A parametric control function approach to estimating the returns to schooling in the absence of exclusion restrictions: an application to the NLSY

An innovation which bypasses the need for instruments when estimating endogenous treatment effects is identification via conditional second moments. The most general of these approaches is Klein and Vella (J Econom 154:154-164, 2010), which models the conditional variances semiparametrically. While this is attractive, as identification is not reliant on parametric assumptions for variances, the nonparametric aspect of the estimation may discourage practitioners from its use. This paper outlines how the estimator can be implemented parametrically. The use of parametric assumptions is accompanied by a large reduction in computational and programming demands. We illustrate the approach by estimating the return to education using a sample drawn from the National Longitudinal Survey of Youth 1979. Accounting for endogeneity increases the estimate of the return to education from 6.8 to 11.2%.