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Understanding the Kuznets Process—An Empirical Investigation of Income Inequality in China: 1978–2011

Abstract

This paper investigates income inequality in post-reform China using both national time series and provincial panel data from 1978 to 2011. We identify a Kuznets inverted-U relationship between economic development and income inequality and show that this relationship was driven by the process of urbanization. We estimate that the Kuznets turning point occurred in the mid-1980s, and argue that increased urbanization after the mid-1980s had the effect of narrowing income inequality but its effect was more than offset by other factors. In particular, we found that low productivity in agriculture relative to that of the economy as a whole (i.e., dualism) and inflation were significant contributing factors to income inequality. We also present evidence to suggest that secondary education and higher education may have different effects on income inequality at the national level and at the provincial level.

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Fig. 1

Notes

  1. 1.

    Greater income disparity in urban areas may be due to greater occupational diversity and the large income gap between established professionals and recently arrived migrants.

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Acknowledgments

This project was supported by China Postdoctoral Science Foundation (Grant No. 2012M510736), Chinese State Scholarship Fund (China Scholarship Council, Visiting Scholar, Grant No. 201406725004), and College of Mathematics and Computer Science, Key Laboratory of High Performance Computing and Stochastic Information Processing (Ministry of Education of China), Hunan Normal University, Changsha, Hunan 410081, P. R. China.

Author information

Correspondence to Yongzheng Wu.

Appendices

Appendix 1: Calculation of the Theil Index

The Theil index has its origin in Shannon’s (1948) information theory. Theil (1967) adapted Shannon’s formula of expected information content to measure inequality, leading to the now well-known Thei’s TT (Conceicao and Galbraith 2000):

$$TT = \sum {\frac{{y_{i} }}{Y}} \ln \frac{{y_{i} /Y}}{1/n} = \frac{1}{n}\sum {\frac{{y_{i} }}{\mu }} \ln \frac{{y_{i} }}{\mu }{\kern 1pt} {\kern 1pt}$$
(3)

where n is the number of individuals in the population, Y is the total income of the population, \(y_{i}\) is the income of individual i, \(\mu\) is the average income of the population.

The Theil index can be understood as a summary statistic that measures the extent to which the distribution of income across groups differs from the distribution of population across the same groups (Conceição and Ferreira 2000). Groups that have higher income shares than their population shares contribute positively to the Theil index; those that have lower income shares than their population shares contribute negatively. If each groups has their “fair” share of income (i.e., each group has the same share of income as its share of population), the Theil index is at its minimum value of zero.

If we consider a population that is divided into i groups each with j subgroups, the Theil index can be written as:

$$TT = \sum\limits_{i} {\sum\limits_{j} {\frac{{Y_{ij} }}{Y}} } \ln \left( {{\kern 1pt} {{\frac{{Y_{ij} }}{Y}} \mathord{\left/ {\vphantom {{\frac{{Y_{ij} }}{Y}} {\frac{{N_{ij} }}{N}}}} \right. \kern-0pt} {\frac{{N_{ij} }}{N}}}} \right)$$
(4)

where \(Y_{ij}\) is the income of subgroup j in group i; \(N_{ij}\) is the population size of subgroup j in group i.

To calculate the national time series Theil index given provincial data of China, we rewrite Eq. (4) as:

$$TT = \sum\limits_{i} {\sum\limits_{j} {\frac{{Y_{ij} }}{Y}} } \ln \left[ {\frac{{\frac{{Y_{ij} }}{Y}}}{{\frac{{N_{ij} }}{N}}}} \right]\quad = \sum\limits_{i} {\sum\limits_{j} {\frac{{N_{ij} }}{N}\frac{{\bar{Y}_{ij} }}{{\bar{Y}}}} } \ln \left[ {\frac{{\frac{{Y_{ij} }}{Y}}}{{\frac{{N_{ij} }}{N}}}} \right]\quad = \sum\limits_{i} {\sum\limits_{j} {\frac{{N_{ij} }}{N}\frac{{\bar{Y}_{ij} }}{{\bar{Y}}}} } \ln \left( {\frac{{\bar{Y}_{ij} }}{{\bar{Y}}}} \right)$$
(5)

where i = 1, 2 representing the urban area and rural area, respectively; j = 1, 2,…, 31, representing 31 provinces (including autonomous regions and directly-administered municipalities); \(N_{ij}\) is the urban (i = 1) or rural (i = 2) population in province j; \(N\) is the total population of China; \(\bar{Y}_{ij}\) is the average urban or rural income in province j; \(\bar{Y}\) is the average income in China.

To calculate the provincial panel Theil index, we rewrite Eq. (4) to

$$TT = \sum\limits_{i = 1}^{2} {\frac{{Y_{i} }}{Y}} \ln \frac{{Y_{i} /Y}}{{N_{i} /N}}{\kern 1pt}$$

where \(Y_{1}\) = total annual disposable income of urban households, \(Y_{2}\) = total annual net income of urban households, \(Y\) = \(Y_{1} + Y_{2}\), \(N_{1}\) = urban population, \(N_{2}\) = rural population

$$N = N_{1} + N_{2}$$

Appendix 2

See Table 8.

Table 8 National time series data

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Cheng, W., Wu, Y. Understanding the Kuznets Process—An Empirical Investigation of Income Inequality in China: 1978–2011. Soc Indic Res 134, 631–650 (2017). https://doi.org/10.1007/s11205-016-1435-x

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Keywords

  • Kuznets curve
  • Income inequality in China
  • Theil index
  • Urbanisation
  • Dualism