Child Endowments, and the Quantity and Quality of Children

Abstract

Introductionrn an earl ie.r paper, Becker and Lewis explained why the quantity and quality of children (and, by extension, of riany other commodities) are more closely related than are any two commodities chosen at random, without assuming that substitution in consumption between quantity and quality is greater than average. It is sufficient to recognize than an Increase In the quantity of children raises the cost or shadow price of the quality of children, and vice versa. This was used to explain, among other things, why the observed Income elasticity of demand for quality of children is high at the same time that the observed quantity elasticity is low and often even negative.As part of a more recent paper on social interactions,1 Becker discussed some other determinants of the demand for quality of children. These include the preferences of parents with regard to their own consumption relative to that of their children, public expenditures on schooling, and genetic inheritance.Becker shows that "social interactions" can also explain the high observed income elasticity of demand for quality of children.This paper brings together and integrates social interactions and the special relation between quantity and quality. We are able to show that the observed quality income elasticity would be relatively high and the quantity e1astcity relatively low and sometimes negative, even if the true "unobserved" Income elasticities for quantity and quality were equal and of average value.Moreover, the observed quality elasticity would fall, and the observed quantity elasticity would rise, as parental income rose. These and related results on the relation of, observed quantity and quality Income elasticities to social 2 mobility and economic growth are discussed in Section 2.Section 3 drops the assumption made in Section 2 that all children are of equal quality, and considers differences in endowment and quality. It analyzes how parental expenditures are related to their children's endowment: in particular, whether better endowments are reinforced or poorer endowments are compensated.It explores the resulting biases in estimates of rates of return on investments In human capital, and in estimates of the direct effect of family background on earnings. It also shows why compensatory education programs may appear to "fail," even when the children being "compensated" were as able and well motivated as other children.2. Interaction between the Quantity and Quality of Children2We assume in this section that each household has a utility function of the following form U -U(n, w, y), (2.1) where n Is the number of children, w the quality of each child, and y the aggregate amount of all other commodities. By saying "the" quality we have introduced the assumption that the quality of each child Is the same. This quality Is partly controlled by the household through its expenditures on children, and Is partly outside its control because inherited ability,3 public investments in children, "luck" and other variables also affect quality. ...

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“…According to the quality-quantity trade off models of household production parents maximize a one period utility as a function of number of children, quality of children, a composite consumption good and the leisure of household members subject to income and time constraints for the household members and the production functions (Becker, 1965;Becker and Lewis, 1973;Becker and Tomes, 1976;1979;and Becker, 1991). Optimization results in a set of reduced form household demand equations for the number of children, children's education, consumption good, leisure and the derived demand equations for the market goods and the labor force participation.…”

The Incentive Effects of Higher Education Subsidies on Student Effort

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“…Policymakers in developing countries, including a number in Latin America, have often advocated policies promoting smaller families as a way of improving human capital accumulation and economic development. Though the quantity-quality model suggests that this type of policy is likely to be effective -since as quantity (number of children) rises, the total cost of quality (investment into children) also rises, thus decreasing the demand for quality (Becker 1960;Becker and Lewis 1973;Becker and Tomes 1976) -other fields such as psychology suggest that large families may be advantageous for children's human capital due to the potentially beneficial effects of children on each other's development (Zajonc 1976). …”