Kakwani decomposition of redistributive effect: origins, criticism and upgrades Ivica Urban...
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Kakwani decomposition of redistributive effect: origins, criticism and upgrades Ivica Urban Institute of Public Finance, Zagreb to be presented at the Fourth Winter School on Inequality and Collective Welfare Theory January 2009
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Transcript of Kakwani decomposition of redistributive effect: origins, criticism and upgrades Ivica Urban...
Kakwani decomposition of redistributive effect: origins, criticism and upgrades
Ivica UrbanInstitute of Public Finance, Zagreb
to be presented at the Fourth Winter School on Inequality and Collective Welfare Theory
January 2009
Kakwani decomposition of redistributive effect
Kakwani (1984) decomposition of redistributive effect into vertical and reranking (horizontal inequity) terms
One of the most important tools in income redistribution literature in last 25 years
Its popularity rests on...
simplicity and ease of computation comprehensiveness: captures two
different notions of redistributive justice availability for straightforward policy
interpretation: for example, “redistributive power can be enhanced if horizontal inequity is reduced”
decomposability
This presentation...
a critical overview of development of Kakwani dec.
the context in which reranking and vertical index have emerged and how they fit into Kakwani dec.
short review of upgrades
Outline
1 Introduction 2 The decomposition 3 Horizontal inequity or reranking? 4 Origins of the vertical effect 5 Origins of the reranking effect 6 Criticism of Lerman and Yitzhaki and their new
framework 7 Extension to the net fiscal system 8 Frameworks capturing vertical and horizontal
inequity and reranking 9 Kakwani-Lambert “new approach” 10 Approach based on relative deprivation
References
Kakwani (1984) On the measurement of tax progressivity and redistributive effect of taxes with applications to horizontal and vertical equity
Kakwani (1986) Analyzing redistribution policies: A study using Australian data
Section title in both works: “Measures of horizontal and vertical equity”
Modern presentation
TXN
concentration coefficient of post-tax income xN
D
XGN
G Gini coefficients of pre- and post-tax income
xt the average tax rate
and
Kakwani progressivity index
APK RVRE
x
KT
xK
t
PtV
1
0 xNN
AP DGR
NX GGRE
decomposition:
concentration coefficient of tax
XxT
KT GDP
xTD
Comparison of presentations
APK RVRE
x
KT
xK
t
PtV
1
0 xNN
AP DGR
NX GGRE
VHR
0
X
NxN
G
GDH
X
NX
G
GGR
Xx
KT
x
Gt
PtV
)1(
OriginalModern
Derivation using L/C curves
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
_
_
_O
)( pLX
)( pC xT
KTP
x
KT
xK
t
PtV
1
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
_
_
_O
)( pLX
)( pC xN
KV
Derivation using L/C curves
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
_
_
_
_O
)( pLX
)( pLN
)( pC xN
APR
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
_
_
_O
)( pLX
)( pC xN
KV
Derivation using L/C curves
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
_
_
_O
)( pLX
)( pLN
RE
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
_
_
_
_O
)( pLX
)( pLN
)( pC xN
APK RVRE
Horizontal inequity or reranking?
The principle of vertical equity requires that people with larger incomes pay higher taxes than those with lower incomes
Horizontal equity in taxation requires that people with equal incomes pay equal taxes
Violation of this principle gives rise to horizontal inequity
Following several other authors, Kakwani identifies horizontal inequity with reranking
Horizontal inequity or reranking?
it is common to name the effect “reranking” instead of “horizontal inequity”
Kaplow (1989) Horizontal Equity: Measures in Search of a Principle
Aronson, Johnson, Lambert (1994) Redistributive effect and unequal income tax treatment
Horizontal inequity or reranking?
