Why checking for robustness?

• What do you think are the main reasons why poverty may not be robust?

1. Arbitrariness of the choice of Poverty Index
2. Arbitrariness of the choice of Poverty Line
3. Equivalence of scale used
4. Sampling error

• What else?

Elasticity of FGT poverty measure with respect to per capita consumption

$$\eta = \frac{\Delta\%FGT_\alpha(x,z)}{\Delta\%PCE}$$

• Shift the distribution without changing its relative shape

• Poverty line remains constant

• What would happen if there is a concentration of marginal poor around the poverty line?

• What are the main reasons why the consumption aggreagte may change?

Graphical representation of change in PCE

The same is true if we change the poverty lines

• Each component of the absolute poverty line (i.e. CBN) is a function of several variables that affects results

  • Food component

  • “Reference” Group could lead to different poverty lines even using the same method;

  • Nutritional requirement

  • Average or median of the “reference” population not only for quantities but also for prices

  • Nonfood component

  • How do we define the interval (“close”) to the poverty line?

  • Lower poverty line & upper poverty line

Graphical representation of change in poverty lines

Poverty Dominance Analysis

• Dominance analysis is a comparison of multiple distributions.

• It allows us to compare results for all poverty lines when comparing across time/subpopulations

• Three relevant poverty curves:

  • Poverty incidence curves

  • Poverty deficit curves

  • Poverty severity curves

Poverty incidence curves

1. First Order Dominance

• If the poverty incidence curve for distribution A is above that for B for all poverty lines (up to $z_{max}$)...
• ... there is more poverty in A than in B for all poverty measures and all poverty lines (up to $z_{max}$)

1. First Order Dominance

Graphically it looks like this

1. First Order Dominance

but,

• What if the poverty incidence curves intersect?

1. First Order Dominance

but,

• What if the poverty incidence curves intersect?

  • Ambiguous poverty ranking

• What could you do?

  • Restrict range of poverty lines

  • Restrict class of poverty measures

1. First Order Dominance

Poverty Deficit curves

• Area under poverty incidence curve

• The height is proportional to the poverty gap measure, the larger the height the larger the poverty gap measure for a given poverty line or level of welfare aggregate

• Each point gives average poverty gap = poverty gap index times the poverty line $z$

1. First Order Dominance

Graphically, it look like this

layout: false

2. Second Order Dominance

• If the poverty deficit curve for distribution A is above that for B for all poverty lines (up to $z_{max}$)...

• ...there is more poverty in A than in B for all poverty measures which are strictly decreasing and weakly---convex in welfare aggregate (i.e. consumption or income) of the poor such as the Poverty Gap and Severity but not Headcount Ratio

2. Second Order Dominance

2. Second Order Dominance

But,

• What if the poverty deficit curves intersect?

2. Second Order Dominance

But,

• What if the poverty deficit curves intersect?

  • Ambiguous poverty ranking- What could you do?

  • Restrict range of poverty lines

  • Restrict class of poverty measures- ... And so on and so forth with poverty severity

Poverty dominance analysis - Recommendations

• First Order: construct the poverty incidence curves up to highest admissible poverty line for each - distribution
  • Do not cross $\rightarrow$ Unambiguous comparison (2nd and 3rd Order holds too)
  • Do cross $\rightarrow$ perform Second Order Dominance test
• Second Order: build poverty deficit curves and restrict range of proper measures
  • Do not cross $\rightarrow$ Unambiguous comparison for higher order poverty indexes
  • Do cross $\rightarrow$ perform Third Order Dominance Test
• Third Order: create poverty severity curves
  • Do not cross $\rightarrow$ Unambiguous comparison
  • Do cross $\rightarrow$ nothing left to do

Equivalence of Scales

• Two options for the arbitrary approack
  • OECD - Modified scale

$$AE_{OECD} = 1 + 0.5 \times (N_A - 1) + 0.3 \times N_C$$ Where,

• $N_A =$ Total number of adults

• $N_C =$ Totol number of children

• LSMS (National Research Council '95)

$$AE_{LSMS} = (N_A - \alpha N_C)^\theta$$

Where,

• $\alpha =$ Adult equivalent $\in (0,1)$
• $\theta =$ Economies of scale $\in (0,1)$

Equivalence of Scales

To check the sensitivity of the paremeters

• Select a "pivot" household which is unaffected by changes in parameters

  • It could be any household composition that would be chosen as modal type: $(N_{A0};N_{A0})$
  • Ex: Two adults and two children

$$x^* = \frac{x} {(N_A + \alpha N_C)^\theta} \frac{(N_{A0} + \alpha N_{C0})^\theta} {(N_{A0} + N_{C0})}$$

• $x^*$ is always equal to per capita expenditure for the reference household because $N_A = N_{A0} \text{ and } N_C = N_{C0}$

• For all other household,

  • $1^{st}$ term if expenditure per adult equivalent
  • $2^{nd}$ term is a constant ($N{A0} \text{ and } N{C0}$ and fixed)

Equivalence of Scales