Do we tend to overestimate poverty gaps? The impact of equivalency scales on the calculation of the poverty gap

Consider a population that consists of only two households. The ®rst household has a total household income of 500 and is composed of three people: 2 adults and a child. Let, for simplicity, the equivalence scale be such that each adult counts for 1, and each child for 0.5. That the household’s income per consumption unit is 200 (500 divided by 2.5 equivalent units). The second household has a total income of 450 and is composed of 2 people: 1 adult and a child. Its per consumption unit income is 300 (450 divided by 1.5). Let now the poverty line per equivalent unit be 400. The analysis is conducted in terms of consumption units, and a household is considered as poor if its income per consumption unit is less than the poverty line. Both households are poor, and poverty headcount (P0) is 1. The question is: What is the amount of the poverty gap? The overall poverty gap is de®ned as the total amount of money that should be given to the households to bring them up to the level of the poverty line. For the ®rst household, the total `required’ income not to be poor is 1000 (400 times 2.5 equivalent units). For the second household, it is 600 (400 times 1.5). Since the combined income of the two households is 950, and the `required’ amount is 1600, the overall poverty gap is 650. This study will now show what the application of the standard formulae will yield. Overall poverty gap is equal to: