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Inference in High Dimensional Panel Models with an Application to Gun Control

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  • Alexandre Belloni
  • Victor Chernozhukov
  • Christian Hansen
  • Damian Kozbur

Abstract

We consider estimation and inference in panel data models with additive unobserved individual specific heterogeneity in a high dimensional setting. The setting allows the number of time varying regressors to be larger than the sample size. To make informative estimation and inference feasible, we require that the overall contribution of the time varying variables after eliminating the individual specific heterogeneity can be captured by a relatively small number of the available variables whose identities are unknown. This restriction allows the problem of estimation to proceed as a variable selection problem. Importantly, we treat the individual specific heterogeneity as fixed effects which allows this heterogeneity to be related to the observed time varying variables in an unspecified way and allows that this heterogeneity may be non-zero for all individuals. Within this framework, we provide procedures that give uniformly valid inference over a fixed subset of parameters in the canonical linear fixed effects model and over coefficients on a fixed vector of endogenous variables in panel data instrumental variables models with fixed effects and many instruments. An input to developing the properties of our proposed procedures is the use of a variant of the Lasso estimator that allows for a grouped data structure where data across groups are independent and dependence within groups is unrestricted. We provide formal conditions within this structure under which the proposed Lasso variant selects a sparse model with good approximation properties. We present simulation results in support of the theoretical developments and illustrate the use of the methods in an application aimed at estimating the effect of gun prevalence on crime rates.

Suggested Citation

  • Alexandre Belloni & Victor Chernozhukov & Christian Hansen & Damian Kozbur, 2014. "Inference in High Dimensional Panel Models with an Application to Gun Control," Papers 1411.6507, arXiv.org.
  • Handle: RePEc:arx:papers:1411.6507
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    References listed on IDEAS

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    1. Hansen, Christian B., 2007. "Asymptotic properties of a robust variance matrix estimator for panel data when T is large," Journal of Econometrics, Elsevier, vol. 141(2), pages 597-620, December.
    2. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    3. Anders Bredahl Kock, 2013. "Oracle inequalities for high-dimensional panel data models," CREATES Research Papers 2013-20, Department of Economics and Business Economics, Aarhus University.
    4. Chao, John C. & Swanson, Norman R. & Hausman, Jerry A. & Newey, Whitney K. & Woutersen, Tiemen, 2012. "Asymptotic Distribution Of Jive In A Heteroskedastic Iv Regression With Many Instruments," Econometric Theory, Cambridge University Press, vol. 28(01), pages 42-86, February.
    5. Marianne Bertrand & Esther Duflo & Sendhil Mullainathan, 2004. "How Much Should We Trust Differences-In-Differences Estimates?," The Quarterly Journal of Economics, Oxford University Press, vol. 119(1), pages 249-275.
    6. Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2011. "Inference on Treatment Effects After Selection Amongst High-Dimensional Controls," Papers 1201.0224, arXiv.org, revised May 2012.
    7. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
    8. Bester, C. Alan & Hansen, Christian, 2009. "Identification of Marginal Effects in a Nonparametric Correlated Random Effects Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(2), pages 235-250.
    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. Joseph G. Altonji & Rosa L. Matzkin, 2005. "Cross Section and Panel Data Estimators for Nonseparable Models with Endogenous Regressors," Econometrica, Econometric Society, vol. 73(4), pages 1053-1102, July.
    11. Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2013. "Supplementary Appendix for "Inference on Treatment Effects After Selection Amongst High-Dimensional Controls"," Papers 1305.6099, arXiv.org, revised Jun 2013.
    12. Cook, Philip J. & Ludwig, Jens, 2006. "The social costs of gun ownership," Journal of Public Economics, Elsevier, vol. 90(1-2), pages 379-391, January.
    13. Tomohiro Ando & Jushan Bai, 2015. "Asset Pricing with a General Multifactor Structure," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 13(3), pages 556-604.
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    Citations

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    Cited by:

    1. Achim Ahrens & Christian B. Hansen & Mark E. Schaffer, 2019. "lassopack: Model selection and prediction with regularized regression in Stata," Papers 1901.05397, arXiv.org.
    2. Duncan Sheppard Gilchrist & Emily Glassberg Sands, 2016. "Something to Talk About: Social Spillovers in Movie Consumption," Journal of Political Economy, University of Chicago Press, vol. 124(5), pages 1339-1382.
    3. Alexandre Belloni & Victor Chernozhukov & Denis Chetverikov & Christian Hansen & Kengo Kato, 2018. "High-dimensional econometrics and regularized GMM," CeMMAP working papers CWP35/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. Damian Kozbur, 2013. "Inference in additively separable models with a high-dimensional set of conditioning variables," ECON - Working Papers 284, Department of Economics - University of Zurich, revised Apr 2018.
    5. 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.
    6. Damian Kozbur, 2017. "Sharp convergence rates for forward regression in high-dimensional sparse linear models," ECON - Working Papers 253, Department of Economics - University of Zurich, revised Apr 2018.
    7. 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.
    8. Damian Kozbur, 2017. "Testing-Based Forward Model Selection," American Economic Review, American Economic Association, vol. 107(5), pages 266-269, May.
    9. Achim Ahrens, 2015. "Civil conflicts in Africa: Climate, economic shocks, nighttime lights and spill-over effects," SEEC Discussion Papers 1501, Spatial Economics and Econometrics Centre, Heriot Watt University.
    10. Borgschulte, Mark & Vogler, Jacob, 2019. "Did the ACA Medicaid Expansion Save Lives?," IZA Discussion Papers 12552, Institute of Labor Economics (IZA).
    11. Anders Bredahl Kock & Haihan Tang, 2014. "Inference in High-dimensional Dynamic Panel Data Models," CREATES Research Papers 2014-58, Department of Economics and Business Economics, Aarhus University.
    12. Rossmann, Tobias, 2019. "Does Experience Shape Subjective Expectations?," Rationality and Competition Discussion Paper Series 181, CRC TRR 190 Rationality and Competition.
    13. Hansen, Christian & Liao, Yuan, 2019. "The Factor-Lasso And K-Step Bootstrap Approach For Inference In High-Dimensional Economic Applications," Econometric Theory, Cambridge University Press, vol. 35(03), pages 465-509, June.
    14. repec:spr:empeco:v:55:y:2018:i:1:d:10.1007_s00181-017-1415-2 is not listed on IDEAS
    15. Christian Hansen & Yuan Liao, 2016. "The Factor-Lasso and K-Step Bootstrap Approach for Inference in High-Dimensional Economic Applications," Papers 1611.09420, arXiv.org, revised Dec 2016.
    16. Harold D. Chiang & Joel Rodrigue & Yuya Sasaki, 2019. "Post-Selection Inference in Three-Dimensional Panel Data," Papers 1904.00211, arXiv.org, revised Apr 2019.
    17. Harold D. Chiang, 2018. "Many Average Partial Effects: with An Application to Text Regression," Papers 1812.09397, arXiv.org, revised Sep 2019.
    18. 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.

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