Timing of Childbearing, Family Size, and Economic Growth

Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 573 November 1996 TIMING OF CHILDBEARING, FAMILY SIZE AND ECONOMIC GROWTH Murat F. Iyigun NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References in publications to International Finance Discussion Papers (other than an acknowledgment that the writer has had acccess to unpublished material) should be cleared with the author or authors.

Abstract This paper incorporates the timing of childbearing into a growth model with endogenousfertility. It analyzes a modelin whichindividuals’human capitalstockdepends positively on their education and parental human capital and in which producing and raising children and acquiring human capital are time intensive. The model highlights how changes in the human capital stock interact with individuals’ timing of childbearing in afiecting the evolution of the economy. It shows that, if the complementarity between parental human capital and education in determining individuals’ human capital is relatively large, then increases in the human capital stock raise the opportunity cost of having children while young and induce individuals to delay childbearing. That, in turn, accelerates human capitalaccumulation in the future. The model also demonstrates that early childbearing may lead to a development trap with low human capital.

TIMING OF CHILDBEARING, FAMILY SIZE AND ECONOMIC GROWTH Murat F. Iyigun1 1. Introduction Thelinkbetweeneconomicdevelopment,educationalattainmentandfertilityyields one of the most well-documented empirical regularities in economics and demographics: As economies develop, fertility rates fall, the level of educational attainment and the average age of childbearing increase2. The economics literature has provided some explanations for why fertility is negatively related to human capital accumulation. So far, however, it has neglected to adress how timing of childbearing relates to economic development. This paper incorporates the timing of childbearing{as part of individuals’ fertility decisions{into an economic growth model. In doing so, it demonstrates the mutually reenforcing efiects of economic growth on delayed childbearing and delayed childbearing on growth. In the nineteenth century, Thomas Malthus made the pioneering theoretical contribution on fertility and economic growth. His model predicts that death rates fall and fertility rises when incomes exceed the equilibrium per capita income. However, empirical evidence has revealed that fertility rates and economic development were negatively related during the past century and a half. It has also provided strong support for 1The author is a stafi economist in the Division of International Finance, Board of Governors of the FederalReserveSystem. Thispaper representstheviewsoftheauthorandshouldnotbeinterpretedas re(cid:176)ecting those of the Board of Governors of the Federal Reserve System or other members of its stafi. Please send all correspondence to: Division of International Finance, Mail Stop 23, Washington, D.C. 20551. Phone: (202) 452-3798. Fax: (202) 452-6424. E-mail: iyigunm@frb.gov 2The historical experience of industrialized countries, as well as cross-country studies, conflrm these trends. In the U.S. and most other developed countries, studies show that working women are more educatedandbearfewerchildrenlater thantheir counterpartstwodecadesago. The1993 Handbook on Women Workers: Trends and Issues (1994) states that in the United States, \. . . many women delay marriage, and when they domarry,they have fewer children than mothershad in previousgenerations. In the mid-seventies a trend began toward delayed childbearing and births among women in their later childbearing years rose markedly in the 1980’s. Between 1980 and 1988, births among women aged 30 to 34 increased from 35 to 45 per 1,000 women . . . During the 1980’s the proportion of . . . women workers completing 4 or more yearsof collegeincreased steadily. In 1989, 24 percent of women workers had completed 4 years of college or more (up from 17.6 percent in 1979) . . ." 1

