Financial and human capital inequalities, public education expenditures and the
access to education: A theoretical and empirical analysis.
By: Ben Mimoun Mohamed*
Abstract:
This paper elucidates the role of both financial and human capital distributions in the presence of credit market
imperfections in human capital accumulation and explores some ways in which public education provisions may be
effective. We show that when individuals are credit constrained, more egalitarian distribution of either physical or
human capital is associated with more aggregate investment in education. This arises because the borrowing
constraint is less severe for individuals with higher parental human capital. Thus, as parental human capital
creates economic mobility for individuals, the fraction of population investing in higher education in the long run
depends not only on the initial wealth distribution, but also on the one of the initial human capital.
Concerning the effect of increasing public resources invested in education, our empirical estimates show only a nonsignificantly positive impact of these resources on enrolment rates in the secondary and higher education. However,
we find that the distribution of these resources across the educational stages matter significantly in producing intercountry differences in human capital investment.
Keywords: Wealth distribution, human capital distribution, credits-market
imperfection, public education expenditure, higher education investment
-------------------------------------* TEAM-CED, Université de Paris 1-Panthéon Sorbonne.
106-112 Bd de l’Hôpital 75013 Paris.
1
Introduction:
Investment in human capital is of great importance in explaining long-run development in
countries’ productive capacities and economic growth.
Education, a major source of human capital accumulation, is often provided by the state or
subject to extensive state intervention. An important reason for such intervention is that purely
private provision of education would involve market failures.
Several theoretical works have concentrated on the role of credit market imperfections when
individuals are heterogeneous in their initial wealth. Examples include Loury [1981], Galor and
Zeira [1993], Banerjee and Newman [1993], Aghion and Bolton [1997], and W.Chiu [1998].
Credits-market imperfections are indeed pervasive in the case of education loans due, in part, to
the fact that as human capital does not fully act as collateral for loans, there is a moral hazard
problem in lending to finance education. The amount of loan that borrowers could obtain
appears then as an increasing function of their physical parental wealth.
Researches in this area suffer unfortunately from at least three major insufficiencies. First, on the
theoretical side, previous works have neglected the distribution of parental education as another
important factor explaining differences in human capital performances although several studies (1)
have demonstrated the existence of the intergenerational education mobility phenomena.
Indeed, when credits-market are imperfect, individuals with a given level of parental education
receive education if their parental wealth is higher than a threshold level and this threshold is
likely to be lower for individuals having more parental human capital. Consequently, aggregate
human capital investment should depend not only on the distribution of initial wealth but also on
the initial human capital stock distribution. Thus, neglecting the effect that could exert the
distribution of human capital on education investment will bias upward the one of wealth
distribution.
The second insufficiency in this research area raises from the absence of exploring explicit ways
in which public education policy may provide a remedy.
In fact, most of the studies, which have shown the negative impact of wealth inequalities on
human capital accumulation, did not explicitly investigate possible policy implications of public
educational provision.
However, studying human capital investment determinants might not be comprehensive if the
supply side of education is not introduced since the demand of education could confront an
insufficient supply of public education or of low quality.
--------------------------------(1) : See G.Becker [1964], Bourdieu & Passeron [1970], Glomm.G [1997] and Birdsall [1999].
2
Some theoretical (2) models of political economy show the positive incidence of increasing public
resources invested in education on human capital investment and income equality (Glomm &
Ravikumar [1992], Saint Paul & Verdier [1992], Bénabou [1996] and Fernandez.R & R.Rogerson
[1998, 1999]).
However, these studies assume that the quality of public education is the same for all educated
children, that is, per pupil received expenditures are uniform, which is surely an unrealistic
assumption.
We try in this work to remedy for this inconsistency by suggesting an heterogeneous received
quality for each child depending on his educational stage.
Desegregating public education budget is necessary in the case of an hierarchical investment such
as human capital investment. It allows us to study the effect of different schemes of public
resources allocation between stages of education on aggregate human capital investment.
When initial physical and human capital are randomly distributed among individuals, their
impacts on schooling decisions are often compounded by the skewed allocation of public
resources between basic and higher levels of education.
The third element of insufficiency consists in the existence of only few papers tackling the
credits-market imperfection issue on the empirical background.
Some recent empirical works like Li, Squire and Zou [1998], Flug, Spilimbergo and Wachtenheim
[1998] and Clarke, Xu and Zou [2003] have tried to display the existence of credit market
imperfections, but are not really convincing for at least two reasons.
The first one is that they do not make use satisfactory proxy variables of credit constraint.
These authors test for the credit constraint hypothesis by using either the financial depth as
measured by M2/GDP or the ratio M3/GDP. However, these ratios are only a crude proxy for
credit constraints. They give the level of monetarisation of the economy. Surely in a country
where money is more pregnant is likely to be a country where it’s easier to get loan from a more
developed financial system. But these proxies are so wide that we can not exactly know the
signification of the coefficient we get as a result when we put this variable in regressions on
educational investment.
----------------------------------------(2) : On the empirical side however, conclusions about the effects of public resources invested in education on
student achievements are far from of being unanimous. While Hanushek [1986, 1995] argues that increasing these
resources exerts only a weak effect on the quality of school and hence on students achievements, many other studies
show on the contrary a significantly positive relationship between increasing these resources and students
achievement as measured either by scores obtained in mathematics and sciences or by repetition and abandon rates
or by rates of returns while working. These studies include D.Card & A.Krueger [1992], Fuller & Clark [1994], Betts
[1996,1999], Barro & Lee [1997], A.Case & M.Yogo [1999] and Guryan.J [2001].
3
The second unsatisfactory feature of these studies is the fact they do not test for the robustness
of their regressions’ results of income inequality or educational investment to the add of another
kind of explanatory variables mainly those related to the education distribution or to public
expenditures.
The present paper aims thus to supply suitable solutions for the insufficiencies discussed above in
a jointly theoretical and empirical framework.
On the theoretical side, we show that in the presence of imperfect credits-market, aggregate
investment in higher levels of education depends in the short as well in the long-run on both
initial physical and human capital distributions. That is, the threshold physical wealth dividing the
population into skilled and unskilled workers is decreasing in the initial human capital stock. This
arises because parental human capital as a social capital inheritance allows economic mobility
since individuals endowed with more parental human capital, once educated, will earn a higher
income and leave a bigger bequest. Our empirical estimations support this conjecture since we
find that more unequal distribution of either financial or human capital stocks are associated with
less enrolment rates in the secondary and tertiary education. Moreover, these enrolment rates are
found to be significantly affected by the credit constraint degree.
Our theoretical model shows that total public expenditures as well their allocation across
successive educational stages are important factors in explaining aggregate investment in higher
education. Two effects of public expenditures are examined: the relaxing financial constraint
effect and the quality improvement effect. The first effect consists in weakening the impact of the
credit constraint, and consequently that of inequality, on human capital accumulation by reducing
the private cost of this investment.
The second effect implies that for a given demand of schooling, increasing public education
provisions improves the quality of education which should directly affect the size of the
population capable to continue investing in next stages of education.
Our empirical results show in particular that the policy reallocation’ effect of public resources
across educational stages on higher education investment is not monotonic. As far as the quality
of basic education is low relative to that of higher educational level, transferring more public
resources in favour of students in higher education and away from those in basic education leads
to less investment in higher education since the quality effect outweighs the liquidity constraint
effect. When the relative quality of basic education becomes too high, transferring more public
resources to this educational stage, results in less aggregate investment in higher education
because, in this case, the liquidity effect outweighs the quality effect. Unfortunately, our empirical
4
estimates of the effect of increasing total public expenditures on the investment rates in
secondary and tertiary education reveal only a weak and non-significant effect.
The plan of the rest of the paper is as follow. Section I spells out briefly the theoretical model
and determines aggregate investment in higher education in the short and long-run.
Section II elucidates the impact of total public resources and their distribution across basic and
higher education on higher education investment. Section III briefly discusses the data used in
the paper and presents the empirical results regarding the determinants of secondary and tertiary
enrolment rates.
I- The model:
I-1- The household’s problem:
Each individual lives for three periods. We assume that the time spent in school is discrete. In the
first period, an individual can either leave the education system immediately after the basic level
and work as unskilled worker during his two other periods. He can also continue to study by
investing in higher education in the second period of life and will be in this case skilled worker in
the last period.
An individual who invests in higher education must pay an education cost denoted by   0 .
Each individual has one parent and one child such that there is no population growth. The
population born in each period is normalised to have measure 1. There is an intergenerational

altruism: in the first period, each child inherits from his parent a financial wealth, x p  x p , x p

and leaves a bequest to his offspring in his last period of life. Denote the distribution function of
this wealth by G  x p  , with G ' x p  0 . It’s also assumed that individuals consume in the third
period of life only.
Formally, individual derives utility both from consumption and from bequest to his offspring:
V   log C  1   log B
(1)
where C is consumption in third period, B is bequest, and 0    1 .
Labour factor prices are a dependent function of the accumulated human capital stock. We
suppose the following:

