Risk, Entrepreneurship, and Human Capital Accumulation

July 1997 Risk, Entrepreneurship and Human Capital Accumulation .-. Murat F. Iyigun iyigunm@frb.gov Ann L. Owen aowen@frb.gov Board of Governors of the FederalReserve System Abstract a important role in countries, human time professional may end up in a returns, or Keywords: Human Capital, Occupational Choice, Education, Entrepreneurship,Growth JEL Clmsification Numbers: J24, 011, 040 JohnM. Heitkempeprrovidedvaluableresearchassistance.Thispaperrepresentstheviewsof the authorsandshotidnotbe interpretedasreflectingthoseof theBoardof Governorsof theFederal ReserveSystemorothermembersofitsstaff.Pleasesendallcorrespondencteo:TheBoardofGovernors oftheFederaRl eserveSystem,MailStop23,WashingtonD, .C.20551.

1. Introduction Both entrepreneursand professionals are important components of an economy’s human capital stock. But each provide differentskillsto the economy and influence the level of technology and the utilization of the existing technology in potentially different ... ways. This paper explores the implications for growth of the existence of more than one type ofhumancapital, showinghowthechoice betweenentrepreneurshipandprofessional employment evolves as an economy develops and examining how individuals’ decisions to accumulate differenttypes of human capital affect the economy’s long-run potential. There arethreemainresults. First,entrepreneurialhumancapital playsarelatively more important role in intermediateincome countries,whereasprofessionalhuman capital isrelativelymore abundant inrichereconomies. We demonstrate that asaneconomy develops, individuals choose to investmore time accumtiating professionalskillsthrough schooling than accumulating entrepreneurialhuman capital. The resultingchange in the relativestocks of entrepreneurialand professionalhuman capital is a direct consequence of our assumption that providing professional services is a relatively safe activity and providing entrepreneurialskillsis risky. As per capita income grows and the payoff to being a professional increases, individuals are less willing to gamble on entrepreneurial ventures. This phenomenon occurs even though the expected value of entrepreneurship riseswith per capita income. While entrepreneursin a more developed economy face a clearly better lottery than entrepreneursin a less developed economy, the price of the lottery ticket–foregoneprofessionalearnings-is higherin the developed economy, making individuals lesswilling to take the bet. Second, we find that, in an economy where both entrepreneurialand professional human capital affect the future level of technology, the initial stocks of bothtypes of human capital areimportant for the process of development. If a country startsoff with too little of either entrepreneurial or professional human capital, it may end up in a 1

development trap in which production is carried out only with unskilledlabor and there is no human capital investmentof any type. Our third result is the natural outcome of considering more than one type of human capital in the presence of a production externality–an inefficientallocation of time between schooling and experience can result. By identifying alternative means of ac- ‘-” cumulating human capital, we are able to show that an economy in the early stages of development may have too little education, but in later stagesof development may have too much education. Whether there is too much education or too little, however, depends on how professionaland entrepreneurialskillsaffect the levelof technology. When entrepreneurialhuman capital is more important than professionalhuman capital in determining the level of technology, the steady state will have too many professionals and too fewentrepreneurs. Thus, areduction in education and anincreasein entrepreneurial experience could increase per capita income. Appropriate tax policy may be able to achieve the efficientoutcome. This paper is motivated, in part, by a stylized fact–in economies with higher per capita income, fewer individuals are employers compared to the number of individuals who work for others (see Figure 1). If we equate working for another with less risk, our model would generatesuch an outcome, with individuals choosing the relativelysafe return of schooling in greaterproportion as per capita income grows. We arealsomotivated by previousworkthat hasexaminedhowoccupational choice is affected by development. Banerjee and Newman (1993) show how the distribution of wealth and credit market imperfections influence an individual’s ability to become an entrepreneur. In their model, there is a fixed cost to becoming an entrepreneurand the distribution of wealth determines the percent of the population that undertakes such a venture and becomes an employer. We take a slightly different view on defining entrepreneurship, choosing to focus on the element of risk inherent in the concept rather 2

