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.

Decomposing the change in a regression coefficient from adding more variables

When new variables are added to a regression, the coefficients on existing variables will typically change. This document shows how to decompose this change according to the share each of the new variables is responsible for.

Difference-in-differences 201

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.

Regression difference-in-differences

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.