Using municipal level data, there is no evidence that federal social program spending benefited the PAN. One objection to the regression analysis I made might be that there is a problem of ecological inference, namely, that one cannot infer from the aggregate municipal voting behavior whether individuals actually shifted their voting behavior as a response to the allocation of social spending. Ecological inference techniques usually deal with discrete variables, while the allocation of social funds across municipalities is a continuous variable. It is possible, however, to analyze continuous variables as though they were discrete through the simulation method proposed by King (1997) and implemented through EzI.

The King (1994) method calculates a posterior density function that best fits a set of bounds calculated for each unit, in this case a municipality. The bounds refer to the limits of possible values that an ecological inference might take, given the observed frequencies of the two variables of interest in the marginals of a 2X2 table (An overview of the method is here). For example, one can estimate the share of PRI supporters among poor households, inferred from the overall marginals of PRI support obtained from electoral results (T) and the marginals of poverty data coming from household surveys (X). The underlying proportions are frequencies from data counts (i.e. a certain number of individuals falling in each cell of a 2x2 table of T and X).

In the case of continuous variables, once the variable of interest has been transformed into a [0,1] metric, the implementation of the EzI software is rather mechanical, although the interpretation of results changes. In the classic ecological inference, one obtains an estimate of shares of discrete counts underlying a certain population. In the continuous variable version of ecological inference, instead, one calculates a conditional mean, estimated for the specific value taken by the X variable.

In the specific problem at hand, the goal is to estimate the share of votes that were cast for each candidate depending on the intensity with which a given municipality received funds from Oportunidades and FISM. One can transform the per capita allocation of Oportunidades and FISM into a [0,1] segment, so that the value represents how much a given municipality receives from those funds compared to the per capita allocation in the municipality with the highest allocation in the country (the highest allocations of FISM and Oportunidades are both found in municipalities in Oaxaca characterized by extreme poverty and a small size). Since both FISM and Oportunidades are allocated taking into account poverty levels, it is clear that the proportion will reflect the degree to which there are more poor households in the municipality (One can control with covariates for the different poverty levels across municipalities in Mexico, although this is left for future work).

The table shows the estimated shares of votes each of the main presidential candidates might have obtained in the 2006 election, expressed as a conditional mean on the average funds allocated to Oportunidades or FISM. The standard errors of the estimations are shown in parentheses. The way to read these results is to compare them to the vote shares that each candidate obtained. The table presents two estimation alternatives, one based on a parametric bivariate normal distribution, and the other based on a non-parametric kernel density function. The reason why the non-parametric estimates are also included is that some of the distributions are not clearly unimodal, so using the non-parametric technique, which does not require the restrictive distributional assumptions of the bivariate normal (although it is not consistent with a Bayesian approach, my apologies to my colleagues), affords greater confidence in the inferences.

The table suggests that Oportunidades beneficiaries were more likely to shift their vote in favor of Roberto Madrazo and Andrés Manuel López Obrador. This conclusion is based on the fact that the conditional mean is much higher than the vote share those candidates actually obtained. For those two candidates the parametric and the non-parametric estimations yield very similar results. However, for Felipe Calderón the estimations suggest a decrease in his vote support conditional on the mean allocation of Oportunidades funds. The FISM estimations behave in the same way, although the effect for AMLO is even stronger. The estimates for Calderón differ quite markedly depending on the technique of estimation used, but they both point in the same direction, in the sense that his vote support is lower conditioned on the mean FISM allocation.

The findings can perhaps be more clearly understood by plotting the estimated values of the vote share of each candidate in each individual municipality, according to the value of per capita Oportunidades funds they receive. The figures suggests that while the Madrazo and López Obrador vote shares are generally higher than what they got from the unconditional mean (i.e. most of the estimated vote shares are in the 40 to 50 percent range), particularly in municipalities with allocations of Oportunidades below 291 pesos (which in the standardized metric corresponds to 0.2). After 291 pesos both the AMLO and RM estimated vote shares become quite dispersed, although the trend, is there is any, is for the votes to increase as Oportunidades becomes more important in a municipality. Calderón, instead, shows in the below average range of Oportunidades funds (less than 0.2) a similar vote share to what he actually got, and although there is also a large degree of dispersion, his support clearly declines as the mean Oportunidades funding increases.