educational investment as a determinant of economic growth [See, for example, Barro (1991) and Mankiw, Romer and Weil (1992)]. Accordingly, economists have developed theoretical models that incorporate the interactions among fertility, educational investment and economic growth. Becker and Barro (1988) construct a model with a dynastic utility function in which parents with more children discount the future consumption of each ofispring more. According to their model, technological progress leads to lower fertility and higher consumption. Becker, Murphy and Tamura (1990) consider a model in which human capital investment exhibits increasing returns, at least to a point, and individuals’ discount rate of future generations’ utility is identical to the one developed in Becker and Barro (1988). They demonstrate that families have fewer children and educate each child more in economies with higher human capital levels. They also show that high fertility leads to slower economic growth. The important feature of these models is the speciflc nature in which the discount factor of parents depends on the number of their ofispring. Sundstrom and David (1988) and Azariadis and Drazen (1990) explain the negative relation between fertility and economic development by individuals’ desire to provide for their old age. In these models, increases in the wage rate improve the bargaining power of children with their parents and reduce parents’ perceived value of having children. Galor and Weil (1996) present a model in which household fertility is determined by the relative wages of men and women. They consider a production function where capital is more complementary to women’s labor input than it is to men’s. Thus, increases in capital per worker raise women’s relative wages and reduce fertility by increasing the cost of children more than household income. Iyigun (1995) considers a model in which having and rearing children take away time from human capital investment, and shows that the trade-ofi between education and childrearing leads to the negative relation between fertility and economic development. This paper difiers from existing related work in three main aspects: First, it provides an explanation for the well-documented empirical relation between economic de- 2

velopment and timing of childbearing. In existing work, this relation arises implicitly and only as a by-product of individuals’ fertility decisions. (i.e. In any given period, if individuals face a trade-ofi between work and producing and rearing children, the fact that they have fewer children due to a higher opportunity cost implies that they also delay childbearing provided that individuals allocate the latter part of the period to producing and rearing children.) Second, unlike existing work that has mostly emphasized time taken away from employment as the main opportunity cost of having children [See, Birdsall (1988) for a review], this paper includes time diverted from education as well as employment as part of the opportunity cost. Thus, it shows that both lower fertility and delayed childbearing are consequences of the higher opportunity cost associated with time taken away from education relative to that associated with time taken away from employment. And third, the model presented below highlights how the human capital stock interacts with individuals’ timing of childbearing in determining the evolution of the economy. It demonstrates that human capital accumulation raises the cost of having children while young relative to lifetime wage income. As a result, individuals delay childbearing and spend more time acquiring education when they are young. Since delayed childbearing, in turn, leads to higher future human capital levels, the model identifles the importance of the positive feedback between human capital accumulation and delayed childbearing in economic development. Inwhatfollows,athreeperiodover-lappinggenerationsmodel{inwhichindividuals receive utility from consumption in the last period and from the total number of their ofispring{is considered. In the model, individuals acquire a minimum mandatory level of education in the flrst period; they devote time to education and producing and rearing children in the second period; and they work, consume and produce and rear children in the last period. By assumption, accumulating human capital and producing and rearing children are time intensive. An important feature of the model is that human capital accumulation depends positively on thetime spent on education and the parental human 3

capital stock, which are assumed to be complements in human capital formation. The role parental human capital plays in human capital formation has been explored both theoretically and empirically. For the empirical signiflcance of parental human capital, see for example, Coleman et al. (1966), Becker and Tomes (1986) and Fuchs and Reklis (1994). In this setup, individuals’ most productive time in acquiring human capital and having children coincide. Therefore, when individuals are young, they face a trade-ofi between getting educated and having children. Moreover, if the degree of complementarity between parental human capital and education in determining individuals’ human capital is su–ciently large, then producing and rearing children in the second period becomes more costly with increases in parental human capital. In response, individuals devote more time to education and delay having children. Thus, as parental human capital increases, the fertility rate of young women declines while that of older women who are in the labor force increases. Nonetheless, since the efiect of substitution of time to education from childrearing in the second period (due to higher parental human capital) always dominates the efiect of higher income on the number of children individuals choose to have in the last period, total fertility declines as the economy evolves. The model described below also shows that multiple steady-state equilibria, where the initial stock of human capital of each country will determine the evolution of its economy, may exist. More speciflcally, countries that start out with a low initial human capital stock will converge to a development trap in which individuals are less educated and bear more children early. In contrast, those countries that start with a higher value of the initial human capital stock will converge to a steady-state in which individuals are more educated and have fewer children later. The remainder of the paper is organized as follows: The next section describes the technology of production and the behavior of individuals. Section three discusses the evolution of the economy. And, section four ofiers some concluding remarks. 4

