TAX PROGRESSION:
INTERNATIONAL &
INTERTEMPORAL COMPARISONS
USING LIS DATA
Kirill Pogorelskiy, SU-HSE, Moscow, Russia
Christian Seidl, University of Kiel, Germany
Stefan Traub, University of Bremen, Germany
July 24, 2010
X International Meeting of the Society for Social Choice and Welfare
Moscow
Methodology
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Conventional approach: use measures of tax progression to make
comparisons
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Local, global, uniform with identical income distributions
Lacks applicability to real world
Situations to be compared have different income distributions

Local measures, e.g., tax and residual elasticities, disregard income
distribution (only use the properties of the tax schedule)
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
Suits (1977), p. 725: “There is nothing inherently regressive about a sales tax or even a
poll tax. They are regressive because income is unequally distributed, and the more
unequally income is distributed, the more regressive they become.”
Global measures, e.g., based on Gini coefficients, ignore structural differences
in the objects being compared

They can compensate intervals with less progression or even regression with intervals
with high progression.
Uniform measures, e.g., first-moment distribution functions of taxes or net
incomes, use dominance relations of the respective curves and require
identical income distributions (equal supports) to hold in both situations
 Second, uniform measures establish just sufficient conditions of greater tax
progression if considered not for all possible income distributions, but for
particular ones being compared
•Both taxes in this figure would be classified as proportional taxes.
•Familiar problem with any sort of average

Uniform measures of tax progression for
identical income distributions
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Let us start with the first moment functions
(1)
(2)
(3)
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These functions indicate the share of Total Income /Tax Revenue/ Net
Income received (or paid) by the income recipients with gross incomes
less or equal to Y
Varying Y from the lowest income level Y* to the highest income Y*,
comparing tax progression  comparing the concentration curves
(1)-(3) are not suitable if the income distributions in the situations to be
compared have different supports, because in such case 100% of TI1 /
TR1 / NI1 is not equal to 100% of TI2 /TR2 / NI2
Uniform measures of tax progression for different
income distributions…
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1)
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2)
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Several ways to cope with this situation
Transplant and compare: remaining in the domain of incomes,
deform the income distribution of 1st situation to the distribution
of the 2nd; then subject both to the taxation of the 2nd (and vice
versa, Dardanoni and Lambert, 2002).
Independence of the baseline distribution holds iff the candidate
reference income distributions are isoelastic transformations of
one another, which hardly ever occurs in the real world.
Approach from Seidl (1994): transform the income domain into
the domain of population quantiles q or income quantiles p →
the range of both dominance curves is the same unit interval.
Hence, we compare the same population or income quantiles in
different countries/ time periods with respect to taxes/net
incomes.
Formally, apply the transformations of variables Y=F-1(q) and
to(1)-(3) Y  FY1 ( p)
Uniform measures of tax progression for
different income distributions
FY(q) [FT(q), FY-T(q)]: Lorenz curve(s) of gross income /tax schedule /net incomes;
share of total GI / TR / NI received/paid by the fraction q of the poorest taxpayers
,
: Suits (1977) curve(s) of taxes and net incomes; share of total TR/NI
paid/received by the poorest taxpayers whose compound GI is the fraction p of total GI
Note that we have
for any progressive tax schedule if 0<q=p<1, because the
fraction q of the poorest taxpayers holds only a fraction of total gross income, FY(q), which is
smaller than
Moreover, for co-monotonic GI,T,NI and progressive tax schedules we have:
Definitions of greater tax progression
1) A tax schedule T1 is uniformly more progressive than T2 whenever the
concentration curve of FT1 relative to FT2 does not cross the diagonal of the unit
square except at the endpoints (0,0) and (1,1).
• This means that for the same fractions q or p as applied to the two income
distributions, T1 collects a smaller fraction of aggregate taxes from smaller
incomes than does T2.
• A sufficient condition for the concentration curve of FT1 relative to FT2 to lie
wholly below the diagonal of the unit square is that it is strictly convex.
2) Uniformly greater tax progression can also be defined in terms of second-order
differences of first moment distribution functions.
