Title: Income Inequality Dynamics: Evidence from a Pool of Major Industrialized Countries
1Income Inequality Dynamics Evidence from a Pool
of Major Industrialized Countries
- F. Clementi1,3 and M. Gallegati2,3
1Department of Public Economics, University of
Rome La Sapienza, Via del Castro Laurenziano 9,
I00161 Rome, Italy fabio.clementi_at_uniroma1.it
2Department of Economics, Università Politecnica
delle Marche, Piazzale Martelli 8, I60121
Ancona, Italy gallegati_at_dea.unian.it
3S.I.E.C., Università Politecnica delle Marche,
Piazzale Martelli 8, I60121 Ancona,
Italy http//www.dea.unian.it/wehia/
21. Outline
3- THE DATA
- THE CROSS-NATIONAL EQUIVALENT FILE (1980-2002)
- THE SURVEY ON HOUSEHOLD INCOME AND WEALTH
(1987-2002) - EMPIRICAL FINDINGS
- THE SHAPE OF THE DISTRIBUTIONS
- TEMPORAL CHANGE OF THE DISTRIBUTIONS
- THE SHIFT OF THE DISTRIBUTIONS
- FLUCTUATIONS OF THE INDEXES SPECIFYING THE
DISTRIBUTIONS - TOTAL INCOME COMPOSITION PATTERN
- INEQUALITY DECOMPOSITION BY INCOME SOURCE
- GENERAL FRAMEWORK
- STATIC DECOMPOSITION BY INCOME SOURCE
- DYNAMIC DECOMPOSITION BY INCOME SOURCE
42. The Data
52.1 The Cross-National Equivalent File (1980-2002)
- CROSS-NATIONAL EQUIVALENT FILE DATA SOURCES. We
use income data from the US Panel Study of Income
Dynamics (PSID), the British Household Panel
Survey (BHPS), and the German Socio-Economic
Panel (GSOEP) as released in a cross-nationally
comparable format in the Cross-National
Equivalent File (CNEF). Our data refer to the
period 1980-2001 for the US, and to the period
1991-2001 for the UK in order to perform
analyses that represent the population of
reunited Germany, we refer to the subperiod
1990-2002 for the GSOEP. - DEFINITION OF INCOME. In this paper, the measure
of income for each individual is based on the
pre-government annual income of the household to
which they belong, adjusted for differences in
household size using the so-called OECD-scale of
equivalence, which deflates household income by
the square root of household size. The household
pre-government income is equal to the sum of
household labour income, household asset income,
household private transfers, and household
private retirement income. - SAMPLE SIZE. In the most recent release, the
average sample size varies from about 7,300
households containing approximately 20,200
respondent individuals for the PSID-CNEF to 6,500
household with approximately 16,000 respondent
individuals for the BHPS-CNEF for the GSOEP-CNEF
data from 1990 to 2002, we have about 7,800
households containing approximately 20,400
respondent individuals. - CURRENCY UNIT. All the variables are in current
year currency therefore, we use the Consumer
Price Index (CPI) to convert into constant
figures for all the CNEF countries. The base year
is 1995. For longitudinal consistency, all German
CNEF income variables are expressed in euros
(11,95583DM).
62.2 The Survey on Household Income and Wealth
(1987-2002)
- THE DATA SOURCE. The Historical Archive (HA) of
the Survey on Household Income and Wealth (SHIW),
made publicly available by the Bank of Italy for
the period 1977-2002, was carried out yearly
until 1987 (except for 1985) and every two years
thereafter (the survey for 1997 was shifted to
1998). In 1989 a panel section consisting of
units already interviewed in the previous waves
was introduced in order to allow for better
comparison over time. As the incomes from
financial assets started to be recorded only in
1987, our data refer to the subperiod 1987-2002. - DEFINITION OF INCOME. The basic definition of
income provided by the SHIW-HA is net of taxation
and social security contributions. It is the sum
of four main components compensation of
employees (including net wages and salaries and
fringe benefits) net income from self-employment
(including income from self-employment,
depreciation, and entrepreneurial income)
pensions and net transfers (including pensions
and arrears and other transfers) property income
(including income from buildings and income from
financial assets). The following components of
net disposable income are used in this study
labour income (equal to the sum of compensation
of employees and net income from
self-employment), pensions and net transfers, and
property income. - SAMPLE SIZE. The average number of income-earners
surveyed from the SHIW-HA is about 10,300. - CURRENCY UNIT. All the amounts are expressed in
lire, except for 2002, where the income variables
are reported in euros. For longitudinal
consistency, we report all the data in 1995
prices using the CPI, and convert them in euros
(11936,27LIT).
