THE MICROECONOMICS
OF INCOME DISTRIBUTION
DYNAMICS
IN EAST ASIA AND LATIN AMERICA
François Bourguignon
Francisco H. G. Ferreira
Nora Lustig
Editors
THE MICROECONOMICS OF
INCOME DISTRIBUTION
DYNAMICS IN EAST ASIA
AND LATIN AMERICA
THE MICROECONOMICS OF
INCOME DISTRIBUTION
DYNAMICS IN EAST ASIA
AND LATIN AMERICA
François Bourguignon
Francisco H. G. Ferreira
Nora Lustig
Editors
A copublication of the World Bank and Oxford University Press
© 2005 The International Bank for Reconstruction and Development / The World Bank
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First printing September 2004
1 2 3 4 08 07 06 05
A copublication of the World Bank and Oxford University Press.
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Cataloging-in-Publication Data has been applied for.
Contents
Preface xiii
Acknowledgments xv
Contributors xvii
Abbreviations and Acronyms xix
1 Introduction 1
François Bourguignon, Francisco H. G. Ferreira,
and Nora Lustig
2 Decomposing Changes in the Distribution of
Household Incomes: Methodological Aspects 17
François Bourguignon and Francisco H. G. Ferreira
3 Characterization of Inequality Changes through
Microeconometric Decompositions: The Case of
Greater Buenos Aires 47
Leonardo Gasparini, Mariana Marchionni, and
Walter Sosa Escudero
4 The Slippery Slope: Explaining the Increase in
Extreme Poverty in Urban Brazil, 197696 83
Francisco H. G. Ferreira and Ricardo Paes de Barros
5 The Reversal of Inequality Trends in Colombia,
197895: A Combination of Persistent and
Fluctuating Forces 125
Carlos Eduardo Vélez, José Leibovich, Adriana
Kugler, César Bouillón, and Jairo Núñez
6 The Evolution of Income Distribution during
Indonesia's Fast Growth, 198096 175
Vivi Alatas and François Bourguignon
7 The Microeconomics of Changing Income
Distribution in Malaysia 219
Gary S. Fields and Sergei Soares
v
vi CONTENTS
8 Can Education Explain Changes in Income
Inequality in Mexico? 275
Arianna Legovini, César Bouillón, and Nora Lustig
9 Distribution, Development, and Education in Taiwan,
China, 197994 313
François Bourguignon, Martin Fournier, and
Marc Gurgand
10 A Synthesis of the Results 357
François Bourguignon, Francisco H. G. Ferreira, and
Nora Lustig
Index 407
Figures
3.1 Gini Coefficient of Equivalent Household Income
Distribution in Greater Buenos Aires, 198598 49
3.2 Hourly EarningsEducation Profiles for Men
(Heads of Household and Other Family
Members), Age 40 55
3.3 Hourly EarningsEducation Profiles for
Women (Spouses), Age 40 56
3.4 Weekly Hours of Work by Educational Level for
Men (Heads of Household), Age 40 59
4.1 Macroeconomic Instability in Brazil: Inflation 84
4.2 Macroeconomic Instability in Brazil: Per Capita GDP 84
4.3 Truncated Pen Parades, 197696 87
4.4 Plotted Quadratic Returns to Education
(Wage Earners) 88
4.5 Plotted Quadratic Returns to Experience
(Wage Earners) 89
4.6 Combined Price Effects by Sector 106
4.7 Price Effects Separately and for Both Sectors
Combined 107
4.8 Occupational-Choice Effects 108
4.9 The Labor Market: Combining Price and
Occupational-Choice Effects 109
4.10 Demographic Effects 110
4.11 Shift in the Distribution of Education, 197696 111
4.12 Education Endowment and Demographic Effects 112
4.13 A Complete Decomposition 113
5.1 Average Household Size by Income Decile in
Urban Colombia, Selected Years 135
CONTENTS vii
5.2 Change in Income from Changes of Returns to
Education, Relative to Workers Who Have
Completed Secondary Education: Male and
Female Wage Earners in Urban Colombia,
Selected Periods 140
5.3 Change in Income from Changes of Returns to
Education, Relative to Workers Who Have
Completed Secondary Education: Male and
Female Self-Employed Workers in Urban
Colombia, Selected Periods 141
5.4 Probability of Being Employed or a Wage Earner
in Urban Colombia according to Various
Individual or Household Characteristics, Various
Groups of Household Members, Selected Years 146
5.5 Simulated Occupational-Choice and Participation
Changes in Percentage Points by Percentile of
Earnings for Urban Males and Females, 197888 154
5.6 Simulated Occupational-Choice and Participation
Changes in Percentage Points by Percentile of
Earnings for Urban Males and Females, 198895 156
5.7 Changes in Employment Rate by Income Percentile,
Females in Urban Colombia, Selected Periods 157
6.1 Summary Decomposition of Changes in the
Equivalized Household Distribution of Income 213
7.1 Changing Quantile Functions 221
7.2 Differences in Quantile Functions 222
7.3 Changing Lorenz Curves 224
7.4 Differences in Lorenz Curves 225
7.5 Household Quantile Curves: 1984 Baseline 253
7.6 Household Quantile Curves: 1989 Baseline 255
7.7 Quantile Curves: Simulated Values Minus 1984
Actual Values 257
7.8 Quantile Curves: Simulated Values Minus 1989
Actual Values 258
7.9 Lorenz Curves: Simulated Values Minus 1984
Actual Values 262
7.10 Lorenz Curves: Simulated Values Minus 1989
Actual Values 263
7.11 Household Quantile Curves: 1989 Baseline 265
7.12 Household Quantile Curves: 1997 Baseline 267
7.13 Quantile Curves: Simulated Values Minus 1989
Actual Values 269
7.14 Quantile Curves: Simulated Values Minus 1997
Actual Values 270
viii CONTENTS
8.1 Observed Change in Individual Earnings by Percentile
in Mexico, 198494 276
8.2 Change in Women's Labor-Force Participation by
Education Level in Mexico, 198494 281
8.3 Returns to Education for Men by Location,
Education Level, and Type of Employment in
Mexico, 1984 and 1994 292
8.4 Effect of Labor Choices on Earnings by Percentile
in Mexico, 198494 298
8.5 Effect of Educational Gains on Earnings by
Percentile in Mexico, 198494 300
8.6 Effect of Changes in Returns to Education on
Earnings by Percentile in Mexico, 198494 301
8.7 Effect of Urban-Rural Disparities on Earnings
by Percentile in Mexico, 198494 303
9.1 Evolution of Income Inequality, 197994 318
9.2 Elasticity of Spouses' Occupational Choice with
Respect to Head of Household's Earnings 332
9.3 197994 Variation in Individual Earnings Caused
by the Price Effect, by Centiles of the 1979 Earnings
Distribution 336
9.4 Simulated Entries into and Exits from the Wage
Labor Force 337
9.5 Simulation of the 1994 Education Structure on
the 1979 Population 340
9.6 197994 Variation in Household Income Caused by
the Price Effect, by Centiles of the 1979 Distribution of
Equivalized Household Income Per Capita (EHIP) 344
9.7 Entries into and Exits from the Labor Force: Overall
Participation Effect 345
9.8 Effects of Imposing the 1994 Education Structure
on the 1979 Population 348
9.9 Effects of Imposing the 1994 Children Structure on the
1979 Population: Relative Variation by Centile of the
1979 Distribution of Equivalized Household Income 351
Tables
1.1 Selected Indicators of Long-Run Structural Evolution 3
3.1 Distributions of Income in Greater Buenos
Aires, Selected Years 49
3.2 Hourly Earnings by Educational Levels in Greater
Buenos Aires, Selected Years 50
3.3 Log Hourly Earnings Equation Applied to
Greater Buenos Aires, Selected Years 52
CONTENTS ix
3.4 Hourly Earnings by Gender in Greater Buenos Aires,
Selected Years 57
3.5 Weekly Hours of Work by Educational Levels in
Greater Buenos Aires, Selected Years 59
3.6 Hours of Work Equation for Greater Buenos Aires,
Selected Years 60
3.7 Labor Status by Role in the Household in Greater
Buenos Aires, Selected Years 62
3.8 Composition of Sample by Educational Level in
Greater Buenos Aires, Selected Years 63
3.9 Decompositions of the Change in the Gini Coefficient:
Earnings and Equivalent Household Labor Income in
Greater Buenos Aires, 198692 71
3.10 Decompositions of the Change in the Gini Coefficient:
Earnings and Equivalent Household Labor Income in
Greater Buenos Aires, 199298 72
3.11 Decompositions of the Change in the Gini Coefficient:
Earnings and Equivalent Household Labor Income in
Greater Buenos Aires, 198698 73
3.12 Decomposition of the Change in the Gini Coefficient:
Average Results Changing the Base Year in Greater
Buenos Aires, Selected Periods 74
4.1 General Economic Indicators for Brazil, Selected
Years 86
4.2 Basic Distributional Statistics for Different Degrees
of Household Economies of Scale 91
4.3 Stochastic Dominance Results 93
4.4 Educational and Labor-Force Participation Statistics,
by Gender and Race 94
4.5 Equation 4.2: Wage Earnings Regression for
Wage Employees 99
4.6 Equation 4.3: Total Earnings Regression for the
Self-Employed 101
4.7 Simulated Poverty and Inequality for 1976, Using
1996 Coefficients 104
4A.1 Real GDP and GDP Per Capita in Brazil, 19761996 115
4A.2 PNAD Sample Sizes and Missing or Zero Income
Proportions 116
4A.3 A Brazilian Spatial Price Index 117
4A.4 Brazilian Temporal Price Deflators, Selected Years 118
4A.5 Ratios of GDP Per Capita to PNAD Mean
Household Incomes, 197696 118
4B.1 Evolution of Mean Income and Inequality:
A Summary of the Literature 119
x CONTENTS
5.1 Decomposition of Total Inequality between Rural
and Urban Areas, Selected Years 129
5.2 Labor-Market Indicators in Urban and Rural
Areas, Selected Years 132
5.3 Changes in Sociodemographic Characteristics
in Urban and Rural Areas, Selected Years 134
5.4 Earnings Equations of Wage and Self-Employed
Male and Female Urban Workers, Selected Years 138
5.5 Earnings Equations of Wage and Self-Employed
Male and Female Rural Workers, Selected Years 139
5.6 Marginal Effect of Selected Variables on Occupational
Choice among Wage Earners, Self-Employed Workers,
and Inactive Individuals for Urban Heads of Household,
Spouses, and Other Household Members, and All
Rural Workers, Selected Years 144
5.7 Decomposition Income Distribution Changes for
Households and Individual Workers in Urban and
Rural Colombia: Changes in the Gini Coefficient,
Selected Periods 150
5.8 Mean Income: Effect of Change in the Constant of
the Earnings Equation 153
5.9 Simulated Changes in Participation and Occupational
Choice in Urban Colombia, Selected Periods 153
6.1 Evolution of Mean Household Income, 198096 178
6.2 Evolution of the Socioeconomic Structure of the
Population, 198096 179
6.3 Evolution of the Personal Distribution of Income,
198096 180
6.4 Individual Wage Functions by Gender and Area,
198096 186
6.5 Household Profit Functions and Nonfarm
Activities, 198096 188
6.6 Simulated Evolution of Typical Incomes: Price Effect 192
6.7 Decomposition of Changes in the Distribution of
Individual Earnings 194
6.8 Decomposition of Changes in the Distribution of
Household Income Per Capita 198
6.9 Mean and Dispersion of Household Incomes
according to Some Characteristics of Heads of
Households 200
6.10 Occupational-Choice Behavior, 198096 202
6.11 Simulated Changes in Occupational Choices,
Whole Population 205
CONTENTS xi
6.12 Simulated Changes in Occupational Choices, Rural
and Urban Population 206
7.1 Location of Actual Distribution of Per Capita
Household Income, 1984 and 1989, 1989 and 1997 223
7.2 Inequality of Actual Distribution of Per Capita
Household Income, Selected Periods 226
7.3 Occupational-Position Equations for Male Heads
of Household 231
7.4 Occupational-Position Equations for Female Heads
of Household 233
7.5 Occupational-Position Equations for Male Family
Members Who Are Not Heads of Household 235
7.6 Occupational-Position Equations for Female Family
Members Who Are Not Heads of Household 237
7.7 Earnings Functions for Male Wage Earners 240
7.8 Earnings Functions for Female Wage Earners 242
7.9 Earnings Functions for Male Self-Employed Workers 244
7.10 Earnings Functions for Female Self-Employed Workers 246
7.11 Distribution of Per Capita Household Income,
Substituting 1989 Values into 1984 Distribution 259
7.12 Distribution of Per Capita Household Income,
Substituting 1984 Values into 1989 Distribution 260
7.13 Rising Educational Attainments in Malaysia, 198497 261
7.14 Actual and Simulated Inequality for Disaggregated
Gender and Occupational-Position Groups 264
7.15 Distribution of Per Capita Household Income,
Substituting 1997 Values into 1989 Distribution 271
7.16 Distribution of Per Capita Household Income,
Substituting 1989 Values into 1997 Distribution 272
8.1 Inequality in Earnings and Household Income in
Mexico, 1984 and 1994 277
8.2 Characteristics of the Labor Force in Mexico, 1984
and 1994 279
8.3 Selected Results from Earnings Equations for Mexico 290
8.4 Decomposition of Changes in Inequality in Earnings
and Household Income in Mexico, 198494 295
8.5 Rural Effect in the Decomposition of Changes in
Inequality in Earnings and Household Income in
Mexico, 198494 297
9.1 Evolution of the Structure of the Population at
Working Age, 197994 316
9.2 Wage Functions for Men, Corrected for Selection
Bias, Selected Years 327
xii CONTENTS
9.3 Wage Functions for Women, Corrected for Selection
Bias, Selected Years 328
9.4 Decomposition of the Evolution of the Inequality of
Individual Earnings, 197980 and 199394 334
9.5 Decomposition of the Evolution of the Inequality
of Equivalized Household Incomes, 197980 and
199394 335
10.1 A Summary of the Decomposition Results 359
10.2 Interpreting the Decompositions: A Schematic
Summary 381
Preface
The process of economic development is inherently about change.
Change in where people live, in what they produce and in how they
produce it, in how much education they get, in how long and in
how well they live, in how many children they have, and so on. So
much change, and the fact that at times it takes place at such sur-
prising speed, must affect the way incomes and wealth are distrib-
uted, as well as the overall size of the pie. While considerable efforts
have been devoted to the understanding of economic growth, the
economic analysis of the mechanisms through which growth and
development affect the distribution of welfare has been rudimentary
by comparison. Yet understanding development and the process of
poverty reduction requires understanding not only how total income
grows within a country but also how its distribution behaves over
time.
Our knowledge of the dynamics of income distribution is
presently limited, in part because of the informational inefficiency
of the scalar inequality measures generally used to summarize dis-
tributions. Single numbers can often hide as much as they show. But
recent improvements in the availability of household survey data for
developing countries, and in the capacity of computers to process
them, mean that we should be able to do a better job comprehend-
ing the nature of changes in the income distribution that accompany
the process of economic development. We hope that this book is a
step in that direction.
By looking at the evolution of the entire distribution of income
over reasonably long periods--10 to 20 years--and across a diverse
set of societies--four in Latin America and three in East Asia--we
have learned a great deal about a variety of development experi-
ences, and how similar building blocks can combine in unique ways,
to shape each specific historical case. But we have also learned about
the similarities in some of those building blocks: the complex effect
of educational expansion on income inequality, the remarkable role
of increases in women's participation in the labor force, and the
importance of reductions in family size, to name a few.
xiii
xiv PREFACE
We have learned that the complexity of the interactions between
these forces is so great that aggregate approaches to the relationship
between growth and distribution are unlikely to be of much use for
any particular country. We have also learned that some common
patterns can be discerned and, with appropriate care and humility,
understanding them might be helpful to policymakers seeking to
enhance the power of development to reduce poverty and inequity.
We hope that readers might share some of the joy we found in
uncovering the stories behind the distributional changes in each of
the countries studied in this book.
François Bourguignon
Francisco H. G. Ferreira
Nora Lustig
Acknowledgments
This book started as a joint research project organized by the Inter-
American Development Bank (IDB) and the World Bank, and we
are grateful to the many people in both institutions who supported
it throughout its five-year lifespan. We would like to thank particu-
larly Michael Walton, who supported the birth of the project when
he directed the Poverty Reduction Unit at the World Bank, as well
as Carlos Jarque and Carlos Eduardo Vélez of the IDB, who sup-
ported the project's completion.
We are also very grateful to Martin Ravallion, who commented
on various versions of the work, from research proposal to finished
papers; to James Heckman, who acted as a discussant for three
chapters at a session in the 2000 Meetings of the American Eco-
nomic Association; to Ravi Kanbur, who provided very useful sug-
gestions at an early stage of the research process; and to Tony
Shorrocks, who gave us many insights into the nature of the decom-
positions we undertook. We are similarly indebted to a number of
participants in seminars and workshops that took place at various
meetings of the Econometric Society (in particular in Latin America
and the Far East); of the European Economic Association (in
Venice); of the Network on Inequality and Poverty of the IDB, World
Bank, and LACEA (Latin American and Caribbean Economic
Association); and at the Universities of Brasília, Maryland, and
Michigan, The Catholic University of Rio de Janeiro, the European
University Institute in Florence, and DELTA (Département et
Laboratoire d'Economie Théorique et Appliquée) in Paris.
Our greatest debt, of course, is to the authors of the seven case
studies, who really wrote the book. Their names and affiliations are
listed separately in the coming pages, and we thank them profoundly
for their commitment and endurance during the long process of pro-
ducing this volume. Finally, the book would not have been possible
without the dedication, professionalism, and attention to detail of
Janet Sasser and her team at the World Bank's Office of the Publisher.
xv
Contributors
Vivi Alatas Economist in the East Asia and
Pacific Region at the World Bank,
Jakarta, Indonesia
César Bouillón Economist in the Poverty and
Inequality Unit of the Inter-American
Development Bank, Washington, D.C.
François Bourguignon Senior vice president and chief econo-
mist of the World Bank, Washington,
D.C.
Walter Sosa Escudero Professor of econometrics at the Uni-
versidad de los Andes, Buenos Aires,
Argentina, and at the Universidad
Nacional de La Plata, Argentina;
researcher at Centro de Estudios
Distributivos, Laborales y Sociales
(CEDLAS) at the Universidad
Nacional de La Plata
Francisco H. G. Ferreira Senior economist in the Development
Research Group at the World Bank,
Washington, D.C.
Gary S. Fields Professor of labor economics at
Cornell University, Ithaca, New York
Martin Fournier Researcher at the Centre d'Etudes
Français sur la Chine Contemporaine
(CEFC), Hong Kong, China, and
associate professor at the Université
d'Auvergne, Clermont-Ferrand,
France
Leonardo Gasparini Director of CEDLAS, as well as pro-
fessor of economics of income distrib-
ution and professor of labor econom-
ics at the Universidad Nacional de La
Plata, Argentina
xvii
xviii CONTRIBUTORS
Marc Gurgand Researcher at the Département et
Laboratoire d'Economie Théorique et
Appliquée (DELTA) at the Centre
National de la Recherche Scientifique
(CNRS), Paris, France
Adriana Kugler Associate professor of economics at
the Universitat Pompeu Fabra,
Barcelona, Spain, and assistant pro-
fessor of economics at the University
of Houston, Texas
Arianna Legovini Senior monitoring and evaluation
specialist in the Africa Region at the
World Bank, Washington, D.C.
José Leibovich Assistant director of the Departamento
Nacional de Planeación (Department
of National Planning), Bogotá,
Colombia
Nora Lustig President of the Universidad de Las
Americas, Puebla, Mexico
Mariana Marchionni Professor of econometrics at the
Universidad Nacional de La Plata,
Argentina, and researcher at CEDLAS
Jairo Núñez Researcher at the Universidad de los
Andes, Bogotá, Colombia
Ricardo Paes de Barros Researcher at the Instituto de
Pesquisa Econômica Aplicada (IPEA),
Rio de Janeiro, Brazil
Sergei Soares Senior education economist in the
Latin America and Caribbean Region
at the World Bank, Washington,
D.C., and researcher at IPEA, Rio de
Janeiro, Brazil
Carlos Eduardo Vélez Chief of the Poverty and Inequality
Unit at the Inter-American Develop-
ment Bank, Washington, D.C.
Abbreviations and Acronyms
CPI Consumer price index
DANE Departamento Nacional de Estadística (National
Department of Statistics, Colombia)
DGBAS Directorate-General of Budget, Accounting, and
Statistics (Taiwan, China)
EH Encuesta de Hogares (Household Survey,
Colombia)
EHIP Equivalized household income per capita
ENIGH Encuesta Nacional de Ingresos y Gastos de los
Hogares (Household Income and Expenditure
Surveys, Mexico)
EPH Encuesta Permanente de Hogares (Permanent
Household Survey, Argentina)
GDP Gross domestic product
IBGE Instituto Brasileiro de Geografia e Estatística
(Brazilian Geographical and Statistical Institute)
ICV-DIEESE Índice do Custo de VidaDepartamento
Intersindical de Estatística e Estudos Sócio-
Econômeios (Cost of Living IndexInter Trade
Union Department of Statistics and Socioeco-
nomic Studies, Brazil)
IGP-DI Índice Geral de PreçosDisponibilidade Interna
(General Price Index, Brazil)
INEGI Instituto Nacional de Estadística, Geografia y
Informática (National Institute of Statistics,
Geography, and Informatics, Mexico)
INPC-R Índice Nacional de Preços ao ConsumidorReal
(National Consumer Price Index, Brazil)
MIDD Microeconomics of Income Distribution
Dynamics
xix
xx ABBREVIATIONS AND ACRONYMS
OLS Ordinary least squares
PNAD Pesquisa Nacional por Amostra de Domicílios
(National Household Survey, Brazil)
Progresa Programa de Educación, Salud y Alimentación
(Program for Education, Heath, and Nutrition,
Mexico)
1
Introduction
François Bourguignon,
Francisco H. G. Ferreira, and Nora Lustig
This book is about how the distribution of income changes during
the process of economic development. By its very nature, the process
of development is replete with structural change. The composition of
economic activity changes over time, generally away from agriculture
and toward industry and services. Relative prices of goods and factors
of production change too, and their dynamics involve both long-term
trends and short-term shocks and fluctuations. The sociodemo-
graphic characteristics of the population evolve, as average age rises
and average family size falls. Patterns of economic behavior are not
constant either: female labor-force participation rates increase, as do
the ages at which children leave school and enter employment.
Generations save, invest, and bequeath, and so holdings of both phys-
ical and human capital change. But although change is everywhere
and although some patterns can be discerned across many societies,
no single country ever follows exactly the same development path.
The combination, sequence, and timing of changes that are actually
observed in any given country, at any given period, are always unique,
always unprecedented.
Each one of these processes of structural change is likely to have
powerful effects on the distribution of income. Social scientists in
general--and economists in particular--have long been searching
for some general rule about how development and income distribu-
tion dynamics are related. Karl Marx (1887) concluded that, under
the inherent logic of capital accumulation by a few and relentless
1
2 BOURGUIGNON, FERREIRA, AND LUSTIG
competition in labor supply by many, social cleavages would grow
increasingly deeper, until revolution changed things forever. Simon
Kuznets (1955)--drawing on W. Arthur Lewis (1954)--believed
that the migration of labor and capital from traditional, less pro-
ductive sectors of the economy toward more modern and produc-
tive ones would result first in rising inequality, followed eventually
by declining inequality. Jan Tinbergen (1975) argued that the cru-
cial struggle in modern economies was that between the rival forces
of (a) technological progress--ever raising the demand for (and the
pay of) more educated workers--and (b) educational expansion--
ever raising the supply of such workers. More recently, economists
have developed models with multiple equilibria, each characterized
by its own income distribution, with its own mean and its own level
of inequality.1 These models show that different combinations of
initial conditions--and of the historical processes that might follow
them--could lead to diverse outcomes.
In this book, we do not suggest yet another grand theory of the
dynamics of income distribution during the process of development.
Instead, we propose and apply a methodology to decompose distri-
butional change into its various driving forces, with the aim of
enhancing our ability to understand the nature of income distribu-
tion dynamics.2 In fact, rather than searching for a unifying expla-
nation, we explore the incredible diversity in the distributional
experiences and outcomes across economies. Why do changes in
inequality differ so markedly across economies that have similar
rates of growth in gross domestic product (GDP) per capita, such as
Colombia and Malaysia (see table 1.1)? Why do we observe rising
inequality both in growing economies (Mexico) and in contracting
ones (Argentina)? Why do educational expansions sometimes lead
to greater equality (as in Brazil and Taiwan, China) and sometimes
to greater inequality (as in Indonesia and Mexico)?
The microeconomic empirics reported in this volume suggest that
this diversity in outcomes results from the various possibilities that
arise from the interaction of a number of powerful underlying social
and economic phenomena. We group these phenomena into three
fundamental forces: (a) changes in the underlying distribution of
assets and personal characteristics in the population (which includes
its ethnic, racial, gender, and educational makeup); (b) changes in
the returns to those assets and characteristics; and (c) changes in
how people use those assets and characteristics, principally in the
labor market.
At a general level, our approach to addressing these themes con-
sists of simulating counterfactual distributions by changing how
markets and households behave, one aspect at a time, and by observ-
ing the effect of each change on the distribution, while holding all
and
China 6.0 5.7 6.0 9.5 70 84 46 50 4.9 4.2
3,786 0.271 0.290 initial
197994 in
aiwan,T
veys
sur
2.4 1.1 5.6 6.9 63 58 33 41 5.3 4.9
5,758 0.491 0.549
Mexico 198494
household
by
c c
4.0 5.2 42 55 60 58
7.9 8.3 4.9 4.4
5,548 0.486 0.499 given
Malaysia 198497 As
b.
.
6
5.7 5.1 3.8 23 35 32 48 5.0 4.4 only
1,430 0.384 0.402
Indonesia 198096 Aires
d d Buenos
3.7 3.8 4.6 6.9 57 61 27 41 5.4 4.3
2,520 .
0.502 0.544
Colombia 197895 Greater
Evolution only
to
refer sector
d d
1.0 0.2 3.2 5.3 68 77 28 42 4.6 3.6
data
4,499
Structural Brazil 0.595 0.591 Urban
197696 d.
.
Argentine
a over
c c all
0.0
Long-Run 6,506 1.0- 86 88 45 56
8.7 9.8 4.4 4.4 and
0.417 0.501 data, 14
of Argentina 198698
age
US$) urbanization
Indicators in the population
in and
GDP For
of percent) household size- c.
1980 parity (percent) (percent) GDP
b
in schooling
rate mean women (household the
Selected of capita,
power of rate of (percent)
households) years.
from
capita (198096, income
rate years year year force year year per year
1.1 analyzed growth
per year year year size year year
coefficient
capita capita Apart terminal
ableT Indicator Period GDP (purchasing Annual per Growth per verageA Initial rminaleT Urbanization Initial rminaleT labor
Participation Initial rminaleT Family Initial rminaleT income weighted
Gini Initial rminaleT a.
3
4 BOURGUIGNON, FERREIRA, AND LUSTIG
other aspects constant. We construct a simple income generation
model at the household level, which allows us to separate the
observed changes in the distribution of income into the three key
forces just described. The first force comprises the changes in the
sociodemographic structure of the population, as characterized by
area of residence, age, education, ownership of physical and finan-
cial assets, and household composition (collectively referred to as
endowment effects, or population effects). The second force comes
from changes in the returns to factors of production, including the
various components of human capital, such as education and expe-
rience (price effects). The third force has to do with changes in the
occupational structure of the population, in terms of wage work,
self-employment, unemployment, and inactivity (occupational
effects).
Of course, those causes of changes in the distribution of income
are not independent of one another. For instance, a change in the
sociodemographic structure of the population--such as higher
education levels in some segments of the population--will proba-
bly generate a change in the structure of prices, wages, and self-
employment incomes, which may in turn modify the way people
choose among alternative occupations. Conversely, exogenous
changes in returns to education (say, from skill-biased technological
change) are likely to induce some response from households in terms
of the desired level of education for their children. Like all of its rel-
atives in the Oaxaca-Blinder class of decompositions, the technique
discussed in this volume is not designed to model those general equi-
librium effects. It simply separates out how much of a given change
would not have been observed under a well-defined statistical coun-
terfactual (for example, if returns to education had not changed),
without making any statement about the economic foundations
of that counterfactual (for example, the conditions under which
no change in the returns to education would be consistent with
the other observed changes, in an economic sense). Nevertheless, as
we hope the case studies in chapters 3 through 9 will show, the
insights gained from the statistical decomposition and some basic
microeconomic intuition allow analysts to improve their under-
standing of the nature of changes in income distribution in a partic-
ular economy.
The microeconometric approach applied in this volume should
be seen as complementary to the more prevalent macroeconometric
(cross-country) studies of the relationship between growth and
inequality (or the reverse). (See, for instance, Alesina and Rodrik
1994; Dollar and Kraay 2002; Forbes 2000.) Cross-country regres-
sions can, if well specified and run on comparable data, tell us much
about average relationships between measures of income dispersion
INTRODUCTION 5
and other indicators of economic performance (such as economic
growth). However, for two reasons they should be complemented
by more detailed country studies of the sort included in this volume.
First, one can argue that endogeneity and omitted variable biases
inevitably plague most macroeconometric cross-country studies.
Suppose, for instance, that inequality is on the left-hand side of a
regression, and growth is treated as an explanatory variable.3 Vari-
ous case studies in this volume suggest that changes in the distribu-
tion of years of schooling affect income inequality. Standard growth
and wealth dynamics theory suggests that such changes would also
affect the rate of economic growth. Those changes cannot be ade-
quately captured by the mean years of schooling alone. If they are
not somehow included as explanatory variables (which they usually
are not), then their correlation with growth would bias the esti-
mated coefficient of mean schooling. Even if the changes were not
correlated with growth (which is unlikely), their omission would
increase the variance of the residuals, inflate standard errors, and
compromise hypothesis testing.
Second, even if the average relationships identified by the cross-
country studies were true, they might not be particularly relevant to
individual countries whose specific circumstances (some of which
may not be observed at the macro level) place them at some point
other than that average. Although useful lessons can be learned
from the average relationships estimated macroeconometrically,
specific country analysis and policy recommendations should also
be informed by more in-depth country studies.
The method proposed is applied to seven economies in this
volume: three in East Asia and four in Latin America.4 The East
Asian economies are Indonesia, Malaysia, and Taiwan (China). The
Latin American ones are Argentina (Greater Buenos Aires), Brazil
(urban), Colombia, and Mexico.5 Latin America and East Asia have
had rather different experiences with trends in the distribution of
income and with the pace of economic development (see table 1.1).
For example, during 19802000, growth in GDP per capita was
considerably higher in East Asia than in Latin America. Also, Latin
America showed higher initial levels of income inequality and (with
the exception of Brazil) sharper upward trends as well. In most
economies, however, the average years of schooling, the share of
urban population, and the participation of women in the labor force
rose, while the average size of households fell. Given the similar
demographic and educational trends in practically all the economies,
what explains the differences in the evolution of inequality? We
hope that learning about the forces at work in the Asian and Latin
American contexts will provide new insights for development ana-
lysts and policymakers.
6 BOURGUIGNON, FERREIRA, AND LUSTIG
The volume is organized as follows. In this introductory chapter,
we first review the broad changes in structure observed in the
economies under study. We then present a nonmathematical descrip-
tion of the methodology, placing it within the context of the litera-
ture. The formal presentation of the method is found in chapter 2.
Chapters 3 to 9 contain the analyses for each of the seven economies.
Chapter 10 presents a synthesis of the results and some concluding
remarks.
Indicators of Structural Change in Seven
Selected Economies
The magnitude of the structural changes that a society undergoes
during the development process is well illustrated by the figures
reported in table 1.1. The table lists changes in average education
levels, in the urban-rural structure of the economy, in female labor-
force participation, and in family sizes over intervals ranging from
one to two decades, from the mid-1970s to the late 1990s. It also
includes two measures of economic growth (in GDP per capita and
in household survey mean income) and the Gini coefficient for
household per capita income. Although the exact initial and final
years vary, some general trends emerge. In all economies, the
changes achieved on these four fronts in the span of 10 to 20 years
were most impressive. The importance of the rural sector declined
drastically everywhere, including Indonesia, where it was initially
much larger than in the other economies in our sample. The educa-
tional level of the population also rose dramatically across all
economies. Educational attainment measured by average years of
schooling rose by 50 percent in Colombia and by even more in
Brazil, Indonesia (urban), and Taiwan (China). (In the latter, educa-
tional attainment rose from an already high initial level of six years.)
In the Greater Buenos Aires area of Argentina, in Malaysia, and in
Mexico, the change was less dramatic. The participation rate of
women in the labor force was largely unchanged in Malaysia and
increased only slightly in Taiwan, China, but it rose substantially in
Indonesia and in the Latin American countries. Average family sizes
went down everywhere, falling by a full person or more in Brazil
and Colombia.
In terms of economic growth, the disparity of experiences fits
neatly into the expected continental lines. The three Asian
economies grew so fast since the end of the 1970s that income per
capita practically doubled during the 15 or so years under analysis.
In the four Latin American countries, growth performance was dis-
appointing. It was close to zero in Argentina and Brazil, positive but
INTRODUCTION 7
small in Mexico, and moderate in Colombia. Taiwan, China, was
poorer than both Brazil and Mexico in 1980, but substantially richer
in the mid-1990s.
All of those changes are likely to have had strong effects on the
distribution of income, because many of them are known to be
strongly income selective. Changes in female participation in the
labor force or in fertility behavior are certainly not uniform across
the population. Moreover, they directly affect per capita income in
the households in which they take place. Likewise, per capita growth
rates as high as 6 percent a year during 15-year periods are likely to
be accompanied by changes in the structure of the economy that
have repercussions on income distribution. Nevertheless, the net
outcome in terms of the change in the Gini coefficient is far from
uniform. It ranges from a decline of 0.4 Gini points in (urban) Brazil
to a rise of 8.4 Gini points in (the Greater Buenos Aires area of)
Argentina.
However, these changes are not perfectly comparable across the
seven economies. For a start, the periods over which each economy
was observed differ somewhat. So does the coverage of the survey,
particularly for Argentina and Brazil. Nevertheless, it is probably
safe to assert that, despite facing broadly similar trends in terms of
demographics, education, urbanization, and female participation,
the seven economies have experienced very different changes in
inequality. How should this observation be interpreted? Can all the
differences be attributed to differences in growth rates or in the sec-
toral composition of output? Did the distributional effects of struc-
tural changes tend to compensate one another more in Brazil and
Malaysia than in Indonesia and Mexico? Or are the distributional
effects of each structural change themselves of smaller size in the
first two economies? How is the net result produced in each eco-
nomy, and why does it differ so much between them? Are changes
in the distribution of income associated with changes in the stock of
education more important than changes in the returns to skills? Are
educational factors more or less important than changes in occupa-
tional choices or fertility patterns? Those questions are taken up
for each economy in chapters 3 through 9 and are summarized in
chapter 10.
