**Ethics in Accounting**

[42] Benston GJ, Bromwich M, Wagenhofer A. Principles versus rules based accounting stan-

[43] Sprouse RT. Accounting for what-you-may-call-its. Journal of Accountancy. 1966;122(4):

[45] Camfferman K, Zeff SA. Financial Reporting and Global Capital Markets: A History of the International Accounting Standards Committee, 1973–2000. Oxford University Press on

dards: The FASB's standard setting strategy. Abacus. 2006;42(2):165-188

[44] Johnson LT. Understanding the Conceptual Framework. FASB Report. 2014

45-53

Demand; 2007

26 Accounting from a Cross-Cultural Perspective

**Chapter 2**

**Provisional chapter**

**Ethical Awareness, Ethical Decision Making, and**

**Ethical Awareness, Ethical Decision Making, and** 

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.76867

Nida Türegün

**Abstract**

**1. Introduction**

Nida Türegün

**Transparency: A Study on Turkish CPAs in Istanbul**

This research aims to reveal the connections among ethical awareness, ethical decision making, and transparency from the perspective of certified public accountants (CPAs) in Istanbul. Data are collected from Turkish CPAs' survey responses, which are based on a seven-point Likert scale, and analyzed using explanatory factor analysis. Hypotheses were tested using ordinary least squares regression, and the results show that, based on the participants' average responses, CPAs are affected mainly by the level of their ethical awareness in decision making about an ethical issue or transparency of financial reports,

Accounting is the language of business; it records information to present the overall financial picture of a firm to related parties and help them make decisions. Economic systems rely on accounting; without which they would eventually collapse [1]. However, the structure of economic systems and strong competition have prompted some accountants to pursue unethical behaviors occasionally, with the aim of maximizing their or their companies' interests [2].

The nature of the accounting profession necessitates a high level of ethics and transparency since the financial figures on statements must be accurate, true and relevant for a better decision making process. Accountants may find themselves in a conflict with the interests of firms or personal gains while making decisions. They may desire to manipulate

which indicates that the three concepts are strongly connected to each other.

**Keywords:** ethical awareness, ethical decision making, transparency

**Transparency: A Study on Turkish CPAs in Istanbul**

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

and reproduction in any medium, provided the original work is properly cited.

DOI: 10.5772/intechopen.76867

#### **Ethical Awareness, Ethical Decision Making, and Transparency: A Study on Turkish CPAs in Istanbul Ethical Awareness, Ethical Decision Making, and Transparency: A Study on Turkish CPAs in Istanbul**

DOI: 10.5772/intechopen.76867

#### Nida Türegün Nida Türegün

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.76867

#### **Abstract**

This research aims to reveal the connections among ethical awareness, ethical decision making, and transparency from the perspective of certified public accountants (CPAs) in Istanbul. Data are collected from Turkish CPAs' survey responses, which are based on a seven-point Likert scale, and analyzed using explanatory factor analysis. Hypotheses were tested using ordinary least squares regression, and the results show that, based on the participants' average responses, CPAs are affected mainly by the level of their ethical awareness in decision making about an ethical issue or transparency of financial reports, which indicates that the three concepts are strongly connected to each other.

**Keywords:** ethical awareness, ethical decision making, transparency

#### **1. Introduction**

Accounting is the language of business; it records information to present the overall financial picture of a firm to related parties and help them make decisions. Economic systems rely on accounting; without which they would eventually collapse [1]. However, the structure of economic systems and strong competition have prompted some accountants to pursue unethical behaviors occasionally, with the aim of maximizing their or their companies' interests [2].

The nature of the accounting profession necessitates a high level of ethics and transparency since the financial figures on statements must be accurate, true and relevant for a better decision making process. Accountants may find themselves in a conflict with the interests of firms or personal gains while making decisions. They may desire to manipulate

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

accounting numbers in order to favor firm with attracting potential investors by presenting higher income or lower income before a potential management acquisition.

compliance to the law of land, anxiety for health and security, and for the natural habitat. Ethics influence how individuals settle on choices and direct their lives. The perception of ethics differs from country to country since the notions of ethics have been originated from

Ethical Awareness, Ethical Decision Making, and Transparency: A Study on Turkish CPAs in Istanbul

http://dx.doi.org/10.5772/intechopen.76867

31

On the other hand, for ethical financial reporting transparency plays an important role. Transparency denotes a clear, complete, and understandable reporting. It creates a setting where information is understandable, accessible and visible to all participants. Moreover, it creates a fair presentation of financial statements. Transparent financial reporting allows users of financial information to evaluate the financial position of a business. It assists investors to make better decisions and build confidence in the fairness of the markets. It is important that companies provide clear, complete and reliable financial statements in order users of financial information to be less likely astonished by unknown transactions or events [5]. However, transparency can be violated by showing more detailed information, which may release confidential information, by showing less information or by covering some transac-

The central aim of unethical behavior and violation of transparency is to mislead investors by announcing financial information, which does not represent the real financial position and performance of the company. Unethical behavior and violation of transparency block decision makers to make rational, logical and realistic decisions. Therefore, uncovering and block-

According to Küçüksözen and Küçükkocaoğlu, there are 10 aims of unethical behavior and violation of transparency. They take place to influence stock prices and risk of a company; meet the financial conditions in debt contracts; keep good relations with investors, creditors and employees; manipulate management fees; increase the amount of funds provided by public offerings or capital increase; avoid risks that may arise from political and legal arrangements; reduce the perceived risk of investors on the company; signal about the company's

The following part is going to give a brief explanation about ethical awareness, ethical deci-

Ethical awareness is the eagerness and ability to designate moral situations and dilemmas; critically analyze, evaluate, and additionally change one's own moral esteems; and look up the effects of one's own attitude for the lives of others. All sizes of enterprises must be conscious of the ethical implications of their way of acting. Ethical awareness begins with watch-

A person is ethically aware if he/she realizes that a problem he/she experiences incorporates an ethical problem [1]. A person can make right and moral decisions only if that person is aware of an ethical problem. Additionally, that person can identify the potential effects of a

ing unethical behavior or violation of transparency is extremely important [6].

future performance; provide tax advantage, and also for insider trading [7].

ful thinking to guarantee an enterprise's activities are morally right.

problem on the benefits, desires, and welfare of all related parties [8].

religions, attitudes, and cultures.

tions in the financial statements.

sion, and transparency concepts.

**2.1. Ethical awareness**

Moreover, accountants may have the motivation to manage reported earnings so as to meet earnings targets and, therefore, to get performance-related payment or bonuses, which are related to company's earnings. This situation generates an information asymmetry as managers practice the discretion they hold on accruals, which alternately decreases the reliability together with the relevance of reported earnings and the entire financial statements. External and internal users of financial statements require transparent and reliable information to make appropriate decisions [3]. Only knowledge of ethics can help accountants make ethical decisions to overcome ethical dilemmas, to benefit external users, especially the public, and maintain their trust in the company [4]. Accountants need to be aware of ethical behaviors, make ethical decisions under uncertain situations, and ensure transparent financial reports.

Thus, the aim of this research in this chapter is to reveal the relationships among ethical awareness, ethical decision making, and transparency from the perspective of CPAs. This study contributes to the literature in three ways. First, unlike most existing research, which focuses on ethical awareness and ethical decision making, this study includes transparency. Therefore, it extends the limited research to the relationships among the three concepts.

Second, to the best of my knowledge, this is the first field study to investigate the connections among ethical awareness, ethical decision making, and transparency in Turkey. This study focuses on Turkey since the country represents a setting that is closer to those of many emerging economies. Moreover, Turkey is one of the countries in the new set of emerging economies that is important to the world economy, and it has attracted the attention of investors. Istanbul, in particular, is chosen because of the diversity of CPAs who come to the city from every region of the country, owing to the city's better working conditions. This study also contributes to the literature by revealing the perspective of Turkish CPAs on ethical awareness, ethical decisions, and transparency, and on the relationships among these three concepts.

Third, by highlighting the relationships among these three concepts, this study recommends an area for further study. The rest of the chapter is structured as follows. In the next part of the study, the definitions and importance of ethics and transparency concepts are stated. In the third part, account profession and CPAs in Turkey are explained in details. In the fourth part, the results and analysis are discussed. In the final part, conclusions are presented.

#### **2. Ethics and transparency**

In order to understand the study in this chapter, the term ethics and transparency must be explained. Ethics is the essential concept and important value of human behavior. Ethics is a part of an attitude that includes classifying, supporting and advising concepts of right and wrong behavior. The word ethics originates from Greek with a meaning of habit. Ethics tries to determine inquiries of human ethical quality by characterizing ideas, for example, right or wrong, good or bad, virtue and vice, etc. It embraces the study of worldwide morals like compliance to the law of land, anxiety for health and security, and for the natural habitat. Ethics influence how individuals settle on choices and direct their lives. The perception of ethics differs from country to country since the notions of ethics have been originated from religions, attitudes, and cultures.

On the other hand, for ethical financial reporting transparency plays an important role. Transparency denotes a clear, complete, and understandable reporting. It creates a setting where information is understandable, accessible and visible to all participants. Moreover, it creates a fair presentation of financial statements. Transparent financial reporting allows users of financial information to evaluate the financial position of a business. It assists investors to make better decisions and build confidence in the fairness of the markets. It is important that companies provide clear, complete and reliable financial statements in order users of financial information to be less likely astonished by unknown transactions or events [5]. However, transparency can be violated by showing more detailed information, which may release confidential information, by showing less information or by covering some transactions in the financial statements.

The central aim of unethical behavior and violation of transparency is to mislead investors by announcing financial information, which does not represent the real financial position and performance of the company. Unethical behavior and violation of transparency block decision makers to make rational, logical and realistic decisions. Therefore, uncovering and blocking unethical behavior or violation of transparency is extremely important [6].

According to Küçüksözen and Küçükkocaoğlu, there are 10 aims of unethical behavior and violation of transparency. They take place to influence stock prices and risk of a company; meet the financial conditions in debt contracts; keep good relations with investors, creditors and employees; manipulate management fees; increase the amount of funds provided by public offerings or capital increase; avoid risks that may arise from political and legal arrangements; reduce the perceived risk of investors on the company; signal about the company's future performance; provide tax advantage, and also for insider trading [7].

The following part is going to give a brief explanation about ethical awareness, ethical decision, and transparency concepts.

#### **2.1. Ethical awareness**

accounting numbers in order to favor firm with attracting potential investors by present-

Moreover, accountants may have the motivation to manage reported earnings so as to meet earnings targets and, therefore, to get performance-related payment or bonuses, which are related to company's earnings. This situation generates an information asymmetry as managers practice the discretion they hold on accruals, which alternately decreases the reliability together with the relevance of reported earnings and the entire financial statements. External and internal users of financial statements require transparent and reliable information to make appropriate decisions [3]. Only knowledge of ethics can help accountants make ethical decisions to overcome ethical dilemmas, to benefit external users, especially the public, and maintain their trust in the company [4]. Accountants need to be aware of ethical behaviors, make ethical decisions under uncertain situations, and ensure transparent financial reports. Thus, the aim of this research in this chapter is to reveal the relationships among ethical awareness, ethical decision making, and transparency from the perspective of CPAs. This study contributes to the literature in three ways. First, unlike most existing research, which focuses on ethical awareness and ethical decision making, this study includes transparency. Therefore, it extends the limited research to the relationships among the three concepts.

Second, to the best of my knowledge, this is the first field study to investigate the connections among ethical awareness, ethical decision making, and transparency in Turkey. This study focuses on Turkey since the country represents a setting that is closer to those of many emerging economies. Moreover, Turkey is one of the countries in the new set of emerging economies that is important to the world economy, and it has attracted the attention of investors. Istanbul, in particular, is chosen because of the diversity of CPAs who come to the city from every region of the country, owing to the city's better working conditions. This study also contributes to the literature by revealing the perspective of Turkish CPAs on ethical awareness, ethical decisions, and transparency, and on the relationships among these three concepts.

Third, by highlighting the relationships among these three concepts, this study recommends an area for further study. The rest of the chapter is structured as follows. In the next part of the study, the definitions and importance of ethics and transparency concepts are stated. In the third part, account profession and CPAs in Turkey are explained in details. In the fourth part,

In order to understand the study in this chapter, the term ethics and transparency must be explained. Ethics is the essential concept and important value of human behavior. Ethics is a part of an attitude that includes classifying, supporting and advising concepts of right and wrong behavior. The word ethics originates from Greek with a meaning of habit. Ethics tries to determine inquiries of human ethical quality by characterizing ideas, for example, right or wrong, good or bad, virtue and vice, etc. It embraces the study of worldwide morals like

the results and analysis are discussed. In the final part, conclusions are presented.

**2. Ethics and transparency**

30 Accounting from a Cross-Cultural Perspective

ing higher income or lower income before a potential management acquisition.

Ethical awareness is the eagerness and ability to designate moral situations and dilemmas; critically analyze, evaluate, and additionally change one's own moral esteems; and look up the effects of one's own attitude for the lives of others. All sizes of enterprises must be conscious of the ethical implications of their way of acting. Ethical awareness begins with watchful thinking to guarantee an enterprise's activities are morally right.

A person is ethically aware if he/she realizes that a problem he/she experiences incorporates an ethical problem [1]. A person can make right and moral decisions only if that person is aware of an ethical problem. Additionally, that person can identify the potential effects of a problem on the benefits, desires, and welfare of all related parties [8].

Most of the people think acting ethically is its personal reward, however, an enterprise likely consumes monetary motivations too. Unethical behaviors may spoil the position, reputation, and relations of an employee. Moreover, it may damage an enterprise's image, which will end up with losing current and potential customers. Indorsing ethical awareness among employees stops issues from developing in any way.

they are transparent. Investors need more transparent data about the monetary information of the organization. Actually, transparency is the quality of report that supports investors in settling on certain investment choice. It is worthy of recommendation to the investors that those organizations who do not comprehend the significance of transparency in financial reporting ought to be kept away from. Making interests in such organizations is unsafe.

Ethical Awareness, Ethical Decision Making, and Transparency: A Study on Turkish CPAs in Istanbul

http://dx.doi.org/10.5772/intechopen.76867

33

Organizations that comprehend the significance of transparency in their statements are moreover knowledgeable about the investor-state of mind. A nontransparent financial report presents no information regarding the true risks attached to the organization. Here is a basic case of this. An essential marker of future development of an organization is the means by which it has contributed the cash. As an investor, when you search for the invested amount you cannot find a solid data with respect to the speculations made by the organization, at that point evaluating investments turns out to be hard. Nontransparent financial statements also mask the debt level. In this way, an organization may hide whether the organization is on the

It is clearly accepted that preparing financial statement takes in the usage of judgment and assumptions. It means that prepared financial statements might demonstrate different results than if they had been produced for the identical company, identical period but by different equally qualified professional. Nevertheless, both kinds of financial statements meet the prevailing requirement of displaying a true and a fair view. The flexibility of management decision, used to affect the reported results, might generate opportunities so-called "earnings management". A number of individuals argues that numerous companies legally practice earnings management. The common reason behind this is to fulfill the expectancies of ana-

Accounting scandals that were taken place in the beginning of 2000s put forward the significance of reliability in accounting information. Enron misrepresented earnings and reserved massive debts off the balance sheets, WorldCom increased revenues with fake journal entries and capitalized expenses; Tyco International siphoned millions of dollars over unapproved loans and deceitful stock sales and so on. After these scandals, many investors at different levels experienced big losses, and capital markets came under question. Accordingly, new regulations come into charge to assure faithful representation and prevent healthy pricing in the market. As a result of these scandals and other situations regulations on ethics have been made.

The significant international ethical regulations in accounting consist of "The Ethical Standards of the Accounting Profession", published by the American Institute of CPAs in 1966, and revised and republished in 1988 as the "Code of Professional Conduct"; the "Code of Ethics", published by the International Organization of Supreme Audit Institutions in 1998 [16]; the Sarbanes-Oxley Act, which came into force in 2002 [17]; the "Rulebook for Code of Ethics", published by the Institute of Internal Auditors in 2010 [18]; and the "Code of Ethics",

Meanwhile, the significant Turkish ethical regulations in accounting include "General Accounting Practice Implementation", published by the Ministry of Finance in 1992, and the ethics-related

lysts, regardless of the inspection from auditors, investors, and authorities [15].

published by the International Federation of Accountants (IFAC) in 2005 [19].

precarious edge of liquidation.

**2.4. Ethical regulations in accounting**

#### **2.2. Ethical decision**

A person's moral choice from among the many possible choices is called an ethical decision [1]. An ethical decision is one that is acknowledged on moral grounds by most of the general public or one that is acknowledged legally. On the other hand, an unethical decision is one that is acknowledged as illegal or immoral. Ethical decision making induces a person to make an ethical decision in uncertain conditions or in ethical dilemmas, relying on his/her assessment at that moment [9].

Making decent ethical decisions needs an educated understanding of ethical concerns, besides a trained manner for discovering the ethical features of a decision and evaluating the thoughts that would affect our decision of a course of action. It is important to have a way ethical decision making.

The more different and problematic the ethical choice we confront, the more we have to depend on talk and exchange with others about the situation. Just through watchful investigation of the issue, supported by the bits of knowledge and alternate points of view of others, we would be able to settle on great moral decisions in such circumstances.

Each profession group is faced with ethical dilemmas while carrying on their activities. Moreover, some professionals may be a threat to society by acting unethically. Some professionals, who are unethical, may advocate various misconceptions such as "everyone is doing it", "moral if it is legal", "possibility of being exposed and punished" in order to justify unethical behavior in the face of ethical dilemma [10, 11]. Ethical values must be taken into account in the practice of professional activities since legal sanctions and written rules designed to prevent unethical behavior are not enough alone. Accountants who hold the foresight of society's interests should be willing to act ethically in the face of ethical dilemmas. In addition, ethical dilemmas should be tried to prevent unethical behavior and contribute to ethical decision making efforts [12].

#### **2.3. Transparency**

The word transparency means straight, very clear, honest, and true. Transparency for financial reporting means financial statements that are true and reliable.

The level of access to a firm's financial information by internal and external users, especially investors, is called transparency [13]. Transparency helps decrease price volatility since all users of financial information have the same data for making decisions. It is a very important concept for companies because the more transparent financial reports become, the more investment companies will receive, and the higher their stock prices will be [14].

Nobody can disregard the significance of transparency in financial reporting since individuals make their investments with respect to the financial reporting. Investors believing that they are transparent. Investors need more transparent data about the monetary information of the organization. Actually, transparency is the quality of report that supports investors in settling on certain investment choice. It is worthy of recommendation to the investors that those organizations who do not comprehend the significance of transparency in financial reporting ought to be kept away from. Making interests in such organizations is unsafe.

Organizations that comprehend the significance of transparency in their statements are moreover knowledgeable about the investor-state of mind. A nontransparent financial report presents no information regarding the true risks attached to the organization. Here is a basic case of this. An essential marker of future development of an organization is the means by which it has contributed the cash. As an investor, when you search for the invested amount you cannot find a solid data with respect to the speculations made by the organization, at that point evaluating investments turns out to be hard. Nontransparent financial statements also mask the debt level. In this way, an organization may hide whether the organization is on the precarious edge of liquidation.

#### **2.4. Ethical regulations in accounting**

Most of the people think acting ethically is its personal reward, however, an enterprise likely consumes monetary motivations too. Unethical behaviors may spoil the position, reputation, and relations of an employee. Moreover, it may damage an enterprise's image, which will end up with losing current and potential customers. Indorsing ethical awareness among employ-

A person's moral choice from among the many possible choices is called an ethical decision [1]. An ethical decision is one that is acknowledged on moral grounds by most of the general public or one that is acknowledged legally. On the other hand, an unethical decision is one that is acknowledged as illegal or immoral. Ethical decision making induces a person to make an ethical decision in uncertain conditions or in ethical dilemmas, relying on his/her assess-

Making decent ethical decisions needs an educated understanding of ethical concerns, besides a trained manner for discovering the ethical features of a decision and evaluating the thoughts that would affect our decision of a course of action. It is important to have a way ethical deci-

The more different and problematic the ethical choice we confront, the more we have to depend on talk and exchange with others about the situation. Just through watchful investigation of the issue, supported by the bits of knowledge and alternate points of view of others,

Each profession group is faced with ethical dilemmas while carrying on their activities. Moreover, some professionals may be a threat to society by acting unethically. Some professionals, who are unethical, may advocate various misconceptions such as "everyone is doing it", "moral if it is legal", "possibility of being exposed and punished" in order to justify unethical behavior in the face of ethical dilemma [10, 11]. Ethical values must be taken into account in the practice of professional activities since legal sanctions and written rules designed to prevent unethical behavior are not enough alone. Accountants who hold the foresight of society's interests should be willing to act ethically in the face of ethical dilemmas. In addition, ethical dilemmas should be tried to prevent unethical behavior and contribute to ethical decision making efforts [12].

The word transparency means straight, very clear, honest, and true. Transparency for finan-

The level of access to a firm's financial information by internal and external users, especially investors, is called transparency [13]. Transparency helps decrease price volatility since all users of financial information have the same data for making decisions. It is a very important concept for companies because the more transparent financial reports become, the more

Nobody can disregard the significance of transparency in financial reporting since individuals make their investments with respect to the financial reporting. Investors believing that

investment companies will receive, and the higher their stock prices will be [14].

we would be able to settle on great moral decisions in such circumstances.

cial reporting means financial statements that are true and reliable.

ees stops issues from developing in any way.

**2.2. Ethical decision**

32 Accounting from a Cross-Cultural Perspective

ment at that moment [9].

sion making.

**2.3. Transparency**

It is clearly accepted that preparing financial statement takes in the usage of judgment and assumptions. It means that prepared financial statements might demonstrate different results than if they had been produced for the identical company, identical period but by different equally qualified professional. Nevertheless, both kinds of financial statements meet the prevailing requirement of displaying a true and a fair view. The flexibility of management decision, used to affect the reported results, might generate opportunities so-called "earnings management". A number of individuals argues that numerous companies legally practice earnings management. The common reason behind this is to fulfill the expectancies of analysts, regardless of the inspection from auditors, investors, and authorities [15].

Accounting scandals that were taken place in the beginning of 2000s put forward the significance of reliability in accounting information. Enron misrepresented earnings and reserved massive debts off the balance sheets, WorldCom increased revenues with fake journal entries and capitalized expenses; Tyco International siphoned millions of dollars over unapproved loans and deceitful stock sales and so on. After these scandals, many investors at different levels experienced big losses, and capital markets came under question. Accordingly, new regulations come into charge to assure faithful representation and prevent healthy pricing in the market. As a result of these scandals and other situations regulations on ethics have been made.

The significant international ethical regulations in accounting consist of "The Ethical Standards of the Accounting Profession", published by the American Institute of CPAs in 1966, and revised and republished in 1988 as the "Code of Professional Conduct"; the "Code of Ethics", published by the International Organization of Supreme Audit Institutions in 1998 [16]; the Sarbanes-Oxley Act, which came into force in 2002 [17]; the "Rulebook for Code of Ethics", published by the Institute of Internal Auditors in 2010 [18]; and the "Code of Ethics", published by the International Federation of Accountants (IFAC) in 2005 [19].

Meanwhile, the significant Turkish ethical regulations in accounting include "General Accounting Practice Implementation", published by the Ministry of Finance in 1992, and the ethics-related regulations that came into force with Law No. 3568 in 1989 [2]. In Turkey, the increased public interest to the ethics concept has arisen with the 2001 economic crisis. The reforms in ethics inevitably took place in the period following the crisis. For the purpose of recovery and improvement of ethics, the "Code of Ethics" has been issued by the Union of Chambers of Certified Public Accountants of Turkey in 2013 [20]. Additionally, the "Ethical Rules for Independent Auditors", published by the Public Oversight, Accounting, and Auditing Standards Authority in a bulletin in 2015 [21]; and the ethics-related regulations published by the Capital Markets Board (CMB) in its bulletins, especially Bulletins No. 1 and 16 [22, 23].

Intended for accounting profession protection of public confidence and increase the credibility of the profession in the community connected with having ethical values in addition to complying with legal regulations related to practice of professional accountants. As in every profession, there are not only specific legal rules in accounting profession, but also ethical

Ethical Awareness, Ethical Decision Making, and Transparency: A Study on Turkish CPAs in Istanbul

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35

The factors, legal regulations, free electoral rights and ethics that affect professional decisions and behaviors of accountants are the points of action in professional decisions for them. According to these points, a profession in the context of the mentioned factors, making professional decisions in the knowledge of ethical and ethical dilemma of professionals is the

An accountant should act within the framework of ethics and responsibilities as well as professional knowledge and experience, resolve any dilemmas with professional ethics when confronted with any value judgment contradiction. Otherwise, it will be inevitable that new financial crises and scandals will come out again. Therefore, technical information for accountants as well as professional knowledge and experience harmonized with ethical values are so

It would be useful to talk about some ethical theories that affect the professional ethics decisions of accountants. Theories of teleological and deontological ethics from these theories mainly emerge in the profession decision making stages of profession members. While teleological ethics is based on the principle that utopia is the right choice based on utility-cost comparison, while deontological ethics developed by Kant is based on the fact that the forms

The moral principles and rule-of-thumb of the community also play an active role in the attitudes and behaviors of accountants in the practice of the profession. Therefore, it is obvious that these troubles will affect every part of the society, which is caused by a number of troubles, especially corruption, in societies not sensitive to moral rules. It should be kept in mind that the accounting profession is performing its services as part of the society in which it is located.

Oriented toward ethics in the accounting profession extensive work has been done and ethical principles and rules have been set not only at Turkey from TÜRMOB according to 3568 code and related regulations, but also from International corporations as The International Federation of Accountants, American Institute of Certified Public Accountants (AICPA), The Federation of European Accountants and Institute of Management Accountants. The study on professional ethics in the United States, where the largest regulations in the accounting profession are found, is the "Professional Ethics Standards in the Accounting Profession" published by AICPA.

Although there are partial differences in principle, it is possible to count rules as "independence, integrity, honesty, confidentiality, public benefit, professional dignity, professional care, professional competence, compliance with accounting principles and standards, confidentiality, social responsibility, impartiality, unfair competition, advertising and incitement prohibition" [12].

Oriented toward accountant profession in Turkey, set of principles and rules have been established in order to enable accountants to have a sense of higher professional knowledge, social

of movement of individuals and groups depend on moral obligations and duties [12].

principles and rules that made by accounting organizations [25].

vital in terms of society and the credibility of the profession.

responsibility to them against the public.

## **3. Account profession and CPAs in Turkey**

An accountant is a person who records, classifies, summarizes, analyzes, interprets, and reports results to related parties, creates accounting policies, and generates financial information for budget and audit purposes to help strategic management and planning [24].

The accounting profession has reached the status of "profession" with the Law on Public Practice Accounting, independent accountant, and financial advisor and Certified Public Accountant numbered 3568 and amended by the Law No. 5786 published in Official Newspaper in 1989, in Turkey. Occupational practitioners keep records that should be held by the enterprises, arrange financial statements and declarations, establish accounting information system, conduct consultancy, and expertise.

Professionals in Turkey are carrying out their activities under the name of two types of professional titles: independent accountant and financial advisor and certified public accountant (CPA). Independent accountant and financial advisors perform bookkeeping, prepare financial statements and declarations, establish accounting information system, conduct consultancy, and expertise in accordance with generally accepted accounting principles and related legislative provisions [12]. On the other hand, CPAs have more credibility and expertise since they have to pass particular tests and meet licensing requirements. They can prepare and sign tax returns and moreover prepare audited financial statements. However, they cannot open an accounting office and cannot be partners in any accounting offices.

Union of Chambers of Certified Public Accountants and Sworn-In Certified Public Accountants of Turkey (TÜRMOB) is a center that gathers the accounting profession under a single roof in Turkey.

#### **3.1. Accounting profession ethics**

Accounting profession ethics is a set of rules that should be implemented by professional accountants during the execution of the activities and even in situations and periods in which professional activity is not carried out for any reason, to provide reliable information by paying attention to the value judgments of the society as well as making transactions in accordance with the laws and relations with customers, society, colleagues, and related sectoral organizations [12].

Intended for accounting profession protection of public confidence and increase the credibility of the profession in the community connected with having ethical values in addition to complying with legal regulations related to practice of professional accountants. As in every profession, there are not only specific legal rules in accounting profession, but also ethical principles and rules that made by accounting organizations [25].

regulations that came into force with Law No. 3568 in 1989 [2]. In Turkey, the increased public interest to the ethics concept has arisen with the 2001 economic crisis. The reforms in ethics inevitably took place in the period following the crisis. For the purpose of recovery and improvement of ethics, the "Code of Ethics" has been issued by the Union of Chambers of Certified Public Accountants of Turkey in 2013 [20]. Additionally, the "Ethical Rules for Independent Auditors", published by the Public Oversight, Accounting, and Auditing Standards Authority in a bulletin in 2015 [21]; and the ethics-related regulations published by the Capital Markets Board (CMB) in

An accountant is a person who records, classifies, summarizes, analyzes, interprets, and reports results to related parties, creates accounting policies, and generates financial informa-

The accounting profession has reached the status of "profession" with the Law on Public Practice Accounting, independent accountant, and financial advisor and Certified Public Accountant numbered 3568 and amended by the Law No. 5786 published in Official Newspaper in 1989, in Turkey. Occupational practitioners keep records that should be held by the enterprises, arrange financial statements and declarations, establish accounting infor-

Professionals in Turkey are carrying out their activities under the name of two types of professional titles: independent accountant and financial advisor and certified public accountant (CPA). Independent accountant and financial advisors perform bookkeeping, prepare financial statements and declarations, establish accounting information system, conduct consultancy, and expertise in accordance with generally accepted accounting principles and related legislative provisions [12]. On the other hand, CPAs have more credibility and expertise since they have to pass particular tests and meet licensing requirements. They can prepare and sign tax returns and moreover prepare audited financial statements. However, they cannot open

Union of Chambers of Certified Public Accountants and Sworn-In Certified Public Accountants of Turkey (TÜRMOB) is a center that gathers the accounting profession under a single roof

Accounting profession ethics is a set of rules that should be implemented by professional accountants during the execution of the activities and even in situations and periods in which professional activity is not carried out for any reason, to provide reliable information by paying attention to the value judgments of the society as well as making transactions in accordance with the laws and relations with customers, society, colleagues, and related sectoral

tion for budget and audit purposes to help strategic management and planning [24].

its bulletins, especially Bulletins No. 1 and 16 [22, 23].

34 Accounting from a Cross-Cultural Perspective

**3. Account profession and CPAs in Turkey**

mation system, conduct consultancy, and expertise.

in Turkey.

organizations [12].

**3.1. Accounting profession ethics**

an accounting office and cannot be partners in any accounting offices.

The factors, legal regulations, free electoral rights and ethics that affect professional decisions and behaviors of accountants are the points of action in professional decisions for them. According to these points, a profession in the context of the mentioned factors, making professional decisions in the knowledge of ethical and ethical dilemma of professionals is the responsibility to them against the public.

An accountant should act within the framework of ethics and responsibilities as well as professional knowledge and experience, resolve any dilemmas with professional ethics when confronted with any value judgment contradiction. Otherwise, it will be inevitable that new financial crises and scandals will come out again. Therefore, technical information for accountants as well as professional knowledge and experience harmonized with ethical values are so vital in terms of society and the credibility of the profession.

It would be useful to talk about some ethical theories that affect the professional ethics decisions of accountants. Theories of teleological and deontological ethics from these theories mainly emerge in the profession decision making stages of profession members. While teleological ethics is based on the principle that utopia is the right choice based on utility-cost comparison, while deontological ethics developed by Kant is based on the fact that the forms of movement of individuals and groups depend on moral obligations and duties [12].

The moral principles and rule-of-thumb of the community also play an active role in the attitudes and behaviors of accountants in the practice of the profession. Therefore, it is obvious that these troubles will affect every part of the society, which is caused by a number of troubles, especially corruption, in societies not sensitive to moral rules. It should be kept in mind that the accounting profession is performing its services as part of the society in which it is located.

Oriented toward ethics in the accounting profession extensive work has been done and ethical principles and rules have been set not only at Turkey from TÜRMOB according to 3568 code and related regulations, but also from International corporations as The International Federation of Accountants, American Institute of Certified Public Accountants (AICPA), The Federation of European Accountants and Institute of Management Accountants. The study on professional ethics in the United States, where the largest regulations in the accounting profession are found, is the "Professional Ethics Standards in the Accounting Profession" published by AICPA.

Although there are partial differences in principle, it is possible to count rules as "independence, integrity, honesty, confidentiality, public benefit, professional dignity, professional care, professional competence, compliance with accounting principles and standards, confidentiality, social responsibility, impartiality, unfair competition, advertising and incitement prohibition" [12].

Oriented toward accountant profession in Turkey, set of principles and rules have been established in order to enable accountants to have a sense of higher professional knowledge, social responsibility, understanding of ethical values, and maximizing the public interest by providing quality services.

operating in Balıkesir province in Turkey. Honesty is one of the main principles of ethics. The study has detected that this principle is perceived by accountants as protecting the taxpayer and public interest equally, being principled, protecting professional reputation and giving confidence. However, in general, it seems that there is little knowledge about the subject of profes-

Ethical Awareness, Ethical Decision Making, and Transparency: A Study on Turkish CPAs in Istanbul

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37

It has been revealed in the "Occupational Ethics, and The Effects of Occupational Ethics on Professional Life" that accountants are aware that they will suffer from their inability to act in

The main focus on "The Role of Personal Value in the Emergence of Ethical Dilemma: An Application on Accountants" is to disclose whether accountants in Kars and Erzurum have experienced ethical dilemma or not. The study reveals that accountants have experienced ethical dilemma in relation to factors such as income, age and losing customers. It has been found that the accountants, who are old and have low income, have experienced more ethical dilemmas, while other accountants, who have lower level education in terms of education fac-

"Accounting Ethics-Responsibility Versus Creativity" suggests that accountants, who face ethical dilemma, must develop their values and virtues in order to overcome an obstacle like creative accounting. Also, suggests that there should be a regulatory accounting system, which will help to strengthen the existing accounting standards. The ethics have a direct impact on the credibility of the accounting profession, and directly affect the perspective of the society to the profession and its members. In addition, the study emphasizes the necessity of ethical education, since the crises and scandals that have been experienced, is a result of

The study in the "Accounting Professional Ethics and An Application in Sivas Province" reveals that social pressure, education level, auditing activities, penal sanctions and conscientious responsibilities have impact on accountants to follow the ethical rules. Responses from accountants indicate three factors, which are desire to earn more money, moral weakness, and

The study conducted on "A Research About Ethical Judgment Levels of Accountants" measures the level of ethical judgment of accountants by using value determination test. Moreover, the study reveals the demographic variables to see whether they are differentiated at the levels of ethical judgment. It was found that the level of ethical judgment is in compliance with Kohlberg Conventional Level and accountants comply with the in house published rules and principles [31]. It has been revealed in the "Occupational Ethics in Accounting Profession and an Application in Kayseri Province" that accountants care about ethics and 97% of the accountants think that there is a need for ethics training. Moreover, accountants think that the occurrence of unethical cases is due to conflicts of interest regarding to monetary relations, and lack of laws and

The survey on "Attitudes of Accounting Professionals and Businesses on Ethics" found that members of the accounting profession believe that honesty, trustworthiness and objectivity should be based on profession and that only self-employed professionals should be

line with ethical principles, however, they have not been sufficiently rigorous [28].

tor, give more importance to ethical values at the outset of ethical dilemmas [10].

inadaqute attitude of accountants in ethical issues [29].

lack of professional ethics education in educational institutions [30].

sional ethics [27].

legislations [32].

