Bayesian Analysis of a Probit Panel Data Model with Unobserved Individual Heterogeneity and Autocorrelated Errors

In this paper, we perform Bayesian analysis of a panel probit model with unobserved individual heterogeneity and serially correlated errors. We augment the data with latent variables and sample the unobserved heterogeneity component as one Gibbs block per individual using a flexible piecewise linear approximation to the marginal posterior density. The latent time effects are simulated as another Gibbs block. For this purpose we develop a new user-friendly form of the Efficient Importance Sampling proposal density for an Acceptance-Rejection Metropolis-Hastings step. We apply our method to the analysis of product innovation activity of a panel of German manufacturing firms in response to imports, foreign direct investment and other control variables. The dataset used here was analyzed under more restrictive assumptions by Bertschek and Lechner (1998) and Greene (2004). Although our results differ to a certain degree from these benchmark studies, we confirm the positive effect of imports and FDI on firms' innovation activity. Moreover, unobserved firm heterogeneity is shown to play a far more significant role in the application than the latent time effects.