Resolve the ambiguity caused by unobserved treatment history

Determine whether an observed treatment event is the corresponding event occurrence in a unit’s complete treatment history when treatment events occurring before the observation window are unobserved.

Background

The sequential imputation estimator requires identifying the number and timing of treatment events, but panel data may begin after a unit has already experienced one or more events. In that case, the first observed event need not be the first event ever experienced.

The paper states that without complete treatment histories, researchers cannot distinguish the count of events observed during the panel from the count of events ever experienced. This leaves the interpretation of event-specific estimates unresolved: they must be treated as effects of the first, second, or later observed event rather than necessarily the corresponding event in the full history.

References

If the full treatment trajectory is not observed in the data, it is unclear whether the $X$-th observed treatment event is the $X$-th treatment event ever experienced.

— First as Tragedy? Second as What? Estimating Dynamic Effects of Recurrent Events  (2609.30007 - Keiller, 24 Sep 2026) in Section 5, subsection “Initial Conditions”