income inequality dynamics: evidence from a pool of major industrialized countries

International Workshop on "Econophysics of Wealth Distributions", Saha Institute of Nuclear Physics, Kolkata, India, 15-19 March, 2005 1

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

CountriesCountries

F. ClementiF. Clementi1,3 and M. Gallegati2,3

1Department of Public Economics, University of Rome “La Sapienza”, Via delCastro Laurenziano 9, I–00161 Rome, Italy

[email protected]

2Department of Economics, Università Politecnica delle Marche, Piazzale Martelli 8, I–60121 Ancona, Italy

[email protected]

3S.I.E.C., Università Politecnica delle Marche, Piazzale Martelli 8, I–60121 Ancona, Italyhttp://www.dea.unian.it/wehia/


1. Outline1. Outline


THE DATA:THE DATA:THE CROSS-NATIONAL EQUIVALENT FILE (1980-2002)THE CROSS-NATIONAL EQUIVALENT FILE (1980-2002)

THE SURVEY ON HOUSEHOLD INCOME AND WEALTH (1987-2002)THE SURVEY ON HOUSEHOLD INCOME AND WEALTH (1987-2002)

EMPIRICAL FINDINGS:EMPIRICAL FINDINGS:THE SHAPE OF THE DISTRIBUTIONSTHE SHAPE OF THE DISTRIBUTIONS

TEMPORAL CHANGE OF THE DISTRIBUTIONSTEMPORAL CHANGE OF THE DISTRIBUTIONSTHE SHIFT OF THE DISTRIBUTIONSTHE SHIFT OF THE DISTRIBUTIONS

FLUCTUATIONS OF THE INDEXES SPECIFYING THE DISTRIBUTIONSFLUCTUATIONS OF THE INDEXES SPECIFYING THE DISTRIBUTIONS

TOTAL INCOME COMPOSITION PATTERNTOTAL INCOME COMPOSITION PATTERN

INEQUALITY DECOMPOSITION BY INCOME SOURCEINEQUALITY DECOMPOSITION BY INCOME SOURCEGENERAL FRAMEWORKGENERAL FRAMEWORK

STATIC DECOMPOSITION BY INCOME SOURCESTATIC DECOMPOSITION BY INCOME SOURCE

DYNAMIC DECOMPOSITION BY INCOME SOURCEDYNAMIC DECOMPOSITION BY INCOME SOURCE


2. The Data2. The Data


2.1 The Cross-National Equivalent File (1980-2.1 The Cross-National Equivalent File (1980-2002)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 (1€=1,95583DM).


2.2 The Survey on Household Income and 2.2 The Survey on Household Income and Wealth (1987-2002)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 (1€=1936,27LIT).


3. Empirical Findings3. Empirical Findings


3.1 The Shape of the Distributions3.1 The Shape of the Distributions THE BODY OF THE DISTRIBUTIONS. We observe that the lognormal complementary cumulative

distribution function:

log1 1

yF y P Y y

with 0≤y<∞, -∞<μ<∞, and σ>0, gives a very accurate fit until the 98th-99th percentile of the distribution for all the countries.

1k

F y P Y yy

where k,α>0, and k≤y<∞.

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:


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)


3.1 The Shape of the Distributions3.1 The Shape of the Distributions THE BODY OF THE DISTRIBUTIONS. We find that the lognormal complementary cumulative

distribution function:

log1 1

yF y P Y y

with 0≤y<∞, -∞<μ<∞, and σ>0, gives a very accurate fit until the 98th-99th percentile of the distribution for all the countries.

1k

F y P Y yy

where k,α>0, and k≤y<∞.

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:

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.


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)


3.2 Temporal Change of the Distributions: 3.2 Temporal Change of the Distributions: The Shift of the DistributionsThe 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:

1, exp

2

yf y P Y y

where -∞<y<∞, -∞<μ<∞, and σ>0. 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.


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)


3.2 Temporal Change of the Distributions: 3.2 Temporal Change of the Distributions: The Shift of the DistributionsThe 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:

1, exp

2

yf y P Y y

where -∞<y<∞, -∞<μ<∞, and σ>0. 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.


