It may seem strange to some that economists feel they have something useful to say about the way in which family members relate to one another in the home. Concerned as they are with market transactions and the performance of industry, economists may appear too crass and heartless to deal with such fine and loving relationships. However, this view of the economist's proper role and area of con­cern is comparatively recent in origin. Economics began as the study of household activities. In fact, the word economics stems from the Greek oeconomia, meaning household management. Aristotle used a completely different word, chrematis-tike, to refer to the pursuit of gain in the market place, an activity which he quite despised.¹

Still, it is true that the economics developed since the eighteenth century has been particularly unsuited to the analysis of intrafamily activities, and it is only recently that extensions of the so-called classical and neoclassical traditions have enabled contemporary economists to tread this unfamiliar ground. There is the fundamental tenet of received economic theory, that the utility of each individual depends wholly on the goods and services that he or she consumes and not at all on what anyone else consumes. As the principle underlying Adam Smith's notion of the "invisible hand," this premise dates at least from the eighteenth century. However, its careful formalization and virtual sanctification are the works of the more recent neoclassical economists.

The assumption of utility independence has proved highly useful in analyzing a wide variety of market-related problems. Those who criticize the concept of "eco­nomic man" as being unrealistic or extreme, even when it allows of useful predic­tions of group behavior, would seem to have missed the point of positive inquiry.²

Nevertheless, economists have been reluctant to extend the model of market be­havior to cover the interaction among family members. The attitude of a wife toward her husband or of a father toward his child is thought to be essentially different from the egoism that characterizes "the consumer" in microeconomic theory.

As a means of skirting the issue, economic pedagogy does not distinguish be­tween "the consumer" and "the household." The two are treated as synonyms. "When economists speak of the consumer, they are in fact referring to the group of individuals composing the household."³

Whereas in the past this terminological convention amounted to an admission by economists that internal family behavior was outside their purview, some economists have now begun to advance the opposite view. It is argued that for many purposes, which include "nonmarket" decisions about family size, family location, education of children, and participation of different family members in the labor force, the family group does behave as if it were one person maximizing a single utility function.

Making this point, Robert Willis writes:

The family exists as an institution because, given altruism and the nonmarket mechanisms by which it is able to allocate commodities and welfare among its members, it has both the incentive and the capacity to resolve allocative prob­lems involving public goods, externalities, and the like that in impersonal markets inevitably lead to market imperfections. The capacity of the family to resolve these problems efficiently provides a basis for a positive theory of fam­ily behavior, because, given efficient allocation, the family will tend to respond systematically to changes in the position or shape of the constraints it faces.⁴

In other words, it is possible to combine all the individual and group consumption that goes on in the family unit into one "family consumption package" and, using economic theories designed for analyzing individual decisions, to make valid and useful statements about family activities.

At the same time, however, to extend the neoclassical notion of the household as a consistent decision-making unit, so that it covers realms of behavior pre­viously considered to be "noneconomic," as Willis and a number of his colleagues at the National Bureau of Economic Research have done, is not to illuminate the process by which group decisions are reached. Willis alludes to the efficacy of "altruism" within the family, and a few economists, prompted by family examples and also by observations of social welfare programs and private philanthropy, have begun to examine the implications of "love" and "charity" for the theory of consumer choice. One school posits a "family welfare function," grafted on the separate utility functions of the different family members.⁵ An alternative ap­proach extends the traditional theory of choice by making the consumption of one person an argument in the utility function of another: "... if M cares about F, M's utility would depend on the commodity consumption of F as well as on his own."⁶

Yet all existing versions of consumer theory may imply competition between any two individuals by attributing a unique utility function to each individual. If, in the extreme case of altruism, M and F are both saints, such that each would devote all of their combined resources to increasing the other's consumption level, it is not possible for both to be satisfied. They are competing to serve one another just as, in the simpler model, consumers compete to serve themselves. Thus the incorporation of altruism into utility theory does not tell us whose preferences among the members of a family are to be satisfied. When economists treat the household as a single decision-making unit, they are relying at this point on explanations from outside their discipline—on what Willis calls "the nonmarket mechanisms." We might imagine, as does J. Kenneth Galbraith in a recent article, a dominant husband/father imposing his will on the rest of the family,⁷ or picture a more democratic form of family politics.

