Robust inference for the Two-Sample 2SLS estimator
推导了异方差下两样本两阶段最小二乘估计量的渐近方差公式，并给出稳健方差估计量，附Stata代码和蒙特卡洛结果，适用于变量在不同数据集中未完全联合观测的情形。
The Two-Sample Two-Stage Least Squares (TS2SLS) data combination estimator is a popular estimator for the parameters in linear models when not all variables are observed jointly in one single data set. Although the limiting normal distribution has been established, the asymptotic variance formula has only been stated explicitly in the literature for the case of conditional homoskedasticity. By using the fact that the TS2SLS estimator is a function of reduced form and first-stage OLS estimators, we derive the variance of the limiting normal distribution under conditional heteroskedasticity. A robust variance estimator is obtained, which generalises to cases with more general patterns of variable (non-)availability. Stata code and some Monte Carlo results are provided in an Appendix. Stata code for a nonlinear GMM estimator that is identical to the TS2SLS estimator in just identified models and asymptotically equivalent to the TS2SLS estimator in overidentified models is also provided there.