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Post-Selection and Post-Regularization Inference in Linear Models with Many Controls and Instruments

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  • Victor Chernozhukov
  • Christian Hansen
  • Martin Spindler

Abstract

In this note, we offer an approach to estimating causal/structural parameters in the presence of many instruments and controls based on methods for estimating sparse high-dimensional models. We use these high-dimensional methods to select both which instruments and which control variables to use. The approach we take extends BCCH2012, which covers selection of instruments for IV models with a small number of controls, and extends BCH2014, which covers selection of controls in models where the variable of interest is exogenous conditional on observables, to accommodate both a large number of controls and a large number of instruments. We illustrate the approach with a simulation and an empirical example. Technical supporting material is available in a supplementary online appendix.

Suggested Citation

  • Victor Chernozhukov & Christian Hansen & Martin Spindler, 2015. "Post-Selection and Post-Regularization Inference in Linear Models with Many Controls and Instruments," Papers 1501.03185, arXiv.org.
  • Handle: RePEc:arx:papers:1501.03185
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    References listed on IDEAS

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    1. repec:eme:aecozz:s0731-905320140000034020 is not listed on IDEAS
    2. 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.
    3. Eric Gautier & Alexandre Tsybakov, 2011. "High-Dimensional Instrumental Variables Regression and Confidence Sets," Working Papers 2011-13, Center for Research in Economics and Statistics.
    4. 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.
    5. 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.
    6. Zhu Liu, 2015. "???????," Working Paper 269181, Harvard University OpenScholar.
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    8. 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.
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    Cited by:

    1. Ahrens, Achim & Hansen, Christian B. & Schaffer, Mark E, 2019. "Iassopack: Model Selection and Prediction with Regularized Regression in Stata," IZA Discussion Papers 12081, Institute of Labor Economics (IZA).
    2. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2018. "Double/debiased machine learning for treatment and structural parameters," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-68, February.
    3. Guber, Raphael, 2018. "Instrument Validity Tests with Causal Trees: With an Application to the Same-sex Instrument," MEA discussion paper series 201805, Munich Center for the Economics of Aging (MEA) at the Max Planck Institute for Social Law and Social Policy.
    4. Alexandre Belloni & Mingli Chen & Victor Chernozhukov, 2016. "Quantile Graphical Models: Prediction and Conditional Independence with Applications to Systemic Risk," Papers 1607.00286, arXiv.org, revised Dec 2017.
    5. Christoph Breunig & Enno Mammen & Anna Simoni, 2018. "Ill-posed Estimation in High-Dimensional Models with Instrumental Variables," Papers 1806.00666, arXiv.org.
    6. Steven Shuye Wang & Kuan Xu & Hao Zhang, 2019. "A Microstructure Study of Circuit Breakers in the Chinese Stock Markets," Working Papers daleconwp2019-02, Dalhousie University, Department of Economics.
    7. repec:eee:econom:v:207:y:2018:i:1:p:175-187 is not listed on IDEAS
    8. Frank Windmeijer & Helmut Farbmacher & Neil Davies & George Davey Smith, 2016. "On the Use of the Lasso for Instrumental Variables Estimation with Some Invalid Instruments," Bristol Economics Discussion Papers 16/674, Department of Economics, University of Bristol, UK, revised 08 Aug 2017.
    9. 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.
    10. Krüger, Jens J. & Rhiel, Mathias, 2016. "Determinants of ICT infrastructure: A cross-country statistical analysis," Darmstadt Discussion Papers in Economics 228, Darmstadt University of Technology, Department of Law and Economics.
    11. Seojeong Lee & Youngki Shin, 2018. "Optimal Estimation with Complete Subsets of Instruments," Department of Economics Working Papers 2018-15, McMaster University.
    12. 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.
    13. Ruf, Daniel, 2017. "Agglomeration Effects and Liquidity Gradients in Local Rental Housing Markets," Working Papers on Finance 1702, University of St. Gallen, School of Finance.
    14. De Luca, Giuseppe & Magnus, Jan R. & Peracchi, Franco, 2018. "Weighted-average least squares estimation of generalized linear models," Journal of Econometrics, Elsevier, vol. 204(1), pages 1-17.
    15. Peter C. B. Phillips & Zhentao Shi, 2019. "Boosting the Hodrick-Prescott Filter," Papers 1905.00175, arXiv.org.
    16. Alexandre Belloni & Victor Chernozhukov & Ivan Fernandez-Val & Christian Hansen, 2013. "Program evaluation with high-dimensional data," CeMMAP working papers CWP77/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    17. repec:wly:emetrp:v:85:y:2017:i::p:233-298 is not listed on IDEAS
    18. Seojeong Lee & Youngki Shin, 2018. "Complete Subset Averaging with Many Instruments," Papers 1811.08083, arXiv.org, revised Aug 2019.
    19. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2016. "Double/Debiased Machine Learning for Treatment and Causal Parameters," Papers 1608.00060, arXiv.org, revised Dec 2017.
    20. Susan Athey & Guido Imbens, 2016. "The Econometrics of Randomized Experiments," Papers 1607.00698, arXiv.org.
    21. Cocker Liu & Adam Nowak & Patrick Smith, 2017. "Some Remarks on Real Estate Pricing," Working Papers 17-20, Department of Economics, West Virginia University.
    22. A. Belloni & V. Chernozhukov & I. Fernández‐Val & C. Hansen, 2017. "Program Evaluation and Causal Inference With High‐Dimensional Data," Econometrica, Econometric Society, vol. 85, pages 233-298, January.
    23. Sander Gerritsen & Mark Kattenberg & Sonny Kuijpers, 2019. "The impact of age at arrival on education and mental health," CPB Discussion Paper 389, CPB Netherlands Bureau for Economic Policy Analysis.

    More about this item

    JEL classification:

    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis

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