why did universities precede primary schools? a …

WHY DID UNIVERSITIES PRECEDE PRIMARY SCHOOLS? A POLITICALECONOMY MODEL OF EDUCATIONAL CHANGE

FALI HUANG∗

Universities were first established in Europe around the twelfth century, althoughprimary schools did not appear until the nineteenth. This paper accounts for thisphenomenon using a political economy model of educational change on who areeducated (the elite or the masses) and what is taught (general or specific/vocationaleducation). A key assumption is that general education is more effective than specificeducation in enhancing one’s skills in a broad range of tasks, including political rent-seeking. Its findings suggest that specific education for the masses is compatible withthe elite rule, whereas mass general education is not, which refines the conventionalassociation between education and democracy. (JEL O10, O40, P16, N10)

I. INTRODUCTION

Modern school systems are usually operatedon a well-structured, hierarchical ladder of gradelevels starting from primary school, then mov-ing to secondary school, and finally completed atthe university of higher learning. This sequencehas become so natural to us in modern timesthat it may be surprising to be reminded that thiswas not the case in most parts of human history.In fact, “as a formal structure, the university orhighest level of education was invented beforesecondary schools, and in a sense, even beforeelementary schools” (Collins 2000, p. 213). Uni-versities were first established in Europe aroundthe twelfth century, although primary schoolsdid not appear until the nineteenth. Universi-ties provided general education for a very smallelite who would become the future leaders forState and Church, whereas primary schools aswell as vocational secondary schools were ini-tially created for the poor masses to teach thembasic reading, writing, arithmetic, and some spe-cific vocational skills. There is some consensusthat the modern education system for the massesarose around 1870 in western Europe and theUnited States, whereas mass general educationat the university level started after the second

*I thank the editor, Vincenzo Quadrini, and an anony-mous referee as well as participants at WEAI 2009 Kyotoconference for very helpful comments.Huang: Assistant Professor, School of Economics, Singa-

pore Management University, 90 Stamford Road, Singa-pore 178903, Singapore. Phone 65-68280859, Fax 65-68280833, E-mail [email protected]

World War and is still an ongoing process (Trow1967; Mueller, Ringer, and Simon 1977; Meyer,Ramirez, and Soysal 1992; Goldin 1999; Bowen2003).

So during a long time in history, only a fewruling elite were educated and the elite educa-tion focused on general education, while massschooling occurred much later, around the timeof industrialization, and it started from specificor vocational education and gradually moved togeneral education. This seems to be a generaltrend of educational change at least in the historyof western Europe. This paper uses a politicaleconomy model to account for such a histori-cal trend in terms of who are educated (the eliteor the masses) and what is taught (general orspecific education). A main theoretical puzzleis why, on the one hand, specific education pre-ceded general education for the masses, while onthe other hand, the elite were trained exclusivelyin general education.1

The intuition begins with the conventionaldifferences between general and specific edu-cation or human capital (Becker 1964; Bennett

1. This paper focuses on the evolution of organizededucation conducted in schools, while treating unorganizedlearning in daily life as the default starting point. SeeSection 5 for more discussions on this.

ABBREVIATIONS

FOC: First Order ConditionLHS: Left-Hand Side

418

Economic Inquiry(ISSN 0095-2583)Vol. 50, No. 2, April 2012, 418–434

doi:10.1111/j.1465-7295.2010.00308.xOnline Early publication June 16, 2010© 2010 Western Economic Association International

HUANG: WHY DID UNIVERSITIES PRECEDE PRIMARY SCHOOLS? 419

1967).2 General education increases one’s gen-eral ability in learning new knowledge and tech-nologies, but it is more costly to acquire in termsof intellectual effort because it needs to buildon a broad and abstract knowledge base. Skill-specific education, in contrast, teaches task-specific skills and is thus less costly to acquire,but it is narrow in knowledge coverage and notdeep enough to facilitate further learning andeasy adaptation to new things.3 An implicationof the differences in these two kinds of edu-cation is that, when technological changes areslow, it is more beneficial to obtain specificskills than general education because there isless need to adapt to new technologies. This par-tially explains why specific education precededgeneral education for the masses.

Another important difference between gen-eral and specific education is from the polit-ical aspect. General education increases one’sgeneral productivity in solving problems, whichimplies that it also increases one’s skills ofextracting gains and defending one’s interestswhen there are political conflicts. Franklin D.Roosevelt, for example, observed that “A manwho has never gone to school may steal froma freight car, but if he has a university educa-tion he may steal the whole railroad.” And ingeneral there is evidence that better educatedpeople are better organized and more activepolitically (Meyer and Rubinson 1975; Collins1971). Specific skills, in contrast, increase one’stask-specific productivity but not necessarilytheir political rent-seeking skills or organiz-ing efficiency. So when the potential rent islarge enough, the elite will focus only on gen-eral education even when the knowledge stockchanges slowly, thus not following the natural

2. The theoretical distinction between general andspecific human capital has become widely adopted ineconomics; see, for example, Gould, Moav and Wein-berg (2001), Lazear (2003), Bertocchi and Spagat (2004),Krueger and Kumar (2004a, 2004b), Wasmer (2006), Iyigunand Owen (1999, 2006).

3. In reality, an education program may contain a mix-ture of both specific and general education, which makesit less straightforward to classify it into either category.It is still possible, however, to ascertain the main compo-nent and purpose of an education program and categorizeit accordingly. The primary school under the elite rule, forinstance, by teaching pupils preliminary reading and num-ber skills in preparation for later vocational training and byindoctrinating blind obedience, can be categorized as spe-cific education. In contrast, the primary school that preparespupils for future academic endeavors has to cultivate inde-pendent thinking besides teaching the basic skills, and so itbelongs to an organic part of general education.

precedence of specific education that arises frompure economical concerns.

The implication for mass education, however,is the opposite. On the one hand, the elite benefitfrom a better educated and hence more produc-tive workforce through larger tax revenues, themore so when the capital-labor ratio is larger.But on the other hand, the elite’s political priv-ileges may be reduced or threatened when themasses acquire more general education, whichmakes them better equipped in defense of theirown interests. This is consistent with Alexis deTocqueville’s famous proposition “To enlightenthe people is to destroy kings.”4 So the rulingelite may find it beneficial to support mass spe-cific education, but not mass general education,especially when the potential loss of politicalrent is large relative to the productivity gain.It suggests that under the elite rule mass gen-eral education is more likely to be repressed anddelayed than specific education.

These results are applicable not only to thedistinction between general and specific educa-tion, but also to different subjects in generaleducation such as humanities versus natural sci-ences; if humanities are more likely to increaseone’s political rent-seeking skills than do thenatural sciences, then an implication is thatthe ruling elite will invest earlier and more inhumanities than in natural sciences, the moreso when the political rent is larger. In stark con-trast, the political elite would be more willing toteach the masses natural sciences than human-ities.5 These results bring new insights to ourunderstanding of educational change over timeand across countries.

This paper contributes to the literature in sev-eral ways. First, it proposes a simple politicaleconomy model to account for the major edu-cational change in history, especially in termsof who are educated and what is taught. Thisis an important issue itself that warrants serious

4. The landed elite in England, for example, opposedmass schooling because they believed that “giving educationto the labouring classes of the poor . . . would render themfactious and refractory, . . . would render them insolent totheir superiors” (quoted in Lindert 2004, p. 100). And suchattitudes “could be found on the part of propertied conserva-tives in practically any country and century” (Lindert 2004,p. 101).

5. For similar reasons, the elite would be willing to teachthe masses social, moral, and civic values that help solidifytheir rule, which is one of the reasons for the public supportof mass education (see, e.g., Bowles and Gintis 1976; Lott1990; Gradstein and Justman 2002). This is also consistentwith the state building rationale of mass schooling (Green1990; Lindert 2004).

420 ECONOMIC INQUIRY

research effort, given the crucial role of knowl-edge and human capital in promoting economicgrowth and general welfare. Second, this modelcan be readily extended to address importantquestions such as why in history the progressof natural sciences lagged behind humanities,and the more so in societies with larger politicalrents or with an open-elite system such as thatin pre-modern China. Third, this paper generatesnew insights in the relationship between edu-cation, political regimes, and economic growth.For example, it shows that specific education forthe masses can be supported by the elite ruleor other forms of non-democratic political sys-tems because it is not necessarily conducive todemocratization.

