This PDF is a selection from an out-of-print volume from the NationalBureau of Economic Research

Volume Title: Economics of the Family: Marriage, Children, and HumanCapital

Volume Author/Editor: Theodore W. Schultz, ed.

Volume Publisher: University of Chicago Press

Volume ISBN: 0-226-74085-4

Volume URL: http://www.nber.org/books/schu74-1

Publication Date: 1974

Chapter Title: Education and the Derived Demand for Children

Chapter Author: Robert T. Michael

Chapter URL: http://www.nber.org/chapters/c2965

Chapter pages in book: (p. 120 - 159)

Education and the DerivedDemand for Children

DERIVED DEMAND FOR CHI

Princeton University. Theformal model with precise,explore channels of influen(

II. The Theoretical

Robert T. MichaelUniversity of California, Los Angeles, and National Bureau of Economic Research

I. IntroductionA negative correlation across households between parent's education andcompleted fertility is one of the most widely and frequently observed rela-tionships in the empirical literature on human fertility behavior. In thispaper I utilize the emerging economic theory of household behavior, whichis also employed in other papers in this volume, to formulate an ex-planation for this observed negative correlation. In particular, the paperhas two objectives: (1) to consider the mechanisms through which acouple's level of education might affect their fertility and (2) to documentthe effects of education on one of these mechanisms that is an aspect offertility control—the choice of a contraceptive technique.

The following section briefly outlines the theoretical framework, and inSection III I discuss the mechanisms through which education's influencemay operate. Throughout, the discussion is restricted to channels ofinfluence from education to fertility; that is, the reverse causation is ruledout by assumption. The specific focus of this discussion should not beinterpreted as an assertion of the exclusiveness or the primacy of educa-tion's influence on fertility. Section IV considers the fertility-control de-dsion in greater detail. It also reports on my initial empirical work withthe 1965 National Fertility Study, a nationwide sociological survey of5,600 U.S. women undertaken by the Office of Research at

I would like to thank Gary S. Becker, Barry R. Chiswick, Victor R. Fuchs,Reuben Gronau, Michael Grossman, Edward P. Lazear, Jacob Mincer, Norman B.Ryder, T. W. Schultz, T. Paul Schultz, and Robert J. Willis for constructive sugges-tions on this project, and Anne 0. Stevens for her able research assistance. MargaretG. Reid's discussion of an earlier draft has been helpful to me. I would like also tothank the Office of Population Research at Princeton University and Professor CharlesF. Westoff in particular for making available to me data tapes from the 1965National Fertility Survey. My work has been supported by a grant from the FordFoundation to the National Bureau of Economic Research for study of the economicsof population.

120

To delineate mechanisms tfertility behavior requiresanalyzed. Since thewhich the analysis takesmechanisms emphasized. Ihavior emerging from pionby Becker (1960, 1965) ain predicting broaddimensions of fertility. Sindevelop specific and detaiexposition to a few particu

i) An Analytical FranzewAssume the household h

where is the amountwhere each commodity inproduction function

where represents purcmember's time used infeature of these commoinseparable; thus, theseholds.

The household is assuduction-function constrstraint,

ap4,

x4tt=1 4=1 —1--r,

and a time-budget const

DERIVED DEMAND FOR CHILDREN 121

Princeton University. The paper does not attempt to set out an explicit,formal model with precise, testable implications, but rather attempts toexplore channels of influence in a relatively flexible analytical context.

IL The Theoretical Considerations

weau of Economic Research

en parent's education andI frequently observed rela-fertility behavior. In thishousehold behavior, whichme, to formulate an ex-

In particular, the paperianisms through which aility and (2) to documentisms that is an aspect of:hnique.retical framework, and inhich education's influencerestricted to channels ofreverse causation is ruleddiscussion should not beor the primacy of educa-s the fertility-control de-itial empirical work withle sociological survey of

Research at

Chiswick, Victor R. Fuchs,Jacob Mincer, Norman B.

iillis for constructive sugges-research assistance. Margaretto me. I would like also to

versity and Professor Charlesdata tapes from the 1965by a grant from the Fordfor study of the economics

To delineate mechanisms through which a couple's education affects theirfertility behavior requires a framework in which that behavior can beanalyzed. Since the choice of a framework determines the structure inwhich the analysis takes place, it thereby influences the nature of themechanisms emphasized. Fortunately, the theory of human fertility be-havior emerging from pioneering work on a theory of household behaviorby Becker (1960, 1965) and Mincer (1962a, 1963) is clearly useful bothin predicting broad patterns of completed fertility and in analyzing otherdimensions of fertility. Since other studies reported herein, notably Willis's,develop specific and detailed versions of this model, I intend to limit myexposition to a few particular points.

1) An Analytical FrameworkAssume the household has the intertemporal utility function

U = . . . , t = 1, . . . , (1)

where is the amount of the commodity i consumed in period t andwhere each commodity in each period is produced according to a householdproduction function

= Ti,), (2)

where Xj represents purchased market goods and T1, is the jth householdmember's time used in the production and enjoyment of An essentialfeature of these commodities is that their production and enjoyment areinseparable; thus, these commodities cannot be exchanged among house-holds.

The household is assumed to maximize equation (1) subject to the pro-duction-function constraints as in equation (2), a money-income con-straint,

A

_______

rt=i (1 +r)t = t j [(1 +r)t +

(1 +r)n]'

and a time-budget constraint,

T

(3)

for all j, (4)

122 ROBERT T. MICI-IAEL

where i is an index over the n commodities, j is an index over the adult'family members, r is the household's rate of time discount, is the marketprice of good W is the real wage rate of individual .1, is the timespent at work by individual 3, is the property income of individual 3, and

T is the total time available to each individual per period.In applying this typical representation of the household production-

function model to the household's fertility behavior, we consider two of theproduction processes in equation (2) more explicitly. The analysis will befor a single period of time. First, assume that one of the commodities, sayZ1, is "family life" and is related to the stream of satisfaction obtainedfrom the couple's offspring. More specifically, for a single time peripd

= f1(x1, T,,, C), (5)

where x1 and T1, are the goods and the adult's own time, which are com-bined with a flow of "child services," C, to produce the stream Z,, whichenters the household's utility function. The C, then, is an intermediateproduct used in J' and is itself produced from the quality-adjusted stock ofchildren in the household.

It will be assumed that C is proportional to the number of offspring inthe household, N:

C=aN (6)

where the factor of proportionality varies across households but is assumedto be constant among children within a given household. The N is a stockof offspring or children, and C is a flow of services per unit of time. Theterm a therefore indicates the rate of flow per unit of the stock. The"quality" of the household's children is then defined to be monotonicallyrelated to a, Q = F(a), 1'> 0, and although a can in principle beobjectively determined, the scaling of Q is arbitrary. The productionfunction for Q is assumed to be

Q=T and and e represents

the household environment to which the child is exposed. This lattervariable will be discussed more extensively below.

A second commodity in the utility function which is analytically relatedto the level of N (the household's number of children) is the commodity"sexual gratification." This commodity, designated as is also producedby one of the household production functions in equation (2) using bothpurchased inputs and the couple's own time. The relationship betweenand N results from the effects of the level of production of upon theprice of acquiring a unit of N. Abstracting from the uncertainties associatedwith the acquisition by a consumer of any durable good, "children" as adurable good is subject to a rather unique risk: the uncertainty of con-

PH

DERIVED DEMAND FOR CHI

ception. Given a positiveexposed to a positiveby the couple's age,The couple may expendlower) this probability. Ttime, will be treated as th

where F is the couple'sand there is evidence sugthe probability of concepgiven level of Z2 and F:

GZ2,F

wherellp is the price ofwould exist at the given Ithe level of P. For examper month, but with an emethod, the couple mayception, P, to .05. Similand a given (low) levelequal to .10, but by an eof their own time in folto, say, .25. Since G, thnegative, flp is negativexpending resources to lo

In the case of contracepflects the fact that the i

1 Potter, Sagi, and Westofiception during the intervalunder twice, to twice, to thia conception fell from 11,0and Gold (1953, p. 29) fouiand the time required forthat the percentage ofwith coital frequency. Fortfrom less than twice a weejor more times a week, theconclude "The frequencyconception, no matter whaof the expected effects ofmathematical model of bi,Although the commoditythe two are positively rela

ROBERT T. MICHAEL IDERIVED DEMAND FOR CHILDREN 123

ception. Given a positive level of production of Z2, a fecund couple isexposed to a positive probability of conception. That probability is affectedby the couple's age, fecundity at each given age, and its coital frequency.The couple may expend resources of time and money to alter (raise orlower) this probability. Thus P, the probability of a conception per unit oftime, will be treated as the outcome of a distinct production process:

P = Z2,F), (8)

where F is the couple's unadjusted fecundity. By definition, t9P/OF > 0,and there is evidence suggesting > The direct expenditure onthe probability of conception, G, will be defined as the expenditure at agiven level of Z2 and F:

G = — P*) + TPPT, (9)Z2,F

whereflp is the price of a unit change in P and is the level of P whichwould exist at the given levels of Z2 and F if no effort were made to affectthe level of P. For example, for a fecund couple, P" may be equal to 0.20per month, but with an expenditure of money and time on a contraceptivemethod, the couple may be able to lower its monthly probability of con-ception, P, to .05. Similarly, a subfecund couple with a given level of Z2and a given (low) level of F may have a monthly birth probability, Pa',equal to .10, but by an expenditure on medical advice and the use of someof their own time in following that advice, they may be able to raise Pto, say, .25. Since G, the total expenditure on the probability P, is non-negative, fl p is negative or positive, depending on whether the couple isexpending resources to lower P below or to raise P above

(10)

In the case of contraception, the negative price of a unit of P simply re-flects the fact that the intermediate good being produced is a reduction in

is an index over the adultdiscount, is the market

lividual j, is the timeincome of individual j, and

per period.household production-

ior, we consider two of thecitly. The analysis will be

of the commodities, sayof satisfaction obtained

r a single time period

(5)

own time, which are com-luce the stream Zi, which

then, is an intermediatequality-adjusted stock of

number of offspring in

(6)

households but is assumedusehold. The N is a stockces per unit of time. Ther unit of the stock. Thefined to be monotonicallyh a can in principle berbitrary. The production

(7)

wn time and e representsis exposed. This latter

ich is analytically relatedidren) is the commodity

as is also producedequation (2) using bothrelationship between

oduction of Z2 upon thee uncertainties associatedle good, "children" as athe uncertainty of con-

1 Potter, Sagi, and Westoff (1962, p. 5 4) indicate that, for couples using no contra-ception during the interval prior to the first pregnancy, as coital frequency rose fromunder twice, to twice, to three or more times per week, the mean period required fora conception fell from 11.0 months, to 7.1 months, to 6.6 months. Earlier, MacLeodand Gold (1953, p. 29) found a strong positive relationship between coital frequencyand the time required for conception. Using husband's age-specific data, they foundthat the percentage of couples with conception occurring in less than 6 months rosewith coital frequency. For example, for husbanth under age 25, as frequency rosefrom less than twice a week, to two to three times, to three to four times, to fouror more times a week, the percentages rose from 37.5, to 70.6, to 83.9, to 94.6. Theyconclude: "The frequency of intercourse is a strong determining factor in ease ofconception, no matter what the age of the husband" (p. 29). For a brief statementof the expected effects of differences in coital frequency on childbearing, in a simplemathematical model of births as a perpetual renewal process, see Keyfitz (1971).Although the commodity Z2 is not defined exclusively in terms of coital frequency,the two are positively related, so the evidence cited here suggests dP/dZ., > 0.

[.

124 ROBERT T. MICHAEL

P; that is, Xp and have negative marginal products in since they areused in an effort to reduce P.

Given an appropriately explicit set of assumptions about the nature ofthe household production functions, cost curves, and utility function, wecan specify a relatively complete model of household fertility behavior. Thedecisions to construct such a model in a static or in a dynamic frameworkand to suppress or to include any particular production relationship (suchas the production of Z2), any intermediate stage of production (such asthe production of Q), or any simultaneous or joint production (such asthe relationship between Z2 and P) depend, of course, upon the specificpurpose of the analysis. The household production function framework it-self is not wedded to any particular formulation. At one level, it simplyprovides a means by which the complexities of observed fertility behaviorcan be sorted out and an economic language in which the various inter-relationships can be discussed.

ii) The Fertility-Control DecisionTo illustrate an application of this framework, consider the family's de-cision regarding fertility control. It will be assumed for now that the de-cision makers suffer from a particular type of myopia: specifically, althoughthey consider long-run repercussions of their fertility-control decision interms of future costs and benefits of children, they do not make long-runfertility-control plans. Thus, the assumption is that the couple does notdetermine an optimal fertility-control strategy: in each period an inde-pendent decision is made with respect to fertility control.

The first stage in the fertility-control decision is the determination ofthe net benefit from an additional child. The net benefit, B, is computedfrom the stream of costs and benefits attributable to the child over time:it may be positive or negative (see Appendix). The term B is function-ally related to all the arguments in the completed-fertility demand func-tion and simply represents the household's effective excess demand forchildren at the prices, income level, level of production of complementsand substitutes, and so on, which are implicit in the calculation of B. If Bis positive, the household's excess demand for children is positive and thecouple may seek to raise their probability of conception. If, on the otherhand, B is negative, the couple may engage in fertility control.2

2 It was pointed out above that the level of production of Z.. is positively re'ated tothe probability of conception P. If the first-order condition for the optimal level ofproduction of Z0 is considered (see Appendix):

f .9NäP

where B is defined as in (A4) and 11., is the direct marginal ccst of Z2. So the shadowprice of Z2 in a given period, is equal to the term in parentheses above. Sinceboth derivatives in the above equation are positive, the shadow price of Z2 is higherthan its direct marginal cost when B is negative. That is, when the net benefit from

Furthermore, it isthe total Cost to the iiP. This cost curve isand coital frequencythese two monetarygiven period can be defunctions for a couple weducation, parityfertility demand. If thcurrent parity is two, tiland marginal benefit ofat a level P1. Since B1stead, the same paresperhaps their B = B2.control up to the pointbenefit functions (P2 II

ifi. Channels of IThe household ismoney-wealth constrail

an additional child is negaits direct cost, and symmeis lower than the direct casee Grossman fi9711). Iceffective demand for Z0 (duction) in the latterof Z2.

