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

Author

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  • Victor Chernozhukov
  • Christian Hansen
  • Martin Spindler

Abstract

We consider estimation of and inference about coefficients on endogenous variables in a linear instrumental variables model where the number of instruments and exogenous control variables are each allowed to be larger than the sample size. We work within an approximately sparse framework that maintains that the signal available in the instruments and control variables may be effectively captured by a small number of the available variables. We provide a LASSO-based method for this setting which provides uniformly valid inference about the coefficients on endogenous variables. We illustrate the method through an application to demand estimation.

Suggested Citation

  • 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.
  • Handle: RePEc:aea:aecrev:v:105:y:2015:i:5:p:486-90
    Note: DOI: 10.1257/aer.p20151022
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    References listed on IDEAS

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    1. 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.
    2. Eric Gautier & Alexandre Tsybakov, 2011. "High-Dimensional Instrumental Variables Regression and Confidence Sets," Working Papers 2011-13, Center for Research in Economics and Statistics.
    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.
    4. Zhu Liu, 2015. "???????," Working Paper 269181, Harvard University OpenScholar.
    5. Carrasco, Marine, 2012. "A regularization approach to the many instruments problem," Journal of Econometrics, Elsevier, vol. 170(2), pages 383-398.
    6. 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.
    7. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
    8. Gary Chamberlain & Guido Imbens, 2004. "Random Effects Estimators with many Instrumental Variables," Econometrica, Econometric Society, vol. 72(1), pages 295-306, January.
    9. Hansen, Christian & Kozbur, Damian, 2014. "Instrumental variables estimation with many weak instruments using regularized JIVE," Journal of Econometrics, Elsevier, vol. 182(2), pages 290-308.
    10. Okui, Ryo, 2011. "Instrumental variable estimation in the presence of many moment conditions," Journal of Econometrics, Elsevier, vol. 165(1), pages 70-86.
    11. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Christoph Breunig & Enno Mammen & Anna Simoni, 2018. "Ill-posed Estimation in High-Dimensional Models with Instrumental Variables," Papers 1806.00666, arXiv.org.
    10. 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.
    11. Susan Athey & Guido Imbens, 2016. "The Econometrics of Randomized Experiments," Papers 1607.00698, arXiv.org.
    12. 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.

    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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