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Difference in Differences and Ratio in Ratios for Limited Dependent Variables

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  • Myoung-jae Lee
  • Sanghyeok Lee

Abstract

Difference in differences (DD) is widely used to find policy/treatment effects with observational data, but applying DD to limited dependent variables (LDV's) Y has been problematic. This paper addresses how to apply DD and related approaches (such as "ratio in ratios" or "ratio in odds ratios") to binary, count, fractional, multinomial or zero-censored Y under the unifying framework of `generalized linear models with link functions'. We evaluate DD and the related approaches with simulation and empirical studies, and recommend 'Poisson Quasi-MLE' for non-negative (such as count or zero-censored) Y and (multinomial) logit MLE for binary, fractional or multinomial Y.

Suggested Citation

  • Myoung-jae Lee & Sanghyeok Lee, 2021. "Difference in Differences and Ratio in Ratios for Limited Dependent Variables," Papers 2111.12948, arXiv.org, revised Aug 2023.
    • Handle: RePEc:arx:papers:2111.12948
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    References listed on IDEAS

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    1. Myoung-jae Lee & Yasuyuki Sawada, 2020. "Review on Difference in Differences," Korean Economic Review, Korean Economic Association, vol. 36, pages 135-173.
    2. Ariella Kahn-Lang & Kevin Lang, 2020. "The Promise and Pitfalls of Differences-in-Differences: Reflections on 16 and Pregnant and Other Applications," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(3), pages 613-620, July.
    3. Joshua D. Angrist & Jörn-Steffen Pischke, 2009. "Mostly Harmless Econometrics: An Empiricist's Companion," Economics Books, Princeton University Press, edition 1, number 8769, December.
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    6. Myoung-Jae Lee, 2018. "Simple least squares estimator for treatment effects using propensity score residuals," Biometrika, Biometrika Trust, vol. 105(1), pages 149-164.
    7. Myoung‐Jae Lee & Satoru Kobayashi, 2001. "Proportional treatment effects for count response panel data: effects of binary exercise on health care demand," Health Economics, John Wiley & Sons, Ltd., vol. 10(5), pages 411-428, July.
    8. Angrist, Joshua D. & Krueger, Alan B., 1999. "Empirical strategies in labor economics," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 3, chapter 23, pages 1277-1366, Elsevier.
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    10. Myoung‐jae Lee, 2021. "Instrument residual estimator for any response variable with endogenous binary treatment," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(3), pages 612-635, July.
    11. J. M. C. Santos Silva & Silvana Tenreyro, 2006. "The Log of Gravity," The Review of Economics and Statistics, MIT Press, vol. 88(4), pages 641-658, November.
    12. Santos Silva, J.M.C. & Tenreyro, Silvana, 2011. "Further simulation evidence on the performance of the Poisson pseudo-maximum likelihood estimator," Economics Letters, Elsevier, vol. 112(2), pages 220-222, August.
    13. Lee, Myoung-jae, 2005. "Micro-Econometrics for Policy, Program and Treatment Effects," OUP Catalogue, Oxford University Press, number 9780199267699.
    14. 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.
    15. Papke, Leslie E & Wooldridge, Jeffrey M, 1996. "Econometric Methods for Fractional Response Variables with an Application to 401(K) Plan Participation Rates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(6), pages 619-632, Nov.-Dec..
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