eee37 9 | Biblioteca motores auton

groups component for the groups of the second partition. Similarly, overall convergence along

component converges naturally to the overall inequality when the number of groups

This procedure can be generalized to any finite multilevel decomposition in subpartitions.

which has the property that

along the subpartition S within any group of the first partition K. The weighting scheme is the

Proposition 1

We shall follow Wodon (1998) and call the new second term of the right-hand side expression,

the second partition can be divided into two components: (1) convergence along the first

the within-groups component decreases since

,...,

)

the two between-groups of the two partitions. Second, it is non-negative, indicating that the

Also, if the inequality index is additively decomposable, then we obtain

inequality along the second partition within the groups of the first partition, plus (3) a within-

(

larger the number of groups, the larger the between-groups component. The between-groups

of the first partition K. It is obtained as a weighted sum of the between-groups inequality

approaches the number of individuals. Note also that it increases exactly the same amount as

between-groups inequality along the first partition, plus (2) a second-order between-groups

First, the second-order between-groups inequality can be computed as the difference between

partition plus (2) a second-order convergence of the second partition along the first partition.

B,SK , the second-order between-groups inequality along the subpartition S within the groups

Overall inequality can then be divided into the following three components: (1) a first-order

same as the within-groups component weights.