Difference-in-Differences for Continuous Treatments and Instruments with Stayers *

50 Pages Posted: 4 Mar 2022 Last revised: 12 Mar 2024

See all articles by Clément de Chaisemartin

Clément de Chaisemartin

SciencesPo - Sciences Po - Department of Economics

Xavier D'Haultfœuille

Center for Research in Economics and Statistics (CREST)

Félix Pasquier

National Institute of Statistics and Economic Studies (INSEE) - Center for Research in Economics and Statistics (CREST)

Gonzalo Vazquez‐Bare

University of California, Santa Barbara (UCSB) - Department of Economics

Date Written: January 18, 2022

Abstract

We propose difference-indifferences estimators in designs where the treatment is continuously distributed at every period, as is often the case when one studies the effects of taxes, tariffs, or prices. We assume that between consecutive periods, the treatment of some units, the switchers, changes, while the treatment of other units remains constant. We show that under a placebo-testable parallel-trends assumption, averages of the slopes of switchers' potential outcomes can be nonparametrically estimated. We generalize our estimators to the instrumental-variable case. We use our estimators to estimate the price-elasticity of gasoline consumption.

Keywords: differences-in-differences, continuous treatment, two-way fixed effects regressions, heterogeneous treatment effects, panel data, policy evaluation, instrumental variable JEL Codes: C21, C23

JEL Classification: C21, C23

Suggested Citation

de Chaisemartin, Clément and d'Haultfoeuille, Xavier and Pasquier, Félix and Vazquez‐Bare, Gonzalo, Difference-in-Differences for Continuous Treatments and Instruments with Stayers * (January 18, 2022). Available at SSRN: https://ssrn.com/abstract=4011782 or http://dx.doi.org/10.2139/ssrn.4011782

Clément De Chaisemartin (Contact Author)

SciencesPo - Sciences Po - Department of Economics ( email )

28, rue des Saints-Pères
Paris, Paris 75007
France

Xavier D'Haultfoeuille

Center for Research in Economics and Statistics (CREST) ( email )

5 avenue Henry le Chatelier
Palaiseau, 91120
France

Félix Pasquier

National Institute of Statistics and Economic Studies (INSEE) - Center for Research in Economics and Statistics (CREST) ( email )

15 Boulevard Gabriel Peri
Malakoff Cedex, 1 92245
France

Gonzalo Vazquez‐Bare

University of California, Santa Barbara (UCSB) - Department of Economics ( email )

Santa Barbara, CA

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