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When Is Parallel Trends Sensitive to Functional Form?

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  • Jonathan Roth
  • Pedro H. C. Sant'Anna

Abstract

This paper assesses when the validity of difference-in-differences depends on functional form. We provide a novel characterization: the parallel trends assumption holds under all strictly monotonic transformations of the outcome if and only if a stronger ``parallel trends''-type condition holds for the cumulative distribution function of untreated potential outcomes. This condition for parallel trends to be insensitive to functional form is satisfied if and essentially only if the population can be partitioned into a subgroup for which treatment is effectively randomly assigned and a remaining subgroup for which the distribution of untreated potential outcomes is stable over time. These conditions have testable implications, and we introduce falsification tests for the null that parallel trends is insensitive to functional form.

Suggested Citation

  • Jonathan Roth & Pedro H. C. Sant'Anna, 2020. "When Is Parallel Trends Sensitive to Functional Form?," Papers 2010.04814, arXiv.org, revised Sep 2022.
    • Handle: RePEc:arx:papers:2010.04814
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    1. Douglas Almond & Hilary W. Hoynes & Diane Whitmore Schanzenbach, 2011. "Inside the War on Poverty: The Impact of Food Stamps on Birth Outcomes," The Review of Economics and Statistics, MIT Press, vol. 93(2), pages 387-403, May.
    2. Susan Athey & Guido W. Imbens, 2006. "Identification and Inference in Nonlinear Difference-in-Differences Models," Econometrica, Econometric Society, vol. 74(2), pages 431-497, March.
    3. Sant’Anna, Pedro H.C. & Zhao, Jun, 2020. "Doubly robust difference-in-differences estimators," Journal of Econometrics, Elsevier, vol. 219(1), pages 101-122.
    4. Stéphane Bonhomme & Ulrich Sauder, 2011. "Recovering Distributions in Difference-in-Differences Models: A Comparison of Selective and Comprehensive Schooling," The Review of Economics and Statistics, MIT Press, vol. 93(2), pages 479-494, May.
    5. Brantly Callaway & Tong Li, 2019. "Quantile treatment effects in difference in differences models with panel data," Quantitative Economics, Econometric Society, vol. 10(4), pages 1579-1618, November.
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    Cited by:

    1. Ruonan Xu, 2023. "Difference-in-Differences with Interference," Papers 2306.12003, arXiv.org, revised Feb 2024.
    2. Weill, Joakim A. & Stigler, Matthieu & Deschenes, Olivier & Springborn, Michael R., 2021. "COVID-19 Mobility Policies Impacts: How Credible Are Difference-in-Differences Estimates?," IZA Discussion Papers 14682, Institute of Labor Economics (IZA).
    3. Jonathan Roth & Pedro H. C. Sant’Anna, 2023. "Efficient Estimation for Staggered Rollout Designs," Journal of Political Economy Microeconomics, University of Chicago Press, vol. 1(4), pages 669-709.
    4. Kirill Borusyak & Peter Hull & Xavier Jaravel, 2023. "Design-based identification with formula instruments: A review," CeMMAP working papers 12/23, Institute for Fiscal Studies.
    5. Bíró, Anikó & Prinz, Dániel & Sándor, László, 2022. "The minimum wage, informal pay, and tax enforcement," Journal of Public Economics, Elsevier, vol. 215(C).
    6. Joakim A. Weill & Matthieu Stigler & Olivier Deschenes & Michael R. Springborn, 2021. "Researchers' Degrees-of-Flexibility and the Credibility of Difference-in-Differences Estimates: Evidence From the Pandemic Policy Evaluations," NBER Working Papers 29550, National Bureau of Economic Research, Inc.
    7. Jeffrey M Wooldridge, 2023. "Simple approaches to nonlinear difference-in-differences with panel data," The Econometrics Journal, Royal Economic Society, vol. 26(3), pages 31-66.
    8. Sina Akbari & Negar Kiyavash, 2024. "Non-linear Triple Changes Estimator for Targeted Policies," Papers 2402.12583, arXiv.org.
    9. Barkowski, Scott, 2021. "Interpretation of nonlinear difference-in-differences: the role of the parallel trends assumption," MPRA Paper 108975, University Library of Munich, Germany.
    10. Gregory Faletto, 2023. "Fused Extended Two-Way Fixed Effects for Difference-in-Differences with Staggered Adoptions," Papers 2312.05985, arXiv.org.
    11. Riveros-Gavilanes, J. M., 2023. "A simple test of parallel pre-trends for Differences-in-Differences," MPRA Paper 119367, University Library of Munich, Germany, revised 2023.
    12. William Torous & Florian Gunsilius & Philippe Rigollet, 2021. "An Optimal Transport Approach to Estimating Causal Effects via Nonlinear Difference-in-Differences," Papers 2108.05858, arXiv.org, revised Mar 2024.
    13. Kyunghoon Ban & D'esir'e K'edagni, 2022. "Robust Difference-in-differences Models," Papers 2211.06710, arXiv.org, revised Aug 2023.
    14. Jessica Pac & Lawrence M. Berger, 2024. "Quasi‐experimental evidence on the employment effects of the 2021 fully refundable monthly child tax credit," Journal of Policy Analysis and Management, John Wiley & Sons, Ltd., vol. 43(1), pages 192-213, January.
    15. Brendon McConnell, 2023. "What's Logs Got to do With it: On the Perils of log Dependent Variables and Difference-in-Differences," Papers 2308.00167, arXiv.org, revised Aug 2023.
    16. Dmitry Arkhangelsky & Guido Imbens, 2023. "Causal Models for Longitudinal and Panel Data: A Survey," Papers 2311.15458, arXiv.org, revised Mar 2024.
    17. Ohler, Adrienne, 2023. "The Economics of Environmental Health Disparities: Who Benefits from Coal Power Plant Closures?," 2023 Annual Meeting, July 23-25, Washington D.C. 335760, Agricultural and Applied Economics Association.
    18. Roth, Jonathan & Sant’Anna, Pedro H.C. & Bilinski, Alyssa & Poe, John, 2023. "What’s trending in difference-in-differences? A synthesis of the recent econometrics literature," Journal of Econometrics, Elsevier, vol. 235(2), pages 2218-2244.
    19. Lima, Gonçalo & Moeller, Jakob & Schmandt, Marco & Westheide, Christian, 2023. "The Dynamics and Spillovers of Management Interventions: A Comment on Bianchi and Giorcelli (2022)," I4R Discussion Paper Series 66, The Institute for Replication (I4R).

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