Irp Discussion Papers Child Costs as a Percentage of Family Income: Constant or Decreasing as Income Rises?

Although it is generally agreed that a child whose parents live apart should have the same proportion of parental income he or she would have if the parents lived together, what that proportion is remains in doubt. The guidelines issued by the federal Office of Child Support Enforcement rest on the contention that as income rises, the percentage of family income spent for a child decreases. The Wisconsin percentage-of-income standard is based on the assumption that expenditures on children increase in proportion to increases in income up to very high income levels. The economics literature on the topic of equivalence scales does not provide clear-cut answers. Further research is needed to develop more definitive tests to determine the cost of a child in relation to family income and the additional cost of additional children. A new technique using data from the subjective Income Evaluation Question shows promise for further examination of this issue. Child Costs as a Percentage of Family Income: Constant or Decreasing as Income Rises? Child support refers to the transfer of income from a nonresident parent to the child's resident parent. The Child Support Enforcement Amendments of 1984 required all states to establish numerical standards for child support awards that courts may--but are not required to--use in establishing child support obligations. The Family Support Act of 1988 requires states to make their child support standards presumptive (required) for all cases, unless good cause for deviating from the standards is established in court. Furthermore, states must review their standards every four years. A report commissioned by the federal Office of Child Support Enforcement (OCSE) for the purpose of providing guidance to the states in establishing child support guidelines recommends a standard based on the following normative proposition: The child should receive the same proportion of parental income that he or she would have if the parents lived together (Williams, 1987). Although we believe that this is an intuitively appealing place to begin, rather than a place to wind up, we will not focus on the normative underpinning of the report. (See Garfinkel and Melli, forthcoming.) Rather, our focus is on the scientific underpinning to its quantitative recommendations, a set of child support guidelines known as the ItIncome Shares Model." In particular, we focus on the extent to which there is good scientific evidence to justify the report's recommendation that child support awards, as a proportion of parental income, decrease as income rises. In technical terms, this recommendation rests on the contention that expenditures on children in intact families increase less than proportionally with income.' In view of the fact that 23 states have adopted standards based on the Income Shares Model, this scientific question has great policy relevance. In the first section of the paper, we briefly summarize the methodologies used in the conventional economics literature on the costs of children, which are based on the application of the theory of equivalence scales to expenditure data. In the process, we demonstrate that the federal report draws upon a branch of that literature that has some questionable properties. Other studies in the literature suggest that expenditures on children increase in proportion to income up to very high incomes. The second section discusses an alternative approach to measuring equivalence scales and the costs of children, which was developed by a group of Dutch economists and which is based on survey questions that ask people about their families' needs. The third section explains how the Dutch approach can be extended to test whether the proportion of income spent on children decreases as income rises, and the fourth describes the data we use. The results presented in the fifth section suggest that neither the hypothesis of proportionality nor the hypothesis of regressivity can be rejected by the data. The paper concludes with a brief summary, some suggestions for further research, and a few cautions to policymakers. I. CONVENTIONAL METHODS USED IN ESTIMATING THE COSTS OF CHILDREN The definition of the cost of a child (or, more generally, of any change in family composition) most favored in the economics literature is where C(U,a) is the llhousehold cost function" which gives the cost of reaching welfare level U, given family composition, a; and a0 is the composition of the reference household. suppose, for example, the reference household is a childless couple. Then the cost of one child is the amount of extra income the family needs after the child is born to be as well off as before. The Iftrue household equivalence scaleIt1 m, is defined as The proportion of (compensated) family income spent on an additional family member is Thus a higher equivalence scale implies a higher proportion of family income spent on children, and we shall use the expressions interchangeably. In this paper, we seek to test the hypothesis that the proportion of family income spent on each additional child does not vary with income, i.e., that dP/dy = 0, where y is family income. If we assume that tastes and leisure time are the same for all families (an implicit assumption in all of this literature), this is equivalent to testing whether dP/dU = 0, or dm/dU = 0. The models that have been used to estimate equivalence scales from observed expenditure data are based on the economic theory of consumer demand, as generalized from individuals to families, which assumes that families maximize a joint utility function. 2 In order to develop a model that is estimable, the researcher must make two important functional form assumptions. The researcher must specify both the form of the expenditure (or utility) function (and thus of Engel curves) for the reference household, and the way household composition is modeled. (The latter decision includes deciding what type of household should be the reference household.) It is not necessary for these functional form assumptions to restrict the sign of dm/dU, but, in practice, most researchers have chosen specifications that directly or indirectly impose assumptions on the data about the relationship between m and the utility level. The oldest and most empirically tractable approach to the estimation of equivalence scales is to assume that two households with equal budget shares for food have equal welfare. Deaton and Muellbauer show that the assumption that equal budget shares means equal welfare implies that children have only income effects on their parents' consumption (or at least on their spending on food vs. other goods) (1980, pp. 193-195). The equivalence scale, m(U, a), can be interpreted as the number of Itadult equivalents" in the household. If an adult (the "reference person") demands food in the quantity qf = qf (y) , then the household demand for food is qhf = mqq,(y/m). The budget share for food (ignoring prices, which are assumed to be the same for s l f ~ = s t m . everyone) is Y ~ / m Thus households with equal budget shares have equal y/m, or I1income per adult equivalent." Suppose we seek to estimate