• E.g., T1 is uniformly more progressive than T2 whenever FY1-FT1 > FY2-FT2 holds
for the whole support.
• This means that the difference between the first moment distribution curves,
which is due to the influence of taxation, is greater for the situation (Y1,T1) than
for the situation (Y2,T2). The corresponding condition in terms of net incomes
can be written as FY1-T1-FY1 > FY2-T2 – FY2 .
Uniform tax progression for different
income distributions: the challenge

This approach reveals not only dominance relations of tax progression,
but also the structure of tax progression
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Unique curve intersections (bifurcate progression) show that less progression for
one country or time period for the lower income strata is accompanied by more
progression for the upper income strata and vice versa.
But do we end up with sufficiently many clear-cut solutions?
Atkinson (1970), p. 258, asserted that for comparisons among 12
countries “in only 24% of cases the Lorenz curves of incomes do not
intersect”.
Yet Bishop et al. (1991), p. 462, found statistically significant
intersections of Lorenz curves only in 3% of all cases, whereas 97% of
the Lorenz curves were ranked;
In contrast to that, simple numerical comparisons would have ranked as
much as about 75% of the comparisons of Lorenz curves
After all, this works out to become an empirical exercise.
First, one has to transform definitions into a discrete framework.
Uniform Tax Progression for Different
Income Distributions: Discrete Version
(Empirical) Questions
1. Do we have a substantial fraction of dominance relations for
comparisons of tax progression, or dominance is the exception
rather than the rule? What kind of dominance curves do we
usually observe?
2. What happens when dominance relations do not hold? Do we
mainly encounter bifurcate or some other progression patterns?
3. What is the relative performance of the 6 methods we use to
compare tax progression? Are there interrelationships?
4. What classifications can result from international/intertemporal
comparisons of tax progression?
5. How can we measure the degree of greater tax progression?
6. Are there relations between changes in tax progression over
time and changes in the ruling parties and their ideologies?
7. How sensitive are our results to equivalence scale parameter?
Data…

Luxembourg Income Study (LIS) www.lisproject.org
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Information required
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around year 2000, as maximizing the # of available country data
Intertemporal comparisons
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Australia, Canada, Denmark, Germany, Finland, France, Netherlands,
Norway, Poland, Sweden, Switzerland, United Kingdom, United States
International comparisons

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Gross Incomes, Net Incomes, Direct Taxes, Payroll Taxes
NI1=GI-DT;
or
NI2=GI-(DT+PT)
Countries we studied (total 13)


Detailed, real, harmonized, standardized, representative microdata; not
second-hand data simulations
Both household-based and individual-based
at least 3recent survey periods (waves III - VI, if data allowed)
This is the first paper that performs international and intertemporal
comparisons of uniform tax progression with actual data.
Data


Direct data access is not permitted by LIS
To access the LIS data, we wrote a program in SPSS that
computed and returned the values of FY(q), FT(q), etc., for 20
equally-spaced quantiles.

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We used 5% steps (i.e., 20 quantiles) because:


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Thereby we avoid data noise for too narrow quantiles
This is a rather fine grid as compared to other work. E.g., Sala-i-Martin
(2006) worked with quintiles. Bishop et al. (1991) worked with deciles
for constructing Lorenz curves, arguing that “increasing the number of
quantiles does not necessarily improve the quality of the overall test” .
We used household and equivalized data both for direct taxes only
and for direct taxes + payroll taxes.


This allowed us to carry out the remaining related computations off-line,
which is much faster and easier
We used a Visual Basic macro to facilitate processing of the LIS output.
Hence we analyzed four datasets: HT, HT+, ET, ET+
Furthermore, we carried out computations for all six definitions.
