The Accumulation of Human Capital: Alternative Methods and Why They Matter

Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 551 .May 1996 THE ACCUMULATION OF HUMAN CAPITAL: ALTERNATIVE METHODS AND WHY THEY MATTER 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to International Finance Discussion Papers (other than an acknowledgement that the writer has had access to unpublished material) should be cleared with the author or authors.

Abstract We show how the abilit~ [o accumulate human capital through formal education and through a learning-by-doing process that occurs on the job affects the dynamic behavior of the human capital stock under a liquidity constrained and a non-constrained case. When there are alternatives to formal school ing in the accumulation of human capital, investing resources in increasing school enrollment rates in low-income countries may not be the most efficient means of increasing the human capital stock. In addition, removal of the liquidity constraints may not be sufficient to escape a development trap. ——

THE ACCUMULATION OF HUMAN CAPITAL. ALTERNATIVE METHODS AND WHY THEY MAITER Murw F. Iyigun Am L. Owen’ 1, Introduction A SUIVCY oj the rcccnt growth Iileralure w(mld reveal tit Ieasl one consistent policy prescripuon: mvesl in humw] cupilal Al[htmgh the impommce of human cupital has t)ccn csutblishcd. should be implcmemed s[ill remains to be answered. Wc lake thIS question Up in this p~per, comsidenng how hC ability [() accumulate human capital tlmwgh both formal training and through on-the-job cxpenence affects (iw dynamic twhavior of the human cupiM S[ock, Emplncal eviderwc from micro datu hits umsislently shown that work cxpericncc is an important determinant of ml individual humun capmd. The model wc prescnl In this piIpCr acknowledges this evidence. Mowlenmg the derini[mn of human ctipitd [() mducic on-the-job learning as well M general educution. The ins@ts gamed dmmgh this approach allow us to dmw several ~mportant conclusions. First. a policy that focuses exclus]vcly on achieving large increases in enrollment rates may not be the mm efficient policy for increasing m economy’s stock of human capital. Alternative policies that encourage industries which produce jobs that allow for more on-thejob learning could achieve the sune objective in u similar time frame with less resources. This conclusion is consistent with the recenl experiences of several developing countries that have ‘Murat F. Ivlgun is an eu(m(ml]si m the Dlv]smn of Imemationa] Finance. Board of Governors of the Federal Reserve System tild Ann L. Owen 1s an economist in the Divisicm of Monetary Affairs, Board of Govcm(ws of the Fclleral Reserve Sysrem. This paper represents the views of the tiuthotx and should no[ be imerpre[ed M re!lec[mg those of the Board of Governors of the Federal Reserve System or other memhers of i[s staff. Plewe send all correspondence to: Division of International Fimmce, Mail Stop 23. W“wshington. D.C. 205s ]. Phone: (202)452-3798. Fax: (202)452-6424. —

.?. experienced ltirgc incrcuses it) cnrollmen[ r~[e~ huI n~l ~{)rresponding increases in outpu[.j In contrust. many of the E&si Asiwl eutm{mlies specitiizing in manufacturing high-tech goods have experienced htrge mmu.ses m (wIpuI with less drarmuic rwcs of increuse in school enrollment. Rcucm wt)rk in [hc cu(m(mllcs Ii[era[urc htis provided mixed evidence in support of educu!iontii 991 ) and Mankiw. mly to include educalionul U[[M]UIWIU, Jlrcu[l} ~t’tect~ ecoll~)mlc grow[h. 01] the ()[hcr hand. Bcnhabih und Spiegel ( 1994) find empirical supp(m f(lr their claim Iha[ human capiud is not u fticmr of production and is (rely relevam m dctcrm irung the level of technology cmpl[)yed in w] ccon[) my. Pri[chc[t ( 1995) makes an even wronger poinl, showing tha[ incrca.ses in cduutiti(mal cfipital due to improvcmcnLs in [he Wucational ti.. mmeru of the labor force hw d ncgtit. ivc immux on the gn)wth of (mtpul per worker. lr~ C(mtrmt IO rnixcd cvidencc from aggrega[e datu. micro dwu has cunsistcntly shown that earnings md pro(fuctiwty mcreuse with an mdividuak education.’ Our imerprcttition IS umsistcnt with both the micro and macro cvidencc; i[ allows Indivlciuais prt)duc[ivi[y [() incrc~sc with their level of educatio~ hu[ recogmzes [hat [he ex[ent (.)t (he producuvity increase will depend on the existing level of’ human ctipital Ill this regwtl. our mode) IS similar [() some 01” the current work m the growth 2Pritchett (1995) provides a summary of reievml stylized facts: In the yew-s between 1960 and 1985, the educational attainment of the labor force m the Sub-Saftaran Africa grew at a fawer rate t.hn that in any other region. Yet growth of output WM about half that of Latin America and about quarter that of more rapidly growing regions [See Easterly and Levine (1995) for u detailed account of the economic performance of countries in Suh-Sahar~ Africa]. Similarly. in other less developed countries as a whole, enrollment rwes have increfised significantly in the last thirty years while growth rates huve been stagrmting or even falling. In c(mntnes wd regions that have recorded considerably high levels of educatiomd tittainment such as Sri Lanka, Costa Rica, Jamaica. the Philippines and parts of” India. output Ievcls have been sigmficanrly low for educational levels. 3See. for example. Mincer ( 1993).

