Stacked Triple Differences

Meng Hsuan Hsieh

Papers from arXiv.org

Abstract: Triple differences (DDD) is a workhorse quasi-experimental design in applied economics. But, under staggered adoption, its conventional three-way fixed-effects (3WFE) implementation inherits the forbidden-comparison and interpretation issues now well understood in the difference-in-differences literature. To resolve these issues, I introduce stacked DDD. I extend the stacked difference-in-differences approach to the DDD setting by creating self-contained stacks, each consisting of four cells over an event window: treated and clean comparison cohorts, each with treatment-eligible and treatment-ineligible units. Appending these stacks yields a unified dataset for estimating treatment effects without making forbidden comparisons. I prove that, at each post-treatment event-time, a linear regression with fully saturated fixed-effects applied to the stacked dataset identifies a strictly positive, cell-size-weighted average of stack-level conditional average treatment effects, with stack weights proportional to stack-level cell sizes. Building on this characterization, I outline alternative weighting schemes that recover distinct, transparent causal estimands with clear interpretations. Stacked DDD complements recent GMM and imputation-based frameworks by trading efficiency for regression-based transparency, pairwise (rather than global) parallel trends, and direct control over aggregation weights. I provide two empirical illustrations where stacked DDD yields substantially different quantitative conclusions compared to existing procedures.

Date: 2026-04
References: Add references at CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/2604.22982 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2604.22982

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().