econ 450 development economics - … · measuring inequality and poverty econ 450 development...

Measuring Inequality and Poverty

ECON 450Development Economics

Measuring Poverty and Inequality

University of Illinois at Urbana-Champaign

Summer 2017

Henrique Veras de Paiva Fonseca ECON 450 Development Economics


Introduction

In this lecture we’ll introduce appropriate measures of inequalityand poverty.



Introduction

Although our main focus is on economic poverty and inequalitiesin the distribution of incomes and assets, it is important to keepin mind that this is only part of the broader inequality problem inthe developing world.Of equal or even greater importance are inequalities of power,prestige, status, gender, job satisfaction, conditions of work,degree of participation, freedom of choice, and many otherdimensions of the problem.


Measuring Inequality and Poverty Measuring InequalityMeasuring Absolute Poverty

Outline

1 Measuring Inequality and PovertyMeasuring InequalityMeasuring Absolute Poverty



Measuring InequalitySize Distributions

The personal or size distribution of income is the measure mostcommonly used by economists.It simply deals with individual persons or households and thetotal incomes they receive.




Economists and statisticians therefore like to arrange allindividuals by ascending personal incomes and then divide thetotal population into distinct groups, or sizes.A common method is to divide the population into successivequintiles (fifths) or deciles (tenths) according to ascendingincome levels and then determine what proportion of the totalnational income is received by each income group.




A common measure of income inequality that can be derivedfrom column 3 is the ratio of the incomes received by the top20% and bottom 40% of the population.This ratio, sometimes called a Kuznets ratio after Nobel laureateSimon Kuznets, has often been used as a measure of the degreeof inequality between high- and low-income groups in a country.

In our example, this inequality ratio is equal to 51 divided by 14, orapproximately 3.64.



Measuring InequalityLorenz Curves

Another common way to analyze personal income statistics is toconstruct what is known as a Lorenz curve

Lorenz curve is defined as a graph depicting the variance of thesize distribution of income from perfect equality.

The figure in the next slide shows how it is done.




The numbers of income recipients are plotted on the horizontalaxis, not in absolute terms but in cumulative percentages.

For example, at point 20, we have the lowest (poorest) 20% of thepopulation; at point 60, we have the bottom 60%; and at the end ofthe axis, all 100% of the population has been accounted for.

The vertical axis shows the share of total income received byeach percentage of population.




At every point on that diagonal, the percentage of incomereceived is exactly equal to the percentage of income recipients.The Lorenz curve shows the actual quantitative relationshipbetween the percentage of income recipients and the percentageof the total income they did in fact receive during, say, a givenyear.




Point A shows that the bottom 10% of the population receivesonly 1.8% of the total income, point B shows that the bottom 20%is receiving 5% of the total income, and so on for each of theother eight cumulative decile groups.




The more the Lorenz line curves away from the diagonal (line ofperfect equality), the greater the degree of inequalityrepresented.The greater the degree of inequality, the greater the bend andthe closer to the bottom horizontal axis the Lorenz curve will be.



Measuring InequalityGini Coefficients and Aggregate Measures of Inequality

Four possible Lorenz curves such as might be found ininternational data are drawn in the next figure.In the "Lorenz criterion" of income distribution, whenever oneLorenz curve lies above another Lorenz curve, the economycorresponding to the upper Lorenz curve is more equal than thatof the lower curve.




Thus economy A may unambiguously be said to be more equalthan economy D.Whenever two Lorenz curves cross, such as curves B and C, theLorenz criterion states that we "need more information" oradditional assumptions before we can determine which of theunderlying economies is more equal.One could use an aggregate measure such as the Gini

coefficient to decide the matter.




The Gini concentration ratio or Gini coefficient, named after theItalian statistician who first formulated it in 1912, can be obtainedby calculating the ratio of the area between the diagonal and theLorenz curve divided by the total area of the halfsquare in whichthe curve lies.




Gini coefficients are aggregate inequality measures and can varyanywhere from 0 (perfect equality) to 1 (perfect inequality).In fact, the Gini coefficient for countries with highly unequalincome distributions typically lies between 0.50 and 0.70, whilefor countries with relatively equal distributions, it is on the orderof 0.20 to 0.35.



Measuring InequalityThe Coefficient of Variation (CV)

One final measure of inequality is the coefficient of variation(CV), which is simply the sample standard deviation divided bythe sample mean.Note that this is a measure of dispersion common in statistics.



Measuring Absolute Poverty

Absolute Poverty is defined as the situation of being unable oronly barely able to meet the subsistence essentials of food,clothing, and shelter.We can define the extent of absolute poverty as the total number,or "headcount", H, of those whose incomes fall below a specifiedminimum level of real income – an international poverty line – Yp.



Measuring Absolute PovertyHow to Determine the Absolute Poverty Line?

One practical strategy for determining a local absolute povertyline is to start by defining an adequate basket of food, based onnutritional requirements from medical studies of requiredcalories, protein, and micronutrients.Then, using local household survey data, one can identify atypical basket of food purchased by households that just barelymeet these nutritional requirements.



Measuring Absolute PovertyHow to Determine the Absolute Poverty Line?

One then adds other expenditures of this household, such asclothing, shelter, and medical care, to determine the localabsolute poverty line



Measuring Absolute PovertyThe Headcount Index

We define the headcount index as the proportion of a country’spopulation living below the poverty line, H/N.



Measuring Absolute PovertyLimitation of the Headcount Index

In many respects, however, simply counting the number ofpeople below an agreed-on poverty line can have its limitations.For example, if the poverty line is set at U.S. $450 per person, itmakes a big difference whether most of the absolute poor earn$400 or $300 per year.Both are accorded the same weight when calculating theproportion of the population that lies below the poverty line.



