So here is a thread to explain why/when the fuzzydid @Stata package may be useful. Many papers use regressions with group and time fixed effects to estimate effect of treatment on an outcome.
In papers.ssrn.com/sol3/papers.cf… , we conduct a lit review and find that 20% of applied papers published in the AER between 2010 and 2012 estimate these regressions.
As these regressions look very much like the one you would estimate in your canonical 2*2 sharp DID à la Card and Krueger 2000, people have implicitly assumed that those regressions estimate the treatment effect of interest under the standard common trends assumption.
It turns out this is not the case. In papers.ssrn.com/sol3/papers.cf… , we show that if you only assume common trends, those regressions estimate weighted sums of the effect of treatment in each and time period, where some groups and time periods may receive a negative weight.
Negative weights are an issue: because of them, the two-way fixed effects regression coefficient may be <0 even if the treatment effect is > 0 in every group and period, see page 9 of papers.ssrn.com/sol3/papers.cf… for a simple numerical example.
Weights can be estimated, and used as a diagnostic tool. If all / most weights >0, you may be fine using the two ways fe regression. But if many weights <0, and you worry that treatment effect may be heterogeneous across time/groups, you may want to use other estimation method
Stata programs computing the weights and allowing you to do that diagnostic check are available here: sites.google.com/site/clementde…
You may want to use the fuzzydid package when diagnostic check not conclusive (many negative weights, and you worry that treatment effect heterogeneous over time and between groups). Why?
Because fuzzydid package computes Wald-TC estimator, that is valid even if treatment effect heterogeneous over time and between groups. Only relies on common trends assumptions, like standard DID estimator. Those assumptions can be "tested" by looking at pre-trends, as in DID.
The theory underlying the Wald-TC estimator is presented here: papers.ssrn.com/sol3/papers.cf… and here: academic.oup.com/restud/article…
Want to see an example of how you can use the fuzzydid package?
We use package to revisit paper by @MattGentzkow , Jesse Shapiro, and @MSinkinson : aeaweb.org/articles?id=10… (thanks to them for putting their data online!). The Stata code to estimate the wald-tc estimator, do placebo tests etc in this application is here: sites.google.com/site/clementde…
I hope these resources will be helpful if you are interested in using the package, and I am obviously happy to chat some more over twitter or by email.
Finally, several recent papers also study two-way fixed effects regressions and / or propose other estimators in such settings, see e.g. imai.fas.harvard.edu/research/files… scholar.harvard.edu/borusyak/publi… economics.mit.edu/files/14964 nber.org/papers/w25018 papers.ssrn.com/sol3/papers.cf…
In the introduction of papers.ssrn.com/sol3/papers.cf… , we explain the connection between these and our papers. End of thread.
