3.1. A Social Accounting Matrix for Mexico

A SAM is a square matrix in which rows and columns are labeled an “account” or “institutional sector.” Since the SAM reflects where the income comes from (income row) and how it is spent (expenditure column), it must balance perfectly: For each account, the income must be equal to the expenditure. In general, the accounts are divided into economic sectors, factors of production and institutions (e.g., households, the government, the rest of the world). In this way, a SAM identifies the circular flow of income between the agents participating in an economy: Households, primary factors, enterprises or sectors, the government, and foreign transactions.

For our estimations, we use a SAM built in 2008 (^{Chapa and Ramírez, 2018})¹. The SAM was constructed using a “bottom up” method, implying that the Input-Output Table (IOT) is disaggregated by labor and household types using microdata of surveys. For example, the sectorial labor income from the IOT is displayed by gender and occupation using the microdata of the Encuesta Nacional de Ocupación y Empleo 2008 (ENOE 2008) compiled by the Instituto Nacional de Estadística y Geografía (^{INEGI, 2008}). Meanwhile, the income and expenditure by household types are disaggregated using the Encuesta Nacional de Ingresos y Gastos de los Hogares 2008 (ENIGH 2008), also from ^{INEGI (2009)}. Other sources used are the Cuentas por Sectores Institucionales 2008 (CSI) from ^{INEGI (2014)}, Secretaría de Hacienda y Crédito Público (^{SHCP, 2010}) and the ^{Banco de México (no date)}.

One of the main characteristics of the used SAM is that the mixed income is split into labor income and capital payments, following the methodology developed by ^{Ayala and Chapa (2014)}. This methodology involves calculating correction factors by sector and adjusting the sectorial labor income from the IOT to consider the shadow value of employers’ labor, self-employees, and unpaid workers. The shadow value of these jobs is calculated estimating Mincerian equations (^{Aguayo, 2018}).

Hence, the SAM includes the income-expenditure relationships of 31 economic sectors (EA), 10 family types identified by the income decile where they are classified (H), owners of the private capital factor (CORP), 4 types of work (L) classified according to their occupation (employee, employer, self-employee and non-paid worker), private and public capital (K and PK, respectively), government (G), the saving and investment identity (S-I) and the rest of the world (ROW). The online Annex of the paper comprises the modified SAM and the details of the accounts included in the matrix².

3.2. The fixed price multipliers model

Since the seminal works of ^{Stone (1985)} and ^{Pyatt and Round (1979)}, several structural analyses and public policy impact applications and studies have been conducted using this model. The accounting multipliers model is static. It is formulated assuming fixed average expenditure propensities, fixed prices or an economy with idle capacity, and linear production. This last assumption means that intermediate products and the factors of production are complementary.

Economic sectors, households, labor types and private capital are accounts considered endogenous. In this sense, the exogenous variables include the government, the rest of the world, and investment since they can be used as economic policy instruments.

The accounting multipliers, M _A , are obtained as follows:

where n denotes the number of endogenous accounts, y_n is the vector of endogenous income (order n×1), I is the identity matrix (order n×n), A_n is a matrix of average endogenous expenditure propensities (order n×n), and x is a vector of exogenous income (order n×1). The element m_ij of the matrix M_A represents the overall income increase of the endogenous account i when the endogenous account j receives a unitary and exogenous income injection.

However, ^{Pyatt and Round (1979)} suggests that these accounting multipliers cannot be interpreted directly as measures of the effects of exogenous injections on the endogenous accounts' income, because the relevant parameters are the marginal and not the average propensities to spend. The authors propose, using the marginal multipliers, instead:

where C_n is a matrix of marginal expenditure propensities to consume (order n(n). Estimating the proper M_C allows us finding the real change of y_n due to income injections. This matrix comprises the fixed price multipliers. Where the difference between A_n and C_n is that, while A_n considers households' average expenditure propensities in goods and services sold by economic activities, C_n involves marginal expenditure propensities to consume.

As stated in the introduction, a major objective of this paper is to evaluate the economic impact of poverty alleviation programs by employing an extraction simulation. In the context of the fixed price multiplier model, the exercise involves a transmission effects mechanism: The elimination of transfers implies a reduction in families' income, causing a decrease in the consumption of goods and services. In turn, the economic sectors' production, the demand for intermediate inputs, and payment to primary factors (labor and capital) do the same, starting the process again until it converges.

Once estimated, the element mc_ij of the matrix M_C indicates the increase in income of the endogenous account i when exogenous account j receives a unit injection of income. In this sense, we can calculate two types of fixed price multipliers, the diffusion effect and the absorption effect. The diffusion effect captures the income increase of the entire economy in the face of a unit injection of income in account j, obtained from the sum of the elements of the matrix of fixed price multipliers that correspond to the column of the account j. The absorption effect involves the income increase of a certain account i when a unit injection of income is made to all the endogenous accounts j at the same time, so it results from adding the elements of the multipliers' matrix that correspond to the row account i.