W b   b h b


W h   h h h
(2)
5
where W h and W b denote respectively skilled and unskilled labour earning.
h h and h b are human capital stock of skilled and unskilled workers respectively, and  h and
 b are the respective rates of return of these two types of human capital.
Aggregate labour income is consequently given by:
1

Y  W j dj   b H b   h H h
(3)
0
where j denotes individuals, and H b and H h are respectively basic and higher aggregate
human capital.
Accumulated human capital of a young individual depends on the one of his parent and on the
quality of public school received when educated.
The human capital production function is assumed to have the following form:



hb  h p Eb



 hh  hb E h
(4)
where 0   1 , 0    1 , 0   1 , and 0    1 .
h p represents the parental human capital stock, E b and E h are respectively the quality of public
education at the basic and higher stages. This quality is simply proxied by the average amount of
public resources received by each pupil.
The assumed functional form captures three key characteristics of the education sector.
First, there is diminishing return to the parental human capital effect in the educational
production function of the child (i.e.,
2hj
h p2
 0  j , j  b , h ).
Second, the production function of human capital is characterised by complementarity between
the parental human capital effect and the public provided expenditures (i.e.,
 2hj
 h p E j
0
 j , j  b , h ). The assumption of this complementary relationship is also consistent with the
formulations presented by Lucas [1988], Bénabou [1996], Loury [1981], S.Paul et T.Verdier
[1993], Glomm et Ravikumar [1992] and Glomm et Kaganovich [2003].
However, on the contrary of these studies where the quality of public education is assumed to be
uniform for all educated children, our specification suggests a different received quality provided
for each child depending on his educational stage.
Finally, human capital investment is hierarchic in the sense that to obtain a unit of higher human
capital, the accumulation of basic human capital must be fully completed. Hence, the hierarchical
6
nature of this investment generates dependence between the stocks of the various capital types.
This hierarchical structure is however completely absent in the case of physical investment.


It’s assumed that parental human capital h p vary in the interval h p ,h p , and has a distribution
function denoted by F  h p
F h p
 where
F ' h p  0. Further, we assume for analytical tractability that
 and G  x  are independent.
p
I- 2- Government policy
The government finances education by taxing proportionally the labour income of working
population. If we denote the tax rate by  , then total resources will be  Y .
These resources are allocated between basic and higher education with shares e b and e h
respectively.
The quality received by each student in higher education depends on aggregate public
expenditures in the following way:
Eh 
eh  Y
(5)
S0
where S 0 denotes the actual proportion of population enrolled in higher education, and it is
known.
Since all children receive basic education, the per-pupil quality of education provided at this stage
is simply given by:
Eb  eb  Y
(6)
We assume that the government budget is balanced at each period, that is:
e b  e h 1
(7)
Increasing E h implies not only an improvement in the quality of higher education, but also a
reduction of the private cost of this education  . We can in fact envisage that this cost is higher
as per-pupil public expenditures are lesser.
Precisely, we assume that higher education cost is related to per-pupil public expenditures in
higher education as follow:
  E h   e h / S 0 Y 

(8)
where: 0    1
7
Capital is assumed to be perfectly mobile so that, individuals can borrow and lend in the capital
market at the world rate of interest of r .
The unskilled workers save their second period wage and their parental inheritance. Skilled
workers save their inheritance and repay the loan that has served to finance higher education cost
 . We can illustrate individual behaviour during their life and their respective levels of wealth as
follow:
Figure 1: Sequence of actions in the basic framework
Period
1st
2nd
3th
Unskilled worker
skilled worker
initial wealth ( x p ) +
initial wealth ( x p ) +
basic education ( h b )
basic education ( h b )
initial wealth ( 1 r ) x p +
initial wealth [( 1 r ) x p -
remuneration ( ( 1 ) W b )
higher education ( h h )
initial wealth ( 1 r )² x p +
initial wealth ( 1 r )[ ( 1 r ) x p -  ]+
remuneration [ ( 2  r )(1 )W b ]
remuneration ( ( 1 ) W h )
]+
I- 3- Optimal behaviour:
I-3-1-Perfect credits-market case:
If credits-markets are perfect, an individual decides to invest or not in higher education
depending solely on his accumulated stock of basic human capital. Since, all students in basic
education benefit from the same amount of public expenditures E b , this decision will be taken
on the basis of the stock of parental human capital h p .
Consider an individual who inherits an amount x p in first period of life. If this individual decides
to work as unskilled and not invest in higher education, his lifetime utility is given by:
V b  ( 1  ) W b  2  r   x p  1  r  ²  
(9)
where:
   log   ( 1  ) log ( 1  )
This unskilled worker is a lender who leaves a bequest of size:
B b ( x p )  ( 1  )  ( 1  ) W b  2  r   x p  1 r  ² 
(10)
8
An individual who invests in higher education, enjoys an utility:
V h  ( 1 ) W h ( 1  r ) ( 1 r ) x p     
and leaves a bequest of:
B h ( x p )  ( 1  )  ( 1 ) W h ( 1  r ) ( 1 r ) x p   
(11)
In equilibrium, i.e., when V b t  V h t , an individual is indifferent between the two types of
occupation.
Substituting W b and W h by their respective expressions given in (2) and (4), we get a threshold
level of parental human capital h p , under which an individual prefers not to invest in higher
education. It’s given by:
1


 1 r  
h p  



 ( 1 ) E b  h E h  b  2  r   
(12)
Replacing  , E b and E h by their respective expressions given above, this threshold can be rewritten as:

1 r 
h p  

 ( 1 ) (  Y )    e b ( e h / S )   h  ( e h / S ) Y    b  2  r 

Hence, all individuals with h
p

1



(13)
 h p attend higher education, while the others leave the
education system with only basic education. The lower the parental human capital is, the lower
will be the basic human capital stock of the child which will find acquiring higher education more
difficult.
We assume that the lowest possible parental human capital h p is always less than h p such that
some individuals will always choose to remain unskilled.
The threshold level is a function of public expenditure variables, aggregate labour income and
rates of return of the two types of human capital.
It’s then important to notice that the occupational choice of an individual does not depend on
his/her initial wealth.
Therefore, the fraction of population investing in higher education does not depend on the
distribution of financial endowments. It’s simply given by:
S tP M  1  Ft
h 

p
(14)
where: the notation ( P M ) refers to the perfect capital-market case.
9
I-3-2- Imperfect credits-market case:
A simple form of imperfection in the credits market is assumed as in Galor and Zeira [1993]. The
credits-market is characterised by the possibility that a borrower may not pay back his debt. But
this activity is costly.
Lenders can avoid such defaults by keeping track of borrowers, but such precautionary measures
are costly as well. Assume that if lenders spend an amount T at keeping track of a borrower, this
borrower can still evade the lenders, but only at the cost of  T , where   1 . These costs create
a capital market imperfection, where individuals can borrow only at an interest rate higher than
r.
It follows that an individual who borrows an amount M pays an interest rate i which covers
lenders’ interest rate and lenders’ costs T . That is:
M .i  M . r  T
(15)
This can be re-written as:
T  M (i  r )
(16)
The tracking costs are then increasing with the amount borrowed M since the incentive to
default rises as M increases.
Lenders choose T to be high enough to make evasion disadvantageous:
M ( 1  i )  T
(17)
Equations (16) and (17) determines the borrowers’ interest rate i :
i
1 r
 1
r
(18)
Consider an individual who inherits an amount x p in first period of life. If this individual decides
to work as unskilled and not invest in higher education, his lifetime utility is given by:
V b  ( 1  ) W b  2  r   x p  1  r  ²  
(19)
where:
   log   ( 1  ) log ( 1  )
This unskilled worker is a lender who leaves a bequest of size:

B b ( x p )  ( 1  ) ( 1 ) W b
 2  r   x 1 r  ² 
p
(20)
An individual with inheritance ( 1  r ) x p   , who invests in higher education is a lender
with utility:


