Sen-Shorrocks-Thon Index

THE SEN-Shorrocks-Thon (SST) Index is a poverty index proposed by A.F. Shorrocks in 1995, based on the pioneering work of A.K. Sen in 1976. It has also received the name “modified Sen Index” in discourse by Shorrocks and Sen. As noted by B. Zheng, this index is identical to the limit of D. Thon's modified Sen Index.

In 1976, Sen proposed an axiomatic approach to poverty measures. He argued that poverty indexes should satisfy certain ethically defensible criteria, or axioms, and that the desirability of a poverty measure should be evaluated in terms of these axioms. Therefore, if we evaluate antipoverty policies according to their ability to reduce this type of poverty index, our evaluation will be consistent with the ethical criteria that inspire the poverty measure.

The index is a weighted sum of the poverty gap ratios of the poor. The weights decrease with the rank order in the income distribution such that more weight is given to the poverty gap of the poorer individuals. The index is normalized to take values between zero and one: it is equal to zero when all the incomes are above the poverty line and so there are no poor people; it reaches a unit value in the extreme case when all the individuals are poor and they have zero income.

Of course, these are extreme hypothetical cases. In a comparative study of 23 Organization for Economic Cooperation and Development (OECD) countries, L. Osberg and K. Xu report a range of indexes between .014 in Austria and .125 in the United States during the 1990s.

This index has some very attractive properties:

• 1)
  Homogeneous of degree zero: The index is invariant to changes in the scale of the income distribution and the poverty line.
• 2)
  Focus axiom: The index does not depend on the income levels of the nonpoor.
• 3)
  Impartiality axiom: It depends only on the vector of ordered incomes and not on the identity of the individuals.
• 4)
  Replication invariant: The poverty index does not change if it is computed based on an income distribution that is the k-fold replication of the original income distribution.
• 5)
  Monotonicity axiom: A reduction in a poor per-son's income, holding other incomes constant, increases the poverty index.
• 6)
  Continuity axiom: The index is a continuous function of individual incomes.
• 7)
  Transfer axiom: The index increases whenever a pure transfer is made from a poor person to someone with more income.

In order to understand the relevance of these properties, it is useful to compare this index with other commonly used poverty measures. The poverty rate or headcount ratio, H, is a commonly used poverty measure. It is defined as the proportion of people whose incomes are under the poverty line. This measure meets properties 1) to 4), but it violates the monotonicity, the continuity, and the transfer axioms because it does not depend on how far and how unevenly the individual incomes of the poor fall below the poverty line.

Using this index to design and to evaluate antipoverty policies can lead to undesirable results. For instance, the easiest way to reduce the poverty rate is to subsidize the richest of the poor with just barely enough additional income to lift them out of poverty. This seems a very controversial policy action. Another commonly used poverty measure is the average poverty [Page 971]gap ratio of the poor (APGR). This index violates the transfer axiom because it is insensitive to the distribution of income among the poor. An income transfer from one poor person to another poor person without lifting any of the two out of poverty will not change the average poverty gap ratio. Finally, the Sen Index satisfies properties 1) to 5), but it violates the continuity and the transfer axioms. These limitations of the Sen Index led Shorrocks to propose the modified Sen Index, or SST index.

...