Difference-in-Differences with Variation in Treatment Timing

Andrew Goodman-Bacon

No 25018, NBER Working Papers from National Bureau of Economic Research, Inc

Abstract: The canonical difference-in-differences (DD) model contains two time periods, “pre” and “post”, and two groups, “treatment” and “control”. Most DD applications, however, exploit variation across groups of units that receive treatment at different times. This paper derives an expression for this general DD estimator, and shows that it is a weighted average of all possible two-group/two-period DD estimators in the data. This result provides detailed guidance about how to use regression DD in practice. I define the DD estimand and show how it averages treatment effect heterogeneity and that it is biased when effects change over time. I propose a new balance test derived from a unified definition of common trends. I show how to decompose the difference between two specifications, and I apply it to models that drop untreated units, weight, disaggregate time fixed effects, control for unit-specific time trends, or exploit a third difference.

JEL-codes: C1 C23 (search for similar items in EconPapers)
Date: 2018-09
New Economics Papers: this item is included in nep-ecm
Note: CH DAE LS PE
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Citations: View citations in EconPapers (380)

Published as Andrew Goodman-Bacon, 2021. "Difference-in-differences with variation in treatment timing," Journal of Econometrics, vol 225(2), pages 254-277.

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