V h  ( 1 )W h ( 1  r ) ( 1 r ) x p    
(21)
and a bequest of:
10


B h ( x p )  ( 1  ) ( 1 )W h ( 1  r ) ( 1 r ) x p  

(22)
An individual with inheritance ( 1 r ) x p   , but invests in higher education is a borrower with
utility:
V h  ( 1 ) W h ( 1  i ) ( 1 r ) x p     
(23)
and a bequest of:
B h ( x p )  ( 1  )  ( 1 ) W h ( 1  i ) ( 1 r ) x p   
We assume that: ( 1 ) W h  W b ( 2  r )    ( 1 r )
(24)
(25)
This condition guarantees that lenders prefer always to invest in higher education since this
investment pays back more than unskilled labour, as is seen from equations (19) and (21).
Borrowers invest in higher education as long as V h  V b . This condition implies the following
threshold level of collateral:
x p 
1
( 1 i )   ( 1 ) W h  W b ( 2 r ) 
( 1 r )( i  r )
(26)
Individuals who inherit an amount smaller than x p would prefer not to invest in higher
education, but work as unskilled. Higher education is, therefore, limited to individuals with high
enough initial wealth, due to a higher interest rate for borrowers.
Using equations (2) and (4), this threshold can be re-written as follow:
x p  h p  
1
( 1 i )   ( 1 ) h p E b  h E h   b ( 2 r ) 
( 1 r )( i  r )
(27)
It can be easily seen that the threshold level of collateral is decreasing in the stock of parental
human capital h p . What this implies is that the higher is this human capital stock, the less will be
the credit constraint. This is because individuals can borrow partially against their future earnings.
The higher is the parental human capital, the higher will be the future child’ earning, and
therefore, the less will be the borrowing constraint.
It’s possible to express the critical point dividing the population into skilled and unskilled
workers in terms of the endowment in parental human capital stock.
Thus, from equation (27), this critical threshold of parental human capital is:
 ( 1 i )   x P ( 1 r )( i  r )   1
~

h p  x p  
 ( 1 ) E   E    ( 2  r )  
b
h
h
b


(28)
11
The following relation gives the fraction of the population enrolled in higher education at period
t:
h
S
IM
t
 1
p
 G  x  h  d  h 
t

p
p
(29)
p
hp
where: ( I M ) refers to imperfect credits-market situation.
It’s interesting to underline from equation (29) that in the presence of credits-market
imperfections, the distribution of initial wealth G  x p
 becomes an important determinant of the
aggregate investment in higher education. The following proposition is proved in the appendix.
Proposition 1: As far as h  ( x p )  0 , an improvement in a generation’s distribution of initial
~
wealth in the sense of second-order stochastic dominance implies higher investment in higher
education.
The intuition for this result is simple. Since richer individuals can afford to invest in higher
education even if their parental human capital is low, if we redistribute income from the rich to
the poor, some lower-parental human capital individuals will drop out of higher education and be
replaced by higher-parental human capital ones. Aggregate investment in higher education will
consequently increase since extra-enrolments exceed extra-dropouts as guarantied by the property
~
h  ( x p )  0 . This property implies indeed that the rate of decrease of the threshold parental human
capital is decreasing with parental physical wealth. If however, this threshold decreases at an increasing
rate, which means that it declines faster for richer individuals, then, transferring income from the richer to
the poorer will result in more dropouts than extra-enrolments.
The following proposition shows the impact of parental human capital distribution on higher education
investment.
 
Proposition 2: A more unequal distribution of parental human capital F h p is associated with
lower investment in higher education.
To understand this result, we refer to the concept of Lorenz dominance curves associated to
human capital distributions. In the manner of income Lorenz curves, human capital Lorenz
curves show the share of aggregate human capital received by the poorest fraction j of the
population as j varies from 0 to 1.
Formally, the Lorenz curve associated to distribution of human capital F , is the graphic of the
function L F  j  :  0 , 1   0 , 1  such as:
12
F 1 ( j )
h
LF
 j

p
dF
hp
(30)
hp
h
p
dF
hp
We say distribution F1 Lorenz dominates distribution F2 if L
F
 j
1
 L
F
 j
 j . That is,
2
the entire curve of distribution F1 lies above that of F2 . Lorenz dominance is a sufficient
condition for a reduction in inequality. Figure (3) illustrates a typical Lorenz curve dominance for
this economy where distribution F1 dominates that of F2 .
Increasing the share of human capital among the poorest individuals in the parental population
would imply a transition of some individuals of the population being initially below the critical
~
threshold of parental human capital ( h p ) to above this threshold. This redistribution would then
increase the fraction of skilled population.
Figure 2 : Lorenz curves dominance
1
LF ( j )
F1
F2
LF 1 ( j)
LF 2 ( j )
0
j
1
Indeed, since there are decreasing returns to parental human capital ( 0 1 ), the marginal
impact of a poor parent’s human capital on his or her child’s human capital exceeds that of a rich
parent. In particular, this implies that marginal increase in the higher education participation rate
among the poorest dynasty of population is higher than its decrease among the richest one. It
follows that a more equally distribution of initial human capital would be associated with greater
investment in higher education.
In definitive, both initial physical and human capital distributions affect children’s educational
investment decisions.
13
Figure (3) below exhibits the distribution of occupational choices in the population with respect
to the distribution of parental human and financial capital.
The fraction of population investing in higher education and becoming next skilled workers is
represented in the figure by the discontinuous crosshatched surface area. This proportion
contains all those having x
p
 x p . The unskilled population is represented by the continuous
crosshatched surface area.
Figure 3: Initial physical and human capital
distributions and occupational choices
xp
x p  h p

hp
xp
hp
I- 4- Intergenerational wealth mobility and the dynamics of higher education investment:
This sub-section derives the dynamics of inheritances’ transfer and describes how individuals
move across educational classes. The fraction of skilled population in the long-run is thus
determined. The transfer an individual gives is as seen above a function of that individual’s
transfer receipt and net labour income (income after paying for taxes and education cost). In
turn, the distribution of inheritances in period t determines next distribution of bequests G t  1
following this rule:
x p t 1
 B b ( x p t )  ( 1   )  ( 1   ) W b  2  r   x p t 1  r  ² 
if x p t  x p t

  B h ( x p t )  ( 1  )  ( 1 ) W h ( 1  i ) ( 1 r ) x p t    if x p t  x p t  (  /1 r )

 B h ( x p t )  ( 1  )  ( 1 ) W h ( 1  r ) ( 1 r ) x p t    if (  /1 r )  x p t
(30)
14
Equation (30) defines a Markov process where the probability of inheriting a particular value,
x p t  1 , is conditional on the value, x p t .
Figure (4) below illustrates the dynamic relationship between inheritances and bequests for
unskilled and skilled workers. Notice that x p is determined by the intersection of B b and B h .
Because the distribution of parental human capital h p is bounded, it’s easy to show that there
exists a recurrent distribution of x p that will also be bounded. Lower and upper bounds are
respectively represented in the figure by x b and x h .
Individuals who inherit less than x p work as unskilled and so are their descendants in all future
generations. Their inheritances converge to a long-run level x b :

xb 
( 1  )( 1 )( 2  r )  b E b h p
(31)
1 ( 1  )( 1 r ) 2
Indeed, individuals who received a transfer of less than x b , even if they had the lowest possible
parental human capital, would pass on their children a transfer larger than the one they received.
Those having received a transfer more than x b , will pass on their children a transfer less than the
one they received.
Figure 4: The dynamics of physical wealth distribution
x t 1
Bh
Bb
xb
x p
k
 /1 r
xh
xt
15
Individuals who inherit more than x p invest in higher education but not all their descendants will
remain in the skilled labour sector in future generations. The critical point is k  in figure 4:
k 


( 1  ) ( 1 i )  ( 1 ) h E b E h h p

( 1  )( 1 i )( 1 r )  1
(32)
Individuals who inherit less than k  in period t , even if their parents have the maximum
possible level of human capital, would pass on their children a bequest less than the one they
received. Hence, these individuals may work as skilled workers, but after some generations their
descendants become unskilled workers and their inheritances converge to x b .
Individuals who inherit more than k  would bequeath a value higher than the one they received.
Thus, they will be skilled workers and so do their descendants, generation after generation. Their
bequests converge to x h :
xh

( 1  ) ( 1 )  h E b E h h p  ( 1 r )

