Estimation of Dynamic Nonlinear Random Effects Models with Unbalanced Panels

This paper presents and evaluates estimation methods for dynamic non-linear models with correlated random effects (CRE) when we have unbalanced panels. Accounting for the unbalancedness is crucial in dynamic non-linear models and ignoring it produces inconsistent estimates of the parameters even if the process that drives it 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. In this paper we allow the sample selection process that determines the unbalancedness structure of the data to be arbitrarily 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 our proposed estimation approaches perform better both in terms of bias and RMSE than the approaches that ignore the unbalancedness or that balance the sample.