INDEX

Note: Page numbers followed by b indicate boxes, f indicate figures and t indicate tables.

A

Absolute bipolarization indices, 335—336

Absolute inequality, 739-740

Absolute poverty, 607-608, 609-610, 788t, 789

Accountable effort, 230, 283

Administrative tax registers, 858

Aggregate deprivation, 1156

Aggregate welfare, 740-743

Aggregator function, xxvii-xxviii

Agnosticism, 112-113

Alienation, 342-348

All the Ginis (ATG) data set, 709-710

American Time Use survey, 1076

Anchored poverty, 609-610

OECD countries, 617f

vs.

Annual disposable family income, 863

Annual labor earnings, 873-874

Antipoverty agenda, 886

Arrow’s theorem, 72

Assets

nonfinancial, 513-514 poverty, 607 real, 513-514

ATK. See Atkinson Index (ATK)

Atkinson-Bourguignon utility-of-income function, 821

Atkinson Index (ATK), 173, 621

Australian Time-Use Survey, 1081

B

Bargaining power, xlviii

Bayesian Information Criterion (BIC), 385-386

Becker’s theory, 1071-1073

Better Life Index, 153-154

BIC. See Bayesian Information Criterion (BIC)

Big Mac Index, 129-130

Bipolarization, 304-305

extensions, 333-335

income polarization and, 332-333 middle class size measurement, 318-322 with ordinal data, 336-337

Bipolarization dominance, 326-328

first-order, 326-328

second-order, 328

Bipolarization indices, 328-332

absolute and relative, 335-336

properties, 322-325

Bivariate density estimation, nonparametric, 904-905

Bivariate income distribution, 857-858

Bootstrap

approach, 418

confidence intervals, 413-414, 414t, 417t methods, 412-413 semiparametric, 415-416

British

income data, 826, 826f

income mobility, 886

British Cohort Study (BCS), 897

British Household Panel Survey (BHPS), 858, 1154

British Industrial Revolution, 477

Budget majorization criterion, 190

C

Canada

earnings decile groups, 913, 914t intergenerational decile transition matrices,

906, 907t

intergenerational earnings mobility, 908, 908t

Capability approach, 75-85, 78f 148-149 aggregation and respect for

preferences, 82-85

choice of dimensions, 80-82

freedom, 79, 80

implementation, 81

influential stream within, 82

refined functionings, 79, 80

researchers and, 80-81, 83

responsibility, 78-79

Capital gains, 498—502, 501f, 657 income for top 1% share trends, 659f top income shares, 658—660

Capital incomes, 498-502, 499f

Cardinal continuous variables, 151

Career interruptions, 1029-1031

Cash-equivalent, 123 estimation, 123 income and needs, 125f valuation method, 123-124, 124f

CGE models.

Chartbook of Economic Inequality, 703 Childcare costs, 1047-1048

Child Poverty Act 2010, liv

Chow test, 390

Chronic poverty, 849

Civil liberties, 220

Clark, John Bates, 47-48

Classical measurement error model, 893

Classical theory

factor prices, 11-12

profits, 10

Class-predicted incomes, 911

Clientele effect, 657

Cobb-Douglas aggregation, 252

Cobb-Douglas indexes, 130

Composite index approach, 158-160

Computable general equilibrium (CGE) models, 746

Conditional cash transfer programs (CCTs), 750-751

Conditional density function, 370, 370f

Conditional density plots, 829, 830f Conditional-distribution equality, 285

Conditional quantiles, 905, 905f

Confidence intervals, 417-418 asymptotic, 412 bootstrap, 412-413, 415-416, 417 coverage rate, 413-414, 414t, 417t inequality and poverty measures, 432t inequality indices with, 362t

Conflict, social, 307-308, 354-355

Consequentialism, 233

Consumer Price Index, 597

Consumption, 596-597

inequality, 705

poverty, 607, 757, 758f

Contamination, 437-441 concept of robustness, 437-440 model estimation, 440-441

Continuous income polarization, 314-317 Counting approach, 146-147

association rearrangement, 173-179 counting deprivations vs. measuring poverty, 179-183

deprivation count distribution, 160-161 dual approach, 167-169 independence axioms, 164-167 partial orderings, 161-164 Pigou-Dalton principle, 160 primal approach, 169-173

welfare criteria, 160

Counting deprivations, 179-183

Cribsheet, 458

Cross-National Equivalent File (CNEF), 859 Cross-nationally comparative household panel surveys, 888

Cross-validation (CV), 380-381

Cumulative effects, taxes, 554-557

Curse of dimensionality problem, 382

D

Dashboard approach, 143

Data-driven methods, 380

Data heterogeneity implications, xxxvii-xxxix Data on inequality

care with data, xxxi-xxxii checklist of questions, xxxiv-xxxvii, xxxiv-xxxv, xxxv-xxxvi, xxxix-xli

international databases, xxxiii relation with national accounts, xxxvi-xxxvii

source of data, xxxvi

Data problems

data contamination, 366-367 incomplete information, 367-368 measurement error, 366-367

Data reduction technique, 155-156

Data sources, 364-365

administrative data, 365 comparability, 601-604 survey data, 365

Data structure complex design, 366 simple design, 365-366

Decile mobility, 867

Decision makers, 221, 222

Decision utility vs.

Deprivation, 1155—1156

Developing countries, 700—701

inequality, 706—711

poverty, 792f

DHI. See Disposable household income (DHI) Dictator game, 1164

Directional majorization criterion, 190 Direct unfairness (DU) vs. fairness gap (FG) approach, 286—288

Discrete income polarization, 310—313, 317—318 Disposable household income (DHI), 630f, 895

distributions, 630—633, 632f

vs. household market income, 634f

Disposable income, 121, 595, 596, 598, 863, 908, 909f, 914, 915t

Distribution matrix, 105—106, 112

Distribution of wealth, l—liii

Distributive justice, 37, 43, 47—48, 50—51, 57, 61, 229, 242, 259-260, 261-262, 268

Domain-specific deprivation, 155-156 Dominance

agnosticism on preferences, 112-113

indices, 423-425

multidimensional inequality and, 105-113

principle, 83, 84f, 104, 423, 444

Dual cut-off approach, 147-148

Dual independence axiom approach, 167-169 Dutch postcode lottery, 1153

Dworkin’s hypothetical insurance market, 224 Dynamic bargaining game, 1164

E

Earnings, 1055-1057

annual labor, 873-874

elasticity, 912

individual, 856-857

labor-market experience and, 390, 391f

long-run, 917, 918t

Mincer equations, 3911

mobility, 873, 908, 908t

transitory, 886-887

true, 861

volatility, 852

wage, 552-557

East Asia and Pacific

inequality, 727-729

poverty, 772-774

Easterlin paradox, 86

Eastern Europe and Central Asia

inequality, 729-730

poverty, 774-775

Economic Freedom Index, 1037-1038

Economic theory, xli-liii

distribution of wealth, l-liii

endogenous technological change, xlvi-xlvii race between technology/globalization and education, xliif, xli-xliii

steady states and transitional dynamics, xliii-xlvi supply and demand, xlviii

EDF. See Empirical distribution function (EDF) Edgeworth, Francis Ysidro, 49

Egalitarian-equivalent approach, 244-245 Egalitarianism, 218, 233, 267-268

Egalitarian political philosophy, 220-229

Egalitarian theory, 218

EKS.

