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ADJUSTING POVERTY THRESHOLDS 175 the scale should be. This has been done in a number of social surveys by asking respondents how much they would need to just avoid poverty and then linking the results to variations in family size. The 1979 Income Survey Development Program (ISDP) Research Panel asked the following question: "Living where you do now and meeting the expenses you consider necessary, what would be the very smallest income you (and your family) would need to make ends meet?" The answers were converted to a logarithmic scale and regressed on the logarithm of family after-tax income, the logarithm of family size, and the age and gender of the head of the family. The coefficients from this equation were then used to predict an income that yielded a consistent level of well-being for families of different sizes and composition. The equivalence scale was created by dividing the predicted income for any size family by the predicted income for the reference family (Danziger et al., 1984); see Table 3-2. Rainwater (1990: Table 5) analyzed Gallup Poll data on the "smallest amount of money a family of four needs each week to get-along in this community," regressing the logarithm of the annualized amounts on the logarithm of income, the logarithm of family size, and the respondent's age. With one exception (the increment in the scale value for two-person families), the Rainwater and ISDP scales are remarkably similar considering the different questions, samples, and estimated equations (see Table 3-2). Statistics Canada, however, found that such scales are typically sensitive both to question wording and to the model estimated (Wolfson and Evans, 1989:41). Subjective scales are attractive because they ask the opinion of the same people for whom the scales are devised. But it does appear that the precise question wording may affect answers, and people may take their "wants" into account as well as their needs. The scales often do not consistently decrease with each additional household member (see Table 3-2). These inconsistencies may reflect general difficulties with answers to subjective questions: respondents are being asked about topics that may be far from their everyday experience and to which they may never have given serious thought. And interviewers do not have any way of cross-checking absurd or nonsensical responses (see Bradbury, 1989, on problems with subjective equivalence scales). Recommended Procedure We do not believe that any of the published methods for adjusting poverty thresholds provide a fully defensible rationale for calculating the kind of equivalence scale that is needed for different family types. But we do believe that the poverty line must be adjusted for differences in family sizes and composition; we also believe that some correction is better than no correction; and we believe that it is possible to do better than scaling in proportion to the number of people in the family.

ADJUSTING POVERTY THRESHOLDS 176 Our recommended procedure recognizes the differences between adults and children and allows for economies of scale so that the cost per adult equivalent falls as the number of adult equivalents rises. We explicitly recognize the arbitrariness that is inherent in all scales. We have selected a set of scale values for which internal consistency is guaranteed by their derivation from a single rule, but for which ultimate support comes from their transparency and plausibility. At the same time, we have tried to check that the scale values are at least roughly consistent with the Rothbarth procedure as applied to data from the CEX, because the Rothbarth method is the most defensible of existing methods. We recognize that our proposed equivalence scale is crude and makes no allowance for the effects of relative prices, location, or variations in scale values that may relate to the level of living of the family. Nor does our procedure anchor economies of scale to the particular commoditiesâprimarily housingâ that generate them. However, we note that several of the adjustments that might conceivably be made through an equivalence scale (such as for child care or commuting expenses) are made on the resource side of the poverty measure, rather than to the thresholds, and are thus taken into account (see Chapter 4). But many omitted issues are left for future research, and we regard our recommendation as no more than a sensible way that is a clear improvement on current practice. Our recommended equivalence scaleâas well as the relationship to other equivalence scalesâcan be described through the use of the general formula introduced above (for a family with A adults and K children): Both parameters P and F lie between 0 and 1.0. If P is set to 1.0, children and adults are assumed to consume the same amount at the poverty line. If F is set to 0, household economies of scale are assumed (unrealistically) to be so large that the scale values are unity for all family types, and the poverty line will be the same for all; a family of four would need only as much as a single individual. If F is set to 1.0. no economies of scale are assumed. Setting both F and P equal to 1.0 gives the per capita result in Table 3-2. Ruggles (1990:77) recommends using the square-root of family size as an equivalence scale short of extensive revisions in the current scale and, in conversation with the panel, Harold Watts also endorsed this approach. This proposal is a special case of the formula, in which P is unity and F is 0.5: Ruggles argues that setting F to 0.5 maintains the overall elasticity of the Orshansky scales while smoothing out some of the irregularities. Entering this recommendation into our general equation makes obvious the fact that the relationship of child to adult consumption is not directly addressed, although

