Alternatives in Human Capital Accumulation: Implications for Economic Growth

Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 550 May 1996 ALTERNATIVES IN HUMAN CAPITAL ACCUMULATION: IMPLICATIONS FOR ECONOMIC GROWTH Murat F. Iyigun and Ann L. Owen 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to International Finance Discussion Papers (other than an acknowledgment that the writer has had acccess to unpublished material) should be cleared with the author or authors.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 demonstrates that considering alternative means of human capital accumulation, such as learning-by-doing, overturns the presumption that formal education is unconditionally beneflcial for economic growth. It analyzes a model in which the average level of human capital creates externalities in future human capital accumulation and individuals can augment their human capital with work experience or education. The model shows that in the early stages of development, education enhances growth by creating a positive externality, and, in later stages, it may depress growth by leading to a negative externality. It also demonstrates the possibility of multiple equilibria in which low-income equilibria are characterized by under-education and high-income equilibria are characterized by over-education.

ALTERNATIVES IN HUMAN CAPITAL ACCUMULATION: IMPLICATIONS FOR ECONOMIC GROWTH Murat F. Iyigun and Ann L. Owen1 1. Introduction An overwhelming number of papers on the role of human capital in the growth process conclude that increased levels of human capital lead to either increased growth rates or increased levels of per capita income. Since, in many of these models, more education leads unequivocally to more human capital, the policy implications of this body of work are straightforward. A topic which has recieved considerably less attention in the growth literature, however, is the complex manner in which individuals increase their human capital and its implications for growth. We take this issue up in this paper, examining how individual decisions to accumulate difierent types of human capital afiect the growth of an economy. By identifying alternative means of accumulating human capital, we are able to show that an economy in the early stages of development may be under-educated but, at a later stage, may become over-educated. In addition, we show the possibility of multiple equilibria in which all equilibria are ine–cient{in the low-income equilibria, individuals do notchoose enough education, and, in thehigh-income equilibria they choose too much education. Thus, our model questions the presumption that more education always leads to higher growth and/or higher income and allows us to qualify the policy recommendations of earlier work, showing that the goals of the best educational policy change as an economy grows. To achieve these ends, we draw on well established ideas regarding the accumula- 1MuratF.IyigunisaneconomistintheDivisionofInternationalFinance,BoardofGovernorsofthe Federal Reserve System and Ann L. Owen is an economist in the Division of Monetary Afiairs, Board of Governors of the Federal Reserve System. This paper represents the views of the author and should not beinterpreted as re(cid:176)ecting those of theBoard ofGovernors of theFederalReserve 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. 1

tion of human capital and its efiect on growth found in several difierent strands of the literature. One of the main tenets of this paper is that the skills individuals accumulate through work experience are an important part of human capital. Support for this idea can be found in microeconomic studies of wage determinants [see for example Becker (1993) and Mincer (1993, 1996)], and also in macroeconomic examinations of growth through a learning-by-doing process [e.g. Lucas(1993) and Stokey (1988)]. A second element of our model is the role that the existing level of human capital plays in the accumulation of future human capital{the efiectiveness of an individual’s timespent accumulating human capitalincreases with theaverage level of human capital of the previous generation. The importance of the existing level of human capital in generating furtherhumancapitalhasbeenemphasizedinthegrowthliterature[seeLucas (1988), Azariadis and Drazen (1990), Romer (1990) and Galor and Tsiddon (1996) to name a few]. In addition, this speciflcation is also consistent with empirical flndings that show that family background plays an important role in educational attainment [See, for example, Coleman (1966)]. However, our deflnition of human capital that includes speciflc skills accumulated through work experience as well as improvements to overall mental ability enriches the usual story and allows us to examine the role that education plays in determining the growth and level of per capita income with a slightly difierent perspective. Thus, in our model, the level of human capital efiectively employed in an economy depends on the total skills of the workforce and not just those accumulated by investing in formal education. Becausea keyresult ofourmodelis thattheroleoffurtherinvestmentin education changes as an economy develops, in addition to the papers mentioned above, our work is also related to a few recent papers that have begun to question exactly how education afiects long-run growth2 . Benhabib and Spiegel (1994) argue that educated labor is not 2While severaloften cited studies[e.g. Barro (1991), Mankiw, Romer,Weil(1992)]that haveshown positive correlations between growth rates and school enrollment ratios might seem to suggest that schooling is always better for growth than its alternative, these cross-sectional results are not able to identify the possibility that higher growth could be achieved by a sub-sample of countries if they had a 2