- 3- Iilera[ure.’ However. hy ackm~wledging alternative methods of accumulating human capital, it differs slgnific~tly trom the cxistlng work in thal it provides an explanation for why advocating increases in enrollmem rules may INN bc the rmxl efficiem policy recornmendauon for economic development. fac[. m cmmrics in which the ex]s[ing level of’ human cuplud 1s very iow. (mr model identifies the possibilt;y thw increases m cnrollmcn[ rates c(mld mually decrwst the economy’s stock of human cfinitfil lli the sh(m I() inlemlediwc lcrm. $ The mlr(duction ot anolher method o!’ accumulating human capital creates the possibility of muluple equilibnu. even for preferences and technology thw w(ndd otherwise not gencmtc such u result Imp(mantly. this possibiltly is not er~sed when credit market impcrfectitms arc removed and there IS no explicit cos[ [() cduw.ion. Another conclusion we are tihle to draw from our model is [hw the amount of educfition mdividua.ls desire may increase with the level of development. Thus, the causality between education and growth rum both wtiys. This conclusion is particularly strong when mdividuais cannot obttun loam r[~ finance firs[ period consumption. Another conclusion of our amdys]s thw IS relevuru to policy makers ]s thu[ Ilquidity constraints. even when there are ml (wi-of-pockel expenses for schooling, may limit the growth und level of per capita income. While the Important role of liquidity consu-ain[s is not new to our paper. we add to this discussion the obsemation thar although removal of iiquidi[y constraints is u necessary 4Some studies, such as Tarnuru ( 1991 j and Galor and Tsiddon (1994) have focused on WI educanon-type mvesunent M the pnmwy channel for humun capml accumulation. Others, such as Stokey (1988) and Young ( 1991) have exammed the growth effects of leurning-hy -doing. Our formulation for human ctipittd accumulation. imwever, IS perhaps most closely related to work that has been done by labor economists who huve long recognized the importance of both work experience and education as a determinant of individual e~ings (See. for example. Becker (1993), Mincer ( 1993) und ,Mincer (1995)]. %t a rela[ed pqer. Fershtwn. Murphy and Weiss ( 1996) also develop a mode! in which w] increase in the number of educated wi)rkers cm be assocluled witi a decre~e in me growth rtite. In their model. u high social srwus of educated workerx can result in an inefficient idlocatlon of education M high-mcornc. k~w-abili(y people “crowd (ret” low-income, high-ability people from grmvth-produc in: educated occupations.”

-4conditwn I(M m WJm IZ, III: pcr ~:[pit~ inc(mm i! IS nor d sufficient cwndit ion. Economies with very low m]uul levels ot hunlan cup][~l nmy ni)[ he uhle to cscupe ~ deveiopmen[ [rtip through a policy (hal t(mses exclusively (Ill rctn[wlng Iiquhhly C(mslramts. Our umulusi(ms arc rcachcd ill [he (ollowmg” tour seclwns. Seclion 2 provides ml twcrview 01” [he model. Sccti(m 3 dcscnbcs [he hmic clcmcn[s of production MM.I individual decision muking. Secll(m 4 c(msldcrs Ihc cv(~lutlo!l !~l lhc llUlllUli curwal ,s[ock with und with(mt liquidiry ~t)ttstr:lints ulld SCLXIO1”! 5 U:) IILIULICS 2. Overwew The model twhw considers d small i~pel~ euon(m]~ m an (wcrlappmg generations lrumcwork in which both physul ctipllal und J labor mpw uc itictors i)t producUon. In the first puiod 0(” Iii’C. mdlviuuids divide tilcir [imc between working and going lo SCINWI. Both w[ivi[ics incrcasc an individuals second period human capmd and. tnus. increase the amoum of’ the labor inpul the indiwdual can supply m the seumd pcnod. A mgh parcxmd level of human capital influences the effectiveness of time spcili m training more dlan it influences the effectiveness of accumulating human capital through tie learning-hy-domg tlmi occurs on the JOb As iI result. when the previ(ms gcncratton has a knv level of humari ctiplud. mdiwduals may preier [(J wxxlmtdme human ~apltti through WOrk experience i.ind nm throuuh frwnmg. As the level of rx.ucnml human cupltal rises. however. schooling becomes ~ more efiec[ive mcms {)t uucumuia[mg humun capltai und individuals choose more education over work in dlc tirs[ pemxl. When loans for Iirsl. period consumpuon twe no[ uvtiilahle, the amount of time spent in school in the first period gradually increases with the pwenta.1 stock of human capital. When indivi(!uu]s an borrow aguinst second -period income m finance first period umsumpmm. ht)wever. they either spend M or none of’ their nme m school. This SCIUP gencrwcs [hc ptwsibiliry of multiple equilihri~. When crcdil murkels are perfecl. there cm] be two s[eudy SMICS: ~ low humm upitd stedy slate in which individuals accumulate

-5human ctipIIal (My through work experience Md d tigh human capita] steady s[ale in which mdiwduals spend d]] of the lirsl period m school Both of these s[eady states are s[able. 11 there are credi[ m~ket impcfiec[itm>. [here cwl he lhree sleady .$[a[ es: the low human cupim.1 steudy state analogous to [he low human capital steody S(W mentioned ahovc and two additional sleudy states in which individuals spend [Jme hoth working and getting an education in the first period. in [his case. however,, only the upper ;ind lower s(eidy states are stable. The following section dcscrihcs LIm nl[xlcl economy more c(m)ple[ cl> 3. The Model 3.1. Production The output of’ the econorn}r is u single homogeneous good produced by a CRS production function that uses capital and labor a!! inputs. The ourpu[ produced w time t, Y,, is given by K Yt = F’(K,Lt) = I@,); k, = ~ (1) r where Kt and L, denote the quantities of physic~ c~pi[~ and labor employed at time L The production function f:R+ + R satisfies the standard neoclassical assumptions. Namely, f ‘(~) >0, + f “(W <0. Iimku f ‘(~) = ~ and ]imk-$-. f ‘(~t! = (), We assume that production is earned out in ti perfectly competitive environment. and both factors eam their marginal products. Thus. rt = /’(kt) and Wt = fikt) - f’(kt)kt (2) where r{ and w, denote the imerest rate on physical capital and the wage rate paid to labor at time [. -..