DERIVED DEMAND FOR

in since they are

tions about the nature ofand utility function, we

dd fertility behavior. Thein a dynamic frameworkuction relationship (suche of production (such asolnt production (such ascourse, upon the specificn function framework it-• At one level, it simplybserved fertility behaviorwhich the various inter-

:onsider the family's de-led for now that the de-)ia: specifically, although'tility-control decision in

do not make long-runhat the couple does notin each period an inde-control.is the determination ofbenefit, B, is computedto the child over time:

['he term B is function-d-fertility demand func-tive excess demand forduction of complementste calculation of B. If Bdren is positive and theeption. If, on the otherility control.2

d is positively related toon for the optimal level of

112) =0,

I cest of Z.). So the shadowin parentheses above. Sinceadow price of Z2 is higherwhen the net benefit from

Furthermore, it is assumed that there is a cost function G representingthe total cost to the household of producing various levels of the probabilityP. This cost curve is presumably functionally related to the parents' ageand coital frequency and their religion and level of education. Thus, fromthese two monetary relationships, B and G, the optimal level of P for agiven period can be determined. Figure 1 depicts hypothetical G and Bfunctions for a couple with a specific age, level of production of Z2, religion,education, parity (current number of children), and effective completed-fertility demand. If the parents demand, say, four children and theircurrent parity is two, then perhaps B = B1. In this case, the marginal costand marginal benefit of altering the probability of conception are equatedat a level P5. Since B1 > 0, the couple would produce a P> If, in-stead, the same parents' current parity were, say, five children, thenperhaps their B = B2. In this case, the couple would engage in fertilitycontrol up to the point of equality between the marginal-cost and marginal-benefit functions (P2 in fig. 1). Thus, when 0.

ifi. Channels of InfluenceThe household is viewed as maximizing a utility function subject to amoney-wealth constraint, a time constraint for each adult, and a set of

an additional child is negative, the shadow price of sexual gratification is higher thanits direct cost, and symmetrically, when the net benefit is positive, the shadow priceis lower than the direct cost (for an extended discussion of this joint production issue,see Grossman [19711). In the former case the household is induced to reduce itseffective demand for Z9 (or to substitute toward less coitus-intensive means of pro-duction) in the latter case the household is induced to increase the quantity demandedof Z2.

ROBERT T. MICHAEL DERIVED DEMAND FOR CHILDREN 125

P/mo.

FIc. 1

B,N,

126 ROBERT T. MICHAELI DERIVED DEMAND FOR C

household production functions. By definition, the parents' education levelmay influence their fertility behavior by affecting any of these four rela-tionships.

Before these relationships are discussed, the term "education," which isso frequently used to mean so many different things, needs defining. Anindividual attends school for a period of time, and the "number of years ofschooling," S, is an objectively quantifiable number. As a product or out-come of that schooling, knowledge and physical and mental skills areacquired. The accumulated stock of knowledge and the acquired physicaland mental skills constitute productive human capital. These stocks ofknowledge and skills acquired from schooling are here defined as "educa-tion." Thus, education is human capital, but education does not necessarilyrepresent the individual's entire stock of human capital, since this capitalmay also be acquired from activities other than schooling.3 While educa-tion is analytically a particular portion of one's stock of human capital,empirically it is generally measured by years of schooling completed. Ourtheories indicate how human capital, E, might affect behavior, but weinvestigate how years of schooling, S, are correlated with observed be-havior.

i) The Utility FunctionEconomists have neither developed for themselves nor had available fromother behavioral sciences a viable theory about the formation of preferencesor the determinants of "tastes." Schooling represents exposure to a differ-entiated type of experience. If experience influences preferences, theneducation may affect preferences in some as yet unspecified manner. Econo-mists have dealt with the implications of differences in, say, risk or timepreferences,4 but until a theory of the formation of preferences is available,little can be said, a priori, about the relationship between education andtastes or about the possible influence of education on the preferencefunction.

ii) The Wealth ConstraintThe influence of education on fertility through the money-wealth con-straint has been much explored. The other papers in this volume focuspredominantly upon the effects on completed fertility of differences in

3 For an important attempt to distinguish operationally between schooling, educa-tion, and human capital, see Welch (1966). For a thorough discussion of the conceptof health capital, see Grossman (1972b).

4 If the evidence on average rates of return to successive levels of schooling (seeT. W. Schultz [1972a]) reflects differential marginal rates of time discount byeducation level, then the higher one's education, the longer one's time horizon. Alonger time horizon, however, may simply reflect consideration of longer-run effectsor the absence of myopia, and if so, it might be treated as an effect on long-runproduction functions rather than as a "taste" phenomenon. For the effects of educationon money savings behavior and attitudes toward savings objectives, see Solmon(1974).

(1) levels of wealth andof the strong accumulatiture of the effects of schcchannel of influence isone's earnings capacity, iraise one's full money mcprices of children and ciwell as the changes in wihousehold demands.quantity of Zpends upon the nature aC, and between C and Z1

In addition to pure mcthe marginal time valuefor an individualeffect of an increasechildren depends upongoods and finalof a change in thedepends upon itsfertility, it is generallyis relatively intensive iaraise the price ofhaps the key economicbetween the wife'sIt should be evident thmediate product N whiQ and of Z1. The timetives to substitute in thtime intensity of Z1 ibetween commodities.

Differences in thehigher the husband'sthe greater is his incewhich are intensive intion uses relatively lit,production falls as hisN (and perhaps Z1)explain the observedmore negatively relatesectional regressions onhusband's income andeffect of the former veffect, since the incre

ROBERT T. MICHAEL DERIVED DEMAND FOR CHILDREN 127

e parents' education levelg any of these four rela-

rm "education," which isneeds defining. An

I the "number of years of)er. As a product or out-

and mental skills arend the acquired physicalcapital. These stocks ofhere defined as "educa-

ation does not necessarilycapital, since this capitalschooling.3 While educa-stock of human capital,chooling completed. Ouraffect behavior, but welated with observed be-

nor had available fromformation of preferencesnts exposure to a differ-ences preferences, thenpecified manner. Econo-es in, say, risk or timepreferences is available,between education and

tion on the preference

the money-wealth con-s in this volume focustility of differences in

between schooling, educa-discussion of the concept

levels of schooling (seetea of time discount byger one's time horizon. Aation of longer-run effects

as an effect on long-runor the effects of educationB objectives, see Solmon

(1) levels of wealth and (2) value of time of household members. In lightof the strong accumulated evidence reported in the human-capital litera-ture of the effects of schooling on wage rates and thus money income, thischannel of influence is well established. Investments in education enhanceone's earnings capacity, increase one's time value in the labor market, andraise one's full money income. These changes may in turn affect the relativeprices of children and child services, and these relative price changes (aswell as the changes in wealth) may alter the quantity of child services thehousehold demands. Given an effect of a "pure" income change on thequantity of Z demanded, the effect on the derived demand for N or Q de-

pends upon the nature of the production relationships between N, Q, and

C, and between C and Z1.In addition to pure income effects from an increase in market wage

the marginal time value or the "price of time" also rises with the wage ratefor an individual optimally allocating time to the labor market. Theeffect of an increase in the price of time on the derived demand forchildren depends upon its effects on the relative prices of intermediategoods and final commodities. As Becker (1965) has emphasized, the effectof a change in the price of time on the relative price of a commoditydepends upon its time intensity. In the current literature on humanfertility, it is generally assumed that children or child-related consumptionis relatively intensive in the wife's time. Thus, increases in her time valueraise the price of children and lower the quantity demanded. This is per-haps the key economic explanation for the observed negative relationshipbetween the wife's education level and the (completed) number of children.It should be evident that it is not simply the time intensity of the inter-mediate product N which is relevant here, but also the time intensity ofQ and of Z1. The time intensity of N relative to Q determines the incen-tives to substitute in the production of child services, C, while the relativetime intensity of Z1 influences the induced substitution in consumptionbetween commodities.

Differences in the value of time of the husband also affect fertility. Thehigher the husband's education level, the higher is his time value and thusthe greater is his incentive to substitute away from nonmarket activitieswhich are intensive in his time. If, as is frequently assumed, child produc-tion uses relatively little of his time, the relative price of child-relatedproduction falls as his time value rises. This induced substitution towardN (and perhaps Z1) as the value of the husband's time rises can helpexplain the observed phenomenon that the wife's education is generallymore negatively related to fertility than is his. Furthermore, in cross-sectional regressions on number of children with two variables representinghusband's income and value of wife's time, the often-observed positiveeffect of the former variable cannot be interpreted as a "pure" incomeeffect, since the increase in the husband's wage rate induces substitution

128 ROBERT T. MICHAEL

toward the production of children. So the parents' levels of education mayaffect their fertility behavior by raising income and the value of theirtime. In addition, there are other, somewhat more subtle, effects onfertility emanating from changes in the income constraint and in the formin which wealth is held.

First, an increase in income results initially in an increase in the ratioof market goods and services to own time in household production. This,in turn, will raise the marginal product of time, given the usual assumptionsabout the nature of production functions. Only if individuals can exchangesome of this additional money income (or these additional units of x) forown time (or T,) by removing time from the labor market to restore theoptimal ratio of x to T will there be no price effects (Becker [1965]explores this point at some length). If, however, an individual were unableto substitute sufficiently (i.e., initially he or she spent no time in thelabor market or spent too little time to permit a full adjustment), then theincome effect also would represent an increase in the time value of theindividual (see Willis's paper in this book for a detailed discussion of thispoint, as well as Ben-Porath's paper herein).

Second, the nature of the household production function model empha-sizes joint production in the household, and one aspect of joint productiongoes far in resolving the dispute in the literature about the mechanismthrough which income affects the relative demand for "quality" and num-ber of children. By definition, parents with more income spend more ongoods and services, and empirically they spend proportionately more onsuch items as durable goods, housing, and travel. Many of these expendi-tures on goods for the couple's own use in various production processesmay yield externalities to their children through the children's unavoidableexposure to these goods. Put differently, the purchase of a durable good,say a hi-fl set, may be motivated by the demand for some commodity quiteunrelated to children, but once acquired, the item assumes some of thecharacteristics of a "public good" within the household. The couple'schildren are necessarily exposed to the good; it represents a part of theenvironment in which the child lives. If these goods .and services which areacquired for the parents' own use are complementary with the directexpenditures used in the production of "quality" in their children. house-holds with larger amounts of these goods and services face a lower marginalcost of child quality, ceteris paribus. Thus, the relative price of quality toquantity of children may be lower for wealthier couples.5 If so, wealthierhouseholds would be induced to shift toward fewer, more quality-intensivechildren, other things held constant.6

5 From eq. (7) the marginal products of x0 and T,, in the production of quality,0,. and 07,, may be affected by the level of e, the environmental variable positivelyrelated to the couple's wealth. If > 0 and > 0, the direct marginal cost of Q.is negatively related to e.

6 Note that the argument here is not that of Duesenberry (1960) and Okun (1960).

DERIVED DEMAND FOR

A final relative price effheld. Education, or humanis by its nature embeddedcapital cannot be separalConsequently, the incomepart of the opportunity oother capital assets is' noin wealth among individtime value: the proporticapital, as well as the q

Pursuing this point lusense that some investmenot in others, and if tis negatively related to ittime incorporates the "uscific uses of one's time.7volves a relatively low roffers relatively little othen the user cost of hrearing.8 In this case, thto the shadow price othe shadow price of tiObviously, the argumebut the point, I think,is neither a homogeneoone's time may emboinvestment opportunitietime. Education may a

Their points were, respecmechanically linked to thatraise their own level of liviIt is not the case that thetied to income: the househon children and achieve thcost of "quality" is lowerethus shifts toward "quality.from some inexorability.

In discussing the usernormal conditions "the useis necessary" (p. 73). It isdepreciation and utilizatiohowever, it seems morenegative correlation betweeis higher in uses which recapital, in contrast to phlittle use of the capital.

8 Michael and Lazearattachment, the shadow pthe net human capital lorates of depreciation on e

H

ROBERT T. MICHAEL ( DERIVED DEMAND FOR CHILDREN 129

levels of education mayand the value of their

more subtle, effects ononstraint and in the form

an increase in the ratiosehold production. This,en the usual assumptionsindividuals can exchange

additional units of x) foror market to restore theeffects (Becker [19651

an individual were unablee spent no time in the

adjustment), then thein the time value of thedetailed discussion of this

n function model empha-spect of loint productionre about the mechanism

for "quality" and num-re income spend more onproportionately more on

I. Many of these expendi-ious production processesthe children's unavoidablerchase of a durable good,for some commodity quiteem assumes some of thehousehold. The couple'srepresents a part of the

ds .and services which arementary with the directin their children, house-

ices face a lower marginalprice of quality to

couples.5 If so, wealthierer, more quality-intensive

in the production of quality,Lronmental variable positivelythe direct marginal cost of Q.

rry (1960) and Okun (1960).

A final relative price effect pertains to the form in which one's wealth isheld. Education, or human capital in general, is but one form of wealth andis by its nature embedded in the individual. The income flow from humancapital cannot be separated from the individual's use of his own time.Consequently, the income or benefit flow from human capital becomes apart of the opportunity cost of one's time. Since the flow of benefits fromother capital assets is' not so wedded to the individual's time, differencesin wealth among individuals do not identically reflect differences in theirtime value: the proportion of one's wealth held in the form of humancapital, as well as the quantity of wealth, affects time values.

Pursuing this point further, if human capital is not homogeneous in thesense that some investments yield benefits in certain specific activities butnot in others, and if this "specific" capital depreciates at a rate whichis negatively related to its rate of utilization, then the shadow price of one'stime incorporates the "user cost" of this capital and may differ among spe-cific uses of one's time.7 If, for example, time spent in child rearing in-volves a relatively low rate of utilization of one's knowledge capital andoffers relatively little opportunity for additional on-the-job investment,then the user cost of human capital will be particularly high in childrearing.8 In this case, the couple's education level may be positively relatedto the shadow price of time used in child rearing, relative even tothe shadow price of time used in other household production activities.Obviously, the argument here is no more than a logical possibility,but the point, I think, merits attention. By its nature, human capitalis neither a homogeneous nor a static quantity, and the various uses ofone's time may embody different rates of depreciation and differentinvestment opportunities which, in turn, affect the opportunity cost oftime. Education may affect fertility by altering relative prices subtly, but

Their points were, respectively, that the "standard of living of the children ismechanically linked to that of the parents" (p. 234) and "automatically, when parentsraise their own level of living . . . quality expenditures per child must rise" (p. 236).It is not the case that the "quality" of the child is "mechanically" or "automatically"tied to income: the household could reduce its direct expenditure of time and goodson children and achieve the same level of "quality." It is, rather, that the marginalcost of "quality" is lowered as incomes rise and that the "quantity to quality" mixthus shifts toward "quality." The shift results from a change in relative prices and notfrom some inexorability.

In discussing the user cost of capital equipment, Keynes (1936) suggests that innormal conditions "the use of equipment brings nearer the date at which replacementis necessary" (p. 73). It is suggested, with respect to physical capital, that the rates ofdepreciation and utilization are positively related. With regard to human capital,however, it seems more likely that depreciation increases with disuse, implying anegative correlation between its rates of use and depreciation. The "user cost" of capitalis higher in uses which represent relatively high net rates of depreciation. For humancapital, in contrast to physical capital, such uses are those activities which makelittle use of the capital.

8 Michael and Lazear (1971) show that for an individual with a labor-marketattachment, the shadow price of nonmarket time is the observed wage foregone plusthe net human capital lost through foregone investment opportunities and higherrates of depreciation on existing capital.

