Robustness against priors and mixing distributions

Neyman and Scott define the incidental-parameter problem. In panel data with $T$ observations per individual, the estimator of the common parameter is usually constistent with O(1/T). This paper shows that the integrated likelihood estimator becomes consistent with O(1/T^2) if an information-orthogonal likelihood is used. Information-orthogonal likelihoods for the general linear model are derived along with an index model with weakly exogenous variables. An approximate solution for the incidental-parameter problem for a wide range of models is given. The paper further argues that reparametrizations are easier in a Bayesian framework. An example shows how to use the O(1/T^2) result to increase robustness against choosing the mixing distribution. Likelihood methods that use sufficient statistics for the individual effects are seen to be a special case of the integrated-likelihood estimator.