EDUCATIONAL STANDARDS IN PRIVATE AND PUBLIC...

EDUCATIONAL STANDARDS IN PRIVATE AND PUBLICSCHOOLS*

Giorgio Brunello and Lorenzo Rocco

When school quality increases with the educational standard set by schools, education before collegeneed not be a hierarchy with private schools offering better quality than public schools. In ourmodel, private schools can offer a lower educational standard at a positive price because they attractstudents with a relatively high cost of effort, who would find the high standards of public schoolsexcessively demanding. We estimate the key parameters of the model and show that majority votingsupports a system where private schools have higher quality in the US and public schools have higherquality in Italy.

Do private schools always provide better service than public schools? The answer isapparently straightforward: since private schools charge a positive price (tuition), theycan only attract students by providing better service than public schools, which arefunded by the taxpayer (see De Fraja, 2004). Yet quality is not the only service thatprivate schools can provide. In a recent scandal, Italian prosecutors have found thatsome private schools in the country used to sell high school diplomas at a price. The socalled �Diploma no problem� organisation provided �good service� to its customers:answers were supplied in advance for written and oral exams, and attendance recordswere fixed. The national examination for the leaving high school certificate was alsoby-passed by having customers take the examinations in places where the outcome wasassured (The Economist, June 12th, 2004, p. 31).

In this admittedly extreme example, private schools can charge a fee by allowingcustomers to obtain the degree with little effort: the service offered is not quality butleisure. Less extreme is the evidence discussed by Bertola and Checchi (2002) who findthat Italian public high schools are associated on average with better performance,followed by religious private schools and lay private schools. They interpret this asevidence that private schools in Italy appear to focus more on the recovery of lessbrilliant students than on across the board high quality education. Italy is not anisolated case. Vandenberghe and Robin (2004) look at the results of standardised testsin mathematics, reading and science reported in the 2000 OECD Program for Inter-national Student Assessment survey and find that public schools can outperform pri-vate schools in France and Austria. De Fraja (2004) reports evidence on the UK byMarks and coauthors, who find that there is considerable variation in the quality of UKreligious – and private – schools: some are very good but others are very poor.1

* We are grateful to the Editor in charge and three anonymous referees, to Sebastiano Bavetta, FrancescaGambarotto, Maria De Paola, David Figlio, Hideshi Itoh, Luciano Greco, Eric Hanushek, Antonio Nicolo,Anna Sanz de Galdeano and to the audiences in Padova, Siena, Udine, Uppsala and Tokyo (Hitotsubashi) forcomments and suggestions. This article was completed while the first author was visiting CIRJE at TokyoUniversity, which provided excellent hospitality. The usual disclaimer applies.

1 He also quotes evidence by Feinstein and Symons (1999), who find that attendance at private schoolsdoes not on average affect individual performance in the UK. Hanushek (2002), argues that �..it seems naturalto believe that Catholic schools also exhibit wide variation in performance, although none of the existinganalyses document either the magnitude or the potential causes of such differences� (p. 74).

The Economic Journal, 118 (November), 1866–1887. � The Author(s). Journal compilation � Royal Economic Society 2008.

Published by Blackwell Publishing, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main Street, Malden, MA 02148, USA.

[ 1866 ]

Across the Atlantic, several studies have investigated the relative effectiveness andquality of private and public schools, with mixed results. On the one hand, Evans andSchwab (1995) and Neal (1997) find evidence that private Catholic schools increasestudent achievement with respect to public schools, especially for minorities. On theother hand, Figlio and Stone (1999) assess the effect of religious and non-religiousUS private schools on educational outcomes and find that, in general, only theformer increase individual outputs relative to public schools. In a review of thisempirical literature, McEwan (2000) concludes that private Catholic secondaryschools in the US have consistent effects in improving college attendance and highschool graduation but almost no effect on individual achievement in standardisedtests. Broadly, this evidence suggests that private schools are heterogeneous, withsome offering poorer academic quality and some others offering better quality thanpublic schools. Why do households pay to send their offspring to schools of loweracademic quality? Figlio and Stone (1999) argue that parents who enrol theiroffspring in private schools may care about other outcomes, such as discipline,extracurricular activities, religious matters and the opportunity to interact with acertain peer group.

In spite of the evidence, the theoretical literature – to our knowledge – does notentertain the possibility that private schools can be of lower academic quality thanpublic schools. Recent exceptions are Oliveira (2006) and McMillan (2004). Oliveirastudies a market with two universities, which compete for students by setting admissionstandards. McMillan has a model where rent-seeking public schools find it optimal toreduce productivity when a voucher is introduced.

An important paper in this area is Epple and Romano (1998) who model the edu-cation market as a stratified hierarchy of school qualities, with private schools doingsystematically better than public schools. Schools in their model are clubs of studentswho differ in their academic ability, and school quality is simply the average quality ofenrolled pupils. The essential reason for the existence of a hierarchy with publicschools dominated by private institutions is that the latter must be of higher peerquality than the former, otherwise no student would be willing to pay to attend a privateschool. In their model, state schools act as residual repositories, taking in all thosestudents who do not enrol in private schools.

In this article we question the assumptions that private schools offer only qualityfor a price and that public schools act as residual repositories. First, private schoolscan charge a positive price for leisure, access to networks or for religious education.2

Second, the view that public schools are of the poorest quality is both not alwaysconsistent with the stylised facts and not grounded in a policy decision rule, be it themaximisation of a social welfare function or a political equilibrium based on majorityvoting.

Until recently, the literature on school quality has been dominated by the educationproduction function approach, with its emphasis on school resources. This importantapproach has not yet produced a consensus on the importance of resources for schoolquality; see Hanushek (2002) for a review. Following recent research, we believe that akey factor affecting school quality not explored enough by the literature is the set of

2 Cohen Zada and Justman (2001) study the role of religion in private education.

� The Author(s). Journal compilation � Royal Economic Society 2008

[ N O V E M B E R 2008] 1867E D U C A T I O N A L S T A N D A R D S

incentives facing students.3 Student time, ability and effort are important inputs ineducation, which can be affected by adequate incentives, including educational stan-dards (Costrell, 1994). When a school increases its standard it raises its quality for tworeasons: first, most students respond by working harder and learning more. Second,since the cost of effort declines with ability, higher standards attract better students.

As in Costrell (1994), we define the educational standard as the productivity levelneeded to graduate. The higher the level, the higher the standard. Depending on thecountry, the selected standard is enforced by a combination of curriculum choice, testsand grading standards.4 In this article, we treat educational standards as incentiveswhich affect the quality of public and private schools because they promote individualeffort and the self-selection of students by ability.

We consider a simplified market for education with only a public and a private schooland a sequential structure. In the first stage of the sequential game, the governmentdecides the educational standard of the public school, which charges no admission fees.The decision criterion used by the government is majority voting. We believe that this isan appealing and intuitive criterion for the US system of primary and secondary edu-cation (see Fernandez and Rogerson, 1995), where individuals vote on the level ofeducation provision in their district and on the associated local property taxation. We areaware, however, that there are other possible decision rules, such as welfare maximisa-tion (De Fraja, 2002). Therefore, in the article we also compare the outcome of majorityvoting with the choice by a social planner who maximises a utilitarian welfare function.