1 ( 1  )( 1 r ) 2
(33)
Individuals who received a transfer larger than x h , even if their parents have the maximum
possible level of human capital, would pass on their children a transfer smaller than the one they
received. The inheritances of these individuals converge to the long-run level given by x h .
In the whole, dynasties in this economy are concentrated in the long run in two groups: rich
dynasties, where generation after generation invest in higher education, and poor ones, where
generation after generation are unskilled workers.
Notice that the slopes of B b and B h in figure (4) are lower than one, at points x b and x h ,
respectively, and that means that we assume that  and r satisfy:
( 1  )( 1 r ) 2  1
(34)
Moreover, the slope of B h at the point k  is higher than one. Indeed, it can be seen from (18)
that:
( 1  )( 1 r )( 1 i ) 

( 1  )( 1 r ) 2  1
 1
(35)
It’s clear from (31) and (33) that long-run poor dynasties’ bequest is increasing with the lowest
initial human capital, h p . The one of rich dynasties increases with the highest initial human
capital, h p . Further, as is seen from equation (32), the critical wealth dividing the population into
16
skilled and unskilled workers, k  is decreasing with the highest initial human capital h p . This
implies that the long-run fraction of the population who invests in higher education and be
skilled is increasing in the highest level of initial human capital.
Parental human capital as a social capital inheritance allows in fact economic mobility since
individuals endowed with more parental human capital, once educated, will earn a higher income
and leave a bigger bequest.
Thus, the long-run equilibrium in our model does not depend on the solely initial distribution of
wealth even though the investment in education in our model is indivisible as in Galor and Zeira
[1993]. The intuition is: since in Galor and Zeira [1993] individuals are only heterogeneous in
initial wealth, the presence of indivisibility in human capital investment means that the initial
wealth alone determines whether one receives education. It follows that the poorest who finds
the wealth-enhancing education unaffordable will end up giving their offspring insufficient
bequest to afford education. A poverty trap is thus created. In contrast, since we assume in our
model that individuals differ not only in their initial wealth but in their parental human capital as
well, the dynamic process will depend on the parental human capital too. The latter creates a
mechanism of economic mobility.
In definitive, the long-run relative size of the skilled dynasties is defined such that:

S I M  1  G k  h
p

(36)
II- The impact of public education expenditures:
The model allows us to elucidate the impact on higher education investment of two public
policies related to educational expenditures.
The first one is an increase in total public educational expenditures via an increase in the tax rate
(  ). The second policy consists in reallocating these resources between educational stages while
holding total resources ( Y ) fixed. The latter policy is particularly interesting in developing
economies where public educational resources are relatively scarce.
A rise in E b or in E h exerts a negative effect on the thresholds given in (27) and (28) and
consequently leads to more important investment in higher education. This effect seems obvious
because of the hierarchical nature of schooling investment.
17
That is, increasing E b implies -ceteris paribus- an improvement of per-pupil quality of basic
education that would raise the human capital accumulated at this stage and hence would facilitate
acquiring higher education.
Similarly, increasing E h implies not only an improvement of the per-pupil quality in higher
education, but also a reduction in the private cost of this education  as it can be seen in (8).
This lowers the two parental thresholds and raises investment in this education stage.
Until now, it was assumed that the increase in E b is independent of the level of E h and vice
versa. That is the increase in E b or in E h is done only via an increase in the total amount of
public education resources  Y .
However, it’s possible to subsidy higher education (raising E h ) by a transfer of public resources
from basic education, that is, by a reduction in E b while keeping total resources (  Y ) fixed. This
kind of policy may obviously reduce the accumulated basic human capital stock and raise
consequently the required parental human capital threshold to invest in higher education. Higher
education participation may hence decrease even if the cost of this education decreases.
It’s also possible to improve basic education quality (an increase in E b ) by shifting public
expenditures away higher education, without varying the total budget of education. This policy
may reduce too higher education participation because it raises the cost of this education  ,
which exacerbates more and more, the liquidity constraint.
Hence, the allocation of public resources between the different levels of education is likely to be
an important factor explaining schooling transition.
On the whole, the potential impacts of different reallocation schemes on higher education
enrolment seem to be the net results of quality and liquidity effects. Notice that in the case of
perfect credits market, the second effect disappears.
In order to study the impact of different reallocations on investing decisions, it’s convenient to
let  denote the relative per-pupil public expenditures:

Eb
Eh

eb
( e h /S 0 )
(37)
For a given education budget  Y , an increase in  indicates a transfer of public resources from
higher education toward basic education. A decrease in  implies however a transfer in the
opposite sense.
Using the fact that e b  e h  1 , we can get:
18
e  
 b S 
0


e  S0
 h S 0  
(38)
Performing variable changes in equations (27) and (28), we can announce these two propositions
which are proved in the appendix.
Proposition 3: For a given ratio  , increasing total educational budget by increasing the tax
rate    rises higher education enrolment rate.
~
h p
 x p
This may be seen from
 0.
 0 and


Increasing    would in fact rise at the same time the per-pupil public expenditures in all levels
of education as can be seen in (5) and (6). This means both an improvement in the quality of
these education levels and a reduction in the cost of higher education, which alleviate the
borrowing constraint for poorest individuals and consequently raise the fraction of the
population investing in higher education.
Proposition 4: There exist   such that, for a given educational public budget (  Y ), increasing
 rises higher education enrolment rate if     , and decreases it if     .
This means that the reallocation of public resources from one educational level toward another
one has a non-monotonic effect on higher education investment.
As long as the relative basic education quality is low (     ), transferring public resources in
favour of basic education improves higher education enrolment because the quality improvement
effect of basic education outweighs that of the increasing in the private cost of higher education.
This result claims that the policy of improving basic education quality should be prior to that of
subsidising higher education cost.
However, if this transfer becomes excessive such that     , shifting more resources in favour
of basic education reduces higher education investment since the effect of increasing the cost of
this education will prevail that of improving the quality of basic education.
19
III- Empirical analysis:
III-1-Data description:
We use gross secondary enrolment ratio and higher education enrolment ratio from 1965 to 1997
as our measures of investment in human capital. These data have been extracted from UNESCO
database [1998].
Primary education is not considered here because it is free almost everywhere, such that all
children can afford this investment. The same is not true for secondary and tertiary education,
however.
We need data on measures of credit market imperfections. We use recent data from T.Beck and
R.Levine [1999] on credits to the private sector by credit banks over GDP available for a big
number of countries between 1965 and 1997. We believe this ratio is an indicator of credits
abundance degree, so a proxy of credit rationing degree denoted later by (RF) could be the
inverse of this ratio, that means GDP/private credits. We think this measure is better than other
monetary aggregate ratios like (M2 or M3 to GDP) usually used as an indicator of financial
development degree because it excludes credits to the public sector.
As far as data on distribution are concerned, ideally we need data on the distribution of wealth,
which are hard to find. Some data compiled by Alesina and Rodrik [1994] on the distribution of
land ownership (GiniLand) in 1960 for some countries are available, which is the closest we can
get to the distribution of wealth. We use both data on the distribution of incomes and lands as
proxies for the distribution of wealth. Gini coefficient of incomes (Gini) and the bottom quintile
(Q1) are our measures of the spread of income distribution. These measures are taken from
Deininger and Squire data set [1996], which promise to be of higher quality and broader in
coverage than any other available data set on the income distribution.
We include only observations labelled « accepted » so of higher quality. These observations have
to meet three criteria: national coverage of the population, comprehensive coverage of the
income source and comprehensive method of calculation.
In addition to the income distribution we include in our analysis data on the Gini index of
education (GiniEdu) to refer to the degree of inequality in the education distribution among the
parental population. This index is from Thomas, Wang and Fan [2000] constructed from Barro
and Lee data set [2000] which gives educational achievements and average years of schooling of
the population more than 25 years old from 1965 to 1995. The construction method of the
GiniEdu is reported in the appendix.
20
On the supply side of schooling, we concentrate on the effects of government expenditures on
education and use mainly two proxy variables describing respectively the two governmental
education policies discussed above.

