Empirical Analysis And Theoretical Model For Income Distribution In Chinese Market

In recent years, econophysics, as an emerging interdisciplinary field, has attracted widespread attention among both physicists and economists. It is found that many tech-niques rooted in statistical physics can be very useful in solving the stochastic and non?linear problems existing in the theoretical econometrics. These techniques provide a set of powerful tools in the studies of financial markets. The work illustrated in this thesis is mainly devoted to understanding the statistical feature of the personal income in finan-cial markets. We performed an empirical study on the correlation between the personal income and the company size in China by comparing our model calculation and network simulation results with the collected data.Our work investigates the large-size Chinese personal income data over a long-term observation. Based on the maximum likelihood method, we analysed the Chinese personal income distribution. A two-stage pattern, which is similar to that observed in the personal income data for developed countries, can be extracted from the analysis: the low and middle personal income fit the log-normal distributions, while the high personal income can be described by the power-law distribution. To further confirm our findings in the empirical studies, we examined the collected personal income data sample in every year.A similar two-stage pattern exists ill all the power-law fits to the yearly data. It is found that the log-nomal exponent inereases year-by-year, while the power-law exponent is rather flat over the years. The power-law exponent of Chinese personal income is found to be larger than the counterparts for the developed countries.On the other hand the size and growth rate of the Chinese companies have been explored by estimating the asset and the number of employees in a company A power-law fit to these quantities indicate that the power-law exponent is quite large for the employee number and no significant dependence for the two indexes over time is observed. To unsettle the controversial issue on the funetional form for the growth rate of the companies,we performed a fit to the data with the Subbotin family funetion. A Laplace distribution is found to be more favored in characterizing the company assets and employee numbers rather than the Gaussian distribution. Similar to the analysis made by Stanley for the American company data, we found a power-law behavior in the scaling relations between the company assets and the standard variation of the employee growth rate in China.Similar scaling behavior also exists in the standard variation of the employee growth rate and the company age.We proposed a long-range stochastic interaction model to understand the power-law behavior observed in the data. A power-law distribution can be obtained for the high-income people in the mean-field analysis, if no additional diffusion process is considered.We also performed a numeric analysis for the stochastic exchange dynamics on networks with additional diffusion process by including the excess wealth. We set the exchange wealth between agents and to be , where is a constant. It turns out that, on homogeneous networks, the system income is related to the average degree in a Gaussian or Poissorn form. On the other hand, the same relation shows a power-law behavior on heterogeneous networks. Further studies were performed upon the time evolution of the game theory models on complex networks. We studied the number of cooperators varying with time on ,scale-free networks based on the prisoner's dilemma model and obtained the group income distributions dependent on the network degrees.The stochastic interaction model has been simulated on BA scale-free networks, static scale-free networks and small-world networks. It is indicated in our simulation that the agent's wealth interaction is mainly dependent on its interaction strength with its neigh-bors and the income is strongly related to the average network degree, which means the long- range interaction does not contribute to wealth trading process. We also investigat-ed the stochastic interaction model on the bipartite network by taking the urban residents and rural residents as two groups of nodes on the network. The final income distribution displays a bimodal structure, with the average rural resident income increasing during the evolution of the system. We also explored the prisoner's dilemma game and snow drift game on static scale-free networks. It has been shown both game theory models lead to the power-law income distribution. The power-law exponent fit to the income distribution is not sensitive to the heterogeneity on scale-free networks.