Efficient kernel-based semiparametric Ⅳ estimation with an application to resolving a puzzle on the estimates of the return to schooling

摘要

An interesting puzzle in estimating the effect of education on labor market earnings (Card in Econometrica 69:1127-1160, 2001) is that the 2SLS estimate for the return to schooling typically exceeds the OLS estimate, but the 2SLS estimate is fairly imprecise. We provide a new explanation that it could be due to the restrictive linear functional form specification on the covariates and the reduced form. For the parameters of endogenous regressors, we propose two kernel-based semiparametric Ⅳ estimators that relax the tight functional form assumption on the covariates and the reduced form. They have explicit algebraic structures and are easily implemented without numerical optimizations. We show that they are consistent, asymptotically normally distributed, and reach the semiparametric efficiency bound. A Monte Carlo study demonstrates that our estimators perform well in finite samples. We apply the proposed estimators to estimate the return to schooling in Card (Aspects of labour market behavior: essays in honour of John Vanderkamp. University of Toronto Press, Toronto, pp. 201-222, 1995). We find that the semiparametric estimates of the return to schooling are much smaller and more precise than the 2SLS estimate, and the difference largely comes from the misspecification in the linear reduced form.