Semiparametric Bayesian Inference in Autoregressive Panel Data Models

Abstract

This paper develops semiparametric Bayesian methods for inference in dynamic linear panel data models, and applies them to longitudinal data on labor earnings from the Panel Study of Income Dynamics. We focus on characterizing not only parameters related to conditional means and variances, but the entire joint distribution of earnings. Full distributional inference in semiparametric panel data models must solve a nonparametric deconvolution problem arising from the existence of unobserved additive individual-specific terms. A computational Bayesian approach based on variable augmentation can deal with such latent-variable models effectively, and can allow considerable flexibility in distributional assumptions. We use relatively simple, low-order linear models with individual heterogeneity, but estimate the distribution of the disturbances without requiring that it belong to a restrictive parametric class, such as the class of normal distributions. A prior distribution on the space of probability distributions is used to impose smoothness on an otherwise general specification for the disturbance terms. This nonparametric prior is constructed using a countable mixture of normals representation, where the mixing distribution is given a Dirichlet process prior.