Decomposing Changes in Inequality: An Introduction
This study is certainly not the first one in which economists have
tried to decompose changes in inequality in order to gain some
insight into the processes that underlie them. Because the number of
reliable data sets with the required time coverage before World War II
8 BOURGUIGNON, FERREIRA, AND LUSTIG
was very small, it is probably fair to say that the first well-known
empirical study of long-term income distribution dynamics was by
Simon Kuznets (1955). Since then, a good number of studies have
looked at the determinants of changes in poverty and inequality.
The literature is too large to be done justice here, and we do not
propose to survey it comprehensively. However, it may be useful to
distinguish between two broad approaches to distributional change
that are present in the literature. We will refer to the first, which
relies primarily on aggregated data, as the macroeconomic
approach. By contrast, empirical studies relying on fully disaggre-
gated data from household surveys fall under the microeconomic
approach.
Macroeconomic approaches can be further classified into two
groups. The first includes those that use standard regression analy-
sis, relating aggregate poverty or inequality indices as dependent
variables to a set of macroeconomic or structural (supposedly) inde-
pendent variables. There are examples in which the variation occurs
on a time series, as in Blejer and Guerrero (1990) and Ferreira and
Litchfield (2001), and there are examples in which it occurs in a
cross-section, as in Dollar and Kraay (2002), Ravallion (1997), and
Ravallion and Chen (1997). These papers were, to a large extent,
inspired by an earlier literature related to the empirical Kuznets
curve (see, for example, Ahluwalia 1976), which also belongs in this
group.
This approach has at least two serious shortcomings. First, con-
cerns about the endogeneity of many right-hand-side variables that
are included--as well as about biases arising from others that are
not6--mean that the regressions can at best be interpreted as (very)
reduced-form estimates of the relationship between summary
measures of poverty and inequality and a few macroeconomic vari-
ables. Second, although single inequality and poverty indices are
useful summary statistics, they are informationally restricted and
often are not robust to changes in the assumptions underlying their
construction (see Atkinson 1970).
The second group of approaches relies on computable general
equilibrium models. Once again, there is a long lineage. Some
important contributions include Adelman and Robinson (1978);
Bourguignon, de Melo, and Suwa (1991); Decaluwé and others
(1999); and Lysy and Taylor (1980). Computable general equilib-
rium models introduce more structure, but they are still essentially
macroeconomic in nature and capture the distributional effect of
only a limited number of variables, and then only on a limited num-
ber of classes or groups. They are also pure simulation models,
which rely on rough calibration procedures rather than on time-
series or detailed household-level data. These approaches do not
INTRODUCTION 9
capture the most interesting and revealing factors that explain the
evolution of individual or household incomes and thus often appear
inconclusive. This happens because the inherent diversity of indi-
vidual situations and the complexity that characterizes the interac-
tion of endowments, human behavior, and market conditions in
determining individual incomes require a microeconomic focus.
Of course, in parallel with these macroeconomic strands of the
literature on income distribution dynamics there is also an estab-
lished microeconomic tradition. Its distinguishing feature is that
whereas the macroeconomic work relies on aggregated data for
countries or regions, the microeconomic work relies on household-
level data. The most common microeconomic approach found in
the literature is based on decompositions of changes in poverty or
inequality measures by population subgroups.7 In the case of
inequality, the change in some scalar measure is decomposed into
what is due to changes in the relative mean income of various pre-
determined groups of individuals or households, what is due to
changes in their population weights, and--residually--what is due
to changes in the inequality within those groups. When groups are
defined by some characteristic of the household or household head,
such as location, age, or schooling, the method identifies the contri-
bution of changes in those characteristics to changes in poverty or
inequality. The decomposition of changes in the mean log deviation
of earnings in the United Kingdom, by Mookherjee and Shorrocks
(1982), is the best illustration of this type of work.
The comparison of poverty profiles over time (Huppi and
Ravallion 1996) or of poverty probit analyses (Psacharopoulos and
others 1993) belong to the same tradition.8 There are at least
four principal limitations to these approaches. First, the analysis
again relies on summary measures of inequality and poverty, rather
than on the full distribution. Second, the decomposition of changes
in inequality or poverty measures often leaves an unexplained resid-
ual of a nontrivial magnitude. Third, the decompositions do not
easily allow for controls: it is impossible, for instance, to identify the
partial share attributable to each factor in a joint decomposition of
inequality changes by education, race, and gender subgroups.
Finally, they shed no light on whether the contribution of a particu-
lar attribute to changes in overall inequality is due to changes in its
distribution or due to changes in market returns to it. A large share
for education, for instance, might be consistent with large shifts in
the distribution of years of schooling, with changes in returns, or--
indeed--with various combinations of the two.
An alternative approach, which seeks to address all four of these
shortcomings in scalar decompositions, is the counterfactual simu-
lation of entire distributions on the basis of the disaggregated
10 BOURGUIGNON, FERREIRA, AND LUSTIG
information contained in the household survey data set. This
approach was first applied by Almeida dos Reis and Paes de Barros
(1991) for Brazil. Juhn, Murphy, and Pierce (1993) use a technique
of this kind to study the determinants of the increase in wage
inequality in the United States during the 1970s and 1980s. Blau
and Khan (1996) use this approach to compare wage distributions
across 10 industrial countries. A semiparametric version of this
approach is provided by DiNardo, Fortin, and Lemieux (1996) in a
study of U.S. wage distribution between 1973 and 1992, which
essentially relies on reweighing observations in kernel density esti-
mates of continuous distributions of earnings so as to construct
appropriate counterfactual distributions that shed light on the
nature of the change in the actual distribution over time.9
As in the studies cited in the preceding paragraph, the method
proposed and applied in this volume follows in the tradition estab-
lished by Oaxaca (1973) and Blinder (1973). All of these approaches
seek to shed light on what determines differences across income dis-
tributions by simulating counterfactual distributions that differ from
an observed distribution in a controlled manner. Unlike Blau and
Khan (1996); Juhn, Murphy, and Pierce (1993); or, indeed, any of
the aforementioned studies, all of which were concerned with wage
distributions, the analysis in this book seeks to understand the more
complex dynamics of the distribution of welfare, proxied by the dis-
tribution of (per capita or equivalized) household income. The
underlying determinants of this distribution are more complex. In
addition to the quantities and prices of individual characteristics
that determine earnings rates, household incomes depend also on
participation and occupational choices, on demographic trends, and
on nonlabor incomes.
As a result, the approach followed here generalizes the counter-
factual simulation techniques from the single (earnings) equation
model to a system of multiple (nonlinear) equations that is meant to
represent mechanisms of household income generation. This system
comprises earnings equations, equations for potential household
self-employment income, and occupational-choice models that
describe how individuals at working age allocate their time between
wage work, self-employment, and nonmarket time. In some cases, it
also includes equations for determining educational levels and the
number of children living in the household.
In each economy, the model is estimated entirely in reduced form,
thus avoiding the insurmountable difficulties associated with joint
estimation of the participation and earnings equations for each
household member. We maintain some strong assumptions about
the independence of residuals. Therefore, the estimation results are
never interpreted as corresponding to a structural model and no
INTRODUCTION 11
causal inference is drawn. We interpret the parameter estimates gen-
erated by these equations only as descriptions of conditional distri-
butions, whose functional forms we maintain hypotheses about.
Yet, even in this limited capacity, these estimates help us gain useful
insights into the nature of differences across distributions and about
the underlying forces behind their evolution over time.
The most important methodological contribution undertaken in
this book is to generalize the counterfactual simulation approach
to distributional change from earnings to household income distrib-
utions. The approach thus applies to problems related to the dis-
tribution of total income, rather than only those related to the
distribution of earnings. The method can shed light on the evolution
of the entire distribution, rather than merely on the path of sum-
mary statistics. And it can decompose any change in the incomes of
a set of households into its fundamental sources: changes in the
amounts of resources at their disposal (reflected in the population or
endowments effects), changes in how the markets remunerate those
resources (reflected in the price effects), and changes in the decisions
made about how to use those resources (reflected in the occupa-
tional effects).
Within each such category, this approach also allows us to iden-
tify the contributions from specific endowments and prices. Thus,
we can distinguish the effect of changes in returns to education from
those of other "prices," such as the effect of experience or of the
gender wage gap. Analogously, we are able to understand the effect
of changes in the distribution of education separately from that of
changes in demographics. We can then shed some light on how one
affects the other, always in terms of understanding how the condi-
tional distributions of those variables have evolved, rather than
seeking to establish directions of causation. This is as far as our
econometrics allows us to go. But it is farther than we have gone
before.
The proposed methodology has some important advantages over
others that have been used in the field. First, as we shall see, small
changes in aggregate indices of inequality can hide strong counter-
vailing forces. For example, a large reduction in dispersion in the
distribution of years of education could be partially offset by the
inequality-increasing effect of a rising skill premium. Substantial
changes in spatial premiums (such as those evident from wage gaps
between urban and rural areas) may be offset by migration and
changes in labor-force participation (as in the Indonesian case). A
rise in household income inequality arising from increases in the
labor-force participation rates of educated women can be partly off-
set by "progressive" declines in family size (as in the case of Taiwan,
China). Methods that rely on decomposing a scalar measure of
12 BOURGUIGNON, FERREIRA, AND LUSTIG
inequality will gloss over those dynamics. As we show in the subse-
quent chapters, the evolution of the distribution of income is the
result of many different effects--some of them quite large--which
may offset one another in whole or in part. Researchers and policy-
makers may find it useful to disentangle those effects, rather than to
focus on a single dimension.
Finally, the approach used here has an additional advantage.
Because it analyzes the entire distribution of income, one can assess
how different factors affect different parts of the distribution. That
assessment can shed light on how different groups (for example, the
urban versus the rural poor) are affected by changes in the distribution
of assets, changes in the returns to those assets, and changes in how
individuals and households choose to use their assets. The next chap-
ter contains a formal presentation of the approach used in this book,
which we refer to as generalized Oaxaca-Blinder decompositions.
Notes
1. See, among others, Banerjee and Newman (1993), Galor and Zeira
(1993), and Bénabou (2000). For good surveys, see Aghion, Caroli, and
Garcia-Penalosa (1999) and Atkinson and Bourguignon (2000).
2. This volume is the result of a five-year multicountry research effort,
known as the project on the Microeconomics of Income Distribution
Dynamics (MIDD), which was sponsored by the Inter-American Develop-
ment Bank and the World Bank.
3. A slightly modified version of the argument that follows could just as
easily be made for the reverse specification (with inequality explaining
growth) or, indeed, for the joint estimation of a two-equation model.
4. Data availability played a role in selecting economies from these two
regions. The proposed methodology requires the availability of at least two
comparable household surveys, separated by an interval of at least one
decade, so that medium- to long-run structural effects of economic devel-
opment and of changes in the sociodemographic characteristics of the pop-
ulation on the distribution of income may be captured.
5. During the period in which this research project was conducted, a
number of other excellent applications of the methodology have been pro-
duced. They include Altimir, Beccaria, and Rozada (2001) on Argentina;
Bravo and others (2000) on Chile; Dercon (2001) on Ethiopia; Grimm
(2002) on Côte d'Ivoire; and Ruprah (2000) on the República Bolivariana
de Venezuela.
6. Sometimes only GDP is used as the explanatory variable, as in the
Kuznets curve literature.
INTRODUCTION 13
7. This approach draws on earlier, static, decomposition approaches
suggested by Bourguignon (1979), Cowell (1980), and Shorrocks (1980).
8. A related approach decomposes changes in scalar poverty measures
into a component attributable to growth in the mean and one attributable
to changes in the Lorenz curve (a "redistribution component"; see Datt and
Ravallion 1992).
9. An alternative semiparametric approach to the estimation of density
functions, which relies on their close relationship to hazard functions, was
proposed by Donald, Green, and Paarsch (2000).
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2
Decomposing Changes in
the Distribution of
Household Incomes:
Methodological Aspects
François Bourguignon and
Francisco H. G. Ferreira
Many different forces are behind long-run changes in income distri-
butions or, more generally, distributions of economic welfare, within
a population. Some of those forces have to do with changes in the
distribution of factor endowments and sociodemographic charac-
teristics among economic agents, others with the returns these
endowments command in the economy, and others still with modi-
fications in agents' behavior such as labor supply, consumption pat-
terns, or fertility choices. Of course, those forces are not indepen-
dent of one another. In some cases, they tend to offset one another,
whereas in others they could reinforce one another. They are also
likely to be affected by exogenous economic shocks as well as by
government policies and development strategies. For all of these
reasons, it is generally difficult to precisely identify fundamental
causes and mechanisms behind the dynamics of income distribu-
tion. Yet, extracting information about the nature and magnitude of
those forces from observed distributional changes is crucial for an
understanding of the development process and the scope of policy
intervention in the distributional sphere.
17
18 BOURGUIGNON AND FERREIRA
This is a difficult analytical task, and it is tempting to rely on sta-
tistical decomposition techniques that are meant to more or less
automatically identify the main causes for distributional changes.
Such techniques have long been in use in the fields of income and
consumption distribution analysis. Largely for computational rea-
sons, however, they have been limited to explaining differences in
scalar summary measures of distributions, rather than in the full
distributions. In other words, the techniques focused on some spe-
cific definition of aggregate social welfare (or inequality) rather than
on the distribution of individual welfare. Among the best examples
of these techniques are the well-known Oaxaca-Blinder decomposi-
tion of differences in mean incomes across population groups with
different characteristics (Blinder 1973; Oaxaca 1973) and the
variance-like decomposition property of the so-called decomposable
summary inequality measures (Bourguignon 1979; Cowell 1980;
Shorrocks 1980). In both cases, the underlying logic is that the
aggregate mean income (or inequality measure) in a population is
the result of the aggregation of various sociodemographic groups or
income sources. Thus, changes in the overall mean or inequality
measure can be explained by identifying changes in the means and
inequality measures within those groups or income sources, and in
their weights in the population or in total income.
These early decomposition techniques proved to be extremely
useful in several circumstances, and they should still be used as a
first step in explaining changes in distributions of some economic
attributes. Indeed, the Oaxaca-Blinder approach is still often used
to analyze wage discrimination across genders or union status. Like-
wise, decomposing inequality measures such as the Theil coefficient
or the mean logarithmic deviation according to gender, education,
or age groups may often be quite informative about the broad struc-
ture of inequality in a society. At the same time, there is both a
growing need and an increasing computational capacity to work
with the entire distribution, rather than merely with its first moment
or a few inequality indices. In particular, the focus on poverty reduc-
tion, which increasingly drives development policy, requires analysis
of the shape of the distribution in the neighborhood of and below
the poverty line. In terms of the Oaxaca-Blinder approach, the issue
is to know not so much whether mean earnings are lower for women
than for men because the former have less average education, as
whether the differences are greater or smaller for the bottom part of
the earnings distribution. Answering this kind of question requires
handling the whole distribution, rather than summary measures.
Several techniques for decomposing distributional change, rather
than merely changes in individual inequality or poverty measures,
DECOMPOSING CHANGES IN THE DISTRIBUTION 19
have been developed in the past decade or so--in part because of
increasing computational capacity.
The technique used to analyze long-run distributional changes in
this book belongs to this recent stream of new decomposition
methodologies. It is based on a parametric representation of the
way in which household income per capita or individual earnings
are linked to household or individual sociodemographic character-
istics, or endowments. From this point of view, it bears great resem-
blance to the Oaxaca-Blinder approach, except for two points: (a) it
deals with the entire distribution, rather than just the means of
income or earnings, and (b) the parametric representation of the
income-generation process for a household is more complex than
the determination of individual earnings, in ways that we shall dis-
cuss below. As in the Oaxaca-Blinder method, however, the decom-
position of distributional change essentially consists of contrasting
representations of the income-generation process (that is, evaluating
differences in estimated parameters) for two different distributions
(for example, two points in time), on the one hand, and accounting
for changes in the joint distribution of endowments, on the other
hand. Other methods, which do not rely so much on a parametric
representation of individual or household income generation, could
also have been applied to the case studies in the chapters that
follow.1 Yet, it turns out that the parametric representation used
throughout this volume is actually of inherent interest, because
the parameters lend themselves directly to relevant economic
interpretations.
This chapter presents this methodology for decomposing
observed changes in the (entire) distribution of household income
per capita. It opens with a brief survey of decomposition techniques
applied to the mean or to summary measures of income inequality. It
continues with a general statement of the decomposition techniques
that handle the whole distribution, focusing on the parametric
method used in this volume. It then shows the detail of the paramet-
ric representation of household income-generation processes that, in
one way or another, underlies all case studies in this volume. The last
section addresses a number of general econometric issues that arise
in the estimation of the model.
Decomposing Distributional Change: Scalar Methods
The general problem is that of comparing two distributions of
income--or of any other welfare measure2--in a population at two
points in time, t and t . Without too much loss of generality, the two
20 BOURGUIGNON AND FERREIRA
distributions will be represented by their density functions: ft(y) and
ft (y). The objective is to explain the change from ft(y) to ft (y) by a
series of elementary changes concerned with changes in the socio-
demographic structure of the population, in income disparities
across sociodemographic groups or, possibly, in the relative impor-
tance and distribution of a particular income source. Before consid-
ering this general functional problem, we briefly review simple ways
of performing that decomposition when density functions are
replaced by some scalar summary index.
The Oaxaca-Blinder Decomposition of Changes in Means
Although it refers to a decomposition of differences in means,
rather than in distributions, it is convenient to start this short
review with the so-called Oaxaca-Blinder method. Indeed, this
method relies on a general principle that will be extensively used
later. In addition, dealing with the first moments of the distribu-
tions ft(y) and ft (y) should provide some indication as to how one
could deal with higher order moments and, therefore, with inequal-
ity or poverty.
Oaxaca (1973) and Blinder (1973) independently found the fol-
lowing way for comparing the mean earnings of two different pop-
ulations.3 Assume that income may satisfactorily be approximated
by the following linear model in both periods t and t :
(2.1) yit = Xit · t + uit
yjt = Xjt · t + ujt .
In other words, the income of individual i observed in period t is
supposed to depend linearly on a vector of his or her observed char-
acteristics, Xit, and on some unobserved characteristics summa-
rized by the residual term, uit. The same relationship holds for indi-
vidual j observed in period t , who presumably is different from the
individual observed in period t. The coefficients t and t simply
map individual characteristics, X, into income, y. If the components
of X are seen as individual endowments, then the coefficients may
be interpreted as rates of return on those endowments, or as the
"prices" of the services associated with them. Given a sample of
individual observations at time t and another at time t , these prices
may be estimated by ordinary least squares, under the usual
assumption that the residual terms are independent of the observed
endowments.
Consider now the change in mean earnings or income between
periods t and t . Under the innocuous assumption that the expected
value of the residual terms is zero, an elementary transformation
DECOMPOSING CHANGES IN THE DISTRIBUTION 21
leads to the following decomposition of the change in (the cross-
sectional) means:
(2.2) y = yt - yt = t · (Xt - Xt) + Xt · (t - t) .
The change in mean earnings thus appears as the sum of two effects:
(a) that of a change in mean endowments at constant prices (that is, the
endowment effect), and (b) that of a change in prices at constant mean
endowments (that is, the price effect). In other words, the change in the
mean earnings of the population between times t and t is explained by
a change in its mean characteristics (education, age, area of residence,
and so on) and by a change in the rates of return to these characteris-
tics. For instance, when the Oaxaca-Blinder decomposition bears on
gender differences, the gender gap is decomposed into what is due to
(a) the fact that working women and men do not have the same char-
acteristics in terms of education, age, or occupation, and (b) the fact
that, at constant characteristics, they are not paid the same rate.
The practical interest of a decomposition such as equation 2.2 is
obvious. If economic analysis were able to predict or explain
changes in the price system, , then it would be easy to figure out
what such changes may imply for the evolution of mean earnings or
incomes. Of course, this decomposition ignores any possible causal
relationship between the two sources of change. Yet it is likely that
observed changes in prices may be caused at least partly by changes
in the sociodemographic structure of the population, and also that
changes in prices in turn induce some changes in the socio-
demographic structure of the population. For instance, a more edu-
cated labor force may lead to narrower wage-skill gaps, and a wider
wage-skill gap may be an incentive for part of the population to
become more educated.
Three additional points must be noted about the Oaxaca-Blinder
decomposition. First, the decomposition identity (equation 2.2) is path
dependent. Indeed, an identity similar to equation 2.2 is as follows:
y = yt - yt = t (Xt - Xt) + Xt · (t - t) .
In this case, the endowment effect is evaluated using the prices at
period t , whereas the price effect is estimated using the initial mean
endowments. There is no reason for this decomposition to give the
same estimates of the price and endowment effect as equation 2.2.
The path that is used for the decomposition matters.4
A second point to be stressed is that different interpretations may
be given to the endowment and the price effects identified by the
preceding decomposition formula. For instance, the endowment
effect may be interpreted as the effect of simply changing the weight
of various population subgroups that are predefined by common
22 BOURGUIGNON AND FERREIRA
endowments. The price effect could then be interpreted as the effect
of changing the relative mean incomes of these groups. This inter-
pretation may be closer to the definition of the decomposition of
distributional changes given at the beginning of this chapter. Note
also that the decomposition formula (equation 2.2) may be inter-
preted simply as the effect on the mean income of changing the
importance of various income sources, either through the coeffi-
cients, or through the mean endowmentsX. In effect, the decompo-
sition operates through the components tXt of the scalar product
k k
tXt, which may rather naturally be interpreted as different sources
of income.
Finally, the way the Oaxaca-Blinder approach was just presented
might give the impression that it has little to do with the analysis of
inequality, because it is concerned with means. This impression is not
entirely appropriate. Suppose that the decomposition formula (equa-
tion 2.2) is applied at time t to the difference in the mean incomes of
two population groups A and B--men and women, for instance--
rather than being applied to a time difference. Equation 2.2 could
then be rewritten as
y = yB - yA = A · (XB - XA) + XB · (B - A).
This earnings differential represents part of the inequality in
the distribution of earnings (at time t): that part which is due to
differences between groups A and B. The change in inequality
between periods t and t will therefore include, among other
things, the change in the A/B earnings differential. It might thus
be decomposed into a change in the difference in endowments
between groups A and B and a change in the difference in prices
faced by the two groups. This argument simply combines an
application of the Oaxaca-Blinder decomposition in a cross-
section with an application over time. We will see below that the
generalization of the Oaxaca-Blinder method to handle entire dis-
tributions, rather than their first-order moments, involves an
argument of this type.
Decomposing Changes in Income Inequality Measures
The principle behind the foregoing decomposition may also be
applied to higher moments and, in particular, to summary inequal-
ity measures. The "decomposable" or Generalized Entropy inequal-
ity measures are endowed with very convenient decomposition
properties.5 Suppose that the population of income earners is
partitioned into G groups, g = 1, 2, . . . ,G, and denote by Ig the
inequality measure for group g and by I the inequality for the whole
DECOMPOSING CHANGES IN THE DISTRIBUTION 23
population. These measures satisfy the following general property:
G
(2.3) I = Igw(ng, mg) + I¯(n1, y1; n2, y2; ... ; nG, yG) = IW + IB
g=1
where ng and mg stand respectively for the population and income
shares of group g within the whole population and I¯(. . .) is the inequal-
ity between groups--that is to say, the inequality that would be
observed in the population if all incomes were equal within each group
g. The distribution of income would thus consist of n1 times the income
y1, n2 times the income y2, and so forth. Total inequality, I, thus decom-
poses into two terms: the mean within-group inequality, where each
group g is weighted by a weight, w, which depends on population and
income shares, and the between-group inequality, I¯(. . .).
The preceding property is intuitive because it resembles the well-
known decomposition of variances across population subgroups. In the
present context, however, we are less interested in the decomposition
among groups at a point in time than in that of the change in inequal-
ity between two points in time. Differentiating equation 2.3, it follows
that the change in overall inequality, I, may be expressed as the sum
of the change in within-group inequality, IW, and the change in
between-group inequality, IB. In turn, both changes may be expressed
as linear combinations of changes in within-group inequality measures
Ig, and changes in population and income shares, ng and mg.6
The mean logarithmic deviation is the simplest of all decompos-
able measures. Its expression for a population of n individuals i is
the following:
n
L = 1Log( y/yi).
n
i=1
It is easily shown that the preceding decomposition formula
(equation 2.3) writes, in this case
G G
L = ngLg + ngLog(y/yg) = IW + IB.
g=1 g=1
Finally differencing this expression between two periods t and t
yields the following:7
G y
L yg
ng -
y
g=1 yg
G G
(2.4) + Lg + Log(y/yg) ng + ng Lg.
g=1 g=1
The total change in inequality is thus expressed as the sum of
three types of effects: (a) changes in the relative mean income of the
24 BOURGUIGNON AND FERREIRA
groups, (b) changes in group population weights,8 and (c) changes
in within-group inequality. Analogous expressions can be derived
for the other members of the family of decomposable inequality
measures.
For practical purposes, this decomposition methodology is imple-
mented as follows. Suppose that the population of earners has been
partitioned by educational attainment: no schooling, primary, lower
secondary, and so forth. Then, following the preceding decomposi-
tion, the change in overall inequality between year t and t may be
analyzed as the sum of (a) the effects of changes in relative earnings
by educational level, (b) the effects of changes in the educational
structure of the population, and (c) the effects of changes in inequal-
ity within educational groups. Thus, the last term is often taken as a
kind of residual, corresponding to that part of the change in inequal-
ity that is not explained by the change in mean incomes across edu-
cational groups and the educational structure of the population.
Of course, the preceding decomposition can be implemented for
all possible observed characteristics of individuals in the population
and, indeed, for all possible combinations of characteristics. For
instance, groups may be defined simultaneously by the education of
the household head, his or her age, his or her area of residence, or the
number of people in the household. There are numerous applications
of this decomposition methodology, starting with the analysis of the
evolution of inequality in the United Kingdom by Mookherjee and
Shorrocks (1982). One of the reasons for its appeal is its analogy
with the Oaxaca-Blinder decomposition: changes in group relative
incomes play a role similar to the changes in the price coefficients, ,
whereas the change in groups' population weights is another way of
representing the changes in the sociodemographic structure of the
population, Xt - Xt. There are two basic differences between these
two approaches, beyond the fact that one is applied to mean incomes
and the other to income inequality. First, the inequality decomposi-
tion formula is nonparametric, whereas the Oaxaca-Blinder relies on
a linear income model.9 Second, the inequality decomposition has a
residual term--the change in within-group inequality--which is inde-
pendent of the inputs of the Oaxaca-Blinder decomposition.10
This residual is one of the sources of dissatisfaction with the pre-
ceding methodology. In empirical applications, it turns out to be an
important component of observed change in inequality, even though
it does not lend itself to an economic interpretation as easily as the
other two components. Another source of dissatisfaction is that it
seems somewhat restrictive to analyze changes in distribution
through a single summary inequality measure. Of course, this
decomposition might be combined with the Oaxaca-Blinder decom-
position, thus yielding information on the change in the mean as
DECOMPOSING CHANGES IN THE DISTRIBUTION 25
well as on the disparity of incomes. But that disparity is still sum-
marized by a single index. Using alternative indices belonging to the
general class of decomposable inequality measures is always possi-
ble but never quite as convincing as looking at differences across the
entire distribution.
A final problem with the decomposition of changes in decompos-
able inequality measures is that it applies to a disaggregation of the
population into subgroups, but not to a disaggregation of income
by sources. Suppose that the income of individual i may be expressed
as the sum of incomes coming from two sources, say, wages (1) and
self-employment (2): yi = y1 + y2 .
i i
It may be interesting to decompose the change in the inequality
of total income into what is due to the changes in the means and in
the inequality of income sources 1 and 2. The preceding decompo-
sition formulas do not work in this case. In particular, it is simply
not true that total inequality is the weighted average of the inequal-
ity of each income source. The covariance of the two sources within
the population is of obvious importance.
Shorrocks (1982) shows the way in which total inequality Iy at a
point in time can be decomposed into the inequality coming from
the various income sources. In particular, he shows that, for E2, the
Generalized Entropy measure with = 2, it is identically true that
(2.5) E2 = cov(yj, y) yj (E2 E2 )1/2
j
j var(yj)var(y) y
where cov(yj, y) is the covariance between the income source j
(= 1, 2) and total income in the population. In other words, the
ratio of this covariance and the variance of total income may be
interpreted as the percentage contribution of income source j to
total inequality, whatever the inequality measure being used.
It turns out that this decomposition is somewhat difficult to use
when time changes are considered. Indeed, to analyze how a change
in the distribution of an income source--say, source 1--may modify
the overall inequality of income, one must first figure out how this
change may modify the covariance between that income source and
total income. Doing so requires figuring out how the change in the
distribution of source 1 may itself modify the covariance between
the incomes of sources 1 and 2. In other words, the analyst must not
operate only at the level of the marginal distribution of income of
one source but at the level of the joint distribution of incomes aris-
ing from the various sources. The need to handle this joint distribu-
tion may explain why the preceding property of decomposability by
income source is seldom used in empirical work on distributional
changes.11
26 BOURGUIGNON AND FERREIRA
Decomposing Changes in Poverty and the Need for
Distributional Analysis
Poverty measures are scalars that summarize the shape of the distri-
bution of income up to some arbitrary poverty line, z. The simplest
poverty measure is the headcount ratio, H, which is simply the value
of the cumulative distribution function at the poverty line. Other
poverty measures may be defined on the basis of specific axioms.
There is an infinity of poverty measures associated with any given
poverty line, z, as there is an infinity of inequality measures. Among
the properties frequently desired from poverty measures is subgroup
decomposability, which simply requires poverty to be additive with
respect to a partition of the whole population into two groups.
Thus, if Pz is the poverty measure for the whole population when
the poverty line is z and if Pj measures poverty in group j, the
z
following property should hold:
Pz = wj · Pj
z
j
where wj stands for the demographic weight of group j, as before.
Clearly, this property holds for the headcount ratio. In effect, all
poverty measures based on the sum of individual income depriva-
tion (z - yi) caused by poverty, whatever way in which this depri-
vation is measured, satisfy this property.12
Given the linear structure implied by subgroup decomposability,
something akin to the Oaxaca-Blinder decomposition principle
applies. Differencing the preceding expression with respect to time,
we obtain the following:
(2.6) Pz = wj · Pj +
z Pj
z wj.
j j
In other words, the change in total poverty is decomposed into a
component that is due to changes in poverty within groups and into
a component that is due to changes in the population weights of the
groups. If groups are defined by common sociodemographic char-
acteristics, it may be said that the second term corresponds to the
endowment effect in the Oaxaca-Blinder decomposition. The first
term partly accounts for changes in prices and behavior that may
generate changes in the mean income of a group and, therefore,
changes in total poverty. But the change in total poverty also partly
depends on changes in the distribution of income within groups.
This was already the case with the residual term in the decomposi-
tion of a change in inequality (see equation 2.4). Unlike in the
decomposition of inequality, however, here it is not possible to
DECOMPOSING CHANGES IN THE DISTRIBUTION 27
isolate these two effects. The basic reason is that inequality is defined
on relative incomes, and it is therefore independent from the general
scale of incomes and from the mean. On the contrary, poverty
depends on the distribution of absolute incomes. As a consequence,
a change in the general scale of incomes--and therefore in mean
income--has a complex effect on poverty, which depends on the
shape of the distribution around (and below) the poverty line.
It is, therefore, impossible to have changes in group mean
incomes--which we have suggested are analogous to price and pos-
sibly behavioral effects--appearing explicitly in a simple way in the
decomposition formula for poverty changes, as was the case for
decomposable inequality measures. For poverty measurement,
changes in mean incomes cannot be straightforwardly disentangled
from distributional changes. Thus, poverty changes cannot be
decomposed into endowment, price, and behavioral effects without
considering the actual distribution within groups, rather than merely
some summary poverty measure for each of those groups.13
A better understanding of changes in poverty thus requires a
more disaggregated approach to distributional dynamics. And
poverty is not the only reason to invest in developing such an
approach. As indicated earlier, a combination of the standard
Oaxaca-Blinder decomposition of changes in means with various
inequality decompositions by population subgroup is hardly a direct
and effective method to understand disaggregated changes in a dis-
tribution of income. The next section proposes a generalization of
the Oaxaca-Blinder framework to deal directly with full distribu-
tions, rather than just means or other scalar indices.
Decomposing Distributional Change: Nonparametric
and Parametric Methods for Entire Distributions
A Simple Generalization of Oaxaca-Blinder: Distributional
Counterfactuals
This section offers a general formulation of the way in which the
preceding scalar decomposition analysis may be extended to the
case of distributional changes. Let ft(y) and f t(y) be the density
functions of the distribution of income, y, or any other definition of
economic welfare, at times t and t . The objective of the analysis is
to identify the factors responsible for the change from the first to the
second distribution.
To do so, it seems natural to depart from the joint distributions
(y, X), where X is a vector of observed individual or household
28 BOURGUIGNON AND FERREIRA
characteristics, such as age, education, occupation, and family size.
The superscript (= t, t ) denotes the period in which this joint dis-
tribution is observed. The distribution of household incomes, f(y),
is of course the marginal distribution of the joint distribution
(y, X):
(2.7) f (y) = ··· (y, X) dX
C(X)
where the summation is over the domain C(X) on which X is
defined. Denoting g(y|X), the distribution of income conditional
on X, an equivalent expression of the marginal income distribution
at time is
(2.8) f (y) = ··· g (y |X) (X) dX
C(X)
where (X) is the joint distribution of all elements of X at time .
Given that elementary decomposition, it is a simple matter to
express the observed distributional change from ft( ) to f t ( ) as a
function of the change in the two distributions appearing in equa-
tion 2.8--that is to say, the distribution of income conditional on
characteristics X, g(y|X), and the distribution of these character-
istics, (X) . To do so, define the following counterfactual
experiment:
(2.9) fgtt (y) = ··· gt (y |X) t (X) dX.
C(X)
This distribution would have been observed at time t if the distribu-
tion of income conditional on characteristics X had been that
observed in time t . This counterfactual distribution may be calcu-
lated easily once the conditional distributions gt(y|X) and gt ( y|X),
as well as the marginal distribution t(X), have been identified. Like-
wise, one may define the counterfactual
(2.10) ftt (y) = ··· gt (y |X) t (X) dX
C(X)
where, this time, it is the joint distribution of characteristics that has
been modified. Note that this latter distribution could also have
been obtained starting from the period t and replacing the condi-
tional income distribution of that period by the one observed in
DECOMPOSING CHANGES IN THE DISTRIBUTION 29
period t. In other words, it is identically the case that, with obvious
notations,
(2.11) fg tt (y) f t t(y) and f tt (y) fg t t(y).