This new insight on compatibility betweenmass specific education with the elite rule refinesthe conventional association between educationand democracy (Acemoglu et al. 2005). It sug-gests that the average schooling level may notbe a sufficient statistic for education, and whatchildren are taught in terms of general versusspecific education is of great importance. Specif-ically, it may shed light on the puzzling factthat Prussia (and then Germany) was the firstto start mass education but a stable democracywas established much later than others (Lindert2004); a possible explanation is that mass educa-tion in Germany was predominantly vocationalwith a heavy dose of obedient and patriotic con-ditioning (Green 1990), which could work wellfor the elite or authoritarian rule. In contrast,another leader in mass education, the UnitedStates, emphasized general education and estab-lished democracy from early on (Goldin 1999,2001).

This paper is related to a number of studies.The evidence for the initial increase and thendecline of vocational education in the processof economic development is shown by Bertoc-chi and Spagat (2004), who propose that the eliterestrict access to general education because itbrings more social status compared with voca-tional education. The externalities of individualeducation on the distribution of human capitallevel and economic growth are studied by Galorand Tsiddon (1997), while Galor, Moav, andVollrath (2009) show that mass education maybe delayed by land owners instead of industri-alists. Brezis and Crouzet (2006) focus on thetraining of elites in history. Grossman and Kim(2003) examine the choice between an egalitar-ian and an elitist education policy where prop-erty of the rich may be threatened by the poor.

None of these studies, however, analyzes theevolution of the entire education system thatcovers historical periods both before and afterthe Industrial Revolution in addition to majortrends in both the elite and mass education.

The paper proceeds as follows. The nextsection sets up the basic model. The analysis ofthe benchmark model is provided in Section III,while the main results of the political economymodel are analyzed in Section IV. Some impor-tant extensions of the model are consideredin Section V. The final section concludes. Alltechnical proofs are relegated to Appendix A.Some relevant historical evidence of educationalchange in western Europe and the United Statesis briefly described in Appendix B.

II. THE BASIC MODEL

There are overlapping generations with afixed population of measure N . Each individuallives for two periods, accumulating human cap-ital in childhood and participating in productionat adulthood.

Technology and Endowment. In every periodthe economy produces a single homogeneousgood that can be used for consumption andinvestment. The production function at timet + 1 is

Yt+1 = H αt+1K

1−αt+1 ,

where Ht+1 is the aggregate stock of human cap-ital and Kt+1 is the aggregate physical capital.They depreciate fully after one period that isequivalent to an individual’s adulthood.

The total amount of human capital Ht+1 iscomposed of two distinct forms, general humancapital Hg,t+1 and task-specific human capitalHs,t+1, where

Ht+1 ≡ At+1Hg,t+1 + AtHs,t+1.

This suggests that workers with general humancapital can access the current knowledge stockAt+1, while those with specific human capitalcan only access At , the knowledge stock inthe previous period. It captures an essentialdifference between these two kinds of humancapital, where general human capital allows oneto transform new knowledge into productivity,whereas specific human capital does not.6

6. Similar results can be obtained if some degree ofcomplementarity between Hg,t+1 and Hs,t+1 exists, forexample, as in Ht+1 = [(At+1Hg,t+1)

ρ + (AtHs,t+1)ρ]1/ρ

where ρ ≤ 1.


The knowledge stock At+1 grows at anendogenously determined speed φ(Hg,t ) suchthat

At+1 = At [1 + φ(Hg,t )],(1)

where φ′ > 0 and φ(0) is a very small positivenumber. That is, the speed of knowledge accu-mulation is strictly increasing in general humancapital Hg,t , but constant with regard to thestock of specific skills. This assumption reflectsthe fact that general human capital is more effec-tive in generating new knowledge than specificskills. The initial stock of knowledge A0 > 0 isexogenously given.

Preferences. Individuals are identical in pref-erences, which are represented by a log-linearutility function7

uti = (1 − β) log cti + β log(z + bti),

where cti is the adulthood consumption ofindividual i in generation t , bti is his bequest foroffspring, β ∈ (0, 1) indicates the relative weightof bequest, and z > 0 represents some thresholdlevel of income. The budget constraint is cti +bti ≤ Iti , where Iti is individual i’s income atadulthood. As a result of utility maximization,his optimal bequest is bti = max{β(Iti − z(1 −β)/β), 0}. That is, only when an individual’sincome is higher than a certain level indicated byZ ≡ z(1 − β)/β, would there be any resourcesleft as bequest. The bequest bti can be investedin physical capital or human capital for the nextgeneration. The total bequest in society is

Bt =∑

i

bti =∑

i

max{β(Iti − Z), 0}.

Investment in Physical and Human Capital. Letmkti , mgti , and msti denote respectively theamount of material resources invested in thethree capital forms, namely physical capital,general human capital, and specific human cap-ital. The sum of them cannot exceed the totalsavings so that mkti + mgti + msti ≤ bti musthold. The aggregate physical capital is thus

Kt+1 =∑

i

mkti .

Each worker is endowed with a basic unit ofspecific human capital, namely the raw labor,

7. As long as a person with a higher income saves more,the exact specifications of utility function are not essentialfor the qualitative results.

even without any education expenditure; toacquire human capital above the basic level,however, a positive amount of material isneeded. The human capital production func-tion h(·) is the same for both general and spe-cific human capital, where h(·) is concave withh(0) = 0 and h′(0) = γ < +∞. An individualcan invest in only one type of human capital,which is either

hg,t+1,i = h(mgti) or hs,t+1,i = h(msti) + 1.

The aggregate general and specific human cap-ital are thus Hg,t+1 = ∑

i hg,t+1,i and Hs,t+1 =∑i hs,t+1,i , respectively.Individuals have heterogenous innate abili-

ties, which affect their costs of investing in gen-eral human capital. The ability distribution isidentical across generations, so is the individualability in the same family. Specifically, the abil-ity of an individual i in any generation t is ai ,which has a distribution of F(·) on the inter-val [al, ah] ⊂ [0,+∞). The investment cost ofgeneral human capital is C(ai, hgti) > 0, whereC1 < 0 and C2 < 0. That is, it is less costly ineffort to invest in general education if one hasa higher ability or if one’s parent has highergeneral human capital. The cost of investing inspecific human capital is normalized to zero forall individuals. This captures another differencebetween general and specific human capital, thatis, it is more costly to acquire general humancapital because it needs to build on a muchbroader and more abstract knowledge base.

III. EDUCATIONAL CHANGE: THEBENCHMARK CASE

We first consider the benchmark case wherethere is no political conflict and individuals areendowed with an identical amount of physicalcapital K0/N . It is straightforward to showthat as knowledge accumulates over time, theeconomy first invests in physical capital, thenin specific human capital, and finally in generalhuman capital, where individuals with higherabilities invest earlier.

Production. Production is operated in a per-fectly competitive environment. Given the cap-ital return rate rt+1, the wage rate per unit ofspecific human capital ws,t+1 and the wage rateper unit of general human capital wg,t+1, pro-ducers in period t + 1 choose the amount ofphysical capital and two types of human capital


to maximize profits. That is,

{K∗t+1,H

∗s,t+1,H

∗g,t+1}

= arg max(At+1Hg,t+1 + AtHs,t+1)α

× K1−αt+1 − rt+1Kt+1 − ws,t+1

× Hs,t+1 − wg,t+1Hg,t+1.

The inverse demand functions for these produc-tion factors are

rt+1 = (1 − α)k−αt+1,(2)

ws,t+1 = αAtk1−αt+1 ,(3)

wg,t+1 = αAt+1k1−αt+1 ,(4)

where kt+1 ≡ Kt+1/Ht+1 is the ratio betweenthe stock of physical capital and the aggregatehuman capital. Not surprisingly, the wage rateof general human capital is higher than that ofspecific skills, and both increase in the capital-labor ratio kt+1.