3.3. Estimation of the marginal propensities to consume

To make SAM simulations, usually average ratios are taken as constants, for example the proportions of inputs per unit of output or the proportion of government purchases among the sectors of the economy. Even though this assumption is reasonable for intermediate consumption and many of the final demand components, it is not so for the case of consumption. The problem is that using average propensities to consume, instead of marginal ones, we implicitly assume all income elasticities are equal to one, what clearly denies the heterogeneity of the goods and services. As consumption is the largest block of total demand, assuming all income elasticities are unitary might lead to significant biases in the marginal propensities to consume and lastly in SAM multipliers.

To this end, we proceed to estimate a flexible parametric Engle Curve, the QAIDS introduced by ^{Banks, Blundell, and Lewbel (1997)}. In a cross-section perspective, assuming consumers face the same prices, the QAIDS system is practically the ^{Deaton and Muellbauer (1980)} AIDS systems with a quadratic term. This system has proved to be very useful in the context of Input-Output and SAM models as the Fidelio Model in Europe (^{Mongelli, Neuwahl and Rueda-Cantuche, 2010}; ^{Kratena et al. 2013}).

The estimated model is given in Equation [3].

The subindex i denotes households, j categories of goods and services, w is the share of the spending in category j in total spending, E is total expenditure, x is a vector of household control variables, such as size of the household and others, and ( and ( are regression coefficients. The income elasticities of these demands are given by Equation [4]:

To estimate the QUAIDS system, we employ the Mexico’s expenditure survey for 2008 (ENIGH 2008) comprising information about purchases and income of 30,000 families. The information was converted to basic prices using trade and transportation margins and mapped out to the North American Industry Classification System (NAICS). The system was estimated for each decile by ordinary least squares, adding as controls the size of the household and its square, the age of the head of the family and its square, and a dummy for urban locations. Income elasticities for each good and income decile are calculated inserting the estimated coefficients, average income, and the mean consumption share of each decile in Equation [4].

Table 1 presents the estimated income elasticities showing the significance for the Wald test where the null hypotheses is that income elasticity is unitary at the mean values of the income and consumption share by decile. From the total of 150 income elasticity estimations, the null hypothesis that income elasticity is unitary is rejected at 5% significance in 101 of the cases, 74 of these cases seem to belong to the necessary goods, 27 to luxury goods, and none of them to inferior goods. Also, the proportion of non-unitary income elasticities increases sharply by decile.

Once the income elasticities are estimated, we obtain point estimations for the marginal propensities to consume for each decile i, for every category of goods j, just as the product of the income elasticities times the consumption share. Table 2 presents these estimates.

For instance, the marginal propensity to consume agricultural products of the 10^th income percentile is one half of the average propensity to consume and just a third for food products. In contrast, it is fifty percent larger for education services.

3.4. Poverty elasticities to income and inequality

The SAM model can be used to simulate the direct and indirect effects in production, income, and inequality of the cash transfers given by the social development programs. But how these outcomes are transmitted to specific poverty measures? For this end we used the poverty index developed by ^{Foster, Greer and Thorbecke (1984)}, known as Foster-Greer-Thorbecke (FGT) poverty indexes defined by Equation [5]:

where P _α is a poverty index depending on the parameter α that reflects the aversion to poverty, z is the line of poverty, H is the total households, h is the number of households whose income is below the poverty line, and y _i is the per capita income of household i.

When α = 0, P₀ = h/H, that is the headcount rate, i.e., the proportion of individuals below the poverty line, what is called the poverty incidence. When α = 1, P₁ measures the gap between the mean income of the poor to the line of poverty, what is known as the depth of poverty, whereas P₂ takes into consideration the inequality among the poor, this measure gives more weight to the poorest among all the individuals below the poverty line, hence it reflects the severity of poverty.

FGT Poverty indexes are affected by mean and dispersion of incomes. If mean income grows, holding inequality constant, FGT indexes diminishes. On the other hand, if inequality increases, holding constant mean income, then poverty increases as well. ^{Huppi and Ravallion (1991)} developed analytical expressions for the income elasticities of poverty for the FGT indexes. They are defined by Equation [6]:

where f(z) is the density function of the poverty distribution evaluated at the line of poverty. On the other hand, ^{Kakwani (1993)} showed that the proportional change in the FGT poverty indexes occasioned by a proportional change in the Gini coefficient, the most popular measure of inequality, is:

where q = F(z) and F is the cumulative distribution function of income. Therefore P ₀ = h/H or the incidence of poverty at the poverty line z, q* = F(z*) and z* = (z + δμ)/(1 + δ), acts as a modified poverty line after the inequality shock, and δ y μ are the percentual change in the Gini coefficient and the mean income of the whole distribution.

