Lies, Damn Lies and OLS Weights Part 4
Todays substack is the penultimate fourth part in a five part series on Tymon Słoyzński’s 2022 paper on OLS under heterogenous treatment effects and the weird weighting it uses for estimation. I have tried to think of the best way to organize this material and decided to use the K.I.S.S. Principle — Keep It Simple, Scott. So what I’ll do is this.
Introduce a particular DGP on potential outcomes and the propensity score used for selection into treatment
Run a simulation 500 times, each time estimating the ATT using 6-7 methods
Report a table of coefficients per model, where each column is the method, and each cell is the mean and standard deviation and a title saying what the mean ATT had been for that DGP
Kernel densities showing the bias of the method
And that’s really it. The focus of this exercise isn’t exactly to put Tymons OLS theorem to the test because to do that, I need two crucial assumptions:
Linear propensity score
Expected Potential outcomes linear in the propensity score
One of t…
Keep reading with a 7-day free trial
Subscribe to Scott's Substack to keep reading this post and get 7 days of free access to the full post archives.