In the second stage, a private school enters the market and chooses both the positivetuition fee and its own educational standard, which could be above or below thestandard set by the public school. The private school maximises profits by taking intoaccount that its choice of price and standard affects the demand for its services. Profitmaximisation is an assumption used in most of this literature, see for instance Stiglitz(1974) and Epple and Romano (1998). By restricting entry to a single private school,we focus on the relative quality of public and private schools at the cost of overlookingthe heterogeneity of private schools. We feel that the treatment of this heterogeneity isimportant but would require a separate paper.

An equilibrium in this economy is the combination of the public and private schooleducational standards and the non-negative tuition fee set by the private school, whichsatisfy both majority voting and profit maximisation. We show that there are two pos-sible equilibria:

(a) the private school sets a higher educational standard than the public school;(b) the private school sets a lower educational standard than the public school.

3 See for instance Betts (1997, 1998), Brunello and Ishikawa (1999), Figlio and Lucas (2004) and De Frajaand Landeras (2006). Betts argues that �...the education production function, which has dominated theschool quality literature for the past 25 years, treats students and school resources as symmetric inputs in aneoclassical production function. It thus neglects the fact that the most important ‘‘inputs’’ – students – arebetter characterized as economic agents with their own objectives..� (1997, p. 2).

4 Bishop (1995, 1997), attributes the relatively poor performance of American high school students ininternational tests to the fact that US high schools tend on average not to reward effort and learning as muchas Japanese and European schools do. Moreover, assessment in the US is not measured as elsewhere againstan absolute, external standard, which makes it difficult to convey valuable information on individual ability tothe labour market. Betts (1998) argues in favour of higher educational standards as a key element in highschool reform in the US.

1868 [ N O V E M B E RT H E E C O N O M I C J O U R N A L


While case (a) is consistent with Epple and Romano’s story, case (b) is not as itproduces a hierarchy with private schools providing lower quality than public schools.We estimate the key parameters of the model by using empirical evidence from the USand Italy and find that majority voting selects �low quality public school – high qualityprivate school� in the former country and �low quality private school – high qualitypublic school� in the latter country. Interestingly, the choice made by majority votingturns out to be the same taken by a social planner who maximises the welfare of all thehouseholds in the economy. We interpret the difference in standards between publicand private schools in these two countries as two different equilibria in our model ofeducational standards.

Our results have interesting policy implications. A lot of the policy debate and a non-negligible amount of policy practice, such as school vouchers, is based on theassumption that private schools are better from an educational viewpoint. If insteadprivate schools turn out to be better because they provide some other non-educationalservice, then a substantial part of policy justification for vouchers falls by the wayside.

The article is organised as follows. Section 1 introduces the model. Section 2 con-siders both the outcome of majority voting and the one produced by a utilitarian socialplanner. An application to the US and Italy is discussed in Section 3. Conclusionsfollow.

1. The Model

We consider a sequential Hotelling-type model where education before college isprovided by a public and a private school. The timing of the model is as follows: first,the government decides the educational standard of the public school sG 2 [1,2];second, a private school decides entry, tuition p and its educational standard sP 2 [1,2];third, a continuum of households, with unitary mass, enrol their offspring in one ofthe available schools, after observing the educational standard of each school and thetuition price set by the private school.

Learning the more sophisticated mathematics and science implied by a higherstandard requires both higher effort by students and adequate facilities such as labor-atories and libraries. Notice that higher standards are not synonymous with moreschool resources: while the former require better facilities, the latter without appro-priate incentives can fail to improve school quality.5 Let k 2 [0,1] be the unit cost ofsetting the standard, independently of whether the school is public or private.6 Anincrease in the standard requires higher total costs. The costs borne by the publicschool, ksG, are funded by a proportional tax s paid by all households, independently ofwhether they send their offspring to the public school or not. The private school fundsits costs by setting a tuition fee p.

Attaining the standard requires that students spend individual effort. Since effort iscostly, students either spend the minimum level needed to attain the standard or makeno effort at all (Costrell, 1994). The individual cost of effort depends on innate ability.

5 See Minter Hoxby (1996) for a similar point in the context of teachers� unions.6 We intend to show that schools can end up with different standards even in the presence of a common

technology. Needless to say, this differentiation is further emphasised if we introduce heterogeneous unitcosts.

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Since individuals differ in innate ability, not all the pupils in this economy attain thestandard and complete secondary school.

The private school decides whether to enter in the market for education and choosesthe standard sP and the price p to maximise (expected) profits. Its profit function is

p ¼ pD � ksP ð1Þ

where D is expected demand, which results from the aggregation of individualenrolment choices. Once the educational standard has been set, the marginal costs ofsupplying school services are assumed to be zero.7

An equilibrium

fsG ; ½sP ðsG Þ; pðsG Þ�;DðsG ; sP ; pÞg

is such that:

(i) D(sG, sP, p) is the demand function obtained by aggregating individual optimalchoices, given sG, sP, p;

(ii) [sP(sG), p(sG)] is the vector of optimal responses to sG by the private school,which takes into account the function D(sG, sP, p);

(iii) sG is determined by majority voting involving all households, given the functions[sP(sG), p(sG)] and D(sG, sP, p). Alternatively, (iii) can be replaced by

(iii0) sG is determined by the government to maximise welfare, given the functions[sP(sG), p(sG)] and D(sG, sP, p).

The sequential structure of the model implies that we can characterise the equilib-rium by using backward induction. We start with the last stage of the game, theenrolment decision of households, which in turn determines the demand for theservices of the public and private school.

1.1. Household Choice

Following De Fraja (2002) each household in this economy consists of a mother and adaughter. Let y be the log endowed income of the mother and w the log earnings of thedaughter. We exclude liquidity constraints by assuming that each household can freelyborrow against the future income of the daughter w.

This assumption simplifies the algebra drastically and is not wholly unrealistic.Carneiro and Heckman (2002) find that between 4% and 8% of children in the USare constrained in their college investment decisions. Given that public providers aremuch more important before college than at college, this percentage is likely to besignificantly lower for decisions concerning primary and secondary education.8

We discuss the consequences for our model of introducing liquidity constraints inSection 3.

The discount factor is equal to 1. Daughters and households are heterogeneous andthese differences are described by the pair (h,y), where h is the log of the reciprocal ofthe daughter’s ability – or minus log ability – lower for higher ability. We assume that h

7 Positive marginal costs complicate the algebra without providing further insights.8 See also Cameron and Taber (2004).



and y are jointly normally distributed, with marginal distributions h � N(0, r2) andy � N(ly,w

2). Therefore, both ability A and income Y are log-normally distributed. Forfuture use, we define l as the mean of Y. In the real world, students can drop out ofschool and fail to graduate.9 In the simplified economy described in this article,daughters either enrol in school and attain the standard or do not enrol at all, which isequivalent to spending zero effort.

We posit that household utility U is

U ¼ y � s� p þ wðe; s; h; yÞ � hse ð2Þ

where log Y(1 � s) � y � s, s ¼ sG, sP, e is a dummy equal to one in the event ofenrolment and school completion10 and to zero otherwise, p is the tuition fee – zero inthe public school and positive in the private school – and hs is the effort cost ofattaining the educational standard s: the higher the standard, the higher the effortrequired to attain it, but the effort cost is lower for higher innate log ability.11 Whenthe daughter fails to enrol, her cost of effort is zero and her reservation utility is UR ¼y � s � p þ w(0, s, h, y).