qhf = mqf (y/m) from expenditure data. If we posit that m depends on family composition alone, we impose the assumption dm/dU = 0. If we allow m to depend on income as well, we can then test the assumption. In practice, most researchers have specified qhf = q(y,a) a priori, so that it is difficult to detect the assumptions they are imposing on m. For example, in Espenshade (1984), the study upon which the Williams report for OCSE is based, a quadratic Engel curve specification is used for the reference household, so that We would expect Espenshade to set where m = m(a,y). Instead, he uses where only the intercept is allowed to depend on family characteristics. If m = m(a), and does not depend on y, he would need to allow c, also to depend on family characteristics, for the model to be consistent. He is thus implicitly allowing m to depend on y.3 It is possible to calculate the formula for dm/dy.4 The only restriction on dm/dy that is obvious from the formula is that dm/dy = 0 if c, = 0. Other restrictions may be implicit. It seems preferable to choose a specification for m(a, y) directly so that one is only imposing the restrictions one wants to impose. The other widely used method for including household composition effects in demand functions was first suggested by Barten (1964). The two major studies that use the Barten method are Muellbauer (1977) and van der Gaag and Smolensky (1981). Each uses a different utility function specification. Muellbauerts estimated equivalence scales declined with rising income, whereas van der Gaag and Smolenskyls scales were the same over a wide range of income levels. The Barten method allows children to have both price and income effects, because it allows for goods-specific equivalence scales, which are then averaged to get an overall equivalence scale (so that the needs of children relative to adults may be larger for some goods than for others). While family purchases of goods that children need relatively more of will tend to increase to meet these needs, there is also an effect in the opposite direction. The adult decision-makers perceive goods that they have to share in larger proportions as relatively more expensive, so they tend to substitute away from these goods. If the good with a large good-specific equivalence scale also has a large enough own-price elasticity of demand (larger than one in absolute value), purchases of the good will actually decline when children are added to the household. This counterintuitive result has led many economists to believe that the Barten method allows children to have excessively large price effects. One implication is that if purchases of goods with high price elasticities increase with family size, then the estimates of the goods-specific equivalence scales will be implausibly low--and can even be negative (Deaton and Muellbauer, 1980, p. 200). It is not unusual for luxuries to have higher own-price elasticities than necessities. Muellbauer's PIGLOG utility function requires this to be the case (Muellbauer, 1977). Income and price elasticities tend to be roughly proportional for the linear expenditure system used by van der Gaag and Smolensky as well (Deaton and Muellbauer, 1980, p. 139). Luxuries will thus tend to have lower than average goods-specific equivalence scales. Because high-income households spend a larger proportion of their incomes on luxuries, the overall equivalence scale, m, will be lower for those households. Thus we find that the Barten specification implies dm/dy 5 0. The extent of this effect depends on the demand function specification, as well as on the data. The difference between Muellbauer's regressive results and van der Gaag and Smolensky's proportionality finding may result from the different specifications of the Engel curves in the two studies. In general, the estimation of household equivalence scales from expenditure data requires functional form assumptions. Most research in this area has not been concerned with the relationship between the costs of children and family income, and has thus imposed functional form restrictions that constrain this relationship. Espenshade's study (1984) is particularly ad hoc in its choice of functional form, and thus it is difficult to derive the precise restrictions it places on the relationship dm/dy. The Barten model of household equivalence scales imposes the assumption that the costs of children increase at a rate less than or equal to the increase in family income, and some results using this technique support proportionality. 11. EQUIVALENCE SCALES BASED ON SURVEY QUESTIONS ON FAMILY NEEDS Another branch of the literature attempts to measure family cost functions by directly asking people about their own family's needs. By comparing the answers of families of different sizes, we can make inferences about the costs of children. These methods, developed by a group of scholars in the Netherlands, have been widely used to develop measures of poverty in Europe (Hagenaars, 1986; van Praag, Goedhart, and Kapteyn, 1980; van Praag, Hagenaars, and van Weeran, 1982). One of these "directu or ltsubjectivell approaches starts by asking a random sample of the population of interest the minimum income question (MIQ). In the Wisconsin Basic Needs Study, the question was phrased as follows: Living where you do now and meeting the expenses you consider necessary, what would be the very smallest amount of income per month--after taxes--your household would need to make ends meet? In order to derive an equivalence scale, we regress people's answers on their current family income (using a linear regression in logs of the variables). We define the poverty line as the income at which the regression line crosses the 45 degree line, because someone at this income level would see his or her current income as just sufficient to make ends meet. Those below this poverty line say they need more income to make ends meet, while those above say they need less. A separate poverty line is calculated for each family size (by including the log of family size in the regression), and an equivalence scale is then constructed by comparing the poverty-level income for various family sizes (Goedhart et al., 1977). This equivalence scale applies only to those at the poverty line, as defined by this technique; there is no reason to assume costs of children would be proportional for those with middle or high incomes. The second of these 'lsubjectivell methods, known as the Welfare Function of Income (WFI), was devised by van Praag (1968). It involves asking the income evaluation question (IEQ), phrased as follows in our data set, the Wisconsin Basic Needs Study : I'm going to ask you to think about the amount of money per month--after taxes--that would make you feel terrible about your household's income; then we will work up to an amount that would make you feel deliqhted about your household's income. It may help if you look at this list with me while I ask the questions. Let's start at the top with terrible. How much money per month and after taxes would leave you feeling terrible about your householdls income? Now let's move to unhappv. As we move to each next level, each of your answers should be larger than the one before, of course. Amount