Elterngeld reform, 1049-1050 Eltetoo-Kooves-Szulc (EKS) method, 949-950 quantity indices, 127

Empirical distribution function (EDF), 375-376

Empirical polarization, 353

Empirical validity, EOp, 262-266

Employment, 1010-1011

Employment Retirement Income

Security Act, 1064

EOp. See Equality of opportunity (EOp)

Episodic luck, 246-247, 284

Equality of opportunity (EOp)

dynamics, 256-259

economic development, 248-256

empirical analysis, 259-261

empirical validity, 262-266

experiments, 266-270

Fleurbaey-Maniquet approach, 243-248 general approach, 239-243 implementing, 260-261

life expectancy, 235, 237-238

model and algorithm, 229-239,

238f, 239f

as multidimensional problem, 273

as process, 273-274

Equality of opportunity (EOp) (Continued) progress report, 270—272 results, 289-294

Equal-luck opportunity, 285

Equal-opportunity theory, 219

Equal sacrifice theories, 54-56

Equity vs. economic development, 254

Equivalence scales

household, 71, 114-120

noncash income, 126

Equivalent income approach, 93-95, 95f choice of reference values, 95-97 concavity failures, 95-97 freedom and responsibility, 98 with incomplete preferences, 101-103, 103f revealed preferences method, 99 satisfaction data method, 100-101 stated preferences method, 99-100

Equivalized pretax pretransfer household income, 877

Estimated Household Income Inequality (EHII), 704-705

Ethnicity, 307

Euler’s theorem, 21

EUROMOD model, 1043-1044

European Community Household Panel (ECHP), 602-603, 859

European Statistics on Income and Living Conditions (EU-SILC), 859-860

Exchange mobility, 811

Experienced utility vs. decision utility, 90, 101-102

Experimental economics

deservingness, 1166-1167 dictator game, 1164 dynamic bargaining game, 1164 equal distribution of wages, 1183 Gini coefficient, 1184-1185 grandchild’s income, 1182 hypothetical-choice experiments, 1181 hypothetical preferences and neuro evidence, 1167-1170

income distribution models, 1161-1163 interdependent preferences, 1160-1161 leaky-bucket experiment, 1182

Lorenz dominance criterion, 1183 public-good contributions and punishment, 1164-1166

Rawlsian maxi-min strategy, 1181

Robin Hood redistribution, 1184

social welfare function, 1180 ultimatum game, 1163-1164 uniform income range, 1181

Extended income approach, 121-122

F

Factor prices, 6-16, 508-509

Family-friendly policies, 1036-1037, 1045-1046, 1048-1049

Family income risk, 871

Family pay gap, 1031-1033

Family policy instruments, 1044-1048 Female-dominated occupations, 1019-1020 Female labor supply, 1029

FGT.

Finite mixture models, density estimation

finite mixture of regressions, 390-392 group decomposition approach, 383-384 group profiles explanation, 387-389 number of components/groups, 385-387

Finite sample properties

asymptotic methods, 412-413

bootstrap methods, 412-413

density estimation, 392-394

heavy-tailed distributions, 414-417 simulation evidence, 413-414

Firm-targeted policies, 1037-1040 First-order dominance, 423-424 Fiscal policy, 750

Fisher price indices, 951

Fisher quantity index, 127-128 Fixed cost approach, 125-126 Fleurbaey-Maniquet approach, 243-248, 262-263 Foster-Greer-Thorbecke (FGT) poverty measure, 408-409

Fractionalization (FRAC), 309, 339f, 340

France

long-run inequality, 478-479

wealth inequality, 524-526, 525f French Time Use survey, 1076 Frequency-based approach, 154-155 Friedman-Savage theory, 27 Frisch-Waugh theorem, 280-281 Full compensation principle, 262-263 Full-imputation system, 657, 664-665

Functional income distribution, 6—16

classical theory, 11—12

determinant, 11

development, 36

Marx’s theory, 14—15

sophisticated theory, 14

Fuzzy sets approach, 151—152

G

Gallup World Poll, 704, 713—715

Gamma distributions, 374—375

Gaussian reference distribution, 380

GDP. See Gross domestic product (GDP)

Geary-Allen International Accounts (GAIA), 950-951

Geary-Khamis (GK)

indices, 128

method, 949-950

Gender banking discrimination, 1058-1059 Gender-based taxation (GBT), 1043 Gender-deviance neutralization effect, 1101 Gender division of labor

contexts, 1101-1103

doing gender approach, 1100-1101

economic approach, 1093-1095 methodological issues, 1097-1100 patterns, 1101-1103

social norms, 1096-1097

sociological approach, 1095-1096

Gender ideology, 1097

Gender inequality

dimensions, 984, 984f

division of labor, 1093-1105

economic well-being, 985-986 economies of scale, 986-987 gender wage gap, 1005-1050 household-level conceptualization, 983 income measurement, 987-988 income statistics, 985

intrahousehold distribution of income, 999-1005 intrahousehold finances, 996-999 methodological and empirical issues, 992-993 neglect of intrahousehold inequality, 1000-1004 nonmarket work/household production,

1071-1079

nonunitary models of household, 994-996 pensions, 1059-1068

productive time, 1079-1093 self-employment, 1050-1059 socioeconomic approach, 987 standard assumptions and assessment, 1004-1005 statistical approach, 988-991

unitary model of household behavior, 991-992 wealth, 1105-1117

western/industrialized countries, 984

Gender segregation, labor market occupations and sectors, 1016-1021 vertical segregation and glass ceiling, 1021-1025 wage differential, 1013-1016

Gender wage gap

cross-country differences, 1006-1013 educational level, 1005-1006 family constraints, 1028-1036 gender segregation, 1013-1025 institutions and policies, 1036-1050 psychology and social norms, 1025-1028 women’s human capital, 1006

General equilibrium theory, 22-23

Generalized beta distribution, 374-375

Generalized entropy (GE) class, 400-403 Generalized-errors-in-variables (GEIV) model, 893 Generalized Lorenz curve (GLC), 424

German Socio-Economic Panel (GSOEP), 858, 1033, 1154

Gini-based Shorrocks

M index, 882

rigidity measure, 874

Gini coefficients (Gini Index), 313, 316-317, 324, 340, 404-406, 628, 707, 707f 708, 708/ 7091, xxii-xxiii

absolute and relative, 739-740, 740f household income, 621 market income, 646t

OECD countries, 634t

post-tax/transfer income, 646t redistribution, 646t for rich nations, 635-637, 636f vs.

