Table Of ContentStudies in
Contemporary Economics
Camilo Oagum Michele Zenga (Eds.)
Income and Wealth
Distribution, Inequality
and Poverty
Proceedings of the Second International
Conference on Income Distribution by Size:
Generation, Distribution, Measurement and
Applications, Held at the University of Pavia,
Italy, September 28-30, 1989
Springer-Verlag
Berlin Heidelberg New York London
Paris Tokyo Hong Kong Barcelona
Editorial Board
D. Bos G. Bombach B. Felderer B. Gahlen K. W. Rothschild
Editors
Prof. Camilo Dagum
Prof. Michele Zenga
Universita degli Studi di Milano
Istituto di Scienze Statistiche e Matematiche "Marcello Boldrini"
Via Conservatorio, 7, 1-20122 Milano, Italy
Mathematical Subject Classification: 6206. 62E20, 62J02, 9006
ISBN-13:978-3-540-52863-0 e-ISBN-13:978-3-642-84250-4
001: 10.1007/978-3-642-84250-4
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Research on personal income distribution stems from Pareto (1895, 1896, 1897)
and is concerned with the distribution of income among a set of economic units,
such as family, household and individual.
This stream of research deals with the total income received by each economic
unit regardless of the factors of production property right, unless the object of
research includes the distribution by category or source of income, e.g. wages and
salaries, selfemployment income, investment income, interest, transfer payments
and others. It is called the size or personal income distribution and purports to
explain the generation and the shape of the income distribution among a set of
microeconomic units.
This collection of essays deals with this theme and was presented and discus
sed at the Second International Conference on the Size Distribution of Income:
Generation, Distribution, Measurement and Applications held at the University of
Pavia, Italy, September 28-30, 1989. One of the driving forces leading to the orga
nization of this Conference was the successful outcome of the first one held in 1985
at the University of Brescia, Italy, and organized by its Faculty of Economics. The
proceedings of this Conference were edited by M. Zenga (1987).
The themes of income distribution by size and income inequality measures has
been introduced to the economic science and the theory and methods of probability
and statistics by the Italian School of Statistics and Economics. This new stream of
research recognizes V. Pareto as its founder. It was further enriched and developed
by outstanding italian scholars such as C. Gini, R. Benini, F.P. Cantelli, G.
Mortam, C. Bresciani-Turroni, C.E. Bonferroni, L. Amoroso, G. Pietra and R.
D'Addario.
The 1985 University of Brescia Conference signalled a renaissance of the Italian
School of Income Distribution and Income Inequality. It was the leading school
since its birth in 1895 until the mid of the XXth Century.
Following the University of Brescia stimulating breakthrough the Italian Society
of Statistics organized a plenary and several invited sessions on income distribu
tion and the measurement of income inequality and poverty during its XXXIIIrd
Scientific Meetings held in Bari, April 1986. The enthusiastic and decisive support
of the Institutes of Statistics of the University of Pavia and the University of Mi
lano, and the Interdepartmental Research Centre on Income Distribution (C.R.I.
DI. RE.) of the University of Siena contributed to the success of the University
of Pavia Conference. Besides Italian scholars, this conference was attended by
scholars from the U.S.A., Canada, the United Kingdom, Germany, Poland and
A ustria. They presented scientific contributions and took active participation du
ring the conference sessions. They brought to the Conference the rich experience
IV
of their respective national statistical offices. We gratefully acknowledge the con
tributions of the U.S. Bureau of Labor Statistics, the U.S. Bureau of the Census,
Statistics Canada and the Polish Institute of Statistics. The Organizing and Pro
gram Committee was integrated by Professors M. Zenga (President) and M.B.
Civardi (Coordinator). Professors L. Pasinetti, L. Biggeri, M. Zenga, A. Predetti,
B. V. Frosini, C. Dagum and A. Zanella kindly agreed to chair the Conference ses
sions. The contributions to the Conference can be organized under the following
main topics:
1. Models of Income and Wealth Distribution, Specification and Estimation.
C. Dagum presents a systemic analysis of income distribution models and or
ganizes almost all the specified models as members of three generating systems of
probability distribution functions. Following Pareto rationale to the specification of
his Type I model, R. Colombi deduces a three-parameter model from the assump
tion that the income variable is the product of two components having respectively
a Paretian and a lognormal distribution. G. Stoppa also starts with the Paretian
model and generalized it introducing a power transformation. A second contribu
tion by C. Dagum deals with the specification and application of a general model
of net wealth distribution. It describes the net wealth distribution of the economic
units including those with zero and negative net wealth.
2. Causal Structure of Income and Wealth Distribution.
R. Targetti Lenti deals with a structural economic analysis purporting to identify
the causal variables generating the functional and personal distribution of income.