Investment in Physical and Human Capital.The initial income of individuals is assumed tobe larger than Z so that bequests are positive.8 Inany period t , the bequest bt is allocated amongmkt and mst or mgt to maximize a child’s adultincome minus any relevant investing cost.9 Sothe relevant objective function is max{I ∗

s,t+1,

I ∗g,t+1 − C(ai, hgti)} where

I ∗s,t+1 ≡ max

mst

rt+1(bt − mst )

+ ws,t+1h(mst ) + ws,t+1,

I ∗g,t+1 ≡ max

mgt

rt+1(bt − mgt )

+ wg,t+1h(mgt ) + ws,t+1,

taking as given rt+1, ws,t+1, and wg,t+1. IncomeI ∗s,t+1 is obtained when a child invests in specific

human capital, while I ∗g,t+1 applies when he

invests in general human capital.Define ψ(kt+1) as the extra income of having

general education than specific education:

ψ(kt+1) ≡ I ∗g,t+1 − I ∗

s,t+1.(5)

8. When the initial income is smaller than Z, there isno capital investment in the initial periods. Suppose the firstperiod that investment starts is t0 so that It0 = Z holds,which uniquely determines t0, because the income It strictlyincreases over time because of �(0) > 0. Then we can useperiod t0 as our new initial period.

9. The subscript i is suppressed whenever possible tosimplify the notations. Here we implicitly assume that thechild makes the allocation decision, possibly under parentalguidance.

The following lemma shows that it is morebeneficial to pursue general education when thecapital-labor ratio kt+1 is higher.

LEMMA 1. ψ(kt+1) > 0 and ψ′(kt+1) > 0.

An individual i will invest in general educa-tion if and only if I ∗

g,t+1 − C(ai, hgti) ≥ I ∗s,t+1,

which is equivalent to ψ(kt+1) ≥ C(ai, hgti). Asindividuals are identical except for their innateabilities, it is straightforward to establish the fol-lowing lemma.

LEMMA 2. There exists a unique thresholdability a∗

t+1 in each generation t + 1 where

ψ(kt+1) − C(a∗t+1, 0) = 0(6)

such that individuals with higher abilities ai ≥a∗

t+1 invest m∗gt in general education, while oth-

ers invest m∗st in specific education. For interior

solutions, m∗gt and m∗

st are determined respec-tively by

αAt+1kt+1h′(m∗

gt ) = 1 − α,(7)

αAtkt+1h′(m∗

st ) = 1 − α.(8)

The threshold ability a∗t+1 declines over time as

kt+1 increases.

This lemma suggests that in each period t + 1it is optimal for individuals with lower abilitiesthan the threshold level a∗

t+1 to invest in specificeducation m∗

st and others to invest in generaleducation m∗

gt . And over time more and morepeople switch from specific to general educationas the threshold ability a∗

t+1 declines. Note thatthe optimal education investments m∗

gt and m∗st ,

once positive, are independent of individualabilities and thus constant across individuals.

Market Equilibrium. In the market equilib-rium, the demand and supply of physical capitalas well as those of the two types of human cap-ital are equal:

H ∗s,t+1 = NF (a∗

t+1)h(m∗st ) + N,

H ∗g,t+1 = N [1 − F(a∗

t+1)]h(m∗gt ),

K∗t+1 = Bt − NF (a∗

t+1)m∗st

− N [1 − F(a∗t+1)]m

∗gt ,

which determine their respective market pricesin each period.

Educational Change. Let t1 denote the firsttime that specific human capital starts to accu-mulate. The comparative statics of a∗

t+1 imply


FIGURE 1Educational Change in the Basic Model: From Specific to General Education

1t

1

Average SpecificHuman Capital Average General

Human Capital

Mass SpecificEducation

Dual-TrackEducation

Mass GeneralEducation

Time2t 3t0

that when the capital-labor ratio kt+1 is toosmall, a∗

t+1 > ah is possible for some periods sothat no one acquires general education. Let t2denote the first time when (6) holds for individ-uals with the highest ability ah, or equivalently,

ψ(kt2) − C(ah, 0) = 0.(9)

Then general human capital starts to accumu-late from t2 onward. The following proposi-tion shows that when the exogenous knowledgeaccumulation speed φ(0) is small enough weobtain t1 < t2, that is, specific education pre-cedes general education.

PROPOSITION 1. Before t1 all savings areinvested in physical capital accumulation, wheret1 is determined by

At1−1kt1 = 1 − α

αγ.(10)

When φ(0) is small enough, specific educationstarts earlier than general education. That is,0 < t1 < t2.

The intuition is as follows. Before t1, noone invests in human capital because invest-ing in physical capital yields higher returns,as there is a natural endowment of specifichuman capital N even without investment. Onlywhen the capital-labor ratio exceeds a certainthreshold level, which happens after period t1,does the investment in human capital start.During the early periods t ∈ [t1, t2], only spe-cific human capital is invested, as the knowl-edge gap across periods, φ(0)At , is too small

to justify the investing cost of general educa-tion.10 After period t2, however, the knowledgegap becomes large enough for the ablest indi-viduals to acquire general education, and as aresult, knowledge starts to accumulate at everfaster speeds φ(Hgt ) > φ(0) than before, grad-ually making it beneficial for less able individ-uals to invest in general education, too. Eventu-ally, when the knowledge stock increases fastenough, all individuals will invest in generaleducation after a certain period t3, where t3 isuniquely determined by

ψ(kt3) − C(al, 0) = 0.(11)

It is obvious that t2 < t3 must hold.The evolution of these two types of human

capital over time is illustrated in Figure 1. Theaverage level of specific human capital remainsat the endowment level 1 before period t1,since then it gradually increases over time asall individuals start to acquire specific educationfrom t1; it starts to decline some time after t2when the ablest individuals switch from specificto general education, and eventually returnsback to its initial level 1 at period t3 when allhave switched. This inverted-U shape of specificeducation is observed in many countries duringtheir economic development process (Bertocchiand Spagat 2004). The accumulation of generalhuman capital, in contrast, starts later (at periodt2) than specific education but its stock keepsincreasing over time.

10. In the alternative case with large φ(0), it is possiblefor general education to precede specific education. Thenthe political economy model can be used to explain why theopposite path occurs for mass education. See Section 5 forfurther discussions.


This benchmark model demonstrates theimplications on the educational change by dif-ferent technical features of general and specificeducation. They are consistent with the changeof mass education, but not with elite educa-tion. Indeed, to account for differences betweeneducation of the elite and the masses, a polit-ical economy model is needed. Furthermore,note that investment in general human capital isinefficient because of its positive externality onthe knowledge stock and hence on productivity.That is, compared to the social optimal result,individuals tend to invest too late and too lit-tle in general human capital. Such inefficienciesmay be partially mitigated in a political econ-omy model where rent-seeking opportunities areavailable.

IV. EDUCATIONAL CHANGE: A POLITICALECONOMY MODEL

In the beginning of the political economymodel, individuals are of two types, the rul-ing elite and the masses. Each elite member isendowed with an identical amount of physicalcapital K0/Ne, where Ne denotes the measureof the elite, while the masses have no capitalendowment. The elite have the political powerand thus can impose tax and other public poli-cies on the masses.

The tax-extracting ability of an elite memberis increasing and concave in his general humancapital he

gt , but decreases in the average gen-eral human capital of the masses denoted byh

p

gt . Specifically, an elite individual gets a taxrevenue

τ(hegt )[1 − d(h

p

gt )]Ipt ,

where τ′ > 0, τ′′ < 0, and τ(·) ≤ 1/Ne. Ipt

denotes the aggregate income of the masses;d(h

p

gt ) denotes the ability of the masses tocounter-act the elite’s political ruling and taxextraction, where d ′ > 0 and d(0) = 0 for nor-malization.

Let h denote the threshold level of workers’average general human capital such that

1 − d(h) ≡ 0.

Note that when the masses acquire enough gen-eral human capital such that h

p

gt ≥ h, their abili-ties to defend their own interests become so highthat the tax revenue of the elite becomes zeroor negative, because 1 − d(h

p

gt ) ≤ 1 − d(h)= 0.In other words, the cost of ruling exceeds the

benefit for the elite when hp

gt ≥ h, and so theyare better off by extending political power to themasses. That is, the political transition from theelite rule to democracy occurs when the massesbecome too difficult to rule.11 In this context,democracy is defined as the political systemwhere all individuals share the political powerso that there is no expropriating tax, and publicpolicies are chosen through majority voting byall individuals. The other elements of the modelare the same as before.