a factor of production but only afiects per capita income through its efiect on the level of technology. Fershtman, Murphy and Weiss (1996) investigate conditions under which nonmonetary rewards in the form of occupational status lead to ine–ciencies in investment in education and a lower growth rate. Pritchett (1995) goes further in challenging the role education plays in determining per capita income, empirically flnding a negative association between the growth of education and total factor productivity. Iyigun and Owen (1995) also explore the role that increases in education play in development in a model in which there are alternative means of accumulating human capital and in which, depending on the stage of development, a parent’s level of human capital afiects the child’s ability to learn through schooling and work experience difierently. In what follows, we consider a three period overlapping generations model. In the flrst period of life, individuals work and go to school. Both of these activities compete for an individual’s time and enhance his skills in difierent ways. Education increases an individual’s general skills (critical thinking and general problem-solving skills) while workexperienceincreaseshisspeciflcskills (theamountofjob-speciflcskillsanindividual accumulates throughrepetition). Inthesecond period, individuals work; andin thethird period, they consume. There is one critical feature of this economy: the way job-speciflc and general skills are combined in output production is difierent than the way the two types of skills interact in human capital production. This setup creates a disparity between the sociallyandindividuallyoptimalchoicesofeducation. Intheearlystagesofdevelopment, increases in the average level of education serve as a positive externality, increasing the average level of human capital and therefore the efiectiveness of both education and work experience in accumulating future human capital. This leads to higher levels of human capital and per capita output for given levels of investment in education and work experience. However, because work experience also contributes to speciflc skills slightly less educated labor force. In addition, these studies typically focus on primary and secondary enrollment rates levels of schooling for which the negative externality we identify is not likely to exist. 3

but competes for time in the flrst period of life, at later stages of development, increased education \crowds out" investment in speciflc skills. In this case, further education may act as a negative externality, decreasing the efiectiveness of education and work experience in accumulating human capital and, as a result, decreasing per capita income. Therefore, when multiple equilibria exist in this economy, low-income equilibria will be characterized by under-education and high-income equilibria may be characterized by over-education. Our results are developed in the following four sections: Section 2 describes the basic model, Section 3 discusses its dynamic behavior, Section 4 considers social externalities, and Section 5 concludes. 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, Y ; is a single homogeneous good produced by a CRS production function that t usesphysicalcapital,K ;rawlabor,L ;generalskills, G ;andspeciflc-skills,S ;asinputs. t t t t The total output produced at time t, Y , is given by t Y = KfiG fl S1¡fi¡fl +L (1) t t t t t where fi;fl > 0 and fi+fl < 1: Thus, physical capital and the two types of skills are complements in forming a capital aggregate which substitutes for raw labor in production3. Capital-skillcomplementarity wasanideaadvancedbyGriliches (1969), and Hamermesh (1986) reports on a number of studies that support Griliches’ initial result. 3Our results would hold with alternative production functions (i.e. raw labor could complement the capital aggregate). When raw labor enters the production function as a substitute, however, the dimension of the dynamical system is reduced and the following analysis is considerably simplifled. 4

