Open AccessLinear regression with many controls of limited explanatory power
Author(s) -
Li Chenchuan Mark,
Müller Ulrich K.
Publication year - 2021
Publication title -
quantitative economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 4.062
H-Index - 27
eISSN - 1759-7331
pISSN - 1759-7323
DOI - 10.3982/qe1577
Subject(s) - heteroscedasticity , inference , linear regression , monte carlo method , mathematics , explanatory power , linear model , regression analysis , quadratic equation , scalar (mathematics) , statistics , econometrics , mathematical optimization , computer science , artificial intelligence , physics , geometry , quantum mechanics
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 R 2 ‐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.