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Program evaluation with high-dimensional data

Author

Listed:
  • Alexandre Belloni

    (Institute for Fiscal Studies)

  • Victor Chernozhukov

    () (Institute for Fiscal Studies and MIT)

  • Ivan Fernandez-Val

    (Institute for Fiscal Studies and Boston University)

  • Christian Hansen

    (Institute for Fiscal Studies and Chicago GSB)

Abstract

In this paper, we provide efficient estimators and honest confidence bands for a variety of treatment effects including local average (LATE) and local quantile treatment effects (LQTE) in data-rich environments. We can handle very many control variables, endogenous receipt of treatment, heterogeneous treatment effects, and function-valued outcomes. Our framework covers the special case of exogenous receipt of treatment, either conditional on controls or unconditionally as in randomized control trials. In the latter case, our approach produces efficient estimators and honest bands for (functional) average treatment effects (ATE) and quantile treatment effects (QTE). To make informative inference possible, we assume that key reduced form predictive relationships are approximately sparse. This assumption allows the use of regularization and selection methods to estimate those relations, and we provide methods for post-regularization and post-selection inference that are uniformly valid (honest) across a wide-range of models. We show that a key ingredient enabling honest inference is the use of orthogonal or doubly robust moment conditions in estimating certain reduced form functional parameters. We illustrate the use of the proposed methods with an application to estimating the effect of 401(k) eligibility and participation on accumulated assets. The results on program evaluation are obtained as a consequence of more general results on honest inference in a general moment condition framework, where we work with possibly a continuum of moments. We provide results on honest inference for (function-valued) parameters within this general framework where modern machine learning methods are used to fit the nonparametric/highdimensional components of the model. These include a number of supporting new results that are of major independent interest: namely, we (1) prove uniform validity of a multiplier bootstrap, (2) offer a uniformly valid functional delta method, and (3) provide results for sparsity-based estimation of regression functions for function-valued outcomes.

Suggested Citation

  • Alexandre Belloni & Victor Chernozhukov & Ivan Fernandez-Val & Christian Hansen, 2015. "Program evaluation with high-dimensional data," CeMMAP working papers CWP55/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:55/15
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    References listed on IDEAS

    as
    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January.
    3. Cattaneo, Matias D., 2010. "Efficient semiparametric estimation of multi-valued treatment effects under ignorability," Journal of Econometrics, Elsevier, vol. 155(2), pages 138-154, April.
    4. Hahn, Jinyong, 1997. "Bayesian Bootstrap of the Quantile Regression Estimator: A Large Sample Study," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(4), pages 795-808, November.
    5. Kline Patrick & Santos Andres, 2012. "A Score Based Approach to Wild Bootstrap Inference," Journal of Econometric Methods, De Gruyter, vol. 1(1), pages 23-41, August.
    6. Jeffrey M Wooldridge, 2010. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232588, January.
    7. A. Belloni & D. Chen & V. Chernozhukov & C. Hansen, 2012. "Sparse Models and Methods for Optimal Instruments With an Application to Eminent Domain," Econometrica, Econometric Society, vol. 80(6), pages 2369-2429, November.
    8. Victor Chernozhukov & Christian Hansen & Martin Spindler, 2015. "Post-Selection and Post-Regularization Inference in Linear Models with Many Controls and Instruments," American Economic Review, American Economic Association, vol. 105(5), pages 486-490, May.
    9. Koenker, Roger, 1988. "Asymptotic Theory and Econometric Practice," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 3(2), pages 139-147, April.
    10. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-475, March.
    11. Abadie, Alberto, 2003. "Semiparametric instrumental variable estimation of treatment response models," Journal of Econometrics, Elsevier, vol. 113(2), pages 231-263, April.
    12. Rothe, Christoph & Firpo, Sergio Pinheiro, 2013. "Semiparametric estimation and inference using doubly robust moment conditions," Textos para discussão 330, FGV/EESP - Escola de Economia de São Paulo, Getulio Vargas Foundation (Brazil).
    13. Han Hong & Denis Nekipelov, 2010. "Semiparametric efficiency in nonlinear LATE models," Quantitative Economics, Econometric Society, vol. 1(2), pages 279-304, November.
    14. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
    15. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
    16. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    17. A. Belloni & V. Chernozhukov & L. Wang, 2011. "Square-root lasso: pivotal recovery of sparse signals via conic programming," Biometrika, Biometrika Trust, vol. 98(4), pages 791-806.
    18. Leeb, Hannes & P tscher, Benedikt M., 2008. "Can One Estimate The Unconditional Distribution Of Post-Model-Selection Estimators?," Econometric Theory, Cambridge University Press, vol. 24(02), pages 338-376, April.
    19. Eric M. Engen & William G. Gale & John Karl Scholz, 1996. "The Illusory Effects of Saving Incentives on Saving," Journal of Economic Perspectives, American Economic Association, vol. 10(4), pages 113-138, Fall.
    20. Hong, H. & Scaillet, O., 2006. "A fast subsampling method for nonlinear dynamic models," Journal of Econometrics, Elsevier, vol. 133(2), pages 557-578, August.
    21. Victor Chernozhukov & Christian Hansen, 2004. "The Effects of 401(K) Participation on the Wealth Distribution: An Instrumental Quantile Regression Analysis," The Review of Economics and Statistics, MIT Press, vol. 86(3), pages 735-751, August.
    22. Edward Vytlacil, 2002. "Independence, Monotonicity, and Latent Index Models: An Equivalence Result," Econometrica, Econometric Society, vol. 70(1), pages 331-341, January.
    23. Benjamin, Daniel J., 2003. "Does 401(k) eligibility increase saving?: Evidence from propensity score subclassification," Journal of Public Economics, Elsevier, vol. 87(5-6), pages 1259-1290, May.
    24. Hansen, Lars Peter & Singleton, Kenneth J, 1982. "Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models," Econometrica, Econometric Society, vol. 50(5), pages 1269-1286, September.
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    Citations

