Generation and distribution of income in Mexico, 1990-2015

Purpose – This paper aims to review the efficient use of economic and social resources to generate income and, at the same time, reduce the concentration of wealth in the 32 states of the Mexican Republic during the period 1990-2015. Design/methodology/approach – Data envelopment analysis with the inclusion of a bad output was used to diagnose the efficiency of Mexican entities, and the Malmquist–Luenberger index was applied to understand how this efficiency evolves. Findings – The results clearly show that only 3 of the 32 units studied generated and distributed wealth efficiently, while the other 29must increase their level of income and its distribution. Originality/value – According to the authors’ knowledge, this is the first work that performs a temporal analysis of the efficiency in the generation of Human Development Index using bad outputs and the Malmquist–Luenberger index.


Introduction
In Mexico, the Human Development Index (HDI) during the period 1990-2015 increased by 17.6 per cent. However, this indicator of welfare is still lower than that of other Latin American economies; one of the main causes is the low level of per capita income in the economy (UNDP, 2018b). At the level of federal entities, Mexico City, Nuevo Le on, Chihuahua, Baja California, Sonora and Aguascalientes stand out as the states with the highest levels of human development, while Hidalgo, Michoacán, Chiapas, Oaxaca and Guerrero have the lowest HDI levels, thus presenting a strong state and regional disparity in social welfare (UNDP, 2011(UNDP, , 2016. The dynamics of variables such as public expenditure, level of education and employed personnel, despite the positive trends throughout the study period, reveal the need for higher levels of investment, employment and education as its impact on the income dimension of the national and state HDI has been low (INEGI, 2018a(INEGI, , 2018b(INEGI, , 2018c(INEGI, , 2018d. In turn, the income concentration data in Mexico indicate that a significant percentage of the states has an asymmetric distribution of wealth, affecting negatively the level of welfare of the society (Tello, 2010;Quiroz and Salgado, 2016;Ortiz et al., 2017). For this reason, it is relevant to establish as a research question how efficient were the 32 entities of the Mexican Republic in the use of their economic and social resources to generate and distribute income during the period 1990-2015. The results of this study allow to quantify the efficiency in the management of the resources during the analyzed period and, therefore, contribute to the design of strategies and policies that energize the behavior of the income dimension of the HDI. Harttgen and Klasen (2012) conceive human development as the process that expands the opportunities of the persons for lives the life that they value and, therefore, reach a higher level of well-being. Understanding as opportunities the possibility to have a long and healthy life; be literate and possess knowledge; have economic resources that grant a decent standard of living; and be involved in the community life. If we do not own them, many other options and opportunities of life are inaccessible (UNDP, 2018a). Determining the level of human development of an economy is key to establish public policies as it allows to evaluate the evolution of the living conditions of the population; diagnose the problems; and enrich the design of government objectives and strategies (L opez-Calva et al., 2004).
In the measurement of human development, the HDI highlights, proposed by the United Nations Development Program (UNDP). This index combines three elements to evaluate the progress of countries in terms of human development: the Gross Domestic Product (GDP) per capita, health and education; each one is included with the same weight in the index (Griffin, 2011;Harttgen and Klasen, 2012). It is due to its simplicity and easy access to the statistical information that is required for its calculation that the HDI has become the most used mechanism to measure human development and social welfare (Le on, 2002;Ord oñez, 2014). Under the vision of human development, and consequently of the HDI, the individual must be the center of the design of public policies and, at the same time, the fundamental instrument of their own development (Griffin, 2011).
The distribution of income is the way in which the national product is distributed among those who have contributed to its production, grouping them into homogeneous categories according to the function exercised or according to the nature of the contribution made (Salinas, 1977;Medina, 2001). The concentration of income is caused by multiple factors. The way in which this asymmetry is measured is through inequality indices, which are measures that summarize the distribution of a variable among a set of individuals. Consequently, the inequality in the distribution of wealth is given by the degree of dispersion of income with respect to a reference value (Ruza, 1978;Carrillo and Vázquez, 2005;Ospina and Giraldo, 2005). The indicators of inequality are usually classified as positive and normative measures (Carrillo and Vázquez, 2005;Ospina and Giraldo, 2005;Mazaira et al., 2008). This research uses positive measures as the normative depends on ethical judgments that are reflected in the values chosen for the parameters of the social welfare function (Acevedo, 1986). Of the divers positive inequality measures, this research uses the Gini Coefficient (Cg), because it allows a simple interpretation of the degree of income concentration and meets the four basic properties of an inequality indicator: is sensitive to the effect of socioeconomic factors of inequality, considers the influence of any social hierarchy on changes of the composition of the population, is consistent with the argument of the Lorenz curve and shows invariance in the face of proportional increases in income (Gradín and del Río, 2001;Medina, 2001;Yáñez, 2010).
