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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.

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  • 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. 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.
    2. Barbaresco, Silvia & Courtemanche, Charles J. & Qi, Yanling, 2015. "Impacts of the Affordable Care Act dependent coverage provision on health-related outcomes of young adults," Journal of Health Economics, Elsevier, vol. 40(C), pages 54-68.
    3. Myoung-Jae Lee, 2018. "Simple least squares estimator for treatment effects using propensity score residuals," Biometrika, Biometrika Trust, vol. 105(1), pages 149-164.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Lee, Myoung-jae, 2005. "Micro-Econometrics for Policy, Program and Treatment Effects," OUP Catalogue, Oxford University Press, number 9780199267699.
    9. 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.
    10. 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..
    11. Myoung-jae Lee & Yasuyuki Sawada, 2020. "Review on Difference in Differences," Korean Economic Review, Korean Economic Association, vol. 36, pages 135-173.
    12. 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.
    13. Joshua D. Angrist & Jörn-Steffen Pischke, 2009. "Mostly Harmless Econometrics: An Empiricist's Companion," Economics Books, Princeton University Press, edition 1, number 8769.
    14. 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.
    15. Heckman, James J. & Lalonde, Robert J. & Smith, Jeffrey A., 1999. "The economics and econometrics of active labor market programs," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 3, chapter 31, pages 1865-2097, Elsevier.
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