it seems that by Kakwani dec. we obtain two measures that both deal with unequal treatment of unequals
Example:
pre-fiscal income
post-fiscal income
A 100 500
B 500 100
Origins of the vertical effect
Kakwani (1977) Measurement of Progressivity: An International Comparison
criticizes RE as a progressivity index: it should be an index of redistributive effect
appropriate index of tax progressivity will indicate that two tax systems with equal elasticity (everywhere) are equally progressive
Origins of the vertical effect Kakwani then proposes an index that does
satisfy the requirement:
...and shows why RE doesn’t... (assume there is no reranking: )
(of two systems having the same elasticity, the one with higher ATR will be deemed as more progressive by RE)
XxT
KT GDP
REV K
x
KT
xK
t
PtREV
1
Origins of the reranking effect: Atkinson
Atkinson: some empirical studies used the measure , which understates the true post-fiscal inequality,
in other words, a measure overstates the redistributive effect of fiscal system,
One motive for measurement of reranking: to estimate redistribution correctly
NGxNX DG
xND
RE
Atkinson: “Changes in the ranking of observations as a result of taxation do not in themselves affect the degree of inequality in the post-tax distribution. They do, however, influence certain ways of representing the redistribution and of calculating summary measures of inequality.”
In other words: Reranking is a by-product, not a causing factor;
Reranking does not contribute, positively or negatively, to the redistributive effect
Origins of the reranking effect: Atkinson
In Plotnick’s model: “the structure of postredistribution income inequality is taken as a datum by the measure.”
“...given the change in inequality, the measure should tell us how seriously the redistributive activities violated the norms of horizontal equity.”
the measure of reranking “should not attempt to compare the actual extent of redistribution or change in inequality to some exogenous criterion. Doing so would be an exercise in measuring vertical inequity.”
Origins of the reranking effect: Plotnick
Advice: How to use it
Atkinson and Plotnick: although aware of the strong connection between the concepts of vertical and horizontal equity, they do not attempt to build comprehensive model capturing both of them
they suggest to future users and developers to be cautious about introduction of reranking measure into other, more comprehensive frameworks
Was the advice taken?
However, for Kakwani, the reranking measures the reduction of the redistributive effect caused by fiscal activities or “increase in inequality”
Reranking is not only a by-product, it is a causing factor
Usual interpretation: Progressive fiscal system reduces inequality and is positive: vertical inequity is “good”; In presence of reranking, is positive and increases inequality; this is evidence of the notion that horizontal inequity is “bad”.
KV
APR
Was the advice taken?
Furthermore, actual redistribution is only . Here, measures a potential redistributive effect; one that could be attained if reranking were somehow eliminated:
APK RVRE KV
APKpotential RREVRE
Popular recipe
researcher may offer straightforward advice to policymakers: by reduction of horizontal inequity, without additional resources, you can increase redistributive effect by x percent
Although this interpretation was not present in Kakwani (1984 and 1986), it might be said that these works encouraged it
New decomposition
Lerman and Yitzhaki (1995) Changing ranks and the inequality impacts of taxes and transfers
criticism of Kakwani decomposition They develop their own decomposition of
redistributive effect following the “philosophy” of Kakwani, but arrive at different conclusions about the role of reranking:
it positively contributes to inequality reduction, together with “gap narrowing” (which corresponds to vertical effect)
Comparison of presentations
APK RVRE
0 xNN
AP DGR
NX GGRE
Lerman and Yitzhaki Kakwani
LYLY RVRE
0 nXX
LY DGR
NnT
LYT GDP X
xT
KT GDP
NnXn
LYT
nLY GD
t
PtV
1
xNXx
KT
xK DG
t
PtV
1
Derivation using L/C curves
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
_
_
_
_O
)( pLX
)( pLN
)( pC xN
APK RVRE
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
_
_
_
_O
)( pLX
)( pLN
)( pC nX
LYLY RVRE
Interpretations...
the method enables decomposition of redistributive effect “into two exclusive, exhaustive terms”.
As Kakwani, they regard reranking as an independent source of redistributive effect: “...policies may reduce inequality by rearranging rankings as well.”
They even claim that Atkinson supported this view: he indicated “that the reranking effect might be important in explaining a proportion of the impact of taxes on inequality.”
