Title

Linear Regression with Many Controls of Limited Explanatory Power

Author(s)

Chenchuan (Mark) Li Chenchuan (Mark) Li (Princeton University)

Ulrich K. Müller Ulrich 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.

Creation Date

2020-03

Section URL ID

Paper Number

2020-57

URL

http://www.princeton.edu/~umueller/L2reg.pdf

File Function

Jel

C30, C39

Keyword(s)

high dimensional linear regression, limit of experiments, L2 bound, invariance to linear reparameterizations

Suppress

false

Series

13