than the structure of employment. Thus, while both models generate the result that high income economies will have more employer-employee relationships, our model focuses particularly on how the incentivesto accumulate professional and entrepreneurial human capital change m an economy grows. Specifically, while Banerjee and Newman (1993) demonstrate that economic development may foster entrepreneurialinvestment, ‘-our model shows that, as economies develop, the increasing risk of entreprenuerialventures has an offsetting negative effect on resourcesdevoted to entrepreneurshiprelative to that devoted to professional activities. Our useof more than one type of human capital also tiesinto recentwork that has begun to question the role education plays in development and growth. Benhabib and Spiegel (1994) argue that educated labor is not a factor of production but only affects per capita income through its effect on the levelof technology. Fershtman,Murphy and Weiss (1996) investigate conditions under which nonmonetary rewards in the form of occupational status lead to inefficienciesin investmentin education and a lower growth rate. Pritchett (1995) goes furtherin challengingthe role education playsin determining per capita income, empirically finding a negative msociation between the growth of education and total factor productivity. By acknowledgingthe validity of more than one type of human capital, our paper points out that alternativesto schooling can also play an important role in development, implicitly downplaying the importance of education. The groundwork for our model hm been laid in many previous papers on related topics. 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 macroeconomic studies of wage determinants [seefor 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 3

determination of future technology, a theme that has been emphasized in the growth literature [seeLucas (1988), Azariadis and Drazen (1990), Romer (1990) and Galor and Tsiddon (1997) to name a few]. However, our definition of human capital that includes entrepreneurialhuman capital accumulated through work experience enrichesthe usual ... story and allowsus to examine the role that education plays in determining the growth and level of per capita income with a slightly differentperspective. Thus, in our model, the levelof human capital effectivelyemployed in an economy depends on the total skills of the workforce and not just those accumulated by investing in formal education. Inwhat follows, we presenta three-period overlapping-generationsmodel. Human capital and a labor aggregate are the only factors of production, but human capital is the sum of both professional and entrepreneurial human capital. When the wages paid to human capital providers are greaterthan the wagesearnedby labor, individuals accumulate professional human capital by investing time in schooling and accumulate entrepreneurial human capital by investing time working as an entrepreneur. A key differencebetweenthe two types of human capital isthat the rewardpaid to professional human capital is certain but the payoff to entrepreneurialhuman capital is not. The level of technology employed by any one generation of workersis determined by the levelof professionalandentrepreneurialhumancapital of the previous generation. Thus, m the stock of professional and entrepreneurialskillsgrow, the compensation to professional human capital and the expected compensation to entrepreneurial human capital increase. However,asthe returnto the safeactivity increases,individuals devote more time to schooling and lesstime to gaining entrepreneurialexperience. In essence, individuals in high income economies with higher wages to professionals have more to lose by gambling on an entrepreneurialventure. [f the way professional and entrepreneurialhuman capital are combined in output production is different from the way the two types of human capital are combined to 4

determine the level of technology, then time devoted to schooling will be inefficient. In other words, if developing the technology utilizes the two types of human capital in a different way than implementing the technology, individuals, whose compensation is based on their contribution to output production, will not choose the socially optimal ... combination ofschooling andentrepreneurialinvestment. Inparticular, ifentrepreneurial ventures are more important in determining the level of technology and less important in its utilization, then the steady state levelof education will be too high and per capita income would be higher with more entrepreneursand fewerprofessionals. These restits 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 an economy that operates in a perfectly competitive world in which economic activity extends over an infinite discrete time. The output of the economy, Yt,is a single homogeneous good produced by a CRS production function that uses a labor aggregate, Lt, and human capital, inputs. The total output produced at time t, Yt, is given by Yt= At + (1) where the technology level in period t, denoted by At,complements the human capital input, Thus, technological change in this economy is skill-biased. We assume that markets are competitive which implies that factor inputs earn 5