In this political economy model, generalhuman capital enhances an individual’s polit-ical bargaining ability as represented by thetax-generating skill τ(he

gt ) of the elite and thetax-evading skill d(h

p

gt ) of the masses, whilespecific human capital does not or is at least lesseffective in doing so. This is a natural implica-tion of the essence of general human capital,which is the ability to transform knowledge intoproductivity in whatever task at hand; the spe-cific human capital, in contrast, only increasesan individual’s productivity in the specific taskin which he is trained.

A. Elite Education

An individual elite’s objective function ismax{I e∗

s,t+1, Ie∗g,t+1 − C(ai, h

egti )} where

I e∗s,t+1 ≡ max

mest

rt+1(bet − me

st ) + ws,t+1h(mest )

+ ws,t+1 + τ(0)[1 − d(hp

g,t+1)]Ip

t+1,

I e∗g,t+1 ≡ max

megt

rt+1(bet − me

gt ) + wg,t+1h(megt )

+ ws,t+1 + τ[h(megt )][1− d(h

p

g,t+1)]Ip

t+1.

The two new terms that associate with taxrevenues are the only structural difference froma typical individual’s incomes in the benchmarkcase.

The net benefit of having general educationover specific education for an elite

ψe(kt+1) ≡ I e∗g,t+1 − I e∗

s,t+1

is higher than that in the benchmark case, as

ψe(kt+1) = ψ(kt+1) + τt+1,

11. Other models of political transition, either forced orvoluntary (see Huang 2008, for more discussions), wouldnot change the main results on educational change in thispaper.


where τt+1 ≡ [τ[h(megt )] − τ(0)][1 − d(h

p

g,t+1)]Ip

t+1 > 0 is the extra tax revenue obtained byan elite member with general human capitalh(me

gt ). This means that, ceteris paribus, beingin the ruling group makes one more likely toinvest in general human capital than in specificskills, and the more so when the extra tax rev-enue τt+1 is larger.

Let ae∗t+1 denote the threshold ability among

the elite to invest in general education. Similaras (6), it is uniquely determined by

ψe(kt+1) − C(ae∗t+1, 0) = 0.

Let the denote the first time the elite start toinvest in general education and tle denote theperiod after which all elite members acquiregeneral education; then following similar argu-ments as in (9) and (11) of the basic model, the

and tle are determined respectively by

ψe(kthe) − C(ah, 0) = 0,

ψe(ktle ) − C(al, 0) = 0.

PROPOSITION 2. The elite education startsearlier and invests more compared with thebenchmark case; when the potential tax revenueis large enough, the elite invest only in generaleducation. Specifically, the < t2 and tle < t3.

In this political economy model, concentra-tion of capital endowment in the few elite andthe extra tax revenue they can extract are twochannels for the society to have a higher totalbequest, and hence a larger aggregate stock ofphysical capital in each period. As a result, ifthe elite ever invest in specific or general humancapital, they will do so at a much earlier time andinvest more in it than in the benchmark model.Furthermore, this proposition suggests that whenthe potential tax revenue is large enough, theelite may skip the stage of specific education tostart directly with general education, which is insharp contrast with the benchmark case wherespecific education precedes general education.Such a reverse of order in educational changearises because general education, by increasingone’s skills in political rent seeking, brings highreturns to individuals over and above its role inproduction.12

12. The propertied elite, for example, could have takenspecific education in order to enhance the management andvalues of their properties rather than going through classicalstudies and assuming positions in the state and church. Thefact that the opposite did happen in history is what thisproposition tries to account for.

B. Stratified Education under Elite Rule

Consistent with broad historical trends, weassume that, even after period tle, the after-taxincome of workers is still too low for them tohave bequest. The elite, however, may find itbeneficial for their own sake to provide freepublic education, because it increases workers’productivity and hence the tax revenue. Asspecific education is less harmful than generaleducation in raising workers’ political threatto the elite, it is the natural focus of publiceducation under the elite rule.

Let mpgt and m

pst denote per student pub-

lic education investment in general and spe-cific education, respectively. The elite choosethe optimal general education level m

p∗gt to maxi-

mize their joint pool of tax revenue Tg,t+1 takinginto consideration the public education expendi-ture (N − Ne)m

pgt , where

T ∗g,t+1 ≡ max

mpgt

[1 − d[h(mpgt )]][I

p

t+1 − (N − Ne)mpgt ].

The optimal specific education level mp∗st is

similarly chosen to obtain

T ∗s,t+1 ≡ max

mpst

[1 − d(hp

g,t+1)][Ip

t+1 − (N − Ne)mpst ],

taking as given the average general humancapital h

p

g,t+1 of the masses, which stays at thebasic level 0 for most times under the elite ruleand starts to increase only after period t2e deter-mined in Equation (13). The optimal choices aresummarized in the following proposition.

PROPOSITION 3. Under the elite rule, freemass education in specific skills starts in someperiod t1e, which is determined by

At1ek1−αt1e+1 = 1/αγ,(12)

and t1e > tle. General education for the masseswill never be supported when d ′(0) ≥ 1 or aslong as he∗

gt ≤ h, where φ(Neh) = d ′(0)/[1 −d ′(0)]; and if ever supported, it will never gobeyond h.

This proposition suggests that when thecapital-labor ratio kt+1 becomes large enough,investing in physical capital becomes less prof-itable than investing in public education toincrease the human capital of the masses andthus their productivity. Then the decision on


which type of education, general or specific edu-cation, to provide for the masses depends onthe trade-off between their different effects onincreasing the tax base versus reducing the taxrate; the more effective general education is inlowering the tax rate through 1 − d(h

p

g,t+1) thanenlarging the tax base I

p

t+1, the less likely itis to be supported by the elite. In fact, it willnever be supported under the elite rule whend ′(0) ≥ 1 holds, in which case general educa-tion is too powerful in enabling the masses toresist the elite rule and evade taxes. Althoughit is possible for the elite to provide generaleducation for the masses when it is less harm-ful politically (d ′(0) < 1) and when the elite areskillful enough in political ruling (he∗

gt > h), theinvestment of mass general education is cappedabove because the elite rule cannot be sustainedonce the masses’ average general human capitalreaches the threshold level h.

The following analysis focuses on the casewith d ′(0) ≥ 1 where the elite won’t supportmass general education. So from t1e onward,workers begin to acquire specific human capi-tal through public education. This enables theincome of workers to grow at a faster speedthan before, and it will eventually reach thethreshold Z at some period tZ .13 Then from tZonward workers start to have bequest and maychoose to invest in general education h

p∗gt by

themselves.The net benefit of investing in general edu-

cation over receiving free specific education is

ψp(kt+1) ≡ {1 − Neτ(he∗g,t+1)[1 − d(h

p

g,t+1)]}× [wg,t+1h(m

p∗gt ) − ws,t+1h(m

p∗st )

− rt+1mp∗gt ]

for a worker, which is smaller than ψ(kt+1) inthe benchmark case not only because of theconfiscatory tax, but also because of the freespecific education provided by the elite; bothelements discourage the poor’s investment ingeneral education and thus help preserve theelite rule.

When the knowledge stock becomes largeenough, however, workers with high abilitiesmay find it beneficial to invest in general edu-cation h

p∗gt , instead of receiving the free spe-

cific education. Let t2e denote the first period

13. Note that tZ > t1e is guaranteed when 1/γ < Z, asws,t1e+1 = αAt1e

k1−αt1e+1 = 1/γ by conditions (3) and (12).

when the ablest workers start to acquire generaleducation. Then following similar arguments asbefore it is uniquely determined by

ψp(kt2e+1) − C(ah, 0) = 0.(13)

The level of general education hp∗gt among the

masses, however, is still lower than that ofthe elite, as the masses lack the rent-seekingopportunity to generate tax revenues.

C. Mass Education under Democracy: FromDual-Track to General Education

Let tm denote the first period when thethreshold level of workers’ average generalhuman capital h is reached; that is, from periodtm onward, d(h

p

g,t ) ≥ 1 holds so that the rulingcost becomes too high for the elite to obtain anytax revenues. This either forces or induces theelite to extend political power to the masses.14

Without loss of generality, we assume that atperiod tm democracy replaces the elite rule sothat confiscatory tax is abolished.