2. The Model 2.1. Production Consider a small open economy that operates in a perfectly competitive world in which economic activity extends over an inflnite discrete time. The output of the economy is a single homogeneous good produced by a CRS production function that uses physical and human capital as input. The output produced at time t, Y , is given t by Y = F(K ; H ) = H f(k ); k · K =H (1) t t t t t t t t where K and H respectively denote the quantities of physical and human capital t t employed in production at time t. The production function f: R ! R satisfles the + + 0 00 0 standard neoclassical assumptions. Namely, f (k t ) > 0, f (k t ) < 0, lim kt !0 f (k t ) = 1 0 and lim kt !1f (k t ) = 0; 8 k t ‚ 0. Competitive markets imply that both factors earn their marginal products: 0 0 r = f (k ) and w = f(k )¡f (k )k (2) t t t t t t where r and w respectively denote the interest rate on physical capital and the wage t t rate paid to human capital. Suppose that the world interest rateis constant at r„: Since thesmall open economy permits unrestricted physical capital mobility, its interest rate is constant at r„ as well. This implies that the ratio of physical capital to human capital, k , and the wage rate t paid to human capital, w , are also constant: t r = r„= f 0 (k ) ) k = k „ = f 0¡1(r„) (3) t t t 5

and, w = f(k „ )¡f 0 (k „ )k „ = w„ (4) t 2.2. Individuals Individuals live for three periods in overlapping generations and they are endowed with one unit of time in every period. In the flrst period, they acquire a minimum level of education, e; mandated by law. In the second period, they get educated if investing in human capital is feasible, and they produce and rear children. In the third and flnal period, individuals work, consume and produce and rear children. Thus, in this model, individuals endogenouslydecide what portionoftheir lifetimeto devoteto child rearing3. In the second period, individuals born at time t¡1 invest in human capital. The acquisition of human capital requires time. An individual of generation t ¡ 1; who is born to a parent with h units of human capital, invests i , i †[0;1], units of time to t t t acquiring h units of human capital. These h units constitute the individuals labor t+1 t+1 supply in the last period of life. ‰ ‰ 1 h t+1 = `(h t ; e t ) = A:[h t + e t ]‰ (5) where A > 0; ¡1 • ‰ < 1 and where e ; e = e + i ; denotes the total amount of t t t education that the individiual accumulates throughout her lifetime: For the remainder of the discussion, we will follow the conventional notation that ` = @ht+1; ` = @ht+1; 1 @ht 2 @et ` = @2ht+1; ` = @2ht+1 and ` = @2ht+1 = ` = @2ht+1: 11 @h2 t 22 @e2 t 12 @h t @et 21 @e t @ht Let n and n respectively denote the number of children that the individual t t+1 chooses to have in the second and third periods. Since, in the second period, individuals 3This setup, without loss of generality, can be extended to include second period consumption. The crucial component of the model is not that individuals allocate their time between education and having children in the second period of life. Rather, it is that producing and rearing children take away some time from individuals’ human capital investment. Including in the analysis the assumption that individuals work in the second period as well will not alter the qualitative nature of the results. Similarly, the results of the model are not dependent on the assumption that the time costs of rearing children do not spillover in to the last period of life. 6