The income dimension of human development apart of the GDP per capita includes other indicators such as the concentration of income to determine in a more inclusive way the economic well-being of society (Hicks, 1997;Alkire and Foster, 2011). Thus, it reaffirms the fact that there can be no economic well-being if the income generated by a society is not properly distributed among the population that generated it (Mazaira et al., 2008;Yáñez, 2010). Hence, an excessive concentration of income can be considered as negative and, therefore, its decrease is recommended (Quiroz and Salgado, 2016). For it, is possible to point out that the concentration of income has a behavior similar to an unwanted output, while income itself would behave as a desired output.
Given that income generation involves the use of resources, it is important, prior to any manipulation of factors, to determine under which combination of socioeconomic inputs an economy is achieving the highest level of income per capita with the lowest concentration of it. In other words, it is relevant to analyze the efficiency in the generation of income. Several studies point the importance of the efficient use of resources to increase the economic well-being of an economy. It is argued that the welfare of society depends on the application of public policies aimed at the efficient use of resources and the promotion of greater equity in the distribution of wealth (Marti c and Savi c, 2001;Cortés, 2003;Stimson et al., 2006;Vargas, 2009;Halkos and Tzeremes, 2010;Tello, 2010;Poveda, 2011;Torres and Rojas, 2015;Quiroz and Salgado, 2016;Ortiz et al., 2017). Thus, the hypothesis of the research is that very few entities of the Mexican Republic were efficient in the usage of their economic and social resources to generate and distribute income, during the period 1990-2015. This has important repercussions on the economic and social well-being of the Mexican population.
For the analysis of the efficiency, the literature offers different methodologies. Data envelopment analysis (DEA), developed initially by Charnes et al. (1978), is a methodology widely used as an alternative to parametric methods (Banker et al., 1984;Bemowski, 1991). In essence, DEA compares an observed production unit with a virtual unit, which obtains the same or more product with the same or lesser number of factors. However, unwanted outputs often are produced together with desirable results. In this sense, Pittman (1983) introduces unwanted outputs in the calculation of productivity indexes, adapting the methodology of Caves et al. (1982), and determines the shadow prices of these. The result of this new approach allows to deduce an efficiency measure that, while maximizing the good outputs, minimizes the undesired outputs from a benchmarking process (Serra, 2004). Although the applications of DEA have been mostly in productive units, it is also applied in studies of quality of life, economic well-being, human development and social welfare (Mahlberg and Obersteiner, 2001;Despotis, 2005;Yago et al., 2010;Giménez et al., 2017). Mariano et al. (2015) perform an extensive review of the literature that use DEA for the analysis of human development. According to our knowledge, this work is the first that analyzes the efficiency in the generation of income considering bad outputs from a temporal perspective. For it, the Malmquist-Luenberger (ML) index is used to measure changes in the efficiency, technological change and productivity over time, taking into consideration the undesirable outputs of the productive process (Chung et al., 1997).
The research is structured in five sections: Section 1 analyzes the socioeconomic aspects of economic well-being. In Section 2, the theoretical elements of human development and income distribution are addressed. In Section 3, the methodological features of the generation and distribution of income DEA model are presented. In Section 4, the main results of the DEA model are exposed, indicating the entities that efficiently used their resources. Finally, the conclusions are established in Section 5, where the fundamental aspects of the research are highlighted.

The income dimension of human development in the entities of Mexico
The study of the dynamics of the income dimension of the HDI shows that during the period 1990-2010, the highest income indices were held by the states of Nuevo Le on, Mexico City, Chihuahua, Campeche and Sonora. On the other hand, the entities with the lowest income indices were Chiapas, Oaxaca, Guerrero, Tlaxcala and Hidalgo, which is directly related to the behavior of the GDP per capita (UNDP, 2011(UNDP, , 2016. Table 1 shows that GDP per capita had an increase of 58 per cent during the period 1990-2015 as a result of increase in public spending and investment attraction policies. The states of the country with the highest GDP per capita levels are Campeche, Mexico City, Jalisco, Nuevo Leon, Queretaro, Quintana Roo and Tabasco.