The first variable is the ratio   

public education exp enditures 

GDP

and captures the level of total
public resources invested in all stages of education. The second variable is the ratio
Ep
per  pupil public exp enditures in primary educaion 


 Es
per  pupil public exp enditures in secondary education 

if the dependent variable is secondary
E
per  pupil public exp enditures in secondary education 
enrolment rate, and  s 
if the dependent
E
 h
per  pupil public exp enditures in higher education 

variable is higher education enrolment rate. The two latter ratios indicate how public education
expenditures are allocated between two successive education levels.
Hence, public resources invested in education would affect the schooling decisions by two
effects: the relaxing financial constraint effect and the quality improvement effect.
The first effect consists in weakening the role of the credit constraint, and consequently that of
inequality, in human capital accumulation by reducing the private cost of this investment.
The second effect implies that for a given demand of schooling, increasing public education
provisions improves the quality of education which should directly affect the size of the
population capable to continue investing in next stages of education (by raising potential abilities
of children for example).
Data on public expenditures are obtained from the UNESCO data set.
On the whole, our data set covers 86 countries from them 64 are developing. Data on schooling
enrolment rates, per capita GDP, educational expenditures and credit-rationing degree are annual.
Data on the distribution of education are quinquennial. Missing informations (mainly on income
distribution) have dramatically reduced the size of our data set transforming it into unbalanced
panel. Descriptive statistics about variables used in the estimations are reported in the appendix.
III-2-The results
Before presenting our estimation’s results, it’s necessary to make some clarifications.
For the effect of credit market rationing, we suggest as Clark Xu and Zou [2003] that it depends
on the composition structure of the economy, that is, on the economic development level of
countries.
21
Indeed, financial development and economic development as measured by per-capita GDP
involve in general in the same sense. So, the credit constraint tends to be more severe in less
developing countries where the financial system is not enough developed. We estimate therefore
to obtain an effect more important of this credit constraint on schooling investment in countries
with less GDP/capita.
To test for this sensibility of the reduction of credit constraint to the economic development
level, we add in our regressions an interactive variable between the level of credit rationing and
that of per capita GDP (3).
In letting the effect of credit rationing depend on the development stage of countries we have
also control for the heterogeneity of our sample of countries.
Further, including the per capita GDP as another determinant of schooling decisions is
consistent with our theoretical result given in proposition (1). Since the result is valid for second
order stochastic dominance, which corresponds to Lorenz dominance for distributions with the
same mean, the inclusion of per capita GDP permits to control for the mean level of income.
For the educational variables, we believe that both average and distribution of (parental)
education affect the enrolment rates
(4)
. However, including these two variables in the same
specification will be problematic because of the strong correlation between them as it can be seen
in the graphic below.
That’s why we use in the regressions only the distribution of education (GiniEdu) in light to
abstract for the multicolinearity issue.
Figure 5: The relation between average and distribution of education
Gini index of education (%)
89.42
5.34126
.069043
12.7608
Average education (years)
----------------------------------(3) : GDP per capita is that calculated in PPP by Summers & Heston [1994].
(4): Mean population’ education could affect children’s educational decisions by the externality effect as in Lucas
[1988].
22
III-2-1-Secondary education enrolment rates:
We present in the table (1) below the results of regressing the enrolment rate in secondary
education on factors describing only the demand side of schooling decisions. So we abstract for
now for the potential impact of the government founding.
Table 1: Estimation of secondary education enrolment: 1965-1997.
Dependent variable : secondary
enrolment rate (%)
Constant
GDP/capita
Gini
(%)
(1)
(2)
(3)
(4)
(5)
6.74
(0.46)
12.91
(10.47)
- 0.776
(- 5.89)
36.05
(3.07)
13.98
(9.80)
2.673
(0.18)
14.17
(10.89)
- 0.752
(- 5.77)
29.18
(2.58)
15.73
(10.63)
51.37
(3.50)
18.28
(15.95)
2.386
(3.85)
Quintile 1 (%)
GiniLand
- 0.532
(- 5.03)
145
- 2.025
(- 2.44)
0.269
(2.55)
- 0.540
(- 5.68)
162
- 2.707
(- 3.07)
0.355
(- 3.15)
- 0.887
(- 55.83)
145
- 0.363
(- 2.96)
- 2.878
(- 3.01)
0.376
(2.83)
- 0.310
(- 3.09)
221
51
51
51
51
37
0.808
0.785
0.816
0.799
0.797
 2 (4) =
 2 (4) =
 2 (5) =
 2 (5) =
 2 (4) =
16.34
0.002
39.98
0.000
13.16
0.021
25.83
0.000
32.62
0.000
(%)
RF
- 2.159
( - 2.42)
- 2.044
(- 2.29)
- 0.498
(- 5.29)
162
RF*(GDP/capita)
GiniEdu (%)
Number of observations
Number of countries
R² (overall)
Hausman test: fixed versus
random effects
Prob >
2.515
(4.14)
 (.)
2
- t-statistics are in brackets.
Looking at the first column, we find that both income and education distributions are strongly
correlated to the school enrolment. In fact, Gini index of incomes and GiniEdu come out
significantly negative at less than 1 % of standard error.
A 1 % decline in the income Gini index (more egalitarian distribution) induces an increase of 0.77
% in the secondary enrolment rate. Moreover, a 1 % decrease in the GiniEduc leads to a rise in
secondary enrolment rate by 0.49 %.
Further, the coefficient of our credit-rationing variable (RF) is highly significant and has the
predicted negative sign. A lesser degree of credit rationing is associated with greater investment in
secondary education which is an evidence supporting the liquidity constraint thesis.
23
Finally, mean income is positively related to the secondary schooling investment. The richer the
country is, the greater is its investment in human capital. This seems to be evidence in supporting
the non-convergence of countries in terms of economic growth because more material wealth
(GDP/capita) creates more human capital investment, which is a potential of more rapid growth,
and vice-versa. Note that the variables considered till now have a large explanatory power. They
explain 80 % of the variation of the dependent variable.
In column (2), we use the first quintile instead of the Gini index as the measure of income
inequality. Similarly, it appears that a more egalitarian distribution of income (an increase in
quintile 1) is associated with a rise in education investment. The other variables are robust to this
change.
In the third specification, we use Gini index of incomes and add the interactive variable between
credit rationing and per-capita GDP to test the hypothesis of different impacts of credit rationing
depending on the economic development stage of countries.
The regression indicates a positive sign for the interactive variable implying the impact of credit
rationing is less important in countries with more GDP per capita. In other words, the impact of
financial development on human capital investment is stronger in developing countries than in
developed ones. Of course, this result comforts the conjecture that we have stipulated above.
For the rest of explanatory variables, they have the same sign and significance degree as in the
first column.
In column (4), we test for the heterogeneous effect of credit rationing on the secondary
education enrolment across countries with different development levels by using the first quintile
of income distribution. Once again, the hypothesis of the heterogeneous effect is well verified.
These results must be however analysed with some caution.
Indeed, since investment in human capital affects the distribution of income as well, there is an
issue of endogeneity in using data on income distribution to explain investment in human capital.
The distribution of lands, however, is unlikely to be affected by investment in human capital.
Therefore, the Gini index for the distribution of lands can be treated as exogenous in explaining
the variation in human capital investment.
The last column of table (1) exhibits the estimations’ results with the GiniLand instead of the
Gini of incomes. The results are qualitatively and quantitatively very similar to the ones obtained
using the bottom quintile or the Gini coefficient for the distribution of incomes.
The sign and significance of all other variables are robust to this latter specification.
24
III-2-2-The role of public education expenditures:
Table (2) includes the supply side explanatory variables, i.e., public education expenditures.
First, and before all, we can observe that the addition of these variables improves the explanatory
power of our specifications relative to that obtained in table (1).
Table 2: Estimation of secondary education enrolment using different variables for educational resources: 1965-1997.
Dependent variable : secondary
enrolment rate (%)
Constant
GDP/capita
Gini
(%)
(1)
(2)
(3)
(4)
(5)
2.673
(0.18)
14.17
(10.89)
- 0.752
(- 5.77)
12.45
(1.45)
8.694
(1.94)
- 0.414
(- 1.98)
23.48
(1.44)
10.99
(7.75)
- 0.594
(- 4.55)
22.59
(1.26)
12.16
(7.24)
42.35
(2.46)
15.31
(10.61)
2.137
(3.478)
Quintile 1 (%)
GiniLand
- 2.159
(- 2.81)
0.267
(2.76)
- 0.559
(- 5.69)
- 2.658
(- 3.25)
0.331
(3.21)
- 0.563
(- 5.14)
- 0.144
(- 1.78)
- 3.188
(- 3.02)
0.408
(2.80)
- 0.356
(- 3.25)
0.269
(0.39)
0.072
(1.99)
- 0.0008
(- 2.13)
- 0.025
(- 6.20)
112
0.319
(0.49)
0.150
(2.41)
- 0.0005
(- 2.24)
- 0.025
(- 4.97)
162
(%)
RF
RF*(GDP/capita)
GiniEdu (%)
- 2.025
(- 2.44)
0.269
(2.55)
- 0.540
(- 5.68)
Per pupil government
expenditures in secondary
education / per capita GDP (%)
Per pupil government
expenditures in primary
education / per capita GDP (%)
 = government expenditures on
education / GDP (%)
Ratio : (Ep / Es)
(%)
- 3.333
( - 2.42)
0.379
(1.48)
- 0.652
(- 2.09)
0.134
(1.03)
0.664
(3.34)
Ratio: (Pop.enrolled.Prim /
Pop.enrolled.Sec) (%)
Number of observations
162
29
0.067
(0.11)
0.060
(2.01)
- 0.0004
(- 2.08)
- 0.024
(- 6.05)
127
Number of countries
51
21
41
41
31
0.816
0.836
0.878
0.878
0.860
Ratio : (Ep / Es)²
R² (overall)
Hausman test: fixed versus
random effects
Prob >
 2 (.)
 2 (5) =
13.16
0.021
 2 (7)=  2 (9) =  2 (9)=
10.02
0.187
9.55
0.388
17.53
0.041
 2 (8) =
7.86
0.447
- t-statistics are in brackets.
25
The first column reports simply the estimations’ results obtained in column (3) of the table 1
above.
In the second column of table (2) we consider the effect of increasing government expenditures
at the secondary and primary levels proxied by the corresponding ratios of per-pupil public
expenditures to per capita GDP. The results indicate a positive -but statistically non significanteffect on secondary enrolment associated with increasing per-pupil resources at the secondary
level and a positive - and highly significant- effect related to increasing public resources at the
primary education level.
The fact that public expenditures in primary education exert a significantly positive effect on the
secondary enrolment rates is consistent with our theoretical predictions and is attributed to the
hierarchical nature of the human capital accumulation generating interdependence between
sequential stages of education. Hence, to raise secondary participation rates, government priority
should be first attributed to the improvement of the quality of primary education.
The inefficacy of secondary education expenditures in raising secondary enrolment rates could be
however explained in this manner. Following our theoretical conjecture, more public resources
invested in secondary education should reflect a lower cost of this education which consequently
should promote the access to the secondary education of individuals who had completed primary
education. This means that increasing public resources invested in the secondary education
should affect positively the enrolment rate in this stage via the liquidity effect.
However in practice, raising public expenditures may only imply an increase in teachers’