II

We come now to a subtle but crucial distinction between traditional microeconomic theory and the theory upon which the economic analysis of most intrafamily behavior must rest.⁸ It has to do with the objects of human choice. The neoclas­sical model suggests that the consumer derives utility from the goods and services purchased in the market place out of money income. The critical "discovery," in what Gary S. Becker, an important progenitor and proponent, and others have called "the new home economics," is that market purchases seldom (if ever) contribute directly to satisfaction. They are, instead, inputs used in the production of primary items of satisfaction, which Becker calls "basic commodities."⁹ When an individual buys a book, what he desires and ultimately consumes is reading, or home decoration, or the appearance of intellectualism, or some combination of these. The book is a means to an end or, in the economist's language, an input in the production of some desired output or commodity.

However, the enjoyment of most (if not all) commodities requires that the con­sumer use his own time in addition to market purchases. Reading is a relatively time-intensive consumption activity, and what is more, there is little the individual can do to increase his output of reading without increasing proportionately his input of time. (He might enroll first in a speed-reading course, but this is an investment that presumably alters the productivity of his time spent in this activ­ity.) In the production of other commodities there is a wide choice of production techniques, which is to say that it is possible to substitute increasing amounts of purchased inputs for decreasing amounts of family time inputs. To enjoy a gour­met meal, it is possible, at one extreme, to purchase it at La Caravelle, using up only as much of one's own time as is necessary to ingest the food (without violat­ing the sensibilities of the chef or one's fellow patrons) or, at the other extreme, to spend the entire day at the produce markets and in the kitchen before sitting down to dine en famille.

The full cost of any commodity includes the cost of the purchased inputs plus the cost of the time used in production. The cost of the purchased inputs is, in principle, easy to figure, since each item was priced in the market. The cost of the time input presents more of a problem, since unlike the time spent in market employment, there is no explicit wage attached to the time spent in home employ­ment. In evaluating the time a person spends, say, cleaning the house, an econo­mist asks the question: What could have been produced in the best alternative use of this time? Assuming that market employment represents the most productive alternative, then the individual's potential market earnings serve as an indicator of what it costs the family to have that person cleaning the house. The foregone earnings (and this is equally true of the price of any purchased good) serve as a measure of what the family gives up.¹⁰

There are two variables especially that economists always have liked to ex­amine with regard to their effects on consumption. One is income, the other, price. Their effects are no less interesting in the new analysis of commodity con­sumption than they were in the older analysis of the demand for goods and ser­vices. We would expect that, other things being equal, a family with more income will be able to consume more of all commodities than a family with less income. At the very least, it will be able to afford more purchased inputs and, in this manner, increase the quantity of commodities produced. A family's decision with regard to the consumption of a particular commodity as income changes is an indicator of how highly it regards this commodity in relation to other commodities.

Given the level of family income, we would expect that the amount of a com­modity a family consumes will vary as the price of the commodity varies. For example, when the price of gasoline increases, the family can afford less transpor­tation. Similarly, if a wife's time becomes more valuable in the market, we might expect the family to choose to have fewer home-cooked gourmet meals and to substitute other inputs (husband's time or children's time or time-saving ma­chines) for her time in the production of the washing and the waxing. In other words, a family in which time inputs are costly would tend to favor commodities and production techniques that are relatively goods-intensive, whereas a family in which time inputs are cheap, meaning that the market opportunities are limited, would tend to favor commodities and production techniques that use relatively large amounts of family time.

