Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty...
Transcript of Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty...
![Page 1: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/1.jpg)
Measurement of poverty and inequality
Econ 1910 – Poverty and distribution in developing countries
Tarjei Havnes
![Page 2: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/2.jpg)
Introduction
I How many are poor?
I How large is inequality?
I How did the financial crises affect poverty?
To answer these questions, we need summary measures.
I to understand the present
I to compare over time
I to compare across countries
![Page 3: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/3.jpg)
Introduction
In order to make useful summary measures, we need to specify whatwe want them to capture.
I How should a poverty measure respond to changes in income
I among the poor?I among the rich?I among the middle class?
I How should an inequality measure respond to these changes?
![Page 4: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/4.jpg)
Introduction
In order to make useful summary measures, we need to specify whatwe want them to capture.
I How should a poverty measure respond to changes in income
I among the poor?I among the rich?I among the middle class?
I How should an inequality measure respond to these changes?
![Page 5: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/5.jpg)
Introduction
In order to understand statements like “poverty has decreased”
I we need to understand what measure is used,
I what the measure captures, and
I what the measure does not capture
![Page 6: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/6.jpg)
Poverty in Norway, 1998–2012
Audun Lysbakken (leader of the Socialist Left Party), said in the 2013election that
“The share of poor people in the Norwegian population is thelowest since 1998.”
![Page 7: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/7.jpg)
Poverty in Norway, 1998–2012
23
45
67
89
10
Po
ve
rty (
%)
1998 2000 2002 2004 2006 2008 2010 2012year
![Page 8: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/8.jpg)
Poverty in Norway, 1998–2012
23
45
67
89
10
Po
ve
rty (
%)
1998 2000 2002 2004 2006 2008 2010 2012year
EU50
EU60
![Page 9: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/9.jpg)
Poverty in Norway, 1998–2012
23
45
67
89
10
Po
ve
rty (
%)
1998 2000 2002 2004 2006 2008 2010 2012year
EU50
EU60
OECD50
OECD60
![Page 10: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/10.jpg)
Poverty in Norway 1998–2012, incl. students
23
45
67
89
10
Po
ve
rty (
%)
1998 2000 2002 2004 2006 2008 2010 2012year
OECD60, incl. students
EU60, incl. students
![Page 11: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/11.jpg)
Plan for today
1. Measures of poverty
I the income distribution
I the incidence of poverty
I poverty lines: absolute poverty vs relative povertyI the head count ratio
I the extent of poverty
I the poverty gap ratioI the income gap ratioI Foster–Greer-Thorbecke
![Page 12: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/12.jpg)
Plan for today
2. Measures of inequality
I four criteria
I the Lorenz curve
I percentile ratios
I the coefficient of variation
I the Gini index
3. Some additional issues
I what income measure?
I what observation unit?
I what time frame?
![Page 13: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/13.jpg)
Example
Individual Adam John Emily Mark Ted Total
Income 400 600 1,300 2,700 5,000 10,000Quintile 1st 2nd 3rd 4th 5th All% of income 4 6 13 27 50 100
![Page 14: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/14.jpg)
Example: Income by rank
01
00
02
00
03
00
04
00
05
00
0
Inco
me
1 2 3 4 5
Rank
![Page 15: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/15.jpg)
Population share below income levels
01
23
45
Ra
nk
0 1000 2000 3000 4000 5000
Income
![Page 16: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/16.jpg)
The cumulative density function (CDF)
0.2
.4.6
.81
Po
pu
latio
n s
ha
re
0 1000 2000 3000 4000 5000Income
![Page 17: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/17.jpg)
Histogram
02
.0e
−0
44
.0e
−0
46
.0e
−0
48
.0e
−0
4D
en
sity
0 1000 2000 3000 4000 5000Income
![Page 18: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/18.jpg)
The probability density function (PDF)
.00
00
5.0
00
1.0
00
15
.00
02
.00
02
5d
en
sity:
Inco
me
0 1000 2000 3000 4000 5000Income
![Page 19: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/19.jpg)
Household expenditure in Uganda, 2006
0.2
.4.6
.81
Po
pu
latio
n s
ha
re
0 1 2 3 4 5Household expenditure
![Page 20: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/20.jpg)
Household expenditure in Uganda, 2006
0.1
.2.3
.4.5
de
nsity:
Ho
use
ho
ld e
xp
en
ditu
re
0 1 2 3 4 5Household expenditure
![Page 21: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/21.jpg)
Absolute poverty vs relative poverty
Poverty is defined in either relative or absolute terms
1. Absolute poverty: Income below a fixed limit
I survival, calories
2. Relative poverty: Income below a limit defined from “normal”income
I OECD50 vs EU60 (median)
What do you think is the best way to measure poverty?
