**3.2. Method of analysis**

This study constructs simultaneous equations to control the inverse causal relationship between welfare expenditures and fiscal sustainability by examining the effects of tax structure on the fiscal sustainability of the welfare state. Existing studies have focused on the impact of fiscal spending on fiscal soundness [55, 64]. It is not only welfare expenditures that affect national finances, but also the government's fiscal capacity for welfare expenditures, which will be limited if finances are not sufficient in the long term. In other words, the financial condition of the state also affects welfare expenditures. If the effect of financial power on welfare expenditures is not reflected in the analytical model, there is a possibility that the estimation will be biased due to the endogeneity problem. In this study, the simultaneous equations model is set and analyzed. Thus, this study constructs a simultaneous equations model with two dependent variables. The first dependent variable is the fiscal sustainability of the welfare state and is measured by the fiscal space of each year on each welfare state. The second dependent variable is the level of public social welfare expenditures, which reflects public welfare efforts or the level of benefits enjoyed by the public.

Model estimations are adopted as a three-step least-squares method devised by Zellner and Theil [75]. This is a combination of the two-step least-squares method and the seemingly unrelated regression model, and all of the equations comprising the simultaneous equations are simultaneously estimated so that the correlation between the error terms of each equation is reflected in the analysis [75]. Using this method, we can derive the coincidental estimator from the simultaneous equations model and find a more efficient estimator than the one using the two-step least-squares method. Additional consideration utilizing national panel data is also considered for treating the endogeneity problem caused by non-modeled factors in the use of national panel data, which may lead to bias in statistical estimation. Specifically, a fixed-effects model with national dummy variables is constructed and analyzed in each equation of simultaneous equations. Additionally, the financial capacity of advanced welfare states has undergone structural changes since late 2000s [76], so the equations analyzed reflect the effect of timing changes, including year dummy (before 2008 and after then) variables.

#### **3.3. Operational definition of variables**

#### *3.3.1. Dependent variables*

The fiscal sustainability of the welfare state, the first dependent variable, is measured as fiscal space, which can be specified by the gap between current debt levels and debt limits according to Ostry et al.'s [56] and Ghosh et al.'s [57] method of calculating. Fiscal space is not merely a source of funds to meet the current welfare needs of the public. Rather, it plays an important role in resource mobilization to cover future spending, as well as cushioning against unexpected risks [77, 78]. In other words, the issue of fiscal space is a question of whether countries can finance their obligations, including social security, without sacrificing economic growth and stability based on fiscal sustainability [5, 50]. Therefore, fiscal space can be a useful tool in examining the fiscal sustainability of the welfare state.

apparent, but, rather, come after a certain period of time, this study has limited its analysis to late 1980s, specifically since 1986 (independent variables since 1985). In addition, until early 1990s, most advanced welfare states demonstrated a relatively moderate increase in national debt. However, since mid-1990s, sovereign debt has soared, and concerns about the national debt have become more widespread since the 2008 global financial crisis. Therefore, it is possible to derive timely policy implications for ensuring the fiscal sustainability of the welfare state by analyzing the period when the national debt had soared and a widespread financial crisis occurred.

This study constructs simultaneous equations to control the inverse causal relationship between welfare expenditures and fiscal sustainability by examining the effects of tax structure on the fiscal sustainability of the welfare state. Existing studies have focused on the impact of fiscal spending on fiscal soundness [55, 64]. It is not only welfare expenditures that affect national finances, but also the government's fiscal capacity for welfare expenditures, which will be limited if finances are not sufficient in the long term. In other words, the financial condition of the state also affects welfare expenditures. If the effect of financial power on welfare expenditures is not reflected in the analytical model, there is a possibility that the estimation will be biased due to the endogeneity problem. In this study, the simultaneous equations model is set and analyzed. Thus, this study constructs a simultaneous equations model with two dependent variables. The first dependent variable is the fiscal sustainability of the welfare state and is measured by the fiscal space of each year on each welfare state. The second dependent variable is the level of public social welfare expenditures, which reflects

Model estimations are adopted as a three-step least-squares method devised by Zellner and Theil [75]. This is a combination of the two-step least-squares method and the seemingly unrelated regression model, and all of the equations comprising the simultaneous equations are simultaneously estimated so that the correlation between the error terms of each equation is reflected in the analysis [75]. Using this method, we can derive the coincidental estimator from the simultaneous equations model and find a more efficient estimator than the one using the two-step least-squares method. Additional consideration utilizing national panel data is also considered for treating the endogeneity problem caused by non-modeled factors in the use of national panel data, which may lead to bias in statistical estimation. Specifically, a fixed-effects model with national dummy variables is constructed and analyzed in each equation of simultaneous equations. Additionally, the financial capacity of advanced welfare states has undergone structural changes since late 2000s [76], so the equations analyzed reflect the effect of timing changes, including year dummy (before 2008 and after then) variables.

