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On the Use of the Harmonic Mean Estimator for Selecting the Hypothetical Income Distribution from Grouped Data

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  • Kazuhiko Kakamu

    (School of Data Science, Nagoya City University, Nagoya 467-8601, Japan)

Abstract

It is known that the harmonic mean estimator is a consistent estimator of the marginal likelihood and is easy to implement, but it has severe biases and does not change as much as the prior distribution changes. In this study, we investigate the use of the harmonic mean estimator to select the hypothetical income distribution from grouped data through Monte Carlo simulations and apply it to real data in Japan. From the results, we confirm that there are significant biases, but it can be reliably used to select an appropriate model only when the sample size is large enough under appropriate prior settings.

Suggested Citation

  • Kazuhiko Kakamu, 2025. "On the Use of the Harmonic Mean Estimator for Selecting the Hypothetical Income Distribution from Grouped Data," JRFM, MDPI, vol. 18(2), pages 1-16, February.
    • Handle: RePEc:gam:jjrfmx:v:18:y:2025:i:2:p:72-:d:1582008
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    References listed on IDEAS

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    3. Tobias Eckernkemper & Bastian Gribisch, 2021. "Classical and Bayesian Inference for Income Distributions using Grouped Data," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 83(1), pages 32-65, February.
    4. Singh, S K & Maddala, G S, 1976. "A Function for Size Distribution of Incomes," Econometrica, Econometric Society, vol. 44(5), pages 963-970, September.
    5. Chan, Joshua C.C. & Grant, Angelia L., 2015. "Pitfalls of estimating the marginal likelihood using the modified harmonic mean," Economics Letters, Elsevier, vol. 131(C), pages 29-33.
    6. Goffe, William L. & Ferrier, Gary D. & Rogers, John, 1994. "Global optimization of statistical functions with simulated annealing," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 65-99.
    7. Higbee, Joshua D. & McDonald, James B., 2024. "A comparison of the GB2 and skewed generalized log-t distributions with an application in finance," Journal of Econometrics, Elsevier, vol. 240(2).
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