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Linear Regression with Many Controls of Limited Explanatory Power

Author

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  • Chenchuan (Mark) Li

    (Princeton University)

  • Ulrich K. Müller

    (Princeton University)

Abstract

We consider inference about a scalar coefficient in a linear regression model. One previously considered approach to dealing with many controls imposes sparsity, that is, it is assumed known that nearly all control coefficients are zero, or at least very nearly so. We instead impose a bound on the quadratic mean of the controls’ effect on the dependent variable. We develop a simple inference procedure that exploits this additional information in general heteroskedastic models. We study its asymptotic efficiency properties and compare it to a sparsity-based approach in a Monte Carlo study. The method is illustrated in three empirical applications.

Suggested Citation

  • Chenchuan (Mark) Li & Ulrich K. Müller, 2020. "Linear Regression with Many Controls of Limited Explanatory Power," Working Papers 2020-57, Princeton University. Economics Department..
    • Handle: RePEc:pri:econom:2020-57
    as

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    File URL: http://www.princeton.edu/~umueller/L2reg.pdf
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    References listed on IDEAS

    as
    1. Graham Elliott & Ulrich K. Müller & Mark W. Watson, 2015. "Nearly Optimal Tests When a Nuisance Parameter Is Present Under the Null Hypothesis," Econometrica, Econometric Society, vol. 83, pages 771-811, March.
    2. Timothy B. Armstrong & Michal Kolesár, 2018. "Optimal Inference in a Class of Regression Models," Econometrica, Econometric Society, vol. 86(2), pages 655-683, March.
    3. Ted Joyce, 2004. "Did Legalized Abortion Lower Crime?," Journal of Human Resources, University of Wisconsin Press, vol. 39(1).
    4. Leeb, Hannes & Pötscher, Benedikt M., 2005. "Model Selection And Inference: Facts And Fiction," Econometric Theory, Cambridge University Press, vol. 21(1), pages 21-59, February.
    5. Rocco Macchiavello & Ameet Morjaria, 2015. "The Value of Relationships: Evidence from a Supply Shock to Kenyan Rose Exports," American Economic Review, American Economic Association, vol. 105(9), pages 2911-2945, September.
    6. Guido W. Imbens & Donald B. Rubin & Bruce I. Sacerdote, 2001. "Estimating the Effect of Unearned Income on Labor Earnings, Savings, and Consumption: Evidence from a Survey of Lottery Players," American Economic Review, American Economic Association, vol. 91(4), pages 778-794, September.
    7. Guido W. Imbens & Jeffrey M. Wooldridge, 2009. "Recent Developments in the Econometrics of Program Evaluation," Journal of Economic Literature, American Economic Association, vol. 47(1), pages 5-86, March.
    8. 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(1), pages 42-86, February.
    9. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    10. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    11. Christopher L. Foote & Christopher F. Goetz, 2008. "The Impact of Legalized Abortion on Crime: Comment," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 123(1), pages 407-423.
    12. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881.
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    Cited by:

    1. Timothy B. Armstrong & Michal Koles'ar & Soonwoo Kwon, 2020. "Bias-Aware Inference in Regularized Regression Models," Papers 2012.14823, arXiv.org, revised Aug 2023.

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    More about this item

    Keywords

    high dimensional linear regression; limit of experiments; L2 bound; invariance to linear reparameterizations;
    All these keywords.

    JEL classification:

    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C39 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Other

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