The aggregate inputs in production are the sum of individual values, and, as will be explained further in the next section, general and job-speciflc skills and raw labor can all be supplied by a single individual. We consider S (job-speciflc skills) and G (general t t skills) to be the two components of human capital. Speciflcally, we deflne job-speciflc skills as the portion of an individual’s labor supply that is enhanced by the acquisition of knowledge about completing speciflc tasks. The more tasks an individual can complete, the higher is his level of speciflc skills. In contrast, general skills is the portion of an individual’s labor that allows him to critically analyze and solve problems. The distinction we make is analogous to the distinction labor economists have traditionally made between flrm-speciflc and general skills. In our one-sector model, however, speciflc skills can be transferred between flrms. Suppose that the world interest rate is stationary at a level r„: Since the small open economy allows unrestricted capital movement, its interest rate is stationary at r„as well. G fl S1¡fi¡fl G fl S1¡fi¡fl r = fi t t = r„ ) t t · ' > 0; (2) t " K t 1¡fi # " K t 1¡fi # Due to the existence of competitive markets, factors of production earn their marginal products. Namely, 1¡fi¡fl w g = w„fl S t 1¡fi t G (cid:181) t¶ fl G 1¡fi ws = w„(1¡fi¡fl) t (3) t ˆS t! wl = 1 t where w„ · 1='1¡ fi fi and where w t g; w t s and w t l respectively denote the wage rates paid to general skills, speciflc skills and raw labor at time t. 5

2.2. Individuals Individuals live for three periods in overlapping generations. The size of the population is normalized to one and there is no population growth. Individuals are endowed with one unit of time and raw labor input in every period. At birth, they are endowed with no amount of general or speciflc skills. In the flrst period, individuals divide their time between education and work. Both activities help individuals augment their total labor input. In the second period, they supply all of their labor endowment, including any general and speciflc skills they have accumulated, to the labor market, and they save. In the third period, individuals consume. Weassumethatthetimedevotedto education, et¡1;increases anindividual’sstock t¡1 of general skills, gt¡1; whereas time devoted to work, xt¡1; increases his speciflc skills, t t¡1 st¡1 (We will follow the convention that a subscript denotes the time period in which t the variable is observed and the superscript denotes with which generation a variable is associated.) : g t t¡1 = (cid:176)‚ t¡1 g(et t ¡ ¡ 1 1 ) (4) and, st t ¡1 = (1¡(cid:176))‚ t¡1 s(xt t ¡ ¡ 1 1 ) (5) 0 0 00 00 0 0 where 0 • (cid:176) • 1;g (:);s(:) > 0; g (:);s (:) < 0;and where (1¡(cid:176))s(1) < (cid:176)g (0) < 1:In the above equations, ‚ t¡1 denotes the externality that the average level of human capital in period t¡1 generates by making the amount of time spent working or in school more efiective in generating human capital, and, (cid:176) is a parameter that represents the relative importance of education in the accumulation of human capital. Let ht¡1denote the individuals’ total human capital stock in the second period, t which is a function of general skills, gt¡1 and the stock of speciflc skills accumulated t; through work experience, st¡1: t 6

ht¡1 = f(gt¡1; st¡1) (6) t t t where f(gt¡1; 0); f(0; st¡1) > 0; @ht t ¡1 = f (:); @ht t ¡1 = f (:) ‚ 0; @2ht t ¡1 = f (:); t t @gt¡1 1 @st¡1 2 @(gt¡1)2 11 t t t @2ht¡1 @2ht¡1 @2ht¡1 t = f (:) • 0; t = f (:) = t = f (:) ‚ 0: We assume that the @(st¡1)2 22 @gt¡1@st¡1 12 @st¡1@gt¡1 21 t t t t t function f(gt¡1;st¡1) is homogenous of degree 1. Thus, we can rewrite equation (6) as t t ht t ¡1 = ‚ t¡1 f[(cid:176)g(et t ¡1); (1¡(cid:176))s(1¡et t ¡1)] (7) Weassumethattheexternalityinhumancapitalaccumulationinperiodt¡1, ‚ t¡1 ; is an increasing concavefunctionoftheaveragehuman capitalstockinthatperiod, h t¡1 : 0 00 ‚ t¡1 = ‚(h t¡1 ); where ‚(h t¡1 ) ‚ 0; ‚ (h t¡1 ) • 0 (8) Note that since all individuals are identical within a generation, the old do not work, and the young have no human capital, the average level of human capital, h t¡1 ; is equal to the level of human capital of a middle-aged worker, ht t ¡ ¡ 2 1 . Thus, ‚ t¡1 represents the older generations’ efiect on the human capital of the young{an individual’s work experience and schooling is more efiective in producing human capital if members of the older generation have higher levels of human capital. Individuals receive utility from consumption in the third period. The utility of an individual of generation t¡1 is ut¡1 = u(ct¡1) (9) t+1 where u 0 (:) > 0;u 00 (:) < 0 , and, where ct¡1 denotes the consumption of the individual t+1 in the last period. 7

