中国市场收入分布的实证和模型研究

发布时间：2018-02-02 20:04

本文关键词： 复杂经济系统复杂网络经济物理学收入分布公司规模分布幂律分布无标度　出处：《华中师范大学》2016年博士论文　论文类型：学位论文

【摘要】：经济物理学作为一个新兴的、跨学科的研究领域,近年来吸引了很多物理学家以及经济学家的注意,运用基于统计物理的统计金融方面的知识来研究金融、经济市场常常能起到很好的作用。本文主要研究了经济市场中个体收入分布的统计特性。通过理论模型的数值分析和Monte Carlo模拟,将理论分析结果和模拟结果与实证研究对比,探讨了中国个人收入分布以及公司规模分布的性质。我们采用样本量较大、观测年份较长的实证数据研究了中国的个人收入分布。运用最大似然法,对中国个人收入分布进行了拟合,得到了与国外发达国家基本一致的特性:中、低收入人群的个人收入符合log-normal分布;而高收入部分则满足幂律分布。为了验证实证分析结果的准确性,对全部观测年份的收入数据进行了拟合,也发现了类似的两段式收入分布。在对拟合参数分析时发现,随着观测年份的推移,中、低收入部分的log-normal指数逐渐增大,而高收入部分的幂律指数则无明显变化趋势。与国外发达国家相比,中国个人收入分布的幂律指数相对较大。分析了中国的公司规模以及增长率分布。用资产和员工数作为公司的规模指标,分别分析了二者的分布。拟合显示这两项指标的分布均符合幂律分布,其中员工数分布具有较大的幂律指数,二者的幂律指数在全部观测年间均无明显变化。对函数形式特点不明的公司增长率分布,通过Subbotin family函数的拟合,发现公司资产和员工数的增长率分布均符合Laplace分布,而非Gaussian分布。分析了公司增长率的标准方差与公司规模之间的标度关系,与Stanley在美国公司数据中发现的标度关系类似。公司资产和员工数增长率的标准方差均为公司规模的幂律函数。另外,在增长率的标准方差与公司开业年份之间同样也存在幂律的标度关系。提出了包含长程相互作用的随机交易模型。为了与实证数据分析相比较,首先运用平均场的方法对模型进行了分析,当不考虑加法扩散过程时,得到了高收入部分的幂律分布。随后,讨论了网络上的长程随机交易过程,假定个体i和j之间交易的财富量为个体i的连接度ki以及它们之间最短路径dj的函数,即交易量Qij = (qo)/(kidij),其中qo为常量。并将个体交易收入之外的财富作为加法扩散过程。发现在均匀网络上,系统的收入分布与网络的平均度相关,符合高斯分布或者泊松分布;而在非均匀网络上,收入分布则与网络的连接度分布一致,满足幂律分布。分析了两人两策略博弈模型在网络上的演化过程,讨论了在均匀混合种群中,个体收益与合作者比例演化的关系。以囚徒困境模型为例,探讨了无标度网络上的演化博弈,得到了种群的收入分布与网络连接度分布之间的函数关系。在复杂网络上对两种收入分布模型进行了Monte Carlo模拟。首先是长程随机交易模型,在BA无标度网络、静态无标度网络以及小世界网络上的研究发现,个体的财富交易主要依赖于邻居间的相互作用,收入分布与网络的连接度分布高度相关,长程相互作用被局部交易所覆盖。讨论了二分网络上的随机交易模型,将城镇居民和农村居民看作二分网络上的两类节点,发现收入分布符合一种双峰分布,且系统稳定后,农村居民的平均收入有所增长。在静态无标度网络上进行了囚徒困境博弈模型和雪堆博弈模型的模拟。通过网络上的博弈过程,两种博弈模型均得到了幂律形式的收益分布。对于异质性程度不同的无标度网络,收益分布的幂律指数无明显变化。
[Abstract]:Economic physics as an emerging, interdisciplinary research field in recent years, attracted a lot of attention of physicists and economists, financial statistics using statistical physics based knowledge to study finance, financial markets often can play a good role. This paper mainly studies the statistical characteristics of individual income distribution in the market economy. By numerical analysis and Monte Carlo model simulation, the comparison between theoretical analysis and simulation results and empirical research, discusses the Chinese personal income distribution and company size distribution properties. We use a large amount of samples, the empirical data of the year long observation of personal income distribution China. Using the maximum likelihood method for personal China the income distribution of the fitting, get the characteristics consistent with the developed countries, the low income crowd: personal income in accordance with log-no Rmal distribution; and the high income part meet the power-law distribution. In order to validate the results of the empirical analysis, the income data of all observed years fitted, found a similar two segment income distribution. Based on the analysis of the fitting parameters, with the observation year goes on, in low income part the log-normal index increased gradually, and the power-law index of high income is no obvious trend. Compared with the developed countries, the income distribution of power-law index is relatively large. China personal analysis of China company size and growth rate distribution. With assets and number of employees as the scale index, respectively, analyzes the distribution of the two the fitting shows the distribution of these two indicators are in line with the power-law distribution, the number of employees with the distribution of power-law index is larger, the power-law index of the two did not change significantly in all years. The function of observation The form characteristics of unknown company growth rate distribution, by fitting the Subbotin family function, found that the company assets and number of employees, the growth rate distribution conformed to Laplace distribution, and Gaussian distribution. To analyze the relationship between corporate growth rate standard deviation and the scale of the company scale, similar to the Stanley company in the United States found in the data standard the relationship between the growth rate of the company's assets. The standard deviation and the number of employees are power law function of the size of the company. In addition, the relationship between years there is also a power-law scaling in the growth rate of the standard deviation of business with the company. Put forward the stochastic trading model including the long-range interaction. In order to analysis and empirical data comparison first of all, the model is analyzed by using the method of mean field, when not considering the addition of the diffusion process, the power-law distribution of high income part. Then, discusses on the network long Cheng Sui For the transaction process, assuming the amount of wealth transactions between individual I and j as a function of connectivity between individual ki I and their DJ shortest path, namely the trading volume of Qij = (Qo) / (kidij), where Qo is a constant. And the individual trading income wealth as a diffusion process. The addition of uniform network, income distribution and the average degree of the network system, in line with the Gauss distribution or Poisson distribution; and in heterogeneous network, the connection degree distribution of income distribution is consistent with a network of, meet the power-law distribution. Analysis of the two two game model evolution on the network, discussed in the mixed population, the relationship between individual income and the proportion of cooperative evolution. In the prisoner's dilemma model as an example, discusses the evolutionary game of scale-free network, the function of income distribution and population distribution network connectivity relationship. In complex networks Two kinds of income distribution model and Monte Carlo simulation. The first is the long-range random trading model, the BA scale-free network, the static research on scale free networks and small world networks found that the interaction of individual wealth trading mainly depends on the connection between neighbors, is highly correlated with income distribution and degree distribution network, long-range interactions are local exchange coverage. This paper discusses stochastic trading model of two points on the network, the urban residents and rural residents as two class two nodes on the network, found that the income distribution in line with a Shuangfeng distribution, and the system is stable, the average income of rural residents increased. In the static scale-free the network simulates the prisoner's dilemma game model and the snowdrift game model. Through the process of network game, two game models are the return distribution of power-law form for different degree of heterogeneity. There is no obvious change in the power law index of the income distribution in the scale-free network.

【学位授予单位】：华中师范大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：F126.2;O157.5

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