Measuring Absolute PovertyThe Total Poverty Gap (TPG)

Economists therefore attempt to calculate a total poverty gap

(TPG) that measures the total amount of income necessary toraise everyone who is below the poverty line up to that line.The next figure illustrates how we could measure the totalpoverty gap as the shaded area between poverty line, PV , andthe annual income profile of the population.




Even though in both country A and country B, 50% of thepopulation falls below the same poverty line, the TPG in countryA is greater than in country B.Therefore, it will take more of an effort to eliminate absolutepoverty in country A.




The TPG – the extent to which the incomes of the poor lie belowthe poverty line – is found by adding up the amounts by whicheach poor person’s income, Yi , falls below the absolute povertyline, Yp, as follows:

TGP =HX

i=1

(Yp � Yi)



Measuring Absolute PovertyThe Average Poverty Gap (APG)

On a per capita basis, the average poverty gap (APG) is foundby dividing the TPG by the total population:

APG =TPG

N



Measuring Absolute PovertyThe Normalized Poverty Gap (NPG)

Often we are interested in the size of the poverty gap in relationto the poverty line, so we would use as our income shortfallmeasure the normalized poverty gap (NPG):

NPG =APGYp

This measure lies between 0 and 1 and so can be useful whenwe want a unitless measure of the gap for easier comparisons.



Measuring Absolute PovertyThe Average Income Shortfall (AIS)

Another important poverty gap measure is the average income

shortfall (AIS), which is the total poverty gap divided by theheadcount of the poor:

AIS =TPG

H

The AIS tells us the average amount by which the income of apoor person falls below the poverty line.



Measuring Absolute PovertyThe Normalized Income Shortfall (NIS)

Finally, the AIS can also be divided by the poverty line to yield afractional measure, the normalized income shortfall (NIS):

NIS =AISYp



Measuring Absolute PovertyThe Foster-Greer-Thorbecke Index

We are also often interested in the degree of income inequalityamong the poor, such as the Gini coefficient among those whoare poor, Gp, or alternatively, the coefficient of variation (CV ) ofincomes among the poor, CVp.One reason that the Gini or CV among the poor can be importantis that the impact on poverty of economic shocks can differgreatly, depending on the level and distribution of resourcesamong the poor.




Thus, the Foster-Greer-Thorbecke (FGT) index, often called theP↵ class of poverty measures, is given by

P↵ =1N

HX

i=1

✓Yp � Yi

Yp

◆↵

Depending on the value of ↵, the P↵ index takes on differentforms.

If ↵ = 0, the numerator is equal to H, and we get the headcountratio, H/N.If ↵ = 1, we get the normalized poverty gap (why?).




If ↵ = 2, the resulting measure, P2, can be rewritten as

P2 =HN[NIS2 + (1 � NIS)2(CVp)

2]

The impact on measured poverty of a gain in income by a poorperson increases in proportion to the distance of the person fromthe poverty line.




P2 has become a standard of income poverty measure used bythe World Bank and other agencies, and it is used in empiricalwork on income poverty because of its sensitivity to the depthand severity of poverty.For the same reason, the P2 measure has now become part ofthe Mexican constitution (chap. 5, art. 34).



Measuring Absolute PovertyThe Newly Introduced Multidimensional Poverty Index

The idea of the Multidimensional Poverty Index (MPI) is thatpoverty cannot be adequately measured with income.Income is imperfectly measured, but even more important, theadvantages provided by a given amount of income greatly differ,depending on circumstances.




To capture this idea the United Nations Development Program(UNDP) developed the MPI.The MPI approach identifies the very poor by measuring a rangeof important household deprivations directly, rather than onlyindirectly through income, then building the index from householdmeasures up to the aggregate measure.




Rather than using already aggregated statistics in an index, theapproach takes into account the multiplied or interactive harmdone when multiple deprivations are experienced by the sameindividual or family.




The first step in measuring poverty is to know which people arepoor.In the multidimensional poverty approach, a poor person isidentified through what is called the "dual cutoff method"

first, the cutoff levels within each of the dimensions, and second,the cutoff of the number of dimensions in which a person must bedeprived (below the line) to be deemed multidimensionally poor.




Three dimensions:1 Health (1/3)2 Education (1/3)3 Standard of living (1/3)




In applied studies, we need proxy measures, called indicators,for each of the selected dimensions.




Health Indicators1 whether any child has died in the family (1/6);2 whether any adult or child in the family is malnourished (1/6).




Education indicators1 whether not even one household member has completed five years

of schooling (1/6);2 whether any school-age child is out of school for grades one

through eight (1/6).




Living Standard indicators1 lack of electricity (1/18);2 insufficiently safe drinking water (1/18);3 inadequate sanitation (1/18);4 inadequate flooring (1/18);5 unimproved cooking fuel (1/18);6 lack of more than one of five assets – telephone, radio, television,

bicycle, and motorbike or similar vehicle (1/18).




Calculating deprivation in this way, individuals in a family are thenidentified as "multidimensionally poor" when deprived by a"weighted sum" of 0.3 or more (3 out of 10 points as calculated inpractice).




A multidimensionally poor person might live in a household thathas experienced a child death and is also deprived in at leastthree of the six living standards indicators, which sums to 1/6 +1/18 + 1/18 + 1/18 = 1/3, or 33%.Or they could live in a household that is deprived in the otherthree living standard indicators and in which there is aschool-age child not attending school.




Finally, the actual MPI for the country (or region or group) iscomputed.The United Nations Development Program (UNDP) reports theMPI for 104 developing countries, based on the currentlyavailable data.


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