Frontiers in Practice:
Reducing Poverty Through Better Diagnostics
PREM Workshop, World Bank, March 2006
Measuring and Modeling
Poverty: An Update
Martin Ravallion
Development Research Group, DEC
World Bank
Part 1: Measuring poverty
1.1
1.2
1.3
1.4
1.5
1.6
1.7
What is a “poverty line”?
Objective poverty lines
Subjective poverty lines
Poverty measures revisited
Robustness tests
Growth incidence curves
Measuring the impacts of policies
Part 2: Modeling poverty
2.1
2.2
2.3
2.4
2.5
Static models
Poverty mapping
Dynamics: Repeated cross-sections
Dynamics: Panel data
Micro growth models
Part 1: Measuring poverty
1.1: What is a “poverty line”?
• 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:”
pi qi
yi 
zi
pi = price vector facing person i
qi = quantities consumed by i
But what is z?
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:
zi  e( pi , xi , wz )
e=expenditure function, giving minimum cost of achieving
welfare level wz when facing prices p and with characteristics x
Welfare function:
wi  w(qi , xi )
Poverty line as the “cost of basic needs”
e( pi , xi , wz ) m
zi   pij
  pij qij*
pij
j 1
j 1
m
qij* = quantity consumed of good j by i
 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:
wi  w(qi , xi )
• 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.
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 wi  w(qi , xi ) 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.
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:
w  w( y, y / m) (where m = mean income)
• Welfare poverty line: wz  w( z, z / m)
• which gives poverty line as a function of the mean: z  z (m)
Poverty lines across countries
Log poverty line
$1/day
Mean consumption
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 method
Poverty 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
Cost-of-basic needs
method
Tunisia
Food share method
Cost-of-basic needs
method
16.8
10.7
14.3
23.6
7.3
3.5
5.7
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.
Food-energy intake
rural
2100
urban
Income
zr
zu
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
f(y)
poverty line.
bf
45°
y
2bf – f(b f) f-1(bf)
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?“
Subjective minimum
income
45°
z*
Actual
income
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
General class of additive (“subgroup consistent”/
”subgroup decomposable”) measures:
1 n
Pi   p ( yi , zi )
n i 1
Aggregate poverty index
Individual poverty index
• non-increasing in y
• non-decreasing in z
Unidimensional approach: y and z are scalars
Multidimensional approach: y and z are vectors
“Money-metric welfare” vs.
“multidimensional poverty measures”
1. Multidimensional poverty measurement:
{Person i is poor iff p( y1i , z1i ; y2i , z2i )  0}
2. Welfare function approach to poverty measurement:
{Person i is poor iff w( y1i , y2i )  z w } or equivalently:
{Person i is poor iff y1i  z1i where w( z1i , y2i )  z w }
• Surely these must be consistent, so why do we
need both approaches?
• The real issue is how to implement multidimensional welfare metrics, whether or not one
uses a “multidimensional” poverty measure.
FGT measures

p( yi , zi )  [max(1  yi / zi ,0)] (  0)
  0 Headcount index (H): % living in households with
income per person below the poverty line.
  1 Poverty gap index (PG): mean distance below the
poverty line as a proportion of the poverty line
  2 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).
FGT: multidimensional version
pi  v1[max(1  y1i / z1 ,0)]  v2 [max(1  y2i / z2 ,0)]   /
(Bourguignon and Chakravarty, 2003)
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:
p( yi , zi )  max[log( zi / yi ),0]
• 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:
pi  v1[max(log( z1 / y1i ),0)]  v2 [max(log( z2 / y2i ),0)]   /
1.5: Testing robustness
The three poverty curves:
1. The poverty incidence curve
= H for each possible poverty line
Each 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
1
A
.8
B
.6
.4
.2
0
0
100
200
300
400
500
Income per capita
600
700
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 test
If 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:
yt ( p )  Ft 1 ( p )  Lt( p ) t
• Then calculate growth rates at each percentile to give
the growth incidence curve:
Lt( p )
gt ( p )  1 
( g t  1)
Lt1 ( p )
• Note that if the Lorenz curve does not change then
g t ( p)  g t
Example 1: China and India in 1990s
Figure 1: Growth incidence curves for China and India in the 1990s
Annual growth in income/expenditure per person (%)
10
9
8
7
China 1990-1999
6
5
4
3
2
India 1993/94-1999/00
1
0
0
10
20
30
40
50
60
70
80
90
The poorest p% of population ranked by per capita incom e/expenditure
But looked what happened in China
around mid 1990s
Figure 2: Growth incidence curve for China, 1993-1996
12.00
Annual growth in income per person (%)
11.00
10.00
Median
9.00
Mean
8.00
7.00
6.00
5.00
4.00
3.00
0
10
20
30
40
50
60
70
80
The poorest p% of population ranked by per capita incom e
90
Example 2: Indonesia in a crisis
Growth Incidence curve: 1996-1998
-9
Growth incidence curve
Growth rate in mean
-10
Annual growth rate %
-11
-12
-13
-14
-15
-16
0
20
40
60
Percentiles
80
100
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.)