Results: International Comparisons – Dominance I
Summary statistics: household data; taxes
Summary statistics: household data; taxes + payroll
Results: International Comparisons – Dominance I
Summary statistics: equivalized data; taxes
Summary statistics: equivalized data; taxes + payroll
Results: International Comparisons – Consistency I
Consistency for Strict Dominance
46.15
47.44
43.59
42.31
67.96
61.54
Consistency for Bifurcate Dominance
71.79
67.94
Results: International Comparisons – Consistency II
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The table below contains rough indications of similarities and dissimilarities
among the progression comparison concepts
It is based on pairwise comparisons of the entries in Tables 2 to 7 (which
report the results corresponding to Definitions 1-6; see Handouts) counting the
dominance and bifurcate relationships that are identical between pairs of tables
The first entries in the cells of this table contain the percentages (as averages
of all four datasets) of congruence of the respective D’s and R’s in the cells of
the pairs of the compared tables, the second entries contain the percentages
(as averages of all four datasets) of cases in which a D or R is not matched by
the respective symbol in the other table.
Multiple crossings were ignored.
Definition 3 is at variance with the other concepts.
Results: International Comparisons – Categorical Data I
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Each cell in Tables 2 -7 contains 4 entries: those in the 1st row refer to
household data, those in the 2nd row to equivalized data using the Luxembourg
equivalence scale m- with = 0.5.
The left-hand side entries in a cell refer to direct taxes only, while the right-hand
side entries to direct taxes + payroll taxes.
Only few left-hand side and right-hand side columns of Tables 2 -7 differ within
each cell. Basically the same observation applies to the rows within each cell.
This means that comparative progression is not changed much if we extend the
direct taxes by payroll taxes.


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This is remarkable since payroll taxes (which consist mainly of employees’ share of social
security contributions) are by and large proportional to income for the lower and middle
income strata, but they expire for incomes beyond some benchmark. Moreover, for the
lower income strata they are usually considerably higher than the direct taxes => they have
a regressive effect on overall tax progression.
The tables also show that high tax countries, e.g., Germany, medium tax
countries, e.g., France, and low tax countries, e.g., the US are classified as
more progressive than most other countries.
This is because the measures in this paper are developed to compare uniform
tax progression, not the level of taxation.

Sweden and Denmark have taxes that reach a high percentage of income rather fast and
remain there, which is more akin to proportional taxation; the same pattern applies to the
UK for a medium tax burden, and to Switzerland for a low tax burden. In contrast to that, the
income interval for which taxation is steadily increasing as a percentage of income is
comparatively extensive in Germany, France, and the US. This explains their dominance
with respect to comparisons of tax progression. For similar results using another approach
see Peichl & Schäfer (2008).
Results: International Comparisons – Categorical Data II
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The next few slides show Hasse diagrams of
progression dominance for our 4 data sets for all 6
definitions of greater tax progression.
These are precisely the entries with a D in Tables
2-7.
Note that these diagrams concern only categorical
relationships.
Information about the intensity of progression can
be gained from the differences of the respective
curves (will be shown in the graphs below)
Finally, we will present graphs showing the effect
of different parameter values of equivalence
scales.
HT, Definitions 1 and 2
ET, Definitions 1 and 2
Uniform Tax Progression for Different Income
Distributions: International Comparisons – UK/US
Def. 1: US m.p. than UK
Def. 2: US m.p. than UK
Def. 3: first UK, then US
Def. 4: US m.p. than UK
Def. 5: US m.p. than UK
Def. 6: US m.p. than UK
Def. 1: US m.p. than UK
Def. 2: US m.p. than UK
Def. 3: first UK, then US
Def. 4: US m.p. than UK
Def. 5: US m.p. than UK
Def. 6: US m.p. than UK
Uniform Tax Progression for Different Income
Distributions: International Comparisons – UK/US
Def. 1: US m.p. than UK
Def. 2: US m.p. than UK
Def. 3: US m.p. than UK
Def. 4: US m.p. than UK
Def. 5: US m.p. than UK
Def. 6: US m.p. than UK
Except for Definition 3, US is uniformly more
progressive than UK. For Definition 3 we
haveUK
for household data first UK, then US.
Def. 1: US m.p. than
Def. 2: US m.p. than UK
Def. 3: US m.p. than UK
Def. 4: US m.p. than UK
Def. 5: US m.p. than UK
Def. 6: US m.p. than UK
Uniform Tax Progression for Different Income
Distributions: Intertemporal Comparisons - US
The characterization of periods to be compared by
the respective governments should not impart the
impression of strict causality. Progression effects
are also due to shifts in household structure,
income distribution, shifts in individuals’ behavior,
etc. The association to the governments should
just provide a label for the periods to be compared.
