Two-Stage Conditional Maximum Likelihood Estimation of Econometric Models

Recent works on Maximum Likelihood (ML) estimation have focused on the behavior of the ML estimator when the model is possibly misspecified [Gourieroux, Monfort and Trognon (1984), Vuong (1983), White (1982, 1983a, b)]. This paper studies a general method, called two-stage conditional maximum likelihood (2SCML) estimation, for generating consistent estimates. In particular, asymptotic properties of 2SCML estimators are derived under correct and incorrect specification of the statistical model. Necessary and sufficient conditions for asymptotic efficiency of 2SCML estimators for all or some of the parameters are obtained. It is also argued that 2SCML estimators can readily be used to construct tests for exogeneity and model misspecification of the Hausman (1978) and White (1982) type. Examples are given to illustrate the applicability of the method. These include the linear simultaneous equation model, the simultaneous probit model and the simple Tobit model.