Revisiting Event Study Designs: Robust and Efficient Estimation

85 Pages Posted: 20 Aug 2016 Last revised: 20 Apr 2022

See all articles by Kirill Borusyak

Kirill Borusyak

University College London - Department of Economics

Xavier Jaravel

London School of Economics & Political Science (LSE) - Department of Economics

Jann Spiess

Stanford Graduate School of Business

Date Written: April 19, 2022

Abstract

We develop a framework for difference-in-differences designs with staggered treatment adoption and heterogeneous causal effects. We show that conventional regression-based estimators fail to provide unbiased estimates of relevant estimands absent strong restrictions on treatment-effect homogeneity. We then derive the efficient estimator addressing this challenge, which takes an intuitive “imputation” form when treatment-effect heterogeneity is unrestricted. We characterize the asymptotic behavior of the estimator, propose tools for inference, and develop tests for identifying assumptions. Extensions include time-varying controls, triple-differences, and certain non-binary treatments. We show the practical relevance of these insights in a simulation study and an application. Studying the consumption response to tax rebates in the United States, we find that the notional marginal propensity to consume is between 8 and 11 percent in the first quarter — about half as large as benchmark estimates used to calibrate macroeconomic models — and predominantly occurs in the first month after the rebate.

Keywords: Difference-in-differences, Event study, Imputation estimator, Panel data

JEL Classification: C21, C23, E62

Suggested Citation

Borusyak, Kirill and Jaravel, Xavier and Spiess, Jann, Revisiting Event Study Designs: Robust and Efficient Estimation (April 19, 2022). Available at SSRN: https://ssrn.com/abstract=2826228 or http://dx.doi.org/10.2139/ssrn.2826228

Kirill Borusyak (Contact Author)

University College London - Department of Economics

Drayton House, 30 Gordon Street
30 Gordon Street
London, WC1H 0AX
United Kingdom

Xavier Jaravel

London School of Economics & Political Science (LSE) - Department of Economics ( email )

Houghton Street
London WC2A 2AE
United Kingdom
7456842728 (Phone)
NW12AR (Fax)

Jann Spiess

Stanford Graduate School of Business ( email )

655 Knight Way
Stanford, CA 94305-5015
United States

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