Robust Priors in Nonlinear Panel Data Models

Abstract

Many approaches to estimation of panel models are based on an average or integ-rated likelihood that assigns weights to different values of the individual effects. Fixed effects, random effects, and Bayesian approaches all fall in this category. We provide a characterization of the class of weights (or priors) that produce estimators that are first-order unbiased. We show that such bias reducing weights will depend on the data in general unless an orthogonal reparameterization or an essentially equivalent condi-tion is available. Two intuitively appealing weighting schemes are discussed. We argue that asymptotically valid confidence intervals can be read from the posterior distribu-tion of the common parameters when N and T grow at the same rate. Next, we show that random effects estimators are not bias reducing in general and discuss important exceptions. Moreover, the bias depends on the Kullback-Leibler distance between the population distribution of the effects and its best approximation in the random effects family. Finally, we show that in general standard random effects estimation of marginal effects is inconsistent for large T, whereas the posterior mean of the marginal effect is large-T consistent, and we provide conditions for bias reduction. Three examples and some Monte Carlo experiments illustrate the results. JEL code: C23.