Econometrica: Jan 2017, Volume 85, Issue 1

Program Evaluation and Causal Inference with High-Dimensional Data

DOI: 10.3982/ECTA12723
p. 233-298

A. Belloni, V. Chernozhukov, I. Fernández‐Val, C. Hansen

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 control variables, receipt of treatment, treatment effects, and 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.

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Supplement to "Program Evaluation and Causal Inference with High-Dimensional Data"

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Supplement to "Program Evaluation and Causal Inference with High-Dimensional Data"

This supplement contains 11 appendices with additional results and some omitted proofs.  Appendices F-J include additional results for Sections 2-7, respectively.  Appendix K gathers auxiliary results on algebra of covering entropies.  Appendices L and M contain the proofs of Sections 4 and 5 omitted from the main text.  Appendix N contains the proofs of Sections 6 omitted from the main text, together with the proofs of the additional results for Section 6 in Appendix I.  Appendix O reports the results of a simulation experiment.

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