The education policy under democracy ischaracterized by (md∗

gt , md∗st ), where md∗

gt andmd∗

st denote each person’s contribution to thepublic investment in general and specific educa-tion, respectively. It is determined by majorityvoting, where each individual votes for the pol-icy that is closest to his favorite choice of pub-lic education investment, which maximizes thefuture income of his child. Opting out of publicspecific education to pursue privately financedgeneral education is allowed, in which case anindividual still needs to pay his share of the edu-cation tax.15 If mass general education is pub-licly provided, very few, if any, would choose toopt out of it, and so to simplify exposition, weassume that opting out of public general educa-tion is not allowed by law.

14. The elite may try to control how the masses areeducated in order to prevent h

p

g,t from being too high, buttheir success is not always guaranteed. The declining costof print, for example, may have contributed to the failure ofsuch elite control.

15. If individuals opting out of public specific educationdo not need to pay their share of the education tax, itessentially leads to a similar situation as if the educationchoice is purely left to individuals; in this case their choiceproblems become exactly the same as in the benchmarkcase, where mass education also evolves from dual-trackto general education.


If a child is going to take general education,his future income will be

I d∗g,t+1 ≡ max

mdgt ,m

dst

rt+1(bti − mdst − md

gt )

+ wg,t+1h(mdgt ) + ws,t+1 − C(ai, hgti).

The first order condition (FOC) for the interiorsolution md∗

gt > 0 is αAt+1kt+1h′(md∗

gt ) = 1 − α,the same as (7) in the benchmark case. So forall individuals who take general education, md∗

gt

will be identical, independent of a child’s abilityand parental bequest or education level. It isstraightforward to see that one’s preferred publicinvestment in specific education is zero if hischild takes general education.

Similarly, if the child is going to take specificeducation, his future income will be

I d∗s,t+1 ≡ max

mdgt ,m

dst

rt+1(bti − mdst − md

gt )

+ ws,t+1h(mdst + ε∗) + ws,t+1,

where ε∗ denotes the extra educational invest-ment that arises if some individuals opt out ofpublic specific education but still pay the edu-cational tax md∗

st . The FOC for the interior solu-tion md∗

st > 0 is αAtkt+1h′(md∗

st + ε∗) = 1 − α,which implies that md∗

st will be the same for allindividuals. And one’s preferred public invest-ment in general education is zero if his childtakes specific education.

These results imply that, conditional on thetype of education, there is a consensus over theamount of investment. The conflict of interestthus lies in the different choices of educationtype across individuals. If a simple majority ofpeople choose to attend public specific educa-tion, then the dual-track education policy will bethe equilibrium choice under majority voting; ifthe opposite is true, then general education willinstead be publicly financed.

If free public specific education is provided,every individual has to pay the education taxmd∗

st , and those who choose to pursue generaleducation instead need to pay the extra invest-ment md∗

gt ; so the net benefit of having generaleducation over specific education is

ψd(kt+1) ≡ I d∗s,t+1 − I d∗

s,t+1

= wg,t+1h(md∗gt ) − ws,t+1h(md∗

st + ε∗)

− rt+1md∗gt ,

which has to be at least as large as the costC(ai, hgti) for an individual to choose generaleducation.

As the benefit of general education ψd(kt+1)under democracy is larger than ψp(kt+1) underthe elite rule, workers whose parents acquiredgeneral education under the elite rule will con-tinue to do so, and so will workers who areslightly less smart. Let aw

t denote the abilityof the threshold worker that invests in generaleducation. It is thus uniquely determined by

ψd(kt+1) = C(awt , 0).

It is less clear whether children of the oldelite will still acquire general education, becauseseveral forces affect their choices in the oppositedirections. On the one hand, the knowledgestock is larger than before and their parents’general education levels are higher than beforeand than others, both of which would make themmore likely to invest in general education; onthe other hand, the disappearing of the politicalrent would reduce the benefit of having generaleducation. What happened in history seems tosuggest that the old elite children will continueto acquire general education, which is assumedhere. So if specific education is to be publiclysupported, individuals from the old elite familiesand workers with ai ≥ aw

t will opt out of publicspecific education and pursue privately financedgeneral education, while the rest with measure(N − Ne)F (aw

t ) will attend it.16

Let amedian denote the threshold ability levelthat is determined by

Ne/N + [1 − F(amedian)](1 − Ne/N) = 1/2.

When amedian < awt holds, less than half of the

population choose to invest in general education,so free specific education will be provided undermajority voting. So the lower amedian is, the morelikely the specific education is publicly providedand the later the free general education policy isto be adopted. Note that, based on the aboveidentity,

∂amedian/∂(Ne/N)

= −F(amedian)

/[−F ′(amedian)(1 − Ne/N)] > 0,

16. This means ε∗ = N/[(N − Ne)F (awt )] − 1)md∗

stmust hold for a balanced budget for public specificeducation, and it is uniquely determined.


which implies that a smaller number of old eliteleads to a lower amedian and thus delays thearrival of mass general education under democ-racy. As the knowledge stock keeps increasingover time, aw

t decreases so that more and moreworkers will choose general education. In a cer-tain period t3m such that

awt3m

≥ amedian

holds for the first time, the education policywill switch from the dual-track system to freegeneral education for all. Thus we have provedthe following proposition.

PROPOSITION 4. Under democracy, the dual-track education system of free specific educa-tion plus private general education is more likelyto continue and to last longer when Ne/N issmaller (or when the initial income inequalityis higher); it will eventually be replaced by freegeneral education for all.

It is useful to note that the existence of dual-track education system in this proposition is notbecause of the usual suspect that insiders whoreceive general education protect their own priv-ileges by restricting access to general education(Collins 1971; Bertocchi and Spagat 2004). Thedriving force is the heterogenous costs amongindividuals: Those with higher abilities and withparents who already acquired general education(the old elite belong to this group) have lowercosts C(ai, hgti) than others. When the initialincome inequality is high, a large proportion ofthe population have high costs of investing ingeneral education and thus prefer to continuewith free specific education. In other words, the

dual-track education system under democracy isthe rational choice of the majority, not the con-spiracy of the privileged. The majority supportfor mass general education, however, will even-tually arise when the knowledge stock changesfast enough to warrant so. That said, one shouldbe aware of the positive externalities of gen-eral education over knowledge accumulation,and hence an earlier adoption of mass generaleducation than mandated by majority voting canbe welfare improving.

D. Summary

The timing of educational change in this pol-itical economy model is illustrated in Figure 2.The elite start to invest in general educationafter the, before which all savings are investedin physical capital accumulation. As the aggre-gate stock of general human capital, althoughso far composed completely by that of the elite,keeps increasing, the knowledge stock expandsat ever faster speeds than before, and it even-tually induces the elite for their own intereststo support public specific education for work-ers starting from t1e. Although the elite maynever want to support general education for themasses, the ablest workers invest in general edu-cation themselves from period t2e onward. Whenthe average general human capital of workersreaches the threshold level h in period tm, theelite rule becomes too costly to maintain and isthus replaced by democracy, under which thereis no expropriating tax and public education ischosen by majority voting. The dual-track edu-cation system includes public specific educationfor majority and private general education for

FIGURE 2Educational Change in the Political Economy Model: From Elite to Mass General Education

het 1et 2et 3mt

1

Average GeneralHuman Capital (Elite)

Average SpecificHuman Capital (Masses)

Average GeneralHuman Capital (Masses)

Elite Education Stratified Education Mass General Education

Time

Dual-Track Education

mt0


the rest, which will finally give way to publicgeneral education for all after period t3m.

The existence of political rent-seeking oppor-tunities facilitates investment in general humancapital for the elite and encourages public edu-cation in specific skills for workers; it thusmay increase productivity in general, especiallywhen the distortion caused by such rent-seekingactivities is relatively minor. In the later stageof development, however, it tends to prolongspecific education and delay investment in gen-eral human capital for the masses. More impor-tantly, this political economy model accountsfor the sharp contrasts between the elite educa-tion and mass education in terms of timing andcontent: elite education starts much earlier andfocuses on general education, while mass edu-cation starts much later and initially focuses onspecific education; although mass specific edu-cation is compatible with and thus can be wellsupported by the elite rule, mass general educa-tion is much less so, and hence most likely tooccur under democracy.

V. EXTENSIONS AND DISCUSSIONS

Humanities versus Natural Sciences. In themodel, the contents of general education areassumed homogenous in terms of their contribu-tions to productivity and rent-seeking effective-ness. They are not necessarily so. For example,humanities seem to be more effective in increas-ing one’s rent-seeking skills than natural sci-ences, while the opposite tends to be true forimproving production productivity in general(Murphy, Shleifer, and Vishny 1991).

