Model Selection in the Presence of Incidental Parameters

This paper considers model selection of nonlinear panel data models in the presence of incidental parameters. The main interest is in selecting the model that approximates best the structure with the common parameters after concentrating out the incidental parameters. New model selection information criteria are developed, either using the Kullback-Leibler information criterion based on the profile likelihood or using the Bayes factor based on the integrated likelihood with robust priors. These model selection criteria impose heavier penalties than those of the standard information criteria such as AIC and BIC. The additional penalty, which is data-dependent, properly reflects the model complexity from the incidental parameters. As a particular example, a lag order selection criterion is examined in the context of dynamic panel models with fixed individual effects, and it is illustrated how the over/under selection probabilities are controlled for.