According to the "General Communique on Accounting System Application" published by the Ministry of Finance, the regulations on accounting profession ethics are composed of 12 basic concepts. Constitution of accounting, social responsibility, neutrality and faithful representation, consistency, full disclosure and substance over form are the concepts related to ethics. From these concepts, the concept of social responsibility requires accountants to engage in ethics in their profession and to take care of the public interest. Other concepts indirectly concern the ethics dimension of the profession [25].

Moreover, CMB has published bulletins based on the Public Disclosure principle in which it was addressed issues related to professional ethics. The Board has undertaken efforts to regulate professional ethics in the bulletins by covering professional competence, independence, care and diligence, under the title of occupational standards.

In accordance with another regulation on accounting ethics in Turkey, Law No. 3568 "Regulations Regarding Working Methods and Principles" published in the direction of work discipline, professional confidence and professional ethics. This law regulates issues related to the ethical and moral values such as the activities that the professions would fulfill or unable to engage in, and the occasions incompatible with profession and professional honor. The "Disciplinary Regulation", which was published for accountants in the Official Newspaper No. 20556 in 1990, states that it is necessary to act within the framework of profession ethics and morality. Otherwise, punishment and sanctions will be subjected. It should also be noted that the Code of Professional Ethics, published in the Official Newspaper No. 24557 in 2001, is a direct regulation of the accounting profession ethics. In addition, TÜRMOB published IFAC publications in the name of "The Code of Ethics Handbook for Professional Accountants", translating the regulations into Turkish, which is related to professional ethics.

"Public Oversight, Accounting and Auditing Standards Authority", which is established by Provision No. 660 and published in the Official Newspaper No. 28103 in 2011, provides the accounting and auditing standards in accordance with the regulations on occupational ethics and regulations in line with the regulations on occupational ethics in the bulletin on "Independent Auditing Regulation" that contributes to the development of the audit profession.

#### **3.2. Ethics literature on accountants**

Empirical studies in the "Ethics and Accounting Education in the UK – A Professional Approach?" suggest that even the best accountant is below the average in terms of ethical behavior, despite the expectations from accountants to operate in a state of high ethical standards. The study emphasizes the difference between what is expected and realized, is the result of inadequate education. Universities are not able to adequately fulfill the ethical training that their future professionals need, and as a result of this, accountants are experiencing failures in the face of ethical dilemmas [26].

The work on "Accounting Professional Ethics Rules and Perceptions of Those Rules by Professionals" was carried out to reveal the knowledge, thoughts and perceptions of accountants operating in Balıkesir province in Turkey. Honesty is one of the main principles of ethics. The study has detected that this principle is perceived by accountants as protecting the taxpayer and public interest equally, being principled, protecting professional reputation and giving confidence. However, in general, it seems that there is little knowledge about the subject of professional ethics [27].

responsibility, understanding of ethical values, and maximizing the public interest by provid-

According to the "General Communique on Accounting System Application" published by the Ministry of Finance, the regulations on accounting profession ethics are composed of 12 basic concepts. Constitution of accounting, social responsibility, neutrality and faithful representation, consistency, full disclosure and substance over form are the concepts related to ethics. From these concepts, the concept of social responsibility requires accountants to engage in ethics in their profession and to take care of the public interest. Other concepts indirectly

Moreover, CMB has published bulletins based on the Public Disclosure principle in which it was addressed issues related to professional ethics. The Board has undertaken efforts to regulate professional ethics in the bulletins by covering professional competence, independence,

In accordance with another regulation on accounting ethics in Turkey, Law No. 3568 "Regulations Regarding Working Methods and Principles" published in the direction of work discipline, professional confidence and professional ethics. This law regulates issues related to the ethical and moral values such as the activities that the professions would fulfill or unable to engage in, and the occasions incompatible with profession and professional honor. The "Disciplinary Regulation", which was published for accountants in the Official Newspaper No. 20556 in 1990, states that it is necessary to act within the framework of profession ethics and morality. Otherwise, punishment and sanctions will be subjected. It should also be noted that the Code of Professional Ethics, published in the Official Newspaper No. 24557 in 2001, is a direct regulation of the accounting profession ethics. In addition, TÜRMOB published IFAC publications in the name of "The Code of Ethics Handbook for Professional Accountants", translating the regula-

"Public Oversight, Accounting and Auditing Standards Authority", which is established by Provision No. 660 and published in the Official Newspaper No. 28103 in 2011, provides the accounting and auditing standards in accordance with the regulations on occupational ethics and regulations in line with the regulations on occupational ethics in the bulletin on "Independent Auditing Regulation" that contributes to the development of the audit profession.

Empirical studies in the "Ethics and Accounting Education in the UK – A Professional Approach?" suggest that even the best accountant is below the average in terms of ethical behavior, despite the expectations from accountants to operate in a state of high ethical standards. The study emphasizes the difference between what is expected and realized, is the result of inadequate education. Universities are not able to adequately fulfill the ethical training that their future professionals need, and as a result of this, accountants are experiencing

The work on "Accounting Professional Ethics Rules and Perceptions of Those Rules by Professionals" was carried out to reveal the knowledge, thoughts and perceptions of accountants

ing quality services.

36 Accounting from a Cross-Cultural Perspective

concern the ethics dimension of the profession [25].

care and diligence, under the title of occupational standards.

tions into Turkish, which is related to professional ethics.

**3.2. Ethics literature on accountants**

failures in the face of ethical dilemmas [26].

It has been revealed in the "Occupational Ethics, and The Effects of Occupational Ethics on Professional Life" that accountants are aware that they will suffer from their inability to act in line with ethical principles, however, they have not been sufficiently rigorous [28].

The main focus on "The Role of Personal Value in the Emergence of Ethical Dilemma: An Application on Accountants" is to disclose whether accountants in Kars and Erzurum have experienced ethical dilemma or not. The study reveals that accountants have experienced ethical dilemma in relation to factors such as income, age and losing customers. It has been found that the accountants, who are old and have low income, have experienced more ethical dilemmas, while other accountants, who have lower level education in terms of education factor, give more importance to ethical values at the outset of ethical dilemmas [10].

"Accounting Ethics-Responsibility Versus Creativity" suggests that accountants, who face ethical dilemma, must develop their values and virtues in order to overcome an obstacle like creative accounting. Also, suggests that there should be a regulatory accounting system, which will help to strengthen the existing accounting standards. The ethics have a direct impact on the credibility of the accounting profession, and directly affect the perspective of the society to the profession and its members. In addition, the study emphasizes the necessity of ethical education, since the crises and scandals that have been experienced, is a result of inadaqute attitude of accountants in ethical issues [29].

The study in the "Accounting Professional Ethics and An Application in Sivas Province" reveals that social pressure, education level, auditing activities, penal sanctions and conscientious responsibilities have impact on accountants to follow the ethical rules. Responses from accountants indicate three factors, which are desire to earn more money, moral weakness, and lack of professional ethics education in educational institutions [30].

The study conducted on "A Research About Ethical Judgment Levels of Accountants" measures the level of ethical judgment of accountants by using value determination test. Moreover, the study reveals the demographic variables to see whether they are differentiated at the levels of ethical judgment. It was found that the level of ethical judgment is in compliance with Kohlberg Conventional Level and accountants comply with the in house published rules and principles [31].

It has been revealed in the "Occupational Ethics in Accounting Profession and an Application in Kayseri Province" that accountants care about ethics and 97% of the accountants think that there is a need for ethics training. Moreover, accountants think that the occurrence of unethical cases is due to conflicts of interest regarding to monetary relations, and lack of laws and legislations [32].

The survey on "Attitudes of Accounting Professionals and Businesses on Ethics" found that members of the accounting profession believe that honesty, trustworthiness and objectivity should be based on profession and that only self-employed professionals should be prohibited from taking custody from customers in the case of work done on a Turkey basis for attitudes toward ethics by accounting professionals and businesses. In addition, it has been determined that the members of the profession do not participate in certain provisions of TÜRMOB's ethical code, but they are mostly engaged in professional activities in accordance with the principles and rules [33].

**H1:** The level of ethical awareness of CPAs affects their ethical decision making positively. No study has examined the relationships between ethical decision making and transparency from the perspective of CPAs, although the literature has provided some explanations related to the linkage between these two concepts. Logically, if a person is ethically aware, then he/ she can make ethical decisions, and consequently, can create transparent reports and have the desire to increase transparency. In other words, there is a chain effect among these three

Ethical Awareness, Ethical Decision Making, and Transparency: A Study on Turkish CPAs in Istanbul

http://dx.doi.org/10.5772/intechopen.76867

39

Finally, hypothesis 3 is developed to determine whether ethical awareness directly affects

The aim of this field study is to reveal the connections among ethical awareness, ethical decision making, and transparency from the perspective of CPAs. Certain measurement tools were utilized to test the hypotheses and achieve the study's aims. A 30-item multi-factorial scale was developed to reflect the ethics and transparency concepts. This scale enables the study to find answers to the research questions, such as what CPAs believe and why they believe them. Each participant was requested to specify his/her response on a 7-point Likert scale, the format of which is coded as strongly agree (−3) to strongly disagree (+3). The survey questionnaires were distributed to 600 CPAs in Istanbul. A total of 162 questionnaires were returned, but only 138 questionnaires were completed and processed for data analysis, since

SPSS is used for the data analysis. Specifically, explanatory factor analysis and OLS regression were performed to analyze the survey data and test the hypotheses. According to the CPA respondents' demographic data, 85% of the respondents are male, 37% have a high school

The suitability of the ethical awareness, ethical decision making, and transparency variables for the factor analysis are tested using Barlett's test of sphericity and the Kaiser-Meyer-Olkin measure of sampling adequacy test (KMO). The KMO yields a value of 0.781, and the Bartlett is smaller than 0.05, which means the observed variables are suitable for factor analysis. The explanatory factor analysis results with the variable factor loads are shown in **Table 1**, and the

**Table 1** shows the factor analysis results for the statements for each of the three factors of ethical behavior awareness, ethical decision making, and transparency. Meanwhile, the results

**H2:** The level of ethical decision making of CPAs affects transparency positively.

**H3:** The level of ethical awareness of CPAs affects transparency positively.

24 of the returned questionnaires were excluded due to incomplete responses.

average responses based on the Likert scale are shown in **Table 2**.

concepts. Therefore, hypothesis 2 is developed as follows:

**5. Study methodology and implementation**

diploma, and 63% have a college degree.

**6. Results and analysis**

transparency.

It was mentioned in "The Contribution of Islamic Ethics Towards Ethical Accounting Practices" that individual ethical developments of accountants improve their business ethics [34]. It is stated in "Ethics in Accounting Professionals: Research on Accountants in Ankara Province" that accountants should give importance to in-service training and it would be beneficial to increase the efforts toward the trial to prevent possible unethical behaviors that may be encountered in the profession [24]. According to the study conducted on "Ethical Perceptions of Independent Accountant and Financial Advisor: Erzurum Case" the accountants were aware of ethical principles; however, they were unaware of unethical behaviors. It has been suggested that more education should be given to organizations and accountants about ethics. In addition, it has been determined that the commitment to ethical principles is directly proportional to the level of education and income [35].

It was found in "The Problems and Ethical Attitudes of Accounting Professionals Toward Accounting Errors and Frauds: A Model Practice in City of Erzurum" that apprentices do not have sufficient knowledge about ethics and that there are instabilities in the unethical cases, investigation of ethical aspects of accounting mistakes and mistakes of city of Erzurum accountants and candidate trainees. As a result of the study, it was concluded that vocational training is necessary [36].

It was stated in "The Role of Personal Value in the Emergence of Ethical Dilemma: An Application on Professional Accountants" that the ethical dilemma is the process of indecision that arises when there are truths that can be discussed on opposite sides of an event. In the process of preparing financial statements, accountants often face ethical dilemmas. In addition to legal and regulatory compliance of accountants, it is also important to be committed to ethical principles [37].

It was found in "Perspectives of Professional Accountants on Professional Ethics: A Research in Kırklareli Province" that about 81% of the accountants had an ethical dilemma in their professional activities. Dominant factors revealed as religious beliefs, values about the cultural environment, and anxiety about losing taxpayers. Additionally, it has been observed that accountants are interested in teaching accounting profession ethics [38].

## **4. Hypothesis development**

Studies that investigate the relationships among accountants' levels of ethical awareness and ethical decision making have obtained similar results. According to Shafer et al., accountants' levels of ethical awareness affect their behavior toward aggressive financial reporting [39]. According to Uyar and Ozer, and Liyanapathirana and Samkin,accountants' levels of ethical awareness affect their ethical decision making positively,in Turkey and Sri Lanka, respectively [1, 40]. Based on the findings of these studies, hypothesis 1 is developed as follows:

**H1:** The level of ethical awareness of CPAs affects their ethical decision making positively.

No study has examined the relationships between ethical decision making and transparency from the perspective of CPAs, although the literature has provided some explanations related to the linkage between these two concepts. Logically, if a person is ethically aware, then he/ she can make ethical decisions, and consequently, can create transparent reports and have the desire to increase transparency. In other words, there is a chain effect among these three concepts. Therefore, hypothesis 2 is developed as follows:

**H2:** The level of ethical decision making of CPAs affects transparency positively.

Finally, hypothesis 3 is developed to determine whether ethical awareness directly affects transparency.

**H3:** The level of ethical awareness of CPAs affects transparency positively.

#### **5. Study methodology and implementation**

The aim of this field study is to reveal the connections among ethical awareness, ethical decision making, and transparency from the perspective of CPAs. Certain measurement tools were utilized to test the hypotheses and achieve the study's aims. A 30-item multi-factorial scale was developed to reflect the ethics and transparency concepts. This scale enables the study to find answers to the research questions, such as what CPAs believe and why they believe them. Each participant was requested to specify his/her response on a 7-point Likert scale, the format of which is coded as strongly agree (−3) to strongly disagree (+3). The survey questionnaires were distributed to 600 CPAs in Istanbul. A total of 162 questionnaires were returned, but only 138 questionnaires were completed and processed for data analysis, since 24 of the returned questionnaires were excluded due to incomplete responses.

SPSS is used for the data analysis. Specifically, explanatory factor analysis and OLS regression were performed to analyze the survey data and test the hypotheses. According to the CPA respondents' demographic data, 85% of the respondents are male, 37% have a high school diploma, and 63% have a college degree.

#### **6. Results and analysis**

prohibited from taking custody from customers in the case of work done on a Turkey basis for attitudes toward ethics by accounting professionals and businesses. In addition, it has been determined that the members of the profession do not participate in certain provisions of TÜRMOB's ethical code, but they are mostly engaged in professional activities in accor-

It was mentioned in "The Contribution of Islamic Ethics Towards Ethical Accounting Practices" that individual ethical developments of accountants improve their business ethics [34]. It is stated in "Ethics in Accounting Professionals: Research on Accountants in Ankara Province" that accountants should give importance to in-service training and it would be beneficial to increase the efforts toward the trial to prevent possible unethical behaviors that may be encountered in the profession [24]. According to the study conducted on "Ethical Perceptions of Independent Accountant and Financial Advisor: Erzurum Case" the accountants were aware of ethical principles; however, they were unaware of unethical behaviors. It has been suggested that more education should be given to organizations and accountants about ethics. In addition, it has been determined that the commitment to ethical principles is

It was found in "The Problems and Ethical Attitudes of Accounting Professionals Toward Accounting Errors and Frauds: A Model Practice in City of Erzurum" that apprentices do not have sufficient knowledge about ethics and that there are instabilities in the unethical cases, investigation of ethical aspects of accounting mistakes and mistakes of city of Erzurum accountants and candidate trainees. As a result of the study, it was concluded that vocational

It was stated in "The Role of Personal Value in the Emergence of Ethical Dilemma: An Application on Professional Accountants" that the ethical dilemma is the process of indecision that arises when there are truths that can be discussed on opposite sides of an event. In the process of preparing financial statements, accountants often face ethical dilemmas. In addition to legal and regulatory compliance of accountants, it is also important to be committed to ethical principles [37]. It was found in "Perspectives of Professional Accountants on Professional Ethics: A Research in Kırklareli Province" that about 81% of the accountants had an ethical dilemma in their professional activities. Dominant factors revealed as religious beliefs, values about the cultural environment, and anxiety about losing taxpayers. Additionally, it has been observed

Studies that investigate the relationships among accountants' levels of ethical awareness and ethical decision making have obtained similar results. According to Shafer et al., accountants' levels of ethical awareness affect their behavior toward aggressive financial reporting [39]. According to Uyar and Ozer, and Liyanapathirana and Samkin,accountants' levels of ethical awareness affect their ethical decision making positively,in Turkey and Sri Lanka, respectively [1, 40]. Based on the findings of these studies, hypothesis 1 is developed

that accountants are interested in teaching accounting profession ethics [38].

dance with the principles and rules [33].

38 Accounting from a Cross-Cultural Perspective

training is necessary [36].

**4. Hypothesis development**

as follows:

directly proportional to the level of education and income [35].

The suitability of the ethical awareness, ethical decision making, and transparency variables for the factor analysis are tested using Barlett's test of sphericity and the Kaiser-Meyer-Olkin measure of sampling adequacy test (KMO). The KMO yields a value of 0.781, and the Bartlett is smaller than 0.05, which means the observed variables are suitable for factor analysis. The explanatory factor analysis results with the variable factor loads are shown in **Table 1**, and the average responses based on the Likert scale are shown in **Table 2**.

**Table 1** shows the factor analysis results for the statements for each of the three factors of ethical behavior awareness, ethical decision making, and transparency. Meanwhile, the results in **Table 2** are obtained by considering the five highest average responses to the statements for each of the three factors. Based on the responses to first group of statements for the factor of ethical awareness, most of the CPAs disagree that other CPAs in their company engage in unethical practices. They may have answered so to protect the reputations of fellow CPAs, but their response may also simply indicate that they trust other CPAs. Most of the CPAs are aware that if they engage in unethical practices under any conditions, they will be fired. Likewise, most of them are aware that if they participate in unethical practices for their own interests, they will be immediately reprimanded.

Ethical behavior awareness

There are numerous opportunities for CPAs inside my

There are numerous opportunities for CPAs outside of my

CPAs in my company usually participate in practices that I

CPAs outside of my company usually participate in

In my company, unsuccessful CPAs are usually more

In my company, CPAs are aware that under no conditions

If a CPA inside my company is found to have participated

His/her own interest (rather than the company's interest),

If a CPA inside my company is found to have participated

The company's interest (rather than his/her own interest,)

CPAs are aware of sanctions and penalties for unethical

I ask what is the right thing to do when something has

If I notice a mistake or manipulation in financial

If I notice a mistake or manipulation in financial

To be successful in my company, sometimes it is appropriate to compromise one's ethics

I learned to make ethical decisions from my ethics

I will fulfill top management's request for something that I

If I could protect myself from punishments and sanctions,

Being a whistle-blower is not always a bad thing 0.749

I learned to make ethical decisions from my family 0.638

Most CPAs are aware of the code of ethics 0.845

Ethical Awareness, Ethical Decision Making, and Transparency: A Study on Turkish CPAs in Istanbul

0.901

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41

0.893

0.813

0.804

0.791

0.771

0.745

0.722

0.625

0.603

0.542

0.900

0.859

0.856

0.837

0.803

0.772

0.711

0.541

company to take part in unethical practices

company to take part in unethical practices

practices that I think are unethical

will unethical behaviors be tolerated

in unethical behaviors that serves

in unethical behaviors that serve

Ethical decision making I check what is the right thing to do when I am uncertain

statements, I try to fix it myself

statements, I do not tell anyone

I would engage in unethical practices

think to be unethical

training/lessons

behaviors

of what to do

gone wrong

he/she will be immediately reprimanded

he/she will be immediately reprimanded

unethical than successful ones

think are unethical

Most of them are also aware that if they participate in unethical practices for their company's interests, they will be immediately reprimanded, but the average response to this statement is distinctly lower than that to the former statement. Some of the CPAs may think that if they engage in unethical practices on behalf of their companies, top management may ignore what was done or may even promote them since their actions may have increased profits to a desired level without drawing the attention of anyone inside or outside of the company. The last item in the factor group is that most of the CPAs think that unsuccessful CPAs engage more in unethical practices than successful ones to achieve a short-cut to success. The last three items in the factor group are an indicator that companies have not yet fully complied with the Turkish ethical system for accounting, and still exhibit unethical behaviors.

Based on the responses to the second group of statements for the factor of ethical decision making, most of the CPAs check what is the right thing to do when they are uncertain of what to do, and they do not hesitate to ask what is the right thing to do when something has gone wrong. They do not make decisions by themselves, to avoid making mistakes under certain conditions. According to **Table 2**, most of the CPAs learned how to make ethical decisions from their family, and not from the ethics training or lessons they took. The reason behind this finding is Turkey's family-centered culture. The development of a person's ethical beliefs starts with learning solid family values at home. On the other hand, most of the CPAs think that being a whistle-blower is not always a bad thing. This line of thinking may be explained by signaling theory, which is the idea that one party convincingly signals information to another party. They think whistle-blowing is efficient if managers signal their private information to outsiders to improve their awareness and support dialog among the public, owners, and managers [41, 42]. With regard to the last item in this factor group, most of the CPAs think that it is not appropriate to compromise one's ethics to be successful, not even for a promotion.

Based on the responses to the third group of statements for the factor of transparency, most of the respondents think that transparency is vitally important for companies, and agree that financial reports are trustworthy and reliable if CPAs prepare them. Additionally, they think that it is not easy to violate transparency in their companies. This result indicates that they are aware of the consequences of engaging in unethical practices. On the other hand, they believe their financial reports are not fully transparent. This result indicates that even though they prepare trustworthy financial reports, they do not trust top managers or owners of their companies, who they think may interfere with the numbers for their own or their companies' interests. This result indicates a possible problem with the implementation of penalties under related laws, and compels us to think about whether audit organizations' work should improve and be more detailed.

in **Table 2** are obtained by considering the five highest average responses to the statements for each of the three factors. Based on the responses to first group of statements for the factor of ethical awareness, most of the CPAs disagree that other CPAs in their company engage in unethical practices. They may have answered so to protect the reputations of fellow CPAs, but their response may also simply indicate that they trust other CPAs. Most of the CPAs are aware that if they engage in unethical practices under any conditions, they will be fired. Likewise, most of them are aware that if they participate in unethical practices for their own

Most of them are also aware that if they participate in unethical practices for their company's interests, they will be immediately reprimanded, but the average response to this statement is distinctly lower than that to the former statement. Some of the CPAs may think that if they engage in unethical practices on behalf of their companies, top management may ignore what was done or may even promote them since their actions may have increased profits to a desired level without drawing the attention of anyone inside or outside of the company. The last item in the factor group is that most of the CPAs think that unsuccessful CPAs engage more in unethical practices than successful ones to achieve a short-cut to success. The last three items in the factor group are an indicator that companies have not yet fully complied

with the Turkish ethical system for accounting, and still exhibit unethical behaviors.

Based on the responses to the second group of statements for the factor of ethical decision making, most of the CPAs check what is the right thing to do when they are uncertain of what to do, and they do not hesitate to ask what is the right thing to do when something has gone wrong. They do not make decisions by themselves, to avoid making mistakes under certain conditions. According to **Table 2**, most of the CPAs learned how to make ethical decisions from their family, and not from the ethics training or lessons they took. The reason behind this finding is Turkey's family-centered culture. The development of a person's ethical beliefs starts with learning solid family values at home. On the other hand, most of the CPAs think that being a whistle-blower is not always a bad thing. This line of thinking may be explained by signaling theory, which is the idea that one party convincingly signals information to another party. They think whistle-blowing is efficient if managers signal their private information to outsiders to improve their awareness and support dialog among the public, owners, and managers [41, 42]. With regard to the last item in this factor group, most of the CPAs think that it is not appropriate to compromise one's ethics to be successful, not even for a promotion. Based on the responses to the third group of statements for the factor of transparency, most of the respondents think that transparency is vitally important for companies, and agree that financial reports are trustworthy and reliable if CPAs prepare them. Additionally, they think that it is not easy to violate transparency in their companies. This result indicates that they are aware of the consequences of engaging in unethical practices. On the other hand, they believe their financial reports are not fully transparent. This result indicates that even though they prepare trustworthy financial reports, they do not trust top managers or owners of their companies, who they think may interfere with the numbers for their own or their companies' interests. This result indicates a possible problem with the implementation of penalties under related laws, and compels us to think about whether audit organizations' work should

interests, they will be immediately reprimanded.

40 Accounting from a Cross-Cultural Perspective

improve and be more detailed.


#### 42 Accounting from a Cross-Cultural Perspective


Method of factor determination: principal component; rotation method: Varimax, revealed variance: 77.43%.

**Table 1.** Explanatory factor analysis concerning ethical awareness, ethical decision making, and transparency.


OLS regression is performed to test the hypotheses, and the results are presented in **Table 3**. The first column of **Table 3** shows that the ethical awareness variable affects ethical decision making positively (F = 17.023, p = 0.00). Accordingly, hypothesis 1 is accepted. Therefore, as the level of ethical awareness of CPAs increases, their ability to make ethical decisions also increases. This outcome suggests that CPAs know when situations they face are ethically problematic or include ethical dilemmas, and that they need to make ethical decisions.

**Questionnaire item Average** 

*Ethical decision making*

anyone

unethical

one's ethics

*Transparency*

responsibility

through unethical practices

unethical practices

10. CPAs are aware of sanctions and penalties for unethical behaviors −0.99 1.03

Ethical Awareness, Ethical Decision Making, and Transparency: A Study on Turkish CPAs in Istanbul

1. I check what is the right thing to do when I am uncertain of what to do −2.67 1.05 2. I ask what is the right thing to do when something has gone wrong −2.20 1.27 3. If I notice a mistake or manipulation in financial statements, I try to fix it myself 1.04 1.89

7. Being a whistle-blower is not always a bad thing 2.29 2.13

9. I learned to make ethical decisions from my family −2.12 1.01 10. I learned to make ethical decisions from my ethics training/lessons 0.15 1.13

1. Transparency is vitally important for companies −2.72 1.01 2. It is easy to violate transparency in financial reports in my company 2.29 1.29 3. I believe my company's financial reports are fully transparent 2.17 2.21 4. My company tries to create a culture of transparency 0.04 1.92

6. Trust is based on the transparency of financial reporting −2.03 1.26 7. Financial reports are generated by trustworthy CPAs in my company −2.19 1.09 8. Financial reports are generated by trustworthy CPAs in other companies −1.85 1.39

10. It is easy to violate transparency in financial reports in other companies 1.22 1.26

**Table 2.** CPAs' responses to ethical behavior awareness, ethical decision making, and transparency.

4. If I notice a mistake or manipulation in financial statements, I do not tell

5. I will fulfill top management's request for something that I think to be

6. If I could protect myself from punishments and sanctions, I would engage in

8. To be successful in my company, sometimes it is appropriate to compromise

5. My company is more concerned with the bottom line than creating moral

9. I know the consequences of inadequate and deceitful financial reports created

**response**

http://dx.doi.org/10.5772/intechopen.76867

1.25 1.93

−1.02 1.22

−1.03 1.73

2.38 1.51

1.92 1.78

−1.08 2.04

**Standard deviation** 43


**Table 2.** CPAs' responses to ethical behavior awareness, ethical decision making, and transparency.

**Questionnaire item Average** 

Transparency Transparency is vitally important for companies 0.905

creating moral responsibility

company

42 Accounting from a Cross-Cultural Perspective

transparent

my company

other companies

other companies

It is easy to violate transparency in financial reports in my

My company is more concerned with the bottom line than

Financial reports are generated by trustworthy CPAs in

Financial reports are generated by trustworthy CPAs in

I know the consequences of inadequate and deceitful financial reports created through unethical practices

It is easy to violate transparency in financial reports in

Method of factor determination: principal component; rotation method: Varimax, revealed variance: 77.43%.

**Table 1.** Explanatory factor analysis concerning ethical awareness, ethical decision making, and transparency.

My company tries to create a culture of transparency 0.860

Trust is based on the transparency of financial reporting 0.777

I believe my company's financial reports are fully

3. Most CPAs are aware of the code of ethics −1.01 2.01 4. CPAs in my company usually participate in practices that I think are unethical 2.26 1.01

1. There are numerous opportunities for CPAs in my company to take part in

2. There are numerous opportunities for CPAs outside of my company to take

5. CPAs outside of my company usually participate in practices that I think are

6. In my company, unsuccessful CPAs are usually more unethical than successful

7. In my company, CPAs are aware that under no conditions will unethical

8. If a CPA in my company is found to have participated in unethical behaviors that serve his/her own interests (rather than the company's interest), he/she

9. If a CPA in my company is found to have participated in unethical behaviors that serve the company's interests (rather than his/her own interest), he/she

*Ethical behavior awareness*

part in unethical practices

behaviors be tolerated

will be immediately reprimanded

will be immediately reprimanded

unethical practices

unethical

ones

**response**

0.896

0.869

0.794

0.664

0.620

0.504

0.501

0.62 2.07

−1.34 1.47

−0.05 1.67

−1.52 1.69

−2.10 1.34

−2.11 1.25

−1.84 1.21

**Standard deviation**

> OLS regression is performed to test the hypotheses, and the results are presented in **Table 3**. The first column of **Table 3** shows that the ethical awareness variable affects ethical decision making positively (F = 17.023, p = 0.00). Accordingly, hypothesis 1 is accepted. Therefore, as the level of ethical awareness of CPAs increases, their ability to make ethical decisions also increases. This outcome suggests that CPAs know when situations they face are ethically problematic or include ethical dilemmas, and that they need to make ethical decisions.


and motivation to act in their own interests. This finding reveals a problem of trust among accountants in Turkey; specifically, it indicates a problem in the implementation of the penalties under related laws, even when such laws are considered inadequate and deterrent.

Ethical Awareness, Ethical Decision Making, and Transparency: A Study on Turkish CPAs in Istanbul

http://dx.doi.org/10.5772/intechopen.76867

45

Thus, ethical awareness affects ethical decision making and transparency and therefore, when the levels of ethical decision making and transparency increase, the level of ethical awareness also increases. Hence, it would be helpful to provide ethics lessons in schools or raise more

The major accounting scandals (e.g. Enron, Lehman Brothers) from around the world have prompted the public to question the accountants' ethics. While accountants embrace their significant roles in generating and auditing financial information for the benefit of society, they face many ethical problems in their daily lives. Their unethical practices can damage all interested parties, and for this reason, they should adapt to rapid changes in accounting standards and legislation to maintain their competitive power, and consequently, their ethics. Therefore, the concepts of ethical awareness, ethical decision making, and transparency

This chapter clearly indicates the importance of ethics to accounting profession. Ethical awareness, ethical decision making, and transparency are important concepts for every profession, individual and society. However, in terms of the accounting profession, it is not exaggerated to attach vital importance to the subject. The accounting profession at the production center of qualified information is important for all segments of the society in the light of the information they provide. Therefore, efforts to raise ethical awareness, ethical decision making and

[1] Uyar M, Özer G. The ethical orientation and professional commitment: An EMPIRICAL EXAMINATION ON Turkish accountants. African Journal of Business Management.

[2] Demir B. Muhasebe ve Denetim Mesleğinde Etik [Ethics in accounting and auditing profession]. Eğitim ve Öğretim Araştırmaları Dergisi [Journal of Research in Education

public awareness about ethics.

should be understood more clearly.

transparency for professionals are needed.

Address all correspondence to: nida.turegun@ozyegin.edu.tr

Ozyegin University, Çekmeköy, İstanbul, Turkey

2011;**5**(23):10023-10037. DOI: 10.1.1.844.5791

and Teaching]. 2015;**4**(4):341-352

**Author details**

Nida Türegün

**References**

**Table 3.** Regression results.

The second column of **Table 3** shows that the ethical decision variable affects transparency positively (F = 15.198, p-value = 0.00). Accordingly, hypothesis 2 is accepted. Therefore, as the level of ethical decisions of CPAs increases, their desire to create transparency also increases. This outcome suggests that these three concepts are strongly related to each other. Thus, there is a chain effect, where ethical awareness affects ethical decision making, which, in turn, affects the level of transparency.

The third column of **Table 3** shows that the ethical awareness variable affects transparency positively (F = 21.267, p-value 0.00). Accordingly, hypothesis 3 is accepted. Therefore, as the level of ethical awareness of CPAs increases, their desire to create transparency also increases. This outcome suggests that even though we exclude the ethical decisions variable, transparency is directly affected by ethical awareness. Consequently, ethical awareness is a noteworthy factor that affects ethical decision making and transparency.

#### **7. Conclusion**

Based on the average of the CPAs' survey responses, in the process of their decision making about an ethical issue or transparency of financial reports, CPAs are affected mainly by their level of ethical awareness. CPAs check what is the right thing to do when they are uncertain of what to do, and they do not hesitate to ask what is the right thing to do when something has gone wrong. This outcome indicates that they are ethically aware, which also allows them to make ethical decisions. The results of this study's analysis show that the three concepts of ethical awareness, ethical decision making, and transparency are strongly connected to each other.

Because of Turkey's family-centered culture, development of the knowledge of ethics begins in the family, and this tendency ensures that an individual is raised with morally sensitive feelings and a higher level of ethical awareness. Therefore, according to the results of the analysis of the survey responses, most of the CPAs believe they generate transparent reports, but they still hesitate to trust their top managers and owners, who have the power and motivation to act in their own interests. This finding reveals a problem of trust among accountants in Turkey; specifically, it indicates a problem in the implementation of the penalties under related laws, even when such laws are considered inadequate and deterrent.

Thus, ethical awareness affects ethical decision making and transparency and therefore, when the levels of ethical decision making and transparency increase, the level of ethical awareness also increases. Hence, it would be helpful to provide ethics lessons in schools or raise more public awareness about ethics.

The major accounting scandals (e.g. Enron, Lehman Brothers) from around the world have prompted the public to question the accountants' ethics. While accountants embrace their significant roles in generating and auditing financial information for the benefit of society, they face many ethical problems in their daily lives. Their unethical practices can damage all interested parties, and for this reason, they should adapt to rapid changes in accounting standards and legislation to maintain their competitive power, and consequently, their ethics. Therefore, the concepts of ethical awareness, ethical decision making, and transparency should be understood more clearly.

This chapter clearly indicates the importance of ethics to accounting profession. Ethical awareness, ethical decision making, and transparency are important concepts for every profession, individual and society. However, in terms of the accounting profession, it is not exaggerated to attach vital importance to the subject. The accounting profession at the production center of qualified information is important for all segments of the society in the light of the information they provide. Therefore, efforts to raise ethical awareness, ethical decision making and transparency for professionals are needed.

## **Author details**

Nida Türegün

The second column of **Table 3** shows that the ethical decision variable affects transparency positively (F = 15.198, p-value = 0.00). Accordingly, hypothesis 2 is accepted. Therefore, as the level of ethical decisions of CPAs increases, their desire to create transparency also increases. This outcome suggests that these three concepts are strongly related to each other. Thus, there is a chain effect, where ethical awareness affects ethical decision making, which, in turn,

**Variable Ethical decisions Transparency Transparency**

Constant 0.702 4.137 0.659 3.264 0.432 1.783 Ethical awareness 0.564 3.287\*\*\* 0.263 1.189\*\*

Ethical decisions 0.535 4.738\*\*\*

R<sup>2</sup> 0.307 0.278 0.102 F 17.023\*\*\* 15.198\*\*\* 21.267\*\*\*

**β<sup>i</sup> t β<sup>i</sup> t β<sup>i</sup> t**

The third column of **Table 3** shows that the ethical awareness variable affects transparency positively (F = 21.267, p-value 0.00). Accordingly, hypothesis 3 is accepted. Therefore, as the level of ethical awareness of CPAs increases, their desire to create transparency also increases. This outcome suggests that even though we exclude the ethical decisions variable, transparency is directly affected by ethical awareness. Consequently, ethical awareness is a notewor-

Based on the average of the CPAs' survey responses, in the process of their decision making about an ethical issue or transparency of financial reports, CPAs are affected mainly by their level of ethical awareness. CPAs check what is the right thing to do when they are uncertain of what to do, and they do not hesitate to ask what is the right thing to do when something has gone wrong. This outcome indicates that they are ethically aware, which also allows them to make ethical decisions. The results of this study's analysis show that the three concepts of ethical awareness, ethical decision making, and transparency are strongly connected to each other. Because of Turkey's family-centered culture, development of the knowledge of ethics begins in the family, and this tendency ensures that an individual is raised with morally sensitive feelings and a higher level of ethical awareness. Therefore, according to the results of the analysis of the survey responses, most of the CPAs believe they generate transparent reports, but they still hesitate to trust their top managers and owners, who have the power

thy factor that affects ethical decision making and transparency.

affects the level of transparency.

