Estimation of Dynamic Nonlinear Random Effects Models with Unbalanced Panels

This paper presents and evaluates estimation methods for dynamic nonlinear correlated random effects (CRE) models with unbalanced panels. Accounting for the unbalancedness is crucial in dynamic non-linear models and it cannot be ignored even if the process that produces it is completely at random. Available approaches to estimate dynamic CRE models accounting for the initial conditions problem were developed for balanced panels and they do not work with unbalanced panels. In this type of dynamic models, just ignoring the unbalancedness produces inconsistent estimates of the parameters. Another potential "solution", used by some practitioners, is to take the sub-sample that constitutes a balanced panel and then to estimate the model using the available methods. Nonetheless, this approach is not feasible in some cases because the constructed balanced panel might not contain enough number of common periods across individuals. Moreover, when feasible, it discards useful information, which, as we show, leads to important efficiency losses. In this paper we consider several scenarios in which the sample selection process can be arbitrarily correlated with the permanent unobserved heterogeneity. The approaches we propose exploit all the observations available, can be implemented using standard solutions to the initial conditions problem, and can be easily applied in the context of commonly used models, such as dynamic binary choice models.The authors gratefully acknowledge research funding from the Spanish Ministry of Education, Grants ECO2009-11165 and ECO2012-31358