빈곤 지수의 공리적 접근

Axiomatic Approach of Poverty Indices

In his pioneering article on the measurement of poverty, Sen(1976) noted that the evaluation of poverty was required the solution of two distinct but not related exercises : first, how to identify the set of the poor in the total population, and second, how to aggregate the available information of the poor into a device that will quantify the extent of poverty. Sen proposed three axioms for an index of poverty - the focus axiom, the monotonicity axiom and the transfer axiom. After the Sen’s pioneering work, a number of articles have considered some properties of indices - additive decomposability axiom, impartiality axiom, axiom of increasing in subsistence income, continuity axiom, population invariant axiom, population growth axiom. We may formally define two crude indices ; Head-count ratio and Poverty-gap ratio. The head-count ration satisfies the focus axiom but violates the monotonicity and transfer axioms. The poverty-gap ratio goes against the transfer axioms. While the Sen-Blackorby -Donaldson- Kakwani indices violate the strong upward transfer axiom and the Takayama index violates the weak monotonicity axiom, the general ethical indices introduced by Clark-Hemming- Ulph-Charkravaty satisfy these axioms. These indices are based on the equally distributed equivalent income corresponding to a censored income profile. Anand (1977) suggested the simple variation of the Sen index but his axiom violates the focus axiom. Foster-Greer-Thorbecke(1984) proposed a class of decomposable poverty indices that vary with a poverty aversion parameter. In this paper, a class of poverty is derived, that serves to clarify an explicit or implicit choice for several axiomatic requirements simultaneously. We conclude that in the situation of grouped data, the performance of Foster-Greer-Thorbecke’s index is better than any others, if the notion of decreasing marginal welfare is accepted.