allocate their one unit of time between acquiring human capital and having and raising children, it follows that i + zn • 1; (6) t t where z; z > 0; is the time cost of producing and raising one child. Similarly,sinceindividuals allocatetheironeunitoftimeendowmentbetween work and producing and rearing children in the last period of life, l +zn • 1; (7) t+1 t+1 where l denotes the amount of time individuals allocate to work in the third period. t+1 Individualsreceiveutilityfromconsumptionandthetotalnumberoftheirchildren. There is no uncertainty and bequest motive. The utility of an individual of generation t¡1 is u t¡1 = u(n T ;c t+1 ) = a ln(n T ) + (1¡a) ln(c t+1 ) (8) where 0 < a < 1; n ; n = n +n ; denotes the total number of children the individual T T t t+1 chooses to have and where c denotes the consumption of the individual in the last t+1 period. Individuals maximize their utility as given by equation (8), subject to equations (6), (7) and the following budget constraint: c • w„ h l : (9) t+1 t+1 t+1 Therefore, the number of children that theindividuals choose to have in thesecond and third periods, n n ; respectively satisfy the following flrst order conditions: t; t+1 7

a z(1¡a)` a z(1¡a) 2 ¡ = ¡ ‚ 0 (10) n +n `(:) n +n e1¡‰ [h ‰ + e ‰ ] t t+1 t t+1 t t t a z(1¡a) ¡ • 0 (11) n +n (1¡zn ) t t+1 t+1 ~ Let h denote the level of parental human capital that makes the individuals indifferent to acquiring education. From equation (10), we derive that @i e z(1¡‰)(1¡a)n ¡ae1¡‰ [h ‰ + e ‰ ] t = t T t t t 8h > ~ h: (12) @h t h t 1¡‰ ( z(1¡‰)(1¡a)n T h ‰ t +e t [h ‰ t + e ‰ t ] ) t Thus, the optimal amount of time devoted to education by an individual born in period t¡1; i ; is strictly monotonicand non-vanishing 8h > h ~ , if e‚ 2(1¡a)(1¡‰) and the t t a¡‰ complementaritybetweentheparentalhumancapitalstockandeducationindetermining individuals’ human capital level is su–ciently large (i.e. the parameter ‰ is relatively small4). In that case, equation (12) is strictly positive 8h > ~ h, and, there exists a t difierentiable and invertable function, i(h ); that determines the optimal amount of time t individuals allocate to acquiring education, i ; and to producing and raising children in t the second period, n : t 0 for h • h ~ t i = (cid:176)(h ) = ; (13) t t 8 > < i(h ) < 1 for h > h ~ t t > : e = e+(cid:176)(h ) · e(h ); (14) t t t 4A necessary but not su–cient condition is for ‰ to be strictly less than zero. Therefore, ‰ is assumed to be strictly negative for the remainder of the discussion. 8

and 1¡i 1¡(cid:176)(h ) t t n = = : (15) t z z From equations (10) and (11), we also conclude that there exists a threshold ⁄ parental human capital level, h ; that equates the marginal costs of having and rais- ⁄ ing children in the second and third periods [i.e. when h = h ; ` (1 ¡zn ) = `(:)]. t 2 t+1 ⁄ When the parental human capital is less than or equal to h ; the marginal cost of having and rearing children in the second period is strictly lower than that in the third period. If as stated previously, e ‚ 2(1¡a)(1¡‰);increases in theparentalhuman capital stock raise a¡‰ the marginal cost of having children in the second period relative to that in the third. Consequently, max 0; 2a¡1 for h • h ⁄ z t n = ‡(h ) = 8 h i (16) t+1 t >> >< 1 z `2[ht; ` e( 2 h [h t) t ] ; ¡ e ` (h [h t) t ] ;e(ht)] = 1 z h ¡ t ‰(1¡ h e ¡ t t ‰ )¡e1 t ¡‰ for h t > h ⁄ >> and, >: @nt+1 = [e1¡‰h‰ + e ]f(a¡‰)e ¡z(1¡a)(1¡‰)n g > 0 @ht t t t t T (17) if e ‚ 2(1¡a)(1¡‰): a¡‰ Equations (13)-(16) imply the following about the behavior of individuals: When the stock of parental human capital, h ; is less than or equal to the threshold level of t ~ human capital, h; individuals do not flnd it optimal to invest time in education, i ; in t order to enhance their human capital stock in the following period, h : As a result, t+1 they choose to devote all of their time endowment in the second period to producing and rearing children. In addition, depending on the value that individuals place on having 9

