The purpose of this paper is to discuss a method of calculating the Gini Coefficient of Inequality, with particular reference to the Kenyan data. This method is simple, precise and straightforward, and is free of ambiguities that beset the other conventional method.
Moreover, it can be readily applied to a series of data that cover a long period of time. As such, the method can be used to analyse readily the extent to which inequality is increasing or decreasing over time in the country or region

Aseto, Oyugi

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A METHOD OF MEASURING THE GINI RATIO OF INCOME 
INEQUALITY : THE KENYAN CASE 
Oyugi Aseto 
i N S T m m of 
OEVEiofwewr shubes 
llSiMf* 
11 11111 M-:M. i.. 
WORKING PAPER NO. 313 
INSTITUTE FOR DEVELOPMENT STUDIES 
CH UNIVERSITY OF NAIROBI 
P.O. BOX 30197 
NAIROBI, KENYA. 
June 19 77 
Views expressed in this paper are those of the author. 
They snould not be interpreted as reflecting the views 
of the Department of Economics, University of Nairobi. 
IDS/WP 313 
ABSTRACT; 
:.- :: t ! The purpose of this paper is to discuss a \» -v 
method of calculating./tha^ini Coefficient of Inequality, 
with particular reference to the Kenyan data. This method 
is simple, precise and straightforward, and is free of 
ambiguities that beset the other conventional method. 
Moreover;hit can be readily applied tc a series of data 
that cover a long period of time. As such, the method 
can be used to analyse readily the extent to which 
inequality is increasing or decreasing over time in the 
country or region. ,. .. . ..,. .-
i " • ••.; !' > V i" :• 
:jf!h SP 
••• 'y.Li 
1 !. f /'. .1 • 
t t : , : 
5 IDS/W P 313 
A METHOD OF. MEASURING THE GIMI RATIO INCOME INEQUALITY; 
THE KENYAN CASE. 
... r ~ u . . ••• ... . - : 
... . . -. : ;:. .. : • :;-•- . , . f. , Mjilijj.'. • •  • • " " o i r 
I: The Kenya's Policy Concerning Equality: . n . .</p..; 
Since independence, tne question of equality of 
.... . >;.!.' ' •• r-.'r.'.X 3! J T income distribution in the country has occupied the . .... • ? • • >u ..•••" . • )i eonxc, attention of decision-makers. This preoccupation was 
V; . • !{: c >! .:. "IT natural. Inequality was one of the evils of colonialism . frr : — • . - -. • y "• : . > ••. .. .  • .'- » >-.>.'<i 
in Kenya. The'colonial society was divided into three 
layered racial groups: Europeans at the top, Asians in the 
middle, and Africans at the bottom. The fighters for 
independence pledged that the inequality of income 
distribution must be eradicated or reduced. Thus, soon 
after independence, the Government produced an official 
document, African Socialism and Its Application to Planning 
— • - - : - : • • ..... ,. to .• ~ 0*? vTTT ' in Kenya, otherwise known as Sessional Paper No. '10 of 1955 
(henceforth to oe referredr to as the Paper) in which the 
issue;of•equitable distribution of income was accorded a 
prominent attention. For example, tne Paper says that 
"Kenya is already committed to (the objective of) high 
and growing per capita incomes, equitably distributed" 
(p.2) .and to M: -vi-. 
fiv? o.: ' wol ra/iwages and incomes policy that recognizes'' ,J L 
the need for differential incentives as well, j 
as an equitable distribution of income, (p.8). 
All the subsequent Develop Plans, I, II and III, for the 
periods 1966 - 1970, 1970 - 1974, and 1974 - 1978, 
respectively, have paid attention to the subject of 
equitable distribution of income. But the greatest attention 
to the matter has been given by the ILO/UNDP visiting mission 
which devoted many pages to the question, especially chapter 
5 and tne Technical Appendix 4 of. their Report: Employment, 
Incomes and Equality (Geneva s 1972). This Report high-
lighted the extent and degree of inequality in the country, 
and prescribed measures to deal with the problem.. Thus, the iv.-. ''. -v. illj < . . • i. • .' 
matter of equality of income distribution has received much 
official attention during the post-independence period. 
