Linear regression with many controls of limited explanatory power

Chenchuan Li, Ulrich K. Müller

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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 (very nearly) zero. We instead impose a bound on the quadratic mean of the controls' effect on the dependent variable, which also has an interpretation as an R2-type bound on the explanatory power of the controls. 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.

Original languageEnglish (US)
Pages (from-to)405-442
Number of pages38
JournalQuantitative Economics
Issue number2
StatePublished - May 2021

All Science Journal Classification (ASJC) codes

  • Economics and Econometrics


  • C12
  • C21
  • High dimensional linear regression
  • L2 bound
  • invariance to linear reparameterizations


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