(...but that is not what he meant)
Why new decomposition?
they criticize Kakwani vertical effect: for given redistributive effect it increases automatically when reranking is increased
“the after-tax ranking is the appropriate ranking for calculating progressivity” (because the after-tax ranking is proper ranking in analysis of marginal changes in the tax system)
Case of “total reranking”
0 nXX
LY DGR
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
_
_
_
_
_
)( pLX
)( pLN
)( pC nX
)( pC xN
O
5 2008 100
10 8020 3530 3035 2080 10
100 8200 5
X xN
0 REGG NX
xN
nXNX DDGG
02 XnXX
LY GDGR
02 XxNN
AP GDGR
02 LYXN
nX
LY RGGDV
02 APX
xNX
K RGDGV
LYLY RV
APK RV
Case of “total reranking”
more reranking results in an increase of Kakwani vertical effect, based on pre-tax rankings
this suggests that even more taxation of the “now poor” is desired
unfortunately, they do not involve in deeper technical elaboration of their criticism
no followers, despite interesting framework
Redistributive effect of the net fiscal system
Lambert (1985) On the redistributive effect of taxes and benefits
decomposes Kakwani vertical effect on tax and benefit contributions
xx
KB
xKT
xK
BT bt
VbVtV
1
)1()1(&
xTXX
xxKT
KT DGttPV )1/(
xBXX
xxKB
KB DGbbPV 1/
Redistributive effect of the net fiscal system
The decomposition helps to reveal an interesting interaction: even if overall tax system is regressive ( ),
taxes do reinforce the redistributive effect of the net fiscal system, so that .
0KTV
KB
KBT VV &
Vertical and horizontal inequity and reranking effects
Aronson, Johnson, Lambert (1994) Redistributive effect and unequal income tax treatment
decomposition of redistributive effect into vertical inequity, horizontal inequity and reranking effects
problem: the model works only with true equals – units with identical income
Vertical and horizontal inequity and reranking effects
AJLAJLAJL RHVRE
xNXX
xTx
xAJL DGGD
t
tV ~~
1
J
ijNjj
AJL GH1
,
APAJL RR
Vertical and horizontal inequity and reranking effects
Duclos, Jalbert and Araar (2003) Classical horizontal inequity and reranking: an integrated approach
DJADJADJA RHVRE
PNN
EN
PN
ENXNX IIIIIIIIRE
dpvpwpXUvWX ,,1
0
1/1yyU 11, vpvvpw
XX WU 1 xX
XI
1
“PIT decomposition”
Pfähler (1990) Redistributive Effect of Income Taxation: Decomposing Tax Base and Tax Rates Effects
decomposes vertical effect (or progressivity index) of tax into four contributions / effects: allowance, deductions, tax credits and tax-schedule
Kakwani-Lambert “New approach”
Kakwani and Lambert (1998) On Measuring Inequity in Taxation: A New Approach
three axioms dealing with both horizontal and vertical equity
A1: „minimal progression“: tax should increase monotonically with income
A2: „progressive principle“: higher income people must be faced with higher tax rates
A3: „no reranking“ criterion: marginal tax rate should not exceed 100 percent
Kakwani-Lambert “New approach”
321 SSSRPtRE AKn
3SPtRE Kn
from calculations based on Australian income tax data in 1984:
0.0240RE
0.1382 AKn RPt
xAAA DGR
(Kakwani decomposition)
RE could be improved by removal of inequities “without change to the marginal rate structure which governs incentives.”
Approach based on relative deprivation
Duclos (2000) Gini Indices and the Redistribution of Income
Gini coefficient can be represented as an average of relative deprivation in population
based on this principle the concepts of “fiscal harshness”, “fiscal looseness” and “ill-fortune” emerge
for each concept a measure is derived
Relative deprivation based approach
all the terms in Kakwani decomposition(s) are “reinvented” using these measures
Kakwani index of progressivity: a difference between the (mean-normalized average) fiscal harshness and average relative deprivation in the population.
Kakwani index of vertical inequity: a difference between the (mean-normalized average) relative deprivation and average fiscal looseness.
Atkinson-Plotnick index of reranking is (mean-normalised average) of ill-fortune in the population
