Linear regression with many controls of limited explanatory power
解释力有限的大量控制变量下的线性回归
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…