She also discusses the relationship between these two types of income distribution
using the social accounting matrices (SAM). The SAM framework provides to M.B.
Civardi the methodological tools to deal with the causal socioeconomic structures
in order to analyse and deduce the family income multiplier matrix.
3. Theory and Applications of Concentration Curves and Measures.
M. Zenga specifies a set of properties that concentration curves and measures
should fulfil. He applies this conceptual framework to a comparative analysis of
the Lorenz and Zenga curves and their corresponding concentration measures. L.
Dancelli makes further analysis of Zenga concentration curve and measure, inve
stigates the causes underlying this curve behaviour and analyses the sensibility of
v
the Zenga concentration curve and associated inequality measure due to single and
double truncations of the income distributions. The analytical results are applied
to a selected set of 'i ncome distribution models. G. Zanardi performs a geometric
and analytical study of the Gini mean difference and the mean of the absolute de
viation within the context of the income concentration inquiry. G. Latorre analyses
the asymptotic behaviour of the Gini and Zenga concentration measure,~ under the
parametric assumption of Paretian and lognormal distributions. The lower bound
of the sample size that will lend support to the use of the normal distribution is
investigated. E. Castagnoli and P. Muliere discuss the Pigou-Dalton principle of
transfer and consider an intermediate case between the strong and weak principles
of transfer in the analysis of income concentration measures. A. Pollastri analyses
the estimator properties of the inequality parameter a specified in the Pareto and
Gini models of income distribution. Besides the estimator properties she considers
the goodness of fit of population and income quantiles respectively. T. Salvaterra
makes a comparative study and evaluation of the Lorenz L(p), Zenga Z(p) and
Zenga )..(p) concentration curves and their corresponding measures of income con
centration given by the Gini G and Zenga ( and)" ratios respectively.
4. The Decomposition of Income Inequality Measures.
B. V. Frosini deals with the ordinal decomposition of inequality measures assu
ming Dagum distributions. An apropriate criterion supporting the choice of the
within groups income inequality as a primitive assumption is advanced and the
between groups inequality is obtained as a derived proposition. A. Tarsitano re
views the theoretical and statistical properties of the Bonferroni measure of income
inequality, examines its values corresponding to four distribution models, analyses
the disaggregation of the Bonferroni measure by factor incomes and its decompo
sition by population subgroups.
5. Social Welfare, Poverty and Inequality.
G. Pyatt attempts to relax the Pareto conditions to achieve a more comprehen
sive and socially valid evaluation criterion consistent with that of Pareto to rank
income distributions over time or between different groups of households. It pur
ports to provide a clear ordering of alternatives in some of those cases where the
ordering is ambiguous from the Pareto perspective.
G. Carbonaro makes an incisive review and a comparative evaluation of the
strength and limitations of several well known poverty measures. Starting from the
observation that the dichotomic classification between poor and non-poor implied
VI
by a poverty line is much too rigid and that the concept of poverty is a multidimen
sional one, S. Zani and A. Cerioli make use of the fuzzy sets theory to support the
specification of a poverty measure that takes into account the intensity of a set of
socioeconomic characteristics that determine the relative wellbeing of a population.
6. Statistical Surveys and Case Studies of Income, Expenditures and Wealth Di
stributions.
T. Garner and S. Shipp examine the data provided by the U.S. Bureau of La
bor Statistics household and expenditure surveys and present results from recent
studies in which these data have been used to examine the distribution of hou
sehold expenditures. J. Mc Neil reviews the U.S. Bureau of the Census' program
to measure the distribution of income, discusses recent efforts to go beyond the
annual measures of money income before taxes, and outlines an agenda for future
improvements. A. Rashid investigates the impact of wife's work status on family
wealth in Canada by comparing the wealth positions of working and non-working
wife families based on the data collected by the 1984 Statistics Canada Survey of
Consumer Finances. L. Cannari and G. D'Alessio deal also with the distribution
of wealth. They analyse the 1987 Banca d'Italia Survey of the family balance sheets
to investigate the consistency of the real state assets and distribution, comparing
them with macroeconomic estimates with the purpose of identifying the sources of
non-sampling errors. J. Kordos provides a brief survey of theoretical and applied
research on income distribution in Poland during the last quarter of this Century.
Then this author analyses the sources of data, several statistical and conceptual
issues and concludes with a comparative study of the goodness of fit of a selected
set of income distribution models applied to Polish data. W. Oberhofer provides
a thorough analysis of family expenditures in the German Federal Republic. B.M.
Zavanella discusses the issue of statistical matching from different sources and its
potential application to income distribution data. L. Bernardi analyses the public
budget impact on the personal income distribution and social welfare. Hence, the
income redistribution effects of taxes and budget allocations. A. Chilosi performs
a documented study of the distribution and redistribution of income during the so
cialist experience of several Eastern European countries. L. Grassini analyses the
possible effects of changes in the personal income distribution and income inequa
lity on the private consumption.