130 ROBERT T. MICHAEL DERIVED DEMAND FOR

perhaps substantially, through these dynamic aspects of the ownership ofan array of different human capital assets.

iii) The Production Function ConstraintsThe household faces a set of production function constraints, and itsmembers' education levels may affect these in many ways. Since it isinferred from evidence pertaining to effects on market earnings thateducation raises one's productive capacity in labor-market activities, ithas more recently been argued that education may affect one's productivecapacity in nonmarket production activities as well. It might do so eitherby influencing the choice of productive techniques employed (by improvingthe couple's capability to acquire, assimilate, and implement knowledgeabout alternative production techniques) or by affecting the marginalproductivity of the inputs used in a given production technique (seeWelch [1970] and Michael [19721). In general, the possible direct in-fluences of education through these productive activities are limitless,since specific effects of education on particular production functions canalter the relative prices of commodities and the relative proficiencies offactors of production, and thereby induce substitution in consumption(between commodities) and substitution in production (between inputs).These shifts can also affect the real income of the household and therebycreate "pure" wealth effects (see Michael [1972]).

Focusing upon two production effects which seem, intuitively, to meritparticular attention regarding fertility behavior, consider the influence ofeducation on child quality and on fertility control.° If the flow of childservices per child, a, is directly related to the child's age-adjusted stockof human capital, then it seems plausible that the parents' stock of suchcapital would be particularly productive in producing human capital intheir children.'° If so, education would be negatively related to the relative

9That is, the variable E will be added to eqq. (7) and (8) as an additional in-fluence on the environment in which this production takes place: Q = 9(XQ, TQ; e, E)and P = Z2, F, E).

10 It has been suggested that education, or human capital in general, may be tech-nologically biased. Specifically, education may raise one's productivity in producing addi-tional human capital more than it improves one's productivity in producing othernonmarket products and, perhaps, more than it improves one's productivity in produc-ing market earnings (see, in particular, Ben-Porath [1970c1 and Mincer 11970b1).It is but an extension of this argument to suggest that human capital is relativelytechnologically biased toward producing human capital in one's children as well.(Current research by Mincer and by Leibowitz, as well as completed work byLeibowitz [19721, pursues this point in the context of preschool investment inchildren. See also De Tray's paper in this volume.) It should perhaps be pointedout that this contention is not inconsistent with the discussion above. It may well bethat education has a disproportionately large effect on lowering the cost of producinghuman capital in children, but that this production represents a relatively low rate ofutilization of the parents' human capital. In short, child rearing by the more-educated may be both quite productive and quite costly.

price of Q, other things ccin the production of any

Finally, since one of tlition is an awareness of antion of fertility controlduction which require var:to be a productive activitately strong effect. Ifceteris pan bus, more-edproduce a relatively loeducation lowered the sbthe optimal P would becouples exposed to a lowtions and hence lower fe

iv) The Time ConstrainConsider, finally, the i

Expressed in nominal (ain which this constrainperiods to which the coat marriage determinesexpectancy determinesdoes the couple's educatiWork on a theory offunction framework isthis model for the effectshere (although some obs

In a recent study of tthe individual's decisionof a model which treathat the lower the cosoptimal length of life,suggests that the largersured by years of forhealth capital. Hence,by extending life expecon the optimal stock of

v) ConclusionIn the context of thechildren are viewed a

11 Of course, it wouldreducing the relevant marcost functions is not specifi

ROBERT T. MICHAEL DERIVED DEMAND FOR CHILDREN 131

pects of the ownership of

tion constraints, and itsmany ways. Since it is

n market earnings thatibor-market activities, itty affect one's productiveelI. It might do so eitheremployed (by improving

id implement knowledgeaffecting the marginal

oduction technique (seeI, the possible direct in-

activities are limitless,Droduction functions canrelative proficiencies of

ltitutiOn in consumption(between inputs).

household and thereby

em, intuitively, to merit:onsider the influence of

If the flow of childage-adjusted stock

parents' stock of suchucing human capital inly related to the relative

d (8) as an additional in-place: Q=9(xQ, e, E)

al in general, may he tech-ductivity in producing addi-ctivity in producing otherc's productivity in produc-

Oci and Mincer [1970b1).human capital is relativelyin one's children as well.II as completed work byI preschool investment inhould perhaps be pointedion above. It may well bering the cost of producingts a relatively low rate of

Id rearing by the more-

price of Q, other things constant, inducing technical substitution toward Qin the production of any given level of child services.

Finally, since one of the behavioral attributes often ascribed to educa-tion is an awareness of and receptivity to new ideas, and since the produc-tion of fertility control encompasses a broad range of techniques of pro-duction which require varying degrees of precision in use, this, too, appearsto be a productive activity in which education may have a disproportion-ately strong effect. If education lowers the relative cost of fertility control,ceteris pan bus, more-educated contracepting couples would choose toproduce a relatively lower probability of conception, P. (In fig. 1, ifeducation lowered the slope of the cost curve at all levels of P < thenthe optimal P would be lower than P,.)11 Over extended periods of time,couples exposed to a lower risk of conception would expect fewer concep-tions and hence lower fertility on the average, all else equal.

iv) The Time ConstraintConsider, finally, the individual household member's time constraint.Expressed in nominal (as distinct from effective) time units, the only wayin which this constraint can be altered is by affecting the number ofperiods to which the constraint applies, lithe formation of the householdat marriage determines the initial time period of the analysis and if lifeexpectancy determines the time horizon, then the question becomes, Howdoes the couple's education affect the age at marriage and life expectancy?Work on a theory of marriage in the context of a household productionfunction framework is presented below by Becker. The implications fromthis model for the effects of education on age at marriage will not be pursuedhere (although some observed correlations are discussed below).

In a recent study of the demand for health, Grossman (1972b) analyzedthe individual's decision regarding an optimal length of life in the contextof a model which treats health as a depreciable capital stock. He showedthat the lower the cost of investment in health capital, the longer theoptimal length of life, cetenis panibus. Empirically, Grossman's evidencesuggests that the larger an individual's stock of knowledge capital, as mea-sured by years of formal schooling, the lower his cost of investment inhealth capital. Hence, one's education level may affect one's time horizonby extending life expectancy, through the endogenous effect of educationon the optimal stock of health capital.

v) ConclusionIn the context of the household production function framework in whichchildren are viewed as a durable asset, there are several mechanisms

11 Of course, it. would be possible for the total cost curve to be lowered withoutreducing the relevant marginal cost curve. At this point, the specific form of thesecost functions is not specified.

132 ROBERT T. MICHAEL

through which the couple's education may affect fertility behavior. In addi-tion to the frequently discussed effects through changes in money incomeand the value of time of household members, effects through the proficiencyof household production functions and through indirect changes in relativeprices have been emphasized. Effects through the utility function and thelength of the couple's time horizon have also been noted.

Too often, the husband's or wife's education level is interpreted inempirical work as a good proxy variable for whatever is of interest to theresearcher. As emphasized here, education may affect behavior in manyways. Thus, it seems to me, high priority in empirical research should begiven to an attempt to parcel out some of these separate effects and toestablish their relative order of importance. The work I report below is acontribution toward that end.

IV. Education and Fertility ControlIt has long been argued that more-educated couples have greater accessto fertility-control information and are therefore more successful in pre-venting unwanted pregnancies. Indeed, there is considerable evidence, fromsociological surveys in the United States—notably the Growth of AmericanFamilies (GAF) studies conducted in 1955 and 1960 and the sequel, theNational Fertility Studies (NFS), to which I referred earlier as the database for this study—that standardized, say, for religion or for age,more-educated couples do use contraceptive techniques more extensively,approve of their use more thoroughly, and adopt contraception at anearlier birth interval. Consequently, more-educated couples are morelikely to have "completely planned" fertility (as to both the timing andthe number of their children) and are less likely to have "excess fertility"or "unwanted" births.12

Similar findings are reported for other countries as well. Vaukey (1961)finds, in a study of some 900 Lebanese women, that the use of contracep-tion and particularly the use of appliance methods rise with education.Roberts et al. (1967), utilizing a 1964 survey of 1,500 women of child-bearing age in Barbados, found that general knowledge of contraception,the average number of contraceptive methods known per woman whoknew of at least one method, and the percentage who had ever usedcontraception rose with the woman's education level. Broadly comparablefindings for India (see Dandekar [1967] and Morrison [1957]), PuertoRico (see Stycos [19671), Japan (see Matsunaga 119671), and Ghana(see Caldwell 11967]), for example, offer supporting evidence of greateruse and acceptance of contraception among the relatively better-educated.

12 The principal reports on the 1955, 1960, and 1965 surveys are, respectively,Freedman, Whelpton, and Campbell (1959), Whelpton, Campbell, and Patterson(1966), and Ryder and Westoff (1971).

DERIVED DEMAND FOR CH

In studies inthe more educated aremethods of contraception.

i) Contraceptive EfficiencWhile it may appear intuiaffect knowledge ofat a time when such knquestion whether existinU.S. data would still refithink that with the relin the past decade or sohave little effect on ferover extended periods ofciency can indeed have alowing Keyfitz (1971), dreduction in the monthlythe monthly probabilityP is the monthly probabiIf a couple used a conteffective, in a 15-year2.7 births (assuming thwas as long as 17 montfertility outcome wouldceptive technique whichconception in a 5-yearperfect) contraception dthink.13

A contraceptive techntion used along with oAs such, the observedindependently from theit is employed. Compacontraceptive techniquaverage products, say, oIt would be preferableductivity of the time inor contraceptive is cornaffected by the precisio

Noting this major Iiobserved use effectiven

13 The chance of a con

number of years of exposution, and the relevant figucoital frequency. The inte

H

ROBERT T. MICHAEL DERIVED DEMAND FOR CHILDREN 133

fertility behavior. In addi-changes in money income

cts through the proficiencyndirect changes in relativee utility function and then noted.n level is interpreted intever is of interest to theaffect behavior in many

pirical research should bee separate effects and towork I report below is a

pies have greater accessmore successful in pre-

nsiclerable evidence, fromthe Growth of American

1960 and the sequel, theferred earlier as the datafor religion or for age,niques more extensively,opt contraception at ancated couples are more

to both the timing andto have "excess fertility"

as well. Yaukey (1961)at the use of contracep-

ods rise with education.f 1,500 women of child-wledge of contraception,known per woman whoage who had ever usedvel. Broadly comparableorrison 119571), Puertoa [19671), and Ghanating evidence of greaterlatively better-educated.

5 surveys are, respectively,Campbell, and Patterson

In studies in less-developed countries, the evidence further indicates thatthe more educated are also more aware of the possibility of and themethods of contraception.

i) Contraceptive Efficiency\Vhiie it may appear intuitively plausible that differences in education levelaffect knowledge of contraception at a relatively low level of education orat a time when such knowledge is generally not widespread, one mightquestion whether existing differences in education levels in contemporaryU.S. data would still reflect much difference in use. Moreover, one mightthink that with the relatively effective contraceptive methods availablein the past decade or so, the specific technique a couple adopted wouldhave little effect on fertility outcome. However, the cumulative effectsover extended periods of time of less than near-perfect contraceptive effi-ciency can indeed have an appreciable influence on expected outcomes. Fol-lowing Keyfitz (1971), define contraceptive efficiency, e, as the percentagereduction in the monthly birth probability: e = (P° — p)/p*, where is

the monthly probability for the fecund couple with no fertility control andP is the monthly probability with a specific contraceptive technique in use.If a couple used a contraceptive technique which was "only" 90 percenteffective, in a 15-year period their expected fertility outcome would be2.7 births (assuming the period of infertility associated with pregnancywas as long as 17 months; with instantaneous replacement, the expectedfertility outcome would be 3.6 conceptions). Or, if a couple used a contra-ceptive technique which was "only" 99 percent effective, the chance of aconception in a 5-year interval exceeds 10 percent. "Good" (but notperfect) contraception does not provide the long-run protection one mightthink.13

A contraceptive technique, as emphasized above, is a factor of produc-tion used along with other factors to reduce the probability of conception.As such, the observed efficiency of the technique should not be treatedindependently from the complementary factors of production with whichit is employed. Comparing the observed effectiveness in use of differentcontraceptive techniques across households is equivalent to comparingaverage products, say, of different types of lawn mowers across households.It would be preferable to attempt to standardize for the amount and pro-ductivity of the time input (and other inputs) with which the lawn moweror contraceptive is combined. In short, the observed effectiveness in use isaffected by the precision and care with which it is used.

Noting this major limitation of such data, consider next the relativeobserved use effectiveness of the most common techniques of contracep-

13The chance of a conception is calculated as 1— (1— P)12Y, where V is thenumber of years of exposure. There are, of course, assumptions implicit in the calcula-tion, and the relevant figures would be affected by such factors as age, fecundity, andcoital frequency. The interested reader is referred to Keyfitz (1971).

L.

134

TABLE 1

ROBERT T. MICHAEL

ESTIMATES OF EFFECTIVENESS OF CONTRACEPTIVE TECHNIQUES

Proba-bility

Observed Monthly Contra- Expected of a Con-Use Birth ceptive Time ception

Effective- Proba- Effi- to Con- in anessR

bilityP

ciencye

ception(Months)

10-YearPeriod

Technique (1) (2) (3) (4) (5)

Pill 1.0 .0008 .9958 1200 .097IUD 2.5 .0021 .9895 480 .222Condom 13.8 .0115 .9425 87 .750DiaphragmWithdrawal

14.416.8

.0120

.0140.9400.9300

8371

.765

.816

Jelly 18.8 .0157 .9217 64 .850Foam tablets 20.1 .0168 .9162 60 .868Suppositories 21.9 .0182 .9088 55 .890Rhythm 38.5 .0321 .8396 31 .980Douche 40.3 .0336 .832 1 30 .983No method ... .2000 .0000 5 1.000

NoTE—Cot. I, R = (number of conceptions >1 l,200)/(number of months of exposure); see Tietze(1962). The rates of use effectiveness are estimates derived from several sources. See in particularTietze (19596, 1962, 1970). I adjusted the rates obtained from different populations by usingrelative links from overlapping estimates. Col. 2, P = (R -i- 1,200). Cot. 3, e = (P — P)/P, whereP is assumed to be .20. Lot. 4, Time = 1/P. Col. 5, Probability in 10 years= 1— (1

tion. The use effectiveness of each technique is its computed failure rateper 100 years of use and as such reflects its reliability in use by a givensample of couples. It does not reflect the physiological or potential effec-tiveness of the technique used under ideal circumstances.14 Table I makesuse of published estimates of use effectiveness. Although the relativelypoor techniques lower the risk of conception per month by more than80 percent on the average (see col. 3), the expected waiting time until aconception is only years (col. 4); over a 10-year period the likelihoodof an accidental pregnancy is as high as 98 percent (col. 5). So a couple

14 Tietze has emphasized in several studies the difficulties in estimating the useeffectiveness of various contraceptive techniques and the qualifications which mustaccompany any such estimates. For an excellent discussion of some of these, see Tietze(1959a, 1962) and Potter, McCann, and Sakoda (1970). To illustrate the difficulty, ifthe computation of contraceptive failure rates includes months of use soon after thetermination of pregnancy, the low rates of pregnancy resulting from the naturalinfertility following delivery will be incorrectly attributed to the technique, biasingdownward the estimate of the failure rate. Likewise, a downward bias is also possibleif the computation excludes too many months beyond the period of postpartuminfertility, since the remaining cohort of users will have excluded the most fecundcouples. The use effectiveness, furthermore, will be affected by the distributions ofthe duration of use among couples and of the parity of couples in the sample, sincelong-period users are more likely to be less fecund and higher-parity users are generallymore careful in their use of contraceptives (see n. 17). The set of estimates in table 1represents a "ball park" estimate of the relative ranking of the techniques by theirobserved use effectiveness.

r DERIVED DEMAND FOR CHIt.

using the rhythm or douchtcannot expect to avoid CCItechnique as the diaphragmconception, on the average,ability equal to .75 of

ii) Simple Correlates of IaThe 1965 National Fertili'selection of contraceptivetionally, some 5,600 womewith their husbands at theand able to participate inapproximately 75 minutesfemale interviewers.'5 Negseparately in the results rel

These data containused within separatepregnancy, between the fininstances, of course, no tesmall number of instancesinterval-specific statistics 1less than 0.5 percent ofwhich the couple did not

The first task undertallin this paper, was toselected in a givenables (in particular, theRather than contend withof the diffusion of specifi

'5For a complete descripearlier GAF surveys and withSurvey data, see Ryder anddata set, only 1,963remainder were Catholicsor over age 40 (1,352) or(37 observations). Anotherinformation on the educatioø

10 Excluding couples that bpregnancy builds in a selectireflect contraceptivea contraceptive failure. So itcontraceptors will be systehowever, has several characwith the closed intervals.time span of the open interend of the open intervaldifferent set of survey quethe open interval. I intendbut have not yet done so.

