Measuring and Modeling Poverty: An Update

Martin RavallionDevelopment Research Group, DEC

World Bank

Frontiers in Practice: Reducing Poverty Through Better Diagnostics

PREM Workshop, World Bank, March 2006

Part 1: Measuring poverty

1.1 What is a “poverty line”?1.2 Objective poverty lines1.3 Subjective poverty lines1.4 Poverty measures revisited1.5 Robustness tests1.6 Growth incidence curves1.7 Measuring the impacts of policies

Part 2: Modeling poverty

2.1 Static models

2.2 Poverty mapping

2.3 Dynamics: Repeated cross-sections

2.4 Dynamics: Panel data

2.5 Micro growth models

Part 1: Measuring poverty

• The welfare ratio: Add up expenditures on all commodities consumed (with imputed values at local market prices) and

• Deflate by a poverty line (depending on household size and composition and location/date)

• => “real expenditure” or “welfare ratio:”

i

iii z

qpy

iq = quantities consumed by i

But what is z?

1.1: What is a “poverty line”?

= price vector facing person iip

The poverty line as money-metric welfare

For informing anti-poverty policies, a poverty line should be absolute in the space of welfare

• This assures that the poverty comparisons are consistent in that two individuals with the same level of welfare are treated the same way.

• Welfare consistency in poverty comparisons will be called for as long as:– the objectives of policy are defined in terms of welfare, and– policy choices respect the weak Pareto principle that a welfare

gain cannot increase poverty,

The poverty line as money-metric welfare

The ideal poverty line should then be the minimum cost to a given individual of a reference level of welfare fixed across all individuals:

),,( ziii wxpez

e=expenditure function, giving minimum cost of achieving welfare level wz when facing prices p and with characteristics x

Welfare function:

),( iii xqww

Poverty line as the “cost of basic needs”

m

jijij

m

j ij

ziiiji qp

p

wxpepz

1

*

1

),,(

= quantity consumed of good j by i*ijq

Poverty line is the cost of a bundle of goods needed to assure a minimum level of welfare

How then do we measure “welfare”?

Traditional approach in economics: an interpersonally comparable utility function defined on consumptions, with differences in tastes represented by a vector of household characteristics:

• Consistent with choices over private goods, i.e., q maximizes w(q, x) at given x.

• But interpersonal comparisons of utility are essential, and x also serves this role.

),( iii xqww

Sen’s capability-based approach: an interpretation

Welfare depends on the functionings (‘beings and doings’) that a person is able to achieve.

• “Poverty” means not having an income sufficient to support specific normative functionings.

• Functionings depend on goods consumed and characteristics. Utility depends on functionings.

• Thus we can still derive as the reduced form.

• Functioning-consistency requires that fixed normative funtionings are reached at the poverty line.

• Multiple solutions for the poverty bundle:– Minimum income s.t. all normative functionings are met– Income level at which functionings are met in expectation.

),( iii xqww

Two generic problems

Identification problem: how to weight aspects of welfare not revealed by market behavior.

• How do family characteristics (such as size and composition) affect individual welfare at given total household consumption?

• How to value command over non-market goods (including some publicly supplied goods)?

• How to measure the individual welfare effect of relative deprivation, insecurity, social exclusion?

Referencing problem: what is reference level of welfare above which one is not poor, i.e., the poverty line in welfare space, which must anchor the money-metric poverty line.

Poverty measurement in practice attempts to expand the information base for addressing the identification and referencing problems

Absolute vs. relative poverty • Poverty should be absolute in the space of “welfare” but

relative in the space of commodities

• Welfare depends on relative income:

(where m = mean income)

• Welfare poverty line:

• which gives poverty line as a function of the mean:

)/,( myyww

)(mzz Poverty lines across countries

Log poverty line

Mean consumption

)/,( mzzwwz

$1/day

Evidence for Malawi

Relative deprivation amongst the poor? • Test for perceived welfare effects of relative deprivation using

self-assessed welfare and perceived welfare of friends and neighbors (Lokshin and Ravallion)

• Subjective welfare addresses the identification problem.