The assumption that household utility is concave in income and earnings but linearin the tuition fee and in the cost of effort is in line with the existing literature in thearea – see De Fraja (2002)12 – and greatly simplifies the algebra, making the modeltractable. The linearity of utility with respect to the tuition fee implies that the enrol-ment decision – conditional on the educational standards and the tuition price –depends exclusively on individual ability and is independent of endowed log income y,consistent with our assumption of no liquidity constraints.

A key finding of the empirical labour economics literature since Mincer – see forinstance Murnane et al. (1995), Bowles et al. (2001) and Hanushek and Kimko (2000),Dearden et al. (2002) – is that earnings are a log-linear function of individualcharacteristics, including school quantity and quality. Drawing from this literature, wespecify the daughter’s earnings as

wðe; s; h; yÞ ¼ k0 þ k1sð Þe þ k2hþ k3y þ k4X ð3Þ

where the constant term k0 2 [0,1] captures the gains associated to the attained schooldegree, k1 2 [0,1] is the labour market return to the educational standard s, k2 and k3

are the returns to log individual ability and log family income and X is a vector ofresidual individual characteristics. The empirical earnings function (3) suggests thatthe labour market recognises both the quantity and the quality of education – theformer corresponding to the school degree and the latter to the educational standard.Individuals who fail to enrol in school lose k0 þ k1s in terms of expected log earningsbut save the effort costs of attaining the standard s.

9 The dropout rate of young Americans – aged 16 to 24 – from high school was 10.9% in 2000.10 Secondary school completion is a ticket for college education. While we do not directly consider college

education, we do so indirectly, because graduation from high quality primary and secondary schools isexpected to increase enrolment in a high quality college.

11 Linear costs of effort when s 2 [1,2] generate corner solutions for the educational standard. Since weare mainly interested in the relative standard of the private and public school, this is a convenient simplifi-cation.

12 In De Fraja the household utility function is concave in the mother’s consumption and linear in thedaughter’s income.



Conditional on enrolment, households choose either the private or the publicschool, depending on the tuition fee, individual abilities and educational standards.There are two regimes – sP > sG and sG > sP. Since household preferences can vary withthe relative ranking of educational standards, we must consider each regime in turn.

1.1.1. Regime 1: sP > sG

The choice of the private school occurs when UPi � UGi – where the subscripts P and Grefer to the private and public school respectively – and UPi P URi. Using (2) and (3)these conditions can be written as

hOk1 �p

sP � sG; h � k1 þ

k0 � p

sP: ð4Þ

Since sP > sG, the second condition is redundant, because all the households whichprefer the private to the public school also prefer the public school to dropping out.Hence, the demand for private education is

DH ¼ Uk1 �

p

sP � sG

r

0B@

1CA ð5Þ

where U is the standard normal distribution. More able students – with lower h – have lowercosts of effort and enrol in the private school, where the educational standard is higher.A second order Taylor expansion of (5) around U(0) yields

Uk1 �

p

sP � sG

r

0B@

1CA ¼ Uð0Þ þ uð0Þ

rk1 �

p

sP � sG

� �ð6Þ

where u is the normal density. Since the normal distribution is symmetric around themean, u0(0) ¼ 0 and the second order term vanishes. Moreover, Uð0Þ ¼ 1=2.

1.1.2. Regime 2: sP < sG

If sP < sG, the private school is selected if

h � k1 þp

sG � sP; h � k1 þ

k0 � p

sPð7Þ

and the demand for private education is

DL ¼ Uk1 þ

k0 � p

sP

r

0BB@

1CCA� U

k1 þp

sG � sP

r

0B@

1CA: ð8Þ

Using a second order Taylor expansion, we can re-write DL as

DL ¼uð0Þ

rk0 � p

sP� p

sG � sP

� �: ð9Þ

This demand is non-negative if

p < k0sG � sP

sG: ð10Þ



Therefore, the higher the (percentage) difference in the educational standard be-tween the public and the private school the higher the tuition fee that the privateschool can set and still attract a positive demand for its services. Conditions (4) and (7)show that the private school has no incentive to set the standard at the same level of thepublic standard, because with a positive price it would attract no student.

1.2. The Private School

Since the distribution of pupils between schools depends on whether the privateschool selects a standard higher or lower than sG, we need to distinguish twoseparate cases, sP > sG and sP < sG . Consider first the case where sP > sG and let theprofits of the private school be pH ¼ pDH � ksP. For a given sG, profit maximisationwith respect to p yields

p ¼ ðsP � sGÞr

4uð0Þ þk1

2

� �ð11Þ

which implies that the demand for private school services (5) is positive for anyeducational standard sP > sG. The optimal price increases in the standard sP anddecreases in the standard set by the public school. Using (11) in the first ordercondition for the optimal standard yields

@pH

@sP¼ uð0Þ

rr

4uð0Þ þk1

2

� �2

�k:

Since the right-hand side of this expression is independent of sP, the optimal standard

is a corner solution, and the regime sP > sG requires k <uð0Þ

rr

4uð0Þ þk1

2

� �2

. When

this condition is verified, the optimal educational standard is sP ¼ 2. Upon substitution,optimal profits are13

pH ¼ð2� sG Þ16uð0Þr rþ 2uð0Þk1½ �2�2k: ð12Þ

Next, consider the case sP < sG and let the profits of the private school be pL ¼ pDL �ksP. Profit maximisation yields

p ¼ k0ðsG � sP Þ2s

G

ð13Þ

and

@pL

@sP¼ �p

uð0Þr

k0 � p

s2P

þ p

ðsG � sP Þ2

" #� k < 0

13 A detailed description of the relationship between profits and the educational standard of the publicschool can be found in the discussion paper version of this article. See Brunello and Rocco (2005).



sincek0 � p

s2P

þ p

ðsG � sP Þ2

" #> 0. Therefore the optimal standard is sP ¼ 1. The

optimal profits of the private school in this regime are

pL ¼k2

0uð0ÞðsG � 1Þ4rsG

� k: ð14Þ

1.2.1. The choice of the standard above or below sG

We now determine how the private school chooses between regime sP < sG and regimesP > sG. Noticing that, at the optimal pricing policy, the profit functions (profit up) and(profit down) depend on the standard set by the government for public schools, sG, weestablish the following Proposition:

Proposition 1. Assume that k � K. Then there exists a unique value s�G such that theprivate school optimally chooses sP ¼ 1 for any sG > s�G and sP ¼ 2 for any sG < s�G. In eithercase the school makes positive profits.14

Proof. See Appendix

The Proposition characterises the private school’s best reply function and shows that, ifthe private school enters in the education market, it chooses either a higher or a lowereducational standard than the public school. If it chooses a higher standard, it sets it to themaximum feasible value. If it chooses a lower standard, it sets it to the minimum feasiblevalue.15 In spite of the fact that households always pay positive tuition fees for privateeducation, only the former case corresponds to the hierarchical model of Epple andRomano (1998) where the public school is of lower quality than the private school.

