Illustrating the bias of TWFE in event studies

Pretty little horrible pictures!

Introduction

The last few years in empirical micro and the broader quant social sciences has been a little stressful because of a series of papers by econometricians focused on the popular "difference-in-differences" design. Even Netflix uses that design. People may prefer A/B tests, but for some things, it's not feasible or realistic. Uber may not be able to run an A/B test on, for instance, a large new product because it would require flipping the switch across many geographic areas that could be very jarring for customers. So sometimes, these observational design approaches are valuable even if they aren't the slam dunk that you come to expect from an A/B test where physical randomization literally deletes from equations confounding selection bias terms.

But back to diff-in-diff. Starting in 2016, when a paper by Kirill Borusyak and Xavier Jaravel (then grad students) came out finding a lot of serious problems with a canonical specification of OLS models (called "twoway fixed effects…