Difference-in-Differences Estimators with Continuous Treatments and No Stayers

4 Pages Posted: 19 Feb 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)

Gonzalo Vazquez‐Bare

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

Date Written: February 8, 2024

Abstract

Many treatments or policy interventions are continuous in nature. Examples include prices, taxes or temperatures. Empirical researchers have usually relied on two-way fixed effect regressions to estimate treatment effects in such cases, see e.g. Deschênes and Greenstone (2012). However, such estimators are not robust to heterogeneous treatment effects in general (De Chaisemartin and D’Haultfoeuille, 2020); they also rely on the linearity of treatment effects. We propose estimators for continuous treatments that do not impose those restrictions, and that can be used when there are no stayers: the treatment of all units changes from one period to the next. This is for instance the case when the treatment is precipitations or temperatures: for instance, temperatures of all US counties change, if ever so slightly, between two consecutive years. We start by extending the nonparametric results of de Chaisemartin et al. (2023) to cases without stayers. We also present a parametric estimator, and use it to revisit Deschênes and Greenstone (2012).

Suggested Citation

de Chaisemartin, Clément and d'Haultfoeuille, Xavier and Vazquez‐Bare, Gonzalo, Difference-in-Differences Estimators with Continuous Treatments and No Stayers (February 8, 2024). Available at SSRN: https://ssrn.com/abstract=4720535 or http://dx.doi.org/10.2139/ssrn.4720535

Clément De Chaisemartin

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

Gonzalo Vazquez‐Bare (Contact Author)

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

Santa Barbara, CA

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
1,162
Abstract Views
2,439
Rank
38,432
PlumX Metrics