IMPACT OF TAXES AND TRANSFERS

Enami, Lustig, Aranda, No. 25, November 2016
Using equation 12, we can derive the general condition for the case in which the combination
of one tax and one transfer (that is, the net fiscal system) is equalizing, neutral, or unequalizing.
As noted, when there is no reranking, П N RS is equal to the change in the Gini coefficient (that
is, G X – G X-T+B ). If G X – G X-T+B > 0, the net fiscal system is equalizing, which simply means that
equation 12 must be positive. Since the denominator is positive by definition, the condition
implies that the numerator has to be positive. In other words,
(13) П RS N = (1−g)П T RS RS
+(1+b)ρ B
> 0 ⟺ (1 − g)П RS T + (1 + b)ρ RS B > 0
1−g+b
(14) ⟺ П T RS > − (1+b)
(1−g) ρ B RS
(15) ⟺ П T K > − (b)
(g) ρ B K
where П T
K
and ρ B
K
are the Kakwani index of the tax and transfer, respectively, and 1 − g is
positive.
Therefore, we can state the following conditions.
Condition 16:
If and only if П RS T > − 1+b
ρ 1−g B RS (ρ RS B >− 1−g
П 1+b T RS ) or П K T > − (b)
ρ (g) B
K (ρ K
B
the net fiscal system reduces inequality.
> − (g)
(b) П T K ),
Condition 17:
If and only if П RS T = − 1+b
ρ 1−g B RS (ρ RS B =− 1−g
П 1+b T RS ), or П K T = − (b)
ρ (g) B K (ρ K
B
the net fiscal system leaves inequality unchanged.
= − (g)
(b) П T K ),
Condition 18:
RS
If and only if П T < − 1+b
ρ 1−g B RS RS
(ρ B