居民收入分布及其变迁的统计研究
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摘要
居民收入分布(Income Distribution)是反映居民收入和财富分配结构状态、变化趋势最重要的概念之一,是经济发展过程中收入和财富分配结果的表现,是定量研究居民收入分配问题的基础。从统计学意义上讲,居民收入分布是指不同收入水平与相应人口比重之间的统计规律或函数形式,最常见的表现形式是收入分布函数(CumulativeDistribution Function,简称CDF)和收入密度函数(Probability Density Function,简称PDF)。如果能合理估计居民收入分布,则几乎可以掌握居民收入分配的全部信息,就能清晰地描述居民收入分布的结构和规律。
非参数统计(Non-parameter Statistics)方法可以分为传统和现代两大类。其中,传统非参数统计方法主要是基于秩的、以检验为主的非参数统计推断,需要假设居民收入服从某些分布形式,并通过非参数检验进行判断和选择。现代非参数统计方法主要是指近二三十年发展起来的非参数回归、非参数密度估计等方法。现代非参数统计方法中的核密度估计方法,能够在总体收入分布未知的情况下,尽量从数据本身来获得所需要的信息,估计居民收入分布。
论文研究目的。针对实际研究中居民收入分布大多未知的情况,基于现代非参数统计方法中的核密度估计方法,围绕估计居民收入分布、测度居民收入分布变迁、分解影响居民收入分布变迁的因素方法进行拓展和创新,并将所有方法应用到我国实际问题研究中。具体包括:
(1)对比研究估计居民收入分布的参数统计方法、传统非参数统计方法与现代非参数统计方法;
(2)研究居民收入分布的现代非参数方法中核密度估计方法;
(3)系统提出测度居民收入分布变迁的相对分布方法;
(4)完整构建居民收入分布变迁影响因素的点分解和区间分解的非参数统计方法;
(5)使用微观数据,对我国居民收入分布及其变迁进行实证分析。估计我国居民收入分布、测算我国居民收入分布变迁过程,定量分解影响我国居民收入分布变迁的增长因素和分配因素,分析我国居民收入分布变迁的经济意义;
(6)将现代非参数统计方法应用到我国中等收入问题研究中。静态标准和动态标准相结合,估计我国中等收入群体比重及其变化趋势,对影响我国中等收入群体比重变化的增长因素、分配因素以及标准线变动因素进行分解和测度。
论文理论、方法基础与创新。综合对比居民收入分布的各种估计理论和方法,分析各种估计方法的特点,分析核密度估计方法具有的不可替代的优势,提出居民收入分布核密度估计方法的改进及其步骤,在计算机上通过R语言编程实现。这部分内容构成本论文的理论和方法基础,由此形成本论文力图创新的第一个方面内容。
论文研究重点、难点与创新。居民收入分布估计、居民收入分布变迁测度、影响收入分布变迁的因素分解等现代非参数方法研究,构成为本论文的核心内容和显著特色。其一,综合提出测度居民收入分布变迁的相对分布方法,完整阐述其经济含义。通过相对密度函数取值变化判断不同收入水平下人口比重的变动,通过相对分布函数取值变化判断不同收入区间累计人口比重的变动;其二,发现和描述了居民收入相对分布不动点现象,并在研究中加以分析运用;其三,引入补偿的居民收入密度曲线,提出影响居民收入分布变迁因素的点分解方法,构建影响不同收入区间居民比重变动的区间分解和测度方法,将影响收入分布变迁的因素分解为增长因素、分配因素和标准线变动因素三部分,既可以用来分解和测度整体收入分布变迁的影响因素,也可以用来分解和测度任何收入水平下或收入区间收入分布变迁的增长效应、分配效应和标准线变动效应,首次从方法上实现了居民收入分布变迁影响因素的静态和动态完全分解。这部分内容构成本论文的研究重点和难点,也是现代非参数统计方法在居民收入分布研究中的拓展,是本论文力图创新的第二个方面内容。
论文实践特色与创新。使用调查的微观收入数据,将论文的所有方法用于实证分析我国居民收入分布和中等收入问题,给出比较符合实际趋势的重要解释和结论。对我国中等收入群体含义和界定标准进行系统梳理,基于中等收入群体的静态标准和动态标准,测算对中等收入群体比重,分析其变迁过程。首次动态分解、测算影响我国中等收入群体比重变动的增长因素、分配因素和标准线变动因素及各自的影响效应,给出比较符合实际情况的解释和结论。此部分内容形成本论文理论与实际相结合的实证特色,也是本论文力图创新的第三个方面内容。
Resident income distribution is one of the most important definitions which reflect the structural status and changes of income and wealth distribution in residents. It is also the basis of further quantitative researches on income distribution. In the view of Statistics, resident income distribution is law or function of the relationship between income levels and the corresponding population scale. The most common forms are the Cumulative Distribution Function (CDF) and Probability Density Function (PDF). If the income distributin can be estimated suitably, we can find all information about the income distribution, then find the structure and law of the distribution.
