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Date: Dec. 13, 2018 (Thu.), 2:30 pm – 4:20 pm
Venue: Raphael, GIS NTU Convention Center
集思台大會議中心拉斐爾廳 (台北市羅斯福路四段 85 號 B1)
Topic: Intersecting Lorenz curves, Transfer Sensitivity, and Inequality Indices
Speaker: Professor W. Henry Chiu, Economics, School of Social Sciences, University of Manchester
Hosts: Center for Research in Econometric Theory and Applications (CRETA), NTU
Registration: Please register before Dec. 10, 2018. Space is limited.
The fundamental axiom of inequality measurement, known as the principle of transfers, is that a transfer from a poor person to someone richer raises inequality. This principle explains the central role of Lorenz curves since, for distributions with the same mean, the Lorenz curve for one lies above the other if and only if the distribution with the lower Lorenz curve can be obtained from the other by a series of regressive transfers. It is well-known nevertheless that intersecting Lorenz curves are not uncommon. In fact, in many studies of real-world income distributions the Lorenz criterion can provide a ranking for only a minority of all possible pairwise comparisons. In view of the limited ability of the Lorenz criterion in ranking income distributions, many authors propose to strengthen the criterion by adopting the additional principle of ``transfer sensitivity'' or equivalently ``aversion to downside inequality''. These authors argue that, for a fixed income gap, the same amount of income transfer from a poorer to a richer person should be considered more disequalizing the lower it occurs in the distribution.
In the first part of the lecture, we clarify the conceptual distinction between inequality aversion (or the principle of transfers) and downside inequality aversion. Specifically, we show, first of all, that when the Lorenz curves of two distributions intersect, one distribution can often be obtained from the other by a combination of an increase in downside inequality and a decrease in inequality (i.e., a series of progressive transfers). Secondly, the inequality aversion and the downside inequality aversion of a given inequality index can work against, as well as reinforce, each other in determining the ranking of two distributions. If we restrict our attention to additive inequality indices, we can show that a measure characterizing the strength of an index's downside inequality aversion against its inequality aversion determines the ranking by the index of two income distributions whose Lorenz curves cross only once. In the case where the Lorenz curves of two distributions cross more than once, since the difference between the two distributions may or may not be decomposed into a change in downside inequality and a change in inequality, we identify the precise condition under which the measure can determine the ranking of two distributions by an index.
Conceptually clarifying as the results pertaining to additive indices are, they do not apply to the best-known inequality index---the Gini coefficient---since it is not additive but is instead a member of the family of “linear inequality indices”. In the second part of the lecture, we discuss this family of inequality indices and the notion of “positional transfer sensitivity”, which says that for a given rank difference, a regressive transfer should be considered less desirable if the individuals involved in the transfer are ranked lower in the income distribution. We will show in particular that analysis analogous to what we have with additive indices and transfer sensitivity obtains in this context: positional transfer sensitivity is equivalent to aversion to “inverse downside inequality” and a measure characterizing the strength of an index's aversion to inverse downside inequality against its inequality aversion can determine the ranking by the index of two income distributions whose Lorenz curves intersect.
14:00 - 14:30 Registration
14:30 - 15:10 First Session (40 mins)
15:10 - 15:30 Tea Break (20 mins)
15:30 - 16:00 Second Session (30 mins)
16:00 - 16:20 Q&A