The fiscal sustainability of the welfare state, the first dependent variable, is measured as fiscal space, which can be specified by the gap between current debt levels and debt limits according to Ostry et al.'s [56] and Ghosh et al.'s [57] method of calculating. Fiscal space is not merely a source of funds to meet the current welfare needs of the public. Rather, it plays

public welfare efforts or the level of benefits enjoyed by the public.

**3.3. Operational definition of variables**

*3.3.1. Dependent variables*

**3.2. Method of analysis**

106 Taxes and Taxation Trends

In order to derive the abovementioned fiscal space as shown in **Figure 1**, it is necessary to estimate the fiscal reaction function and select the appropriate gap between the interest rate and the growth rate [57]. This is because it is necessary to determine the debt limit of each country on the basis of the intersection of the estimated base on the fiscal reaction function and the interest repayment schedule. This study estimates the fiscal reaction function through pooled time series analysis and uses a vector autoregressive model for estimation to establish the gap between the appropriate interest rate and the growth rate. The description of variables used for estimating the fiscal reaction function is shown in **Table 1**. 4

Next, one of the most important points to be considered in determining the national debt limit, along with the estimation of the fiscal reaction function, is how to define the long-term interest rate [56].5 This study estimates the interest rate through vector autoregulation (VAR), similar to the works of Polito and Wickens [62, 63]. This is because it not only avoids arbitrary problems, but also reflects the endogenous relationship between the interest rate and the national debt level (**Table 2**). In this study, the autoregressive model is used to model the endogenous relationship between the interest rate and the national debt, adding government revenue, government spending, debt, the economic growth rate, the inflation rate, and short- and long-term interest rates [62, 63]. The gap between these estimates and the average real growth rates of the countries from 1985 to 2013 are used to calculate the debt limit and determine fiscal space based on this. The contents and data sources of the variables used for estimating the fiscal reaction function are shown in **Table 3**.

The second dependent variable is public welfare expenditures. This is the level of public (general government) social welfare spending that reflects public welfare efforts or the level of benefits enjoyed by the public. Total public welfare expenditures divided by the gross domestic product is used to control differences in the welfare expenditure level according to the level of economic scale by country.

<sup>4</sup> The dependent variable is the primary balance, and the independent variables are the financial factors (national debt, public welfare expenditures, output gap, inflation rate), the economic structural factors (unemployment rate, service industry ratio, portion of involuntary part-time work, economic openness, aging rate, future old age portion), and political and financial institutional factors (election, change of ideology, mandatory political system, concentration index, fiscal rule index). In this study, it is based on the works of Ostry et al. [56] and Ghosh et al. [57], but some variables are excluded in consideration of multicollinearity.

<sup>5</sup> Ostry et al. [56] determined long-term interest rates in two ways. The first assumes that the observed interest rate itself reflects the perceived probability of bankruptcy of a country, so the current market rate is used as the long-term interest rate. In this case, it is possible to overestimate the maximum value of sustainable debt by overlooking the fact that the interest rate rises as the debt level approaches its limit, and the risk of bankruptcy increases. An alternative method of overcoming this limitation is to use the interest rate, which is calculated by taking into account the endogenous relationship between debt levels and interest rates. Specifically, they used the calculated interest rate, assuming a recovery rate of 90% when bankruptcy occurred. Alternative methods which they used help to accurately estimate fiscal space by reflecting endogenous relationships between interest rates and macroeconomic variables. However, the abovementioned study does not provide a clear basis for assumptions used in interest rate estimation. Therefore, it is not free of the problems caused by an arbitrary definition of the recovery rate [80]. In order to overcome these limitations, this study uses the estimates through VAR.