Non-parametric statistical methods can be divided into two parts: Traditional Non-parametric Statistics and Modern Non-parametric Statistics. Basing on the rank and non-parametric statistical tests, the former mainly assumes the specific form of resident income distribution and make inferences. The latter are methods developing in the past three decades which includes non-parametric regression, nonparametric density estimation and so on. When the exact form of resident income distribution is unknown, non-parametric kernel estimation methods estimate the income distribution form basing on the information from the real data.
Purposes of this paper are doing researches on the non-parametric methods when the income distribution is unknow. These researches include estimating the distributional form of resident income, measuring the changes of income distribution, decomposing the factors affecting the changes and applying all the methods in our country's practice. Concretely speaking, they are as followings:
(1) Comparing and analyzing the methods of Modern Non-parametric Statistics, Parametric Statistics and Traditional non-parametric Statistics in estimating the form of resident income distribution.
(2) Researching the non-parametric kernel estimation method and applying it to estimating the form of resident income distribution.
(3) Presenting the relative distribution method which can measure the income distribution changes systematically.
(4) Constructing the point and interval decomposition methods which can decompose the factors affecting the income distribution changes.
(5) Using the real micro-data, this paper analyzes the resident income distribution in China. Mainly includes: estimating Chinese resident income distribution form, measuring its changing process, decomposing and measuring the growth effect and distribution effect which lead to the changes, analyzing the economic meanings of the changes.
(6) Applying the modern non-parametric methods to the researches of the middle-income matters. Basing on the static and dynamic standards, this paper estimates the scale of Chinese middle-income residents; decomposes the growth effect, distribution effect and the standard effect which affect the changes of the scale.
Theory, Methods, and Innovation: Through a comprehensive comparison to different theories and methods estimating the income distribution form, analyzing the irreplaceable advantages of non-parametric kernel estimation method; presenting the operation steps of kernel method in estimating income distribution forms and applying them in the R language software. All the above contents form the foundation of the theories and methods in this paper which constitutes the first innovation of this paper.
Focuses, Difficulties and Innovation: Researching on the methods of estimating resident income distribution form, measuring its changes, decomposing the factors affecting the changes is the core and significant feature of this paper. First, this paper puts forward the relative distribution methods measuring the changes of income distribution and expounds its economic meanings perfectly. Through the relative distribution function and relative density function values, it measures the changes of the population scale at different income point and the cumulative population scale in different income intervals. Secondly, this paper describes the fixed points in income distribution changing process and applying this phenomenon in practical researches. Thirdly, this paper originally introduces the compensated income distribution density curve and constructs the decomposition methods. The method concludes point decomposition and range decomposition, both of which can be used to measure the overall impact of changes in income distribution. This part is not only the most important and difficult content in this paper, but also constitute the second innovation in this paper.
