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Title: Income Inequality Dynamics: Evidence from a Pool of Major Industrialized Countries


1
Income 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/
2
1. 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

4
2. The Data
5
2.1 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).

6
2.2 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).

7
3. Empirical Findings
8
3.1 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.
9
The 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)
10
3.1 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.

11
Time 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)
12
3.2 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.
13
The 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)
14
3.2 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.

15
3.3 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.

16
The 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)
17
3.3 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.

18
Fluctuations 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)
19
3.4 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.

20
The 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)
21
3.4 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.

22
The 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)
23
4. Inequality Decomposition by Income Source
24
4.1 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.
25
4.2 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.

26
Total 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)
27
4.2 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.

28
Total 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)
29
4.3 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.

30
One-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
31
4.3 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.

32
One-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
33
5. 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.

35
5. 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/

37
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