N

using the rhythm or douche technique at its average observed efficiencycannot expect to avoid conception for long. Even using as effective atechnique as the diaphragm or the condom, the typical couple can expect aconception, on the average, after about 7 years of use and faces a prob-ability equal to .75 of incurring a conception in 10 years of exposure.

ii) Simple Correlates of Interval-specific Contraception BehaviorThe 1965 National Fertility Study that I have used to investigate theselection of contraceptive techniques among households surveyed, na-tionally, some 5,600 women under age 55, currently married and livingwith their husbands at the time of the interview (around November 1965)and able to participate in an English-language interview. Interviews ofapproximately 75 minutes were conducted by specially trained professionalfemale interviewers.'5 Negroes were double-sampled and are dealt withseparately in the results reported below.

These data contain information on the specific contraceptive techniquesused within separate pregnancy intervals (between marriage and the firstpregnancy, between the first and second pregnancy, and so on). In manyinstances, of course, no technique was used within a given interval. In asmall number of instances, no information was obtained. For each of theinterval-specific statistics below, these few cases of missing data (typicallyless than 0.5 percent of the subsample) were deleted, as were cases inwhich the couple did not have that closed interval.'6

The first task undertaken with these data, and the only one reportedin this paper, was to examine the relationship between the techniqueselected in a given interval and various economic and demographic vari-ables (in particular, the levels of schooling of the husband and wife).Rather than contend with each specific technique separately, as in a studyof the diffusion of specific technological innovations, the techniques were

rROBERT T. MICHAEL

Acepilva TECHnIQUES

FI

DERIVED DEMAND FOR CHILDREN

Proba-

ontra- Expectedbility

of a Con-eptiveEffi-

Timeto Con-

ceptionin a

icncy Ception 10-Yeare (Months) Period

(3) (4)

135

9958 1,2009896 4801425 871400 83300 71217 64162 60388 55396 31321 30100 5

.097.222.750.765.816.850.868.890.980.983

1.000

er of months of exposure); see Tietzerem several sources. See in particularfrom different populations by using

00). Col. 3, e = (/5* — P)/P, wherey ix tO years= I — (I

is its computed failure rateeliability in use by a givenfological or potential effec-mstances.14 Table I makess. Although the relativelyper month by more than

waiting time until a-year period the likelihoodcent (col. 5). So a couple

ficulties in estimating the usethe qualifications which muston of some of these, see Tietze• To illustrate the difficulty, ifmonths of use Soon after the

resulting from the naturalted to the technique, biasingownward bias is also possibled the period of postpartumre excluded the most fecundcted by the distributions ofCouples in the sample, sinceher-parity users are generallyhe set of estimates in table 1

of the techniques by their

15 For a complete description of this data set and its comparability with theearlier GAF surveys and with the 1960 US. census and subsequent Current PopulationSurvey data, see Ryder and Westoff (1971). Of the 5,617 observations in the NFSdata set, only 1,963 observations have been used in the analysis here (see table 2). Theremainder were Catholics (1,271 observations) or non-Catholics under age 25 (806)or over age 40 (1,352) or age 25—40 but designated by race as "other nonwhite"(37 observations). Another 188 observations initially deleted contained either noinformation on the education level of a spouse or no income information.

16 Excluding couples that had not "closed" a specific birth interval by a subsequentpregnancy builds in a selectivity bias. While the closed intervals do not necessarilyreflect contraceptive failures, the open interval by definition has not been closed bya contraceptive failure. So in successively higher pregnancy intervals, some successfulcontraceptors will be systematically omitted. The open-ended pregnancy interval,however, has several characteristics which make it somewhat inappropriate to includewith the closed intervals. These characteristics include (a) the considerably longertime span of the open interval, (b) the availability of the oral contraceptive near theend of the open interval (the survey date), and (c), most importantly, a somewhatdifferent set of survey questions pertaining to the contraceptive techniques used inthe open interval. I intend to study the contraceptive behavior in the open intervalbut have not yet done so.

136 ROBERT T. MICHAEL DERIVED DEMAND FOR C

collapsed into a single variable defined in terms of the monthly birthprobability applicable to that technique. This was done by assigning toeach technique its corresponding monthly birth probability from table 1.So, for example, a couple that used a diaphragm in the first pregnancyinterval was assigned a value of .0120 (from col. 2 of table 1). This as-signment was made for each of the first three closed pregnancy intervalsfor each household. Couples with no such interval were excluded forpurposes of that variable, and couples who used no method in a giveninterval were assigned a value of .2000 (which is a value often quoted asa typically fecund couple's unadjusted monthly birth probability). Formany of the statistics, couples who used no method of contraception in aspecific interval were excluded; these statistics are designated below asreferring to "users only."

It must be stressed that the average observed use effectiveness of agiven contraceptive technique was assigned to each pregnancy intervalfor each household on the basis of information on the technique the coupleused in that interval. So the variable to be examined is not the couple'sown monthly birth probability computed from its own experience. Rather,the assigned values simply rank the techniques and scale their averageeffectiveness in a reasonably appropriate manner. This enables us toinvestigate the selection of a contraceptive technique in terms of its rela-tive average effectiveness.

It should also be emphasized that the unit of analysis here is a preg-nancy interval. The lengths of these intervals vary across households andby parity. The procedure used assigns a probability to an interval onthe basis of the best technique used in that interval without regard tohow extensively or exclusively that technique was used by that couple inthat interval. Table 2 indicates mean values for subsamples of the 1965NFS data. Cell sizes decline in successive pregnancy intervals becausehouseholds for which the interval has not been closed are excluded. Thetable reflects a few of the findings from this data set reported by others(see especially Ryder and Westoff [1971]).

Looking at the extent of use of contraception as shown in table 2,there is a systematic reduction in the fraction of women using no contra-ception from interval to interval for each age-specific and color-specificgroup. There is not, however, a pronounced tendency for users to usemore effective techniques as they progress to successive intervals (i.e.,the average probability among "users only" does not decline) Compared

1TThis finding is not new. On the basis of the Princeton Study (a longitudinalsurvey, begun in 1957, of 1,165 urban couples having a second child born in September1956), Westoff, Potter, and Sagi (1963, pp. 232—35) report that the observed improve-ment in fertility control across birth intervals "is clearly not a matter of couplesshifting from ineffective to effective methods" nor is it related to any important"practice effect" or to a declining fecundity or reduced coital frequency. Instead, theauthors suggest that "the chief mechanism in the improvement of contraception

MEAN VALUES orAS INDI&

VARIABLE ANDPREGNANCY

INTERVAL

All women (cell size)Income of husband ($)Education of wifeEducation of husbandTotal number of birthsNumber of childrenPill: current users (%)Pill: ever used (%)Pill: never heard of itMarriage date

First pregnancy interval (cellUsed no method (%)Probability (all)Probability (users only)

Second pregnancy interval(cell size)Used no method (%)Probability (all)Probability (users only)

Third pregnancy interval(cell Size)Used no method (%)Probability (all)Probability (users only)

with whites, blacks tenlevel of contraceptivestatement pertains tointerest is thecohorts.18

In examining theand parity-specific mttions between contractand family-size variabreflect some of the us

appears to be greater regutack of shifting toward nof assigning the overall rthe differences in actualin the data summarized ii

is For the age groupblacks to whites is 1.651.93 and 1,70. For the Cspecific nonuse rates fallsfrequency of nonuse of coto whites in younger

ROBERT T. MICHAEL

s of the monthly birthas done by assigning torobability from table 1.

in the first pregnancy2 of table 1). This as-

osed pregnancy intervalsrval were excluded forno method in a given

a value often quoted asbirth probability). For

od of contraception in aare designated below as

use effectiveness of aeach pregnancy intervalthe technique the couplemed is not the couple'sown experience. Rather,and scale their averageer. This enables us toue in terms of its rela-

analysis here is a preg-across households and

ility to an interval onerval without regard toused by that couple in

subsamples of the 1965ancy intervals because

losed are excluded. Theset reported by others

as shown in table 2,omen using no contra-

ecific and color-specificdency for users to useccessive intervals (i.e.,ot decline) 17 Compared

eton Study (a longitudinalnd child born in Septemberthat the observed improve-

not a matter of couplesrelated to any important

ital frequency. Instead, theovement of contraception

DERIVED DEMAND FOR CHILDREN

TABLE 2MEAN VALUES or SELECTED VARIABLES BY COLOR, AGE, AND PREGNANCY INTERVAL

AS INDICATED (NON-CATHOLIC WOMEN ONLY)

137

VARIABLE ANDPREGNANCYINTERVAL

WHI

25—29

m Wos

30—34

SEN

35—39

BLA

25—29

CII Woa

30—34

SEN

35—39

All women (cell size) (466) (506) (508) (160) (166) (157)Income of husband ($) 7,227 8,048 8,532 4,897 4,855 4,615

Education of wife 12.1 11.8 11.8 10.9 10.8 10.3

Education of husband 12.2 11.9 11.8 10.7 10.5 9.5

Total number of births 2.32 2.85 2,92 3.34 3.87 3.95

Number of children intended 2.85 3.06 3.00 3.82 4.28 4.04

Pill: current users (%) 24.2 16.0 9.2 22.5 12.0 5.1Pill: ever used (%) 38.8 28.7 15.2 30.0 18.1 8.9Pill: never heard of it (%) 0.9 2.4 2.4 4.4 5.4 11.5Marriage date 1958 1953 1949 1958 1953 1949

First pregnancy interval (cellsize) . . . (431) (477) (474) (146) '158) (145)Used no method (%) 43.2 38.2 36.5 45.2 54.4 60.7Probability (all) 0949 .0869 .0832 .1008 .1181 .1292Probability (users only) 0150 .0171 .0160 .0190 .0202 .0198

Second pregnancy interval(ceilsize) (381) (431) (434) (135) (137) (126)Used no method (%) 27.6 26.4 26.7 31.8 40.9 51.6Probability.(all) 0665 .0652 .0653 .0763 .0927 .1127Probability (users only) 0157 .0168 .0161 .0185 .0185 .0196

Third pregnancy interval(cell size) (228) (330) (317) (117) (112) (109)

Used no method (%) 23.2 26.7 24.9 30.8 34.8 42.2

Probability (all) 0589 .0654 .0620 .0738 .0823 .0957Probability (users only) 0161 .0165 .0162 .0178 .0195 .0195

with whites, blacks tend to have a larger fraction of nonusers and a lowerlevel of contraceptive efficiency among users (keep in mind that such astatement pertains to the choice of techniques only). Of considerableinterest is the reduction in nonuse by blacks relative to whites acrosscohorts.18

In examining the relationships between variables within age-, color-,and parity-specific intervals, table 3 indicates various simple correla-tions between contraceptive-choice variables and income, and educationand family-size variables for non-Catholic women. The first three rowsreflect some of the usual relationships in terms of positive correlations

appears to be greater regularity of practice." The results in table 2 relate only to thelack of shifting toward more effective techniques on the average. By the procedureof assigning the overall mean use effectiveness to a technique regardless of interval,the differences in actual use effectiveness for specific techniques cannot be observedin the data summarized in table 2.

18 For the age group 3 5—39, the ratio of norsuse in the first pregnancy interval forblacks to whites is 1.65 (=60.7 ÷ 36.5) and for the two successive intervals it is1.93 and 1.70. For the cohort of the ages 25—29, however, this ratio of interval-specific nonuse rates falls to 1.05, 1.14, and 1.33 for respective intervals. That is, thefrequency of nonuse of contraception for blacks is considerably reduced by comparisonto whites in younger cohorts.

TAB

LE 3

SIM

PLE

OF

SELE

CTE

D V

AR

IAB

LES

WIT

H IN

CO

ME,

ED

UC

ATI

ON

, AN

D IN

TEN

DED

FA

MIL

Y-S

IZE

VA

RIA

BLE

S, B

Y C

OLO

R A

ND

AG

E(N

oN-C

ATH

oLIc

WO

MEN

Seco

nd p

regn

ancy

inte

rval

:U

sed

no m

etho

dfB

irth

prob

abili

ty (a

ll)(C

ell s

ize

=13

7)—

209

—10

0—

226

—12

0—

287

-—

326

WH

ITE

WO

MEN

BLA

CK

WO

MEN

Num

ber o

fN

umbe

r of

Hus

band

'sW

ife's

Hus

band

'sC

hild

ren

Hus

band

'sW

ife's

Hus

band

'sC

hild

ren

Inco

me

Educ

atio

nEd

ucat

ion

Inte

nded

Inco

me

Educ

atio

nEd

ucat

ion

Inte

nded

All

wom

en:

A. W

omen

Age

25—

29

(Cel

l siz

e =

466)

(Cel

l siz

e16

0)W

ife's

educ

atio

n31

9...

...—

236

323

. ..

...

—34

8H

usba

nd's

educ

atio

n37

464

7...

—17

240

063

0.