Practical Characteristics and Innovation: Basing on the micro data, this paper applies the modern non-parametric methods developed in this paper to the research of the resident income distribution and the middle-income issues, giving reasonably explaination and conclusion. This paper systematically analyzes the meaning and the standards of the middle-income residents, puts forward the static and dynamic standards of their income, estimates their scale, measures the scale changes, decomposes the factors affecting the changes. This paper dynamically decomposes and measures the growth effect, distribution effect and standard effect which affect the Chinese middle-income residents for the first time and give out the explainations and conclusions consistent with the fact. This paper implements all the methods into empirical study which constitutes the third innovation.
非参数统计(Non-parameter Statistics)方法可以分为传统和现代两大类。其中,传统非参数统计方法主要是基于秩的、以检验为主的非参数统计推断,需要假设居民收入服从某些分布形式,并通过非参数检验进行判断和选择。现代非参数统计方法主要是指近二三十年发展起来的非参数回归、非参数密度估计等方法。现代非参数统计方法中的核密度估计方法,能够在总体收入分布未知的情况下,尽量从数据本身来获得所需要的信息,估计居民收入分布。
论文研究目的。针对实际研究中居民收入分布大多未知的情况,基于现代非参数统计方法中的核密度估计方法,围绕估计居民收入分布、测度居民收入分布变迁、分解影响居民收入分布变迁的因素方法进行拓展和创新,并将所有方法应用到我国实际问题研究中。具体包括:
(1)对比研究估计居民收入分布的参数统计方法、传统非参数统计方法与现代非参数统计方法;
(2)研究居民收入分布的现代非参数方法中核密度估计方法;
(3)系统提出测度居民收入分布变迁的相对分布方法;
(4)完整构建居民收入分布变迁影响因素的点分解和区间分解的非参数统计方法;
(5)使用微观数据,对我国居民收入分布及其变迁进行实证分析。估计我国居民收入分布、测算我国居民收入分布变迁过程,定量分解影响我国居民收入分布变迁的增长因素和分配因素,分析我国居民收入分布变迁的经济意义;
(6)将现代非参数统计方法应用到我国中等收入问题研究中。静态标准和动态标准相结合,估计我国中等收入群体比重及其变化趋势,对影响我国中等收入群体比重变化的增长因素、分配因素以及标准线变动因素进行分解和测度。
论文理论、方法基础与创新。综合对比居民收入分布的各种估计理论和方法,分析各种估计方法的特点,分析核密度估计方法具有的不可替代的优势,提出居民收入分布核密度估计方法的改进及其步骤,在计算机上通过R语言编程实现。这部分内容构成本论文的理论和方法基础,由此形成本论文力图创新的第一个方面内容。
论文研究重点、难点与创新。居民收入分布估计、居民收入分布变迁测度、影响收入分布变迁的因素分解等现代非参数方法研究,构成为本论文的核心内容和显著特色。其一,综合提出测度居民收入分布变迁的相对分布方法,完整阐述其经济含义。通过相对密度函数取值变化判断不同收入水平下人口比重的变动,通过相对分布函数取值变化判断不同收入区间累计人口比重的变动;其二,发现和描述了居民收入相对分布不动点现象,并在研究中加以分析运用;其三,引入补偿的居民收入密度曲线,提出影响居民收入分布变迁因素的点分解方法,构建影响不同收入区间居民比重变动的区间分解和测度方法,将影响收入分布变迁的因素分解为增长因素、分配因素和标准线变动因素三部分,既可以用来分解和测度整体收入分布变迁的影响因素,也可以用来分解和测度任何收入水平下或收入区间收入分布变迁的增长效应、分配效应和标准线变动效应,首次从方法上实现了居民收入分布变迁影响因素的静态和动态完全分解。这部分内容构成本论文的研究重点和难点,也是现代非参数统计方法在居民收入分布研究中的拓展,是本论文力图创新的第二个方面内容。
论文实践特色与创新。使用调查的微观收入数据,将论文的所有方法用于实证分析我国居民收入分布和中等收入问题,给出比较符合实际趋势的重要解释和结论。对我国中等收入群体含义和界定标准进行系统梳理,基于中等收入群体的静态标准和动态标准,测算对中等收入群体比重,分析其变迁过程。首次动态分解、测算影响我国中等收入群体比重变动的增长因素、分配因素和标准线变动因素及各自的影响效应,给出比较符合实际情况的解释和结论。此部分内容形成本论文理论与实际相结合的实证特色,也是本论文力图创新的第三个方面内容。
Resident income distribution is one of the most important definitions which reflect the structural status and changes of income and wealth distribution in residents. It is also the basis of further quantitative researches on income distribution. In the view of Statistics, resident income distribution is law or function of the relationship between income levels and the corresponding population scale. The most common forms are the Cumulative Distribution Function (CDF) and Probability Density Function (PDF). If the income distributin can be estimated suitably, we can find all information about the income distribution, then find the structure and law of the distribution.