Uniform Tax Progression for Different Income
Distributions: Intertemporal Comparisons - US
Def. 1: US94 m.p. than US91
Def. 2: US94 m.p. than US91
Def. 3: US91 m.p. than US94
Def. 4: US94 m.p. than US91
Def. 5: first US91, then US94
Def. 6: US94 slightly m.p. than US91
Def. 1: US94 m.p. than US91
Def. 2: US94 m.p. than US91
Def. 3: US91 m.p. than US94
Def. 4: US94 m.p. than US91
Def. 5: first US91, then US94
Def. 6: US94 slightly m.p. than US91
Uniform Tax Progression for Different Income
Distributions: Intertemporal Comparisons - US
Def. 1: US94 m.p. than US91
Def. 2: US94 m.p. than US91
Def. 3: US91 m.p. than US94
Def. 4: US94 m.p. than US91
Def. 5: first US91, then US94
Def. 6: US94 slightly m.p. than US91
The same pattern for
all four graphs!
Def. 1: US94 m.p. than US91
Def. 2: US94 m.p. than US91
Def. 3: US91 m.p. than US94
Def. 4: US94 m.p. than US91
Def. 5: first US91, then US94
Def. 6: US94 slightly m.p. than US91
Uniform Tax Progression for Different Income
Distributions: Intertemporal Comparisons - US
Def. 1: first US94, then US00
Def. 2: US94>US00>US94
Def. 3: first US00, then US94
Def. 4: first US00, then US94
Def. 5: US94>US00>US94
Def. 6: US00 m.p. than US94
Def. 1: first US94, then US00
Def. 2: US94>US00>US94
Def. 3: first US00, then US94
Def. 4: first US00, then US94
Def. 5: US94>US00>US94
Def. 6: US00 m.p. than US94
Uniform Tax Progression for Different Income
Distributions: Intertemporal Comparisons - US
Def. 1: first US94, then US00
Def. 2: US94>US00>US94
Def. 3: first US00, then US94
Def. 4: first US00, then US94
Def. 5: first US00, then US94
Def. 6: US00 m.p. than US94
For Definition 5, H:
US94>US00>US94
for E: first US00, then US94.
Def. 1: first US94, then US00Everything else the same.
Def. 2: US94>US00>US94
Def. 3: first US00, then US94
Def. 4: first US00, then US94
Def. 5: first US00, then US94
Def. 6: US00 m.p. than US94
Uniform Tax Progression for Different Income
Distributions: Intertemporal Comparisons - US
Def. 1: US04 m. p. than US00
Def. 2: US04 m.p. than US00 (exc.
T/B)
Def. 3: US00 m.p. than US04
Def. 4: US00 m.p. than US04
Def. 5: first US00, then US04
Def. 6: US00 m.p. than US04
Def. 1: US04 m. p. than US00
Def. 2: US04 m.p. than US00
Def. 3: US00 m.p. than US04
Def. 4: US00 m.p. than US04
Def. 5: US00 largely m.p. than US04
Def. 6: US00 m.p. than US04
Uniform Tax Progression for Different Income
Distributions: Intertemporal Comparisons - US
Def. 1: first US04 , then US00
Def. 2: first US04, then US00
Def. 3: first US00 , then US04
Def. 4: US00 m.p. than US04
Def. 5: first US00, then US04
Def. 6: US00 m.p. than US04
More progression for HT [HT+] becomes bifurcate
progression for ET [ET+] for Definitions 1, 2, and 3
[1 and 3 ] [effect of transforming data by
equivalence scales]. Bifurcate progression for HT
and ET for Definition 5 becomes progression for
HT+ and ET+; bifurcate progression for ET for
Definition 2 becomes progression for ET+ [effect of
Def. 1: first US04 payroll
, then US00
taxes]. .