—27

6M

arria

ge d

ate

092

514

353

—27

303

330

534

2—

398

Firs

t pre

gnan

cy in

terv

al:

(Cel

l siz

e =

431)

(Cel

l siz

e =

146)

Use

d no

met

hodt

—11

2—

236

—27

112

3—

034

—18

0—

075

206

Birt

h pr

obab

ility

(all)

—11

6—

243

—27

812

6—

044

—19

0—

095

210

Birt

h pr

obab

ility

(use

rs)

—07

1—

166

—15

707

2—

224

—18

0—

366

076

Seco

nd p

regn

ancy

inte

rval

:(C

ell s

ize

=38

1)(C

ell s

ize

= 13

5)U

sed

no m

etho

dt—

079

—16

8—

136

159

—14

5—

270

—13

910

4B

irth

prob

abili

ty (a

ll)—

079

—17

7—

146

167

—15

5—

280

—15

210

3B

irth

prob

abili

ty (u

sers

)00

1—

145

—16

813

2—

157

—16

3—

189

—00

8Th

ird p

regn

ancy

inte

rval

:(C

ell s

ize

=22

8)(C

ell s

ize

117)

Use

d no

met

hodf

—00

7—

095

—01

508

7—

211

—37

4—

223

201

Birt

h pr

obab

ility

(all)

—00

5—

106

—02

109

2—

227

—38

5—

237

208

Birt

h pr

obab

ility

(use

rs)

All

wom

en:

021

—13

5—

081

075

—21

3—

180

—20

209

9

B. W

omen

Age

30—

34

(Cel

l siz

e =

506)

(Cel

l siz

e =

166)

Wife

's ed

ucat

ion

380

..

..

..

—22

835

3.

...

.—

300

Hus

band

's ed

ucat

ion

491

624

—14

944

250

8...

—30

7M

arria

ge d

ate

092

440

293

—23

431

933

126

6—

331

Firs

t pre

gnan

cy in

terv

al:

(Cel

l siz

e =

477)

(Cel

l siz

e =

158)

Use

d no

met

hodt

—20

0—

264

—22

921

6—

229

—29

0—

211

118

Birt

h pr

obab

ility

(all)

Birt

h pr

obab

ility

(use

rs)

—20

6—

117

—27

3—

237

224

—18

0—

147

190

—23

0—

028

—29

7—

217

—15

2—

116

122

095

TAB

LE 3

(Con

tinue

d)

WH

ITE

WO

MEN

WO

MEN

Hus

band

'sIn

com

e

Num

ber o

fW

ife's

Hus

band

'sC

hild

ren

Educ

atio

nEd

ucat

ion

Inte

nded

Hus

band

'sIn

com

eW

ife's

Hus

band

'sEd

ucat

ion

Educ

atio

n

Num

ber o

fC

hild

ren

Inte

nded

I

(Cel

l siz

e =4

31)

—17

1—

260

—19

0—

184

—27

1—

206

227

236

—15

0—

169

—28

8

176

199

TAB

LE 3

(Con

tinue

d)

WR

ITE

WO

MEN

BLA

CK

WoM

EN

Num

ber o

fN

umbe

r of

Hus

band

'sW

ife's

Hus

band

'sC

hild

ren

Hus

band

'sW

ife's

Hus

band

'sC

hild

ren

Inco

me

Educ

atio

n Ed

ucat

ion

Inte

nded

Inco

me

Educ

atio

nEd

ucat

ion

Inte

nded

Seco

nd p

regn

ancy

inte

rval

:(C

ell s

ize

431)

(Cel

l siz

e13

7)U

sed

no m

etho

dt—

171

—26

0—

190

227

—15

0—

209

—10

017

6B

irth

prob

abili

ty (a

ll)—

184

—27

2—

206

236

—16

9—

226

—12

019

9B

irth

prob

abili

ty (u

sers

)—

183

—17

4—

217

155

—28

8—

287

—32

639

4Th

ird p

regn

ancy

inte

rval

:(C

ell s

ize

—33

0)(C

ell s

ize

= 11

2)U

sed

no m

etho

dt—

162

—20

4—

180

174

—14

3—

275

—15

120

9B

irth

prob

abili

ty (a

ll)—

175

—22

1—

198

185

—14

4—

279

—16

422

3B

irth

prob

abili

ty (u

sers

)

All

wom

en:

—17

0—

244

—25

619

0—

024

—05

8—

172

209

C. W

omen

Age

35—

39

(Cel

l siz

e =

508)

(Cel

l siz

e =

157)

Wife

's ed

ucat

ion

330

..

..

-.

—18

835

7.

..

..

.—

182

Hus

band

's ed

ucat

ion

526

570

..

.—

120

399

457

...

—14

9M

arria

ge d

ate

048

354

248

—24

102

617

310

0—

202

Firs

t pre

gnan

cy in

terv

al:

(Cel

l siz

e =

474)

(Cel

l siz

e =

145)

Use

d no

met

hodt

—16

2—

207

—18

015

1—

019

—16

0—

113

025

Birt

h pr

obab

ility

(all)

—17

0—

218

—18

815

4—

027

—17

1—

119

031

Birt

h pr

obab

ility

(use

rs)

—13

2—

195

—15

006

2—

163

—24

9—

131

169

Seco

nd p

regn

ancy

inte

rval

:(C

ell s

ize

= 43

4)(C

ell s

ize

= 12

6)U

sed

no m

etho

dt—

165

—17

5—

155

141

—07

5—

103

—17

116

2B

irth

prob

abili

ty (a

ll)—

172

—18

8—

163

147

—07

9—

117

—18

216

8B

irth

prob

abili

ty (u

sers

)—

104

—18

7—

113

104

—07

9—

280

—19

913

9Th

ird p

regn

ancy

inte

rval

:(C

ell s

ize

= 31

7)(C

ell s

ize

= 10

9)U

sed

no m

etho

dt—

051

—13

5—

124

153

—03

5—

105

—15

509

6B

irth

prob

abili

ty (a

ll)—

064

—14

6—

137

159

—03

5—

110

—16

609

6B

irth

prob

abili

ty (u

sers

)—

172

—15

5—

170

100

010

—09

2—

157

—00

0

* T

heco

rrel

atio

ns a

re e

xpre

ssed

in w

iits m

ultip

lied

by 1

,000

(i.e

., th

e de

cim

al p

oint

has

bee

n om

itted

).t D

umm

y va

riabl

e de

fined

as I

if no

met

hod

used

in th

at in

terv

al a

nd a

s zer

oan

y co

ntra

cept

ive

met

hod

used

in th

at in

terv

al.

—I

S

rnet

hodt

Birt

h pr

obab

ility

(all)

Birt

h pr

obab

ility

(use

rs)

All

wom

en:

—00

502

1—

106

—13

5—

021

—08

1

087

092

075

211

—22

7—

213

(Cel

lsi

ze =

506

)(C

ell

size

=16

6)W

ife's

educ

atio

n38

0...

...—

228

353

...H

usba

nd's

educ

atio

n49

162

4...

—14

944

250

8M

arria

ge d

ate

Firs

t pre

gnan

cy in

terv

al:

Use

d no

met

hodf

Birt

h pr

obab

ility

(all)

Birt

h pr

obab

ility

(use

rs)

092

—20

0—

206

—11

7

440

(Cel

l—

264

—27

3—

180

293

size

= 4

77)

—22

9—

237

—14

7

—23

4

216

224

190

319

—22

9—

230

—02

8

331

(Cel

l—

290

—29

7—

152

size

=

B. W

omen

Age

30—

34

——

-,—

-.1

—37

4—

223

201

—38

5—

237

208

—18

0—

202

099

266

158)

—21

1—

217

—11

6

—30

0—

307

—33

1

118

122

095

between spouses' education levels and between income and education, anda negative correlation between education (particularly the wife's) andfertility measures. Notice the relatively strong correlation, especially forwomen and more particularly for whites, between education and marriagedate: the more-educated marry at a later date.

The first row in each of the interval-specific sets of rows of table 3indicates the simple correlation between the column variable and a dummyvariable defined as 1 if the couple used no contraceptive method in thatinterval and zero if a method was used. In every instance, this correlationis negative for the income and education variables and positive for the"intended number of children" variable (for a definition of this lattervariable, see n. 20). Holding age, parity, and color constant, couples withhigher husband's income or higher wife's education or higher husband'seducation (separately) are more likely to have used a contraceptivemethod at some time in the given pregnancy interval. While many ofthese simple correlations are not high, their consistency over so manygroups is corroborative.

The remaining two rows of simple correlations for each pregnancyinterval in table 3 are related to the value of the monthly probabilityassigned to that interval for each couple on the basis of information aboutthe contraceptive method used in that interval. The variable "birth prob-ability (all)" includes the nonusers—those couples who used no methodand were assigned the value .2000. Thus, this variable has an essentiallybimodal distribution, with many observations at .20 and a distributionof the remainder centered around a value somewhat less than .02. Thecorrelations with the variable defined as "birth probability (users)" ex-clude all couples who used no method in that specific interval.

Not only is each spouse's education level negatively correlated withnonuse of contraception, but each is also negatively correlated with theprobability of birth (or positively correlated with the effectiveness ofthe technique chosen) among "users only" for every specific birth interval.In other words, there is a consistent systematic selection by more-educated husbands and wives (for each pregnancy interval) of contra-ceptive techniques which are, on the average, relatively more effective.For whites, the correlations with education tend to decline in successiveintervals, relatively more for the dichotomous variable than for the "prob-ability (users)" variable.

To obtain some indication of the relationship between techniquesselected in successive pregnancy intervals and between the use andnonuse of contraception in successive pregnancy intervals, simple correla-tions were computed for pairs of intervals as indicated in table 4. Part Asuggests that nonuse is significantly correlated from interval to interval,especially in the later-interval pair. Part B suggests a strong correlationacross intervals in the techniques selected (in terms of their average oh-

140 ROBERT T. MICHAEL.

DERIVED DEMAND FOR CH

SIMPLE CORRELATIONS IN CWITH RESPECT to NONUS

AMONG USERS

PREGNANCY INTERVALS

(Cell size)First and secondFirst and thirdSecond and thirdBoth first and second,

and thirdFirst and both Second

and third

(Cell size)First and secondFirst and thirdSecond and third

NoTe-—Cell size applies to thethey had not completed the first t]not used a contraceptive techniqueunits multiplied by 1,000 (i.e., deci

served use effectiveness)among the later pair of

iii) Regression AnalysisTurning to the partialcontraceptive behavior,It was stated that B, ta child, is positively i

children at that point irdemand as N* (thefertility demand functionAll the factors whichincome, time values,corporated in N*. Itdiscrepancy (N* — N),This framework, then,benefits from contracepthe probability P) negdesired and the actual s

ROBERT T. MICHAEL

income and education, andarticularly the wife's) andg correlation, especially forèen education and marriage

Ic sets of rows of table 3iimn variable and a dummyntraceptive method in thatry instance, this correlationjables and positive for thea definition of this latterolor constant, couples withation or higher husband'save used a contraceptiveinterval. While many ofonsistency over so many

tions for each pregnancythe monthly probability

basis of information aboutThe variable "birth prob-pies who used no method,ariable has an essentiallyat .20 and a distributionewhat less than .02. The

probability (users)" ex-)ecific interval.egatively correlated with

correlated with thethe effectiveness of

specific birth interval.atic selection by more-ncy interval) of contra-relatively more effective.

to decline in successiveiable than for the '1prob

hip between techniquesbetween the use and

intervals, simple correla-Lcated in table 4. Part A

interval to interval,tests a strong correlation

of their average ob-

DERIVED DEMAND FOR CHILDREN 141

TABLE 4SIMPLE CORRELATIONS IN CONTRACEPTIVE BEHAVIOR ACROSS PREGNANCY INTERVALS

WITH RESPECT TO NONUSE (PART A) AND SELECTION OF SPECIFIC TECHNIQUESAMONG USERS (PART B) (NON-CATHOLIC WOMEN ONLY)

PREGNANCY INTERVALS

WHITE WOMEN BLACIc WOMEN

25—29 30—34 35—39 25—29 30—34 35—39

A. Simple Correlations between Dummy VariablesRepresenting Nonuse in Specified

(Cell size)

Pregnancy Intervals(228) (330) (317) (116) (112) (109)

First and second 421 571 521 567 596 652First and third 368 439 373 483 531 481Second and third 698 640 639 627 753 705Both first and second,

and third 632 614 587 632 755 630First and both second

and third 349 487 449 513 543 513

B. Simple Correlations between Birth Probabilitiesamong Users Only in Specified

(Cell size)

Pregnancy Intervals

(100) (165) (165) ( 52) C 43) ( 38)First and second 574 662 719 572 548 838First and third 627 646 690 795 649 834Second and third 708 733 782 649 726 966

Noxe.—.-CeIl size applies to the entire column for each part. For Part A, couples were excluded ifthey had not completed the first three birth intervals. For Part 8, couples were excluded if they hadnot used a contraceptive technique in each of the three birth intervals. Correlations are expressed inunits multiplied by 1,000 (i.e., decimal point is omitted).

served use effectiveness). The latter correlations appear to be strongeramong the later pair of intervals and stronger among the older cohorts.

iii) Regression Analysis of Interval-specific Contraception BehaviorTurning to the partial relationships between variables correlated withcontraceptive behavior, the earlier analysis (including fig. 1) is helpful.It was stated that B, the present value of the net marginal benefit ofa child, is positively related to the household's excess demand forchildren at that point time. Define the household's completed-fertilitydemand as N* (the outcome from the household's static, completed-fertility demand function) and define the household's current parity as N.All the factors which affect the couple's completed-fertility demand—income, time values, relative productivities, revealed preferences—are in-corporated in N*. It will be assumed that the greater the (positive)discrepancy (N* — N), the larger the arithmetic value of the term B.This framework, then, is a simple stock-adjustment model, with thebenefits from cQntraception (the negative benefits from an increase inthe probability P) negatively related to the discrepancy between thedesired and the actual stock of children. The benefits from contraception

142 ROBERT T. MICHAEL

continue to increase as the discrepancy (N* — N) becomes negative.Thus, ceteris paribus, we would expect to observe a positive relationshipbetween the couple's monthly birth probability and (N* — N).

The discussion in Section II also suggests that the cost function offertility control (the portion of the discontinuous cost curve below pointP*) is presumably related to the couple's fecundity, coital frequency,religion, and education. We will treat the wife's age A as a (negativelyrelated) proxy variable for fecundity and coital frequency, and we expectage, ceteris paribus, to be negatively related to the couple's monthly birthprobability, P. If education lowers the costs of fertility control, we shouldexpect to observe a negative partial relationship between education, E(measured as the number of years of schooling), and P. If Catholicsselect a contraceptive technique from a subset of possible techniques, andparticularly if the subset excludes the relatively more efficient techniques,the cost of fertility control will be higher for Catholics, ceteris paribus.Thus, a dummy variable R (1 if Catholic and zero if non-Catholic) wouldbe expected to be positively related to P.