The public spending had a major expansion from 33,938m pesos in 1990 to 1,955,597m pesos in 2015. The educational level of the society presented an increase of 45.5 per cent, this is, in 1990, the average level of education was 6.3 years, and in 2015, it was 9.1 years. The employed population grew 116 per cent, excelling Mexico City, State of Mexico, Nuevo Le on, Jalisco, Puebla and Veracruz (Table 1). The establishment of companies during this stage was incentivized as they went from 736,860 in 1990 to 5,654,014 in 2015, factor that had a direct impact on the generation of jobs and on the remunerations of the population. An element that also presented development was the Gross Capital Formation, Foreign direct investment being the variable that showed the highest growth during the years studied. Specifically, the states of Baja California, Chihuahua, Guanajuato, Jalisco, State of Mexico, Mexico City, Nuevo Le on, Puebla and Veracruz were the more benefited (INEGI, 2018a(INEGI, , 2018b(INEGI, , 2018c(INEGI, , 2018d. Despite the positive behavior of these indicators, the low impact of the income dimension on the national and state HDI reflects the importance of increasing per capita income levels, as this would lead to higher levels of well-being in the entities of the country. The concentration of income in Mexico decreased during the period 1990-2015, going from 0.519 in 1990 to 0.469 in 2015. When carrying out the analysis by states, it was observed that Baja California Sur, Tlaxcala, Colima, Baja California and State of Mexico presented the highest levels of income distribution, while Oaxaca, Guerrero, Hidalgo, Querétaro and Campeche were the ones that had the highest concentration of income. These results have, as a background, the poor performance of these last entities in terms of generation and distribution of GDP (Table 2).

Methodology
The idea of Farrell (1957), who explains that to measure the efficiency of a set of productive units, it s necessary to know the function of production and the frontier of efficiency, has been applied empirically through two methodologies: stochastic frontiers estimation and DEA measurements. The first involves the use of econometrics, and the second involves linear programming algorithms and benchmarking. DEA is a technique used to measure the comparative efficiency of homogeneous units. Starting from the inputs and outputs, this method provides a classification of the Decision Making Unit (DMU), giving them a relative efficiency score. A DMU is efficient when there is no other (or combination of them) that produces more output, without generating less of the rest and without consuming more inputs. In this case, we speak of an output-oriented model, while in the opposite case, it is called an input-oriented model. DEA models take

JEFAS 25,49
advantage of the know-how of the DMUs and once determined who is efficient and who is not, set improvement goals for the inefficient, and based on the achievements of the efficient (Bemowski, 1991;Navarro and Torres, 2003;Serra, 2004). In our case, the model was oriented to the output because the ultimate goal of economic well-being is to maximize income and minimize the concentration of it.
Due to the existence of undesirable outputs, for the calculation of the annual efficiency levels, a model based on a directional distance function (DDF) was used (Färe et al., 1994), precisely with the objective to maximize income while minimizing the concentration of it, given the amount of available resources. The DDF models has been widely used in efficiency studies (Sueyoshi and Goto, 2010;Färe et al., 2005;Watanabe and Tanaka, 2007). The mathematical expression of it is as follows:  where b is the maximum increase and reduction achievable simultaneously in the good and bad outputs, y t km represents the output m of the unit k in the year t, b t kh the bad output h of the unit or country k in the year t, x t kn the input n used by the country k in the year t and y ot m , b ot h and x ot kn denote the observed levels of good and bad outputs and inputs for the country evaluated in the year t. The linear mathematic equation (1) is solved for each unit analyzed.