Individuals maximize their utilityas given by equation (9), subject to et¡1+xt¡1 • t¡1 t¡1 1 and to the following budget constraint: ct¡1 • (1+r„)It¡1 = (1+r„)[(1+(1+r„)xt¡1)+w g gt¡1 +wsst¡1] (10) t+1 t t¡1 t t t t Therefore, the optimal amount of time allocated to education by the individual, et¡1, satisfles the following flrst order condition: t¡1 1+r„ (cid:176)g 0 (et¡1)wg ¡(1¡(cid:176))s 0 (1¡et¡1)ws = (11) t¡1 t t¡1 t ‚(h t¡1 ) Equation (11) implies that the optimal amount of time devoted to education by an indiviudal born in period t¡1, et¡1 is a non-decreasing function of the average parental t¡1 human capital stock in period t¡1. Namely, 0 for h t¡1 • h ~ ; @et¡1 @h t t ¡ ¡ 1 1 = 8 >> >> < >>> ¡ (cid:176) ‰ w t gg00(:)+g0(:) @ @ e w t t ¡ ¡ t g 1 1(cid:190) + 1+ (1 r„ ¡(cid:176)) ‰ w t ss00(:)¡s0(:) @ @ e w t t ¡ ¡ t s 1 1(cid:190) [‚ ‚ ( 0 : ( ) : ] ) 2 > 0 for h t¡1 ( > 12 h ) ~ >: ~ where h is the highest value of the parental human capital stock for which individuals choose no education. Thus, 0 for h t¡1 • ~ h et¡1 = (13) t¡1 8 > < e(h t¡1 ) for h t¡1 > h ~ and, > : lim et¡1 < 1 (14) h t¡1 !1 t¡1 8

3. The Evolution of the Economy In this economy, the human capital stock in period t; h ; is determined by the t human capital stock in the previous period; h : Namely, t¡1 ‚(h t¡1 )f[(cid:176)g~; (1¡(cid:176))s~] for h t¡1 • ~ h h t = ˆ(h t¡1 ) = 8 > < ‚(h t¡1 )ff(cid:176)g[e(ht t ¡1)]; (1¡(cid:176))s[1¡e(ht t ¡1)]g for h t¡1 > ~ h (15) >: where g~ · g(0); s~· s(1) and where the initial stock of human capital, h is historically 0; given. The evolution of the economy can be further characterized by 0 ~ ‚(h t¡1 )f[(cid:176)g~; (1¡(cid:176))s~] ‚ 0 for h t¡1 • h 8 > >> >> @ @ h h t¡ t 1 = ˆ 0 (h t¡1 ) = >>> >> >> >> ‚ 0 (h t¡1 )ff(cid:176)g[e(ht t ¡1)]; (1¡(cid:176))s[1¡e(ht t ¡1)]g for h t¡1 > ~ h < > >> >> >> +‚(h t¡1 )f(cid:176)f 1 (:)g 0 [e(h t¡1 )]¡(1¡(cid:176))f 2 (:)s 0 [1¡e(h t¡1 )]g @ @ h et t t ¡ ¡ ¡ 1 1 1 >>> >> >> (16) : When h t¡1 • ~ h, the human capital stock is increasing in the previous generation’s level. When h t¡1 > ~ h, it is not possible to sign @ @ h h t¡ t 1 in all cases. For low values of h t¡1 , 0 0 e(h t¡1 ) is also low and (cid:176)f 1 (:)g [e(h t¡1 )] > (1¡(cid:176))f 2 (:)s[1¡e(h t¡1 )], and a non-negative slope for ˆ(h t¡1 ) is ensured. However, for su–ciently high values of h t¡1 , it is possible that (cid:176)f 1 (:)g 0 [e(h t¡1 )] < (1¡(cid:176))f 2 (:)s 0 [1¡e(h t¡1 )], and, thus, for some speciflcations, @ @ ht h ¡ t 1 may be negative. Nonetheless, we are able to establish 0 lim ˆ (h t¡1 ) = 0 (17) ht¡1 !1 9