• Findings: Relative deprivation is not a concern for most of the sample, although it is for the comparatively well off (upper fifth, esp., in urban areas).

=> welfarist explanation for the high priority given to absolute poverty in poor countries.

1.2: Objective poverty lines

1. Cost-of-basic-needs methodPoverty line = cost of a bundle of goods deemed sufficient for “basic needs”.

Food-share version: poverty line = Cost of food-energy requirement Food-share of “poor”

2. Food-energy intake method Find expenditure or income at which food-energy requirements are met on average.– i.e., functioning consistency in expectation, but only one

functioning

Methods of setting poverty lines matter!

Head-count index (% poor) Urban Rural Indonesia Food energy method 16.8 14.3 Cost-of-basic needs method

10.7 23.6

Tunisia Food share method 7.3 5.7 Cost-of-basic needs method

3.5 13.1

Problems to be aware of

1. Defining "basic consumption needs"• Setting food energy requirements (variability; multiple equilibria;

activity level).• Setting "basic non-food consumption needs" (behavioral

approaches).

2. Consistency in terms of welfare • Is the same standard of living being treated the same way in

different sub-groups of the poverty profile? If not, then the profile may be quite deceptive.

• Is the definition of welfare consistent with the definition of poverty? If some good is purchased by poor people why should it not be included in the poverty bundle?

Key question: how sensitive are the rankings in a poverty profile to these choices?

Inconsistent poverty lines?

Example 1: “Cost-of-basic-needs method”

% of calories from each source

"urban" rural"

rice 50 40

cassava 10 40

vegetables 20 10

meat 20 10

• The two bundles yield same food-energy intake.• But the "urban" bundle is almost certainly preferable• The standard of living at the urban poverty line is higher than at the rural line. • This makes the poverty comparison inconsistent, which can distort policy making based on the poverty profile.

Example 2: "Food-energy intake method"

Different sub-groups attain food energy requirements at different standards of living, in terms of real consumption expenditures. e.g., "rich" urban areas buy more expensive calories than "poor" rural areas.

zuIncome

Food-energy intake

2100

zr

rural

urban

Do your poverty lines have the same real value to the poor across the poverty profile? Much evidence that they do not!

Allowing for differences in relative prices

• Ideally we only want to adjust the poverty bundle for differences in relative prices

• The problem is how to implement this ideal in practice• The identification problem remains

Parametric demand models: If we know the parametric utility function then or we can figure it out from demand behavior then use this to determine the cost of the reference welfare level in each region

Numerical methods: • Look at consumption behavior of poorest x% nationally in

each region of the country• Cost the consumption bundle of that group in each region• Calculate the poverty rate nationally• Iterate if the answer differs too far from x

When non-food prices are missing

Step 1: Find the cost at prevailing prices of a single national food consumption bundle that assures that recommended caloric requirements are met at prevailing tastes nationally. This gives the food poverty line.

Step 2: Set the non-food allowance, consistent with consumption behavior of those who can either just attain or just afford the food poverty line.

bf

f(y)

yf-1(bf)2bf – f(bf)

45°

Utility-consistency can still be a problem!

Testing poverty lines

• Well-defined “poverty bundles” by area

+

• Complete price matrix (commodity x area)

Revealed preference test for utility-consistency (Lokshin and Ravallion)

• This assumes homogeneous preferences (given x).

• The problem of welfare comparisons across different tastes remains.

• A promising clue: subjective welfare data

1.3: The social subjective poverty line

The Minimum Income Question (MIQ)"What income do you consider to be absolutely minimal, in that you

could not make ends meet with any less?“

z* Actualincome

Subjective minimumincome

45°

Is this method suitable for developing countries?

Can one estimate z* without the MIQ?