Def. 2: US00 m.p. than US04
Def. 3: first US00 , then US04
Def. 4: US00 m.p. than US04
Def. 5: US00 m.p. than US04
Def. 6: US00 m.p. than US04
Uniform Tax Progression for Different Income
Distributions: Equivalence Scales
Equivalence Scales Matter!
It is interesting to see that equivalence scales matter very much for some definitions.
It is in particular Definitions 1 and 3 which are extremely sensitive to equivalence
scales. They can account for up to 8% of progression comparisons.
Definition 1: As the parameter α of the LIS equivalence scale, m-α, decreases, tax
progression according to Definition 1 increases.
Definition 2: As α increases, tax progression according to Definition 2 increases, but
much less than for Definition 1. This is much less distinctive than for Definition 1, and
is hardly seen for US data.
Definition 3: As α increases, tax progression according to Definition 3 increases.
Definition 5: As α increases, tax progression according to Definition 5 increases for
the lower income strata and decreases for the upper income strata (bifurcate
progression).
There are no major effects of equivalence scales for Definitions 4 and 6.
Uniform Tax Progression for Different Income
Distributions: Equivalence Scales- US
Conclusions…
In the conclusion of this paper we come back to the issues to be investigated:
1. Do we have a substantial fraction of dominance relations for comparisons of tax
progression, or is dominance the exception rather than the rule? We have
about two thirds of strict progression dominance relations and one fifth of
bifurcate progression dominance. Only in about one tenth do we
encounter multiple crossings. Statistically significant crossings are even
less. What kind of dominance curves do we usually observe? For household
data, about three quarters of the cases of progression dominance
conforms with strict convexity or concavity; for equivalized data, it is
about two thirds.
2. What happens when dominance relations do not hold? Do we mainly encounter
bifurcate or some other progression patterns? Bifurcate progression holds in
about three thirds of these cases; only in about one third (10% of all
cases) do we encounter multiple crossings; some of them are so weak that
they may well be ignored.
3. What is the relative performance of the six proposed measures of the
comparison of tax progression? Are there interrelationships? We have
remarkable congruence among Definitions 1,2, 4. and 5. It is, in particular,
Definition 3 which marches to a different drummer.
4. What classifications can result from international/intertemporal comparisons of
tax progression? Countries with high taxation levels such as the
Scandinavian countries tend to have lower tax progression. Low-tax
countries like the US and medium-tax countries like Germany have high
progression. UK has lower progression than both. Payroll taxes tend to
lower tax progression; however, this effect is not very pronounced.
Conclusions
How can we measure the degree of greater tax progression? Can
be seen from the graphs (but note that they are differently
calibrated). Definitions 5 and 6 tend to show least intensity of
progression.
6. Are there relations between changes in tax progression over time
and changes in the ruling parties and their ideologies? In the US,
there has been slight increase in progression from Bush sen.
to Clinton; not much change during the Clinton government,
and less progression under Bush jun.
In the UK there was less progression from Major to Blair.
In Germany, progression increased from 1989 to 2000.
5. How sensitive are our results to equivalence scale parameter?
Equivalence scales matter much for Definitions 1 and 3 in
opposite ways, and less for Definitions 2 and 5.
5.
References
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Atkinson, AB 1970, ‘On the measurement of inequality’, Journal of Economic
Theory, vol. 2, pp. 244-63.
Bishop, JA, Formby, JP and Smith, WJ 1991, ‘International comparisons of
income inequality: tests for Lorenz dominance across nine countries’,
Economica, vol. 58, pp. 461-77.
Dardanoni, V and Lambert PJ 2002, ‘Progressivity comparisons’, Journal of
Public Economics, vol. 86, pp. 99-122.
Luxembourg Income Study (LIS) Database 2010,
http://www.lisproject.org/techdoc.htm (multiple countries).
Musgrave, RA and Thin, T 1948, ‘Income tax progression, 1929-48’, Journal of
Political Economy, vol. 56, pp. 498-514.
Peichl, A and Schäfer, T 2008, Wie progressiv ist Deutschland? Das Steuerund Transfersystem im europäischen Vergleich, EUROMOD Working Paper No.
EM 01/08
Sala-i-Martin, X 2006, ‘The world distribution of income: falling poverty and ...
convergence, period’, The Quarterly Journal of Economics, vol. 121, pp. 351-97.
