Model selection in the presence of incidental parameters

This paper considers model selection in panels where incidental parameters are present. Primary interest centers on selecting a model that best approximates the underlying structure involving parameters that are common within the panel. It is well known that conventional model selection procedures are often inconsistent in panel models and this can be so even without nuisance parameters. Modifications are then needed to achieve consistency. New model selection information criteria are developed here that use either the Kullback-Leibler information criterion based on the profile likelihood or the Bayes factor based on the integrated likelihood with a bias-reducing prior. These model selection criteria impose heavier penalties than those associated with standard information criteria such as AIC and BIC. The additional penalty, which is data-dependent, properly reflects the model complexity arising from the presence of incidental parameters. A particular example is studied in detail involving lag order selection in dynamic panel models with fixed effects. The new criteria are shown to control for over/under-selection probabilities in these models and lead to consistent order selection criteria.