children, which depends positively on the parameter a, individuals may devote part of their third period endowment to producing and raising children as well. Speciflcally, if a • 1; individuals choose not to get educated and have 1 children in the second period, 2 z and, no children in the last period. And if a > 1; individuals choose not to get educated 2 and have 1 children in the second period, and 2a¡1 children in the third period. When z z ~ the parental human capital stock, h ; exceeds the threshold level, h; individuals flnd it t optimal to allocate a positive amount of time to education. Since i = 1 ¡ zn ; this t t implies that they choose to have fewer children in the second period. Note also that equations (10) and (11) imply h ~ < h ⁄ if a • 1; and h ~ = h ⁄ if 2 a > 1: Hence, if a • 1 and when ~ h < h • h ⁄ ; individuals choose to have fewer 2 2 t children in the second period and they continue to have no children in the last period in response to increases in the parental human capital stock. In this case, individuals put relatively little emphasis on the total number of children compared to consumption that the amount of time that they devote to producing and rearing children in the second period is su–cient for them to have the optimal number of total children. Moreover, it is still optimal for them to have all of their children when they are young since the opportunity cost of doing so is still lower than that in the third period (or, alternatively ⁄ ⁄ because h • h ): Only when parental human capital reaches a level such that h > h ; t t do individuals choose to have more children in the third period and continue to have fewer children in response to increases in the parental human capital stock. In contrast, if a > 1 and when ~ h = h ⁄ < h ; individuals choose to have fewer children in the second 2 t period and more children in the third period in response to increases in parental human capital. In this case, individuals put relatively more emphasis on the total number of children compared to consumption that they need to devote some fraction of their time to producing and rearing children in the last period. Unlike the previous case, however, increased time devoted to education in the second period immediately leads to delayed childbearing and an increase in the number of children that individuals choose to have 10

in the third period, 8 h > h ~ . In sum, without examining whether human capital t accumulation leads to lower fertility, we can conclude that individuals choose to delay childbearing in response to increases in parental human capital5 . The intuition behind this conclusion is straighforward: increases in the stock of parental human capital raise the cost of childbearing in the second period relative to that in the last period and make not acquiring education in the second period \too costly". ~ Finally, we can easily establish that, when h > h; individuals choose to have fewer t children in total as the parental stock of human capital increases. Equation (11) implies that, when h > h ⁄ ; n = a 1¡znt+1: Thus, @nT = ¡ a @nt+1 < 0; 8 h > h ⁄ . In t T 1¡a z @ht 1¡a @ht t addition, if a • 1 and h ~ < h • h ⁄ ; then n n and @nT = ¡1 @it < 0: When h > ~ h, 2 t T= t @ht z@ht t totalfertilitydeclines asthereturnto educationincreasessimplybecausetheefiectofthe substitution of time devoted to education from childrearing in the second period always dominates the efiect of higher income on the number of children individuals choose to have in the last period. Figures 1 and 2 summarize the above discussion. 3. The Evolution of the Economy The evolution of this economy, and, in particular, the evolution of the stock of 1 human capital, fh g , is governed by an autonomous, non-linear, flrst-order difiert t=0 1 ence equation. The evolution of the human capital stock, fh g , in turn, determines t t=0 1 the evolutions of the amount of time allocated to education, fe g , the number of t t=0 1 children individuals choose to have in the second and third periods and in total, fn g , t t=0 1 1 fn g ; n = n +n ; and of per capita income, fy g . We derive equation (18) t+1 t=0 T t t+1 t t=0 by combining equations (5) and (14): 5Notethat,inthecontextofthemodelpresentedhere,delayedchildbearingarisesbecausetheaverage age of childbearing increases (as the fertility rate of young women declines while that of older women who are in the labor force rises with increases in the human capital stock) and not so much because individuals choose to have fewer children in the second period. Put difierently, delayed childbearing is not strictly a consequence of the order of activities in the second period as the model does not rely on the assumption that, in the second period, individuals flrst get educated and then they produce and rear children. 11

