I need to consider using a custom-built estimator for this "close elections DiD" thing.
Under the close election assumption, I have treatment randomization over wards. However, because the "treatment" is having a "tied" alderman replaced, I dosage correlates to net votes. Furthermore, under the close election assumption, precinct-level net votes don't significantly change when treated or untreated.
Thus, I effectively see the "counter-factual dosage" each precinct would have gotten if their alderman had been reelected. I'm effectively matching on this "dosage" and then running a DiD, but this leads to a lower power than if I can use all of the 50 precincts available in each ward.
I need to consider using a custom-built estimator for this "close elections DiD" thing.
Under the close election assumption, I have treatment randomization over wards. However, because the "treatment" is having a "tied" alderman replaced, I dosage correlates to net votes. Furthermore, under the close election assumption, precinct-level net votes don't significantly change when treated or untreated.
Thus, I effectively see the "counter-factual dosage" each precinct would have gotten if their alderman had been reelected. I'm effectively matching on this "dosage" and then running a DiD, but this leads to a lower power than if I can use all of the 50 precincts available in each ward.
Traditional DiD estimators (e.g., https://bcallaway11.github.io/posts/five-minute-did-continuous-treatment) assume that you can't see this "counterfactual dosage," but in this case, we can.