RERANKING AND THE ANALYSIS OF INCOME REDISTRIBUTION*
| Published date | 01 February 1988 |
| Author | Stephen Jenkins |
| Date | 01 February 1988 |
| DOI | http://doi.org/10.1111/j.1467-9485.1988.tb01030.x |
Sconirh
Journal
of
Polrrical
Economy,
Vol.
35,
No.
I,
February
19RR
0
1988
Scortish
Economic
Society
RERANKING AND THE ANALYSIS
OF
INCOME REDISTRIBUTION*
STEPHEN
JENKINS
School
of
Humanities and Social Sciences, University
of
Bath
I
INTRODUCTION
Ron’s income before tax is
$500
per week and Mike’s is $450, while their
after-tax incomes are $400 and $425 respectively. The redistributive effect of
the tax system in this case is clearly equalizing as the “distance” between
Ron’s and Mike’s income is reduced, but their relative rankings in the income
distribution have been reversed. Does this reranking matter?
The answer provided by the literature is affirmative,
with
the predominant
reason given being that
reranking violates the principle
of
horizontal
equity-that “equals” should be treated equally and “unequals” treated
accordingly (see Plotnick 1982, for a recent survey). However reranking is
also important for other reasons, and in this paper
I
show this with reference
to
the analysis
of
income redistribution,
and in particular, the calculation of
summary measures based upon the Gini coefficient and Lorenz curve. This
second argument for studying reranking has been advanced in a few
theoretical papers previously but there is, as far as
I
am aware, little hard
empirical evidence about whether
not
taking reranking into account leads to
significant inaccuracies
in
estimates, and also the magnitude of such biases
relative to those induced by data grouping (the problem that has received the
most attention to date).’ Such information
is
important particularly because
many empirical studies of redistribution are based on secondary analysis of
previously published tables
in
which the data on incomes, taxes and transfers
are grouped, with the groupings all based on the same ranking; by average
income before taxes and transfers.
(A
leading example
of
such tables is the
“Summary of the effects of taxes and benefits” published annually by the
CSO
in
Economic Trends.)
Presented at the European Economic Association meeting, Vienna, August 29-31,
1986. The paper derives from research
on
“Distributional change, horizontal equity, and
the British tax-transfer system” financed by the ESRC (Grant number B00232123) and
carried out in conjunction with Stephen Hope and Michael O’Higgins. Thanks are due
to
Frank Cowell
for
his LORENZ program which was used to do some
of
the calculations and
draw Figure
1,
to
Peter Lambert for helpful discussions, and
to
Robert Plotnick for the
Smeeding reference.
The
only
related figures
I
am aware
of
are given by Smeeding (1979, pp 941-942) as part
of
his critique of Browning (1976). Smeeding argues e.g. that
“If
families could be
reranked, Browning’s estimate
of
the income share
of
the bottom quintile would be less
than 9.5 percent
of
net income, rather than 10.7 percent
of
net income (1979, p. 942).
65
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