A:[h ‰ t + e‰]‰ 1 if h t • ~ h h t+1 = ˆ(h t ) = 8 (18) >> < A:[h ‰ t + e(h t )‰] 1 ‰ if h t > h ~ > >: where the initial stock of human capital, h , is historically given. 0 Along the dynamic path, h , evolves monotonically. Namely, t @h A:[1 + e‰h ¡ t ‰] 1¡ ‰ ‰ > 0 if h t • h ~ t+1 0 = ˆ (h t ) = 8 @h t >> < A:[1 + e(h t )‰h ¡ t ‰] 1¡ ‰ ‰ +A:[1 + e(h t ) ¡‰h‰ t ] 1¡ ‰ ‰ @ @ h et t > 0 if h t > ~ h > (19) >: A:(‰¡1)[h ‰ t + e‰] 1¡ ‰ 2‰ e‰ h t ‰¡2 < 0 if h t • ~ h 8 @2 @ h h t 2 t +1 = ˆ 00 (h t ) = >> >> >> >> A:(‰¡1)[h ‰ t + e(h t )‰] 1¡ ‰ 2‰ e ‰ t h t ‰¡2 +h ‰ t e(h t )‰¡2@ @ 2 h e 2 t t if h t > ~ h < n o > >> >> >>> +A:[h ‰ t + e(h t )‰] 1¡ ‰ 2‰ h t ‰¡1e(h t )‰¡1 @ @ h et t (20) : Furthermore, as obtained from equations (18) and (19) ˆ(0) = 0 (21) and, 0 lim ˆ (h ) = A > 0 (22) t ht !0 lim ˆ 0 (h t ) = A:[1 + e‰h ¡ t ‰] 1¡ ‰ ‰ +A:[1 + e ¡‰h‰ t ] 1¡ ‰ ‰ @e t > (23) ht !~h+ @h t 12

lim ˆ 0 (h t ) = A:[1+e‰h ¡ t ‰ ] 1¡ ‰ ‰ ht !~h ¡ 0 lim ˆ (h ) = 0 (24) t ht !1 „ A steady-state equilibrium is deflned as a stationary stock of human capital, h such that „ „ h = ˆ(h): (25) „ Once the stock of human capital is in its steady-state, h, per capita income, the total number of children individuals have and the amount of time individuals allocate to education reach their steady-state levels, respectively denoted by y„; n„ ;e„ as well. T Given equations (21)-(24) and ˆ(h ) is a continuous function of the human capital t stock, h ,weareableto establishthatanon-trivialstablesteady-stateexistsifA > 1. In t addition, multiple steady state equilibria may exist under certain parameter restrictions. Sincelim ht !0 ˆ 0 (h t ) = A, ˆ 00 (h t ) < 0 8 h t • h ~ , and ~ hdepends positively on the minimum ~ level of required education, e; non-trivial multiple steady-state equilibria exist if h > 0; ˆ( ~ h) < ~ h; 9 h t > ~ h such that ˆ(h t ) > h t and lim ht !1ˆ 0 (h t ) < 1: From equations (18)- (24), it follows that the above conditions are satisfled if A > 1 and the complementarity between parentalhuman capitaland education is su–cientlylargefor a given set ofother parameter values (i.e. for relatively small values of ‰): Note also that, as can be verifled from equation (23), the slope of the dynamical system in a close neighborhood to the ~ right of h is larger than that in a close neighborhood to the left of it. Figures 3 and 4, respectively illustrate the dynamical evolution of the system with unique and multiple steady state equilibria. 13