\*\*Significant at the 0.05 level. \*\*\*Significant at the 0.01 level.

44 Accounting from a Cross-Cultural Perspective

**Table 3.** Regression results.

**7. Conclusion**

Address all correspondence to: nida.turegun@ozyegin.edu.tr

Ozyegin University, Çekmeköy, İstanbul, Turkey

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**Chapter 3**

**Provisional chapter**

**Theoretical Perspectives on Sustainability Reporting: A**

**Theoretical Perspectives on Sustainability Reporting: A** 

This study analyzes the perspectives of the institutional theory, the legitimacy theory, and the stakeholders' theory in the accounting changing process and sustainability reports. The objective is to explore how these theories are used in corporate social responsibility (CSR) disclosure. Through this analysis, it is provided a better theoretical understanding of these theories, which support and promote research on accounting and sustainability reporting. This chapter analyzes each theory and the relationship between them. We conclude that, although the legitimacy theory is the dominant theory used in accounting and sustainability reporting studies, it is related to the other theories. The selection and

**Keywords:** institutional theory, legitimacy theory, accounting, stakeholders' theory,

The present business language takes for granted that no business may be successful without the approval of its stakeholders as a socially and environmentally responsible entity [1]. As there is a greater awareness and concern about the organization's activity and its effects [2], the sustainability reporting offers them quite a lot in terms of transparency regarding environmental and social performance issues. Thus, the voluntary disclosure of these social, environmental, and economic variables, known as triple bottom line (TBL), should be seriously and responsibly perceived. Accordingly, Elkington [3] suggested combining the social and environmental

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

DOI: 10.5772/intechopen.76951

**Literature Review**

**Literature Review**

Alcina Portugal Dias

Alcina Portugal Dias

**Abstract**

Maria da Conceição da Costa Tavares and

Maria da Conceição da Costa Tavares and

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

application will depend on the study focus.

sustainability reports

**1. Introduction**

http://dx.doi.org/10.5772/intechopen.76951

#### **Theoretical Perspectives on Sustainability Reporting: A Literature Review Theoretical Perspectives on Sustainability Reporting: A Literature Review**

DOI: 10.5772/intechopen.76951

Maria da Conceição da Costa Tavares and Alcina Portugal Dias Maria da Conceição da Costa Tavares and Alcina Portugal Dias

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.76951

#### **Abstract**

This study analyzes the perspectives of the institutional theory, the legitimacy theory, and the stakeholders' theory in the accounting changing process and sustainability reports. The objective is to explore how these theories are used in corporate social responsibility (CSR) disclosure. Through this analysis, it is provided a better theoretical understanding of these theories, which support and promote research on accounting and sustainability reporting. This chapter analyzes each theory and the relationship between them. We conclude that, although the legitimacy theory is the dominant theory used in accounting and sustainability reporting studies, it is related to the other theories. The selection and application will depend on the study focus.

**Keywords:** institutional theory, legitimacy theory, accounting, stakeholders' theory, sustainability reports

#### **1. Introduction**

The present business language takes for granted that no business may be successful without the approval of its stakeholders as a socially and environmentally responsible entity [1]. As there is a greater awareness and concern about the organization's activity and its effects [2], the sustainability reporting offers them quite a lot in terms of transparency regarding environmental and social performance issues. Thus, the voluntary disclosure of these social, environmental, and economic variables, known as triple bottom line (TBL), should be seriously and responsibly perceived. Accordingly, Elkington [3] suggested combining the social and environmental

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

reports with the traditional financial report to achieve an excellent TBL performance for which new types of economic, social, and environmental partnerships are necessary.

In fact, the rising number of social and environmental consequences the economic activity is producing [13] has led to an increase of empirical studies in social and environmental accounting, despite most of them approach the private sector [14–16]. However, traditional financial reporting is unable to explain and present complexities associated with several issues of public interest. They do not adequately deal with the measurement of social and environmental impact given that social issues may not always carry monetary values. The social and environmental reporting pays more attention to the social and environmental impact of organizations. Consequently, there is a need for broader sustainability reporting in

Theoretical Perspectives on Sustainability Reporting: A Literature Review

http://dx.doi.org/10.5772/intechopen.76951

53

Accounting, in its broadest sense, may be considered a record and control system by which the "elements of civil society, the state and the market define, articulate and monitor the behaviors by which they will be judged and held accountable". "Social accounting is concerned with exploring how the social and environmental activities undertaken (or not, as the case may be) by different elements of a society can be‑and are‑expressed" ([17], p. 240). Thus, the disclosure of the social impact of an organization is important, and the disclosure of accurate and relevant information on corporate behavior can bring stakeholders, organizations, and society some benefits [18]. Hence, disclosure is a way through which organizations

Recently, the focus has been the content and development of stand-alone sustainability reports, such as the Global Reporting Initiative (GRI) (see [16, 20, 21]). The GRI, developed in cooperation with the United Nations Environment Programme (UNEP), is particularly wellknown and challenging [18]. It came forward in 1999 as an answer to a unified system of CSR reports' standards missing [21], following the USA's financial system model for disclosure (FASBI) [20, 21]. The GRI offers a set of principles for the CSR report and a structured content with indicators for the social, environmental, and economic domains, with the mission of developing and globally spreading guidelines applicable to sustainability reports, enabling organizations to voluntarily report their activities in those dimensions [18, 22]. It has then

The main driver of the IT is that organizations work within a social grid, whose practices are instigated by golden social rules and norms on what is an adequate or acceptable behavior in the environment they operate in [23, 24]. As a result, the social reality becomes the "guidelines for social behavior" ([25], p. 1). Organizations yield to institutional pressures for change since an increasing stability, legitimacy, resources, and survival capacity will reward them for

The IT focuses particularly on the pressures and constraints of the institutional environment and "illustrates how the exercise of strategic choice may be preempted when organizations are unconscious of, blind to, or otherwise take for granted the institutional processes to which they adhere" ([26], p. 148). It limits organizational choices and focuses on how the cultural and social environment influences organizations [27]. The IT is urged by the question of why different organizations, operating in such different environments, are so often similar in their structures [28].

become an internationally recognized reporting framework.

**2.1. Overall vision on the institutional theory in the organizational practices**

organizations [13, 15, 16].

can present their CSR [19].

doing so [8, 23, 24].

Accounting literature has shown a significant growth of concern for sustainability matters and the accounting practice [4]. Sciulli [2] considers that the phrase *environmental and social accounting research* has been replaced by the term *sustainability reporting research*. Thus, accounting researchers perceive "accounting as a social and institutional practice", rather than as a mere technical practice ([5], p. 5). In this sense, this study looks into (better) understanding that accounting is not a mere daily sustained and due practice, a result of years of habits and self-indulgence [6], but that it also involves and brings about social and institutional pressures that lead entities to take certain measures and decisions in behalf of those institutions' legitimacy [7], which originates constant shifts and changes, not only at the accounts level, but also at the technological and social levels.

Institutional, legitimacy, and stakeholder theories offer different explanatory perspectives of similar sustainability phenomena. In this paper, these theoretical perspectives will be analyzed. They have been applied and taught separately [8] but they together provide a broad theoretical understanding for the research advancement in social and environmental accounting. Therefore, this study aims to explore the IT relation with the accounting shifting processes, as well as the forms of institutional pressure influencing decisions to adopt accounting practices and sustainability reports. The drivers of change and the reasons for those changes will be made known according to the new institutional sociology (NIS) [9]. This paper may be of interest for researchers who need to apply these theories and the relationships among them in accounting research and sustainability reports.

The results enable us to conclude that we may have compatible understandings of theoretical evidence under different perspectives, according to Gray et al. [10] and Chen and Roberts [8].

In this paper we start with a general insight over the IT and responsible accounting practices. Next, we provide an answer to accounting issues related to isomorphism, the legitimacy theory (LT), and the stakeholders' theory (ST). The paper discusses the relationship between these theories and their importance in accounting research and sustainability reports. Final considerations, limitations, and recommendations for future research will also be presented.

#### **2. Institutional theory and accounting practices**

According to authors such as DiMaggio and Powell [9], organizations were seen as closed systems, depending on themselves, and had no relationship with their institutional environment. In the 1960s and 1970s, after acknowledging the importance of the institutional environment for organizations, the IT gained a preponderant role in understanding the existing phenomena in the life of organizations [11]. Thus, the IT has been used to study and analyze the establishment of accounting practices in an organization. By studying the reasons for adopting certain accounting practices rather than others, and who the players are in the establishment of such practices and their reasons, it may answer some questions influencing institutional social choices [9, 12].

In fact, the rising number of social and environmental consequences the economic activity is producing [13] has led to an increase of empirical studies in social and environmental accounting, despite most of them approach the private sector [14–16]. However, traditional financial reporting is unable to explain and present complexities associated with several issues of public interest. They do not adequately deal with the measurement of social and environmental impact given that social issues may not always carry monetary values. The social and environmental reporting pays more attention to the social and environmental impact of organizations. Consequently, there is a need for broader sustainability reporting in organizations [13, 15, 16].

reports with the traditional financial report to achieve an excellent TBL performance for which

Accounting literature has shown a significant growth of concern for sustainability matters and the accounting practice [4]. Sciulli [2] considers that the phrase *environmental and social accounting research* has been replaced by the term *sustainability reporting research*. Thus, accounting researchers perceive "accounting as a social and institutional practice", rather than as a mere technical practice ([5], p. 5). In this sense, this study looks into (better) understanding that accounting is not a mere daily sustained and due practice, a result of years of habits and self-indulgence [6], but that it also involves and brings about social and institutional pressures that lead entities to take certain measures and decisions in behalf of those institutions' legitimacy [7], which originates constant shifts and changes, not only at the accounts level, but

Institutional, legitimacy, and stakeholder theories offer different explanatory perspectives of similar sustainability phenomena. In this paper, these theoretical perspectives will be analyzed. They have been applied and taught separately [8] but they together provide a broad theoretical understanding for the research advancement in social and environmental accounting. Therefore, this study aims to explore the IT relation with the accounting shifting processes, as well as the forms of institutional pressure influencing decisions to adopt accounting practices and sustainability reports. The drivers of change and the reasons for those changes will be made known according to the new institutional sociology (NIS) [9]. This paper may be of interest for researchers who need to apply these theories and the relationships among them

The results enable us to conclude that we may have compatible understandings of theoretical evidence under different perspectives, according to Gray et al. [10] and Chen and Roberts [8]. In this paper we start with a general insight over the IT and responsible accounting practices. Next, we provide an answer to accounting issues related to isomorphism, the legitimacy theory (LT), and the stakeholders' theory (ST). The paper discusses the relationship between these theories and their importance in accounting research and sustainability reports. Final considerations, limitations, and recommendations for future research will also be presented.

According to authors such as DiMaggio and Powell [9], organizations were seen as closed systems, depending on themselves, and had no relationship with their institutional environment. In the 1960s and 1970s, after acknowledging the importance of the institutional environment for organizations, the IT gained a preponderant role in understanding the existing phenomena in the life of organizations [11]. Thus, the IT has been used to study and analyze the establishment of accounting practices in an organization. By studying the reasons for adopting certain accounting practices rather than others, and who the players are in the establishment of such practices and their reasons, it may answer some questions influencing institutional

new types of economic, social, and environmental partnerships are necessary.

also at the technological and social levels.

52 Accounting from a Cross-Cultural Perspective

in accounting research and sustainability reports.

**2. Institutional theory and accounting practices**

social choices [9, 12].

Accounting, in its broadest sense, may be considered a record and control system by which the "elements of civil society, the state and the market define, articulate and monitor the behaviors by which they will be judged and held accountable". "Social accounting is concerned with exploring how the social and environmental activities undertaken (or not, as the case may be) by different elements of a society can be‑and are‑expressed" ([17], p. 240). Thus, the disclosure of the social impact of an organization is important, and the disclosure of accurate and relevant information on corporate behavior can bring stakeholders, organizations, and society some benefits [18]. Hence, disclosure is a way through which organizations can present their CSR [19].

Recently, the focus has been the content and development of stand-alone sustainability reports, such as the Global Reporting Initiative (GRI) (see [16, 20, 21]). The GRI, developed in cooperation with the United Nations Environment Programme (UNEP), is particularly wellknown and challenging [18]. It came forward in 1999 as an answer to a unified system of CSR reports' standards missing [21], following the USA's financial system model for disclosure (FASBI) [20, 21]. The GRI offers a set of principles for the CSR report and a structured content with indicators for the social, environmental, and economic domains, with the mission of developing and globally spreading guidelines applicable to sustainability reports, enabling organizations to voluntarily report their activities in those dimensions [18, 22]. It has then become an internationally recognized reporting framework.

#### **2.1. Overall vision on the institutional theory in the organizational practices**

The main driver of the IT is that organizations work within a social grid, whose practices are instigated by golden social rules and norms on what is an adequate or acceptable behavior in the environment they operate in [23, 24]. As a result, the social reality becomes the "guidelines for social behavior" ([25], p. 1). Organizations yield to institutional pressures for change since an increasing stability, legitimacy, resources, and survival capacity will reward them for doing so [8, 23, 24].

The IT focuses particularly on the pressures and constraints of the institutional environment and "illustrates how the exercise of strategic choice may be preempted when organizations are unconscious of, blind to, or otherwise take for granted the institutional processes to which they adhere" ([26], p. 148). It limits organizational choices and focuses on how the cultural and social environment influences organizations [27]. The IT is urged by the question of why different organizations, operating in such different environments, are so often similar in their structures [28].

The IT is one of the dominant theoretical perspectives and may facilitate a wider representation of accounting as an object of institutional practices and better coordinate the part of accounting in the institutionalization process. It is more and more applied in the accounting research to study the accounting practice in organizations [29]. The main premise of the IT, which DiMaggio and Powell [27] have related to voluntary corporate disclosures, is that it may help explain why organizations tend to act and communicate in a homogeneous way in the organizational field [30].

ecological reasons [40]. As Scott states [25], the IT has a long past and a promising future. It is a widely positioned theory to help face questions such as the similarity and differentiation foundations of the organization, the relationship between structure and behavior, the role of symbols in social life, the relationship between ideas and interests, and the tensions between

Theoretical Perspectives on Sustainability Reporting: A Literature Review

http://dx.doi.org/10.5772/intechopen.76951

55

"Organizational fields rich in myths and ceremonies are constructed when pressure is exerted on organizations by forces in the surrounding environment" ([41], p. 285). The organizational field, as a model within the organization, tends to become infused with a quality taken as certain, where the actors unconsciously accept the model as prevailing, good, and adequate [27]. It is in this sense that the IT is usually used, to account for the resemblance and stability of organizational arrangements within a population or organization field to which compliance

Organizational change is not so much due to efficiency and rivalry competitiveness but rather due to bureaucracy reduction and organizations' attempt to become more identical with each other to achieve legitimacy in the market and in their organizational context, and not necessarily to become more efficient [27]. Usually, the IT is not considered an organizational change theory but an explanation to the similarity (isomorphism) and stability, although recently, the NIS has attempted to answer the emerging questions on changing [39], and some argue that

While national institutions are path dependent, according to the traditional IT, and organizations tend to behave the same way (that is, displaying isomorphism), the NIS's intraorganizational dynamic "precipitate and facilitate organizational change, and the adoption of governance elements that the organization finds efficient and/or legitimate" ([33], p. 489).

Branco and Rodrigues [44, 45] argue that organizations get involved in CSR activities and disclosure for two reasons: because they assume that fruitful relations with stakeholders boost an increase in financial return and because they are adapting to stakeholders' norms and expectations, which constitute a legitimacy instrument, to show their compliance to such norms and expectations (consistent with the IT explanations, in particular with the LT).

There are several authors with important studies combining several theories. For example, Chen and Roberts [8] explore how the IT, LT, ST, and resources dependency theory (RDT) can inform and supply important theoretical frameworks for environmental and social accounting research, as they share a common interest: to explain how organizations survive in a changing society. Golob and Bartlett [18] follow the LT and ST theoretical framework in their comparative study of CSR reports in Australia and Slovenia. Oliver [26] focuses her study on the IT and RDT to analyze the convergent and divergent assumptions relevant to characterize

standards have followed [42]. Isomorphism is a key element of the IT [43].

organizations are strategic in their answers to imposed institutional pressures [26].

**3. The explanatory theoretical framework for sustainability** 

the strategic responses to external pressures and expectations.

freedom and order.

**disclosure: the thesis**

The IT, specifically the NIS, is particularly useful to often complete functional explanations of accounting practices [31]. The contemporary IT (NIS) has attracted the attention of a wide range of scholars in the social science areas, and it is followed to analyze the systems which range from the micro to the macro global framework of interpersonal interactions [25].

The two-main precursor works of the NIS are Meyer and Rowan [32] and DiMaggio and Powell [27]. The NIS applied to accounting began around the 1970s, by the investigator Anthony Hopwood, with publications in scientific magazines such as *Accounting*, *Organizations*, and *Society* [6]. The NIS is founded on the premise that organizations answer to their institutional environment pressures and "adopt structures and/or procedures that are socially accepted as being the appropriate organizational choice" ([24], p. 569). According to the NIS, accounting practices are the result of the institutional nature and of the economic pressures from their institutional environment, operating in an open system. IT appears as a response to the main stream in accounting research, which sees accounting practices as an economic, rational, and logical result [11]. DiMaggio and Powell [9] believe that the NIS rejects the rational actors' models, standing up for an interest in institutions as independent variables. For such, they attempt to give cognitive and cultural explanations to those models.

The NIS is being used to obtain proposals about the general governance change. Because of the globalization, organizations can choose different elements of any system that suit their requirements. The timing differences for firms to adopt institutional changes show the potential value of the NIS to predict circumstances that make the acceptance of an institutional innovation likely. Here, the key element is the organization's insertion degree in traditional institutions [33]. According to the NIS, "organizations use formal structures for purposes of legitimization, independently of consequences in terms of efficiency" ([34], p. 852).

The NIS model holds that survival of the organization is motivated by the orientation toward the institutional environment. This alignment enables organizational actors to depict the organization as legitimate [35]. The NIS emphasizes the influences of the institutional environment, molding the social and organizational behavior, thereby reducing ambiguity and uncertainty [36–38].

NIS research analyses how organizations seek practices that are not explained by efficiency maximization. Organizations do not always adopt strategies, structures, and processes to enhance their performance; instead, they react and look for ways to accommodate external and regulative pressures, seeking legitimacy before their stakeholders [27, 28]. The IT supplies a basis for analyzing the nature of the messages of organizational communication, determining how far organizations seek competitive advantage, legitimacy, and responsiveness to ecological reasons [40]. As Scott states [25], the IT has a long past and a promising future. It is a widely positioned theory to help face questions such as the similarity and differentiation foundations of the organization, the relationship between structure and behavior, the role of symbols in social life, the relationship between ideas and interests, and the tensions between freedom and order.

The IT is one of the dominant theoretical perspectives and may facilitate a wider representation of accounting as an object of institutional practices and better coordinate the part of accounting in the institutionalization process. It is more and more applied in the accounting research to study the accounting practice in organizations [29]. The main premise of the IT, which DiMaggio and Powell [27] have related to voluntary corporate disclosures, is that it may help explain why organizations tend to act and communicate in a homogeneous way in

The IT, specifically the NIS, is particularly useful to often complete functional explanations of accounting practices [31]. The contemporary IT (NIS) has attracted the attention of a wide range of scholars in the social science areas, and it is followed to analyze the systems which range from the micro to the macro global framework of interpersonal interactions [25].

The two-main precursor works of the NIS are Meyer and Rowan [32] and DiMaggio and Powell [27]. The NIS applied to accounting began around the 1970s, by the investigator Anthony Hopwood, with publications in scientific magazines such as *Accounting*, *Organizations*, and *Society* [6]. The NIS is founded on the premise that organizations answer to their institutional environment pressures and "adopt structures and/or procedures that are socially accepted as being the appropriate organizational choice" ([24], p. 569). According to the NIS, accounting practices are the result of the institutional nature and of the economic pressures from their institutional environment, operating in an open system. IT appears as a response to the main stream in accounting research, which sees accounting practices as an economic, rational, and logical result [11]. DiMaggio and Powell [9] believe that the NIS rejects the rational actors' models, standing up for an interest in institutions as independent variables. For such, they

The NIS is being used to obtain proposals about the general governance change. Because of the globalization, organizations can choose different elements of any system that suit their requirements. The timing differences for firms to adopt institutional changes show the potential value of the NIS to predict circumstances that make the acceptance of an institutional innovation likely. Here, the key element is the organization's insertion degree in traditional institutions [33]. According to the NIS, "organizations use formal structures for purposes of

The NIS model holds that survival of the organization is motivated by the orientation toward the institutional environment. This alignment enables organizational actors to depict the organization as legitimate [35]. The NIS emphasizes the influences of the institutional environment, molding the social and organizational behavior, thereby reducing ambiguity and

NIS research analyses how organizations seek practices that are not explained by efficiency maximization. Organizations do not always adopt strategies, structures, and processes to enhance their performance; instead, they react and look for ways to accommodate external and regulative pressures, seeking legitimacy before their stakeholders [27, 28]. The IT supplies a basis for analyzing the nature of the messages of organizational communication, determining how far organizations seek competitive advantage, legitimacy, and responsiveness to

legitimization, independently of consequences in terms of efficiency" ([34], p. 852).

attempt to give cognitive and cultural explanations to those models.

the organizational field [30].

54 Accounting from a Cross-Cultural Perspective

uncertainty [36–38].

"Organizational fields rich in myths and ceremonies are constructed when pressure is exerted on organizations by forces in the surrounding environment" ([41], p. 285). The organizational field, as a model within the organization, tends to become infused with a quality taken as certain, where the actors unconsciously accept the model as prevailing, good, and adequate [27]. It is in this sense that the IT is usually used, to account for the resemblance and stability of organizational arrangements within a population or organization field to which compliance standards have followed [42]. Isomorphism is a key element of the IT [43].

Organizational change is not so much due to efficiency and rivalry competitiveness but rather due to bureaucracy reduction and organizations' attempt to become more identical with each other to achieve legitimacy in the market and in their organizational context, and not necessarily to become more efficient [27]. Usually, the IT is not considered an organizational change theory but an explanation to the similarity (isomorphism) and stability, although recently, the NIS has attempted to answer the emerging questions on changing [39], and some argue that organizations are strategic in their answers to imposed institutional pressures [26].

While national institutions are path dependent, according to the traditional IT, and organizations tend to behave the same way (that is, displaying isomorphism), the NIS's intraorganizational dynamic "precipitate and facilitate organizational change, and the adoption of governance elements that the organization finds efficient and/or legitimate" ([33], p. 489).

## **3. The explanatory theoretical framework for sustainability disclosure: the thesis**

Branco and Rodrigues [44, 45] argue that organizations get involved in CSR activities and disclosure for two reasons: because they assume that fruitful relations with stakeholders boost an increase in financial return and because they are adapting to stakeholders' norms and expectations, which constitute a legitimacy instrument, to show their compliance to such norms and expectations (consistent with the IT explanations, in particular with the LT).

There are several authors with important studies combining several theories. For example, Chen and Roberts [8] explore how the IT, LT, ST, and resources dependency theory (RDT) can inform and supply important theoretical frameworks for environmental and social accounting research, as they share a common interest: to explain how organizations survive in a changing society. Golob and Bartlett [18] follow the LT and ST theoretical framework in their comparative study of CSR reports in Australia and Slovenia. Oliver [26] focuses her study on the IT and RDT to analyze the convergent and divergent assumptions relevant to characterize the strategic responses to external pressures and expectations.

Thus, in the analytical framework presented, accounting and sustainability reports will be seen through three different lenses: the IT and isomorphism (see [24, 27, 32, 39, 41, 46–49]), the LT as a source of competitive advantage, differentiating from their competitor and legitimizing their position and compliance with norms (see [2, 8, 10, 14, 44, 45, 50–55]), and the ST, responding to their expectations (see [8, 10, 19, 38, 54, 55]).

also mention that uncertainty may lead to isomorphism, and within an organizational field, this tends to be stronger. Thus, these three types of institutional pressures promote homoge-

Theoretical Perspectives on Sustainability Reporting: A Literature Review

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57

In an institutional perspective, the "most important aspect of isomorphism with environmental institutions is the evolution of organizational language" ([32], p. 348). So, the IT explains accounting choice through organizational actors being subject to institutional pressure normative, or coercive, or mimetic [47]. In accounting studies, the IT has been used [24] based on this list of institutional mechanisms, which work differently, "which is important to notice in order to fully understand how decision makers are influenced by institutions" ([47], p. 151). It would be expected that coercive, normative, and mimetic pressures regarding the adoption of sustainable practices would arise at the state level as this is one of the entities that constitute organizational fields with which firms will be congruent [62]. Hillebrand et al. [49], according to the institutional perspective, which conceptualizes that organizations operate in a social context, sees social pressures as strong predictors of isomorphism. It has shown that mimetic reasons can reduce an organization's capacity to obtain valuable insights from their customers. Frumkin and Galaskiewicz [41] state that, although the PS is seen as an institutionalization conductor, it is also susceptible to these types of pressures, adapting and changing if exposed to institutional forces. Through legitimacy practices it demonstrates social and economic aptitude by conforming to institutional pressures. Touron [34] verifies in his study that the IT partly allows explaining the actions of organizations according to international accounting standards, in which normative isomorphism has a crucial part, and mimicry helps

Campbell [63] presents an IT of CSR that consists of a series of propositions, specifying the conditions in which organizations are susceptible to behaving in a socially responsible way. Trevino et al. [48] believe that the cognitive, normative, and regulative pillars represent the processes leading to institutional change and influence the organization's results. Bebbington et al. [46] have used the IT theoretical framework in the narrative analysis to explore how regulative, normative, and cognitive institutions combine with organizational dynamics to influence sustainable development (SD) reports' activity and the institutionalization of this practice. Chen and Roberts [8] state that the focus of the IT study, applicable to social and environmental studies, is the adoption of a certain structure, system, program, or practice of an organization that is normally implemented by similar organizations. Jamali [42] has followed the IT theoretical framework to account for the similarity and stability of organizational practices within a specific organizational area. These practices are affected by the

Jackson and Apostolakou [58] investigate the institutional determinants of CSR, in a comparative institutional analysis, to understand how institutional differences between countries may influence how organizations get involved with CSR. They show that national and institutional level factors have an asymmetric effect: they strongly influence the likelihood of an organization to adopt the "minimal norms" of CSR but have little influence on the adoption of "better practices." Also, using a NIS framework, Schultz and Wehmeier [35] have shown that organizations suffer enormous and conflicting pressures in economic, social, and environmental

normative, regulative, and cognitive aspects of the institutional environment.

neity within organizational fields [61].

justifying the adoption of accounting norms.

These theories, applied as complementary, can enhance our understanding of the practice and choice of GRI sustainability reports, as disclosing instruments of accounting practices and sustainability reports.

#### **3.1. Institutional isomorphism and sustainability pressures**

IT literature emphasizes how organizational structures and processes become isomorphic within the norms of specific types of organizations. For those defending the NIS, organizations sharing the same organizational environment are under the same pressures, tending to be isomorphic [9, 27]. Leaptrott [56] states that isomorphism is NIS's focus, which results from the necessity to obtain and maintain legitimacy, to deal with uncertainty and the normative influences of authorized sources. Isomorphism is a synonym for *convergence*, and when an organization becomes similar to the characteristics of another, an isomorphism process happens [43]. This way, DiMaggio and Powell [27] define isomorphism as the process through which organizations adopt similar structures and systems, making their practices identical. The concept of isomorphism does not address the mentality of the intervenient actors in the organizational behaviors but the structure that determines the decision choices those actors will make as rational and cautious.

The IT attempts to explain the existing institutional isomorphic changing process in organizations, arguing that there are forces encouraging the convergence of business practices [57]. The IT claims that organizations' operations comply with social rules, values, and assumptions on what is an acceptable behavior [26, 50]. Some sectors or institutional areas have powerful environmental agents able to impose structural practices in subordinated organizational units [23], which under isomorphic pressures adopt "institutionalized" norms and practices in order to be perceived as "legitimate" [12]. However, to authors such as DiMaggio and Powell [27], these organizational characteristics change to increase compatibility with the characteristics of the institutional environment. In this sense, "isomorphism is a key element of" the IT and assumes that organizations adopt management structures and practices considered legitimate and socially acceptable by other organizations in their field, regardless their real usefulness" ([43], p. 742).

In institutional isomorphism, organizations are not mere production systems; they are also social and cultural systems [12, 36]. Thus, they tend to adopt the same practices over time as an institutional response to common pressures from similar industries or organizations [12, 27, 32, 36, 43]. Institutional isomorphism leads to the organizational success and endurance [32], enabling the identification of three different types of mechanisms making organizations adapt to their institutional environment, leading to isomorphic institutional change: normative, coercive, and mimetic (see [8, 24, 27, 34, 41, 43, 46, 47, 57–61]). DiMaggio and Powell [27] also mention that uncertainty may lead to isomorphism, and within an organizational field, this tends to be stronger. Thus, these three types of institutional pressures promote homogeneity within organizational fields [61].

Thus, in the analytical framework presented, accounting and sustainability reports will be seen through three different lenses: the IT and isomorphism (see [24, 27, 32, 39, 41, 46–49]), the LT as a source of competitive advantage, differentiating from their competitor and legitimizing their position and compliance with norms (see [2, 8, 10, 14, 44, 45, 50–55]), and the ST,

These theories, applied as complementary, can enhance our understanding of the practice and choice of GRI sustainability reports, as disclosing instruments of accounting practices

IT literature emphasizes how organizational structures and processes become isomorphic within the norms of specific types of organizations. For those defending the NIS, organizations sharing the same organizational environment are under the same pressures, tending to be isomorphic [9, 27]. Leaptrott [56] states that isomorphism is NIS's focus, which results from the necessity to obtain and maintain legitimacy, to deal with uncertainty and the normative influences of authorized sources. Isomorphism is a synonym for *convergence*, and when an organization becomes similar to the characteristics of another, an isomorphism process happens [43]. This way, DiMaggio and Powell [27] define isomorphism as the process through which organizations adopt similar structures and systems, making their practices identical. The concept of isomorphism does not address the mentality of the intervenient actors in the organizational behaviors but the structure that determines the decision choices those actors

The IT attempts to explain the existing institutional isomorphic changing process in organizations, arguing that there are forces encouraging the convergence of business practices [57]. The IT claims that organizations' operations comply with social rules, values, and assumptions on what is an acceptable behavior [26, 50]. Some sectors or institutional areas have powerful environmental agents able to impose structural practices in subordinated organizational units [23], which under isomorphic pressures adopt "institutionalized" norms and practices in order to be perceived as "legitimate" [12]. However, to authors such as DiMaggio and Powell [27], these organizational characteristics change to increase compatibility with the characteristics of the institutional environment. In this sense, "isomorphism is a key element of" the IT and assumes that organizations adopt management structures and practices considered legitimate and socially acceptable by other organizations in their field, regardless their

In institutional isomorphism, organizations are not mere production systems; they are also social and cultural systems [12, 36]. Thus, they tend to adopt the same practices over time as an institutional response to common pressures from similar industries or organizations [12, 27, 32, 36, 43]. Institutional isomorphism leads to the organizational success and endurance [32], enabling the identification of three different types of mechanisms making organizations adapt to their institutional environment, leading to isomorphic institutional change: normative, coercive, and mimetic (see [8, 24, 27, 34, 41, 43, 46, 47, 57–61]). DiMaggio and Powell [27]

responding to their expectations (see [8, 10, 19, 38, 54, 55]).

**3.1. Institutional isomorphism and sustainability pressures**

and sustainability reports.

56 Accounting from a Cross-Cultural Perspective

will make as rational and cautious.

real usefulness" ([43], p. 742).

In an institutional perspective, the "most important aspect of isomorphism with environmental institutions is the evolution of organizational language" ([32], p. 348). So, the IT explains accounting choice through organizational actors being subject to institutional pressure normative, or coercive, or mimetic [47]. In accounting studies, the IT has been used [24] based on this list of institutional mechanisms, which work differently, "which is important to notice in order to fully understand how decision makers are influenced by institutions" ([47], p. 151).

It would be expected that coercive, normative, and mimetic pressures regarding the adoption of sustainable practices would arise at the state level as this is one of the entities that constitute organizational fields with which firms will be congruent [62]. Hillebrand et al. [49], according to the institutional perspective, which conceptualizes that organizations operate in a social context, sees social pressures as strong predictors of isomorphism. It has shown that mimetic reasons can reduce an organization's capacity to obtain valuable insights from their customers. Frumkin and Galaskiewicz [41] state that, although the PS is seen as an institutionalization conductor, it is also susceptible to these types of pressures, adapting and changing if exposed to institutional forces. Through legitimacy practices it demonstrates social and economic aptitude by conforming to institutional pressures. Touron [34] verifies in his study that the IT partly allows explaining the actions of organizations according to international accounting standards, in which normative isomorphism has a crucial part, and mimicry helps justifying the adoption of accounting norms.

Campbell [63] presents an IT of CSR that consists of a series of propositions, specifying the conditions in which organizations are susceptible to behaving in a socially responsible way. Trevino et al. [48] believe that the cognitive, normative, and regulative pillars represent the processes leading to institutional change and influence the organization's results. Bebbington et al. [46] have used the IT theoretical framework in the narrative analysis to explore how regulative, normative, and cognitive institutions combine with organizational dynamics to influence sustainable development (SD) reports' activity and the institutionalization of this practice. Chen and Roberts [8] state that the focus of the IT study, applicable to social and environmental studies, is the adoption of a certain structure, system, program, or practice of an organization that is normally implemented by similar organizations. Jamali [42] has followed the IT theoretical framework to account for the similarity and stability of organizational practices within a specific organizational area. These practices are affected by the normative, regulative, and cognitive aspects of the institutional environment.