Combining both elasticities, it is possible to evaluate the effect of the direct and indirect economic effects of the social programs on poverty. Hence an exogenous injection (extraction) of resources in sector j in the SAM matrix produces an increase (decrease) in the mean income of all the economy, reducing (increasing) poverty. But if the inequality in income distribution (e.g., Gini coefficient) increases, poverty tends to rise, counterbalancing the income effect. On the other hand, if inequality decreases, the distribution effect reinforces the income effect on poverty. We can capture the overall effect through Equation [8]:

y-i is the mean income of household i, dx-j is the exogenous income injection in sector j, m _ij is the i income SAM multiplier associated to the injection in j and dG is the change in the Gini coefficient (G).

4.1. On sectorial activity and household income

Two simulations are proposed depending on what is done with the resources that are extracted from the social programs. In both scenarios the social programs are eliminated. Under the simulation labeled Absolute, the released resources are devoted to external pay government debt. Under the simulation labeled Net, they are transferred back to taxpayers according to the proportion they contributed to the labor income tax.

As the simulations assume an exogenous extraction of income of the households that were beneficiary of these programs, the results depend on the importance of these transfers in the total income. Figure 1 shows these proportions for the ten deciles of the income distribution. Note a negative relationship between the proportion of the Oportunidades program benefits that families receive on total income and the decile of the income distribution to which they belong. In the case of the other two programs, a U-shaped relationship is observed. Clearly, the Oportunidades program is better targeted to low-income families than the Procampo and Adulto Mayor programs. The 35% of Procampo’s budget is absorbed by the ninth and tenth decile of income, 13.6% in the Adulto Mayor program and only 3.9% in the Oportunidades one.

Source: Authors own elaboration with microdata from ENIGH 2008 from ^{INEGI (2009)}.

Figure 1 Social programs distribution by income decile, 2008 

The results of the Absolute simulation are shown in Table 3. The sectors that are most affected are: Apparel Manufacturing, Leather and Allied Product Manufacturing; Accommodation and Food Services; Educational Services; Other Services (except Public Administration) and Utilities. The effect on the gross production of these sectors ranges between -2.96% to -1.92% in the case of Oportunidades, -1.23% to -0.78% for Procampo, and -0.70% to -0.45% for the Adulto Mayor program. Nonpaid workers are the most affected by the elimination of the programs. For Oportunidades, the effects range between -1.63% for nonpaid workers to -1.06% for private capital owners. With respect to Procampo, the impact ranges between -0.64% to -0.43%, and for Adulto Mayor, from -0.38 to -0.25. The most affected households are the low-income deciles. Eliminating Oportunidades reduces income between -5.16% and -1.04%, eliminating Procampo, between -1.84% and -0.55%, and removing Adulto Mayor, between -1.27% and -0.26%.

The numbers are cold and might not express in the right dimension the consequences of aborting these social programs. If the burden of the income contraction of the first decile under the Absolute scenario were experienced by the 20% poorest households of the first decile, that would represent an income cut of 56%; if it were levied on the poorest ones, that would be equivalent to leaving 223,000 families without any income.

In the short term, the elimination of social programs and the allocation of resources to pay the debt has a negative impact on the country’s gross value added of 0.94% due to the elimination of the Oportunidades program, of 0.38% for Procampo and 0.22% for the Adulto Mayor Program.

We consider the scenario where the released resources of the eliminated social programs are transferred back to the families according to the current labor income tax burden, what we call the Net scenario. Because the programs, especially Oportunidades and Adulto Mayor, are concentrated in the low-income deciles, whereas 83.50% of the labor income tax is concentrated in the three highest income deciles, this policy combination generates initial positive net impacts for households in deciles 7 to 10 and initial negative impacts for households from deciles 1 to 6.

Table 4 shows the main outcomes of the simulation under the Net scenario. The sectors presenting the largest percentual contractions are Agriculture, Forestry, Fishing and Hunting; Food Manufacturing; Beverage and Tobacco Product Manufacturing; Transportation and Warehousing; Wholesale and Retail Trade; and Paper Manufacturing, and Printing and Related Support Activities. Those sectors that benefited the most are Educational Services; Information; Arts, Entertainment, and Recreation; Other Services (except Public Administration); and Health Care and Social Assistance. Note that deciles 1 to 6 have high marginal propensities to consume in the goods and services sold by the affected sectors, and deciles 7 to 10 in the goods and services sold by the benefited sectors. Most of the productive factors are negatively affected, except for employees, who benefit under this scenario. As the initial shock dictates, the households that benefit are the richest ones, from deciles 7 to 10. In the aggregate, under this scenario the effect on gross value added is practically zero.

