A0275
Title: Difference-in-Differences: A Functional data perspective
Authors: Chencheng Fang - University of Bonn (Germany) [presenting]
Dominik Liebl - University Bonn (Germany)
Abstract: Difference-in-Differences (DiD) is typically constructed in a panel data setting, which considers time-series processes in discrete time. We argue, however, that the underlying processes typically can be viewed as (relatively) smooth processes in continuous time, which leads to a functional data perspective. Our theoretical framework takes into account the interpolation errors due to the fact that the underlying functional data are not observed in continuous time, but need to be constructed using natural spline interpolations. We show that the interpolation errors are uniformly negligible under a large $n, T$ asymptotic. It is proved that our functional treatment effects estimator is point-wise asymptotically normal. Moreover, we also adopt a fully functional perspective and show that our functional treatment effects estimator converge to a Gaussian process in the Banach space of continuous functions. The latter result allows us to derive powerful simultaneous confidence bands for the functional treatment effect parameter. One major contribution of our functional perspective on DiD is that we can do functional registration. This provides a completely new possibility for relaxing the critical parallel trends assumption of classic DiD. We show that our registration procedure is consistent, and we derive conditions under which the estimation errors from the registration procedure are asymptotically negligible in the inference about the functional treatment effects.