Subjective poverty lines for developing countries

• Minimum income question is of doubtful relevance to most countries

• Subjective poverty lines can be derived using simple qualitative assessments of consumption adequacy.

• Consumption adequacy question: “Concerning your family’s food consumption over the past one month,

which of the following is true?” Less than adequate ...1 Just adequate .......…. 2 More than adequate.. .3 "Adequate" means no more nor less than what the respondent

considers to be the minimum consumption needs of the family.

Modeling consumption adequacy

Individual needs are a latent variable:

Z =βY + πX + ε

Subjective poverty line identified from qualitative data using the model:

Prob(Y > Z) = F[(1-β)Y-α- πX)/σ]

(Pradhan and Ravallion)

Examples for Jamaica and Nepal

• Respondents asked whether their food, housing and clothing were adequate for their family’s needs. • The implied poverty lines are robust to alternative methods of dealing with other components of expenditure. • The aggregate poverty rates turn out to accord quite closely with those based on independent “objective” poverty lines. • However, there are notable differences in the geographic and demographic poverty profiles.

1.4: Poverty measures revisited

n

iiii zyp

nP

1

),(1

General class of additive (“subgroup consistent”/ ”subgroup decomposable”) measures:

Aggregate poverty index Individual poverty index• non-increasing in y• non-decreasing in z

Unidimensional approach: y and z are scalarsMultidimensional approach: y and z are vectors

“Money-metric welfare” vs. “multidimensional poverty measures”

1. Multidimensional poverty measurement: {Person i is poor iff }2. Welfare function approach to poverty measurement:

{Person i is poor iff } or equivalently:{Person i is poor iff where }

• Surely these must be consistent, so why do we need both approaches?

• The real issue is how to implement multi-dimensional welfare metrics, whether or not one uses a “multidimensional” poverty measure.

0),;,( 2211 iiii zyzyp

wii zyyw ),( 21

ii zy 11 wii zyzw ),( 21

FGT measures

Headcount index (H): % living in households with income per person below the poverty line.

Poverty gap index (PG): mean distance below the poverty line as a proportion of the poverty line

Squared poverty gap index (SPG): poverty gaps are weighted by the gaps themselves, so as to

reflect inequality amongst the poor (Foster et al., 1984).

)0()]0,/1[max(),( iiii zyzyp

0

1

2

FGT: multidimensional version

(Bourguignon and Chakravarty, 2003)

/222111 )]0,/1[max()]0,/1[max( zyvzyvp iii

Four groups of parameters:v weights attached to each dimension elasticity of substitution (shape of contours) poverty aversion parameter (concavity) z poverty lines (how can they be constant?

Watts measure

• Watts index based on the aggregate proportionate poverty gaps of the poor:

• This is the only index that satisfies all accepted axioms for poverty measurement including: focus axiom, monotonicity axiom; transfer axiom, transfer-sensitivity and subgroup consistency (Zheng)

• Multidimensional Watts index:

]0),/max[log(),( iiii yzzyp

/222111 )]0),/[max(log()]0),/[max(log( iii yzvyzvp

1.5: Testing robustness

The three poverty curves:1. The poverty incidence curve

= H for each possible poverty lineEach point gives the % of the population deemed poor if the point on the horizontal axis is the poverty line.

2. The poverty depth curve = area under poverty incidence curve

Each point on this curve gives aggregate poverty gap per capita.

3. The poverty severity curve = area under poverty depth curve

Each point gives the squared poverty gap per capita.

First-order dominance test

If the poverty incidence curve for A is above that for B for all poverty lines up to zmax then there is more poverty in A than B for all poverty measures and all poverty lines up to zmax

Income per capita 0 100 200 300 400 500 600 700

0

.2

.4

.6

.8

1 A

B

What if the PICs intersect at some point < zmax?e.g., higher rice prices in Indonesia: very poor lose, those near the poverty line gain.

Second-order dominance test

If the poverty deficit curve for A is above that for B up to zmax then there is more poverty in A for all poverty measures which are strictly decreasing and weakly convex in consumptions of the poor (e.g. PG and SPG; not H).