The choice of the standard by the private school depends crucially on the standardselected by the public school. Independently of the selected regime, private tuition is afunction of the difference between the public and the private standard. Suppose thatthe government sets a low standard for the public school. In this case, the privateschool can charge a high price by choosing a high educational standard. As the stan-dard in the public school increases, however, the relative benefit that the private schoolhas from setting a high standard declines, and after a given threshold – s�G – the privateschool finds it more profitable to switch to a low standard. By so doing, it can increasesboth tuition and profits.16

The type of equilibrium which prevails depends critically on government choice. Thegovernment chooses the educational standard of the public school by taking intoaccount the subsequent entry by the private school. We turn to this decision in the nextsection of the article.

14 In Brunello and Rocco (2005) we relax the condition k � K and show that the private school can refrainfrom entry for some values of sG.

15 The choice of the extreme values is dictated by the assumption that the costs of attaining the standard inthe individual utility function are linear in the standard.

16 At the optimal price and private standard, the demand for private schools is a constant, and so is thetotal cost of setting the standard. Therefore, profits vary only with private tuition p.



2. The Choice of the Standard for the Public School

We assume that the public sector budget, which consists only of educational expen-ditures and income taxes, is always balanced. This is equivalent to requiringZ

sY dF ðY Þ ¼ sl ¼ ksG ð15Þ

where F(Y) is the log-normal cumulative distribution of Y, which yields, uponintegration

s ¼ ksG

l: ð16Þ

Therefore, a higher educational standard increases the proportional tax rate paid by allthe households in this economy.

We posit that the choice of the public school standard sG is based on majority voting –as in Stiglitz (1974) and Fernandez and Rogerson (1995) – and describe the outcomeof the voting as follows: first, we select the value of sG preferred by the majority ofhouseholds in each of the two regimes – the private school with lower and higherstandard than the public school. Second, we compare preferred outcomes across re-gimes and choose the one favoured by the majority of voters. Last, we contrast theoutcome of majority voting with the one produced by a social planner who maximises autilitarian social welfare function.

2.1. Regime 1: High Quality Public School (sG � s�G Þ

In the regime sG � s�G the private school chooses sP ¼ 1 and p ¼ k0ðsG � 1Þ=2sG . Weask how utilities UPi and UGi vary with the public standard sG. It turns out that

@UPi

@sG¼ � k

l� k0

2s2G

< 0

for students enrolled in the private school. Since this derivative is negative, householdswith students in private schools unambiguously prefer the lowest value of sG in theregime, s�G . On the other hand

@UGi

@sG

> 0 if hi < k1 �k

l

< 0 if hi > k1 �k

l

8><>:

for students enrolled in the public school. More able students, for whom the derivativeis positive, profit from a higher public standard because of their relatively low cost ofeffort and vote for sG ¼ 2; less able individuals, for whom the derivative is negative,gain from a lower standard, and vote for sG ¼ s�G . The marginal student with abilityhi ¼ k1 � k/l is indifferent to the level of the standard but we assume hereafter thatshe votes with the group having hi < k1 � k/l. We establish the following

Lemma 1. If the group of individuals with hi � k1 � k/l is the majority, it chooses sG ¼ 2.If the group with hi > k1 � k/l is the majority, it chooses sG ¼ s�G.



Proof. See the Appendix

2.2. Regime 2: Low Quality Public School (sG � s�G Þ

In the regime sG � s�G , the private school selects sP ¼ 2 and p ¼ r4uð0Þ þ

k1

2

� �ð2 � sG Þ.

Thus, we get

@UPi

@sG¼ � k

lþ r

4uð0Þ þk1

2

� �

for individuals enrolled in the private school, and

@UGi

@sG

> 0 if hi < k1 � k=l ! sG ¼ s�G< 0 if hi > k1 � k=l ! sG ¼ 1

�

for individuals in the public school. Again, the marginal individual is indifferent to thestandard.

Lemma 2. If k � K, thenkl<

r4uð0Þ þ

k1

2

� �.


This Lemma implies that @UPi/@sG is always positive if Proposition 1 holds, as weassume. Then, sG ¼ s�G , because the cost of setting up a higher standard in the publicschool – relative to average income – is lower than the expected return. We have

Lemma 3. If the group of individuals with hi � k1 � k/l is the majority, it choosessG ¼ s�G. If the group with hi > k1 � k/l is the majority, it chooses sG ¼ 1.


2.3. The Choice Between Regimes

We use the results in the previous sub-sections to compare regimes and establish thefollowing

Proposition 2. If the group with hi � k1 � k/l is the majority, it chooses the regime sG �s�G and sG ¼ 2. If the majority is with the group h > k1 � k/l, it votes for sG � s�G and sG ¼ 1.


We conclude that the group with hi � k1 � k/l is the majority when

Uk1 � k=l

r

� �>

1

2ð17Þ

i.e. when the size of the group is larger than 50%. This is equivalent to the followingcondition



k1 �k

l> 0

which is satisfied when the difference between the marginal benefit of the educationalstandard, k1, and the marginal cost, k, – relative to average household income – ishigher than 0.

Notice that the majority voting condition must be consistent with the conditionk � K required for Proposition 1 to hold. When k1 � k/l > 0 we need to check thatk < min(lk1, K). Similarly, when k1 � k/l < 0 we must verify that lk1 < k�K,otherwise the voted equilibrium where the public school offers a lower standard thanthe private school cannot exist.

In other words, Proposition 2 tells us that, when the benefit of increasing thestandard is relatively high, not only the very able but also the households withdaughters of intermediate ability can profit enough from the higher standard tocompensate for the cost of attaining it. Therefore the outcome of the vote is sG ¼ 2.If the benefit declines, however, fewer voters will find it sufficient to compensate theeffort required by a high standard, and eventually the majority will shift to sG ¼ 1.

2.4. The Social Planner

In the �political economy� approach, households vote on the quality of educationprovision – measured by the educational standard – and take into account that a higherpublic quality needs to be financed with higher income taxes. In this sub-section webriefly characterise the market for education when the government acts as a socialplanner and contrast the results with the findings obtained using the �political equi-librium� approach. We assume that the welfare function used by the government isutilitarian and consists of the simple aggregation of the utilities of all the households inthe economy. Moreover, we limit our attention to the case where the private schoolexists in either regime. It turns out that the social welfare function is always convex insG.17 Therefore, the social optimum is a corner solution in both regimes. In the nextSection, we apply the model to Italy and the US and compare the outcomes of majorityvoting and of social welfare maximisation in these two countries.

3. An Application to Italy and the US

We apply the model to Italy and the US. The earnings function (3) postulates thatindividual earnings increase both in the quantity of education and in the level of theeducational standard. Following Card (1999) and Brunello (2002) the monetary returnto a year of secondary education is estimated to be equal to 11% for the US and to 8.8%for Italy.

