Abstract
AbstractThis paper provides a normative model for distributional comparisons that can be easily adapted for the evaluation of public policies. This model considers individuals whose well‐being is characterized by a monetary and a nonmonetary dimension. It also accounts for inequality at the top and bottom of the distribution of both dimensions. It derives third‐order inverse stochastic dominance conditions for classes of social welfare functions satisfying: (i) threshold dependent positional transfer (TDPT) sensitivity with respect to the monetary dimension; (ii) TDPT combined with downside inequality aversion with respect to the nonmonetary dimension; (iii) TDPT combined with upside inequality aversion with respect to the nonmonetary dimension. This paper's results emerge along with the existing one supporting downside inequality aversion both with respect to the monetary and nonmonetary dimension, and upside inequality aversion with respect to the monetary dimension.
Highlights
In recent years a growing effort has been devoted to expand the classical notion of income inequality towards a multidimensional space of achievements
We develop third order inverse stochastic dominance conditions for classes of social welfare functions satisfying: i) Threshold Dependent Positional Transfer Sensitivity with respect to the monetary dimension (TDPT); ii) TDPT combined with downside inequality aversion with respect to the non-monetary dimension; iii) TDPT combined with upside inequality aversion with respect to the non-monetary dimension
Due to the transferability typical of income, it is used to compensate for deficiencies concerning the other dimension. They divide the populations to be compared into subgroups, each one of them being characterized by a different level of needs, and impose certain sign restrictions on the utility functions reflecting some desirable properties, requiring essentially that the needier is a household the higher is her marginal evaluation of income at any income level, and that such marginal evaluation decreases as income increases
Summary
In recent years a growing effort has been devoted to expand the classical notion of income inequality towards a multidimensional space of achievements. In their paper, referred to a unidimensional context based on income only, they develop a third order inverse downward dominance condition, that places more emphasis on differences in the upper part of the distribution and holds for classes of social welfare functions satisfying the principle of upside positional transfer sensitivity. We draw together the arguments introduced above, namely the concern for the multidimensional evaluation of social welfare, the interest in inequalities affecting the top of the distribution and the application of the framework in other contexts To this end, we develop third-degree inverse stochastic dominance conditions suitable for a rank-dependent and bidimensional framework and able to encompass different attitudes towards inequality aversion. The remainder of the paper is organized as follows: Section 2 outlines the framework, Section 3 presents the theoretical results, Section 4 concludes
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