Dear Applied Statistics Workshop Community,
Our next meeting of the semester will be on September 28 (12:00 EST). Luke
Miratrix and Dae Woong Ham will present "A devil’s bargain? Repairing a
Difference in Differences parallel trends assumption with an initial
matching step."
<Where>
In-person: CGIS K354
Bagged lunches are available for pick-up at 11:40 (CGIS K354).
Zoom:
https://harvard.zoom.us/j/99181972207?pwd=Ykd3ZzVZRnZCSDZqNVpCSURCNnVvQT09
<Abstract>
The Difference in Difference (DiD) estimator is a popular estimator built
on the "parallel trends" assumption that the treatment group, absent
treatment, would change "similarly" to the control group over time. To
increase the plausibility of this assumption, a natural idea is to match
treated and control units prior to a DiD analysis. In this paper, we
characterize the bias of matching under a class of linear structural models
with both observed and unobserved confounders that have time varying
effects. Given this framework, we find that matching on baseline covariates
generally reduces the bias associated with these covariates, when compared
to the original DiD estimator. We further find that additionally matching
on pre-treatment outcomes has both cost and benefit. First, matching on
pre-treatment outcomes will partially balance unobserved confounders, which
mitigates some bias. This reduction is proportional to the outcome's
reliability, a measure of how coupled the outcomes are with the latent
covariates. On the other hand, we find that matching on pre-treatment
outcomes also undermines the second "difference" in a DiD estimate by
forcing the treated and control group's pre-treatment outcomes to be equal.
This injects bias into the final estimate, creating a bias-bias tradeoff.
We extend our bias results to multivariate confounders with multiple
pre-treatment periods and find similar results. We summarize our findings
with heuristic guidelines on whether to match prior to a DiD analysis,
along with a method for roughly estimating the reduction in bias. We
illustrate our guidelines by reanalyzing a recent empirical study that used
matching prior to a DiD analysis to explore the impact of principal
turnover on student achievement.
<2022 Schedule>
GOV 3009 Website:
https://projects.iq.harvard.edu/applied.stats.workshop-gov3009
Calendar:
https://calendar.google.com/calendar/embed?src=c_3v93pav9fjkkldrbu9snbhned8…
Best,
Shusei