Gini mobility index, 842, 867

GLC. See Generalized Lorenz curve (GLC) Glivenko-Cantelli theorem, 397-398 Global distribution of income

beta convergence, 944

between-and within-country inequality, 963-967

Global distribution of income (Continued)

China, 943-944

concepts, 943, 943t

egalitarian principles, 940

estimation, 952-963

global inequality, 955-963

global poverty, 968-973

household final consumption expenditure, 939

household surveys and national accounts, 945-947

international markets, 942

international social arrangements, 940-941

market exchange rates, 941-942

national income, 942

occupy movement, 939-940

per capita household income, 938

Philippines, 944-945

population unit, 942-943

PPP exchange rates, 948-952

purchasing power parity exchange rates, 938-939 relative and absolute global inequality, 967-968 sigma convergence, 944 top income, 948

within-and between-country components, 941

Global Entrepreneurship Monitor (GEM), 1052-1053

Global inequality

alternative estimation, comparison, 959-960

NA means, 960-963

with and without top income data, 955-959

Globalization, 548-549, 748-749

Global poverty

estimation, 971-973

methodology, 968-971

Goodness-of-fit test, 375-377

Gossen’s law, 17

Great Gatsby curve, 889, 890/ 917

Great Recession (GR), 616-619

Gross domestic product (GDP), 369-370, 369/

Gross national income (GNI), 700, 719-720 Grouped data, 368

Growth-incidence curve (GIC), 723-725, 724/ Growth-inequality-poverty triangle, 772, 773t

H

Happiness economics, 1171

Happiness equations, 153-154

Heavy-tailed distributions, 414-417

Heckscher-Ohlin model, 548-549 Hedonic welfarism, 88, 89

Heterogeneity of income distributions, xxxvii-xxxix

Hicks-Hansen identity for income, 595-596 High-wage income earners, 498-499 Hirschman-Herfindahl index, 340 Hirschman’s tunnel effect, 1155 Homotheticity (HOM), 194-195 Household-based income tax, 1042-1043 Household behavior

living standards, 985-1005 nonunitary model, 994-996 unitary model, 991-992

Household equivalence scales

family relations, 114 identification of scales, 115-116 income evaluation question, 118-119 individual indifference scales, 117-118 modified OECD scale, 114-115 resource-based approach, 116 satisfaction approach, 118-119 sharing rule-approach, 117-118 subjective approach, 118-119, 120 traditional approach, 117 Van Praag approach, 119

Household final consumption

expenditure (HFCE), 939, 946

Household income, 825-826, 825/ 947 distribution, 619-620 Gini coefficient, 621

LIS countries using equivalized, 629/ Household, Income and Labour Dynamics in Australia (HILDA) survey, 858 Household market income vs. disposable household income, 634t

Household panel surveys, 858

Household production

inequality between households, 1081-1084 markets, 1079-1081

nonmarket work, 1071-1079

Household surveys and national accounts, 945-947

Housework

leisure and well-being, 1088-1093 methodological issues, 1097-1100 sociological approach, 1095-1096 wages, 1085-1088

Human capital endowments, 913

Human capital theory, 25—26

Human Development Index (HDI), 153, 700—701

Human opportunity index, 252—253

Human opportunity measure, 253

Human Poverty Index (HPI), 158-159

Humphrey-Hawkins Full Employment and

Balanced Growth Act of 1978, lix-lx

Hypothesis testing

null of dominance, 435-436

null of nondominance, 436

I

IF. See Influence function (IF)

IGE. See Intergenerational elasticity (IGE)

Immobility ratio (IR), 840

Imputed rent, 598-599

Income decomposition, 676-679

Income equivalent approach, xxviii

Income equivalent variations, 132

Income flux, 866, 883-884

Income group boundaries, 823-825

Income growth

Britain, 831-832, 832f

equiproportionate, 837

individual, 812-813, 834-835 median real, 865, 865f proportional, 843-844 rates, differential, 817-818

Income immobility, 875-877

Income inequality, xxv-xxxi

between-and within-group, 341-342 global, xxxviii-xxxix

international databases on, xxxiii

relative poverty and, 618-619, 618f

Income inequality attitudes

altruism, 1197

charitable giving, 1198 comparative reference group, 1149-1150 distribution of income, 1187-1190 experimental economics, 1160-1170,

1180-1185

normative reference group, 1149-1150 outcome variables, 1185-1187

redistribution, 1190-1196

relative deprivation and satisfaction, 1150 subjective well-being, 1152-1160

transfer elasticity, 1199

volunteering opportunities, 1198

well-being, 1171-1180

Income inequality, long-run trends in, 477-511 capital gains, 498-502, 501f

capital incomes, 498-502, 499f

evidence, 492-502

factor prices, 508-509

France, 478-479

industrialization, 510-511 interpolation techniques, 488-489 life prospects, 509-510 measurement, 474, 502-510

reference total for income, 485-488 reference total for population, 483-485 tax avoidance, 489-491

tax evasion, 489-491

tax statistics, 480-483, 481t, 484t

top income, 474, 479-491, 486t, 492-495, 493f 494f 496-498, 497f

wage dispersion, 507-508

Income measurement, 987-988

Income mobility

intergenerational mobility, 889-922

intragenerational mobility, 855-888 measurement, 822-855

multiple dimensions, 811-814

single bivariate joint distribution, 808-809 socially desirable, 814-818

social welfare, 818-821

variance components models, 809-810

Income polarization, 303-304, 332-333 continuous, 314-317

discrete, 310-313, 317-318

Income risk, 814

Income states, 511

Income units, 599-601

Incomplete data

censored and truncated data, 441-443

trimmed data, 443-447

Independence axioms, 164-167

Indirect taxes, 598-599

Individual earnings, 856-857

Individual income growth, 812-813, 834-835 Individual labor earnings mobility, 873

Inequality

absolute, 739-740, 967-968

aggregate welfare, 740-743

for all ages, 645, 649t

Inequality (Continued)

between-and within-country, 963—967 Brazil, 732b

of capabilities, xxix

CGE models, 746

China, 729b

consumption, 705

convergence, 737-738 cross-country regressions, 746 data on (see Data on inequality)

decile shares, 712, 712t, 713, 714t, 725, 725f decompositions, 745

defined, xxvii-xxviii

determinants of, 546-567

developing countries, 706-711 developments, 548-549, 717-720 different facets of, xxi-xxxi

distribution of national Ginis, 721-722, 722f East Asia and Pacific, 727-729

Eastern Europe and Central Asia, 729-730 extended Human Development Index, xxvii-xxviii

fiscal and social policy, 750

Gallup World Poll, 713-715 gender (see Gender inequality) globalization, 748-749

growth and development, 747-748 growth-incidence curve, 723-725, 724f high-and middle-income countries in 2000s, 622-633

income (see Income inequality)

