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Interpretation of nonlinear difference-in-differences: the role of the parallel trends assumption

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  • Barkowski, Scott

Abstract

I argue interpretation of nonlinear difference-in-differences models depends on the form of the parallel trends assumption. When they are assumed in the natural scale of the dependent variable, the treatment effect is the interaction effect (a cross-difference). If they are assumed in the transformed scale, it is a single difference. I further note that assuming parallel trends in one scale implies they do not hold in the other, except in special cases. Finally, I consider log-linear (and related) difference-in-differences models and provide a constant form of the treatment effect that is comparable across applications with different parallel trends assumptions.

Suggested Citation

  • Barkowski, Scott, 2021. "Interpretation of nonlinear difference-in-differences: the role of the parallel trends assumption," MPRA Paper 108975, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:108975
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    3. Lechner, Michael, 2011. "The Estimation of Causal Effects by Difference-in-Difference Methods," Foundations and Trends(R) in Econometrics, now publishers, vol. 4(3), pages 165-224, November.
    4. Puhani, Patrick A., 2012. "The treatment effect, the cross difference, and the interaction term in nonlinear “difference-in-differences” models," Economics Letters, Elsevier, vol. 115(1), pages 85-87.
    5. 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.
    6. Ai, Chunrong & Norton, Edward C., 2003. "Interaction terms in logit and probit models," Economics Letters, Elsevier, vol. 80(1), pages 123-129, July.
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    Cited by:

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    4. Berger, Michael & Six, Eva & Czypionka, Thomas, 2024. "Policy implications of heterogeneous demand reactions to changes in cost-sharing: Patient-level evidence from Austria," Social Science & Medicine, Elsevier, vol. 340(C).

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    More about this item

    Keywords

    Difference-in-differences; Nonlinear Models; Model Interpretation; Identification; Probit; Logit; Log-linear; Semilogarithmic;
    All these keywords.

    JEL classification:

    • 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
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities

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