On the basis of the definition of these counterfactuals, the observed
distributional change f t (y) - ft(y) may now be identically decom-
posed into
(2.12) f t (y) - f t(y) fgtt(y) - f t(y) + f t (y) - fgtt (y) .
As in the Oaxaca-Blinder equation, the observed distributional
change is expressed as the sum of a price-behavioral effect and an
endowment effect. Indeed, the first term on the right-hand side of
equation 2.12 describes the way in which the distribution of
income has changed over time because of the change in the distri-
bution conditional on characteristics X. In other words, it shows
how the same distribution of characteristics--that of period t--
would have resulted in a different income distribution had the
conditional distribution g(y|X) been that of period t . To see that
the second term is indeed the effect of the change in the distribu-
tion of endowments that took place between times t and t , one
can use equation 2.11 and rewrite the preceding decomposition
formula as follows:
(2.13) f t (y) - f t(y) = fgtt (y) - f t(y) + f t (y) - ft t (y) .
The main difference with respect to the Oaxaca-Blinder approach
and the decomposition of scalar inequality measures reviewed ear-
lier is that this decomposition--and the counterfactuals it relies
on--refer to full distributions, rather than just to their means. Tak-
ing means on equation 2.12 or 2.13 under the parametric assump-
tion that the conditional mean of g(y|X) may be expressed as X
would actually lead to the Oaxaca-Blinder equation (equation 2.2).
More generally, the decomposition formula (equation 2.13) may be
applied to any statistic defined on the distribution of income, f (y):
mean, summary inequality measures (and not only those which are
explicitly decomposable), poverty measures for various poverty
lines, and so forth.
The only restrictive property in the preceding decomposition is
the path dependence already discussed in connection with the
Oaxaca-Blinder equation. In the present framework, this property
means that changing the conditional income distribution from the
one observed in t to that observed in t does not have the same effect
on the distribution when this is done with the distribution of
30 BOURGUIGNON AND FERREIRA
characteristics X observed in t, as when X is observed in t . In the
present general case, this means that
fg
tt (y) - f t(y) = f t (y) - fg t t (y) .
However, the difference is likely to be small when the change in
conditional income distributions g(y |X) is small.14
Extending the Scope of Counterfactuals
In the preceding specification, all the characteristics X were consid-
ered on the same footing. But it might be of interest in some
instances to decompose further the change in the distribution of
these characteristics. For example, one might want to single out the
effect of the change in the distribution of schooling or of family size.
Doing so simply requires extending the conditioning chain in equa-
tion 2.8 and defining new counterfactuals as described below.
For any partition (V, W) of the variables in X, the conditioning
chain (equation 2.8) may be rewritten as
f (y) = ··· g(y |V, W)h(V |W)(W) dV dW
C(V,W)
whereh(V |W) is the distribution of V conditional on W and (W)
the marginal distribution of W. The set of counterfactuals may then
be enlarged by modifying the conditional distribution of V. All com-
binations of the three distributions--gg(y |V, W), hh(V |W), and
(W) with g, h, = t or t --may be considered as generating a
specific counterfactual. Two particular counterfactuals are the actual
distributions themselves. They are obtained with the combinations
g = h = = t or t .
Comparing two counterfactuals that differ by only one distribu-
tion gives an estimate of the contribution of the change in that partic-
ular distribution to the overall distributional change. Of course, there
are many paths for evaluating this contribution, with no guarantee
that all these paths will generate the same estimate. For instance, the
contribution of the change in the distribution of V conditional on W
may be evaluated by comparing f t(y) and the following:
fh
tt (y) = ··· gt(y |V, W) ht (V |W) t(W) dV dW.
C(V,W)
But, with obvious notations, it could also be obtained by com-
paring fg tt (y) and fgtt (y) and f t (y).
,h (y) or fh t t
If necessary, a more detailed conditioning breakdown of vari-
ables in V could be considered. For instance, it might be of interest
DECOMPOSING CHANGES IN THE DISTRIBUTION 31
to analyze the effect of a change in the distribution of some compo-
nents of V conditional on the others, thus breaking down ht(V |W)
into h1(V1|V-1, W) h-1(V-1|W), where V-1 stands for the compo-
nents of V different from V1. Following the same steps as above, this
breakdown opens other counterfactuals and other decomposition
paths.15
A Parametric Implementation of the Decomposition of
Distributional Change
This decomposition analysis may be directly implemented using non-
parametric representations--such as kernel density estimates--of the
appropriate distributions. With enough observations, it is indeed
possible to obtain a nonparametric representation of all the condi-
tional distributions involved in defining counterfactuals. In practical
terms, however, this may require a discretization of the distribution
of the conditioning variables (V, W) or, in other words, defining
groups of individuals with specific combinations of variables V and
W. An example of such a use of the general decomposition principle
above is provided by DiNardo, Fortin, and Lemieux (1996).16
For reasons that have mostly to do with the interpretation of the
results of this decomposition, the various studies in this book rely
instead on a parametric representation of some of the distributions
used for defining counterfactuals. Indeed, dealing with changes in
parameters with direct economic meaning, such as the return to
education or the age elasticity of labor force participation, makes
the discussion of the decomposition results quite fruitful. This sec-
tion discusses the general principles behind this parametric analysis.
A general parametric representation of the conditional functions
g(y |V, W) and h(V |W) relates y and (V, W), on the one hand,
and V and W on the other hand, according to some predetermined
functional form. These relationships may be denoted as follows:
y = G[V, W, ; ]
V = H[W, ; ]
where and are sets of parameters and and are random
variables-- is a vector if V is a vector. These random variables play
a role similar to the residual term in standard regressions. They are
meant to represent the dispersion of income y or individual charac-
teristics V for given values of individual characteristics (V, W), and
W, respectively. They are also assumed to be distributed indepen-
dently of these characteristics, according to density functions ( )
and µ( ). Finally, the functions G and H have preimposed func-
tional forms.
32 BOURGUIGNON AND FERREIRA
With this parameterization, the marginal distribution of income
in period may be written as follows:
f (y) = () d
G(V,W,; )=y
(2.14) × µ() d (W) dV dW.
H(W,, )=V
Counterfactuals may be generated by modifying some or all of the
parameters in sets and , the distributions ( ) and µ( ), or the
joint distribution of exogenous characteristics, (W). These coun-
terfactuals may thus be defined as follows:
D[ , , µ; , ] = () d
G(V,W,; )=y
(2.15) × µ() d (W) dV dW
H(W,, )=V
where any of the three distributions ( ), µ( ), and µ( ), and the two
sets of parameters, and can be those observed at time t or t .
For instance, D[ t, t, µt; t, t] would correspond to the distrib-
ution of income obtained by applying to the population observed at
time t, the income model parameters of period t , while keeping con-
stant the distribution of the random residual term, , and all that is
concerned with the variables V and W. Thus, the contribution of the
change in parameters from to may be measured by the differ-
t t
ence between D[ t, t, µt; t , t] and D[ t, t, µt; t, t], which
is ft(y). But, of course, other decomposition paths may be used. For
instance, the comparison may be performed using the population
observed at time t as a reference, in which case the contribution
of the change in the parameters would be given by
D[ t, t , µt ; t, t] - D[ t, t , µt ; t, t ] (where the notation
"-" stands for distributional differences). Note that the decompo-
sition may also bear on some subset of the and parameters.
In this parametric framework, the number of decomposition
paths may become very large. Thus, the contribution of each indi-
vidual change in the and parameters, in the distribution of the
random or residual terms, ( ) and µ( ), and finally in the whole dis-
tribution of exogenous characteristics, ( ), may be evaluated in
many different ways. The choice depends on what value is given to
DECOMPOSING CHANGES IN THE DISTRIBUTION 33
the other parameters or the functions used for the other distribu-
tions. In general, a single decomposition path is used. But it is impor-
tant to compare the results with those obtained on different paths to
see whether they are very different and, if so, to understand the rea-
sons for the differences.17
A Parametric Representation of the Income-Generation
Process
This section is devoted to particular applications of the preceding
methodology--that is, to a specific set of variables X = (V, W) and
some specification of the functions G( ) and H( ) above. The actual
specifications used in the various chapters in this volume differ
somewhat across economies, but they do share a common base,
which is described below.
The Simple Case of Individual Earnings
If it were to be applied to the distribution of individual earnings, the
preceding methodology would be rather simple. If we ignore for the
moment the partition of X into exogenous characteristics (W) and
nonexogenous individual characteristics (V), a simple and familiar
parametric representation of individual earnings as a function of
individual characteristics is given by the following:
(2.16) Log y = X · + .
In this particular case, the function G( ) thus writes as follows:
G(X, ; ) = eX · + .
To obtain estimates for the set of parameters and for the distri-
bution of the random term , one may rely on standard econometric
techniques. Running a regression on samples of observations i avail-
able at time ,
Log yi = Xi ·
+ i
yields an estimate of the set of parameters , as well as of the
distribution ( ) of the random term. Then, the counterfactuals
D( ) defined earlier in (2.15) can be computed easily. Without
the (V, W) distinction, a counterfactual is now defined as
D(, ; ), where (W, ) is the joint distribution of the exogenous
components of (V, W). Switching to a discrete representation
{yi} = (y1, y2, ..., yN) of the distribution at time , where N is
34 BOURGUIGNON AND FERREIRA
the number of observations in the sample available at time = t, t ,
it is identically the case that
D(t, t, t) = {yi}t.
The counterfactual, D(t, t, t) = {yi}tt , is obtained by
computing
Log (yi)t t = Xi ·
t ^ t + ^i
t for i = 1, 2, ... , Nt
where the notation ^ stands for ordinary least squares estimates.
This counterfactual is thus obtained by simulating the preceding
model on the sample of observations available at time t. This simu-
lation shows what would have been the earnings of each individual
in the sample if the returns to each observed characteristics had
been those observed at time t rather than the actual returns
observed at time t.18 The returns to the unobserved characteristics
that may be behind the residual term ^i are supposed to be
t
unchanged, though. This is equivalent to the evaluation of the price
effect for observed characteristics in the Oaxaca-Blinder calcula-
tion. The difference is that the evaluation is carried out for every
individual in the sample.
The counterfactual on the distribution of the random term
D(t, t , t) = {yi}tt is a little more difficult to construct. Import-
ing the distribution of residuals from time t to time t requires an
operation known as a rank-preserving transformation, whereby the
residual in the nth percentile (of residuals) at time t is replaced by the
residual in the nth percentile at time t , for all n. As this operation is
not immediate when the number of observations is not the same in
the two samples, an approximate solution is used. It consists of
assuming that both distributions of residual terms are the same up
to a proportional transformation. An example would be if residuals
were normally distributed, with mean zero. The rank-preserving
transformation is then equivalent to multiplying the residual
observed at time t by the ratio of standard deviations at time t and
t.19 D(t, t , t) = {yi}tt is thus defined by
Log (yi)tt = Xi ·
t ^ t + ^i · (^ /^)
t t t for i = 1, 2, ... , Nt.
With those counterfactuals at hand, estimates of the contribution to
the observed overall distributional change between t and t of the
change in the parameters, in the distribution of residuals (), and
possibly of these two changes taken together may easily be found.
The effect of changing the distribution of individual endowments,
X, is obtained as the complement of the two previous changes:
{yi}t - D(t, t , t ).
DECOMPOSING CHANGES IN THE DISTRIBUTION 35
This technique is intuitively simple, and a very similar methodology
has been in use in the literature on earnings distribution ever since it
was introduced by Juhn, Murphy, and Pierce (1993). Things are
slightly more complicated when dealing with household incomes.
The additional complication arises from the need to take into
account behavior related to participation in the labor force or,
equivalently, the presence of various potential earners within a
household.
A Household IncomeGeneration Model
Moving from individual earnings to household income per capita
requires adding the earnings of the various members of the house-
hold and dividing by the total number of persons, or adult equiva-
lents. This computation in turn requires considering not only the
earnings of those people who are active but also the participation
behavior of all the people of working age. Indeed, one reason the
distribution of household income may change over time is that mem-
bers may change occupation.20 In an imperfect labor market, more-
over, it may also be necessary to take into account the segment of
the labor market in which active people work. The model presented
below incorporates these various aspects in the specification of the
function G(V, W, ; ).
The first component of the model is an identity that defines
income per capita in a household h, with nh persons in it:
1 nh J
(2.17) yh = j j se .
nh Ihi yhi + yh + y0h
i=1 j=1
In this expression, household income is defined as the aggregation
of the earnings yhi across individual members i and activities j, of
joint household self-employment income yh , and of unearned
se
income such as transfers or capital income, y0 . Individual earnings
h
may come from different activities, j = 1, 2, ... , J . The variables
Ihi are indicator variables that take the value 1 if individual i par-
j
ticipates in earning activity j, and 0 otherwise. The set of activities
may differ across studies. In studies in which self-employment
income is reported at the individual level, this set essentially com-
prises wage work or self-employment, both full- and part-time, and
possibly a combination of part-time wage work and self-employ-
ment. In studies in which self-employment income is reported at the
household level, being employed in the family business may be taken
as an additional activity, J + 1, whereas J would include full-time or
part-time wage work, possibly combined with part-time work in the
36 BOURGUIGNON AND FERREIRA
family business. Since some of these alternative occupations involve
both wage work and self-employment, each occupation in the J + 1
set is exclusive of another occupation. It is thus the case that
J +1 j
j=1 Ihi = 0 or 1, with 0 corresponding to inactivity.
The allocation of individuals across these J or J + 1 activities is
represented through a multinomial logit model. It is well known
(see McFadden 1974) that this model may be specified in the
following way:
Ihi = 1 if Zhi
s Ls+ i > Max(0, Zhi
Ls Lj + i ),
Lj
j = 1, ... , J + 1, j = s
(2.18)
Ihi = 0 for all s = 1, ... , J + 1 if Zhi
s Ls + i 0
Ls
for all s = 1, ... , J + 1
where Zhi is a vector of characteristics specific to individual i and
household h, Ls are vectors of coefficients, and Ls are random
variables identically and independently distributed across individu-
als and occupations according to the law of extreme values. Within
a discrete utility-maximizing framework, Zhi Ls+ i is to be inter-
Ls
preted as the utility associated with occupation s, with Ls standing
for unobserved utility determinants of occupation s and the utility
of inactivity being arbitrarily set to 0.21 Note, however, that this
interpretation in terms of utility-maximizing behavior is not fully
justified because occupational choices may actually be constrained
by the demand side of the market, as in the case of selective
rationing, rather than by individual preferences.
Observed heterogeneity in earnings in each occupation j can be
described by a log-linear model reminiscent of the well-known
Mincer model:
(2.19) log yhi = Xhi
j wj + wjhi wj for i = 1, ... , nh
where Xhi is a vector of individual characteristics, wj a vector of
coefficients, and hi a random variable supposed to be distributed
wj
identically and independently across individuals and occupations,
according to the standard normal law. Under those conditions, wj
is to be interpreted as the unobserved heterogeneity of individual
earnings in occupation j. To simplify, earnings functions are often
assumed to differ across activities only through the intercepts, so
that all components of wjbut one are identical across occupations
and wj = w. Finally, self-employment income at the household
level is assumed to be given by
se
(2.20) Log yh = Yh,
se Ihi ,
se Ihi Xhi
se · se+ seh . se
i Ihi
DECOMPOSING CHANGES IN THE DISTRIBUTION 37
The first component of the vector in brackets is a set of household
characteristics, including available assets in the self-employment
activity. The second component is the number of family members
involved in that activity, and the third is a vector that corresponds
to their average individual characteristics. As before, se is a vec-
tor of coefficients, and h is a random variable distributed as a stan-
se
dard normal. Thus, se stands for the unobserved heterogeneity of
household-level self-employment income.
The model is now complete. Together, equations 2.17 to 2.20
give a full description of household incomegeneration behavior
and correspond to the function G( ) discussed earlier. The (V, W)
variables are now replaced by the X, Y, and Z characteristics of
households and household members. Parameters are all the coeffi-
cients included in ( Lj , wj, se), and random variables are the
residual terms in the occupational-choice model, Lj ; the earning
equations, wj; and the self-employment function, se. The only dif-
ference with respect to the general parametric formulation discussed
earlier is that the parameterization now extends to the distribution
of the random variable terms. These terms are now assumed to be
distributed according to some prespecified law, with parameters
given by the standard errors (w, se) in the case of the normal dis-
tributions for (wj, se). This parameterization of the distribution of
random terms introduces some approximation in the decomposition
methodology. However, because the normal distribution fits rather
well with distributions of (log) earnings or self-employment income,
the approximation error is likely to be small.
Econometric estimates of all parameters ( ^Lj wj se
, ^ , ^ ), of the
standard errors (^ , ^ ), and of individual residual terms
wj s
se
(^ , ^ , ^s ) may be obtained on the basis of samples of observa-
Ly¨ wy¨ se
tions available in t and t . Then the parametric decomposition
technique described in the preceding section may be applied, after
substituting the distributions ( ) and µ( ) by (^ , ^ ). Typically,
wj se
the model described in equations 2.17 through 2.20 is evaluated for
each household in the sample of period t after substituting the para-
meters ( ^Lj wj se
, ^ , ^ s ), or a subset of them, by their counterpart in
period t . This microsimulation exercise is less simple than the
derivation of counterfactual distributions in the case of individual
earnings but does not involve any particular difficulty.
Some issues concerning the econometric estimation of the model
are discussed in the next section. Yet an important point must be
stressed at this stage. The estimates of the earnings functions (equa-
tion 2.19) and self-employment functions (equation 2.20) are based
on subsamples of individuals and households with nonzero earnings
or income in the corresponding activity, which requires controlling
38 BOURGUIGNON AND FERREIRA
for selection biases. The residual terms (^ , ^s ) are directly
wj se
observed only for those individuals or households with nonzero
earnings or self-employment income. Simulating the complete
household income model (equations 2.17 to 2.20) requires that an
estimate be available for every random term ( , s ). For instance,
wj se
it is possible that individual i in household h who is observed as
inactive in period t would become a wage worker when the coeffi-
cients of year t , ^Lj, are used in the occupational model (equa-
t
tion 2.18). The earnings to be imputed to that individual in this
counterfactual experiment are given by equation 2.19. The first part
on the right-hand side of that equation is readily evaluated, but
some value must be given to the corresponding random term in hi , wj
because it is not observed. A simple solution consists of drawing
that value randomly in a standard normal distribution. In effect,
doing so involves drawing from conditional distributions rather
than a standard normal distribution because of the obvious endoge-
nous selection of people into the various types of occupations (see
below for more detail). Note also that the same remark applies to
the residual terms, , which are also unobserved. They must be
Lj
drawn from extreme value distributions in a way that is consistent
with observed occupational choices.
The preceding specification of the income-generation model may
appear as unnecessarily general. The reason for such a general formu-
lation is that it encompasses different specifications used in the case
studies in this book. Each of these specifications is individually sim-
pler than the preceding general model in some aspects and slightly
more complicated in others. A simplification common to all case stud-
ies is that both the occupational model (equation 2.18) and the indi-
vidual earnings equation (equation 2.19) are logically defined on
household members at working age. Another important simplifica-
tion is that individual and household self-employment income are
never observed simultaneously. Thus, equation 2.20 is irrelevant when
self-employment income is observed at the individual level, and equa-
tion 2.19 is estimated only for wage employment (rather than allow-
ing for individual self-employment) when self-employment income is
registered at the household level. Additional complexity arises from
the facts that (a) some studies rely on earnings functions that differ
across labor-market segments (defined by gender and by rural and
urban areas) and (b) most studies rely on different occupational-
choice models for household heads, spouses, and other household
members of working age. Those variations do not modify the under-
lying logic of the income-generation model (2.172.20). They were
ignored in the preceding discussion for the sake of notational simplic-
ity. At the same time, they show how rich the representation of the
income-generation model summarized by the function G( ) can be.
DECOMPOSING CHANGES IN THE DISTRIBUTION 39
Before turning to some econometric issues linked to the estima-
tion of the model, we should say a word about the specification
adopted for the second stage of decomposition--that is to say, the
function H( ), which relates the set of variables V to those in W and
. Two characteristics are treated as conditional at this second stage:
individual education and the number of children in the household.
The conditional distribution of the latter variable is represented
through a multinomial logit, as in equation 2.18:
nch = m if Yh D Nm + hNm> Max 0, Yh D Nj + h Nj ,
j = 1, ... , M, j = m
(2.21)
nch = 0 if Yh D Nj+ h 0 for all j = 1, ..., M
Nj
where Yh is a subset of household and individual characteristics--
D
essentially the age, the education level, and the region of residence of
the household head and of his or her spouse, if present. Here Nj is
a vector of coefficients, h are independent random variables dis-
Nj
tributed according to the law of extreme values, and M is some upper
limit on the number of children. Likewise the number of years of
schooling, Xhi , of an individual i in household h is related to some
E
simple demographic variables Xhi such as age, gender, and region of
D
residence, through the same type of multinomial logit specification:
Xhi = s if Xhi
E D Es + hi > Max 0, Xhi
Es D Ej+ hi ,
Ej
j = 1, ... , S, j = s
(2.22)
Xhi = 0 if Xhi
E D Ej+ h 0 for all j = 1, ..., S
Ej
where Ej is a matrix of coefficients, hi a set of independent ran-
Ej
dom variables distributed according to the law of extreme values,
and S the maximum number of years of schooling.22
The preceding multinomial logit specification is not particularly
restrictive. As before, applying the microsimulation methodology to
this specification amounts to modifying the distribution of educa-
tion or family size conditionally on demographic characteristics, by
replacing the coefficients estimated for period t with those for period
t in the preceding conditional system. Doing so requires drawing
values for the residual variables, , in a way that is consistent with
observed choices. But then, it may readily be seen that this is equiv-
alent to changing the distribution of education or family sizes
through simple rank-preserving transformations, conditionally on
demographic characteristics.
It is worth concluding the discussion of the income-generation
model used in the rest of this book with an important warning on
the epistemological nature of this decomposition exercise. It will
have been noted that equations 2.21 and 2.22 are not proper
40 BOURGUIGNON AND FERREIRA
economic models of fertility or schooling. They are purely statistical
models, aimed at representing in a simple way the distribution of
some variable conditionally on others, thus enabling us to perform
the switches required by the methodology for decomposing distri-
butional changes in a manner consistent with the covariance pat-
terns observed in the data. To some extent, the same may be said of
the income-generation model shown in equations 2.17 through
2.20. Earnings or income equations 2.19 and 2.20 might be inter-
preted as the outcome of the labor market and self-employment
production. In that sense, there is something of an economic model
behind these equations. This injunction is not true, however, of sys-
tem 2.18, which describes the allocation of individuals across occu-
pations. If this discrete choice specification were to be taken as a
structural model of labor supply, then it would be necessary to
explicitly introduce the wage rate or productivity of self-employ-
ment in that specification, as well as to introduce nonlabor income.
Instead, equation 2.18 should be seen as a reduced-form specifica-
tion. Comparing it at two points in time provides information on
the identity of the individuals who modified their occupation over
time, but not on the reasons they did so.
It would thus be incorrect to rely on counterfactual distributions
where only earnings equations are modified to identify the total dis-
tributional effect of changes in wages. Only the direct effects can be
captured in this way. Indirect effects that operate through the impact
of these wage changes on labor supply cannot be identified sepa-
rately from changes in the occupational structure of the labor force.
Without a structural specification of occupational choices, instead
of the reduced form (equation 2.18)23 and additional economywide
modeling, there unfortunately is no solution to this identification
problem. It is important to keep this "partial equilibrium" nature of
the decomposition methodology in mind when analyzing the results
obtained in the case studies in this book.24
Some General Econometric Issues
Estimating the complete household income model (2.172.20) in its
general form above would be a formidable undertaking, for several
reasons. First, all the equations of the model clearly should be esti-
mated simultaneously, with nonlinear estimation techniques,
because of the discrete occupational-choice model and because of
the likely correlation among the unobservable terms in the various
equations. In particular, if the allocation of individuals across occu-
pations is in some sense consistent with utility maximization, then
the random term L cannot be considered independent from the
DECOMPOSING CHANGES IN THE DISTRIBUTION 41
random terms in the earnings and self-employment equations, w
and se. Indeed, if an individual finds a salaried job with higher earn-
ings than individuals who have the same observable characteristics,
he or she is likely to be observed in that job, too. Although extremely
intricate, such simultaneous estimation might be manageable--
probably under some simplifying assumptions--if every household
comprised a single individual. But the obvious correlation across the
earnings equations and labor-supply equations of the working-age
members of the same household, the number of which varies across
households, makes things hopelessly complicated. An additional
risk is that the estimates obtained with such a complex econometric
specification might not be robust. They might, in particular, show
artificially high time variability, thus jeopardizing the decomposition
principle shown above.
The microeconometric estimation work undertaken in the case
studies reported in this volume relies on a simplified, but possibly
more robust, specification, based on the following three principles:
1. Individual earnings functions and household self-employment
functions, if applicable, are estimated separately and consistently
through the instrumentation of endogenous right-hand-side vari-
ables and the usual two-step Heckman correction for selection bias.
This standard correction for selection bias allows us to draw the
unobserved residual terms, w and se , of those individuals with no
earnings (or households with no self-employment income) in the
appropriate conditional distribution. In particular, it accounts for
the fact that the latter should logically expect earnings and self-
employment income that are smaller than those who are actually
observed in a wage-earning job or a self-employment activity. Yet
we do not attempt to link this selection bias correction procedure
and the drawing of residuals in the earnings and self-employment
income equations to the estimation of the occupational-choice
model and to the drawing of residuals in that model.25 This is
unlikely to be a problem if no significant bias is present in the earn-
ings and self-employment equations, as occurs in most cases. It is
less satisfactory, of course, when the bias is strongly significant.
2. The simultaneity between household members' labor-supply
decisions is taken into account by considering the behavior of house-
hold heads and that of the other members sequentially, as conven-
tionally done in much of the labor-supply literature. Thus, the
occupational decision of the household head is estimated first with
the preceding multinomial logit model and using both the general
exogenous characteristics of the household, as well as those of all
household members, as explanatory variables. Second, the labor-
supply and occupation decision of other members is estimated
42 BOURGUIGNON AND FERREIRA
conditionally on the decision made by the head of household and
possibly on his or her income. In addition, different models were
sometimes estimated depending on the position of a person in the
family. Indeed, it seems natural that, other things being equal, the
spouse does not behave in the same way with respect to labor supply
as the daughter of the head of household. The categories for which
distinct labor-supply models were estimated include spouses, sons,
daughters, and other household members.
3. The drawing of residual terms in the multinomial logit model
raises some difficulties. First, none of the error terms is actually
observed. What is observed is that the J + 1 random terms lie in
some region of RJ +1 , such that all the inequality conditions are sat-
isfied for the observed choice Ihi in system 2.18. Specifically, if indi-
vidual i is observed in occupation 2, rather than in any of the other
J occupations ( j = 2) that he or she might have chosen, then the vec-
tor of i must be such that Zhi
L L2 + iL2 > Zhi Lj+ i , j = 2
Lj
and Zhi L2+ i L2> 0. Drawing consistent values for these residual
terms essentially consists of independently drawing J + 1 values in
the law of extreme values and checking whether they satisfy the
above condition for the observed Ihi, that is, the occupation observed
for individual hi. Drawings for which these conditions are not satis-
fied are discarded, and the operation is repeated until a (single) set of
values is drawn such that the conditions in system 2.18 hold.26
Finally, combined with the random drawing of residual terms for
the potential earnings and self-employment incomes of individuals
not observed in such an activity, this procedure for drawing multi-
nomial logit residuals implies that any counterfactual distribution
generated by the microsimulation of the model is, in effect, random.
This is not too great a problem if the microsimulation relies on a suf-
ficiently large number of observations. For this practical reason, the
law of large numbers was supposed to hold in the case studies gath-
ered in this book. If that were not the case, one should repeat each
microsimulation a large number of times, so as to obtain a distribu-
tion of counterfactual distributions. In the context of the large sam-
ple sizes available to the case studies in the chapters that follow, the
computation time necessary to generate these Monte Carlo experi-
ments was generally judged excessive. How much the results of sin-
gle-draw simulations differ from analogous Monte Carlo microsim-
ulations remains an interesting question for further research.
Another concern that is left for future research is perhaps even
more basic. Estimates of distributions in this book--whether they
are scalar measures or quantile interval means in some curve--are
derived from samples and are thus subject to sampling error. Ideally,
therefore, one would present confidence intervals for the various
DECOMPOSING CHANGES IN THE DISTRIBUTION 43
statistics and seek to determine their implications for the estimated
counterfactual distributions. Recent analytical and software devel-
opments in the realm of inference for stochastic dominance may be
a promising avenue for further investigation of this important issue
(see, for instance, Davidson and Duclos 2000). As microeconomic
simulation research evolves, a more rigorous treatment of its statis-
tical inference properties is certain to become necessary.
Notes
1. A powerful semiparametric method for constructing counterfactual
distributions that is very similar in spirit to the parametric alternative we
use here has been proposed by DiNardo, Fortin, and Lemieux (1996). We
return to it later in this chapter.
2. In theory, using income or consumption per capita as a welfare mea-
sure should not make any difference for a number of methods discussed in
this chapter. Yet the parametric model discussed later is definitely better
suited to an income view of welfare. Hence, this chapter generally refers to
income distribution or income inequality, rather than to their consumption
expenditure counterparts.
3. They were both interested by earning discrimination across individ-
ual characteristics such as gender or race. Therefore, the populations they
considered were defined by some given sociodemographic characteristic.
Conceptually, this is no different than considering two populations at two
different points in time, as in what follows.
4. To avoid this problem, some authors use the mean characteristics
across periods t and t to evaluate the price effect and use the time average of
prices to evaluate the endowment effect. It will be seen later that such efforts
are an application of a more general method to deal with path dependence.
5. For an introduction to decomposable inequality measures, see Cowell
(2002) and the references therein.
6. To see this, note that the mean income in group g is such that:
yg = y · mg/ng.
7. The approximation in equation 2.4 tends to an equality as the
changes become infinitesimally small.
8. Note that the change in population group weights is also present in
the change in the overall mean, but this point is overlooked for the sake of
simplicity.
9. But, of course, the Oaxaca-Blinder method could also be cast in terms
of groups' means and group weights, rather than in terms of a linear income
model.
10. Conversely, the inequality decomposition is path independent.
11. Two exceptions are Fields and O'Hara (1996) and Morduch and
Sicular (2002). In both cases, however, the authors ignore the preceding
44 BOURGUIGNON AND FERREIRA
point and the need to handle the joint distribution rather than the marginal
distributions of income by sources.
12. The concept of subgroup decomposability was first introduced by
Foster, Greer, and Thorbecke (1984). For a discussion of the normative
implications of this property, see Sen (1997, appendix).
13. Poverty changes can, of course, be decomposed into a growth com-
ponent (changes in means) and an inequality component (changes in Lorenz
curves). See Datt and Ravallion (1992). But this decomposition is not anal-
ogous to a decomposition into price effects, endowment effects, and behav-
ioral changes, because both components are influenced by all three effects.
14. One way to investigate how small these differences are--and to
address the problem of path dependence--would be to consider a large
number of paths and to estimate the "average" contribution of a particular
change over them. Shorrocks (1999) provides a formal definition of the
appropriate "averaging" concept, on the basis of Shapley values.
15. A general formulation of these various decomposition paths is given
in Bourguignon, Ferreira, and Leite (2002).
16. See also the semiparametric technique proposed by Donald, Green,
and Paarsch (2000).
17. An alternative would be to use the Shapley-value approach referred
to in note 14.
18. Because the simulation actually bears on micro data rather than
aggregate data, this operation is often referred to as microsimulation.
19. For situations in which selection into the sample differs across t and
t (say, because participation behavior has changed), an alternative
approach exists for generating a counterfactual distribution of residuals.
This approach, discussed in Cunha, Heckman, and Navarro (2004), relies
on factor analysis (and a number of assumptions) to decompose the variance
of residuals into a component due to predictable individual heterogeneity
and another due to pure uncertainty (or "luck"). Such a decomposition
would enable one to consider estimates of "unobserved" individual fixed
effects separately from pure randomness.
20. This change in the population of earners because of changing labor-
force participation behavior was only implicit in the preceding analysis of
individual earnings. It was simply part of the endowment effect or, in other
words, the change in the sociodemographic characteristics of the active
population.
21. Ex ante, the probability that individual i of household h takes occu-
pation s is given by the following:
Ls
Ps Zhi, L eZhi
=
1 + eZhi Lj
j
whereas the probability of inactivity, P0(Zhi, L), is such that all prob-
abilities sum to unity.
DECOMPOSING CHANGES IN THE DISTRIBUTION 45
22. The multinomial logit specification is also compatible with school-
ing being defined by achievement levels, rather than by number of years.
23. The occupational models are not always in pure reduced form. For
instance, many case studies model the occupational choice of spouses or sec-
ondary household members as a function of the income of the household head,
as in much of the standard labor-supply literature. Such studies allow account-
ing for the typically structural effect of a change in the occupation or earnings
of the household head on the occupation of other household members.
24. The same caveat about the partial equilibrium nature of the exercise
applies to the original Oaxaca-Blinder decomposition; to the semiparamet-
ric approach of DiNardo, Fortin, and Lemieux (1996); and, indeed, to all
other approaches previously reviewed.
25. An equivalent to the well-known Heckman two-stage procedure for
the correction of selection bias in the case of a dichotomous choice repre-
sented by a probit exists with polychotomous choice and the multinomial
logit model (see Lee 1983). Yet this method has been shown to be problem-
atic (see Bourguignon, Fournier, and Gurgand 2002; Schmertmann 1994).
26. Specific i terms can be obtained as i = - log[- log(x)], where x
L L
is a random draw in a uniform distribution in [0, 1]. An alternative method
is proposed in Bourguignon, Fournier, and Gurgand (2001).
References
Blinder, Alan S. 1973. "Wage Discrimination: Reduced Form and Structural
Estimates." Journal of Human Resources 8(Fall): 43655.
Bourguignon, François. 1979. "Decomposable Income Inequality Mea-
sures." Econometrica 47: 90120.
Bourguignon, François, Francisco Ferreira, and Phillippe Leite. 2002.
"Beyond Oaxaca-Blinder: Accounting for Differences in Household
Income Distributions across Countries." Policy Research Working Paper
2828. World Bank, Washington, D.C.
Bourguignon, François, Martin Fournier, and Marc Gurgand. 2001. "Fast
Development with a Stable Income Distribution: Taiwan, 19791994."
Review of Income and Wealth 47(2): 125.
------. 2002. "Selection Bias Correction Based on the Multinomial Logit
Model." Working paper. DELTA, Paris.
Cowell, Frank A. 1980. "On the Structure of Additive Inequality Mea-
sures." Review of Economic Studies 47: 52131.
