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Income inequality and nations
by Emilio José Chaves
16 June 2002 00:36 UTC
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Income inequality and nations

In a draft paper of mine, called "Survey Errors, Distorted Gini Indexes and Social Classes -Critique and Proposal based on a General Paretian Distribution Model-", it is shown that the national statistics bureaus may be reporting around 70% of the real Gini index they should. This is due to the survey mutilation of those with an income greater than 20 average real incomes, and from different practices of income under-reporting, which gather to account for only 50-60% of total real income and of real income per capita in the surveys.

The following table, show results for 108 nations -based on available data from UN-2000 report which uses programm POVCAL with another fitting technique-. You may build the Lorenz curve for each nation applying the mentioned formulas to the A, B, parameters obtained from the published quantiles data. A derived series proxy formula to compute the area under Lorenz curve, L, using A,B, is given in the table, so Gini index may be computed from G = 2.L – 1

In order to approach a Gini index closer to the real value, instead of the official one, multiply this later one times 1.4.

Observe that the most unequal nations are located in Africa and Latin America –an old new-. Also, important nations like Argentina, Iran, Irak, Kuwait, the Emirates, Saudi Arabia .. do not inform their distributions. I also have reasons to believe that U.S., England, Australia, Canada and New Zealand statistics gov bureaus tend to distort the topic with a common pattern. And it is not a problem of anglo-phobia.

My intention is to offer an alternative way to analyze and to build related graphs of distribution curves from published quintils/decils/shares data, in a quick and precise way with any standard electronic page. I would appreciate some comments from one or two of you with some math-stats expertise, that might be interested in reading the draft, so please write me to email: (chavesej@hotmail.com) to send the text .

Thanks and cordial regards, Emilio J. Chaves, Pasto, Colombia

Appendix 6. World Nations Oficial and Theoretical Ginis Indexes, Estimated values of A, B, a*

Notes:

Source of Income/Spendings Quantiles and Official Gini Indexes: UNDP-2000 Report

R2 correlation (G1,G3)=

0.9999

R2 correlation (G3,G2)=

0.9998

GPD Lorenz curve, rich to poor y(t) = t ^ (2 - A - B.t)

UPD Lorenz curve for same GPD-Gini Index, y(t) = t ^ ( 2 - a*)

GPD= General Paretian Distribution

UPD= Uniform Paretian Distribution

L(area)= [1/(3-A]+[B/(3-A)/(4-A)]+[(B^2-B) /(3-A)/(4-A)/(5-A)]+[(B^3-3.B^2-B)/(3-A)/(4-A)/(5-A)/(6-A)]

GPD Gini Index formula (Proxy) = 2.L - 1

L= Area under Lorenz curve

Nations

GPD

GPD

UNDP

GPD

GPD

a*(G3)

Inequa-

Nations

with

Value

Value

Official

Proxy

Numeric

UPD

lity

without

Quantiles

of

of

Gini

Gini

Gini

Param.

rank

aproved

Data

A

B

G1

G2

G3

a*

#

data

Algeria

1.3911

0.3628

0.3530

0.3651

0.3555

1.5245

69

Albania

Australia

1.3456

0.4866

0.3520

0.3704

0.3572

1.5263

66

Angola

Austria

1.2433

0.3395

0.2310

0.2391

0.2323

1.3770

106

Argentina

Bangladesh

1.4305

0.2043

0.3360

0.3432

0.3380

1.5052

72

Armenia

Belarus

1.2649

0.2450

0.2170

0.2253

0.2205

1.3614

107

Azerbaijan

Belgium

1.2518

0.3948

0.2500

0.2631

0.2547

1.4060

102

Benin

Bolivia

1.4737

0.3383

0.4200

0.4320

0.4217

1.5933

36

Bosnia/Herz.

Brazil

1.6592

0.2907

0.6000

0.6147

0.6023

1.7518

3

Botswana

Bulgaria

1.2994

0.3825

0.2830

0.2956

0.2869

1.4459

94

Cameroon

Burkina Faso

1.5772

0.2192

0.4820

0.4903

0.4827

1.6511

26

Congo,D.R.

Burundi

1.3912

0.3021

0.3330

0.3436

0.3359

1.5029

74

Congo,Rep

Cambodia

1.4917

0.2378

0.4040

0.4112

0.4041

1.5756

45

Cuba

Canada

1.3267

0.4156

0.3150

0.3290

0.3188

1.4834

87

Chad

Central Afr.R.

1.6649

0.3091

0.6130

0.6301

0.6166

1.7629

2

Eritrea

Colombia

1.6334

0.2876

0.5710

0.5822

0.5706

1.7266

7

Gabon

Costa Rica

1.5027

0.4014

0.4700

0.4858

0.4722

1.6415

28

Georgia

Côte d'Ivoire

1.4304

0.3011

0.3670

0.3777

0.3695

1.5396

56

Haiti

Croatia

1.2964

0.3373

0.2680

0.2782

0.2708

1.4262

98

Hong Kong,Ch.

