Fuzzy Differences-in-Differences

By C. Chaisemartin, X. d'Haultfoeuille. 2015

266 citations recorded by the source corpus.

In many applications of the differences-in-differences (DID) method, the treatment increases more in the treatment group, but some units are also treated in the control group. In such fuzzy designs, a popular estimator of treatment effects is the DID of the outcome divided by the DID of the treatment, or OLS and 2SLS regressions with time and group fixed effects estimating weighted averages of this ratio across groups. We start by showing that when the treatment also increases in the control group, this ratio estimates a causal effect only if treatment effects are homogenous in the two groups. Even when the distribution of treatment is stable, it requires that the effect of time be the same on all counterfactual outcomes. As this assumption is not always applicable, we propose two alternative estimators. The first estimator relies on a generalization of common trends assumptions to fuzzy designs, while the second extends the changes-in-changes estimator of Athey & Imbens (2006). When the distribution of treatment changes in the control group, treatment effects are partially identified. Finally, we prove that our estimators are asymptotically normal and use them to revisit applied papers using fuzzy designs.

Subfields: Education, Sociology and Political Science, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/84ec3150f6c7f135228579f091945bc70871a134

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Citations in the corpus

Difference-in-Differences Estimators of Intertemporal Treatment Effects (2020, unknown): “Then, δtru + and δtru − are similar to the switcher’s average treatment effect considered in de Chaisemartin and D’Haultfœuille (2020). Another special case where δtru + may reduce to a standard average treatment effect are staggered adoption designs, where groups can switch in but not out of the tr”
Can Technology Solve the Principal-Agent Problem? Evidence from China’s War on Air Pollution (2020, unknown): “More discussions can be found in de Chaisemartin and D’HaultfŒuille (2018, 2019); Goodman-Bacon (2018); Imai and Kim (2018). significant post-automation discontinuity of 3.0 ppb or 6.0% in NO2 concentrations and a statistically insignificant effect on reported SO2 concentrations.”
Two-Way Fixed Effects Estimators with Heterogeneous Treatment Effects (2018, methodology): “On the other hand, if the proportion of treated units is randomly assigned to each group, negative weights are not a concern.4 The DIDM estimator can also be generalized to fuzzy designs, see point 2 of Theorem S1 in the Web Appendix of de Chaisemartin and D’Haultfœuille (2018) for further details.”
Two-Way Fixed Effects and Differences-in-Differences with Heterogeneous Treatment Effects: A Survey (2021, methodology): “de Chaisemartin and D’Haultfœuille (2020b) review Gentzkow et al. (2011) and Enikolopov et al. (2011), two papers that have estimated TWFE regressions with a non-binary treatment. In both cases, more than half of the weights attached to β̂fe are negative, and the sum of the negative weights is large”
Capital market effects of media synthesis and dissemination: evidence from robo-journalism (2017, unknown): “%) of quarters before (after) automation (i.e., a Bsharp^ instead of Bfuzzy^ treatment (de Chaisemartin and D’Haultfoeuille 2015)).”
Difference-in-Differences with multiple time periods (2018, methodology): “…of DID methods focus on this standard two periods, two groups setup, see e.g. Heckman et al. (1997, 1998), Abadie (2005), Athey and Imbens (2006), Qin and Zhang (2008), Bonhomme and Sauder (2011), Botosaru and Gutierrez (2017), de Chaisemartin and D’Haultfœuille (2017), and Callaway et al. (2018).”
What’s trending in difference-in-differences? A synthesis of the recent econometrics literature (2022, unknown): “Other work has considered DiD settings with non-binary treatments. de Chaisemartin and D’Haultfoeuille (2018) study ‘‘fuzzy’’ DiD settings in which all groups are treated in both time periods, but the proportion of units exposed to treatment increases in one group but not in the other.”