Robust Multidimensional Poverty Comparisons

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Robust Multidimensional Poverty Comparisons
Jean-Yves Duclos Université Laval David E.
Sahn Cornell University Stephen D.
Younger Cornell University
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Credits and Advertisements
This research is supported by the SAGA project,
funded by USAID. For more information, see
http//www.saga.cornell.edu.
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Motivation and Goals

• Poverty is a multidimensional phenomenon
• Widely accepted in principle
• Rarely applied in practice
• We want to explore how to compare
  multidimensional poverty in two different samples
• sub-groups
• or two points in time

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Methodological Approach

• Poverty dominance approach
• Poverty comparisons should be
• Robust to choice of poverty measure (index)
• (including aggregation procedure)
• Robust to choice of poverty line
• Statistical

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Specific Application

• Spatial poverty comparisons in Uganda
• Regions (four)
• Urban/rural
• Well-being/poverty measures in two dimensions
• Household expenditures per capita
• Childrens standardized heights

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Methods
Robust Univariate Poverty Comparisons Poverty
incidence curves (cdfs)
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Methods

• If one poverty incidence curve is everywhere
  below another, then poverty is lower for that
  group for any poverty line and for any poverty
  index (measure) in a large class of indices, viz.
  those that are
• non-decreasing (non-satiation)
• anonymous
• continuous at the poverty line
• This is a robust (very general) comparison with
  respect to the poverty line and the poverty index
• We call this poverty dominance

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Methods

• What if the poverty incidence curves cross?
• see next slide
• cost of generality
• possibility of defining a maximum poverty line
  for which we can establish poverty dominance
• Restrict the set of poverty indices for which the
  dominance result is valid higher orders of
  poverty comparisons

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Methods
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Methods

• Second-order poverty dominance
• The poverty incidence curves establish
  first-order poverty dominance
• Now consider a smaller class of poverty indices
• All the above characteristics (non-decreasing,
  anonymous, and continuous at the poverty line),
  plus
• The Dalton transfer principle
• We can get a dominance result for any poverty
  index in this class and for any poverty line by
  comparing the integral of the poverty incidence
  curves

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Methods

• Third-order poverty dominance
• Now consider an even smaller class of poverty
  indices
• All the above characteristics plus
• The principle of transfer sensitivity
• In theory, we can keep going, although this is
  the highest order for which we have a ready
  intuition
• Relation to FGT(a) poverty measures

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Methods

• Bivariate poverty comparisons
• We want to extend the univariate comparisons to
  two (and more) dimensions or measures of
  well-being
• Much of the intuition is the same
• Rather than comparing two-dimensional curves, we
  will compare three- (and more) dimensional
  surfaces (see next slide)
• There are a couple interesting complications when
  we move to multiple dimensions

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Figure 3 Bidimensional Poverty Surface
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Methods
Intersection, Union, and Intermediate Poverty
Measures

• Intersection poverty must be poor in both x and
  y dimensions
• Union poverty must be poor in either dimension
• Intermediate poverty see Figure 1

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Figure 1 Poverty Domains
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Theorem 1

• Consider a class of bidimensional poverty
  indices
• defined by

Then
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Theorem 1 (continued)

• So we compare the dominance surfaces over the
  domain in Figure 1.
• Note that in this case of first-order dominance
  in both dimensions, we are just comparing the
  bivariate, intersection headcount, but at every
  point in the relevant test domain defined by
  ?(?).
• The test is conceptually the same for union,
  intersection, and intermediate poverty
  comparisons. Only the test domain varies.
• Tests at higher orders of dominance, in either
  dimension or both, are possible, analogous to the
  univariate case, for increasingly restricted
  classes of poverty measures
• Main limitation the correlation increasing
  switch assumption.

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Figure 4 Poverty Surface Difference
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Relevance of the methods

• First, note that we can integrate out one
  dimension of the poverty dominance surface to get
  a univariate dominance curve
• So on Figure 4, univariate comparisons are
  possible at the extremes of the surface
• One-at-a-time comparisons vs. bivariate
  comparisons
• Could have univariate dominance in one or both
  dimensions, but no bivariate dominance. (Shift
  Figure 4 down.)
• Could have no dominance in one or both univariate
  dimensions, but (intersection) bivariate
  dominance. (See Figure 4.)

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Relevance of the methods (continued)

• Comparison with Human Development-type indices
• The HDI takes each dimension individually,
  integrates it to get a scalar, and then takes a
  weighted sum of those scalars
• A more general approach would be to first sum
  each individuals values and then integrate over
  the (unidimensional) weighted Sum. This has an
  interpretation in Figure 1 -- ?(?) is a ray from
  the origin.

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Table 1 Basic Data for Uganda
Stunted height-for-age z-score lt 2. We
generated a poverty line internal to this dataset
of children only in such a way that it yields a
national poverty headcount of 0.35, equal to that
calculated by the Uganda Bureau of Statistics.
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Table 3 Central vs. Eastern regions
Source Uganda 1999 NHS and authors
calculations Blue shading indicates a
significantly positive t-statistic. Yellow
shading indicates a significantly negative
t-statistic. All tests are at the 5 percent
level of significance.
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Table 6 Eastern vs. Western regions
Source Uganda 1999 NHS and authors
calculations Blue shading indicates a
significantly positive t-statistic. Yellow
shading indicates a significantly negative
t-statistic. All tests are at the 5 percent
level of significance.
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Table 8 Western vs. Northern regions
Source Uganda 1999 NHS and authors
calculations Blue shading indicates a
significantly positive t-statistic. Yellow
shading indicates a significantly negative
t-statistic. All tests are at the 5 percent
level of significance.
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Table 10 Rural Central vs. Urban Eastern
Source Uganda 1999 NHS and authors
calculations Blue shading indicates a
significantly positive t-statistic. Yellow
shading indicates a significantly negative
t-statistic. All tests are at the 5 percent
level of significance.
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Table 12 Rural Central vs. Urban Northern
Source Uganda 1999 NHS and authors
calculations Blue shading indicates a
significantly positive t-statistic. Yellow
shading indicates a significantly negative
t-statistic. All tests are at the 5 percent
level of significance.
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Critical Poverty Frontiers

• Rather than testing for dominance over an
  arbitrary ?(?), search for a maximum set ?(?)
  for which multidimensional dominance holds
• Analogous to a maximum poverty line in one
  dimension
• Note that this is not necessary if one surface is
  everywhere above the other. ?(?) is the entire
  domain.

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Table 27 Rural Eastern vs. Urban
Northern Critical Poverty Frontiers
Source Uganda 1999 NHS and authors
calculations Critical frontier for ?1,1 is pink
for ?2,2 is purple for ?3,3 is red. Standard
errors show in cells.
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