Sina Akbari, Negar Kiyavash, AmirEmad Ghassami
arXiv 27 Feb 2025 · Econometrics
arXiv:2502.19788 · PDF · DOI · OpenAlex · Extracted main text
The triple difference causal inference framework is an extension of the well-known difference-in-differences framework. It relaxes the parallel trends assumption of the difference-in-differences framework through leveraging data from an auxiliary domain. Despite being commonly applied in empirical research, the triple difference framework has received relatively limited attention in the statistics literature. Specifically, investigating the intricacies of identification and the design of robust and efficient estimators for this framework has remained largely unexplored. This work aims to address these gaps in the literature. From the identification standpoint, we present outcome regression and weighting methods to identify the average treatment effect on the treated in both panel data and repeated cross-section settings. For the latter, we relax the commonly made assumption of time-invariant composition of units. From the estimation perspective, we develop semiparametric estimators for the triple difference framework in both panel data and repeated cross-sections settings. These estimators are based on the cross-fitting technique, and flexible machine learning tools can be used to estimate the nuisance components. We characterize conditions under which our proposed estimators are efficient, doubly robust, root-n consistent and asymptotically normal. As an application of our proposed methodology, we examined the effect of mandated maternity benefits on the hourly wages of women of childbearing age and found that these mandates result in a 2.6% drop in hourly wages.
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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 | Alberto Abadie (2005) Semiparametric difference-in-differences estimators | 0.811 | 4 | 2 | 100% |
| 2 | Jonathan Gruber (1994) The incidence of mandated maternity benefits | 0.737 | 3 | 2 | 100% |
| 3 | Andreas Olden and Jarle Men (2022) The triple difference estimator | 0.585 | 3 | 1 | 100% |
| 4 | Pedro HC Sant'Anna and Qi Xu (2025) Difference-in-differences with compositional changes | 0.585 | 3 | 1 | 100% |
| 5 | Joseph D. Y. Kang and Joseph L. Schafer (2007) Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data | 0.511 | 3 | 2 | 33% |
| 6 | Victor Chernozhukov, Denis Chetverikov, Mert Demirer, Esther Duflo,… (2018) Double/debiased machine learning for treatment and structural parameters, 2018 | 0.511 | 2 | 1 | 100% |
| 7 | James J Heckman, Hidehiko Ichimura, and Petra E Todd (1997) Matching as an econometric evaluation estimator: Evidence from evaluating a job training programme | 0.511 | 2 | 1 | 100% |
| 8 | Seung-Hyun Hong (2013) Measuring the effect of napster on recorded music sales: difference-in-differences estimates under compositional changes | 0.511 | 2 | 1 | 100% |
| 9 | Pedro HC Sant’Anna and Jun Zhao (2020) Doubly robust difference-in-differences estimators | 0.511 | 2 | 1 | 100% |
| 10 | Castiel Chen Zhuang (2024) A way to synthetic triple difference | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 33 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Three’s a crowd: Identification challenges in the triple difference model with spillover effects | 0.405 | 1 | 1 |