Estimation of Dynamic Nonlinear Random Effects Models with Unbalanced Panels

Abstract

This paper presents estimation methods for dynamic nonlinear models with correlated random effects (CRE) when having unbalanced panels. Unbalancedness is often encountered in applied work and ignoring it in dynamic nonlinear models produces inconsistent estimates even if the unbalancedness process is completely at random. We show that selecting a balanced panel from the sample can produce efficiency losses or even inconsistent estimates of the average marginal effects. We allow the process that determines the unbalancedness structure of the data to be correlated with the permanent unobserved heterogeneity. We discuss how to address the estimation by maximizing the likelihood function for the whole sample and also propose a Minimum Distance approach, which is computationally simpler and asymptotically equivalent to the Maximum Likelihood estimation. Our Monte Carlo experiments and empirical illustration show that the issue is relevant. Our proposed solutions perform better both in terms of bias and RMSE than the approaches that ignore the unbalancedness or that balance the sample.