73. Empirical Findings
83.1 The Shape of the Distributions
- THE BODY OF THE DISTRIBUTIONS. We observe that
the lognormal complementary cumulative
distribution function
with 0ylt8, -8ltµlt8, and sgt0, gives a very
accurate fit until the 98th-99th percentile of
the distribution for all the countries.
- THE UPPER INCOME TAIL. The upper income tail of
the income distributions is rather well fitted by
a Pareto or power-law complementary cumulative
distribution function
where k,agt0, and kylt8.
9The binned cumulative probability distribution of
the equivalent and personal income along with the
lognormal and Pareto fits for some randomly
selected years (a) United States (1996) (b)
United Kingdom (1998) (c) Germany (2002) (d)
Italy (2000)
103.1 The Shape of the Distributions
- THE BODY OF THE DISTRIBUTIONS. We find that the
lognormal complementary cumulative distribution
function
with 0ylt8, -8ltµlt8, and sgt0, gives a very
accurate fit until the 98th-99th percentile of
the distribution for all the countries.
- THE UPPER INCOME TAIL. The upper income tail of
the income distributions is rather well fitted by
a Pareto or power-law complementary cumulative
distribution function
where k,agt0, and kylt8.
- UNIVERSAL STRUCTURE. The distribution pattern of
the personal income expressed as the lognormal
with power law tail seems to hold all over the
years covered by our data sets. However, we
observe a shift of the distributions and a change
of the indexes specifying them over time.
11Time development of the income distribution for
all the countries and years (a) United States
(1980-2001) (b) United Kingdom (1991-2001) (c)
Germany (1990-2002) (d) Italy (1987-2002)
123.2 Temporal Change of the Distributions The
Shift of the Distributions
- GDP AND INDIVIDUAL INCOME GROWTH RATE
DISTRIBUTION. We assume that the origin of the
observed shift of the income distributions over
the years covered by our data sets consists in
the growth of the countries. To confirm this
assumption, we study the fluctuations in the
(logarithmic) growth rate of GDP and individual
income. We find that the distributions of both
GDP and personal income growth rate display a
tent-shaped form hence, they are remarkably
well approximated by a Laplace or double
exponential distribution
where -8ltylt8, -8ltµlt8, and sgt0. Moreover, after
normalization all the points representing both
GDP and personal income growth rates collapse
relatively well close to the peak upon the solid
lines representing the Laplace probability
density function.
13The probability distribution of GDP and PI growth
rates for all the countries and years (a) United
States (1980-2001) (b) United Kingdom
(1991-2001) (c) Germany (1990-2002) (d) Italy
(1987-2002)
143.2 Temporal Change of the Distributions The
Shift of the Distributions
- GDP AND INDIVIDUAL INCOME GROWTH RATE
DISTRIBUTION. We assume that the origin of the
observed shift of the income distributions over
the years covered by our data sets consists in
the growth of the countries. To confirm this
assumption, we study the fluctuations in the
(logarithmic) growth rate of GDP and individual
income. We find that the distributions of both
GDP and personal income growth rate display a
tent-shaped form hence, they are remarkably
well approximated by a Laplace or double
exponential distribution
where -8ltylt8, -8ltµlt8, and sgt0. Moreover, after
normalization all the points representing both
GDP and personal income growth rates collapse
relatively well close to the peak upon the solid
lines representing the Laplace probability
density function.
- UNIVERSAL FEATURES IN THE GROWTH DYNAMICS OF BOTH
GDP AND INDIVIDUAL INCOME. These findings
(reminiscent of the concept of universality found
in statistical physics, where different systems
can be characterized by the same fundamental
laws, independent of microscopic details) lead
us to the conclusion that the temporal evolution
of both GDP and personal income is governed by
similar mechanisms, pointing in this way to the
existence of correlation between them as one
would expect.
