abdelkrim araar, sami bibi and jean-yves...

Poverty line PEP and UNDP June 2010 – 1 / 23

Setting a poverty line

Abdelkrim Araar, Sami Bibi and Jean-Yves Duclos

Workshop on poverty and social impact analysisDakar, Senegal, 8-12 June 2010

Outline


Relative poverty lines

Absolute poverty lines

Conclusion

Objectives


� Understand the normative distinctions between absolute and relativeapproaches to the measurement of poverty;

� Discuss the links between inequality and poverty;� Assess the challenges in setting an absolute poverty line;� Examine procedures for estimating food and non-food poverty lines.


Outline

Objectives


Definition

Arguments forrelativity

Implications forpoverty assessment

Comparing relativeinequalityacross groups


Conclusion


Definition


� The relative approach to assessing and comparing poverty defines thepoverty line in relation to a social “norm” that is context specific;

� Practically, this involves setting the poverty line to a fractionλ of themean or the median (or some other quantile) of the distribution ofwell-being that is assessed (income, expenditure, consumption,functionings,etc.) within a population. In the popular case of choosingthe mean, we have:

z = λµ. (1)

Arguments for relativity


� “We maintain that if a state is to avoid the greatest plague ofall (...),extreme poverty and wealth must not be allowed to arise in anysection ofthe citizen-body. That is why the legislator must now announce theacceptable limits of wealth and poverty. The lower limit of poverty mustbe the value of the holding. The legislator will use the holding as his unitof measure and allow a man to possess twice, thrice, and up to four timesits value.” (Plato,The Laws, Book V, quoted in Cowell, 1995, p. 21–22).

� “By necessaries I understand, not only the commodities which areindispensably necessary for the support of life, but whatever the customof the country renders it indecent for creditable people, even of the lowestorder, to be without.” (Adam Smith,The Wealth of Nations)

� “I would like to say that poverty is an absolute notion in the space ofcapabilities but very often it will take a relative form in the space ofcommodities and characteristics.” (Sen (1985), p.335).

Implications for poverty assessment


� Relative poverty measures fulfilthe scale invariance principle, whichstates that poverty should be invariant to any uniform proportional changeof individuals’ income.

� Because of this, relative poverty measures resembleinequality measuressince these also obey thescale invariance principle.

Thus:

� A growth pattern that raises the incomes of all, but proportionally morethose of the non-poor, will worsen poverty, albeit the absolute income ofthe poor increases.

� Conversely, a recession that decreases everyone’s income butproportionally more that of the non-poor, will reduce poverty, althoughthe absolute income of the poor falls.

Comparing relative inequalityacross groups


To contrast relative poverty across two groups,l andm say:

1. should we use the same relative poverty linez = λµ for the two groups?or,

2. should we use a specific relative poverty line for each group, i.e.,zl = λµl for l andzm = λµm for m?

Comparing relative inequalityacross groups


Table 1: Relative poverty across Uganda’s regions, 1999

Region P l(0; 0.4µ) P l(0; 0.4µl)Central 4.76 14.9

(1) (2)Eastern 12.3 8.5

(1.3) (1)Northern 37.3 11.2

(3.4) (1.3)Western 6.85 7.1

(1.2) (0.8)

Uganda 13.5 13.5(1.1) (1.1)


Outline

Objectives



Definition

Example: The WorldBank poverty line

Two-step estimationstrategy

Determination of afood poverty line

Determination of alower total povertyline

Estimationprocedures

Determination of anupper poverty line

Lower and upperpoverty lines

Conclusion


Definition


� The minimum standard, under which a person would not be able to“make both ends meet” if he enjoyed less, is a fixed cut-off level that isapplied across the distribution of income.

� In making comparisons across distributions (over time or space), thestandard is unchanged inreal or purchasing power terms, even in thepresence of changes in the income distribution (through economic growthfor instance).

� Two main reasons have usually guided this choice:

1. to obtain “consistent” poverty profiles, in that any two individualswith the same real living standards should be treated identically interms of poverty assessment;

2. to avoid situations in which differences in assessed poverty couldcome from variants in poverty assessment methods instead ofgenuine difference in living standards — analogous to “moving thegoalposts”.

Example: The World Bank poverty line


� For the purpose of international comparisons of poverty, the World Bankhas until recently been promoting a poverty line set to approximately 1.08dollar a day per person in 1993 purchasing power parity (PPP).

� When initially set, this line corresponded to the median of the nationalpoverty lines of 10 developing countries (Bangladesh, China, India,Indonesia, Nepal, Pakistan, Thailand, Tanzania, Tunisia,and Zambia).

� Note: PPP adjusts for cost-of-living differences between countries.� Should also adjust for cost-of-livingwithin countries, though this has

been rare in international comparisons.

