A model of income evaluation: income comparison on subjective reference income distribution
Summary (3 min read)
- This article focuses on individuals’ evaluations of their own income in relation to others within the income distribution.
- It is assumed that evaluation of income would be obtained by recognizing the relative position of one’s own income in the distribution through comparison with others.
- Hence, this is also related to the empirical validity of the “relative income hypothesis” in economics.
- This study focuses on the empirical validity of this assumption.
- Figure 1 shows the income distribution is well fitted by a lognormal distribution as theoretically expected (Hamada, 2003, 2004).
2.1 Model Assumption
- The authors assume that an individual evaluates their relative position of income by repeatedly comparing themselves with others whom they randomly encounter on a subjective reference income distribution.
- It is further assumed that the subjective reference distribution reflects the biased pattern of an individual’s daily encounters and/or their expectations about the distribution that are not based on their experience but on media information or rumors.
- In addition, when evaluating their income, the individual is assumed to respond according to the number of times they have outperformed others in the last m comparisons.
- From equation (2), x can be expressed as the inverse CDF of the subjective reference distribution, i.e. x = F−1s (p).
2.2 Model Derivations
- First, the authors assume, as a special case, that the subjective reference income distribution is equal to the objective income distribution, because there is no encounter bias.
- This is an ideal situation of income evaluation, assumed by the relative income hypothesis, where people perceive the objective income distribution correctly and evaluate their income with respect to the exact relative position in the objective income distribution.
- Now, the authors move on to more general situations where there is a difference between the objective income distribution and subjective reference income distribution, which is biased from the objective distribution.
- (8) From these derivations, the condition for the appearance of the centralization effect in terms of income evaluation can be summarized as follows.
3.2 Model Derivation
- Let us perform some derivation from the model.
- First, to determine the condition of a local maximum point of the distribution p, the authors specify the growth rate of the objective and subjective reference income distribution3.
- They also show that the larger δ is, the smaller the maximum point of p∗ becomes.
- Conversely, behind the middle-concentrated distribution of income evaluation, the authors can assume the existence of a subjective income distribution that is more dispersed than the objective distribution.
- The data used for the analysis are from the Stratification and Social Psychology Project Survey (SSP2015), which is a Japanese national sampling survey of class identity, social images, and other related attitudes toward social inequality and social stratification.
- The survey was conducted between January and June 2015.
- The sampling procedure was a three-stage stratified random sampling.
- The sampling list was the Japanese electoral roll and the basic resident registration.
- As mentioned in the introduction, the main variables in the model are individual annual income and the 10-scaled income evaluation .
- In addition, the authors introduce gender (male and female) and age cohort as covariates to examine the differences in the income evaluation within different social categories and the differences in the subjective income distributions across the categories assumed to be behind the evaluation.
4.3 Common Subjective Distribution Model
- In the following, the authors construct the model as a Bayesian statistical model and estimate the parameters.
- First, as a baseline model, the authors analyze a common subjective distribution model in which all members of a society potentially have the same subjective distribution, regardless of their social category.
- The authors conducted four chains of sampling for 6,000 iterations each, which included 1,000 initial iterations as warm-up samples.
- Because R̂ of each parameter is approximately 1.000, the authors can safely conclude that the MCMC sampling converged (Gelman et al., 2013, 284–6).
- Table 1 and Figure 5 show that the subjective income distribution has a slightly larger mean and a much larger variance than the objective one.
4.4 Different Subjective Distributions Model
- Next, the authors prepare a more complex and more realistic model with the additional assumption that each social category shares a different subjective income distribution, reflecting differences in social experience.
- Figure 8 shows estimated parameters of objective and subjective income distribution for each social category represented by posterior mean and interval between 0.05 and 0.95 quantiles.
- This may reflect the fact that women’s participation in the labor market is still lower than that of men, and many women participate in the labor market as a marginal labor force in Japan.
- Again, the authors can see that women have a subjective income distribution that is farther from the objective one than men, and among men, the 45-54 age cohort has a subjective distribution that is closest to reality.
- Thus far, the authors have developed a model that assumes income comparison on a subjective income reference distribution to explain the centralization phenomenon of income evaluation and have conducted theoretical analysis and empirical parameter estimation using Bayesian statistical modeling.
- The theoretical analysis shows that income evaluation centralization occurs when the subjective distribution is more dispersed than the objective distribution.
- Furthermore, in a specific model assuming a lognormal distribution, the authors could parametrically analyze the effect of the relationship between the subjective and objective distributions on the distribution of income evaluation.
- Furthermore, the authors found that the relationship between the subjective and objective distributions differed depending on gender and age cohorts with different social experiences.
- This can lead to biased income assessments, which has important implications for understanding people’s satisfaction in unequal societies.
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Q1. What are the contributions in "A model of income evaluation: income comparison on subjective reference income distribution" ?
The authors develop a model that assumes income comparison on a subjective income reference distribution to explain the centralization phenomenon of income evaluation. The authors conduct theoretical analysis and empirical parameter estimation using Bayesian statistical modeling. 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.