India, 735b

Indonesia, 729b

labor market, 747

labor policies, 753

Latin America and Caribbean, 730-732

Lorenz curves, 622-624 macroeconomic crises, 751 market reforms, 749-750

Middle East and North Africa, 733-734 monetary, xxi-xxv

multidimensional, xxvii-xxviii multidimensional measurement

(see Multidimensional inequality measurement)

per capita consumption expenditures, 720-721, 721f

polarization and, 351-353

relative, 967-968

spatial, xxiv

South Africa, 737 b

South Asia, 734-735

sub-Saharan Africa, 735-737

tax records, 743-745

technology and education, 749

top incomes, 715-717

trends, structural changes, and shocks, 548-552 United States from 1913, xixf

using life satisfaction, xxviii-xxix

Inequality-adjusted Human Development Index (IHDI), 194

Inequality adverse reward principle, 285-286

Inequality aversion, 1161, 1166

Inequality indices, 361-362, 362t

Inequality measurement, 619-620

coefficient estimates and variances for, 457t distributional statistics, 620-622

GE class, 376-377, 400-403

Gini coefficient, 404-406

high-and middle-income countries in late 2000s, 622-633

income distribution, since 1970, 633-645

LIS country statistics and rankings, 628-629, 629f, 630t

mean deviation, 403-404

testing equality, 417-420

United Kingdom, 1992 and 1999, 456-458

Inequality of opportunities, xxix-xxxi

Inequality of opportunity measurement

age and sex, 277

choice of an index, 288-289

DU vs. FG approach, 286-288

lack of relevant information, 274-276 methodological issues, 272-277 poor data set case, 282-284 rich data set case, 278-282

types vs. tranches approach, 284-286

Inequality of opportunity ratio (IOR), 250 Influence function (IF), 397-398

Inheritance, determinant of income distribution, 36-37

Institutional theories of income distribution, 34-36 Instrumental variables (IV) method, 899-900 Integrated squared error (ISE), 380-381

Intergenerational decile transition matrices,

906, 907t

Intergenerational elasticity (IGE), 890, 912

Intergenerational mobility, 888

class mobility, 921

cross-national comparative evidence, 908—914 cross-national differences, 889

data and issues, empirical implementation, 891-899

evidence on sibling correlations, 914-920

Great Gatsby curve, 889, 890f

income persistence, 922

intergenerational elasticity, 890

linear bivariate regression line, 889 occupation, 921

socioeconomic advantage, 920-921

socioeconomic status, 921

United States, 899-907

International prices, 950

Interpolation techniques, 488-489

Intersection approach, 83

Intragenerational mobility

data and issues, empirical implementation, 856-863

evidence, 881-887

United States, 863-875

Intrahousehold inequality measurement, 114

IOR. See Inequality of opportunity ratio (IOR)

K

Karl Marx’s positive economic theory, 14-16 Kernel density estimation, 827-828

adaptive kernel estimator, 378-379, 381, 382f bandwidth selection, 380-381

GDP, 369f

from histogram to kernel estimator, 377-379 multivariate and conditional density, 382-383 Kolmogorov-Smirnov test, 375-376

Kuznets curve, 478, 551-552

Kuznets series to household surveys, 471-473

L

Labor-capital decomposition, 554

Labor force

participation, 1008-1009, 1009f supply, 1041-1044

Labor market

average gender pay gap, 1007, 1007f employment, 1010-1011

experience, earnings and, 390, 391f

female participation, 1045-1046

gender segregation, 1013-1025 labor force participation, 1008-1009, 1009f part-time work, 1011-1012

unemployment, 1012-1013

United States, 1008

wage structure, 1009-1010 women educational level, 1008 women’s participation, 1040-1050

Labor policies, 753

Labor supply elasticity, 1042

Lander-Year Gini coefficient, 1178

Latin America and Caribbean

inequality, 730-732 poverty, 775-776

Laws of distribution, 14

Legitimate inequality, 1192

Life in Transition Survey (LiTS), 1158

Life satisfaction, 87-89, 90, 91, 1151, 1159, 1177

Linear model approach, 392

LIS. See Luxembourg Income Study (LIS)

Log annual family income, 871, 872f

Lognormal distribution, 373, 373f

Log-normal income distributions,

1187-1188, 1187f

Longer-term income, 813, 869-870, 869f

Long run

defined, 471

earnings, 917, 918t

equilibrium, wages, 9 trends in wealth distribution, 474-475

Lorenz curves, 362-363, 363f, xxiiif, xxii-xxiii of equivalized DHI, 622, 623f inequality, 622-624 net worth, 450-451, 451f

Luck egalitarianism, 218

Luxembourg Income Study (LIS), 328, 472, 594, 702-703, 710, 946, 1188-1189

LuxembourgWealth Study, 1117

M

Maasoumi-Zandvakili-Shorrocks indices, 878

Macroeconomic crises, 751

Mahatma Gandhi National Rural Employment Guarantee Act in 2005, lix-lx

Malthus’s theory, 8, 9

Marginal effective tax rate (METR), 1041

Marginalist revolution, 16-18, 28

Marginal tax rates, 555—556, 556/, 557,

657, 661/ 663

Market

income, 646t, 912

reforms, 749-750

Marketization hypothesis, 1080-1081

Marshall, Alfred, 18-20

Material deprivations, 148-149, 161-163,

162/ 162t

Maternal and parental leaves, 1046-1047

Maximum likelihood estimators (MLEs), 440-441

Maximum likelihood method, 371

MDGs. See Millennium Development Goals (MDGs)

Mean integrated absolute errors (MIAE) measurement, 392-393, 394t

Mean integrated squared error (MISE), 380-381

Mean logarithmic deviation (MLD), 250, 400-401 Measurement error, 366-367

Median real income growth, 865, 865/ Metaphors, 218

METR. See Marginal effective tax rate (METR)

MIAE measurement. See Mean integrated absolute errors (MIAE) measurement

Middle class size measurement, 318-322

Middle East and North Africa

inequality, 733-734

poverty, 776

Millennium Development Goals (MDGs), 698, 968-969, liv

Mill, John Stuart, 41-43

Mincer earnings equations, 3911

MISE. See Mean integrated squared error (MISE) MLD. See Mean logarithmic deviation (MLD) MLEs. See Maximum likelihood

estimators (MLEs)

