Efficient Monte Carlo Likelihood Analysis of Panel Data Models with Unobserved Heterogeneity in Time and across Individual Units

Unobserved random heterogeneity plays a central role in many socio-economic studies based upon panel data. When jointly present across individual units and over time its treatment requires (very) high-dimensional integrations which are analytically intractable in non-linear models and, therefore, have to be estimated by Monte Carlo simulation techniques. Existing procedures, essentially Methods of Simulated Moments and Scores (MSM, MSS) are somewhat limited in scope and, moreover, being based upon joint simulation of the unobservables and observables, do not allow for ex-post estimation of the heterogeneity components themselves, a key component of the validation of any empirical panel data models. In the present contribution I demonstrate how to apply Efficient Importance Sampling (EIS) to a high-dimensional logit model with unobserved heterogeneity along both dimensions to compute numerically accurate ML estimators as well as likelihood based test statistics. Most importantly I also provide estimates for the posterior expectations of the heterogeneity components themselves and discuss how these estimates can be used for (mis)specification analysis. I also discuss a number of important numerical issues in relation with the development of numerically robust and users-friendly computer programs for these procedures. Extensions to a broad range of non- linear panel data models with unobserved heterogeneity are also discussed. Last but not least real-life applications in progress will be used to illustrate the performance of these programs.