The model can be readily extended to accom-modate such heterogeneity in general education.For example, the production function can beadjusted by replacing Hg,t+1 with σ1H

Rg,t+1 +

σ2HNg,t+1, where HR

g,t+1 denotes the aggregatehuman capital in humanities, HN

g,t+1 denotes theaggregate human capital in natural sciences, andσ1 ≤ σ2; the rent-seeking skill τ(hg,t+1) can bechanged to τ(σ3h

Rg,t+1 + σ4h

Ng,t+1), where σ3 ≥

σ4; and finally an individual can invest simul-taneously in these two types of general humancapital.

Following similar arguments as in the model,it is easy to obtain the following results. Inthe basic model without rent-seeking oppor-tunities, individuals will invest more in natu-ral sciences than in humanities, which is alsotrue under democracy in the political economy

model. Under the elite rule, in contrast, theelite will invest more in humanities than in nat-ural sciences, the more so if the gains fromrent-seeking are larger. And everything elseequal, societies with relatively more gains fromrent-seeking than others would invest more inhumanities but less in natural sciences. It wouldbe interesting to test these results empirically infuture research.

Closed-Elite versus Open-Elite. The politicaleconomy model adopted in this paper is a modelof closed-elite in that the elite group is fixed anddetermined by birth, and as a result only a fixedgroup in society is entitled to gains from rent-seeking. An alternative is an open-elite model,such as the bureaucratic system in feudal China,where the elite were recruited through standardexams that were open to all members in society(Collins 2000). In such a model, the accessto rent-seeking gains is endogenous, becauseanyone can choose to invest in general educationto become the elite, if the benefit of doing sooutweighs the cost.

From a naive point of view, the open-elitemodel seems to be better because it gives every-one a more equal chance to join the elite thanthe closed-elite model. A quite surprising resultemerging from our analysis shows that the oppo-site is true, however, at least from the wholesociety’s perspective. Following similar argu-ments in the model, one can find that the open-elite system is more effective in stabilizing theelite rule in comparison to the closed-elite sys-tem, because the richest and smartest individualswill invest in general education and join theelite, which implies that the repressed massesacquire either no education at all or only specificeducation and thus have much limited ability toachieve political power and overthrow the eliterule. Furthermore, societies with the open-elitesystem tend to over-invest in humanities andunder-invest in natural sciences than those withthe closed-elite system. Both results seem con-sistent with the contrasting differences betweenfeudal China and western Europe.

Educational Differences across Countries. Animplication of the model is that general edu-cation of the masses starts earlier and thus itsknowledge stock grows faster in society witha more diverse talent pool. This may speak tothe educational differences between the UnitedStates and Europe where vocational educationis emphasized more in Europe than in theUnited States (Goldin 2001; Krueger and Kumar2004b). A possible reason could be that the


United States as an immigrant country has a rel-atively more diverse distribution of talent andhence started mass general education earlier.Specifically, suppose that talent ai is distributedon [aU

l , aUh ] in society U and on [aE

l , aEh ] in

society E, where aUl < aE

l , aUh > aE

h , and themedian is kept the same. So abilities are morediversely distributed in society U than in soci-ety E. As C1 < 0 and aU

h > aEh , it follows from

(13) that tU2e < tE2e must hold, which means thatgeneral education of the masses starts earlierin society U than in society E; and this inturn leads to earlier democratization (tUm < tEm )and earlier beginning of mass general education(tU3m < tE3m).

Discussions on Modeling Choices. As brieflymentioned in the Introduction, the model focuseson the changing level and content of organizedlearning conducted in schools. This is by nomeans intended to deny the ubiquitous pres-ence of informal learning in daily life, whichlong preceded any form of organized learning inhistory and has always been playing an impor-tant role in knowledge accumulation. In fact,its existence is acknowledged in the assump-tion that each individual is endowed with abasic unit of specific human capital even with-out organized education, and its indispensablerole is also reflected in the assumption φ(0) >0, which means that the knowledge stock stillgrows, although slowly, even when there is noorganized education. Furthermore, investment inorganized education becomes worthwhile in themodel only after the knowledge stock accumu-lated by such informal learning becomes largeenough.

This paper does not explicitly model whylearning becomes organized in schools at somepoint for a couple of reasons. First, the exactorganization of learning presumably involvesdifferent economic forces than those consideredin the model, and thus its analysis is beyondthe scope of this paper. Second, considering itexplicitly is not likely to change the main resultsof this paper. One may argue, for example, thatif the economy of scale is more easily reachedin general education than vocational education,this may explain why organized education beganfrom universities among the elite.17 This argu-ment by itself, however, does not explain why,on the contrary, vocational education precededgeneral education for the masses. A plausible

17. This may also be achieved by assuming largeenough φ(0); see Proposition 1.

explanation is readily provided by the samepolitical economy model as before: Even thoughit is best in this scenario to provide generaleducation for the masses from pure economicconsiderations, the elite may choose the oppo-site because of the political concerns that gen-eral education makes the masses more difficultto rule. This suggests that the political econ-omy model captures some fundamental forcesunderlying the different paths taken by elite andmass education, which are the main focus of thispaper.18

VI. CONCLUSIONS

For many years in history only the few rul-ing elite were educated and the elite educationfocused on general education rather than tech-nical or specific skills, while the masses startedto receive education in the nineteenth century inwestern Europe together with industrialization;and the mass education was initially focusingon specific vocational skills and then graduallymoving to general education. Such educationalchange in terms of who are educated and whatthey learn is accounted for in this paper in aframework of long run economic and politicaldevelopment.

The main results of this paper suggest that theeducational change can be categorized into threephases, namely, the elite education phase whereonly the elite are educated and it focuses on gen-eral education; the stratified education phase thatincludes both general education for the elite asbefore and specific education for the masses; andfinally, the mass education phase under democ-racy, which continues with the dual-track edu-cation system including general education forsome and specific education for majority, andeventually converges to providing general edu-cation for all. These results are broadly consis-tent with the historical evidence.

More interestingly, the paper finds that,although mass specific education may be sup-ported under the elite rule, this is very unlikelyfor mass general education, which occurs typi-cally under democracy. In other words, the eliterule is often associated with a lack of general

18. To be clear, this political economy story is notnecessarily the only path to explain the educational change,although it is a potentially useful way of looking at theissue because it links up democracy, education, and growthin a way consistent with our general understanding of theirempirical relationship.


education for the masses. This is probably drivenby an important difference between general andspecific education, where general education ismore likely to increase an individual’s skillsin whatever tasks at hand, which by definitioninclude skills of extracting gains and defend-ing one’s own interests in political conflicts.The same insights suggest that if humanities andsocial sciences are more effective in improvingone’s rent-seeking skills than natural sciences,the elite will invest more in the former than inthe latter, the more so in societies where thegains from rent-seeking are larger. As shownin the paper, the model can also be readilyextended in other ways to yield intriguing resultsthat may account for cross-country differencesin education and its effects on economic andpolitical development.

APPENDIX A: PROOFS

Proof of Lemma 1

Proof. Note that the incomes I ∗g,t+1 and I ∗

s,t+1 arise froma common function I ∗

t+1 ≡ rt+1(bt − m∗t ) + wt+1h(m∗

t ) +ws,t+1 where wt+1 can take two distinct values, eitherws,t+1 or wg,t+1. By the Envelope Theorem we know∂I ∗

t+1/∂wt+1 = h(m∗t ) > 0 if m∗

t > 0, that is, the incomeI ∗t+1 strictly increases in wage rate wt+1; but then wg,t+1 >

ws,t+1 implies I ∗g,t+1 > I ∗

s,t+1, which is equivalent toψ(kt+1) > 0.

Observe that

ψ′(kt+1) = (∂I ∗g,t+1/∂kt+1) − (∂I ∗

s,t+1/∂kt+1)

= w′g,t+1h(m∗

gt ) − w′s,t+1h(m∗

st ) − r ′t+1(m

∗gt − m∗

st )

= α(1 − α)k−αt+1[At+1h(m∗

gt ) − Ath(m∗st )]

+ α(1 − α)k−α−1t+1 (m∗

gt − m∗st ),

where the second equality follows from the EnvelopTheorem. As At+1 ≥ At and h′ ≥ 0, ψ′(kt+1) > 0 holds ifm∗

gt ≥ m∗st , which is indeed true.

