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Linear Regression with Many Controls of Limited Explanatory Power

Author

Listed:
  • 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
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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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