EFFICIENT ESTIMATION OF SEMIPARAMETRIC MODELS BY SMOOTHED MAXIMUM LIKELIHOOD∗

A smoothed likelihood function is used to construct efficient estimators for some semiparametric models that contain unknown density functions together with parametric index functions. Smoothing the likelihood makes maximization with respect to the unknown density functions more tractable. The method is used to show the efficiency gains from knowledge of population shares in three cases: (1) binary choice; (2) binary choice when only one outcome is sampled, supplemented by random sampling of the explanatory variables; and (3) linear regression, where the shares are defined by a threshold value of the dependent variable. Semiparametric efficiency is achieved both for parametric components and for a class of functionals of the error density.