Non-parametric statistical methods can be divided into two parts: Traditional Non-parametric Statistics and Modern Non-parametric Statistics. Basing on the rank and non-parametric statistical tests, the former mainly assumes the specific form of resident income distribution and make inferences. The latter are methods developing in the past three decades which includes non-parametric regression, nonparametric density estimation and so on. When the exact form of resident income distribution is unknown, non-parametric kernel estimation methods estimate the income distribution form basing on the information from the real data.
Purposes of this paper are doing researches on the non-parametric methods when the income distribution is unknow. These researches include estimating the distributional form of resident income, measuring the changes of income distribution, decomposing the factors affecting the changes and applying all the methods in our country's practice. Concretely speaking, they are as followings:
(1) Comparing and analyzing the methods of Modern Non-parametric Statistics, Parametric Statistics and Traditional non-parametric Statistics in estimating the form of resident income distribution.
(2) Researching the non-parametric kernel estimation method and applying it to estimating the form of resident income distribution.
(3) Presenting the relative distribution method which can measure the income distribution changes systematically.
(4) Constructing the point and interval decomposition methods which can decompose the factors affecting the income distribution changes.
(5) Using the real micro-data, this paper analyzes the resident income distribution in China. Mainly includes: estimating Chinese resident income distribution form, measuring its changing process, decomposing and measuring the growth effect and distribution effect which lead to the changes, analyzing the economic meanings of the changes.
(6) Applying the modern non-parametric methods to the researches of the middle-income matters. Basing on the static and dynamic standards, this paper estimates the scale of Chinese middle-income residents; decomposes the growth effect, distribution effect and the standard effect which affect the changes of the scale.
Theory, Methods, and Innovation: Through a comprehensive comparison to different theories and methods estimating the income distribution form, analyzing the irreplaceable advantages of non-parametric kernel estimation method; presenting the operation steps of kernel method in estimating income distribution forms and applying them in the R language software. All the above contents form the foundation of the theories and methods in this paper which constitutes the first innovation of this paper.
Focuses, Difficulties and Innovation: Researching on the methods of estimating resident income distribution form, measuring its changes, decomposing the factors affecting the changes is the core and significant feature of this paper. First, this paper puts forward the relative distribution methods measuring the changes of income distribution and expounds its economic meanings perfectly. Through the relative distribution function and relative density function values, it measures the changes of the population scale at different income point and the cumulative population scale in different income intervals. Secondly, this paper describes the fixed points in income distribution changing process and applying this phenomenon in practical researches. Thirdly, this paper originally introduces the compensated income distribution density curve and constructs the decomposition methods. The method concludes point decomposition and range decomposition, both of which can be used to measure the overall impact of changes in income distribution. This part is not only the most important and difficult content in this paper, but also constitute the second innovation in this paper.