Combining the effects on P through the benefit and cost functions, thereduced-form equation for the probability P would be

(11)

In estimating some of these effects empirically, several qualificationsmust be noted. First, since the structure of the benefit and cost functionshas not been made explicit, the form of this reduced-form equation is notgiven. Consequently, equation (11) has not been estimated directly.Instead, the data have been partitioned by the variables N, A, and R andlinear regressions have been run within parity-, age-, and religion-specificgroups.'° In addition, both because of disproportionate representation inthe sample and because of an interest in any observed difference in be-havior per Se, the groups were further partitioned by race. So the regres-sions reported below pertain to religion-, age-, race-, and parity-specificgroups and regress P as a function of the education levels of the spousesand a variable representing N*.bo

T

I.DERIVED DEMAND FOR CH,

A second important qmonthly birth probabilityfig. 1) is the actual probabut the dependent variaassigned to that coupleemployed for that pregnatheoretical discussion shthe regressions do not Stregressions attempt to mvcontrol behavior, namelyaverage observed use effe

Table 5 indicates regCatholic women for thevariable is the monthlytechnique (the units arewho used no contracepticludes the nonusers frothat the wife's educatioto the monthly birth pconstant, achieve a loweris measured in terms ofno contraception as one oalso appears to be generamagnitude and is more eexpected, the proxy forprobability.21

While the regressionsception in the specific i

the mean value of the debelow 200 (or a probab

present pregnancy] ?" A "dowhat is your best guess?"sidered the number of childrN*. The number of childrena rather complicated seriesRyder and Westoff and thintended number of childrenintended and as the currentfrom retrospective questionsall other women [see Rydechildren "wanted" by the wi

21 In other regressions (nwithout any additional vanvariables representing the hthe couple's marriage datevariables). These results sueffect of the wife's educatiogenerally negative effect of

19 The parity-specific groups are defined in terms of pregnancy intervals rather thanlive-birth intervals, Some checks on the effects of this distinction are planned. Also,no resufts are reported for Catholic women, because an analysis has not yet beenmade. Ryder and Westoff (1971, pp. 244—52) report a similar aspect of these datawhich does include Catholics.

20 variable N* might be estimated for each subgroup from an auxiliaryregression, but for the analysis conducted to date, the variable is defined as either(a) the number of children the couple "intends" to have or (b) the number ofchildren "wanted" by the wife. The intended number of children was computed byadding to the respondent's current parity her intended number of additional children.(After the woman's current pregnancy status and the couple's current fecundity weredetermined, the respondent was asked: "Do you intend to have a[nother] child[after the one you are expecting now] ?" If the answer was yes, the respondent wasthen asked: "How many more children do you intend to have [not counting your

ROBERT T. MICHAEL

— N) becomes negative.a positive relationship

and (N*_N).that the cost function ofus cost curve below pointcundity, coital frequency,'s age A as a (negativelyfrequency, and we expecthe couple's monthly birthertility control, we shouldip between education, Eg), and P. II Catholics

f possible techniques, andmore efficient techniques,

Catholics, ceteris pan bus.ro if non-Catholic) would

fit and cost functions, thebe

(11)

Ily, several qualificationsbenefit and cost functions

equation is notbeen estimated directly.riables N, A, and R and

age-, and religion-specifictionate representation inbserved difference in be-

by race. So the regres-race-, and parity-specificion levels of the spouses

egnancy intervals rather thanlistinction are planned. Also,

analysis has not yet beensimilar aspect ol these data

Libgroup from an auxiliaryvariable is defined as eitherave or (b) the number of

children was computed byimber of additional children.pie's current fecundity wered to have a[notherl childwas yes, the respondent was

have [not counting your

r DERIVED DEMAND FOR CHILDREN 143

A second important qualification which must be noted is that themonthly birth probability in the theoretical analysis (eqq. [8]—[ 11] andfig. 1) is the actual probability produced by the households for themselves,but the dependent variable in the empirical analysis is the probabilityassigned to that couple from information on the contraceptive techniqueemployed for that pregnancy interval (as discussed above). So while thetheoretical discussion sheds light on the partial relationships observed,the regressions do not strictly test the implications of that analysis. Theregressions attempt to investigate partial effects on one aspect of fertility-control behavior, namely, the selection of techniques ranked by theiraverage observed use effectiveness.

Table S indicates regression results for age- and color-specific non-Catholic women for the first three pregnancy intervals. The dependentvariable is the monthly birth probability assigned for each contraceptivetechnique (the units are multiplied by 1,000). Part A includes coupleswho used no contraceptive technique in that interval, while Part B ex-cludes the nonusers from the regressions. It would appear from Part Athat the wife's education level is quite systematically negatively relatedto the monthly birth probability: more-educated women, other thingsconstant, achieve a lower risk of conception, on the average, when that riskis measured in terms of the contraceptive technique selected (includingno contraception as one of the techniques). The education of the husbandalso appears to be generally negatively related, but this effect is of smallermagnitude and is more erratic, especially for the youngest age group. Asexpected, the proxy for N* is positively related to the monthly birthprobability.21

While the regressions in Part A include couples who used no contra-ception in the specific interval, Part B excludes nonusers. Consequently,the mean value of the dependent variable is considerably lower, somewhatbelow 200 (or a probability of .02), compared with a mean of 600 to

present pregnancy] ?" A "don't know" answer resulted in the further question: "Well,what is your beat guess?" The resulting total [not additional] births was then con-sidered the number of children intended and is used [tables 5 and 71 as the proxy forN*. The number of children "wanted" by the wife is a constructed variable based ona rather complicated series of questions. The value is in fact an inference made byRyder and Westoff and their associates. (Briefly, the variable is defined as theintended number of children for women whose current parity is less than the numberintended and as the current parity minus the number of unwanted births [determinedfrom retrospective questions about the circumstances at the time of conception] forall other women [see Ryder and Westoff (1971, p. 93)1. This variable, number ofchildren "wanted" by the wife, is used in table 6.)

21 In other regressions (not shown here), the two education variables were enteredwithout any additional variables, and the two education variables were entered withvariables representing the husband's current income, the wife's current income, andthe couple's marriage date (plus appropriate missing-data dummies for the incomevariables). These results support the conclusion of a generally significant negativeeffect of the wife's education level and a considerably weaker, somewhat erratic, butgenerally negative effect of the husband's education level.

* M

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of ten

statistically

signific

matically

to select

more

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The

"intended

number

generally

positive

as

about

30 percent

of the si

sions.

Since

by its definiti

(defined

in n.

20)

is

be that

the regressions

poorer

contraceptors

achi

be a reverse

causation

f

number

of cbildren"

van

regressions

in table

6rep

by the

"number

of childr

n.

20).

This

variable

cornis also,

by definition,

les

behavior

in the early

preis its inferential

nature:

basis

of the respondent's

comparable

to Part

II of

tions

for

the same

age-,

c

employs

one

proxy

varia

alternative

proxy.

In a

wife's

education

effect

a

Part

I of table

6 while

th

and more

significant.

Th

tween

Parts

B of the

two

in their

significance,

an

appear

small.23

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economic

incentiv

related

to (N* —

N) an

greater)

when

(N* —

N)

22 Using

a slope

coefficientis a rough

average

of the

effe

an

additional

4 years

of scho

birth

probability

by about

.0

effect

on

the long-term

believe

the

estimate

would

be

23 While

nofle

of the regre

included

an

intercept

term.

'I

the proxy

for

N* was

the

"number

of children

inferred

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146

L

DERIVED DEMAND FOR CHILDREN 147

1,300 (or a probability of .06—.13) in Part A. Furthermore, the coefficientof variation of the dependent variable in Part B is around .5, while inPart A it is about 1. In Part B, one observes quite consistent, small,negative effects of both education levels, although the coefficients are notoften statistically significant. More-educated couples do appear syste-matically to select contraceptive techniques which are, on the average,more efficient.22

The "intended number of children" variable, the proxy for N*, isgenerally positive as expected, but it is statistically significant in onlyabout 30 percent of the separate age-, color-, and interval-specific regres-sions. Since by its definition the "intended number of children" variable(defined in n. 20) is never smaller than a woman's current parity, it maybe that the regressions in table 5 suffer from a simultaneity problem:poorer contraceptors achieve higher parities, ceteris paribus, so there maybe a reverse causation from the dependent variable to the "intendednumber of children" variable. To overcome this problem somewhat, theregressions in table 6 replace the "intended number of children" variableby the "number of children inferred wanted by the wife" (also defined inn. 20). This variable comes closer to the theoretical concept of N*, and itis also, by definition, less likely to have been affected by contraceptivebehavior in the early pregnancy intervals. Its weakness as a proxy for N*is its inferential nature: the value is inferred by social scientists on thebasis of the respondent's retrospective introspection. Part I of table 6 iscomparable to Part II of table 5, for both use precisely the same observa-tions for the same age-, color-, and interval-specific regressions; the latteremploys one proxy variable for N* while Part I of table 6 employs analternative proxy. In a comparison of Parts A of these two tables, thewife's education effect appears to be somewhat smaller and weaker inPart I of table 6 while the husband's education effect is somewhat strongerand more significant. There appear to be few important differences be-tween Parts B of the two tables. Overall, the differences in the coefficients,in their significance, and in the explanatory power of the regressionsappear small 23

The economic incentives related to contraception are assumed to berelated to (N* — N) and may in fact be distinctly different (presumablygreater) when (N* — N) 0. As a first approximation to separating the

22 Using a slope coefficient of —4.0 per year of schooling for each spouse (whichis a rough average of the effects for each spouse across estimates in table 5, Part II),an additional 4 years of schooling for each would be expected to lower the monthlybirth probability by about .003 on the average. One could then calculate the impliedeffect on the long-term risks of conception, but I will not do so here because Ibelieve the estimate would be too crude to be meaningful.

23 While none of the regressions in table 5 or 6 reports intercepts, all regressionsincluded an intercept term. These intercepts, too, appear to be insensitive to whetherthe proxy for N* was the "number of children intended" (as in table 5) or the"number of children inferred wanted" (as in table 6).

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TAB

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REG

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30—

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OR

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Wife

Husband

Wife

(s.e

.e.)t

White women:

I.W

hole

Sam

ple

Firs

t int

erva

l47

71

869

1—

78.0

5—

37.2

3(1

8.51

)10

.00

(3.0

4).1

02 848.

295

r 171

1(8

8)j

—5.

84(3

.13)

—2.

04(2

.40)

1.37

(0.4

5).0

64 86.

Second interval

431

r 652

1

—82

.23

(22.

97)

—20

.17

(17.

72)

8.12

(3.0

1).0

91 777.

317

r 168

]

[(85

)]—2.32

(2.96)

—5.91

(2.23)

0.88

(0.41)

.064

82.

Tiiird interval

330

654

—58.83

(27.26)

—31.88

(20.55)

4.35

(3.4

8).060

795.

242

r16

5 1

L (8

6)]

—5.60

(3.49)

—5.88

(2.61)

0.80

(0.47)

.089

82.

Bla

ck w

omen

:First interval

158

11181

1—102.99

(35.68)

—27.86

(33.98)

2.61

(3.50)

.097

864.

72r 2

02 1

[(10

2)]

—5.

95(5

.79)

—0.

70(5

.43)

1.28

(0.6

0).0

88 100.

Seco

nd in

terv

al13

71

927

1—

98.3

0(3

8.74

)16

.45

(37.

01)

9.16

(3.7

4).0

92 866.

81 185

1[(

93]

—8.

08(4

.69)

—7.

61(4

.60)

1.05

(0.5

0).1

77 86.

Third

inte

rval

112

r 823

1[(

868)

]

—12

8.88

(44.

52)

—14

.38

(40.

08)

6.83

(3.7

6).1

09 830.

731

195

1[(

100)

]

—2.

87(6

.22)

—7.

01(5

.46)

1.00

(0.5

8).0

71 98.

TAB

LE 6

(Con

tinue

d)

I I

—318g

435

060

242

—560

—588

080

089

F65

41

(27.

26)

(20.

55)

(3.4

8)79

5.1

165

1(3

.49)

(2.6

1)(0

.47)

82.

L(81

6).J

[(86

)]Black

wom

en:

Firs

t int

erva

l.

158

—10

2.99

—27

.86

2.61

.097

72—

5.95

—0.

701.

28.0

88ril

si 1

(35.

68)

(33.

98)

(3.5

0)86

4.r 2

02 1

(5.7

9)(5

.43)

(0.6

0)10

0.[(

901)

][(

102)

]Se

cond

inte

rval

137

—98

.30

16.4

59.

16.0

9281

—8.

08—

7.61

1.05

.177

192

71

(38.

74)

(37.

01)

(3.7

4)86

6.r 1

85 1

(4.6

9)(4

.60)

(0.5

0)86

.[(

898)

j[93]

Third

inte

rval

112

—12

8.88

—14

.38

6.83

.109

73—

2.87

—7.

011.

00.0

71r 8

23 1

(44.

52)

(40.

08)

(3.7

6)83

0.r 1

95 1

(6.2

2)(5

.46)

(0.5

8)98

.[(

sos)

][0

00)j

HT

AB

LE6

(Con

tinue

d)

A.

CO

NTR

AC

EPTI

VEUSERS AND

NO

NU

SER

SB

.U

SER

S O

NLY

(Exc

No

LIJD

ES C

oyM

ETilO

D)

PLES

TnA

TU

sto

Num

-N

um-

ber o

fbe

r of

Chi

l-:

Chi

l-dr

en In

-dr

en In

-C

OLo

Rfe

rred

ferr

edA

ND

Num

ber

Educ

a-Ed

uca-

Wan

ted

Num

ber

Educ

a-Ed

uca-

Wan

ted

PREG

NA

NC

Yof

Ob-

tion

oftio

n of

byR

2of

Ob-

tion

oftio

n of

byR

2IN

TER

VA

Lse

rvat

ions

*W

ifeH

usba

ndW

ife(s

.e.e

.)tse

rvat

ions

*W

ifeH

usba

ndW

ife(s

.e.e

.)t

II.

Chi

ld S

pace

rs O

nly

Whi

te w

omen

:Fi

rstin

terv

al46

4—

79.6

9—

31.0

012

6.63

.109

289

—5.

76—

1.97

14.4

9.0

63r 8

61 1

(23.

68)

(18.

63)

(32.

38)

843.

r 171

1(3

.17)

(2.4

3)(4

.83)

86.

—L(

890)

][(

88)]

Seco

nd in

terv

al39

4—

92.3

5—

3.95

128.

80.1

1229

2—

1.31

—6.

5510

.02

.065

r 643

1(2

3.73

)(1

8.47

)(3

5.47

)76

3.r 1

69 1

(3.1

2)(2

.33)

(4.9

0)82

.L(

806)

J[(

85)]

Third

inte

rval

234

—87

.13

—16

.06

165.

27.1

1917

1—

3.64

—6.