![Page 22: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/22.jpg)
The incidence of poverty: HCR
The head count ratio (HCR) is the most common poverty measure
I counts the number of people below a poverty line p
I as a share of the population n
HCR =HCn
=
∑1 (yi < p)
n
This is used to measure both absolute and relative poverty
I Relative: OECD50, EU60
I Absolute: Dollar-a-day measures
![Page 23: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/23.jpg)
HCR in Uganda, 2006
HCR = 0.33
0.2
.4.6
.81
Po
pu
latio
n s
ha
re
0 1 2 3 4 5Household expenditure
![Page 24: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/24.jpg)
The incidence of poverty: HCR – Issues
Key problem: HCR is that it does not take into account the extent (orintensity) of poverty.
I HCR does not change if the poor’s living standards improve ifthey remain below the poverty line
I the “bang for the buck” problem
I most efficient way of reducing HCR is to help the least poor
I even at the expense of the poorest!
![Page 25: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/25.jpg)
The extent of poverty: PGR
The poverty gap ratio (PGR)
I totals the income short-fall of the poor, (p − yi)
I as a fraction of total income in the population,n ×m = n 1
n
∑ni=1 yi
PGR =
∑HCi=1 (p − yi)
nm
where we have ordered incomes so that
y1 ≤ y2 ≤ · · · ≤ yn
![Page 26: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/26.jpg)
PGR in Uganda, 2006
PGR = 0.05
0.2
.4.6
.81
Po
pu
latio
n s
ha
re
0 1 2 3 4 5Household expenditure
![Page 27: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/27.jpg)
The extent of poverty: PGR – Issues
PGR can be interpreted as
I the minimum cost of bringing the poor out of poverty
I disregarding implementation costs and distortions
But what if society is highly unequal,
I wealthy overall
I a large number of poor
![Page 28: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/28.jpg)
The extent of poverty: IGR
The income gap ratio (IGR)
I totals the income short-fall of the poor, (p − yi)
I as a fraction of minimum total income if all poor were brought outof poverty, p × HC
IGR =
∑HCi=1 (p − yi)
p × HC
![Page 29: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/29.jpg)
IGR in Uganda, 2006
IGR = 0.30
0.2
.4.6
.81
Po
pu
latio
n s
ha
re
0 1 2 3 4 5Household expenditure
![Page 30: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/30.jpg)
The extent of poverty: FGT
All previous measures fail the basic test
I Income transfers from richer to poorer,
I between two poor people,
I should increase poverty
The Foster-Greer-Thorbecke measure (FGT) passes this test, as longas α > 1 .
FGT (α) =1n
HC∑i=1
(p − yi
p
)α
Note also that
FGT (0) = HCR
FGT (1) = PGR
![Page 31: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/31.jpg)
FGT in Uganda, 2006 (α = 2)
FGT(2) = 0.13
0.2
.4.6
.81
Po
pu
latio
n s
ha
re
0 1 2 3 4 5Household expenditure
![Page 32: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/32.jpg)
Poverty in Uganda, 2006
IGR = 0.30 PGR = 0.05
FGT(2) = 0.13
HCR = 0.33
0.2
.4.6
.81
Po
pu
latio
n s
ha
re
0 1 2 3 4 5Household expenditure
![Page 33: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/33.jpg)
Measurement of inequality
Four criteria for inequality measures
1. Anonymity principle
I who earns what does not matter
2. Population principle
I population size does not matter
3. Relative income principle
I only relative income should matter, not income levels
4. The Pigou–Dalton principle
I if the giver stays poorer than the recipient, thenI transfer from poorer to (weakly) richer increases inequality
![Page 34: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/34.jpg)
Example
Individual Adam John Emily Mark Ted Total
Income 400 600 1,300 2,700 5,000 10,000Quintile 1st 2nd 3rd 4th 5th All% of income 4 6 13 27 50 100
![Page 35: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/35.jpg)
Anonymity principle
Permutations of the income distribution should not affect inequality
I (y1, y2, . . . yk−1, yk+1, . . . , yn) = I (y1, y2, . . . yk+1, yk−1, . . . , yn)
Individual Adam John Emily Mark Ted Total
OriginalIncome 400 600 1,300 2,700 5,000 10,000Quintile 1st 2nd 3rd 4th 5th All% of income 4 6 13 27 50 100After permutationsIncome 1,300 400 5000 2,700 600 10,000Quintile 3rd 1st 5th 4th 2nd All% of income 13 4 50 27 6 100
![Page 36: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/36.jpg)
Population principle
The size of the population should not matter
I i.e. if we clone the current distribution, then inequality should bethe same
I (y1, y2, . . . , yn) = I (y1, y2, . . . , yn, y1, y2, . . . , yn)
![Page 37: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/37.jpg)
Relative income principle
Only relative incomes should affect inequality
I differences in a rich country should be counted equally as
I differences in a poor country
Individual Adam John Emily Mark Ted Total
OriginalIncome 400 600 1,300 2,700 5,000 10,000Quintile 1st 2nd 3rd 4th 5th All% of income 4 6 13 27 50 100After scalingIncome 800 1,200 2,600 5,400 10,000 20,000Quintile 1st 2nd 3rd 4th 5th All% of income 4 6 13 27 50 100
![Page 38: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/38.jpg)
Pigou–Dalton principle
If a distribution F can be constructed from another G
I by a set of regressive transfers (poor to rich)
I then inequality is larger in F
I that is, for h > 0,
I (y1, y2, . . . , ys, . . . , yt , . . . , yn)
< I (y1, y2, . . . , ys − h, . . . , yt + h, . . . , yn)
![Page 39: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/39.jpg)
Pigou–Dalton principle
Note that we should define with regressive transfers, not progressive.
