Counting and multidimensional poverty measurement

Counting and multidimensional poverty measurement. Sabina Alkire, James Foster. 2011. Journal of Public Economics. 12 pp.

Introduction

Challenges:

1. Ordinal variables, rather than cardinal. Hard to aggregate in a single number.
2. Who is poor if there are multiple dimensions?

The Alkire-Foster Method:

1. Counting-based method
2.  Adjusted FGT measures
3. Identifies breadth and depth

Two cutoffs:

1. First, benchmarking in each dimension
2. Second, count the number of dimensions below the line

Identifying the poor

Criterions:

1. Union. Poor if deprived in one or more dimensions. Overestimates.
2. Intersection. Poor if deprived in all dimensions. Underestimates
3. Dual cutoff. Intermediate. Poor in at least k dimensions.
1. Poverty focused
2. Deprivation focused
3. Invariant to monotonic transformations

Measuring poverty

• Dimensions: d
• Population: n
• Vector of Achievements: y
• Dimensional cutoff: z
• Identification function: p
• Poor people: q(z)
• Non-poor people:  r(z) = n - q
• Measure of poverty: M
• Methodology: X(p, M)
• Headcount ratio H = q/n
• Vector of deprivation counts: c(k)
• Average deprivation share: A = c/qd
• Adjusted headcount ratio: Mo = HA
• Average poverty gap: G
• Adjusted poverty gap: M1 = HAG
• Average severity of deprivations: S
• Adjusted FGT measure: M2 = HAS

General weights

An equal weight of w = 1 to each dimension is appropriate when the dimensions are of relatively equal importance. However, in other settings there may be good arguments for using general weights.

Properties

• Decomposability. Overall poverty is the weighted average of subgroup poverty levels, where weights are subgroup population shares. 
• Invariance. Poverty is evaluated relative to the population size, so as to allow meaningful comparisons across different sized populations.
• Symmetry. If two or more persons switch achievements, measured poverty is unaffected. This ensures that M does not place greater emphasis on any person or group of persons.
• Poverty focus. If x = y + r, then M(x) = M(y)
• Deprivation focus. If x = y + non deprived, then M(x) = M(y)
• Monotonicity.
• Nontriviality. M achieves at least two distinct values.
• Normalization. M achieves a minimum value of 0 and a maximum value of 1.
• Weak transfer. An averaging of achievements among the poor generates a poverty level that is less than or equal to the original poverty level.
• Weak rearrangement.

Adjusted headcount ratio

1. Methodology delivers identical conclusions when monotonic transformations are applied to both variables and cutoffs. 
2. Methodology is a better choice when key functions are fundamentally ordinal (or categorical) variables.
3. Methodology conveys tangible information on the deprivations of the poor in a transparent way. Its simple structure ensures that M0 is easy to interpret and straightforward to calculate.
4. Methodology is fundamentally related to the axiomatic literature on freedom. M can be viewed as a measure of ‘unfreedom’. It may be more tractable to monitor deprivations than attainments.

Cutoffs

Two general forms of cutoffs must be chosen:

1. The deprivation cutoffs zj. 
2. The poverty cutoff k. Setting k establishes the minimum eligibility criteria for poverty in terms of breadth of deprivation and reflects a judgement regarding the maximally acceptable multiplicity of deprivations. Check robustness for values near the original cutoff, or even to opt for dominance tests that cover all possible values of k.