III

To review our discussion thus far, we have seen that the economic theory for­mulated by the great economic thinkers of the past two hundred years was quite unsuited to the analysis of internal family behavior. However, recent develop­ments, which extend rather than supplant the traditional theory, give the econo­mist a firm foot in the family door. The family is viewed as a cohesive and consis­tent decision-making unit, which allocates the time of different family members in combination with purchased articles in order to produce desired commodities.

One such desired commodity is the raising of children. In fact, the basic human desire to raise one's own children helps to explain the ubiquity of the institution of marriage in different societies throughout the world.¹¹ Progeny are valued for the psychic income (utility) that they can be expected to yield over many years. As such, they may be called "consumer durables."¹² In poorer societies especially, children are valued as well for their productive services in the home, in the family fields, and for the money income that, it is hoped, they will earn and remit to their parents. As such, children qualify as "producer durables." In many countries, children are the sole source of old-age security, and where due to market imper­fections the rural-urban income differential is great for individuals of the same skill level, so that there is keen competition for urban jobs, parents often feel compelled to rear large families, "counting each child as another chance in the national lottery for [urban] wage employment."¹³

In analyzing parental behavior with regard to the raising of children, we must recognize the inextricable link that exists between a couple's fertility deci­sion (the number of children born) and what might be called in aggregative fashion "its nurturing decision" (the level of household resources expended per child). In other words, the single commodity, raising children, has both a quantity dimension and a quality dimension. The same is true of most other objects of human consumption. In the words of Becker: "For nearly all other consumer durables, such as cars, houses, or refrigerators, families purchase more units as well as better quality units at higher income levels, with the quantity income elas­ticity usually being small compared to the quality elasticity."¹⁴ This insight helps to explain the (positive but) very weak correlation observed cross-sectionally and over time between number of children and family wealth, other things, such as wife's market wage and birth-control knowledge, held constant (the simple corre­lation usually is found to be negative, that is, poorer families have more children). Thus with children as with automobiles, the response to a higher level of income is frequently to trade in the family Chevrolet for a Buick rather than to purchase a second Chevrolet.

As our discussion moves from the general theoretical framework that enables today's economist to analyze family behavior broadly defined to focusing on the family's educative role—the particular component of family behavior specified in our title—we necessarily lose sight of the many interrelated behavioral compo­nents. Most researchers who concentrate on the allocation of family (or societal) resources to the intellectual and physical development of children simply accept the number of children as "given," that is, as an exogenous variable. Clearly, it is not "a given" in the broader context of family (societal) decision-making. Econo­mists, no less than other social scientists, are willing to engage in partial analysis of this kind but, possessing a general theoretical framework, are able to recognize it as such.

IV

Having isolated the commodity, education, from the rest of the family's wants, what is the economist able to say about it? Like all other household commodities, education is produced by combining market inputs and family time. The public school movement in the United States, which shifted the burden of educational responsibility for children over the age of five from the family to the state, can be described in economic terms as a substitution of market inputs for parents' time (not for children's time, of which American schools have been unnecessarily wasteful, treating it as a "free good").¹⁵ A similar, though in most cases less com­plete, process of substitution has occurred historically with respect to a number of other household commodities, for example, the preparation of meals in which families have relied increasingly on precleaned, precut, precooked food inputs in order to save on family members' time. However, for children under the age of five, despite the growing availability of nursery schools and day-care facilities, education remains largely a home-produced commodity, consuming large quan­tities of family time.

