Flexible Correlated Random Effects Estimation in Panel Models with Unobserved Heterogeneity

In this paper, we consider identification in a correlated random effects model for panel data. We assume that the likelihood for each individual in the panel is known up to a finite dimensional common parameter and an individual specific parameter. We allow the distribution of unobserved individual specific effects to depend on observed explanatory variables and make no assumptions about the particular functional form of this dependence. This leads to a semiparametric problem where the parameters include a finite dimensional common parameter, θ and an infinite dimensional conditional density, q, that describes the distribution of unobserved individual specific effects. For a given likelihood, we establish restrictions on the space of functions H for the distribution of unobserved heterogeneity under which {θ, q} are identified. We show the model parameters may be consistently estimated by sieve maximum likelihood for a fixed panel length, T. The conditions on H, which include assumptions about the support of explanatory variables and smoothness of q in its arguments, are relatively mild and are similar to those required for nonparametric density estimation.