Mobility dominance correlation-reducing transformation, 834 cumulative bivariate distribution, 833 discount factor, 835-836

individual income growth, 834-835 inequality aversion, 834

intergenerational income data, 834 social weights, 834-835

social welfare, 833 steady-state income distribution, 835 transition matrices, 835-836

univariate income distributions, 836

Mobility indices

absolute income movement, 853-854

average jump index, 841 canonical random effects model, 850 chronic poverty, 849

correlation-decreasing transformations, 844-845 counterfactual income distributions, 837-838 decomposability properties, 837 directional income growth, 843-844 directionality, 837 earnings volatility, 852

equiproportionate income growth, 837 fixed-window calculation, 846 generalized entropy indices, 847-848 generic properties, 836 Gini coefficient, 838 Gini mobility index, 842 idiosyncratic unpredictable income change, 850 immobility ratio, 840 income flux, 853

income-generation process, 851-852 income rigidity, 845 income volatility, 853 intertemporal consistency, 838 King index, 843

log-income change, 854-855 log-linear regression line, 840 longer-term inequality values, 848 low-income persistence, 841 normalizations, 836-837 Pearson correlation, 838 per-capita relative movement index, 854 permanent variance, 852 personal characteristics, 850-851 positional mobility, 838-839 poverty spell distribution, 841-842 proportional income growth, 843-844 quantile regressions, 839 regression analysis, 839-840 relative inequality index, 849 Shorrocks indices, 846-847 single-parameter generalized Gini scheme, 845 social calculus, 843

Spearman rank correlation, 838-839

survival probabilities, 841 T-averaged incomes, 845-846 Theil generalized entropy index, 852 transitory poverty, 849

United States, 863—864, 864t

window-averaging method, 851—852 within-generation mobility, 846

Mobility matrix, 822—823

Mobility measurement

description, 822—833

dominance, 833—836

indices, 836—855

Modified OECD scale, 114-115

Monetary inequality, xxi-xxv

Mortality multipliers, 518

Motherhood wage gap. See Family pay gap

Mother labor supply, 1047-1048 Multidimensional inequality measurement, xxvii-xxviii

agnosticism on preferences, 112-113 binary variables, 198-200 dominance and, 105-113

extended income approach, 121-122

Paretian egalitarian impossibility, 110-112 partial orderings and sequential dominance criteria, 192-193

Pigou-Dalton transfer principle, 108-110, 190-192

two-stage approaches, 194-198

two-step aggregation procedure, 106-108 welfarism, 189

Multidimensional Pigou-Dalton transfer principle, 108-110

Multidimensional polarization, 305-306, 348-351

Multidimensional poverty, 82, 606-607

Multidimensional Poverty Index (MPI), 183

Multidimensional poverty measurement association-rearrangement principle, 185-187 attribute-specific poverty thresholds, 184-185 axiomatic simultaneous aggregation approach, 184

cardinal variables, 183-184 composite index approach, 156-157, 158-160 continuous nonincreasing convex function, 185 dichotomous variables, 185-187 distribution of deprivations, 157-158, 157t factor decomposability, 185

focus axiom, 185

material deprivation, 156

normative rearrangement principles, 158 partial orderings, 187-189

subgroup decomposability, 185

union and intersection criteria, 157-158

Multivariate statistical techniques, 154-155

N

National Longitudinal Survey

ofYouth (NLSY), 891

Natural arithmetic average reward principle, 285-286

Natural reward principle, 262-263

Neoclassical economics, marginalist approach, 16-28

Alfred Marshall, 18-20

general equilibrium theory, 22-23

human capital theory, 25-26

imperfect competition, 23-25

Knut Wicksell, 20-21

marginalist revolution, 16-18

risk taking, 27-28

Neoclassical economists, efficiency

and justice, 43-49

J. B. Clark, 47-48

Marshall, 45-46

Pareto, 48-49

Walras, 43-45

Net worth (net wealth), 513-514

New home economics, 1071-1073

Noncash income, 126

Nonfinancial assets, 513-514

Nonmarginalist approaches

institutional theories, 34-36

macroeconomic approach, 33-34

Pareto distribution, 28-32

property ownership and inheritance, 36-37 statistical approach, 32-34

Nonmarket dimensions, 130-133

Nonmarket work/household production

conceptual revolutions, 1071-1074 measurement and valuation issues, 1074-1079

Nonparametric density estimation, 392-393, 904-905

Nonparametric method, 368

Nontransferable attributes, 145

Normative economics

Adam Smith, 38-40

John Stuart Mill, 41-43

Malthus and Ricardo on poor laws, 40-41

Null hypothesis, dominance/nondominance, 432-435

O

OBRE. See Optimal Bias-Robust Estimators (OBRE)

Occupational gender segregation, 1016, 1018—1019, 1026-1027

OECD. See Organization for Economic Cooperation and Development’s (OECD)

Oil-rich economies, 733

Old-age pension schemes, 1063 Opportunity-cost method, 1077-1078

Optimal Bias-Robust Estimators (OBRE), 440-441

Option luck, 246-247

Ordered probit model, 389

Organization for Economic Cooperation and Development’s (OECD) pensions reform, 1063-1064 scale, modified, 114-115

Organization for Economic Cooperation and Development’s (OECD) countries anchored poverty, 617f disposable household income Gini, 642f

Gini coefficients, 634t, 643-645, 644f pretax and transfer income distribution, 640-645, 641f

redistribution, 640-645

relative poverty, 612-613, 612f self-employment, 1051-1052 S80/S20 and P90/P10 measures, 637-640,

638/ 639f

P

Palma Index, 621, 628

Panel Study of Income Dynamics (PSID), 858 Parametric density estimation, 370, 371-377 Parametric modeling, 368, 447-448

Parametric utility function, 266-267

Parental income, 894

Parental investments, 902-904

Parent-child conditional income expectation, 913

Pareto coefficient, 488-489

Pareto distribution, 371-372

Pareto’s law, 28-29, 30, 32

Part-timework, 1011-1012, 1029-1031

Paternity leave, 1049-1050

Pearson chi-square test, 375-376

PennWorldTable (PWT), 128, 129

Pension gap, 1061, 1062f

Pensions family matters, 1066-1068 gendered effects, 1062-1066 male breadwinner model, 1059-1060 noncontributory, 1060 reform, OECD, 1063-1064 schemes, old-age, 1063 sparse and noncomparable statistics, 1060-1062

survivor’s, 1068 wealth, 515

Permanent incomes, 866, 891 Personal income distribution, 23 Personal-preference principle, 84, 84f 95, 104 Personal wealth, 513-514

Pigou-Dalton transfer principle, 96, 105, 108-110, 146, 190-192, 304-305, 1148, xxviii

