Semiparametric estimation of Nelson–Olson simultaneous Tobit model

Abstract

In this article we study the semiparametric estimation of the Tobit model simultaneously jointed with an endogenous regressor. The model usually is estimated by maximum likelihood method and two-stage estimation under the normality assumption of the error terms. The possible misspecification motivates our semiparametric study. We first construct a semiparametric estimator for the parameters in the reduced form equations and prove its consistency and asymptotical normality. Then the parameters in the structural models are recovered by system minimum distance estimator. The simulation shows that our estimator performs well in different designs in finite samples. Finally, an empirical application is given to show the usefulness of the estimator.