4.2. Mexico’s social programs impact on poverty: An extraction simulation

Employing the microdata of the ENIGH 2008 (^{INEGI, 2009}) we estimate the FGT poverty indexes for α = 0, 1 and 2. Besides, using the consumption per adult equivalent distribution, a Lorenz Curve was fitted employing ordinary least squares following ^{Kakwani (1980)}, and the second derivative of this curve at the head count measure of poverty was estimated to infer the density evaluated at the poverty line. With all these inputs we are able to estimate the poverty elasticities regarding mean income and Gini coefficient, presented in Table 5.

Using the initial and simulated incomes, the Gini coefficient of the income distribution, and the poverty elasticities, we arrive to estimates of the percentual increase in the poverty indexes due to eliminating the social programs. Table 6 presents the main results of the impact of the three social programs, one program at a time under both scenarios. Annual mean income and Gini coefficients are reported, as well as the estimated percentual variations in poverty due to the income and inequality changes, and the total effect. As it is natural, the decrease in mean income is larger for the Absolute than for the Net scenarios because in the latter the elimination of the social programs’ cash transfers is compensated with tax rebates for the rest of the families, hence the net effect dilutes. The Net scenario presents the major increases in the Gini coefficient, because the simulation takes money from the poorest families and transfer it to the highest income families. For this reason, the income effect on the FGT poverty measures is more important in the Absolute scenario and the distribution effect is more relevant in the Net simulation.

Oportunidades is clearly the program with the largest impact in the FGT poverty indexes. Cancelling the program means a rise in the poverty indexes from 6.04 to 13.18 percent, depending on the definition of poverty in the Absolute scenario, whereas eliminating Procampo rises poverty in a range of 1.87 to 3.46 percent, and 1.27 to 3.63 for the Adulto Mayor program. The differential impact might be explained because Procampo weakly targets poverty and the Adulto Mayor program is relatively new and with smaller budgets, compared to Oportunidades.

In all cases the distribution effect runs in the same direction as the income effect, that is, the first reinforces the second. In the case of the incidence of poverty or the head count index, both effects are roughly of the same magnitude. In the case of Oportunidades, the contraction of the mean income of the poor, directly by the cash transfer and indirectly by the multiplier effects in the SAM model, produce a rise in poverty of the same size than the one produced by the increase in the Gini coefficient. Rises in poverty under the Net scenario are due almost entirely to the distribution effect.

Let assess the contribution of the social programs on poverty incidence. Our extraction exercise in the Absolute scenario leads us to conclude that the proportion of households in poverty would increase 9.18% if all three social programs were eliminated. As in 2008 the head count poverty in Mexico was 12.83%, then poverty incidence would rise to 14.01%, an increase of 1.21 percentual points, meaning 1.4 million more poor individuals in the economy.

Is the impact of the three programs in terms of poverty alleviation small or large? Clearly the alleviation of poverty of the social programs considered is not minor, but it can be insufficient depending on Mexico’s goals and its commitments regarding poverty. It is difficult to establish a desired goal for poverty in the next decade for Mexico but let us advance two possible goals: The first one is to accomplish the parameters established in the Sustainable Development program of the World Bank that pretends to eradicate extreme poverty by 2030; the second is to drop poverty incidence to levels compatible with the degree of Mexico´s development.

According to the World Bank’s parameters, then every household should have an income to afford at least 1.25 US dollars per person per day³. In 2008, poverty line in Mexico was approximately 805.1 pesos monthly and the 1.25 US dollars line was equivalent to 417.35 pesos, then under a uniform distribution, making all population having an income greater than the World Bank poverty line is equivalent to reduce the poverty incidence in Mexico by 52%.

The second standard also implies a huge drop in the poverty incidence in Mexico. Taking 71 country observations of World Bank extreme poverty incidence estimations and Gross Domestic Product (GDP) per capita, we estimate that according to their per capita income level, Mexico’s poverty incidence should be 50% lower compare with its actual level⁴. In order of magnitude, both standards point to a goal of dropping the poverty incidence in Mexico by half in the next decades.

Our results indicate that to achieve such a reduction, the social programs should be increased by a factor of 8 if they remain as they operate. Some gains might be achieved changing the rules of operation in the case of Procampo and making sure the transfers from Oportunidades and Adulto Mayor programs trickle down to the first and second decile of the income distribution. Although, even in this scenario, the amount of resources devoted to alleviating poverty should increase dramatically to cut poverty in Mexico by half.