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Program evaluation with high-dimensional data

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  • Victor Chernozhukov
  • Ivan Fernandez-Val
  • Christian Hansen

Abstract

We consider estimation of policy relevant treatment effects in a data-rich environment where there may be many more control variables available than there are observations. In addition to allowing many control variables, the setting we consider allows heterogeneous treatment effects, endogenous receipt of treatment, and function-valued outcomes. To make information inference possible, we assume that reduced form predictive relationships are approximately sparse. That is, we require that the relationship between the covariates and the outcome, treatment status, and instrument status can be captured up to a small approximation error using a small number of controls whose identities are unknown to the researcher. This condition allows estimation and inference for a wide variety of treatment parameters to process after selection of an appropriate set of control variables formed by selecting controls separately for each reduced form relationship and then appropriately combining this set of reduced form predictive models and associated selected controls. We provide conditions under which post-selection inferences is uniformly valid across a wide-range of models and show that a key condition underlying uniform validity of post-selection inference allowing for imperfect model selection is the use of approximately unbiased estimating equations. We illustrate the use of the proposed treatment effect estimation methods with an application to estimating the effect of 401(k) participation on accumulated assets.

Suggested Citation

  • Victor Chernozhukov & Ivan Fernandez-Val & Christian Hansen, 2013. "Program evaluation with high-dimensional data," CeMMAP working papers 57/13, Institute for Fiscal Studies.
  • Handle: RePEc:azt:cemmap:57/13
    DOI: 10.1920/wp.cem.2013.5713
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    3. Alexandre Belloni & Victor Chernozhukov & Christian Hansen & Damian Kozbur, 2016. "Inference in High-Dimensional Panel Models With an Application to Gun Control," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(4), pages 590-605, October.
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    8. Susan Athey & Guido W. Imbens, 2017. "The State of Applied Econometrics: Causality and Policy Evaluation," Journal of Economic Perspectives, American Economic Association, vol. 31(2), pages 3-32, Spring.
    9. Danquah, Michael & Iddrisu, Abdul Malik & Boakye, Ernest Owusu & Owusu, Solomon, 2021. "Do gender wage differences within households influence women's empowerment and welfare? Evidence from Ghana," Journal of Economic Behavior & Organization, Elsevier, vol. 188(C), pages 916-932.
    10. 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.
    11. Kasy Maximilian, 2019. "Uniformity and the Delta Method," Journal of Econometric Methods, De Gruyter, vol. 8(1), pages 1-19, January.
    12. Alexandre Belloni & Victor Chernozhukov & Lie Wang, 2013. "Pivotal estimation via square-root lasso in nonparametric regression," CeMMAP working papers 62/13, Institute for Fiscal Studies.
    13. Ning Xu & Jian Hong & Timothy C. G. Fisher, 2016. "Finite-sample and asymptotic analysis of generalization ability with an application to penalized regression," Papers 1609.03344, arXiv.org, revised Sep 2016.
    14. Susan Athey & Julie Tibshirani & Stefan Wager, 2016. "Generalized Random Forests," Papers 1610.01271, arXiv.org, revised Apr 2018.
    15. Guo, Zijian & Kang, Hyunseung & Cai, T. Tony & Small, Dylan S., 2018. "Testing endogeneity with high dimensional covariates," Journal of Econometrics, Elsevier, vol. 207(1), pages 175-187.
    16. 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.
    17. Thai T. Pham & Yuanyuan Shen, 2017. "A Deep Causal Inference Approach to Measuring the Effects of Forming Group Loans in Online Non-profit Microfinance Platform," Papers 1706.02795, arXiv.org.
    18. Christian Hansen & Damian Kozbur & Sanjog Misra, 2016. "Targeted undersmoothing," ECON - Working Papers 282, Department of Economics - University of Zurich, revised Apr 2018.
    19. Denis Chetverikov & . ., 2016. "On cross-validated Lasso," CeMMAP working papers CWP47/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
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    21. Matias D. Cattaneo & Michael Jansson, 2014. "Bootstrapping Kernel-Based Semiparametric Estimators," CREATES Research Papers 2014-25, Department of Economics and Business Economics, Aarhus University.
    22. Kaspar W thrich, 2015. "Semiparametric estimation of quantile treatment effects with endogeneity," Diskussionsschriften dp1509, Universitaet Bern, Departement Volkswirtschaft.
    23. Shao, Shuai & Xu, Le & Yang, Lili & Yu, Dianfan, 2024. "How do energy-saving policies improve environmental quality: Evidence from China’s Top 10,000 energy-consuming enterprises program," World Development, Elsevier, vol. 175(C).

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