Chapter 1: Introduction
• The fourth property is scale invariance, which requires the poverty measure to be unchanged if all incomes and the poverty line are scaled up or down by the same factor. This approach makes sure that the measure is independent of the unit of measurement of income. The first four properties are invariance properties, which indicate how various changes in the distribution should not be taken into account by the measure. The next two properties are dominance properties that require the measure to be consistent with certain basic changes in the distribution. • The fifth property is weak monotonicity, which requires poverty to rise or be unchanged if the income of a poor person falls—in other words, a decrement in a poor income cannot decrease poverty. Weak monotonicity is a central property of a poverty measure and is often presented in a stronger form, known as monotonicity, which requires an increment in a poor income to (strictly) decrease poverty. • The final property considers the effect of a transfer on poverty. The weak transfer property requires poverty to fall or be unchanged as a result of a progressive transfer (from richer to poorer) between two poor people. This property also has a stronger version, known as the transfer principle, which requires poverty to (strictly) increase as a result of a regressive transfer (from poorer to richer) between two poor people. Notice that both the monotonicity axiom and the transfer principle allow the number of poor to be altered in the process, whereas the weaker versions do not. The headcount ratio, the poverty gap measure, and the FGT index satisfy all six basic axioms. The headcount ratio satisfies weak monotonicity and the weak transfer principle (because it is unaffected by the distributional changes specified in the two properties), but it violates the two stronger versions. The poverty gap measure satisfies the monotonicity axiom, but it violates the transfer principle (because it is unaffected by a small regressive transfer). The FGT index satisfies both stronger axioms. Some additional properties can also be helpful in evaluating poverty measures. Transfer sensitivity requires a decrement in the income of a poor person, when combined with an equal-sized increment in the income of a richer poor person, to raise poverty. It ensures that a given-sized transfer has a larger poverty-reducing effect at lower poor incomes. Decomposability and
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