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