-6. The economy under coflsldertition IS open md small. and the world interes[ rate IS consl~t at r. .Smce the open txxmtm); permits perfecl cfipltti mohility. its interesl ralc is cons[iml al r. M well. r, = F = f(k) - k, = z = f’-’(i) (3) (4) 3.2. lndiwcluats Individuals live for [w() periods in (werlupping generwicms. The size of the Population is normalized to one and there IS ml population growth lndiwduds uc endowed with onc unit of time and with u. u >0, uni[s of physlual iuhor mpul m tmrh periods. In the first period. r-hey alhwtilc their time ~and physical Iuhor tietween work ~d eductilion und tney umsume. In rhe second pcnod, they supply all of their ume and physical Itibor plus Ihe hurmm capnal they accumula[cd in tic firsl period to the labor market and consume. Thus. firs~ period income is Npw, and second perrod income is (p + L+,)v:. where X, M the fraction of Ume spent woriimg in the first period and ~+1 is the humm ctipitd supplied iri the second period. Becuuse there are no (mt-ot. pocket expenses assocmred with formal training. gemng un eductilion ~ftkcts firsf Pen(d resources ~m)y by reducing the umounl of labor income Both work expencnce w]d for-mid [rwnmg m the first period incre~e the umounl of human ctipital supplied in the second period. In addition. the y.rent’s level of humun ctipital enhances the child “s human capital uccumulu[ ion. Specifically. an mdivldual ‘S second period human capital is given i-l)’

-7- /++, = V(lzf)x, + z(h,)e, (5) where ~ is the paren[a.1 level of human ctipital. x, is the time spent working. c, is the fraction {~1” {ime spent in trwmng. imd v(h) and z(h) wc mm-decreasing functions of the parental human ctipimi such thal V’(h,), M+) 0, vq~l), z “(h) ~ 0. v h, > f) 2 v(h,) z 2(/2,) v h, < /i (6) V@t) ‘ Z(ht) V h, > h lim~_ Z’(h,) = o A key fcwure o~ the spculfiuation ubove is Ww at low levels of’ parental human cupilai, w(wking m the firsl period will provide for higher levels of human ciIpita~ m the second pcnod; bu[ til higher Icvcls of parental human capital. formal rr~ining results m higher human capital uccun~ultition.” We should uiso note tha[ m the context of our model, education can be interpreted browi]y to include not only traditional schooling bur also other forms of formal training such iLS vocattcmal training or apprenticeships, Thus, in our formulation. the humim ciqxtai uucumul ated through work experience is exclusively a result of leammg by doing. The Important role that a parent’s human capml plays in increasing the efficiency with which u child accumulates human ctipItai can be justif]ed in Iighr of Coleman et al. ( 1966). Ha.nushek ( 1986) and Fuchs and Reklis ( 1994) which show thal parent’s education is important in determining the child’s level of education. More specifically. Coleman et al. (1966) investigate the relative importance of family backgrounds in educational attainment and conciude thw differences m Iwckgrounds and bAn example of d function [ha[ sa(isfies the properties discussed above is: ht+l = ah[xt + bh~et ; O s ~ c a c I ; @ >0

-ti - Churac[enshcs ot peers m sch{ml play ~ m[~re lmportam role than qualiry differences urnong schools. Ha.nushek ~ 19X()). in d sum’ej <)[ the litcramre i)n duculii)ntil studies. rernark.s thal genertil conceptual fm)dels Jeplc[ lhc dchievenlcnl {)1 d gI\JeII studcnl d.k d runcut)n of the II)puI\ of famil}. peers A [ctichers mterwln: with HUMIC pcrs( mai ~hill[]es. Fuchs u.nd Reklis ( 1994) pr{widc evidence that family and child chuructcnsllus, hu[ n(N SCINN)lS. influence math achievement of eighth-grade students III the U.S. In uddili(m 10 Ihis cvidencc of) ptircntul roles in children’s cducaiional uchievemem in ti developed cxmn[ry. other s[udics huvc cmphus]zcd [he ]mp(mancc of” Ieuming-hy-dt)ing and lhe [ransmmon 01 Ih]s knowlcd~c u) other t’iunil) mcmbcrs III developing ctmn[ries, Roscnzwci: and Wolpin ( 1985) documcni the posi[ivc inllucncc Ihm older. more cxpcrien~ed. family mcmhcrs have {m farm profitabill[y in lndia. finding thal the prescncc OJ an i)lder family memhcr increases txd-weather profits by 14% (compared U; an 8.5% mcrea.se resulting from an addiuonaf year of schooling to the mos[ educa[ed mdiwdual m the household). F(w[cr and Rosenzwc]g ( 1995) also show the irnporla.rwe of ieanung-by-domg In developing tx)unmes. fmfing thi,u expencncc Witil i]igh.yieilfmg seal vmcties is essenwi for generating profl[s with their usc (Me of the results of’ this study of Indian households is that experienced farmers were uhie to earn profits whiie reexperienced fanners. both educaied and uneducated. couid not. Losses to inexperienced educated farmers were smaller than those to inexperienced and uneducated farmers, indicating that educti[ ion did add to d farmer’s human capital, but to a lesser degree than previous expenencc. Since. in the firsl period. individuals allocate their lime between e(lucati(m and work. it follows that et + xr s ] (7) Individuals receive u[ility fkm] consumption in both periods, with the util]t}’ of an individual of genertit[(m t yven hy —

