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ADJUSTING POVERTY THRESHOLDS 172 be used to compare any family type with any other family type and so to produce a complete set of equivalence scale values. This method will presumably also capture any economies of scale so long as they are reflected in the food share, as they must be if the Engel assertion is correct. It is also possible to extend the Engel method beyond the share of food to the share of other necessities; this iso-prop approach was introduced by Watts (1967; see also Seneca and Taussig, 1971) and underlies the Canadian low- income cut-offs (LICOs) (see Wolfson and Evans, 1989). When goods other than food are included, the assumption is that the share of those goods indicates family welfare. Hence, the procedure will work in the same way as does Engel's, provided that the share falls with income (because the goods are necessities) and rises with family size. The Engel method and its iso-prop variants are only as good as the basic assumption that the food (or other necessity) share correctly indicates family welfare, which can be argued. Even if Engel's Law is correct, and even if larger families spend a larger share of their budget on food, there is no automatic implication that the food share is a valid indicator of the standard of living. Engel's Law says that richer families have lower food shares, so that, among families of the same composition, it makes sense to argue that families with higher food shares are poorer than families with lower food shares, which is no more than a restatement of the law. Larger families spend a larger share on food, as do poorer families, but it does not follow that larger families spend more on food because they are poorer or that one can measure how much poorer they are by calculating the income drop that would have produced the same effect. Nicholson (1976) has convincingly argued that the food share is a poor indicator of the standard of living. Consider again a married couple who have their first child, and suppose for the purposes of the argument that one has managed to calculate the correct compensation and that the appropriate amount has been paid to the family. What will happen? The parents have been fully compensated and so are expected to spend, out of their share of family resources, the same fraction on food as they did before the birth of the child. But a child consumes mostly food and clothing, so this fully compensated family actually spends a larger share of its total budget on food. According to Engel, the family is worse off than it was before because its food share is higher, and it must be paid more to compensate it for the cost of the child. By this argument, the compensation calculated according to the Engel method assigns too large a cost to children. Nicholson's argument is a persuasive one, and we do not believe that the food (or necessities) share should be used to calculate equivalence scale values. The Rothbarth and Other Methods Instead of using food share, Rothbarth (1943) used expenditures on adult goods as an indicator of the standard of
ADJUSTING POVERTY THRESHOLDS 173 living, if not of the whole family, at least of its adult members. Using the same example of a married couple with a child, the argument is that the child brings needs but no resources and that those needs can be met only by making cuts elsewhere in the budget. If one can find some goods that children do not consume âalcohol, tobacco, and adult clothing being the most obvious and frequently used examplesâtheir consumption should decline when a child is added to the family. The decline is caused by the diversion of income to the child, so that if one can calculate the reduction in income that would produce that same decline, one has calculated the amount of income diverted to the child, and, thus, its cost. The mechanics of the procedure are similar to those of the Engel method and are illustrated in Figure 3-3. Again, there is curve A for the original family and curve B for the larger family containing the child, but now they slope upwards, since expenditure on adult goods is assumed to rise with income. And it is the lower curve, curve B, that is associated with the larger family because expenditures on adult goods are cut to make room for the additional expenses associated with the child. The original family with income y0 spends a0 on adult goods, which is reduced to a1 in the presence of the child. If income is increased to y1 from y0, the original level of expenditure on adult goods is restored, and, according to Rothbarth, so are the living standards of the parents. The difference y1 â y0 is therefore the cost of the child, and the ratio of y1 to y0 is the equivalence scale value for the two family types. FIGURE 3-3 Rothbarth method for equivalence scales. (See text for discussion.)