------. 2002. "Measurement of Inequality." In Anthony Atkinson and
François Bourguignon, eds., Handbook of Income Distribution, Vol. 1.
Amsterdam: Elsevier.
Cunha, Flávio, James Heckman, and Salvador Navarro. 2004. "Counter-
factual Analysis of Inequality and Social Mobility." University of
Chicago. Processed.
46 BOURGUIGNON AND FERREIRA
Datt, Gaurav, and Martin Ravallion. 1992. "Growth and Redistribution
Components of Changes in Poverty Measures." Journal of Development
Economics 38: 27595.
Davidson, Russell, and Jean-Yves Duclos. 2000. "Statistical Inference for
Stochastic Dominance and for the Measurement of Poverty and Inequal-
ity." Econometrica 68(6): 143564.
DiNardo, John, Nicole Fortin, and Thomas Lemieux. 1996. "Labor Market
Institutions and the Distribution of Wages, 19731992: A Semi-
Parametric Approach." Econometrica 64(5): 100144.
Donald, Stephen, David Green, and Harry Paarsch. 2000. "Differences in
Wage Distributions between Canada and the United States: An Applica-
tion of a Flexible Estimator of Distribution Functions in the Presence of
Covariates." Review of Economic Studies 67: 60933.
Fields, Gary, and Jennifer O'Hara. 1996. "Changing Income Inequality in
Taiwan: A Decomposition Analysis." Cornell University. Ithaca, New
York. Processed.
Foster, James, Joel Greer, and Erik Thorbecke. 1984. "A Class of Decom-
posable Poverty Measures." Econometrica 52: 76165.
Juhn, Chinhui, Kevin Murphy, and Brooks Pierce. 1993. "Wage Inequality and
the Rise in Returns to Skill." Journal of Political Economy 101: 41042.
Lee, Lung-Fei. 1983. "Generalized Econometric Models with Selectivity."
Econometrica 51: 50712.
McFadden, Daniel L. 1974. "Conditional Logit Analysis of Qualitative
Choice Behavior." In Paul Zarembka, ed., Frontiers in Econometrics.
New York: Academic Press.
Mookherjee, Dilip, and Anthony Shorrocks. 1982. "A Decomposition
Analysis of the Trend in U.K. Income Inequality." Economic Journal 92:
886902.
Morduch, Jonathan, and Terry Sicular. 2002. "Rethinking Inequality
Decomposition, with Evidence from Rural China." Economic Journal
112: 93106.
Oaxaca, Ronald. 1973. "Male-Female Wage Differentials in Urban Labor
Markets." International Economic Review 14: 673709.
Schmertmann, Carl P. 1994. "Selectivity Bias Correction Methods in Poly-
chotomous Sample Selection Models." Journal of Econometrics 60:
10132.
Sen, Amartya. 1997. On Economic Inequality. Oxford, U.K.: Clarendon
Press.
Shorrocks, Anthony. 1980. "The Class of Additively Decomposable
Inequality Measures." Econometrica 48: 61325.
------. 1982. "Inequality Decomposition by Factor Components." Econo-
metrica 50(1): 193211.
------. 1999. "Decomposition Procedures for Distributional Analysis: A
Unified Framework Based on the Shapley Value." University of Essex,
Essex, U.K. Processed.
3
Characterization of Inequality
Changes through
Microeconometric
Decompositions: The Case
of Greater Buenos Aires
Leonardo Gasparini, Mariana Marchionni, and
Walter Sosa Escudero
The main economic variables have oscillated widely in the past two
decades in Argentina in association with deep macroeconomic and
structural transformations. After reaching a peak of 172 percent
monthly in 1989, the inflation rate decreased to less than 1 percent
each year in a few years; gross domestic product drastically fell at
the end of the 1980s and then grew at unprecedented rates in the
first half of the 1990s; unemployment rose steadily from around
5 percent to 14 percent in a short period of time. Income inequality
was not an exception in this turbulent period. The Gini coefficient
increased from 41.9 to 46.7 between 1986 and 1989, fell to 40.0
toward 1991, and rose steadily in the following seven years, reach-
ing a record level of 47.4 in 1998.1 In recent economic history, it is
difficult to find periods with such marked changes in inequality,
both in Argentina and in the rest of the world.
The reasons for these changes in inequality are varied and com-
plex. The main aim of this chapter is to assess the relevance of some
forces believed to have affected income inequality in the Greater
47
48 GASPARINI, MARCHIONNI, AND ESCUDERO
Buenos Aires area between 1986 and 1998. More specifically, the
microeconometric decomposition methodology proposed in chap-
ter 2 is used to measure the relevance of various factors that appear to
have driven changes in inequality. In particular, this methodology is
used to identify to what extent changes in (a) returns to education and
experience, (b) endowments of unobservable factors and their returns,
(c) the wage gap between men and women, (d) labor-market partici-
pation and hours of work, and (e) the educational structure of the
population contribute to the observed changes in income distribution.
The results presented in this chapter suggest that the observed
similarity between the inequality indices of 1986 and 1992 is in fact
the consequence of mild forces that operated in different directions
but compensated for each other in the aggregate. On the contrary,
between 1992 and 1998, nearly all the determinants under study
contributed to increased inequality. The dominating forces appear
to be the increase in the returns to education; a higher dispersion
in the endowments or in the returns to unobservable factors; and
the dramatic fall in the hours of work of less skilled, low-income
people. Perhaps surprisingly, neither the narrowing of the gender
wage gap nor the increase in average education of the population
were significant equalizing factors. In addition, the dramatic jump
in unemployment in the 1990s does not appear to have had a very
significant direct effect on household income inequality.
The rest of this chapter is organized as follows. The basic facts and
some issues that might have affected inequality in the past two decades
aredescribedfirst.Nextthedecompositionmethodologyimplemented
to assess the relevance of those factors is presented, and the estimation
strategy is explained. The main results of the analysis are then pre-
sented. The chapter concludes with some brief final comments.
Income Inequality: Basic Facts and Sources of Changes
Income inequality in Argentina has fluctuated considerably around
an increasing trend initiated in the mid-1970s. Figure 3.1 shows the
Gini coefficient of equivalent household income between 1985 and
1998 in the Greater Buenos Aires area.2 After a substantial increase
in the late 1980s, inequality plunged in the first two years of the
1990s. A new stage of rising inequality started in 1992 and has not
stopped yet. Until 1998, the Greater Buenos Aires area had never
experienced the level of income inequality reached in that year, at
least since reliable household data sets were available.3
For simplicity, this study focused on three years of relative macro-
economic stability separated by equal intervals: 1986, 1992, and
1998. In addition, we restricted the analysis mainly to labor income
CHARACTERIZATION OF INEQUALITY CHANGES 49
Figure 3.1 Gini Coefficient of Equivalent Household Income
Distribution in Greater Buenos Aires, 198598
Gini coefficient
48
47
46
45
44
43
42
41
40
39
38
1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998
Source: Authors' calculations based on the EPH, Greater Buenos Aires, October.
Table 3.1 Distributions of Income in Greater Buenos Aires,
Selected Years
(Gini coefficient)
Type of distribution 1986 1992 1998
Earnings 39.4 37.7 44.9
Equivalent household labor income 40.3 41.0 49.5
Source: Authors' calculations based on the EPH, Greater Buenos Aires, October.
(that is, wage earnings and self-employment earnings) for two
reasons: (a) the Permanent Household Survey (Encuesta Permanente
de Hogares, or EPH) has various deficiencies in capturing capital
income, and (b) modeling capital income and retirement payments is
not an easy task, especially considering the scarce information con-
tained in the EPH. We also ignored those households whose heads or
spouses were older than 65 or received retirement payments.
Table 3.1 shows the basic facts characterized in this chapter.
Inequality in individual labor income and in equivalent household
labor income, as measured by the Gini, did not change very much
between 1986 and 1992; on the contrary, both measures rose dra-
matically in the next six years.4,5
50 GASPARINI, MARCHIONNI, AND ESCUDERO
A countless number of factors may have caused the changes
in inequality documented in table 3.1. We concentrate on seven:
(a) returns to education, (b) the gender wage gap, (c) returns to expe-
rience, (d) unobservable factors and their returns, (e) hours of work,
(f) employment, and (g) the education of the working-able popula-
tion. The objective of this chapter is to estimate the sign and the rel-
ative magnitude of the effect of those factors on the distribution of
earnings and the equivalent household labor income. Although
microeconometric decompositions will be used toward that aim, this
section begins with an analysis of the basic statistics and regressions
to provide some intuitions about the results and to understand the
need and usefulness of a microsimulation decomposition technique.
Returns to Education
An increase in the returns to education implies a widening of the
wage gap between workers with high levels of education and those
with low levels of education. This wider gap, in turn, would imply
a more unequal distribution of earnings and probably a more
unequal distribution of household income.6 Table 3.2 shows hourly
earnings in real pesos (Arg$) for workers between 14 and 65 years
old by educational level. The average wage fell 19 percent between
1986 and 1992 and increased 9.3 percent over the following
six years. Changes were not uniform among educational groups.
Although in the first period of the analysis the most dramatic drop
in hourly earnings was for the college complete group, that group
enjoyed the greatest increase in wages during the 199298 period.
Table 3.2 is a first piece of evidence that changes in relative wages
Table 3.2 Hourly Earnings by Educational Level in Greater
Buenos Aires, Selected Years
Means (Arg$ 1998) Changes (percent)
Educational level 1986 1992 1998 198692 199298 198698
Primary incomplete 6.6 5.7 5.3 -13.6 -6.8 -19.5
Primary complete 7.7 6.3 5.9 -18.1 -6.0 -23.0
Secondary incomplete 9.2 6.8 6.6 -26.1 -2.8 -28.1
Secondary complete 11.6 9.1 9.1 -21.2 -0.4 -21.5
College incomplete 14.5 11.9 10.6 -17.5 -11.1 -26.7
College complete 24.1 16.3 19.4 -32.3 19.1 -19.4
Total 10.4 8.4 9.2 -19.0 9.3 -11.4
Note: Data cover workers between ages 14 and 65 with valid answers.
Source: Authors' calculations based on the EPH, Greater Buenos Aires, October.
CHARACTERIZATION OF INEQUALITY CHANGES 51
among schooling groups implied a decrease in earnings inequality
between 1986 and 1992 and an increase thereafter.
Table 3.3 shows the results of Mincerian log hourly earnings
functions, estimated using the Heckman procedure to correct for
sample selection. The first three columns refer to household heads
(mostly men), the second three columns refer to spouses (nearly all
women), and the last three columns refer to other members of the
family (roughly half men and half women). Because the EPH does
not record years of education, we included dummy variables that
capture the maximum educational level achieved. The omitted cate-
gory is primary incomplete. A gender dummy variable, age and age
squared, and a dummy variable for youths younger than 18 years
old (only relevant for other family members) also were included in
the regression. In addition to those variables, the selection equation
included marital status, number of children, and a dummy variable
that takes the value 1 when the individual attends school. Following
Bourguignon, Fournier, and Gurgand (2001), our analysis assumed
that labor-market participation choices were made within the house-
hold in a sequential fashion. Spouses consider the labor-market sta-
tus of the head of household when deciding whether to enter the
labor market themselves. Other members of the family consider the
labor-market status of both the head of household and the spouse
before deciding to enter the labor market.
The coefficients of most educational levels are positive, signifi-
cant, and increasing with the educational level; that is, the returns to
education are always positive.7 For family heads in 1998, an indi-
vidual who had completed primary school had an hourly wage
18 percent greater than an individual whose primary education was
incomplete, if all other factors were constant. The same figures for
individuals whose secondary education was incomplete, those who
completed secondary school, those whose college education was
incomplete, and those who completed college education are 36, 65,
94, and 146 percent, respectively, all with respect to individuals
who had not completed primary school. In many cases, returns to
education are increasing; that is, the hourly wage gap between edu-
cational levels increases with education.8 For heads of household in
1998, the difference in wages between an individual who had
completed primary school and one whose secondary education
was incomplete is 18 percent, whereas the difference between an
individual at the latter level and one who completed secondary
school is 29 percent. The greatest jump is between individuals who
did not complete and who completed college: 52 percent.
Figure 3.2 shows predicted hourly earnings for all educational
levels. The first panel refers to male household heads and the second
1998 0.0417 (0.287) 0.1366 (0.953) 0.3646 (2.447) 0.6699 (4.592) 0.9456 (5.830) 0.1678 (3.250) 0.0846 (4.138) 0.0011- 3.735)-( 0.3601- 2.811)-( 0.3190- 0.799)-(
members
1992 0.3349 (2.884) 0.4361 (3.795) 0.5726 (4.546) 0.7100 (5.919) 0.8109 (5.432) 0.0701 (1.405) 0.0797 (4.267)
family 0.0009- 3.545)-( 0.0338- 0.406)-( 0.2793- 0.749)-(
Other
earsY 1986 0.0407 (0.441) 0.2278 (2.400) 0.4053 (3.927) 0.5646 (5.289) 0.7439 (5.577) 0.0454 (0.827) 0.0766 (4.351) 0.0009- 3.646)-( 0.0218- 0.250)-( 0.1849 (0.577)
Selected 1998 0.0575 (0.462) 0.2306 (1.848) 0.4841 (3.861) 0.6579 (4.347) 0.9607 (5.600) 0.2859 (1.706) 0.0454 (2.028) 0.0005- 1.813)-( 0.6169 (1.178)
Aires,
Spouse 1992 0.1731- 1.695)-( 0.0243- 0.211)-( 0.2652 (2.445) 0.5173 (3.666) 0.5764 (4.183) 0.2626 (1.280) 0.0343 (1.533) 0.0004- 1.393)-( 1.1095 (2.283)
Buenos
1986 0.0393 (0.496) 0.2241 (2.342) 0.5595 (6.720) 0.6446 (5.210) 0.8607 (7.824) 0.1865- 0.774)-( 0.0413 (2.120) 0.0005- 2.057)-( 1.0778 (2.554)
Greater
to
1998 0.1828 (2.978) 0.3630 (5.620) 0.6534 (9.664) 0.9382 1.4634 0.1675 (3.474) 0.0452 (3.951)
(12.714) (20.282) 0.0004- 3.155)-( 0.2051 (0.792)
Applied
household
of 1992 0.2162 (4.011) 0.3367 (5.661) 0.6229 0.9516 1.2607 0.1834 (3.707) 0.0546 (4.882)
(10.185) (12.713) (18.242) 0.0006- 4.661)-( 0.1959 (0.806)
Equation Head
1986 0.2150 (5.496) 0.3994 (9.206) 0.6219 0.9121 1.3079 0.2915 (5.106) 0.0401 (3.969)
(12.649) (15.469) (22.778) 0.0004- 3.295)-( 0.5599 (2.400)
Earnings
equation
Hourly
Log 18
earnings incomplete complete
3.3 complete incomplete complete than
hourly squared
ableT ariableV Log Primary Secondary Secondary College College Male Age Age oungerY Constant
52
)
page
0.2573 (1.126) 0.2308 (1.021) 0.4376 (1.829) 0.5657 (2.284) 0.8389 (2.752) 0.5007 (6.182) 0.2719 (9.111) 0.0036- 8.656)-( 0.4761- 3.360)-( 0.5995- 4.087)-( 0.9050- 7.556)-(
following
0.5917 (2.874) 0.8538 (4.015) 0.7899 (3.296) 1.5396 (5.794) 1.3888 (3.766) 0.4630 (4.703) 0.1686 (4.836) 0.0022- 4.832)-( 0.4060- 2.373)-( 0.3063- 1.925)-( 1.7389- 11.237)-( the
on
0.2137 (1.203) 0.2258 (1.215) 0.4315 (1.901) 0.8123 (3.441) 0.8274 (2.101) 0.8164 (8.451) 0.1960 (5.682) 0.0029- 6.385)-( 0.7813- 4.386)-( 0.5983- 3.823)-( 1.6477- 11.458)-( Continued(
0.1975- 1.346)-( 0.0398 (0.258) 0.2299 (1.489) 0.4153 (2.102) 1.3115 (7.588) 1.3967 (5.353) 0.1203 (4.279) 0.0015- 4.353)-( 0.1768- 5.477)-( 0.2020 (0.900)
0.0513- 0.381)-( 0.0129 (0.083) 0.1556 (1.066) 0.5239 (2.433) 1.0577 (5.620) 1.7185 (2.970) 0.1757 (5.577) 0.0023- 5.668)-( 0.1797- 5.460)-( 0.3501 (1.040)
0.3295- 3.289)-( 0.1980- 1.612)-( 0.0736- 0.639)-( 0.4776 (2.355) 0.7033 (4.467) 1.2982 (2.235) 0.1288 (4.907) 0.0017- 5.117)-( 0.1929- 6.496)-( 0.3036- 0.963)-(
0.3955 (3.052) 0.4556 (3.234) 0.5866 (3.736) 0.4125 (2.177) 0.8111 (4.537) 0.6528 (5.263) 0.1045 (3.748) 0.0014- 4.269)-( 0.0588 (0.477) 0.0464- 1.387)-( 0.5569- 2.509)-(
0)
>
0.2212 (1.429) 0.5737 (2.987) 0.5575 (2.827) 1.0563 (3.318) 1.0181 (3.750) 0.7840 (4.001) 0.1141 (3.012) 0.0016-
earnings 3.589)-( 0.1559 (0.841) 0.0178- 0.442)-( 1.0407- 3.280)-(
hourly
if 0.2931 (2.240) 0.3494 (2.238) 0.4875 (2.580) 0.4760 (1.827) 1.2176 (3.085) 0.8594 (5.175) 0.1099 (3.160)
1 0.0014- 3.541)-( 0.1986 (1.204) 0.0087- 0.202)-( 0.8669- 2.850)-(
=.
var
(dep.
18
incomplete complete
equation school
complete incomplete complete than
squared
Selection Primary Secondary Secondary College College Male Age Age Married Children oungerY Attending
53
with
1998 0.2210- 1.951)-( 0.0488 (0.547) 4.0987- 8.127)-( 1,631
861.41 0.3600 0.5569 0.2005 65
1,191.27- and
members 14
1992
family 0.1624- 1.112)-( 0.0005- 0.005)-( 2.6912- 4.358)-( 1,090
590.80 769.56- 0.3726 0.4770 0.1777 ages
between
Other
1986 0.0351- 0.212)-( 0.0763- 0.706)-( 2.6080- 4.233)-( 1,292
767.13 841.52- 0.1705 0.4848 0.0827
individuals
all
1998 0.6148- 4.386)-( 1.8346- 3.390)-( 1,413
303.14
1,354.19- 0.1035- 0.6434 0.0666- cover
Data
Spouse 1992 0.6382- 3.314)-( 2.7184- 4.571)-( 1,116
154.13 998.04 0.0379 0.5492 0.0208
parentheses.
.
in
1986 0.7922- 3.982)-( 1.5356- 3.015)-( 1,575
164.62
1,311.55- 0.1691- 0.5603 0.0948- are
October
values
z Aires,
1998 1.3239- 2.296)-( 1,967
148.96 0.1247 0.6361 0.0793
2,281.71- Buenos
estimation;
household 1,404
of 1992 1.3567- 1.682)-( 124.61 0.6786 0.5747 0.3900 Greater
1,368.31-
likelihood EPH,
Head
the
1986 1.3555- 1.892)-( 1,961
153.77 0.2179 0.5562 0.1212 on
1,888.35- maximum
based
)
Heckman
calculations'
Continued(
observations represent
household of Authors
3.3 employed Data
of
likelihood answers.
2
ableT ariableV employed Note: Source:
Head Spouse Constant Number Chi Log Rho Sigma Lambda valid
54
CHARACTERIZATION OF INEQUALITY CHANGES 55
Figure 3.2 Hourly EarningsEducation Profiles for Men
(Heads of Household and Other Family Members), Age 40
A. Heads of household
Hourly earnings (Arg $)
25
20
15
10
5
0
Prii Pric Seci Secc Coli Colc
Educational level
B. Other family members
Hourly earnings (Arg $)
14
12
10
8
6
4
2
0
Prii Pric Seci Secc Coli Colc
Educational level
1986 1992 1998
Note: Prii = primary incomplete, Pric = primary complete, Seci = secondary
incomplete, Secc = secondary complete, Coli = college incomplete, Colc = college
complete.
Source: Predicted hourly earnings from models in table 3.3.
56 GASPARINI, MARCHIONNI, AND ESCUDERO
to other male household members, both with age kept constant at
40. The wage-education profiles for family heads have a marked
positive slope and are almost parallel everywhere, except for the
substantial increase in the slope between 1992 and 1998 in the
highest educational levels. This situation certainly contributes to
increased earnings inequality among household heads. For other
male family members, the wage-education profile became flatter
between 1986 and 1992 and substantially steeper and more convex
in the following six years. The latter movement could imply a dra-
matic widening of the earnings gap by educational level.
Figure 3.3 shows the profiles for 40-year-old females. As in the case
of men, the wage-education profiles show a decreasing slope between
1986 and 1992 and an opposite movement between 1992 and 1998.
In summary, the changes in the returns to education appear to have
been mildly inequality reducing between 1986 and 1992 and strongly
inequality increasing in the next six years. Those conclusions are the
most detailed we can draw with basic statistics and regressions. To
get a more complete assessment of the relative significance of these
effects on the income distribution, we need to go beyond this simple
Figure 3.3 Hourly EarningsEducation Profiles for Women
(Spouses), Age 40
Hourly earnings (Arg $)
18
16
14
12
10
8
6
4
2
0
Prii Pric Seci Secc Coli Colc
Educational level
1986 1992 1998
Note: Prii = primary incomplete, Pric = primary complete, Seci = secondary
incomplete, Secc = secondary complete, Coli = college incomplete, Colc = college
complete.
Source: Predicted hourly earnings from models in table 3.3.
CHARACTERIZATION OF INEQUALITY CHANGES 57
analysis. Later sections present a microsimulation methodology that
builds from the results of this section and allows a richer analysis.
Gender Wage Gap
Table 3.4 presents mean hourly wages by gender. Wages were higher
for males in every year. In 1986, males' hourly wages were on aver-
age 16 percent higher than females' hourly wages. The gender gap
narrowed to 3 percent in 1998. A conditional analysis also shows a
shrinking wage gap for household heads. From table 3.3, the coeffi-
cients of the male dummy variable in the regression for household
heads are always positive and significant but clearly decrease over
time.9 This narrowing gender wage gap has undoubtedly been an
equalizing factor on the earnings distribution.
The effect of the narrowing gender wage gap on the distribution
of equivalent household labor income depends on the relative posi-
tion of working women in that distribution. Two factors play in
different directions. On the one hand, female workers are more con-
centrated in the upper part of the distribution than male workers
(partly because of their own labor decisions), and hence a relative
wage change in favor of women implies an increase in household
income inequality.10 On the other hand, a proportional wage increase
for all women is more relevant in low-income families because
women's earnings are a more significant part of total resources in
those households than in rich families. An extreme example is the
disproportionate number of poor households headed by working
women. The total effect of a shrinking gender wage gap on the house-
hold income distribution is then ambiguous. We need a more power-
ful methodology to get a more precise assessment of that effect.
Returns to Experience
Age is used as a proxy for experience in the labor market. The coef-
ficients of age and age squared in the log hourly earnings equation
Table 3.4 Hourly Earnings by Gender in Greater Buenos
Aires, Selected Years
Means (Arg$ 1998) Changes (percent)
Gender 1986 1992 1998 198692 199298 198698
Female 9.3 8.1 9.0 -12.6 10.2 -3.7
Male 10.8 8.5 9.3 -21.2 9.0 -14.1
Total 10.4 8.4 9.2 -18.9 9.3 -11.4
Note: Data cover workers between 14 and 65 with valid answers.
Source: Authors' calculations based on the EPH, Greater Buenos Aires, October.
58 GASPARINI, MARCHIONNI, AND ESCUDERO
of table 3.3 suggest an inverted U-shaped wage-age profile. The
comparison between 1986 and 1998 reveals no major changes in
the returns to experience. In contrast, the relevant coefficients did
change in subperiods 198692 and 199298. For instance, between
1992 and 1998, the wage-age profile for heads of household and
spouses changed in favor of workers older than 50. Because the
mean hourly wage of this group is somewhat lower than the overall
mean, in principle we expect a mild equalizing effect on the earnings
distribution.11 Older workers are better located in the distribution
of equivalent household income than in the earnings distribution,
perhaps because of smaller families; thus, the effect of the change in
the returns to experience on that distribution is not clear.12 The
results presented in this chapter help assess the quantitative rele-
vance of those arguments.
Unobservable Factors
Earnings equations allow the estimation of returns to observable
factors such as education and experience. The error term usually is
interpreted as capturing the joint effect of the endowment of unob-
servable factors (such as individual ability) and their market value
on earnings. In general, the variance of this error term captures the
contribution of dispersion in unobservable factors to general
inequality. Table 3.3 reports the standard deviation of the error
terms of each log hourly earnings equation (labeled as "sigma").
For instance, for household heads, the standard deviation took a
value of 0.56 in 1986, 0.57 in 1992, and 0.64 in 1998. The sub-
stantial increase between 1992 and 1998 also is present in the
spouses' and other members' equations. According to these results,
the effect of changes in unobservable factors would have been mildly
unequalizing between 1986 and 1992 and substantially unequaliz-
ing in the next six-year period.
Hours of Work
During the period under analysis, there has been a slight fall in
weekly hours of work: one hour between 1986 and 1992 and less
than one-half hour in the next six years. This fall was not uniform
across categories of workers. Table 3.5 classifies workers by educa-
tional level and records the average hours of work of each group.
Although there is not a clear pattern of changes between 1986 and
1992, the 1990s witnessed a dramatic fall in hours of work by work-
ers with low levels of education. This change would have a nonneg-
ligible unequalizing effect on the earnings and income distributions.
CHARACTERIZATION OF INEQUALITY CHANGES 59
Table 3.5 Weekly Hours of Work by Educational Levels in
Greater Buenos Aires, Selected Years
Means (Arg$ 1998) Changes (percent)
Educational level 1986 1992 1998 198692 199298 198698
Primary incomplete 45.7 45.6 40.2 -0.3 -11.7 -12.0
Primary complete 48.5 46.8 46.5 -3.3 -0.8 -4.1
Secondary incomplete 47.0 47.0 47.5 0.1 1.0 1.1
Secondary complete 46.9 45.1 46.7 -3.9 3.5 -0.5
College incomplete 42.7 41.9 41.8 -1.9 -0.1 -2.0
College complete 42.6 42.3 42.8 -0.5 1.1 0.5
Total 46.5 45.5 45.2 -2.1 -0.8 -2.9
Note: Data cover workers between 14 and 65 with valid answers.
Source: Authors' calculations based on the EPH, Greater Buenos Aires, October.
Figure 3.4 Weekly Hours of Work by Educational Level for
Men (Heads of Household), Age 40
Weekly hours of work
55
50
45
40
35
30
25
20
Prii Pric Seci Secc Coli Colc
Educational level
1986 1992 1998
Note: Prii = primary incomplete, Pric = primary complete, Seci = secondary
incomplete, Secc = secondary complete, Coli = college incomplete, Colc = college
complete.
Source: Predicted weekly hours of work from models in table 3.6.
A conditional analysis yields similar results. Figure 3.4 shows
predicted weekly hours of work for male household heads from the
Tobit censored data model presented in table 3.6. Although hours of
9.4156
1998 (1.467) 9.4008 (1.484) 12.4789 (1.890) 21.8096 (3.152) 13.3421 (1.777) 15.2718 (7.018) 7.5266 (9.468) 0.1020- 8.948)-( 12.1374- 3.241)-( 23.3702- 5.426)-(
members
1992 16.5169 (3.094) 19.4012 (3.583) 17.9790 (3.009) 39.7456 (5.859) 23.1498 (3.108) 14.8407 (6.134) 3.4066 (4.049)
family 0.0468- 4.130)-( 7.6537- 1.818)-( 14.6823- 3.618)-(
Other
1986 9.5376 (2.186) 6.1322 (1.352) 8.5914 (1.686) 24.1386 (4.185) 8.2748 (1.156) 21.8135 (9.650) 4.7870 (6.111) 0.0714- 6.934)-( 15.8565- 3.813)-( 18.8104- 4.861)-(
earsY 1998 3.7478- 0.694)-( 5.4827 (0.973) 12.0399 (2.135) 20.2824 (2.858) 36.5539 (6.181) 43.9907 (6.512) 4.4250 (4.335) 0.0562- 4.368)-( 7.3587- 6.414)-(
Selected
Spouse 1992 0.8331- 0.158)-( 1.6344 (0.270) 8.1426 (1.432) 18.4916 (2.277) 32.6159 (4.806) 44.9860 (3.380) 6.5939 (5.414) 0.0850- 5.455)-( 7.3819- 5.847)-(
Aires,
1986 12.8134- 3.047)-( 8.1969- 1.583)-( 1.4443- 0.301)-( 16.6182 (2.095) 21.8548 (3.546) 45.2329 (2.677) 5.4816 (4.942) 0.0722- 5.098)-( 8.7386- 7.070)-(
Buenos
1998 9.1412 (4.416) 13.2170 (6.057) 13.1584 (5.770) 10.8928 (3.979) 13.2734 (5.535) 15.1987 (8.093) 1.3565 (3.351)
Greater 0.0186- 3.895)-( 4.4988 (2.608) 0.4745- 1.036)-(
for
household
of 1992 2.9998 (1.690) 7.4547 (3.780) 3.7789 (1.853) 5.7436 (2.149) 5.2378 (2.255) 11.0772 (4.845) 0.9534 (2.468) 0.0150- 3.248)-( 3.3768 (1.652) 0.0064 (0.015)
Equation Head
ork 1986 3.6994 (3.059) 3.6777 (2.722) 4.6707 (3.075) 3.1701 (1.552) 1.7271 (0.985) 1.5803 2.7919 0.2807
W 13.0310 (7.291) (4.980) 0.0212- 5.620)-( (1.826) (0.835)
of
Hours 18
incomplete complete
3.6 complete incomplete complete than
squared
ableT ariableV Primary Secondary Secondary College College Male Age Age Married Children oungerY
60
982 valid
1,631
33.9044- 10.203)-( 3.6361- 1.224)-( 0.0257 (0.011)
108.5699- 7.913)-( 0.1163
33.2833
941.1300 with
3,576.4700- 65
and
609
14
54.3772- 13.539)-( 5.6771- 1.619)-( 1.2688 (0.478) 43.2795- 2.895)-( 1,090
658.90 0.1124
2,602.48- 31.4037
ages
780 between
51.2882- 14.003)-( 4.0485- 1.095)-( 3.5146- 1.327)-( 51.8461- 3.641)-( 1,292
877.47 0.1368
2,769.37- 30.5604
individuals
848 all
2.5146 (0.330) 19.6188- 4.138)-( 70.4622- 3.570)-( 1,413
252.91 0.0363
3,352.46- 40.6468
cover
Data
705
9.0871 (0.772) 25.8924- 3.669)-( 99.8388- 4.321)-( 1,116
129.49 0.0252
2,502.00- 42.6309
.
81 parentheses.
in
October
13.9652- 1.077)-( 28.5008- 3.686)-( 70.2406- 3.282)-( 1,575
143.34 0.0225
3,111.35- 45.6327 are
Aires,
ratiost
201
Buenos
13.1575- 3.902)-( 3.6110- 0.435)-( 1,967
292.40 0.0172
8,369.46- 24.0450
estimation; Greater
97
16.2041- 4.315)-( 1,404 EPH,
17.5783 (2.193) 174.00 0.0146
5,880.39- 19.6320
likelihood the
on
112
1,961 based
14.2282- 4.665)-( 3.5987 (0.559) 279.96 0.0169 maximum
8,148.67- 18.2014
obitT
calculations'
represent
school
household of 2 Authors
employed R Data
of
likelihood
2
employed observations Note: Source:
Attending Head Spouse Constant Number Censored Chi Log Pseudo Sigma answers.
61
62 GASPARINI, MARCHIONNI, AND ESCUDERO
work clearly decreased between 1986 and 1998 for the less edu-
cated male household heads, changes in hours for the rest of the
educational groups were only marginal.
Employment
Household income inequality can change not only because of
changes in hours of work but also because of changes on the exten-
sive margin of the labor market. This aspect is particularly interest-
ing in the case of Argentina, because many analysts consider the
dramatic jump in the unemployment rate in the 1990s to be the
main reason for the increase in inequality.
In table 3.7, adults are grouped according to whether they are
employed, unemployed, or out of the labor force (inactive). The per-
centage of unemployed individuals rose from 2.3 percent in 1986 to
6.5 percent in 1998.13 The major increase took place between 1992
and 1998. However, the increase in unemployment between 1986
and 1998 was accompanied by a decrease in inactivity of roughly
the same magnitude. Despite the jump in the unemployment rate,
Table 3.7 Labor Status by Role in the Household in Greater
Buenos Aires, Selected Years
Proportions by group (percent)
Labor status 1986 1992 1998
All
Employed 59.4 60.9 59.5
Unemployed 2.3 3.5 6.5
Inactive 38.3 35.6 34.0
Head
Employed 94.6 93.1 89.8
Unemployed 2.0 3.1 5.2
Inactive 3.4 3.8 5.0
Spouse
Employed 31.7 36.8 40.1
Unemployed 1.4 1.7 5.6
Inactive 66.9 61.5 54.3
Other
Employed 39.6 44.1 39.8
Unemployed 4.0 5.9 8.8
Inactive 56.3 50.0 51.4
Note: Data cover individuals between ages 14 and 65 with valid answers.
Source: Authors' calculations based on the EPH, Greater Buenos Aires, October.
CHARACTERIZATION OF INEQUALITY CHANGES 63
the proportion of working-able people with zero income remained
roughly unchanged between 1986 and 1998. Notice that for
inequality measures, it is irrelevant whether the individual has zero
income because he or she is unemployed or because he or she is not
looking for a job. Hence, it is not likely that aggregate changes in
labor-market participation played a significant role on inequality
changes.14
Table 3.7 suggests three different stories in the labor market--for
household heads, spouses, and other family members. Some house-
hold heads lost or quit their jobs, especially in the period between
1992 and 1998, becoming either unemployed or out of the labor
force. By contrast, many of the spouses tried to enter the labor force
between 1986 and 1992; most of them found a job, but some of
them did not. Other family members were less fortunate; nearly all
members of this group who started to look for a job became unem-
ployed (or caused another employed individual to move into the
unemployed category).
Education
In Argentina, as in many developing countries, substantial changes
in the educational composition of the population have been taking
place in recent decades. Table 3.8 presents the proportion of indi-
viduals between 14 and 65 years old by level of education. Between
1986 and 1998, there was a strong contraction in the proportion of
youths and adults with primary education (both those who com-
pleted primary schooling and those who did not). Simultaneously,
the share of individuals in all other educational groups increased,
particularly in the secondary complete group between 1986 and
1992 and in the college group between 1992 and 1998.
