Linear Regression with Many Controls of Limited Explanatory Power

Chenchuan (Mark) Li and Ulrich Müller
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Chenchuan (Mark) Li: Princeton University
Ulrich Müller: Princeton University

Working Papers from Princeton University. Economics Department.

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.

Keywords: high dimensional linear regression; limit of experiments; L2 bound; invariance to linear reparameterizations (search for similar items in EconPapers)
JEL-codes: C30 C39 (search for similar items in EconPapers)
Date: 2020-03
New Economics Papers: this item is included in nep-ban, nep-ecm and nep-ore
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:pri:econom:2020-57

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