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Difference-in-Differences Estimators for Treatments Continuously Distributed at Every Period

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

Abstract

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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43
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Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1de Chaisemartin, C. and X. D'Haultfuille (2025) Difference-in-differences estimators of intertemporal treatment effects0.6597186%
2Li, S., J. Linn, and E. Muehlegger (2014) Gasoline taxes and consumer behavior0.64441100%
3Callaway, B., A. Goodman-Bacon, and P. H. Sant'Anna (2021) Difference-in-differences with a continuous treatment0.58531100%
4Graham, B. S. and J. L. Powell (2012) Identification and estimation of average partial effects in “irregular” correlated random coefficient panel data models0.58531100%
5Andrews, D. W (1991) Asymptotic optimality of generalized cl, cross-validation, and generalized cross-validation in regression with heteroskedastic e…0.51121100%
6Borusyak, K., X. Jaravel, and J. Spiess (2024) Revisiting event-study designs: robust and efficient estimation0.51121100%
7Coglianese, J., L. W. Davis, L. Kilian, and J. H. Stock (2017) Anticipation, tax avoidance, and the price elasticity of gasoline demand0.51121100%
8de Chaisemartin, C (2010) A note on instrumented difference in differences0.51121100%
9de Chaisemartin, C. and X. D'Haultfuille (2020) Two-way fixed effects estimators with heterogeneous treatment effects0.51121100%
10Fajgelbaum, P. D., P. K. Goldberg, P. J. Kennedy, and A. K. Khandelwal (2020) The return to protectionism0.51121100%

Showing the top 10 of 43 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Difference-in-Differences Estimators with Continuous Treatments and no Stayers0.69351
2What Do We Get from Two-Way Fixed Effects Regressions? Implications from Numerical Equivalence0.64422
3An Effective Treatment Approach to Difference-in-Differences with General Treatment Patterns0.40511