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Difference in Differences, Ratio in Ratios, and Ratio in Odds Ratios for Limited Dependent Variables: A Review and More

Author

Listed:
  • Lee Sanghyeok

    (School of Economics and Trade, Kyungpook National University, Daegu 41566, South Korea)

  • Lee Myoung-jae

    (Department of Economics, Korea University, Seoul 02841, South Korea)

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” and “ratio in odds ratios”, to LDV’s under the unifying framework of ‘generalized linear models with link functions’. We review and 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

  • Lee Sanghyeok & Lee Myoung-jae, 2026. "Difference in Differences, Ratio in Ratios, and Ratio in Odds Ratios for Limited Dependent Variables: A Review and More," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 30(3), pages 295-319.
    • Handle: RePEc:bpj:sndecm:v:30:y:2026:i:3:p:295-319:n:1007
    DOI: 10.1515/snde-2024-0125
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    JEL classification:

    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C34 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Truncated and Censored Models; Switching Regression Models
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions

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