The economic analysis of home production is not easily separated from the study of female labor force participation, a topic that Jacob Mincer at Columbia University pioneered in the context of time allocation theory three years before the appearance of Becker's celebrated article in which the approach was given a generalized formulation.¹⁶ In general, married women spend more time at non-market activities, especially at child care, and less time in the labor force than their husbands do. Contrary to the rhetoric of militant feminism, the explanation is not simply one of cultural inertia, although if one digs deeply enough, ascribed sex roles can probably be found to be at the root of the phenomenon. At the simplest level of economic decision-making, a family allocates members' time to different activities according to their relative productivity levels in each of the activities. If, perhaps as the result of more schooling and on-the-job experience, the husband's market wage rate is higher than the wife's, then there is incentive for the family to devote more of the husband's time to market employment or, put differently, more of the wife's time to home employment, even if the wife is no more productive than the husband in home employment. The cultural bias is reflected, not perhaps in the lower wage rate nor in the family decision that fol­lows from it, but in the fact that the woman has had less (marketable) human capital invested in her from the start. As indicated in a recent article by Mincer and Polachek, women spend less time in the labor force because they earn less, and they earn less because they spend less time in the labor force (and in school).¹⁷

Ceteris paribus, women with more education spend more time in the labor force (and less time in the home) than women with less education. The most thorough study to date of the relationship between these two variables is the Columbia University doctoral dissertation of Arleen Leibowitz.¹⁸ Leibowitz sup­ports the explanation "that education raises productivity in the labor market more than the productivity of time spent in home production, so that the 'cost' of not being in the labor force rises [with educational attainment]"¹⁹ However, her most interesting observation taken from United States census data is an exception to the above rule. The exception occurs between the ages of twenty-five and forty. During this time, the years when young children are in the home, better educated women spend no more time in the labor force than other women (and during these years all women spend less time in the labor force than immediately before or after, a gradual increase in labor force participation occurring when women are in their thirties and the children are growing up). Moreover, in another study using microlevel time-allocation data, Leibowitz demonstrates that women with more education actually spend more time at child care (and so do their husbands) than women with less education, despite the greater cost of their time as measured by foregone market earnings.²⁰

Apparently, child care differs from other home activities in one or more ways that are discernible in economic analysis. To verify the differences, Leibowitz runs separate regressions with which to compare the determinants of the wife's time (minutes over two days) devoted to four different categories of household work: meal preparation, laundering, physical care, and "other care" of children. The final category is of particular interest in the present context, as it was defined by the Cornell researchers who gathered the data, for a sample of some 1,300 fam­ilies, as "all activities related to the social and educational development of family members, such as: helping with lessons, reading to children, taking children to social and educational functions."²¹

Leibowitz finds weak support for the hypothesis that the amount of child care "purchased" (produced by combining market purchases and family time) is re­sponsive to changes in income, everything else (such as the price of purchased inputs and the cost of time) remaining the same.²² Leibowitz uses two proxies for family income, husband's education and the number of rooms per capita. The regression coefficients for these variables in the equation for wife's time supplied to "other care" of children are positive but not significant.

Husband's education is taken as a proxy for income because education is known to raise one's productivity in the market, that is, one's wage. The reader should note that a wife's education in the context of this research is not a proxy for family income but rather an indicator of the "price" of child care. That is, the cost of the wife's time devoted to this activity is her potential market wage, which the family gives up. If education affects productivity in home production as well as in market production, then the net effect of a wife's education on the use of her time is not predictable ex ante. The greater market productivity and the greater home productivity pull her in two directions. In Leibowitz' study, the net effect is found to be in the direction of child care, but the coefficient is not significant.

The most striking of Leibowitz' conclusions concerns differences in the avail­ability of effective substitutes for a woman's time at child care as opposed to substitutes for her time in other household work. As would be expected, the time given to laundering is much reduced by the presence of laundering machines in the house. In contrast, one is hard pressed to think of machines that can substitute for a mother's time in the production of child care, especially in the production of social and educational development.²³

Leibowitz analyzes as well the human substitutes for the mother's time. Whereas the "husband's time in meal preparation is a substitute (albeit a highly imperfect one!) for the wife's time,"²⁴ it appears that his time and her time are complementary in child care. Controlling for the family's expressed taste in child care, as well as for other variables identified a priori as determinants of  the wife's time input, the analysis shows that ten minutes of a husband's time given to child care is accompanied by an additional three to four minutes of a wife's time.

