seminario

[Pietro Muliere <pietro.muliere@uni-bocconi.it>]

Istituto Metodi Quantitativi - Università L. Bocconi
Viale Isonzo, 25 - 20135 Milano
Tel. 02-58365629  - Fax 02-58365630

SEMINARIO


The normative significance of using inverse
stochastic dominance in inequality, welfare and poverty comparisons

Claudio Zoli
School of Economics, Univ. of Nottingham

giovedì, 17 maggio 2001 - ore 16.00
aula IMQ - stanza 137
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Abstract:
We investigate the relationship between dominance conditions associated to 
non-additive linear rank-dependent indices and the criterion of inverse 
stochastic dominance. The results obtained are dual to those relating 
dominance for classes of additive indices to the standard stochastic 
dominance criteria. Results are provided both for different degrees of 
inverse stochastic dominance evaluated over homogeneous populations, and 
for comparisons involving heterogeneous populations. The restrictions on 
the rank-dependent indices associated to the various inverse stochastic 
dominance conditions considered are characterised in terms of effectiveness 
of income transfers between and within groups of homogenous individuals. 
Results are applied both to inequality, welfare and poverty analysis.
  More precisely:
A)We investigate the relationship between the third degree inverse 
stochastic dominance criterion introduced in Muliere and Scarsini (JET 
1989) and inequality dominance when Lorenz curves intersect. We propose a 
new definition of transfer sensitivity aimed at strengthening the 
Pigou-Dalton Principle of Transfers. Our definition is dual to that 
suggested by Shorrocks and Foster (RES 1987). It involves a regressive 
transfer and a progressive transfer both from the same donor, leaving the 
Gini index unchanged. Finite sequences of these transfers and/or 
progressive transfers characterize the third degree inverse stochastic 
dominance criterion. This criterion allows us to make unanimous inequality 
judgements even when Lorenz curves intersect. The Gini coefficient becomes 
relevant in these cases in order to conclusively rank the distributions
.B) We provide characterizations of sequential stochastic 
dominance  conditions which are dual to those introduced in Atkinson and 
Bourguignon (1987). Instead of evaluating social welfare according to the 
utilitarian approach, we apply the rank-dependent dual approach to the 
measurement of welfare and inequality suggested in Weymark (MaSS 1981) and 
Yaari (Econometrica 1987, JET 1988). Different interpretations of the results,
in terms of either welfare comparisons of populations decomposed into 
needs-based subgroups, or intertemporal income comparisons are 
suggested.The dual SWF is shown to be consistent with a class of 
satisfaction and    deprivation indices. The sequential dominance criteria 
based on this class of indices is introduced, they require comparisons 
involving generalized satisfaction curves and deprivation curves of the 
reference groups in the population. The connections with dominance criteria 
associated to rank-dependent poverty indices and the sequential dominance 
results
introduced is investigated. A poverty dominance condition for 
rank-dependent comparisons over heterogenous populations is suggested, it 
involves combinations of the poverty-gap curves of the different groups 
of  individuals.