Table 3.8 Composition of Sample by Educational Level in
Greater Buenos Aires, Selected Years
Educational level 1986 1992 1998
Primary incomplete 15.4 11.0 7.3
Primary complete 32.0 31.1 25.2
Secondary incomplete 26.0 26.8 30.6
Secondary complete 13.5 15.8 15.2
College incomplete 7.1 8.1 11.7
College complete 6.0 7.3 10.0
Note: Data cover individuals between ages 14 and 65 with valid answers.
Source: Authors' calculations based on the EPH, Greater Buenos Aires, October.
64 GASPARINI, MARCHIONNI, AND ESCUDERO
To understand the effects of these changes, one can think of over-
all inequality as a function of inequality between educational groups
and a weighted average of inequality within educational groups. An
increase in the share of a given educational group in the population
can increase inequality (a) if the mean income of that group is far
from the overall mean (or median) so that inequality between that
group and the others grows, and (b) if inequality within that group
is high so that the weighted average of inequalities within the group
increases. In Argentina, the educational structure has changed in the
1990s in favor of a group with an earnings distribution with a rela-
tively high mean and dispersion--the college group. This change
feeds the presumption of an unequalizing education effect on the
earnings and income distribution, operating through both of the
previously mentioned channels.15 The first channel is linked to
Kuznets's (1955) observation: if the highly educated rich are a
minority and only some poor children manage to achieve the high-
est educational (and income) levels, it is likely that inequality grows
as the average education of the population increases, at least until
the highly educated group is relatively large. The second channel lies
on the convexity of the returns to education, which implies higher
wage dispersion for the group of highly educated people.
So far we have analyzed several factors that might have affected
inequality. Although we have offered some evidence to argue for
each effect, we still do not have a consistent framework to use to
confirm the sign of each effect and to assess its quantitative rele-
vance. Were changes in the returns to education really an unequal-
izing force? Were they really a significant force compared with other
factors? The next section presents a framework to tackle these
questions.
Methodology
To assess the relevance of the various factors discussed in the previ-
ous section on income inequality changes, we adapted the micro-
econometric decomposition methodology proposed in chapter 2 to
our case.16
Let Yit be individual i's labor income at time t, which can be writ-
ten as a function F of the vector Xit of individual observable
characteristics that affect wages and employment, the vector it of
unobservable characteristics, the vector t of parameters that deter-
mine market hourly wages, and the vector t of parameters that
affect employment outcomes (participation and hours of work).
(3.1) Yit = F(Xit, it, t, t) i = 1, . . . , N
CHARACTERIZATION OF INEQUALITY CHANGES 65
where N is total population. The distribution of individual labor
income can be represented as follows:17
(3.2) Dt = {Y1 , . . . , YNt}.
t
We can simulate individual labor incomes by changing one or some
arguments in equation 3.1. For instance, the following expression
represents labor income that individuals i would have earned in
time t if the parameters determining wages had been those of time t,
keeping all other things constant:
(3.3) Yit(t ) = F(Xit, it, t , t) i = 1, . . . , N.
More generally, we can define Yit(kt ), where k is any set of argu-
ments in equation 3.1. Hence, the simulated distribution will be
(3.4) Dt(kt ) = {Y1 (kt ), . . . , YNt(kt )}.
t
The contribution to the overall change in the distribution of a
change in k between t and t , holding all else constant, can be
obtained by comparing equations 3.2 and 3.4. Although we can
make the comparisons in terms of the whole distributions, in this
chapter, we compared inequality indices I(D). Therefore, the effect
of a change in argument k on the earnings distribution is given by
(3.5) I[Dt(kt )] - I(Dt).
As discussed in the previous section, this chapter is devoted to
discussing the following effects:
· Returns to education (k = ed) measures the effect of changes
in the parameters that relate education to hourly wages (ed) on
inequality.
· Gender wage gap (k = g) measures the effect of changes in
the parameters that relate gender to hourly wages (g) on inequality.
· Returns to experience (k = ex) measures the effect of changes
in the parameters that relate experience (or age) to hourly wages
(ex) on inequality.
· Endowment and returns to unobservable factors (k = w) mea-
sures the effect of changes in the unobservable factors and their
remunerations affecting hourly wages (w) on inequality.
· Hours of work and employment (k = ) measures the effect of
changes in the parameters that determine hours of work and labor-
market participation () on inequality.
· Education (k = Xed) measures the effect of changes in the
educational levels of the population (Xed) on inequality.
The previous discussion refers to the distribution of earnings.
However, from a social point of view, it is more relevant to study
the distribution of household income because a person's utility
66 GASPARINI, MARCHIONNI, AND ESCUDERO
usually depends not on his or her own earnings but on the house-
hold income and the demographic composition of the family. Equiv-
alent household income for each individual in household h in time t
is defined as
(3.6) Yht =
q Yjt + Yjt0 ajt h = 1, . . . , H
jht jht
where Yq stands for equivalent household income, h indexes house-
holds, Y0 is income from other sources, a stands for the equivalent
adult of each individual, and is a parameter that captures house-
hold economies of scale.18 The distribution of equivalent household
income for the population of N individuals can be expressed as
follows:
(3.7) Dt = Y1 , . . . , YNt .
q q q
t
Changing argument k to its value in t yields the following simulated
equivalent household income in year t:
(3.8) Yht(kt ) =
q Yjt(kt ) + Yjt
0 ajt h = 1, . . . , H.
jht jht
Hence, the simulated distribution is
(3.9) Dt (kt ) = Y1 (kt ), . . . , YNt(kt ) .
q q q
t
The effect of a change in argument k, holding all else constant, on
equivalent household income inequality is given by
(3.10) I Dt (kt ) - I Dt .
q q
Estimation Strategy
To compute expressions 3.5 and 3.10, we need to estimate parame-
ters and and the residual terms . Also, because we do not have
panels, we need a mechanism to replicate the structure of observ-
able and unobservable individual characteristics of one year into the
population of another year. This section is devoted to explaining the
strategies to address these problems.
Estimation of and
Let Li denote the number of hours worked by person i and wi be the
hourly wage received. Total labor income is given by Yi = Liwi . The
number of hours of work Li comes from a utility maximization
process that determines optimal participation in the labor market,
whereas wages are determined by market forces. The estimation
CHARACTERIZATION OF INEQUALITY CHANGES 67
stage specifies models for wages and hours of work, which are used
in the simulation stage described earlier.
The econometric specification of the model is similar to the one
used by Bourguignon, Fournier, and Gurgand (2001), which corre-
sponds to the reduced form of the labor decisions model originally
proposed by Heckman (1974). Heckman shows how it is possible to
derive an estimable reduced form starting from a structural system
obtained from a utility maximization problem of labor-consumption
decisions. Leaving technical details aside, the scheme proposed by
Heckman has the following structure. Individuals allocate hours to
work and domestic activities (or leisure) to maximize their utility
subject to time, wealth, wages, and other constraints. As usual, the
solution to this optimization problem can be characterized as
demand relations for goods and leisure as functions of the relevant
prices. Under general conditions, it is possible to invert these func-
tions to obtain prices and wages as functions of quantities of goods
and leisure consumed (or their counterpart, hours of work). In par-
ticular, the wages obtained in this fashion (denoted as w) are inter-
preted as marginal valuations of labor, which will be a function of
hours of work and other personal characteristics, and represent the
minimum wage for which the individual would accept work for a
determined number of hours. In equilibrium, if the individual
decides to work, the number of hours devoted to labor should
equate their marginal value w with the wage effectively received.
Conversely, a decision not to work is made if the marginal value is
greater than the wage offered, given the individual's personal
characteristics.
This discussion suggests a way to determine wages demanded by
individuals. In parallel it is possible to model market determinants
of wages offered (w) as a function of characteristics such as years
of education, experience, and age as a standard Mincer equation
(Mincer 1974). In equilibrium, it is assumed that the number of
hours of work adjusts to make w = w.
The demand-supply relations discussed so far are structural forms
in the sense that they reflect relevant economic behavior in which
wages offered and demanded depend on the number of hours of
work. Under general conditions, it is possible to derive a reduced
form for the equilibrium relations in which wages and hours of
work are expressed as functions of the variables taken as exoge-
nous. In this way, the model has two equations--one for wages (w)
and one for the number of hours of work (L)--and both are a
function of factors taken as given that affect wages (X1) and hours
(X2), which may or may not have elements in common. The error
terms 1 and 2 represent unobservable factors that affect the deter-
mination of endogenous variables.
68 GASPARINI, MARCHIONNI, AND ESCUDERO
According to the characteristics of the problem, we observe pos-
itive values of w and L for a particular individual if and only if the
individual actually works. If the person does not work, we only
know that the offered wage is smaller than the wage demanded.
Consequently, the reduced form model for wages and hours of work
is specified as follows:
(3.11) wi = X1 + 1
i i i = 1, . . . , N
(3.12) Li = X2 + 2
i i
with
wi = wi if Li > 0
wi = 0 if Li 0
Li = Li if Li > 0
Li = 0 if Li 0
where wi and Li correspond to observed wages and hours of work,
respectively. This notation emphasizes that, consistent with the data
used for the estimation, observed wages for a nonworking individ-
ual are zero.
Following Heckman (1979), for estimation purposes we assume
that 1 and 2 have a bivariate normal distribution with E(1 ) =
i i i
E(2 ) = 0, variances 12 and 22, and correlation coefficient . This
i
particular specification corresponds to the Tobit type III model in
Amemiya's (1985) classification.
Even though it is possible to estimate all the parameters using a full
information maximum likelihood method, we adopted a limited
information approach that has notable computational advantages. If
instead of hours of work, we had information only about whether or
not the individual works, the model would correspond to the type II
model in Amemiya's classification, whose parameters can be esti-
mated on the basis of a simple selectivity model. More specifically, the
regression equation would be the wage equation, and the selection
equation would be a censored version of the labor supply equation,
simply indicating whether or not the individual works. Table 3.3
shows the estimation results of these equations for our case.
Conversely, the hours of work equation corresponds to the Tobit
type I model in Amemiya's classification in which the variable is
observed only if it is positive. In this case, the parameters of interest
could be estimated using a standard censored regression Tobit model
(see table 3.6). This strategy is consistent but not fully efficient. In
any case, the efficiency loss is not necessarily significant for a small
sample.
CHARACTERIZATION OF INEQUALITY CHANGES 69
Unobservable Factors
Unobservable factors that affect wages are modeled as regression
error terms of the wage equation 3.11. Their mean is trivially nor-
malized to zero, and their variance is estimated as an extra parame-
ter in the Heckman procedure. To simulate the effect of changes in
those unobservable factors between t and t on inequality, we have
rescaled the estimated residuals of the wage equation of year t by
t /t, where is the estimated standard deviation of the wage
equation.19
To study employment effects, the decomposition methodology
requires simulating earnings for people who do not work. Because
we do not observe wages, we cannot apply equations 3.11 and 3.12
to estimate the unobservables. For each individual in that situation,
we assigned as an "error term" a random draw from the bivariate
normal distribution implicit in the wage-labor supply model (equa-
tions 3.11 and 3.12), whose parameters are consistently estimated
by the Heckman procedure. Error terms were drawn from the bivari-
ate normal distribution and a prediction (based on observable
characteristics, estimated parameters, and sampled errors) was com-
puted for wages and hours worked. If the resulting prediction yields
positive hours of work (and the prediction is inconsistent with
observed behavior in this group), the error term is sampled again
until nonpositive hours of work are predicted.
Individual Characteristics
For the estimation of the education effect, it is necessary to simulate
the educational structure of year t on year t population. Instead of
following Bourguignon, Fournier, and Gurgand (2001) and estimat-
ing a parametric equation that relates individual educational level to
other individual characteristics (age and gender), we apply a rough
nonparametric mechanism. We divide the adult population in
homogeneous groups by gender and age and then replicate the edu-
cational structure of a given cell in year t into the corresponding
cell in year t.
Results
This section reports the results of performing the decompositions
described in the methodology using the estimation strategy outlined
in the previous section. The objective is to shed light on the quanti-
tative relevance of the various phenomena discussed earlier in this
chapter on inequality changes during 198698.
70 GASPARINI, MARCHIONNI, AND ESCUDERO
Before we show the results, two explanations are in order. First,
the decompositions are path dependent. Hence, we report the results
using alternatively t and t as the base year. Second, the simulations
are carried out for the whole distribution. To save space, we show
only the results for the Gini coefficient. There were not significant
variations when other indices were used.20
Tables 3.9 to 3.11 show the results both with t and t as base
years. Table 3.12 reports the average of these results.21 A positive
number indicates an unequalizing effect. A large number compared
with the other figures in the column suggests a significant effect. For
instance, the price effect of education on the earnings distribution in
the 199298 period (column ii) is 2.9. This finding roughly means
that the Gini would have increased 2.9 points if only the returns to
education (that is, the coefficients of the educational dummy vari-
ables in the wage equation) had changed between those years. The
number 2.9 tells us two things: (a) because it is a positive number, it
implies that the returns to the education effect increased inequality,
and (b) because it is large compared with the other numbers in the
column, it indicates that the change in the returns to education was
a very significant factor affecting inequality in the distribution of
earnings.
The rest of this section is devoted to studying the effects on the
earnings and equivalent household labor income distributions of the
seven factors that were discussed earlier, with the help of tables 3.9
to 3.12.
Returns to Education
Table 3.12 confirms the presumptions of the earlier section on basic
facts and sources for change. Changes in the returns to education
had an equalizing effect on the individual labor income distribution
between 1986 and 1992 and a strong unequalizing effect over the
next six years. The effects on the equivalent income distribution
were similar. Over the whole period from 1986 to 1998, changes in
the returns to education (in terms of hourly wages) represented an
important inequality increasing factor.
Gender Wage Gap
As expected, changes in the gender parameter of the wage equation
implied an equalizing effect on the earnings distribution. During the
past decade, the gender wage gap has shrunk substantially. Given
that women earn less than men, that movement had an unambigu-
ous inequality-decreasing effect on the earnings distribution.
CHARACTERIZATION OF INEQUALITY CHANGES 71
Table 3.9 Decompositions of the Change in the Gini
Coefficient: Earnings and Equivalent Household Labor
Income in Greater Buenos Aires, 198692
Using 1992 coefficients
Earnings Equivalent income
Indicator Level Change Level Change
1986 observed 39.4 40.3
1992 observed 37.7 -1.7 41.0 0.7
Effect
1. Returns to education 38.9 -0.5 39.7 -0.6
2. Gender wage gap 38.4 -1.0 40.4 0.1
3. Returns to experience 41.5 2.1 40.0 -0.3
4. Unobservable factors 39.9 0.5 40.7 0.4
5. Hours of work 39.8 0.4 41.7 1.4
6. Employment 39.4 0.0 40.1 -0.3
7. Education 39.2 -0.2 40.5 0.1
8. Other factors -3.1 -0.1
Using 1986 coefficients
Earnings Equivalent income
Indicator Level Change Level Change
1986 observed 39.4 -1.7 40.3 0.7
1992 observed 37.7 41.0
Effect
1. Returns to education 39.2 -1.5 42.2 -1.2
2. Gender wage gap 38.8 -1.1 40.9 0.1
3. Returns to experience 36.4 1.3 41.7 -0.7
4. Unobservable factors 37.2 0.5 40.7 0.3
5. Hours of work 38.8 -1.2 40.4 0.6
6. Employment 37.6 0.1 41.0 0.0
7. Education 38.6 -1.0 40.8 0.2
8. Other factors 1.2 1.2
Average changes
Indicator Earnings Equivalent income
198692 observed -1.7 0.7
Effect
1. Returns to education -1.0 -0.9
2. Gender wage gap -1.0 0.1
3. Returns to experience 1.7 -0.5
4. Unobservable factors 0.5 0.4
5. Hours of work -0.4 1.0
6. Employment 0.0 -0.1
7. Education -0.6 0.2
8. Other factors -0.9 0.5
Note: The earnings distribution includes those individuals with Yit > 0 and
Yit(kt ) > 0. The equivalent household labor income distribution includes those indi-
viduals with Yit 0 and Yit(kt ) 0. Nonlabor income is not considered.
q q
Source: Authors' calculations based on the EPH, Greater Buenos Aires, October.
72 GASPARINI, MARCHIONNI, AND ESCUDERO
Table 3.10 Decompositions of the Change in the Gini
Coefficient: Earnings and Equivalent Household Labor
Income in Greater Buenos Aires, 199298
Using 1998 coefficients
Earnings Equivalent income
Indicator Level Change Level Change
1992 observed 37.7 41.0
1998 observed 44.9 7.2 49.5 8.5
Effect
1. Returns to education 40.8 3.2 43.8 2.7
2. Gender wage gap 37.3 -0.4 41.0 0.0
3. Returns to experience 36.8 -0.9 41.9 0.8
4. Unobservable factors 39.9 2.2 42.8 1.8
5. Hours of work 40.7 3.0 42.9 1.9
6. Employment 37.5 -0.2 41.0 0.0
7. Education 38.2 0.5 41.3 0.2
8. Other factors -0.2 1.0
Using 1992 coefficients
Earnings Equivalent income
Indicator Level Change Level Change
1992 observed 37.7 7.2 41.0 8.5
1998 observed 44.9 49.5
Effect
1. Returns to education 42.2 2.7 46.5 3.0
2. Gender wage gap 45.3 -0.4 49.6 -0.1
3. Returns to experience 45.9 -1.0 48.8 0.7
4. Unobservable factors 43.1 1.8 48.0 1.5
5. Hours of work 43.0 1.9 47.8 1.7
6. Employment 44.8 0.1 49.2 0.3
7. Education 44.8 0.1 48.7 0.8
8. Other factors 2.0 0.6
Average changes
Indicator Earnings Equivalent income
199298 observed 7.2 8.5
Effect
1. Returns to education 2.9 2.8
2. Gender wage gap -0.4 -0.1
3. Returns to experience -0.9 0.7
4. Unobservable factors 2.0 1.7
5. Hours of work 2.5 1.8
6. Employment -0.1 0.1
7. Education 0.3 0.5
8. Other factors 0.9 0.8
Note: The earnings distribution includes those individuals with Yit > 0 and
Yit(kt ) > 0. The equivalent household labor income distribution includes those indi-
viduals with Yit 0 and Yit(kt ) 0. Nonlabor income is not considered.
q q
Source: Authors' calculations based on the EPH, Greater Buenos Aires, October.
CHARACTERIZATION OF INEQUALITY CHANGES 73
Table 3.11 Decompositions of the Change in the Gini
Coefficient: Earnings and Equivalent Household Labor
Income in Greater Buenos Aires, 198698
Using 1998 coefficients
Earnings Equivalent income
Indicator Level Change Level Change
1986 observed 39.4 40.3
1998 observed 44.9 5.5 49.5 9.2
Effect
1. Returns to education 41.1 1.7 42.0 1.7
2. Gender wage gap 38.1 -1.3 40.5 0.1
3. Returns to experience 39.8 0.4 40.6 0.2
4. Unobservable factors 42.2 2.8 42.7 2.4
5. Hours of work 42.3 3.0 43.5 3.2
6. Employment 39.2 -0.2 40.1 -0.2
7. Education 39.8 0.4 41.2 0.9
8. Other factors -1.3 0.9
Using 1986 coefficients
Earnings Equivalent income
Indicator Level Change Level Change
1986 observed 39.4 5.5 40.3 9.2
1998 observed 44.9 49.5
Effect
1. Returns to education 43.0 1.9 47.6 1.9
2. Gender wage gap 46.4 -1.5 49.7 -0.2
3. Returns to experience 44.5 0.4 49.2 0.3
4. Unobservable factors 42.7 2.2 47.7 1.8
5. Hours of work 43.5 1.4 46.7 2.8
6. Employment 44.7 0.2 49.4 0.1
7. Education 45.7 -0.8 48.5 1.0
8. Other factors 1.7 1.6
Average changes
Indicator Earnings Equivalent income
198698 observed 5.5 9.2
Effect
1. Returns to education 1.8 1.8
2. Gender wage gap -1.4 0.0
3. Returns to experience 0.4 0.3
4. Unobservable factors 2.5 2.1
5. Hours of work 2.2 3.0
6. Employment 0.0 -0.1
7. Education -0.2 0.9
8. Other factors 0.2 1.2
Note: The earnings distribution includes those individuals with Yit > 0 and
Yit(kt ) > 0. The equivalent household labor income distribution includes those indi-
viduals with Yit 0 and Yit(kt ) 0. Nonlabor income is not considered.
q q
Source: Authors' calculations based on the EPH, Greater Buenos Aires, October.
in
(vi) 9.2 1.8 0.0 0.3 2.1 3.0
earY 0.1- 0.9 1.2 includes
198698
Base income
distribution
the
(v) 8.5 2.8
household 0.1- 0.7 1.7 1.8 0.1 0.5 0.8 income
199298
labor
Changing
Equivalent
household
Results (iv) 0.7 0.9- 0.1 0.5- 0.4 1.0 0.1- 0.2 0.5
198692
equivalent
verageA The
0.
>)
cient:fi t
(iii) 5.5 1.8 1.4- 0.4 2.5 2.2 0.0 0.2- 0.2 k( .
it
198698 Y
Coef and October
0
> considered.
Gini it
Y not Aires,
is
the (ii) 7.2 2.9
in
Earnings 199298 0.4- 0.9- 2.0 2.5 0.1- 0.3 0.9 with
Buenos
income
Greater
individuals
Change Nonlabor EPH,
the Periods those 0.
(i) the
of
198692 1.7- 1.0- 1.0- 1.7 0.5 0.4- 0.0 0.6- 0.9- )
t
k( on
q
includes it
Y
Selected based
and
0
q it
Aires, distribution Y
gap factors
Decomposition with calculations'
education experience
Buenos to wage to work earnings
of factors Authors
3.12 The
individuals
ableT Returns Gender Returns Unobservable Hours Employment Education Other Note: Source:
Greater Indicator Observed Effect 1. 2. 3. 4. 5. 6. 7. 8. those
74
CHARACTERIZATION OF INEQUALITY CHANGES 75
However, the gender effect becomes negligible in the equivalent
household labor income distribution. Earlier, we argued that, on the
one hand, the shrinking gender wage gap could increase inequality
in the household income distribution because of the concentration
of female workers in the upper part of that distribution. On the
other hand, however, it could decrease inequality because women's
earnings are a more significant part of total resources in low-income
households. It appears that these two factors cancel each other out.
Returns to Experience (Age)
The age coefficients in the wage equations of 1986 and 1998 are not
substantially different. This fact is translated into a small value for
the effect of returns to experience seen in columns iii and vi of
table 3.12. Changes were greater in the two subperiods. For
instance, the relative increase in earnings for people older than 50
between 1992 and 1998 implies a sizable equalizing effect on the
earnings distribution. Instead, the sign of the returns to the experi-
ence effect in column v is positive, perhaps because of the different
location of the age groups in the earnings and household income
distributions, as argued in the section on basic facts and sources for
changes.
Unobservables
Changes in endowments and returns to unobservable factors have
implied unequalizing changes in wages, which have translated into
unequalizing changes in the earnings and equivalent household
labor income distributions. These effects were particularly strong in
the 199298 period. The results of the decompositions suggest that
the increase in the dispersion of unobservables was one of the main
factors affecting earnings and household inequality over the period
under analysis.
Hours of Work
To assess the relevance of changes in hours of work and employ-
ment status on inequality, we simulate the distribution in a base
year using the parameters of the Tobit employment equations of
table 3.6 for a different year. To single out the effect of changes in
hours worked, we ignore observations for people who changed
labor status between the base year and the simulation (that is, we
keep their actual earnings) and change hours of work only for indi-
viduals who worked both in the base year and in the simulation. As
76 GASPARINI, MARCHIONNI, AND ESCUDERO
discussed earlier, the 1990s witnessed a substantial fall in hours of
work by low-income workers and an increase in hours of work for
the rest. From columns ii and v of table 3.12, it appears that this
fact has had a very significant effect on the earnings and household
income distributions.
Employment
To assess the effect of changes in individual employment status, we
assign zero earnings to people with nonpositive simulated hours of
work, whereas people who worked in the simulation are assigned
the actual base year earnings.22
Unemployment rates skyrocketed in the mid-1990s and have
remained very high since then. There is a widespread belief that the
increase in unemployment is the main cause of the strong increase
in household inequality. Results in column v of table 3.12 suggest
that we scale down those conclusions because the employment
effect is positive but negligible.23 Two reasons contribute to reduce
the effect of the great increase in unemployment on household
inequality. First, during 199298, the unemployment rate jumped,
but the employment rate did not change much, implying a minor
change in the number of individuals without earnings. As stressed
earlier, this number, rather than the number of unemployed people,
is the relevant number for household inequality. The second point
is that the newly unemployed (those who did not work in 1998 but
who would have worked given the 1992 parameters) had extremely
low individual labor incomes in 1992 (just 10 percent of the rest),
but their equivalent household incomes were not far from the
median (75 percent of the median). This finding implies that in
the simulation using the 1992 parameters, the change in labor
status (from unemployed to employed) of some individuals
would not have a very strong effect on household inequality
because (a) those individuals had very low incomes anyway, and
(b) they were not concentrated in the lower tail of the household
income distribution.
Education
Argentina has witnessed a dramatic change in the educational com-
position of its population in the past two decades. According to the
results shown in table 3.12, that change had a mild inequality-
increasing effect on the earnings and equivalent household income
distributions in the 1990s. This result is not surprising given our
earlier discussion on sources for change.
CHARACTERIZATION OF INEQUALITY CHANGES 77
Other Factors and Interactions
The last row in table 3.12 is calculated as a residual. It encompasses
the effects of interaction terms and of many factors not considered
in the analysis. According to table 3.12, these terms are not too
large, implying either that the factors not considered in the analysis
are not extremely important or that they tend to compensate for
each other.
Concluding Remarks
This chapter contributes to a highly discussed topic in Argentina--
the increase in income inequality--by using microeconometric
decompositions methodology. This technique allows us to assess the
relevance of various factors that affected inequality between 1986
and 1998. The results of the chapter suggest that the small change
in inequality between 1986 and 1992 is the result of mild forces that
compensated for each other. In contrast, between 1992 and 1998,
nearly all effects played in the same direction. Changes in the returns
to education and experience, in the endowments of unobservable
factors and their remunerations, and in hours of work and employ-
ment status, as well as the transformation of the educational
structure of the population, have all had some role in increasing
inequality in Argentina to unprecedented levels. Even the decrease
in the wage gap between men and women, which is a potential force
for reducing inequality, has not induced a significant decrease in
household income inequality.
The increase in the returns to education and unobservable factors
and the relative fall in hours of work for unskilled workers are
particularly important to characterize the growth in inequality. Per-
haps surprisingly, although Argentina witnessed dramatic changes
in the gender wage gap, the unemployment rate, and the educa-
tional structure, these factors appear to have had only a mild effect
on the household income distribution.
Notes
This article is part of a project on income distribution financed by the
Convenio Ministerio de Economía de la Provincia de Buenos Aires and the
Facultad de Ciencias Económicas de la Universidad Nacional de La Plata.
We appreciate the financial support of these institutions. We are grateful to
the editors of this volume and seminar participants at the Universidad
Nacional de La Plata, Universidad Torcuato Di Tella, Latin American and
78 GASPARINI, MARCHIONNI, AND ESCUDERO
Caribbean Economic Association meetings in Rio de Janeiro, meetings of
the Asociación Argentina de Economía Política in Córdoba, and Hewlett
Foundation Conference at the University of California at Los Angeles for
helpful comments and suggestions. We also thank Verónica Fossati and
Alvaro Mezza for efficient research assistance. All opinions and remaining
errors are the responsibility of the authors.
1. These values correspond to the distribution of the equivalent house-
hold income in Greater Buenos Aires. All figures in this chapter were calcu-
lated from the Permanent Household Survey (Encuesta Permanente de
Hogares, or EPH) for the Greater Buenos Aires area, because data for the
rest of urban Argentina are available only from the beginning of the 1990s.
Following Buhmann and others (1988), the equivalent household income
was obtained by dividing household income by the number of equivalent
adults--taken from the National Institute of Statistics and Census
(INDEC)--raised to 0.8, a parameter that implies mild household
economies of scale.
2. The use of other indices does not change the main conclusions
derived from the graph. See Gasparini and Sosa Escudero (2001).
3. These broad trends are also reported by other authors. See Altimir,
Beccaria, and González Rozada (2001); Gasparini, Marchionni, and Sosa
Escudero (2001); Lee (2000); and Llach and Montoya (1999).
4. All households with valid incomes (including those with no income)
were considered in the equivalent household labor income statistics.
Ignoring those with zero income did not alter the main results; see our
companion paper, Gasparini, Marchionni, and Sosa Escudero (2000). Only
workers with positive earnings were included in the individual labor income
statistics. Results in table 3.1 are robust to changes in inequality indices (see
our companion paper).
5. Gasparini and Sosa Escudero (2001) used bootstrap methods to
show that it is possible to reject the null hypothesis that the Gini coefficients
of 1986 and 1998 are equal. Although the same is true for the Gini coeffi-
cients of 1992 and 1998, one cannot reject the null hypothesis that the Gini
coefficients of 1986 and 1992 are equal.
6. Throughout the paper, wage refers to hourly labor income earned
by wage workers and self-employed workers.
7. We refer to returns to education as the change in hourly wages
owing to a change in the educational level (and not in years of education).
It takes approximately seven years to complete primary school, five or six
additional years to complete high school, and approximately five years to
complete college.
8. The increasing returns to education could be caused by a selectivity
bias in the schooling decision. High-ability people have lower costs of
acquiring knowledge and hence are more prone to make a higher human
capital investment.
CHARACTERIZATION OF INEQUALITY CHANGES 79
9. Surprisingly, the time pattern is the opposite for other members of
the household. However, because the number of working individuals in this
group is much smaller than in the head of household group, the global con-
clusion of a narrowing gender wage gap holds.
10. Although 44 percent of working women are in the highest income
quintile of the equivalent household labor income distribution, only 25 per-
cent of men are in that quintile (the Greater Buenos Aires area, 1998). At
the other extreme, 6 percent of working women are in the lowest income
quintile, whereas 9 percent of men are in that quintile.
11. In 1998, the mean wage for workers between 50 and 60 years old
was 86 percent of the overall mean.
12. For instance, although 22 percent of working household heads in
their 50s are in the richest quintile of the earnings distribution, 28 percent
are in the top quintile of the equivalent household labor income distribu-
tion (the Greater Buenos Aires area, 1998). Instead, for working household
heads in their 30s, the figures are 36 percent and 28 percent.
13. This implies an unemployment rate of 3.8 percent in 1986 and 9.9 per-
cent in 1998. These figures refer to our restricted sample. The unemployment
rates reported by INDEC for the whole country are somewhat higher.
14. Furthermore, there are no signs that the strong increase in unem-
ployment has translated into a disproportionate increase in adults with no
income in any of the educational groups. The results of the selection equa-
tions in table 3.3 are in line with this conclusion. See Gasparini,
Marchionni, and Sosa Escudero (2000) for more information.
15. Between 1986 and 1992, the greatest increase in share was for adults
who had completed or not completed secondary school, a group with wages
close to the mean and with relative low dispersion; therefore, we expect an
equalizing education effect on the earnings distribution.
16. See also Altimir, Beccaria, and González Rozada (2001) and the
other chapters in this book.
17. It is typical to restrict this distribution to those individual with
Yit > 0. We followed that practice in the empirical implementation.
18. In the empirical implementation, we ignore Yjt. 0
19. Under bivariate normal assumptions implicit in the Heckman
model, once the correlation between unobservable factors affecting wages
and hours worked is kept constant, all remaining effects of unobservable
factors on wages come through the variance. Machado and Mata (1998)
allowed for heterogeneous behavior of the error term using quintile regres-
sion methods.
20. See Gasparini, Marchionni, and Sosa Escudero (2000).
21. According to table 3.12, the observed Gini coefficient of the indi-
vidual earnings distribution grew 7.2 points between 1992 and 1998. The
return to education in column ii is 2.9. This figure is the average of two
numbers: (a) the difference between the Gini that results from applying
80 GASPARINI, MARCHIONNI, AND ESCUDERO
1998 vector ed of educational dummy variables to the 1992 distribution
and the actual Gini in 1992, and (b) the difference between the actual Gini
in 1998 and the Gini that results from applying 1992 vector ed to the 1998
distribution.
22. Some people did not work in the base year but did work in the sim-
ulation. For those individuals, we simulated the base year hours of work
and wages using the base year parameters of equations 3.11 and 3.12 and
adding error terms obtained by following the procedure described the
section on estimation strategy.
23. Naturally, the role of unemployment as the main source of the
increase in inequality can be stressed again if it is argued that the fall in the
relative wages of the poorest workers was generated by a relative increase
in the unemployment rate of that group. However, the evidence on this
point is far from conclusive.
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Evolución de la Distribución del Ingreso Familiar en la Argentina: Un
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Maestría en Finanzas Públicas Provinciales y Municipales, Universidad
Nacional de La Plata, La Plata, Argentina.
Amemiya, Takeshi. 1985. Advanced Econometrics. Cambridge, Mass.:
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Bourguignon, François, Martin Fournier, and Marc Gurgand. 2001. "Fast
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Gasparini, Leonardo, and Walter Sosa Escudero. 2001. "Assessing Aggre-
gate Welfare: Growth and Inequality in Argentina." Cuadernos de
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Gasparini, Leonardo, Mariana Marchionni, and Walter Sosa Escudero.
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CHARACTERIZATION OF INEQUALITY CHANGES 81
Kuznets, Simon. 1955. "Economic Growth and Income Inequality."
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4
The Slippery Slope: Explaining
the Increase in Extreme Poverty
in Urban Brazil, 197696
Francisco H. G. Ferreira and
Ricardo Paes de Barros
By both the standards of its own previous growth record during the
"Brazilian miracle" years of 196873 and those of other leading
developing countries thereafter (notably in Asia), the two decades
between 1974 and 1994--between the first oil shock and the return
of stability with the Real plan--were dismal for Brazil. Primarily,
these years were characterized by persistent macroeconomic dis-
equilibrium, the main symptoms of which were stubbornly high and
accelerating inflation and a gross domestic product (GDP) time
series marked by unusual volatility and a very low positive trend.
Figures 4.1 and 4.2 plot annual inflation and GDP per capita growth
rates for the 197696 period.
The macroeconomic upheaval involved three price and wage
freezes (during the Cruzado Plan of 1986, the Bresser Plan of 1987,
and the Verão Plan of 1989), all of which were followed by higher
inflation rates. Then there was one temporary financial asset freeze
(with the Collor Plan of 1990), and finally a successful currency
reform followed by the adoption of a nominal anchor in 1994 (the
Real Plan). In less than a decade, the national currency changed
names four times.1 Throughout the period, macroeconomic policy
was almost without exception characterized by relative fiscal laxity
and growing monetary stringency.
