A model of income evaluation: income comparison on subjective reference income distribution

ABSTRACT

People’s evaluation of the relative position of their income is not as accurate as the relative income hypothesis assumes. It is observed from empirical survey data that income evaluation is concentrated in the middle. We develop a model that assumes income comparison on a subjective income reference distribution to explain the centralization phenomenon of income evaluation. We conduct theoretical analysis and empirical parameter estimation using Bayesian statistical modeling. The theoretical analysis shows that the centralization of income evaluation distribution occurs when the subjective reference distribution is more dispersed than the objective distribution. Empirical analysis using Japanese data from 2015 shows that the relationship between subjective and objective distributions differed depending on social categories with different social experiences. Women had a more ambiguous distribution than men. Among men, those aged 45–54 had a subjective distribution closest to the objective distribution. Thus, the subjective reference income distributions that potentially define people’s evaluation of their income and their differences based on social category were only clarified by constructing the model.

KEYWORDS:

• Income distribution
• relative income hypothesis
• Bayesian statistical modeling

Acknowledgments

We thank the SSP Project for permission to use the SSP2015 survey. This work was supported by JSPS KAKENHI Grant Numbers JP19H00609 and JP19K02065 as part of the SSP Project (http://ssp.hus.osaka-u.ac.jp/)

Notes

1. The unit of income is the Japanese yen. We treated 344 cases with no individual income and three cases with 100 million yen as missing.

2. The question in the questionnaire was as follows: Thinking about present-day Japanese society, how would you rate your own level of income below on a scale of 1 (the highest level) to 10 (the lowest level)?.

3. In general, the canonical form of exponential family of distribution can be expressed as

$f(x|\theta )=\mathrm{e}\mathrm{x}\mathrm{p}\left(xb\left(\theta \right)+c\left(\theta \right)+d\left(x\right)\right)$

where $b\left(\theta \right)$ is called a natural parameter (Dobson & Barnett, 2008, p. 46). Then, the growth rate and that in terms of the second derivative of $f$ would be

$\frac{f^{\prime }\left(x|\theta \right)}{f\left(x|\theta \right)}=\hspace{0.17em}b\left(\theta \right)+d^{\mathrm{\prime }}\left(x\right),\frac{f^{\prime \prime }\left(x|\theta \right)}{f\left(x|\theta \right)}=\hspace{0.17em}(b\left(\theta \right)+d^{\mathrm{\prime }}\left(x\right))+d^{\prime \prime }(x).$

Additional information

Funding

This work was supported by the JSPS KAKENHI [JP19H00609, JP19K02065].