Two-stage regression without exclusion restrictions

Klein and Vella (2010) propose an estimator to fit a triangular system of two simultaneous linear equations with a single endogenous regressor. Models of this form are generally analyzed with two-stage least squares or IV methods, which require one or more exclusion restriction. In practice, the assumptions required to construct valid instruments are frequently difficult to justify. The KV estimator does not require an exclusion restriction; the same set of independent variables may appear in both equations. To account for endogeneity, the estimator constructs a control function using information from the conditional distribution of the error terms. Conditional variance functions are estimated semiparametrically, so distributional assumptions are minimized. I will present my Stata implementation of the semiparametric control function estimator, kvreg, and discuss the assumptions that must hold for consistent estimation. The kvreg estimator contains an undocumented implementation of Ichimura’s (1993) semiparametric least squares estimator, which I plan to fill-out into a stand-alone command.