Jackson and Apostolakou [58] investigate the institutional determinants of CSR, in a comparative institutional analysis, to understand how institutional differences between countries may influence how organizations get involved with CSR. They show that national and institutional level factors have an asymmetric effect: they strongly influence the likelihood of an organization to adopt the "minimal norms" of CSR but have little influence on the adoption of "better practices." Also, using a NIS framework, Schultz and Wehmeier [35] have shown that organizations suffer enormous and conflicting pressures in economic, social, and environmental aspects. In Escobar and Vredenburg's study [59] on multinational oil organizations and the adoption of SD, an interpretative approach based on the RDT and the IT was used. They state that to embrace SD, there must be some kind of power exerted on the organizations.

to change the perceptions of its relevant public without changing its real behavior; third, to manipulate perception by deviating attention from a problem to another; and fourth, to change the external expectations of its performance. He shows that social disclosure may be

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Gifford and Kestler [38] noticed that multinational companies should be embedded in the civilian society, in local community groups, and in the PS. With these trust partnerships and SD engagement, they keep their authority and credibility in communities and gain local legitimacy in the long term. SD is the ultimate corporate aim by which organizations must genuinely perform their CSR, as big and sanctioned organizations because of environmental

The CSR disclosure is one of the strategies sought by organizations to be accepted and approved for their actions in society. By disclosing CSR information, they convey a social image of responsibility, legitimizing their behaviors and improving external reputation by showing their conformity to such norms and expectations, leading to the increase of financial profitability [58]. Legitimacy from society is the reward when organizations comply with

The LT suggests that CSR disclosure is an important form of communication that aims to convince stakeholders that the organization is meeting expectations. Organizations disclose CSR information due to external pressures. They seek compliance with what organizations meeting society's expectations do; otherwise they would suffer some harm in their profits and survival [44, 45]. The vision incorporated in this theory, which is publicly embraced by management, is that organizations are sanctioned if they do not comply with the society's

An organization's legitimacy is granted and controlled by people outside the organization. Thus, it attempts to implement certain strategies in order to change stakeholders' perception and divert their attention from certain issues so as to change their expectations regarding the organization's performance. Thus, organizations are encouraged to disclose appropriate environmental information to their stakeholders to ensure that their behavior is perceived as legitimate [19]. The organizational LT predicts that organizations will do what they consider to be necessary to keep

Wilmshurst and Frost [51] state that the LT offers an explanation for the management motivation to disclose environmental information in the annual report. When activities have an adverse impact on the environmental management, the organizations will try to restore its credentials through additional information disclosure to ensure their activities and performances are acceptable to the community. This way, the LT suggests that it would be expected that organizations with poorer environmental performance would provide more environmental disclosures, extensive and positive, in their financial reports, as an effort to diminish

Chen and Roberts [8] state that the focus of the LT, when applicable to environmental and social studies, is how organizations manage their image when the social expectation is assumed and the public target is not clearly identified, for example, in voluntary environmental and social disclosures. Branco and Rodrigues [67] believe that for some organizations,

their image as valid, with legitimate purposes and methods to attain them [65].

applied in all of these cases.

expectations [64].

infractions get more attention from the government [19].

institutionalized social expectations [8, 44, 45].

the increase of threats to their legitimacy [52].

Institutional theorists claim that organizations face similar institutional pressures, ending up with the adoption of similar strategies. This happens because they integrate a society, and their actions are influenced by stakeholders, "including governments (through regulations), an industry (through standards and norms), competitors (through better business models), and consumers (through loyalty)" ([59], p. 40). Power exerted by regulators leads to coercive isomorphism as it induces organizations to adopt similar SD strategies and practices. Power induced by the industry leads to normative isomorphism as it induces standards to step in to prevent coercive measures from emerging (voluntary norms may be anticipated through written regulations, which may put at risk the competitiveness of a multinational). Power exerted by competitors leads mimetic isomorphism to induce the existence of successful, proven competitive models that should be adopted as they diminish the uncertainty or complexity related to SD pressures.

#### **3.2. Legitimacy theory as explanatory theory in the organizations' image management**

The process of legitimacy search is directly related to the IT, as it suggests the institutionalization of the normative values of an integrated social system for concrete behaviors of institutions. Theorists believe that compliance with institutional norms established for a long time leads to institutional legitimacy. This legitimization process also strengthens the legitimacy of the existing social values system [8]. These authors present in their study a group of researchers who have used the LT to explain the motivation behind the voluntary disclosures of organizations. This theory postulates that organizations attempt to continuously assure that they operate within society's norms and limits. In this sense, there is a "social contract" between organizations and people affected by their operations [64]. Thus, conformity with social myths emphasizes the social legitimacy of organizations, convincing the public that they are worthy of support and enhancing their survival perspectives [32, 34].

The IT postulates that it is not enough for organizations to compete for resources and clients; it also has to deal with the pressure to comply with shared notions of adequate norms and behaviors, as violating them may put at risk the organization's legitimacy and affect their capacity to ensure resources and social support [57].

LT is more used in the research literature on environmental and social accounting to support the idea that social disclosure will be kept in the present levels, or increase over time, to avoid legitimacy crisis. However, literature contains some references to reasons, and incidents of social disclosure decrease [65].

In a pluralist world, the LT is concerned with organization‑society negotiation [10]. Gray et al. [10] consider Lindblom's [66] exposition of the LT to be the clearest as it argues that, first, we should distinguish legitimacy from legitimation. Lindblom [66] identified four strategies a corporation should adopt when seeking legitimation; first, to educate and inform its "relevant public" about the real changes on performance and activities of the organization; second, to change the perceptions of its relevant public without changing its real behavior; third, to manipulate perception by deviating attention from a problem to another; and fourth, to change the external expectations of its performance. He shows that social disclosure may be applied in all of these cases.

aspects. In Escobar and Vredenburg's study [59] on multinational oil organizations and the adoption of SD, an interpretative approach based on the RDT and the IT was used. They state

Institutional theorists claim that organizations face similar institutional pressures, ending up with the adoption of similar strategies. This happens because they integrate a society, and their actions are influenced by stakeholders, "including governments (through regulations), an industry (through standards and norms), competitors (through better business models), and consumers (through loyalty)" ([59], p. 40). Power exerted by regulators leads to coercive isomorphism as it induces organizations to adopt similar SD strategies and practices. Power induced by the industry leads to normative isomorphism as it induces standards to step in to prevent coercive measures from emerging (voluntary norms may be anticipated through written regulations, which may put at risk the competitiveness of a multinational). Power exerted by competitors leads mimetic isomorphism to induce the existence of successful, proven competitive models that should be adopted as they diminish the uncertainty or

The process of legitimacy search is directly related to the IT, as it suggests the institutionalization of the normative values of an integrated social system for concrete behaviors of institutions. Theorists believe that compliance with institutional norms established for a long time leads to institutional legitimacy. This legitimization process also strengthens the legitimacy of the existing social values system [8]. These authors present in their study a group of researchers who have used the LT to explain the motivation behind the voluntary disclosures of organizations. This theory postulates that organizations attempt to continuously assure that they operate within society's norms and limits. In this sense, there is a "social contract" between organizations and people affected by their operations [64]. Thus, conformity with social myths emphasizes the social legitimacy of organizations, convincing the public that

The IT postulates that it is not enough for organizations to compete for resources and clients; it also has to deal with the pressure to comply with shared notions of adequate norms and behaviors, as violating them may put at risk the organization's legitimacy and affect their

LT is more used in the research literature on environmental and social accounting to support the idea that social disclosure will be kept in the present levels, or increase over time, to avoid legitimacy crisis. However, literature contains some references to reasons, and incidents of

In a pluralist world, the LT is concerned with organization‑society negotiation [10]. Gray et al. [10] consider Lindblom's [66] exposition of the LT to be the clearest as it argues that, first, we should distinguish legitimacy from legitimation. Lindblom [66] identified four strategies a corporation should adopt when seeking legitimation; first, to educate and inform its "relevant public" about the real changes on performance and activities of the organization; second,

that to embrace SD, there must be some kind of power exerted on the organizations.

**3.2. Legitimacy theory as explanatory theory in the organizations' image** 

they are worthy of support and enhancing their survival perspectives [32, 34].

capacity to ensure resources and social support [57].

social disclosure decrease [65].

complexity related to SD pressures.

58 Accounting from a Cross-Cultural Perspective

**management**

Gifford and Kestler [38] noticed that multinational companies should be embedded in the civilian society, in local community groups, and in the PS. With these trust partnerships and SD engagement, they keep their authority and credibility in communities and gain local legitimacy in the long term. SD is the ultimate corporate aim by which organizations must genuinely perform their CSR, as big and sanctioned organizations because of environmental infractions get more attention from the government [19].

The CSR disclosure is one of the strategies sought by organizations to be accepted and approved for their actions in society. By disclosing CSR information, they convey a social image of responsibility, legitimizing their behaviors and improving external reputation by showing their conformity to such norms and expectations, leading to the increase of financial profitability [58]. Legitimacy from society is the reward when organizations comply with institutionalized social expectations [8, 44, 45].

The LT suggests that CSR disclosure is an important form of communication that aims to convince stakeholders that the organization is meeting expectations. Organizations disclose CSR information due to external pressures. They seek compliance with what organizations meeting society's expectations do; otherwise they would suffer some harm in their profits and survival [44, 45]. The vision incorporated in this theory, which is publicly embraced by management, is that organizations are sanctioned if they do not comply with the society's expectations [64].

An organization's legitimacy is granted and controlled by people outside the organization. Thus, it attempts to implement certain strategies in order to change stakeholders' perception and divert their attention from certain issues so as to change their expectations regarding the organization's performance. Thus, organizations are encouraged to disclose appropriate environmental information to their stakeholders to ensure that their behavior is perceived as legitimate [19]. The organizational LT predicts that organizations will do what they consider to be necessary to keep their image as valid, with legitimate purposes and methods to attain them [65].

Wilmshurst and Frost [51] state that the LT offers an explanation for the management motivation to disclose environmental information in the annual report. When activities have an adverse impact on the environmental management, the organizations will try to restore its credentials through additional information disclosure to ensure their activities and performances are acceptable to the community. This way, the LT suggests that it would be expected that organizations with poorer environmental performance would provide more environmental disclosures, extensive and positive, in their financial reports, as an effort to diminish the increase of threats to their legitimacy [52].

Chen and Roberts [8] state that the focus of the LT, when applicable to environmental and social studies, is how organizations manage their image when the social expectation is assumed and the public target is not clearly identified, for example, in voluntary environmental and social disclosures. Branco and Rodrigues [67] believe that for some organizations, being seen as socially responsible will bring them competitive advantage. LT is particularly useful to explain any type of disclosure trying to close a particular existing legitimacy gap. Thus, LT focuses disclosure used to repair or to defend lost or threatened legitimacy, to gain or to extend legitimacy and to maintain levels of current legitimacy.

Inherent to the notion that corporate social disclosures have been driven by the need of organizations to legitimize their activities, management will react to the community's expectations [51]. Organizations are part of a social system, and if they show that their values go against social norms, their legitimacy is, potentially and substantially, threatened. They need to consider all the stakeholders when elaborating their strategies so as not to take the risk of their support to be withdrawn, using environmental and social reports as the means of com-

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Organizations are seen as having the obligation to consider what society wants and needs in the long term, which implies that they get involved in activities that promote benefits for society and minimize the negative impacts of their actions [67]. However, environmental and social reports may not be as important in some countries as legitimacy is not perceived as

By definition, there is some kind of a relationship between an organization and each of its stakeholders [68]. They are the ones offering organizations a set of resources they need to accomplish their businesses [14, 18]. There should be a reciprocal relationship: stakeholders supply vital resources or contribute to the organization, and this fulfills their needs [17]. Thus, it is the vision that the stakeholders have within the community that determines the accept-

The ST suggests an extensive variety of groups in the social environment, which may affect an organization, groups with legitimate claims because of concepts of the agency and property theories [69]. When the ST is used in the management interpretation, the managers' tendency to implement changes regarding the LT gets under focus [65]. As the stakeholders' influence is crucial for corporate image and comparative advantage, organizations manage their relationships with stakeholders by providing them information often as voluntary disclosure in their

Branco and Rodrigues [67] try to show that the CSR term must be based on stakeholders and able to attend to both normative and instrumental aspects. CSR is analyzed as a basis of competitive advantage. Huang and Kung [19] show that the environmental and social disclosure level is influenced by the search of stakeholders' groups—internal, external, and intermediaries—such as shareholders and employees, governments, debtors, suppliers, competitors, consumers, organizations of environmental protection, and accounting organizations, which

Manetti [70] shows in his study that he tries to understand the stakeholders' role in sustainability reports. He concludes that it is important to get them involved in the environmental and social accounting for the definition of strategic sustainable aims and coherence in management activities. Chen and Roberts [8] state that focus of the ST, applicable to environmental and social studies, is the unexpected environmental and social activities performed by organizations, such as voluntary participation in activities benefitting society or the natural

The ST sees the world through the management perspective of the organization strategically concerned about the continuous success of the organization. From this perspective, the

being threatened or because stakeholders are not concerned with these issues [65].

able activities expected to be undertaken by organizations [51].

exert a strong influence on management intentions and organizations.

environment, without explicit self-promotion or publicity.

munication between them [19].

annual reports or in their websites [55].

The consensus among researchers seems to be that corporate disclosure is growing and will increase over time. Organizations may decrease environmental disclosures or alter the disclosure type when they notice a change or threat to their legitimacy, making reports more specific and accurate [65]. Organizations that are seen as innovative are often imitated by others to become legitimate [12].

The LT is often referred to as an explanation to environmental and social reports of the private sector [50]. However, Deegan [14] believes that the LT explains why and how managers benefit an organization by using externally‑focused reports. This theory can be further refined to clarify corporate social and environmental reporting practices. Sciulli [2] adopted the LT as the theoretical model in his study on sustainability reports in the PS.

Golob and Bartlett [18] believe that the LT is informed by two other perspectives that contribute to the study and analysis of CSR reports: the RDT, which focuses on the role of legitimacy and the organization's capacity to acquire resources, and the IT [27], which considers the restrictions to organizations in complying with external expectations.

In their work, Tilling and Tilt [53] follow a longitudinal case study using the LT to understand the organizations' motivation to voluntarily disclose environmental and social information. Sciulli [30] argues in his works on sustainability reports in the PS that no theory is predominantly adequate to the investigation on sustainability. Instead, there is a series of theories that, isolated or together, offer suitable information and clarifications for behaviors and management practices, namely, the LT, the IT, and the ST. The LT has been widely used in this context [13, 14, 30, 53]. It suggests that social responsibility disclosure provides an important way of communicating with stakeholders, and of convincing them that the organizations is fulfilling their expectations [67].

Also, Mahadeo et al. [54] follow the LT and the ST in their study on practices of environmental and social disclosure (in annual reports) in emerging economies (Maurice Islands). Based on the LT and the ST, a manager must communicate with several groups to attain the perceived legitimacy [19].

According to Suttipun [55], despite the different theoretical approaches that are used to explain TBL reports, the LT and the ST are the theoretical perspectives more widely put forward in literature on environmental and social accounting.

#### **3.3. Stakeholders' theory as explanatory theory of voluntary sustainability disclosure**

The ST is closely aligned with the LT, and both are often used as complements [14]. Both enrich, rather than compete, the understanding of corporate social and environmental disclosure practices, despite their different points of view. Both are concerned with "mediation, modification and transformation" ([10], p. 53).

Inherent to the notion that corporate social disclosures have been driven by the need of organizations to legitimize their activities, management will react to the community's expectations [51]. Organizations are part of a social system, and if they show that their values go against social norms, their legitimacy is, potentially and substantially, threatened. They need to consider all the stakeholders when elaborating their strategies so as not to take the risk of their support to be withdrawn, using environmental and social reports as the means of communication between them [19].

being seen as socially responsible will bring them competitive advantage. LT is particularly useful to explain any type of disclosure trying to close a particular existing legitimacy gap. Thus, LT focuses disclosure used to repair or to defend lost or threatened legitimacy, to gain

The consensus among researchers seems to be that corporate disclosure is growing and will increase over time. Organizations may decrease environmental disclosures or alter the disclosure type when they notice a change or threat to their legitimacy, making reports more specific and accurate [65]. Organizations that are seen as innovative are often imitated by

The LT is often referred to as an explanation to environmental and social reports of the private sector [50]. However, Deegan [14] believes that the LT explains why and how managers benefit an organization by using externally‑focused reports. This theory can be further refined to clarify corporate social and environmental reporting practices. Sciulli [2] adopted the LT as

Golob and Bartlett [18] believe that the LT is informed by two other perspectives that contribute to the study and analysis of CSR reports: the RDT, which focuses on the role of legitimacy and the organization's capacity to acquire resources, and the IT [27], which considers the

In their work, Tilling and Tilt [53] follow a longitudinal case study using the LT to understand the organizations' motivation to voluntarily disclose environmental and social information. Sciulli [30] argues in his works on sustainability reports in the PS that no theory is predominantly adequate to the investigation on sustainability. Instead, there is a series of theories that, isolated or together, offer suitable information and clarifications for behaviors and management practices, namely, the LT, the IT, and the ST. The LT has been widely used in this context [13, 14, 30, 53]. It suggests that social responsibility disclosure provides an important way of communicating with stakeholders, and of convincing them that the organizations is fulfilling their expectations [67].

Also, Mahadeo et al. [54] follow the LT and the ST in their study on practices of environmental and social disclosure (in annual reports) in emerging economies (Maurice Islands). Based on the LT and the ST, a manager must communicate with several groups to attain the perceived

According to Suttipun [55], despite the different theoretical approaches that are used to explain TBL reports, the LT and the ST are the theoretical perspectives more widely put for-

The ST is closely aligned with the LT, and both are often used as complements [14]. Both enrich, rather than compete, the understanding of corporate social and environmental disclosure practices, despite their different points of view. Both are concerned with "mediation,

or to extend legitimacy and to maintain levels of current legitimacy.

the theoretical model in his study on sustainability reports in the PS.

restrictions to organizations in complying with external expectations.

ward in literature on environmental and social accounting.

modification and transformation" ([10], p. 53).

**3.3. Stakeholders' theory as explanatory theory of voluntary sustainability** 

others to become legitimate [12].

60 Accounting from a Cross-Cultural Perspective

legitimacy [19].

**disclosure**

Organizations are seen as having the obligation to consider what society wants and needs in the long term, which implies that they get involved in activities that promote benefits for society and minimize the negative impacts of their actions [67]. However, environmental and social reports may not be as important in some countries as legitimacy is not perceived as being threatened or because stakeholders are not concerned with these issues [65].

By definition, there is some kind of a relationship between an organization and each of its stakeholders [68]. They are the ones offering organizations a set of resources they need to accomplish their businesses [14, 18]. There should be a reciprocal relationship: stakeholders supply vital resources or contribute to the organization, and this fulfills their needs [17]. Thus, it is the vision that the stakeholders have within the community that determines the acceptable activities expected to be undertaken by organizations [51].

The ST suggests an extensive variety of groups in the social environment, which may affect an organization, groups with legitimate claims because of concepts of the agency and property theories [69]. When the ST is used in the management interpretation, the managers' tendency to implement changes regarding the LT gets under focus [65]. As the stakeholders' influence is crucial for corporate image and comparative advantage, organizations manage their relationships with stakeholders by providing them information often as voluntary disclosure in their annual reports or in their websites [55].

Branco and Rodrigues [67] try to show that the CSR term must be based on stakeholders and able to attend to both normative and instrumental aspects. CSR is analyzed as a basis of competitive advantage. Huang and Kung [19] show that the environmental and social disclosure level is influenced by the search of stakeholders' groups—internal, external, and intermediaries—such as shareholders and employees, governments, debtors, suppliers, competitors, consumers, organizations of environmental protection, and accounting organizations, which exert a strong influence on management intentions and organizations.

Manetti [70] shows in his study that he tries to understand the stakeholders' role in sustainability reports. He concludes that it is important to get them involved in the environmental and social accounting for the definition of strategic sustainable aims and coherence in management activities. Chen and Roberts [8] state that focus of the ST, applicable to environmental and social studies, is the unexpected environmental and social activities performed by organizations, such as voluntary participation in activities benefitting society or the natural environment, without explicit self-promotion or publicity.

The ST sees the world through the management perspective of the organization strategically concerned about the continuous success of the organization. From this perspective, the existence of the organization involves the search of the stakeholders' support and approval, and activities have to be adjusted toward profit [10]. The ST acknowledges that the impact of each stakeholder group on the organization is different, and the expectations of the different stakeholders are different and incompatible. Thus, the ST is adequate for research studies concerned with the connection and interaction of organizations or groups [8]. According to Freeman [69], the original intention of the ST is to allow managers to go beyond business practices, if necessary.

to ensure resources and social support [57]. The IT is not generally considered an organizational change theory but rather as enlightenment for the resemblance and stability of organizational commitments to a community or organizational field. The intra‑organizational dynamic of the NIS rushes and facilitates the organization to change as well as to adopt governance elements organizations find efficient and/or legitimate. Thus, organizations tend to behave similarly [33]. The IT argues that there are forces promoting the convergence of business practices, and it attempts to clarify the institutional isomorphic change process in organizations [57]. The IT explains that organizations not only take into account the economic aspects in their structural decisions and management practices but try to legitimize themselves before the stakeholders [27]. Thus, a reason for the isomorphic behavior is to attain legitimacy and social acceptance [24, 43, 60] to improve the organization's reputation as rational, modern, responsible, and legally compatible [60]. The IT has been used in accounting studies [24] because it justifies accounting choice with the organizational actors being under institutional pressure, and it is important to understand these institutional mechanisms, which work differently, and how

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From the IT perspective, Brown et al. [20] showed in their study how the institutionalization process is deeply influenced by the initial strategies of the GRI founders. GRI is a brand tool of organizations—private and public—whether it is for management, comparability, sustainability, or reputation. GRI's influence has also been proved by the study of Nikolaeva and Bicho [21]. Organizations are part of the social system, and if they prove that their values are going against social norms, their legitimacy is potentially threatened [19]. The IT holds that organizations imitate others when practices are broadly accepted and shared by the main interveners [2, 46]. Therefore, the IT suggests that the institutionalization of value standards is integrated in concrete behaviors of its institutions. Institutional theorists believe that compliance with institutional norms established for a long time is the way to institutional and social legitimacy [8].

Sustainability reports have been explored as a tool for boosting change, attitudes, and actions necessary to put forward a different kind of organization and decision making compatible to ecological and social sustainability. Oliver [26] presents an example of CSR and organizational ethics maintenance, which may lead organizations to act not because of any kind of direct connection to a positive organizational result but quite simply it would be unthinkable to do differently. So, the organization would not be invariably reducible to strategic behaviors

Following previous studies, Ball et al. [71] have discussed several approaches to sustainability reports on the role of public services promoting sustainability, and they observe, through a case study in the local government of the United Kingdom, that environmental accounting is pressed—political, social, and functional pressures—toward changing the organization. This is called "deinstitutionalization" (discontinuity of organizational practices or activities).

Cho and Patten [52] believe that some environmental disclosures in reports are used as a legitimacy tool, but others are not. However, organizations with poorer environmental performance provide higher disclosure levels. To Branco and Rodrigues [45], some organizations believe that being seen as socially responsible will bring them "competitive advantage".

institutions influence decision makers [47].

encouraged by the expectation of organizational profit.

Environmental and social disclosure integrates the dialog between the organization and the stakeholders, and CSR reports are fairly successful in negotiating those relationships. This practice is a intricate activity that may not be completely explained by a single theoretical perspective [10]. To Gray et al. ([68], p. 333), organizations today voluntarily disclose environmental and social information as "part of a legitimacy and/or social construction process".

## **4. Analysis and discussion**

Several scholars have used the institutional, legitimacy, and stakeholder theories to enlighten the existence and content of accounting environmental and social reports [13]; and they acknowledge that these theories share some common characteristics.

The aim of this essay is to provide a wider vision and theoretical support for research on accounting and sustainability reports. We reinforced the idea that accounting is not a mere due and daily sustained technique and practice. Accounting research should consider social and institutional pressures, which lead entities to adopt certain measures and decisions to increase their legitimacy [7]. This allows to understand how and why accounting changes. The IT can help in the development of explanations for accounting change or of the accounting practice [39].

Institutional change can come from "pressures resulting from functional, political, or social sources". This "change involves a decrease in institutional forces or a substitution of one set of behaviors or structures for another" ([56], p. 217). Institutional pressures do not affect organizations in the same way. "Organizations do not always embrace strategies, structures, and processes that enhance their performance but, instead, react to and seek ways to accommodate pressures following external scrutiny and regulation" ([41], p. 285). Organizational change is not so much due to efficiency and rivalry competitiveness but rather to bureaucracy reduction and the attempt of organizations to become more identical to each other to achieve legitimacy without necessarily becoming more efficient [27].

The literature review confirms the close relationship of the IT with accounting environmental and social reports, also designated as TBL or sustainability, and the existence of coercive, normative, and mimetic pressure over organizations, influencing the adoption of certain accounting practices.

The IT postulates that it is not sufficient for organizations to compete for resources and clients; instead, they also have to deal with the pressure to comply with shared notions of adequate behaviors and paths, as their violation may put at risk their legitimacy and influence their capacity to ensure resources and social support [57]. The IT is not generally considered an organizational change theory but rather as enlightenment for the resemblance and stability of organizational commitments to a community or organizational field. The intra‑organizational dynamic of the NIS rushes and facilitates the organization to change as well as to adopt governance elements organizations find efficient and/or legitimate. Thus, organizations tend to behave similarly [33].

existence of the organization involves the search of the stakeholders' support and approval, and activities have to be adjusted toward profit [10]. The ST acknowledges that the impact of each stakeholder group on the organization is different, and the expectations of the different stakeholders are different and incompatible. Thus, the ST is adequate for research studies concerned with the connection and interaction of organizations or groups [8]. According to Freeman [69], the original intention of the ST is to allow managers to go beyond business

Environmental and social disclosure integrates the dialog between the organization and the stakeholders, and CSR reports are fairly successful in negotiating those relationships. This practice is a intricate activity that may not be completely explained by a single theoretical perspective [10]. To Gray et al. ([68], p. 333), organizations today voluntarily disclose environmental and social information as "part of a legitimacy and/or social construction process".

Several scholars have used the institutional, legitimacy, and stakeholder theories to enlighten the existence and content of accounting environmental and social reports [13]; and they

The aim of this essay is to provide a wider vision and theoretical support for research on accounting and sustainability reports. We reinforced the idea that accounting is not a mere due and daily sustained technique and practice. Accounting research should consider social and institutional pressures, which lead entities to adopt certain measures and decisions to increase their legitimacy [7]. This allows to understand how and why accounting changes. The IT can help in the development of explanations for accounting change or of the accounting practice [39]. Institutional change can come from "pressures resulting from functional, political, or social sources". This "change involves a decrease in institutional forces or a substitution of one set of behaviors or structures for another" ([56], p. 217). Institutional pressures do not affect organizations in the same way. "Organizations do not always embrace strategies, structures, and processes that enhance their performance but, instead, react to and seek ways to accommodate pressures following external scrutiny and regulation" ([41], p. 285). Organizational change is not so much due to efficiency and rivalry competitiveness but rather to bureaucracy reduction and the attempt of organizations to become more identical to each other to achieve

The literature review confirms the close relationship of the IT with accounting environmental and social reports, also designated as TBL or sustainability, and the existence of coercive, normative, and mimetic pressure over organizations, influencing the adoption of certain

The IT postulates that it is not sufficient for organizations to compete for resources and clients; instead, they also have to deal with the pressure to comply with shared notions of adequate behaviors and paths, as their violation may put at risk their legitimacy and influence their capacity

acknowledge that these theories share some common characteristics.

legitimacy without necessarily becoming more efficient [27].

practices, if necessary.

62 Accounting from a Cross-Cultural Perspective

accounting practices.

**4. Analysis and discussion**

The IT argues that there are forces promoting the convergence of business practices, and it attempts to clarify the institutional isomorphic change process in organizations [57]. The IT explains that organizations not only take into account the economic aspects in their structural decisions and management practices but try to legitimize themselves before the stakeholders [27]. Thus, a reason for the isomorphic behavior is to attain legitimacy and social acceptance [24, 43, 60] to improve the organization's reputation as rational, modern, responsible, and legally compatible [60]. The IT has been used in accounting studies [24] because it justifies accounting choice with the organizational actors being under institutional pressure, and it is important to understand these institutional mechanisms, which work differently, and how institutions influence decision makers [47].

From the IT perspective, Brown et al. [20] showed in their study how the institutionalization process is deeply influenced by the initial strategies of the GRI founders. GRI is a brand tool of organizations—private and public—whether it is for management, comparability, sustainability, or reputation. GRI's influence has also been proved by the study of Nikolaeva and Bicho [21].

Organizations are part of the social system, and if they prove that their values are going against social norms, their legitimacy is potentially threatened [19]. The IT holds that organizations imitate others when practices are broadly accepted and shared by the main interveners [2, 46]. Therefore, the IT suggests that the institutionalization of value standards is integrated in concrete behaviors of its institutions. Institutional theorists believe that compliance with institutional norms established for a long time is the way to institutional and social legitimacy [8].

Sustainability reports have been explored as a tool for boosting change, attitudes, and actions necessary to put forward a different kind of organization and decision making compatible to ecological and social sustainability. Oliver [26] presents an example of CSR and organizational ethics maintenance, which may lead organizations to act not because of any kind of direct connection to a positive organizational result but quite simply it would be unthinkable to do differently. So, the organization would not be invariably reducible to strategic behaviors encouraged by the expectation of organizational profit.

Following previous studies, Ball et al. [71] have discussed several approaches to sustainability reports on the role of public services promoting sustainability, and they observe, through a case study in the local government of the United Kingdom, that environmental accounting is pressed—political, social, and functional pressures—toward changing the organization. This is called "deinstitutionalization" (discontinuity of organizational practices or activities).

Cho and Patten [52] believe that some environmental disclosures in reports are used as a legitimacy tool, but others are not. However, organizations with poorer environmental performance provide higher disclosure levels. To Branco and Rodrigues [45], some organizations believe that being seen as socially responsible will bring them "competitive advantage". Frumkin and Galaskiewicz [41] believe that government agencies have a fundamental part in implanting and triggering institutional change, applying pressure through their funding control, which is sometimes exerted by their regulation power. Government action has the core function of starting the structural transformation of other organizations. However, Chen and Roberts [8] state that the IT [27, 32] is similar to the LT [66] but is focused on the connection between the environment and organizations, mainly in the stability and survival of the organization. It is the institutional legitimacy process that is directly related to the IT [8].

Here, legitimacy is the only reward. But others may start those practices as a result of their

Theoretical Perspectives on Sustainability Reporting: A Literature Review

http://dx.doi.org/10.5772/intechopen.76951

65

There is an urgent need for investigation on accounting practices and sustainability reports to compare really sustainable organizations in this global world, leading to future benefits. In short, this is a present, pertinent, promising, and interesting theme for everyone: citizens, organizations, community, state, shareholders, among others, inclusively to literature and

This study concludes that there are three important theoretical considerations for future research studies on accounting and sustainability reports. Firstly, it must be acknowledged that some organizations start sustainability activities based on pressure to change or on direct interaction with stakeholders, while others can perform analogous activities to achieve their social level of legitimacy; secondly, from the analysis of the perspectives of the institutional, legitimacy and stakeholder theories, it is possible to reach compatible interpretations with economic, social, and environmental business phenomena (of sustainability); thirdly, all these phenomena will be part of executives' motivations to voluntarily get involved and engaged in CSR practices and disclosure. The choice and use of these theories depend on the study theme. Although these perspectives may complement responses to the present issues on accounting and sustainability reports, it is necessary to understand the concepts and potential applications of each theory; thus, they should be simultaneously studied, mutually complementing

Therefore, the limitations of this study are the gaps in deeper considerations about these and other theories in the explanation and motivation of organizations' sustainability practices. In this sense, the results recommend opportunities for further research studies, namely, using case studies, which may allow more conclusive inferences on these theories, singly or together, to get a more coherent and complete approach to the understanding of accounting

\* and Alcina Portugal Dias2

[1] Gray R. Is accounting for sustainability actually accounting for sustainability. And how would we know? An exploration of narratives of organizations and the planet.

engagement with pertinent stakeholders' groups.

investigators, as there is little research work in this area.

each other.

**Author details**

**References**

practice and sustainability reports.

Maria da Conceição da Costa Tavares1

1 University of Aveiro, Aveiro, Portugal

\*Address all correspondence to: mariatavares@ua.pt

Accounting, Organizations and Society. 2010;**35**(1):47-62

2 Polytechnic Institute of Porto, Porto, Portugal

The LT claims that legitimacy is a state achieved when an organizational value system is coherent with society's wider value system, but it does not offer a solution in terms of how it can be achieved or empirically analyzed in practice. However, the organizational or structural legitimacy process is more related to the ST, which recognizes that legitimacy is subjectively assessed according to the value standards of the stakeholders' groups [8]. Freeman [69] highlights that the will to interact and engage is the necessary solution for the approval and support of the stakeholders.

However, as there are no normative or coercive pressures for organizations to adhere to GRI standards yet, mimetic isomorphism would be best for the voluntary adoption of CSR reports since the mimetic behavior may be the right response to the environmental uncertainty, and it may really help managers save resources by copying their competitors' behaviors [21]. These authors consider their own study as the first to explore the voluntary adoption of the world's framework of CSR reports (GRI) by organizations. Results suggest that managers are encouraged to disclose CSR reports, according to the GRI, increasing the organization's legitimacy.

Summing up, each theory gives its contribution, completing each other according to its perspective. Thus, it is possible to incorporate various theories in an attempt to attain a more comprehensible and full understanding of an organization's connection with society, the value of researching a specific social event from various theoretical perspectives should be emphasized.

## **5. Concluding remarks**

We are in a global community, in a new environment and before a new strategic model, where future organizations have to generate value for stakeholders. Socially responsible organizations generate value for others and achieve better results for themselves. CSR is not a mere choice of organizations; it is a matter of strategic vision and survival. The GRI, the internationally acknowledged standard for sustainability disclosure, contributes to the dialog among the diverse stakeholders [22].

Understanding the different theoretical perspectives and the institutional pressures for change, organizations will tend to adopt sustainability practices and the path of social responsibility. This study reveals that those theories are different in their specificity, perspective, and solution levels, but their aims are the same: they have a shared interest of explaining how organizations survive and grow. They stress that financial performance and efficiency are crucial but not enough for organizations to continue surviving. Some organizations may perform some sustainability performance merely to satisfy mutual expectations of doing business. Here, legitimacy is the only reward. But others may start those practices as a result of their engagement with pertinent stakeholders' groups.

There is an urgent need for investigation on accounting practices and sustainability reports to compare really sustainable organizations in this global world, leading to future benefits. In short, this is a present, pertinent, promising, and interesting theme for everyone: citizens, organizations, community, state, shareholders, among others, inclusively to literature and investigators, as there is little research work in this area.

This study concludes that there are three important theoretical considerations for future research studies on accounting and sustainability reports. Firstly, it must be acknowledged that some organizations start sustainability activities based on pressure to change or on direct interaction with stakeholders, while others can perform analogous activities to achieve their social level of legitimacy; secondly, from the analysis of the perspectives of the institutional, legitimacy and stakeholder theories, it is possible to reach compatible interpretations with economic, social, and environmental business phenomena (of sustainability); thirdly, all these phenomena will be part of executives' motivations to voluntarily get involved and engaged in CSR practices and disclosure. The choice and use of these theories depend on the study theme.

Although these perspectives may complement responses to the present issues on accounting and sustainability reports, it is necessary to understand the concepts and potential applications of each theory; thus, they should be simultaneously studied, mutually complementing each other.

Therefore, the limitations of this study are the gaps in deeper considerations about these and other theories in the explanation and motivation of organizations' sustainability practices. In this sense, the results recommend opportunities for further research studies, namely, using case studies, which may allow more conclusive inferences on these theories, singly or together, to get a more coherent and complete approach to the understanding of accounting practice and sustainability reports.

#### **Author details**

Frumkin and Galaskiewicz [41] believe that government agencies have a fundamental part in implanting and triggering institutional change, applying pressure through their funding control, which is sometimes exerted by their regulation power. Government action has the core function of starting the structural transformation of other organizations. However, Chen and Roberts [8] state that the IT [27, 32] is similar to the LT [66] but is focused on the connection between the environment and organizations, mainly in the stability and survival of the organization. It is the institutional legitimacy process that is directly related to the IT [8].

The LT claims that legitimacy is a state achieved when an organizational value system is coherent with society's wider value system, but it does not offer a solution in terms of how it can be achieved or empirically analyzed in practice. However, the organizational or structural legitimacy process is more related to the ST, which recognizes that legitimacy is subjectively assessed according to the value standards of the stakeholders' groups [8]. Freeman [69] highlights that the will to interact and engage is the necessary solution for the approval and sup-

However, as there are no normative or coercive pressures for organizations to adhere to GRI standards yet, mimetic isomorphism would be best for the voluntary adoption of CSR reports since the mimetic behavior may be the right response to the environmental uncertainty, and it may really help managers save resources by copying their competitors' behaviors [21]. These authors consider their own study as the first to explore the voluntary adoption of the world's framework of CSR reports (GRI) by organizations. Results suggest that managers are encouraged to disclose CSR reports, according to the GRI, increasing the

Summing up, each theory gives its contribution, completing each other according to its perspective. Thus, it is possible to incorporate various theories in an attempt to attain a more comprehensible and full understanding of an organization's connection with society, the value of researching a specific social event from various theoretical perspectives should be emphasized.

