arXiv 26 Feb 2025 · Econometrics
arXiv:2502.19620 · PDF · DOI · OpenAlex · Extracted main text
Triple difference designs have become increasingly popular in empirical economics. The advantage of a triple difference design is that, within a treatment group, it allows for another subgroup of the population -- potentially less impacted by the treatment -- to serve as a control for the subgroup of interest. While literature on difference-in-differences has discussed heterogeneity in treatment effects between treated and control groups or over time, little attention has been given to the implications of heterogeneity in treatment effects between subgroups. In this paper, I show that the parameter identified under the usual triple difference assumptions does not allow for causal interpretation of differences between subgroups when subgroups may differ in their underlying (unobserved) treatment effects. I propose a new parameter of interest, the causal difference in average treatment effects on the treated, which makes causal comparisons between subgroups. I discuss assumptions for identification and derive the semiparametric efficiency bounds for this parameter. I then propose doubly-robust, efficient estimators for this parameter. I use a simulation study to highlight the desirable finite-sample properties of these estimators, as well as to show the difference between this parameter and the usual triple difference parameter of interest. An empirical application shows the importance of considering treatment effect heterogeneity in practical applications.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Gruber, Jonathan (1994) The Incidence of Mandated Maternity Benefits | 1.000 | 13 | 5 | 100% |
| 2 | Olden, Andreas, Møen, Jarle (2022) The Triple Difference Estimator | 1.000 | 9 | 3 | 100% |
| 3 | Callaway, Brantly, Sant’Anna, Pedro H. C (2021) Difference-in-Differences with Multiple Time Periods | 0.902 | 15 | 6 | 73% |
| 4 | Sant’Anna, Pedro H. C., Zhao, Jun (2020) Doubly Robust Difference-in-Differences Estimators | 0.860 | 11 | 5 | 64% |
| 5 | Callaway, Brantly, Goodman-Bacon, Andrew, Sant'Anna, Pedro H. C (2021) Difference-in-Differences with a Continuous Treatment | 0.737 | 3 | 2 | 100% |
| 6 | Chaisemartin, Clément, D'Haultfœuille, Xavier (2020) Two-Way Fixed Effects Estimators with Heterogeneous Treatment Effects | 0.737 | 3 | 2 | 100% |
| 7 | Ortiz-Villavicencio, Marcelo, Sant'Anna, Pedro H. C (2025) Better Understanding Triple Differences Estimators | 0.644 | 4 | 1 | 100% |
| 8 | Baum, Charles L (2003) The Effect of State Maternity Leave Legislation and the 1993 Family and Medical Leave Act on Employment and Wages | 0.644 | 2 | 2 | 100% |
| 9 | Chaisemartin, Clément, D’Haultfœuille, Xavier (2018) Fuzzy Differences-in-Differences | 0.644 | 2 | 2 | 100% |
| 10 | Derenoncourt, Ellora, Montialoux, Claire (2020) Minimum Wages and Racial Inequality | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 31 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | 2606.24785 | 0.874 | 12 | 2 |
| 2 | Three’s a crowd: Identification challenges in the triple difference model with spillover effects | 0.843 | 3 | 3 |
| 3 | Difference-in-Differences Designs: A Practitioner's Guide | 0.405 | 1 | 1 |
| 4 | Better Understanding Triple Differences Estimators | 0.405 | 1 | 1 |