Control variables approach to estimate semiparametric models of mismeasured endogenous regressors with an application to U.K. twin data

We study the identification and estimation of semiparametric models with mismeasured endogenous regressors using control variables that ensure the conditional covariance restriction on endogenous regressors and unobserved causes. We provide a set of sufficient conditions for identification, which control for both endogeneity and measurement error. We propose a sieve-based estimator and derive its asymptotic properties. Given the sieve approximation, our proposed estimator is easy to implement as weighted least squares. Monte Carlo simulations illustrate that our proposed estimator performs well in the finite samples. In an empirical application, we estimate the return to education on earnings using U.K. twin data, in which self-reported education is potentially measured with error and is also correlated with unobserved factors. Our approach utilizes the twin’s reported education as a control variable to obtain consistent estimates. We find that a one-year increase in education leads to an 11% increase in hourly wage. The estimate is significantly higher than those from OLS and IV approaches which are potentially biased. The application underscores that our proposed estimator is useful to correct for both endogeneity and measurement error in estimating returns to education.