While there is substantial evidence on the labour market effects of years ofeducation, much less is known on the effects of a higher educational standard. In theonly empirical study for the US we are aware of, Betts and Grogger (2000) estimate theeffects of a higher grading standard on the earnings of young workers using the High

17 Further details are available in Brunello and Rocco (2005).



School and Beyond survey. According to their definition, a school’s grading standard isa measure of how stringently it grades its students. They find that a 1% increase in thegrading standard increases earnings by 0.0147,18 a small effect. In order to obtain fromthis an estimate of k1, we assume that the estimated elasticity from Betts and Grogger isequal to the elasticity associated to the standard s, which varies between 1 and 2, andobtain @w/@s ¼ 0.0147/s, which we evaluate at the average s ¼ 1.5. We get k1 ¼ 0.0098.

Compared to the US, Italian high schools are organised into an academic (licei classiciand licei scientifici) and a vocational track. The latter track can be further divided intovocational schools (istituti professionali) and technical schools (istituti tecnici), with theformer having lower educational standards than the latter. While vocational schoolscan last from 3 to 5 years, technical schools and the schools in the academic trackusually last 5 years.

The following evidence supports our view that the academic track in Italy has highereducational standards than the vocational track. First, students enrolled in the aca-demic track exert higher effort. Based on the data collected by the Programme forInternational Student Assessment survey (OECD, 2004a), the average number of hoursper week spent doing homework is 13 in the academic track and 7 in the vocationaltrack. Second, the former track attracts the best performing students from lower sec-ondary education. According to the Italian Survey on the School and Work Experienceof 1998 High School Graduates (IHSG), close to 33% of the students enrolled in theacademic track completed their lower secondary education with high marks, comparedto only 13% in the vocational track.19 Third, the average standardised test score inmathematics, reading and problem solving of students aged 15 – who have just startedtheir academic or technical track – is significantly higher in the former (average score:542) than in the latter (average score: 477).20 Last but perhaps most important, whenwe use IHSG data and regress individual graduation marks at the end of high school onage, gender, parental background dummies, the marks attained in junior high schooland a dummy equal to 1 if the student has graduated from the academic track and to 0if she has graduated from the vocational track, we find that the latter dummy attracts anegative and statistically significant coefficient, pointing to a higher standard in theacademic track.21

We use data from the National Survey on the Income and Wealth of ItalianHouseholds (SHIW), carried out by the Bank of Italy on a bi-annual basis, whichinclude information on earnings and school curriculum for a nationally representativesample of Italians, and restrict our attention to the sub-sample of individuals agedbetween 20 and 30, who have attained at most a 5-years high school diploma. The agerestriction is motivated by comparability, as Betts and Grogger focus on entry-levelwages.

18 This elasticity is computed by multiplying the estimated coefficient reported in the first column of theirTable 4 (0.0053) by the sample mean value of the grading standard, 2.78.

19 This difference is broadly confirmed by Gasperoni (1996) who uses a different survey of high schoolstudents.

20 Source: Programme for International Student Assessment (PISA), OECD (2004a).21 We estimate that – conditional on the controls listed in the text – the average graduation mark in the

academic track (which include licei classici and licei scientifici) is 4.85% lower than in the vocational track(which includes istituti tecnici e professionali). Details are available from the authors upon request.



We generate a discrete indicator of educational standards, equal to 1 if the individualgraduated from a vocational school, to 2 if she graduated from a technical school andto 3 for graduation from the academic track, and specify an empirical earnings func-tion which is as close as possible to the one used by Betts and Grogger for the US. Afterpooling the data for the period 1995 to 2004, we estimate that the elasticity of earningsto the selected measure of educational standards is 0.072.22

We also use an alternative dataset, the Italian survey on the School and WorkExperience of 1998 High School Graduates, carried out by the national statistical officein 2001, three years after graduation. Compared to the SHIW data, these data have theadvantage of also including the high school graduates who are attending college, as inBetts and Grogger, and the disadvantage that they do not distinguish between 3-yearand 5-year vocational schools. We restrict our attention to individuals aged 24, closeenough to the age group considered by Betts and Grogger (25 to 27). It turns out thatthe estimated elasticity of earnings to the educational standard is 0.055, smaller thanthe value obtained from the SHIW data but still substantially higher than the elasticityfound in the US data.23

We prudentially choose the smaller estimate and assume, as for the US, that theestimated elasticity is equal to the elasticity associated with the standard si. This impliesthat for Italy k1 ¼ 0.0371, about four times as large as the US estimates. The substan-tially lower return to the educational standard experienced by the US is in line withBishop’s analysis of US high schools. Bishop (1995) points out that not only is studenteffort poorly rewarded at school but it is also poorly signalled to the external labourmarket, because of the limited use of external statewide achievement examinations,which are more common in Europe and available in Italy. As a consequence, the USlabour market �. . .fails to reward effort and achievement in high school� (p. 18).

Next, we estimate the variance of the distribution of log ability. We use as a measureof ability the scores obtained by more than 5 thousand high school American studentsand more than 10 thousand Italian students in the mathematics, reading, science andproblem solving tests reported by the OECD 2003 PISA Study (OECD, 2004a). Aftertaking a simple average of these scores for each individual, we compute the coefficientof variation associated to the empirical distribution, which is 0.1847 for the US and0.1677 for Italy. Since ability in our model is lognormally distributed, we imposeequality between the coefficient of variation and the empirical measure. Therefore, wehave

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffier2ðer2 � 1Þ

p=e

12r

2 ¼ 0:1847 for the US, which yields r ¼ 0.183, andffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffier2ðer2 � 1Þ

p=e

12r

2 ¼ 0:1689 for Italy, which yields r ¼ 0.168.We notice that the number of public schools in the real world is much higher than 1.

If M is the number of public schools, the budget constraint should be written morerealistically as Mk/l ¼ s/sG, which corresponds to (16) when l is opportunelyredefined as l/M. The cost of setting the standard should include the educational

22 The estimated coefficient associated with the indicator of educational standards is 0.037 (standard error:0.018) The elasticity reported in the text is obtained by multiplying this coefficient by 1.93, the sampleaverage value of the standard in this dataset. The detailed estimates are available from the authors uponrequest.

23 The estimated coefficient associated with the indicator of educational standards is 0.038 (standard error:0.012). The elasticity reported in the text is obtained by multiplying this coefficient by 1.44, the sampleaverage value of the standard in this dataset. The detailed estimates are available from the authors uponrequest.



expenditures for teachers, laboratories, libraries and other facilities, because more orbetter teachers and facilities are required to enforce a higher standard. These con-siderations suggest that a reasonable measure of s is the share of public educationalexpenditure for primary and secondary education on GDP. According to the OECD(2004b) this share in 2000 was equal to 3.5% for the US and to 3.2% for Italy.We provide an appropriate scale to these numbers by dividing them by the averagestandard sG ¼ 1.5 and obtain estimates of s/sG of 0.023 for the US and 0.021 for Italy.

Average income l in 2000 converted in international dollars using PPP was equal to$34,360 in the US and $20,170 in Italy (source: The World Bank). The number ofpublic schools in the US in the same year was 93,273, compared with 28,133 for Italy.24

Furthermore, we assume that the variance of log income is as estimated by Baudourianet al. (2002) and equal to 0.961 for the US and to 0.67 for Italy. Finally, we set thecorrelation between ability and income q ¼ 0.018, using the estimates of the rela-tionship between test scores and parental income contained in Blau (1999).25 Byapplying the formulas for the mean of a lognormal distribution, we obtain ly ¼ 9.964for the US and ly ¼ 9.577 for Italy.