We are in a global community, in a new environment and before a new strategic model, where future organizations have to generate value for stakeholders. Socially responsible organizations generate value for others and achieve better results for themselves. CSR is not a mere choice of organizations; it is a matter of strategic vision and survival. The GRI, the internationally acknowledged standard for sustainability disclosure, contributes to the dialog among the

Understanding the different theoretical perspectives and the institutional pressures for change, organizations will tend to adopt sustainability practices and the path of social responsibility. This study reveals that those theories are different in their specificity, perspective, and solution levels, but their aims are the same: they have a shared interest of explaining how organizations survive and grow. They stress that financial performance and efficiency are crucial but not enough for organizations to continue surviving. Some organizations may perform some sustainability performance merely to satisfy mutual expectations of doing business.

port of the stakeholders.

64 Accounting from a Cross-Cultural Perspective

organization's legitimacy.

**5. Concluding remarks**

diverse stakeholders [22].

Maria da Conceição da Costa Tavares1 \* and Alcina Portugal Dias2


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**Section 3**

**Insurance Contracts**


**Section 3**

**Insurance Contracts**

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**Chapter 4**

Provisional chapter

**An Inequality for Reinsurance Contract Annual Loss**

DOI: 10.5772/intechopen.76265

For reinsurance contract simulated annual losses, an inequality relating their standard

square root of the ratio of numbers of zero losses years to numbers of non-zero losses years. The largest such coefficient is also proved to be the universal upper bound. As direct application of this inequality, bounds for other risk measures of reinsurance contract, the TVaR (average of the annual losses that are larger than a given loss), the probability of attaching (greater than a given attachment loss), and the probability of exceeding (the annual loss limit) are obtained, which in turn reveal the capability upper limit of the

Keywords: reinsurance contract, simulation, standard deviation, coefficient of variation,

In reinsurance industry, simulated losses from catastrophe events combined with reinsurance contract financial terms are used to calculate the contract expected annual loss, the standard deviation of the expected annual loss, and quantiles of the losses (such as the AEP: Aggregate Exceedance Probability, or TVaR: Tail Value at Risk, in Ref. [1]). These numbers are in turn used for pricing or risk management of the contract. There are two kinds of model risks in this approach: independent simulations may give different results without any model change, and simulations vary before or after model change such as from the yearly catastrophe events sets or parameters updates. Empirically, the distribution of the contract expected annual loss may be more like a Beckmann, MaxStable, Gamma, Inverse Gaussian, or even a Lognormal Distribution

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

, where the coefficient in the inequality is the

ffiffiffiffiffiffiffiffiffiffi <sup>μ</sup> AC ð Þ μð Þ A r

An Inequality for Reinsurance Contract Annual Loss

**Standard Deviation and Its Application**

Standard Deviation and Its Application

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.76265

deviation and mean is found, σ<sup>f</sup> ≥ mf

inequality, ratio distribution, model risk

simulation approach.

1. Introduction

Frank Xuyan Wang

Frank Xuyan Wang

Abstract

#### **An Inequality for Reinsurance Contract Annual Loss Standard Deviation and Its Application** An Inequality for Reinsurance Contract Annual Loss Standard Deviation and Its Application

DOI: 10.5772/intechopen.76265

#### Frank Xuyan Wang Frank Xuyan Wang

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.76265

#### Abstract

For reinsurance contract simulated annual losses, an inequality relating their standard deviation and mean is found, σ<sup>f</sup> ≥ mf ffiffiffiffiffiffiffiffiffiffi <sup>μ</sup> AC ð Þ μð Þ A r , where the coefficient in the inequality is the square root of the ratio of numbers of zero losses years to numbers of non-zero losses years. The largest such coefficient is also proved to be the universal upper bound. As direct application of this inequality, bounds for other risk measures of reinsurance contract, the TVaR (average of the annual losses that are larger than a given loss), the probability of attaching (greater than a given attachment loss), and the probability of exceeding (the annual loss limit) are obtained, which in turn reveal the capability upper limit of the simulation approach.

Keywords: reinsurance contract, simulation, standard deviation, coefficient of variation, inequality, ratio distribution, model risk

#### 1. Introduction

In reinsurance industry, simulated losses from catastrophe events combined with reinsurance contract financial terms are used to calculate the contract expected annual loss, the standard deviation of the expected annual loss, and quantiles of the losses (such as the AEP: Aggregate Exceedance Probability, or TVaR: Tail Value at Risk, in Ref. [1]). These numbers are in turn used for pricing or risk management of the contract. There are two kinds of model risks in this approach: independent simulations may give different results without any model change, and simulations vary before or after model change such as from the yearly catastrophe events sets or parameters updates. Empirically, the distribution of the contract expected annual loss may be more like a Beckmann, MaxStable, Gamma, Inverse Gaussian, or even a Lognormal Distribution

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

than a Normal Distribution, but consider that the mean annual loss is the average of a large number of losses, and especially for simplicity, if we assume they obey a Normal Distribution, to quantify the model risk, we can use Hinkley formula [2] or Marsaglia formula [3] to calculate the probability of two simulations have expected annual loss deviated from each other by more than say 50%. Their formulas, in our model risk quantification context and the simplest scenario, depend on only two factors: the correlation coefficient r of the distribution in the two simulations, and the coefficient of variation (CV) of the distribution, that is, the ratio of the standard deviation to the mean. Most reinsurance contracts, due to the carefully selected financial terms, have many or the majority of simulated year's losses zero. Thus call for a study of the CV range or bounds of those scarcely payout contracts.

#### 2. Results

#### 2.1. CV range

Starting from Hölder's inequality (https://en.wikipedia.org/wiki/Hölder's\_inequality):

$$\|f\mathbf{g}\|\_1 \le \|f\|\_p \|\mathbf{g}\|\_{q'} \tag{1}$$

<sup>¼</sup> mf <sup>a</sup> � mf <sup>a</sup>μð Þþ <sup>A</sup> mf <sup>b</sup><sup>μ</sup> AC � � (7)

An Inequality for Reinsurance Contract Annual Loss Standard Deviation and Its Application

<sup>b</sup> <sup>¼</sup> <sup>μ</sup> AC ð Þ

σ<sup>f</sup> ≥ 31:6069612585582mf (9)

σ<sup>f</sup> ≥ 9:9498743710662mf (10)

<sup>μ</sup>ð Þ <sup>A</sup> , increasing on [0, <sup>μ</sup> AC ð Þ

http://dx.doi.org/10.5772/intechopen.76265

/mf = 1.25783054243641 > [math]::

<sup>μ</sup>ð Þ <sup>A</sup> ]

75

(8)

The maximum of the right-hand side of Eq. (3) is achieved by <sup>a</sup>

� �, and then we get:

then we will get [math]::sqrt((1e5-100)/100) = 31.6069612585582:

mean loss mf = 1,874,487 and standard deviation σ<sup>f</sup> = 2,357,787, σ<sup>f</sup>

losses and higher CV (more explanation in the following section).

sqrt((1e5-41,143)/41,143) = 1.19605481319037.

σ<sup>f</sup> ≥ mf

ffiffiffiffiffiffiffiffiffiffiffiffiffi μ A<sup>C</sup> � � μð Þ A

s

As a corollary, if we use the 2-sigma or 3-sigma rule for the confidence interval of the estimate of the mean, for those contracts that have most years 0 losses, these interval will be very large. For example, if we have only 100 years have nonzero losses out of the 100,000 simulated years,

And if we have 1000 years nonzero losses, we get the constant [math]::sqrt((1e5-1000)/

Checking against some concrete examples, for a contract we see 2220 nonzero losses records, suppose all of them are in different years, then we get the ratio [math]:: sqrt((1e5-2220)/ 2220) = 6.63664411016931, and we have its mean loss mf = 3848 and standard deviation

Another contract have unique 41,143 nonzero losses years out of the 100,000 simulated years, with

Typically, more than half of the contracts may have nonzero losses years count below 10,000, for which we can see their σ<sup>f</sup> ≥ 3mf, since [math]::sqrt((1e5-1e4)/1e4) = 3. More than 80% of the contracts may have nonzero losses years count below 50,000, for which there is the simple

This inequality Eq. (8) can explain the observation that when we sort the contracts by the mean annual loss, the lower quarter of contracts may have more than tens of percent deviation from different simulations, since smaller mean loss usually corresponding to fewer years of nonzero

To get an upper bound for CV, suppose the total simulated years is n and each year has the loss

σ<sup>f</sup> = 37,149 from the simulation, 37,149/3848 = 9.65410602910603 > 6.63664411016931.

From these examples, we see that our lower bound formula for CV is relatively close.

inequality σ<sup>f</sup> ≥ mf, since sqrt((1e5-5e4)/5e4) = 1. These bounds are collected in Table 1.

<sup>μ</sup>ð Þ <sup>A</sup> ; <sup>∞</sup>

and decreasing on <sup>μ</sup> <sup>A</sup><sup>C</sup> ð Þ

1000) = 9.9498743710662:

xi ≥ 0. Then:

suppose f in the formula is the contract annual loss with mean mf deducted, that is, is of the form f � mf and p = q = 2, g is some nonnegative weights on the discrete probability space of the simulated years Ω, for example, the set {1,2,…,100,000} for 100,000 years of simulations, each element with a probability of 1e-5 (a typical setting in practice). Then we get:

$$\int |f - m\_f| \gcd \mu \le \left[ \int |f - m\_f|^2 d\mu \right]^{1/2} \left[ \int g^2 d\mu \right]^{1/2} = \sigma\_f \left[ \int g^2 d\mu \right]^{1/2} \tag{2}$$

Suppose f is nonnegative and zero outside of a subset A of Ω and g is constant a on A and constant b on AC: f|AC = 0, f|<sup>A</sup> > 0, g|AC = b ≥ 0, g|<sup>A</sup> = a ≥ 0. Then we can deduct that:

$$\sigma\_f \ge m\_f \frac{a\mu\left(A^{\triangle}\right) + b\mu\left(A^{\triangle}\right)}{\sqrt{a^2\mu(A) + b^2\mu\left(A^{\triangle}\right)}}\tag{3}$$

due to

$$|f - m\_f| \ge f - m\_f \tag{4}$$

and

$$\int |f - m\_f| \mathrm{gd}\mu = \int\_A |f - m\_f| \mathrm{ad}\mu + \int\_{A^C} m\_f b d\mu \tag{5}$$

$$\rho \geqslant \int\_{A} f d\mu - \int\_{A} m\_f a d\mu + m\_f b \mu \left(A^{\mathbb{C}}\right) \tag{6}$$

An Inequality for Reinsurance Contract Annual Loss Standard Deviation and Its Application http://dx.doi.org/10.5772/intechopen.76265 75

$$0 = m\_f a - m\_f a \mu(A) + m\_f b \mu\big(A^\complement\big) \tag{7}$$

The maximum of the right-hand side of Eq. (3) is achieved by <sup>a</sup> <sup>b</sup> <sup>¼</sup> <sup>μ</sup> AC ð Þ <sup>μ</sup>ð Þ <sup>A</sup> , increasing on [0, <sup>μ</sup> AC ð Þ <sup>μ</sup>ð Þ <sup>A</sup> ] and decreasing on <sup>μ</sup> <sup>A</sup><sup>C</sup> ð Þ <sup>μ</sup>ð Þ <sup>A</sup> ; <sup>∞</sup> � �, and then we get:

than a Normal Distribution, but consider that the mean annual loss is the average of a large number of losses, and especially for simplicity, if we assume they obey a Normal Distribution, to quantify the model risk, we can use Hinkley formula [2] or Marsaglia formula [3] to calculate the probability of two simulations have expected annual loss deviated from each other by more than say 50%. Their formulas, in our model risk quantification context and the simplest scenario, depend on only two factors: the correlation coefficient r of the distribution in the two simulations, and the coefficient of variation (CV) of the distribution, that is, the ratio of the standard deviation to the mean. Most reinsurance contracts, due to the carefully selected financial terms, have many or the majority of simulated year's losses zero. Thus call for a study of the CV range

Starting from Hölder's inequality (https://en.wikipedia.org/wiki/Hölder's\_inequality):

element with a probability of 1e-5 (a typical setting in practice). Then we get:

f � mf � � � � 2 dμ � �<sup>1</sup>=<sup>2</sup> ð

σ<sup>f</sup> ≥ mf

∣f � mf ∣gdμ ¼

⩾ ð A fadμ �

ð

suppose f in the formula is the contract annual loss with mean mf deducted, that is, is of the form f � mf and p = q = 2, g is some nonnegative weights on the discrete probability space of the simulated years Ω, for example, the set {1,2,…,100,000} for 100,000 years of simulations, each

Suppose f is nonnegative and zero outside of a subset A of Ω and g is constant a on A and

<sup>a</sup><sup>μ</sup> <sup>A</sup><sup>C</sup> � � <sup>þ</sup> <sup>b</sup><sup>μ</sup> <sup>A</sup><sup>C</sup> � � ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>a</sup><sup>2</sup>μð Þþ <sup>A</sup> <sup>b</sup><sup>2</sup>

q � �

∣f � mf ∣adμ þ

μ A<sup>C</sup>

ð AC

constant b on AC: f|AC = 0, f|<sup>A</sup> > 0, g|AC = b ≥ 0, g|<sup>A</sup> = a ≥ 0. Then we can deduct that:

ð A

ð A

g2 dμ � �<sup>1</sup>=<sup>2</sup>

k k fg <sup>1</sup> ≤ k kf <sup>p</sup>k kg <sup>q</sup>, (1)

¼ σ<sup>f</sup> ð g2 dμ � �<sup>1</sup>=<sup>2</sup>

∣f � mf ∣ ≥ f � mf (4)

mf ad<sup>μ</sup> <sup>þ</sup> mf <sup>b</sup>μ Α<sup>C</sup> � � (6)

mf bdμ (5)

(2)

(3)

or bounds of those scarcely payout contracts.

74 Accounting from a Cross-Cultural Perspective

ð

∣f � mf ∣gdμ ≤

ð

2. Results

2.1. CV range

due to

and

$$
\sigma\_f \ge m\_f \sqrt{\frac{\mu(A^\odot)}{\mu(A)}}\tag{8}
$$

As a corollary, if we use the 2-sigma or 3-sigma rule for the confidence interval of the estimate of the mean, for those contracts that have most years 0 losses, these interval will be very large. For example, if we have only 100 years have nonzero losses out of the 100,000 simulated years, then we will get [math]::sqrt((1e5-100)/100) = 31.6069612585582:

$$
\sigma\_f \ge 31.6069612585582 m\_f \tag{9}
$$

And if we have 1000 years nonzero losses, we get the constant [math]::sqrt((1e5-1000)/ 1000) = 9.9498743710662:

$$
\sigma\_f \ge 9.94987437106662 \, m\_f \tag{10}
$$

Checking against some concrete examples, for a contract we see 2220 nonzero losses records, suppose all of them are in different years, then we get the ratio [math]:: sqrt((1e5-2220)/ 2220) = 6.63664411016931, and we have its mean loss mf = 3848 and standard deviation σ<sup>f</sup> = 37,149 from the simulation, 37,149/3848 = 9.65410602910603 > 6.63664411016931.

Another contract have unique 41,143 nonzero losses years out of the 100,000 simulated years, with mean loss mf = 1,874,487 and standard deviation σ<sup>f</sup> = 2,357,787, σ<sup>f</sup> /mf = 1.25783054243641 > [math]:: sqrt((1e5-41,143)/41,143) = 1.19605481319037.

From these examples, we see that our lower bound formula for CV is relatively close.

Typically, more than half of the contracts may have nonzero losses years count below 10,000, for which we can see their σ<sup>f</sup> ≥ 3mf, since [math]::sqrt((1e5-1e4)/1e4) = 3. More than 80% of the contracts may have nonzero losses years count below 50,000, for which there is the simple inequality σ<sup>f</sup> ≥ mf, since sqrt((1e5-5e4)/5e4) = 1. These bounds are collected in Table 1.

This inequality Eq. (8) can explain the observation that when we sort the contracts by the mean annual loss, the lower quarter of contracts may have more than tens of percent deviation from different simulations, since smaller mean loss usually corresponding to fewer years of nonzero losses and higher CV (more explanation in the following section).

To get an upper bound for CV, suppose the total simulated years is n and each year has the loss xi ≥ 0. Then:

$$\text{CV} \equiv \frac{\sigma\_f}{m\_f} = \sqrt{n \frac{\sum\_{i=1}^{n} \mathbf{x}\_i^2}{\left(\sum\_{i=1}^{n} \mathbf{x}\_i\right)^2} - 1} \tag{11}$$

The overall upper bound ffiffiffiffiffiffiffiffiffiffiffi

using importance sampling), then:

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

to the mean mf is bound below by:

mean mf is bound above by:

losses years, respectively. The lower bound

max <sup>1</sup> p1 ; 1 p2 ;…; <sup>1</sup> pn � � � <sup>1</sup>

r

From the fact that the minimum of the expression in Eq. (11) is attained at

P<sup>n</sup> <sup>i</sup>¼<sup>1</sup> <sup>x</sup><sup>2</sup> i

P<sup>n</sup> <sup>i</sup>¼<sup>1</sup> xi � �<sup>2</sup> <sup>≥</sup>

P<sup>n</sup> <sup>i</sup>¼<sup>1</sup> <sup>x</sup><sup>2</sup> i pi

P<sup>n</sup> <sup>i</sup>¼<sup>1</sup> xipi � �<sup>2</sup> <sup>≥</sup>

The minimum value of the right side is attained when x<sup>1</sup> ¼

We summarize our deduction and discussion into the following:

.

arbitrarily close to 0.

that:

<sup>n</sup> � <sup>1</sup> <sup>p</sup> for CV is approachable when we let all but one of the xi

An Inequality for Reinsurance Contract Annual Loss Standard Deviation and Its Application

P<sup>n</sup> <sup>i</sup>¼<sup>2</sup> <sup>x</sup><sup>2</sup> i P<sup>n</sup> <sup>i</sup>¼<sup>2</sup> xi � �<sup>2</sup>

> P<sup>n</sup> <sup>i</sup>¼<sup>2</sup> <sup>x</sup><sup>2</sup> i pi

P<sup>n</sup> <sup>i</sup>¼<sup>2</sup> xipi � �<sup>2</sup>

P<sup>n</sup> <sup>i</sup>¼<sup>2</sup> xipi � �<sup>2</sup> <sup>þ</sup> <sup>1</sup>

> P<sup>n</sup> <sup>i</sup>¼<sup>2</sup> <sup>x</sup><sup>2</sup> i p <sup>P</sup> <sup>i</sup> n <sup>i</sup>¼<sup>2</sup> xipi

P<sup>n</sup> <sup>i</sup>¼<sup>2</sup> <sup>x</sup><sup>2</sup> i P<sup>n</sup> <sup>i</sup>¼<sup>2</sup> xi � �<sup>2</sup> <sup>þ</sup> <sup>1</sup>

More generally, if year is have possibly unequal probability pi of occurrence (such as when

p1 P<sup>n</sup> <sup>i</sup>¼<sup>2</sup> <sup>x</sup><sup>2</sup> i pi

tively to give an "elementary" proof of our lower bound results, and additionally can show that the lower bound is attained when all the nonzero losses are equally valued which using the Hölder's inequality cannot arrive. Similarly we can show that the upper bound is

Theorem 1. For reinsurance contract simulated annual losses f, the standard deviation σ<sup>f</sup> with respect

s

where μ(AC) and μ(A) are the measure of the numbers of zero losses years and the numbers of non-zero

s

if and only if all the non-zero losses are of the same value. The standard deviation σ<sup>f</sup> with respect to the

ffiffiffiffiffiffiffiffiffiffi <sup>μ</sup> <sup>A</sup><sup>C</sup> ð Þ μð Þ A

r

σ<sup>f</sup> ¼ mf

ffiffiffiffiffiffiffiffiffiffiffiffiffi μ A<sup>C</sup> � � μð Þ A

is attended:

ffiffiffiffiffiffiffiffiffiffiffiffiffiffi μ A<sup>C</sup> � � μð Þ A

σ<sup>f</sup> ≥ mf

P<sup>n</sup> <sup>i</sup>¼<sup>2</sup> <sup>x</sup><sup>2</sup> <sup>P</sup> <sup>i</sup> <sup>n</sup> <sup>i</sup>¼<sup>2</sup> xi

http://dx.doi.org/10.5772/intechopen.76265

. we can see

(14)

77

(15)

(16)

. This can be used induc-

, (17)

For the expression P<sup>n</sup> <sup>i</sup>¼<sup>1</sup> <sup>x</sup><sup>2</sup> i P<sup>n</sup> <sup>i</sup>¼<sup>1</sup> xi � �2, by taking the partial derivative with respect to <sup>x</sup>1, we can know that it is decreasing in 0; P<sup>n</sup> <sup>i</sup>¼<sup>2</sup> <sup>x</sup><sup>2</sup> <sup>P</sup> <sup>i</sup> <sup>n</sup> <sup>i</sup>¼<sup>2</sup> xi � � and increasing in P<sup>n</sup> <sup>i</sup>¼<sup>2</sup> <sup>x</sup><sup>2</sup> <sup>P</sup> <sup>i</sup> <sup>n</sup> <sup>i</sup>¼<sup>2</sup> xi ; ∞ � �. So the maximum must be attained at either 0 or ∞, that is, is the value of P<sup>n</sup> <sup>i</sup>¼<sup>2</sup> <sup>x</sup><sup>2</sup> <sup>P</sup> <sup>i</sup> <sup>n</sup> <sup>i</sup>¼<sup>2</sup> xi or 1. Recursively, we know that the final maximum is 1. So we get:

$$CV \le \sqrt{n-1} \tag{12}$$

For the extreme case when only one year have nonzero losses, we thus verified that the coefficient [math]::sqrt((1e5-1)/1) = 316.226184874055 is exact, that is, we have:

$$
\sigma\_f = 316.226184874055 m\_f \tag{13}
$$


For given years of nonzero losses out of 100,000 simulated years, the lower bound as given by our formula Eq. (8).

Table 1. CV lower bound.

The overall upper bound ffiffiffiffiffiffiffiffiffiffiffi <sup>n</sup> � <sup>1</sup> <sup>p</sup> for CV is approachable when we let all but one of the xi arbitrarily close to 0.

From the fact that the minimum of the expression in Eq. (11) is attained at P<sup>n</sup> <sup>i</sup>¼<sup>2</sup> <sup>x</sup><sup>2</sup> <sup>P</sup> <sup>i</sup> <sup>n</sup> <sup>i</sup>¼<sup>2</sup> xi . we can see that:

$$\frac{\sum\_{i=1}^{n} \mathbf{x}\_i^2}{\left(\sum\_{i=1}^{n} \mathbf{x}\_i\right)^2} \ge \frac{\frac{\sum\_{i=2}^{n} \mathbf{x}\_i^2}{\left(\sum\_{i=2}^{n} \mathbf{x}\_i\right)^2}}{\frac{\sum\_{i=2}^{n} \mathbf{x}\_i^2}{\left(\sum\_{i=2}^{n} \mathbf{x}\_i\right)^2} + 1} \tag{14}$$

More generally, if year is have possibly unequal probability pi of occurrence (such as when using importance sampling), then:

$$\frac{\sum\_{i=1}^{n} \mathbf{x}\_i^2 p\_i}{\left(\sum\_{i=1}^{n} \mathbf{x}\_i p\_i\right)^2} \ge \frac{\frac{\sum\_{i=2}^{n} \mathbf{x}\_i^2 p\_i}{\left(\sum\_{i=2}^{n} \mathbf{x}\_i p\_i\right)^2}}{p\_1 \frac{\sum\_{i=2}^{n} \mathbf{x}\_i^2 p\_i}{\left(\sum\_{i=2}^{n} \mathbf{x}\_i p\_i\right)^2} + 1} \tag{15}$$

The minimum value of the right side is attained when x<sup>1</sup> ¼ P<sup>n</sup> <sup>i</sup>¼<sup>2</sup> <sup>x</sup><sup>2</sup> i p <sup>P</sup> <sup>i</sup> n <sup>i</sup>¼<sup>2</sup> xipi . This can be used inductively to give an "elementary" proof of our lower bound results, and additionally can show that the lower bound is attained when all the nonzero losses are equally valued which using the Hölder's inequality cannot arrive. Similarly we can show that the upper bound is ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r

$$\sqrt{\max\left(\frac{1}{p\_1}, \frac{1}{p\_2}, \dots, \frac{1}{p\_n}\right)} - 1.$$

CV � <sup>σ</sup><sup>f</sup> mf ¼

For the expression

that it is decreasing in 0;

76 Accounting from a Cross-Cultural Perspective

maximum is 1. So we get:

P<sup>n</sup> <sup>i</sup>¼<sup>1</sup> <sup>x</sup><sup>2</sup> i P<sup>n</sup> <sup>i</sup>¼<sup>1</sup> xi

attained at either 0 or ∞, that is, is the value of

P<sup>n</sup> <sup>i</sup>¼<sup>2</sup> <sup>x</sup><sup>2</sup> <sup>P</sup> <sup>i</sup> <sup>n</sup> <sup>i</sup>¼<sup>2</sup> xi � � ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

� �2, by taking the partial derivative with respect to <sup>x</sup>1, we can know

P<sup>n</sup> <sup>i</sup>¼<sup>2</sup> <sup>x</sup><sup>2</sup> <sup>P</sup> <sup>i</sup> <sup>n</sup> <sup>i</sup>¼<sup>2</sup> xi ; ∞ � �

vuut (11)

. So the maximum must be

or 1. Recursively, we know that the final

<sup>n</sup> � <sup>1</sup> <sup>p</sup> (12)

σ<sup>f</sup> ¼ 316:226184874055mf (13)

ffiffiffiffiffiffiffiffiffiffi <sup>μ</sup> <sup>A</sup><sup>C</sup> ð Þ μð Þ A r

n P<sup>n</sup> <sup>i</sup>¼<sup>1</sup> <sup>x</sup><sup>2</sup> i

and increasing in

P<sup>n</sup> <sup>i</sup>¼<sup>2</sup> <sup>x</sup><sup>2</sup> <sup>P</sup> <sup>i</sup> <sup>n</sup> <sup>i</sup>¼<sup>2</sup> xi

CV ≤ ffiffiffiffiffiffiffiffiffiffiffi

For the extreme case when only one year have nonzero losses, we thus verified that the

coefficient [math]::sqrt((1e5-1)/1) = 316.226184874055 is exact, that is, we have:

Nonzero losses years CV lower bound

 316.226184874055 99.9949998749938 31.6069612585582 9.9498743710662

5000 4.35889894354067

30,000 1.52752523165195 40,000 1.22474487139159

90,000 0.333333333333333 99,000 0.100503781525921 99,900 0.0316385998584166 99,990 0.0100005000375031 99,999 0.00316229347167527

For given years of nonzero losses out of 100,000 simulated years, the lower bound as given by our formula Eq. (8).

2000 7

10,000 3 20,000 2

50,000 1 80,000 0.5

Table 1. CV lower bound.

P<sup>n</sup> <sup>i</sup>¼<sup>1</sup> xi � �<sup>2</sup> � <sup>1</sup>

We summarize our deduction and discussion into the following:

Theorem 1. For reinsurance contract simulated annual losses f, the standard deviation σ<sup>f</sup> with respect to the mean mf is bound below by:

$$\sigma\_f \ge m\_f \sqrt{\frac{\mu\left(A^{\widehat{C}}\right)}{\mu(A)}}\tag{16}$$

where μ(AC) and μ(A) are the measure of the numbers of zero losses years and the numbers of non-zero losses years, respectively. The lower bound ffiffiffiffiffiffiffiffiffiffi <sup>μ</sup> <sup>A</sup><sup>C</sup> ð Þ μð Þ A r is attended:

$$
\sigma\_f = m\_f \sqrt{\frac{\mu \langle \mathbf{A}^\circ \rangle}{\mu \langle \mathbf{A} \rangle}},
\tag{17}
$$

if and only if all the non-zero losses are of the same value. The standard deviation σ<sup>f</sup> with respect to the mean mf is bound above by:

$$
\sigma\_f \le m\_f \sqrt{\max\left\{\frac{1}{p\_1}, \frac{1}{p\_2}, ..., \frac{1}{p\_n}\right\} - 1} \tag{18}
$$

σ2

≥ m<sup>2</sup> f 1

¼ mf <sup>1</sup>

@

mf <sup>1</sup>

The inequality Eq. (22) is arrived by the fact that mf = mf<sup>1</sup> + mf<sup>2</sup> and

@

: TVaR(q) ≤

ffiffiffiffiffiffiffiffiffiffi

s

s

domain with zero value for f<sup>2</sup> include the set B. Hence:

1�q

no matter what the distribution of the annual loss is.

� Prob{f > 0}, with respect to the CV is bound below by:

ffiffiffiffiffiffiffiffiffiffi μð Þ B q ffiffiffiffiffiffiffiffiffiffiffiffiffi μ BC q � �

<sup>q</sup> or the return period <sup>r</sup> � <sup>1</sup>

TVaR upper bound (now simply σ<sup>f</sup>

for the probability of attaching:

<sup>f</sup> ¼ E f <sup>1</sup> þ f <sup>2</sup>

<sup>¼</sup> <sup>σ</sup><sup>2</sup> <sup>f</sup> <sup>1</sup> <sup>þ</sup> <sup>σ</sup><sup>2</sup>

μ B<sup>C</sup> � � <sup>μ</sup>ð Þ <sup>B</sup> <sup>þ</sup> <sup>m</sup><sup>2</sup>

s

ffiffiffiffiffiffiffiffiffiffiffiffiffi μ B<sup>C</sup> � � μð Þ B

ffiffiffiffiffiffiffiffiffiffiffiffiffi μ BC � � μð Þ B

0 s

þ

ffiffiffiffiffiffi q 1�q q

If we let the subset B be {x|f(x) >0}, then Eq. (22) become Eq. (16). If we let the subset B be {x|CDFf (x) ≥ q,0 ≤ q ≤ 1}, we get the so called AEP TVaR upper bound for the given quantile

<sup>r</sup> � <sup>1</sup> <sup>p</sup> <sup>þ</sup> mf ) is in Table 2.

Numerical example shows that our TVaR upper bound is relatively close in the quantile range [0.8,0.9], with the theoretical upper bound deviated from the simulated value by less than 20%,

Notice that the measure of the numbers of nonzero losses years is also called the probability of attaching in insurance, we can rearrange the terms in the formula Eq. (8) to get a lower bound

Corollary 3. For a reinsurance contract simulated annual losses f, the probability of attaching, ProbA

As an application of Corollary 3, we see that if CV ≤ 3, then ProbA ≥ 0.1, the 0.9 quantile of f is larger than zero. Equivalently, if the 0.9 quantile of f (the so called AEP in insurance) is zero, we

1

ProbA ≥

� �<sup>2</sup> h i � E f <sup>1</sup> <sup>þ</sup> <sup>f</sup> <sup>2</sup>

<sup>f</sup> <sup>2</sup> � 2mf <sup>1</sup>

μð Þ B <sup>μ</sup> <sup>B</sup><sup>C</sup> � � � <sup>2</sup>mf <sup>1</sup>

> ffiffiffiffiffiffiffiffiffiffiffiffiffi μð Þ B μ BC � �

An Inequality for Reinsurance Contract Annual Loss Standard Deviation and Its Application

ffiffiffiffiffiffiffiffiffiffiffiffiffi μð Þ B <sup>μ</sup> BC � � <sup>s</sup>

1

ffiffiffiffiffiffiffiffiffiffiffiffiffi μð Þ B μ B<sup>C</sup> � � 1 A

2

� mf <sup>2</sup>

from Theorem 1 and the fact that the domain with zero value for f<sup>1</sup> include the set BC and the

≤ mf <sup>2</sup>

f 2

ffiffiffiffiffiffiffiffiffiffiffiffiffi μ BC � � μð Þ B

0 s

� � � � <sup>2</sup> (23)

mf <sup>2</sup> (24)

http://dx.doi.org/10.5772/intechopen.76265

mf <sup>2</sup> (25)

þ σ<sup>f</sup> (27)

<sup>A</sup> <sup>¼</sup> <sup>μ</sup> BC � � <sup>þ</sup> <sup>μ</sup>ð Þ¼ <sup>B</sup> <sup>1</sup> (28)

σ<sup>f</sup> þ mf . For the usually used return period, the

CV<sup>2</sup> <sup>þ</sup> <sup>1</sup> (29)

(26)

79

□

where the pi is the probability of occurrence of year i. The upper bound is attained if and only if the smallest occurrence probability year is the only year of non-zero losses. And when only year i have nonzero losses:

$$
\sigma\_{\mathbf{f}} = \mathbf{m}\_{\mathbf{f}} \sqrt{\frac{1}{\mathbf{p}\_{\mathbf{i}}} - 1} \tag{19}
$$

For not necessarily nonnegative loss contracts (such as contracts with complex layers structure and hedging design), and for contracts that have significant concentration on the upper bound (due to limit and annual limit), replacing f by f � m or M� f, where m and M are the minimum and the maximum annual loss, from the theorem we get the following lower bounds:

Corollary 1. For arbitrary reinsurance contract simulated annual losses f, the standard deviation σ<sup>f</sup> with respect to the mean mf, minimum annual loss m, and maximum annual loss M, is bound below by:

$$
\sigma\_f \succeq \left( m\_f - m \right) \sqrt{\frac{\mu \left( L^{\complement} \right)}{\mu \left( L \right)}} \tag{20}
$$

$$
\sigma\_f \ge \left(M - m\_f\right) \sqrt{\frac{\mu\left(\mathcal{U}^\mathbb{C}\right)}{\mu\left(\mathcal{U}\right)}}\tag{21}
$$

where μ(LC ) and μ(L) are the measure of the numbers of minimum losses years and the numbers of notminimum losses years, μ(UC ) and μ(U) are the measure of the numbers of maximum losses years and the numbers of not-maximum losses years, respectively. The equality hold if and only if f is a bivalued distribution.

From Theorem 1, we can get an upper bound for the average annual loss on an arbitrary subset of the years:

Corollary 2. <sup>1</sup> For a nonnegative random variable f on a probability space Ω, an arbitrary subset B ⊂ Ω, the average Ð B fdμ <sup>μ</sup>ð Þ <sup>B</sup> is bound above by the standard deviation <sup>σ</sup><sup>f</sup> and the mean mf by:

$$\frac{\int\_{\mathcal{B}} f d\mu}{\mu(B)} \le \sigma\_f \sqrt{\frac{\mu\left(B^C\right)}{\mu(B)}} + m\_f. \tag{22}$$

Proof:

Define two functions f<sup>1</sup> and f<sup>2</sup> from f such that they are the restrictions of f on the subset B and BC: f1|BC = 0, f1|<sup>B</sup> = f|B, f2|BC = f|BC, f2|<sup>B</sup> = 0. Then we have f = f<sup>1</sup> + f<sup>2</sup> and f<sup>1</sup> f<sup>2</sup> = 0. The standard deviation:

<sup>1</sup> The nonnegative condition can be relax to f is bound below.

