Controlling for “X”?

Understanding linear regression mechanics via the Frisch-Waugh-Lovell Theorem

Introduction

Applied econometrics is generally interested in establishing causality. That is, what is the “treatment” effect of T on some outcome y. In a simple bivariate case, we can imagine randomly assigning treatment T=1 to some individuals and T=0 to others. This can be represented by the following linear regression model:

If we assume the treatment is truly randomly assigned, then T is orthogonal to the …

causal inference econometrics theory