Practical Characteristics and Innovation: Basing on the micro data, this paper applies the modern non-parametric methods developed in this paper to the research of the resident income distribution and the middle-income issues, giving reasonably explaination and conclusion. This paper systematically analyzes the meaning and the standards of the middle-income residents, puts forward the static and dynamic standards of their income, estimates their scale, measures the scale changes, decomposes the factors affecting the changes. This paper dynamically decomposes and measures the growth effect, distribution effect and standard effect which affect the Chinese middle-income residents for the first time and give out the explainations and conclusions consistent with the fact. This paper implements all the methods into empirical study which constitutes the third innovation.
引文
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[1]本文强调“中等收入者”的收入水平并非摒弃了中等收入者质的特征,而是认为:质的形成,即中等收入者的政治见解、生活方式、文化心理、审美情趣、道德意识的形成是一个历史的自然的过程,收入水平提高是其形成的根本前提条件,在我国当前条件下,“中等收入者”应该强调其“前提条件”——收入水平。正如许海峰(2003)所说“与西方社会的‘中产'悠闲自由的生活方式相比,中国‘新中产'显得更为紧张和忙碌,也许只能算是正在形成的‘中产',或者说算是当前‘具有中国特色的中产”'。本文认为用中等收入者来替用“具有中国特色的中产”更好,中国人要达到外国中产阶级或中产阶层的生活水准,还需要走很长的路,所以从收入角度研究我国中等收入群体具有很强的现实意义。
[2]反映到统计学上就是一个中等收入区间。
[3]国家发改委宏观经济研究院课题组(课题组成员:陈新年、杨宜勇、常兴华、曾智泽、徐振斌、常虹、程凯、温运娟),《进一步扩大中等收入者比重》,红旗文稿,2006年12期。
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[2]刁永祚,《中等收入群体的基本分析》,北京社会科学,2006年第3期。
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[1]陈新年(2005)详细阐述了我国中等收入者收入水平的界定方法,并对得到的中等收入者收入水平进行了评价,参见:陈新年,《中等收入者论》,中国计划出版社,2005:pp30-34.
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[2]郑杭生:《中国社会结构变化趋势变化》,中国人民大学出版社,2004年第1版,34页。
[1]本文强调“中等收入者”的收入水平并非摒弃了中等收入者质的特征,而是认为:质的形成,即中等收入者的政治见解、生活方式、文化心理、审美情趣、道德意识的形成是一个历史的自然的过程,收入水平提高是其形成的根本前提条件,在我国当前条件下,“中等收入者”应该强调其“前提条件”——收入水平。正如许海峰(2003)所说“与西方社会的‘中产'悠闲自由的生活方式相比,中国‘新中产'显得更为紧张和忙碌,也许只能算是正在形成的‘中产',或者说算是当前‘具有中国特色的中产”'。本文认为用中等收入者来替用“具有中国特色的中产”更好,中国人要达到外国中产阶级或中产阶层的生活水准,还需要走很长的路,所以从收入角度研究我国中等收入群体具有很强的现实意义。
[2]反映到统计学上就是一个中等收入区间。
[3]国家发改委宏观经济研究院课题组(课题组成员:陈新年、杨宜勇、常兴华、曾智泽、徐振斌、常虹、程凯、温运娟),《进一步扩大中等收入者比重》,红旗文稿,2006年12期。
[1]纪玉山等《中等收入者比重的扩大及“橄榄型”财富结构的达致》,社会科学研究,2005年2期。
[2]刁永祚,《中等收入群体的基本分析》,北京社会科学,2006年第3期。
[1]王开玉.中国中等收入者研究[M].社会科学文献出版社,2006:15-15.
[1]国家发改委宏观经济研究院课题组(课题组成员:陈新年、杨宜勇、常兴华、曾智泽、徐振斌、常虹、程凯、温运娟),《进一步扩大中等收入者比重》,红旗文稿,2006年12期。
[1]陈新年(2005)详细阐述了我国中等收入者收入水平的界定方法,并对得到的中等收入者收入水平进行了评价,参见:陈新年,《中等收入者论》,中国计划出版社,2005:pp30-34.
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