Measuring Poverty: A New Approach (1995)

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ADJUSTING POVERTY THRESHOLDS 170 calibrate the scales, a result that has been formally demonstrated by Pollak and Wales (1979). Although calculating the cost of a change in family size may appear to be analogous to the problem of calculating the money needed to compensate for a price change—something that is routinely done in applied economics—the two problems are not the same. In the case of a price increase, one can observe how much a family consumes and so get a good idea of how much a price increase will cost it. But when a child is added to a family, one does not know how much the child consumes (or how much the parents alter their own consumption accordingly) and so cannot price out its cost. The situation is not quite hopeless. If one can devise a general rule that indicates when households of different compositions are equally well off, one can use it to calculate the scale. The discussion above showed that such a rule cannot be deduced from the data. In principle, postulating such a rule is not very different from picking a set of arbitrary but plausible values to constitute an equivalence scale, but it is easier to propose and defend a single rule than a whole set of scale values. The use of a single principle guarantees that the scale values for different family types are internally consistent, unlike the scale values implicit in the current official poverty thresholds. In the next two subsections, we discuss two different rules for determining when households are equally well off and the procedures for calculating equivalence scale values that are associated with each. (See Table 3-2 for examples of scales developed by these rules.) The Engel and Iso-Prop Methods The most famous of the procedures for determining equivalence scales dates back to the work of Ernst Engel and uses the share of a family budget devoted to food as an indicator of living standards (E. Engel, 1895). Engel's Law, that the share of food expenditure in the budget declines as people become better off, is one of the earliest and most widely confirmed empirical generalizations in economics. It is also true that, at the same level of income or total expenditure, households with more children spend a larger share of their budget on food. Engel went beyond these two empirical facts to assert that the share of food in the budget correctly indicates the standard of living across families of different types. If one accepts this assertion, one has a simple and easily applied rule for detecting which of two families is better off, even when the families have different compositions. If the food share for two families is the same—that is, if they are on the same food "iso-prop" curve—they are equally well off. Hence, all one needs to do to calculate the cost of an additional family member is to calculate how much must be added to the budget to restore the family's food share to its original value. Figure 3-2, which shows the relationship between the food share and family income for two families, illustrates how Engel's procedure works. Line 

ADJUSTING POVERTY THRESHOLDS 171 FIGURE 3-2 Engel method for equivalence scales. (See text for discussion.) A is for a two-adult family, and line B is for that family with the addition of a child. Line B is higher at all levels of income: that is, more is spent on food at all income levels. In the original situation, the small family has income y0 and food share w0, which rises to w1 after the addition of the child. According to Engel, this family is restored to its original standard of living when its food share returns to its original value. This would happen if the family's income was increased to y1, or if the family received some compensation equivalent to y1 – y0. The equivalence scale value for a two-adult/one-child family relative to a two-person family is given by the ratio of y1 to y0. In practice, the Engel method would be implemented, not diagrammatically, but by fitting an Engel curve in which food expenditures—or the share of expenditures on food—is linked to income and family characteristics. The estimated equation can then be used to calculate what increase in income is equivalent to an additional family member (of various types), and the equivalence scale values are calculated exactly as above. The example was cast in terms of two parents having their first child, but so long as one is prepared to accept Engel's basic assertion that food shares indicate welfare, the method can