83
Figure 4.1 Macroeconomic Instability in Brazil: Inflation
Inflation rate (percent)
1,800
1,706
1,600
1,509
1,400 1,328
1,200
1,107
1,000
900
800
703
600
400
319 350
200 158 174 190
42 36 38 62 80 84 86 57
20 9
0
1976 1977 1978 1979 19801981 1982 1983 1984 19851986 1987 1988 1989 1990 19911992 1993 1994 19951996
Source: Fundação Getulio Vargas 1999 and Instituto Brasileiro de Geografia e
Estatística 1999.
Figure 4.2 Macroeconomic Instability in Brazil: Per Capita
GDP
Per capita GDP growth rate (percent)
10
8 8 7
6 6
5
4 4
4
3 3
2 2 3
2 2 1 1
0
1
2 1
2 2
4
5
6
6 6
8
1976 1977 1978 1979 19801981 1982 1983 1984 19851986 1987 1988 1989 1990 19911992 1993 1994 19951996
Source: Instituto Brasileiro de Geografia e Estatística 1999.
84
THE SLIPPERY SLOPE: EXPLAINING THE INCREASE 85
In addition, substantial structural changes were taking place.
Brazil's population grew by 46.6 percent between 1976 and 19962
and became more urban (the urbanization rate rose from 68 percent
to 77 percent). The average education of those 10 years or older
rose from 3.2 to 5.3 effective years of schooling.3 Open unemploy-
ment grew steadily more prevalent. The sectoral composition of the
labor force moved away from agriculture and manufacturing and
toward the service industries. The degree of formalization of the
labor force declined substantially: the proportion of formal workers
(wage workers with formal documentation) dropped by nearly half,
from just less than 60 percent to just more than 30 percent of all
workers (see table 4.1). However, despite the macroeconomic tur-
moil and continuing structural changes, a casual glance at the head-
line inequality indicators and poverty incidence measures reported
at the bottom of table 4.1 suggests that little changed in the Brazil-
ian urban income distribution between 1976 and 1996.
Nevertheless, as is often the case, casual glances at the data can
be misleading. This apparent distributional stability belies a number
of powerful, and often countervailing, changes in four realms: the
returns to education in the labor markets, the distribution of educa-
tional endowments over the population, the pattern of occupational
choices, and the demographic structure resulting from household
fertility choices. In this chapter, we discuss two puzzles about the
evolution of Brazil's urban income distribution in the 197696
period and suggest explanations for them.
The first puzzle is posed by the combination of growth in mean
incomes and stable or slightly declining inequality on the one hand
and rising extreme poverty on the other hand. We argue that this
enigma can be explained only by the growth in the size of a group
of very poor households, who appear to be effectively excluded both
from the labor markets and the system of formal safety nets. This
group is trapped in indigence at the very bottom of the urban
Brazilian income distribution and contributes to rises in poverty
measures, particularly to bottom-sensitive measures like the depth
[P(1)] and severity [P(2)] of poverty.4 This is especially the case when
poverty is defined with respect to a low poverty line. E(0) fails to
respond to this group because of a rise in the share of families report-
ing (valid) zero incomes.5 Other inequality measures, which also fell
slightly between 1976 and 1996, compensated for these increases in
poverty by declining dispersion further along the distribution. How-
ever, the reality of the loss in income to the poorest group of urban
households is starkly captured by figure 4.3, which plots the
observed (truncated) Pen parades for the four years being studied.6
The main endogenous channel through which the marginalization
86 FERREIRA AND PAES DE BARROS
Table 4.1 General Economic Indicators for Brazil,
Selected Years
Economic indicator 1976 1981 1985 1996
Gross national product
per capita (in constant
1996 reais)a 4,040 4,442 4,540 4,945
Annual inflation
rate (percent)a,b 42 84 190 9
Open unemployment
(percent)c 1.82 4.26 3.38 6.95
Average years of schoolingd,e 3.23 4.01 4.36 5.32
Rate of urbanizatione 67.8 77.3 77.3 77.0
Self-employed workers (as a
percentage of the
labor force)e 27.03 26.20 26.19 27.21
Percentage of formal
employmente,f 57.76 37.97 36.41 31.51
Mean (urban) household
per capita income
(in constant 1996 reais)e,g 265.10 239.08 243.15 276.46
Inequality (Gini)e 0.595 0.561 0.576 0.591
Inequality (Theil T)e 0.760 0.610 0.657 0.694
Poverty incidence
(R$30 per month)e 0.0681 0.0727 0.0758 0.0922
Poverty incidence
(R$60 per month)e 0.2209 0.2149 0.2274 0.2176
a. Annual figure is given.
b. Rate shown is for January to December. The 1976 figure is based on the Índice
Geral de PreçosDisponibilidade Interna (General Price Index). All other years are
based on the Índice Nacional de Preços ConsumidorReal (National Consumer Price
Index).
c. Rate is based on the Instituto Brasileiro de Geografia e Estatística (Brazilian
Geographical and Statistical Institute) Metropolitan Unemployment Index.
d. Rate is for all individuals 10 years of age or older in urban areas.
e. Rate is calculated from the urban Pesquisa Nacional por Amostra de Domicilios
(National Sample Survey) samples by the authors. See appendix 4A.
f. Defined as the number of formal sector (com carteira) employees as a fraction of
the sum of all wage employees and self-employment workers.
g. Urban only, monthly and spatially deflated.
Source: Authors' calculations.
of this group is captured in our model is a shift in their occupational
"decisions" away from either wage or self-employment, toward
unemployment or out of the labor force.7
Second, the evidence we examine reveals general downward shifts
in the earnings-education profile, controlling for age and gender, in
both the wage and self-employment sectors over the 20-year data
THE SLIPPERY SLOPE: EXPLAINING THE INCREASE 87
Figure 4.3 Truncated Pen Parades, 197696
Income (R$)
200
180
160
140
120
100
80
60
40
20
0
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61
Percentile
1976 1981 1985 1996
Source: Authors' calculations.
period, 197696 (figure 4.4). Despite a slight convexification of the
profile, the magnitude of the shift implies a decline in the (average)
rate of return to education for all relevant education levels. Simi-
larly, average returns to experience also fell unambiguously for 0 to
50 years of experience (figure 4.5). The combined effect of changes
in these returns--the price effects--was an increase in simulated
poverty for all measures and for both lines. Simulated inequality
also rose, albeit much more mildly. Both effects were exacerbated
when the changes (to 1996) of the determinants of labor-force par-
ticipation decisions also were taken into account. The second puz-
zle, then, is what forces counterbalance these price and occupa-
tional choice effects to explain the observed stability in inequality
and "headline poverty."8 We found that these forces were funda-
mentally the combination of increased educational endowments,
which move workers up along the flattening earnings-education
slopes, with an increase in the correlation between family income
and family size, caused by a more-than-proportional reduction in
dependency ratios and family sizes for the poor. This demographic
88 FERREIRA AND PAES DE BARROS
Figure 4.4 Plotted Quadratic Returns to Education
(Wage Earners)
Returns
25
20
15
10
5
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Years of schooling
1976 1981 1985 1996
Source: Authors' calculations.
factor had direct effects on per capita income--through a reduction
in the denominator--but also had indirect effects--through partici-
pation decisions leading to higher incomes.
Naturally, the coexistence of these two phenomena or puzzles
implies that these last combined educational and demographic
effects did not extend to all of Brazil's poor. At the very bottom,
some of the poor are being cut off from the benefits of greater edu-
cation and economic growth and remain trapped in indigence.
We address these issues by means of a microsimulation-based
decomposition of distributional changes, which builds on the work
of Almeida dos Reis and Paes de Barros (1991) and of Juhn,
Murphy, and Pierce (1993). The approach, which was described in
chapters 1 and 2 of the book, has two distinguishing features. First,
unlike other dynamic inequality decompositions, such as the
approach proposed by Mookherjee and Shorrocks (1982), it decom-
poses the effects of changes on an entire distribution rather than
on a scalar summary statistic (such as the mean log deviation).
This approach allows for much greater versatility: within the same
THE SLIPPERY SLOPE: EXPLAINING THE INCREASE 89
Figure 4.5 Plotted Quadratic Returns to Experience
(Wage Earners)
Returns
6
5
4
3
2
1
0
0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69
Years of experience
1976 1981 1985 1996
Source: Authors' calculations.
framework, a wide range of simulations can be performed to inves-
tigate the effects of changes in specific parameters on any number of
inequality or poverty measures (and then for any number of poverty
lines or assumptions about equivalence scales). Second, the evolving
distribution, which it decomposes, is a distribution of household
incomes per capita (with the recipient unit generally being the indi-
vidual). Therefore, moving beyond pure labor-market studies, the
approach explicitly takes into account the effect of household com-
position on living standards and participation decisions. As it turns
out, these factors are of great importance for a fuller understanding
of the dynamics at hand.
The remainder of the chapter is organized as follows. The next
section briefly reviews the main findings of the literature on income
distribution in Brazil over the period of study and presents summary
statistics and dominance comparisons for the four observed distri-
butions analyzed: 1976, 1981, 1985, and 1996. The methodology
section outlines how the basic model in chapter 2 of this book was
adapted to the case of Brazil. The section on estimating the model
90 FERREIRA AND PAES DE BARROS
presents the results of the estimation stage and discusses some of its
implications. It is followed by a section presenting the main results
of the simulation stage and decomposing the observed changes in
poverty and inequality. The chapter then concludes and draws some
policy implications.
Income Distribution in Brazil from 1976 to 1996:
A Brief Review of the Literature and the Data Set
There is little disagreement in the existing literature about the broad
trends in Brazilian inequality since reasonable data first became
available in the 1960s. The Gini coefficient rose substantially during
the 1960s, from around 0.500 in 1960 to 0.565 in 1970 (see Bonelli
and Sedlacek 1989).9 There was a debate over the causes of this
increase, spearheaded by Albert Fishlow (1972) on the one hand
and Carlos Langoni (1973) on the other. However, there was gen-
eral agreement that the 1960s saw substantially increased disper-
sion in the Brazilian income distribution.10
The 1970s displayed a more complex evolution. Income inequal-
ity rose between 1970 and 1976, reached a peak in that year, and
then fell--both for the distribution of total individual incomes in
the economically active population and for the complete distribu-
tion of household per capita incomes--from 1977 to 1981. This
decline was almost monotonic, except for an upward blip in 1980
(Bonelli and Sedlacek 1989; Hoffman 1989; Ramos 1993). The
recession year of 1981 was a local minimum in the inequality series,
whether measured by the Gini coefficient or the Theil T index. From
1981, income inequality rose during the recession years of 1982 and
1983. Some authors report small declines in some indices in 1984,
but the increase resumed in 1985. In 1986, the year of the Cruzado
Plan, a break in the series was caused both by a sudden (if short-
lived) decline in inflation and by a large increase in reported house-
hold incomes. Stability and economic growth led to a decline in mea-
sured inequality, according to all of the authors cited in table 4B.1
in appendix 4B. Thereafter, with the failure of the Cruzado stabi-
lization attempt and the return to stagflation, inequality resumed its
upward trend, with the Gini coefficient finishing the decade at 0.606.
Table 4B.1 summarizes the findings of this literature, both for per
capita household incomes and for the distribution of total individ-
ual incomes in the economically active population.
The general trends identified in the existing literature are mir-
rored in the statistics for the years covered in this chapter: 1976,
1981, 1985, and 1996. The distributions for each of these years
were taken from the Pesquisa Nacional por Amostra de Domicílios
THE SLIPPERY SLOPE: EXPLAINING THE INCREASE 91
(National Sample Survey, or PNAD), run by the Instituto Brasileiro
de Geografia e Estatística (Brazilian Geographical and Statistical
Institute, or IBGE). Except where otherwise explicitly specified, we
deal with distributions for urban areas only, where the welfare con-
cept is total household income per capita (in constant 1996 reais,
spatially deflated to adjust for regional differences in the average
cost of living), and the unit of analysis is the individual. Details of
the PNAD sampling coverage and methodology, sample sizes, defi-
nitions of key income variables, spatial and temporal deflation
issues, and adjustments with respect to the national accounts base-
line are discussed in appendix 4A.
Table 4.2 presents a number of summary statistics for these dis-
tributions in addition to the mean, which was provided in table 4.1.
The four inequality indices used throughout this chapter are the
Gini coefficient and three members of the generalized entropy class
Table 4.2 Basic Distributional Statistics for Different
Degrees of Household Economies of Scale
Statistic 1976 1981 1985 1996
Median (1996 R$)a 127.98 124.04 120.83 132.94
Inequality
Gini, = 1.0 0.595 0.561 0.576 0.591
Gini, = 0.5 0.566 0.529 0.548 0.567
E(0), = 1.0 0.648 0.542 0.588 0.586
E(0), = 0.5 0.569 0.472 0.524 0.534
E(1), = 1.0 0.760 0.610 0.657 0.694
E(1), = 0.5 0.687 0.527 0.580 0.622
E(2), = 1.0 2.657 1.191 1.435 1.523
E(2), = 0.5 2.254 0.918 1.134 1.242
Poverty, R$30 per month
P(0), = 1.0 0.0681 0.0727 0.0758 0.0922
P(0), = 0.5 0.0713 0.0707 0.0721 0.0847
P(1), = 1.0 0.0211 0.0337 0.0326 0.0520
P(1), = 0.5 0.0235 0.0315 0.0303 0.0442
P(2), = 1.0 0.0105 0.0246 0.0224 0.0434
P(2), = 0.5 0.0132 0.0226 0.0204 0.0357
Poverty, R$60 per month
P(0), = 1.0 0.2209 0.2149 0.2274 0.2176
P(0), = 0.5 0.2407 0.2229 0.2382 0.2179
P(1), = 1.0 0.0830 0.0879 0.0920 0.1029
P(1), = 0.5 0.0901 0.0875 0.0927 0.0960
P(2), = 1.0 0.0428 0.0525 0.0534 0.0703
P(2), = 0.5 0.0471 0.0508 0.0521 0.0625
a. For urban areas only, and spatially deflated. See appendix 4A.
Source: Authors' calculations.
92 FERREIRA AND PAES DE BARROS
of inequality indexes, E(). Specifically, we chose E(0), also known
as the mean log deviation or the Theil L index; E(1), better known
as the Theil T index, and E(2), which is one-half of the square of the
coefficient of variation. These indices provide a useful range of sen-
sitivities to different parts of the distribution. E(0) is more sensitive
to the bottom of the distribution, whereas E(2) is more sensitive to
higher incomes. E(1) is somewhere in between, whereas the Gini
places greater weight around the mean.
We also present three poverty indices from the Foster, Greer, and
Thorbecke (1984) additively decomposable class P(). P(0), also
known as the headcount index, measures poverty incidence. P(1) is
the normalized poverty deficit, and P(2) is an average of squared
normalized deficits, thus placing greater weight on incomes furthest
from the poverty line. We calculated each of these indices with
respect to two poverty lines, representing R$1 and R$2 per day, at
1996 prices.11
Each of these poverty and inequality indices is presented both for
the (individual) distribution of total household incomes per capita
and for an equivalized distribution using the Buhmann and others
(1988) parametric class of equivalence scales (with = 0.5). This
method provides a rough test that the trends described are robust to
different assumptions about the degree of economies of scale in con-
sumption within households. Although a per capita distribution
does not allow for any such economies of scale, taking the square
root of family size allows for economies of scale to a rather gener-
ous degree. As usual, per capita incomes generate an upper bound
for inequality measures, whereas allowing for some extent of local
public goods within households raises the income of (predominantly
poor) large households and lowers inequality. In the case of the
poverty measures, the poverty lines were adjusted as follows:
z = z[µ(n)]1 - , where µ(n) is the mean household size in the dis-
tribution (see Deaton and Paxson 1997).
Table 4.2 also confirms that the evolution of inequality over the
period was marked by a decline from 1976 to 1981 and by a subse-
quent deterioration over the remaining two subperiods. Further-
more, this trend is robust to the choice of equivalence scale, proxied
here by two different values for , although the inequality levels are
always lower when we allow for economies of scale within house-
holds. It is also robust to the choice of inequality measure, at least
with regard to the inequality increases from 1981 to 1996 and from
1985 to 1996, as the Lorenz dominance results identified in table 4.3
indicate.
The results for poverty are more ambiguous. With respect to the
higher poverty line, incidence is effectively unchanged throughout
THE SLIPPERY SLOPE: EXPLAINING THE INCREASE 93
Table 4.3 Stochastic Dominance Results
1976 1981 1985 1996
1976 F
1981 L
1985 L
1996
Source: Authors' calculations.
the period (and even displays a slight decline for the equivalized
distribution). P(1) and P(2), however, showed increases over the
period, which become both more pronounced and more robust with
respect to as the concavity of the poverty measure increases. This
trend suggests that depth and severity of poverty, affected mostly by
falling incomes at the very bottom of the distribution, were rising.
These results are reflected in table 4.3, in which a letter L (F) in
cell (i, j) indicates that the distribution for year i Lorenz dominates
(first order stochastically dominates) that for year j. Both 1981 and
1985 display Lorenz dominance over 1996, as suggested earlier.
There is only one case of first-order welfare dominance throughout
the period, and symptomatically, it is not a case of a later year
over an earlier one. Instead, money-metric social welfare was
unambiguously higher in 1976 than in 1985. Indeed, all poverty
measures reported for both of our lines (and for = 1.0) are higher
in 1985 than in 1976.12 This finding is conspicuously not the case
for a comparison between 1976 and 1996. Although poverty mea-
sures very sensitive to the poorest are higher for 1996, poverty
incidence for "higher" lines fall from 1976 to 1996, suggesting a
crossing of the distribution functions. Figure 4.3 shows this cross-
ing by plotting the Pen parades [F-1(y)], truncated at the 60th
percentile for all four years analyzed. Note that although 1976 lies
everywhere above 1985, all other pairs cross. In particular, 1976
and 1996 cross somewhere near the 17th percentile.
Before we turn to the model used to decompose changes in the
distribution of household incomes, which will shed some light on all
of these changes, it is helpful to gather some evidence on the evolu-
tion of educational attainment (as measured by average effective
years of schooling) and on labor-force participation, for different
groups in the Brazilian population, partitioned by gender and eth-
nicity. Table 4.4 presents these statistics. As seen, there was some
progress in average educational attainment in urban Brazil over this
period. Average effective years of schooling for all individuals 10
years or older, as reported in table 4.1, rose from 3.2 to 5.3 years.
94 FERREIRA AND PAES DE BARROS
Table 4.4 Educational and Labor-Force Participation
Statistics, by Gender and Race
Statistic 1976 1981 1985 1996
Average years of schooling
Males 3.32 4.04 4.36 5.20
Females 3.14 3.99 4.37 5.43
Blacks and mixed-race
individuals -- -- -- 4.20
Whites -- -- -- 6.16
Asians -- -- -- 8.13
Labor-force participation
(percent)
Males 73.36 74.63 76.04 71.31
Females 28.62 32.87 36.87 42.00
Blacks and mixed-race
individuals -- -- -- 55.92
Whites -- -- -- 56.41
Asians -- -- -- 54.88
-- Not available.
Notes: Table shows the average effective years of schooling for persons age 10 or
older in urban areas. Labor-force participation rates are for urban areas only.
Source: Authors' calculations.
In fact, this piece of good news was vital in preventing a more
pronounced increase in poverty. Table 4.4 now reveals that the
male-female educational gap has been eliminated, with females
10 years or older being on average slightly more educated than
males of the same age. Clearly, this finding must imply a large dis-
parity in favor of girls in recent cohorts. Although a cohort analysis
of educational trends is beyond the scope of this chapter,13 such a
rapid reversal may in fact warrant a shift in public policy toward
programs aimed at keeping boys in school, without in any way dis-
couraging the growth in schooling of girls. Finally, note the remark-
able disparity in educational attainment across ethnic groups, with
Asians substantially above average and blacks and those of mixed
race below average.
As for labor-force participation, the persistent and substantial
increase in female participation from 29 percent to 42 percent over
the two decades was partly mitigated by a decline in male partici-
pation rates. Those trends notwithstanding, the male-female partic-
ipation gap remains high, at around 30 percentage points. There is
little evidence of differential labor-force participation across ethnic
groups.
THE SLIPPERY SLOPE: EXPLAINING THE INCREASE 95
The Model and the Decomposition Methodology
Let us now turn to the Brazilian version of the general semireduced-
form model for household income and labor supply in chapter 2. It
is used here to investigate the evolution of the distribution of house-
hold incomes per capita over the two decades from the mid-1970s
to the mid-1990s. Specifically, we analyzed the distributions of
1976, 1981, 1985, and 1996 and simulated changes between them.
As stated earlier, this chapter covers only Brazil's urban areas (which
account for some three-quarters of its population). The general
model, therefore, collapses to two occupational sectors: wage earn-
ers and self-employed workers in urban areas.14
Total household income (Yh) is given by
n n
(4.1) Yh = wi Li +
w i Li + Y0
se
h
i=1 i=1
where wi is the total wage earnings of individual i; Lw is a dummy
variable that takes the value 1 if individual i is a wage earner (and 0
otherwise); i is the self-employment profit of individual i; Lse is a
dummy variable that takes the value 1 if individual i is self-employed
(and 0 otherwise); and Y0 is income from any other source, such as
transfer income or capital income. Equation 4.1 is not estimated
econometrically. It aggregates information on right-hand-side terms
1 (from equations 4.2 and 4.4), 2 (from equations 4.3 and 4.4), and
3 directly from the household data set.
The wage-earnings equation is given as follows:
(4.2) Log wi = Xi w + i
P w
where Xi = (ed, ed2, exp, exp2, Dg) and ed denotes completed effec-
P
tive years of schooling. Experience (exp) is defined simply as (age -
education - 6), because a more desirable definition would require
the age when a person first entered employment, a variable that is
not available for 1976.15 Dg is a gender dummy variable, which
takes the value of 1 for females and 0 for males; wi is the monthly
earnings of individual i; and i is a residual term that captures any
other determinant of earnings, including any unobserved individual
characteristics, such as innate talent. This extremely simple specifi-
cation was chosen to make the simulation stage of the decomposi-
tion feasible, as described below. Analogously, the self-employed
earnings equation is given as follows:
(4.3) Log i = Xi se + i .
P se
Equations 4.2 and 4.3 are estimated using ordinary least squares
(OLS). Equation 4.2 is estimated for all employees, whether or not
96 FERREIRA AND PAES DE BARROS
they are heads of household and whether or not they have formal
sector documentation (com or sem carteira). Equation 4.3 is esti-
mated for all self-employed individuals (whether or not they are
heads of households). Because the errors are unlikely to be inde-
pendent from the exogenous variables, a sample selection bias cor-
rection procedure might be used. However, the standard Heckman
procedure for sample selection bias correction requires equally
strong assumptions about the orthogonality between the error terms
and (from the occupational-choice multinomial logit below).
The assumptions required to validate OLS estimation of equations
4.2 and 4.3 are not more demanding than those required to validate
the results of the Heckman procedure. We assume, therefore, that
all errors are independently distributed and do not correct for sam-
ple selection bias in the earnings regressions.
We now turn to the labor-force participation model. Because we
had a two-sector labor market (segmented into the wage employ-
ment and self-employment sectors), labor-force participation and the
choice of sector (occupational choice), could be treated in two dif-
ferent ways. One could assume that the choices were sequential, with
a participation decision independent from the occupational choice
and the latter conditional on the former. That approach, which would
be compatible with a sequential probit estimation, was deemed less
satisfactory than an approach in which individuals face a single three-
way choice, between staying out of the labor force, working as
employees, or being self-employed. Such a choice can be estimated
by a multinomial logit model. According to that specification, the
probability of being in state s = (0, w, se) is given by equation 4.4:
eZis
(4.4) Pi =
s
eZis + eZij where s, j (0, w, se)
j=s
where the explanatory variables differ for household heads and
other household members, by assumption, as follows. For house-
hold heads,
1
P
X1 ; n0-13, n14-65, n>65, D14 -65ed,
n14
-65 -1
Z1 =
h 1 2 1
D14-65 ed , D14 -65age, .
n14-65 -1 n14 -65 -1
1 2 1
D14 age , D14 Dg, D
n14 -65 -65
-65 -1 n14 -65 -1
Notice that this is essentially a reduced-form model of labor
supply, in which own earnings are replaced by the variables that
THE SLIPPERY SLOPE: EXPLAINING THE INCREASE 97
determine them, according to equation 4.2 or 4.3. For other mem-
bers of the household,
1
Xi P; n0
-13, n14-65, n>65, D14 -65ed,
n14
-65 -i
Zi =
h 1 2 1
D14 -65ed , D14-65age,
n14 -65 -i n14-65 -i
1 2 1
D14 age , D14 se
n14 -65 -65Dg, D1 , Lww1,D
1
-65 -i n14-65 -i
where nk is the number of persons in the household whose age
m
falls between k and m, D14 is a dummy variable that takes the
65
value of 1 for individuals whose age is between 14 and 65, Dse is a
dummy variable for a self-employed head of household, and the
penultimate term is the earnings of a wage-earning head. These last
two variables establish a direct conduit for the effect of the house-
hold head's occupational choice (and possibly income) on the par-
ticipation decisions of other members. D is a dummy variable that
takes the value 1 if there are no individuals age 14 to 65 years in the
household. The sums defined over {-j} are sums over {i h| j}.
The multinomial logit model in equation 4.4 corresponds to the
following discrete choice process:
(4.5) s = Argj max Uj = Zi j + y, j = (0, w, se)
h
¨
where Z is given above, separately for household heads and other
members; the y are random variables with a double exponential
¨
density function; and Uj may be interpreted as the utility of alterna-
tive j. Once the vector j is estimated by equation 4.4, and a random
term is drawn, each individual chooses an occupation j so as to
maximize the above utility function.
Once equations 4.2, 4.3, and 4.4 have been estimated, we have
two vectors of parameters for each of the four years in our sample
(t {1976, 1981, 1985, 1996}): t from the earnings equations for
both wage earners and the self-employed (including constant terms
t) and t from the participation equation. In addition, from equa-
tion 4.1, we have Y0 and Yht. Let Xht = {Xi , Zi |i h} and
P h
ht ht=
{wi, sei, ji|i h}. We can then write the total income of household h
at time t as follows:
(4.6) Yht = H (Xht, Y0 ,
ht ht; t, t) h 1, . . . , m.
On the basis of this representation, changes in the distribution
of incomes can be decomposed into price effects ( ), occupational-
choice effects (), endowment effects (X, Y0), and residual
98 FERREIRA AND PAES DE BARROS
effects ( ), as outlined in chapter 2. Calculating the price and
occupational-choice effects is reasonably straightforward once the
relevant exogenous parameters have been estimated. Estimating
individual endowment effects requires a further step because
elements of the X and Y vectors are jointly distributed and a change
in the value of any one variable must be understood conditionally
on all other observable characteristics.
Specifically, if we are interested in the effect of a change in the
distribution of a single specific variable Xk on the distribution of
household incomes between times t and t , it is first necessary to
identify the distribution of Xk conditional on other relevant charac-
teristics X-k (and possibly other incomes Y0). This can be done by
regressing Xk on X-k at dates t and t , as follows:
(4.7) Xkit = X-kitµt + ukit
where k is the variable, i is the individual, and t is the date. The vec-
tor of residuals ukit represents the effects of unobservable character-
istics (assumed to be orthogonal to X-k) on Xk. The vector µt is a
vector of coefficients capturing the dependency of Xk on the true
exogenous variables X-k, at time t. For the sake of simplicity, let us
assume that the error terms u are normally distributed with a mean
of zero and a common standard deviation t.
The same equation can, of course, be estimated at date t , gener-
ating a corresponding vector of coefficients µt, and a standard error
of the residuals given by t . We are then ready to simulate the effect
of a change in the conditional distribution of Xk from t to t by
replacing the observed values of Xkit in the sample observed at time
t, with
t
(4.8) Xkit = X-kitµt + ukit
.
t
The contribution of the change in the distribution of the variable
Xk to the change in the distribution of incomes between t and t may
now be written as follows:
Rtt =D[{Xkit , X-kit, Y0 ,
x
ht ht}, t, t]
(4.9) - D[{Xkit, X-kit, Y0 ,
ht ht }, t, t].
In this study, we perform four regression estimations such as
equation 4.7, and hence four simulations such as equation 4.8. The
four variables estimated are Xk = {n0 -13, n14-65 , n>65, ed). In the case
of the education regression, the vector of explanatory variables X-kit
was (1, age, age2, Dg, regional dummy variables). In the case of the
regressions with the numbers of household members in certain age
THE SLIPPERY SLOPE: EXPLAINING THE INCREASE 99
intervals as dependent variables, the vector X-kit was (1, age, age2,
ed, ed2, regional dummy variables), where age and education are
those of the household head. The simulations permitted by these
estimations allow us to investigate the effects of the evolution of the
distribution of educational attainment and of the demographic
structure on the distribution of income. We now turn to the results
of the estimation stage of the model.
Estimating the Model
The results of the OLS estimation of equation 4.2 for wage earners
(formal and informal) are shown in table 4.5. The static results are
not surprising. All variables are significant and have the expected
signs. The coefficients on education and its square are positive and
significant. The effect of experience (defined as age - education -
6) is positive but concave. The gender dummy variable (female = 1)
is negative, significant, and large.
The dynamics are more interesting. Between 1976 and 1996, the
earnings-education profile changed shape. After rising in the late
1970s, the linear component fell substantially between 1981 and
1996. Meanwhile, the coefficient of squared years of schooling fell
to 1981 but then more than doubled to 1996, ending the period
substantially above its initial 1976 value. Overall, the relationship
Table 4.5 Equation 4.2: Wage Earnings Regression for
Wage Employees
Variable 1976 1981 1985 1996
Intercept 4.350 4.104 3.877 4.256
(0.0001) (0.0001) (0.0001) (0.0001)
Education 0.123 0.136 0.129 0.080
(0.0001) (0.0001) (0.0001) (0.0001)
Education squared (× 100) 0.225 0.181 0.283 0.438
(0.0001) (0.0001) (0.0001) (0.0001)
Experience 0.075 0.085 0.087 0.062
(0.0001) (0.0001) (0.0001) (0.0001)
Experience squared (× 100) -0.105 -0.119 -0.121 -0.080
(0.0001) (0.0001) (0.0001) (0.0001)
Gender (1 = female) -0.638 -0.590 -0.635 -0.493
(0.0001) (0.0001) (0.0001) (0.0001)
R2 0.525 0.538 0.547 0.474
Note: P-values are in parentheses.
Source: Authors' calculations based on the PNAD.
100 FERREIRA AND PAES DE BARROS
became more convex, suggesting a steepening of marginal returns to
education at high levels. However, plotting the parabola that mod-
els the partial earningseducation relationship from equation 4.2,
the lowering of the linear term dominates. The profile shifts up from
1976 to 1981 and again to 1985, before falling precipitously
(although convexifying) to 1996 (see figure 4.4). The net effect
across the entire period was a fall in the cumulative returns to edu-
cation (from zero to t years) for the entire range. This effect coex-
isted with increasing marginal returns at high levels of education.
The implications for poverty and inequality are clear, with the edu-
cation price effect leading to an increase in the former and a decline
in the latter, all other things being equal.
Returns to experience also increased from 1976 to 1981 and
from 1981 to 1985 with a concave pattern and a maximum at
around 35 years of experience (see figure 4.5). However, from 1985
to 1996, there was a substantial decline in cumulative returns to
experience, even with respect to 1976, until 50 years of experience.
The relationship became less concave, and the maximum returns
moved up to around 40 years. Over the entire period, the experience
price effect was mildly unequalizing (although it contributed to
increases in inequality until 1985, which were later reversed) and
seriously poverty increasing.
The one piece of good news comes from a reduction in the male-
female earnings disparity. Although, when we controlled for both
education and experience, female earnings remained substantially
lower in all four years (suggesting that some labor-market discrimi-
nation may be at work), there was nevertheless a decline in this
effect between 1976 and 1996. As we will see from the simulation
results, this effect was both mildly equalizing and poverty reducing.
Let us now turn to equation 4.3, which seeks to explain the earn-
ings of the self-employed with the same set of independent variables
as equation 4.2. The results are reported in table 4.6. This table
reveals that education is also an important determinant of incomes
in the self-employment sector. The coefficient on the linear term has
a higher value in all years than for wage earners, but the quadratic
term is lower. This result implies that, all other things equal, the
return to low levels of education might be higher in self-employment
than in wage work, but these returns eventually become lower
as years of schooling increases. This result will have an effect on
occupational choice, estimated through equation 4.4. Dynamically,
the same trend was observed as for wage earners: the coefficient on
the linear term fell over time, but the relationship became more con-
vex.16 The coefficients on experience and experience squared follow
a similar pattern to that observed for wage earners, as shown in
THE SLIPPERY SLOPE: EXPLAINING THE INCREASE 101
Table 4.6 Equation 4.3: Total Earnings Regression for the
Self-Employed
Variable 1976 1981 1985 1996
Intercept 4.319 4.192 3.853 4.250
(0.0001) (0.0001) (0.0001) (0.0001)
Education 0.196 0.148 0.165 0.114
(0.0001) (0.0001) (0.0001) (0.0001)
Education squared (× 100) -0.206 0.021 0.012 0.219
(0.0001) (0.4892) (0.6545) (0.0001)
Experience 0.074 0.079 0.084 0.063
(0.0001) (0.0001) (0.0001) (0.0001)
Experience squared (× 100) -0.101 -0.108 -0.111 -0.082
(0.0001) (0.0001) (0.0001) (0.0001)
Gender -1.092 -1.148 -1.131 -0.714
(0.0001) (0.0001) (0.0001) (0.0001)
R2 0.431 0.434 0.438 0.336
Note: P-values are in parentheses.
Source: Authors' calculations based on the PNAD.
figure 4.5. Once again, the cumulative return to experience fell over
the bulk of the range from 1976 to 1996, contributing to the
observed increase in poverty. The effect of being female, all other
things equal, is even more markedly negative in this sector than in
the wage sector. It also fell from 1976 to 1996, despite a temporary
increase in disparity in the 1980s.
A cautionary word is in order before proceeding. All of the esti-
mation results reported in table 4.6 refer to equations with total
earnings as dependent variables. The changes in coefficients will,
therefore, reflect changes not only in the hourly returns to a given
characteristic but also in any supply responses that may have taken
place. The analysis is to be understood in this light.
