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Model averaging in semiparametric estimation of treatment effects

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  • Kitagawa, Toru
  • Muris, Chris

Abstract

Choosing the covariates and functional form of the propensity score is an important choice for estimating treatment effects. This paper proposes a data-driven way of averaging the estimators over candidate specifications to resolve the specification uncertainty in the propensity score weighting estimation of the ATT. The proposed procedures minimize the estimated MSE of the ATT estimator in a local asymptotic framework. We formulate model averaging as a statistical decision problem in a limit experiment, and derive an averaging scheme that is Bayes optimal with respect to a given prior. The averaging estimator outperforms selection estimators and the estimators in any of the candidate models in terms of Bayes asymptotic MSE. Our Monte Carlo studies illustrate the size of the MSE gains. We apply the averaging procedure to evaluate the effect of a labor market program.

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  • Kitagawa, Toru & Muris, Chris, 2016. "Model averaging in semiparametric estimation of treatment effects," Journal of Econometrics, Elsevier, vol. 193(1), pages 271-289.
    • Handle: RePEc:eee:econom:v:193:y:2016:i:1:p:271-289
    DOI: 10.1016/j.jeconom.2016.03.002
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    1. Song, Kyungchul, 2014. "Point Decisions For Interval–Identified Parameters," Econometric Theory, Cambridge University Press, vol. 30(2), pages 334-356, April.
    2. Richard K. Crump & V. Joseph Hotz & Guido W. Imbens & Oscar A. Mitnik, 2009. "Dealing with limited overlap in estimation of average treatment effects," Biometrika, Biometrika Trust, vol. 96(1), pages 187-199.
    3. LaLonde, Robert J, 1986. "Evaluating the Econometric Evaluations of Training Programs with Experimental Data," American Economic Review, American Economic Association, vol. 76(4), pages 604-620, September.
    4. Keisuke Hirano & Jack R. Porter, 2009. "Asymptotics for Statistical Treatment Rules," Econometrica, Econometric Society, vol. 77(5), pages 1683-1701, September.
    5. Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2011. "Inference on Treatment Effects After Selection Amongst High-Dimensional Controls," Papers 1201.0224, arXiv.org, revised May 2012.
    6. Matias Busso & John DiNardo & Justin McCrary, 2014. "New Evidence on the Finite Sample Properties of Propensity Score Reweighting and Matching Estimators," The Review of Economics and Statistics, MIT Press, vol. 96(5), pages 885-897, December.
    7. Hansen, Bruce E., 2005. "Challenges For Econometric Model Selection," Econometric Theory, Cambridge University Press, vol. 21(1), pages 60-68, February.
    8. 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.
    9. Hansen, Bruce E., 2016. "Efficient shrinkage in parametric models," Journal of Econometrics, Elsevier, vol. 190(1), pages 115-132.
    10. Shakeeb Khan & Elie Tamer, 2010. "Irregular Identification, Support Conditions, and Inverse Weight Estimation," Econometrica, Econometric Society, vol. 78(6), pages 2021-2042, November.
    11. Farrell, Max H., 2015. "Robust inference on average treatment effects with possibly more covariates than observations," Journal of Econometrics, Elsevier, vol. 189(1), pages 1-23.
    12. Bryan S. Graham & Cristine Campos de Xavier Pinto & Daniel Egel, 2016. "Efficient Estimation of Data Combination Models by the Method of Auxiliary-to-Study Tilting (AST)," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(2), pages 288-301, April.
    13. Bryan S. Graham & Cristine Campos De Xavier Pinto & Daniel Egel, 2012. "Inverse Probability Tilting for Moment Condition Models with Missing Data," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 79(3), pages 1053-1079.
    14. Guido W. Imbens & Whitney Newey & Geert Ridder, 2005. "Mean-square-error Calculations for Average Treatment Effects," IEPR Working Papers 05.34, Institute of Economic Policy Research (IEPR).
    15. Gerda Claeskens & Raymond J. Carroll, 2007. "An asymptotic theory for model selection inference in general semiparametric problems," Biometrika, Biometrika Trust, vol. 94(2), pages 249-265.
    16. Millimet, Daniel L. & Tchernis, Rusty, 2009. "On the Specification of Propensity Scores, With Applications to the Analysis of Trade Policies," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(3), pages 397-415.
    17. Naoya Sueishi, 2013. "Generalized Empirical Likelihood-Based Focused Information Criterion and Model Averaging," Econometrics, MDPI, vol. 1(2), pages 1-16, July.
    18. Hidehiko Ichimura & Oliver Linton, 2001. "Asymptotic expansions for some semiparametric program evaluation estimators," CeMMAP working papers 04/01, Institute for Fiscal Studies.
    19. Carrasco, Marine & Florens, Jean-Pierre & Renault, Eric, 2007. "Linear Inverse Problems in Structural Econometrics Estimation Based on Spectral Decomposition and Regularization," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 77, Elsevier.
    20. Jinyong Hahn, 1998. "On the Role of the Propensity Score in Efficient Semiparametric Estimation of Average Treatment Effects," Econometrica, Econometric Society, vol. 66(2), pages 315-332, March.