their marginal products: (2) where w: and w: respectively denote the returns to human capital and labor. 2.2. Individuals Individuals live for threeperiods in overlapping generations. The sizeof the population is normalized to one and there is no population growth. Individuals are endowed with one unit of time in every period. At birth, they areendowed with an innate mental ability level, which we assume to be drawn from a uniform distribution function. Therefore, E 1 —da~ = 1. (3) Ig Ii-a where ~,Qrespectively denote the upper and lowerbounds of the ability distribution. Individuals’ innate mentalability levels, augmenttheirhuman capital input. In the firstperiod, individuals decide whetherthey will be labor or human capital suppliers during their lifetime. If they chose to become labor providers, they devote all of their time endowmentinthe firstandsecond periods to work. Ifthey choose to become human capital suppliers, they also decide on what fraction of their time in the first period to devote to accumulating professional human capital through education and to acquiring entrepreneurialhuman capital by workingin an entrepreneurialventurel . In the second period, individuals supply their total human capital endowment and they save. In the third period, individuals consume their savings. l~e have~ho~entfis specificationto keeptheanalysistractable.A morerealisticversionof the model,howeverc,otid incorporateanotherdimensionintoinnatementalability.Inthatcase,those individualswhopossesshigherinnateentreprenueriaablility(relativetoprofessionalw)otidspecialize inentrepreneurshwiphileotherswo~d choosetobecomeprofessionalsT.hequalitativenatureofthe conclusionws ereachbelowshouldnotbeaffectedunderthisalternativeformulation. 6

We assumethat the time devoted to education, s~,increasesan individual’s stock of professional human capital, p~+l, whereas time devoted to work, z;, incre~es his entrepreneurialhuman capital, ej+l: p = (5) where the standard Inada conditions hold and where V zj, S: 20, j’(.) >0, f“(.) <0. One can think of the time devoted to work to augmententrepreneurialhuman capital m a start-up cost for entrepreneurialventures. During this time the individual can learn effective techniques for running a business. We also assumethat there is uncertainty in the return to entrepreneurialventures but that the return to education (which generates professional human capital in the following period) is not subject to any uncertainty. Specifically, individual z’s income from becoming an entrepreneur, (~~+l)e,is ~:+le;+l= ~t+le:+l with probability (1:+,)’ = = with probability {“ and from professional activities, (~~+l)p,is his income ( = W = ~~t+lP;+l.: :+ +l (7) where O< q < 1 In equation (6), # representsthe fixed payoff to being an entrepreneur in the bad state. The probabilities q and 1– q arethe probabilities of successand failure 7

faced by eachindividual. In aggregate,givenasufficientlylargenumberof entrepreneurs, q percent will succeed and 1– q percent will fail. Those that fail essentiallysupply units of unskilledlabor to the economy. Finally,wesssumethat theleveloftechnology inperiod t+l, At+l,isdeterminedby the averagelevelsof the entrepreneurialand professionalhuman capital in the previous ‘--” period. Specifically, ~ = ~ P (8) where Aj+l = ~ aA ‘ ’ , G * > (), ~t+l ~ -~, Afil ~ ~ <0 and ~~~1= ~~;jj; , ~g;l _ a 1 apt~t > 0“ Individuals maximize expected utility from consumption in the third period and their rate of time preferenceis zero. We resume that the expected utility of individual i of generation t takesthe following form2: q)ln[(c~+2)1-ql E[u(c~+2) It] = qln[(c~+2)q] + (1 – (9) l–~ respectively denote the consumption of individual z in the where (c~+2)qand (cj+2) good and bad states. In addition to s; + z: ~ 1,individual i is subject to the budget constraint below: 2 if zis a labor provider = (lo) (~:+l+)e(~;+l)p if zis a human capital provider { zwehavechosenlogmit~c preferencestodemonstrattehatincrewingrelativeriskaversionisnot necessaryto generatethe decliningwillingnessto gambleon entrepreneurshipasper capitaincome grows.Clearly,thisrwdt couldbegeneratedwithanyutilityfunctionthatfeaturesincreasingrelative riskaversion,andsome,butnotall,utilityfunctionsthatfeaturedecreasingrelativeriskaversion. 8