Third-order dominance testIf the poverty severity curve for A is above that for distribution B then there is more poverty in A, if one restricts attention to distribution sensitive (strictly convex) measures such as SPG and the Watts index.

1.6: Growth incidence curves

• Invert the CDF to obtain the quantile function:

• Then calculate growth rates at each percentile to give the growth incidence curve:

• Note that if the Lorenz curve does not change then

1( ) ( ) ( )t t t ty p F p L p

1

( )( ) 1 ( 1)

( )t

t tt

L pg p g

L p

tt gpg )(

Example 1: China and India in 1990s

Figure 1: Growth incidence curves for China and India in the 1990s

0

1

2

3

4

5

6

7

8

9

10

0 10 20 30 40 50 60 70 80 90

The poorest p% of population ranked by per capita income/expenditure

An

nu

al g

row

th in

in

co

me/e

xp

en

dit

ure

per

pers

on

(%

)

China 1990-1999

India 1993/94-1999/00

But looked what happened in China around mid 1990s

Figure 2: Growth incidence curve for China, 1993-1996

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

11.00

12.00

0 10 20 30 40 50 60 70 80 90

The poorest p% of population ranked by per capita income

An

nu

al g

row

th in

inco

me

per

per

son

(%

)

Mean

Median

Example 2: Indonesia in a crisis

-16

-15

-14

-13

-12

-11

-10

-9

Ann

ual g

row

th r

ate

%

0 20 40 60 80 100Percentiles

Growth incidence curve

Growth rate in mean

Growth Incidence curve: 1996-1998

Measuring the rate of “pro-poor growth”

Watts index for the level of poverty implies using the mean growth rate of the poor in measuring the rate of pro-poor economic growth. (Not growth rate in the mean for the poor.)

1990-99 1993-96 Growth rate in the mean

(% per annum) 6.9 8.4 Headcount index (%) Rate of pro-poor growth

(% per annum): 10 3.7 9.4 15 3.9 9.8 20 4.1 10.0 25 4.3 10.1

100 5.9 9.4

])([ ttHt HppgEg

Example: Growth rates for China

1.7: Measuring the poverty impacts of policies and programs

Various measures of “targeting performance:”• SHARE: the share of total payments going to those with

pre-transfer income y<z (or some fixed %)• Concentration index (CI): the area between the

concentration curve and the diagonal (along which everyone receives the same amount).

• SHARE normalized by headcount index• Targeting differential (TD) is the difference between the

participation rate for the poor and that for the non-poor

However, better “targeting” does not imply a higher impact on poverty

There can be no guarantee that better targeting by these measures will enhance a programs’ impact on poverty:

• Coverage maters: avoiding leakage to non-poor may entail weak coverage of the poor.

• Deadweight costs (incentive effects); e.g., income foregone by participants in workfare programs

• Political economy: fine targeting can undermine political support for anti-poverty programs

Example for China’s Di Bao program

Impacts on poverty measured across 35 municipalities Impact on (log) poverty measure: Headcount

index Poverty

gap index Squared

poverty gap

Constant -0.001 -0.056 -0.131 (-0.012) (-0.469) (-0.709) SHARE -0.016 -0.053 -0.039 (-0.316) (-0.870) (-0.340) Concentration index -0.029 0.021 0.075 (-0.181) (0.122) (0.264) SHARE/H 0.003 0.005 0.007 (1.071) (1.669) (1.203) Targeting differential 0.250 0.496 0.753 (4.927) (7.571) (6.689) R2 0.438 0.629 0.542

Only the targeting differential has any predictive power for poverty impacts!

Better to focus directly on the poverty impact, though decompositions help

understand that impact

For example, the impact of a targeted transfer program on poverty (by any FGT measure) can be decomposed into four components:

(1) the budget outlay per capita;

(2) the extent of leakage to the non-poor;

(3) a vertical equity component; and

(4) a horizontal equity component.

