Econometrica
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Опубликовано на портале: 02-12-2003
Francois Bourguignon
Econometrica.
1979.
Vol. 47.
No. 4.
P. 901-920.
A decomposable inequality measure is defined as a measure such that the total inequality
of a population can be broken down into a weighted average of the inequality existing
within subgroups of the population and the inequality existing between them. Thus,
decomposable measures differ only by the weights given to the inequality within the
subgroups of the population. It is proven that the only zero-homogeneous "income-weighted"
decomposable measure is Theil's coefficient (T) and that the only zero-homogeneous
"population-weighted" decomposable measure is the logarithm of the arithmetic mean
over the geometric mean (L). More generally, it is proved that T and L are the only
decomposable inequality measures such that the weight of the "within-components"
in the total inequality of a partitioned population sum to a constant. More general
decomposable measures are also analyzed.


Опубликовано на портале: 13-12-2003
A. F. Shorrocks
Econometrica.
1984.
Vol. 52.
No. 6.
P. 1369-1386.
This paper examines the implications of imposing a weak aggregation condition on
inequality indices, so that the overall inequality value can be computed from information
concerning the size, mean, and inequality value of each population subgroup. It is
shown that such decomposable inequality measures must be monotonic transformations
of additively decomposable indices. The general functional form of decomposable indices
is derived without assuming that the measures are differentiable. The analysis is
suitable for extension to the many other kinds of indices for which a similar relationship
between the overall index value and subaggregates is desirable.


On Inequality Comparisons [статья]
Опубликовано на портале: 03-12-2003
Gary S. Fields, John C.H. Fei
Econometrica.
1978.
Vol. 46.
No. 2.
P. 303-306.
In this paper, we have developed an approach to inequality comparisons which differs
from the conventional one. Beginning by postulating three axioms, we showed that
the axiomatic system so constructed is sufficient to justify the Lorenz criterion
for inequality comparisons. However, like the Lorenz criterion, the axiomatic system
is incomplete. Past researchers have achieved completeness by the use of cardinal
inequality measures. We showed that many but by no means all of the commonly used
indices satisfy our three axioms. The ones which do satisfy the axioms agree on the
ranking of distributions whose Lorenz curves do not intersect. However, when Lorenz
curves do intersect, the various measures partition the income distribution space
differently. Since the three axioms are insufficient to determine the specific partition
to use, the use of any of the conventional measures implicitly accepts the additional
welfare judgments associated with that measure.
The key issue for inequality comparisons is the reasonableness of the ordering criterion,
which in the case of cardinal measures is the index itself. An axiomatic approach
is probably the ideal method for confronting this issue, because the reasonable properties
(i.e., the axioms) are postulated explicitly. At minimum, this approach facilitates
communication by enabling (and indeed requiring) one to set forth clearly his own
viewpoints and value judgments for scrutiny by others. But in addition, to the extent
that one person's judgments (such as those in our three axioms) are acceptable to
others, controversies over inequality comparisons may be resolved. We have seen that
our three axioms are incomplete insofar as they cannot determine the ordinal ranking
uniquely. A feasible and desirable direction for future research is to investigate
what further axioms could be introduced to complete the axiomatic system or at least
to reduce further the zones of ambiguity.
It is conceivable that beyond some point the search for new axioms may turn out to
be unrewarding. In that case, inequality comparisons will always be subject to arbitary
specifications of welfare weights. The selection of suitable weights by whatever
reasonable criterion one cares to exercise is a less desirable but possibly more
practical alternative than a strictly axiomatic approach.
Our research has hopefully made clear that inequality comparisons cannot be made
without adopting value judgments, explicit or otherwise, about the desirability of
incomes accruing to persons at different positions in the income distribution. Even
the Lorenz criterion, which permits us to rank the relative inequality of different
distributions in only a fraction of the cases, embodies such judgments. The traditional
inequality indices such as those considered in Section 3, to the extent they complete
the ordering, embody some value judgments


Опубликовано на портале: 26-11-2003
Amartya Sen
Econometrica.
1976.
Vol. 44.
No. 2.
P. 219-231.
The primary aim of this paper is to propose a new measure of poverty, which should
avoid some of the shortcomings of the measures currently in use. An axiomatic approach
is used to derive the measure. The conception of welfare in the axiom set is ordinal.
The information requirement for the new measure is quite limited, permitting practical
use.