Replacing the calibrated parameters in condition (17), we obtain

U0:0098� 0:023

0:183

� �¼ 0:47 <

1

2

for the US and

U0:0371� 0:021

0:168

� �¼ 0:54 >

1

2

for Italy.Moreover, we can check that k ¼ (s/sG)(l/M) is equal to 0.0086 in the US and to

0.0153 in Italy. The former verifies (l/M)k1 < k < K, as 0.0036 < 0.0086 < 0.0117,while the latter verifies k < min[(l/M)k1,K], as 0.0153 < min[0.0266, 0.0154].26

Therefore, each voting majority is consistent with the condition required forProposition 1 to hold.

Since the returns to a higher standard are low relative to its costs, our calibration ofthe US public education system suggests that the majority of voters in that countryshould favour a low standard in public schools and a high standard in private schools,consistent with the ordering of schools by quality suggested by Epple and Romano(1998). The opposite occurs in Italy, where the returns to a higher standard dominatethe costs. In that country, the majority votes in favour of an equilibrium where publicschools are of higher quality than private schools.

We conclude that these two countries represent two different equilibria of ourmodel of educational standards. We hasten to stress, however, that the size of thesemajorities is likely to be sensitive to measurement errors in the calibration of the keyparameters. Given the paucity of empirical evidence, especially for the US, we believe

24 Sources: US data from the National Center of Educational Statistics. Italian data refer to 2003 and arefrom the Italian Ministry of Education.

25 Given the lack of similar estimates for Italy, we assume that q is the same across the two countries.26 A parallel condition is a fortiori verified for Italy when k1 ¼ 0.0481.



that additional empirical work in the area is needed before reaching more solidconclusions.

Based on our numerical solutions, students with lower ability in the US either dropout or enrol in the public school. Since they have a relatively high cost of effort andthe return to the standard is relatively low, they favour a low quality public school. Theupper part of the ability distribution instead enrols in the private school, where theeducational standard is much higher. Therefore, we reproduce the stratification byability emphasised by Epple and Romano (1998) in their stylised model of theAmerican schooling system. Rather than assuming, as they do, that public schools actas residual repositories, we obtain the relatively low quality of public schools as theoutcome of a voting equilibrium, while allowing private schools to be, in principle, oflower quality than public schools.

Is this equilibrium altered by the presence of liquidity constraints? If these con-straints are effective, they must reduce enrolment in the private school in favour of thepublic school. Since the utility derived from the public school is increasing in thestandard for individuals with high ability, these individuals should vote for a highpublic school standard – exactly as before, given that @UPi/@sG > 0 in the regimesG � s�G . With no change in the majority, the lowest public school standard still pre-vails.

In the Italian equilibrium, the students with lower ability enrol in private schools andfavour a low standard there. Since individuals with intermediate or higher ability enrolin public schools, there is natural pressure for a higher standard in these schools.Again, liquidity-constrained individuals who could not enrol in private schools will endup in public schools. These individuals will vote for a low public school standard,independently of whether they go to a private or a public school. However, since themajority remains in favour of a high public school standard, the voting equilibrium isunaltered.

Finally, we compare the values of the calibrated social welfare function across thetwo regimes. Consider first the US. The local maximum is when sG ¼ 2 in theregime sG � s�G and when sG ¼ 1 in the regime sG � s�G . By comparing localmaxima, we find that the former is higher. Therefore, sG ¼ 1 is the educationalstandard which attains the global maximum. Next we look at Italy. By comparinglocal maxima, we find that sG ¼ 2 is the educational standard which yields thehighest welfare. We conclude that – given the assigned values to the parameters –the choice of the public school standard by majority voting is consistent in bothcountries with welfare maximisation.

4. Conclusions

When school quality increases with the educational standard set by schools andattaining the standard requires costly effort, the market for education before collegeneed not be a hierarchy with private schools offering better quality than public schools.An alternative configuration, with public schools offering a higher educational stand-ard than private schools, can also exist, in spite of the fact that tuition levied by privateschools is strictly positive. In the model presented in this article, private schools canoffer a lower educational standard at a positive price because they attract students with



a relatively high cost of effort, who would find the high standards of the public schoolexcessively demanding. Clearly, costly effort is only one possible factor driving thisresult. Alternatives include the fact that private schools provide access to labour marketnetworks, which provide access to better jobs more easily because of the connectionsthey afford, or that they are �snob� goods, which are consumed because of the repu-tation they offer (Corneo and Jeanne, 1997), even if quality is lower than in the publicschool. In either case, the intuition remains the same: by offering services that are notstrictly related to quality, private schools can charge a positive price, offer lower qualitythan public schools and still make positive profits.

When the educational standard of the public school is chosen by majority voting, weshow that the choice between a configuration with high quality public schools and aconfiguration with high quality private schools depends on the marginal return to theeducational standard relative to the marginal cost of setting up the standard. Wecalibrate the model by using micro-econometric evidence from the US and Italy andfind that, based on the calibrated parameters, majority voting in the US produces asystem with high quality private schools and low quality public schools, as assumed byEpple and Romano (1998). This system is also the one chosen by a social planner whomaximises household welfare using a utilitarian welfare function. In Italy, anothermajority voting equilibrium prevails, with public schools setting higher educationalstandards that private schools. Therefore, Italy and the US can be seen as two differentequilibria of a model of educational standards.

We believe that the model discussed in this article has two important policyimplications. First, high school reforms that improve educational standards andintroduce curriculum-based external exams, as suggested by Bishop (1997) andBetts (1998), may improve the returns to educational standards in the US. If such animprovement is large enough, our model suggests that the system actually in placecould shift away from an equilibrium with low quality public schools. Second, policiessuch as school vouchers require that private schools are better from an educationalviewpoint. If these schools turn out instead to be of lower educational quality thanpublic schools, as in the Italian equilibrium, a key element of the policy justificationfor vouchers is likely to fall.

Appendix

Proof of Proposition 1

Let pH ¼ pH(sP ¼ 2,sG) and pL ¼ pL(sP ¼ 1,sG). Next note that @pH/@sG < 0 and @pL/@sG > 0.Denote D ¼ pL � pH : clearly @D/@sG > 0. Moreover, let s�G be defined in such a way that D ¼ 0 andsuppose that s�G 2 ½1; 2�. Then for sG < s�G we have that D < 0 and the preferred alternative issP ¼ 2. On the other hand, for all sG > s�G we have D > 0, and the preferred alternative is sP ¼ 1.

To guarantee entry by the private school, at least one profitable option (sP ¼ 1 or sP ¼ 2) mustbe available. A sufficient condition for this to happen is that pH valued at s�G is nonnegative, i.e.pH ðsP ¼ 2; s�G Þ � 0 : if so, then pH > 0 for all sG < s�G and pL > 0 for sG � s�G . More explicitly,replace s�G in pH to get

pH ðsP ¼ 2; s�G Þ ¼ �3

2k þ A

2þ B �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðk þ A � 2BÞ2 þ 4AB

q2

ð18Þ



where

A ¼ k20uð0Þ4r

> 0; B ¼ ðrþ 2uð0Þk1Þ2

16uð0Þr > 0 ð19Þ

and@pH ðsP ¼ 2; s�G Þ

@k¼ � 3

2� 1

2

k þ A � 2Bffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðk þ A � 2BÞ2 þ 4AB

q < 0 as j k þ A � 2Bffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðk þ A � 2BÞ2 þ 4AB

q j < 1.