153.3 Temporal Change of the Distributions
Fluctuations of the Indexes Specifying the
Distributions
- TEMPORAL EVOLUTION OF GIBRAT AND PARETO INDEXES.
We observe that the power-law slope and the
curvature of the lognormal fit are different both
in different countries, as well as in different
periods for the same country. This fact means
that Gibrat index and Pareto exponent change in
time.
16The time series of Gibrat and Pareto indexes over
the years covered by our data sets (a) United
States (1980-2001) (b) United Kingdom
(1991-2001) (c) Germany (1990-2002) (d) Italy
(1987-2002)
173.3 Temporal Change of the Distributions
Fluctuations of the Indexes Specifying the
Distributions
- TEMPORAL EVOLUTION OF GIBRAT AND PARETO INDEXES.
We observe that the power-law slope and the
curvature of the lognormal fit are different both
in different countries, as well as in different
periods for the same country. This fact means
that Gibrat index and Pareto exponent change in
time.
- CORRELATION BETWEEN PARETO INDEX AND ASSET PRICE.
From these behaviours we consider that there are
some factors causing no correlation between the
Gibrat and Pareto indexes, mainly affecting the
latter. Therefore, we study the origin of the
temporal change of Pareto index in more detail.
To this end, we consider its correlation with the
asset prices, such as the stock prices and the
housing prices. The stock market dynamics is
characterized by a slight downward trend during
the early 1990s, followed by a rise in the
mid-1990s which dropped at the end of the decade
after the bursting of the speculative bubble. A
similar behaviour is found in the temporal path
of real housing prices. By comparison with the
temporal change of the power-law exponent, we
conclude that both stock market and housing
market dynamics have a considerable effect on the
upper income tail.
18Fluctuations of the stock market indexes and the
housing prices for the countries and years of our
concern (a) New York Stock Exchange (NYSE) index
and CPI Housing (1980-2001) (b) London Stock
Exchange FTSE (Financial Times Stock Exchange)
index and CPI Housing (1991-2001) German Stock
Exchange Composite DAX (CDAX) index and CPI
Housing (1990-2002) Milano Borsa Italia (MIB)
index and CPI Housing (1987-2002)
193.4 Temporal Change of the Distributions The
Composition of Total Income in the Two Sections
of the Distributions
- THE COMPOSITION OF TOTAL INCOME... These results
lead us to check the possibility that non-labour
income sources are responsible for the Pareto
functional form of the observed empirical income
distributions at the high-income range. To this
end, we look at the composition of total income
within the two regimes of the income
distributions by calculating the share of each
income component in the lognormal and power-law
sections of the distributions for all the
countries and years
where µk is the mean of the kth source of income
and µ is the average income of the whole
population in the lognormal and Pareto regimes.
- ...IN THE LOGNORMAL... As expected, individuals
in the low-middle income ranges (98-99 of the
population) rely mostly on labour income.
20The composition of total income in the low-middle
income ranges characterized by the lognormal
distribution (a) United States (1980-2001) (b)
United Kingdom (1991-2001) (c) Germany
(1990-2002) (d) Italy (1987-2002)
213.4 Temporal Change of the Distributions The
Composition of Total Income in the Two Sections
of the Distributions
- THE COMPOSITION OF TOTAL INCOME... These results
lead us to check the possibility that non-labour
income sources are responsible for the Pareto
functional form of the observed empirical income
distributions at the high-income range. To this
end, we look at the composition of total income
within the two regimes of the income
distributions by calculating the share of each
income component in the lognormal and power-law
sections of the distributions for all the
countries and years
where µk is the mean of the kth source of income
and µ is the average income of the whole
population in the lognormal and Pareto regimes.
- ...IN THE LOGNORMAL... As expected, individuals
in the low-middle income ranges (98-99 of the
population) rely mostly on labour income.
- ...AND POWER-LAW REGIMES OF THE INCOME
DISTRIBUTIONS. Individuals in the top percentiles
(1-2 of the population) derive a significant
share of their income in the form of capital
income. This difference seems to corroborate our
conjecture that returns on capital play an
important role in determining the power-law
behaviour in the high-income region.