(Bibi and Duclos, 2005)

Part 2: Modeling poverty

2.1: Static models of poverty

• For all additive measures we can decompose the aggregate measure by sub-groups – e.g., “urban” vs “rural”, “large” vs “small” households

• The poverty profile can be thought of as a simple model of poverty:

Prob(y < z)=

m

jjj DP

1

Sub-group poverty measures (“poverty profile”)

But this is too simple a model

We would like to introduce a richer set of covariates (some continuous) to:

• Account better for the variance in circumstances leading to poverty

• Disentangle which are the key factors, given their inter-correlation.

For example: • poverty profile shows that rural incidence > urban incidence,

and that poverty is greater for those with least education. • But education is lower in rural areas. • Is it lack of education or living in rural areas that

increases poverty?

Multivariate poverty profiles

Welfare indicator modeled as a function of

multiple variables:

or xzy )/log(

xylog

Fixed effects, one for each sub-group with a different poverty line

Probits for poverty make little sense

Probit regression for poverty (normally distributed error):

However: • This is just an inefficient way of estimating the OLS regression parameters.• You do not need a probit/logit when the continuous variable is observed.• You can still estimate poverty impacts:

• And under weaker assumptions (e.g., normality of errors is not required)

/(.)fX

P

)/()Pr()Pr( xFxzy

2.2: Poverty mapping

Impute measure of welfare (e.g. comprehensive real consumption) from household survey into census, using estimated static model:

Note: • Constrained to using x’s that are available in the

census• Can’t have geographic fixed effects• Can’t allow for idiosyncratic local factors • Standard errors can allow for these sources of error

xzy )/log(

2.3: Studying poverty dynamics using

repeated cross-sectional data Decomposing changes in poverty

Decomposition 1: Growth versus redistribution

Growth component holds relative inequalities (Lorenz curve) constant; redistribution component holds mean constant

Change in poverty between two dates =

Change in poverty if distribution had not changed+Change in poverty if the mean had not changed+Interaction effects between growth and redistribution

Example for BrazilPoverty and inequality measures

1981 1988 Headcount index (H) (%) 26.5 26.5 Poverty gap index (PG) (x100) 10.1 10.7 Squared poverty gap index (SPG) (x100)

5.0 5.6

Gini index 0.58 0.62

Very little change in poverty; rising inequality

Example for BrazilPoverty and inequality measures

1981 1988 Headcount index (H) (%) 26.5 26.5 Poverty gap index (PG) (x100) 10.1 10.7 Squared poverty gap index (SPG) (x100)

5.0 5.6

Gini index 0.58 0.62

Very little change in poverty; rising inequality

Decomposition Growth

component Redistribution

component Interaction

effect H -4.5 4.5 0.0 PG -2.3 3.2 -0.2 SPG -1.4 2.3 -0.3

• No change in headcount index yet two strong opposing effects: growth (poverty reducing) + redistribution (poverty increasing). • Redistribution effect is dominant for PG and SPG.

Decomposition 2: Gains within sectors vs population shifts

• Gains within sectors at given pop. shares;

• Population shift effects hold initial poverty measures constant

• Interaction effects.

Example: urban-rural

tP = the poverty measure for date t=1,2

i

tP = the measure for sector i=u,r (urban, rural)

i

tn = population shares

)])([()]()([ 121112212212uuruuuurrr nnPPPPnPPnPP

Within-sector effect Population shift effect

Within-sector effect: the change in poverty weighted by the final year population shares; Population shift effect: the contribution of urbanization, weighted by the initial urban-rural difference in poverty measures. Note: The “population shift effect” should be interpreted as the partial effect of urban-rural migration; it does not allow for any effects of migration and remittances on poverty levels within sectors.

