since large families tend to contain a larger proportion of children, the economies of scale that come from the square-root rule are coincidentally picking up the distinction between adults and children. The alternative is (as we propose) to make F larger and to compensate by setting K to less than 1.0, thus explicitly recognizing the distinction between pure economies of scale and family composition. Since we consider the needs of, say, five adult family members living together to be greater than the needs of a family of two adults and three children, we prefer our formula to that suggested by Ruggles.
The OECD equivalence scale (Organization for Economic Cooperation and Development, 1982) sets a single adult to be 1.0, each additional adult to be 0.7, and each child to be 0.5. This rule can be written in the same general way:
In this case, there is no adjustment for economies of scale beyond the family composition adjustment for the second and additional adults. A third adult adds as much to household needs as does a second or fourth adult. The OECD scale, in contrast to the square-root rule, puts all of the adjustment on adult and child differences, without an explicit recognition of economies of scale except for the difference between the first and second adult. In fact, the OECD scale can be well approximated by ignoring the distinction between adults and children and between the first and second adult and simply raising family size to the power of 0.72 (see Buhmann et al., 1988).
Betson and Michael (1993) provide estimates of the parameters in the general formula from work of Betson (1990), who estimated the cost of children by using the Rothbarth method and data from the 1980-1986 CEX; see Table 3-3. Betson (1990) reported the estimated percentages of total expenditures devoted to children (see first column of Table 3-3) and the proportional cost of children in oneand two-parent families (see second column of Table 3-3). For example, two parents with a child are estimated to spend 24 percent of their budget on their child and hence would need 31 percent more income than a childless couple to be equally well off. The estimates presented in Table 3-3 cannot be directly interpreted in terms of the relationship between the consumption needs of children relative to adults (P) nor the scale economy factor (F). To select which two parameters would best fit the information contained in Table 3-3, Betson and Michael (1993) chose the parameters that minimized the sum of squared deviations of the observed proportional costs of children (the five values in the second column of Table 3-3) from the fitted proportional costs of children expressed in terms of the panel's recommended equivalence scale formula: