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Program evaluation and causal inference 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 con fidence bands for a variety of treatment eff ects including local average (LATE) and local quantile treatment eff ects (LQTE) in data-rich environments. We can handle very many control variables, endogenous receipt of treatment, heterogeneous treatment e ffects, 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 ecient estimators and honest bands for (functional) average treatment eff ects (ATE) and quantile treatment eff ects (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 eff ect 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, which arises from structural equation models in econometrics. Here too the crucial ingredient is the use of orthogonal moment conditions, which can be constructed from the initial moment conditions. We provide results on honest inference for (function-valued) parameters within this general framework where any high-quality, modern machine learning methods can be used to learn the nonparametric/high-dimensional components of the model. These include a number of supporting auxilliary results that are of major independent interest: namely, we (1) prove uniform validity of a multiplier bootstrap, (2) o er 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, 2016. "Program evaluation and causal inference with high-dimensional data," CeMMAP working papers CWP13/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:13/16
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    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. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    3. Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January.
    4. Guido W. Imbens & Whitney K. Newey, 2009. "Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity," Econometrica, Econometric Society, vol. 77(5), pages 1481-1512, September.
    5. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    6. Victor Chernozhukov & Christian Hansen & Martin Spindler, 2016. "hdm: High-Dimensional Metrics," CeMMAP working papers 37/16, Institute for Fiscal Studies.
    7. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects, and Econometric Policy Evaluation," Econometrica, Econometric Society, vol. 73(3), pages 669-738, May.
    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. Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2012. "Gaussian approximation of suprema of empirical processes," CeMMAP working papers CWP44/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    10. 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.
    11. 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.
    12. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function Is Not Smooth," Econometrica, Econometric Society, vol. 71(5), pages 1591-1608, September.
    13. 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.
    14. Chamberlain, Gary & Imbens, Guido W, 2003. "Nonparametric Applications of Bayesian Inference," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 12-18, January.
    15. Jeffrey M Wooldridge, 2010. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232588, April.
    16. 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.
    17. Linton, Oliver, 1996. "Edgeworth Approximation for MINPIN Estimators in Semiparametric Regression Models," Econometric Theory, Cambridge University Press, vol. 12(1), pages 30-60, March.
    18. Juan Carlos Escanciano & Lin Zhu, 2013. "Set inferences and sensitivity analysis in semiparametric conditionally identified models," CeMMAP working papers CWP55/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    19. 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.
    20. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun.
    21. Koenker, Roger, 1988. "Asymptotic Theory and Econometric Practice," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 3(2), pages 139-147, April.
    22. 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.
    23. 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, Fundação Getulio Vargas (Brazil).
    24. Chunrong Ai & Xiaohong Chen, 2003. "Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions," Econometrica, Econometric Society, vol. 71(6), pages 1795-1843, November.
    25. Han Hong & Denis Nekipelov, 2010. "Semiparametric efficiency in nonlinear LATE models," Quantitative Economics, Econometric Society, vol. 1(2), pages 279-304, November.
    26. 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.
    27. Matias D. Cattaneo, 2010. "multi-valued treatment effects," The New Palgrave Dictionary of Economics,, Palgrave Macmillan.
    28. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney K. Newey, 2016. "Double machine learning for treatment and causal parameters," CeMMAP working papers CWP49/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    29. 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.
    30. Andrew Chesher, 2003. "Identification in Nonseparable Models," Econometrica, Econometric Society, vol. 71(5), pages 1405-1441, September.
    31. David A. Wise, 1994. "Studies in the Economics of Aging," NBER Books, National Bureau of Economic Research, Inc, number wise94-1.
    32. 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.
    33. Victor Chernozhukov & Chris Hansen & Martin Spindler, 2016. "High-Dimensional Metrics in R," Papers 1603.01700, arXiv.org, revised Aug 2016.
    34. Mehmet Caner & Hao Helen Zhang, 2014. "Adaptive Elastic Net for Generalized Methods of Moments," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(1), pages 30-47, January.
    35. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    36. Markus Frölich & Blaise Melly, 2013. "Identification of Treatment Effects on the Treated with One-Sided Non-Compliance," Econometric Reviews, Taylor & Francis Journals, vol. 32(3), pages 384-414, November.
    37. 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.
    38. Hong, H. & Scaillet, O., 2006. "A fast subsampling method for nonlinear dynamic models," Journal of Econometrics, Elsevier, vol. 133(2), pages 557-578, August.
    39. 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.
    40. Elizabeth L. Ogburn & Andrea Rotnitzky & James M. Robins, 2015. "Doubly robust estimation of the local average treatment effect curve," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(2), pages 373-396, March.
    41. Abadie A., 2002. "Bootstrap Tests for Distributional Treatment Effects in Instrumental Variable Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 284-292, March.
    42. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881, September.
    43. Edward Vytlacil, 2002. "Independence, Monotonicity, and Latent Index Models: An Equivalence Result," Econometrica, Econometric Society, vol. 70(1), pages 331-341, January.
    44. 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.
    45. Chamberlain, Gary, 1992. "Efficiency Bounds for Semiparametric Regression," Econometrica, Econometric Society, vol. 60(3), pages 567-596, May.
    46. 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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