Misspecification and Conditional Maximum Likelihood Estimation

Recently White (1982) studied the properties of Maximum Likelihood estimation of possibly misspecified models. The present paper extends Andersen (1970) results on Conditional Maximum Likelihood estimators (CMLE) to such a situation. In particular, the asymptotic properties of CMLE's are derived under correct and incorrect specification of the conditional model. Robustness of conditional inferences and estimation with respect to misspecification of the model for the conditioning variables is emphasized. Conditions for asymptotic efficiency of CMLE's are obtained, and specification tests a la Hausman (1978) and White (1982) are derived. Examples are also given to illustrate the use of CMLE's properties. These examples include the simple linear model, the multinomial logit model, the simple Tobit model, and the multivariate logit model.