Czech R.

1.3044

0.2770

0.2540

0.2647

0.2588

1.4112

101

Iran,

Chile

1.6411

0.2531

0.5650

0.5762

0.5661

1.7229

9

Iraq

China

1.4509

0.3493

0.4030

0.4145

0.4042

1.5757

44

Korea,Dem.R

Denmark

1.2515

0.3937

0.2470

0.2626

0.2542

1.4054

103

Kuwait

Dominican R.

1.5469

0.3207

0.4870

0.4992

0.4880

1.6560

23

Lebanon

Ecuador

1.4986

0.3186

0.4370

0.4487

0.4387

1.6099

34

Libya

Egypt, Arab R

1.3705

0.2129

0.2890

0.2958

0.2908

1.4506

93

Macedonia,

El Salvador

1.5736

0.3444

0.5230

0.5379

0.5251

1.6886

14

Malawi

Estonia

1.3615

0.4506

0.3540

0.3710

0.3588

1.5281

65

Mauritius

Ethiopia

1.4933

0.2237

0.4000

0.4075

0.4009

1.5724

48

Montenegro

Finland

1.2953

0.3008

0.2560

0.2655

0.2591

1.4116

100

Myanmar

France

1.3479

0.4018

0.3270

0.3419

0.3317

1.4982

78

Namibia

Gambia,

1.5313

0.3435

0.4780

0.4920

0.4802

1.6488

27

Oman

Germany

1.3270

0.3726

0.3000

0.3144

0.3055

1.4681

90

Palestine

Ghana

1.3931

0.2759

0.3270

0.3361

0.3291

1.4953

82

Puerto Rico

Greece

1.3572

0.3708

0.3270

0.3388

0.3295

1.4957

81

Saudi Arabia

Guatemala

1.6409

0.3336

0.5960

0.6115

0.5974

1.7480

4

Serbia

Guinea

1.4712

0.2969

0.4030

0.4138

0.4051

1.5766

43

Singapore

Guinea-Bissau

1.5882

0.4023

0.5620

0.5794

0.5634

1.7207

10

Sudan

Honduras

1.5954

0.3148

0.5370

0.5499

0.5379

1.6995

12

Syrian A.R.

Hungary

1.3692

0.2794

0.3080

0.3172

0.3105

1.4738

89

Tajikistan

India

1.4865

0.1742

0.3780

0.3829

0.3779

1.5485

55

Togo

Indonesia

1.4585

0.2134

0.3650

0.3714

0.3656

1.5354

59

United Arab E.