Let K be the value of k such that pH ðsP ¼ 2; s�G Þ ¼ 0, i.e.

K ¼ A þ B

2�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiA2 þ B2p

2> 0: ð20Þ

Then, s�G 2 ½1; 2� whenever k � K, for any A and B. Since pH ðsP ¼ 2; s�G Þ > 0 as k < K, theprivate school enters the market and sets sP ¼ 1 if sG > s�G and sP ¼ 2 if sG < s�G .

Proof of Lemma 1

Since the reciprocal of individual log ability h is distributed in the interval [�1,1], we need toexamine in some detail how households vote in regime sG > s�G .

Individuals with hi 2 [�1,k1 þ p/(sG � sP) ¼ k1 þ k0/(2sG)] choose to enrol in thepublic school. Therefore, those with hi < k1 � k/l vote for sG ¼ 2, and those withk1 � k/l < hi < k1 þ k0/(2sG) vote for sG ¼ s�G . The marginal individual with hi ¼k1 � k/l is indifferent.

Individuals with hi 2 [k1 þ k0/(2sG),k1 þ k0/sG] prefer the private school and vote forsG ¼ s�G .

Individuals with hi 2 [k1 þ k0/sG,1] do not participate. Since their utility UR isdecreasing in sG, they vote for sG ¼ s�G .

Proof of Lemma 2

First note thatr

4uð0Þ þk1

2

� �¼

ffiffiffiffiBp ffiffiffiffiffiffiffiffiffiffi

ruð0Þ

rwhere B is defined as in the proof of Proposition 1. We

need to prove that K � l½ r4uð0Þ þ

k1

2� � 0, but we can prove a weaker condition. Replaceffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

A2 þ B2p

in the definition of K with A þ B �ffiffiffiffiffiffiffiffiffi2ABp

, a quantity strictly lower thanffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiA2 þ B2p

.Then we can write

ffiffiffiffiffiffiffiffiffi2ABp

� 2lffiffiffiffiBp ffiffiffiffiffiffiffiffiffiffi

ruð0Þ

r< 0 ð21Þ

which simplifies to

k0

ffiffiffiffiffiffiffiffiffiffiuð0Þ

p2ffiffiffirp �

ffiffiffi2p

lffiffiffiffiffiffiffiffiffiffi

ruð0Þ

r< 0! k0 <

2ffiffiffi2p

uð0Þ rl � 7rl: ð22Þ

The last inequality if verified for all k0 2 [0,1] given reasonable values of r and l (see theapplication in Section 4).

Proof of Lemma 3

In regime sG < s�G , voting occurs as follows:



Individuals with hi 2 �1; k1 � r4uð0Þ þ

k12

� �� choose the private school and vote

sG ¼ s�G given that k=l < r4uð0Þ þ

k12

� �.

Individuals with hi 2 k1 � r4uð0Þ þ

k12

� �; k1 þ k0

sG

� �choose the public school. Those with

hi < k1 � k/l vote sG ¼ s�G , and those with hi > k1 � k/l vote sG ¼ 1. Notice that given

k=l < r4uð0Þ þ

k12

� �holds, k1 � k/l lies within the range k1 � r

4uð0Þ þk12

� �; k1 þ k0

sG

� � Finally, individuals with hi 2 [k1 þ k0/sG, 1] do non participate to upper secondary

school and vote for the minimum value of sG, i.e. sG ¼ 1.

Therefore, all individuals with hi < k1 � k/l vote for sG ¼ s�G while all the others vote for sG ¼ 1.

Proof of Proposition 2

Let the group of students with hi � k1 � k/l in Figure 1 be the majority. Then, the votingoutcome is sG ¼ 2 if sG � s�G and sG ¼ s�G if sG � s�G . When sG � s�G the students belonging tothe group go to the public school; when sG � s�G , they go to the private school if

hi < k1 � r4uð0Þ þ

k12

� �and to the public school if k1 � r

4uð0Þ þk12

� �< hi < k1 � k=l.

Consider the group going to the public school in either regime and compare their utilities. Theregime sG � s�G is preferred because

UG ðsG ¼ 2Þ � UG ðsG ¼ s�G Þ ¼ 2 k1 � hi �k

l

� �� s�G k1 � hi �

k

l

� �> 0:

Next take the group going to the public school in regime sG � s�G and to the private school inthe other regime. The former regime is preferred because

regime sG > sG*

regime sG < sG* Private Public Public

Public Public Public Private No schooling

No schooling

λ1 – (σ/4ϕ + λ1/2) λ1 + λ0/sG λ1 – k/μ

λ1 + λ0/2sG λ1 + λ0(sG + 1)/2sG λ1 – k/μ

Public

If majority, the majority voting outcomes are

sG = 2 for sG > sG*sG = sG* for sG < sG*

If majority, the majority voting outcomes are sG = sG* for sG > sG* sG = 1 for sG < sG*

θ

θ

Fig. 1. Voting



UG ðsG ¼ 2Þ � UP ðsG ¼ s�G Þ ¼ ð2� s�G Þ �k

lþ r

4uð0Þ þk1

2

� �� > 0:

Therefore, when the group with hi � k1 � k/l is the majority, the regime sG � s�G and thepublic school standard sG ¼ 2 are selected.

Turning to the voting behaviour of the group with hi > k1 � k/l, suppose it is the majority.Then the voting outcome is sG ¼ s�G in the regime sG � s�G and sG ¼ 1 in the regime sG � s�G .Under the former regime (sG � s�G Þ, students go to the public school if k1 � k =l <hi < k1 þ k0=ð2s�G Þ and to the private school if k1 þ k0=ð2s�G Þ < hi < k1 þ k0ðs�G þ 1Þ=s�G .Finally, students with hi > k1 þ k0ðs�G þ 1Þ=s�G do not enrol in either school. Under the latterregime (sG � s�G Þ, students endowed with k1 � k/l < hi < k1 þ k0 go to the public school andstudents with hi > k1 þ k0 do not enrol in any secondary school. Notice that the definition ofthresholds already incorporates the majority voting outcome in the regime.