2 IDSA'.'P 313 
Yet there is a good measure of belief that inequality 
: of income distribution, despite official attention, is 
indeed increasing both absolutely^and relatively. The 
ILO/UNDP Report says (p.83) that "... unemployment and 
gross inequality continue, and in some respects may even 
have increased. " -
The idea that income inequality may hayp, increased 
since independence suggests a need for a measure of inequality, 
This kind of measurement will not only assist the policy-
makers in assessing the extent to which the., policy for 
reduction of inequality has been achieved, but. it v/ill also r rr, ncrcXc.'A. *qoJ srus-eq--. --.qixo'ip D'-J > 
help them to device new approaches to dealing with the ere J--fiy.LT ' !';5:)Ij J JfTI , •. 
problem. Without such accurate measurements, there would 
be no way of making precise judgements about•the performance SCtti'i*' , 1' i.': lO i.'-'j,} £>'..• ; • 1 -, r J- ."11 HO IJul.li j i , of the policy instruments deviced to deal with( th§ problem. 
nine, f , rtoi.-Tivoi £qqA. " . mn '••lj- j , ia.^ nuJOOL 
II: The Problems" of Measuring Inequality: ^ Ur. . — —' " •• >0 JO , £.\JIQA n 
3,.. ' But, any attempt to measure income inequality;*!^ the 
3 country isf immediately beset with r.two problem: : lack of data 
on family ineor.es^and expenditure" and.ia method of j to use 
for mqasuringoinequality. Concerning-..the.;.f irst • problem, the 
issu^ tii5r;-sef.ious^ .:.'Ilenya does not have data necessary'for 
the measurement. There are data on output and wages, but 
these data are not relevant for the problem at hand. The 
ILO^IttPPrrJReport :-presents the matter oin-the following way 
(p. 7 3 £ f n i 
A comprehensive analysis of income distribution 
in Kenya is unfortunately precluded by lack of 
data. There are parts of the population/ especia-
lly wage earners in the formal sector, for whom 
the existing data yield a reasonably complete and 
-accurate picture of income distribution, but for 
.ot.her .pajrts only fragmentary aata of limited 
; m s r ^ re'ii abi iity' are avai 1 ab le. I 
f'.-s v.! J )"> : '•'•>• ??:• , :i'"••'>. : • ;..J OJ ; • 1 •-*'"• •* • 
a o'.'i-. Ihe second problem of measurement of incbme inequality 
concerns the technique to be uked for the measurement-. There 
are at least five commonly used alternative measures of 
inequalitys the Gini Concentration'Ratio, the Standard 
Deviation of Logs of Income, the Coefficient of Variation, 
the Shares of the Lowest QUintile, and Shares of the Highest 
Quintile, These techniques give different results when applied 
to a given set of data. Moreover, their results become 
IDS-/WF? 31.3 
amhig.uous when Lor6h2' curves cross. But it is the Gini 
Concentration Patio Itliat is of particular interest in 
this paper,.! - >•>>'' 
.. . • ' ; .. i :' ;',:• ' J "' ' Ii' . • ' 
III. The, Gini Coefficient.Measure of Inequality; 
The Gini Coefficient of inequality is usually obtained 
in the following manner. All income groups are ranked 
cumulatively from zero to one hundred percent. The corres-
ponding incomes of the groups are also likewise ranked 
cumulatively from zero to one hundred percent. Then, using 
a graph paper, one can plot the cumulative percentile .1 I'll'-1". 
income receipts against the cumulative percentile income 
groups. Figure 1 illustrates this point.. - i cH ; ' • • • 
Figure 1. Lorenz Curve of Income Distribution,., ho.3j-Dg 
100 - P C t. r,, 
A V . lOOp 
Percent of Population X 
B 
If income is completely equally distributed, then one 
percent of the population will receive one percent of the 
income, twenty-three percent of tne population will receive 
twenty-three percent of the income, and soon, till one 
hundred percent of the population will receive one hundred 
percent of the income. Such a situation will be depicted by 
the line AC which is a 45° degree diagonal line. 
