OPTIMISING ANTI-POVERTY TRANSFERS WITH QUANTILE ... - Ivie

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to the poorest of the poor. The ‘p-type’ rule is applied to the case of the head-count
index (FGT index with α =0). In that case, ‘p-type’ transfers just express that it
is least costly to start transferring from the poorest of the poor and sweeping up
the income distribution, if the aim is merely to reduce the number of the poor.
For the economically most interesting cases (k convex), the above algorithm
depends on Euler conditions, including the budget condition. No negative transfer
is necessary and the condition of positive transfers is never binding under perfect
targeting. We shall show how to implement a similar procedure under imperfect
targeting and even with X multivariate.
2.1.1. The imperfect information case
Unfortunately, perfect targeting is not feasible because incomes cannot be perfectly
observed.
Nevertheless, since the household living standard is correlated
with some observable characteristics, it is possible, as in Glewwe (1992), to think
about minimizing an expected poverty measure subject to the available budget
for transfers and conditioning on these characteristics. In practice, the approach
followed in the literature falls short from such a lofty ambition. Practitioners, including
Glewwe, design the APTS by merely replacing unobserved living standards
with OLS predictions based on observed variables and working with the observed
sample as if it was the global population. We shall refine this approach.
Under perfect information, the social planner needs to use observed characteristics
X rather than unobserved incomes y to implement the transfers.
We
therefore consider the following optimisation program.
min
{t(X)}
Z +∞ Z +∞
−∞ −∞
P (z, y + t(X)) dF (y, X)