As for the time inputs of other persons, namely, older children, grandmothers, and sitters, these are found to substitute minimally for a wife's time, but only in the case of the less educated subsample of families when the sample is divided by wife's education into those with some college and those with none. Apparently, education increases the productivity of time spent at child care, and the more educated women find these other persons unacceptable substitutes in this activity. In a study that predates Leibowitz' and is less conclusive for our purposes, Hill and Stafford find that the presence of both a thirteen-seventeen year-old child and a three-four year-old child, holding constant the number of children in these and all other age categories, reduces the mother's time spent in household work for all (of three) SES groups defined in the study.²⁵ However, because household work is not broken down into its many productive categories, there is no way of telling whether the time of the older child is substituting for the mother's time in child care or only in other activities. Thus their finding is not necessarily inconsistent with Leibowitz', that college-educated women are generally unwilling to substi­tute the time of less educated persons for their own time in caring for young children.

In another study, Hill and Stafford happen upon a fascinating pattern in the time allocated to preschoolers according to sex of child and education of parents. Using a sample of families surveyed by the Institute of Social Research of the University of Michigan, they find, holding father's education constant, that women with at least some college education spend more time with their preschool daughters than with their preschool sons, whereas the reverse is true for women who have never attended college. In contrast, father's education appears to have no differential impact on the amount of family time devoted to boys and girls. They conclude that father's education, as a proxy for family income, is important in determining the level at which child care in general is produced within the home, whereas mother's education serves to influence the allocation of time inputs to child care by sex.²⁶

The preceding observations on home education, emanating mostly from the research of Arleen Leibowitz at Brown University and Frank Stafford and Russell Hill at the University of Michigan, have to do with the determinants of the inputs of family time allocated to this production activity. The remainder of our discus­sion will look at what economists have been able to say about the effects of home education on school achievement and on future earnings.

V

Most noteworthy about the emergent economic analysis of home education are the implications for social mobility in this country. We have noted in our sum­mary of Leibowitz' work that the more years of schooling a woman has com­pleted, the more time, on average, she spends with her children. This is true, in part, because the better educated woman is likely to come from wealthier parents and to marry a (potentially) wealthier man than is her less educated counterpart and, thus, can afford to devote more of her time to child care. Holding family wealth constant, however, we have seen that the more educated woman tends still to spend more time with her children, especially engaged in activities related to their educational and social development. We may infer that another reason for her giving more of her time to child care is that she is "better," that is, more productive, at it. Thus using the mother's education as an indicator of socioeconomic status, we may conclude that a child in a high SES group receives on average not only a greater input of the mother's time but a greater benefit per unit of mother's time than does a child in a low SES group.

As if the greater quantity and quality of the mother's time were not enough of an advantage, there is evidence of complementarity between mother's time and father's time in child care, with the result that the high SES child is likely to receive a greater input of the father's time as well. With home education, we may conclude that it never rains but it pours.

There is no shortage of evidence assembled by sociologists and economists alike demonstrating that there is significant covariance between the education of one or both parents and a child's success in school or in later life.²⁷ Until recently, howev­er, there was little understanding of the process by which parents' education con­tributed to the child's success. There are at least three hypotheses that explain the observed relationship. The first is the heritability argument, which states that the higher educational attainment of the parents and the greater success of the child are both the results of superior genetic traits that characterize the family. The second is a sociological explanation, that the more educated parents are able to exercise their greater social influence to the benefit of their children. The third, an economic hypothesis, asserts that the more educated parents are successful in endowing their children with greater knowledge and more skills, that is, with a larger investment in early human capital development.