Polarization, 302, 306 bipolarization, 304-305, 318-337 and conflict, 354-355 defined, 302, 306 empirical, 353 importance of, 309 income, 303-304, 310-318 and inequality, 351-353 motivation, 306-309 multidimensional, 305-306, 348-351 notation, 309-310 social, 305, 307, 337-341 socioeconomic, 305, 341-342 Policy to date, impact, liv-lvii objectives, liv prospects for future, lvii-lviii thinking outside the box, li#967;f, lviii-lxi Positional change mobility, 811 Positional income mobility, 867, 867f Positive economics factor prices, 6-16 functional distribution, 6-16 Post-Rawls-Dworkin inequality, 219 Posttax posttransfer

Gini index for, 646t household income, 883-884 income concept, 881-882 real family income measure, 866-867 POUM. See Prospect of upward mobility (POUM)

Poverty

changes in measurement, 764—765, 766t convergence, 778—779

decomposition of changes, 768—769 distribution functions, 762f 763

East Asia and Pacific, 772—774

Eastern Europe and Central Asia, 774—775 focus axiom, 185—187

GDP, 760-762, 762t, 769

global, 968-973 growth, 779-786 growth-inequality-poverty triangle, 772, 773f headcount ratios, 181-183, 182f, 755, 756f, 763-764, 764f, 765f 770, 7711

Latin America and Caribbean, 775-776 level of and trends in, 611-616 mean consumption, 757, 758f

Middle East and North Africa, 776

Millennium Development Goal, 753-754

Moran scatterplot, 758-760, 761f multidimensional measurement

(see Multidimensional poverty measurement)

National Accounts data, 767

PPP conversion rates, 754

regressions, 757-758, 759t relative, 787-789

South Asia, 777

squared poverty gap, 757

sub-Saharan Africa, 757, 777-778 total population poverty vs. child poverty, 613-614, 613f

trends in half-median, 614, 614f

World Bank, 755

Poverty measurement, 407-412, 604f 606-607, 755-757, 756t

FGT, 408-409

origins and development, 604-606

sen poverty index, 409-410

SST, 410-412

Poverty threshold, 153-154

PPP. See Purchasing power parity (PPP) Pragmatic convenience motivate approaches, 126-127

Preference-based approach, 80-81

Preference welfarism, 88, 90

Pregovernment income, 856

Pretax

distributions, 630-633, 632f 640-645 income components, 874-875

Price majorization, 190

Probability density function, 369-370, 372f

Profits

classical theory, 10

ownership structure determination, 10

Progressive tax reduction, 662, 663 Promotion, 1022-1025

Proportional income tax, 1043

Prospect of upward mobility (POUM),

818, 1155, 1194

Public-good contributions and punishment, 1164-1166

Publicly provided services

and benefits, 120-126

extended income approach, 121-122 respect for preferences, 122-124

Public Policy, 1040-1050

Purchasing power parity (PPP), 126-130, 699, 948-952

Pure exchange mobility, 823

PWT. See Penn World Table (PWT)

Q

Quasi-relative poverty, 609

Quintile transition matrices, 879

R

Rank-dependent utility theory, 171, 198

Ranking criteria implementation, 426-436

asymptotic distributions, 426-430 hypothesis testing, 435-436 intuitive approach to dominance, 430-432 null hypothesis, 432-435

Real asset, 513-514

Redistribution

Gini index for, 6461

for OECD countries, 640-645

policy, 37, 44, 56

Redistributive Preferences Index (RPI), 1195-1196

Redistributive taxation, 254

Reference-group income, 1154

Reference period, 599-601

Relative bipolarization indices, 335-336

Relative deprivation, 1156

Relative implicit tax rate, 666—667, 667f

Relative income hypothesis, 1160—1161

Relative Lorenz curve (RLC), 425

Relative poverty, 607-608, 787-789, 788t

vs. anchored poverty, 616-619

and income inequality, 618-619, 618f measurement, 608-610

in OECD nations, 612-613, 612f rates for total population, 611f trends in, 616t

Relative wage, 562f

Rent, 11

Replacement cost method, 1077

Residual luck, 247-248

Resource fetishism, 69

Resource sharing, 599-601 Responsibility cut issue, 260, 270f Responsibility-sensitive fair income distribution, 1190

Retirement income system, 1063-1064 Revealed preferences approach, 99

Ricardo’s theory, 11

Risk aversion, 1026-1027

RLC. See Relative Lorenz curve (RLC) Roemer’s approach, 246, 260

S

Same-preference principle, 92, 98

SBTC hypothesis. See Skill-bias technical change (SBTC) hypothesis

Scandinavian welfare approach,

148-149

Second-order dominance, 424-425 Self-employment

economic crisis, 1051

fuzzy scope, 1052-1053 gender gap, 1053

OECD countries, 1051-1052 self-confidence, 1051 women, 1053-1059

Semiparametric methods, 447-452 choice of #946;, 449

inequality and dominance, 449-452

model estimation, 448-449 parametric model, 448

Sen, Amartya

capability approach, 75-85, 246

choice of dimensions, 81

poverty index, 409-410

welfarism, 72-73

Sen-Shorrocks-Thon (SST) poverty index, 410-412

Sequential dominance criteria, 145,

192-193

Skill-bias technical change (SBTC) hypothesis, xli-xlii, xliii, xhf xlv-xlvi, xlix

wage dispersion, xlix

Shapley-value method, 252

Sharing rule-approach, 117-118

Short-term mobility, 874, 882

Sibling correlations, 914-920

Silverman’s rule-of-thumb bandwidth selection, 380, 394

Skill-biased technological change, 749

Smith, Adam, 38-40

Smith’s theory

wage differentials, 10

wage structure, 12, 13

Social-choice theory, 218, 219

Social conflict, 307-308, 354-355

Social exclusion, 148-149

Socially desirable income mobility

alternative income concept, 817

bivariate joint distribution, 818

constant income flow rate, 817

differential income growth rates, 817-818 dynastic inequality, 816

equality of opportunity, 814-815 fluctuating incomes, 817 generation mobility, 814

income gains, 817

income risk, 817

inequality of longer-term incomes, 815-816

inequality of opportunity, 815 longer-term inequality reduction, 816-817 prospect of upward mobility, 818

