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The authors emphasize that the value judgment between attainment and shortfall gets intertwined in practice with the value judgment of whether it is absolute or relative inequality that matters.
First, when looking at relative inequality levels, it is helpful to use Kjellsson et al.'s ingenious diagrams to identify cases where the choice between attainment and shortfalls does not matter.
The pills example in Kjellsson et al. helped me stumble on what is, as far as I know, a new result, namely that although it does matter when it comes to analyzing (relative) inequality, the choice between attainment and shortfalls does not apparently matter when it comes to analyzing changes in inequality.
Accepting all these as possible viewpoints implies that for a bounded variable the researcher not only has to choose between a relative and an absolute value judgment but must also choose between analyzing relative inequality in either attainments or shortfalls (i.e., choose between an attainment-relative, absolute, or shortfall-relative measure).
But, in contrast to absolute indices, relative indices imply different inequality equivalence criteria depending on whether health is measured with respect to attainments or shortfalls because an equiproportionate change in attainments will not generally constitute an equiproportionate change in shortfalls and vice versa.
However, although health attainments and shortfalls are but 'two sides of the same coin' (Clarke et al., 2002), indices of inequality measured with respect to health attainments and shortfalls need not be equivalent to each other.
On the distinction between attainments and shortfalls, there are also implications of the above that are worth highlighting.
The distinction between attainments and shortfalls has resurfaced recently in the health economics literature in the context of the debate over measuring inequalities in bounded variables.
Typically, though, one's results vis-à-vis levels of relative inequality will be sensitive to the choice between attainments and shortfalls.
For some time in the health economics literature, the importance of the choice between attainments and shortfalls was not widely appreciated.
The health-economic literature has acknowledged that a relative measure may rank populations differently depending on whether attainments or shortfalls are used and have shown that an index cannot, at the same time, measure relative inequality and guarantee consistent rankings of attainments and shortfalls.
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Justyna Jupowicz-Kozak
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