Once we move beyond the simplest two-group, two-period difference-in-differences design, a surprisingly basic question becomes important:
What treatment effect are we actually trying to estimate?
In staggered-adoption settings, different units receive treatment at different times. Treatment effects may also vary across cohorts and evolve with time since adoption.
That means there may be no single treatment effect waiting to be recovered. Instead, there is a collection of economically meaningful effects that can be aggregated in different ways.
Start With the Estimand
Suppose group g first receives treatment in period g. A natural causal parameter is the group-time average treatment effect:
This asks: among units first treated in period g, what is the average treatment effect at calendar time t?
Once we write the question this way, heterogeneity is not a complication added after estimation. It is part of the object we are trying to understand.
A Marketplace Advertising Example
Imagine a marketplace introducing a sponsored-advertising product across cities at different dates.
Some cities adopt early. Others adopt months later. The company wants to know whether access to sponsored advertising increases seller revenue.
But “the effect of advertising” may not be a single number. Sellers may need time to learn how to use the product. Early markets may have different seller composition. Effects may be initially small and grow as adoption matures.
A treatment effect for a city one month after launch is therefore not necessarily the same economic object as the treatment effect twelve months after launch.
Calendar Time and Event Time Answer Different Questions
Calendar time tells us when an outcome was observed. Event time tells us how long a unit has been exposed to treatment.
where e denotes event time.
An event-time effect can summarize treatment effects for units that have been exposed for the same amount of time, even if they entered treatment in different calendar periods.
This is often economically meaningful when treatment effects are dynamic.
There Is More Than One Reasonable Average
After estimating a collection of ATT(g,t) parameters, we may want to summarize them. But several summaries are possible.
We could average across treated groups to obtain an overall treatment effect. We could average within cohorts to understand whether early and late adopters respond differently. Or we could aggregate by event time to study how effects evolve after treatment.
Different aggregation rules answer different economic questions. There is no reason to expect them to produce the same number.
The Weights Are Part of the Economic Question
Suppose a large cohort experiences a modest treatment effect while a small cohort experiences a very large effect.
A population-weighted average emphasizes the experience of the larger group. An equally weighted cohort average gives each cohort the same influence.
Neither is automatically correct or incorrect. They answer different questions.
This is why aggregation should not be treated as a mechanical final step. The weighting scheme helps define the estimand itself.
From Decision to Estimator
In applied work, I find it useful to reverse the usual workflow. Instead of starting with a regression specification, start with the decision that the analysis is intended to inform.
Decision → Causal Question → Estimand → Identification Strategy → Estimator
In the marketplace example, management might be deciding whether to expand the advertising product nationally.
That decision may require understanding the average effect across eligible markets. A product team might instead care about how quickly benefits emerge after launch. Another team may care about whether effects differ systematically across types of markets.
Those are related questions, but they are not the same estimand.
Why This Matters Beyond Difference-in-Differences
This issue is not unique to staggered DiD.
Many empirical disagreements that appear to be disagreements about estimators are actually disagreements about the causal quantity being estimated.
Before debating standard errors, specifications, or algorithms, it is worth asking whether two analyses are even targeting the same parameter.
A statistically correct estimate of the wrong estimand can still be causally uninformative for the decision we care about.
Takeaway
Staggered treatment timing forces us to confront something that is easy to overlook in simpler designs: treatment effects can differ across groups and across time.
Once that happens, asking for “the treatment effect” is incomplete.
We need to define whose effect, at what time, and with what aggregation rule.
The estimator should come after those choices—not before them.