(8) where c, md cl+, dcnolc the consumption of the indivich.ra.i in the first and second peri[xk. 3. ()<SS1. is the discoun[ tuctor [hat [hc mdividwd upplies to second period consumption. and U(c,, c,+,: 5) satisfies the usuid condill(ms thtit ensure an mlcnor soiut.mn. lndividwds maximize [heir utility suhject I() (7) and the following budget c(mstr~nt: (9) 4. The Evolution of the Economy The optmal armwnt oi urne alhu[ed u) cducatml. c,. and to work. XT. by the indivichraf in the flrsr period (and. t.hereforc the evoluuon of the economy w a whole). will depend on whether there exxsts binding liquidity constraints on individuals’ first period consumption choices. In what follows. we first analyze the evolution of u non-liquidity constrained economy in which individuals can borrow m finance consumption. Then. we consider an economy in which individuals are liquidity cons[rtine(l and cannot borrow t( finance first period consumpt.ron The evoiution of this economy. and. m !xrrncuwr. the evolution of the stock of human capml, (h,]-,+, IS governed by an autonomous. fiml-order difference equation. The evolution of the human capltai stock. I ~ 1-,+,, in turn determines the evolutions of the time allocated to educuuon, { e, )-,<,, and to work, { x, )-,4,. imd. therefore. the evolution ot” per-ctipita income. {y, ) ‘(+,. 4.1. The Case of No Liquidity Constraints Let h* be the threshold level of parcnta! human capital below which individuals do not choose any eductitton in the first period. Then, given the assumptions outlined in (6), h“ IS stnctfy grearer than fi since the oppt)nuni[} COS[ of getl ing an educatmn mciudes nor oni}’ the I’oregone human -

j(; . Ctipital ticcumula(ed throug]? work expenencc hur also the earnings associated with working. Since p > 0. w fi tie oppunumty cost ol educution is Svmct.ly greu[er than the opportunity cost of working. Thus, when there ure no binding liquidity constrains on consumption in the first period. the optimal urnoum of [ime allocwed to cductilion by the individual. c,. is given by the following: (lo) where h“ IS such thal v(h”) + u = /.(1?”) When there wc nol liquid]ly u(ms[rwnw. m tlw firsl perifxi. individuals ‘devme W of Iheir lime to either work (Jr K) eductimm. wlt.h the chowc dcpendmg on the rclalive marginal returns ()!’ ctich activity Specifically, individuals borrow [(t finance first period consurnp[ion and alkxxte all of their time in the first period to getting educated when their parental human capital stock is sufficiently high. Otherwise. a[ low levels of the ptirental human capital stock. individuals choose m spend all of their time at work in the first period. Noting that e, ~ x, = !, we cu.n describe the [ime ,path of the human capital stock h} combining equations (5) and ( lo): I v(ht) ifhl < h* ht+, = q(ht) = V(h,)u-o(h,)] - z(h,)o(ht) = (11) I z(h,) ifht > h“ where the initial stock of humun cupittii. h,,. is historically given. Along the dynamic path. k evo]ves nl(motonwally. Namely, (14) —

!1 - I V’(ht) 2 0 lfhl c h 9 aht+l —= q/(ht) = ~ (12) ah, I( z’[hr) > 0 if ht > h” ( v“(ht)s O ifh, < h i?ht+, l — = qr’’(ht) = (13) dh: zlt(ht) s o if ht > h { l Wc UCJ”H)C ii sicudy-s[alc ~quiliimulli ds ~ s[all(mary stock of human capiud, h, such that (15) h = *(F) Once the human capital sl(xk rrxhes its stewfy-sta[e. h. the ammnt of time tha[ individuals dl(KtiIc to education. mm allocated to work, and per capltti income reuch their steady-sta[e levels. rcspec[ivcly - -denoteu by e. x. y, M well 11” yf(()) = v(()) > () or i!” Iml,,+, v ‘(h) > 1. then wc Imnv u non-trivial $Iea(iy .Sta[e eXISL\. - Figure 1 shows three possibilities for v(hJ. In figure 1 A, there is d unique nontrivial steady state in whwh individuals choose no educ~(ion, in 1 B there is u unique non-trivial s[cady state in which mdiwduais do nm choose to work in the first period, and in IC.. there. are two steady states, one m which there is no work and one m which there m m] education m the first period. In Section 4.4. we give an example in which. depending on parameter values. all three cases are possible. 4.2. The Case of Liquidity Constraints When there are liquidity constraints. indwiduals ca.nrn borrow [o finance their consumption in the first permd or their lives. As u resuit. individuals” first period consumption cannot exceed their first period income. Thus. [o ensure positive consumption in both periods, they will alwiIys choose M allocate some portion of’ their time m work in the firs[ period. ‘Even when only the trivud steady suite. h=[). exists. y > () since individuals would still earn wp>O in both periods. This evcm would occur if work ex~enence and education provided relatively little human ctipital.