remuneration. In this case, such increase does not systematically imply a reduction in the private
cost of this education and hence does not lead necessarily to an increase in the schooling access.
The absence of such systematic relationship is argued in Hanushek [1995] who has demonstrated
that the increase in teachers’ remuneration does not lead to a significant improvement in the
schooling achievement in the developing countries.
Moreover, in most of countries in the world, almost 90 % of current public expenditures cover
teachers and administrative employees’ salaries (Berthélemy [2002]). So, the liquidity effect of
public expenditures would likely to be of a weak magnitude.
In the whole, the results in the second column suggest that increasing the resources invested in
one stage of education may be associated with a weak liquidity effect and then be ineffective in
directly raising student participation at that level. However, it generates a significant quality effect,
which is beneficial in favouring the transition to the next stage.
26
These results suggest that to make the liquidity effect active too, it’s necessary to raise the part of
expenditures benefiting directly to the students. This can arise for examples by increasing
scholarship, setting public loans and exemption from education fees.
It’s important at this stage of reasoning to signal that all the variables describing the demand side
of schooling are with the same sign and significance as in column (1). This is evidence in
supporting the robustness of these variables.
In specification (3) of the table, we replace the two variables describing per-pupil public
expenditure at secondary and primary levels by the ratio of these variables denoted by (Ep/Es)
which captures the distribution of public expenditures between these two educational stages.
We introduce the square of this ratio (Ep/Es)² to test the non-monotonic effect of public
resource transfers as has been demonstrated in our theoretical model.
Since the amount of public resources devoted to each pupil depends on the size of the
population enrolled at each level, we include the ratio of these two populations as an additional
explanatory variable.
In addition, we introduce in the regression the variable capturing total public education
expenditures (  ) as a percentage of GDP.
The coefficient of (  ) is positive but non-significant (t = 0.11). This result is similar to that of
Checchi [2000] for whom, the coefficient associated to this variable is in the most of his
specifications significantly negative. However, when he includes an interactive variable between
public expenditures and Gini index of income distribution, Checchi shows that the effect of
public expenditures on schooling enrolment can be positive for high levels of Gini index, i.e. in
highly unequal countries. Unfortunately, we do not find any significant effect for increasing total
educational budget even if we reproduce Checchi’ specification.
Hence increasing total public resources devoted to education does not imply that investment in
education (here the secondary) will systematically be promoted.
When considering the distribution of public expenditures between primary and secondary levels,
we find a significantly positive effect of the variable (Ep/Es) on secondary enrolment. This
evidence argues that reallocation of public expenditures from secondary education in favour of
primary education promotes secondary enrolment and confirms the result obtained in the second
column regarding the supremacy magnitude of the quality impact of the primary education
funding relative to the liquidity effect of the secondary education funding.
27
On the contrary, the variable (Ep /Es)² has a significant and negative sign –although its extent is
low- suggesting that shifting public resources from secondary to primary education could lead to
a decrease in secondary enrolment if the transfer becomes excessive.
The results in the third column show that doubling the ratio (Ep/Es), that is increasing it by 100
% leads to an increase in the secondary enrolment rate by about 3 %, and that the reversal ratio is
about 150 %, that is when per-pupil public expenditures in primary education are 1.5 times that
in secondary education.
The variable giving relative enrolled populations has the expected negative sign implying that the
more pupils are in primary relative to secondary level, the lesser is the secondary rate and viceversa.
Specifications (3) and (4) consider the same explanatory variables except for the income
distribution which is replaced by quintile 1 and GiniLand respectively instead of the Gini index of
income.
Unsurprisingly, the results are typically the same as in the previous columns.
Finally, when comparing the results in table (2) to those in table (1) it’s very important to remark
that the effects associated to the distributions of incomes (or lands) are of lesser amplitude when
public expenditure variables are considered. In our opinion, this is an additional argument that
public expenditures are effective in promoting schooling investment via the reduction of income
inequalities.
III-2-3- Higher education enrolment rates:
We report in the table (3) below our results of regressing higher education enrolment rates on the
same explanatory variables as in the previous section.
We focus in the three first columns on only variables describing the demand side of education
and alternate with the three measures of wealth distribution.
Once more, we find a strong negative correlation between wealth inequality, credit rationing and
educational inequality in one hand, and investment in higher education in the other hand.
As for secondary enrolment regressions, we find here that the negative effect of credit rationing
on higher education investment is higher for developing countries since the interaction variable
RF*(GDP/capita) has a positive singe. This effect is in the most specifications statistically
significant only at 10 %.
28
Table 3: Estimation of tertiary education enrolment using different variables for educational resources: 1965-1997.
Dependent variable : tertiary
enrolment rate (%): 1965-1997
Constant
GDP/capita
Gini
(%)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
26.21
(4.55)
2.344
(2.72)
- 0.311
(- 2.46)
16.22
(5.91)
1.861
(2.81)
30.56
(6.34)
1.343
(3.12)
13.64
(2.18)
2.093
(2.55)
- 0.205
(- 2.08)
11.03
(1.87)
1.711
(2.44)
- 0.200
(- 1.99)
12.64
(3.39)
1.212
(2.09)
20.28
(5.12)
1.222
(2.66)
0.544
(1.87)
Quintile 1 (%)
GiniLand
(%)
RF
RF*(GDP/capita)
GiniEdu (%)
- 2.363
(- 1.96)
0.249
(1.71)
- 0.402
(- 4.81)
- 2.852
(- 1.97)
0.305
(1.74)
- 0.438
(- 4.92)
0.528
(1.65)
- 0.159
(- 1.81)
- 3.382
(- 2.71)
0.419
(2.49)
- 0.508
(- 5.49)
Per pupil government
expenditures in higher education
/ per capita GDP
(%)
Per pupil government
expenditures in secondary
education / per capita GDP (%)
 = Government expenditures
on education / GDP (%)
Ratio : (Es / Eh) (%)
- 2.018
(- 1.82)
0.276
(1.68)
- 0.714
(- 2.60)
0.060
(1.24)
- 1.503
(- 1.73)
0.190
(1.57)
- 0.379
(- 5.07)
- 2.416
(- 1.77)
0.071
(1.46)
- 0.369
(- 5.07)
- 0.132
(- 1.67)
- 1.988
(- 1.76)
0.227
(1.88)
- 0.394
(- 4.68)
0.428
(0.62)
0.195
(2.57)
- 0.0009
(- 1.54)
- 0.001
(- 1.87)
85
0.190
(0.29)
0.135
(2.33)
- 0.0007
(- 1.45)
- 0.010
(- 3.14)
74
0.385
(1.96)
Ratio: (Pop.enrolled.Sec /
Pop.enrolled.Tert) (%)
Number of observations
130
115
174
32
0.018
(0.03)
0.176
(2.41)
- 0.0008
(- 1.77)
- 0.001
(- 1.91)
98
Number of countries
53
52
38
22
42
41
31
0.661
0.624
0.665
0.735
0.897
0.891
0.849
Ratio : (Es / Eh)²
R² (overall)
Hausman test: fixed versus
random effects
Prob >
 (.)
2
 2 (5)  2 (5)  2 ( 4)  2 ( 7 )  2 ( 9 )  2 ( 9 )  2 (8)
= 1.17
0.808
= 1.62
0.626
= 2.74
0.433
= 5.75
0.435
= 9.15
0.329
= 6.84
0.553
= 7.24
0.404
- t-statistics are in brackets.
On the supply side however, we find strong evidence supporting the effectiveness of public
resources invested in previous educational levels in promoting enrolment in next educational
stages. For instance, as it’s shown in column (4), tertiary enrolment rates are strongly affected by
per-pupil public expenditures in secondary education, but no effect of resources devoted to
tertiary education is found. As before, this result implies the quality improvement effect of the
29
educational expenditures outweighs its liquidity effect. The weak effect of the liquidity effect
could once again be attributed to the weak weigh of public resources benefiting directly to
students in total resources devoted to the higher education level.
As for secondary estimations, results in column (5) show unambiguously that increasing total
expenditures do not significantly matter in promoting higher education enrolment rates.
However, we can see that the allocation of public resources across students in secondary and
higher education matters in explaining tertiary education enrolment.
Precisely, the quadratic form of the ratio (Es/Eh) is highly significant and has the right signs
indicating that enrolment in higher education increases as public resources are shifting toward
secondary education, but tends to decline once this reallocation becomes too high. The
estimation indicates that, doubling per-pupil expenditures in secondary education relative to that
in higher education leads to a promotion in higher education rates by 9.6 %.
In addition, the estimated reversal ratio is at 220 %. However, since this ratio is not reached in
our countries’ sample (the maximum ratio is 170.6 % for Korea in 1990), the result in column (5)
should simply suggest that increasing this ratio would have a decreasing positive effect on the
higher education participation rates.
Finally, in columns (6) and (7), we test for the effects of public funding using consecutively the
bottom quintile of income distribution and the Gini index for distribution of lands. Results are
quantitatively and qualitatively unchanged.
Conclusion:
This paper has examined some factors affecting human capital accumulation in economies with
imperfect capital markets. Our principal findings support policies enhancing equality in the
distribution of financial capital in order to promote investment in education. The distribution of
education among the parental generation has also an important role in future aggregate human
capital investment. In some empirical specifications, its impact comes out as the most important
one from the explanatory variables used in our empirical study. More equal distribution in initial
human capital implies a less severe credit constraint for poorest individuals and a higher
probability for these individuals -once educated- to leave bigger bequests for future offspring.
This facilitates economic mobility. On the supply side of education, our theoretical study shows
that the total amount of public resources and their distribution across successive educational
stages matter in making inter-country differences in human capital investment. On the empirical
30
ground, we find that the effect of the resources’ allocation is by far more important than that
exerted by total amount of these resources. Thus, our estimation results support a reallocation
policy of public resources toward lower stages of education (basic education) especially in
developing countries where these resources are relatively limited. In many developing countries
(mainly from sub-Saharan Africa, Latin America and South Asia) these resources are highly
skewed in favour of higher education levels. Such policy had incontestably worsened the quality
of basic education and had prevented important fractions of populations from continuing
studying in higher levels of education. In doing so, these countries had followed a counterproductive policy since they have eroded the quality of basic educational levels at the cost of only
insignificant or even non-existent reduction in the private cost of higher educational levels. Such
policy has unambiguously strengthened the negative impact of initial financial and human capital
inequalities on schooling investment.
31
Appendix:
Proof of proposition 1:
Suppose distribution G 2 ( x p ) stochastically dominates distribution G 1 ( x p ) in the sense of
second order stochastic dominance. Denoting the fraction of population investing in higher
education under distribution G i by S Gi , we can write the difference in this investment under
two distributions using equation (29) as follow.
hp
S G 2  S G1 
 G  x
1