Let us now turn to the estimation of the multinomial logit in
equation 4.4. This estimation was made separately for household
heads and for others because the set of explanatory variables was
slightly different in each case (see the description of vectors Z1 and
Zi in the previous section).17
For household heads, education was not significantly related to
the likelihood of choosing to work in the wage sector compared
with staying out of the labor force, at any time. In addition, the pos-
itive effect of education decreased from 1976 to 1996 to the point
where it was no longer statistically significant. The dominant effect
on the occupational choices of urban household heads over this
period, however, was a substantial decline in the constant term
102 FERREIRA AND PAES DE BARROS
affecting the probability of participating in either productive sector,
as opposed to remaining outside the labor force or in unemploy-
ment. Because it is captured by the constant, this effect is not related
to the educational or experience characteristics of the head of house-
hold or to the endowments of his or her household. We interpret it,
instead, as the effect of labor-market demand-side conditions, lead-
ing to reduced participation in paid work.18 In the occupational-
choice simulations reported in the next section, this effect will be
shown to be both unequalizing and immiserizing.
For other members of the household, education did appear to
raise the probability of choosing wage work compared with staying
out of the labor force, with the relationship changing from concave
to convex over the period. It also enhanced the probability of being
in self-employment compared with being outside the labor force in
both periods, although this relationship remained concave. The
number of children in the household significantly discouraged par-
ticipation in both sectors, although more so in the wage-earning
sector. The change in the constant term was much smaller than for
household heads, suggesting that negative labor-market conditions
hurt primary earners to a greater extent. Consequently, we observed
the effect of the occupational choices of other household members
on poverty and inequality to be much milder than that of the occu-
pational choices of the heads of households. This finding is in con-
trast to those in other economies where similar methodologies have
been applied. For example, in Taiwan, China, changes in labor-
force participation rates of spouses (particularly female spouses)
had important consequences for the distribution of incomes (see
chapter 9).
The results of the estimation of equation 4.7, with education of
individuals 10 years old or older as the dependent variable regressed
against the vector (1, age, age2, Dg, regional dummy variables), are
also given in Ferreira and Paes de Barros (1999). Over time, there is
a considerable increase in the value of the intercept, which will yield
higher predicted values for educational attainment, controlling for
age, gender, and regional location. In addition, the gender dummy
variable went from large and negative to positive and significant,
suggesting that women have more than caught up with men in edu-
cational attainment in Brazil over the past 20 years. The effect of
individual age is stable, and regional disparities persist, with the
South and Southeast ahead of the three central and northern regions.
Regressing the number of household members in the age intervals
013, 1465, and older than 65 years, respectively, on the vector (1,
ed, ed2, age, age2, regional dummy variables) yields the finding that
THE SLIPPERY SLOPE: EXPLAINING THE INCREASE 103
the schooling of the head of household has a large, negative, and
significant effect on the demand for children; hence, as education
levels rise, family sizes tend to fall, all other things equal. In addi-
tion, some degree of convergence across regions in family size can
be inferred, with the positive 1976 regional dummy coefficients for
all regions (with respect to the Southeast) declining over time and
more than halving in value to 1996.
Simulation Results
After estimating earnings equations for both sectors of the model--
wage earners (equation 4.2) and the self-employed (equation 4.3);
participation equations for both household heads and other house-
hold members (equation 4.4); and endowment equations for the
exogenous determination of education and family composition
(equation 4.7), we are now in the position to carry out the decom-
positions described in chapter 1. These simulations, as discussed
earlier, are carried out for the entire distribution. The results are
summarized in table 4.7, through the evolution of (a) the mean
household per capita income µ(y); (b) four inequality indices--the
Gini coefficient, the Theil L index [E(0)], the Theil T index [E(1)],
and E(2); and (c) the standard three members of the Foster, Greer,
and Thorbecke (1984) class of poverty measures--P(), = 0, 1,
2--computed with respect to two monthly poverty lines: an indi-
gence line of R$30 and a poverty line of R$60 (both expressed in
1996 São Paulo metropolitan area prices).19
Table 4.7 contains a great wealth of information about a large
number of simulated economic changes, always by bringing combi-
nations of 1996 coefficients to the 1976 population. To address the
two puzzles posed in the introduction to this chapter--namely, the
increase in extreme urban poverty between 1976 and 1996 despite
(sluggish) growth and (mildly) reducing inequality and the coexis-
tence of a deteriorating labor market with stable headline poverty--
we now plot differences in the logarithms of incomes between the
simulated distribution of household incomes per capita and that
observed for 1976 for a number of the simulations in table 4.7.20
Figure 4.6 plots the combined price effects ( and ) separately for
wage earners and the self-employed. As can be seen, these effects
were negative (that is, they would have implied lower income in
1976) for all percentiles. The losses were greater for wage earners
than for the self-employed and, for the latter, were regressive. Those
losses are exactly what one would have expected from the downward
P(2)
0.0428 0.0703 0.0596 0.0490 0.0673 0.0545 0.0590 0.0488 0.0525 0.0404
R$60
=z month P(1)
0.0830 0.1029 0.1129 0.0932 0.1249 0.1040 0.1114 0.0953 0.1000 0.0797
per
Poverty:
P(0)
0.2209 0.2176 0.2876 0.2399 0.3084 0.2688 0.2837 0.2531 0.2592 0.2160
P(2)
0.0105 0.0434 0.0141 0.0121 0.0169 0.0129 0.0143 0.0110 0.0125 0.0090
R$30
=z month P(1)
cientsfi 0.0211 0.0530 0.0304 0.0250 0.0357 0.0275 0.0303 0.0234 0.0265 0.0191
per
Poverty:
Coef P(0)
0.0681 0.0922 0.0984 0.0788 0.1114 0.0897 0.0972 0.0779 0.0851 0.0650
1996
E(2) 2.657 1.523 2.161 2.787 2.190 2.691 2.055 2.691 2.694 2.590
Using
E(1) 0.760 0.694 0.752 0.770 0.754 0.774 0.736 0.759 0.771 0.751
1976,
for Inequality E(0) 0.648 0.586 0.656 0.658 0.655 0.664 0.644 0.639 0.664 0.649
Gini 0.595 0.591 0.598 0.597 0.598 0.601 0.593 0.593 0.600 0.595
Inequality
and capita
Mean income
per 265.101 276.460 218.786 250.446 204.071 233.837 216.876 232.830 240.618 270.259
Poverty
both
Simulated earners for) both both
both no for for both
4.7 wage self-employed both
observed observed effects for, for
ableT Indicator 1976 1996 Price for, for, for
, (but
only All Education Experience Gender
104
0.0671 0.0454 0.0902 0.0264 0.0677 0.0287 0.0173 0.0561
0.1082 0.0867 0.1466 0.0554 0.1129 0.0567 0.0359 0.0913
0.2471 0.2274 0.3248 0.1711 0.2724 0.1593 0.1131 0.2204
0.0331 0.0119 0.0402 0.0063 0.0321 0.0073 0.0049 0.0296
0.0451 0.0231 0.0597 0.0113 0.0433 0.0136 0.0078 0.0374
0.0944 0.0721 0.1352 0.0365 0.0931 0.0424 0.0225 0.0735
2.633 2.482 2.401 2.432 2.177 2.485 2.320 1.896
0.788 0.757 0.788 0.704 0.727 0.740 0.688 0.727
0.650 0.657 0.649 0.585 0.577 0.650 0.584 0.600
0.609 0.598 0.610 0.574 0.587 0.594 0.571 0.594
PNAD.
the
260.323 265.643 202.325 277.028 210.995 339.753 353.248 263.676 on
based
effects
effects
+
sectors all calculations'
patterns
heads other all
sectors sectors both endowment all all
all
both for for for, for, Authors
for
both both d
only
Occupational-choice for (and others) for (only members) ,, for,,,, ,,
e
only µ, µ, for,,
d d e d e Source:
Demographic µ µ Education µ µ µ
105
106 FERREIRA AND PAES DE BARROS
Figure 4.6 Combined Price Effects by Sector
Difference of log incomes
0.3
0.2
0.1
0.0
0.1
0.2
0.3
0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96
Percentile
Wage earners Self-employment
Source: Authors' calculations.
shifts of the partial earnings-education and earnings-experience
profiles, shown in figures 4.4 and 4.5.
In figure 4.7, we adopt a different tack to the price effects by
plotting the income differences for each price-effect simulation (for
both sectors combined) and then aggregating them. As we would
expect from figures 4.4 and 4.5, the returns to education and expe-
rience are both immiserizing. The change in partial returns to edu-
cation alone is mildly equalizing (as can be seen from table 4.7). The
change in the partial returns to experience is unequalizing as well as
immiserizing. The change in the intercept, calculated at the mean
values of the independent variables, was also negative throughout.
This change proxies for a "pure growth" effect, capturing the effects
on earnings from processes unrelated to education, experience, gen-
der, or the unobserved characteristics of individual workers. It is
intended to capture the effects of capital accumulation, managerial
and technical innovation, macroeconomic policy conditions, and
other factors likely to determine economic growth that are not
included explicitly in the Mincer equation. Its negative effect in this
THE SLIPPERY SLOPE: EXPLAINING THE INCREASE 107
Figure 4.7 Price Effects Separately and for Both
Sectors Combined
Difference of log incomes
0.3
0.2
0.1
0.0
0.1
0.2
0.3
0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96
Percentile
Combined price effect Economic growth Returns to education
Returns to experience Returns to being female
Source: Authors' calculations based on the 1976 and 1996 PNAD.
simulation suggests that these factors were immiserizing in urban
Brazil over the period.
The one piece of good news, once again, comes from the gender
simulation, which reports a poverty-reducing effect as a result of the
decline in male-female earnings differentials captured in tables 4.5
and 4.6. However, this effect was far from being sufficient to offset
the combined negative effects of the other price effects. As the thick
line at the bottom of figure 4.7 indicates, the combined effect of
imposing the 1996 parameters of the two Mincerian equations on
the 1976 population was substantially immiserizing.
Figure 4.8 plots the logarithm of the income differences between
the distribution that arises from imposing the 1996 occupational-
choice parameters (the vector from the multinomial logit in
equation 4.4) on the 1976 population and the observed 1976 distri-
bution. It does so both for all individuals (the lower line) and for
108 FERREIRA AND PAES DE BARROS
Figure 4.8 Occupational-Choice Effects
Difference of log incomes
0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96
Percentile
All s s (nonhead of household)
Source: Authors' calculations based on the 1976 and 1996 PNAD.
nonhousehold heads (the upper line). The effect of this simulated
change in occupational-choice and labor-force participation behav-
ior is both highly immiserizing and unequalizing, as an inspection of
the relevant indices in table 4.7 confirms. It suggests the existence of
a group of people who--by voluntarily or involuntarily leaving the
labor force, entering unemployment, or being consigned to very ill-
remunerated occupations (likely) in the informal sector--are becom-
ing increasingly impoverished.
Combining the negative price and occupational-choice effects
provides a sense of the overall effect of Brazil's urban labor-market
conditions over this period. This finding is shown graphically in
figure 4.9, where the lowest curve plots (a) the differences between
the household per capita incomes from a distribution in which all
s, s, and s change, and (b) the observed 1976 distribution. It
shows the substantially poverty-augmenting (and unequalizing)
combined effect of changes in labor-market prices and occupational-
choice parameters on the 1976 distribution.
THE SLIPPERY SLOPE: EXPLAINING THE INCREASE 109
Figure 4.9 The Labor Market: Combining Price and
Occupational-Choice Effects
Difference of log incomes
0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96
Percentile
s and s All s s, s, and s
Source: Authors' calculations based on the 1976 and 1996 PNAD.
At this point, the second puzzle can be stated clearly: given these
labor-market circumstances, what factors can account for the facts
that mean incomes rose, headline poverty did not rise, and inequal-
ity appears to have fallen slightly? The first part of the answer is
shown graphically in figure 4.10, where the upper line plots the
differences between the log incomes from a distribution arising from
imposing on the 1976 population the transformation (equation 4.8)
for the demographic structure of the population. The changes in the
parameters µd (and in the variance of the residuals in the corre-
sponding regression) have a positive effect on incomes for all per-
centiles and in an equalizing manner. However, when combined with
a simulation in which the values of all s, s, and s also change, it
can be seen that the positive demographic effect is still overwhelmed.
Nevertheless, it is clear that the reduction in dependency ratios--
and subsequently in family sizes--in urban Brazil over this period
had an important mitigating effect on the distribution of incomes.
110 FERREIRA AND PAES DE BARROS
Figure 4.10 Demographic Effects
Difference of log incomes
0.4
0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96
Percentile
(d) (d), s, s, and s
Source: Authors' calculations based on the 1976 and 1996 PNAD.
One final piece of the puzzle is needed to explain why the deteri-
oration in labor-market conditions did not have a worse effect on
poverty. That, as should be evident from the increase in mean years
of effective schooling registered in table 4.1, is the rightward shift
in the distribution function of education. This effect is shown in
figure 4.11, which reveals that gains in educational attainment were
particularly pronounced at lower levels of education and thus, pre-
sumably, among the poor.
A gain in educational endowments across the income distribu-
tion, but particularly among the poor, has both direct and indirect
effects on incomes. The direct effects are through equations 4.2 and
4.3, where earnings are positive functions of schooling. The indirect
effects are both through the occupational choices that individuals
make and through the additional effect that education has on reduc-
ing the demand for children and, hence, family size. A simulation of
the effect of education is thus quite complex.21 After it is completed,
THE SLIPPERY SLOPE: EXPLAINING THE INCREASE 111
Figure 4.11 Shift in the Distribution of Education, 197696
100
90
80
70
60
50
40
30
20
10
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Years of schooling
1976 1996
Source: Authors' calculations based on the 1976 and 1996 PNAD.
one observes, in figure 4.12, a rather flat improvement in log
incomes across the distribution (that is, a scaling effect). However,
when this effect is again combined with changes in the parameters
of the demographic equations, it gains strength and becomes not
only more poverty reducing but also mildly equalizing. The bottom
line in figure 4.12, in keeping with the pattern, combines both of
these effects with the changing s, s, and s. The result is striking:
this complex combined simulation suggests that all of these effects,
during 20 turbulent years, cancel out almost exactly from the 15th
percentile up, hence the small changes in headline poverty. How-
ever, from around the 12th percentile down, the simulation suggests
a prevalence of the negative occupational-choice (and, to a lesser
extent, price) effects, with substantial income losses. These findings
account for the rise in indigence captured by the R$30 per month
poverty line.
The bottom line in figure 4.12 is, in a sense, the final attempt by
this methodology to simulate the various changes that led from the
1976 to the 1996 distribution. Figure 4.13 is a graphical test of the
approach. Here the line labeled "199676" plots the differences in
112 FERREIRA AND PAES DE BARROS
Figure 4.12 Education Endowment and Demographic Effects
Difference of log incomes
0.6
0.4
0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96
Percentile
(e) (d) and (e) (d), (e), s, s, and s
Source: Authors' calculations based on the 1976 and 1996 PNAD.
actual (log) incomes between the observed 1996 and the observed
1976 distributions. Along with it, we also plotted every (cumula-
tive) stage of our simulations: first, the immiserizing (but roughly
equal) price effects; then these effects combined with the highly
immiserizing occupational-choice effects; then the slightly less bleak
picture arising from a combination of the latter with the parameters
of the family size equations; and, finally, the curve plotting the
differences between the incomes from the simulation with all param-
eters changing, and observed 1976. As can be seen in figure 4.13,
the last line does not seem to replicate the actual differences badly.
Of course, the point of the exercise is not to replicate the actual
changes perfectly but rather to learn the different effects of different
parameters and possibly to infer any policy implications from them.
However, the success of the last simulation in approximately match-
ing the actual changes does provide some extra confidence in the
methodology and in any lessons we may derive from it.
THE SLIPPERY SLOPE: EXPLAINING THE INCREASE 113
Figure 4.13 A Complete Decomposition
Difference of log incomes
0.5
0.0
0.5
1.0
1.5
2.0
0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96
Percentile
s and s s, s, and s (d), s, s, and s
(d), (e), s, s, and s 199676
Source: Authors' calculations based on the 1976 and 1996 PNAD.
Conclusions
In the end, does this exercise help improve our understanding of the
evolution of Brazil's urban income distribution over this turbulent
20-year period? Although many traditional analysts of income dis-
tribution dynamics might have inferred from the small changes in
mean income, in various inequality indices, and in poverty incidence
that there was little--if anything--to investigate, digging a little
deeper has unearthed a wealth of economic factors interacting to
determine substantial changes in the environment faced by individ-
uals and families and in their responses.
In particular, we have found that, despite a small fall in measured
inequality (although the Lorenz curves cross, as expected) and a
small increase in mean income, extreme poverty has increased for
sufficiently low poverty lines, or sufficiently high poverty-aversion
parameters. This result appears to have been caused by outcomes
114 FERREIRA AND PAES DE BARROS
related to participation decisions and occupational choices, in com-
bination with declines in the labor-market returns to education and
experience. These changes were associated with greater unemploy-
ment and informality, as one would expect, but more research
appears necessary. Although we appear to have identified the exis-
tence of a group excluded both from the productive labor markets
and from any substantive form of safety net, we have not been able
to interpret fully the determinants of their occupational choices.
Issues of mobility--exacerbated by the current monthly income
nature of the welfare indicator--will also require further under-
standing in this context. Policy implications appear to lie in the area
of self-targeted labor programs or other safety nets, but it would be
foolhardy to go into greater detail before the profile of the group
that appears to have fallen into extreme poverty in 1996 is better
understood.
Second, we have found that, even above the 15th percentile, where
urban Brazilians have essentially stayed put, this lack of change was
the result of some hard climbing up a slippery slope. These urban
Brazilians had to gain an average of two extra years of schooling (still
leaving them undereducated for the country's per capita income level)
and to substantially reduce fertility in order to counteract falling
returns in both the formal labor market and in self-employment.
It may well be, as many now claim, that an investigation of non-
monetary indicators--such as access to services or life expectancy at
birth--would lead us to consider the epithet of "a lost decade" too
harsh for the 1980s. Unfortunately, we find that if one is sufficiently
narrow minded to consider only money-metric welfare, urban Brazil
has in fact experienced two, rather than one, lost decades.
Appendix 4A: Data and Methodology
Macroeconomic Data
All macroeconomic indicators reported in this chapter were based
on original data from the archives of the IBGE. GDP and GDP per
capita figures reported in the introduction came from the series
shown in table 4A.1. This series was constructed from the current
GDP series (A), which was revised in 1995 and backdated to 1990
and from the old series (B), from 1976 to its final year, 1995. The
series reported in table 4A.1 comprises the values of series A from
1990 to 1996 and the values of series B scaled down by a factor of
0.977414 from 1976 to 1989. This factor is the simple average of
the ratios A/B over the years 199095. The series is expressed in
1996 reais, using the IBGE GDP deflator.
THE SLIPPERY SLOPE: EXPLAINING THE INCREASE 115
Table 4A.1 Real GDP and GDP Per Capita in Brazil,
19761996
(constant 1996 prices)
Year GDP (reais) Population GDP per capita (reais)
1976 434,059,220 107,452,000 4,040
1977 455,477,123 110,117,000 4,136
1978 478,113,823 112,849,000 4,237
1979 510,432,394 115,649,000 4,414
1980 562,395,141 118,563,000 4,743
1981 538,474,976 121,213,000 4,442
1982 542,971,306 123,885,000 4,383
1983 527,054,370 126,573,000 4,164
1984 555,515,747 129,273,000 4,297
1985 599,129,793 131,978,000 4,540
1986 644,002,821 134,653,000 4,783
1987 666,708,887 137,268,000 4,857
1988 666,304,312 139,819,000 4,765
1989 687,391,828 142,307,000 4,830
1990 651,627,236 144,091,000 4,522
1991 658,339,124 146,408,000 4,497
1992 654,759,303 148,684,000 4,404
1993 687,004,026 150,933,000 4,552
1994 727,213,139 153,143,000 4,749
1995 757,918,030 155,319,000 4,880
1996 778,820,353 157,482,000 4,945
Source: Instituto Brasileiro de Geografia e Estatística 1999.
The GDP per capita growth rates plotted in figure 4.1 were
derived from this series. Annual inflation and unemployment rates
also came from the relevant IBGE series.
The PNAD Data Sets
All of the distributional analyses performed in this chapter were
based on four data sets (1976, 1981, 1985, 1996) of Brazil's
National Household Survey (Pesquisa Nacional por Amostra de
Domicilios, or PNAD), which is fielded annually by the IBGE. For
the latter three years, the survey was nationally and regionally rep-
resentative, except for the rural areas of the North region (except
the state of Tocantins). For 1976, rural areas were not surveyed in
the North or in the Center-West regions. In this chapter, we were
concerned only with urban areas, which are defined by state-level
legislative decrees. The urban proportions of the population in each
year are given in table 4.1. The PNAD sample sizes, as well as the
proportion of missing income values, are given in table 4A.2.
Each PNAD questionnaire contains a range of questions pertain-
ing to both the household and the individuals within the household.
116 FERREIRA AND PAES DE BARROS
Table 4A.2 PNAD Sample Sizes and Missing or Zero
Income Proportions
Proportion of
Proportion of individuals
Number of Number of individuals with whose income
Year households individuals missing income is zero
1976 84,660 385,282 0.0052 0.0063
1981 110,151 477,607 0.0073 0.0141
1985 127,128 520,069 0.0073 0.0108
1996 91,621 329,434 0.0291 0.0313
Note: Income is total household income per capita.
Source: Authors' calculations based on PNAD.
The household-related questions included regional location, demo-
graphic composition, quality of the dwelling, ownership of durables,
and so forth. The individual questions included age, gender, race,
educational attainment, labor-force status, sector of occupation, and
incomes (in both cash and kind) from various sources. The main
variables used in our analysis were those related to incomes, educa-
tion, demographic structure of the household, and labor-force par-
ticipation. Tables A.6 to A.9 in Ferreira and Paes de Barros (1999)
summarize the main items in the questionnaire for these variables
and the changes from 1976 to 1996.
Most importantly, the distributions analyzed in this chapter
(except where explicitly otherwise indicated) have, as welfare con-
cept, total household income per capita (regionally deflated). It is
constructed by summing all income sources for each individual
within the household and across all such individuals, except for
lodgers or resident domestic servants. The latter two categories con-
stitute separate households. Total nominal incomes were deflated
spatially to compensate for differences in average cost of living
across various areas in the country, according to the spatial price
index given in table 4A.3.
We assumed, largely because of the lack of earlier comparable
regional price information, that the structure of average regional cost
of living described earlier remained constant over the period. Tem-
poral deflation was undertaken on the basis of the Brazilian consumer
price indices--the Índice Geral de Preços--Disponibilidade Interna
(General Price Index, or IGP-DI) for 1976 and the Índice Nacional
de Preços ConsumidorReal (National Consumer Price Index, or
INPC-R) for the three subsequent years. For 1996, the INPC-R was
upwardly adjusted by 1.2199 to compensate for the actual price
increases that took place in the second half of June 1994 and that
were not computed into the July index, because the latter was already
computed in terms of the unidade real de valor (real value unit). This
THE SLIPPERY SLOPE: EXPLAINING THE INCREASE 117
Table 4A.3 A Brazilian Spatial Price Index
(São Paulo metropolitan area = 1.0)
PNAD region Spatial price deflator
Fortaleza metropolitan area 1.014087
Recife metropolitan area 1.072469
Salvador metropolitan area 1.179934
Northeast (other urban areas) 1.032056
Northeast rural 0.953879
Belo Horizonte metropolitan area 0.958839
Rio de Janeiro metropolitan area 1.002163
São Paulo metropolitan area 1.000000
Southeast (other urban areas) 0.904720
Southeast rural 0.889700
Porto Alegre metropolitan area 0.987001
Curitiba metropolitan area 0.987001
South (other urban areas) 0.904720
South rural 0.889700
Belem metropolitan area 1.088830
North (other urban areas) 1.032056
Brasília metropolitan area 1.037915
Center-West (other urban areas) 0.968388
Note: This regional price index is based on the consumption patterns and implicit
prices from the 1996 Pesquisa de Padrões de Vida (Living Standard Measurement
Survey) for the Northeast and Southeast regions and was extrapolated to the rest of
country according to a procedure specified in Ferreira, Lanjouw, and Neri (2003),
where the exact derivation of the index is also discussed in detail.
Source: Ferreira, Lanjouw, and Neri 2003.
adjustment is becoming the standard deflation procedure at the Insti-
tuto de Pesquisa Econômica Aplicada when comparing incomes
across JuneJuly 1994 (see Macrométrica 1994). To center the
indices on the first day of the month, which is the reference date for
PNAD incomes, the geometric average of the index for a month and
for the preceding month were used as that month's deflator. Once
again, this procedure is now best practice for price deflation in hyper-
inflationary periods. Once the deflators were constructed in this way,
the values to convert current incomes into 1996 reais were devel-
oped, as shown in table 4A.4.
A final possible adjustment to the PNAD data concerns devia-
tions between survey-based welfare indicators (such as mean
household income per capita) and national accountsbased prosper-
ity indicators (such as GDP per capita). The international norm is
that household survey means are lower than per capita GNP, both
because the latter includes the value of public and publicly provided
goods and services, which are generally not imputed into the survey
indicators, and because of possible underreporting by respondents.
Given that the levels of the two series are not expected to match
118 FERREIRA AND PAES DE BARROS
Table 4A.4 Brazilian Temporal Price Deflators, Selected Years
Year Value
1976 4.115
1981 49.512
1985 2257.294
1996 1.000
Source: Authors' calculations based on IBGE: IGP-DI and INPC-R.
Table 4A.5 Ratios of GDP Per Capita to PNAD Mean
Household Incomes, 197696
Year GDP per capita (A) Mean PNAD income (B) (A)/(B)
1976 336.6 190.2 1.770
1981 370.2 187.3 1.976
1985 378.3 188.6 2.005
1996 412.1 233.0 1.769
Source: Authors' calculations based on PNAD and National Accounts data.
exactly, analysts are usually concerned by deviant trends, which
may indicate a problem with the survey instrument. Conversely, it
may be argued that national accounts data have errors of their own
and that many of the "correction" procedures applied to household
data rely on reasonably strong assumptions, such as equipropor-
tional underreporting by source.
In deciding whether to adjust the PNAD data with reference to
the Brazilian national accounts over this period, we examined the
evolution of the ratios of GDP per capita to mean household
incomes from the PNAD (for the entire country and without
regional price deflation, for comparability). As table 4A.5 shows,
these ratios were remarkably stable. In particular, the ratios for the
starting and ending points of the period covered, which are of par-
ticular importance for our analysis, are almost identical. In this light
and because even the disparity with respect to 1981 and 1985 is rea-
sonably small, we judged that the costs of making rough adjust-
ments to the PNAD household incomes on the basis of the national
accounts outweighed the benefits.
Appendix 4B: Summary of the Literature
Table 4B.1 shows the evolution of mean income and inequality in
Brazil during the period studied and provides a summary of the
literature.
)
1990 164 0.606 0.745 page
1989 196 0.618 0.796 following
the
1988 166 0.609 0.750 on
1987 166 0.582 0.710
Continued(
1986 5.6 0.586 0.519 213 0.581 0.694 0.577
3112.8
Literature 1985 0.592 4.5 0.592 0.529 150 0.589 0.697 2222.1 0.588
the
1984 125
of 4.0 0.588 0.526 0.577 0.653
1983 0.549 0.589 3.8 0.589 0.523 126 0.584 0.676 1835.6 0.582
Summary
A 1982 4.7 0.587 0.520
1981 0.542 0.584 4.6 0.584 0.519 143 0.574 0.647 2040.6 0.562
Inequality: 1980 4.8 0.597 0.536 2264.0 0.590
and
1979 0.550 0.588 4.7 0.588 0.523 2081.2 0.574
Income 1978
Mean 1977
of
1976 0.561 0.583 2241.8 0.589
) d
Evolution a
b income
(1989 (1996) US$)
(1989)
income cientfi cientfi cientfi cientfi population) cientfi
4B.1 capita (1989) eldfi
(1990
and coef coef c coef T and coef T and e coef
per Sedlacek Litch individual (active Sedlacek
ableT Gini Gini Mean Gini Theil Mean Gini Theil Mean Gini
Indicator Household Bonelli Hoffman Ferreira otalT Bonelli
119
Sul,
1990 the
(Cost do
and
D and
1989 a
Estudos Grosso Estatístico
e PNA
Mato Ferreir
1988 sticaí Anuário 1986 For
Estat and and
1987 s.á Grosso,
de set/1986.
PNAD.
Goi Mato and 1985,
Census;
1985
1986 426.1 0.589 and of
1983,
and
Sul, Intersindical areas set/1985
do income. 1981,
1985 335.7 0.599 94.6 0.545 0.521 0.584 rural 1984,
Demographic
total
Grosso and between 1979,
1983,
1984 293.6 0.587 89.2 0.536 0.498 0.558 -DIEESE). 1980
Mato Departamento week;
ICV years the 1976,
idaV or all -DIEESE per 1982,
the
1983 297.5 0.591 86.8 0.534 0.496 0.565 for ICV
de PNAD;
Grosso, hours 1981, PNAD.
Studies, (1989),
region 1985; 20
1982 91.9 0.520 0.465 0.527 Mato Custo 1986
1979, 1990
of do least and
North August at and
Sedlacek 1978,
1981 331.2 0.572 93.4 0.514 0.457 0.513 states ndiceÍ the 1985,
in until and 1989,
the the Socioeconomic 1977,
working
1980 by
and and 1994,
areas 1988,
values. and Bonelli
atedfl income. 1976,
rural INPC-IBGE 1983, For the
areas 1987,
1979 340.2 0.585 93.6 region de
0.530 0.486 0.560 Statistics income
of positive 1983.
North 1980, ators:fl 1982,
urban (1993), 1986,
Excludes and
1978 89.7 with values.
0.531 0.488 0.571 De in
the missing 1981,
1985,
of
income. August or 1986. force Ramos
1989. lowest force 1982,
of Department 1979,
1977 87.5 0.543 0.511 0.607 zero areas
) and 1984,
income labor labor the 1981, Lauro
with rural wages Union
September the the For 1983,
1976 85.4 zero
0.564 0.556 0.709 in September in
the radeT of highest
1979. of of (1989), 1980,
with
and 65, 1981,
families
Continued( minimum people 18 1979, Census.
h
a,f excludes in Inter 100. the
=
i Cz$1,000 average
cientfi cientfi those people 1976 cruzeiros ages Hoffman
years
in
4B.1 (1989) 1979, value, Index- the (1996),
g coef (1993) j coef L T forsá includes 1980 For
1,000 men,
eighted
Includes For Real Excludes Prices Goi Only In W for Demographic
For Base: eldfi
ableT Mean Gini Mean Gini Theil Theil a. b. c. Living d. e. f. g. h. i. j. Source:
Indicator Hoffman Ramos of and 1985 1980 Litch
120
THE SLIPPERY SLOPE: EXPLAINING THE INCREASE 121
Notes
1. The changes were from the cruzeiro to the cruzado in 1986, to the
novo cruzado in 1989, back to the cruzeiro in 1990, and to the real in
1994.
2. See table 4A.1 in appendix 4A for a complete population series.
3. Effective years of schooling are based on the last grade completed
and are thus net of repetition.
4. All poverty measures reported in this chapter are the P() class of
decomposable measures from Foster, Greer, and Thorbecke (1984). An
increase in implies an increase in the weight placed on the distance
between households' income and the poverty line.
5. E() denote members of the decomposable generalized entropy class
of inequality measures. A lower means an increased weight placed on
distances between poorer people and the mean. E(0), the Theil L index, is
particularly sensitive to the poorest people but ignores zero incomes by con-
struction. See Cowell (1995). For the zero incomes in our sample, see appen-
dix 4A, table 4A.2.
6. Pen parades--or quantile functions--are the mathematical inverse of
distribution functions; that is, they plot the incomes earned by each person
(or group of persons) when these people are ranked by income.
7. The use of terms such as occupational choice or decision should not
be taken to imply an allocation of responsibility. It will become clear when
the model is presented that, as usual, these are choices under constraints.
8. By headline poverty, we mean poverty incidence computed with
respect to the R$60 per month poverty line.
9. Throughout this chapter, this comparison and other comparisons
between sample-based statistics are subject to sampling error, and one would
ideally like to estimate their level of statistical significance. As discussed in
chapter 2, the application of inference procedures to microsimulation-based
decompositions remains an item in the agenda for future research.
10. The Fishlow-Langoni debate concerned the importance of educa-
tion vis-à-vis repressive labor-market policies in determining the high level
of Brazilian inequality. See, for example, Fishlow (1972), Langoni (1973),
and Bacha and Taylor (1980).
11. At 1996 market exchange rates, this amount was roughly equal to
US$1 and US$2. In real terms, this amount would be slightly lower than the
conventional poverty lines of purchasing power parities US$1 and US$2
valued at 1985 prices, which the World Bank often uses for international
comparisons because of U.S. inflation in the intervening decade.
12. Note that this first-order welfare dominance is not robust to a
change in to 0.5.
13. See Duryea and Székely (1998) for such an educational cohort
analysis of Brazil and other Latin American countries.
122 FERREIRA AND PAES DE BARROS
14. In Brazil, wage earners include employees with or without formal
documentation (com or sem carteira). The self-employed are own-account
workers (conta própria).
15. Because education is given by the last grade completed and is thus
net of repetition, this definition overestimates the experience of those who
repeated grades at school and, hence, biases the experience coefficient
downward. The numbers involved are not substantial enough to alter any
conclusions on trends.
16. In this case, the relationship actually switched from concave to
convex.
17. Space constraints prevent the presentation of the tables reporting
these estimations. They are available in Appendix 3 of the working paper
version (Ferreira and Paes de Barros 1999).
18. In terms of the occupational-choice framework, these are changes in
the constraints with respect to which those choices are made.
19. Table 4.7 and the remaining figures in this chapter refer to the sim-
ulation of bringing the coefficients estimated for 1996 on 1976. Similar
exercises were conducted for 1981 and 1985 and are reported in Ferreira
and Paes de Barros (1999). Likewise, the return simulation of applying the
1976 coefficients on 1996 was conducted, and the directions and broad
magnitudes of the changes confirm the results presented here.
20. In computing these differences, we compared the percentiles of the
two different distributions described earlier. A different, but equally inter-
esting, exercise is to compare the percentiles of the simulated distribution
ranked as in the observed 1976 distribution with that 1976 distribution.
These exercises were performed but are not reported because of space con-
straints. In any case, the plots presented are those that correspond to the
summary statistics presented in table 4.7.
21. Note that the different effects are not simply being summed. The
effect of greater educational endowments is simulated through every equa-
tion in which it appears in the model, thereby affecting fertility choices and
occupational statuses, as well as earnings.
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5
The Reversal of Inequality
Trends in Colombia, 197895: A
Combination of Persistent and
Fluctuating Forces
Carlos Eduardo Vélez, José Leibovich, Adriana
Kugler, César Bouillón, and Jairo Núñez
By the late 1970s, the Colombian economy had completed two
decades of consistent reduction in income inequality. For some time,
income inequality in Colombia was exemplary of Kuznets's well-
known inverted U-shaped curve: after the growing inequality of the
first half of the 20th century, substantial reductions in inequality
were observed during the 1960s and 1970s as the economy grew.
