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Inference in Differences-in-Differences with Few Treated Groups and Heteroskedasticity
Abstract
We derive an inference method that works in differences-in-differences settings with few treated and many control groups in the presence of heteroskedasticity. As a leading example, we provide theoretical justification and empirical evidence that heteroskedasticity generated by variation in group sizes can invalidate existing inference methods, even in data sets with a large number of observations per group. In contrast, our inference method remains valid in this case. Our test can also be combined with feasible generalized least squares, providing a safeguard against misspecification of the serial correlation.
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“Ferman and Pinto (2019) extend the approach of Conley and Taber (2011) to allow for heteroskedasticity caused by heterogeneity in group sizes or other observable characteristics, but must still restrict heterogeneity based on unobserved characteristics (e.g. unobserved treatment effect heterogeneity).”
From What's trending in difference-in-differences? A synthesis of the recent econometrics literature (2023) · cites this paper as Ferman and Pinto (2019)
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“It is often assumed that ϵ ijt are iid mean-zero across i and j (and sometimes t ); see, e.g., Donald and Lang (2007), Conley and Taber (2011), and Ferman and Pinto (2019).”
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Metadata
- Authors
- Ferman, B., & Pinto, C.
- Affiliations
- Escola de Economia de São Paulo (BR)
- Venue
- The Review of Economics and Statistics
- Publisher
- MIT Press
- Published
- 2019-07
- Volume
- 101
- Issue
- 3
- Pages
- 452-467
- ISSN
- 0034-6535 (ISSN-L)
- 1530-9142
- OpenAlex
- W2113132502
- Cited by
- 178
- References
- 37
- Citations by year
- 2026: 41 · 2025: 19 · 2024: 20 · 2023: 14 · 2022: 21 · 2021: 24 · 2020: 18 · 2019: 12
- FWCI
- 11.83
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- The Review of Economics and Statistics (publishedVersion)
- 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
- difference-in-differences, heteroscedasticity, inference, serial correlation, feasible generalized least squares, model misspecification, causal inference
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