p
( h p )   G 2  x p ( h p )   dh p
(39)
hp
This can be written as:
x p ( h p )
S G 2  S G1  
 G  x   G  x   x
p
1
p
2
 1
p

(40)
( x p ) dx p
x p ( h p )
x p ( h p )
S G 2  S G1  

x
 1
p
x p ( h p )

 xp


G 1  m   G 2  m  dm 
( x p ) d
 x p ( h p )




(41)
 xp


 1 
Integrating by parts treating x p ( x p ) as the first term and d 
G 1  m   G 2  m  dm 
  ˆ

 xp ( hp )


as the second term we get:
S G 2  S G1

 xp





1

G 1  m   G 2  m  dm   
 ( xp (xp ) 

 x p ( h p )





 xp


 1 
G 1  m   G 2  m  dm  dx p )
xp
(xp ) 
 x p ( hˆ p )

)


x p ( h p )

x p ( h p
(42)



Using from the equation (28), the fact that x p1 ( x p )  0 and x p1 ( x p )  0 , we get the
result S G 2  S G1  0 .
Proof of proposition 3:
Using the change of variables given in (38), we can re-write the threshold levels of human and
physical parental capital as follow:
Equation (27) is rewritten as:
32
 Y


1
  ( 1 i ) 
x p ( h p )  
 S 
 ( 1 r )( i  r )  
 0


  ( 1 )  h h p


  Y

 S 
 0






 h


 Y

 S 
 0



  b ( 2  r )  




(43) Equation (28) transforms to:

 Y
~
h p ( x p )   ( 1i ) 

 S 0 





1

 x p ( 1 r )( i  r ) 


  Y
 ( 1 ) 
 S 

 0








 h

 Y

 S 
 0

  1

  b ( 2  r )   




(44)
Derivation of these expressions with respect to  permits to capture the impact of a tax increase
(an increase in the public education expenditures at all the schooling levels) on the enrolment rate
in higher education ( S t ). We get:



 Y


x p
1
  ( 1 i ) 
  

 ( 1 r )( i  r )   
 S 0 







 Y
 h p  
 S 0 









  Y   (   )( 1 )   
 
  h 
1   


S




 
0



  0


  ( 1 ) 
1 
   b ( 2  r )  





and,






Y



Y


 ( 1i )  


 

 S  
~
~ 

S




 0 
 0 
h p
hp
 ( )


 
A



 Y
where: A  ( 1i ) 
 S 




  Y
and B  ( 1 ) 
 S 


h






 h

 Y 


 S  
 0 

 (   )( 1 ) 
  ( 1 )   

1    b ( 2  r ) 
1   





  
 0

B



 x p ( 1r )( i  r )  0
 Y

 S 



  b ( 2  r )   0



Proof of proposition 4:
The impact of re-allocation of public education resources from higher to basic education on the
investment rate in higher education is not monotonic. This can be seen once we derive the two
thresholds above with respect to  . We get:
x p  C

   S 0 

 Y
   ( 1 i ) 

 S 

 0


  Y
  ( 1 ) h p 

 S 

 0






 h

 Y

 S 
 0





 S0

 S

  b ( 2r ) 0


 

 









1

where C  
 ( 1r )( i  r ) 
33
and,


  Y
 Y 



( 1 ) 

(
1

i
)
 S  
~
~ 
 S 0 
h p  h p  
 0 



  

A ( S 0  )











 h

 Y

 S 
 0





 S0

 S

   b ( 2r ) 0


 

 



B
  







where: A and B are as defined above.
It’s not possible to obtain an analytical solution for the sign of these two derivatives. That’s why
we use a parametric method.
 x p
~
h p