1019

.83

.107

r 660

1(3

1.90

)(2

3.61

)(5

4.10

)77

3.r 1

66 1

(4.3

1)(3

.05)

(7.4

4)82

.L(

818)

J[

(86)

JB

lack

wom

en:

Firs

t int

erva

l14

0—

113.

11—

27.7

79.

33.1

0863

—3.

530.

3816

.89

.106

r119

1 1

(37.

78)

(36.

41)

(41.

05)

859.

r 202

1(6

.33)

(5.8

2)(7

.07)

100.

[(90

0)]

Luo3

']S

econ

din

terv

al11

0—

78.1

516

.6.

107.

28.0

8263

—1.

63—

13.1

517

,33

.281

r 960

1(4

5.44

)(4

2.63

)(5

1.03

)87

9.r 1

85 1

(5.0

7)(4.97)

(6.14)

80.

[(92

)]Th

ird in

terv

al73

—142.37

—51.57

27.08

.150

44

2.35

—8.60

12.25

.074

r92

0 1

(54.

69)

(50.

08)

(63.

13)

835.

r 208

1(8

.14)

(6.85)

(9.99)

100.

L(88

6)J

[('0

')]M

ean

and

stan

dard

dev

iatio

n (in

par

enth

eses

) of d

epen

dent

var

iabl

e ar

e br

acke

ted.

f s.e

.e. =

stan

dard

erro

r of e

stim

ate.

* St

anda

rd e

rror

in p

aren

thes

es.

4

....-

:.,

...

..

1..DERIVED DEMAND FOR CHILI

Finally, table 7 again maII of table 5 and reportsthird intervals only, using diwife and the husband. Inis larger (negative) and sfor the wife's education, aPart A. That is, the effect oieducation appears to be grtive to high school; the Stpairs of coefficients has not.the negative effects reportables 5 and 6 result predschooling (and the high ti

iv) ConclusionThe empirical analysis inserved contraceptive behavThe results reported here,selection of contraceptive tinon-Catholic women betweiobserved effects of theof contraceptives are oftsignificant, the effects areand parity-specificdefinition of the proxy va

If it is tentatively conlevels do have a negativeas defined in this studyselect contraceptive technipreventing pregnancy—thOne cannot distinguish, bquite distinct interpretatireducing information costby raising the marginal pwith any specific contraction for the observed negaon the marginal benefitbigger loss to more-educinduced to make a greater

This third explanation

quite small for these low-palfourth pregnancy interval, hiobservations with (N* — N)these couples differs apprecif>0.

150 ROBERT T. MICHAE

TABLE 7

REGRESSIONS ON MONTHLY BIRTH PROBABILITY SN FIRST AND THOm PREGNANCYINTERVALS FOR NON-CATHOLIC WHITE WOMEN AGE 30—34 BY USER STATUS

(WITH EDUCATION DuMMY VARIABLES)

Num-berof

Chil-dren

PregnancyInterval

In- R2HS(W) COLL(W) HS(H) COLL(H) tended see.

First interval

A. Contraceptive Users and Nonusers—506.11 —261.14 10.22 .102

(128.02)* (95.75) (2.64) 848.—375.77 —187.07 11.32 .093

(110.63) (88.22) (2.62) 852.—373.72 —196.15 —255.45 —80.68 9.82 .114

(137.89) (106.80) (117.19) (97.84) (2.63) 844.

Third

First

interval

interval

—427.09 104.91 7.15 .065(143.32) (116.65) (3.16) 793.

—509.07 48.78 7.88 .087(119.19) (99.30) (3.04) 783.

—266.15 —129.52 —439.20 116.46 6.35 .099(150.10) (129.13) (125.13) (111.28) (3.13) 781.

B. Contraceptive Users Only (Excludes Couples ThatUsed No Method)

—35.95 —21,70 1.13 .058(23.53) (11.36) (0.44) 86.

—1.14 —25.28 1.35 .056(17.11) (10.77) (0.43) 86.

—35.70 —12.99 7.55 —18.80 1.14 .066(24.85) (12.76) (17.96) (12.01) (0.44) 86.

Third interval —47.55 —26.13 0.95 .074(20.98) (13.69) (0.48) 83.

—34.02 —30.68 1.21 .091(16.73) (11.79) (0.45) 82.

—32.29 —8.39 —25.52 —25.82 0.99 .101(21.98) (15.56) (17.59) (13.44) (0.48) 82.

N0TE.—HS(W) is I if wife's schooling level wss 1 year of high school or more; COLL(W) is Iif wife's schooling level was 1 year of college or more; HS(H) and COLL(H) are similarly defineddummy variables for the husband's schooling level.

Standard error in parentheses.

sample into groups for which (N* — N) >. 0 (designated as "childspacers") and (N* — N) 0, Part II of table 6 reestimates the regres-sions in the first part of table 6 for the subset "child spacers." That is,for each pregnancy interval, the couple was included in the regressions inthe second part of table 6 if and only if the "number of children inferredwanted by the wife" was equal to or greater than the interval number;for example, women who "wanted" two children were excluded from theregressions pertaining to the third interval, and' so on.24

24The sample sizes for the residual subsets (couples for which — NJ 0) were

ROBERT T. MICHAE: DERIVED DEMAND FOR CHILDREN 151

Finally, table 7 again makes use of the same observations as does PartII of table 5 and reports regressions for white women for the first andthird intervals only, using dummy variables for the education levels of thewife and the husband. In all cases, the high school dummy's coefficientis larger (negative) and stronger than the college dummy's coefficientfor the wife's education, and similarly for the husband's education inPart A. That is, the effect of high school education relative to grade schooleducation appears to be greater than the effect of college education rela-tive to high school; the statistical significance of the differences in thesepairs of coefficients has not been computed. It clearly is not the case that

__________________________

the negative effects reported for the education coefficients throughouttables 5 and 6 result predominantly from the effects of the high level ofschooling (and the high time values) of the most-educated women.

iv) ConclusionThe empirical analysis in this section has only begun to investigate ob-served contraceptive behavior in the context of an economic framework.The results reported here represent initial findings with respect to theselection of contraceptive techniques in low-parity pregnancy intervals fornon-Catholic women between the ages of 25 and 40 (in 1965). WThile theobserved effects of the husband's and wife's education levels on the useof contraceptives are often not large and frequently not statisticallysignificant, the effects are quite consistently negative for all age-, color-,and parity-specific regressions. They also appear to be insensitive to thedefinition of the proxy variable for N*.

If it is tentatively concluded that the husband's and wife's educationlevels do have a negative partial effect on the monthly birth probabilityas defined in this study—that more-educated couples, ceteris paribus,select contraceptive techniques which on the average are more effective inpreventing pregnancy—the interpretation of this result is not yet clear.One cannot distinguish, by the statistical procedure followed, between twoquite distinct interpretations: (1) education lowers contraceptive costs byreducing information costs; and (2) education lowers contraceptive costsby raising the marginal product of the couple's time used in conjunctionwith any specific contraceptive device. Moreover, an aJ.ternative explana-tion for the observed negative relationship emphasizes an effect of educationon the marginal benefit function: (3) "unwanted children" represent abigger loss to more-educated couples, and hence the more-educated areinduced to make a greater effort to prevent timing and quantity failures.

This third explanation, however, requires information about the shape

quite small for these low-parity intervals and were not, therefore, analyzed. By thefourth pregnancy interval, however, one would expect to find a sizable number ofobservations with (N* — N) 0; I hope to determine whether the behavior ofthese couples differs appreciably from the behavior of those for whom (N* — N)>0.

ANt) Tresxo PREGNANcYGE 30—34 BY USER STArusRIABLES)

Num-berof

Chil-drenIn-

tended(H) COLL(H)R2

see.

Users and Nonusers10.22 .102(2.64) 848.

5,77 —187.07 11.32 .093- ).63)

5,457.19)

(88.22)—80.68

(97.84)

(2.62)9.82

(2.63)

852..114844.

9.07.19)

9.20.13)

48.78(99.30)116.46

(111.28)

7.15(3.16)

7.88(3.04)

6.35(3.13)

.065793.

.087783.

.099781.

sly (Excludes Couples ThatMethod)

.14 —25.28.11) (10.77).55 —18.80.96) (12.01)

1.13(0.44)

1.35(0.43)

1.14(0.44)

.05886.

.05686.

.06686.

0.95 .074(0.48) 83.

.02 —30.68 1.21 .091.73) (11.79) (0.45) 82..52 —25.82 0.99 .101.59) (13.44) (0.48) 82.

h school or more; COLL(W) is 1

ad COLL(H) are similarly defined

0 (designated as "child6 reestimates the regres-"child spacers." That is,ided in the regressions inmber of children inferredan the interval number;were excluded from the

so on.24

which — NJ 0) were

152 ROBERT T. MICHAEL

of the marginal-cost and marginal-benefit functions around the equilibriumat N*.as Also, the use of the interval-specifIc regressions which include aproxy for the desired number of children is designed to standardize forjust such differences in contraceptive motivation. Finally, the finding fromthe regressions in table 7 that the high school dummy variable has astronger effect on the monthly birth probability than does the collegedummy variable does not support explanation (3). Thus, this interpretationof the observed negative education effects does not seem persuasive.

The results in this paper cannot help us distinguish between the firsttwo explanations, since it is not possible to tell whether better-educatedcouples (a) select contraceptive techniques which are inherently moreeffective in use or (b) simply select some techniques systematically andproceed to use them relatively effectively. As long as the selection issystematic—different distributions by education for different techniques—either a differential inherent use effectiveness or a differential effectivenessby education for any given technique could yield the negative effects ob-served in tables 5, 6, and 7. It would be very useful to analyze the observeduse effectiveness of a given technique by education level. This is notfeasible with the data I have used here. Other studies, however, do suggesta differential use effectiveness by socioeconomic status (see, e.g., Tietze[1959b1, table I, p. 353).

The interpretation of the results reported in this section based ondifferential knowledge or awareness of contraceptives may seem strainedfor contemporary U.S. women. It is interesting to note, however, that forthe non-Catholic women in the 1965 NFS data, the correlation of wife'sand husband's education level with a dummy variable for knowledge ofthe pill (defined as 1 for women who had never heard of the "pill" at thetime of the interview) ranged between —.10 and —.30 for all six sub-samples defined in table 2 for each spouse's education level. So knowledgeof new contraceptives may not diffuse uniformly across education groups.26For the period of time covered by the data used in the regressions here—primarily from the late 1940s into the early 1960s—there were few changesin contraceptive technology until the pill became available. So it would

25 It is not sufficient simply to argue that the higher price of time of the better-educated couple raises the cost of a child and thereby creates a differential motivation.The child also yields a flow of benefits, and N* is defined in terms of equality ofthe marginal-benefit and marginal-cost functions, The economic motivation to avoidan additional child is a function of the differences in the heights of these two marginalcurves around their point of intersection.

26 Since medical care or exposure to medical advice is positively related to income,the simple correlations of the knowledge-of-the-pill dummy variable and the husband'sincome, which also range between —.12 and —.24 for the same six color- and age-specific groups, suggest that the information differential may work through thischannel. For more information on the use of the pill ,derived from these data, seeRyder and Westoff (1971, chap. VI).

DERIVED DEMAND FOR CHI:

seem likely that the observetial rates of adoption ofness of a given technique,proficiencies of existing temarket firms, long-run daverage efficiencies can anddecades ago (1937).

V. Other DimensionsThe empirical results aba'educated couples achieveand partial correlations fappears to be a systematiniques by more-educatedhigh levels of efficacy, cefficiency imply quite largso, more-educated coupleceptions, which would betheir observed fertility be

The influence on themost straightforward. Byceptions, more-educated cfertility (if the problemsubfecundity in aggregatcosts reduce completed ftoward quality of childreimplicitly raising the prishadow price of N is deliG raises the price of Nproduction of child servipoint in depth.

An effect of educationexpected to influence the

intervals) of their childattention to these dime:evidence by sociologistswomen) tend to marrymarriage begins (see[1966]). A recent (1968the National Bureau ofCensus contained inforcouples in the relativel

DERIVED DEMAND FOR CHILDREN 153

seem likely that the observed effects result from factors other than differen-tial rates of adoption of new techniques—perhaps differential use effective-ness of a given technique, or perhaps differential knowledge of the differentproficiencies of existing techniques. Unlike the survival test applicable tomarket firms, long-run differences in households' marginal as well asaverage efficiencies can and do exist, as Wesley Mitchell pointed out severaldecades ago (1937).

V. Other Dimensions of Fertility BehaviorThe empirical results above lend support to the contention that more-educated couples achieve greater contraceptive efficiency. In terms of simpleand partial correlations for each of the spouse's education levels, thereappears to be a systematic selection of more effective contraceptive tech-niques by more-educated couples. Over extended periods of time and athigh levels of efficacy, comparatively minor differences in contraceptiveefficiency imply quite large differences in the risk of conception. If this isso, more-educated couples are exposed to lower risks of undesired con-ceptions, which would be expected to affect many other dimensions oftheir observed fertility behavior.

The influence on the completed fertility of more-educated couples ismost straightforward. By lowering the costs of avoiding undesired con-ceptions, more-educated couples, on the average, exhibit lower completedfertility (if the problem of excess fertility dominates the problem ofsubfecundity in aggregate behavior). Not only may lower contraceptivecosts reduce completed fertility, but they may also induce substitutiontoward quality of children, Q, and away from numbers of children, N, byimplicitly raising the price of N relative to the price of Q. Since theshadow price of N is defined net of contraceptive costs, G, a reduction inC raises the price of N and induces substitution toward quality in theproduction of child services. The Becker-Lewis paper above explores thispoint in depth.

An effect of education on a couple's risk of conception could also beexpected to influence the timing (over the life cycle) and spacing (by birthintervals) of their children. Economists have as yet not devoted muchattention to these dimensions of fertility behavior, but the empiricalevidence by sociologists suggests that more-educated coup'es (especiallywomen) tend to marry later and to postpone childbearing longer aftermarriage begins (see especially Whelpton, Campbell, and Patterson11966]). A recent (1968) survey of consumer anticipations conducted bythe National Bureau of Economic Research and the U.S. Bureau of theCensus contained information on the timing and spacing of children bycouples in the' relatively wealthy suburban households surveyed. These

ROBERT T. MICHAEL

ons around the equilibriumegressionS which include aesigned to standardize for

Finally, the finding fromol dummy variable has aity than does the college). Thus, this interpretationnot seem persuasive.tinguish between the first11 whether better-educatedhich are inherently moreniques systematically andlong as the selection isfor different techniques—-a differential effectiveness

Id the negative effects ob-ful to analyze the observedcation level. This is nottidies, however, do suggestc status (see, e.g., Tietze

in this section based onptives may seem strainedto note, however, that for

the correlation of wife'svariable for knowledge ofheard of the "pill" at thend —.30 for all six sub-:ation level. So knowledgeacross education groups.2°in the regressions here—

s—there were few changesie available. So it would

price of time of the better-eates a differential motivation.fined in terms of equality ofconomic motivation to avoidheights of these two marginal

positively related to income,iy variable and the husband'sthe same six color- and age-ial may work through thisderived from these data, see

154 ROBERT T. MICHAEL

data also suggest that more-educated couples—at relatively high levelsof education—begin childbearing at a later age (see Michael [197hz]).