Seidl, C 1994, ‘Measurement of tax progression with nonconstant income
distributions’, in W Eichhorn (ed.), Models and measurement of welfare and
inequality, Berlin: Springer-Verlag, pp. 337-60.
Suits, DB 1977, ‘Measurement of tax progressivity’, The American Economic
Review, vol. 67, pp. 747-52.
Q&A
The paper will be soon available as
a LIS Discussion Paper (see www.lisproject.org)

Backup
Uniform Tax Progression for Different
Income Distributions: Discrete Version
We start by defining the first-moment distribution functions in discrete terms:
Strictly speaking, both components are functions of k. Then we consider the range
of the right-hand function to become the domain of the left-hand function, which
gives us the discrete first-moment distribution functions. For all curves in terms of q
we use the ranking according to gross income, as we have to apply that necessarily
also for the curves in terms of p. Moreover, re-ranking does not have dramatic
effects [see Peichl and Schäfer (2008)].
HT+, Definitions 1 and 2
HT+, Definitions 3 and 4
HT+, Definitions 5 and 6
ET+, Definitions 1 and 2
ET+, Definitions 3 and 4
ET+, Definitions 5 and 6
Uniform Tax Progression for Different Income
Distributions: International Comparisons – DE/UK
Def. 1: DE m.p. than UK
Def. 2: DE m.p. than UK
Def. 3: first UK, then DE
Def. 4: DE m.p. than UK
Def. 5: DE m.p. than UK
Def. 6: DE m.p. than UK
Def. 1: first DE, then UK
Def. 2: first DE, then UK
Def. 3: first UK, then DE
Def. 4: DE m.p. than UK
Def. 5: first UK, then DE
Def. 6 DE m.p. than UK
Uniform Tax Progression for Different Income
Distributions: International Comparisons – DE/UK
Def. 1: DE m.p. than UK
Def. 2: DE m.p. than UK
Def. 3: DE m.p. than UK
Def. 4: DE m.p. than UK
Def. 5: DE m.p. than UK
Def. 6: DE m.p. than UK
For equivalized data, Germany is more progressive
than UK, except ET+ for Definition 2, where we have
first DE, then UK. For HT, Germany ist more
progressive except Definition 3, for which bifurcate
progression, first UK, then DE hold. For HT+, DE>UK
holds only for Definitions 4 and 6; first UK, then DE
holds
Def. 1: first DE, then
UKfor Definitions 3 and 5, and first DE, then UK
holds
Def. 2: DE m.p. than
UKfor definition 2 [effect of payroll taxes for
household
data].
Def. 3: DE m.p. than
UK
Def. 4: DE m.p. than UK
Def. 5: DE m.p. than UK
Def. 6: DE m.p. than UK
Uniform Tax Progression for Different Income
Distributions: International Comparisons – DE/US
Def. 1: first DE, then US
Def. 2: DE m.p. than US
Def. 3: first US, then DE
Def. 4: first US, then DE
Def. 5: US>DE>US
Def. 6: US m.p. than DE
Def. 1: first indefinite, then
US
Def. 2: first US, then DE
Def. 3: first US, then DE
Def. 4: first DE, then US
Def. 5: US m.p. than DE
Def. 6: first indefinite, then
Uniform Tax Progression for Different Income
Distributions: International Comparisons – DE/US
Def. 1: first indefinite, then US
Def. 2: DE m.p. than US
Def. 3: DE m.p. than US
Def. 4: indefinite
Def. 5: first DE, then US
Def. 6: first DE, then US
There are shifts in bifurcate progression:
for household data US more progressive
at the bottom, DE at the top. For
equivalized data, Germany becomes more
at the bottom, US at the top
Def. 1: first indefinite,progressive
then US
(some exceptions). [Effect of greater
Def. 2: DE m.p. than US
families in US?]
