Triple Difference

A triple-difference (DDD) design adds a third contrast to difference-in-differences: within the treated units it compares an affected subgroup to an unaffected subgroup, so the estimate is the difference between two DiDs — e.g. (affected − unaffected group) × (treated − control state) × (after − before). The extra differencing nets out any shock common to the affected group across all states and any state-specific shock common to both subgroups. Its key virtue ([[OldenMoen2022-TripleDifference|Olden & Møen 2022]]): DDD does not require the two underlying DiDs to each satisfy Parallel-Trends; it needs only one parallel-trends assumption — that the trend differential between the two subgroups is the same in treated and control units, so the shared DiD bias cancels.

Relied on by

Difference-in-differences (DiD) applications with a within-unit eligibility/exposure margin; introduced by Gruber1994-IncidenceMandatedMaternity and formalized by OldenMoen2022-TripleDifference.

Referenced by

New-papers pass (2026-07-20): Gruber1994-IncidenceMandatedMaternity (introduces the estimator — maternity mandates on women of childbearing age), OldenMoen2022-TripleDifference (derives its single-parallel-trend identifying assumption).