where (~~+l)eand (~~+l)pare given by equations (6) and (7). Given the problem specified above, there exists a threshold innate ability level for every period t–that, henceforth we will denote tit-below which individual i will choose to be a labor supplier. Combining equations (4)-(7), (9) and (10), we can show that fit satisfiesthe following equality: If individual i’s innate mental ability level is such that ai > fit,individual i–while youg–chooses to accumulate human capital instead of supplying labor. In that case, the optimal amount of time allocated to education by the individual, s;, satisfies (12) Notethat thefirst-ordercondition above impliesthat theamount of timeindividual i devotes to schooling is independent of his innate ability levelai. Put differently,s = s Vi such that ai > tit3. Equations (11) and (12) lead to the propositions below: Proposition 1: V t < innate a 3Analternativemodelling&oice,havingthepayoffto entrepreneurshiinpthebadstatenotde penalon individualability,wodd haveresultedin individualsof differentability choosingdifferent levelsofschooling.We didnotpursuethisalternativemodelinthesubsequenatnalysisbecauseofits intractability. 9

act act < (13) 8et a Proof: Using equation (11) and the implicit function theorem it is straightforward to show (14) and, (15) q The above proposition shows that, in the early stages of development when the returns to both types of human capital input are relatively small, only those with the highest ability levelschoose to supply human capital, whereasa majority of the population chooses to supply labor. As improvementsin technology raisethe relative return to humancapital, however,alargerfraction of the poptiation choosesto accumtiate human capital while young by allocating time to education and working as entrepreneurs4. Proposition 2: (i) V O< q s 1, and V t < i > V q 41n~m model,hum capitalaccu~ation isrationedby ability. It wo~d be straightforwardto adaptourmodeltootherrationingrtiessuchasonethattakwintoaccountparentalwealthandability suchw thatfoundinOwenandWeil (forthcoming). 10

q V t2 C < i increasing average professional (16) ‘-- Proof: (i) Given that the lhs and the firstterm on the rhsof equation (12) arepositive, we establish that the term ~,(~~f~~~fl–~o~n) the rhs needs to be non-positive. Thus, ~ O~ ~ ~V z such that ai > tit. (ii) Using the first-order condition given by (12) and invoking-once again-the implicit function theorem, we get (17) where O – A + — ~,,(st)f,(+l–f’s’t()1–~t)f’(5t) (St)+f(1– St)] [ f ~ is equ~ t. an expression almost identical to (17), where ~~+1is rePlaced bY * A; q Proposition 2showshow increasesin the humancapital stock, which raisethe level of technology and per capita income, affect the accumulation of the two different types 11

of human capital. Specifically, it demonstrates that technological change, by inducing human capital suppliers to devote more time to schooling, leads to a shift away from entrepreneurialhuman capital accumulation. The reason is that technological change not only raisesthe relativereturn to human capital, but it also increasesthe riskof time .-. investedinentreprenuerialhumancapital accumulation inthe sensethat the discrepancy between the payoffsin the good and bad statesincreasesasthe economy develops. As a result, those individuals who find it optimal to become human capital suppliers choose to stay in school longer and develop a higher ratio of professional to entrepreneurial skills. As will be seen in the next section, the change in the ratio of professional to entrepreneurialskillsdoes not necessarilyimply areduction in aggregateentrepreneurial skills,because the aggregate value is also affected by decreasesin titwhich cause more individuals to become human capital providers. 3. The Evolution of the Economy Given (11) and the specification of the technology parameter, At+l, in (8), we identify that there exists a minimum level of technology below which all individuals choose to work as raw labor and noone allocates time to activities that foster human capital accumulation. Let P= (et, p,) qln{~,+~~[$(s,) + f(l - S + ( - q) S { (18) Thus, when (et,pt E p t < ti not even the highest ability individuals choose to devote time to education or work experience and et+l = p = O. 12

