Instrumental variable estimation in a probit measurement error model

Probit regression is studied when normally distributed covariates are subject to normally distributed measurement errors. Under the assumption that surrogate instrumental variables are available, the parameters in the probit model are shown to be identified. The maximum likelihood estimator and an easily computed two-stage estimator are derived and studied. The two-stage estimator is shown to be asymptotically efficient. Simulation results complement the theory and provide evidence of robustness to the normality assumptions.