4. Conclusion In providing an explanation for the well-documented negative relation between human capital accumulation and fertility, existing work in the economics literature emphasizestimedivertedfromemploymentasthemainopportunitycostofhavingchildren,and stresses that increases in the return to human capital make more educated individuals’ time too valuable to care for children. In doing so, however, it ignores how individuals’ most productive periods in having children and acquiring human capital coincide, and, how timing of childbearing is inextricably linked to the fertility decision. The model presented above, incorporates the timing of childbearing into an economic growth model. The results highlight the importance of the feedback mechanism between the return to education (via the existing human capital stock) and timing of childbearing on economic growth: Increases in the human capital stock raise the opportunity cost of bearing children while young and induce individuals to delay childbearing. That, in turn, accelerates human capital accumulation in the future as younger generations devote relatively more time to education. The key feature of the preceeding analysis is the interdependence of parental human capital and education in determining individuals’ human capital stock. The model reveals that, if the complementarity between these variables in human capital formation is relatively large, in response to higher returns to education individuals delay childbearing until they join the labor force. This leads to the possibility of multiple steady-state equilibria: For countries with a low initial human capital stock, the interaction between human capital and timing of childbearing creates a development trap in which individuals are less educated and bear more children early. In contrast, countries with higher initial human capital stock converge to a steady-state in which individuals are more educated and have fewer children later. Moreover, the same interaction between timing of childbearing and human capital that leads to a development trap for other countries stimulates economic growth in these countries. The results also demonstrate that lower 14

fertility as well as delayed childbearing are consequences of the higher opportunity cost associated with time taken away from education relative to that associated with time taken away from employment. 15

5. References Azariadis, C. and Drazen, A., 1990,\Demographic Transition in a Dual Economy", mimeo, University of Pennsylvania. Barro, R. J., 1991, \Economic Growth in a Cross Section of Countries", Quarterly Journal of Economics, 106, 407-444. Becker, G. S. and Tomes N., 1986, \Human Capital and the Rise and Fall of Families", Journal of Labor Economics, 4, S1-S39. Becker, G.S., and Barro, R. J., 1988, \A Reformulation of the Economic Theory of Fertility", Quarterly Journal of Economics, 103, 1-26. Becker, G. S., Murphy, K. M. and Tamura R., 1990, \Human Capital, Fertility, and Economic Growth", Journal of Political Economy, vol. 98, No. 5, S12-S37. Birdsall, N., 1988, \Economic Approaches to Population Growth", in The Handbook of Development Economics, Chenery and T. N. Srinivasan eds., North Holland. Coleman, J. S. et al., 1966, \Equality of Educational Opportunity", (U.S. G.P.O., Washington, D.C.). Fuchs, V. and Reklis, D., 1994, \Mathematical Achievement in Eighth Grade: Interstate and Racial Difierences", NBER Working Paper Series, Paper No: 4784. Galor, O. and Weil D. N., 1996, \The Gender Gap, Fertility and Growth", American Economic Review, vol 86, No. 3, 374-87. Iyigun, M. F., 1995, \Human Capital Accumulation, Fertility and Growth: A Re- Analysis", Board of Governors of the Federal Reserve System, International Finance Discussion Papers, No: 523. Mankiw, N., Romer, D. and Weil, D. N., 1992, \A Contribution to the Empirics of Economic Growth", Quarterly Journal of Economics, 107, 407-437. Sundstrom, W. A. and David, P. A., 1988, \Old-Age Security Motives, Labor Markets and Farm Family Fertility in Antebellum America", Explorations in Economic History, 25, 104-197. 16

U.S. Department of Labor, Women’s Bureau, 1994, \1993 Handbook on Women Workers: Trends and Issues", (U.S. G.P.O., Washington, D.C.). 17

Figure 1: The evolution of fertility by period and total fertility when a • 1 2 18

Figure 2: The evolution of fertility by period and total fertility when a > 1 2 19

Figure 3: A globally stable, unique steady-state equilibrium 20

Figure 4: Locally stable, multiple steady-state equilibria 21