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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

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. Benjamin J. Gillen & Matthew Shum & Hyungsik Roger Moon, 2014. "Demand Estimation with High-Dimensional Product Characteristics," Advances in Econometrics, in: Ivan Jeliazkov & Dale J. Poirier (ed.), Bayesian Model Comparison, volume 34, pages 301-323, Emerald Publishing Ltd.
    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. 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.
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    7. Leeb, Hannes & Pötscher, Benedikt M., 2008. "Can One Estimate The Unconditional Distribution Of Post-Model-Selection Estimators?," Econometric Theory, Cambridge University Press, vol. 24(2), pages 338-376, April.
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    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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