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A Local Projections Approach to Difference-in-Differences Event Studies

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Abstract
Many of the challenges in the estimation of dynamic heterogeneous treatment effects can be resolved with local projection (LP) estimators of the sort used in applied macroeconometrics. This approach provides a convenient alternative to the more complicated solutions proposed in the recent literature on Difference in-Differences (DiD). The key is to combine LPs with a flexible ‘clean control’ condition to define appropriate sets of treated and control units. Our proposed LP-DiD estimator is clear, simple, easy and fast to compute, and it is transparent and flexible in its handling of treated and control units. Moreover, it is quite general, including in its ability to control for pre-treatment values of the outcome and of other time-varying covariates. The LP-DiD estimator does not suffer from the negative weighting problem, and indeed can be implemented with any weighting scheme the investigator desires. Simulations demonstrate the good performance of the LP-DiD estimator in common settings. Two recent empirical applications illustrate how LP-DiD addresses the bias of conventional fixed effects estimators, leading to potentially different results.

Suggested Citation

  • Arindrajit Dube & Daniele Girardi & Òscar Jordà & Alan M. Taylor, 2023. "A Local Projections Approach to Difference-in-Differences Event Studies," Working Paper Series 2023-12, Federal Reserve Bank of San Francisco.
    • Handle: RePEc:fip:fedfwp:96259
    DOI: 10.24148/wp2023-12
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    1. Clément de Chaisemartin & Xavier D'Haultfœuille, 2020. "Two-Way Fixed Effects Estimators with Heterogeneous Treatment Effects," American Economic Review, American Economic Association, vol. 110(9), pages 2964-2996, September.
    2. Javier Alvarez & Manuel Arellano, 2003. "The Time Series and Cross-Section Asymptotics of Dynamic Panel Data Estimators," Econometrica, Econometric Society, vol. 71(4), pages 1121-1159, July.
    3. Òscar Jordà & Alan M. Taylor, 2016. "The Time for Austerity: Estimating the Average Treatment Effect of Fiscal Policy," Economic Journal, Royal Economic Society, vol. 126(590), pages 219-255, February.
    4. Daron Acemoglu & Suresh Naidu & Pascual Restrepo & James A. Robinson, 2019. "Democracy Does Cause Growth," Journal of Political Economy, University of Chicago Press, vol. 127(1), pages 47-100.
    5. Sant’Anna, Pedro H.C. & Zhao, Jun, 2020. "Doubly robust difference-in-differences estimators," Journal of Econometrics, Elsevier, vol. 219(1), pages 101-122.
    6. Shuowen Chen & Victor Chernozhukov & Iván Fernández-Val, 2019. "Mastering Panel Metrics: Causal Impact of Democracy on Growth," AEA Papers and Proceedings, American Economic Association, vol. 109, pages 77-82, May.
    7. Clément de Chaisemartin & Xavier D’Haultfœuille, 2023. "Two-way fixed effects and differences-in-differences with heterogeneous treatment effects: a survey," The Econometrics Journal, Royal Economic Society, vol. 26(3), pages 1-30.
    8. Michelle Marcus & Pedro H. C. Sant’Anna, 2021. "The Role of Parallel Trends in Event Study Settings: An Application to Environmental Economics," Journal of the Association of Environmental and Resource Economists, University of Chicago Press, vol. 8(2), pages 235-275.
    9. Goodman-Bacon, Andrew, 2021. "Difference-in-differences with variation in treatment timing," Journal of Econometrics, Elsevier, vol. 225(2), pages 254-277.
    10. Doruk Cengiz & Arindrajit Dube & Attila Lindner & Ben Zipperer, 2019. "The Effect of Minimum Wages on Low-Wage Jobs," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 134(3), pages 1405-1454.
    11. Sun, Liyang & Abraham, Sarah, 2021. "Estimating dynamic treatment effects in event studies with heterogeneous treatment effects," Journal of Econometrics, Elsevier, vol. 225(2), pages 175-199.
    12. Arellano, Manuel, 2003. "Panel Data Econometrics," OUP Catalogue, Oxford University Press, number 9780199245291.
    13. Òscar Jordà, 2005. "Estimation and Inference of Impulse Responses by Local Projections," American Economic Review, American Economic Association, vol. 95(1), pages 161-182, March.
    14. Nickell, Stephen J, 1981. "Biases in Dynamic Models with Fixed Effects," Econometrica, Econometric Society, vol. 49(6), pages 1417-1426, November.
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    More about this item

    Keywords

    difference-in-differences; two-way fixed effects; event study; negative weights; local projections; clean controls;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models

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