Now we prove that m∗gt > m∗

st holds; that is, when anindividual is considering the optimal investment in these twotypes of human capital, he would invest more resources inacquiring general education than in specific education. Foran individual that invests in h∗

s,t+1, his objective function is

maxmst

rt+1(bt − mst ) + ws,t+1h(mst ) + ws,t+1.

The FOC after plugging in (2) and (3) becomes

Atkt+1h′(m∗

st ) = (1 − α)/α for m∗st > 0,(14)

Atkt+1 ≤ (1 − α)/αγ for m∗st = 0.(15)

So the threshold level for Atkt+1 is (1 − α)/αγ, belowwhich no resources are spent in accumulating specific humancapital. The optimal amount of specific education m∗

st is afunction of At and kt+1 obtained from (14).

For an individual who invests in h∗g,t+1, his objective

function is

maxmgt

rt+1(bt − mgt ) + wg,t+1h(mgt ) + ws,t+1 − C(ai , hgti ).

The FOC is

At+1kt+1h′(mgt ) = (1 − α)/α for mgt > 0,(16)

At+1kt+1 ≤ (1 − α)/αγ for mgt = 0.

For interior solutions, the optimal amount of general educa-tion m∗

gt is a function of At+1 and kt+1, while it is inde-pendent of ai . This implies that h(m∗

gt ) is the same forall who invest in it, regardless of their individual abilities.Note that m∗

gt > m∗st > 0 because h′′(·) < 0 and h′(mgt ) =

[(1 − α)/αAt+1kt+1] < [(1 − α)/αAtkt+1] = h′(mst ) holdsfor interior solutions. As At+1 > At , the threshold condi-tion At+1kt+1 = (1 − α)/αγ for general education invest-ment must hold at some time earlier than that for specificeducation. This means m∗

gt ≥ m∗st is always true. �

Proof of Lemma 2

Proof. The investment cost C(ai , hgti ) is strictly decreasingin ai as C1 < 0, C2 < 0 and hgti = h(m∗

g,t−1) does notdepend on individual ai , which is shown in the aboveproof. As ψ(kt+1) is independent of ai while C(ai , hgti )

strictly decreases in ai , a threshold ability a∗t+1 must

exist so that the marginal person with ability a∗t+1 is

indifferent between investing in either general or specifichuman capital. Note that when it is the first time that anindividual reaches the threshold of starting to invest ingeneral human capital, his parent must have not investedin it so that h(m∗

g,t−1) = 0. The reason is straightforward.If h(m∗

g,t−1) > 0, then ψ(kt ) − C(a∗t+1, 0) ≥ 0 must hold

for the parent, which together with kt+1 > kt then impliesψ(kt+1) − C(a∗

t+1, 0) > 0 is true for the child. But thiscontradicts with (6). Based on (6) we have

∂a∗t+1/∂kt+1 = [ψ′(kt+1)/C1(a

∗t+1, h(m∗

g,t−1))] < 0,

because C1 < 0. Similarly we can show that ∂a∗t+1/∂At+1 <

0 and ∂a∗t+1/∂At < 0. So a∗

t+1 strictly decreases over timeand in capital-labor ratio kt+1. �

Proof of Proposition 1

Proof. The equality in (15) is achieved in period t1, from thenon people start to invest in specific human capital. Whenψ(kt1 ) − C(ah, 0) < 0, no one invests in general educationbefore period t1, which means t1 < t2 will hold. As ψ(kt1 )

strictly increases in φ(0) and is equal to zero when φ(0) = 0,there must exist a unique level of φ(0), denoted by g,such that ψ(kt1 ; g) = C(ah, 0). So a sufficient condition forψ(kt1 ) − C(ah, 0) < 0 is φ(0) < g.

As there is no human capital investment before periodt1, we obtain Hgt = 0, Hst = N , and At = At−1(1 +φ(0)) in any period t ≤ t1; then At+1kt+1 = Kt+1(1 +φ(0))/N by definition. So (10) can be rewritten as Kt1 =[1 − α/αγ][N/(1 + φ(0))]. Thus K1 < Kt1 is sufficient toinsure that t1 > 0, where K1 = β(Aα

−1K1−α0 − NZ). This

condition is equivalent to φ(0) < g where g is determinedby g = [(1 − α)N/αγK1] − 1. So any φ(0) ≤ min{g, g}) issufficient to establish the timing 0 < t1 < t2. �



Proof. For an individual elite that invests in general humancapital he∗

g,t+1, his objective function is

maxme

gt

rt+1(bet − me

gt ) + wg,t+1h(megt ) + ws,t+1

+ τ(h(megt ))(1 − d(h

p

g,t+1))Ip

t+1 − C(ai , hegti ).

The FOC is

[At+1kt+1 + kαt+1I

p

t+1τ′(h(me

gt ))(1 − d(hp

g,t+1))/α]h′(megt )

(17)

= (1 − α)/α for megt > 0,

At+1kt+1 + kαt+1I

p

t+1τ′(0)/α

< (1 − α)/αγ for megt = 0.

For interior solutions, the optimal general education foran elite me∗

gt is higher than that in the benchmark casem∗

gt , because a higher general human capital enableshim to collect a larger tax revenue as reflected bykαt+1I

p

t+1τ′(h(me

gt ))(1 − d(hp

g,t+1))/α in the FOC. And thedifference is larger when the tax base I

p

t+1 is larger. Theinvestment in general education among the elite will startearlier than in the benchmark case as a result of the positiveterm kα

t+1Ip

t+1τ′(0)/α, where 1 − d(h

p

g,t+1) = 1 must holdas a result of h

p

g,t+1 = 0, because the education of the poormasses cannot start before the rich elite.

As in the benchmark case, the threshold ability ae∗t+1

strictly decreases over time and in capital-labor ratio kt+1 aslong as h

p

g,t+1 = 0, which is true well after tle as confirmedin the next proposition. Observe that

ψe′(kt+1) = ψ′(kt+1) + (∂τt+1/∂kt+1) > 0,

where ∂τt+1/∂kt+1 = ∂(τ(h(me∗gt )) − τ(0))I

p

t+1/∂kt+1 > 0as a result of ∂me∗

gt /∂kt+1 > 0, which can be obtained bythe Implicit Function Theorem from Equation (17). Notethat ae∗

t+1 < a∗t+1 holds because ψe(kt+1) > ψ(kt+1) is true

because of the extra positive term τt+1. Given that ae∗t+1 <

a∗t+1 and both decrease over time, we obtain immediately

the < t2 and tle < t3.If one invests in specific human capital, the FOC is the

same as (14) and (15) so that me∗st has the same functional

form as m∗st in the benchmark case. However, their optimal

levels at each period are different. Concentration of capitalendowment in the few hands of the elite and the extra taxrevenue allow the society to have a higher total bequest,and hence a larger aggregate stock of physical capital ineach period. So if the elite ever invest in specific humancapital, they do so at a much earlier time and invest morein it, that is, tse < t1 and me∗

st > m∗st , where tse is the first

time the elite start to invest in specific education such thatAtse−1ktse = (1 − α)/αγ.

When the tax revenue is large enough, the elite willinvest only in general education and never in specific skills.This is true when all elite individuals have invested ingeneral education by period tse , that is, when tle ≤ tse orequivalently ψe(ktse ) > C(al, 0) holds, which is true whenthe extra tax revenue τtse is large enough. As τtes

strictlydecreases in Ne/N , the ratio of the elite versus the masses,there exists a unique level n such that τtse (n) = C(al, 0).This implies that Ne/N ≤ n is a sufficient condition forψe(ktse ) > C(al, 0). �


Proof. The optimal specific education level mp∗st is chosen

to obtain

T ∗s,t+1 ≡ (1 − d(h

p

g,t+1))(Ip∗t+1 − (N − Ne)m

p∗st )

= (N − Ne)(1 − d(hp

g,t+1)) maxm

pst

(ws,t+1h(mpst ) − m

pst ).

