Welfare Gains of the Poor: An Endogenous Bayesian Approach with Spatial Random Effects

Abstract

We introduce a Bayesian instrumental variable procedure with spatial random effects that handles endogeneity, and spatial dependence with unobserved heterogeneity. We take into account the endogeneity through a system of simultaneous equations where a conditional correlation between the stochastic errors captures the endogeneity, and exclusion restrictions are used to treat endogenous regressors. In addition, we propose a Bayesian hierarchical spatial framework to model spatial dependence and heterogeneity. A Gibbs sampling algorithm is used to draw samples from all our conditional posterior distributions. We find through a limited Monte Carlo experiment that our proposal works well in terms of point and interval estimates, as well as prediction, compared with other possible alternatives. Taking advantage of the fact that a Bayesian framework permits easily performing statistical inference related to complicated non-linear functions of parameter estimates, we apply our method to analyze the welfare effects on the poorest households generated by a process of electricity tariff unification. In particular, we deduce an Equivalent Variation measure from a logarithmic demand function and a budget constraint for a two-tiered pricing scheme. We find the posterior distribution of the Equivalent Variation, and estimate the welfare implications in a context where electricity tariffs decreased by as much as 17.53%. We find that 10% of the poorest municipalities attained welfare gains above 2% of their initial income.