In contrast, for all pairs of entrepreneurialand professional human capital in any given period t (et, pt) @ p, the dynamical system is characterized by the two equations that governthe evolution of entrepreneurialand professionalhuman capital stocks. Namely, .-. (19) Given that both titand starefunctions of the technology levelin period t+ 1,It+l, which in turn is a function of the entrepreneurialand professional human capital in the previous period, et and pt, e = r( pt) and P = Q P (20) Inthiseconomy, asteady-stateischaracterizedby (~,p) suchthat, Vt ~ T, ~= r(~, p) and p = W(E,p). Proposition 3: V ~ s q ~ 1 and (eO,p @ p 3 a # 13

Proof: SeeAppendix for the derivation of the dynamical system depicted in Figure 2. [Figure2 about here.] The reason for the first condition is intuitiv~the technology of human capital production must be effectiveenough to induce individuals to accumulate entrepreneurial and professional skills. The remon for the second condition is not m intuitive but, m can be seen in the details of the proof, when @ is too large, the substitution effect of individuals reallocating time awayfrom entrepreneurshipalwaysdominates the effect of a decreasein tit,which incremes the fraction of human capital providers. This makesit more diffictit to establish the existence of a non-trivial steady state. There are several important implications of the dynamics of our model. First, entreprenerialhuman capital plays a relatively (but not absolutely) more important role in intermediate income countries, whereasprofessional human capital is relatively (and absolutely) more abundant in richer economies. For those countries that start off with a sticiently high combination of entrepreneurial and professional human capital, an incre~ing fraction of the population chooses to invest in both types of human capital during the transition to the steady state. Moreover, those who choose to do so devote an incre~ing amount of time to the accumulation of professional human capital and a decreming amount of time to entrepreneurialhuman capital. The remon, as we have 14

stated earlier,is that as per capita income grows and the payoff to being a professional increases,individuals are lesswilling to gamble on entrepreneurialventures. Of course, higherprobabilities of entrepreneurialsuccess (highervaluesof q) generatehigher stocks of entrepreneurialskills, Second, the initialstock of bothentrepreneurialand professionalhuman capital are ‘-important for the process of development. Notably, those countries that start off with too little entrepreneurialor professional human capital end up in a development trap in which production is carried out with raw labor input only and there is no human capital investment of any type. This result obtains because both entrepreneurial and professional human capital play a role in the determination of the level of technology. Therefore, when either type of human capital is relatively small initially, the level of technology and the return to human capital investment relative to raw labor input are also small. As a result, an increasingfraction of individuals choose to become raw labor suppliersinstead of becoming human capital providers. A relevant example of the importance of this second point may be found in the former east-bloc countries. As some have pointed out [e.g. Fan, Overland and Spagat (1996)], these economies have a highly educated labor force and maybe primed for an economic take-off. However, our model highlights the possibility that these economies, if short on entrepreneurs,may be further awayfrom the high-income steady state than education levelsalonewould indicate. In fact, some of them may evenbe unable to reach it. Externalities A third implication of our model is that because the social marginal returns to work and education may differ from the private marginal returns, it is likely that even 15