. 12. The optima] amoum ot lime allocated to education by the individual. et. when there are hmding Ilqu]di[y construims on consumption. is given by the following: Notc [h;u dw wn(mn[ of [mm tillouued [i) cducauon. e,. is u non.dccrcwing limclion of the piwermd humwi ctipittil stock. and [he WI)(NMN of [me ailoca[ed M) work in the fim[ period. A, is & nonmcreasing iunc[l(m 01” 1hc puremul hunuui cupltal stock Thus. O’(IJ) = () when h < h“, ml Q’(h) > () when ~ > h- We ~rc uble [() describe ihc dynamic hehavmr of the human uupiud stock when there are Iicjuld]ry consm,ms by cwmttinmg equatl{ms (5) and ( 16): v(ht) ht s h lf l (17) h f+l = tr(ht) = V(h,)[l -o(h,)] + z(h,)o[hr) = /~ v(h,)[l -e(h,)] + z(ht)e(h,) Wh, > h“ Moreover,. As m the case of no liquidity constrtin[s examined above, ~ evolves monotonically along the dynamic path Specifically. Iv’(ht) z o if hl < ~ “ aht+, (19) — = lp’(ht) = aht z’(ht)e(ht) + v’(@[I -e(h,)] + e’(ht)[z(ht) -Mht)] >0 Zfht > h l

- }3 - ! v“(h) s o zyhr < h I l a%,+, — . ~“(hl) . (20) z “(h,)qhr) + v’IQ+)[I - e(ht)] + 2t?’(@[Z ‘(hr) - v’(k)l ah; . e“(ht)[z(hf) -v@)] if hl > h” where the sgn of ~’ ‘(~) when ~ > h* is lndeteminate. As in the liquidity constrained c~se. if v(()) = v(()) > () or if lim~+(, v’(iQ > 1. u non-trivial stctid}’ SK:C :XiSW When there arc liquidity constraints. however. ~(i~) is a continuous function of the human GIpIIai SKKA, 1~ Figure 2 shows mree pussibiiitles fur the ~(~) function in the liquidity constrained UUSC. Figure 2A genera[es a umgue steady staw w]th no cduutirion, 2B generates a unique s[eufy state m which mdividuais both work imd go u) school and 2C shows the case in which multiple equilibrm ex]sL A1 h ~ there ]s no education and at hz. there M both work and education in the first period. (See the example in Section 4.4 that demonstrates the possibility of each of these three cases. ) 4.3 Discussion of Policy Alternatives In considering the effects of human carnta] uccumulatlon on economic growth. the anafysis above demonstrates that a broader definition of human capital that includes elements of formai trxining and on-the-job learning leads to significantly different policy implications than the ones suggested by models that define human capitai more narrowiy First. the presence of alternative means of human ctipital accumulation implies that increasing school enrollments will not necessarily increwe an economy’s stock of human capital. in filcl. when the level of human capital in the economy is sufficiently low (~ < ~) increasing school enrollments will actually decrease the economy’s stock of human capital in the short mn. This pint is illustrated in Figure 3 which shows the time path of human capmi for three different initial levels of human capital under the assumption t.h a poiicy dewsed so that the amount of time spem in schooi is set equal m the ievel that would he chosen m the Iugh-incorne steady state. Thus. the presence of .-

]4 - Uhemtitlve methods Of hurn;ln uupittd accumu)~[i{)n cw, hetn expltin the observat.i[ms documented in Bermubib ~ Spiegel ( ]994) and Pri[uhen ( IY95 I rcgtirding the luck of increxe in per cupitfi income in low mcomc uounmes that IKIVC rccentl? expcncnced large Increwes in school enrollment rates. In the fihscncc {}!” u scheme lhw u(mlmlts Iuture genera[l(ms h) subsidize the consumption of current generwi(ms. inurcwmg schtwl cnn)lhnen! ru[es Dey(md the level chosen by ulility-mtixirnizing ~gen[~ ~lf=~l~ [r~de~ ,)f~ [h~ wcljurc. (If currcllf wid iulurc generations. Welfare akmg the [runsilioll to [he s[etid} svttc ts Iowcr m the prcscl)cc- 01 such d policy SIIKC. Iefl [(I their own devices. individuals would hu~c choscIl ICSS cduuuf]i)tl. J1 [hc ptdluy is successful in uchieving the high-incornc s[eady s[me however future gencrati{ms will hc much heuer off thn they would have been otherwise.~ W’hile incre~sing school cnn)llment rutes is u p~)Jicy thii[ will be successful in the I(mg-run, us .Pomtect w: move, ]! may be costly m the sh(m-mn An xlditional policy thal our approtich idemifies 1s thtt[ of mracting Jobs I(I an economy ‘hat htivc J higher lcarmng c(mtenl. thus ull~~wing individuals [o increase Weir humun uupitai withou[ imendmg more school and foregoing first pcri(N.I WU:CS. Figure ~ ~h~lws tie time p~th Of }lum~l CUpIItiJ tk)r vwious ]eveis ot” thC m~ghld producllv~t}’ of wofi experience and ]Ilusuwes thw i’acf Wit if the vtilue of” work experience is either to(; high or [()() low the economy will not achieve the high-income .wewly state, When the value of work expericrwe is too low, the economy cwnot accumuiare enough human ca~ltai to make educau(m worthwhile: and when the vaiue or work expenen~e IS [o() h]gh. u~divldu~js choose” IW[ [O ~~ome educti[ed. ‘The analysls above also shows thii! tile existence 01 liquidity constraints affects the optimal amount of time tilloctited to work and to cduculion. Specifically. as we show in the nexl section with ‘While the issue of cductiti(m firumcing is nor specifically uddressed in our model. our analysis allows us to point out t.h. when the accumulation of human capital is positively influenced by the existing le\’eJ of human ctpital. running u govemmenr budget deficit to finance the accumulation of education may he an appropriate out-of -srcudy-state” policy since i[ allows future generations to make transfers to their artcestom. In the sfetidy sutre. however. when the stock of human capital is no Jonger growing. this intergenerational transfer is no longer tippropriate md the government hudget deficit should tie ~pproaching zero.

