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Comparing Latent Inequality with Ordinal Data

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Abstract

We propose new ways to compare two latent distributions when only ordinal data are available and without imposing parametric assumptions on the underlying continuous distributions. First, we contribute identification results. We show how certain ordinal conditions provide evidence of between-group inequality, quantified by particular quantiles being higher in one latent distribution than in the other. We also show how other ordinal conditions provide evidence of higher within-group inequality in one distribution than in the other, quantified by particular interquantile ranges being wider in one latent distribution than in the other. Second, we propose an "inner" confidence set for the quantiles that are higher for the first latent distribution. We also describe frequentist and Bayesian inference on features of the ordinal distributions relevant to our identification results. Our contributions are illustrated by empirical examples with mental health and general health.

Suggested Citation

  • David M. Kaplan & Wei Zhao, 2022. "Comparing Latent Inequality with Ordinal Data," Working Papers 2206, Department of Economics, University of Missouri.
    • Handle: RePEc:umc:wpaper:2206
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    2. Shuo Liu & Nick Netzer, 2023. "Happy Times: Measuring Happiness Using Response Times," American Economic Review, American Economic Association, vol. 113(12), pages 3289-3322, December.
    3. Wu, Qian & Kaplan, David M., 2025. "Regression and decomposition with ordinal health outcomes," Journal of Health Economics, Elsevier, vol. 102(C).
    4. Grimes, Arthur & Jenkins, Stephen P. & Tranquilli, Florencia, 2020. "The Relationship between Subjective Wellbeing and Subjective Wellbeing Inequality: Taking Ordinality and Skewness Seriously," IZA Discussion Papers 13692, Institute of Labor Economics (IZA).
    5. Andrew Chesher & Adam Rosen & Zahra Siddique, 2019. "Estimating Endogenous Effects on Ordinal Outcomes," CeMMAP working papers CWP66/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. Stephen P. Jenkins, 2020. "Comparing distributions of ordinal data," Stata Journal, StataCorp LLC, vol. 20(3), pages 505-531, September.
    7. Kaplan, David M. & Zhuo, Longhao, 2021. "Frequentist properties of Bayesian inequality tests," Journal of Econometrics, Elsevier, vol. 221(1), pages 312-336.
    8. Arthur Grimes & Stephen P. Jenkins & Florencia Tranquilli, 2023. "The Relationship Between Subjective Wellbeing and Subjective Wellbeing Inequality: An Important Role for Skewness," Journal of Happiness Studies, Springer, vol. 24(1), pages 309-330, January.

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    JEL classification:

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

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