An Inequality for Reinsurance Contract Annual Loss Standard Deviation and Its Application http://dx.doi.org/10.5772/intechopen.76265 79

$$
\sigma\_f^2 = \mathbb{E}\left[\left(f\_1 + f\_2\right)^2\right] - \left[\mathbb{E}\left(f\_1 + f\_2\right)\right]^2 \tag{23}
$$

$$=\sigma\_{f\_1}^2 + \sigma\_{f\_2}^2 - 2m\_{f\_1}m\_{f\_2} \tag{24}$$

$$\geq m\_{f\_1}^2 \frac{\mu\left(\mathcal{B}^\complement\right)}{\mu(\mathcal{B})} + m\_{f\_2}^2 \frac{\mu(\mathcal{B})}{\mu\left(\mathcal{B}^\complement\right)} - 2m\_{f\_1}m\_{f\_2} \tag{25}$$

$$= \left( m\_{\mathcal{f}\_1} \sqrt{\frac{\mu\left(\mathcal{B}^{\mathcal{C}}\right)}{\mu\left(\mathcal{B}\right)}} - m\_{\mathcal{f}\_2} \sqrt{\frac{\mu\left(\mathcal{B}\right)}{\mu\left(\mathcal{B}^{\mathcal{C}}\right)}} \right)^2 \tag{26}$$

from Theorem 1 and the fact that the domain with zero value for f<sup>1</sup> include the set BC and the domain with zero value for f<sup>2</sup> include the set B. Hence:

$$m\_{f\_1} \sqrt{\frac{\mu\left(\mathcal{B}^{\complement}\right)}{\mu(\mathcal{B})}} \le m\_{f\_2} \sqrt{\frac{\mu(\mathcal{B})}{\mu\left(\mathcal{B}^{\complement}\right)}} + \sigma\_f \tag{27}$$

□

The inequality Eq. (22) is arrived by the fact that mf = mf<sup>1</sup> + mf<sup>2</sup> and

σ<sup>f</sup> ≤ mf

year i have nonzero losses:

78 Accounting from a Cross-Cultural Perspective

where μ(LC

of the years:

Proof:

deviation:

1

Corollary 2. <sup>1</sup>

B ⊂ Ω, the average

minimum losses years, μ(UC

Ð B fdμ

The nonnegative condition can be relax to f is bound below.

max

σ<sup>f</sup> ¼ mf

and the maximum annual loss, from the theorem we get the following lower bounds:

<sup>σ</sup><sup>f</sup> <sup>≥</sup> mf � <sup>m</sup> � �

σ<sup>f</sup> ≥ M � mf � �

Ð <sup>B</sup>fdμ <sup>μ</sup>ð Þ <sup>B</sup> <sup>≤</sup> <sup>σ</sup><sup>f</sup>

s

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

� �

ffiffiffiffiffiffiffiffiffiffiffiffi 1 pi � 1 � 1

(18)

(19)

(20)

(21)

1 p1 ; 1 p2 ; …; 1 pn

where the pi is the probability of occurrence of year i. The upper bound is attained if and only if the smallest occurrence probability year is the only year of non-zero losses. And when only

s

For not necessarily nonnegative loss contracts (such as contracts with complex layers structure and hedging design), and for contracts that have significant concentration on the upper bound (due to limit and annual limit), replacing f by f � m or M� f, where m and M are the minimum

Corollary 1. For arbitrary reinsurance contract simulated annual losses f, the standard deviation σ<sup>f</sup> with respect to the mean mf, minimum annual loss m, and maximum annual loss M, is bound below by:

> ffiffiffiffiffiffiffiffiffiffiffiffiffi μ L<sup>C</sup> � � μð Þ L

ffiffiffiffiffiffiffiffiffiffiffiffiffiffi μ U<sup>C</sup> � � μð Þ U

) and μ(U) are the measure of the numbers of maximum losses years and the

þ mf : (22)

s

s

) and μ(L) are the measure of the numbers of minimum losses years and the numbers of not-

For a nonnegative random variable f on a probability space Ω, an arbitrary subset

<sup>μ</sup>ð Þ <sup>B</sup> is bound above by the standard deviation <sup>σ</sup><sup>f</sup> and the mean mf by:

ffiffiffiffiffiffiffiffiffiffiffiffiffi μ B<sup>C</sup> � � μð Þ B

s

Define two functions f<sup>1</sup> and f<sup>2</sup> from f such that they are the restrictions of f on the subset B and BC: f1|BC = 0, f1|<sup>B</sup> = f|B, f2|BC = f|BC, f2|<sup>B</sup> = 0. Then we have f = f<sup>1</sup> + f<sup>2</sup> and f<sup>1</sup> f<sup>2</sup> = 0. The standard

numbers of not-maximum losses years, respectively. The equality hold if and only if f is a bivalued distribution.

From Theorem 1, we can get an upper bound for the average annual loss on an arbitrary subset

$$\left(\sqrt{\mu(\mathcal{B})}\sqrt{\mu(\mathcal{B}^{\mathbb{C}})}\right)\left(\sqrt{\frac{\mu(\mathcal{B}^{\mathbb{C}})}{\mu(\mathcal{B})}}+\sqrt{\frac{\mu(\mathcal{B})}{\mu(\mathcal{B}^{\mathbb{C}})}}\right) = \mu(\mathcal{B}^{\mathbb{C}}) + \mu(\mathcal{B}) = 1\tag{28}$$

If we let the subset B be {x|f(x) >0}, then Eq. (22) become Eq. (16). If we let the subset B be {x|CDFf (x) ≥ q,0 ≤ q ≤ 1}, we get the so called AEP TVaR upper bound for the given quantile <sup>q</sup> or the return period <sup>r</sup> � <sup>1</sup> 1�q : TVaR(q) ≤ ffiffiffiffiffiffi q 1�q q σ<sup>f</sup> þ mf . For the usually used return period, the TVaR upper bound (now simply σ<sup>f</sup> ffiffiffiffiffiffiffiffiffiffi <sup>r</sup> � <sup>1</sup> <sup>p</sup> <sup>þ</sup> mf ) is in Table 2.

Numerical example shows that our TVaR upper bound is relatively close in the quantile range [0.8,0.9], with the theoretical upper bound deviated from the simulated value by less than 20%, no matter what the distribution of the annual loss is.

Notice that the measure of the numbers of nonzero losses years is also called the probability of attaching in insurance, we can rearrange the terms in the formula Eq. (8) to get a lower bound for the probability of attaching:

Corollary 3. For a reinsurance contract simulated annual losses f, the probability of attaching, ProbA � Prob{f > 0}, with respect to the CV is bound below by:

$$ProbA \ge \frac{1}{CV^2 + 1} \tag{29}$$

As an application of Corollary 3, we see that if CV ≤ 3, then ProbA ≥ 0.1, the 0.9 quantile of f is larger than zero. Equivalently, if the 0.9 quantile of f (the so called AEP in insurance) is zero, we


Similarly, from Corollary 2, we can easily rearrange terms to get an upper bound for the probability of exceeding a given loss, which is called the Cantelli's inequality in the

Corollary 4. For a reinsurance contract simulated annual losses f, the probability of exceeding a given loss x, ProbE � Prob{f ≥ x}, with respect to the mean loss mf and the standard deviation σf, when x ≥ mf,

> 1 ð Þ <sup>x</sup>�mf 2 σ2 f

þ 1

≤

<sup>N</sup>. If <sup>1</sup>

1

An Inequality for Reinsurance Contract Annual Loss Standard Deviation and Its Application

CV2þ<sup>1</sup> <sup>&</sup>lt; <sup>1</sup>

CV<sup>2</sup> <sup>þ</sup> <sup>1</sup> (31)

http://dx.doi.org/10.5772/intechopen.76265

<sup>N</sup>, that is, CV <sup>&</sup>gt; ffiffiffiffiffiffiffiffiffiffiffiffi

þ mf , the lowest permissible exposure to allow the

þ mf (32)

<sup>M</sup>, respectively, whose CV is then

, respectively, whose

f σ2 <sup>f</sup> <sup>þ</sup>m<sup>2</sup> f

(30)

81

(33)

<sup>N</sup> � <sup>1</sup> <sup>p</sup> , then in

ProbE ≤

σ2 f mf þ mf ( )

> f mf

This bound gives a limitation on simulation with a given number N of simulated years where

given mean mf and given standard deviation σ<sup>f</sup> (to be shown in Lemma 1). In other words, if

Lemma 1. For a reinsurance contract simulated annual losses f that are bound up by M and with a

On the other hand, with the given max loss M and mean loss mf, the standard deviation σ<sup>f</sup> must satisfy:

The maximum standard deviation given mf and M is attained only by a bivalued distribution of values

<sup>þ</sup> mf , with probability q � <sup>σ</sup><sup>2</sup>

<sup>M</sup>, then g is a random variable with values in interval [0,1]. So:

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi M � mf � �mf

<sup>M</sup> and p � mf

. Similarly, the minimal exposure given mf and σ<sup>f</sup> is attained only by a bivalued

f σ2 <sup>f</sup> <sup>þ</sup>m<sup>2</sup> f

and p � <sup>m</sup><sup>2</sup>

M ≥ σ2 f mf

q

σ<sup>f</sup> ≤

<sup>N</sup> � <sup>1</sup> <sup>p</sup> , no such simulation can match both the given mean and the given standard

Prob f ≥

literature (https://en.wikipedia.org/wiki/ Chebyshev's\_inequality):

is bound above by:

Specifically, if x <sup>¼</sup> <sup>σ</sup><sup>2</sup>

CV > ffiffiffiffiffiffiffiffiffiffiffiffi

ffiffiffiffiffiffiffiffiffiffiffiffi M mf � 1 q

CV is then <sup>σ</sup><sup>f</sup>

Proof: Let <sup>g</sup> <sup>¼</sup> <sup>f</sup>

¼

ffiffiffiffiffiffiffiffiffiffi 1 <sup>p</sup> � 1 q

distribution of values either <sup>0</sup> or <sup>σ</sup><sup>2</sup>

ffiffiffiffiffiffiffiffiffiffi 1 <sup>p</sup> � 1 q

:

mf ¼

f mf þ mf , then:

each year have equal probability of occurrence <sup>1</sup>

theory no simulated loss can reach to <sup>σ</sup><sup>2</sup>

deviation closely (see also inequality Eq. (12)).

either <sup>0</sup> or M, with probability q � <sup>1</sup> � mf

given mean loss mf and a given standard deviation σf, we must have:

f mf

For given year of return period, the upper bound as given by our formula Eq. (22).

#### Table 2. TVaR upper bound.


For given range of CV, the lower bound as given by our formula Eq. (29)

Table 3. ProbA lower bound.

know CV > 3: then we will less prone to think that those zero quantiles is due to simulation inaccuracy. The CV bounds for commonly used AEP, related to probability of attaching by the formula ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 ProbA � 1 q , is in Table 3.

Similarly, from Corollary 2, we can easily rearrange terms to get an upper bound for the probability of exceeding a given loss, which is called the Cantelli's inequality in the literature (https://en.wikipedia.org/wiki/ Chebyshev's\_inequality):

Corollary 4. For a reinsurance contract simulated annual losses f, the probability of exceeding a given loss x, ProbE � Prob{f ≥ x}, with respect to the mean loss mf and the standard deviation σf, when x ≥ mf, is bound above by:

$$ProbE \le \frac{1}{\frac{\left(x - m\_f\right)^2}{\sigma\_f^2} + 1} \tag{30}$$

Specifically, if x <sup>¼</sup> <sup>σ</sup><sup>2</sup> f mf þ mf , then:

know CV > 3: then we will less prone to think that those zero quantiles is due to simulation inaccuracy. The CV bounds for commonly used AEP, related to probability of attaching by the

0.577350269189626 0.75 0.25 1.33333333333333

TVaR upper bound σ<sup>f</sup>

ffiffiffiffiffiffiffiffiffiffi <sup>μ</sup> <sup>B</sup><sup>C</sup> ð Þ μð Þ B r

þ mf

� �

formula

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 ProbA � 1

Return period Quantile

80 Accounting from a Cross-Cultural Perspective

100,000 0.99999 316.226184874055σ<sup>f</sup> + mf 10,000 0.9999 99.9949998749938σ<sup>f</sup> + mf 0.9998 70.7036066972541σ<sup>f</sup> + mf 0.999 31.6069612585582σ<sup>f</sup> + mf 0.998 22.3383079036887σ<sup>f</sup> + mf 0.996 15.7797338380595σ<sup>f</sup> + mf 0.995 14.1067359796659σ<sup>f</sup> + mf 0.99 9.9498743710662σ<sup>f</sup> + mf

50 0.98 7σ<sup>f</sup> + mf

10 0.9 3σ<sup>f</sup> + mf 5 0.8 2σ<sup>f</sup> + mf

2 0.5 1σ<sup>f</sup> + mf

For given year of return period, the upper bound as given by our formula Eq. (22).

30 0.966666666666667 5.3851648071345σ<sup>f</sup> + mf 25 0.96 4.89897948556636σ<sup>f</sup> + mf 20 0.95 4.35889894354067σ<sup>f</sup> + mf

4 0.75 1.73205080756888σ<sup>f</sup> + mf

99.9949998749938 0.0001 0.9999 10,000 9.9498743710662 0.01 0.99 100 3 0.1 0.9 10 2 0.2 0.8 5 1.73205080756888 0.25 0.75 4 1 0.5 0.5 2

0.5 0.8 0.2 1.25

CV2þ<sup>1</sup> Beginning quantile with nonzero loss Return period � <sup>1</sup> ProbA

, is in Table 3.

For given range of CV, the lower bound as given by our formula Eq. (29)

q

Table 3. ProbA lower bound.

Table 2. TVaR upper bound.

CV upper bound ProbA lower bound <sup>1</sup>

$$\text{Prob}\left\{f \ge \frac{\sigma\_f^2}{m\_f} + m\_f\right\} \le \frac{1}{\text{CV}^2 + 1} \tag{31}$$

This bound gives a limitation on simulation with a given number N of simulated years where each year have equal probability of occurrence <sup>1</sup> <sup>N</sup>. If <sup>1</sup> CV2þ<sup>1</sup> <sup>&</sup>lt; <sup>1</sup> <sup>N</sup>, that is, CV <sup>&</sup>gt; ffiffiffiffiffiffiffiffiffiffiffiffi <sup>N</sup> � <sup>1</sup> <sup>p</sup> , then in theory no simulated loss can reach to <sup>σ</sup><sup>2</sup> f mf þ mf , the lowest permissible exposure to allow the given mean mf and given standard deviation σ<sup>f</sup> (to be shown in Lemma 1). In other words, if CV > ffiffiffiffiffiffiffiffiffiffiffiffi <sup>N</sup> � <sup>1</sup> <sup>p</sup> , no such simulation can match both the given mean and the given standard deviation closely (see also inequality Eq. (12)).

Lemma 1. For a reinsurance contract simulated annual losses f that are bound up by M and with a given mean loss mf and a given standard deviation σf, we must have:

$$M \cong \frac{\sigma\_f^2}{m\_f} + m\_f \tag{32}$$

On the other hand, with the given max loss M and mean loss mf, the standard deviation σ<sup>f</sup> must satisfy:

$$
\sigma\_f \le \sqrt{(M - m\_f)m\_f} \tag{33}
$$

The maximum standard deviation given mf and M is attained only by a bivalued distribution of values either <sup>0</sup> or M, with probability q � <sup>1</sup> � mf <sup>M</sup> and p � mf <sup>M</sup>, respectively, whose CV is then ffiffiffiffiffiffiffiffiffiffiffiffi M mf � 1 q ¼ ffiffiffiffiffiffiffiffiffiffi 1 <sup>p</sup> � 1 q . Similarly, the minimal exposure given mf and σ<sup>f</sup> is attained only by a bivalued distribution of values either <sup>0</sup> or <sup>σ</sup><sup>2</sup> f mf <sup>þ</sup> mf , with probability q � <sup>σ</sup><sup>2</sup> f σ2 <sup>f</sup> <sup>þ</sup>m<sup>2</sup> f and p � <sup>m</sup><sup>2</sup> f σ2 <sup>f</sup> <sup>þ</sup>m<sup>2</sup> f , respectively, whose CV is then <sup>σ</sup><sup>f</sup> mf ¼ ffiffiffiffiffiffiffiffiffiffi 1 <sup>p</sup> � 1 q :

Proof: Let <sup>g</sup> <sup>¼</sup> <sup>f</sup> <sup>M</sup>, then g is a random variable with values in interval [0,1]. So:

$$\mathbf{g}^2 \le \mathbf{g} \tag{34}$$

2.2. Simulation deviation

Typical correlation coefficient r from yearly model update range from 0.27 to 0.96, the CV range is 0.003–316 as we calculated in Table 1. With these parameters we used Mathematica Manipulate function to explore the probability of the ratio of two simulated annual-mean-loss be within the range of 0.5–1.5, assuming the annual-mean-loss obeys the Normal Distribution. We find that the probability is small when r is close to 0, and is decreasing when CV is increasing, but is stabilized after CV ≥ 7. For an example r = 0.822434, for almost half of the contracts, the simulated annual-mean-loss being within 50% to each other has probability of 0.459, that is, with probability of 0.551 we will see two simulation have simulated annualmean-loss increased or decreased by more than 50% (Figures 1 and 2). These factors should be

An Inequality for Reinsurance Contract Annual Loss Standard Deviation and Its Application

http://dx.doi.org/10.5772/intechopen.76265

83

Figure 1. Probability that two simulated mean are within 50% of each other. The horizontal axis is the CV and the vertical axis is the probability. (a) Using Hinkley formula. Formulas used in (a) is complex and very different which may cast

Figure 2. Probability that two simulated mean are within 50% of each other. The horizontal axis is the CV and the vertical axis is the probability. (b) Using Marsaglia formula. Formulas used in (b) is complex and very different which may cast

considered for model risk management or individual contract evaluation.

doubt for their validity. Our plot is a numerical assurance for their correctness.

doubt for their validity. Our plot is a numerical assurance for their correctness.

and

$$\int\_{\Omega} g^2 d\mu \le \int\_{\Omega} g d\mu \tag{35}$$

$$\int\_{\Omega} \mathrm{g}^2 d\mu - \left(\int\_{\Omega} \mathrm{g} d\mu\right)^2 \le \int\_{\Omega} \mathrm{g} d\mu - \left(\int\_{\Omega} \mathrm{g} d\mu\right)^2 \tag{36}$$

$$
\sigma\_{\mathcal{S}}^2 \le m\_{\mathcal{S}} \left( 1 - m\_{\mathcal{S}} \right) \tag{37}
$$

$$\frac{\sigma\_f^2}{M^2} \le \frac{m\_f}{M} \left(1 - \frac{m\_f}{M}\right) \tag{38}$$

This proves both of our inequalities. Without loss of generality, suppose any nonempty subset of Ω have nonzero measure, the equality hold in Eq. (34) and its subsequent inequalities if and only if g = 0 or g = 1. □

Because of the probability of mf <sup>M</sup> of taking value M, we cannot solve the limitation on CV by increasing M. The only solution is then by increasing N or using unequal probabilities (please refer to Eq. (18)), otherwise we may have to choose to only match the mean loss, and reduce the simulated standard deviation.

By examining the proof of Corollary 2 and Theorem 1 Eq. (17), forcing the inequality in Eq. (25) to be an equality, we can prove that:

Corollary 5. For a nonnegative random variable f on a probability space Ω, an arbitrary subset B ⊂ Ω, assuming <sup>σ</sup><sup>f</sup> <sup>&</sup>gt; <sup>0</sup>, <sup>μ</sup>ð Þ <sup>B</sup> <sup>&</sup>gt; <sup>0</sup>, <sup>μ</sup> BC � � <sup>&</sup>gt; <sup>0</sup>, mf <sup>&</sup>gt; <sup>0</sup>, the average Ð B fdμ <sup>μ</sup>ð Þ <sup>B</sup> attain its upper bound with respect to the standard deviation σ<sup>f</sup> and the mean mf:

$$\frac{\int\_{B} f d\mu}{\mu(B)} = \sigma\_f \sqrt{\frac{\mu\left(B^C\right)}{\mu(B)}} + m\_f \tag{39}$$

if and only if f is a nonzero constant function on the subset B and a constant function on the subset BC.

So the maximum TVaR distribution is bivalued, this corollary provides a guide for implementing relatively high CV distribution simulation: for CV close to ffiffiffiffiffiffiffiffiffiffiffiffi <sup>N</sup> � <sup>1</sup> <sup>p</sup> which do not simulate well, a conservative and simple selection is using bivalued distribution. Similar conclusion about bivalued distribution can be made for the maximum AEP distribution which are bound by TVaR's bound and attain the same upper bound given in Eq. (39). Both conclusions give clue for a risk measure of the maximally likely or best compromise quantile by comparing simulated TVaR or AEP with the theoretical bound for the best match but that is the topic of a different research.

#### 2.2. Simulation deviation

g<sup>2</sup> ≤ g (34)

gdμ (35)

� � (37)

<sup>μ</sup>ð Þ <sup>B</sup> attain its upper bound with respect

þ mf (39)

<sup>N</sup> � <sup>1</sup> <sup>p</sup> which do not simulate well, a

(36)

(38)

ð Ω g<sup>2</sup>dμ ≤ ð Ω

ð Ω gdμ � �<sup>2</sup>

σ2

σ2 f <sup>M</sup><sup>2</sup> <sup>≤</sup> ≤ ð Ω gdμ �

<sup>g</sup> ≤ mg 1 � mg

This proves both of our inequalities. Without loss of generality, suppose any nonempty subset of Ω have nonzero measure, the equality hold in Eq. (34) and its subsequent inequalities if and only if g = 0 or g = 1. □

increasing M. The only solution is then by increasing N or using unequal probabilities (please refer to Eq. (18)), otherwise we may have to choose to only match the mean loss, and reduce

By examining the proof of Corollary 2 and Theorem 1 Eq. (17), forcing the inequality in Eq. (25)

Corollary 5. For a nonnegative random variable f on a probability space Ω, an arbitrary subset B ⊂ Ω,

s

if and only if f is a nonzero constant function on the subset B and a constant function on the

So the maximum TVaR distribution is bivalued, this corollary provides a guide for implementing

conservative and simple selection is using bivalued distribution. Similar conclusion about bivalued distribution can be made for the maximum AEP distribution which are bound by TVaR's bound and attain the same upper bound given in Eq. (39). Both conclusions give clue for a risk measure of the maximally likely or best compromise quantile by comparing simulated TVaR or AEP with the theoretical bound for the best match but that is the topic of a different

ffiffiffiffiffiffiffiffiffiffiffiffiffi μ BC � � μð Þ B

mf <sup>M</sup> <sup>1</sup> � mf M � �

ð Ω gdμ � �<sup>2</sup>

<sup>M</sup> of taking value M, we cannot solve the limitation on CV by

Ð B fdμ

ð Ω g2 dμ �

Because of the probability of mf

82 Accounting from a Cross-Cultural Perspective

the simulated standard deviation.

to be an equality, we can prove that:

to the standard deviation σ<sup>f</sup> and the mean mf:

subset BC.

research.

assuming <sup>σ</sup><sup>f</sup> <sup>&</sup>gt; <sup>0</sup>, <sup>μ</sup>ð Þ <sup>B</sup> <sup>&</sup>gt; <sup>0</sup>, <sup>μ</sup> BC � � <sup>&</sup>gt; <sup>0</sup>, mf <sup>&</sup>gt; <sup>0</sup>, the average

Ð <sup>B</sup>fdμ <sup>μ</sup>ð Þ <sup>B</sup> <sup>¼</sup> <sup>σ</sup><sup>f</sup>

relatively high CV distribution simulation: for CV close to ffiffiffiffiffiffiffiffiffiffiffiffi

and

Typical correlation coefficient r from yearly model update range from 0.27 to 0.96, the CV range is 0.003–316 as we calculated in Table 1. With these parameters we used Mathematica Manipulate function to explore the probability of the ratio of two simulated annual-mean-loss be within the range of 0.5–1.5, assuming the annual-mean-loss obeys the Normal Distribution. We find that the probability is small when r is close to 0, and is decreasing when CV is increasing, but is stabilized after CV ≥ 7. For an example r = 0.822434, for almost half of the contracts, the simulated annual-mean-loss being within 50% to each other has probability of 0.459, that is, with probability of 0.551 we will see two simulation have simulated annualmean-loss increased or decreased by more than 50% (Figures 1 and 2). These factors should be considered for model risk management or individual contract evaluation.

Figure 1. Probability that two simulated mean are within 50% of each other. The horizontal axis is the CV and the vertical axis is the probability. (a) Using Hinkley formula. Formulas used in (a) is complex and very different which may cast doubt for their validity. Our plot is a numerical assurance for their correctness.

Figure 2. Probability that two simulated mean are within 50% of each other. The horizontal axis is the CV and the vertical axis is the probability. (b) Using Marsaglia formula. Formulas used in (b) is complex and very different which may cast doubt for their validity. Our plot is a numerical assurance for their correctness.

The Mathematica code for the plot in Figures 1 and 2 is in Appendix A. The two plots are identical even though their formulas are quite different and we do not know whether they can be analytically proved to be equivalent: our plots are numerical validation of both of their formulas.

gj

ð g2 <sup>d</sup><sup>μ</sup> <sup>¼</sup> <sup>a</sup><sup>2</sup>

<sup>≥</sup> mf � <sup>m</sup> � �aμð Þþ <sup>m</sup>

σ<sup>f</sup> ≥

b

Using the negative form of the inequality f � mf

σ<sup>f</sup> ≥

b

, A <sup>¼</sup> mf � <sup>m</sup> � �μð Þ <sup>m</sup> , B <sup>¼</sup> <sup>M</sup> � mf

� �μð Þþ <sup>m</sup> <sup>M</sup> � mf

a b � �<sup>2</sup>

� �μð Þþ <sup>m</sup> <sup>M</sup> � mf

a b � �<sup>2</sup>

<sup>C</sup> <sup>¼</sup> <sup>μ</sup>ð Þ <sup>m</sup> , D <sup>¼</sup> <sup>c</sup>

� � <sup>c</sup>

<sup>μ</sup>ð Þþ <sup>m</sup> <sup>c</sup> b � �<sup>2</sup>

� � <sup>c</sup>

<sup>μ</sup>ð Þþ <sup>m</sup> <sup>c</sup> b � �<sup>2</sup>

� � c

b � �<sup>2</sup> b

ð

f g f ¼m

ð

∣f � mf ∣gdμ ¼

Then:

ð

due to ∣f � mf ∣ ≥ f � mf .

<sup>¼</sup> mf � <sup>m</sup> � � <sup>a</sup>

<sup>¼</sup> mf � <sup>m</sup> � � <sup>a</sup>

We get:

suppose b > 0.

suppose b > 0.

Define:

<sup>t</sup> <sup>¼</sup> <sup>a</sup> b f g <sup>f</sup> <sup>¼</sup><sup>m</sup> <sup>¼</sup> a, g f g <sup>m</sup><<sup>f</sup> <sup>&</sup>lt;<sup>M</sup> <sup>¼</sup> <sup>b</sup>; <sup>g</sup> �

∣f � mf ∣adμ þ

f g m<f <M

� �

<sup>μ</sup>ð Þþ <sup>m</sup> <sup>b</sup><sup>2</sup> <sup>1</sup> � <sup>μ</sup>ð Þ� <sup>m</sup> <sup>μ</sup>ð Þ <sup>M</sup> � � <sup>þ</sup> <sup>c</sup>

f g m<f <M

f g m<f <M

� �ð Þ <sup>c</sup> � <sup>b</sup> <sup>μ</sup>ð Þ <sup>M</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>a</sup><sup>2</sup> � <sup>b</sup><sup>2</sup> � �μð Þþ <sup>m</sup> <sup>c</sup><sup>2</sup> � <sup>b</sup><sup>2</sup> � �μð Þþ <sup>M</sup> <sup>b</sup><sup>2</sup>

� �ð Þ <sup>c</sup> <sup>þ</sup> <sup>b</sup> <sup>μ</sup>ð Þ <sup>M</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>a</sup><sup>2</sup> � <sup>b</sup><sup>2</sup> � �μð Þþ <sup>m</sup> <sup>c</sup><sup>2</sup> � <sup>b</sup><sup>2</sup> � �μð Þþ <sup>M</sup> <sup>b</sup><sup>2</sup>

ð

ð

fbdμ �

<sup>¼</sup> mf � <sup>m</sup> � �aμð Þþ <sup>m</sup> mf <sup>b</sup> � mbμð Þ� <sup>m</sup> Mbμð Þ� <sup>M</sup> mf <sup>b</sup> <sup>1</sup> � <sup>μ</sup>ð Þ� <sup>m</sup> <sup>μ</sup>ð Þ <sup>M</sup> � � <sup>þ</sup> <sup>M</sup> � mf

<sup>¼</sup> mf � <sup>m</sup> � �ð Þ <sup>a</sup> <sup>þ</sup> <sup>b</sup> <sup>μ</sup>ð Þþ <sup>m</sup> <sup>M</sup> � mf

mf � <sup>m</sup> � �ð Þ <sup>a</sup> <sup>þ</sup> <sup>b</sup> <sup>μ</sup>ð Þþ <sup>m</sup> <sup>M</sup> � mf

b

� � �

mf � <sup>m</sup> � �ð Þ <sup>a</sup> � <sup>b</sup> <sup>μ</sup>ð Þþ <sup>m</sup> <sup>M</sup> � mf

b

�

An Inequality for Reinsurance Contract Annual Loss Standard Deviation and Its Application

f g <sup>f</sup> <sup>¼</sup><sup>M</sup> <sup>¼</sup> <sup>c</sup> (41)

http://dx.doi.org/10.5772/intechopen.76265

μð Þ M (42)

� �cμð Þ <sup>M</sup> (44)

∣f � mf ∣cdμ (43)

85

� �cμð Þ <sup>M</sup> (45)

� �μð Þ <sup>M</sup> (51)

2

mf bdμ þ M � mf

<sup>q</sup> (47)

<sup>q</sup> (49)

� �μð Þ� <sup>M</sup> mf � <sup>m</sup> � �μð Þþ <sup>m</sup> <sup>M</sup> � mf � �μð Þ <sup>M</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

� �μð Þþ <sup>M</sup> mf � <sup>m</sup> � �μð Þ� <sup>m</sup> <sup>M</sup> � mf

μð Þþ M 1 � μð Þ� m μð Þ M (52)

μð Þþ M 1 � μð Þ� m μð Þ M <sup>q</sup> (50)

� �μð Þþ <sup>M</sup> mf � <sup>m</sup> � �μð Þ� <sup>m</sup> <sup>M</sup> � mf � �μð Þ <sup>M</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

μð Þþ M 1 � μð Þ� m μð Þ M <sup>q</sup> (48)

ð

f g f ¼M

� �ð Þ <sup>c</sup> � <sup>b</sup> <sup>μ</sup>ð Þ <sup>M</sup> (46)

� ≥ mf � f, we also get a dual form inequality:

∣f � mf ∣bdμ þ

#### 3. Discussion

The lower bound for CV of reinsurance contract annual loss is established. The largest of those bound are also proved to be the upper bound for all CV. Applying this range information to ratio distribution, we can get theoretical value of the probability that different simulations will have simulated mean annual loss with deviation from each other less than a given percentage, under the Normal Distribution assumption of the mean annual loss. We think this assumption can be removed by using more suitable distributions, with numerical methods, but may still give the probability not too different. Typical example case numerical study confirmed this, and showed that the "Normal approximation" gives probability only a few percent (2–5%) less than using more suitable distributions that do not have explicit formula for the probability.

As the starting point and the application of the CV range, the ratio distribution and the model risk quantification results we get may be only rudimentarily correct due to other factors, such as the distribution modeling, the dependence modeling, and additional parameters dependence than just the CV and r, but our CV inequality itself is mathematically sound.

The less general upper bound ffiffiffiffiffiffiffiffiffiffiffi <sup>n</sup> � <sup>1</sup> <sup>p</sup> where all probabilities are equal is obtained by Katsnelson and Kotz in the literature [4, 5].

Using the same Hölder's inequality and calculus technique which may not have a simple elementary inequality approach counterpart, we can prove a more complex formula:

Theorem 2. For reinsurance contract simulated annual losses f, the standard deviation σ<sup>f</sup> with respect to the mean mf is bound below by:

$$\sigma\_f \ge \sqrt{\left(m\_f - m\right)^2 \mu(m) + \left(M - m\_f\right)^2 \mu(M) + \frac{\left[\left(m\_f - m\right)\mu(m) - \left(M - m\_f\right)\mu(M)\right]^2}{1 - \mu(m) - \mu(M)}}\tag{40}$$

when μ(m) + μ(M) < 1, where σ<sup>f</sup> is the standard deviation, mf is the mean, m is the minimum annual loss, M is the maximum annual loss, μ(m) denote the measure of the numbers of minimum losses years, μ(M) denote the measure of the numbers of maximum losses years.

Proof:

In the inequality Eq. (2), we divide Ω into three subset and let the nonnegative function g be constant in each of the three sets:

An Inequality for Reinsurance Contract Annual Loss Standard Deviation and Its Application http://dx.doi.org/10.5772/intechopen.76265 85

$$\left. \left. g \right|\_{\{f=m\}} = a, \left. g \right|\_{\{m < f < M\}} = b, \left. g \right|\_{\{f=M\}} = c \tag{41}$$

Then:

The Mathematica code for the plot in Figures 1 and 2 is in Appendix A. The two plots are identical even though their formulas are quite different and we do not know whether they can be analytically proved to be equivalent: our plots are numerical validation of both of their

The lower bound for CV of reinsurance contract annual loss is established. The largest of those bound are also proved to be the upper bound for all CV. Applying this range information to ratio distribution, we can get theoretical value of the probability that different simulations will have simulated mean annual loss with deviation from each other less than a given percentage, under the Normal Distribution assumption of the mean annual loss. We think this assumption can be removed by using more suitable distributions, with numerical methods, but may still give the probability not too different. Typical example case numerical study confirmed this, and showed that the "Normal approximation" gives probability only a few percent (2–5%) less than using more suitable distributions that do not have explicit formula for the probability.

As the starting point and the application of the CV range, the ratio distribution and the model risk quantification results we get may be only rudimentarily correct due to other factors, such as the distribution modeling, the dependence modeling, and additional parameters depen-

Using the same Hölder's inequality and calculus technique which may not have a simple

Theorem 2. For reinsurance contract simulated annual losses f, the standard deviation σ<sup>f</sup> with respect

μð Þþ M

when μ(m) + μ(M) < 1, where σ<sup>f</sup> is the standard deviation, mf is the mean, m is the minimum annual loss, M is the maximum annual loss, μ(m) denote the measure of the numbers of minimum losses years,

In the inequality Eq. (2), we divide Ω into three subset and let the nonnegative function g be

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

<sup>n</sup> � <sup>1</sup> <sup>p</sup> where all probabilities are equal is obtained by

mf � <sup>m</sup> � �μð Þ� <sup>m</sup> <sup>M</sup> � mf � �μð Þ <sup>M</sup> � �<sup>2</sup> 1 � μð Þ� m μð Þ M

(40)

dence than just the CV and r, but our CV inequality itself is mathematically sound.

elementary inequality approach counterpart, we can prove a more complex formula:

The less general upper bound ffiffiffiffiffiffiffiffiffiffiffi

to the mean mf is bound below by:

constant in each of the three sets:

s

mf � <sup>m</sup> � �<sup>2</sup>

μð Þþ m M � mf

μ(M) denote the measure of the numbers of maximum losses years.

� �<sup>2</sup>

σ<sup>f</sup> ≥

Proof:

Katsnelson and Kotz in the literature [4, 5].

formulas.