ADJUSTING POVERTY THRESHOLDS 177 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:

ADJUSTING POVERTY THRESHOLDS 178 TABLE 3-3 Estimates of the Cost of Children (Using Rothbarth Method) Family Type Percent of Family Budget Spent Scale Value of the Family Type on Children (P) [1/(1âP)]a Single-Parent Family One child 0.307 1.443 Two children 0.496 1.984 Two-Parent Family One child 0.237 1.311 Two children 0.354 1.548 Three children 0.407 1.686 SOURCE: From Betson and Michael (1993); Betson (1990). (1990). a The scale value in column 2 is derived as the inverse of 1 minus the estimate in column 1. Scale values for children in a single-parent family are expressed relative to a value of 1.00 for a single- adult family; scale values for children in a two-parent family are expressed relative to a value of 1.00 for a two-adult family. The fitted parameters using these estimates are Thus, Betson and Michael's work suggests a scale in which children are treated as 0.70 of an adult and in which the number of adult equivalents is raised to a power of 0.76 to account for scale economies for larger families. We recommend a scale in which children are treated as 0.70 of an adult (as in the Betson and Michael results) and in which the number of adult equivalents in the family is raised to a power in the range of 0.65 to 0.75 (similar to, but not exactly the same as, the Betson and Michael results). The high value of our recommended range represents the Betson and Michael result of 0.76 rounded down to 0.75. The low value of the range is suggested because this value does not make such a large difference for the poverty threshold for single-person families (compared with the official thresholdâsee below). We believe that the general form of the proposed scale satisfies two critical criteria: it recognizes the differences between children and adults and adjusts for scale economies with increasing family size in a consistent manner. In addition, it is easy to explain and implement. Finally, the use of a scale formula of this type acknowledges the inevitable arbitrariness in adjusting the poverty thresholds for different family circumstances rather than disguising it in opaque econometric analysis. Figure 3-4 shows the current scale, the square-root proposal, the proposed scale with scale economy factors of 0.65 and 0.75, and the OECD scale.

ADJUSTING POVERTY THRESHOLDS 179 In comparing these scales, one can see that the current scale generally assumes the greatest economies of scale as family size increases while the OECD scale assumes the least economies of scale. (An exception is the square- root proposal, which assumes greater economies of scale for families of size five or larger.) We rejected the current scale because, as shown above, it is inconsistent across family types. Also, in our opinion, it assumes economies of scale that are too large for large families and for families of two in comparison with one-person families. The square-root proposal is an improvement but ignores the differences between adults and children and is even less generous to large FIGURE 3-4 Alternative equivalence scales: increment for each added family member (relative to a scale value of 1.00 for a single adult): a The OECD scale adds 0.70 for each added adult and 0.50 for each child. b Each child is treated as 0.70 of an adult, and the number of adult equivalents in the family is raised to a power of 0.75. c Each child is treated as 0.70 of an adult, and the number of adult equivalents in the family is raised to a power of 0.65. d Suggested by Ruggles (1990) and Watts (in conversation with the panel): each child is treated as the equivalent of an adult, and the number of people in the family is raised to a power of 0.50. e The current scale is calculated by converting the 1992 threshold for each family type to the 1992 threshold for an unrelated individual under age 65; the threshold for two adults is the one in which the head is under age 65.

