1. Introduction

#### 1.1. Tributary incomes and active base of contributors

In Mexico, within the category of tributary incomes, taxes like ISR (income tax), IVA (valueadded tax), IEPS (special tax on goods and services), IGI (general tax on imports), and other concepts, in the first quarter of 2016, reach \$723,130 million pesos. This quantity represented an increase of 6.1% compared with the value in the first quarter of the previous year [1]. More specifically, these taxes experimented an increase for ISR of 8.3%, IVA in 5.2%, and IGI 1.1% [1, 2].

The collection for the period January–March 2016 is of special importance since it reached \$93,585 more than the expected in LIF (Federal income law) [1, 3–8]. On the other hand, the tax

collection from 2010 to 2015 indicated that more than 90% comes from ISR and IVA and the percentage for ISR was 49.71% in 2010, 55.67% in 2011, 57.74% in 2012, and 57.98% in 2013. The percentage for IVA in the same period was 40.02, 41.51, 44.12, and 35.65%, respectively. It is important to note that the percentage of IEPS with respect to the total reaches only 0.03% in 2010 and presented a deficit in 2011 and 2013. Only until the year 2014, IEPS reach a positive increase of 6.17%. Based on the above information, it is clear that there is a need to estimate the composition of contributors since they are valuable for the tax collection process. This work concentrates in this problem and presents several models that attempt to estimate the expected number of contributors.

of adequate policies that enhance the perception on transparency and accountability are needed. Giarrizzo and Brudersohn [10], on the other hand, considered that the role of the government as a regulatory and executor agency was not always convenient for the public administration; therefore, a positive correlation in the "exert pressure does not necessarily mean more tax collection" cannot be established. In contrast, they propose incentives for individuals and companies which comply properly with the taxpaying process, thus rewarding their efforts via fiscal incentives in a clear and directed way. They consider, however, that although this approach of incentives works well in Argentina, their proposal can be well adapted to the present work by quantifying the number of contributors with maximum tax burden and establishing incentives based on this. Javier Tapia [11] using a more legal research presented the theory of the relation of power, the theory of relation of legal-tributary, and the

A Model for Estimating the Number of Taxpayer That Fullfill Mexican Income Law

http://dx.doi.org/10.5772/intechopen.74375

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Rodriguez [12] highlights the importance of equality to maintain a positive perception of the base number of contributors and considers taxing financial operations. Absalón and Urzúa [13] highlight the need to analyze the base number of contributors per categories or subgroups in the same way this work does. Absalón [13] presented the effect of a fiscal reform and suggests that the negative effects are intimately related to the different regimes, categories, or group of contributors. By the use of microdata, they suggest that the impact could have been

There is a growing interest to quantify the impact of fiscal imposition on social inequality. Flores [14] analyzes the increase of value-added tax (IVA) on the poorest people and emphasizes the need for a deeper revision of a fiscal reform and claims that a tax on certain goods and

Gómez [15] presented a study of the fiscal impact on different population layers and proposed an approach to absorb the taxpaying process to enhance the tax collection. For this, they highlight productivity in the employment via an endogenous model, and they propose direct charges to the level of revenues of people. With this, they claim that it will result in social welfare and tributary equality. For more information regarding the study of fiscal policies, reforms, and the application of mathematical methods for studying contributors, the reader is

The methodologies presented in this chapter are based on optimization models; the interested reader may refer to the following references for the theory [26–31]. The variables for developing an optimization model, applied to the active base of contributors, originated from the expected collection in the income law for the fiscal years 2015 and 2016 and the number of contributors up to the fourth quarter of 2015 and first quarter of 2016. Table 1 shows the number of contributors according to the individuals, employees, and entities categories

theory of tributary function.

identified in specific groups, regimes, or categories.

services should not impact to the poorest ones.

referred to the following studies [16–25].

2.1. Base information for developing the proposed models

2. Methodology

According to official information [1], the active base of contributors is composed by all individuals, employees, and entities which in a determined moment are active in the Federal Taxpayer Registry (RFC in Spanish) under a fiscal regime. Up to the year 2010, the number of individuals with respect to the total represented 36.68%, the employees 59.38%, and entities 4.23%.

Taking into account the number of contributors from the year 2010 until March 2016, it was found that the number of employees is surprisingly high reaching 61.64% followed by individuals which are 34.54% and entities represent only 3.82% [1] (Figure 1).

#### 1.2. Works based on contributors

In the following, a brief description of the works related to the study of tax contributors is presented. The description is focused in a more Latin-American context. Méndez, Morales, and Aguilera [9] presented a study in which contributors were considered a part of a whole and in which the development of people depends on them, but only a few of them are leading the group. The authors claim that when performing an analysis on contributors, compliance to the tributary authorities is demanded since it plays a significant role in the removal or addition of profits in their payments. They conclude that in order to have a wider and efficient number of contributors, consideration on perception, sociocultural profile of individuals, and the design

Figure 1. Composition of the active base of contributors considering general averages in 2010–2016. Source: Compiled by the authors with data from the tributary and management report up to the first quarter of 2016.

of adequate policies that enhance the perception on transparency and accountability are needed. Giarrizzo and Brudersohn [10], on the other hand, considered that the role of the government as a regulatory and executor agency was not always convenient for the public administration; therefore, a positive correlation in the "exert pressure does not necessarily mean more tax collection" cannot be established. In contrast, they propose incentives for individuals and companies which comply properly with the taxpaying process, thus rewarding their efforts via fiscal incentives in a clear and directed way. They consider, however, that although this approach of incentives works well in Argentina, their proposal can be well adapted to the present work by quantifying the number of contributors with maximum tax burden and establishing incentives based on this. Javier Tapia [11] using a more legal research presented the theory of the relation of power, the theory of relation of legal-tributary, and the theory of tributary function.

Rodriguez [12] highlights the importance of equality to maintain a positive perception of the base number of contributors and considers taxing financial operations. Absalón and Urzúa [13] highlight the need to analyze the base number of contributors per categories or subgroups in the same way this work does. Absalón [13] presented the effect of a fiscal reform and suggests that the negative effects are intimately related to the different regimes, categories, or group of contributors. By the use of microdata, they suggest that the impact could have been identified in specific groups, regimes, or categories.

There is a growing interest to quantify the impact of fiscal imposition on social inequality. Flores [14] analyzes the increase of value-added tax (IVA) on the poorest people and emphasizes the need for a deeper revision of a fiscal reform and claims that a tax on certain goods and services should not impact to the poorest ones.

Gómez [15] presented a study of the fiscal impact on different population layers and proposed an approach to absorb the taxpaying process to enhance the tax collection. For this, they highlight productivity in the employment via an endogenous model, and they propose direct charges to the level of revenues of people. With this, they claim that it will result in social welfare and tributary equality. For more information regarding the study of fiscal policies, reforms, and the application of mathematical methods for studying contributors, the reader is referred to the following studies [16–25].