One explanation for this behavior may be that both schooling and childrearing are relatively time-intensive activities, especially for the wife.While engaging in the production of education, one's time value is relativelyhigh, which effectively precludes simultaneously choosing to engage inchildbearing. Thus, child production and education production are donesequentially. Add to this an assumption of asymmetry in the effects ofthe two stocks on the marginal product of time in the production of theother: assume that an acquired stock of education raises the marginalproduct of time in child rearing more than an acquired stock of childrenraises the marginal product of time in the production of education. Thenone has, perhaps, the beginnings of a theory of the optimal timing of childproduction. As long as the optimal strategy involves postponement of childrearing, it is facilitated by contraceptive efficiency.

In addition to beginning childbearing later, more-educated couples alsoappear to space their children closer together (see, e.g., Bumpass andWestoff [1970], chap. 3; Michael [1971]; U.S. Bureau of the Census[19681). Again, there is no well-developed theory of the optimal spacingof children, although the differential rates of increase in earnings profilesby education levels may be sufficient to imply a negative correlationbetween education and child-spacing intervals, other things (including childquality) held constant. Contraceptive efficiency is particularly relevant tothe child-spacing issue, since a reduction in child spacing for a givennumber of children implies a longer period of subsequent exposure to therisk of an undesired conception.

Finally, it is of interest to note a tendency for more-educated women tospace their children more evenly. Michael (1971) analyzed the absoluteand relative variations within the household in the spacing of children andfound that for age- and parity-specific groups, more-educated womenexhibited a lower variation in the spacing of their children. That is, thestandard deviation and the coefficient of variation in the spacing intervalsamong children within a given household decline, on the average, acrosshouseholds as the wife's education level rises. If the higher variation inspacing among less-educated women reflects outlying spacing-intervalobservations, these may reflect contraceptive "failures," although thisargument is admittedly quite conjectural.

I have explored channels of influence from the couple's levels of educa-tion to various dimensions of human fertility in a relatively free format.Obviously, no tightly woven theory of the demand for fertility control orof the optimal timing and spacing of children has been set forth. Whiledifferent aspects of fertility behavior surely interact with each other, thedirections, nature, and magnitudes of these interactions have been con-sidered only in passing. In short, this paper is a progress report on an

'1

DERIVED DEMAND FOR CHII

effort to understand the i

observed fertility behavior,researchers of the viabilityframework to the broad, mt

Appendix

The constrained objective f UI

t '

where i, j, and t are indices,time, respectively, and wherevalue. For the purpose at harin the labor market at the disimay thus be collapsed withto the wage rate

Consider the optimalprobability of conception Pdition is

h

ÔL az1

axPk = L_4 '\ÔZ1 ôC

where C'kt is the discounteiperiod k. The inelegant stnof influence through which sturn the expected number 01and hence the production orewritten thus:

The term in parenthesesadditional child in periodthe term represents the presterm will be designated B:

'SBk =

ROBERT T. MICHAEL

relatively high levels(see Michael [1971a}).

at both schooling and childespecially for the wife.

time value is relativelyly choosing to engage ination production are doneymmetry in the effects ofe in the production of theation raises the marginalacquired stock of childrenuction of education. Thenhe optimal timing of childlves postponement of child

riore-educated couples also(see, e.g., Bumpass and

S. Bureau of the Censusry of the optimal spacingcrease in earnings profilesly a negative correlationher things (including childis particulaHy relevant tohild spacing for a givenibsequent exposure to the

more-educated women to1) analyzed the absolute

spacing of children andmore-educated women

eir children. That is, thein the spacing intervals

e, on the average, acrossf the higher variation inutlying spacing-interval

'failures," although this

couple's levels of educa-a relatively free format.

for fertility control oras been set forth. Whileact with each other, theractions have been con-

progress report on an

DERIVED DEMAND FOR CHILDREN 155

effort to understand the influence of education on several aspects ofobserved fertility behavior. I hope that it will help to convince otherresearchers of the viability of applying the household production functionframework to the broad, interesting, and important area of human fertility.

Appendix

The constrained objective function, from equations (1)—(4) may written

(W',gTw1t+t t tj

— [ ( T111 + — T,1)], (Al)ti i

where i, j, and t are indices over commodities, adult household members, andtime, respectively, and where a prime represents an appropriate time-discountedvalue. For the purpose at hand, it will be assumed that all j adults are employedin the labor market at the discounted wage rate and that the two constraintsmay thus be collapsed with the shadow price of time equal at the marginto the wage rate

Consider the optimal level of the goods input XPk in the production of theprobability of conception P (see eq. [8]) in time period k. The first-order con-dition is

'I(aU aPI

L._4 äC aN1÷1 t äXP1t==k4-1

1rv-' / 6P1\ OG'11+—J =0, (A2)OP1 OXP5

t=k+1where is the discounted total expenditure in period t on a child born inperiod k. The inelegant string of partial derivatives simply reflects the chainof influence through which Xp affects utility: Xp affects the probability P and inturn the expected number of children N, which alters the flow of child servicesand hence the production of Z1 and, therefore, utility. Equation (A2) can berewritten thus:

a( MU1 \ aG'1

1 1 MP0a — C'1 J = . (A3)'A \ / OP1 OXP1 OXp1

The term in parentheses represents the benefits (in constant dollars) of anadditional child in period t net of the costs of the child. Summed over time,the term represents the present value of the net marginal benefit of a child. Theterm will be designated B:

(A4)

156 ROBERT T. MICHAEL

So the first-order conditions for Xp and are

f aN \and

/ aN \B ( ) (AS)\ apk /

Comment

where and are the prices of the goods and time used in the production

I. IntroductionThe basic assumption of 1fertility objective and thaa set of constraints thatFertility decisions are viechild services against stri"education and fertilityStudy of 1965, many finand C. F. Westoff (1971)of the paper and on testsis inferred from informati

IL Theoretical ConsiHousehold models proviianalysis. Households arewithin them and functioirelationships. Interpretatiactivities related to the e:activi ties are not inseparduced. Failure toutility or enjoyment fronor for oneself that mighta source of confusion in a

III. Channels of InfiThe influence of educatiprincipal channels, nam

Margaret G. ReiUniversity of Chicago

of P.The term Bk may be positive or negative. If, at time k, the present value of

the gross benefit stream from an additional child exceeds the present value of thecost of the child, will be positive. Presumably, the sign of the term B is theanalytical analogue of the response to survey questions which seek to determinewhether a given pregnancy was "wanted." Abstracting from the costs of fertilitycontrol, a child would be "wanted" if B > 0 and "unwanted" if B <0. Since0N/äP, the effect of an increase in P on the expected number of children, ispositive and the prices of time and market goods are also positive, equation(AS) implies that and will be positive or negative as B is positiveor negative. That is, if B < 0, the couple will engage in fertility control bypurchasing and using goods and time inputs to reduce P. If, instead, B > 0 andan additional child is "wanted," the couple may expend resources to raise P.Expressed differently, from the first-order condition for optimization withrespect to P itself,

/ 0N äG'k\—=A( Bk——------— 10,\ äPk /or from equation (9),

So equation (10') can be extended to indicate that if Bk is negative (or positive),is less than (or greater than) P*k and FIpk is negative (or positive).

(A6)

ROBERT T. MICHAEL

Comment= PTp1, (AS)

I time used in the production

Margaret G. ReidUniversity of Chicago

I. IntroductionThe basic assumption of Robert Michael's paper is that each family has afertility objective and that decisions concerning it are made in the light ofa set of constraints that are associated with education of the spouses.Fertility decisions are viewed as flowing from the weighing of benefits ofchild services against streams of costs. Empirical estimates presented of"education and fertility control" utilize data of the National FertilityStudy of 1965, many findings from which are reported by N. B. Ryderand C. F. Westoff (1971). I comment briefly on each of the main sectionsof the paper and on tests of "wealth" constraints, the feasibility of whichis inferred from information secured.

IL Theoretical Consideration8Household models provide an intriguing approach to any consumptionanalysis. Households are multiproduct firms with an exchange systemwithin them and function in response to market and external nonmarketrelationships. Interpretation of Michael's equation (2) fails to recognizeactivities related to the exchange system within households. All nonmarketactivities are not inseparable from the enjoyment of the commodity pro-duced. Failure to differentiate explicitly nonmarket activities of personalutility or enjoyment from those that provide products for another person,or for oneself that might be provided by someone else, is, in my opinion,a source of confusion in a general model of household production functions.

ifi. Channels of Influence of EducationThe influence of education on fertility is assumed to flow through fourprincipal channels, namely, utility, money wealth, a set of household

157

time k, the present value ofceeds the present value of thethe sign of the term B is theions which seek to determineng from the costs of fertility"unwanted" if B < 0. Sincected number of children, isare also positive, equationor negative as B is positivegage in fertility control byce P. If, instead, B > 0 andxpend resources to raise P.tion for optimization with

(A6)

Bk is negative (or positive),egative (or positive).

158 MARGARET G. REID

production functions, and time. Michael's review of these is a contributionto all analyses utilizing education as a behavior variable. The hetero-geneity of the economic aspects of education is better documented thanthat of other influences.

a) Michael notes that "until a theory of the formation of preferencesis available, little can be said, a priori, about the relationship betweeneducation and tastes or about the possible influence of education on thepreference function." If knowledge affects preferences, then preferencesare modified by exogenous change. Information theory predicts thatdiffusion of knowledge is affected by channels of information and theoriesof cultural norms and group identification explain resistance to change.The higher a person's education, the more accessible channels of informa-tion tend to be; hence, knowledge of new methods of contraception, suchas the pill, will tend to be greater for better-educated couples. Knowledgeand use of the pill as of 1965, less than 5 years after its introduction,could be expected to increase with education, to be greater for urbanthan for farm families, and to have restricted births after the secondand third pregnancy intervals more than after the first. Cultural normsand group identification affect birth rates. Existing theories of lagspredict that time tends to narrow the effect of their difference as well asthat of knowledge among groups. Further innovation in contraceptivetechniques may continue to cause differences in contraceptive behaviorby education, access to channels of information, and cultural norms.

b) Michael comments briefly on the large literature on human capital.Theoretical models that relate fertility to education through wealth con-straints seem well developed. Empirical investigators still search forreliable variables to fill boxes of the theory. So far, attention has concen-trated on opportunity costs of time rather than on money costs of qualityof children. Even so, money wage rates utilized are often very crude.Those of employed females have considerable measurement error. Evenless is known of the supply wage of mothers out of the labor force becauseof home care of children. Better data on money wealth are, of course, notenough. Purchasing power of money must be considered. Money wagesthroughout the United States, and probably also within other countries,are likely to be positively correlated with the cost of living.

c) The effect of education on "production-function constraints" is ap-propriately viewed as "limitless." Economists are, as it were, warned ofthe maze in which they are likely to be entering in dealing with theirramifications. One production function explicitly dealt with is the effecton efficiency of fertility control due to knowledge and use of new tech-niques of contraception. Such differential efficiency may, however, betemporary. Diffusion of knowledge has been rapid, and utilization of newtechniques calls for little expertise.

Education of mothers tends to increase efficiency of child care. Knowl-

COMMENT

edge of the effects of echsomething be learned frorrmothers, other conditionsof children during early ye

d) Discussion of the tirelation between educationto the negative correlationship is well documented bin testing the effect of cothe age of marriage. Henc

The time constraint isof its relevance to fertilit:explored area of speculaticchildren? They are lookin,and their offspring. Therean additional child restriparents, as it were, tradean extra child?

A consideration of lifeMichael in the hope of poefficiency of household prthis effect is a matter ofexamination of longevitysuredly have little bearin

IV. Education and IUtilization of anceptive technique used issimple and complex quanithe model presented.tively correlated with thcorrelated with the numiamong non-Catholic worconsiderably between seFor the first and secondprobabilities and educaticthan for those using coneffectiveness of contrac€.Wealth, knowledge, ancclosely associated.

MARGARET G. REID I COMMENT 159

edge of the effects of education awaits identification of quality. Couldsomething be learned from infant mortality with respect to education ofmothers, other conditions held constant? Or from the speed of learningof children during early years in school?

d) Discussion of the time constraint first deals with the positive cor-relation between education and age of marriage of women. This contributesto the negative correlation between education and fertility. This relation-ship is well documented by other studies. In this study, criteria imposedin testing the effect of contraception on fertility indirectly hold constantthe age of marriage. Hence, its effect on fertility is not described.

The time constraint is related to life expectancy without considerationof its relevance to fertility. The discussion does, however, suggest an un-explored area of speculation. Do adults who expect a long life desire morechildren? They are looking forward to more years in which to enjoy themand their offspring. There are other conditions. For example, does havingan additional child restrict leisure that contributes to health, so thatparents, as it were, trade an extra year or two of life for themselves foran extra child?

A consideration of life expectancy seems to have been introduced byMichael in the hope of presenting further evidence that education increasesefficiency of household production. It undoubtedly contributes. To isolatethis effect is a matter of great interest. Attempts at its isolation throughexamination of longevity seem unlikely to bring much reward, and as-suredly have little bearing on birth rates.

IV. Education and Fertility ControlUtilization of an estimate of probability of conception due to the contra-ceptive technique used is a unique feature of this study. It lends itself tosimple and complex quantitative estimates of the type necessary for testingthe model presented. The probability of conception is shown to be nega-tively correlated with the education of wife and husband and positivelycorrelated with the number of children intended. The correlations shownamong non-Catholic women by pregnancy interval, age, and race differconsiderably between sets of all women and those using contraception.For the first and second pregnancy intervals, the correlation between birthprobabilities and education of the wife is appreciably greater for all womenthan for those using contraception. What conditions account for this? Iseffectiveness of contraceptive techniques related to wealth constraints?\Vealth, knowledge, and effective use of contraceptive techniques areclosely associated.

w of these is a contributionvior variable. The hetero-is better documented than

formation of preferencest the relationship betweenuence of education on the

then preferencesion theory predicts thatI information and theorieslain resistance to change.sible channels of inforrna-ods of contraception, suchcated couples. Knowledgears after its introduction,to be greater for urbanbirths after the second

the first. Cultural normsxisting theories of lags

their difference as well asovation in contraceptiven contraceptive behaviorand cultural norms.rature on human capital.lion through wealth con-tigators still search for

far, attention has concen-n money Costs of qualityd are often very crude.easurement error. Even

the labor force becauseealth are, of course, not

onsidered. Money wageswithin other countries,

t of living.ction constraints" is ap-e, as it were, warned ofg in dealing with theirdealt with is the effecte and use of new tech-

ëncy may, however, beand utilization of new

y of child care. Knowl-