3. Discussion

84 Accounting from a Cross-Cultural Perspective

$$\int g^2 d\mu = a^2 \mu(m) + b^2 \left(1 - \mu(m) - \mu(M)\right) + c^2 \mu(M) \tag{42}$$

$$\int |f - m\_f| \text{gl} d\mu = \int\_{\{f = m\}} |f - m\_f| \text{ad}\mu + \int\_{\{m < f < \mathcal{M}\}} |f - m\_f| \text{bd}\mu + \int\_{\{f = \mathcal{M}\}} |f - m\_f| \text{cd}\mu \tag{43}$$

$$\geq (m\_{\!\!\!/\!} - m)a\mu(m) + \int\_{\{m < \!\!/\!\!/\!\!/\!\!/\!\!/\!\!\/:\!} \!\!\! d\mu - \int\_{\{m < \!\!\!/\!\!/\!\!/\!\!/\!\!\/:\!} \!\!\!/\!\!\!/\!\!\!/\!\!\/(m - m\_{\!\!\!\!/\!\!\!/\!\!\/)} c\mu(M) \tag{44}$$

$$\mathbf{x} = \left(m\_f - m\right)a\mu(m) + m\_f b - mb\mu(m) - Mb\mu(M) - m\_f b \left(1 - \mu(m) - \mu(M)\right) + \left(M - m\_f\right)c\mu(M) \tag{45}$$

$$=(m\_f - m)(a+b)\mu(m) + (M - m\_f)(c-b)\mu(M) \tag{46}$$

due to ∣f � mf ∣ ≥ f � mf .

We get:

$$\sigma\_f \ge \frac{(m\_f - m)(a+b)\mu(m) + \left(M - m\_f\right)(c-b)\mu(M)}{\sqrt{\left(a^2 - b^2\right)\mu(m) + \left(c^2 - b^2\right)\mu(M) + b^2}}\tag{47}$$

$$=\frac{\left(m\_{\hat{f}}-m\right)\left(\frac{a}{b}\right)\mu(m)+\left(M-m\_{\hat{f}}\right)\left(\frac{c}{b}\right)\mu(M)+\left(m\_{\hat{f}}-m\right)\mu(m)-\left(M-m\_{\hat{f}}\right)\mu(M)}{\sqrt{\left(\frac{a}{b}\right)^{2}\mu(m)+\left(\frac{c}{b}\right)^{2}\mu(M)+1-\mu(m)-\mu(M)}}\tag{48}$$

suppose b > 0.

Using the negative form of the inequality f � mf � � � � ≥ mf � f, we also get a dual form inequality:

$$\sigma\_f \ge \frac{(m\_f - m)(a - b)\mu(m) + (M - m\_f)(c + b)\mu(M)}{\sqrt{(a^2 - b^2)\mu(m) + (c^2 - b^2)\mu(M) + b^2}} \tag{49}$$

$$=\frac{\left(m\_{\hat{f}}-m\right)\left(\frac{\mu}{b}\right)\mu(m)+\left(M-m\_{\hat{f}}\right)\left(\frac{\varepsilon}{b}\right)\mu(M)-\left(m\_{\hat{f}}-m\right)\mu(m)+\left(M-m\_{\hat{f}}\right)\mu(M)}{\sqrt{\left(\frac{\mu}{b}\right)^2\mu(m)+\left(\frac{\varepsilon}{b}\right)^2\mu(M)+1-\mu(m)-\mu(M)}}\tag{50}$$

suppose b > 0.

Define:

$$A = \frac{a}{b}, A = \begin{pmatrix} m\_f - m \end{pmatrix} \mu(m), B = \begin{pmatrix} M - m\_f \end{pmatrix} \begin{pmatrix} \mathcal{C} \\ b \end{pmatrix} \mu(M) + \begin{pmatrix} m\_f - m \end{pmatrix} \mu(m) - \begin{pmatrix} M - m\_f \end{pmatrix} \mu(M) \tag{51}$$

$$\mathcal{C} = \mu(m),\\\mathcal{D} = \left(\frac{c}{b}\right)^2 \mu(\mathcal{M}) + 1 - \mu(m) - \mu(\mathcal{M})\tag{52}$$

$$F(t) = \frac{At + B}{\sqrt{Ct^2 + D}}\tag{53}$$

Then

$$A \succeq 0, \mathsf{C} \succeq 0, D > 0 \tag{54}$$

The derivative

$$F'(t) = \frac{AD - BCt}{\left(D + \mathcal{C}t^2\right)^{\frac{3}{2}}}\tag{55}$$

If B ≤ 0, then F<sup>0</sup> ð Þ<sup>t</sup> <sup>&</sup>gt; 0, <sup>F</sup>(t) take the maximum <sup>A</sup>ffiffi C <sup>p</sup> at ∞. If B > 0, then F(t) increase on (0, AD BC) and decrease on (AD BC, ∞), attain the maximum ffiffiffiffiffiffiffiffiffiffiffiffiffi A2 <sup>C</sup> <sup>þ</sup> <sup>B</sup><sup>2</sup> D q at AD BC.

Apply the same argument to

$$\frac{B}{\sqrt{D}} = \frac{\left(M - m\_f\right)\left(\frac{c}{b}\right)\mu(M) + \left(m\_f - m\right)\mu(m) - \left(M - m\_f\right)\mu(M)}{\sqrt{\left(\frac{c}{b}\right)^2\mu(M) + 1 - \mu(m) - \mu(M)}}\tag{56}$$

with (M � mf)μ(M) > 0 since μ(m) + μ(M) < 1, we have if (mf � m)μ(m) � (M� mf)μ(M) > 0, then Bffiffiffi D <sup>p</sup> attain the maximum ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi M � mf � �<sup>2</sup> <sup>μ</sup>ð Þþ <sup>M</sup> ½ � ð Þ mf �<sup>m</sup> <sup>μ</sup>ð Þ� <sup>m</sup> ð Þ <sup>M</sup>�mf <sup>μ</sup>ð Þ <sup>M</sup> <sup>2</sup> 1�μð Þ� m μð Þ M r at ð Þ <sup>M</sup>�mf ð Þ <sup>1</sup>�μð Þ� <sup>m</sup> <sup>μ</sup>ð Þ <sup>M</sup> ð Þ mf �<sup>m</sup> <sup>μ</sup>ð Þ� <sup>m</sup> ð Þ <sup>M</sup>�mf <sup>μ</sup>ð Þ <sup>M</sup> . If (mf � <sup>m</sup>)μ(m) � (<sup>M</sup> � mf)μ(M) = 0, then <sup>B</sup>ffiffiffi D <sup>p</sup> is monotonically increasing with respect to <sup>c</sup> <sup>b</sup> and attain the maximum M � mf � � ffiffiffiffiffiffiffiffiffiffiffi <sup>μ</sup>ð Þ <sup>M</sup> <sup>p</sup> at <sup>∞</sup>.

If (mf � m)μ(m) � (M � mf)μ(M) < 0, then use the inequality Eq. (50), we can follow the same steps to arrive at the same form of maximum formula. We thus proved the maximal

$$\sqrt{\frac{\mathbf{A}^2}{\mathbf{C}} + \frac{\mathbf{B}^2}{D}} = \sqrt{\left(m\_f - m\right)^2 \mu(m) + \left(M - m\_f\right)^2 \mu(M) + \frac{\left[\left(m\_f - m\right)\mu(m) - \left(M - m\_f\right)\mu(M)\right]^2}{1 - \mu(m) - \mu(M)}} \tag{57}$$

with the specific choice of <sup>c</sup> <sup>b</sup> and <sup>a</sup> b

We can also prove by calculus that:

Theorem 3. In the terminology of Theorem 2, if m = 0,

$$\sqrt{\left(m\_f - m\right)^2 \mu(m) + \left(M - m\_f\right)^2 \mu(M)} + \frac{\left[\left(m\_f - m\right)\mu(m) - \left(M - m\_f\right)\mu(M)\right]^2}{1 - \mu(m) - \mu(M)} \ge m\_f \sqrt{\frac{\mu(m)}{1 - \mu(m)}}\tag{58}$$

. □

Proof:

Define

for t ≥ 0.

F tðÞ¼ mf � <sup>m</sup> � �<sup>2</sup>

The derivative of F(t) is

set {f>m}).

variables.

Then F(t) is continuous at 0 and

μð Þþ m M � mf

<sup>F</sup>ð Þ¼ <sup>0</sup> mf � <sup>m</sup> � �<sup>2</sup>

F0 ðÞ¼ t

jf � mf j1dμ

ð

0 B@

f g m<f <M

� �<sup>2</sup>

t þ

μð Þþ m

Theorem 3 can be combined with the following form of the Hölder's inequality:

1 CA

2 ≤

Eq. (8) when we need a fast first approximation, and hence of less practical interest.

<sup>¼</sup> mf � <sup>m</sup> � �<sup>2</sup> � <sup>m</sup><sup>2</sup>

mf � <sup>m</sup> � �μð Þ� <sup>m</sup> <sup>M</sup> � mf � �t � �<sup>2</sup>

An Inequality for Reinsurance Contract Annual Loss Standard Deviation and Its Application

mf � <sup>m</sup> � �μð Þ <sup>m</sup> � �<sup>2</sup>

f

mf � <sup>M</sup> <sup>þ</sup> ð Þ <sup>M</sup> � <sup>m</sup> <sup>μ</sup>ð Þ <sup>m</sup> � �<sup>2</sup>

which is always nonnegative, so F(t) ≥ 0 for any t ≥ 0. □

ð

f � mf � � � � 2 dμ

f g m<f <M

to give an alternative proof of Theorem 2 and then Eq. (16) (or directly for Eq. (20) by using the

So there is a complex but better lower bounds Eq. (40), and empirical study shows that when μ(m) > 0.86, both bounds are close to the true σ<sup>f</sup> to within 86% with the simple form Eq. (8) 3–4% lower than the complex form Eq. (40). Even though the complex form Eq. (40) is generally valid for any discrete random variable, it may not be as easily applicable as the simple form

With numerical simulation, we can get σ<sup>f</sup> and CV directly, so these formulas seems not to be useful for the numerical results. But since each simulation may arrive at a different value, known a priori their approximate value will be a check for any possible simulation process problem. Our inequalities also reveal that the CV is intrinsically related to important value distribution characteristics of the annual loss random variable. This essentialness of CV is also confirmed by other studies, such as the correlation and cluster analysis of these random

<sup>1</sup> � <sup>μ</sup>ð Þ <sup>m</sup> � <sup>m</sup><sup>2</sup>

<sup>1</sup> � <sup>μ</sup>ð Þ� <sup>m</sup> <sup>t</sup> � <sup>m</sup><sup>2</sup>

f

<sup>1</sup> � <sup>μ</sup>ð Þ <sup>m</sup> <sup>μ</sup>ð Þ¼ <sup>m</sup> <sup>0</sup> (61)

�<sup>1</sup> <sup>þ</sup> <sup>t</sup> <sup>þ</sup> <sup>μ</sup>ð Þ <sup>m</sup> � �<sup>2</sup> (62)

ð

12

dμ (63)

f g m<f <M

μð Þ m

f

http://dx.doi.org/10.5772/intechopen.76265

μð Þ m <sup>1</sup> � <sup>μ</sup>ð Þ <sup>m</sup> (59) 87

<sup>1</sup> � <sup>μ</sup>ð Þ <sup>m</sup> (60)

An Inequality for Reinsurance Contract Annual Loss Standard Deviation and Its Application http://dx.doi.org/10.5772/intechopen.76265 87

Proof:

F tðÞ¼ At <sup>þ</sup> <sup>B</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

AD � BCt <sup>D</sup> <sup>þ</sup> Ct<sup>2</sup> � �<sup>3</sup>

> at AD BC.

� �μð Þþ <sup>M</sup> mf � <sup>m</sup> � �μð Þ� <sup>m</sup> <sup>M</sup> � mf

μð Þþ M 1 � μð Þ� m μð Þ M

<sup>μ</sup>ð Þþ <sup>M</sup> ½ � ð Þ mf �<sup>m</sup> <sup>μ</sup>ð Þ� <sup>m</sup> ð Þ <sup>M</sup>�mf <sup>μ</sup>ð Þ <sup>M</sup> <sup>2</sup> 1�μð Þ� m μð Þ M

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

mf � <sup>m</sup> � �μð Þ� <sup>m</sup> <sup>M</sup> � mf � �μð Þ <sup>M</sup> � �<sup>2</sup> 1 � μð Þ� m μð Þ M

μð Þþ M

� �μð Þ <sup>M</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

C

ffiffiffiffiffiffiffiffiffiffiffiffiffi A2 <sup>C</sup> <sup>þ</sup> <sup>B</sup><sup>2</sup> D

with (M � mf)μ(M) > 0 since μ(m) + μ(M) < 1, we have if (mf � m)μ(m) � (M� mf)μ(M) > 0, then

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

If (mf � m)μ(m) � (M � mf)μ(M) < 0, then use the inequality Eq. (50), we can follow the same

D

steps to arrive at the same form of maximum formula. We thus proved the maximal

� �<sup>2</sup>

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

μð Þþ M

q

2

F0 ðÞ¼ t

ð Þ<sup>t</sup> <sup>&</sup>gt; 0, <sup>F</sup>(t) take the maximum <sup>A</sup>ffiffi

� � <sup>c</sup>

M � mf � �<sup>2</sup>

� � ffiffiffiffiffiffiffiffiffiffiffi

<sup>b</sup> and <sup>a</sup> b

Theorem 3. In the terminology of Theorem 2, if m = 0,

� �<sup>2</sup>

μð Þþ m M � mf

b

c b � �<sup>2</sup>

<sup>μ</sup>ð Þ <sup>M</sup> <sup>p</sup> at <sup>∞</sup>.

μð Þþ m M � mf

BC, ∞), attain the maximum

<sup>p</sup> <sup>¼</sup> <sup>M</sup> � mf

r

If (mf � <sup>m</sup>)μ(m) � (<sup>M</sup> � mf)μ(M) = 0, then <sup>B</sup>ffiffiffi

mf � <sup>m</sup> � �<sup>2</sup>

Then

The derivative

If B ≤ 0, then F<sup>0</sup>

decrease on (AD

Bffiffiffi D

Apply the same argument to

86 Accounting from a Cross-Cultural Perspective

<sup>p</sup> attain the maximum

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi A2 C þ B2 D

s

s

attain the maximum M � mf

¼

with the specific choice of <sup>c</sup>

mf � <sup>m</sup> � �<sup>2</sup>

s

We can also prove by calculus that:

B ffiffiffiffi D Ct<sup>2</sup> <sup>þ</sup> <sup>D</sup> <sup>p</sup> (53)

(55)

BC) and

<sup>b</sup> and

(57)

at ð Þ <sup>M</sup>�mf ð Þ <sup>1</sup>�μð Þ� <sup>m</sup> <sup>μ</sup>ð Þ <sup>M</sup> ð Þ mf �<sup>m</sup> <sup>μ</sup>ð Þ� <sup>m</sup> ð Þ <sup>M</sup>�mf <sup>μ</sup>ð Þ <sup>M</sup> .

≥ mf

s

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi μð Þ m 1 � μð Þ m

(58)

A ≥ 0, C ≥ 0, D > 0 (54)

<sup>p</sup> at ∞. If B > 0, then F(t) increase on (0, AD

<sup>q</sup> (56)

<sup>p</sup> is monotonically increasing with respect to <sup>c</sup>

mf � <sup>m</sup> � �μð Þ� <sup>m</sup> <sup>M</sup> � mf � �μð Þ <sup>M</sup> � �<sup>2</sup> 1 � μð Þ� m μð Þ M

. □

Define

$$F(t) = \left(m\_f - m\right)^2 \mu(m) + \left(M - m\_f\right)^2 t + \frac{\left[\left(m\_f - m\right)\mu(m) - \left(M - m\_f\right)t\right]^2}{1 - \mu(m) - t} - m\_f^2 \frac{\mu(m)}{1 - \mu(m)}\tag{59}$$

for t ≥ 0.

Then F(t) is continuous at 0 and

$$F(0) = \left(m\_f - m\right)^2 \mu(m) + \frac{\left[\left(m\_f - m\right)\mu(m)\right]^2}{1 - \mu(m)} - m\_f^2 \frac{\mu(m)}{1 - \mu(m)}\tag{60}$$

$$\mu = \frac{\left(m\_f - m\right)^2 - m\_f^2}{1 - \mu(m)}\mu(m) = 0\tag{61}$$

The derivative of F(t) is

$$F'(t) = \frac{\left(m\_f - M + (M - m)\mu(m)\right)^2}{\left(-1 + t + \mu(m)\right)^2} \tag{62}$$

which is always nonnegative, so F(t) ≥ 0 for any t ≥ 0. □

Theorem 3 can be combined with the following form of the Hölder's inequality:

$$\left(\int\_{\{m$$

to give an alternative proof of Theorem 2 and then Eq. (16) (or directly for Eq. (20) by using the set {f>m}).

So there is a complex but better lower bounds Eq. (40), and empirical study shows that when μ(m) > 0.86, both bounds are close to the true σ<sup>f</sup> to within 86% with the simple form Eq. (8) 3–4% lower than the complex form Eq. (40). Even though the complex form Eq. (40) is generally valid for any discrete random variable, it may not be as easily applicable as the simple form Eq. (8) when we need a fast first approximation, and hence of less practical interest.

With numerical simulation, we can get σ<sup>f</sup> and CV directly, so these formulas seems not to be useful for the numerical results. But since each simulation may arrive at a different value, known a priori their approximate value will be a check for any possible simulation process problem. Our inequalities also reveal that the CV is intrinsically related to important value distribution characteristics of the annual loss random variable. This essentialness of CV is also confirmed by other studies, such as the correlation and cluster analysis of these random variables.

#### 4. Conclusions

Lower bound for reinsurance contract annual loss standard deviation involving zero losses years counts are obtained, which imply a general upper bound for annual loss TVaR or AEP with no mention of zero losses years. Alternative forms of these bounds give inequalities for probability of attaching and exceeding. These bounds can explain the difficulties or instabilities observed in numerical simulations, show the major reason of the limitation of the simulation is high CV and give clue to alternative solutions.

marsaglia[t\_,p\_,c\_]:=marsaglia[t,p,c] = With[{},Exp[1.0/(1.0 + p)/cˆ2]/Pi/(1.0 + tˆ2)(1.0 + q[t,p,c]

An Inequality for Reinsurance Contract Annual Loss Standard Deviation and Its Application

http://dx.doi.org/10.5772/intechopen.76265

89

M[v\_,p\_,c\_]:=M[v,p,c] = With[{},CDF[NormalDistribution[0,1],1/c (1 p)/Sqrt[1 pˆ2]] + CDF[ NormalDistribution[0,1],1/c] 2 CDF[NormalDistribution[0,1],1/c (1 p)/Sqrt[1 pˆ2]] CDF[.

LogLinearPlot[Evaluate[MA[1.5,0.822434,x]MA[0.5,0.822434,x]],{x,0.1,10},PlotRange>All,

[1] Lloyd's Market Association. Catastrophe Modelling Guidance for Non-Catastrophe Modellers [Internet]. 2013. Available from: http://www.lmalloyds.com/lma/finance/Cat\_

[2] Hinkley DV. On the ratio of two correlated normal random variables. Biometrika 1969; 56(3):635-639. DOI: 10.2307/2334671. Available from: http://www.jstor.org/stable/2334671

[3] Marsaglia G. Ratios of normal variables. Journal of Statistical Software. 2006;16:1-10. DOI: 10.18637/jss.v016.i04. Available from: https://www.jstatsoft.org/article/view/v016i04/v16i04.

[4] Cox NJ. Speaking Stata: The limits of sample skewness and kurtosis. Stata Journal. 2010;10:492- 495. Available from: http://www.stata-journal.com/sjpdf.html?articlenum=st0204 [Accessed:

[5] Katsnelson J, Kotz S. On the upper limits of some measures of variability. Archiv für Meteorologie, Geophysik und Bioklimatologie, Serie B. 1957;8(1):103-107. DOI: 10.1007/ BF02260299. Available from: http://link.springer.com/article/10.1007%2FBF02260299 [Accessed:

GridLines > Full,GridLinesStyle > Directive[Gray,Dashed],Mesh > Automatic,

Exp[q[t,p,c]ˆ2/2.0] Evaluate[Integrate[Exp[yˆ2/2.0],{y,0.0,q[t,p,c]}]])]

MA[v\_,p\_,c\_]:=MA[v,p,c] = With[{},M[(v p)/Sqrt[1.0 pˆ2],p,c]];

Address all correspondence to: frank.wang@validusresearch.com

Modelling\_Guidance.aspx [Accessed: March 5, 2018]

DistributeDefinitions [q,marsaglia,M,MA];

Validus Research Inc., Waterloo, ON, Canada

ImageSize > Full,Frame > on]

[Accessed: May 12, 2016]

pdf [Accessed: May 05, 2016]

July 25, 2016]

July 25, 2016]

Author details

Frank Xuyan Wang

References

NormalDistribution[0,1],1/c] + Evaluate[NIntegrate[marsaglia[u,p,c],{u,0.0,v}]]]

#### Acknowledgements

This research is supported by Validus Research Inc.

#### Conflict of interest

The authors declare no conflict of interest.

#### Thanks

The author thanks Nancy Wang for checking against a C++ application that validated the practical usefulness of our inequality.

#### Appendix-A

hinkley[x\_?NumericQ,c\_,p\_]:=1/Sqrt[2 Pi]/c (x + 1) (1 p)/(xˆ2–2 p x + 1)ˆ1.5 Exp[1/2/cˆ2 (x 1)ˆ2/(xˆ2–2 p x + 1)](CDF[NormalDistribution[0,1],1/c Sqrt[(1 p)/(1 + p)] (x + 1)/Sqrt [xˆ2–2 p x + 1]] CDF[NormalDistribution[0,1],1/c Sqrt[(1 p)/(1 + p)] (x + 1)/Sqrt[xˆ2–2 p x + 1]]) + 1/Pi Sqrt[1 pˆ2]/(xˆ2–2 p x + 1) Exp[1/cˆ2/(1 + p)];

H[x\_,c\_,p\_]:=Integrate[hinkley[y,c,p],{y,Infinity,x}];

LogLinearPlot[Evaluate[H[1.5,x,0.822434] H[0.5,x,0.822434]],{x,0.1,10},PlotRange > All, GridLines > Full,GridLinesStyle > Directive[Gray,Dashed],Mesh > Automatic, ImageSize > Full,Frame > on];

Clear[q,marsaglia,M,MA]

Off[NIntegrate::inumr]

q[t\_,p\_,c\_]:=q[t,p,c] = With[{},1.0/c (1.0 + (1.0 p) t/Sqrt[1.0 pˆ2])/Sqrt[1.0 + tˆ2]]

marsaglia[t\_,p\_,c\_]:=marsaglia[t,p,c] = With[{},Exp[1.0/(1.0 + p)/cˆ2]/Pi/(1.0 + tˆ2)(1.0 + q[t,p,c] Exp[q[t,p,c]ˆ2/2.0] Evaluate[Integrate[Exp[yˆ2/2.0],{y,0.0,q[t,p,c]}]])]

M[v\_,p\_,c\_]:=M[v,p,c] = With[{},CDF[NormalDistribution[0,1],1/c (1 p)/Sqrt[1 pˆ2]] + CDF[

NormalDistribution[0,1],1/c] 2 CDF[NormalDistribution[0,1],1/c (1 p)/Sqrt[1 pˆ2]] CDF[.

NormalDistribution[0,1],1/c] + Evaluate[NIntegrate[marsaglia[u,p,c],{u,0.0,v}]]]

MA[v\_,p\_,c\_]:=MA[v,p,c] = With[{},M[(v p)/Sqrt[1.0 pˆ2],p,c]];

DistributeDefinitions [q,marsaglia,M,MA];

```
LogLinearPlot[Evaluate[MA[1.5,0.822434,x]MA[0.5,0.822434,x]],{x,0.1,10},PlotRange>All,
GridLines > Full,GridLinesStyle > Directive[Gray,Dashed],Mesh > Automatic,
ImageSize > Full,Frame > on]
```
#### Author details

4. Conclusions

88 Accounting from a Cross-Cultural Perspective

Acknowledgements

Conflict of interest

Thanks

Appendix-A

tion is high CV and give clue to alternative solutions.

This research is supported by Validus Research Inc.

The authors declare no conflict of interest.

practical usefulness of our inequality.

ImageSize > Full,Frame > on];

Clear[q,marsaglia,M,MA] Off[NIntegrate::inumr]

x + 1]]) + 1/Pi Sqrt[1 pˆ2]/(xˆ2–2 p x + 1) Exp[1/cˆ2/(1 + p)];

H[x\_,c\_,p\_]:=Integrate[hinkley[y,c,p],{y,Infinity,x}];

Lower bound for reinsurance contract annual loss standard deviation involving zero losses years counts are obtained, which imply a general upper bound for annual loss TVaR or AEP with no mention of zero losses years. Alternative forms of these bounds give inequalities for probability of attaching and exceeding. These bounds can explain the difficulties or instabilities observed in numerical simulations, show the major reason of the limitation of the simula-

The author thanks Nancy Wang for checking against a C++ application that validated the

hinkley[x\_?NumericQ,c\_,p\_]:=1/Sqrt[2 Pi]/c (x + 1) (1 p)/(xˆ2–2 p x + 1)ˆ1.5 Exp[1/2/cˆ2 (x 1)ˆ2/(xˆ2–2 p x + 1)](CDF[NormalDistribution[0,1],1/c Sqrt[(1 p)/(1 + p)] (x + 1)/Sqrt [xˆ2–2 p x + 1]] CDF[NormalDistribution[0,1],1/c Sqrt[(1 p)/(1 + p)] (x + 1)/Sqrt[xˆ2–2 p

LogLinearPlot[Evaluate[H[1.5,x,0.822434] H[0.5,x,0.822434]],{x,0.1,10},PlotRange > All,

GridLines > Full,GridLinesStyle > Directive[Gray,Dashed],Mesh > Automatic,

q[t\_,p\_,c\_]:=q[t,p,c] = With[{},1.0/c (1.0 + (1.0 p) t/Sqrt[1.0 pˆ2])/Sqrt[1.0 + tˆ2]]

Frank Xuyan Wang

Address all correspondence to: frank.wang@validusresearch.com

Validus Research Inc., Waterloo, ON, Canada

#### References


**Section 4**

**Green Accounting**

**Section 4**

**Green Accounting**

**Chapter 5**

Provisional chapter

**Accounting and Measuring Well-being**

The recent literature on the measurement of sustainable income has developed in two important ways for accounting of contribution of natural resource stocks. One set of studies directly addresses the problem of measuring genuine savings or extended wealth formation including changes in human resource capital and natural capital. The second set of studies uses the extended conventional national income accounting methods for accounting of changes in natural resource stocks and environmental extensions of inputoutput tables. This chapter describes the methodology of measuring genuine savings for a country and reviews the estimates available for different countries. It also suggests a way

DOI: 10.5772/intechopen.77066

Keywords: genuine savings, wealth, welfare, sustainable development, natural capital,

Sustainable development of a country depends on its policies related to wealth and capital formation. It requires the measurement of wealth in broader context of including man-made physical capital, human skill capital and natural capital consisting of stocks of exhaustible and renewable resources. The wealth formation during an accounting period has to be measured as the value of changes in man-made and natural resource stocks. Recent research on green

i. United Nations (UN) Methodology of System of Environmental and Economic Account-

ii. European Union (EU) Methodology of Extended Input–Output Tables for Accounting of

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

Accounting and Measuring Well-being

Additional information is available at the end of the chapter

forward for measuring genuine saving for India.

accounting was developed in the following four important ways:

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.77066

M N Murty

M N Murty

Abstract

human skill capital

1. Introduction

ing [20, 21]

Environmental Externalities [5]

#### **Accounting and Measuring Well-being** Accounting and Measuring Well-being

#### M N Murty M N Murty

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.77066

#### Abstract

The recent literature on the measurement of sustainable income has developed in two important ways for accounting of contribution of natural resource stocks. One set of studies directly addresses the problem of measuring genuine savings or extended wealth formation including changes in human resource capital and natural capital. The second set of studies uses the extended conventional national income accounting methods for accounting of changes in natural resource stocks and environmental extensions of inputoutput tables. This chapter describes the methodology of measuring genuine savings for a country and reviews the estimates available for different countries. It also suggests a way forward for measuring genuine saving for India.

DOI: 10.5772/intechopen.77066

Keywords: genuine savings, wealth, welfare, sustainable development, natural capital, human skill capital

#### 1. Introduction

Sustainable development of a country depends on its policies related to wealth and capital formation. It requires the measurement of wealth in broader context of including man-made physical capital, human skill capital and natural capital consisting of stocks of exhaustible and renewable resources. The wealth formation during an accounting period has to be measured as the value of changes in man-made and natural resource stocks. Recent research on green accounting was developed in the following four important ways:


© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


sustainable income is derived as the one that maximizes wealth W, defined as the present value of utility or consumption given a rate of discount and the constraints on changes in man-made physical capital, human skill capital, exhaustible resource stocks and environmental resource stocks during an accounting period. The sustainable income is derived as the following

> dS dt <sup>þ</sup> <sup>μ</sup><sup>n</sup>

where C is aggregate consumption and K, S, N and E are stocks of man-made physical capital, human skill capital, exhaustible resources and environmental resources and μk, μs, μ<sup>n</sup> and μ<sup>e</sup> are their respective shadow prices. The genuine savings G are defined as

> dS dt <sup>þ</sup> <sup>μ</sup><sup>n</sup>

Eq. (3) implies that the negative genuine savings at a point in time means that future consumption must be less than current consumption over some period on the optimal path. In other words, negative genuine savings serves as an indicator of unsustainability. The shadow prices of resource stocks in Eq. (1) are the prices required to support sustainable income path. The prices observed in the marketplace will generally differ from these shadow prices [2]. The policy distortions in a typical economy lead to over-extraction of natural resources and excess pollution emissions [10]. Under these conditions it can be shown that real-world resource rents of exhaustible resources and marginal social costs of pollution exceed their shadow prices. Efficient management of natural resources will reduce the differences in observed market

Gross national savings are measured as in conventional national income accounts of a country. Net national savings or net physical capital formation representing additions to man-made physical capital are obtained by deducting depreciation of physical capital from gross national savings.

Human skill capital is the knowledge, experience and skills embodied in a nation's population. A country augments the stock of human skill capital in large part through its educational

dN dt <sup>þ</sup> <sup>μ</sup><sup>e</sup>

dN dt <sup>þ</sup> <sup>μ</sup><sup>e</sup> dE

dE

G ¼ rW � C (3)

dt (1)

Accounting and Measuring Well-being http://dx.doi.org/10.5772/intechopen.77066 95

dt (2)

current-value Hamiltonian function, which is maximized at each point in time:

dK dt <sup>þ</sup> <sup>μ</sup><sup>s</sup>

H ¼ C þ μ<sup>k</sup>

G ¼ μ<sup>k</sup>

prices and shadow prices and also increase genuine savings.

dK dt )

> dS dt) 2

It could be shown that (Hamilton, 1997)

where r is the rate of discount.

2.2. Measurement

2

See [16, 19].

Manmade capital formation (μ<sup>k</sup>

Human skill capital formation (μ<sup>s</sup>

dK dt <sup>þ</sup> <sup>μ</sup><sup>s</sup>

One set of studies directly addresses the problem of measuring genuine savings or extended wealth formation including changes in human resource capital and natural capital [8–10]. Genuine savings constitute net accumulation of man-made physical capital and human skill capital and depletion of natural resource stocks. It is an indicator of sustainable income path of a country. Genuine savings of a country could be positive or negative depending if net accumulation of man-made capital is higher or lower than the value of depletion of natural resource stocks. Positive and negative genuine savings indicate, respectively, sustainable and unsustainable income paths. Available estimates of genuine savings for different countries show that some countries have negative genuine savings.

Conventional measure of savings does not consider the most of the expenditures on human skill capital formation, for example, expenditures on education, as savings in the economy. The methodology of measuring genuine savings considers education expenditures during an accounting period as part of savings in the economy. The value of depletion of exhaustible resources stocks has to be deducted from savings. The accounting principle for valuing depletion of these resources is based on the concept of weak sustainability [4, 8, 12–16]. It requires that part of net income earned from the extraction of exhaustible resources has to be reinvested in man-made capital say in creating human skill capital so that present as well as future generations share the benefits of resource extraction. Similarly, the value of degradation of renewable resource stocks has to be deducted from genuine savings. The accounting principle for valuing depletion of these resources is based on the concept of strong sustainability. It requires the measuring of environmental degradation as excess pollution or deforestation over threshold or carrying capacity levels of resource stocks and valuing it at the cost of maintaining the threshold levels or social cost of environmental degradation [20]. There are now a number of theoretical and empirical studies on measuring social cost of environmental degradation.<sup>1</sup>

The plan of the remaining chapter is as follows. Section 2 discusses some methodological issues in measuring genuine savings. Section 3 provides a review of estimates of genuine savings for some countries. Section 4 presents a critical assessment of genuine savings studies and lessons for India. Finally Section 5 provides conclusion.

## 2. Methodology

#### 2.1. Genuine savings

Green accounting aggregates of genuine savings and sustainable income are defined in the literature on the basis of an inter-temporal optimization problem [7, 13, 14, 16, 22]. The path of

<sup>1</sup> See [6, 11, 17, 18].

sustainable income is derived as the one that maximizes wealth W, defined as the present value of utility or consumption given a rate of discount and the constraints on changes in man-made physical capital, human skill capital, exhaustible resource stocks and environmental resource stocks during an accounting period. The sustainable income is derived as the following current-value Hamiltonian function, which is maximized at each point in time:

$$H = \mathcal{C} + \mu\_k \frac{dK}{dt} + \mu\_s \frac{dS}{dt} + \mu\_n \frac{dN}{dt} + \mu\_c \frac{dE}{dt} \tag{1}$$

where C is aggregate consumption and K, S, N and E are stocks of man-made physical capital, human skill capital, exhaustible resources and environmental resources and μk, μs, μ<sup>n</sup> and μ<sup>e</sup> are their respective shadow prices. The genuine savings G are defined as

$$\mathbf{G} = \mu\_k \frac{d\mathbf{K}}{dt} + \mu\_s \frac{d\mathbf{S}}{dt} + \mu\_n \frac{d\mathbf{N}}{dt} + \mu\_e \frac{dE}{dt} \tag{2}$$

It could be shown that (Hamilton, 1997)

$$
\mathcal{G} = r\mathcal{W} - \mathcal{C} \tag{3}
$$

where r is the rate of discount.

iii. World Bank Methodology of Measuring Genuine Savings of Countries [8–10]

Green National Accounts in India

94 Accounting from a Cross-Cultural Perspective

show that some countries have negative genuine savings.

and lessons for India. Finally Section 5 provides conclusion.

2. Methodology

2.1. Genuine savings

See [6, 11, 17, 18].

1

iv. Methodology of Arrow et al. [1] and the follow-up Dasgupta Committee Report [3] on

One set of studies directly addresses the problem of measuring genuine savings or extended wealth formation including changes in human resource capital and natural capital [8–10]. Genuine savings constitute net accumulation of man-made physical capital and human skill capital and depletion of natural resource stocks. It is an indicator of sustainable income path of a country. Genuine savings of a country could be positive or negative depending if net accumulation of man-made capital is higher or lower than the value of depletion of natural resource stocks. Positive and negative genuine savings indicate, respectively, sustainable and unsustainable income paths. Available estimates of genuine savings for different countries

Conventional measure of savings does not consider the most of the expenditures on human skill capital formation, for example, expenditures on education, as savings in the economy. The methodology of measuring genuine savings considers education expenditures during an accounting period as part of savings in the economy. The value of depletion of exhaustible resources stocks has to be deducted from savings. The accounting principle for valuing depletion of these resources is based on the concept of weak sustainability [4, 8, 12–16]. It requires that part of net income earned from the extraction of exhaustible resources has to be reinvested in man-made capital say in creating human skill capital so that present as well as future generations share the benefits of resource extraction. Similarly, the value of degradation of renewable resource stocks has to be deducted from genuine savings. The accounting principle for valuing depletion of these resources is based on the concept of strong sustainability. It requires the measuring of environmental degradation as excess pollution or deforestation over threshold or carrying capacity levels of resource stocks and valuing it at the cost of maintaining the threshold levels or social cost of environmental degradation [20]. There are now a number of theoretical and empirical studies on measuring social cost of environmental degradation.<sup>1</sup>

The plan of the remaining chapter is as follows. Section 2 discusses some methodological issues in measuring genuine savings. Section 3 provides a review of estimates of genuine savings for some countries. Section 4 presents a critical assessment of genuine savings studies

Green accounting aggregates of genuine savings and sustainable income are defined in the literature on the basis of an inter-temporal optimization problem [7, 13, 14, 16, 22]. The path of Eq. (3) implies that the negative genuine savings at a point in time means that future consumption must be less than current consumption over some period on the optimal path. In other words, negative genuine savings serves as an indicator of unsustainability. The shadow prices of resource stocks in Eq. (1) are the prices required to support sustainable income path. The prices observed in the marketplace will generally differ from these shadow prices [2]. The policy distortions in a typical economy lead to over-extraction of natural resources and excess pollution emissions [10]. Under these conditions it can be shown that real-world resource rents of exhaustible resources and marginal social costs of pollution exceed their shadow prices. Efficient management of natural resources will reduce the differences in observed market prices and shadow prices and also increase genuine savings.