Social polarization, 305, 307

concepts and motivation, 337-338

index, 339, 339f

measurement, 338-341

Social policy, 750

Social Security benefit income, 870

Social security system, 1067

Social security wealth, 515

Socialwelfare, 189

Atkinson-Bourguignon utility-of-income function, 821

income risk, 820-821

individual-level mobilities, 821

Lorenz curves, 818-819

loss aversion, 821

positional mobility, 819

stochastic dominance checks, 820

utility function, 819-820 utility-of-income functions, 819

Social welfare functions (SWFs), 818-819

Socioeconomic Database for Latin America and the Caribbean (SEDLAC), 702-703

Socioeconomic polarization, 305

between-and within-group income inequality,

341- 342

identification/alienation hybrids,

342- 348

index, 342, 348

South Asia

inequality, 734-735

poverty, 777

Spatial inequality, xxiv

Spearman-rank correlation coefficient, 708

Spousal retirement benefit, 1067

Squaredpoverty gap (SPG), 757

Standardized World Income Inequality Database (SWIID), xxxiii, xxxvii-xxxviii

Standards of living

nonmarket dimensions, 130-133

PPP indexes, 126-130

Stated preferences approach, 99-100

Statistics on Income and Living Conditions (SILC) data, 600-601

Status-quo policy, 232-233

Stochastic dominance, 425-426

Structural mobility, 811

Subjective well-being approach

decision utility, 90

experienced utility, 90

freedom, 92-93

happiness, 85-93

hedonic welfarism, 87-89

life satisfaction, 87-89, 90, 91 preference welfarism, 88, 90 respect for preferences, 92 responsibility, 92-93

Sub-Saharan Africa inequality, 735-737 poverty, 777-778

Subsistence wages, 8

Super-star theories, 475-476 Supply-side theory, 663

Survey of Labour and Income Dynamics (SLID), 858

Survivor’s pension, 1068

Sweden

capital incomes, 498-499

CEO and worker incomes, 560, 561f gross income class, 484f income volatility, 896

intergenerational earnings mobility, 908, 908t share trends in, 658f

tax reform, 882

tax unit concept, 483-485

top income and wealth fractiles in, 554f wages dispersion, 508

wealth inequality, 531-534, 532f

wealth tax data, 518

SWIID. See Standardized World Income Inequality Database (SWIID)

T

Tax, 554-557, 1041-1044

administration records, 870 behavioral responses to, 490-491 benefit policies, 886 benefit principle, 56-58 cumulative effects of, 475-476, 568-569 laws, 514

legislation changes, 655-656, 657

records, 743-745

reform, 657

Tax avoidance, 489-491, 518-519, 660-665

Tax evasion, 489-491, 518-519, 660-665

Tax Reform Act (TRA) of1986, 500-502, 663

Tax units

concept, 483-485

definitions, 665-666

United Kingdom, 665

Theil generalized entropy index, 852

Theil inequality index, 880

Top incomes, 645-652, 715-717, 948 capital gains, 498-502, 501f capital incomes, 498-502, 499f

Top incomes (Continued)

caveats and limitations to data, 653—654

data and methodology, 652—667 definition, 655—660 earners in top decile, 496—498, 496f interpolation techniques, 488—489 labor and capital compositions, 678f methods and data, 479-491, 486t Pareto distribution, 488-489 reference total for income, 485-488 reference total for population, 483-485 tax avoidance, 489-491 tax evasion, 489-491 tax statistics, 480-483, 481t, 484t top shares in late 2000s, 668-669, 669f top tax rates on, 565-566

Top income shares, 474, 492-495, 493f

494/, 497f, 500-502, 652-653, xxiii-xxiv analysis, 651 capital gains for, 658-660 cumulative changes, 674 determinants, 562-566, 564t dynamics of, 652 estimation, 656

vs. Gini coefficients, 679-680, 682f gross and disposable, 666-667 growth in countries, 669-676, 671f household survey data, 680-683 inequality measurement, 503-506 pre-and post-tax, 666-667, 668f as proxies, 683-687 public economics and, 652 reduce tax progressivity, 663 tax-based and survey-based estimation, 502-503

WTID, 668, 670, 674-676

Top tax rates, 565-566

Top wages, 557-562 Total gross income, 480-482, 499f Trade theory, 508-509, 548 Tranche-compensation principle, 284, 287-288 Transfer income distributions, 630-633, 632f, 640-645

Transfer tax, 480-482

Transitional dynamics, steady states and, xliii-xlvi Transitory earnings shocks, 886-887

Transitory poverty, 849

True earnings, 861

Tsui multidimensional inequality measure, 197-198

Two-dimensional poverty measures, 187-188 Type-compensation principle, 284-285, 287-288 Types vs. tranches approach, 284-286

U

Ultimatum game, 1163-1164 Unemployment, 1012-1013

Uniform Pigou-Dalton majorization principle (UMPM), 194-195

United Kingdom

disposable income, 914, 915t income distribution, 1973 and 1979, 386-387, 386f, 388-389, 389f

inequality measurement, 1992 and 1999, 454f, 456-458

National Child Development Study, 897 tax units, 665 wealth inequality, 535-537, 536f

United States

capital gains income, 658-660

CEO and worker incomes in, 560, 561f conditional density plots, 829, 830f decile transition matrices, 823, 824t, 868 General Social Survey, 1172 income data, 828-829, 828f inequality from 1913, xixf intergenerational income persistence, 902, 903f intergenerational mobility, 899-907 intragenerational mobility, 863-875 labor market, 1008 men’s earnings, 861-862

National Longitudinal Survey of Youth, 891 Panel Study of Income Dynamics, 858 relative poverty measurement, 608-610 relative wage, 562f rigidity profiles, 846, 847f share trends in, 658f

Social Security Administration, 900 wealth inequality, 537-540, 538f vs. West Germany income mobility, 875-881 University of Texas Inequality Project (UTIP), xxxiii

Unpaid work, 984, 984f, 1093-1095 Utilitarianism, 49-54, 234

critique, 50-51

sum of utilities, maximizing, 49-50

Utilitarian policy, 234

Utility

and happiness, 72—73, 85—93

mental attitude, 72—73

V

Van Praag approach, 119

W

Wage, 873-874

bargaining, 25

conditional density function estimation, 370, 370f determination, 9

discrimination, 1037-1038

earnings, 552-557

education and training implications, 12-13 housework, 1085-1088

income, 679

inequality, xliii-xliv long-run development, 560-561 long-run equilibrium, 9

lower, 1029

Malthus's theory, 8, 9

structure, 11-13, 1009-1010

subsistence, 8

top, 557-562

Wage dispersion, 507-508, 546-547

Wage shares, 662

Weak comonotonic additivity (WCA), 194-195

Weak Pareto principle, 110, 111f

Wealth, 513-517

augmented, 515

decile, 579t

holding unit, 513

net, 513-514

pension, 515

percentile, 572f, 576t personal, 513-514 shocks, 554-557 social security, 515 wage earnings and, 552-557

Wealth and gender

composition effects, 1111-1113 gender gap measurement, 1114-1115 households, 1107-1108, 1115-1117 inequality, 1105

marital dimension, 1106

strategies and limitations, 1109-1111

Wealth distribution

analysis of, 512

data, 512 long-run trends in, 474-475 measures of, 518-519

Wealth inequality, long-run trends in, 474-475, 511-546

Australia, 520, 521f composition of wealth, 543-544 consumer durables, 516 data and measurement, 512-519 Denmark, 520-521, 522, 522f Finland, 522-524, 524f foreign wealth holdings, 516-517 France, 524-526, 525f long-run evolution, western countries, 540-543, 541t

measurement, 517-518 Netherlands, 526-527, 527f Norway, 528-531, 530f shares-within-shares estimation, 542-543,

