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Cited by 11Advanced Causal Inference TechniquesSpatial and Panel Data AnalysisStatistical Methods and Bayesian Inference

A Flexible, Heterogeneous Treatment Effects Difference-in-Differences Estimator for Repeated Cross-Sections

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Deb, Partha, Norton, Edward, Wooldridge, Jeffrey, Zabel, Jeffrey·2024·National Bureau of Economic Research
DOI 10.3386/w33026
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Abstract

This paper proposes a method to estimate treatment effects in difference-in-differences designs for repeated cross-section data in which the treatment start is staggered over time and treatment effects are heterogeneous by group, time, and observation-level covariates.We show that a linear-inparameters regression specification with a sufficiently flexible functional form consisting of groupby-time treatment effects, two-way fixed effects, and interaction terms yields consistent estimates of heterogeneous treatment effects under general conditions.We also show that our method is identical to an imputation estimator.Under homoskedasticity assumptions the estimators are efficient, and aggregation of the treatment effects and inference are straightforward.We illustrate the use of this flexible linear model estimated by OLS with covariates (X) -FLEX -with an empirical example and provide comparisons to some benchmark estimators.

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  • Many saturated models have been developed to address staggered treatment adoption issues.

    “Many saturated models have been developed to address issues related to staggered treatment adoption [34, 35, 45-48].”

    From Difference-in-Differences for Health Policy and Practice: A Review of Modern Methods (2025) · cites this paper as [45]

    Section 3 says methods for staggered treatment entry have grown rapidly, and Section 4.3 describes alternative techniques that address bias from staggered entry. The paper also describes a fully saturated FLEX specification, but these passages do not establish that many of the developed models are saturated. Page numbers are unavailable in our copy. (LLM, conf=0.79)

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  • Several authors have developed DiD estimators for staggered adoption, where treatment starts at different calendar times for different units.

    “For example, several authors have developed estimators for cases when treatment started at different calendar times for different units (“staggered adoption”) [34, 35, 45-48].”

    From Difference-in-Differences for Health Policy and Practice: A Review of Modern Methods (2025) · cites this paper as [45]

  • Many newer DiD specifications are saturated, estimating an ATT for each post-intervention time period and sometimes for specific units or groups.

    “Many new specifications are “saturated,” estimating an ATT specific to each post-intervention time period and sometimes to specific units or groups of units.”

    From Difference-in-Differences for Health Policy and Practice: A Review of Modern Methods (2025) · cites this paper as [45]

  • The imputation and pooled OLS methods can be extended to the case of repeated cross sections, provided essentially the same assumptions in Sect. 4 are imposed along with a stable population over time.

    “the methods the imputation and pooled OLS methods can be extended to the case of repeated cross sections, provided we impose essentially the same assumptions in Sect. 4 along with a stable population over time.”

    From Two-way fixed effects, the two-way Mundlak regression, and difference-in-differences estimators (2025) · cites this paper as Deb et al. (2024)

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Research works printed but not linked: 18

  1. [1]1. Abadie, A. (2005). Semiparametric Difference-in-Differences Estimators. The Review of Economic Studies, 72(1):1-19.
  2. [3]3. Alsan, M. and Yang, C. S. (2024). Fear and the Safety Net: Evidence from Secure Commu- nities. The Review of Economics and Statistics, 106(6):1427-1441.
  3. [5]5. Borusyak, K., Jaravel, X., and Spiess, J. (2024). Revisiting Event-Study Designs: Robust and Efficient Estimation. The Review of Economic Studies, 91(6):3253-3285.
  4. [7]7. Callaway, B. and Sant'Anna, P. H. C. (2021). Difference-in-Differences with Multiple Time Periods. Journal of Econometrics, 225(2):200-230.
  5. [8]8. Cengiz, D., Dube, A., Lindner, A., and Zipperer, B. (2019). The Effect of Minimum Wages on Low-Wage Jobs. The Quarterly Journal of Economics, 134(3):1405-1454.
  6. [9]9. de Chaisemartin, C. and D'Haultfœuille, X. (2020). Two-Way Fixed Effects Estimators with Heterogeneous Treatment Effects. American Economic Review, 110(9):2964-2996.
  7. [10]10. de Chaisemartin, C. and D'Haultfœuille, X. (2023). Two-way fixed effects and difference- indifferences with heterogeneous treatment effects: a survey. Econometrics Journal, 26:C1- C30.
  8. [12]12. Dette, H. and Schumann, M. (2024). Testing for Equivalence of Pre-Trends in Difference-in- Differences Estimation. Journal of Business & Economic Statistics, 1-13.
  9. [13]13. Dube, A., Girardi, D., Jorda, O., and Taylor, A. M. (2025). A Local Projections Approach to Difference-in-Differences. Journal of Applied Econometrics, 40(7):741-758.
  10. [14]14. East, C. N., Hines, A. L., Luck, P., Mansour, H., and Velásquez, A. (2023). The Labor Market Effects of Immigration Enforcement. Journal of Labor Economics, 41(4):957-996.
  11. [16]16. Goodman-Bacon, A. (2021). Difference-in-differences with Variation in Treatment Timing. Journal of Econometrics, 225(2):254-277.
  12. [18]18. MacKinlay, A. C. (1997). Event Studies in Economics and Finance. Journal of Economic Literature, 35(1):13-39.
  13. [19]19. Roth, J. (2022). Pretest with Caution: Event-Study Estimates after Testing for Parallel Trends. American Economic Review: Insights, 4(3):305-322.
  14. [21]21. Roth, J., Sant'Anna, P. H. C., Bilinski, A., and Poe, J. (2023). What's Trending in Difference- in-differences? A Synthesis of the Recent Econometrics Literature. Journal of Economet- rics, 235(2):2218-2244.
  15. [22]22. Sant'Anna, P. H. C. and Zhao, J. (2020). Doubly robust difference-in-differences estimators. Journal of Econometrics, 219(1):101-122.
  16. [23]23. Sun, L. and Abraham, S. (2021). Estimating Dynamic Treatment Effects in Event Studies with Heterogeneous Treatment Effects. Journal of Econometrics, 225(2):175-199.
  17. [25]25. Wooldridge, J. M. (2010). Econometric Analysis of Cross Section and Panel Data. The MIT Press.
  18. [26]26. Wooldridge, J. M. (2023). Simple Approaches to Nonlinear Difference-in-differences with Panel data. The Econometrics Journal, 26(3):C31-C66.

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Authors
Deb, P., Norton, E., Wooldridge, J., & Zabel, J.
Affiliations
  • Hunter College (US)
  • University of Michigan (US)
  • Michigan State University (US)
  • Tufts University (US)
Corresponding author
Deb, Partha
ORCID
Venue
National Bureau of Economic Research
Publisher
National Bureau of Economic Research
Published
2024-10
DOI
10.3386/w33026
OpenAlex
W4403173907
Cited by
10
References
0
Citations by year
2026: 4 · 2025: 5 · 2023: 1
Type
report
Language
en
Open access
Locations
  • National Bureau of Economic Research (publishedVersion)
  • SSRN Electronic Journal (acceptedVersion)
  • RePEc: Research Papers in Economics (submittedVersion)
Topics
  • Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
  • Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Spatial and Panel Data Analysis
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
Keywords
treatment effect heterogeneity, repeated cross-sections, difference-in-differences, two-way fixed effects, interaction terms, estimator consistency, estimator efficiency

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