Difference-in-Differences with Unequal Baseline Treatment Status

49 Pages Posted: 27 Mar 2023 Last revised: 16 Nov 2024

See all articles by Alisa Tazhitdinova

Alisa Tazhitdinova

University of California, Santa Barbara (UCSB)

Gonzalo Vazquez‐Bare

University of California, Santa Barbara (UCSB) - Department of Economics

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Date Written: March 2023

Abstract

We study a difference-in-differences (DiD) framework where groups experience unequal treatment statuses in the pre-policy change period. This approach is commonly employed in empirical studies but it contradicts the canonical model's assumptions. We show that in such settings, the standard DiD approach fails to recover the average treatment effect (ATT), unless the treatment effect is immediate and constant over time. Furthermore, the usual parallel trends test is invalid, meaning one may find pre-trends when the parallel trends assumption holds, and vice versa. We discuss two solutions. First, we show that including a linear term trend will recover the ATT if the differences in trends are constant over time (both in unequal baseline and canonical DiD settings) but not otherwise. Second, estimation in reverse also recovers the ATT if the potential outcomes do not depend on past treatments and post-policy statuses are converging.

Suggested Citation

Tazhitdinova, Alisa and Vazquez‐Bare, Gonzalo, Difference-in-Differences with Unequal Baseline Treatment Status (March 2023). NBER Working Paper No. w31063, Available at SSRN: https://ssrn.com/abstract=4400705

Alisa Tazhitdinova (Contact Author)

University of California, Santa Barbara (UCSB) ( email )

South Hall 5504
Santa Barbara, CA 93106
United States

Gonzalo Vazquez‐Bare

University of California, Santa Barbara (UCSB) - Department of Economics ( email )

Santa Barbara, CA

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