Step

Definitions

Notations and equations

Identification

Defining the set of indicators which will be considered in the multidimensional poverty measure.

x ij . is the achievement of person i in dimension j

Setting the level of achievement considered sufficient to be considered as non-deprived in each indicator using the deprivation cutoff points (z)

( z 1 ⋯ z d )

Applying the cutoff points to ascertain whether each person is deprived or not in each indicator ( g 0 ).

g ij 0 ={ 1 x ij < z j 0 x ij ≥ z j (1)

Selecting for each indicator the relative weight or value (w). The sum of the relative weight is equal to one.

( w 1 ⋯ w d )

Computing “deprivation score” which is the weighted sum of deprivations for each person.

c ij = ∑ j=1 d w j g ij 0 (2)

Determining (normatively) the proportion of weighted deprivations a person needs to experience to be considered multidimensionally poor. The poverty cutoff point k and ρ k ( x i ;z ) identification function which identifies each person as multidimensionally poor or not according to the selected poverty cutoff point k .

ρ k ( x i ;z )={ 1 c i >k 0 otherwise (3)

Aggregation

Censoring deprivations of the non-poor and computing the proportion of people who have been identified as multidimensionally poor (q) in the population (n). It’s also called Headcount Ratio and noted: H

H= q n (4)

Computing the average share of weighted indicators in which poor people are deprived (A).

A= ∑ i=1 q c i ( k ) q (5)

Computing the M0 measure as the association of the headcount ratio (H) and the average share of weighted indicators (A).

M 0 =H∗A (6)