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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 |
|||
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