Today I want to give a shout-out to @TymonSloczynski paper, "Interpreting OLS Estimands When Treatment Effects Are Heterogeneous: Smaller Groups Get Larger Weights", that is currently available here:
people.brandeis.edu/~tslocz/Sloczy…
Paper is conditionally accepted at ReStat!
people.brandeis.edu/~tslocz/Sloczy…
Paper is conditionally accepted at ReStat!
This is a very interesting paper that highlights some potential pitfalls of not separating the identification and estimation/inference steps when doing causal inference.
In other words, OLS may be messing up your regression interpretations.
So good to see that I am not alone!
In other words, OLS may be messing up your regression interpretations.
So good to see that I am not alone!
Let go straight to the main message of Tymon's paper.
We all have seen and probably run linear regressions like this and attach causal interpretation to \tau after invoking selection on observables type of assumptions.
We all have seen and probably run linear regressions like this and attach causal interpretation to \tau after invoking selection on observables type of assumptions.
But the key question here is: "what is the causal parameter that \tau recovers when treatment effects are heterogeneous?"
Easy answer is that it is a weighted average of causal effects. But that is a cheap answer.....
Easy answer is that it is a weighted average of causal effects. But that is a cheap answer.....
If we want to attach causal interpretation to tau, we need to understand the weights!
Knowing if that tau is closer to the ATE, ATT or ATU is important as the policy implications may differ.
This is what @TymonSloczynski paper is essentially about: understand these weights!
Knowing if that tau is closer to the ATE, ATT or ATU is important as the policy implications may differ.
This is what @TymonSloczynski paper is essentially about: understand these weights!
He shows that \tau is a convex combination of the ATT and the ATU, but these weights are *somehow weird*: The more units are treated, the less weight is placed on ATT.
This is exactly what you *did not* want, I am sure!
This is exactly what you *did not* want, I am sure!
@TymonSloczynski also propose simple diagnostic tools that we can use in our applications to see if the OLS linear regression mentioned way above is a "reasonable" choice.
For the sake of #EconTwitter, @TymonSloczynski does not engage in the #Stata vs #rstats war! What does that mean?
It means he provides both Stata and R packages that implement his diagnostic tools.
It means he provides both Stata and R packages that implement his diagnostic tools.
Main take-way message is: please, separate the identification from the estimation/inference steps when doing causal inference!
If you do not want to do that, at least make sure you are aware what you are estimating.
That's all!
If you do not want to do that, at least make sure you are aware what you are estimating.
That's all!
