Measuring and Modeling Poverty: An Update

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Measuring and Modeling Poverty An Update
Frontiers in Practice Reducing Poverty Through
Better Diagnostics PREM Workshop, World Bank,
March 2006

• Martin Ravallion
• Development Research Group, DEC
• World Bank

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• Part 1 Measuring poverty
• 1.1 What is a poverty line?
• 1.2 Objective poverty lines
• 1.3 Subjective poverty lines
• 1.4 Poverty measures revisited
• 1.5 Robustness tests
• 1.6 Growth incidence curves
• 1.7 Measuring the impacts of policies

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• 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

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• Part 1 Measuring poverty

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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)
• gt real expenditure or welfare ratio

price vector facing person i
quantities consumed by i
But what is z?
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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,

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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

eexpenditure function, giving minimum cost of
achieving welfare level wz when facing prices p
and with characteristics x Welfare function
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Poverty line as the cost of basic needs
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

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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.

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Sens 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.

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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

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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

1/day
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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).
• gt welfarist explanation for the high priority
  given to absolute poverty in poor countries.

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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

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Methods of setting poverty lines matter!
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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?

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Inconsistent poverty lines?

• Example 1 Cost-of-basic-needs method

of calories from each source 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.

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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.

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

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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.

Utility-consistency can still be a problem!
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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

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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?

• Is this method suitable for developing countries?
• Can one estimate z without the MIQ?

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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 familys 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.

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Modeling consumption adequacy

• Individual needs are a latent variable

Subjective poverty line identified from
qualitative data using the model
(Pradhan and Ravallion)
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• Examples for Jamaica and Nepal
• Respondents asked whether their food, housing
  and clothing were adequate for their familys
  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.

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1.4 Poverty measures revisited
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
scalars Multidimensional approach y and z are
vectors
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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.

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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).

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FGT multidimensional version

• (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?
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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

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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.

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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

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

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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

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Example 1 China and India in 1990s
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But looked what happened in China around mid 1990s
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Example 2 Indonesia in a crisis
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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.)
Example Growth rates for China
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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 yltz (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

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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

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Example for Chinas Di Bao programImpacts on
poverty measured across 35 municipalities
Only the targeting differential has any
predictive power for poverty impacts!
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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)

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• Part 2 Modeling poverty

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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 lt z)
Sub-group poverty measures (poverty profile)
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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 gt
  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?

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Multivariate poverty profiles

• Welfare indicator modeled as a function of
• multiple variables
• or

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

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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 xs that are available in
  the census
• Cant have geographic fixed effects
• Cant allow for idiosyncratic local factors
• Standard errors can allow for these sources of
  error

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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

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Example for Brazil

• Poverty and inequality measures

Very little change in poverty rising inequality
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Example for Brazil

• Poverty and inequality measures

Very little change in poverty rising
inequality Decomposition

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

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• 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.

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Example urban-rural
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Example for China

• 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.

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Static models on repeated cross-sections

• Two time periods, or two sets of households

• How much has the change in poverty been due to
• Change in the joint distribution of the Xs?
• Change in the parameters (return to the Xs)?
• 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

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2.4 Studying poverty dynamics using panel data

• PROT ("Protected") Change in proportion who
  fell into poverty.
• PROM ("Promotion") Change in proportion who
  escaped poverty.

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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
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Models of transient and chronic poverty
Transient poverty model Chronic poverty
model
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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.

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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)

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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

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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
• gt Geographic poverty traps

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Example for China Geographic poverty traps
ggt0
glt0

• The results strengthen the equity and efficiency
  case for public investment in lagging poor areas
  in this setting.