Def. 3: DE m.p. than US
Def. 4: indefinite
Def. 5: first DE, then US
Def. 6: first DE, then US
Uniform Tax Progression for Different Income
Distributions: International Comparisons – DE/SE
Def. 1: DE m.p. than SE
Def. 2: DE m.p. than SE
Def. 3: first SE , then DE
Def. 4: DE m.p. than SE
Def. 5: DE m.p. than SE
Def. 6: DE m.p. than SE
Def. 1: first DE, then SE
Def. 2: DE m.p. than SE
Def. 3: first SE, then DE
Def. 4: DE m.p. than SE
Def. 5: DE m.p. than SE
Def. 6: DE m.p. than SE
Uniform Tax Progression for Different Income
Distributions: International Comparisons – DE/SE
Def. 1: DE m.p. than SE
Def. 2: DE m.p. than SE
Def. 3: first SE, then DE
Def. 4: DE m.p. than SE
Def. 5: DE m.p. than SE
Def. 6: DE m.p. than SE
DE more progressive than SE, except for
Definition 3, which asserts bifurcate progression:
first SE, then DE. For Definition 1, first DE, then
SE for HT+, becomes DE>SE for ET+.
Def. 1: DE m.p. than SE
Def. 2: DE m.p. than SE
Def. 3: first SE, then DE
Def. 4: DE m.p. than SE
Def. 5: DE m.p. than SE
Def. 6: DE m.p. than SE
Uniform Tax Progression for Different Income
Distributions: Intertemporal Comparisons - UK
Uniform Tax Progression for Different Income
Distributions: Intertemporal Comparisons - UK
Def. 1: UK95 m.p. than UK91
Def. 2: first UK95, then UK91
Def. 3: first UK95, then UK 91
Def. 4: UK91 slightly m.p. than
UK95
Def. 5: UK95 m.p. than UK91 (exc.
top)
Def. 6: UK 91 slightly m.p. than UK
95
Def. 1: UK95 m.p. than UK91
Def. 2: first UK95, then UK91
Def. 3: first UK95, then UK 91
Def. 4: UK95 m.p. than UK91
(m.exc.)
Def. 5: UK95 m.p. than UK91 (exc.
top)
Uniform Tax Progression for Different Income
Distributions: Intertemporal Comparisons - UK
Def. 1: UK95 m.p. than UK91
Def. 2: UK95 m.p. than UK91
Def. 3: UK91 m.p. than UK95
Def. 4: UK91 slightly m.p. than UK95
Def. 5: first UK91, then UK95
Progression reversal from UK91>UK95
to slightly m.p. than UK95
Def. 6: UK91
UK95>UK91 when moving from HT to HT+
for Definitions 4 and 6, and reversal at top
when moving from ET to ET+ for Definition
4 [effect of payroll taxes]. Progression
reversal for Definitions 2, 3, and 5 when
moving from HT to ET, and for Definitions
Def. 1: UK95 m.p. 2,
than
UK91
3, 4,
and 5 when moving from HT+ to
Def. 2: UK95 m.p. ET+
than [effect
UK91 of transforming data by
Def. 3: UK91 m.p. equivalence
than UK95 scales].
Def. 4: UK91>UK95>UK91
Def. 5: first UK91, then UK95
Def. 6: UK95 m.p. than UK91 (exc.
bot.)
Uniform Tax Progression for Different Income
Distributions: Intertemporal Comparisons - DE
Uniform Tax Progression for Different Income
Distributions: Intertemporal Comparisons - DE
Def. 1: first DE94, then DE89
Def. 2: first DE94, then DE89
Def. 3: DE94 m.p. than DE 89 (exc.)
Def. 4: DE89 slightly m.p. than DE94
Def. 5: DE94 m.p. than DE89 (exc.)
Def. 6: DE89 slightly m.p. than DE94
Def. 1: first DE94, then DE89
Def. 2: first DE94, then DE89
Def. 3: DE94 m.p. than DE 89
(exc.)
Def. 4: first DE94 , then DE89
Def. 5: DE94 m.p. than DE89 (exc.)
