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Efficient Estimation of Data Combination Models by the Method of Auxiliary-to-Study Tilting (AST)

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  • Bryan S. Graham
  • Cristine Campos de Xavier Pinto
  • Daniel Egel

Abstract

We propose a locally efficient estimator for a class of semiparametric data combination problems. A leading estimand in this class is the Average Treatment Effect on the Treated (ATT). Data combination problems are related to, but distinct from, the class of missing data problems analyzed by Robins, Rotnitzky and Zhao (1994) (of which the Average Treatment Effect (ATE) estimand is a special case). Our estimator also possesses a double robustness property. Our procedure may be used to efficiently estimate, among other objects, the ATT, the two-sample instrumental variables model (TSIV), counterfactual distributions, poverty maps, and semiparametric difference-in-differences. In an empirical application we use our procedure to characterize residual Black-White wage inequality after flexibly controlling for 'pre-market' differences in measured cognitive achievement as in Neal and Johnson (1996).

Suggested Citation

  • Bryan S. Graham & Cristine Campos de Xavier Pinto & Daniel Egel, 2011. "Efficient Estimation of Data Combination Models by the Method of Auxiliary-to-Study Tilting (AST)," NBER Working Papers 16928, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:16928
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    References listed on IDEAS

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    1. Currie, Janet & Yelowitz, Aaron, 2000. "Are public housing projects good for kids?," Journal of Public Economics, Elsevier, vol. 75(1), pages 99-124, January.
    2. DiNardo, John & Fortin, Nicole M & Lemieux, Thomas, 1996. "Labor Market Institutions and the Distribution of Wages, 1973-1992: A Semiparametric Approach," Econometrica, Econometric Society, vol. 64(5), pages 1001-1044, September.
    3. Chris Elbers & Jean O. Lanjouw & Peter Lanjouw, 2003. "Micro--Level Estimation of Poverty and Inequality," Econometrica, Econometric Society, vol. 71(1), pages 355-364, January.
    4. Judith K. Hellerstein & Guido W. Imbens, 1999. "Imposing Moment Restrictions From Auxiliary Data By Weighting," The Review of Economics and Statistics, MIT Press, vol. 81(1), pages 1-14, February.
    5. Bryan S. Graham, 2011. "Efficiency Bounds for Missing Data Models With Semiparametric Restrictions," Econometrica, Econometric Society, vol. 79(2), pages 437-452, March.
    6. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2003. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometrica, Econometric Society, vol. 71(4), pages 1161-1189, July.
    7. Fortin, Nicole & Lemieux, Thomas & Firpo, Sergio, 2011. "Decomposition Methods in Economics," Handbook of Labor Economics, Elsevier.
    8. Bryan S. Graham & Cristine Campos De Xavier Pinto & Daniel Egel, 2012. "Inverse Probability Tilting for Moment Condition Models with Missing Data," Review of Economic Studies, Oxford University Press, vol. 79(3), pages 1053-1079.
    9. Barsky R. & Bound J. & Charles K.K. & Lupton J.P., 2002. "Accounting for the Black-White Wealth Gap: A Nonparametric Approach," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 663-673, September.
    10. Neal, Derek A & Johnson, William R, 1996. "The Role of Premarket Factors in Black-White Wage Differences," Journal of Political Economy, University of Chicago Press, vol. 104(5), pages 869-895, October.
    11. Keisuke Hirano & Guido W. Imbens & Geert Ridder & Donald B. Rubin, 2001. "Combining Panel Data Sets with Attrition and Refreshment Samples," Econometrica, Econometric Society, vol. 69(6), pages 1645-1659, November.
    12. Patrick Kline, 2011. "Oaxaca-Blinder as a Reweighting Estimator," American Economic Review, American Economic Association, vol. 101(3), pages 532-537, May.
    13. Alessandro Tarozzi & Angus Deaton, 2009. "Using Census and Survey Data to Estimate Poverty and Inequality for Small Areas," The Review of Economics and Statistics, MIT Press, vol. 91(4), pages 773-792, November.
    14. William A. Darity & Patrick L. Mason, 1998. "Evidence on Discrimination in Employment: Codes of Color, Codes of Gender," Journal of Economic Perspectives, American Economic Association, vol. 12(2), pages 63-90, Spring.
    15. Alberto Abadie & Guido W. Imbens, 2006. "Large Sample Properties of Matching Estimators for Average Treatment Effects," Econometrica, Econometric Society, vol. 74(1), pages 235-267, January.
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    Citations

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    Cited by:

    1. Bryan S. Graham & Guido Imbens & Geert Ridder, 2016. "Identification and efficiency bounds for the average match function under conditionally exogenous matching," CeMMAP working papers CWP10/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Huber, Martin & Lechner, Michael & Wunsch, Conny, 2013. "The performance of estimators based on the propensity score," Journal of Econometrics, Elsevier, vol. 175(1), pages 1-21.
    3. repec:eee:csdana:v:115:y:2017:i:c:p:91-102 is not listed on IDEAS
    4. Knaus, Michael C., 2018. "A Double Machine Learning Approach to Estimate the Effects of Musical Practice on Student's Skills," IZA Discussion Papers 11547, Institute for the Study of Labor (IZA).
    5. Frölich, Markus & Huber, Martin & Wiesenfarth, Manuel, 2017. "The finite sample performance of semi- and non-parametric estimators for treatment effects and policy evaluation," Computational Statistics & Data Analysis, Elsevier, vol. 115(C), pages 91-102.
    6. Susan Athey & Raj Chetty & Guido Imbens & Hyunseung Kang, 2016. "Estimating Treatment Effects using Multiple Surrogates: The Role of the Surrogate Score and the Surrogate Index," Papers 1603.09326, arXiv.org, revised Jun 2016.
    7. Nikolay Doudchenko & Guido W. Imbens, 2016. "Balancing, Regression, Difference-In-Differences and Synthetic Control Methods: A Synthesis," NBER Working Papers 22791, National Bureau of Economic Research, Inc.
    8. Toru Kitagawa & Chris Muris, 2013. "Covariate selection and model averaging in semiparametric estimation of treatment effects," CeMMAP working papers CWP61/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    9. Susan Athey & Guido W. Imbens & Stefan Wager, 2016. "Approximate Residual Balancing: De-Biased Inference of Average Treatment Effects in High Dimensions," Papers 1604.07125, arXiv.org, revised Jan 2018.
    10. Susan Athey & Guido Imbens, 2016. "The State of Applied Econometrics - Causality and Policy Evaluation," Papers 1607.00699, arXiv.org.
    11. repec:aea:jecper:v:31:y:2017:i:2:p:3-32 is not listed on IDEAS
    12. Susan Athey & Guido Imbens & Thai Pham & Stefan Wager, 2017. "Estimating Average Treatment Effects: Supplementary Analyses and Remaining Challenges," Papers 1702.01250, arXiv.org.

    More about this item

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • J31 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - Wage Level and Structure; Wage Differentials
    • J7 - Labor and Demographic Economics - - Labor Discrimination

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