Estimating linear regressions with mismeasured, possibly endogenous, binary explanatory variables

This paper is concerned with mismeasured binary explanatory variables in a linear regression. Modification of a technique in Hausman et al. (J. Econometrics 87 (1998) 239) allows simple computation of bounds under relatively weak assumptions. When one has instruments, we show how to obtain consistent parameter estimates using GMM. We show how to incorporate the estimated measurement error bounds into the GMM estimates, and we develop a specification test based on the compatibility of the GMM estimates with the measurement error bounds. When the mismeasured variable is endogenous, the IV estimate and the measurement error bounds can be used to bound its coefficient.