In addition, ‚ 00 (h t¡1 )f[(cid:176)g~; (1¡(cid:176))s~] • 0 for h t¡1 • h ~ 8 > >> >>> >> >> >> >> ‚ 00 (h t¡1 )ff(cid:176)g[e(:)]; (1¡(cid:176))s[1¡e(:)]g for h t¡1 > ~ h >>> @ @ h 2 2 t h ¡ t 1 = ˆ 00 (h t¡1 ) = >> >> >> >> >>> >> >> < +2‚ + 0 ( ‚ h ( t¡ h 1 t¡ )f 1 (cid:176) )f f (cid:176) 1 ( 2 : f ) 1 g 1 0 ( ¡ :)( ( g 1 0 ) ¡ 2 + (cid:176)) ( f 1 2 ¡ (:) (cid:176) s 0 ) g 2 @ f @ h e 2 t t t 2 ¡ ¡ ¡ ( 1 1 1 :)(s 0 )2g @ @ h et t t ¡ ¡ ¡ 1 1 1 > >> >> >> >>> >> ¡2(cid:176)(1¡(cid:176))‚(h t¡1 )f 12 (:)g 0 (:)s 0 (:) @ @ h et t t ¡ ¡ ¡ 1 1 1 >> >> >> >>> >> >> +‚(h t¡1 )f(cid:176)2f 1 (:)g 00 +(1¡(cid:176))2f 2 (:)s 00 g @ @ 2 h e 2 t t t ¡ ¡ ¡ 1 1 1 >> >> >>> (18) : Noting that 0 0 lim ˆ (h t¡1 ) = ‚(h t¡1 )f[(cid:176)g~; (1¡(cid:176))s~] ‚ 0 (19) ht¡1 !0 0 and that ˆ (0) can be greater than 1, using (17), we are able to establish the existence of at least one steady state. Figure 1 depicts one possible shape for ˆ(h t¡1 ) when there is one steady state level of h . t It is also possible, however, that multiple steady states exist. We demonstrate the ~ ~ possible existence of multiple steady states by example. In particular, when ˆ(h) < h, a steady state with no education exists. An examination of equation (11) reveals that thereexistsparametervalues suchthattheopportunitycosts of educationare su–ciently high so that individuals allocate no time to education. For example, a su–ciently high value of the world interest rate, r„, and/or a low value of ‚(:) evaluated at et¡1 = 0 would t¡1 10

satisfy this condition. This guarantees the existence of a steady state with no education ~ ~ (i.e. ˆ(h) < h): Moreover, ‚ 0 (h ~ )f[(cid:176)g~; (1¡(cid:176))s~] 8 0 ht¡ l 1 im !~h+ ˆ (h t¡1 ) = >> >> >< + ‚(h ~ )f(cid:176)f 1 (:)g 0 (0)¡(1¡(cid:176))f 2 (:)s 0 (1)g @ @ h et t t ¡ ¡ ¡ 1 1 1 (20) >> >> >: Thus, (20) implies that the slope of the function ˆ(h t¡1 ) can be large enough to 0 guarantee the existence of a steady state with education, provided that (cid:176)f (:)g (0)¡(1¡ 1 0 0 0 (cid:176))f (:)s(1) is su–ciently large. The term (cid:176)f (:)g (0) ¡ (1 ¡ (cid:176))f (:)s(1) identifles the 2 1 2 net marginal efiect of an increase in education when individuals devote no time to it. Thus, if it is su–ciently high, a steady state with a positive amount of time devoted to education exists. The evolution of the human capital level, h ; under these conditions is t depicted in Figure 2. 1 In this economy, the evolution of the human capital stock, fh g , in turn detert t=0 1 mines the evolution of the amount of time allocated to education, fe g ; the stock of t t=0 1 1 general skills, fG g ; the stock of speciflc skills, fS g ; the net amount of raw labor t t=0 t t=0 1 1 input, fL g ; and per capita income, fy g : t t=0 t t=0 4. Externalities In our model, increases in the stock of skills enhance the accumulation of future skills. We have demonstrated that, in response to increases in the average skill level, individuals choose to allocate a positive and increasing amount of time to education ~ once the human capital stock is above the threshold level, h: Thus, when the human capital stock is monotonically increasing as an economy develops, the total stock of general skills, G increases and the stock of speciflc skills accumulated through work t; experience, S declines. t; 11

