Why is the generalized DiD not reported as the Variance Weighted Average Treatment Effect on the Treated (VWATT)?

Question

Normally, when dealing with the staggered implementation of laws we normally use generalized difference-in-differences. I saw that Dasgupta, 2019, p. 2596-2597 did not mention the VWATT which is described by Goodman-Bacon (2018), I am wondering why he did not account for the VWATT? From his model, it appears they simply ran OLS with fixed effects and clustering.

The identification in Dasgupta's paper is:

$Y_{it}$ = $\alpha$ + $\beta$ $(Leniency Law)_{kt}$ + $\delta$$X_{ikt}$ + $\theta$$_t$ + $\gamma$$_i$ +$\epsilon$$_{it}$

where $i$, $k$, and $t$ index firms, countries, and years respectively. $X_{ikt}$ is a vector of the different firm, country, and industry control, while $\gamma$ and $\theta$ are firm and year fixed effects.

Answer 1

It's hard to say.

If may wager a guess, they were likely unaware of the new developments in this area. The manuscript was submitted to the journal in early 2019 which suggests they were doing some of the heavy-lifting for the paper in 2018. Andrew Goodman-Bacon's research surfaced as an NBER working paper in late 2018. There's no guarantee they knew about the potential pitfalls of using the two-way fixed effects estimator, especially in settings with a staggered treatment. There's often a lag before research is shared with the wider scientific community.

Even if they were aware of the downsides, they arguably didn't have enough time to implement Goodman-Bacon's decomposition in software. Note the 2018 working paper did not include any code, at least to my knowledge. The Stata package bacondecomp was first made available in 2019. The command actually calculates the smaller component estimators (i.e., 2x2 estimators) and their weights for you. The R analog of the bacon decomposition was made available in R several months later (e.g., review R Package bacondecomp, published: 2020-01-24). More working papers have surfaced recently and across multiple disciplines, most of which include code. Peruse the work of Callaway and Sant'Anna 2019 and Imai et al. (2020), to name only a few.

Please note this response is somewhat conjectural. It's possible they tried other estimation strategies before publication. Maybe the weighted estimate didn't deviate from their early findings, so they reported the unweighted estimate and just moved on. It's hard to offer a solid post-hoc justification without speaking with the authors.