the steady state with positive human capital investmentis inefficient. However,because in our model the alternative to education is also a productive activity, the source of the inefficiency is not standard-there may be too much investment in education in the steady state. Specifically, when entrepreneursare more important in determining the level of technology than professionals, the high-income steady state may be character- ‘-ized by over-investment in education. Similarly, when professional human capital has greater influence on the technology in use, the high-income steady state has too little education. The keyfeatureof the model that produces theseunique inefficienciesisthat entrepreneurial and professional human capital may be combined in different ways in production and in the formation of the technology of production. A market economy may be able to achieve a more efficient mix of professional and entrepreneurialskillsthrough tax policy which alterstheir relative private returns. Although in our model the cost of becoming either type of human capital provider is simply an opportunity cost, one can imagine a richer model in which out-of-pocket expenses are also necessary. In such a model, tuition tax credits may encourage more investmentineducation andgeneratemoreprofessionalswhilereducedcapital gainstaxes may be ableto increasetherelativeattractivenessof entrepreneurship5. Thus, depending on the nature of the inefficiency, appropriate tax policy may be able to increme steady state income. It is important to note that the inefficiency results not from too much human capital, but from a misallocation of the existing human capital stock between professional and entrepreneurialactivities. In fact, a more efficient ratio of professional and entrepreneurialskillswillraisethe steady statelevelof technology andincreasethe wages paid to human capital providers and the economy’s human capital stock. 50fcour~e,givenexogenomgovement thetaxbreaksgiventoonetypeofworkerwillneed toberecoupedthroughothert~es. These“additional”taxesmustbecollectedinanon-distortionary manner,i.e. alump-sumtax,inordertoensurethatthispolicyiseffective. 16

5. Conclusion The model we present above demonstrates why both entrepreneurs and professionals are important for development. It shows that the private incentives to accumulate entrepreneurialrelative to professional skillsare greater in intermediate income ... countries and that–due to the inherent riskinessof entrepreneurialventures–those incentives decline relative to the incentives to become a professional as countries grow richer. Nonetheless, the initial stock of types of human capital matter, because together they determine the return to human capital relative to raw labor. Thus, the initial conditions are important in determining whether countries converge to an equilibrium in which, for a largerfraction of the population, investingtime in human capital accumulation will be more profitable relative to labor provision. Our model also demonstrates that when more than one type of human capital exists, individuals may not allocate their time efficiently to the accumulation of these differentskills. More generally,our resultsindicate that a thorough macroeconomic investigationof allof the channelsof humancapital accumulation isnecessaryto effectively formulate and implement the most successfd policies. This is a fruitful areafor firther research. 17

References Azariadis, C. and A. Drazen, 1990, “Threshold Externalitiesin Economic Development,” Quarterly Banerjee, A. and A. Newman, 1993, “Occupational Choice and the Process of Economic Development,“ 101, 2, 274-98. Becker,G. S., 1993, A (The Universityof Chicago Press, Chicago). Benhabib, J. and M. M. Spiegel, 1994, “The Role of Human Capital in Economic Development: Evidence from aggregatecross-country Data,” Fan C. S., J. Overland and M. Spagat, 1996, “Human Capital and Russia’s Economic ~ansformation,” Vol. 2, No: 13. Fershtman,C., K.M. Murphy,andY. Weiss, 1996,“Social Status,Education andGrowth,” February,108-132. Galor, O. and D. Tsiddon, 1997, “The Distribution of Human Capital and Economic Growth,” Lucas, R. E., 1993, “Making a Miracle,” Vol. 61, No:2, March, 251-72. Mincer, J., 1993, (Brookfield, VT: Edward Elgar Publishing Company). Mincer, J., 1996, “Economic Development, Growth of Human Capital and the Dynamics of the Wage Structure,” l(l), March, 29-48. OwenA. L.andD. N.Weil, “IntergenerationalEarningsMobility, InequalityandGrowth,” forthcoming. Pritchett, L., 1995, “Where has all the education gone?”, mimeo. Romer, P. M., 1990, “Endogenous Technological Change,” October, 571-602. 18

Stokey, N. L., 1988, “Learning by Doing and the Introduction of New Goods,” XCVI, 701-717. 19