Figure on the left-hand side shows the results of simulating
(5)
the derivative of parental physical
capital threshold with respect to the ratio of public per-pupil expenditures (  ) for different levels
of parental human capital: h p 1, h p  5 & h p  10 . Figure on the right-hand side shows the
results of simulating the derivative of parental human capital threshold with respect to the ratio
of  for different levels of parental physical wealth: x p 15, x p  20 & x p  25 .
We can see that the effect of varying  on the two thresholds is not monotonic.
That is, as far as the ratio of public per-pupil expenditures in the basic educational stage relative
to that in higher education is not too high (      0.4 from our simulations), shifting these
expenditures from higher toward basic education reduces the two thresholds and increases
consequently the rate of enrolment in higher education. This is so, because the positive effect of
improvement in basic education quality outweighs the negative effect of increasing the private
cost of higher education.
-------------------------------------------
i  0.1, r  0.05 ,   0.8,   0.5 ,    0.3 ,  h  0.1,  b  0.12 ,
  0.2 , S 0  0.25 and Y  50 .
(5): Parameter values are set such that:
34
When the quality of basic education relative to that of higher education becomes too high
(     ), shifting more public resources away higher education and toward basic education leads
to a decrease of the investment rate in higher education because in this case, the liquidity
constraint effect of this transfer outweighs its quality improvement effect.
Construction method of the Gini index of human capital distribution
The Gini index of the education distribution among each country has been elaborated from the
updated Barro and Lee [2000] data set. This data set indicates the fraction of the population more
than 25 years old having attend or completed each stage of education. We then get seven
categories of population: without any education, partial primary, completed primary, partial
secondary, completed secondary, partial tertiary and completed tertiary. By associating these data
with the corresponding duration of education stage, Gini index of education can be calculated
following this formula:
GiniEdu 
1

n
i 1
i2
j 1

pi xi  x j p j
where  is the average year of education, x i and x j are years of education of the fractions i
and j of the population. p i and p j are the proportions of the population with some education,
and n refers to the number of stages (here 7).
35
Figure 5: The distribution of public education expenditures and secondary education enrolment rates
Enrolment rate: secondary (%)
142.5
2
8.58078
331.308
Ratio: (Ep/Es) (%)
Figure 6: Distribution of public education expenditures and tertiary education enrolment rates
Enrolment rate: tertiary (%)
81
.3
1.95095
170.672
Ratio: (Es/Eh) (%)
36
Descriptive statistics : averages on 1965 - 1997
Regions
Secondary
Tertiary
h
(years)
Gini
(%)
(%)
GiniLand
(%)

GiniEdu
(%)
RF
(%)
Per
capita
GDP
Quintile 1
(%)
21.36
14.12
4.57
61.79
(19)
2.96
2.57
0.47
12.28
(18)
1110
926
274
3934
(19)
2.53
1.39
0.30
4.91
(15)
46.68
10.16
28.9
62.3
(19)
5.19
2.14
2.02
9.70
(19)
60.35
14.82
42.29
80.4
(5)
64.46
12.87
44.9
82.38
(8)
55.28
15.11
36.16
83.48
(6)
18.09
7.69
9.01
30.27
(6)
1986
880
1013
3478
(7)
3.64
2.00
1.30
7.01
(7)
38.51
2.21
34.53
42.50
(7)
6.66
0.91
5.78
8.71
(7)
60.87
9.54
45.43
71.81
(5)
30.48
16.08
16.52
59.41
(5)
4.42
0.95
2.91
5.89
(5)
585
113
496
805
(5)
1.81
0.77
0.73
2.49
(3)
34.06
4.09
30.06
41.71
(5)
8.00
0.97
6.33
9.11
(5)
62.38
21.02
31.00
93.33
(11)
24.80
14.66
3.3
49.81
(11)
2824
2142
506
6623
(11)
6.56
2.77
3.38
11.10
(10)
38.23
6.48
29.62
50.35
(11)
6.21
1.38
3.95
8.25
(11)
(%)
(Ep/Es)
(%)
(Es/Eh)
(%)
13.33
12.50
2.01
48.00
(19)
4.42
1.50
2.56
7.95
(10)
30.08
14.64
17.10
69.50
(10)
14.71
9.79
6.92
40.63
(10)
61.81
15.76
34.06
76.95
(6)
3.94
1.88
1.70
6.71
(7)
3.81
0.97
2.32
4.87
(4)
74.39
20.61
39.37
92.09
(4)
41.05
12.26
20.24
51.73
(4)
56.15
9.01
41.87
65.73
(4)
68.73
19.42
35.62
82.90
(4)
10.66
6.52
5.17
23.27
(5)
2.26
0.86
0.92
3.16
(4)
64.74
13.00
51.12
84.78
(4)
19.60
10.13
9.34
36.15
(4)
57.1
16.47
33.85
85.31
(8)
39.51
12.65
20.01
57.11
(10)
3.57
1.94
1.15
7.70
(11)
3.09
0.93
1.80
5.05
(9)
78.19
32.87
32.83
123.43
(9)
42.93
26.90
8.30
85.43
(9)
Sub-Sahar.Africa
Mean
Std deviation
Min
Max
(Nbre countries)
M.East & N.Africa
Mean
Std deviation
Min
Max
(Nbre countries)
South Asia
Mean
Std deviation
Min
Max
(Nbre countries)
East Asia & Pacific
Mean
Std deviation
Min
Max
(Nbre countries)
Descriptive statistics : averages on 1965 - 1997 (suite)
Regions
Secondary
Tertiary
(%)
(%)
46.62
18.27
18.04
87.16
(19)
16.79
7.00
6.13
26.64
(19)
87.33
11.70
68.5
110.94
(11)
Per
capita
GDP
h
(years)
Gini
(%)
Quintile 1
GiniLand
(%)
GiniEdu
(%)
RF
(%)
2707
3443
833
6527
(19)
4.88
1.38
2.48
7.41
(17)
48.85
4.43
42.04
57.27
(19)
4.15
0.99
2.72
5.78
(19)
81.36
7.52
60.66
92.30
(13)
46.95
11.68
25.68
69.78
(16)
27.02
7.58
17.39
43.17
(11)
7406
2288
4437
12680
(10)
8.33
0.15
8.18
8.48
(2)
28.24
4.42
20.49
34.65
(11)
9.04
1.46
6.72
11.66
(11)
------
90.17
13.64
53.25
104.44
(12)
38.47
5.49
30.05
50.91
(11)
7659
1102
5660
8711
(12)
8.79
1.18
6.70
10.21
(11)
31.56
4.75
25.98
43.10
(12)
7.36
1.31
4.87
9.46
(12)
93.34
1.71
91.64
95.05
(2)
75.64
4.02
71.63
79.65
(2)
9402
652
8052
9402
(2)
10.89
0.30
10.58
11.19
(2)
33.28
2.02
31.27
35.30
(2)
5.93
0.91
5.03
6.84
(2)

(%)
(Ep/Es)
(%)
(Es/Eh)
(%)
7.84
3.88
2.89
17.57
(19)
3.55
0.93
1.77
5.51
(11)
58.26
12.51
38.46
83.25
(11)
30.31
12.45
10.44
55.20
(11)
29.40
11.49
19.09
47.98
(4)
9.53
6.25
1.83
22.50
(11)
4.17
0.10
4.05
4.29
(3)
72.33
7.16
64.40
81.72
(3)
46.82
23.49
29.41
79.93
(3)
56.50
14.60
39.14
84.46
(9)
28.72
3.81
24.65
36.16
(6)
2.72
0.86
1.77
4.95
(12)
4.93
1.35
1.76
6.91
(12)
115.14
57.00
56.96
227.67
(12)
55.35
15.78
36.46
85.26
(12)
64.12
9.02
55.15
73.1
(2)
18.52
2.76
15.77
21.28
(2)
2.44
0.70
1.73
3.15
(2)
6.02
-6.02
6.02
(1)
133.02
-133.02
133.02
(1)
62.66
-62.66
62.66
(1)
Latin America
(Nbre
Mean
Std deviation
Min
Max
countries)
Centr & East Europe
(Nbre
Mean
Std deviation
Min
Max
countries)
Western Europe
(Nbre
Mean
Std deviation
Min
Max
countries)
North America
(Nbre
Mean
Std deviation
Min
Max
countries)
Notes:
-
Secondary and Tertiary are respectively enrolment rates in secondary and tertiary education.
Per capita GDP is PPP-adjusted 1985 international prices in ($). RF is the credit rationing measure.
 is total public expenditures on education over GDP.
(Ep/Es) is the ratio of per-pupil public expenditure in primary education to per-pupil expenditure in secondary education.
(Es/Eh) is the ratio of per-pupil public expenditure in secondary education to per-pupil expenditure in tertiary education.
37
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