I've been so discombobulated lately that I don't keep track of what's in version of papers and what I include in lectures/teaching. So here's an update on what I've learned about DiD in 2022.
#jwdid (borrowing from @friosavila).
#jwdid (borrowing from @friosavila).
1. The pooled OLS method I proposed, which is the same as TWFE and random effects, is also equivalent to a version of imputation I proposed. That means it is consistent for various ATTs under weak assumptions (but those include no anticipation and parallel trends).
2. Because of this equivalence, POLS uses all possible control units in each time period for each cohort. Under standard assumptions, it is efficient.
3. I've only allowed time-constant covariates. But can see the "moderating effects" directly in the regression that gives ATTs.
3. I've only allowed time-constant covariates. But can see the "moderating effects" directly in the regression that gives ATTs.
4. Standard errors are easy to obtain, as is aggregation and their SEs, with built-in Stata commands. See the recent do file in my shared Dropbox. I've figured out lately how to make this even easier.
5. Both event-study type tests and het trend tests can be used to test for pre-trends. Both are the same on the entire sample and on the untreated units. So there is no contamination in using the tests in the fully flexible equation. The het trends also offer a correction.
6. It's easy to allow for exit by extending the notion of a "cohort." I've been teaching this but it needs to be added to my TWFE/TWM paper.
7. The simulations (that I need to add) look good for POLS/TWFE.
7. The simulations (that I need to add) look good for POLS/TWFE.
8. Once I saw the POLS/TWFE equivalence for the linear case, it seemed the former can extend to nonlinear cases. It does, and the pooled logit, frac logit, Poisson (with exp mean) identify ATTs under index PT assumptions. Hopefully that paper will appear in the Econometrics J.
9. I probably put too much weight on elegance of estimation methods, but how the marginal effects turn into the ATTs is really satisfying. Especially because it is extends cross-sectional regression adjustment to the staggered DiD setting.
10. I now have a very good idea about how to make it all work with repeated cross section, but that's not written down.
Feel free to ask questions about the method or Stata files. It's like the 10th version of some of those do files.
See my pinned tweet for the Dropbox link.
Feel free to ask questions about the method or Stata files. It's like the 10th version of some of those do files.
See my pinned tweet for the Dropbox link.
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