Atkinson Measure of Inequality:
Atkinson Measure of Inequality:
Atkinson defines what he calls "the equally distributed equivalent income" of a given distribution of a total income, and this is defined as that level of per capita income which if enjoyed by everybody would make total welfare exactly equal to the total welfare generated by the actual income distribution. Atkinson measure of inequality has the following formula:
= 1 - for 1
= 1 - for = 1
Now, from BBS data collected from Naogaon in 1996, we had the following data-
|
|
Surveyed households |
% house hold |
Income |
|
,=3 |
|
<1000 |
39 |
7.815631 |
56126.36 |
0.2327325 |
18.46231013 |
|
1000-2000 |
179 |
35.871743 |
290124.32 |
0.2621113 |
14.55554174 |
|
2001-3000 |
107 |
21.442886 |
281048.35 |
0.4247682 |
5.54237693 |
|
3001-4000 |
56 |
11.222445 |
225586.54 |
0.6514482 |
2.35635256 |
|
4001-5000 |
32 |
6.412826 |
162442.64 |
0.8209274 |
1.48385157 |
|
5001-6000 |
22 |
4.408818 |
115243.11 |
0.8471240 |
1.39349689 |
|
6001-7000 |
11 |
2.204409 |
64389.11 |
0.9466173 |
1.11596637 |
|
7001-8000 |
15 |
3.006012 |
136743.99 |
1.4742519 |
0.46010463 |
|
8000+ |
38 |
7.615230 |
784834.07 |
3.3400192 |
0.08964005 |
|
Total |
499 |
100 % |
2116538 |
|
45.45964 |
= 1 - for = 3
= 1 - 0.444947
= 0.555053
See the S-plus / R codes used to calculate this result of the Atkinson's measure.
Similarly, = 0.3287440 for = 1.25
= 0.3754383 for = 1.50
= 0.4164656 for = 1.75
= 0.4523522 for = 2.00
= 0.4836391 for = 2.25
= 0.5108557 for = 2.50
= 0.5345050 for = 2.75
As the value of the parameter increases, the Atkinson measure of inequality becomes more and more sensitive to the relative position of the poorer person. From the results, we see that for parameter value of greater magnitude, Atkinson measure becomes higher and higher indicating relative position of the poorer person more unequal.
Now, from BBS data collected from Naogaon in 1996, we had the following data-
|
|
Surveyed households |
% house hold |
Expenditure |
|
,=3 |
|
<1000 |
39 |
7.815631 |
21266.13 |
0.09065847 |
121.6699257 |
|
1000-2000 |
179 |
35.871743 |
254711.65 |
0.23658124 |
17.8664966 |
|
2001-3000 |
107 |
21.442886 |
281124.15 |
0.43681636 |
5.2408557 |
|
3001-4000 |
56 |
11.222445 |
188828.04 |
0.56061276 |
3.1818085 |
|
4001-5000 |
32 |
6.412826 |
137942.38 |
0.71669151 |
1.9468634 |
|
5001-6000 |
22 |
4.408818 |
135931.97 |
1.02726727 |
0.9476176 |
|
6001-7000 |
11 |
2.204409 |
98167.24 |
1.48374209 |
0.4542377 |
|
7001-8000 |
15 |
3.006012 |
125930.71 |
1.39580553 |
0.5132751 |
|
8000+ |
38 |
7.615230 |
697523.22 |
3.05182477 |
0.1073695 |
|
Total |
499 |
100 % |
1941425 |
|
151.9284 |
= 1 - for = 3
= 1 - 0.2433895
= 0.7566105
Similarly, = 0.4181511 for = 1.25
= 0.4924929 for = 1.50
= 0.5587816 for = 1.75
= 0.6156667 for = 2.00
= 0.6629220 for = 2.25
= 0.7012866 for = 2.50
= 0.7320429 for = 2.75
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This web-site is maintained by - Mohammad
Ehsanul Karim
Institute of Statistical Research and Training University of Dhaka, Dhaka -1000, Bangladesh
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