Ireland

1.3908

0.3851

0.3590

0.3729

0.3625

1.5321

62

Yugoslavia

Israel

1.3917

0.3662

0.3550

0.3669

0.3571

1.5263

67

Italy

1.2862

0.3898

0.2730

0.2878

0.2790

1.4363

96

Jamaica

1.4218

0.3185

0.3640

0.3762

0.3676

1.5375

58

Japan

1.3083

0.2423

0.2490

0.2566

0.2515

1.4019

105

Jordan

1.4426

0.2556

0.3640

0.3723

0.3653

1.5351

60

Kazakhstan

1.3819

0.3890

0.3540

0.3665

0.3561

1.5252

68

Kenya

1.4989

0.3452

0.4450

0.4595

0.4484

1.6191

32

Korea,

1.3329

0.4047

0.3160

0.3304

0.3204

1.4853

86

Kyrgyz

1.4738

0.2939

0.4050

0.4152

0.4066

1.5781

42

Lao

1.3913

0.2045

0.3040

0.3100

0.3051

1.4675

91

Latvia

1.3566

0.3705

0.3240

0.3382

0.3289

1.4950

83

Lesotho

1.6111

0.3333

0.5600

0.5759

0.5626

1.7201

11

Lithuania

1.3613

0.3499

0.3240

0.3349

0.3262

1.4919

84

Madagascar

1.5288

0.3026

0.4600

0.4730

0.4630

1.6329

30

Malaysia

1.5506

0.3057

0.4850

0.4970

0.4864

1.6545

25

Mali

1.5841

0.2633

0.5050

0.5157

0.5062

1.6722

17

Mauritania

1.4339

0.3615

0.3890

0.4032

0.3928

1.5640

53

Mexico

1.6037

0.2905

0.5370

0.5489

0.5379

1.6995

13

Moldova

1.3681

0.3997

0.3440

0.3584

0.3479

1.5162

70

Mongolia

1.3543

0.3918

0.3320

0.3438

0.3338

1.5005

76

Morocco

1.4580

0.3042

0.3950

0.4041

0.3954

1.5667

51

Mozambique

1.4589

0.3103

0.3960

0.4073

0.3983

1.5697

49

Nepal

1.4442

0.2585

0.3670

0.3747

0.3676

1.5376

57

Netherlands

1.3466

0.4026

0.3260

0.3410

0.3308

1.4972

79

New Zealand

1.4002

0.6039

0.4390

0.4657

0.4455

1.6164

33

Nicaragua

1.5685

0.3029

0.5030

0.5150

0.5042

1.6704

19

Niger

1.5131

0.4638

0.5050

0.5225

0.5057

1.6717

18

Nigeria

1.5763

0.2880

0.5060

0.5173

0.5070

1.6728

16

Norway

1.2934

0.3153

0.2580

0.2688

0.2620

1.4152

99

Pakistan

1.4074

0.1913

0.3120

0.3190

0.3143

1.4783

88

Panama

1.5169

0.4045

0.4850

0.5018

0.4878

1.6557

24

Papua N.Guinea

1.5846

0.2710

0.5090

0.5195

0.5096

1.6752

15

Paraguay

1.6392

0.3245

0.5910

0.6053

0.5917

1.7435

6

Peru

1.5073

0.3688

0.4620

0.4774

0.4651

1.6349

29

Philippines

1.5415

0.2643

0.4620

0.4709

0.4621

1.6321

31

Poland

1.3703

0.3487

0.3290

0.3421

0.3333

1.4999

77

Portugal

1.4175

0.3047

0.3560

0.3675

0.3593

1.5287

64

Romania

1.3128

0.3442

0.2820

0.2934

0.2856

1.4443

95

Russian Fed.

1.5501

0.3130

0.4870

0.4994

0.4886

1.6564

22

Rwanda

1.3597

0.2438

0.2890

0.2973

0.2917

1.4516

92

Senegal

1.4899

0.2733

0.4130

0.4229

0.4146

1.5862

38

Sierra Leone

1.6448

0.3926

0.6290

0.6432

0.6258

1.7698

1

Slovak R.

1.2179

0.2869

0.1950

0.2048

0.1995

1.3326

108

Slovenia

1.2566

0.4487

0.2680

0.2845

0.2744

1.4306

97

South Africa

1.6621

0.2692

0.5930

0.6087

0.5973

1.7479

5

Spain

1.3503

0.3902

0.3250

0.3398

0.3300

1.4962

80

Sri Lanka

1.4178

0.2601

0.3440

0.3518

0.3450

1.5130

71

Sweden

1.2526

0.3895

0.2500

0.2620

0.2538

1.4048

104

Switzerland

1.3444

0.4265

0.3310

0.3477

0.3367

1.5038

73

Tanzania

1.4455

0.3039

0.3820

0.3925

0.3839

1.5549

54

Thailand

1.4915

0.2678

0.4140

0.4223

0.4142

1.5858

39

Trinidad&Tob.

1.4341

0.3924

0.4030

0.4150

0.4034

1.5749

46

Tunisia

1.4473

0.3562

0.4020

0.4137

0.4032

1.5747

47

Turkey

1.4712

0.3330

0.4150

0.4276

0.4175

1.5891

37

Turkmenistan

1.4723

0.3065

0.4080

0.4185

0.4094

1.5810

41

Uganda

1.4538

0.3114

0.3920

0.4029

0.3940

1.5653

52

Ukraine

1.3983

0.2493

0.3250

0.3312

0.3250

1.4906

85

United Kingdom

1.3938

0.3836

0.3610

0.3750

0.3646

1.5344

61

United States

1.4340

0.4186

0.4080

0.4249

0.4123

1.5839

40

Uruguay

1.4746

0.3483

0.4230

0.4367

0.4260

1.5975

35

Uzbekistan

1.3661

0.3651

0.3330

0.3443

0.3350

1.5019

75

Venezuela, R.B.

1.5276

0.3798

0.4880

0.5029

0.4897

1.6574

21

Vietnam

1.4518

0.2182

0.3610

0.3670

0.3611

1.5306

63

Yemen,

1.4439

0.3501

0.3950

0.4082

0.3981

1.5695

50

Zambia

1.5609

0.3137

0.4980

0.5113

0.5001

1.6668

20

Zimbabwe

1.6647

0.1911

0.5680

0.5776

0.5697

1.7259

8

Arithmetic Ave.

1.4438

0.3268

0.3946

0.4067

0.3971

1.5613




Emilio José Chaves
Address: Edif. Los Héroes Apto. 604
Av.Panamericana, Pasto (N)
Colombia, S.A.
Tel. +(92)7222889
email: chavesej@hotmail.com


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