#### 2.2. Measurement

#### Manmade capital formation (μ<sup>k</sup> dK dt )

Gross national savings are measured as in conventional national income accounts of a country. Net national savings or net physical capital formation representing additions to man-made physical capital are obtained by deducting depreciation of physical capital from gross national savings.

#### Human skill capital formation (μ<sup>s</sup> dS dt) 2

Human skill capital is the knowledge, experience and skills embodied in a nation's population. A country augments the stock of human skill capital in large part through its educational

<sup>2</sup> See [16, 19].

systems, into which it spends lot of money every year. Conventional national income accounts consider only educational expenditures incurred in man-made physical capital such as school buildings as investments. These expenditures may constitute only 10% of total education expenditures. The other expenditures consisting of teacher salaries, books, etc., are treated as consumption expenditures which are not correct in the context of measuring genuine savings. Education expenditures lead to the formation of human skill capital and therefore treated as the investment. However, the issues related to valuation of human skill capital are not yet completely understood because one dollar worth of educational expenditure may not necessarily yield one dollar worth of human skill capital. Therefore as an initial adjustment, current educational expenditures could be treated as part of genuine savings in the economy.

#### Value of depletion of exhaustible resources (μ<sup>n</sup> dN dt )

Extraction of exhaustible natural resources such as crude oil, natural gas, coal, minerals and metals results in the depletion of resource stock extracted. The conventional national income accounts consider all the revenue earned net of cost of extraction of the resource as part of GDP. It is not a correct accounting method given that present and future generations have property rights for exhaustible resources. Therefore, measurement of genuine savings requires that value of depleted resource stocks has to be deducted from nation's savings. In the literature user cost and net price methods are used for valuing resource depletion.

#### Valuing degradation of environmental resources μ<sup>e</sup> dE dt )

Various developmental activities in the economy contribute to degradation of environmental resources due to pollution, soil erosion and deforestation. Conventional national income accounts do not account for value of environmental degradation. The methods of maintenance cost (cost of maintaining environmental resource stocks at sustainable levels) or social cost (health cost and income loss) are used for valuing environmental degradation.

average of these prices is considered. Table 1 provides recent estimates of rents earned from natural resources (oil, natural gas, coal, minerals and forests) as percentage of GDP in different

Table 1. Rents earned from natural resources (oil, natural gas, coal, minerals and forests) as percentage of GDP in the

Region Natural resource rents as percentage of GDP

Accounting and Measuring Well-being http://dx.doi.org/10.5772/intechopen.77066 97

East Asia and Pacific 1.2 Europe and Central Asia 1.2 Latin America and Caribbean 3.1 Middle East and North Africa 13.8 North America 0.3 South Asia 1.7 Sub-Sahara Africa 8.0 Low income 12.8 Lower middle income 2.9 Upper middle income 2.7 High income 1.1 India 1.9 Source: World Development Indicators, World Bank, 2016.

The adjusted [genuine] savings estimates have to take into account the losses of benefits from environmental services of biodiversity, carbon sequestration, soil conservation and recreation from the unsustainable use of forests. They have to also account for losses due to air and water pollution and soil erosion during the accounting period. The disinvestment arising out of greenhouse gas emissions, a global externality of air pollution, has also to be accounted. The most recent estimates of adjusted savings (genuine savings) of the World Bank made for countries and various regions in the world have tried to take into account to the extent possibly

Estimation of adjusted (genuine) savings of different countries is a pioneering attempt by World Bank economists leading to generalization of national income accounts for estimating green GDP. It is a precursor to now available UN methodology of Environmental and Economic Accounting [UN, 2003]. The World Bank methodology apart from suggesting accounting of depletion of exhaustible resources and degradation of renewable environmental resources suggests also for accounting of human skill formation in measuring genuine savings. Expenditures in human skill formation or educational expenditures will be an addition to conventional net savings, while the value of natural resource depletion is a deletion.

regions of the world including India in the year 2015.

world regions including India in the year 2015.

these losses in environmental services in an accounting period.

3. Estimates of genuine savings

#### 2.3. Data

Studies providing estimates of genuine savings for different countries especially those by World Bank economists [9, 23, 24] provide good insights into how macroeconomic data from secondary sources could be used for this purpose. They have attempted a comprehensive accounting of depletion of exhaustive resources in the measurement of genuine savings for different countries. These studies consider most of exhaustible energy resources including crude oil, natural gas, coal and lignite and minerals and metals comprising bauxite, copper, gold, iron, lead, nickel, phosphate, silver, tin and zinc. Resource rents for each resource are estimated as net price which is defined as unit price minus unit cost of extraction.<sup>3</sup> Unit cost of extraction is taken as the average cost instead of marginal cost because of data limitations. Since the unit cost of resource extraction could be different for different countries, a weighted average of unit costs is taken as the cost of extraction. World prices are taken as per unit resource prices, and since these prices may be different across the countries, again a weighted

<sup>3</sup> The basic approach to calculating resource rents for nonrenewable resources is to subtract country- or region-specific average costs of extraction from the world price for the resource in question, all expressed in current US dollars [19].


Table 1. Rents earned from natural resources (oil, natural gas, coal, minerals and forests) as percentage of GDP in the world regions including India in the year 2015.

average of these prices is considered. Table 1 provides recent estimates of rents earned from natural resources (oil, natural gas, coal, minerals and forests) as percentage of GDP in different regions of the world including India in the year 2015.

The adjusted [genuine] savings estimates have to take into account the losses of benefits from environmental services of biodiversity, carbon sequestration, soil conservation and recreation from the unsustainable use of forests. They have to also account for losses due to air and water pollution and soil erosion during the accounting period. The disinvestment arising out of greenhouse gas emissions, a global externality of air pollution, has also to be accounted. The most recent estimates of adjusted savings (genuine savings) of the World Bank made for countries and various regions in the world have tried to take into account to the extent possibly these losses in environmental services in an accounting period.

#### 3. Estimates of genuine savings

systems, into which it spends lot of money every year. Conventional national income accounts consider only educational expenditures incurred in man-made physical capital such as school buildings as investments. These expenditures may constitute only 10% of total education expenditures. The other expenditures consisting of teacher salaries, books, etc., are treated as consumption expenditures which are not correct in the context of measuring genuine savings. Education expenditures lead to the formation of human skill capital and therefore treated as the investment. However, the issues related to valuation of human skill capital are not yet completely understood because one dollar worth of educational expenditure may not necessarily yield one dollar worth of human skill capital. Therefore as an initial adjustment, current

educational expenditures could be treated as part of genuine savings in the economy.

literature user cost and net price methods are used for valuing resource depletion.

(health cost and income loss) are used for valuing environmental degradation.

dN dt )

> dE dt )

Extraction of exhaustible natural resources such as crude oil, natural gas, coal, minerals and metals results in the depletion of resource stock extracted. The conventional national income accounts consider all the revenue earned net of cost of extraction of the resource as part of GDP. It is not a correct accounting method given that present and future generations have property rights for exhaustible resources. Therefore, measurement of genuine savings requires that value of depleted resource stocks has to be deducted from nation's savings. In the

Various developmental activities in the economy contribute to degradation of environmental resources due to pollution, soil erosion and deforestation. Conventional national income accounts do not account for value of environmental degradation. The methods of maintenance cost (cost of maintaining environmental resource stocks at sustainable levels) or social cost

Studies providing estimates of genuine savings for different countries especially those by World Bank economists [9, 23, 24] provide good insights into how macroeconomic data from secondary sources could be used for this purpose. They have attempted a comprehensive accounting of depletion of exhaustive resources in the measurement of genuine savings for different countries. These studies consider most of exhaustible energy resources including crude oil, natural gas, coal and lignite and minerals and metals comprising bauxite, copper, gold, iron, lead, nickel, phosphate, silver, tin and zinc. Resource rents for each resource are estimated as net price which is defined as unit price minus unit cost of extraction.<sup>3</sup> Unit cost of extraction is taken as the average cost instead of marginal cost because of data limitations. Since the unit cost of resource extraction could be different for different countries, a weighted average of unit costs is taken as the cost of extraction. World prices are taken as per unit resource prices, and since these prices may be different across the countries, again a weighted

The basic approach to calculating resource rents for nonrenewable resources is to subtract country- or region-specific average costs of extraction from the world price for the resource in question, all expressed in current US dollars [19].

Value of depletion of exhaustible resources (μ<sup>n</sup>

96 Accounting from a Cross-Cultural Perspective

Valuing degradation of environmental resources μ<sup>e</sup>

2.3. Data

3

Estimation of adjusted (genuine) savings of different countries is a pioneering attempt by World Bank economists leading to generalization of national income accounts for estimating green GDP. It is a precursor to now available UN methodology of Environmental and Economic Accounting [UN, 2003]. The World Bank methodology apart from suggesting accounting of depletion of exhaustible resources and degradation of renewable environmental resources suggests also for accounting of human skill formation in measuring genuine savings. Expenditures in human skill formation or educational expenditures will be an addition to conventional net savings, while the value of natural resource depletion is a deletion. Educational expenditures which are taken as consumption expenditures in conventional national income accounting constitute a significant part of GDP in both developed and developing countries.

The adjusted [genuine] savings [AS] in an accounting period is estimated as:

adjusted savings [AS] = gross savings [GS] – consumption of fixed capital – depletion of exhaustible resources – degradation of environmental resources [particulate matter and CO2 emissions, water pollution and soil and forest degradation] + additions to human skill capital [educational expenditure].

Tables 2–4 provide estimates of gross savings [GS] and adjusted [genuine] savings [AS] and reduction in gross savings [RGS] due to natural and environmental resource depletion in an accounting period for BRIC countries, developed countries and different regions of the world, respectively. Among BRIC countries, China has to account for the largest reduction in its GS amounting to 44.05% followed by Russia, 19.12; South Africa, 15.21; India, 14.23; and Brazil, 5.38% in the year 2015. Accounting for the particulate matter emissions in the current estimates of AS by the World Bank could be a reason for very steep fall in savings in countries like China and India. For South Africa, estimates of AS have become negative and negligible during


recent years implying negative growth or negligible growth rate of well-being measured as

Table 3. Estimates of gross savings, adjusted savings and reduced gross savings for seven developed countries during

Notes: GS: gross savings; AS: adjusted savings due to depletion of man-made capital and natural capital; RGS: reduction

Country 2010 2011 2012 2014 2014 2015 Australia GS 23.47 24.98 25.82 25.33 24.84 23.60

Canada GS 19.79 21.31 21.33 21.92 22.17 20.03

France GS 19.78 20.66 19.57 19.44 19.63 20.46

Germany GS 24.74 26.53 25.72 25.61 26.49 27.17

Japan GS 24.29 23.50 22.94 23.25 23.78 26.01

UK GS 12.53 13.46 11.92 11.72 12.00 12.11

USA GS 15.16 17.50 18.13 19.04 18.96 17.77

in gross savings in the computation of adjusted net national income (ANNI).

AS 8.38 9.37 10.88 9.99 8.78 8.05 RGS �15.09 �15.61 �14.94 �15.34 �16.06 �15.55

Accounting and Measuring Well-being http://dx.doi.org/10.5772/intechopen.77066 99

AS 6.18 7.87 7.57 8.01 8.14 6.02 AGNI �13.61 �13.44 �13.76 �13.91 �14.03 �14.01

AS 7.15 7.83 6.40 6.28 6.18 7.36 RGS �12.63 �12.83 �13.17 �13.16 �13.45 �13.10

AS 11.29 13.26 12.23 12.14 13.10 13.71 RGS �13.45 �13.27 �13.49 �13.47 �13.39 �13.46

AS 6.14 5.14 5.04 5.18 5.53 6.75 RGS �18.15 �18.36 �17.90 �18.07 �18.25 �19.26

AS 4.28 4.72 3.22 3.33 3.96 4.31 RGS �8.25 �8.74 �8.70 �8.39 �8.04 �7.80

AS 2.73 3.62 5.81 6.26 7.08 7.41 RGS �12.43 �13.88 �12.32 �12.78 �11.88 �10.36

Table 3 shows estimates of AS for developed countries during the period 2010–2015. Estimates show that reduction in savings is highest for Japan amounting to 19.16% followed by Australia 15.55; Canada, 14.01; Germany, 13.46; France, 13.10; the USA, 10.36; and the UK, 7.90%. Accounting for air pollution in estimating AGS could be a reason for the sharp fall in savings

Table 4 provides estimates of AS [genuine savings] for countries in different income brackets [low income, middle income and high income] in the world. During recent 5-year period, lowincome countries have negative genuine savings implying their growth rate of well-being [adjusted national income] is negative. During the same period, the middle-income countries

green national income [GNP].

Source: World Development Report, 2016.

2010–2015 (percentage of gross national income).

even in these developed countries.

Notes: GS: gross savings; AS: adjusted savings due to depletion of man-made capital and natural capital; RGS: reduction in gross savings in the computation of adjusted net national income (ANNI). Source: World Development Indicators, World Bank, 2016.

Table 2. Estimates of gross savings, adjusted savings and reduced gross savings for four BRIC countries during 2010–2015 (percentage of gross national income).


Educational expenditures which are taken as consumption expenditures in conventional national income accounting constitute a significant part of GDP in both developed and devel-

adjusted savings [AS] = gross savings [GS] – consumption of fixed capital – depletion of exhaustible resources – degradation of environmental resources [particulate matter and CO2 emissions, water pollution and soil and forest degradation] + additions to human skill capital

Tables 2–4 provide estimates of gross savings [GS] and adjusted [genuine] savings [AS] and reduction in gross savings [RGS] due to natural and environmental resource depletion in an accounting period for BRIC countries, developed countries and different regions of the world, respectively. Among BRIC countries, China has to account for the largest reduction in its GS amounting to 44.05% followed by Russia, 19.12; South Africa, 15.21; India, 14.23; and Brazil, 5.38% in the year 2015. Accounting for the particulate matter emissions in the current estimates of AS by the World Bank could be a reason for very steep fall in savings in countries like China and India. For South Africa, estimates of AS have become negative and negligible during

Brazil GS 18.50 19.06 18.44 18.56 16.34 14.74

Russia GS 28.05 30.16 28.73 25.54 25.86 28.08

India GS 38.65 35.79 34.43 33.70 34.01 32.88

China GS 51.72 49.93 49.87 49.33 49.49 48.58

South Africa GS 18.41 17.96 15.25 15.79 15.95 16.72

Notes: GS: gross savings; AS: adjusted savings due to depletion of man-made capital and natural capital; RGS: reduction

Table 2. Estimates of gross savings, adjusted savings and reduced gross savings for four BRIC countries during 2010–2015

in gross savings in the computation of adjusted net national income (ANNI).

Source: World Development Indicators, World Bank, 2016.

(percentage of gross national income).

2010 2011 2012 2013 2014 2015

AS 12.45 12.41 12.33 12.66 10.31 9.36 RGS �6.05 �6.65 �6.11 �5.90 �6.03 �5.38

AS 12.09 12.83 10.60 7.30 6.43 8.96 RGS �15.96 �17.33 �8.13 �18.24 �19.43 �19.12

AS 25.00 22.00 20.54 20.10 20.23 18.65 RGS �13.65 �13.79 �13.89 �13.60 �13.78 �14.23

AS 4.66 3.72 3.92 4.85 4.18 4.53 RGS �47.06 �46.21 �45.95 �44.48 �45.31 �44.05

AS 2.49 2.60 0.70 �0.02 0.01 1.51 RGS �15.92 �15.36 �14.55 �15.81 �15.94 �15.21

The adjusted [genuine] savings [AS] in an accounting period is estimated as:

oping countries.

[educational expenditure].

98 Accounting from a Cross-Cultural Perspective

Notes: GS: gross savings; AS: adjusted savings due to depletion of man-made capital and natural capital; RGS: reduction in gross savings in the computation of adjusted net national income (ANNI). Source: World Development Report, 2016.

Table 3. Estimates of gross savings, adjusted savings and reduced gross savings for seven developed countries during 2010–2015 (percentage of gross national income).

recent years implying negative growth or negligible growth rate of well-being measured as green national income [GNP].

Table 3 shows estimates of AS for developed countries during the period 2010–2015. Estimates show that reduction in savings is highest for Japan amounting to 19.16% followed by Australia 15.55; Canada, 14.01; Germany, 13.46; France, 13.10; the USA, 10.36; and the UK, 7.90%. Accounting for air pollution in estimating AGS could be a reason for the sharp fall in savings even in these developed countries.

Table 4 provides estimates of AS [genuine savings] for countries in different income brackets [low income, middle income and high income] in the world. During recent 5-year period, lowincome countries have negative genuine savings implying their growth rate of well-being [adjusted national income] is negative. During the same period, the middle-income countries


in these studies may not be justifiable. There is a need for more studies to find out the relation-

Accounting and Measuring Well-being http://dx.doi.org/10.5772/intechopen.77066 101

The net price or resource rent used in these studies for accounting of depletion of exhaustible resources is not an appropriate method of accounting for depletion. The value of resource stocks valued at net price is already accounted in measuring gross national income [GNI] using conventional methods of national income accounting. Deduction of this amount again from GNI or country's net rate of savings does not give any credit to the country having these resources in comparison to the country not having them. Any method of valuation of resource depletion has to take into account the property rights of both present and future generations to an exhaustible resource stock and the problem of inter-temporal equity in resource use. The user cost could be an appropriate method for valuing the depletion of the resource because it is based on the concept of weak sustainability (man-made capital could be a substitute for natural capital) ensuring the same level of real income to the present as well as future generations from resource extraction. Therefore, in the context of measuring value of depletion of exhaustible resources, studies have to be done to estimate user cost of resource stocks of minerals, metals and fossil fuels.<sup>4</sup> The user cost method of accounting value of depletion takes into account the part of resource rents earned from extraction that is spent in accumulation of man-made physical capital and human skill capital. Therefore, using resource rents for valuing

depletion could result in underestimation of cost of depletion of exhaustible resources.

cost of particulate matter and CO2 emissions for different countries.

resource stock. This is called user cost method of accounting (El Serafy, 1989). Consider

The true or sustainable income from resource extraction is defined as X such that

X: true or permanent income or income to present as well as future generations from resource extraction

for given (O1 .......OT), r and T. Assuming Ot = O, t = 1,....T, the user cost (O-X) could be obtained as

4

used)

PT t¼1 Ot=ð Þ <sup>1</sup> <sup>þ</sup> <sup>r</sup> <sup>t</sup> <sup>¼</sup> <sup>P</sup><sup>∞</sup>

O-X = O/(1 + r)<sup>T</sup>

r: rate of discount or market rate of interest

<sup>X</sup>=ð Þ <sup>1</sup> <sup>þ</sup> <sup>r</sup> <sup>t</sup>

t¼1

T: life of exhaustible resource (proven reserves/rate of extraction)

It is difficult to get data for estimating costs of environmental degradation in the form of soil erosion, air pollution and water pollution for a large number of countries for which genuine savings estimates are obtained by these studies. Therefore, these costs are not fully accounted in the estimation. However, an attempt is made in the recent estimates AS for accounting of

The approach adopted in UN methodology of Environmental and Economic Accounting [UN, 2003] for measuring green GDP is similar to the approach described above for estimating genuine savings. UN methodology prescribes the development of asset and flow accounts of natural resources as satellite accounts of conventional national income accounts. The satellite accounts provide comprehensive information of depletion of exhaustible resources and

User cost depends on the life of proven reserves and rate of discount used to address to the problem of intertemporal equity. It decreases with the rate of discount and life of the resource stock making it resource specific. The rate of discount depends on the value judgments of the government about the property rights of present versus future generations to the

Ot: net operating surplus from resource extraction in year t (Ot = turnover-cost of extraction � return on man-made capital

ship between educational expenditures and human skill formation.

Notes: GS: gross savings; AS: adjusted savings due to depletion of man-made capital and natural capital; RGS: reduction in gross savings in the computation of adjusted net national income (ANNI). Source: World Development Report, 2016.

Table 4. Estimates of gross savings, adjusted savings and reduced gross savings for low-income, middle-income and high-income countries during 2010–2015 as percentage of gross national income.

have experienced a sharp fall of savings amounting to 18%, while high-income countries have experienced a fall of 7–10%. This implies that the genuine or adjusted rate of growth of wellbeing of countries is much lower when accounted for the effects of economic development on environmental and natural resource stocks.

## 4. Critical assessment of genuine savings estimates and lessons for green GDP measurement in India

Estimation of AS [genuine savings] and the methodology used for it in the literature are pioneering contributions toward measurement of well-being or green national income of countries. Even though the accounting of costs of natural resource depletion and degradation is not yet fully done in the available studies, they clearly provided a way forward for the more comprehensive accounting of all costs. The important contribution of these studies is in:


Accounting of educational expenditures as accumulation of human skill capital will significantly increase the genuine savings rates of countries as most of these expenditures are treated as consumption expenditures in conventional national income accounting. However, the assumption that human skill capital is increased by the exact amount of educational expenditures made in these studies may not be justifiable. There is a need for more studies to find out the relationship between educational expenditures and human skill formation.

The net price or resource rent used in these studies for accounting of depletion of exhaustible resources is not an appropriate method of accounting for depletion. The value of resource stocks valued at net price is already accounted in measuring gross national income [GNI] using conventional methods of national income accounting. Deduction of this amount again from GNI or country's net rate of savings does not give any credit to the country having these resources in comparison to the country not having them. Any method of valuation of resource depletion has to take into account the property rights of both present and future generations to an exhaustible resource stock and the problem of inter-temporal equity in resource use. The user cost could be an appropriate method for valuing the depletion of the resource because it is based on the concept of weak sustainability (man-made capital could be a substitute for natural capital) ensuring the same level of real income to the present as well as future generations from resource extraction. Therefore, in the context of measuring value of depletion of exhaustible resources, studies have to be done to estimate user cost of resource stocks of minerals, metals and fossil fuels.<sup>4</sup> The user cost method of accounting value of depletion takes into account the part of resource rents earned from extraction that is spent in accumulation of man-made physical capital and human skill capital. Therefore, using resource rents for valuing depletion could result in underestimation of cost of depletion of exhaustible resources.

It is difficult to get data for estimating costs of environmental degradation in the form of soil erosion, air pollution and water pollution for a large number of countries for which genuine savings estimates are obtained by these studies. Therefore, these costs are not fully accounted in the estimation. However, an attempt is made in the recent estimates AS for accounting of cost of particulate matter and CO2 emissions for different countries.

The approach adopted in UN methodology of Environmental and Economic Accounting [UN, 2003] for measuring green GDP is similar to the approach described above for estimating genuine savings. UN methodology prescribes the development of asset and flow accounts of natural resources as satellite accounts of conventional national income accounts. The satellite accounts provide comprehensive information of depletion of exhaustible resources and

$$\sum\_{t=1}^{T} \mathcal{O}\_t / (1+r)^t = \sum\_{t=1}^{T} \mathcal{X} / (1+r)^t$$

have experienced a sharp fall of savings amounting to 18%, while high-income countries have experienced a fall of 7–10%. This implies that the genuine or adjusted rate of growth of wellbeing of countries is much lower when accounted for the effects of economic development on

Table 4. Estimates of gross savings, adjusted savings and reduced gross savings for low-income, middle-income and

Country 2010 2011 2012 2013 2014 2015 Low income GS 14.53 16.70 16.59 15.67 16.72 15.78

Middle income GS 34.28 34.13 34.11 33.42 33.95 34.74

High income GS 20.64 21.47 21.84 22.02 22.35 22.21

Notes: GS: gross savings; AS: adjusted savings due to depletion of man-made capital and natural capital; RGS: reduction in gross

AS 2.21 �1.51 �2.10 �6.06 �4.10 NA RGS �12.32 �18.21 �18.69 �21.73 �20.82 NA

AGS 17.82 16.12 16.04 15.09 15.81 16.91 RGS �16.46 �18.01 �18.07 �18.33 �18.14 �17.83

AGS 7.11 7.87 8.29 10.40 8.88 9.07 RGS �13.53 �13.60 �13.55 �11.62 �13.47 �13.14

4. Critical assessment of genuine savings estimates and lessons for green

Estimation of AS [genuine savings] and the methodology used for it in the literature are pioneering contributions toward measurement of well-being or green national income of countries. Even though the accounting of costs of natural resource depletion and degradation is not yet fully done in the available studies, they clearly provided a way forward for the more comprehensive accounting of all costs. The important contribution of these studies is in:

A. providing methodologies and data sources for measuring the value of depletion of

B. attempting for loss of environmental services due to air and water pollution and forest

C. presenting a case for considering educational expenditures as contribution to human skill

Accounting of educational expenditures as accumulation of human skill capital will significantly increase the genuine savings rates of countries as most of these expenditures are treated as consumption expenditures in conventional national income accounting. However, the assumption that human skill capital is increased by the exact amount of educational expenditures made

exhaustible resources (energy and mineral resources);

environmental and natural resource stocks.

savings in the computation of adjusted net national income (ANNI).

high-income countries during 2010–2015 as percentage of gross national income.

GDP measurement in India

Source: World Development Report, 2016.

100 Accounting from a Cross-Cultural Perspective

depletion; and

capital formation in a country.

for given (O1 .......OT), r and T. Assuming Ot = O, t = 1,....T, the user cost (O-X) could be obtained as O-X = O/(1 + r)<sup>T</sup>

<sup>4</sup> User cost depends on the life of proven reserves and rate of discount used to address to the problem of intertemporal equity. It decreases with the rate of discount and life of the resource stock making it resource specific. The rate of discount depends on the value judgments of the government about the property rights of present versus future generations to the resource stock. This is called user cost method of accounting (El Serafy, 1989). Consider

X: true or permanent income or income to present as well as future generations from resource extraction

Ot: net operating surplus from resource extraction in year t (Ot = turnover-cost of extraction � return on man-made capital used)

r: rate of discount or market rate of interest

T: life of exhaustible resource (proven reserves/rate of extraction)

The true or sustainable income from resource extraction is defined as X such that

degradation of environmental resources in terms of physical quantities and monetary values. The information available in these accounts could be used to obtain estimates of rate of AS or genuine savings for countries. However, these estimates differ from the ones discussed above in two ways. First of all UN methodology does not consider educational expenditures contributing to formation of human skill capital as part of savings. Secondly, it requires comprehensive accounting of monetary values of environmental degradation. These include losses of both marketable and nonmarketable services from soil erosion, forest degradation, air pollution and water pollution.

We found that genuine savings studies reviewed in this chapter could measure only some important components of genuine savings, especially the cost of depletion of exhaustible resources and degradation of air quality by particulate matter and CO2 emissions. A comprehensive accounting of cost of environmental degradation could not be attempted in these studies because of data limitations. The important contribution of these studies is in discussing secondary data sources of different countries for measuring the value of depletion of exhaust-

Accounting and Measuring Well-being http://dx.doi.org/10.5772/intechopen.77066 103

The satellite accounts of natural resources in UN methodology of Environmental and Economic Accounting provide comprehensive information of depletion of exhaustible resources and degradation of environmental resources in terms of physical quantities and monetary values. The information available in these accounts could be used to obtain very comprehensive estimates of rate of genuine savings for countries. However, these estimates differ from the ones reviewed in this chapter in two ways. First of all UN methodology does not consider educational expenditures contributing to formation of human skill capital as part of savings. Secondly, it requires comprehensive accounting of monetary values of environmental degradation. These include losses of both marketable and nonmarketable services from soil erosion, forest degradation, air pollution and water

In an attempt of having green accounting in developing macro-economic statistics in India, CSO and other concerned organizations could try to get independent estimates of genuine savings using the above-described methodology and the data from secondary sources. Macro-economic aggregates of human skill capital formation and cost of depletion of exhaustible resources could be estimated using data from secondary sources as described above. Estimation of cost of depletion using user costs instead of resource rents as unit costs is possible with data available in India from secondary sources. However, data from secondary sources alone is not sufficient to estimate the cost of degradation of environmental resources. Detailed empirical studies of using data from both primary and secondary sources have to be done in India for estimating the macroeconomic aggregate of cost of environmen-

ible resources such as energy and mineral resources.

\*Address all correspondence to: mn.murty71@gmail.com

1 Institute of Economic Growth, University Enclave, Delhi, India

3 South Asian Network for Development Economics and Environment (SANDEE),

I am grateful to a referee and the editor for very useful suggestions for improving an earlier

pollution.

tal degradation.

Author details

M N Murty1,2,3\*†

Kathmandu, Nepal

draft of this paper

†

2 TERI University, Delhi, India

In an attempt of having green accounting in developing macro-economic statistics in India, the Central Statistical Organization [CSO] and other concerned organizations could try to get independent estimates of AS using the above-described methodology. Macroeconomic aggregates of human skill capital formation and cost of depletion of exhaustible resources could be estimated using data from secondary sources as described above. Estimation of cost of depletion using user costs instead of resource rents as unit costs is possible with data available in India from secondary sources. However, data from secondary sources alone is not sufficient to estimate the cost of degradation of environmental resources. Detailed empirical studies of using data from both primary and secondary sources have to be done in India for estimating the macro-economic aggregate of cost of environmental degradation.

Estimates of adjusted national income or well-being for depletion and degradation of natural resources could be obtained given an estimate of rate of AS or genuine savings. If the difference between GS or conventional gross rate of savings and AS or rate of genuine savings (excluding education expenditure) is positive, the adjusted national income is lower than the conventional national income for a country. As discussed earlier, the World Bank's estimates of AS or genuine savings for India indicate that adjusted national income in India and other countries is lower than the conventional national income. For some low-income countries, AS becomes negative implying negative rate of growth of well-being.

#### 5. Conclusion

Genuine savings or AS consisting of net accumulation of man-made physical capital and human skill capital and depletion of natural resource stocks is an indicator of sustainable income path of a country. They could be positive or negative depending if net accumulation of man-made capital is higher or lower than the value of depletion of natural resource stocks. Negative genuine savings indicate unsustainable income path, and available estimates of genuine savings for different countries show that some low-income countries have negative genuine savings.

The methodology and estimates of genuine savings reviewed in this chapter are pioneering contributions to fast-growing literature on estimation of green national income of a country. The studies of genuine savings apart from suggesting accounting of depletion of exhaustible resources and degradation of renewable environmental resources suggest also for accounting of human skill formation in measuring genuine savings. Expenditures in human skill formation or educational expenditures will be an addition to conventional net savings, while the value of natural resource depletion is a deletion.

We found that genuine savings studies reviewed in this chapter could measure only some important components of genuine savings, especially the cost of depletion of exhaustible resources and degradation of air quality by particulate matter and CO2 emissions. A comprehensive accounting of cost of environmental degradation could not be attempted in these studies because of data limitations. The important contribution of these studies is in discussing secondary data sources of different countries for measuring the value of depletion of exhaustible resources such as energy and mineral resources.

The satellite accounts of natural resources in UN methodology of Environmental and Economic Accounting provide comprehensive information of depletion of exhaustible resources and degradation of environmental resources in terms of physical quantities and monetary values. The information available in these accounts could be used to obtain very comprehensive estimates of rate of genuine savings for countries. However, these estimates differ from the ones reviewed in this chapter in two ways. First of all UN methodology does not consider educational expenditures contributing to formation of human skill capital as part of savings. Secondly, it requires comprehensive accounting of monetary values of environmental degradation. These include losses of both marketable and nonmarketable services from soil erosion, forest degradation, air pollution and water pollution.

In an attempt of having green accounting in developing macro-economic statistics in India, CSO and other concerned organizations could try to get independent estimates of genuine savings using the above-described methodology and the data from secondary sources. Macro-economic aggregates of human skill capital formation and cost of depletion of exhaustible resources could be estimated using data from secondary sources as described above. Estimation of cost of depletion using user costs instead of resource rents as unit costs is possible with data available in India from secondary sources. However, data from secondary sources alone is not sufficient to estimate the cost of degradation of environmental resources. Detailed empirical studies of using data from both primary and secondary sources have to be done in India for estimating the macroeconomic aggregate of cost of environmental degradation.

#### Author details

degradation of environmental resources in terms of physical quantities and monetary values. The information available in these accounts could be used to obtain estimates of rate of AS or genuine savings for countries. However, these estimates differ from the ones discussed above in two ways. First of all UN methodology does not consider educational expenditures contributing to formation of human skill capital as part of savings. Secondly, it requires comprehensive accounting of monetary values of environmental degradation. These include losses of both marketable and nonmarketable services from soil erosion, forest degradation, air pollution and

In an attempt of having green accounting in developing macro-economic statistics in India, the Central Statistical Organization [CSO] and other concerned organizations could try to get independent estimates of AS using the above-described methodology. Macroeconomic aggregates of human skill capital formation and cost of depletion of exhaustible resources could be estimated using data from secondary sources as described above. Estimation of cost of depletion using user costs instead of resource rents as unit costs is possible with data available in India from secondary sources. However, data from secondary sources alone is not sufficient to estimate the cost of degradation of environmental resources. Detailed empirical studies of using data from both primary and secondary sources have to be done in India for estimating

Estimates of adjusted national income or well-being for depletion and degradation of natural resources could be obtained given an estimate of rate of AS or genuine savings. If the difference between GS or conventional gross rate of savings and AS or rate of genuine savings (excluding education expenditure) is positive, the adjusted national income is lower than the conventional national income for a country. As discussed earlier, the World Bank's estimates of AS or genuine savings for India indicate that adjusted national income in India and other countries is lower than the conventional national income. For some low-income countries, AS

Genuine savings or AS consisting of net accumulation of man-made physical capital and human skill capital and depletion of natural resource stocks is an indicator of sustainable income path of a country. They could be positive or negative depending if net accumulation of man-made capital is higher or lower than the value of depletion of natural resource stocks. Negative genuine savings indicate unsustainable income path, and available estimates of genuine savings for different countries show that some low-income countries have negative genuine savings.

The methodology and estimates of genuine savings reviewed in this chapter are pioneering contributions to fast-growing literature on estimation of green national income of a country. The studies of genuine savings apart from suggesting accounting of depletion of exhaustible resources and degradation of renewable environmental resources suggest also for accounting of human skill formation in measuring genuine savings. Expenditures in human skill formation or educational expenditures will be an addition to conventional net savings, while the

the macro-economic aggregate of cost of environmental degradation.

becomes negative implying negative rate of growth of well-being.

value of natural resource depletion is a deletion.

water pollution.

102 Accounting from a Cross-Cultural Perspective

5. Conclusion

M N Murty1,2,3\*†

\*Address all correspondence to: mn.murty71@gmail.com

1 Institute of Economic Growth, University Enclave, Delhi, India

2 TERI University, Delhi, India

3 South Asian Network for Development Economics and Environment (SANDEE), Kathmandu, Nepal

† I am grateful to a referee and the editor for very useful suggestions for improving an earlier draft of this paper

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**Section 5**

**Financial Instruments**