The improvements became marginal during the late 1970s and the
1980s, and income inequality took a U-turn in the late 1980s, com-
pletely reversing the equity gains of the two preceding decades.
The rise in national inequality during the 198895 period in
Colombia was driven by a large increase in inequality in the urban
sector, as well as by the simultaneous increase in inequality between
urban and rural areas. At the same time, Colombia experienced sig-
nificant changes in the sociodemographic characteristics of the pop-
ulation. Between 1978 and 1995, the most significant changes in
those respects were the following: (a) higher educational attainment
of the labor force--particularly among women--and greater work
experience; (b) a drop in fertility, leading to smaller family size; (c) a
decrease in the gender earnings gap; (d) pronounced fluctuations in
125
126 VÉLEZ, LEIBOVICH, KUGLER, BOUILLÓN, AND NÚÑEZ
the structure of wages by educational level; and (e) increased female
participation in the labor market. At the same time, the Colombian
economy was subjected to major structural reforms and macroeco-
nomic changes that modified key labor-market parameters and
affected labor-market performance through different channels. The
structural reforms of the early 1990s covered several areas: trade
liberalization and trade integration agreements with neighboring
countries, liberalization of the capital account, and major changes
in labor and social security legislation. The latter increased the rela-
tive cost of labor with respect to capital and became a source of dif-
ficulty for job creation. In addition, the economy suffered supply
shocks linked to major discoveries of oil reserves.
Rural economic activities experienced a marginal shift from agri-
culture, strictly speaking, and industry to mining and services. In
addition, during the late 1970s and early 1980s, agriculture was
subjected to a faster process of concentration of land and rural
credit. Finally, that sector was hit by a set of negative shocks in the
early 1990s: lower tariff protection, real exchange appreciation,
lower international prices, drought, and violence.
The purpose of this chapter is to decompose the dynamics of
income inequality--urban and rural--so as to measure the specific
contribution of some of the preceding factors to changes in income
inequality. Within a microsimulation framework based on a
reduced-form model of individual earnings and participation in the
labor market, we evaluate the following factors:1 (a) the returns to
observable human assets (such as education or experience) and
individual characteristics (such as gender, location, or occupational
status); (b) the changes in the distribution of these assets and indi-
vidual characteristics in the population; (c) the changes in labor-
force participation and occupational choice behavior; and finally
(d) the changes in the overall effect of unobservable earning
determinants. This approach is used to decompose the changes in
inequality and measure the contribution of each of the preceding
factors for the periods 197888 and 198895 for both individual
earnings and household income.
Our findings show that periods of moderate changes in inequal-
ity conceal strong counterbalancing effects of equalizing and
unequalizing forces. The strongest determinants of individual
income distribution dynamics are returns to education, education
endowments (that is, how many years of education an individual
has), and effects of unobservable factors on earning inequality, in
addition to family size and nonlabor income for household income.
Some of these factors are persistent, while others are less stable and
are strongly dependent on economic conditions. The analysis also
THE REVERSAL OF INEQUALITY TRENDS 127
shows that the forces that determine changes in the distribution of
individual earnings differ in intensity from those that determine
changes in the distribution of household income.
A combination of persistent and fluctuating forces characterizes
the dynamics of income inequality in the urban sector in Colombia
between 1978 and 1995 and explains the reversal that took place in
1988. The persistent forces are linked to demographics and labor
supply: the evolution of family behavior--smaller family size and
increased labor participation by women--and the growth of educa-
tional endowments. The unstable or fluctuating factors tend to
respond to changes in the labor demand function--namely, to its
labor skills profile. Although the aggregate effect of persistent fac-
tors is moderate relative to the effect of fluctuating factors, it is per-
haps the best indicator of long-run trends in inequality. Some of
these effects are also present, but of much less importance, in the
rural sector.
Two of our main findings are contrary to our expectations. First,
and intuitively, a greater and more egalitarian education endowment
in both urban and rural areas is expected to reduce income inequal-
ity. However, according to our decomposition exercise, this intuition
held true only in rural areas. Paradoxically, equalization of educa-
tion endowment led to a deterioration in the income distribution in
urban areas in both periods, 197888 and 198895. This apparent
contradiction is explained by the strong convexity of the earnings
functions and by the larger interquintile differences in returns to edu-
cation prevalent in urban areas, with respect to rural areas. Second,
increasing female participation in the labor market generated asym-
metric effects on per capita income distribution vis-à-vis changes in
the per capita labor earnings distribution. The effects were regressive
for income distribution and progressive for labor earnings distribu-
tion. This surprising discrepancy is easily explained with a simple
statistical line of reasoning, which is laid out later in this chapter.
This chapter is divided into four sections. In the first section, we
examine the evolution of inequality and poverty indicators for three
years: 1978, 1988, and 1995. We examine the changes in some
labor-market indicators and in the distribution of sociodemographic
characteristics. We also briefly review the main structural reforms
and macroeconomic developments that affected labor-market per-
formance. In the second section, we model the income-generating
process and provide estimates of parameters that describe the evo-
lution of the structure of earnings and participation behavior. The
third section discusses the outcome of the decomposition exercises,
which measure the contribution of different factors to the total
change in inequality. Finally, we offer some conclusions.
128 VÉLEZ, LEIBOVICH, KUGLER, BOUILLÓN, AND NÚÑEZ
Colombian Income Distribution between 1978
and 1995
The Recent U-Turn in Inequality
Several authors have identified the mid-1960s as the break point
in the regressive trend of income distribution during the first half
of the 20th century.2 However, the evolution of the income distrib-
ution over the past two decades suggests instead that the regressive
trend of the 1960s only presaged a high-water mark. The reduction
in inequality was steady from the mid-1960s until the late 1970s.
Inequality plateaued from 1978 to 1988 then increased significantly
from 1988 to 1995, practically erasing the equity gains of previous
decades.3
As may be seen in table 5.1, indexes of household income inequal-
ity for urban and rural areas are relatively stable from 1978 to 1988
but exhibit opposite tendencies during the 198895 period. In urban
areas, the Gini coefficient is flat and the Theil index fell a little in the
first period. Some reduction of inequality in the upper tail and some
increase in the lower tail of the urban distribution are revealed by
the simultaneous drop in the transformed coefficient of variation
and the increase in the mean log deviation index.
After 1988, urban inequality deteriorated significantly, as indi-
cated by all summary inequality measures reported in table 5.1.4 In
rural areas, the evolution is almost identical between 1978 and
1988: the Gini coefficient and the Theil index deteriorate a little,
and the lower and upper tail inequalities show the same rise and
decline as in urban areas. From 1988 to 1995, however, rural
inequality follows a different path. A clear improvement is notice-
able in all inequality indices shown in table 5.1.
This improvement in the rural income distribution was not suffi-
cient to prevent national inequality from rising under the pressure
of the increase in the inequality of urban incomes, which represent
approximately 80 percent of national household income. It is true
that the urban-rural income gap increased after 1988, as urban
income per capita nearly doubled between 1978 and 1995 while
rural income increased by only 50 percent. However, this evolution
is of little importance in explaining the overall worsening of the
national distribution of household income. Most of the increase in
national inequality after 1988 is explained by changes within urban
areas, whereas the limited changes in the national distribution of
income during the preceding decade reflect parallel distributional
changes within both urban and rural areas.
ithin 42 63
321
W 39.1 57.4
Female
Urban
13 11 10
Decomposition Between Male 45.0 59.4
1995 otalT 56.1 55.8 74.7
331.5
0.4 Rural 36.6
Rural 40.7 30.0 29.4 45.8 39.3 17.4
earsY 1.4
54.4 50.5 70.6 60.7 82.6
Urban 282.7 Urban 50.3
ithin 04 74
115
W 34.3 59.0
Selected Female
Urban
9 8 7
Areas, Decomposition Between Male 39.5 53.5
1988 otalT 54.1 49.6 55.2
122.2
Urban
0.5 Rural 39.0
and Rural 44.4 37.3 35.0 50.5 39.8 21.0
Hogares.
1.3 de
50.2 42.5 50.3 60.2 79.0
Rural Urban 105.1 Urban 44.7
ithin 63 84 Nacional
163
W 32.7 54.0
Female
between
Urban
8 8 7 Encuesta
Decomposition Between Male 42.1 60.8
DANE,
1978
Inequality otalT 53.9 44.7 56.0
170.4
from
otalT 0.6 38.5
Rural 43.5 33.8 34.6 60.3 42.6 23.9 Rural data
on
of
1.3
50.2 38.0 52.6 57.4 76.1
Urban 153.6 Urban 47.8 based
calculations
E(2)
Decomposition E(0) coefficient
inequality share
5.1 share income mean) Authors'
log E(1)
coefficient variation, the coefficients earner
ableT deviation, of (to individuals
Indicator Household Gini Mean Theil, ransformedT age Source:
Population Income Relative Indicator Gini All W Self-employed
130 VÉLEZ, LEIBOVICH, KUGLER, BOUILLÓN, AND NÚÑEZ
In view of that relative autonomy of the evolution of urban
inequality and rural inequality and their clear contribution to over-
all inequality, the two sectors are analyzed separately in the rest of
this chapter. In urban and rural areas, the inequality of earnings
among all employed persons follows a pattern somewhat similar to
household inequality. Data from 1978 to 1988 reveal a pronounced
decrease in income inequality for all individual urban workers
(see the bottom of table 5.1) and stability for rural workers. From
1988 to 1995, earnings inequality for individual rural workers
decreases slightly, whereas inequality for urban workers increases
quite significantly.
To conclude this short review of the distributional trend in
Colombia since 1978, we should mention that, despite fluctuations
in income inequality, social welfare in urban Colombia improved
substantially and unambiguously both from 1978 to 1988 and from
1988 to 1995. The doubling of income per capita compensated for
all changes in income distribution. In rural areas, welfare improve-
ments are unambiguous between 1978 and 1988 but somewhat
ambiguous between 1988 and 1995. Vélez and others (2001) find
first-order stochastic dominance in both periods in urban areas and
during the first period in rural areas as well. However, from 1988 to
1995 in rural areas, second-order stochastic dominance is only sat-
isfied up to the 90th percentile.
Main Forces Driving the Dynamics of Income Distribution
The purpose of this chapter is to identify the forces that shaped the
changes of income inequality within urban and rural areas during
the 1980s and early 1990s. Before turning to a detailed analysis, we
first review the social and demographic developments that may have
affected the distribution of income either directly or through the
supply of labor. We also assess the simultaneous structural reforms
and macroeconomic events that had major impacts on the demand
side of the labor market.
EVOLUTION OF THE SOCIODEMOGRAPHIC STRUCTURE
OF THE WORKING POPULATION
Greater and More Egalitarian School Attainment. Urban education
levels became higher and more equally distributed throughout the
period. The proportion of urban workers who had only completed or
had not completed primary education fell by nearly 20 percentage
points (see table 5.3), whereas the average number of years of school-
ing went up from 6.4 to 8.9 years. A more detailed analysis also
THE REVERSAL OF INEQUALITY TRENDS 131
shows that the increase in educational attainment was greater among
women--specifically among younger women, who either caught up
with or surpassed men. This general increase in education came with
some equalizing of schooling attainment. For instance, the coefficient
of variation of the number of years of schooling in the cohort born in
1975 was half what it was four decades earlier. Progress in educa-
tional attainment was also observed in the rural population: the aver-
age number of years of schooling went up from 2.1 to 3.9 years.
Overall, however, the rural sector remained considerably behind the
urban sector. As for trends within the urban population, the inequal-
ity of educational achievements fell substantially.
Higher Participation in the Labor Force, Particularly by Women.
Changes in labor-force participation have been substantial over the
period, especially among women. Table 5.2 shows that the average
employment rate for women increased from 37.0 to 51.0 percent in
urban areas and from 18.6 to 27.5 percent in rural areas. Interest-
ingly, most of this gain in labor-force participation was among
female household heads or spouses.
Overall, the share of wage earners in the urban labor force
remained relatively constant at about 44 percent. However, the pro-
portion of men employed as wage earners decreased noticeably, sug-
gesting that a higher proportion of women were employed as wage
workers. This tendency was still clearer in rural areas, where women
entering the labor force tended to concentrate in wage work in com-
merce and services (López 1998).
Decreasing Fertility Rates. Table 5.3 shows that family size fell in
urban areas from 5.1 persons in 1978 to 4.3 in 1988 and 4.1 in
1995. For the average household, this change in size produced, other
things being equal, an increase in per capita income of 24 percent,
which represents a fourth of the total gain in real earnings per capita
for the average Colombian household over the period. This evolu-
tion was even more pronounced in rural areas. Overall, the reduc-
tion in family size affected all income groups, although in different
proportions. Figure 5.1 shows that in urban areas family size fell
proportionally more for lower-middle-income households.
MACRO EVENTS AND CHANGES IN DEMAND FOR LABOR
The growth performance of the Colombian economy was satisfac-
tory between 1978 and 1995. Gross domestic product (GDP) per
capita grew at an average annual rate of 1.8 percent. But the growth
rate was higher by 1 percentage point between 1988 and 1995.5
otalT 69.2 100 8.8
43.7 24.2 32.1 100 261
1995 51.0 43.4 11.4 32.8 16.3 50.9 100 206 1.2
Female
6.8
Male 90.4 56.6 56.3 33.4 10.3 100 296 1.5
otalT 64.4 100 10.3 43.3 19.9 36.8 100 228
earsY Urban 1988 0.9
43.3 41.3 13.9 28.9 12.6 58.5 100 182
Female
7.8
Selected Male 88.6 58.7 59.7 28.3 12.0 100 253 1.2
Areas,
otalT 62.4 100 8.2
43.5 16.5 40.1 100 211
Rural
and
1978 37.0 38.6 10.3 25.6 10.0 64.4 100 150 0.8
Female
Urban
in
6.9
Male 88.9 61.4 64.2 24.0 11.9 100 239 1.3
Indicators
groups
rate by month
-Market earner hour
per
rate
statistics per
Labor gender wage self-employed thousand) thousand)
by of of
5.2 employment population earnings $Col wages $Col
-market
ableT Indicator Labor verageA orking
Employed Unemployment W Percentage Percentage Inactive otalT verageA (1995 verageA (1995
132
otalT 4.7
53.1 31.7 19.3 49.1 100 107
100.0
86
9.70 100
1995 29.6 27.50 16.5 12.5 71.1
Female
2.6
Male 76.1 72.5 46.9 26.0 27.1 100 115
otalT 4.0
53.0 30.6 18.5 50.9 100 111
100.0
86
Rural 1988 8.9
26.5 24.4 13.7 10.1 76.2 100
Female
2.3
Male 79.0 75.6 47.9 27.2 24.9 100 118 Hogares.
de
otalT 2.1 99
49.1 26.7 17.1 56.2 100 Nacional
100.0
Encuesta
5.4 7.6 8.2 68
1978 19.6 18.6 84.2 100
Female
DANE,
from
1.3
Male 76.8 81.4 46.5 26.4 27.1 100 106 data
on
based
groups
rate by month
earner
per calculations
rate
statistics gender wage self-employed thousand)
by of of
employment population earnings $Col Authors'
-market
Indicator Labor verageA orking
Employed Unemployment W Percentage Percentage Inactive otalT verageA (1995 Source:
133
5.3 0.8 0.6 3.9 4.7
1995 40.5 22.1 16.8 20.6 19.8 57.8 15.8 100
3.6 0.5 0.3 3.4 5.1
earsY Rural 1988 44.6 20.7 15.8 18.9 22.1 60.5 13.0 100
Selected
6.6 1.0 0.1 0.1
1978 47.2 18.4 15.0 19.4 37.9 54.3 100 2.1 5.9
Areas,
Rural 8
2.1
1995 23.7 32.7 24.3 19.2 26.8 27.4 24.9 10.8 100 8.9 4.1
and
Urban Hogares.
in 2.1 7.1 9.5 100 7.9 4.3 de
Urban 28.4 32.7 20.9 18 32.8 28.8 19.8
1988
Nacional
4.2 6.3 5.8 6.4 5.1
1978 34.9 27.4 18.5 19.1 43.6 28.9 11.2 100 Encuesta
Characteristics
DANE,
from
data
working on
in
force
Sociodemographic education based
in of
labor
population in years
the of calculations
Changes of
structure incomplete complete size
5.3 complete Authors'
incomplete complete number
(percentage)
structure
ableT age (percentage)
Indicator Age 1224 2534 3544 4565 Education Illiterate Primary Secondary Secondary rtiaryeT rtiaryeT otalT verageA Source:
Household
134
THE REVERSAL OF INEQUALITY TRENDS 135
Figure 5.1 Average Household Size by Income Decile in Urban
Colombia, Selected Years
Average household size (persons)
8
7.5
7
6.5
6
5.5
5
4.5
4
3.5
1 2 3 4 5 6 7 8 9 10
Income decile
1978 1988 1995
Source: Authors' calculations based on data from DANE, Encuesta Nacional de
Hogares.
Labor demand was less dynamic, a change that is likely to have
affected the evolution of income distribution. Employment growth
fell quite significantly after 1990.
Several macroeconomic events and structural reforms during the
early 1990s explain the lack of dynamism of labor demand for less
skilled workers: (a) exchange rate appreciation and labor legislation
reforms in the early 1990s that increased the relative cost of labor
relative to capital; (b) a tendency of domestic industry to invest in
more capital-intensive technology, as exposure to international com-
petition rose because of tariff reductions and regional trade integra-
tion; and (c) a gradual shift of productive activities toward more
capital-intensive activities, as production shifted from agriculture
and industry to mining and services. The substantial rise in payroll
taxation in the 1990s also slowed down the demand for unskilled
labor and the generation of wage-earning jobs,6 despite the labor
reform of 1990 (Ley 50), which reduced labor costs by diminishing
the expected value of the cost of dismissals (cesantías). Only one
136 VÉLEZ, LEIBOVICH, KUGLER, BOUILLÓN, AND NÚÑEZ
factor helped reinforce the demand for low-skilled labor: the five-
fold increase in construction activity in the early 1990s, closely
related to exchange rate appreciation, which derived from unprece-
dented capital inflows.7
On the agricultural side, the first half of the 1990s was charac-
terized by a set of negative circumstances and policy measures that
produced a major reduction in output. The removal of import con-
trols, the lowering of tariffs, the appreciation of the exchange rate,
low international prices, scarce credit, frequent drought, and
increasing violence all contributed to a substantial agricultural
decline (Jaramillo 1998). Changes in rural credit and land owner-
ship should have had more direct effects on the distribution of
income. The 197484 decade witnessed an increase in the concen-
tration of land ownership (Lorente, Salazar, and Gallo 1994). How-
ever, this trend reversed in the subsequent decade, when the Gini
coefficient of land ownership went down from 0.61 to 0.59. The
same egalitarian evolution occurred in the credit market. Until 1984,
credit and interest rate subsidies were concentrated among large-
scale producers. But a shift occurred between 1984 and 1993. The
controls over interest rates gradually crumbled, and credit tended to
deconcentrate (Gutiérrez 1995).
Determinants of Household Income: 1978, 1988,
and 1995
The explanation of the dynamics of income distribution relies on
some representation of household incomegenerating behavior in
the various periods under analysis. Household income is modeled as
the outcome of two interrelated process: (a) the determination of
labor earnings as a function of observed and unobserved individual
characteristics and (b) the individual decision to participate to the
labor force as a wage worker or a self-employed worker and the
probability of being employed.8 This section presents the main
results of the estimation of earning and occupational choice equa-
tions. It also highlights the most prominent changes in underlying
individual or market behavior that are likely to have led to changes
in the distribution of income during the 197895 period.
Urban and rural earnings are modeled independently. In each case,
four separate Mincer earning equations are estimated for the loga-
rithm of self-employed workers' and wage workers' earnings and for
each gender. Explanatory variables are the number of years of school-
ing, potential labor experience, location. Both schooling and experi-
ence include quadratic terms that control for heterogeneity in results
THE REVERSAL OF INEQUALITY TRENDS 137
by levels of schooling or experience. For urban areas, equations for
men are estimated by ordinary least squares (OLS), and a two-stage
Heckman selection-bias correction is used for women. For rural
areas, the Heckman correction is applied to wage earners of both
genders; OLS is used for self-employed workers because the selection
bias failed to be significant.
Occupational choice behavior is estimated as a multinomial logit
model with three possible situations: (a) self-employed, (b) wage
earner, and (c) inactive. This model is estimated separately for house-
hold heads, spouses, and other members of the household--with
gender dummy variables included in each case. The same occupa-
tional model is used for all individuals of working age in rural areas.
Explanatory variables include the variables likely to affect potential
individual earnings--schooling, experience, region, and gender.
These variables describe the earning and domestic production capac-
ity of all other household members--that is, household composition
summarized by number of household members by gender and age
group, average schooling, and average experience.
Changes in the Earnings Equations
The eight panels of tables 5.4 and 5.5 show the individual
regressions for log earnings of male and female wage earners and
self-employed workers in urban and rural areas for the three years
considered in this analysis.
For all years and for all occupational situations, the coefficients
have the expected sign and are generally highly significant. The pos-
itive estimate of the quadratic term for education reveals that the
marginal rate of return to schooling increases with schooling within
all groups--except for male, rural, self-employed workers in 1995--
and the reverse is true of experience, as predicted by the Mincerian
model.
Figures 5.2 and 5.3 show how the changes in parameter estimates
for schooling affected wage differentials across schooling levels for
urban male and female wage and self-employed workers. Changes in
returns to schooling clearly contributed to flattening the earnings-
schooling profile of men between 1978 and 1988 and, therefore, to
equalizing the earnings distribution. Indeed, the relative income of
low-educated workers increased much more than that of those with
more education. No change took place for self-employed women,
whereas middle-educated wage-earning women seemed to lose in
comparison with those women of other educational levels. The evo-
lution of income distribution was radically different between 1988
and 1995. For men, relative incomes increased at both the lower and
844*
1995
earsY 9.3611* 0.0321* 0.0051* 0.0536* 0.0007*- 0.8156 5,059 0.3029 1995 8.8958* 0.0254 0.0061* 0.0448* 0.0006*- 0.9127 11,837
workers workers cancefi
Selected squares)
signi
correction) 792*
least 1988 8.9284* 0.0901* 0.0024* 0.0561* 0.0007*- 0.7913 4,635 0.3216 1988 8.3962* 0.0457** 0.0063* 0.0461* 0.0006*- 0.9159 18,676
orkers, indicates
self-employed self-employed
W ** ,
(ordinary (Heckman
Male Female better
Urban or
834 201*
1978 8.4609* 0.1232* 0.0007 0.0867* 0.0013*- 0.885 0.2818 1978 4,046
8.2978* 0.0361 0.0068** 0.0342** 0.0004- 0.8905 level
Female percent
1
and the
at
Male 1995 8,534
9.8234* 0.0379*- 0.0075* 0.0476* 0.0007*- 0.5211 0.3983 1995 3,082*
9.4141* 0.0015- 0.0062* 0.0337* 0.0006*- 0.4934 17,621
cancefi
signi
squares)
earners earners level.
correction) Indicates
*
Self-Employed least 3229*
wage 1988 9,762
9.5537* 0.0027 0.0055* 0.0541* 0.0007*- 0.457 0.4659 wage 1988 9.3672* 0.0383* 0.0034* 0.0416* 0.0006*- 0.458 18,676
table. percent
and 10
Male the
Female
(ordinary (Heckman the
age at
from
W
of 774*
1978 2,234 cancefi
9.0234* 0.0474* 0.0046* 0.0727* 0.0011*- 0.5142 0.4774 1978 4,046
9.2313* 0.0267 0.0049* 0.0399* 0.0007*- 0.4587 omitted
are signi
Equations
variables indicates
and
dummy calculations.'
Earnings level,
squared squared observations observations
variance squared squared
of variance of Authors
5.4 Regional percent
5
2
ableT ariableV 2
Constant Schooling Schooling Experience Experience Residual Number R ariableV Note: the Source:
Constant Schooling Schooling Experience Experience Residual Number Chi at
138
THE REVERSAL OF INEQUALITY TRENDS 139
Table 5.5 Earnings Equations of Wage and Self-Employed
Male and Female Rural Workers, Selected Years
Male wage earners Male self-employed workers
(Heckman correction) (ordinary least squares)
Variable 1988 1995 1988 1995
Constant 10.4208* 10.7522* 9.2593* 9.2058*
School 0.0221* -0.0050 0.0749* 0.0738*
School squared 0.0021* 0.0042* 0.0005 -0.0005
Age 0.0668* 0.0474* 0.0656* 0.0730*
Age squared -0.0008* -0.0005* -0.0006* -0.0007*
Atlantic -0.3041* -0.2729* -0.0335 -0.0317
Oriental -0.2324* -0.0454* -0.2765* -0.2297*
Central -0.2345* -0.2016* 0.0583 -0.2490*
Model chi2 1,237.2 1,970.0 n.a. n.a.
Adjusted R2 n.a. n.a. 0.1243 0.1180
Number of
observations 4,438 4,691 2,515 2,604
Female wage earners Female self-employed
(Heckman correction) (ordinary least squares)
Variable 1988 1995 1988 1995
Constant 9.8676* 10.0758* 10.5254* 10.0828*
School 0.0800* 0.0527* 0.0636* 0.0647*
School squared 0.0015 0.0021* 0.0014 0.0035*
Age 0.0576* 0.0508* 0.0040 0.0186*
Age squared -0.0005* -0.0005* 0.0000 -0.0001
Atlantic -0.2306* -0.1884* -0.1274 0.1923*
Oriental -0.1947* -0.0025 -0.5907* -0.0297
Central -0.1825* -0.1305* -0.1065 -0.0722
Model chi2 n.a. n.a. 1,028.6 1,081.3
Adjusted R2 0.4211 0.3877 n.a. n.a.
Number of
observations 1,300 1,645 965 1,246
*Significant at the 5 percent level.
n.a. Not applicable.
Source: Authors' calculation based on DANE, Encuesta Nacional de Hogares.
the upper end of the distribution of schooling, with a priori ambigu-
ous effects on inequality. The same was observed for female wage
workers, as in the previous period, whereas the evolution was unam-
biguously equalizing for female self-employed workers.
This evolution of earning differential with respect to education is
broadly consistent with the macroeconomic factors that affected the
labor market through the early 1990s: capital deepening and a
complementary demand for skilled workers at the top of the distri-
bution, and construction boom and a demand for unskilled workers
at the bottom.
140 VÉLEZ, LEIBOVICH, KUGLER, BOUILLÓN, AND NÚÑEZ
Figure 5.2 Change in Income from Changes of Returns to
Education, Relative to Workers Who Have Completed Secondary
Education: Male and Female Wage Earners in Urban Colombia,
Selected Periods
Percent change in relative income
40
30
20
10
0
10
20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Years of schooling
Percent change in relative income
40
30
20
10
0
10
20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Years of schooling
197888 198895
Source: Authors' calculations.
THE REVERSAL OF INEQUALITY TRENDS 141
Figure 5.3 Change in Income from Changes of Returns to
Education, Relative to Workers Who Have Completed Secondary
Education: Male and Female Self-Employed Workers in Urban
Colombia, Selected Periods
Percent change in relative income
40
30
20
10
0
10
20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Years of schooling
Percent change in relative income
40
30
20
10
0
10
20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Years of schooling
197888 198895
Source: Authors' calculations.
142 VÉLEZ, LEIBOVICH, KUGLER, BOUILLÓN, AND NÚÑEZ
Compared with returns to education in the urban labor market,
returns in rural areas behaved similarly but showed more hetero-
geneity over time and across labor groups (table 5.5). Returns to
education increased with years of schooling attained, except for
self-employed male workers in 1988 and 1995. As in the urban
case, the convexity of the earnings equation with respect to years of
schooling decreased from 1978 to 1988 and increased again after.
The variance in the residuals of the earnings equations represents
the joint dispersion across earners of the rewards for unobserved
skills, as well as measurement error and transitory components of
earnings.9 Table 5.4 shows a reduction in that variance between
1978 and 1988 and an increase between 1988 and 1995 for all male
urban earners, whereas changes are somewhat limited for female
urban earners. Observed changes in that variance seem large enough
to affect the inequality of individual earnings and that of household
incomes.10
It is clear from tables 5.4 and 5.5 that shifts in earning differen-
tials across gender and occupational groups depend on the charac-
teristics of earners. For example, for otherwise equal men and
women who have 8 years of schooling and 10 years of experience in
urban areas, we would expect to find a small increase in the male-
female wage differential but a large drop in the differential between
men (wage or self-employed workers) and self-employed women.
Most of the resulting substantial drop in the male-female earnings
gap actually took place between 1988 and 1995. In the rural sector,
equal men and women who have three years of schooling will likely
exhibit a continuous substantial drop in the earning differential
between male self-employed workers and male wage workers but an
increasing gender wage differential in favor of men.
Changes related to experience are of limited amplitude. Regional
differences declined for all groups between 1978 and 1988 but did
the opposite during the 1990s.11
Changes in Participation and Occupational Choice Behavior
Occupational choices are modeled as a multinomial logit. Three
choices are considered: inactivity, wage work, and self-employment.
Dependent variables include all characteristics of individuals as well
as summary characteristics for the household they belong to. The
estimation is made independently for household heads, spouses, and
other male and other female adult members. The main features of
occupational choice behavior within those groups of individuals
and their evolution over time are summarized in the following
paragraphs.
THE REVERSAL OF INEQUALITY TRENDS 143
URBAN
Labor-force participation displays the usual features (see table 5.6).
Higher levels of education increase the probability of being
employed, in particular for spouses.12 Participation decreases with
experience or age for household heads and spouses, but it tends to
increase for other household members. Spouse participation is par-
ticularly sensitive to demographics and household potential income.
It falls with the number of children in the household and with the
average human capital endowment (education and experience) of
other household members. The latter effect is quite strong.13
From 1978 to 1988, changes in the average participation rate are
insignificant among male household heads. Changes are substan-
tially positive for spouses and female household heads and negative
for other household members. All these findings are in full agreement
with the aggregate evolution shown in table 5.3. More interestingly,
this evolution was not neutral with respect to education, but the bias
depends on the group being considered. Married women's participa-
tion increased more among the least educated (see figure 5.4),
whereas participation declined relatively more for the least-educated,
secondary, male household members. From 1988 to 1995, participa-
tion kept increasing for all women, with the same bias toward the
least educated. Other male household members also saw a tilt in par-
ticipation in favor of the least skilled. As in the preceding period,
changes in participation among household heads were negligible.
The negative impact of family size on female participation in the
labor force shifted over time too. It ended up concentrating among
spouses in households with very young children, but most of that
evolution took place between 1978 and 1988 (see figure 5.4). With
respect to the effect of the characteristics of other household mem-
bers on spouse participation, figure 5.4 shows an interesting evolu-
tion. It would seem that the increase in spouse participation tended
to concentrate first in households that had a relatively higher poten-
tial income, as summarized by the average educational level of non-
spouse members. But between 1988 and 1995, that increase con-
centrated more among less educated households. This feature will
prove important.
Concerning the choice between wage work and self-employment,
estimates conform to what is observed elsewhere. Wage work tends
to be more common for younger and more educated individuals.
The effect of education tends to be more pronounced among spouses
and other household members than among heads of household.14
The education gradient for wage employment became positive
and significant for household heads in 1995 also. Over time, two
1995 20.4*- 0.2*- 0.2** 0.0 0.0
11.3* 0.9- 1995 26.8* 3.2*- 0.2*- 4.2*
10.3* 0.8- 9,233
12,104 0.1364 0.0898
Members,
Self-Employed
1988 2.1* 0.8**
Inactive
Earners, Household 19.7*- 0.1**- 0.1 12.8* 1.0- 0.6- 1.1*- 1988
Inactive 28.2* 2.6*- 0.3*- 7.9* 9,586
12,657 0.1418 0.0907
age
W Other
and
1978 0.2 0.0 4.8 2.4* 1.3*
among heads 16.9*- 15.6* 3.7- 0.1 0.9- 1978 23.6*
2,587 1.5- 0.0* 1,931
0.1812 0.0909
spouses
Spouses,
Choice household
Urban
Urban 1995 2.2*- 0.9*- 0.7* 14.7*- 1.0- 1.1 2.6* 1995 0.7* 0.3
12,104 0.1364 22.4**- 2.8**- 0.5**- 1.8* 9,233
0.0898
Household,
Occupational of
on
Heads 1988 23.5*- 0.2- 0.9* 0.8 0.9 0.8
13.0*- 1988 0.7* 0.3*
19.6*- 2.0*- 0.4* 0.2*
9,586
Self-employed 12,657 0.1418 Self-employed 0.0907
ariablesV Urban
for earsY
Selected 1978 4.1 1.7 0.9 0.3 0.2
of 33.8*- 0.1- 1.2* 13.8- 1978
2,587
0.1812 13.1- 3.2- 0.7- 0.3- 1,931
0.0909
Selected
Individuals
Effect
orkers,
Inactive W (percent) (percent) (percent)
2 (percent) 2 (percent)
Marginal (percent) (percent)
and observations observations
Rural (percent) (percent) (percent)
under 52 136 (percent) (percent)
(female) of 2 (percent) under 52 136 of 2
5.6 R R
All
ableT orkers,
W and ariableV Constant Schooling Experience Gender Children Children Children Number Pseudo ariableV Constant Schooling Experience Children Children Children Number Pseudo
144
1995 7.3*- 2.8*- 0.0* 5.5* 1.8
23.2* 12.8* 1.5- 1.8*- years years
11,437 0.1219 19,992 0.3277 table. other 2
of 66
the than
Logit in ber and variables,
num less 18
een
1988 3.4*
Inactive 3.0*- 0.1*- 5.2* 1.6** old, dummy
28.5* 15.1* Inactive 0.9**- 1.9*- included
betw al
12,787 0.1185 18,781 0.3419 Multinomial not years Population
of are 65 region
female
and Rural:
model old, three
14 65.
members 1978 3.2*- 3.2- 0.1*- 34.5* 17.3 0.6*- 4.2* 3,009 1.6- 2.0*- indicators the
0.394 years
0.1432 13,084 in than
65
workers cancefi between household,
used older
family and of
Signi males 18
rural age
other females
0.0* 0.6
1995 10.0**- 7.9- 1.4**- 0.5** 0.4* All 0.7* 0.8* rural. variables other
11,437 0.1219 19,992 0.3277 for of between average
Some other
Urban of
males
persons level. number
old,
number household,
of
0.2* 0.5*
1988 15.1*- 11.9*- 1.1*- 2.0*- 0.7* earner 0.4* 1.0* percent 65, years Hogares.
age 10 9
12,787 0.1185 18,781 0.3419 experience, level de
Self-employed W than
self-employed the of and
at 6
and older
years Nacional
and educational
0.0 0.4
1978 10.0- 9.8- 2.8- 6.1 0.2- 0.9 1.4*