Two-Sample Instrumental Variables Estimators

Following an influential article by Angrist and Krueger (1992) on two-sample instrumental variables (TSIV) estimation, numerous empirical researchers have applied a computationally convenient two-sample two-stage least squares (TS2SLS) variant of Angrist and Krueger's estimator. In the two-sample context, unlike the single-sample situation, the IV and 2SLS estimators are numerically distinct. We derive and compare the asymptotic distributions of the two estimators and find that the commonly used TS2SLS estimator is more asymptotically efficient than the TSIV estimator. We also resolve some confusion in the literature about how to estimate standard errors for the TS2SLS estimator.