Linear regression with many controls of limited explanatory power

• 成果类型: Article
• 署名作者: Li, Chenchuan (Mark); Muller, Ulrich K.
• 署名单位: Princeton University
• 刊物名称: QUANTITATIVE ECONOMICS
• ISSN/ISSBN: 1759-7323
• DOI: 10.3982/QE1577
• 发表日期: 2021
• 页码: 405-442
• 关键词: High dimensional linear regression; L2 bound; invariance to linear reparameterizations; C12; C21

摘要

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.