*3.3.2. Independent variables*

Government expenditure

Economic structure

Political and fiscal systems

Dependent variable

Independent variables

Tax structure, a major independent variable, is divided between the ability to pay principle and the benefit principle. The former is divided into horizontal equity and vertical equity. In

Public debt General government public debt as a percentage of GDP OECD Economic Outlook No. 97 (Edition 2015/1) Government revenue Total government revenue as a percentage of GDP

Total government expenditure as a percentage of GDP

consumer of acquiring a basket of goods and services

the following section, the operation of each principle is described in detail.

**Variables Definition Sources**

**Table 2.** Descriptive statistics of variables for estimating fiscal reaction function.

Output gap Difference between actual GDP and potential GDP Inflation The annual percentage change in the cost to the average

Long-term interest rate Interest rate of government bonds maturing in 10 years

*Note*: Each variable in the estimated variables is included from *t*−1 to *t*−*n*. *t* = 1, …, 27.

Short-term interest rate Interest rate which is money market rate

**Table 3.** Variables for estimating long-term interest rate.

**Categories Mean Standard** 

**deviation**

Primary balance 0.249 3.693 −10.505 15.786

Finance Lagged debt 71.681 28.763 16.079 166.190

Output gap −0.049 2.622 −13.851 9.579 Welfare expenditures 22.763 4.857 10.565 35.517 Inflation 2.935 2.755 −0.900 23.015

How Does a Welfare State achieves Fiscal Sustainability? A Study of the Impact of Tax Equity

Unemployment 7.636 3.940 0.457 24.885 Service industry 2.679 0.793 1.232 5.384 Part-time worker 3.071 1.649 0.295 9.714 Self-employed 15.987 9.116 6.536 50.708 Capital openness 1.929 0.908 −1.188 2.390 Age dependency 15.466 2.015 10.255 21.080 Future dependency 31.238 5.987 18.478 51.991

Election 0.292 0.455 0.000 1.000 Political stability 0.353 0.772 0.000 3.000 Majority system 0.177 0.382 0.000 1.000 Centralization 0.672 0.115 0.370 1.000 Fiscal rule 0.419 0.172 0.242 0.908

**Minimum maximum**

109

http://dx.doi.org/10.5772/intechopen.72527

**Table 1.** Variables for estimating the fiscal reaction function.


**Table 2.** Descriptive statistics of variables for estimating fiscal reaction function.

#### *3.3.2. Independent variables*

**Categories Definition Sources**

Finance Lagged debt General government debt/

Inflation △CPI*<sup>t</sup>*

GDP

Welfare expenditures Public social expenditures

Unemployment (unemployed/labor force

Part-time worker (Non-voluntary part-

Service industry (Workers in service industry/

Self-employed (Self-employed/labor force

Age dependency (People over age 65/total

nominal GDP Output gap Difference between actual and

/CPI*<sup>t</sup>*−1

population) × 100

population) × 100

population) × 100

ages 15–64) × 100, years ahead

(election: 1 no election: 0)

current and former Cabinet

of the bicameral legislature, effective number of parties, and the independence of the financial management organization

rules, legislative base of rules, existence of the multiyear spending limit, exception and financial monitoring system

Future dependency (People over age 65/population of

Election Dummy variable of election

Majority system Majority system:1; others: 0 Centralization Index of federalism, the strength

Fiscal rule Index of introduction of fiscal

Political stability Ideological differences between

total employment) × 100

time workers/labor force population) × 100

Capital openness Chinn-Ito index Chinn-Ito index (KAOPEN)

net lending excluding interest payments on consolidated government liabilities/nominal

potential (calculated using the Hodrick-Prescott filter) real GDP OECD Economic Outlook OECD Social Expenditures

OECD Employment and Labor Market Statistics

http://web.pdx.edu/~ito/ Chinn-Ito\_website.htm

OECD Employment and Labor Market Statistics

Comparative political dataset/IMF fiscal rules

database

database

database

database

Dependent variable Primary balance Government net borrowing or

Independent variables

108 Taxes and Taxation Trends

Economic structure

Political and fiscal systems

**Table 1.** Variables for estimating the fiscal reaction function.

Tax structure, a major independent variable, is divided between the ability to pay principle and the benefit principle. The former is divided into horizontal equity and vertical equity. In the following section, the operation of each principle is described in detail.


**Table 3.** Variables for estimating long-term interest rate.
