A Hierarchical Non-Parametric Mixture Model to Detect Heterogeneity in Preferences for Redistribution
Abstract: This paper proposes a hierarchical semi-parametric Bayesian model that generalizes Generalized Linear Models (GLM) and Generalized Linear Mixed Models (GLMM). It generalizes GLMs and GLMMs in the sense that it can be used whenever using GLM or GLMM is justifiable, either in the context of observational or experimental studies. However, whenever GLM/GLMM are not appropriate because there might be heterogeneity in the effect of the covariates/treatment due to latent or unobserved variables, the proposed model can be used to estimate clusters in the population based on those latent factors. Additionally, the hierarchical structure of the model allows us to investigate if the latent heterogeneity is a function of context-level features. A Gibbs sampler is derived for cases with continuous outcome variable, and a Riemannian Manifold Hamiltonian Monte Carlo within a Blocked Gibbs sampler algorithm is proposed for cases in which the outcome is binary or discrete. A Monte Carlo exercise is conducted and shows, first, that the proposed model and MCMC estimation have good coverage and recover the true value of the linear coefficients when the assumptions underlying the use of GLM or GLMM holds. So, it can be used to estimate the linear coefficients whenever using GLM or GLMM is justifiable. Second, when there is latent heterogeneity in the data and GLM/GLMM are not appropriate, the MC simulations show that the proposed model can be used and estimates the correct clusters of linear coefficients with good coverage. The model is then applied to a real data sets to investigate latent heterogeneity in support for redistributive policies. There are a variety of political economy models designed to explain voters' support for redistribution. The model is applied is to investigate if there are latent sub-populations containing different types of voters for which different behavioral models seem to be adequate. In other words, the proposed model allows us to investigate empirically if there is heterogeneity in the population in terms of how voters' socio-economic characteristics are associated with their support for redistributive policies, and therefore estimate the number and characteristics of types of voters. The hierarchical structure of the model allows the estimation of how country-level features are associated with the number and characteristics of types of voters.
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