Reference period in new DID estimators

[Mustafa Hussein]

Hello all! I am running a few checks using the new heterogeneity-robust diff-in-diff estimators, specifically: csdid, did_imputation, and did_muliplegt. From each estimator, I retrieve the estimates for the leads and lags relative to the time of policy introduction and compare to the lead/lag estimates from a standard event study model (using reghdfe). It seems that these estimators by default choose the reference period as the latest lead, as opposed to the lead at period -1 right before policy introduction. This may be innocuous with simulated data but it creates problems when one tries to estimate the overall average ATT (all lag/lead estimates will be relative to the wrong period). I've seen this issue with simulated data (e.g. Asjad Naqvi 's incredibly helpful code: https://asjadnaqvi.github.io/DiD/docs/code/06_combined/) and with real data across different projects.

I was wondering if anyone has figured out how to somehow force the reference lead to be period -1 or otherwise re-scaled the lead and lag estimates to be relative to this more meaningful reference.

Thanks for chiming in!

P.S. This could be a very simple fix and I am just completely missing it!

[Nevine Elmallakh]

Hello, I am also looking to compare did_imputation results to a normal event study with the omitted period -1. Did you by any chance find a way to force it in did_imputation?

Thanks!!

[Felipe Lozano]

Hi there!
I have the same issue, and I am looking for a solution to this problem, making event studies comparable across multiple methodologies with the same reference period, and just like you both, I realize that did_imputation chooses the period furthest away from treatment. Has any of you managed to change that?
Thanks.

[Felipe Lozano]

I have been thinking about this since yesterday, and I am solving the issue with an extra step and calculating the linear combination with preX - pre1. This will make the pre-period prior to the implementation the reference period. Somewhat cumbersome, but get's me a comparable event study.

[Jeff Wooldridge]

I sort this out in my forthcoming Empirical Economics paper "Two-Way Fixed Effects, the Two-Way Mundlak Regression, and Difference-in-Differences Estimators." It's available free online, I believe.

The estimators underlying did_imputation and jwdid are "lags only" estimators. They do not estimate pre-treatment effects, so they are not "leads and lags" or event study estimators. They effectively average all pre-treatment periods to obtain a suitable reference value. They are not using the first period as the reference period. The "lags only" name comes from the fact that no lead treatment indicators are included. With a balanced panel and time-constant controls, did_imputation and jwdid produce the same estimates; see Wooldridge (2025).

Sun and Abraham (2021)) and Callaway and Sant'Anna (2021) are leads and lags estimators. SA (2021) anchor on the period just before the intervention. The original CS (2021) did not estimate the pre-trends in the most common way, but this is easily done with the long2 option in csdid. When SA (2021) is made fully flexible as in W (2025), and the covariates don't change over time, it's the same as the CS (2021) regression adjustment estimator using the never treated group -- again, I discuss this in W (2025).

So the main difference is lags only (BJS, Wooldridge) versus leads and lags (SA, CS). How one does the actual estimation appears to be less important provided full flexible in the ATTs and covariates is allowed.

[FernandoRios]

That bein said. jwdid also estimate the model with leads and lags. if you have a never treated group
just add option "never"