Working Paper: CEPR ID: DP17247
Authors: Kirill Borusyak; Xavier Jaravel; Jann Spiess
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 Codes: C21; C23; E62
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| conventional regression-based estimators (C51) | biased estimates (C51) |
| treatment effect heterogeneity (C21) | biased estimates (C51) |
| efficient estimator (C51) | unbiased estimates (C51) |
| MPC from tax rebates (H29) | fiscal stimulus potency (E62) |
| MPC predominantly occurs in the first month after rebate (D42) | fiscal stimulus potency (E62) |