Heterogeneous Treatment Effect Difference-in-Differences (HTE-DiD)
Also known as: HTE-DiD, heterogeneous DiD, CATT estimator, group-time ATT
HTE-DiD extends the classic Difference-in-Differences estimator to settings where treatment effects vary across units, time periods, or treatment cohorts. Developed formally by Callaway and Sant'Anna (2021) and Sun and Abraham (2021), it avoids the biases that arise when a conventional two-way fixed-effects regression is used with staggered adoption or effect heterogeneity, by estimating cohort-and-time-specific average treatment effects that can then be aggregated flexibly.
Key highlights
- Correctly handles staggered treatment adoption by avoiding the use of already-treated units as controls, eliminating the negative-weighting bias of two-way fixed effects.
- Provides disaggregated cohort-and-time estimates that reveal how effects evolve and differ across groups, rather than obscuring them in a single number.
- Supports flexible aggregation: researchers can report the overall ATT, dynamic effects relative to treatment date, or cohort-specific effects depending on their research question.
- The cohort-specific parallel-trends assumption is testable using pre-treatment data, making the identification strategy transparent and falsifiable.
- Accommodates never-treated and not-yet-treated control units, maximising the use of available comparison variation.
Intuition
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How it works
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When to use it
Use HTE-DiD when treatment is adopted at different times by different units (staggered rollout), when you suspect treatment effects vary across cohorts or evolve over time, or when standard two-way fixed-effects DiD may produce biased estimates due to heterogeneous effects. It requires panel or repeated cross-section data, a continuous or binary outcome, and multiple pre-treatment periods to test the parallel-trends assumption. Do not use HTE-DiD when all units are treated simultaneously and there is strong prior reason to assume homogeneous effects — classic DiD suffices in that case and is simpler to communicate.
Strengths & limitations
- Correctly handles staggered treatment adoption by avoiding the use of already-treated units as controls, eliminating the negative-weighting bias of two-way fixed effects.
- Provides disaggregated cohort-and-time estimates that reveal how effects evolve and differ across groups, rather than obscuring them in a single number.
- Supports flexible aggregation: researchers can report the overall ATT, dynamic effects relative to treatment date, or cohort-specific effects depending on their research question.
- The cohort-specific parallel-trends assumption is testable using pre-treatment data, making the identification strategy transparent and falsifiable.
- Accommodates never-treated and not-yet-treated control units, maximising the use of available comparison variation.
- Requires sufficient observations within each cohort-period cell; thin cells produce imprecise estimates and may prevent estimation for some cohorts.
- More complex to implement and communicate than classic DiD; requires software such as the csdid (Stata) or did (R) package.
- The never-treated or not-yet-treated parallel-trends assumption, while weaker than classic DiD, is still untestable in the post-treatment periods and must be defended on substantive grounds.
- Aggregated summaries depend on the choice of weights; different aggregations can yield different effect sizes, and the choice should be motivated by theory rather than by which looks best.
- In designs with very few cohorts or short panels, power is limited and CATT estimates for late cohorts may be identified from few pre-treatment periods.
Common pitfalls
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Applications
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Frequently asked
Why can I not just run a two-way fixed-effects regression and report the interaction coefficient?
With staggered adoption and heterogeneous effects, the TWFE estimator implicitly uses already-treated units as controls for later-treated units and applies negative weights to some cohort-period effects. This can produce estimates that are a misleading blend of effects — or even have the wrong sign. Callaway and Sant'Anna (2021) and Goodman-Bacon (2021) document this problem formally.
What is a CATT and why does it matter?
A Cohort-Average Treatment effect on the Treated is the average effect for units that first received treatment in a specific period, evaluated at a specific calendar time. Reporting CATTs preserves the richness of effect heterogeneity and allows researchers to summarise effects in ways that are directly interpretable — for example, the average effect two periods after treatment across all cohorts.
Which units should serve as the control group?
Only never-treated units, or units that have not yet been treated as of the time period being compared. Already-treated units must be excluded from the control group for a given cohort, because their outcomes have already been affected by treatment and they no longer represent the untreated counterfactual.
How do I test the parallel-trends assumption in a staggered design?
Plot or report the CATT estimates for each cohort in the pre-treatment periods. If parallel trends hold, these pre-treatment estimates should be close to zero and statistically insignificant. A formal pre-trend test can be conducted by regressing the pre-treatment CATTs on a time trend and testing whether the coefficients are jointly zero.
What software is available for HTE-DiD?
The did package in R and csdid in Stata implement the Callaway-Sant'Anna estimator. The eventstudyinteract package in Stata implements the Sun-Abraham estimator. Both are well-documented and actively maintained.
Sources
- 1.Callaway, B., & Sant'Anna, P. H. C. (2021). Difference-in-Differences with multiple time periods. Journal of Econometrics, 225(2), 200-230.
- 2.Sun, L., & Abraham, S. (2021). Estimating dynamic treatment effects in event studies with heterogeneous treatment effects. Journal of Econometrics, 225(2), 175-199.
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Cite this page
ScholarGate. (2026, June 3). Heterogeneous Treatment Effect Difference-in-Differences. ScholarGate. https://scholargate.app/causal-inference/heterogeneous-treatment-effect-difference-in-differences