IMPACT OF TAXES AND TRANSFERS

Enami, Lustig, Aranda, No. 25, November 2016
(5) П T
K
= C T − G X ,
where C T is the concentration coefficient of the tax t and G X is the Gini coefficient of pre-tax
income. The conditions for a tax to be equalizing, neutral, or unequalizing are П T K > 0, П T K = 0,
and П T K < 0, respectively.
Table 2 presents a summary of the conditions described above. Of course, if the tax meets the
sufficient condition, it implies that the necessary condition is met too (but not vice versa).
Since we assumed there is no reranking, the disproportionality measures such as the
concentration curves and the Kakwani index translate immediately into measures of
redistribution.
Table 2. Conditions of Equalizing, Neutral, and Unequalizing Taxes
Tax Sufficient Necessary and Sufficient
Equalizing
Neutral
Unequalizing
t’(x) ≥ 0 for all x with
some t’(x) > 0
t’(x) = 0 for all x
t’(x) ≤ 0 for all x with
some t’(x) < 0
C T (p) ≤ L X (p) for all p and for any
distribution of pre-tax income
OR
П T K > 0
C T (p) = L X (p) for all p and for any
distribution of pre-tax income
OR
П T K = 0
C T (p) ≥ L X (p) for all p and for any
distribution of pre-tax income
OR
П T K < 0
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