I to see why, consider an egalitarian distribution, where all incomesare equal
I with regressive transfers, indeed
I (y , y , . . . , y , . . . , y , . . . , y) < I (y , y , . . . , y − h, . . . , y + h, . . . , y)
I but with progressive transfers
I (y , y , . . . , y , . . . , y , . . . , y) < I (y , y , . . . , y + h, . . . , y − h, . . . , y)!
![Page 40: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/40.jpg)
The Lorenz curveThe Lorenz curve summarizes all information necessary for calculatinginequality indices under the above criteria
I income sharesI population shares
0.2
.4.6
.81
Inco
me
sh
are
0 .2 .4 .6 .8 1Population share
![Page 41: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/41.jpg)
A regressive transfer
Individual Adam John Emily Mark Ted Total
Income 1 400 600 1,300 2,700 5,000 10,000Income 2 0 600 1,300 2,700 5,400 10,000
![Page 42: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/42.jpg)
A regressive transfer
0.2
.4.6
.81
Inco
me
sh
are
0 .2 .4 .6 .8 1Population share
Individual Adam John Emily Mark Ted Total
Income 1 400 600 1,300 2,700 5,000 10,000
Income 2 0 600 1,300 2,700 5,400 10,000
![Page 43: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/43.jpg)
Summary measures of inequality
Two problems with the Lorenz curves
1. Often interested in summarizing inequality by a number
2. No ranking when Lorenz curves cross
A summary inequality measure provides a complete ranking
I Different summary measures may disagree in ranking
![Page 44: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/44.jpg)
Percentile ratios (Kuznets ratios)
Percentile ratios take the fraction of percentiles, for instance
d9d1 =p90p10
d5d1 =p50p10
Easy to calculate and understand, but
I ignores incomes between percentiles
I ignores incomes above the highest and below the lowest
I fails Pigou–Dalton
![Page 45: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/45.jpg)
The coefficient of variation
Takes advantage of the entire income distribution
I Consider income distances from the average income
I giving higher weight to larger deviations
CV =1m
√√√√1n
n∑i=1
(yj −m)2
It satisfies all four principles and is therefore Lorenz-consistent.
![Page 46: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/46.jpg)
The Gini coefficient
The Gini coefficient is the most used in empirical work.
I Takes the difference between all pairs of incomes and simplytotals the (absolute) difference.
I Sequentially, compare an individual Joe to all other individuals,1
nm
∑nk=1 |yJoe − yk |
I And then do the same for everybody,
G =1n
n∑i=1
1nm
n∑k=1
|yi − yk |
It satisfies all four principles and is therefore Lorenz-consistent.
![Page 47: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/47.jpg)
Gini coefficient
A
Gini = 2*A
0.2
.4.6
.81
Inco
me
sh
are
0 .2 .4 .6 .8 1Population share
![Page 48: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/48.jpg)
Lorenz curve and Gini in Uganda, 2006
A
Gini = 2*A = 0.444
0.2
.4.6
.81
Ho
use
ho
ld e
xp
. sh
are
0 .2 .4 .6 .8 1Population share
![Page 49: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/49.jpg)
Comparing Gini and CV
Both satisfy all four principles.
I If Lorenz curves do not cross – always rank the same
I If Lorenz curves do cross – may rank differently
In practice,
I Gini is sensitive to the middle of the distribution
I CV is sensitive to the right tail of the distribution (the rich)
I Neither is very sensitive to the poor
Neither is by any means perfect,
I Gini = 0.5
I 50% richest share all income equallyI 75% poorest share 25%, while 25% richest share 75%, both
equally
![Page 50: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/50.jpg)
Some additional issues
What is the basis for calculating poverty (or inequality)?
I Income
I Consumption
I Consumption-potential
What is the unit we are interested in?
I Individuals
I Households
I Equivalence scales
Note that we are essentially ignoring distribution inside the household.
![Page 51: Measurement of poverty and inequality - Universitetet i · PDF fileI How should a poverty measure respond to changes in income ... Measures of poverty ... The extent of poverty: FGT](https://reader034.fdocuments.in/reader034/viewer/2022051522/5a70c38a7f8b9aac538c369c/html5/thumbnails/51.jpg)
Some additional issues
What if high consumption or income today is followed by lowconsumption or income tomorrow?
I transient poverty vs persistent poverty
I income today vs lifetime income
I depends on ability to smooth incomeI how reliant are you on variable income (think about agriculture)I financial markets: insurance, credit and savingsI public safety net: unemployment, disability, social assistance,
income replacement