- 15an example. the threshold level t)f’ parental hum~ capital below which individuals devote no time to educxion. h“. does II(JI depend 011 the discoum factor that individuals apply to future consumption. when no liquidity ums[riun[s ex]s[s. whereds. ]t does depend on the discm.rm facmr when liquidity constraints exisl The reason for ths result is simple--when no liquidity constraints exisi, individuals choose the optimal time devoted to education only co maximize their inter-temporal income: but when con.. traints exis[, they take irm> auc(nrnl their consumption time preference as well. Pu[ differcw!}. the threshold Ievei of parermrl eductitJ(m. h= will hc greater when I iquidity constraints exist i! the discxwm ffictor is relatively low, An inlplica[ion 01 this analysls is thw policies th aim to remove liquidity con.. tmints on indwiduals consumption in the c~lier part of their lives will result in individuals devoting more nme to education, provided that their parental human cupital stock is sufficiently high. Therefore, the removal of liquidity constraints can help those less developed economies that have sufficiently high levels of parental human ctipttd s[octi tivoid d development trap (if it exists). Nevertheless. as we huve shown above. multlple equilihriti mtiy exist even when there ue ml Iiqudity constraints. As u result. when m economy’s s[ock of human capmd is sutllciently 10W. the removal of iiquidity constraints wili not aiiow the economy to avmd the development trip. Another observation that resuits from comparing the iiquidity i.ind non-iiquidity constrained cases is that the ievei of human capitai and per capita income in tie high income steady state is higher when there are no iiquidity constraitms since the presence of’ consumption iouns aiiows individuals to spend aii of the first period getun: an educxmon. Tires. wnen this obserwmon is combined with the discussion m the previous parugruph. it is apparem that removmg iiquidity constraints IS u necessary bu[ not sufflcierii condition to achieve maximum per cap]ta income. Unfortunately. we GJMOI conciucie thrs section with one overriding recommendation appropriate for aii countries. Rather. we arc ohie to use our modei to identify the circumsumces under w’hich certain policies wiil he tipprupriaie and to offer an expiamdion u to why increases in education —...

4.4 An Example III IhIS sccIiim, we pnwidc w exampic thtit ilius[rules the properties discussed ahwe. Let Then. whcr; there arc no liquidity u(mstrtijn[s (22) a (23) bh: o (24) (25) In this economy. Iherc CXISLS d sletidy-sw[e eguilibnum m which indwiduais allocate all of

- 17tnelr ume 10 work m the firsi period it’ ]]mh+h” ~(~) < h“ We find that this occurs when the physicid labor endowmem o! individutis, p. is sut%ciently Iwge and/or tie effec[ of work experience on human capital accumultition, ~J, [~es on an imermediate value. Namely. aa[b - a) ‘a] P’ (26) ]*F Equa[ion (26) stiys [M mdividutis will choose to work m the I-irsl pcn(xl when 1 ) the opportumty” C(NI of educauori is high (,14 M Iarge).or 2) il work experiences is particularly valuable in accurnula[ing human capital (a IS large). Note thtit very small values of a will tiso generate u slcudy state in which there is no education. While the choice not 10 get an euucation when work expencncc provi(fcs Iittlc human capital may appear irrational. it is not A steady state with a low u is consistent only with a small amount of parental human capital. At dus ste’ady s[ate, the low level of paremai human capital results in a low marginat productivity for educmon in producing human ctipi[al, Thus. the positive opportunity cost of becoming educated causes individuals ;O chose work over education. Wherl there are n{) liquidity constraints. a steady s[atc in which individuals choose nw to work in the firs[ period exlsLs if the effecl of’ education OIi humm capital accumulation for a given level of the parental human capital stock. b. IS sufficiently large relative to the effect of work experience on human capital accumulation. a. Specifically. iimti+i,” v(~) > h“ if and ordy if (27) Interpretation of the condition in (27) is siralghtforward--individuals obtain an education when iLs marginal producdvity in accumultifing human cupital ]s rekmvely ~gh (h is large) and Lhe opportunity cost of education is relatively low (a and 1( tire small). When parwne[er values am such that both equztmns (26) and (27) ure sausfied. then without further restrictions. there exists muhiple steady-slate —

equilibnu m lhls cc(momy When lhcrc MC Iiquldily c{mstrainLs,, the op[imal amount of time devnted to education and the cvolunon of Ihc humm ctipIMl SUKA GUI De clxmic[erized ny e, = t$(h,) { (28) q : 8(MzrE -a) - (p - a) >0 ~f hl > h l (1 + a)(bh; -a) [ y- tlt SD h “ i= I ht., = v(ht) = a[l -@(h,)] - bh:t$(h,) Ifh, > h- (29) =~ (bh: . ~) [ 1-8 As in the case of n{) iiqudity c(mstrwnI\ exwnmed move. h, evolves monomrmv.dly a.iong the aynarnlc path, Speclfictilly. (30) {31)