Two-step estimation strategy


� A common approach that is used in developing countries to construct apoverty line uses the relationship between calorie requirements and foodexpenditures as well as some minimum non-food expenditures.

� Actual procedures vary but often follow two steps:

1. The determination of a food poverty line;2. The determination of a non-food poverty line.

Determination of a food poverty line


� The most common technique is the so-called thecost-of-basic-needsapproach.

� Household surveys typically provide information on food expenditureand consumption by households.

� Let qi,k be the consumption of food commodityk made by individualiand letςk be the calorie content of food itemk. Food quantities can beconverted into caloriesci as:

ci =K∑

k=1

ςkqi,k. (2)

Determination of a lower total poverty line


� We can think of a lower poverty line (zlower) using the idea that if aperson’s income is just enough to reach the food threshold (yi = zfood),then anything (sayzlower

non−food) that the person spends on non-food items atzfood has to be be considered as essential as food. Thiszlower

non−food can thusbe thought of as a lower non-food threshold.

� A lower poverty line can then be given by:

zlower = zfood+ zlowernon−food = zfood+(1−food)zfood = (2−food)zfood

(3)wherewfood is the budget share devoted to food consumption.� It is also possible to set an upper poverty line,zupper, by estimating the

level of total expenditures that would be needed for an individual whoactually spendszfood on food. This iszupper = E(y|yfood = zfood).zupper would enable households to meet their food needs withoutsacrificing essential non-food items.

Estimation procedures


� Ravallion (1998) suggested to estimate the parameterfood using afood-share Engel equation:

wfoodi = food + β1ln

yi

zf+ β2

(ln

yi

zf

)2

+ ǫi (4)

� Using equations (3) and (4), the lower poverty line is given by (the“ ˆ food” is a parameter estimate)

zl = (2− ˆ food)zfood (5)

� As before, this procedure would normally be applied after the distributionof food and non-food expenditures has been adjusted for price variabilityand household composition heterogeneity.

Determination of an upper poverty line


� To estimate the upper poverty linezupper requires computing the foodshare of households whose food spending corresponds exactly to zfood:

w∗ =zfood

zupper(6)

� Using (4),zupper can be inferred as

w∗ = food + β1 logzupper

zfood+ β2

(log

zu

zf

)2

= food + β1 log1

w∗

+ β2

(log

1

w∗

)2

(7)

Lower and upper poverty lines


z_food

z_food

z_upper

upper z_nonfood

45° A

B

C D

025

5075

100

125

Foo

d sp

endi

ng

0 25 50 75 100 125Income

food Income

Conclusion

Outline

Objectives



Conclusion

Summary

Relevant DASPcommands

Exercises with Stataand DASP

Additional literature

References


Summary


� The relative approach to assessing and comparing poverty defines thepoverty line in relation to a social “norm” that is valid at a particular timeperiod.

� Relative poverty measures resembleinequality measures since they obeythescale invariance principle.

� An absolute poverty line is unchanged in real in purchasing power termseven in the presence of changes in the income distribution.

� A common absolute-line approach uses the relationship between calorierequirements and food expenditures as well as some minimum non-foodexpenditures.

Relevant DASP commands


� Relative and absolute FGT poverty indices (ifgt).� Difference between relative and absolute FGT poverty indices (difgt).

http://132.203.59.36/DASP/help/DASP_MANUAL_V2.1.htm#_Toc247593921

http://132.203.59.36/DASP/help/DASP_MANUAL_V2.1.htm#_Toc247593922

Exercises with Stata and DASP


� Part I: Exercises 6.1, 6.2, 6.3, 6.4, .6.5, 6.6, 6.7, 6.8

http://dasp.ecn.ulaval.ca/exercises/exercises.htm#_Toc255461631

Additional literature


� The material from this presentation draws largely from Ravallion (1998)and Duclos and Araar (2006).

� Greer and Thorbecke (1986) has been influential in promotingthe use ofthe food-energy-intake method for estimating poverty lines.

� Also see Pradhan and Ravallion (2000) for a method to estimatesubjective poverty lines.

References


DUCLOS, J.-Y. AND A. A RAAR (2006):Poverty and Equity Measurement,Policy, and Estimation with DAD, Berlin and Ottawa: Springer and IDRC.

GREER, J. AND E. THORBECKE(1986): “A Methodology for MeasuringFood Poverty Applied to Kenya,”Journal of Development Economics, 24,59–74.

PRADHAN , M. AND M. RAVALLION (2000): “Measuring Poverty UsingQualitative Perceptions of Consumption Adequacy,”Review of Economicsand Statistics, 82, 462–71.

RAVALLION , M. (1998): “Poverty Lines in Theory and Practice,” LSMSWorking Paper 133, The World Bank.

SEN, A. (1985):Commodities and Capabilities, Amsterdam:North-Holland.

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