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Difference-in-Differences with Unequal Baseline Treatment Status

Author

Listed:
  • Alisa Tazhitdinova
  • Gonzalo Vazquez-Bare

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

  • Alisa Tazhitdinova & Gonzalo Vazquez-Bare, 2023. "Difference-in-Differences with Unequal Baseline Treatment Status," NBER Working Papers 31063, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:31063
    Note: AG CH DEV ED EH LS PE TWP
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    Cited by:

    1. Kortelainen, Mika & Markkanen, Jaakko & Toivanen, Otto & Siikanen, Markku, 2023. "The Effects of Price Regulation on Pharmaceutical Expenditure and Availability," CEPR Discussion Papers 18497, C.E.P.R. Discussion Papers.

    More about this item

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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