Appendix: We prove this proposition in three steps: l Step 1: We assume that the EE and PP loci do not lie within ~ (i.e. fit < ti Vt and equation (19) holds) and demonstrate that they have the form shown in ‘-” Figure 2. l Step 2: We then show that, when q = 1, the EE and PP loci intersect when ~(~) is large enough. We relax the assumption that the entire EE and pp loci derived in step 1lie outside of p, but show that the intersection of the two loci is still outside of p. . Step Finally,weshowthat decreasesinqshiftthe EE andPP loci continuously, guaranteeingthat the EE and PP loci intersectfor V q, ~s qs 1. Step 1: Let = {(et, p [et+~– et = Ae = O} (Al) and, PP = {(et, pt) [pt+l – Pt = ~P = 0}0 (A.2) Assume that tit<6 Vt. Then, using the implicit function theorem, we are able to show that where r. and rP respectively denote ~ and ~. Similarly, 20

whereW,and TPrespectively denote ~ and ~. By combining (14) and (17) with (A.3), we find that if @is relatively small then ~ and ~ are also small and r,, rP ~ OV (et, Pt) @p. Thus, when r, z I 7 (A.5) de~ EE >0 - { when r, c 1 —. and, since V~, VP~ OV (et, @ for all parameter specifications, <0 when Vp >1 apt (A.6) ~et Pp >0 when Wp<1 - { Let e*andp respectively denote (for givenvaluesof and et) the valuesof etand pt that set qln{~t+l~[~(st) + ~(1 – s~)]} + (1 – q)ln{ti[~ + ~t+l~(st)]} = in(2). Given that tit < ~, ~, ~ are positive, and ~, ~are negative–as can be verified from + + (14), (15) and (17)-we determine that - - ) EE ‘0 ) Moreover, given that Stand at are continuous in et and pt implied by Propositions 1 and 2, along the locus 3 (e’, p’) @p such that apt o (A.9) 8et EE = and that, along the locus 3 (e”, p“) ~ p such that apt ~et (A.1o) = Thus, we establish the generalforms of the and loci on the (e, p map as shown in Figure 2. 21

Step 2: Next, we need to demonstrate that, for a non-trivial, stable steady-state to exist, 3 (E,p) @p. First consider the casein which q= 1.When q= 1,s, = ~ and $(s,) =~(1– St)= to @ —@ —0. Thus, (19) simplifies $(~) ~ ~ Vt. Moreover, ~,, – ~P,_ ..when tit> Q (All) when tits Q Underthiscase,ifanon-trivial steadystateequilibrium (E,p) @ p exists,it satisfies ~= ~. It ~so follows directly from (All) that if 3 (2, ~) c EE such that @= @and ~ (Z,@) l PP such that 5= fi, then ~= E= ~and @= P=P (i.e. if the EE and PP loci cross the 45° line, they must cross at the same place.). Suppose that, there does not exist (~, F) @ p. This implies that V et = p (et, pt) < P, ~P and- Ae are both negative. However, (All) indicates that, for a large enough value of ~, 3 (et, @p s.t. et = p and A and Ae are both positive. Thus, we can ensure that 3 (et,pt) ~ p s.t. et= pt and Ap = Ae = O.. Step 3: We now show that as q is reduced, 3 (E,P) @ p. First note that, when q = 1, (A.12) when evaluated at (E,~). Thus, we can rtie out a tangency at (E,~) when q = 1. Using (19), (Al) and (A.2) and the fact that st and titarecontinuous in q we can also establishthat the and the locus shiftcontinuously in responseto changesin q Taken together with the fact that and are not tangent at (z, p) when q = 1, we conclude that 3 q ~ ~ q < 1, such that (z, P) @p (with z < ~) exists. Remark: Note that incremes in the effectiveness of education and experience in human capital accumdation-m given by the function ~(.)–shift and in the opposite direction asdecreasesin Thus, the more effectivej(.) isin converting education and experience into human capital, the loweris ~. 22

4 . 3.5 I 3 . - 1 I - .-- - - . . . 0.5 = . . “*. - . . . - .%- -.- -. - 0 9 0 2000 4000 6000 8000 10000 12000 14000 16000 GDP Capita Figure 1: GDP per capita and the employers to employeesratio6. (1980-Sample of 42 countries) Data Source: The World Bank, 1997. 6Employersincludethosethatarese~-employed. 23

e Figure 2: Entrepreneurialand professional human capital accumulation dynamics. 24