Dynamic Panel Probit with Flexible Correlated Effects

In this paper, we analyze a dynamic panel probit model with two flexible latent effects: first, unobserved individual heterogeneity that is allowed to vary in the population according to an assumption-free nonparametric distribution, and second, with a latent serially correlated common error component. In doing so, we extend the approach developed in Albert and Chib (1993), Albert and Chib (1996), and Chib and Carlin (1999) by releasing restrictive parametric assumptions on the latent individual effect and eliminating potential spurious state dependence with latent time effects. Due to a data augmentation strategy, virtually all model parameters are sampled directly without resorting to Metropolis-Hastings steps that would require additional tuning. The estimation problem is re-cast in the form of an iterative scheme of latent regressions whereby the latent utility is explicitly sampled along with other model parameters. This feature avoids the curse of dimensionality arising in likelihoods specified as high-dimensional integrals. We show in simulations that capturing nonparametrically unobserved heterogeneity of irregular form greatly reduces the bias of estimated average partial effects relative to the random effects probit model. Moreover, the bias reduction is achieved even when the unobserved individual effects are correlated with the observed regressors. We apply our method to the estimation of a patent equation on firm level data. We find statistically significant technology spillover effects as well as clusters in unobserved firm level heterogeneity. JEL: C11, C13, C15, C23, C25