RECENTERED AND RESCALED INSTRUMENTAL VARIABLE ESTIMATION OF TOBIT AND PROBIT MODELS WITH ERRORS IN VARIABLES

Abstract

Since Durbin (1954) and Sargan (1958), instrumental variable (IV) method has long been one of the most popular procedures among economists and other social scientists to handle linear models with errors-in-variables. A direct application of this method to nonlinear errors-in-variables models, however, fails to yield consistent estimators.

This article restricts attention to Tobit and Probit models and shows that simple recentering and rescaling of the observed dependent variable may restore consistency of the standard IV estimator if the true dependent variable and the IV's are jointly normally distributed. Although the required condition seems rarely to be satisfied by real data, our Monte Carlo experiment suggests that the proposed estimator may be quite robust to the possible deviation from normality.

Keywords:

• Instrumental variables
• GMM estimator
• Nonlinear errors in variables
• Elliptically symmetric distribution

ACKNOWLEDGMENTS

I would like to thank an anonymous referee, De-Min Wu and Joe Sicilian for their helpful comments and Yi Geng for his excellent computational assistance.