- 19- When mere are liquldity cfms[rwms. ~(h; is ti umtmuous finc[ion of the human capital sIock. ~. Thus. there exlsrs h s[cwty-stare equilibrium ill this economy” if ~(()) > () WId there exists ~ such that Wh! < h lor s~)nlc h, > [) SIIWC d > (J m! since individuals choose [O idk)cate till of their [ime to work m the iicw period when the parcnud edmxmon srock IS equal to zero. V(()) >(). In the stew.iy 1l.mh-- WZJ = o (32) slare. II c[~uid he the c~sc [hw mdlvldutis ch(wsc no cducwion (Jr choose some cducatmn. A s[cad)’ srate with no cdw.xmon CXISL$ if V(h”) < h“. Equurion (29) implies Ihal ~(h”) < h“ when ~ > CZ”[8L) - (2’-”(1 + 8)] (33) Consequently, if eqwmon (33) N stitlsfied. then withou~ further pwunctcr rcstnclions there exrsts a steady-state equilibrium in which individuals ch(x)sc fo allocate m) umc I(J education. deno[ed by h,. where hl = u. Examinutmn of (33) revetis thw M m the ncm-ltquidity-cons[rtined cue. a steady state with no education is possible if the value of work experience in accumulating human capital. a. is either very high or very low. in contrast, if w(h*) > h*, then the shape of the v@) function characterized by equations (30) through (32) allow us to conclude that u unique steady state with education exists. For a reasonable range of pmuneter vtilues. it is possible that muitipie equilibria exist in this econorn}’. Multiple equilibria will exisl when ~(h”) < h’. ]imh+. y’(~) < 1. and there exisLs an l? > h* such that ~(~) > Q. As established above. ~(h”) < h* if equation (33) is satisfied, and as implied by equation (32). iimt,+<. W’(ii) < 1. In wldition. ~ cioser examination of (30) shows Ihai the slope of W(h) ai h- 1S ]ncrcwng in h and 6 UNI dmw.u.wn: m u. thus ensuring for some range of pwarneter

-20values thw there CXISIS WI tZ > h“ such Ihal ~(~) > h“.’ Therefore. it 10 I1ows tha[ fOr some range of -parameter values. there CXM[S IWO stable steady-wne equilibria. denoted by h, and hj. where hz > h). At h,. mdiwduals obtain m} education. and w hl. Individwds choose (o allocate some of thew time [o — -education. A third. unsudde stcudy state. hq such tha[ h} < hq < ht. is also possible. 1(1 Al this unstable stetidy su.ue individuals would also ch(mse [() h(mh work and go to school. The parental sl(di of humun capittii required for individwds u) choose to allocate u positive armmm of [imc to educti[i(m ili the llrsl period. h“. will he greti[er when there arc binding liquidity constraints und when mchvidwds are sufficicntl) impatlenl (the discoum factor. & relative I() the interest rare. r. is sufficiently low )1 ] As wc discussed Iii the preceding section. this condition allows the removal of liquidity uons[raints u) be u viabic policy idtcmatlve. 5. Conclusion The theory we presem above. focuses on how the aoiliry to accumulate human capttal through both formai training and through on-the-Job experience affects tie dynanm behavior of the human capital stock and of the economy. allowing us m dr~w severai conclusions, some of which have Important policy irnplicti[ions. First. u @icy that focuses exclusively on achieving large increases in enrollment rates may not be the must efficient policy for generating economic development. Alternative policies t.ku encourtige mdusrries whicn proctuce jobs tha[ allow for more learning through on-the-job experience c(wld uchieve rhe s~e t)blec[lve more efficlent)y. AS some empiricui studies have shown, this conclusion is consistent witil the recent experiences of several developing countries devaluating (30) M h“ yields u value greater than 1 when a~b - a’a(l+~) >0. This condition can be satisfied simultaneously with (33) for some parameter wdues. ‘%e third stetidy state is not present when h“ = ~. 1 lhx is greater under tile ]iquidi[v cOns[ralned Uwe when OJ+a)/~ > (1+ r ~~, ‘+

-. J I that htive experienced large incrcuses in enrollment rates withou[ corresponding increases in output. Another conclusmn of [he preceding iuuilysis that is relevant m policy makers is tha[ liquidity Coms[ram[s. even when lhere arc n{) (ml -~)f-pt wket expenses for schooling. may limit the level and -o-rowth t )f per Upi[a inu me. M(m InlporumI}. {he mdel demonswates that although the removal of llquidity c(ms[raims JS iI necessary cx)nditlfm fi)r mcremmg efficiency and for muimizing Iong-mn per t;~plt~ IIICI )rne, II IS INN LI SU!fiCICII[ col]diti{m ECOINMUIeS with very low levels of ini[i~ human capital s[ock may no[ he ahlc It) escape u dcvelopmcn[ [rtip through d policy tha~ focuses exclusively on the rcmowd 01 Iiqudity constraints. Our ptiper also shows the conditions under which there will he multiple equilibria. Specifically, II shows that if the effecl of on-the-job expenencr rela(we [() that of training on human capital accumulation is sufficlentty smalI. then there mtiy exist A development trip. In t.lxu cme, sufficiently low mitml Ieveis of human capital result in low levels of marginal productivity for education in pmducmg human capital Thus. the positive opportunity” COSI of hecoming educa[ed causes individuals m choose work over eduuau(m

