Discussion Papers In Economics
And Business

Dual Poverty Trap

Ryo Horii and Masaru Sasaki

Discussion Paper 06-12

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANDual Poverty Trap

Ryo Horii and Masaru Sasaki

Discussion Paper 06-12
May 2006
この研究は「大学院経済学研究科・経済学部記念事業」
基金より援助を受けた、記して感謝する。
Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANDual Poverty Trap∗
Ryo Horii† and Masaru Sasaki‡
May 11, 2006

Abstract
This paper constructs an overlapping generations model of search equilibriumthat analyzes intergenerational and coordination traps simultaneously. When
parents are uneducated, their children often face diﬃculty in finishing school,
and therefore likely to remain uneducated. In addition, if children expect that
other children of the same generation do not receive education, they anticipate
that firms will not create enough jobs for educated and thus are discouraged fromschooling. These two mechanisms of poverty trap reinforce each other–creating
a dual poverty trap. Escaping from the trap requires a combined, not separate,
implementation of financial assistance for schooling and policies for changing
agents’ expectation.
JEL Classification Numbers: O11, J62, J23.
Keywords: overlapping generations model, education, intergenerational externality, job search.

∗

This research is partially supported by the Japan Society for the Promotion of Science, Grant-in-

Aid for Young Scientists (B), 2004—2006. The authors are grateful to Ryoichi Imai, Noritaka Kudoh,Kazuo Mino, Takashi Shimizu and seminar participants at Osaka University and Kansai University
for their valuable comments and suggestions. Any remaining errors are naturally ours.
†

Graduate School of Economics, Osaka University, 1-7 Machikaneyama, Toyonaka 560-0043,

JAPAN. E-mail: horii@econ.osaka-u.ac.jp‡

Graduate School of Economics, Osaka University, 1-7 Machikaneyama, Toyonaka 560-0043,

JAPAN. E-mail: sasaki@econ.osaka-u.ac.jp1

1

Introduction

It has been argued that many low income countries cannot escape from poverty because people in youth do not acquire suﬃcient education and therefore work only inless productive sectors when they are grown up. A survey by World Bank (2005) reports that the gross school enrollment rate for secondary education among low income
countries (with a GNI per capita of $755 or less) remains only 46% in 2002. Why
don’t they then obtain education? A simple answer proposed in the literature says:
because they are just poor and therefore cannot aﬀord education–that is, they arepoverty-trapped.1 If the aﬀordability of education is the only problem, foreign aids
and assistances that makes education aﬀordable would solve the problem. However,diﬃculties faced by various aid programs suggest that the existence of some deeper
causes.
This paper considers two other mechanisms of poverty traps. In an overlapping
generations model of search equilibrium, we analyze intergenerational linkage in eachfamily or lineage, and the coordination issues among the individuals of the same generation. If parents in a family are not educated, children are less likely to obtain
education than otherwise. If the majority of other individuals of the same generation
within the economy do not receive education, one may expect that the return fromschooling would be low and therefore loses incentives to obtain education.
While each of these two mechanisms can separately create a possibility of a poverty
trap, this paper shows that, when they simultaneously present, they reinforce eachother so that the likelihood that the economy falls into the poverty trap is considerably
higher: that is, a coordination failure triggers the intergenerational trap, whereas thelimited intergenerational mobility makes the coordination trap more persistent. In
addition, it is shown that, in economies trapped in poverty for both reasons–i.e., in

1

Such an argument often relies on the assumption that the financial market is imperfect andtherefore children cannot borrow enough against their future income.

