For a long time, I have been struggling to find a satisfactory explanation for why the regression approach to difference-in-differences (DiD) recovers the correct DiD parameter. I finally found the time to sit down and work it out. This document gives the answer and along the way demonstrates what the least squares coefficients recover when all variables vary only at the group level.

Fixed effects

In this document, I show how to prove what a regression on individual-level and time fixed effects recovers.