gtH  E[ gt ( p) p  H t ]
Example: Growth rates for China
Headcount index (%)
10
15
20
25
100
1990-99
1993-96
Growth rate in the mean
(% per annum)
6.9
8.4
Rate of pro-poor growth
(% per annum):
3.7
9.4
3.9
9.8
4.1
10.0
4.3
10.1
5.9
9.4
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
Constant
Impact on (log) poverty measure:
Headcount
Poverty
Squared
index
gap index poverty gap
-0.001
-0.056
-0.131
(-0.012)
(-0.469)
(-0.709)
SHARE
-0.016
(-0.316)
-0.053
(-0.870)
-0.039
(-0.340)
Concentration index
-0.029
(-0.181)
0.021
(0.122)
0.075
(0.264)
SHARE/H
0.003
(1.071)
0.005
(1.669)
0.007
(1.203)
Targeting differential
0.250
(4.927)
0.438
0.496
(7.571)
0.629
0.753
(6.689)
0.542
R2
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

j 1
Pj D j
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 intercorrelation.
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:
log( y / z )   x  
or
log y   x    
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):
Pr( y  z )  Pr(   x)  F ( x /  )
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.
P
 f (.) / 
• You can still estimate poverty impacts:
X
• And under weaker assumptions (e.g., normality of errors is not
required)
2.2: Poverty mapping
Impute measure of welfare (e.g. comprehensive real
consumption) from household survey into census,
using estimated static model:
log( y / z )   x  
•
•
•
•
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
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 Brazil
Poverty and inequality measures
Headcount index (H) (%)
Poverty gap index (PG) (x100)
Squared poverty gap index
(SPG) (x100)
Gini index
1981
26.5
10.1
5.0
1988
26.5
10.7
5.6
0.58
0.62
Very little change in poverty; rising inequality
Example for Brazil
Poverty and inequality measures
Headcount index (H) (%)
Poverty gap index (PG) (x100)
Squared poverty gap index
(SPG) (x100)
Gini index
1981
26.5
10.1
5.0
1988
26.5
10.7
5.6
0.58
0.62
Very little change in poverty; rising inequality
Decomposition
H
PG
SPG
Growth
component
-4.5
-2.3
-1.4
Redistribution
component
4.5
3.2
2.3
Interaction
effect
0.0
-0.2
-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
Pt = the poverty measure for date t=1,2
Pt i = the measure for sector i=u,r (urban, rural)
nti = population shares
P2  P1  [n2r ( P2r  P1r )  n2u ( P2u  P1u )]  [( P1u  P1r )(n2u  n1u )]
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)
Within rural
Within urban
Population
shift
Total change
H
-32.53
(72.5)
-2.08
(4.6)
-10.27
(22.9)
-44.87
PG
-10.39
(74.0)
-0.32
(2.3)
-3.32
(23.7)
-14.04
SPG
-4.51
(75.0)
-0.09
(1.5)
-1.42
(23.6)
-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 crosssections
Two time periods, or two sets of households
ln Yi   A X i   iA
for i  A
ln Yi   B X i   iB
for i  B
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
Fell into
Persistently
poverty:
non-poor:
Not poor in the
Not poor in
first period, but either period
poor in second
Poor in second
Not poor in
period
second period
Poor in first
period
Not poor in
first 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:
P ( yi1 ,.., yiD )  Ci  Ti
The transient component of poverty is the part attributed to
variability in consumption:
Ti  P( yi1,..., yiD )  P( yi ,..., yi )
The chronic component is:
Ci  P( yi ,..., yi )
Models of transient and chronic poverty
Transient poverty model
Ti   T X i   iT
Chronic poverty model
Ci   C X i   iC
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 (underinvestment in the externality-generating activities)
Micro growth models cont.,
Micro model of the growth process
 ln C it     x it   z i   it
(i=1,..,N; t=4,..,T)
Latent heterogeneity in growth process can be dealt with allowing for
time varying effects
 it   t  i   it
Quasi-differencing to eliminate the fixed effect
 ln Cit   (1  rt )  rt  ln Cit 1   ( xit  rt xit 1 )
  (1  rt ) z i   it  rt  it 1
where rt   t /  t 1
As long as rt  1 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
Example for China
Geographic poverty traps
County wealth
County wealth (log)
8
g>0
7
g<0
6
5
2
4
6
Household wealth (log)
8
10
Household wealth
The results strengthen the equity and efficiency case for
public investment in lagging poor areas in this setting.