We have already seen evidence that more educated parents spend more time per child at child care. However, to determine that this expenditure represents an investment in the child's development and not simply parental consumption, it is necessary to develop a model wherein the success of the child in school and in later life is expressed as a function of the quantity and quality of parental time inputs. Unfortunately, the required longitudinal data, which should span the pe­riod from birth to at least the age of thirty or forty years, are not readily available. The best economic study to date along these lines is provided again by Leibowitz.²⁸

In this study, Leibowitz must resort to a pair of dummy variables as the best available indicator of the quantity of time given to home instruction.²⁹ To indicate the quality of time inputs, she uses the schooling levels reached by mother and father. Although the sample is an exceedingly rarefied group, consisting entirely of men and women whose childhood IQ scores exceeded 140, which stratum represents the top 1 percent of the intelligence distribution, the conclusions are suggestive, nevertheless, and call for additional research in this area, as represen­tative longitudinal data become available.³⁰

The conclusions flow from measures of the partial effects of home education on three indicators of offspring success: IQ at a point in grade school, final schooling level (reported some thirty years later), and income (reported at three points in later life, corresponding roughly to ages thirty, forty, and fifty years). The model is a recursive system, wherein IQ is postulated to affect schooling attainment, and both IQ and schooling attainment are posited as contributors to income. The sample is partitioned by sex in all of the regressions. Although the model explains only a small proportion (less than 20 percent) of the variance in any of the three success indicators, it does underscore the importance of home educational invest­ments, at least as these affect male children.

The quantity of parental time inputs was found to be significantly related to a son's IQ score. The same was true of the mother's education, but not of the fa­ther's, which suggests that the relationship is one primarily of human capital pro­duction instead of heredity. Whereas the quantity of home educational inputs, as measured, was not found to affect schooling attainment, the quality of time inputs showed a significant impact on the final schooling level attained by both male and female children. Finally, although early home investments had no direct effect on income in later life, their indirect effect cannot be ignored in light of the strong, positive relationship between income and schooling, attested to in a host of recent economic studies³¹ and reconfirmed by Leibowitz.

Thus we find initial support for the proposition that the intergenerational transfer of socioeconomic status occurs, at least in part, through a process of investment in the early human capital of children. More educated parents spend more time with their children, and this expenditure "pays off" in the form of greater aptitude in school, which leads ultimately to greater economic success. Hill and Stafford find that religious affiliation, which, like parents' education, is a favorite choice of statisticians as an efficient "predictor" of income, is also closely related to preschool time inputs.³²

The policy implications of these findings concern ways of compensating for a paucity of home inputs, so that children of equal natural ability but coming from different socioeconomic backgrounds have the same opportunity for economic success. There are just two alternatives, broadly defined, that come to mind. The first is to provide compensatory inputs to children from deprived backgrounds once they enter the formal schooling system. This is the strategy that has received more attention in the United States, partly because the public role in the schools was already established and partly because the nature of social "deprivation" was not fully understood. However, by the time a child is five-years old, it may be too late to begin the process of equalization, which is to say that the costs of achieving this goal may be greater than society is willing to bear.

The second alternative is to provide additional inputs, both material and human, for a poor child from the day of birth (and before birth in the form of prenatal care). The preschool time inputs of parents can be supplemented by the time inputs of other adults, presumably the high quality time inputs of specially trained adults. Parents who have been deprived of adequate human capital invest­ment themselves from birth cannot impart the cognitive skills necessary for the scholastic and economic success of their children.

There may be, however, another dimension of quality, which is not the in­creased productivity that education imparts but rather the instinctive concern of parents for their own child. If this, too, contributes to a child's development, as we suspect it must, then it is imperative that public policy not undermine the family unit. We can imagine no institution that could substitute satisfactorily for the family on a full-time basis in the nurturing of children during the critical stages of infancy and early childhood.

The ideal educational policy, in the opinion of this writer, would provide con­venient access to remedial educational facilities for impoverished parents as well as their children. However, mere access to educational facilities does not insure their use. There can be little appreciation for the long-range benefits of education on the part of families struggling for survival from day to day. If an enriched environment is indicated for a child's healthy development, then in the opinion of this writer, the enrichment should begin in the home. Presumably, a way to achieve the more equal provision of early education is to achieve, as a first step, the more equal distribution of income among families.

