Income Distribution and Aggregate Saving: Theory and China’s Evidence

ABSTRACT

Using a parsimonious heterogeneous-agent general equilibrium model, this study reveals a positive causal effect of income inequality on the aggregate saving rate. In the model economy, benevolent individuals save to leave offspring bequests. Since bequests are luxury, the rich have a higher marginal propensity to save. Then, else equal, a fall in income inequality will lower the economy-wide saving rate. The model predicts an augmented aggregate saving function: the aggregate saving rate depends positively not only on the aggregate income level, but also on the dispersion of income. We find some empirical support for this hypothesis using China’s province-level longitudinal data.

KEY WORDS:

• Aggregate saving rate
• China
• income inequality
• panel regression

JEL Codes:

• E21
• E25

Acknowledgments

We thank two anonymous referees for their great suggestions and Meixin Guo, Tao Hu, Qian Jiao, Ali M. Kutan, Shaorong Li, Zhibing Liang, Chen Lin, Chong Liu, Lin Lu, Hong Ma, Min Ouyang, Yulei Peng, Xinqiao Ping, Xue Qiao, Xuezheng Qin, Binzhen Wu, Yuan Xu, Jingyi Ye, Pengfei Zhang, Yaguang Zhang, Jianbo Zhou, Chuanqi Zhu, and seminar participants at Peking University, Tsinghua University, Shandong University, Sun Yat-sen University, the 6th CEA (Europe) and 25th CEA (UK) Annual Conference for their helpful comments. All errors are our sole responsibility.

Notes

^1. http://news.xinhuanet.com/english/china/2013-01/18/c_132111927.htm

^2. We do not deny the existence of causality the other way around, but it is not the focus of present study.

^3. See, e.g., De Nardi (2004) and Aït-Sahalia, Parker, and Yogo (2004).

^4. The model features time-varying cross-sectional distributions (except for that of labor endowment). Simplifying assumptions are made so that all the second- and higher-order moments of a cross-sectional distribution can be described by a single variable. This dramatically reduces the dimensions of state space.

^5. Unfortunately, we are not able to test some interesting theoretical predictions due to data limitations.

^6. See, e.g., Schmidt-Hebbel and Servén (2000), Alvarez-Cuadrado and Vilalta (2012) and Gu et al. (2015).

^7. A notable exception is Alvarez-Cuadrado and Vilalta (2012).

^8. In practice, theorists studying the distribution of income and/or wealth often make some strong assumptions to obtain linear decision rules so that the aggregate level can affect the cross-sectional distribution but not the other way around (see, e.g., Chatterjee 1994; Ríos-Rull 1997; Wen 2009). We cannot follow this strategy since the whole point of this article is to establish an aggregate effect of distribution.

^9. Introducing overlapping generations won’t critically change the main results of the model.

^10. Potential determinants of “labor endowment” include health condition, human capital, luck, etc. All these are assumed to be exogenous.

^11. Admittedly this is a strong assumption. We make it for simplicity. Introducing elastic intergenerational transfer of labor endowment may bring about other interesting results. We leave this for future study.

^12. Negative bequests are not allowed. Put differently, parents are forbidden to borrow from children.

^13. Complete capital depreciation is a reasonable assumption as one “period” covers an individual’s whole life.

^14. That children’s incomes, which rely crucially on parents’ bequests, directly generate utilities for parents’ echoes the “warm glow” bequest motive in the literature.

^15. See De Nardi (2004) and Aït-Sahalia, Parker, and Yogo (2004).

^16. This imposes certain restrictions on the values of parameters and the initial states of the model economy.

^17. Since capital completely depreciates, $K_{t+1}$is also the aggregate investment in period$t$.

^18. Technically, labor endowment follows a linearly transformed Bernoulli distribution.

^19. See, e.g., Ríos-Rull (1997).

^20. For example, under the parameterization$\theta =2$, $\tau =10$, $A=0.8$, $\alpha =0.36$, $n=0.5$, ${\mu }_L=1.2$, ${\mathrm{\Psi }}_0^{-1}{\mathrm{\Psi }}_1$is equal to$\left[\begin{array}{cc}-0.4813& 0.0023\\ -0.0271& 0.6122\end{array}\right]$, the two eigenvalues of which equal $0.4818$ and$0.6117$.

^21. From Proposition 2, an economy featured by a higher degree of labor income inequality tends to have a higher aggregate saving rate and a higher aggregate income. According to Proposition 3, this economy also tends to have a higher degree of capital inequality, and as a result, a higher degree of total inequality.

^22. The 27 provinces, municipalities or autonomous regions are Beijing, Tianjin, Shanghai, Chongqing, Heilongjiang, Jilin, Liaoning, Shandong, Henan, Jiangsu, Zhejiang, Fujian, Guangdong, Guangxi, Hainan, Shaanxi, Shanxi, Anhui, Hubei, Jiangxi, Sichuan, Guizhou, Yunnan, Inner Mongolia, Xinjiang, Ningxia and Qinghai. The other 4 (mainland) provinces or autonomous regions, Hunan, Hebei, Gansu and Tibet, are excluded from the sample due to either incomplete or noncomparable data.

^23. The “average individual” is conceptually different from the “representative individual”. Actually, the present model doesn’t admit a “representative individual”.

^24. Our derivation here relies heavily on Hu (2004).

^25. This, of course, is an accounting effect.