543f

Sweden, 531-534, 532f

Switzerland, 534-535, 534f

tax avoidance, 518-519

tax evasion, 518-519

top wealth shares, 517, 518 United Kingdom, 535-537, 536f United States, 537-540, 538f wealth concept, 513-517 wealth holding unit, 513

Weber-Fechner law, 49

Weibull distributions, 374-375

Welfare indices, 394-425, 438-440

asymptotic inference, 396-400 background results, 398-399 basic cases, 394-396 parametric approaches,

421-423

QAD, 399-400, 445

Welfarism, 189

Amartya Sen, 72-73

hedonic, 87-89

preference, 88, 90

Well-being

dimensions, 148-150

domains, 143

measurement, 75-105

West Germany

conditional density plots, 829, 830f

family incomes, 827—828, 827f

income data, 828—829, 828f nonparametric transition probability plots, 829-830, 831f

rigidity profiles, 846, 847f

vs. United States income mobility, 875-881 Wicksell, Knut, 20-21

WIID. See World Income Inequality Database (WIID)

Willingness-to-pay for the services, 124-126

Within-generation income mobility analysis, 833

Work-family conciliation policies, 1036-1037 World Bank's PovcalNet, 702

World Development Indicators (WDI), 713

World Income Distribution (WYD),

702-703

World Income Inequality Database (WIID), 472, 703, xxxiii

World social welfare function, 967

World Top Incomes Database

(WTID), 651, 668, 670, 674-676

World Values Survey (WVS), 1176

WTID. See World Top Incomes Database

Z

Zero egalitarian equivalence (ZEE)

approach, 244, 245, 246

Zero mobility reference point, 813

Zeuthen's theory, 25

⁵ Since 1997, the official poverty statistic adopted by the Irish government is “consistent poverty,” which is the proportion of people who are both income-poor and deprived of two or more items considered essen­tial for a basic standard of living (Social Inclusion Division, 2014). The British Child Poverty Act 2010 sets four policy targets, among which is a combined low income and material deprivation target (The Child Poverty Unit, 2014). One ofthe five European Union headline targets set by the Europe 2020 strategy for a smart, sustainable, and inclusive growth concerns the share of people “at risk of poverty or social exclusion” (European Commission 2010). This indicator combines income poverty, householdjoblessness, and severe material deprivation, with severe material deprivation occurring whenever a person lives in a household that cannot afford at least four out of nine amenities. For discussions of the use of indicators of material deprivation and, more generally, the multidimensional perspective adopted in the European Union’s pol­icy evaluation of social progress, see Atkinson et al. (2002), Marlier et al. (2007), Maquet and Stanton (2012), and Marlier et al. (2012).

3.3.2.1 Partial Orderings

As is standard in the income distribution literature, the first criterion regards first-degree dominance.^{* 18 19}

Definition 3.1

A deprivation count distribution F₁ is said tofirst-degree dominate a deprivation count distribution F2 if

and the inequality holds strictly for some k.

If F₁ first-degree dominates F₂, then F₁ exhibits less deprivation than F₂. An example is given in Figure 3.1, in which we use the material deprivation indicators in five Euro­pean countries in 2012 drawn from Eurostat (2014) and reported in Table 3.2. Figure 3.1 plots on the vertical axis the cumulative proportion of persons who suffer from

¹⁸ Lasso de la Vega (2010) and Yalonetzky (2014) also identify dominance conditions to rank deprivation count distributions.

¹⁹ The first-degree stochastic dominance relations for integer variables representing the counting of people achievements, rather than deprivations, are studied by Chakravarty and Zoli (2012).

The surge of research on the measurement of inequality in multiple dimensions is fairly recent, but the central question is far from new. In Income Distribution, Value Judgments, and Welfare, Fisher was not interested in money income, a “scalar,” but in “real” income, that is, “a vector whose components are amounts of commodities” (Fisher, 1956, p. 382). His analysis was carried out by aggregating commodities either by using constant prices— to which he assigned “no particular significance... as market valuations of the commod­ities. Any arbitrary set of weights would do as well” (Fisher, 1956, p. 383, fn. 6)—or by means of individual utility functions. Social welfare was thus seen as an aggregation of individual preferences, in the tradition of what Sen (1977) has labeled “welfarism.” The modern approach to measuring inequality in multiple dimensions generally departs from this identification by interpreting the individual utility function as “the observer’s evaluation of the individual’s welfare” (Kolm, 1977, p. 3), so that “the social criterion makes no use of information on individual i’s relative valuation of the different elements of [the vector ofgoods received by person i]” (AtkinsonandBourguignon, 1982, p. 184).

As in the study of a single variable pioneered by Kolm (1969) and Atkinson (1970), the analysis proceeds by investigating the conclusions that can be reached on the ranking of multivariate distributions by making alternative assumptions on the order of aggregation and the shape of the social welfare function, or on the desired properties of inequality indi­ces. We first consider the extension of the Pigou-Dalton transfers principle. We then move to partial orderings and sequential dominance criteria, and lastly to inequality indices.⁴⁰

See Bradburd and Ross (1988) and Fluckiger and Silber (1994) for early proposals of multidimensional inequality indices.

⁴⁶ These estimates are computed dropping countries with few observations in the period.

China

Since 1978, when China started pro-market reforms, GDP has increased at an average rate close to 10%, and household per capita income has grown more than 7% per year. Such remarkable economic transformation has been accompanied by important changes in inequality and poverty. China is a successful story of reduction in absolute poverty (Minoiu and Reddy, 2008; Ravallion and Chen, 2007, 2008; World Bank, 2009). However, it is argued that it will be harder for China to maintain its past rate of progress against absolute poverty without addressing the problem of rising inequality.

The increase in income inequality in China over the last three decades has been widely documented. Ravallion and Chen (2007) and World Bank (2009) show that income inequality rose from the mid-1980s through 1994, dipping a bit in the late 1990s, and then edging upward thereafter. Li et al. (2013), among others, document the increase in the 2000s, a pattern explained by the widening of the rural-urban income gap, and the increase in income from property and assets, driven by the development of urban residential real-estate markets, the expansion of stock and capital markets, the growth of private enterprises, and other property rights.

A significant share of income inequality in China is now accounted for by rural-urban differences in income levels. The concentration of growth in urban areas is creating a

⁵² The increasing availability of surveys in Latin America allowed the creation of databases that make efforts to standardize the generation of poverty and inequality statistics, favoring a close monitoring of the social and labor situation in the region (SEDLAC by CEDLAS and the World Bank, and BADEINSO by UN's ECLAC).