Lies, Damn Lies and OLS Weights Part II

More on Tymon Sloczynski OLS Theorem

In an earlier substack on Tymon Sloczynski‘s 2022 Restat (hereafter “Tymon”) I went through the algebraic properties of this OLS model:

\(Y_i = \alpha + \tau D_i + \beta X_i + \varepsilon_i\quad{\text{ (1)}}\)

I noted that Tymon had a theorem he called the “weighted average interpretation of OLS” that showed the OLS estimate of tau was a weighted average of two average partial linear effect quantities — one for the treatment …