Clément de Chaisemartin, Xavier D'Haultfœuille, Félix Pasquier, Doulo Sow, Gonzalo Vazquez-Bare
arXiv 18 Jan 2022 · Econometrics · 52 citations (OpenAlex)
arXiv:2201.06898 · PDF · DOI · OpenAlex · Extracted main text
When one studies the effects of taxes, tariffs, or prices using panel data, the treatment is often continuously distributed in every period. We propose difference-in-differences (DID) estimators for such cases. We assume that between consecutive periods, the treatment of some units, the switchers, changes, while the treatment of other units, the stayers, remains constant. We show that under a parallel-trends assumption, the slopes of switchers' potential outcomes are nonparametrically identified by difference-in-differences estimands comparing the outcome evolutions of switchers and stayers with the same baseline treatment. Controlling for the baseline treatment ensures that our estimands remain valid if the treatment's effect changes over time. We consider two weighted averages of switchers' slopes, and discuss their respective advantages. For each weighted average, we propose a doubly-robust, nonparametric, and $\sqrt{n}$-consistent estimator. We generalize our results to the instrumental-variable case. We apply our method to estimate the price-elasticity of gasoline consumption.
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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 | de Chaisemartin, C. and X. D'Haultfuille (2025) Difference-in-differences estimators of intertemporal treatment effects | 0.659 | 7 | 1 | 86% |
| 2 | Li, S., J. Linn, and E. Muehlegger (2014) Gasoline taxes and consumer behavior | 0.644 | 4 | 1 | 100% |
| 3 | Callaway, B., A. Goodman-Bacon, and P. H. Sant'Anna (2021) Difference-in-differences with a continuous treatment | 0.585 | 3 | 1 | 100% |
| 4 | Graham, B. S. and J. L. Powell (2012) Identification and estimation of average partial effects in “irregular” correlated random coefficient panel data models | 0.585 | 3 | 1 | 100% |
| 5 | Andrews, D. W (1991) Asymptotic optimality of generalized cl, cross-validation, and generalized cross-validation in regression with heteroskedastic e… | 0.511 | 2 | 1 | 100% |
| 6 | Borusyak, K., X. Jaravel, and J. Spiess (2024) Revisiting event-study designs: robust and efficient estimation | 0.511 | 2 | 1 | 100% |
| 7 | Coglianese, J., L. W. Davis, L. Kilian, and J. H. Stock (2017) Anticipation, tax avoidance, and the price elasticity of gasoline demand | 0.511 | 2 | 1 | 100% |
| 8 | de Chaisemartin, C (2010) A note on instrumented difference in differences | 0.511 | 2 | 1 | 100% |
| 9 | de Chaisemartin, C. and X. D'Haultfuille (2020) Two-way fixed effects estimators with heterogeneous treatment effects | 0.511 | 2 | 1 | 100% |
| 10 | Fajgelbaum, P. D., P. K. Goldberg, P. J. Kennedy, and A. K. Khandelwal (2020) The return to protectionism | 0.511 | 2 | 1 | 100% |
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