ENDNOTES

1    See Robert L. Heilbroner. The Economic Problem. Englewood Cliffs, N.J.: Prentice-Hall, 1968, p. 34.

2   See Milton Friedman, "The Methodology of Positive Economics," in Milton Friedman, ed. Essays in Positive Economics. Chicago: Chicago University Press, 1953.

3   Richard G. Lipsey and Peter O. Steiner. Economics, 3rd ed. New York: Harper & Row, 1972, p. 52.

4   Robert J. Willis, "A New Approach to the Economic Theory of Fertility," in Theodore W. Schultz, ed. New Economic Approaches to Fertility, supplement to Journal of Political Economy, Vol. 81, No. 2, Part 2, March/April 1973, p. S19.

5   See Paul A. Samuelson, "Social Indifference Curves," Quarterly Journal of Economics, Vol. 70, February 1956, pp. 1-22.

6   Gary S. Becker, "A Theory of Marriage: Part II," in Theodore W. Schultz. Marriage, Family Human Capital, and Fertility," supplement to Journal of Political Economy, Vol. 82, No. 2, Part 2, March/April 1974, p. S12.

7   John Kenneth Galbraith, "The Economics of the American Housewife," The Atlantic Monthly, August 1973, pp. 78-83.

8   I am grateful to Charles Skoro for textual and organizational suggestions that contribute enor­mously to the clarity of the following section.

9   Gary S. Becker, "A Theory of the Allocation of Time," The Economic Journal, Vol. 75, No. 299, September 1965, pp. 493-517.

10   Naturally, the potential wage may differ, not only for different family members, but also for any one family member at different times of the day (9 to 5 o'clock versus off hours) and days of the week (weekdays versus weekends). Becker, "A Theory of the Allocation of Time," op. cit. Because of this and other serious problems of measurement, housework is not even included in the official statistics of national production; moreover, the neoclassical model distinguishes only between "work" (that is, market time) and "leisure." Condemned to Doll's House status by these conven­tions of traditional economics are millions of American housewives who devote none of their time to market employment.

11    Gary S. Becker, "A Theory of Marriage: Part I," Journal of Political Economy, Vol. 81, No. 4, July/ August 1973, pp. 813-846.

12   Becker was the first to place children in this category, defined by the social accountants: Gary S. Becker, "An Economic Analysis of Fertility Behavior," in Universities-National Bureau Con­ference Series 11. Demographic and Economic Change in Developed Countries. Princeton, N.J.: Princeton University Press, 1960. For a demographer's angry reaction, see Judith Blake, "Are Babies Consumer Durables? A Critique of the Economic Theory of Reproductive Motivation," Population Studies, Vol. 22, March 1968, pp. 5-25.

13   Peter R. Moock, "Managerial Ability in Small-Farm Production: An Analysis of Maize Yields in the Vihiga Division of Kenya," unpublished Ph.D. dissertation, Teachers College, Columbia Uni­versity, New York, 1973, p. 30.

14   Becker, "An Economic Analysis of Fertility Behavior," op. cit., p. 212. See also Gary S. Becker and H. Gregg Lewis, "On the Interaction Between Quantity and Quality of Children," in Schultz, New Economic Approaches to Fertility, op. cit., pp. S279-S288.

15   Harold Noah points out to me that the public school movement was simply the culmination of a long and gradual process of substitution. Earlier examples of substitutes for parents' time include private tutors, dame schools, church schools, and private commercial and charity schools. See Lawrence A. Cremin. American Education: The Colonial Experience, 1607-1783, Vol. 1. New York: Harper & Row, 1970.