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    Cited by:

    1. Hansen, Christian & Liao, Yuan, 2016. "The Factor-Lasso and K-Step Bootstrap Approach for Inference in High-Dimensional Economic Applications," MPRA Paper 75313, University Library of Munich, Germany.
    2. Xu, Ning & Hong, Jian & Fisher, Timothy, 2016. "Finite-sample and asymptotic analysis of generalization ability with an application to penalized regression," MPRA Paper 73622, University Library of Munich, Germany.
    3. Denis Chetverikov & . ., 2016. "On cross-validated Lasso," CeMMAP working papers CWP47/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. Christian Hansen & Yuan Liao, 2016. "The Factor-Lasso and K-Step Bootstrap Approach for Inference in High-Dimensional Economic Applications," Papers 1611.09420, arXiv.org, revised Dec 2016.
    5. Alexandre Belloni & Victor Chernozhukov & Kengo Kato, 2013. "Valid Post-Selection Inference in High-Dimensional Approximately Sparse Quantile Regression Models," Papers 1312.7186, arXiv.org, revised Jun 2016.
    6. 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.
    7. Matias D. Cattaneo & Michael Jansson, 2014. "Bootstrapping Kernel-Based Semiparametric Estimators," CREATES Research Papers 2014-25, Department of Economics and Business Economics, Aarhus University.
    8. Susan Athey & Julie Tibshirani & Stefan Wager, 2016. "Generalized Random Forests," Papers 1610.01271, arXiv.org, revised Apr 2018.
    9. Huber, Martin & Wüthrich, Kaspar, 2017. "Evaluating local average and quantile treatment effects under endogeneity based on instruments: a review," FSES Working Papers 479, Faculty of Economics and Social Sciences, University of Freiburg/Fribourg Switzerland.
    10. Kaspar Wüthrich, 2015. "Semiparametric estimation of quantile treatment effects with endogeneity," Diskussionsschriften dp1509, Universitaet Bern, Departement Volkswirtschaft.
    11. Susan Athey & Guido Imbens, 2016. "The State of Applied Econometrics - Causality and Policy Evaluation," Papers 1607.00699, arXiv.org.
    12. Christian Hansen & Yuan Liao, 2016. "The Factor-Lasso and K-Step Bootstrap Approach for Inference in High-Dimensional Economic Applications," Departmental Working Papers 201610, Rutgers University, Department of Economics.

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