Stochastic search selection for heterogeneous panel data models

This article presents a method for selecting variables and determining parameter heterogeneity in Bayesian hierarchical panel data models. Mixture distributions are used as priors for the mean and the variance of the individuals’ parameters. Selection indicators determine the best-fitting component of each mixture distribution and indicate whether the mean parameter is non zero and whether the parameters are heterogeneous. The method is applied to two panel data sets. The first is on inflation of US CPI sub-indices, and the results suggest that a heterogeneous panel AR model with a lagged, first principal component is the preferred model. A second application to house price inflation across US metropolitan statistical areas shows that the model includes either the autoregressive component or the lagged spatial components, but not both at the same time.