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In recent years, more and more attention has been focused on the effects of economic growth and inequality changes on income polarization, as well as on the changes in the middle income class fraction. A significant part of the literature that deals with these issues is focused on polarization indices. However, the polarization indices proposed by researchers do not allow for an assessment of impact of the income distribution changes on the disappearance of the middle income class. Moreover, the general income polarization indices do not allow for assessment of polarization within the distinguished income classes. This study proposes a class of median relative polarization partial indices, which allows for a comprehensive assessment of the median relative polarization over time, within the distinguished income classes, as well as the impact of income distribution changes (its polarization or convergence) on the change of the middle income class fraction (its disappearance or increase). Using Social Diagnosis panel data (a study carried out by the Social Monitoring Council), the proposed new tool has been used to verify the hypothesis of whether changes in the household income distribution in Poland during the years 2005–2015 have led to income polarization within the three distinguished income groups—lower, middle and upper income classes. Empirical analysis shows that despite the lack of overall polarization of incomes in the household population, there was a convergence of incomes in the upper and lower income classes and polarization of incomes within the middle income class. It implies that the income distribution has not been petrified, and as on average individuals in the lower and upper income classes tend to reduce the distance to the median income, whereas the members of the middle income class tend to be pushed out of the middle class. Moreover, the flows of households into the middle income class were higher than the outflows from this class, resulting in economic convergence, i.e. changes in income distribution leading to an increase of the middle income class fraction.

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A three-dimensional multivariate model is developed for the analysis of temporal and spatial demographic changes. The model is used to analyze the interaction of eight demographic variables in 22 European countries for the period 1950 to 1980.  相似文献   
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