22The composition of total income in the upper tail
of the income distributions (a) United States
(1980-2001) (b) United Kingdom (1991-2001) (c)
Germany (1990-2002) (d) Italy (1987-2002)
234. Inequality Decomposition by Income Source
244.1 The Contribution of Individual Income Sources
to Total Inequality General Framework
- METHODOLOGY. To further confirm our conjecture
that the capital gains contribution to total
income may be responsible for the observed
power-law behaviour in the tail of the
distributions, we perform a decomposition
analysis of the level of total inequality for
assessing the contribution of a set of individual
income sources. To this end, we express total
inequality, I, as the sum of the contributions of
each source of income
where Sk depends on incomes from source k, and
represents its absolute contribution to total
inequality. If Skgt0, the kth source of income
provides a disequalizing effect, and an
equalizing effect if Sklt0.
- INEQUALITY MEASURE. The inequality measure we
decompose in this way is GE(2), which is a member
of the Generalized Entropy class of inequality
measures
where CV is the Coefficient of Variation, having
the formula
where n is the number of individuals in the
sample, yi is the income of individual i, and µ
the mean income.
254.2 The Contribution of Individual Income Sources
to Total Inequality Static Decomposition by
Income Source
- METHODOLOGY. When the GE(2) inequality measure is
used, the absolute contribution of each source to
total inequality can be written as
where skSk/I is the proportional contribution of
income component k to total inequality, ?k is the
correlation between source k and total income,
?kµk/µ is the share of source k in total income,
and GE(2) and GE(2)k are one-half the squared
coefficient of variation of total income and
source k respectively. A large value of Sk
suggests that income source k is an important
source of total inequality.
- STATIC DECOMPOSITION BY INCOME SOURCE OF OVERALL
INEQUALITY AT THE LOW-MIDDLE... The application
of this method for source decomposition of total
income going to the population belonging to the
low-middle income section of the distributions
points to the contributory influence of labour
earnings in explaining the level of aggregate
inequality.
26Total inequality (GE(2)) and income source
contribution to total inequality (SkskGE(2)) for
the lognormal region of the income distribution
(a) United States (1980-2001) (b) United Kingdom
(1991-2001) (c) Germany (1990-2002) (d) Italy
(1987-2002)
274.2 The Contribution of Individual Income Sources
to Total Inequality Static Decomposition by
Income Source
- METHODOLOGY. When the GE(2) inequality measure is
used, the absolute contribution of each source to
total inequality can be written as
where skSk/I is the proportional contribution of
income component k to total inequality, ?k is the
correlation between source k and total income,
?kµk/µ is the share of source k in total income,
and GE(2) and GE(2)k are one-half the squared
coefficient of variation of total income and
source k respectively. A large value of Sk
suggests that income source k is an important
source of total inequality.
- STATIC DECOMPOSITION BY INCOME SOURCE OF OVERALL
INEQUALITY AT THE LOW-MIDDLE... The application
of this method for source decomposition of total
income going to the population belonging to the
low-middle income section of the distributions
points to the contributory influence of labour
earnings in explaining the level of aggregate
inequality.
- ...AND HIGH END OF THE DISTRIBUTIONS. At the high
end of the income distributions, capital income
plays a significant role in explaining the level
of overall inequality.
28Total inequality (GE(2)) and income source
contribution to total inequality (SkskGE(2)) for
the power-law region of the income distribution
(a) United States (1980-2001) (b) United Kingdom
(1991-2001) (c) Germany (1990-2002) (d) Italy
(1987-2002)
294.3 The Contribution of Individual Income Sources
to Total Inequality Dynamic Decomposition by
Income Source
- DYNAMIC DECOMPOSITION OF GE(2) AGGREGATE VALUE...
We also attempt to account for the impact of
individual income sources on changes in
inequality. Using GE(2) as the inequality index,
our decomposition of changes in overall
inequality builds on the following formula
In this decomposition, the changing impact of a
source depends on changes in the correlation with
total income, changes in the share of total
income, and changes in inequality of the source
therefore, a large value of ?Sk suggests that
changes in factor k have a large influence in
changes in total inequality.
- ...IN THE LOGNORMAL... We observe that labour
income is an important contributor to changes in
total inequality for the great majority of
populations.