We are confident that this collection of essays constitutes a significant socioeco
nomic and statistical contribution to the analysis of income and wealth distribution,
poverty, social welfare and income concentration measures. We expect that the re
search content and the issues raised in the research papers that we are pleased to
VII
present to the readers will attract the interest of young researchers to the manifold
socioeconomic, probabilistic and statistical research topics of income and wealth
distributions.
We finally express our most sincere appreciation and acknowledgement to Pro
fessors Pasquale Scaramozzino, Marisa Bottiroli Civardi and Giovanni Latorre for
their exceptional contribution to the organization and logistic of this Conference.
Camilo Dagum Michele Zenga
REFERENCES
Pareto, V. (1895). La legge della domanda. Giornale degli Economisti, January, pp. 59-68.
Pareto, V. (1896). Ecrits sur la courve de la repartition de la richesse. Complete works of V.
Pareto published under the direction of G. Busino. Geneve: Librairie Droz, 1965.
Pareto, V. (1897). Cours d'economie politique. New edition by G.H. Bousquet and G. Busino.
Geneve: Librairie Droz, 1964.
Zenga, M., editor (1987). La distribuzione personale del reddito: problemi di formazione, di ripar
tizione e di misurazione. Milano: Vita e Pensiero.
Income Distribution by Size: Generation, Distribution,
Measurement and Applications.
Second International Conference, University of Pavia, Italy,
September 28 - 30, 1989.
Scientific Committee:
M. Zenga, President (Milan), L. Biggeri (Florence), C. Dagum (Ottawa), V. B.
Frosini (Milan) and G. Pyatt (Warwick).
Organizing Committee:
P. Scaramozzino, President (Pavia), M. Bottiroli Civardi (Pavia), G. Latorre (Co
senza) and M. Zenga (Milan).
Acknowledgements
The Editors wish to record their thanks to all those who helped with both the
selection and refereeing of papers, and with the organisation of the Meeting. Spon
sorship from the Societa Italiana di Statistica and financial support from Italian
Consiglio Nazionale delle Ricerche, Universita degli Studi di Pavia, Alleanza Assi
curazioni -Trieste, Amministrazione Provinciale di Pavia, Associazione Industriali
di Pavia, Banca del Monte di Lombardia - Milano, Banca Popolare di Milano, Ita
lease S.p.A. - Milano are gratefully acknowledged.
TABLE OF CONTENTS
PART I
MODELS OF INCOME AND WEALTH DISTRIBUTION, SPECIFICATION
AND ESTIMATION
Generation And Properties Of Income Distribution Functions 1
Camilo Dagum
A New Model Of Income Distribution: The Pareto - Lognormal Distribution 18
Roberto Colombi
ANew Model For Income Size Distributions 33
Gabriele Stoppa
A Model Of Net Wealth Distribution Specified For Negative, Null and Positive 42
Wealth. A Case Study: Italy
Camilo Dagum
PART II
CAUSAL STRUCTURE OF INCOME AND WEALTH DISTRIBUTION
Income Distribution And The Structure Of The Economic System: 57
A SAM Approach
Renata Targetti Lenti
Income Multipliers In The Household Institutional Sector 72
Marisa Bottiroli Civardi
PART III
THEORY AND APPLICATIONS OF CONCENTRATION CURVES AND
MEASURES
Concentration Curves And Concentration Indexes Derived From Them 94
Michele Zenga
XII
On The Behaviour Of The Zp Concentration Curve III
Livia Dancelli
Costituent Of The Mean Deviations And Of The Mean Difference And 128
Concentration Scheme
Giampaolo Zanardi
Asymptotic Distributions Of Indices Of Concentration: Empirical 149
Verification And Applications
Giovanni Latorre
A Note On Inequality Measures And The Pigou - Dalton Principle Of 171
Transfers
Erio Castagnoli and Pietro Muliere
A Comparison Of The Traditional Estimators Of The Parameter cy Of The 183
Pareto Distribution
Angiola Pollastri
Comparison Among Concentration Curves And Indexes In Some Empirical 194
Distributions
Tiziano Salvaterra
PART IV
THE DECOMPOSITION OF INCOME INEQUALITY MEASURES
Ordinal Decomposition Of Inequality Measures In Case Of Dagum 215
Distributions
Benito V. Frosini
The Bonferroni Index Of Income Inequality 228
Agostino Tarsitano
PART V
SOCIAL WELFARE, POVERTY AND INEQUALITY
Social Evaluation Criteria 243
Graham Pyatt
Global Indicators Of Poverty 254
Giuseppe Carbonaro