Income in Mexico
For determining the evolution of efficiency and productivity over time, the ML index is used, which has its origins in the Malmquist index (MI) (Caves et al., 1982;Chung et al., 1997). The MI can explain the change in the total productivity of the factors as a product of the efficiency change or catching up and technological change. Chung et al. (1997) modified the MI to apply it to the case of DDF. The new index called ML was decided to use in this investigation as undesirable variables were considered in the income dimension of the HDI. The mathematical expression of the index is as follows (Chung et al., 1997): is the DDF defined for each unit analyzed taking its data for year t (x t , y t , b t ) and as a reference the set of production possibilities for the same year P(x t ). In an analogous way, it could be defined, for example, In this case, the DDF would take the data for year t (x t , y t , b t ) for each unit analyzed and, as a reference, the set of production possibilities for year t þ 1, that is, P(x tþ1 ). In the latter case, the DDF is crossed in the sense that it uses the data of one year for the analyzed units and projects them on the production possibility frontier of a different year. A value of ML t,tþ1 greater than 1 would mean that there has been an improvement in productivity between years t and t þ 1, while a value less than 1 would be interpreted in the opposite way. Any of the DDF needed for calculating the ML index can be calculated using equation (1). Equation (2) can be decomposed using simple algebraic manipulation, such as: where: represents the efficiency change or catch up, that is, if the unit analyzed has approached or moved away in the period with respect to the frontier. If it has been approximated, equation (4) takes a value greater than 1 and less than 1 otherwise. While: Income in Mexico represents technological change, that is, if the frontier has improved or worsened over the period. In case of improvement (positive technological change), equation (5) takes a value greater than 1, and less than 1 otherwise. For the empirical application of the model in this case, it was used as a good output the GDP per capita and as a bad output the concentration of the income, measured by the Cg. This due to the theoretical representativeness that these variables have to explain the economic well-being of a country. The selection of inputs was based on the theoretical pillars that explain the behavior of the components of the HDI income dimension. In this sense, the postulates of the UNDP (2011, 2016, 2018a); Mahlberg and Obersteiner (2001) Hoarau (2011, 2013) were analyzed, arriving at the conclusion that the indicators that explain the behavior of the income dimension of human development are the average annual change in the consumer price index, inequality index, exports, imports, foreign direct investment, total debt service, development assistance, public spending, electricity consumption per capita, proportion of the population that uses the internet, degree of schooling, economically active population, employed personnel, economic units, gross capital formation, remunerations and salary.
Given the availability of statistical information for the states of the Mexican Republic, the number of indicators was reduced. With these data, a statistical analysis was carried out by determining fist a matrix of correlations. Subsequently, factorial analysis was carried out, which is very useful for depurate the correlation matrix. The factorial analysis, under the concept of main components, passed the tests of Kaiser-Meyer-Olkin (KMO), with values higher than 0.70, and the test of sphericity of Bartlett, with a high result and with a small level of significance. Due to the positive results in the tests, we proceeded with the factorial analysis, and a matrix of communalities was obtained, which showed that the inputs that best explain the HDI income dimension are public expenditure, degree of schooling and employed personnel (Tables 3-6).
The statistical information of these variables was possible to obtain it through the databases of the Instituto Nacional de Estadística, Geografía e Informática de México, the Secretaría de Educaci on Pública de México, the Consejo Nacional de Poblaci on, the Consejo Nacional de Evaluaci on de la Política de Desarrollo Social, the Banco de México and the Human Development Reports of UNDP.

Analysis and discussion of results
The states considered efficient in the use of their resources to generate income and at the same time reduce the concentration of income, during the period 1990-2015, were Baja California Sur, Campeche and Mexico City. On the other hand, Quintana Roo and Nuevo Le on stand out as entities that approach efficiency (Table 7). These results are related to the endowment of factors that these states have and the level of life of their population. Specifically, it can be seen in Tables 1 and 2 that Baja California Sur, Campeche and Mexico    City were characterized for occupying the first positions in terms of GDP per capita, public expenditure, employed personnel and average degree of schooling, as well as having the lowest levels of income concentration. Behavior that directly affected the position that they occupied in the national ranking of HDI (UNDP, 2011(UNDP, , 2016(UNDP, , 2018b. Emphasizing with this the preponderant position that they occupy within the regional dynamics of Mexico, being the entities that historically stand out in the country for their socioeconomic dynamism (Garza and Schteingart, 2010;Tello, 2010;Quiroz and Salgado, 2016;Ortiz et al., 2017). Thus, in this case, the efficient use of resources corresponds with the behavior of the main socioeconomic indicators and to the level of human development displayed by these entities during the study period.