Because both general and speciflc skills afiect the externality that the average level of human capital generates and the individual’s private reward difiers from the social reward, a socially ine–cient level of education will result. In particular, individuals’ suboptimal choice of education will generate slower growth during the transition to the steady state. However, contrary to the standard result that individuals do not choose enough education, our model, which includes job-speciflc skills as part of human capital, demonstrates that the nature of the ine–ciency can change as an economy grows and accumulates more human capital. In fact it is trivial to show that, when the marginal efiectoftimeallocatedtoeducationinproducinggeneralskillsisgreaterthanthatoftime 0 0 allocated to work in producing speciflc skills (i.e. (cid:176)f (:)g (:) > (1 ¡ (cid:176))f (:)s(:)), more 1 2 education leads to a higher positive externality in human capital accumulation, faster accumulation of the factors of production and a higher economic growth rate4. During these periods, individuals choose to allocate too little time time to education since they do not take into account the positive efiect increases in their education would have on the human capital of the next generation. In other words, at low levels of development, the efiectiveness of education in producing general skills is not high enough to produce a private return to education that is as high as the social return to education5. Nevertheless, as the stock of human capital increases, individuals choose to devote more time to education. In fact, in later stages of development, if the marginal efiect of time allocated to education in producing general skills becomes less than that of time al- 0 0 locatedtoworkinproducingspeciflcskills(i.e. (cid:176)f (:)g (:) < (1¡(cid:176))f (:)s(:)),theoptimal 1 2 amountoftimethatindividuals devotetoeducation createsa negativesocialexternality{ factor accumulation would be faster at lower levels of education. This situation will occur if the marginal private reward for investing in education, w t g(cid:176)‚(h t¡1 )g 0 (et t ¡ ¡ 1 1 ), is \too high" and does not provide the appropriate incentive to invest in the socially optimal 4Note that ‚(ht¡1) reaches a maximum when (cid:176)f1(:)g0 (:)=(1 ¡ (cid:176))f2(:)s0 (:). 5The distinction between the return to education and the return to general skills is an important one. At lowlevelsof development,thewage return to general skillswould behigh,but education is not very efiective in producing general skills, and thus, the private return to education would be lower. 12

level of education. Of course, the likelihood that this situation will occur will be greater for higher values of fl which, in our formulation, determines the share of general skills in total income: Thus, whentherearemultiplesteadystatesinthiseconomy, itispossiblethatnone are e–cient. At the low-income steady state, individuals invest too little in education, andattheuppersteadystate,individualsinvesttoomuch. Percapitaincomeatthelower steady state can be increased by raising investment in education and per capita income in the upper steady state can be increased by lowering investment in education (and increasing investment in speciflc skills). Even when there is only one steady state, the dichotomy between private and social returns creates ine–ciencies along the transition to it. Growth is flrst slowed by under-investment in education which may, in later stages of development, turn into over-investment in education. It is important to note that the key feature of the model that produces the ine–ciencies is that general and speciflc skills are combined in difierent ways in production and in the formation of the human capital. Insum,includingworkexperienceasavalidmethodofaccumulatinghumancapital and valuing the job-speciflc skills that result from it can have important implications for the dynamic behavior of the economy. To emphasize this point, we could consider a subset of our model that puts little emphasis on the role that work experience plays (For example, this can be done by setting (cid:176) in equation (7) very large). In this subcase, the efiect of work experience is minimized and an overeducated steady state cannot be achieved. Thus, our model resembles the more traditional models in which education is the primary means of accumulating human capital. Because the inclusion of work experience leads to such dramatically difierent results, we are led to conclude that the existence of alternative means of accumulating human capital, such as through work experience, is a possibility to be carefully considered. 13

