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Program evaluation with high-dimensional data


  • 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)


In this paper, we consider estimation of general modern moment-condition problems in econometrics in a data-rich environment where there may be many more control variables available than there are observations. The framework we consider allows for a continuum of target parameters and for Lasso-type or Post-Lasso type methods to be used as estimators of a continuum of high-dimensional nuisance functions. As an important leading example of this environment, we first provide detailed results on estimation and inference for relevant treatment eff ects, such as local average and quantile treatment eff ects. The setting we work in is designed expressly to handle many control variables, endogenous receipt of treatment, heterogeneous treatment eff ects, and possibly function-valued outcomes. To make informative inference possible, we assume that key reduced form predictive relationships are approximately sparse. That is, we require that the relationship between the control variables and the outcome, treatment status, and instrument status can be captured up to a small approximation error by a small number of the control variables whose identities are unknown to the researcher. This condition permits estimation and inference to proceed after datadriven selection of control variables. We provide conditions under which post selection inference is uniformly valid across a wide-range of models and show that a key condition underlying the uniform validity of post-selection inference allowing for imperfect model selection is the use of orthogonal moment conditions. We illustrate the use of the proposed methods with an application to estimating the e ffect of 401(k) participation on accumulated assets.

Suggested Citation

  • Alexandre Belloni & Victor Chernozhukov & Ivan Fernandez-Val & Christian Hansen, 2014. "Program evaluation with high-dimensional data," CeMMAP working papers CWP33/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:33/14

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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Damian Kozbur, 2017. "Testing-Based Forward Model Selection," American Economic Review, American Economic Association, vol. 107(5), pages 266-269, May.
    5. Christian Hansen & Damian Kozbur & Sanjog Misra, 2016. "Targeted undersmoothing," ECON - Working Papers 282, Department of Economics - University of Zurich, revised Apr 2018.
    6. 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.
    7. Denis Chetverikov & . ., 2016. "On cross-validated Lasso," CeMMAP working papers CWP47/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. 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.
    9. Alexandre Belloni & Victor Chernozhukov & Kengo Kato, 2013. "Valid Post-Selection Inference in High-Dimensional Approximately Sparse Quantile Regression Models," Papers 1312.7186,, revised Jun 2016.
    10. Christian Hansen & Yuan Liao, 2016. "The Factor-Lasso and K-Step Bootstrap Approach for Inference in High-Dimensional Economic Applications," Papers 1611.09420,, revised Dec 2016.
    11. Matias D. Cattaneo & Michael Jansson, 2014. "Bootstrapping Kernel-Based Semiparametric Estimators," CREATES Research Papers 2014-25, Department of Economics and Business Economics, Aarhus University.
    12. Susan Athey & Julie Tibshirani & Stefan Wager, 2016. "Generalized Random Forests," Papers 1610.01271,, revised Apr 2018.
    13. Kaspar Wüthrich, 2015. "Semiparametric estimation of quantile treatment effects with endogeneity," Diskussionsschriften dp1509, Universitaet Bern, Departement Volkswirtschaft.
    14. Susan Athey & Guido Imbens, 2016. "The State of Applied Econometrics - Causality and Policy Evaluation," Papers 1607.00699,

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