Example for China

Poverty measures (% point change 1981-2001)

H PG SPG

Within rural -32.53 -10.39 -4.51 (72.5) (74.0) (75.0)

Within urban -2.08 -0.32 -0.09 (4.6) (2.3) (1.5)

-10.27 -3.32 -1.42 Population shift (22.9) (23.7) (23.6)

Total change -44.87 -14.04 -6.01

• 75-80% of the drop in national poverty incidence is accountable to poverty reduction within the rural sector; • most of the rest is attributable to urbanization of the population.

Static models on repeated cross-

sections Two time periods, or two sets of households

Aii

Ai XY ln for Ai

Bii

Bi XY ln for Bi

How much has the change in poverty been due to:

• Change in the joint distribution of the X’s?• Change in the parameters (“return to the X’s)?

Example 1: in Vietnam, returns to education are significantly higher for the majority ethnic group than minorities

Example 2: in Bangladesh, returns to education are higher in urban areas. Strong geographic effects

2.4: Studying poverty dynamics using panel data

Persistently poor:

Poor in both years

Escaped poverty:

Poor in the first period, but not

in second

Poor in first period

Fell into poverty:

Not poor in the first period, but poor in second

Persistently non-poor:

Not poor in either period

Not poor in first period

Poor in second period

Not poor in second period

Panel population

PROT ("Protected") = Change in proportion who fell into poverty.

PROM ("Promotion") = Change in proportion who escaped poverty.

Transient vs. chronic poverty

Measure of poverty for household i over dates 1,2,…,D:

The transient component of poverty is the part attributed to variability in consumption:

The chronic component is:

iiiDi TCyyP ),..,( 1

),...,(),...,( 1 iiiDii yyPyyPT

),...,( iii yyPC

Models of transient and chronic poverty

Transient poverty model

Chronic poverty model

Tii

Ti XT

Cii

Ci XC

Example for rural China Determinants of chronic poverty look quite similar (though

not identical) to that for total poverty (chronic plus transient).

However, the determinants of transient poverty measure are quite different.

• Low foodgrain yields foster chronic poverty, but are not a significant determinant of transient poverty.

• Higher variability over time in wealth is associated with higher transient poverty but not chronic poverty.

• While smaller and better educated households have lower chronic poverty, these things matter little to transient poverty.

• And living in an area with better attainments in health and education reduces chronic poverty but is irrelevant to transient poverty.

Different models are determining chronic versus transient poverty in rural China.

2.5: Micro growth models

With panel data we can also investigate why some households do better than others over time.

• Initial conditions (incl. geographic variables)• Shocks• Policies

Examples of the questions that can be addressed: • Are there geographic poverty traps?• Does where you live matter independently of individual

(non-geographic) characteristics? Poor areas or just poor people?

• Are there genuine externalities in rural development?• Does this help explain under-development (under-

investment in the externality-generating activities)

Micro growth models cont.,

Micro model of the growth process

Latent heterogeneity in growth process can be dealt with allowing for time varying effects

Quasi-differencing to eliminate the fixed effect

itiitit zxC ln

(i=1,..,N; t=4,..,T)

ititit

1

11

)1(

)(ln)1(ln

ittitit

ittititttit

rzr

xrxCrrC

where 1/ tttr

As long as 1tr we can identify the impacts of the time-invariant observables on the growth process.

Example for China

Micro growth model estimated on six-year household panel (Jalan-Ravallion)

• Consumption growth at the household level is a function of household characteristics and geographic characteristics.

• Publicly provided goods, such as rural roads, generate non-negligible gains in consumption relative to the poverty line.– And since latent geographic effects included, these effects

cannot be ascribed to endogenous program placement.

• Convergent effects of private wealth; divergent effects of local geographic wealth

=> Geographic poverty traps

The results strengthen the equity and efficiency case for

public investment in lagging poor areas in this setting.

County wealth

Cou

nty

wea

lth (l

og)

Household wealth (log)2 4 6 8 10

5

6

7

8

Household wealth

Example for ChinaGeographic poverty traps

g<0

g>0