Kyunghoon Ban, Zhengrun Chen, Désiré Kédagni
arXiv 18 Aug 2026 · Econometrics
arXiv:2608.18375 · PDF · Extracted main text
We study difference-in-differences (DiD) designs in which a binary treatment changes an endogenous time-varying (continuous, discrete, or mixed) mediator that in turn affects an outcome. Under our model assumptions, we show that the usual DiD estimand mixes the average direct effect on the treated, the average indirect effect, and a trend bias term. A two-way fixed effects (TWFE) regression that controls for the mediator does not recover the average direct treatment effect on the treated. We show that a DiD estimand conditional on the observed mediator path identifies the conditional average direct effect for treated units at that path, and that averaging over the treated path distribution identifies the average direct effect even when unconditional parallel trends fails. A stable average mediator effect assumption helps recover the average mediator and indirect effects. The framework extends to multivariate mediators, nonlinear DiD, and multiple treatment periods settings. Existing doubly robust estimators can be used to conduct inference. Revisiting the effects of railroad access on agricultural land values, the specification yields a positive direct component not mediated by measured market access, while the corresponding indirect component is small and imprecise. A TWFE benchmark with the same sample and baseline geographic covariates gives a small, imprecise direct coefficient, whereas the original-control TWFE coefficient reverses sign.
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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 | Imai, Kosuke, Luke Keele, and Teppei Yamamoto (2010) Identification, Inference and Sensitivity Analysis for Causal Mediation Effects | 1.000 | 5 | 4 | 100% |
| 2 | Sant’Anna, Pedro HC and Jun Zhao (2020) Doubly robust difference-in-differences estimators | 0.843 | 4 | 3 | 75% |
| 3 | Caetano, Carolina and Brantly Callaway (2024) Difference-in-differences when parallel trends holds conditional on covariates | 0.811 | 4 | 2 | 100% |
| 4 | Athey, Susan and Guido W. Imbens (2006) Identification and Inference in Nonlinear Difference-in-Differences Models | 0.644 | 2 | 2 | 100% |
| 5 | de Chaisemartin, Clément and Xavier D'Haultfuille (2020) Two-Way Fixed Effects Estimators with Heterogeneous Treatment Effects | 0.644 | 2 | 2 | 100% |
| 6 | Pearl, Judea (2001) Direct and Indirect Effects | 0.644 | 2 | 2 | 100% |
| 7 | Donaldson, Dave and Richard Hornbeck (2016) Market Access | 0.511 | 2 | 1 | 100% |
| 8 | Brown, Nicholas L., Kyle Butts, and Joakim Westerlund (2026) Direct and Indirect Treatment Effects With Time-Varying Covariates | 0.405 | 1 | 1 | 100% |
| 9 | Callaway, Brantly and Pedro HC Sant’Anna (2021) Difference-in-differences with multiple time periods | 0.405 | 1 | 1 | 100% |
| 10 | Celli, Viviana (2022) Causal Mediation Analysis in Economics: Objectives, Assumptions, Models | 0.405 | 1 | 1 | 100% |
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