ADJUSTING POVERTY THRESHOLDS 180 families. At the other extreme, the OECD method is straightforward and easy to use, but, in our opinion, it assumes economies of scale that are too small across the family size distribution. The range of scale economy factors that we recommend (0.65 to 0.75) produces results that are between the extremes and more consistent across family size.4 It is because the choice of an equivalence scale cannot avoid arbitrariness that we suggest a range for the scale economy factor, F. Judgement is also involved in setting the parameter P for the proportionate needs of children relative to adults, and we could have suggested a range for P as well as for F. However, it becomes difficult to grasp the implications of alternative equivalence scales across the family size distribution if both parameters are varied. Moreover, the two parameters are, as we have discussed, not independent. Thus, if P is set at 1.0, implying no difference between the needs of children and adults, then it is appropriate to set F closer to zero (as in the square-root proposal), because F then accounts both for economies of scale in the strict sense and also for the fact that larger families include more children. If, however, as we propose, children are assumed to need less than adults, then it is appropriate to raise F closer to a value of 1.0, although how much closer is, to repeat, a matter of judgement. For these reasons, we recommend a value of 0.70 for P and a range for F of 0.65 to 0.75, which is consistent with the value for P. In reaching a judgement on the specific form of the equivalence scale for implementation, it will be important to consider the implications of a particular value of F in relation to the current scale. Although one wants to improve on that scale, there is an argument for making a choice that does not represent a great departure from the current implicit scale for particular population groups. In this regard, we note the importance of applying the scale to the poverty threshold for the reference family of two adults and two children rather than to the threshold for a one-person family. Because the current scale assumes such great scale economies in moving from one-person to two-person families, it is clear that the use of almost any other scale, including those that we propose, will produce significantly higher thresholds for two-person and larger families. The only exception, again, is the square-root proposal, which will produce larger thresholds for small families but smaller thresholds for large families than the current scale. 4 The low-income measure recently adopted on an experimental basis by Statistics Canada to supplement the low-income cut-offs uses an equivalence scale formula to adjust the reference threshold for a one-person family. The formula treats each added adult in the family as 0.40 of the first adult and each added child under age 16 as 0.30 of the first adult, with one exception: in a single-parent family, the first child is treated as 0.40 of the adult (see Statistics Canada, 1991:172-173). This scale gives results similar to the square-root proposal for families of size one to size five and results similar to our proposal with a 0.65 scale economy factor for larger families.

ADJUSTING POVERTY THRESHOLDS 181 TABLE 3-4 Alternative Equivalence Scales, with Scale Values Expressed Relative to a Value of 1.00 for a Family of Two Adults and Two Children Type of Scale Family Current 0.50 Scale 0.65 Scale 0.75 Scale OECDe Type Officiala Economy Economy Economy Factorb Factorc Factord One- 0.513 0.500 0.451 0.399 0.370 person familyf Married 0.660 0.707 0.708 0.672 0.630 couple Plus one 0.794 0.866 0.861 0.841 0.815 child Plus two 1.000 1.000 1.000 1.000 1.000 children Plus three 1.177 1.118 1.130 1.151 1.185 children Plus four 1.318 1.225 1.251 1.295 1.370 children Plus five 1.476 1.323 1.367 1.434 1.556 children a The current scale is calculated by expressing the official 1992 threshold for each family type as a multiple of the 1992 threshold for a family of two adults and two children; the thresholds for unrelated individuals and two-adult families are those for people under age 65. b Suggested by Ruggles (1990) and Watts (in conversation with the panel): each child is treated as the equivalent of an adult, and the number of people in the family is raised to a power of 0.50. The resulting scale value for each family type is converted to a ratio of the scale value for two-adult/two- child families. c Each child is treated as 0.70 of an adult, and the number of adult equivalents in the family is raised to a power of 0.65. The resulting scale value for each family type is converted to a ratio of the scale value for two-adult/two-child families. d Each child is treated as 0.70 of an adult, and the number of adult equivalents in the family is raised to a power of 0.75. The resulting scale value for each family type is converted to a ratio of the scale value for two-adult/two-child families. e The OECD scale adds 0.70 for each added adult and 0.50 for each child. The resulting scale value for each family type is converted to a ratio of the scale value for two-adult/two-child families. f Includes people living alone and with others in a household not related to them. By applying the proposed scale to the threshold for the reference two-adult/ two-child family, the differences from the current scale are reduced for families in most size categories; see Table 3-4 and Figure 3-5. Specifically, for a given value of the reference family threshold, the proposed scale with a scale economy factor of 0.75 produces very similar thresholds as the current scale for all family size categories except for one-person families, for which it produces a threshold value that is less than 80 percent of that produced by the current scale. The proposed scale with a scale economy factor of 0.65 produces thresholds that are reasonably close to the official thresholds for all categoriesâsomewhat lower for one-person families and families of five to seven members and somewhat higher for families of two and three members. In our analysis with March CPS data (see Chapter 5), we explore the implications of the choice of a scale economy factor on poverty rates for families of different sizes and other population groups.