The name is absent



Stata Technical Bulletin

ɪede(ɪ) — / j,
i=l


fi ⅛g(yt)


The Atkinson indices (Atkinson 1970) are defined by

A(e) = 1 - [yede(e)∕nι]

These indices are decomposable but not additively decomposable (Blackorby, Donaldson, and Auersperg 1981):

A(e) = Aw(a) + AB(a) - [A1,y(α)]. [As(α)]

where

and


Aw (ɑ) = 1


fe=l


Ab(o) = 1 -


У de


Social welfare indices (Jenkins 1997) are defined by

We = -ɪ- [yβde(e)]1 e, 0 0 0, e ≠ 1

1 — e

W1 = log[yβde(1)]

Each of these indices is an increasing function of a generalized mean of order (1 — e). All the welfare indices are additively
decomposable:

W(e)


= ∑VkWk(e)
k=l


The Gini coefficient is given by

G = 1 + (1∕2V) -


(ɪ) ∑(jv-i + 1b

∖mJ∖zJ


where persons are ranked in ascending order of yB

The Gini coefficient (and the percentile ratios) are not properly decomposable by subgroup into within- and between-group
inequality components.

Sen’s (1976) welfare index is given by

5 = m(1-G)

Syntax

ineqdeco varname [weight] [if exp] [in range] [, bygroup(groupvar) w summ]
fweights and aweights are allowed.



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