16   Jacob Mincer, "Labor Force Participation of Married Women: A Study of Labor Supply," in Universities-National Bureau Conference Series 14. Aspects of Labor Economics. Princeton, N. J.: Princeton University Press, 1962; Becker, "A Theory of the Allocation of Time," op. cit.

17   Jacob Mincer and Solomon Polachek, "Family Investments in Human Capital: Earnings of Women," in Schultz, Marriage, Family Human Capital, and Fertility, op. cit., pp. S76-S108.

18   Arleen Leibowitz, "Women's Allocation of Time to Market and Non-Market Activities: Differences by Education," unpublished Ph.D. dissertation, Columbia University, New York, 1972.

19   Arleen Leibowitz, "Education and the Allocation of Women's Time," unpublished paper, 1973, p. 3. (A version of this paper is scheduled for publication in F. Thomas Juster, ed. Education, Income and Human Behavior. New York: National Bureau of Economic Research, 1974.)

20   Arleen Leibowitz, "Education and Home Production," American Economic Review, Vol. 64, No. 2, May 1974, pp. 243-250.

21    Ibid., Table 1, p. 245.

22   In technical language, Leibowitz finds that there is positive income elasticity of demand for child care. Her hypothesis was that this elasticity would be greater than those for other household activities, but the data are not conclusive on this point.

23   Television, given Sesame Street and other out-of-the-ordinary programming, may be one. How­ever, many purchased inputs, such as books and educational toys, in order to have their intended impact may require actually an additional input of time. That is, they may complement mother's time, rather than substitute for it.

24   Leibowitz, "Education and Home Production," op. cit., p. 246. The regression shows that ten minutes of the husband's time in meal preparation reduces the wife's time by only five minutes; hence Leibowitz' conclusion that the substitution is far from perfect.

25   C. Russell Hill and Frank P. Stafford, "The Allocation of Time to Children and Educational Opportunity," paper presented at the Econometric Society Meetings, New Orleans, December

1971. (A version of this paper is scheduled for application in the Journal of Human Resources, 1974.)

26   C. Russell Hill and Frank P. Stafford, "Time Inputs to Children," in James N. Morgan, ed. 5000 American Families—Patterns of Economic Progress, Vol. 2. Ann Arbor, Mich.: Institute of So­cial Research, 1974.

27   See, for example, James S. Coleman et al. Equality of Educational Opportunity. Washington, D.C.: U.S. Government Printing Office, 1966; Samuel Bowles, "Schooling and Inequality from Generation to Generation," in Theodore W. Schultz, ed. Investment in Education: The Equity-Efficiency Quandary, supplement to Journal of Political Economy, Vol. 80, No. 3, Part 2, May/ June 1972, pp. S219-S251.

28   Arleen Leibowitz,"Home Investments in Children," in Schultz, Marriage, Family Human Capi­tal, and Fertility, op. cit., pp. S111-S131.

29   A dummy variable is one with just two values, a "yes" value, which by convention is given the numerical equivalent of one, and a "no" value, given the equivalent of zero. In this study, the first variable is defined by the parents' having spent a "considerable number of hours, but chiefly reading, telling stories, and writing," the second variable by there having been "an appreciable amount of instruction along particular lines." Individuals who score one on the second variable may be said to have had much home education; those who score one on the first variable to have had an intermediate amount of home education; those who score one on neither variable, to have had "no instruction, other than the usual amount of reading and telling stories." Ibid., p. S116.

30   The data were collected from 1921 under the direction of Lewis M. Terman, a Stanford Univer­sity psychologist.

31 See, for example, Giora Hanoch, "An Economic Analysis of Earnings and Schooling," Journal of Human Resources, Vol. 2, No. 3, Summer 1967, pp. 310-329; Daniel C. Rogers, "Private Rates of Return to Education in the U.S.: A Case Study," Yale Economic Essays, Spring 1969, pp. 89-134.

32   Hill and Stafford, "Time Inputs to Children," op. cit.