Def. 6: DE89>DE94>DE89
Uniform Tax Progression for Different Income
Distributions: Intertemporal Comparisons - DE
Def. 1: first DE94, then DE89
Def. 2: first DE94, then DE89
Def. 3: first DE89, then DE94
Def. 4: DE89 m.p. than DE94
Def. 5: DE89>DE94>DE89
Def. 6: DE89 slightly m.p. than DE94
Progression shift from DE89>DE94 to bifurcate progression,
first DE94, then DE89, for Definition 4 [to DE89>DE94>DE89
for Definition 6] when moving from HT to HT+ and from ET to
ET+ [effect of payroll taxes]. Progression shift for Definition 3
from DE94>DE89 to bifurcate progression, first DE89, then
DE94 [for Definition 5 to DE89>DE94>DE89] when moving
Def. 1: first DE94, then DE89
from HT to ET and from HT+ to ET+ [effect of transforming data
Def. 2: first DE94, then DE89
by equivalence scales].
Def. 3: first DE89, then DE94
Def. 4: first DE94, then DE89
Def. 5: DE89>DE94>DE89
Def. 6: DE89>DE94>DE89
Uniform Tax Progression for Different Income
Distributions: Intertemporal Comparisons - DE
Def. 1: DE00 m.p. than DE94
Def. 2: DE00 m.p. than DE94
Def. 3: first DEoo, then DE94
Def. 4: DE00 m.p. than DE94
Def. 5: DE00 m.p. than DE94
Def. 6: DE00 m.p. than DE94
Def. 1: DE00 m.p. than DE94
Def. 2: DE00 m.p. than DE94
(exc.)
Def. 3: first DEoo, then DE94
Def. 4: DE00 m.p. than DE94
Def. 5: DE00 m.p. than DE94
Def. 6: DE00 m.p. than DE94
Uniform Tax Progression for Different Income
Distributions: Intertemporal Comparisons - DE
Def. 1: DE00 m.p. than DE94
Def. 2: DE00 m.p. than DE94
Def. 3: first indefinite, then DE94
Def. 4: DE00 m.p. than DE94
Def. 5: DE00 m.p. than DE94
Def. 6: DE00 m.p. than DE94
Slight upward shift for Definition 3 when
moving to equivalized data. Everything else
the same.
Def. 1: DE00 m.p. than DE94
Def. 2: DE00 m.p. than DE94
Def. 3: first indefinite, then
DE94
Def. 4: DE00 m.p. than DE94
Def. 5: DE00 m.p. than DE94
Def. 6: DE00 m.p. than DE94
Uniform Tax Progression for Different Income
Distributions: Intertemporal Comparisons - DE
Def. 1: DE00 m.p. than DE89
Def. 2: DE00 m.p. than DE89 (exc.
top)
Def. 3: DE00 slightly m.p. than DE89
Def. 4: DE00 m.p. than DE89
Def. 5: DE00 m.p. than DE89
Def. 6: DE00 m.p. than DE89
Def. 1: DE00 m.p. than DE89
Def. 2: DE00 m.p. than DE89 (exc.
top)
Def. 3: DE00 m.p. than DE89 (exc.
top)
Def. 4: DE00 m.p. than DE89 (exc.
top)
Def. 5: DE00 m.p. than DE89
Uniform Tax Progression for Different Income
Distributions: Intertemporal Comparisons - DE
Def. 1: DE00 m.p. than DE89
Def. 2: DE00 m.p. than DE89 (exc.
top)
Def. 3: DE89>DE00> DE89
Def. 4: DE00 m.p. than DE89 (exc.
top)
Progression shift for Definition Def.
3 from
5: DE00 m.p. than DE89 (exc.
DE00>DE89 to DE89>DE00> DE89
bot.)
when moving from HT to ET and
from
Def.
6: DE00 slightly m.p. than DE89
HT+ to ET+ [effect of transforming data
by equivalence scales]
Def. 1: DE00 m.p. than DE89
Def. 2: DE00 m.p. than DE89 (exc.
top)
Def. 3: DE89>DE00> DE89
Def. 4: DE00 m.p. than DE89 (exc.
top)
Def. 5: DE00 m.p. than DE89 (exc.
Uniform Tax Progression for Different Income
Distributions: Equivalence Scales- DE
Uniform Tax Progression for Different Income
Distributions: Equivalence Scales- UK