3.3 Temporal Change of the Distributions: 3.3 Temporal Change of the Distributions: Fluctuations of the Indexes Specifying the Fluctuations of the Indexes Specifying the

DistributionsDistributions

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.


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)

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

Year

Gibra

t inde

x (β)

1.7

2.2

2.7

3.2

3.7

4.2

Pareto index (α)

Gibrat index (β)

Pareto index (α)

0.8

0.9

1

1.1

1.2

1.3

1.4

Year

Gibra

t inde

x (β)

1.5

2

2.5

3

3.5

Pareto index (α)

Gibrat index (β)

Pareto index (α)

0.8

0.9

1

1.1

1.2

1.3

1.4

Year

Gibr

at in

dex (

β)

2.1

2.3

2.5

2.7

2.9

3.1

3.3

3.5

3.7

Pareto index (α)

Gibrat index (β)

Pareto index (α)

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

Year

Gibra

t inde

x (β)

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3

3.2

3.4

Pareto index (α)

Gibrat index (β)

Pareto index (α)

(a) (b)

(c) (d)


3.3 Temporal Change of the Distributions: 3.3 Temporal Change of the Distributions: Fluctuations of the Indexes Specifying the Fluctuations of the Indexes Specifying the

DistributionsDistributions

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.


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)


3.4 Temporal Change of the Distributions: 3.4 Temporal Change of the Distributions: The Composition of Total Income in the Two The Composition of Total Income in the Two

Sections of the DistributionsSections 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:

kk

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.


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)


3.4 Temporal Change of the Distributions: 3.4 Temporal Change of the Distributions: The Composition of Total Income in the Two The Composition of Total Income in the Two

Sections of the DistributionsSections 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:

kk

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.


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)


4. Inequality 4. Inequality Decomposition by Decomposition by

Income SourceIncome Source


4.1 The Contribution of Individual Income 4.1 The Contribution of Individual Income Sources to Total Inequality: General Sources to Total Inequality: General

FrameworkFramework 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 Sk>0, the kth source of income provides a disequalizing effect, and an equalizing effect if Sk<0.

kk

I S

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:

212

2GE CV

where CV is the Coefficient of Variation, having the formula:

1

22

1

1 1 n

ii

CV yn

where n is the number of individuals in the sample, yi is the income of individual i, and μ the mean income.


4.2 The Contribution of Individual Income 4.2 The Contribution of Individual Income Sources to Total Inequality: Static Sources to Total Inequality: Static Decomposition by Income SourceDecomposition 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:

2 2 2k k k k kS s GE GE GE

where sk=Sk/I is the proportional contribution of income component k to total inequality, ρk is the correlation between source k and total income, χk=μk/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.


Total inequality (GE(2)) and income source contribution to total inequality (Sk=skGE(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)


4.2 The Contribution of Individual Income 4.2 The Contribution of Individual Income Sources to Total Inequality: Static Sources to Total Inequality: Static Decomposition by Income SourceDecomposition 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:

2 2 2k k k k kS s GE GE GE

where sk=Sk/I is the proportional contribution of income component k to total inequality, ρk is the correlation between source k and total income, χk=μk/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.


Total inequality (GE(2)) and income source contribution to total inequality (Sk=skGE(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)


4.3 The Contribution of Individual Income 4.3 The Contribution of Individual Income Sources to Total Inequality: Dynamic Sources to Total Inequality: Dynamic

Decomposition by Income SourceDecomposition 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:

1

2 2 2

2 2

t t

k k k kk k

GE GE GE

S GE GE

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 ΔSk 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.


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


4.3 The Contribution of Individual Income 4.3 The Contribution of Individual Income Sources to Total Inequality: Dynamic Sources to Total Inequality: Dynamic

Decomposition by Income SourceDecomposition 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:

1

2 2 2

2 2

t t

k k k kk k

GE GE GE

S GE GE

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 ΔSk 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.


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


5. Summary5. Summary


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.


5. Forthcoming 5. Forthcoming EventsEvents


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@ACE). Ancona, Italy, December 2-3, 2005: http://www.dea.unian.it/wehia/


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income inequality dynamics: evidence from a pool of major industrialized countries

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