-A. - rn"/WP §13 
But that kind of situation does not exist. What exists 
is a situation in which a few people receive a disproportion-
ately high income and the majority of the population receives 
a disproportionately smaller income. A line depicting that 
kind of situation can be depicted by the dotted curve 
beloW the lin£ of complete equality. This latter curve is 
the Lorenz curve of inequality. It describes the extent 
to which there is a deviation of inequality from equality " -
for all income groups. 
,-tThis measure, however, is not specific. A single index 
of .inequality is required. Hence the use of the Gini' Ratio 
of. Inequality. The iRatio expresses the shaded area in 
; Figure 1 as a proportion Of the total area of the triangle 
ABC. If there is a..complete equality ih ine&nte1 distribution, 
then the shaded area" will- vanish, arid Inequality will be 
"ero. If there is a complete'inequality in income distribution, 
it means that only one person owns everything, and the 
, . . . - , . i H 
shaded area will embrace the entird triangle. The. Ratio will 
be 1. 
It is obvious that neither of tnese extreme situations 
exists in any society. The normal situation is that in 
which a smaller percentage of people receives a larger per-
centage of income. And the problem then becomes that of 
finding the inequality index or a ratio of inequality in 
income distribution. FIGURE 2. Using an approximation method to calculate the 
Gini Ratio. 
Percent Population X 
5 IDS/W P 313 
The usual procedure of finding tne ratio is to 
approximate the shaded area through the technique of sub-
dividing the shaded area into triangles and rectangles 
and then add up all the so approximated area. The sum of 
' ail' these are ' then expressed as a proportion of the triangle 
ABC. This is then the Ratio required. Figure 2 illustrates 
the point. The areas of all the small triangles and did. ••'" 
' divided by the area of the triangle ABC whose area is 
H ABCD. 
'93-3.['.(r;ooM<Dre generally, the Gini Ratio described above can 
be..!expressed mathematically as '.1 ') -
.:)•:• ••• j j.u(• w .•; 1 jj:,:;r - .to.; Of-:: .:.... " J" 100 -=?v • ,-xni . ' 
o f x - f (X),./ dx 
..... . ... • h (100)2 
where X is cumulative percent population ana f(X) is 
sire sfi-i • • : -
cumulative percent income. b.i •'. ' '.'.••. • • ' -
i .• ' V • " . .. - • • • • : ' 
The method described above has several disadvantages. 
First, adding up all those triangles and rectacles is an 
. arduous undertaking.. It. is t i rne - cons um in g .-'• - S e dOri d 1 y, 
there t.aim likely.'to be mistakes emanating from the approxi-
mations in the partitioning process. Thus, these errors 
may lead to subjective conclusions, since two people will 
"hot make the skme partitions from the same data. And finally, 
!JJne' prok/lism o;f LOrenz curve crossing is never dealt with. 
There is a need therefore for a technique that will take 
care of all these problems. 
IV. The New Method of. Measuring the Gini Coefficient of 
:.)ff i a>Inequality!, yji. • atrv •• • «' :,rt-'- -
fiicir. BJV. r" > '• • • • 
The new technique of measuring the Gini Ratio of, eo'trl.t n t abl' -ao • •• • • -> 1 
Concentration, to be described below, has several advantages 
over the pxistimjr methods , In the . f irst p^ace , _ it .is .,;••• 
very simple, and is therefore non-time consuming. Secondly, 
it is definitely much more accurate and is thus much more 
objective than the others. And lastly, it does solve the 
problem of Lorenz curve crossing. 
i.i.;.fu- - . ,-u. - .IPS/WP 313 
The new method begins to be applied where the Lorenz 
curve has been drawn. Instead of measuring the shaded 
area as a proportion of the triangle, as described above, 
the following procedure is followed. 
