Elsevier

Economics Letters

Volume 146, September 2016, Pages 50-54
Economics Letters

Robust inference for the Two-Sample 2SLS estimator

https://doi.org/10.1016/j.econlet.2016.06.033Get rights and content
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Highlights

  • We derive the variance of the TS2SLS estimator under heteroscedasticity.

  • We propose a new robust variance estimator.

  • We provide Stata code for the TS2SLS estimator and its robust variance estimator.

  • We provide Stata code for an asymptotically equivalent nonlinear GMM estimator.

Abstract

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.

JEL classification

C12
C13
C26

Keywords

Linear model
Data combination
Instrumental variables
Robust inference
Nonlinear GMM

Cited by (0)

We would like to thank Helmut Farbmacher, Tom Palmer, Mark Schaffer, Jon Temple, Kate Tilling and the editor, Costas Meghir, for helpful comments. Windmeijer acknowledges funding by the Medical Research Council, grant no. MC_UU_12013/9.