Stein-type control function maximum likelihood estimator for the probit model in the presence of endogeneity

Abstract

A Stein-type control function maximum likelihood (CFML) estimator is suggested for the probit model in the presence of endogeneity. This novel estimator combines the probit maximum likelihood and CFML estimators. The asymptotic distribution and risk function for the new estimator is derived. It is demonstrated that, subject to certain conditions of the shrinkage parameter, the asymptotic risk of the new estimator is strictly smaller than the risk of the CFML. Monte Carlo simulations illustrate the method's superiority in finite samples. The method is also applied to analyze the impact of managerial incentives on the use of foreign-exchange derivatives.