5. Conclusion We have attempted a look inside the black box called aggregate human capital. In doing so, we have shown that the complex manner in which individuals accumulate human capital and the way in which individuals are rewarded for accumulating human capital of difierent types can have important implications for the evolution of the economy. Our model demonstrates that in countries with a large human capital stock, individuals may obtain more than the socially optimal level of education. At the same time, a less developed economy with the same production technology can be under-educated. Thus, increased time devoted to education can lead to either a positive or negative externality. Thepossiblepresenceofmultipleequilibria addsan interesting twistto theusualstory{it is possible that none of the equilibria generated by our model are e–cient, but they are ine–cient for difierent reasons. Low-income equilibria are characterized by not enough education and high-income equilibria are characterized by too much education. The key mechanism of our model is that the difierent types of skill determine the efiectiveness of investing in education and work experience in a difierent manner than they determine wages. Because there is a tradeofi in accumulating general versus job-speciflc skills, the over-accumulation of one factor causes the under-accumulation of the other. Thus, including work experience as a valid method of accumulating human capital can have important implications for the dynamic behavior and e–ciency of the economy. Giventhemicro-levelevidencefortherolethatexperienceplaysindetermining an individual’s human capital, we believe this to be an important and justifled inclusion in our analysis. Our conclusions are important for policymakers because they suggest that education is not a panacea for slow growing economies. Optimal policies will have goals for increases in educational attainment that evolve with the economy. More generally, our results indicate that a thorough macroeconomic investigation of all of the channels of human capital accumulation is necessary to efiectively formulate and implement the 14

most successful policies. This is a fruitful area for further research. 15

6. References Azariadis, C. and A.Drazen, 1990, \Threshold Externalities in Economic Development", Quarterly Journal of Economics, 105, 501-26. Barro, R. J., 1991, \Economic Growth in a Cross Section of Countries", Quarterly Journal of Economics, 106, 407-444. Becker, G. S., 1993, Human Capital: A Theoretical and Empirical Analysis, with Special Reference to Education, (The University of Chicago Press, Chicago). Benhabib, J. and M. M. Spiegel, 1994, \The Role of Human Capital in Economic Development: Evidencefromaggregatecross-country Data", Journal of Monetary Economics, 34, 143-173. Coleman, J. S. et al., 1966, \Equality of Educational Opportunity", (U.S. G.P.O., Washington, D.C.). Fershtman,C.,K.M.Murphy,andY.Weiss,1996,\SocialStatus,EducationandGrowth", Journal of Political Economy, 104(1), February, 108-132. Galor, O. and D. Tsiddon, 1996, \The Distribution of Human Capital and Economic Growth", Journal of Economic Growth, forthcoming. Griliches, Z., 1969, \Capital-Skill Complementarity", Review of Economics and Statistics, 51(4), November, 465-68. Hamermesh, D. S., 1986, \The Demand for Labor in the Long Run", in Handbook of Labor Economics, Vol. I, edited by O. Ashenfelter and R. Layard, (New York: North Holland), 429-71. Iyigun, M. F. and A. L. Owen, 1995, \The Accumulation of Human Capital: Alternative Methods and Why They Matter", mimeo. Lucas, R. E., 1993, \Making a Miracle", Econometrica, Vol. 61, No:2, March, 251-72. Mankiw, N. G., D. Romer and D. N. Weil, 1992, \A Contribution to the Empirics of Economic Growth", Quarterly Journal of Economics, 107, 407-437. 16

Mincer, J., 1993, Studies in Human Capital: Collected Essays of Jacob Mincer, Vol. 1, (Brookfleld, VT: Edward Elgar Publishing Company). Mincer, J., 1996, \Economic Development, Growth of Human Capital and the Dynamics of the Wage Structure", Journal of Economic Growth, 1(1), March, 29-48. Pritchett, L., 1995, \Where has all the education gone?", mimeo. Romer, P.M., 1990, \Endogenous Technological Change", Journal of Political Economy, 98(5), October, 571-602. Stokey, N. L., 1988, \Learning by Doing and the Introduction of New Goods", Journal of Political Economy, XCVI, 701-717. 17

Figure 1: Figure 2: 18