The results of Table 7 also show that entities such as Oaxaca, Chiapas, Michoacán, Guerrero and Veracruz were the most inefficient in generating economic well-being. These states did not use efficiently their resources to increase their GDP per capita and, at the same time, reduce the concentration of income in the period 1990-2015. Performance that is linked to the unequal allocation of resources (public expenditure, employed personnel and average Source: Own elaboration based on the data of Tables 1 and 2 JEFAS 25,49 grade of schooling) among the entities of the country. Being so historically the most lagging states in economic and social terms of Mexico (INEGI, 2018a(INEGI, , 2018b(INEGI, , 2018c(INEGI, , 2018d; since historically, they have been characterized as being the most lagging in economic and social terms (Garza and Schteingart, 2010;Tello, 2010;Quiroz and Salgado, 2016;Ortiz et al., 2017). Behavior that has been reflected in the three elements or dimensions of the health, education and income (HDI) (UNDP, 2011(UNDP, , 2016(UNDP, , 2018b. Table 8 shows that the entities rated as efficient in the generation of economic well-being (Baja California Sur, Campeche and Mexico City) did not have a similar performance in terms of productivity, during the period 1990-2015. In the case of Baja California Sur, Campeche and Mexico City, the ML index worsened. That is, these states, despite being efficient, did not present substantial improvements in the efficient use of their resources. In general, Table 8 shows that during the period 1990-2015, the 32 entities worsened the use of their resources to generate and distribute income. This deterioration is consistent with the low levels of economic well-being that place Mexico in the ranking of countries with medium degree of HDI (UNDP, 2018b). These results show that the states of the country that received the most resources in the period 1990-2015 (Campeche, Jalisco, Nuevo Leon, Queretaro, Quintana Roo, Tabasco and Mexico City) were not always the most efficient in the generation and distribution of income. Similarly, it is observed that despite the general increase in the efficient use of resources in the country, it is necessary to promote public policies that encourage this type of management and promote investment, employment and education in each of the entities of the Mexican Republic. This is because the efficient use of economic and social resources would generate economic well-being and, therefore, contribute to a higher level of human development in Mexico. Causal relationship that had already been exposed by authors such as Marti c and Savi c (2001) Hoarau (2011, 2013) and Poveda (2011). Thus, the efficiency results of this study match with the theoretical arguments that indicate that the efficient use of resources contributes significantly to the human development of the countries (Mahlberg and Obersteiner, 2001;Despotis, 2005;Yago et al., 2010;Giménez et al., 2017). As with the empirical evidence that highlights that the lack of economic growth and the presence of income concentration in Mexico; as a consequence of the cheapening of the labor force, the absence of employment for the trained personnel, the little social mobility, the growing public debt, and the absence of a social and labor policy; perpetuate poverty and marginalization (Cortés, 2003;Vargas, 2009;Tello, 2010;Torres and Rojas, 2015;Quiroz and Salgado, 2016;Ortiz et al., 2017).

Conclusions
Human development in Mexico as a goal of economic development models has been partial as, on one hand, it exists a positive evolution in terms of health and education, coupled with positive, but not sufficient, growth rates of employed personnel, public expenditure and GDP per capita. On other hand, there are important lags in social matters such as marginalization and concentration of income. In regional terms, there is an uneven development of the entities in Mexico. States such as Campeche, Jalisco, Nuevo Leon, Queretaro, Quintana Roo, Tabasco, Puebla and Mexico City have high levels of well-being, while, others like Oaxaca, Guerrero, Michoacán and Chiapas are distinguished by their economic backwardness. Human development seeks to expand the capabilities of the human being, adding to the economic factor the health and education dimensions to have a holistic vision of social welfare. The concentration of income, understood as the unequal distribution of the product generated by a society among its members, is directly related to the concept of human development from the income dimension as economic well-being is not only the generation of income but also the way in which it is distributed among the population.
Based on the DEA methodology, it was determined how efficient were Mexican entities in the use of the resources to generate income and, at the same time, reduce the concentration of it during the period 1990-2015. The model was elaborated with constant returns to scale, oriented to the output and including a bad output. The output of the model was the GDP per capita, the bad output the Cg, and the inputs were the public expenditure, the degree of schooling and the employed personnel.
Oaxaca, Chiapas, Michoacán, Guerrero and Veracruz were the most inefficient entities in the generation of economic well-being, while, Baja California Sur, Campeche and Mexico City had the highest efficiencies, that is, with the resources, they possess were efficient in the generation of income and in the reduction of the concentration of it. The ML index in this case reflected that all the states presented a negative evolution in their efficiency and productivity over the period studied.
The results obtained in this study show that the states that received the most economic resources (Campeche, Jalisco, Nuevo Le on, Querétaro, Quintana Roo, Tabasco and Mexico City) were not always the most efficient in the generation and distribution of income, making evident the need for a more adequate use of resources, through the establishment of public policies focused by entity for the promotion of investment, employment, education and the reduction of inequity.