30One-year dynamic decomposition of GE(2)
inequality measure by income source for the
lognormal region of the income distribution (a)
United States (b) United Kingdom (c) Germany
(d) Italy
314.3 The Contribution of Individual Income Sources
to Total Inequality Dynamic Decomposition by
Income Source
- DYNAMIC DECOMPOSITION OF GE(2) AGGREGATE VALUE...
We also attempt to account for the impact of
individual income sources on changes in
inequality. Using GE(2) as the inequality index,
our decomposition of changes in overall
inequality builds on the following formula
In this decomposition, the changing impact of a
source depends on changes in the correlation with
total income, changes in the share of total
income, and changes in inequality of the source
therefore, a large value of ?Sk suggests that
changes in factor k have a large influence in
changes in total inequality.
- ...IN THE LOGNORMAL... We observe that labour
income is an important contributor to changes in
total inequality for the great majority of the
populations.
- ...AND POWER-LAW REGIONS OF THE DISTRIBUTIONS. On
the other hand, in the high-end tail of the
distributions capital income makes by far the
most significant contribution to overall changes
in inequality, especially from the mid-1990s, as
a consequence of the increasing personal
ownership of equities.
32One-year dynamic decomposition of GE(2)
inequality measure by income source for the
power-law region of the income distribution (a)
United States (b) United Kingdom (c) Germany
(d) Italy
335. Summary
34- THE SHAPE OF THE INCOME DISTRIBUTIONS. Our
analysis of the data for the US, the UK, Germany,
and Italy shows that there are two regimes in the
income distribution. For the low-middle classes
up to approximately 98-99 of the total
population the incomes are well described by a
two-parameter lognormal distribution, while the
incomes of the top 1-2 is described by a
power-law (Pareto) distribution. - THE SHIFT OF THE DISTRIBUTIONS. This structure
have been observed in the analysis for different
years. However, the indexes specifying the
distributions change in time. Thus we studied the
temporal change of the distributions. Firstly, we
analyze the GDP and individual income growth rate
distributions. We find that after normalization
the resulting empirical probability density
functions appear similar for observations coming
from different populations. This effect, which is
quantitatively the same for countries and
individuals, raises the intriguing possibility
that a common mechanism might characterize the
growth dynamics of GDP and individual income,
pointing to the existence of correlation between
these quantities. - TEMPORAL EVOLUTION OF THE INDEXES SPECIFYING THE
DISTRIBUTIONS. Secondly, from the analysis of the
change of Gibrat and Pareto indexes, we confirmed
that these quantities should not necessarily
correlate each other. This means that different
mechanisms are working in the distribution of the
low-middle income range and that of the high
income range. One possible origin of no
correlation is the change of the asset price,
such as the stock price and the housing price,
which mainly affects the high income
distribution. - DECOMPOSITION OF OVERALL INEQUALITY BY INCOME
SOURCE. By disaggregating the level and time
trend of total inequality into contributory
influences from various income sources, we find
that the low-middle income section of the
distributions comprises almost entirely of labour
income, while earnings from financial or other
assets play an important role in the high-income
section. We conclude that this difference in the
composition and inequality of the income is
likely to be responsible for the lognormal nature
of the former and the power-law behaviour in the
latter region of the distributions.
355. Forthcoming Events
36- COMPLEXITY, HETEROGENEITY AND INTERACTIONS IN
ECONOMICS AND FINANCE (CHIEF). Ancona, Italy, May
2-21, 2005 http//www.dea.unian.it/wehia/AnconaTI
_3.htm - 10th ANNUAL WORKSHOP ON ECONOMICS WITH
HETEROGENEOUS AND INTERACTING AGENTS (WEHIA
2005). Colchester, UK, June 13-15, 2005
http//www.essex.ac.uk/wehia05/ - ECONOPOHYSICS COLLOQUIM. Canberra, Australia,
November 14-18, 2005 http//www.rsphysse.anu.edu.
au/econophysics/index.php - WORKSHOP ON INDUSTRY AND LABOR DYNAMICS. THE
AGENT-BASED COMPUTATIONAL ECONOMICS APPROACH
(WILD_at_ACE). Ancona, Italy, December 2-3, 2005
http//www.dea.unian.it/wehia/
37Dhannabad!