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Robust Inference for the Two-Sample 2SLS Estimator

Author

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  • David Pacini
  • Frank Windmeijer

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.

Suggested Citation

  • David Pacini & Frank Windmeijer, 2016. "Robust Inference for the Two-Sample 2SLS Estimator," Bristol Economics Discussion Papers 16/676, School of Economics, University of Bristol, UK.
  • Handle: RePEc:bri:uobdis:16/676
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    1. Gerard J. van den Berg & Pia R. Pinger & Johannes Schoch, 2016. "Instrumental Variable Estimation of the Causal Effect of Hunger Early in Life on Health Later in Life," Economic Journal, Royal Economic Society, vol. 126(591), pages 465-506, March.
    2. Joshua D. Angrist & Jörn-Steffen Pischke, 2009. "Mostly Harmless Econometrics: An Empiricist's Companion," Economics Books, Princeton University Press, edition 1, number 8769.
    3. Joshua D. Angrist & Alan B. Krueger, 1993. "Split Sample Instrumental Variables," Working Papers 699, Princeton University, Department of Economics, Industrial Relations Section..
    4. Klevmarken, Anders, 1982. "Missing Variables and Two-Stage Least-Squares Estimation from More than One Data Set," Working Paper Series 62, Research Institute of Industrial Economics.
    5. Atsushi Inoue & Gary Solon, 2010. "Two-Sample Instrumental Variables Estimators," The Review of Economics and Statistics, MIT Press, vol. 92(3), pages 557-561, August.
    6. Thomas S. Dee & William N. Evans, 2003. "Teen Drinking and Educational Attainment: Evidence from Two-Sample Instrumental Variables Estimates," Journal of Labor Economics, University of Chicago Press, vol. 21(1), pages 178-209, January.
    7. Ridder, Geert & Moffitt, Robert, 2007. "The Econometrics of Data Combination," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 75, Elsevier.
    8. Newey, Whitney K., 1984. "A method of moments interpretation of sequential estimators," Economics Letters, Elsevier, vol. 14(2-3), pages 201-206.
    9. Angrist, Joshua D & Krueger, Alan B, 1995. "Split-Sample Instrumental Variables Estimates of the Return to Schooling," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(2), pages 225-235, April.
    10. Manuel Arellano & Costas Meghir, 1992. "Female Labour Supply and On-the-Job Search: An Empirical Model Estimated Using Complementary Data Sets," Review of Economic Studies, Oxford University Press, vol. 59(3), pages 537-559.
    11. repec:ieb:wpaper:2013/6/doc2014-35 is not listed on IDEAS
    12. John Jerrim & Álvaro Choi & Rosa Simancas Rodríguez, 2014. "Two-sample two-stage least squares (TSTSLS) estimates of earnings mobility: how consistent are they?," Working Papers 2014/35, Institut d'Economia de Barcelona (IEB).
    13. John Jerrim & Alvaro Choi & Rosa Simancas Rodriguez, 2014. "Two-Sample Two-Stage Least Squares (TSTSLS) estimates of earnings mobility: how consistent are they?," DoQSS Working Papers 14-17, Quantitative Social Science - UCL Social Research Institute, University College London.
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    More about this item

    Keywords

    Linear Model; Data Combination; Instrumental Variables; Robust Inference; Nonlinear GMM.;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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