--)7. . References Barre, R. J. 1991. “Econwnic Growth in a Cross Section or Countries”. Quurtcrl]” Journal of Economics. 106.407-444. Becker G. S. 199Y, f-iunwn Cup ItaI. A Theorv[icui and EmpiriCal Anaivsis. with 5pt~clal Rcf2rencc 10 Edu(arlon. (The University of Chlctigo Press. Chugo). Benhabih. J ml M. M, Spiegel. 1994. “The Role of Human Capital in Econornlc Deveiopmem: Evidence from Aggrcgti!c Cross-country Datti”. Journal of Monczarv Economic.\, .34. 143-173. Coleman. J. S. et uI.. 1966, Equlliit> @ Edu~’atit)nal Opporluni~, (U.S. G.P.O.. Wwhingmn, D.C. ). Easterly. W md R, Levine. 1995. “The Al”ritian Growth Tragedy,” n]lmeo Fershtmari. C. Murph~, K. M and Y Weiss, 1996. “SiNHtil SMtus. Education. and Growth,’” Journu/ u: Politl(ai Econon I\. 1(W 1). I OX- 132, Foster. A. D und M R Rosenzwelg. 1995, “Letirnmg by Doing and Lcaming from Others: Human Capm.i and Techmcal Change m Agriculture,’” Journal of Political Economy. 103(6). 1176- 1209. Fuchs, V and D. Reklis. 1994. “Mathematical Achievement in Eighth Grade: Interstate and Racial Differences”. NBER Working Paper Series, 4784. Galor. 0. and D. Tsiddon, 1994, “Human CapItW Distributmn. Technologwat Progress und Economic Growth”. Brown Uruversity Working Paper Series, 94-2, Hanushek. E. A.. 1986. “The Econom]cs of Schooling. Production and Efficiency in the Public Schools’”. Journal of Econonur Lifcraw-e. 24. 114! -1177. Lucas. R. E.. 1988. “On the Mechamcs of Econonuc Development”, Journal qf klone[a~ Econom/cs, 22. L.lz Mankiw. N.. D. Romer md D. N Weil. 1992, “A C“ontrihmon to the Empirics of Economic Growth”. Quurrcrh Journui of Etonom[cs. 107. 4)7-437. Mincer. J.. 1993. Studies in Human Capital: ColltIcted EAsa\vs of Jacob Min~cr. V’ol. 1. (Brook fieid. VT: Edward Elgar Publishing Company). Mincer, J.. 1995. “Economic Devclopmem. Growth of Human Capital, and the Dymunics of the Wage S[mc[ure”, mime~. Pritchett. L.. 1995. “Where Im M the education gone’!”, mlmeo.

Rosenzweig. M. R. WI(J K. I. Wolpin, 1985. “Specifi~ Experience, Household Structure. and Intergenerationtil Trunsfers: Farm Fw-nily Land and Labor Arrangements m Developing Countries.” Quurfcrh Journal of Econonucs. 100.” 961-987. S[okey. N. L.. 1988. “Learning hy D{)iny WNI the In[nxluction of New Goods”. Journal of Poli(icu/ Econom>. XCV1. 701-717. Ta.rrnm. RoherI. 1991. “income Convergence in M End(~genous Growth Model,” Journal of Po/i~i~a/ Econonz?, 90(,3), 522-540, Young. A,, 1991. “Lcw-ning hy Doing and the Dynwnic Effects of International Trade”, Quarwr/v .IOLO”)IU; [j” ELumn/Ls, 106. 36%406.

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- .27 - International Finance Discussion Papers IFDP Number -s Author(s) ~ 551 The Accumulation of Human Capital: Alternative Murat F. lyigun Methods and Why They Matter Ann L. Owen 550 Alternatives in Human Capital Accumulation: Murat F. Iyigun Implications for Economic Growth Ann L. Owen 549 More Evidence on the Link between Bank Michael S. Gibson Health and Investment in Japan 548 The Syndrome of’ Exchange-Rate-Based Enrique G. Mendoza Stabilization and the Uncertain Duration of Martin Uribe Currency Pegs 547 German Unification: What Have We Learned Joseph E. Gagnon from Milti-Country Models? Paul R. Masson Warwick J. McKibbin 546 Returns to Scale in U.S. Production: Estimates Susanto Basu and Implications John G. Femald 545 Mexico’s Balance-of-Payments Crisis: A Chronicle Guillermo A. Calvo of Death Foretold Enrique G. Mendoza 544 The Twin Crises: The Causes of Banking and Graciela L. Kaminsky Balance-of-Payments Problems Carmen M. Reinhart 543 High Real interest Rates in the Aflertnath of Graciela L. Kaminsky Disinflation: Is It a Lack of Credibility? Leonardo Leiderman 542 Precautionary Portfolio Behavior from a Life-Cycle Carol C. Bertaut Perspective Michael Haliassos 541 Using Options Prices to Infer PDF’s for Asset Prices: William R. Melick An Application to Oil Prices During the Gulf Crisis Charles P, Thomas 540 Monetary Policy in the End-Game to Exchange-Rate Steven B. Kamin Based Stabilizations: The Case of Mexico John H. Rogers 539 Comparing the Welfare Costs and the Initial Dynamics Martin Uribe of Altema;ive Temporary Stabilization Policies Please address requests for copies to International Finance Discussion Papers, Division of International Finance. Stop 24. Board of Governors of the Federal Reserve System, Washington. D.C. 20551. ——

-28- International Finance Discussion Papers IFDP Number Titles Author(s) 538 Long Memory in Inflation Expectations: Evidence Joseph E. Gagnon from International Financial Markets 537 Using Measures of Expectations to Identify the AlIan D. Brunner Effects of a Monetary Policy Shock 536 Regime Switching in the Dynamic Relationship Chan Huh between the Federal Funds Rate and Innovations in Nonborrowed Reserves 535 The Risks and Implications of External Financial Edwin M. Truman Shocks: Lessons from Mexico 534 Currency Crashes in Emerging Markets: An Jeffrey A. Frankel Empirical Treatment Andrew K. Rose 533 Regional Patterns in the Law of One Price: Charles Engel The Roles of Geography vs. Currencies John H. Rogers 532 Aggregate Productivity and the Productivity Susanto Basu of Aggregates John G. Femald 531 A Century” of Trade Elasticities for Canada. Japan, Jaime Marquez and the United States 530 Modelling Inflation in Australia Gordon de Brouwer Neil R. Ericsson 529 Hyperinflation and Stabilisation: Cagan Marcus Miller Revisited Lei Zhang 528 On the Inverse of the Covariance Matrix in Guy V.G. Stevens Portfolio Analysis 526 Uncertainty, instrument Choice, and the Uniqueness Dale W. Henderson of Nash Equilibrium: M icroeconom ic and Ning S. Zhu Macroeconomic Examples 525 Targeting inflation in the 1990s: Recent Challenges Richard T. Freeman Jonathan L. Willis