Lies, Damn Lies and OLS Weights Part III
And how you almost can't avoid extrapolating
Boy has the last week been a joy ride. I was working through this 2022 Restat article, as I said, by Tymon Słoczyński from Brandeis and trying super hard to get a simulation going that I thought would illustrate something cool, but I learned I had unknowingly created the funkiest data generating process and just had no idea why, just kept working at it. But, eventually I learned a thing or two and made a new data generating process and this one better satisfied the key assumptions in Tymons theorem. So today I’ll walk you through the causal interpretation of the theorem using a simulation and then I’ll conclude with comparing a few estimators.
Restatement of the OLS Theorem
We will be working with this OLS model:
Out focus is on the least squares estimate of tau. Tymon shows that under some assumptions, the OLS coefficient on D is equal to a weighted avera…