Functional Framework And Model Construction Of Income Measurement

The study of personal income distribution has been received attention publicly and can not be avoided in any historical periods. In recent years, with the further deepening of China’s rapid economic growth and reform, the contradictions in the field of income distribution have become more apparent. Well understanding the issues of the personal income distribution, we must to investigate the income measurement firstly, which mainly include characteristics of income levels and its changes, of income groups and its changes, income inequality and its decomposition and economic impact analysis of the income distribution.The traditional way of measurement framework could be described as income funetion fittingâ†'inequality indicators calculatingâ†'indicators analyzing. Generally speaking, the income functions as well as the relationship within these curves were considered as the most informational objects, which include income inequality, income changes, etc., while the process of inequality indicators calculating lead to loss of information substantially, as well as solo-function fitting hinder to the measurement of income inequality and of income dynamic changes consequently.According to the problems described bove, this thesis trying to avoid the process of indicators calculating and construct statistical analysis based n income unctions directly. So, in this theisis, the framework that could be concluded as income Junctions fitting functional analyzing was proposed, and statistical inference methods of income functions were constructed under this framework. These include:Firstly, income functional data generation and description:(1) Fitting approachs of income functions was discussed based on basis functions expression, which including non-constraint and constraint forms.(2) The specification of forms, orders, and knots of B-spline basis functions were discussed.(3) According to fitting approachs of basis function expression, statistical description under L2space and relationship to traditional multivariate statistical methods were discussed.(4) As application of fitting approachs and as the data used in subsequent chapter, some China’s income data was fitted and analyzed preliminary, including time series curves family, Lorenz curves family, as well as income distribution function family fitting respectively.Secondly, according to fitting approach of income function described above, statistical model of income functions were constructed, estimated, and application of China’s income data were included. These include:(1) Overall effect model Income functions was constructed and estimated:A location-scale model was proposed in L2space, under this model, trajectory changes of income functions were expressed as parameters of the position translation and scale expansion, which could be used for explaining the whole characteristic of income function’s changes. As application and extension of this model, first, vertical and horizontal location parameter model were constructed for time series curves family from two points of view, and income inequality mode was also discussed under this situation. Second, a location-scale families of income distribution functions was build and estimated, which indicated that the income distribution changes were summarized as changes in the location parameter and scale parameter.(2) Modeling and analyzing of the income functions’characterized exploration. Under the assumptions income groups relyed on data variation performance, according to spectral analysis of covariance operator, this thesis proposed an estimated approach based on double dimensionality reduction method for eigenvalues and eigenfunctions. Under this model, the classification of the relative income groups was discuss based on the functional data of Lorenz curve family, and absolute income groups was discuss based on the functional data of income distribution function family.(3) Pattern recognition and analysis of income functions. Under the assumption of the income regein constitute the same population, a functional cluster analysis model was given out in this chapter. Under the base expression approach, an estimation approach based on dimensional reduction was proposed, and a functional form of income inequality function named variation coefficient function was constructed. Finally, an application of inequality decomposition was discussed for China’s income time-series curves family.(4) Under the framework income function model, research could also be further extended in two ways:the impact factors of income functions analysis and income functions’effects to economic factors. This thesis discusses the effects of the personal income tax system and its reform to income distribution functions, which include: quantitative analysis of the effects of the personal income tax on income distribution, comparative static analysis of the reforms of the personal income tax on income distribution, as well as the dynamic sensitivity analysis of follow-up effects of the personal income tax reforms.