The FOC for the specific education level mp∗st is

αh′(mpst )At k

1−αt+1 = 1 for m

pst > 0,

αγAtk1−αt+1 < 1 for m

pst = 0,(18)

The left-hand side (LHS) of (18) is increasing over time, sothere must exist some period t1e such that the equality holds.As Atse ktse+1 = (1 − α)/αγ, we know that αγAtse ktse+1 =(1 − α) < 1, which means t1e > tse . This, combined withtse > tle , indeed confirms our assumption that t1e > tle .

The optimal general education level mp∗st is chosen to

obtain

T ∗g,t+1 ≡ (1 − d(h(m

p∗gt )))(I

p∗t+1 − (N − Ne)m

p∗gt )

=(N− Ne) maxm

pgt

(1− d(h(mpgt )))(wg,t+1h(m

pgt ) −m

pgt ).

The FOC for the general education level mp∗gt is

αAt+1k1−αt+1 [1 − d(h) − d ′(h))h]h′ + d(h) − d ′(h)h′mp

gt

= 1 for mpgt > 0,

αγAt+1k1−αt+1 (1 − d ′(0)) < 1 for m

pgt = 0.(19)

where h is the shorthand for h(mp∗gt ). If d ′(0) ≥ 1, then (19)

will always hold, which means the ruling elite will neversupport mass general education. If d ′(0) < 1, the LHS of(19) is smaller than that in (18) if

φ(Nehe∗gt ) < d ′(0)/(1 − d ′(0))(20)

given that At+1 = At (1 + φ(Nehe∗gt )). The LHS of (20) is

strictly increasing in he∗gt , which implies that there exists

a unique threshold h such that (20) holds with equality.In other words, before their general education reachesh, the ruling elite will only support mass education inspecific skills. Even after he∗

gt > h is achieved, the elitemay still choose not to support mass general educationif T ∗

g,t+1 < T ∗s,t+1. Specifically, the investment in mass

general education, if any, will never go beyond h underthe elite rule, otherwise the tax revenue will become zero ornegative. �

APPENDIX B: HISTORICAL EVIDENCE

The main results of this paper suggest that the educa-tional change can be categorized into three phases: (1) EliteEducation. The political elite are educated first and in gen-eral education while the masses do not receive any formaleducation for a long time. (2) Stratified Education. Whenthe capital-labor ratio becomes large enough, it may be ben-eficial for the elite to support specific or technical educationfor the masses, while the elite still receive general education,and so the education system is stratified. (3) Mass Educa-tion. After the elite rule is replaced by democracy, which isendogenously determined by the general education level of


the masses, mass education may still be dual-track initially,where both specific education and general education are pur-sued. Over time, however, mass education will eventuallymove toward general education. This is broadly consistentwith the western history.

Before the nineteenth century, the masses hardly receivedany formal education at all, whereas the elites were educatedin classical studies that were designed mainly to train freethinkers, rather than preparing for any specific or narrowvocations. Over the years, and especially during the sev-enteenth and eighteenth centuries, scientific knowledge asto the forces and laws of the physical world was gradu-ally accumulated by scholars. Important development andgreat applications were made in the nineteenth century,which kicked in the era of modern economic growth (Mokyr2002). In the second phase of the Industrial Revolution, therise of science-based new industries such as chemicals andelectricity made the grasp of systematic scientific knowl-edge essential for worker productivity, and the need to trainthe masses with relevant technical knowledge was stronglyfelt. As a consequence, vocational education for the massesstarted in the leading industrial countries around 1870. Theelite education, however, was hardly changed from beforeand run separately from the mass schools. So the educa-tion system was highly stratified, especially in continentalEurope. Although democracy was achieved in the leadingindustrial countries by the end of World War I, the dual-track education system continued for decades, and a unifiedgeneral education system was not attempted or realized untilafter World War II (Collins 2000).

Elite Education. In the late eleventh and early twelfthcenturies, a number of schools, in time known as universi-ties, came into prominence (Cordasco 1976). They representa reaction to the changed conditions of the times such asthe rise of the city and the revival of trade and industry.They offered studies in four traditional faculties, namely,arts, law, medicine, and theology, and trained future lead-ers for State and Church. During the Renaissance in thefifteenth and sixteenth centuries, language and literatureof ancient Greece and Rome formed the main content ofelite education and were known as humanities. The typicalhumanistic schools of Europe were the German Gymnasiumand the English public schools. The grammar school of theAmerican colonies was a transplanted English public school.This humanistic education dominated the training of the eliteclasses of society for the next 400 yr. For example, the formof the English public schools was not drastically modifieduntil the report of the royal commissioners of investigationin 1864.

Stratified and Mass Education. As commercial andindustrial sectors gradually become dominant economicactivities, the Industrial Revolution started first in Englandaround the middle of the eighteenth century and later spreadto other western countries. The industrialization processbrought forth fundamental changes across Europe, trans-forming it from a primarily agrarian society to a matureindustrial society by the end of the nineteenth century; itincreased demand for skilled workers and set the stage forthe beginning of mass education in western Europe andAmerica.

Germany. Prussia was the first modern state to startmass education, and by 1825, it had taken over educationfrom the Church and made it an instrument of the State.Its education system, however, was a highly stratifiedtwo-class school system, and it was continued after theformation of the German Empire in 1871. Children ofthe laboring classes attended the basic elementary schools

(Volksschule: folk-schools), which were designed to createan intelligent but obedient and patriotic citizenship; a vastprogram of vocational education was, about a half centurylater, developed for the graduates of the Volksschule. Forthose who were to form the official and directing class ofsociety, a classical training track composed of Gymnasiumand university was provided. Up at least to 1914, schoolsfor the masses educated about 92% children, while schoolsfor the leaders educated 8% (Cubberley 1920, p. 578). Thebasic pattern of this two-class education system has not beendramatically changed ever because.19 The establishment ofa stable liberal parliamentary republic was not achieved inWest Germany until its major military defeat in World War IIand in East Germany until the reunification of Germanyin 1990.

France. The Law of 1833, which established lower andhigher primary schools, marked the first time in Frenchhistory that an earnest effort was made to provide educationfor the great mass of the people. The basic form of Frenchnational education was achieved under the Third Republic(1870), which started a lasting democracy with universalmale suffrage. The French state school system was also oftwo-class, where schools for the masses were composedby the primary and vocational schools, and schools forthe elite included the lycees and universities. No concerteddrive was made to reform this system until World War I.Reforms eventually took place in the 1960s when the accessto secondary education was opened up for all children,and from the 1980s the lycees and then higher educationwere becoming accessible to the great majority of youngpeople.

England. Starting from the Elementary Education Actof 1870, England started to establish compulsory elementaryeducation for the masses. The curriculum of most elementaryschools was limited to reading and writing. The BalfourAct of 1902 equalized and unified educational provisionsand made the general provision of secondary educationpossible. New modern-type universities were created invarious cities to extend the educational ladder upward.However, even after World War I only a small proportion ofpupils, around 1920 about 10%, transferred from the uppergrades of the elementary into the secondary schools, andonly “1 per cent or less of these former elementary-schoolpupils entered the university” (Ulich 1961, pp. 117-118).It was not until the Education Act of 1944 that the oldclass division of secondary schools for the privileged, onthe one hand, and elementary and vocational schools for themasses, on the other hand, was broken down. Starting fromthe 1960s the number of comprehensive schools has grownso that most state-maintained secondary schools are nowcomprehensive.

United States. The American education was initiallysimilar to that in Europe, focused almost exclusively ontraining a small elite through the Latin grammar schoolsand universities. In the middle of the eighteenth century,the elementary or common school had been established indifferent states to provide the basic education to children ofthe masses. The full white manhood suffrage was largelycomplete by the 1840s in the United States. After 1870, themass secondary school started to grow, which was largelyterminal, providing an increasingly vocational education forthe new body of white-collar workers (Trow 1967). The

19. Currently in Germany about 25% secondary-school–aged children enter the Gymnasium, and the majority restattend some schools that eventually lead to vocationaltraining (Encyclopedia Britannica).


rapid growth of higher education occurred after World WarII, and as a consequence, prompted the transformation of theterminal secondary system into a mass preparatory system(Goldin 1999, 2001).

In summary, the three phases of educational change,namely, elite education, stratified education, and masseducation (from dual track to mass general education)are broadly consistent with historical evidence of west-ern Europe and the United States. Similar school systemshave been reproduced in many other countries, where massgeneral education links closely with democracy (Cubberley1920).

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