Consider first the students going to the public school in both regimes, i.e. those withk1 � k=l < hi < k1 þ k0=ð2s�G Þ. The regime sG � s�G (and the choice sG ¼ 1) is preferredbecause

UG ðsG ¼ s�G Þ � UG ðsG ¼ 1Þ ¼ ðs�G � 1Þð� k

lþ k1 � hiÞ < 0

Take now those with k1 þ k0=ð2s�G Þ < hi < k1 þ k0ðs�G þ 1Þ=ð2s�G Þ who go to the privateschool in the first regime and to the public the second. By comparing their payoffs, we obtain

UP ðsG ¼ s�G Þ � UG ðsG ¼ 1Þ ¼ � k

l� k0

2s�G< 0

which implies that their preferred choice is sG ¼ 1.Next, consider those with k1 þ k0ðs�G þ 1Þ=ð2s�G Þ < hi < k1 þ k0. While in the first regime

they do not enrol in any school, in the second regime they choose the public school. Comparingvoting outcomes we obtain

UN ðsG ¼ s�G Þ � UG ðsG ¼ 1Þ ¼ � k

lðs�G � 1Þ � ðk0 þ k1 � hÞ < 0

and the preferred outcome is sG ¼ 1.Finally, students endowed with hi > k1 þ k0 do not enrol in secondary school and only care

about reducing their tax burden, which is attained by voting on the lowest available standardsG ¼ 1. Therefore, when the group with hi > k1 � k/l is the majority, its preferred alternative isunanimously sG ¼ 1.

University of Padova, CESifo and IZAUniversity of Padova

Submitted: 21 September 2006Accepted: 28 August 2007

ReferencesBaudourian, R., McDonald, J. and Turley, R. (2002). �A comparison of parametric models of income distri-

bution across countries and over time�, mimeo, Brigham Young University.Bertola, G. and Checchi, D. (2002). �Sorting and private education in Italy�, Centre for Economic Policy

Research Discussion Paper No. 3198.Betts, J. (1997). �Do grading standards affect the incentive to learn?�, mimeo, University of California, San

Diego.Betts, J. (1998). �The two-legged stool: the neglected role of educational standards in improving America’s

public schools�, FRBNY Economic Policy Review, March, pp. 97–116.



Betts, J. and Grogger, J. (2000). �The impact of grading standards on student achievement, educationalattainment and entry-level earnings�, NBER Working Paper No. 7875.

Bishop, J. (1995). �Incentives to study and the organization of secondary education�, in (W. Becker andW. Baumol, eds.), Assessing Educational Practice: The Contribution of Economics, pp. 131–182, Cambridge:The MIT Press.

Bishop, J. (1997). �The effect of national standards and curriculum-based exams on achievement�, AmericanEconomic Review, vol. 87(2), pp. 260–4.

Blau, D. (1999). �The effect of income on child development�, Review of Economics and Statistics, vol. 81,pp. 261–76.

Bowles, S., Gintis, H. and Osborne, M. (2001). �The determinants of earnings: a behavioral approach�, Journalof Economic Literature, vol. 39, pp. 1137–76.

Brunello, G. (2002). �Absolute risk aversion and the returns to education�, Economics of Education Review,vol. 21(6), pp. 635–40.

Brunello, G. and Ishikawa, T. (1999). �Elite schools, high tech jobs and economic welfare�, Journal of PublicEconomics, vol. 72(3), pp. 395–419.

Brunello, G. and Rocco, L. (2005). �Educational standards in public and private schools�, IZA DiscussionPaper No. 1854.

Cameron, S. and Taber, C. (2004). �Estimation of education borrowing constraints using returns to school-ing�, Journal of Political Economy, vol. 112(1), pp. 132–82.

Card, D. (1999). �The causal effect of education on earnings�, in (O. Ashenfelter and D. Card, eds.), Handbookof Labor Economics, vol. 3A, pp. 1820–97, Amsterdam: Elsevier.

Carneiro, P. and Heckman, J. (2002). �The evidence on credit constraints in post-secondary schooling�,Economic Journal, vol. 112(482), pp. 705–34.

Cohen Zada, D. and Justman, M. (2001). �Religious education and school vouchers�, Working Paper No. 01–23, Ben Gurion University.

Corneo, G. and Jeanne, O. (1997). �Snobs, bandwagons and the origins of social customs in consumerbehavior�, Journal of Economic Behavior and Organization, vol. 32, pp. 333–47.

Costrell, R. (1994), �A simple model of educational standards�, The American Economic Review, vol. 84, pp. 956–71.De Fraja, G. (2002). �The design of optimal education policies�, The Review of Economic Studies, vol. 69, pp. 437–

66De Fraja, G. (2004). �Private and public schools: theoretical considerations�, in (D. Checchi and C. Lucifora,

eds.), Education, Training and Labour Market Outcomes in Europe, pp. 172–94, London: Palgrave.De Fraja, G. and Landeras, P. (2006). �Could do better: the effectiveness of incentives and competition in

schools�, Journal of Public Economics, vol. 90, pp. 189–213.Dearden, L., Meghir, C. and Ferri, H. (2002). �The effect of school quality on educational attainment and

wages�, Review of Economics and Statistics, vol. 84(1), pp. 1–20.Epple, D. and Romano, R. (1998). �Competition between private and public schools, vouchers and peer group

effects�, American Economic Review, vol. 88, pp. 33–62.Evans, W.N. and Schwab, R.M. (1995). �Finishing high school and starting college: do catholic schools make a

difference?�, Quarterly Journal of Economics, vol. 110(4), pp. 941–74.Feinstein, L. and Symons, J. (1999). �Attainment in secondary schools�, Oxford Economic Papers, vol. 51, pp.

300–21.Fernandez, R. and Rogerson, R. (1995). �On the political economy of education subsidies�, Review of Economic

Studies, vol. 62, pp. 249–62.Figlio, D. and Lucas, M. (2004). �Do higher grading standards affect student performance?�, Journal of Public

Economics, vol. 88, pp. 1815–34.Figlio, D. and Stone, J. (1999). �Are private schools really better?�, Research in Labor Economics, vol. 23, pp. 115–40.Gasperoni, G. (1996). Diplomati e istruiti. Bologna: Il Mulino.Hanushek, E. (2002). �Publicly provided education�, in (A. Auerbach and M. Feldstein, eds.), Handbook of

Public Economics, pp. 2045–141, Amsterdam: Elsevier.Hanushek, E. and Kimko, D. (2000). �Schooling, labor force quality and the growth of nations�, American

Economic Review, vol. 90(5), pp. 1184–208.McEwan, P. (2000). �Comparing the effectiveness of public and private schools: a review of evidence and

interpretations�. Occasional Paper No. 3, Teachers College, Columbia University.McMillan, R. (2004). �Competition, incentives, and public school productivity�, Journal of Public Economics,

vol. 88, pp. 1871–92.Minter Hoxby, C. (1996). �How teachers unions affect education production�, Quarterly Journal of Economics,

vol. 111, pp. 671–718.Murnane, R., Willett, J. and Levy, F. (1995). �The growing importance of cognitive skills in wage determi-

nation�, Review of Economics and Statistics, vol. 77(2), pp. 251–66.Neal, D. (1997). �The effects of catholic secondary schooling on educational achievement�, Journal of Labor

Economics, vol. 15(1), pp. 98–123.OECD (2004a). The 2003 PISA Study, Paris: OECD.



OECD (2004b). Education at a Glance, Paris: OECD.Oliveira, T. (2006). �Tuition fees and admission standards: how do public and private universities really

compete for students?�, Working Paper No. 06/6, University of Leicester.Stiglitz, J. (1974). �The demand for education in public and private school systems�, Journal of Public Economics,

vol. 3, pp. 349–85.Vandenberghe, V. and Robin, S. (2004). �Evaluating the effectiveness of private education across countries:

a comparison of methods�, Labour Economics, vol. 11, pp. 487–506.



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