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) |