Orthogonal parameters and panel data

Abstract

This paper describes a class of consistent estimators for short panels with fixed effects. The method is to find an orthogonal reparametrization of the fixed effects and then to integrate the new effects from the likelihood with respect to an appropriately chosen prior density. The resulting marginal posterior densities of the common parameters have modes that are shown to be consistent in the models examined here. The main result concerns the first-order autoregressive model with agent specific intercepts where the likelihood is conditional on the set of initial observations. This paper provides a consistent likelihood- based estimator for this model. Some numerical illustrations are given. The first-order conditions for the posterior mode can also be thought of as new moment conditions for GMM estimation.