Population regression coefficients
It is well known that the slope coefficient in a bivariate regression equals the covariance between the dependent and independent variable divided by the variance of the independent variable. But did you know that the slope coefficients in a trivariate regression can also be expressed in terms of variances and covariances? See here.
I've written some notes on what you should know if you want to use difference-in-differences yourself. No proofs but goes beyond the basics.
Maybe I was being slow, but it wasn't obvious to me why the regression approach to difference-in-differences (DiD) should recover the correct DiD parameter. 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.
Two-way fixed effects
In this document, I show how to prove what a regression on individual-level and time fixed effects recovers.