(a) rDraw a line parallel to the line of complete 
equality (the:diagonal line which forms the 
45° with the horizontal line) but tangent 
to the Lorenz curve of inequality at F, 
(b) The tangent point F at which the parallel 
line touches the Lorenz curve is the longest 
possible distance that exists between the 
45° line of complete equality and the Lorenz 
curve of inequality1. This proposition should 
be verified by measuring these distances with 
"• a ruler, i.e. GF is the longest distance. 
• t': i • ; " • • ' 
(c) Draw a line GL which joins the1 45° line with 
the horizontal axis, but passing through the 
tangent point .F. 
f -I'V^C • •: » ' . -'^ r IniV•' mtC' JV • ; ik->. 
(d) Measure the distance GF as a proportion of GE. 
The ratio GF/GE gives the desired Gini Ratio 
of inequality. 
V. Application of the Method to the Kenyan Data: 
An jattempt was made by the ILO/UNDP mission to 1 
find out the extent of income inequality in Kenya. Using 
household Budget Survey 1968-69, the mission was able 
to tabulate income groups of various nouseholds in three 
big urban areas in Kenya: Nairobi, Mombasa and Kisumu. 
The result of their findings is reproduced in table 1 
below: 
7 IDS/W P 313 
TABLE I; No. of households an sample by income class for 
Nairobi, Mombasa and Kisuniu, Household Budget Survey, 
1968-1969. • i 
Income groups (shillings per month).. 
Town 
0-199 200-299 300-399 ,400-499 500 
699 
- 700-
999 -
1000 
1399 
1400 
1999 
over 
2000 
N7\robi 27 83 65 47 72 4 7 . . 52, \ j 52 53 
Mombasa 61 73 <O >. 58 ouwc-.uor. 34 
4 8. 43 37 31 39 
i 
Kisumu 10 23 32 28 43 34 24 19 i 11 i 
All 'three • - ' ; 9 8 : 179 15 5 
. • : : • jj!, 
109"*"" 163 
• • •-. i '• 
124 113 102 103 | 
i 
Source ; ILO/UNDP, Employment, Incomes and 
Equality, p. 34 7. 
• • ': '. i <•-' '. * -": : '.V 
8 - - IDS/WP 313 
F i9 u r-g— 4~ Distribution of Income among Households i 
Nairobi, Mombasa, and Kisumu 196 8-196 9. 
! 
Sources ILO/UNDP, Employment, Incomes and Equality, p.347. 
j *J i. 
9 IDS/W P 313 
These data were then transformed into cumulative 
percentage distribution by income groups and by income. A 
curve diagram depicting these distributions was then drawn, 
as in Figure 
The results of calculated Gini Coefficients are as 
follows s 
Table 2s The Gini Ratio's for Kisumu, Nairobi and Mombasa 
Town 
— — — 
i 
Gini Coefficient 
Nairobi 0.5 
Mombasa 0.6 
Kisumu 0.4 
From the results, it is clear that income is more, 
equitably distributed in Kisumu and Nairobi than it is in 
Mombasa, since the Gini Ratios are 0.4, 0,5 and 0.6, 
respectively. 
'7 Conclusion; 
The purpose of this paper has been to discuss a method 
of income inequality measurement by the use of the Gini 
Coefficient of Concentration Ratio. The new method was found 
to be simpler, direct, and less time consuming. It is now 
possible then to undertake to calculate many Gini Ratio's 
for several years and to be able consequently to compare the 
extent to which inequality in income distribution is in-
creasing or decreasing over time in either a region or in 
the country as a whole. 


A method of measuring the Gini ratio of income inequality: the Kenyan case

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A method of measuring the Gini ratio of income inequality: the Kenyan case

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