    21. Qingfeng Liu & Ryo Okui, 2013. "Heteroscedasticity‐robust C(p) model averaging," Econometrics Journal, Royal Economic Society, vol. 16(3), pages 463-472, October.
    22. Bruce E. Hansen, 2014. "Model averaging, asymptotic risk, and regressor groups," Quantitative Economics, Econometric Society, vol. 5(3), pages 495-530, November.
    23. Liu, Chu-An, 2015. "Distribution theory of the least squares averaging estimator," Journal of Econometrics, Elsevier, vol. 186(1), pages 142-159.
    24. Guido W. Imbens, 2004. "Nonparametric Estimation of Average Treatment Effects Under Exogeneity: A Review," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 4-29, February.
    25. Francis DiTraglia, 2011. "Using Invalid Instruments on Purpose: Focused Moment Selection and Averaging for GMM, Second Version," PIER Working Paper Archive 15-027, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 10 Aug 2015.
    26. DiTraglia, Francis J., 2016. "Using invalid instruments on purpose: Focused moment selection and averaging for GMM," Journal of Econometrics, Elsevier, vol. 195(2), pages 187-208.
    27. Magnus, Jan R. & Powell, Owen & Prüfer, Patricia, 2010. "A comparison of two model averaging techniques with an application to growth empirics," Journal of Econometrics, Elsevier, vol. 154(2), pages 139-153, February.
    28. Jinyong Hahn, 2004. "Functional Restriction and Efficiency in Causal Inference," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 73-76, February.
    29. Wan, Alan T.K. & Zhang, Xinyu & Zou, Guohua, 2010. "Least squares model averaging by Mallows criterion," Journal of Econometrics, Elsevier, vol. 156(2), pages 277-283, June.
    30. Claeskens,Gerda & Hjort,Nils Lid, 2008. "Model Selection and Model Averaging," Cambridge Books, Cambridge University Press, number 9780521852258, September.
    31. Hansen, Bruce E. & Racine, Jeffrey S., 2012. "Jackknife model averaging," Journal of Econometrics, Elsevier, vol. 167(1), pages 38-46.
    32. Xu Cheng & Zhipeng Liao & Ruoyao Shi, 2013. "Uniform Asymptotic Risk of Averaging GMM Estimator Robust to Misspecification, Second Version," PIER Working Paper Archive 15-017, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 25 Mar 2015.
    33. James J. Heckman & Hidehiko Ichimura & Petra Todd, 1998. "Matching As An Econometric Evaluation Estimator," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(2), pages 261-294.
    34. Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2013. "Supplementary Appendix for "Inference on Treatment Effects After Selection Amongst High-Dimensional Controls"," Papers 1305.6099, arXiv.org, revised Jun 2013.
    35. Xun Lu, 2015. "A Covariate Selection Criterion for Estimation of Treatment Effects," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(4), pages 506-522, October.
    36. 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.
    37. Bruce E. Hansen, 2007. "Least Squares Model Averaging," Econometrica, Econometric Society, vol. 75(4), pages 1175-1189, July.
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    2. Shi, Pengfei & Zhang, Xinyu & Zhong, Wei, 2024. "Estimating conditional average treatment effects with heteroscedasticity by model averaging and matching," Economics Letters, Elsevier, vol. 238(C).
    3. Jiang Du & Zhongzhan Zhang & Tianfa Xie, 2017. "Focused information criterion and model averaging in censored quantile regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(5), pages 547-570, July.
    4. Raffaella Giacomini & Toru Kitagawa & Alessio Volpicella, 2022. "Uncertain identification," Quantitative Economics, Econometric Society, vol. 13(1), pages 95-123, January.
    5. Shou-Yung Yin & Chu-An Liu & Chang-Ching Lin, 2021. "Focused Information Criterion and Model Averaging for Large Panels With a Multifactor Error Structure," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(1), pages 54-68, January.
    6. Riccardo Lucchetti & Luca Pedini & Claudia Pigini, 2021. "Bayesian Model Averaging For Propensity Score Matching In Tax Rebate," Working Papers 457, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    7. Jiaming Mao & Jingzhi Xu, 2020. "Ensemble Learning with Statistical and Structural Models," Papers 2006.05308, arXiv.org.
    8. Ruoyao Shi, 2021. "An Averaging Estimator for Two Step M Estimation in Semiparametric Models," Working Papers 202105, University of California at Riverside, Department of Economics.
    9. Fang, Fang & Li, Jialiang & Xia, Xiaochao, 2022. "Semiparametric model averaging prediction for dichotomous response," Journal of Econometrics, Elsevier, vol. 229(2), pages 219-245.
    10. Fang, Fang & Yu, Zhou, 2020. "Model averaging assisted sufficient dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    11. Lucchetti, Riccardo & Pedini, Luca & Pigini, Claudia, 2022. "No such thing as the perfect match: Bayesian Model Averaging for treatment evaluation," Economic Modelling, Elsevier, vol. 107(C).
    12. Zulj, Valentin & Jin, Shaobo, 2024. "Can model averaging improve propensity score based estimation of average treatment effects?," Working Paper Series 2024:1, IFAU - Institute for Evaluation of Labour Market and Education Policy.

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    More about this item

    Keywords

    Treatment effects; Propensity score; Model averaging; Limit experiment;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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