2

dually trapped economies–the problem can be solved only when both intergenerationaland coordination issues are tackled simultaneously.
Regarding the intergenerational linkage, there are empirical views supporting thatthe education level of parents has a significantly positive eﬀect on children’s school attendance, even after controlling for income (e.g., Strauss and Thomas 1995, Grootaert
1999, Ray 1998, Patrinos and Psacharopoulos 1997).2 In particular, Bratti (2002)shows that children’s school level depends more largely on family characteristics (parents’ education level and their social class) than on parents’ current income, using the
British data. Following those observations, our model assumes that the cost of acquiring education is higher when one’s parent is unskilled, i.e., when the parent neither iseducated nor obtained some skill on the job. As studied in the literature (e.g. Azariadis and Drazen, 1990; De la Croix and Michel 2002, sec. 5.2), such intergenerational
positive spillovers of education generates increasing returns in obtaining education,and therefore may create multiple steady states. If the initial generation obtains low
education, then the subsequent generation faces a high cost of schooling, and therefore
again do not obtain education. Such a link creates an intergenerational poverty trap.
The other key component of our model is coordination failure. We focus on thetendency that, in low income countries, children often have little prospect of finding agood job even when they acquire education. If they hold such a pessimistic expectation,
it discourages them from attending school even when it is financially aﬀordable. In
fact, the pessimistic expectation is shown to self fulfilling when we explicitly consider
the frictional nature of the labor market: if there are few educated workers, firms are
not willing to create jobs that requires educated workers since they think it diﬃcult tofind appropriate workers successfully.
In the literature, previous studies have shown that multiple equilibria may emerge
if acquiring education on the part of workers and creating jobs on the part of firms
2Behrman (1997, 2002) focuses on the eﬀect of mother’s education level on children’s school at-tainment.

3

are strategic complements (see Burdett and Smith 2002; Laing, Parivos, and Wang
1995; Acemoglu 1997). Rather, given that acquirement of education takes much longer
time than creation of jobs, this paper stresses the importance of expectation among
young people. If one thinks that other agents have a pessimistic expectation, one canrationally expect that other agents do not receive education and that, when they aregrown up, firms observing it will not create enough jobs. Therefore, this bad outcome
cannot be escaped unless all young agents somehow coordinate their expectation: i.e.,a coordination trap emerges.
Previous studies have analyzed intergenerational and coordination traps separately.
However, for low income countries, both of arguments seem equally plausible; i.e., thosecountries may be dually trapped, where two mechanisms of poverty trap reinforce
each other. If a certain mass of people in the previous generation is uneducated, thenot only children of those uneducated agents, but also other agents in the economy
have to choose not to receive education; i.e., the bad intergenerational linkage causesa coordination failure. On the other direction, once a coordination failure occurs,
then the majority of agents in the generation choose not to receive education, whichcauses the intergenerational poverty trap in the subsequent period. We show that,consequently, any policy prescription that aim to solve one of the problem do not work,and that, in fact, it may fail completely without even partially resolving the directed
problem. It would be one of the possible reasons why various forms of development
assistance have been largely unsuccessful. International organizations have recently
recognized the necessity of combined approach to the dual nature of poverty trap.3
This paper is organized as the follows. The next section sets up a simple overlapping
generations (OLG) model in which a parent’s human capital eases the acquirement ofeducation by her child. We derive the young people’s schooling choices given their3

For example, the World Bank (South Asia) budgeted for the Female Education Awareness Pro-

gram as well as for stipend in the Female Secondary Assistance Project of Bangladesh. (see the WorldBank’s web site:www.worldbank.org)

4expectation regarding the prospect of successfully obtaining a job in the modern sector. Firms’s decision of creating job is analyzed in Section 3. Section 4 investigates
the equilibrium of the economy and shows that, under a particular parameter range,
the equilibrium exhibits a dual poverty trap. In Section 5, after explaining why the
one-by-one prescription fails, we consider two types of eﬀective policies: public awareness campaigns combined with subsidy for education or provision of free education.
Concluding Remarks appear in the last section.

2

Households

In the model, there are overlapping two-period-lived agents with an unit population foreach generation. Agents seeks to maximize their utility that are obtained from theirconsumption flow. For simplicity, we assume either that the economy is a small open
country, or that agents are risk neutral. In either case, the discount factor is constantand denoted by β ∈ (0, 1).

2.1

Childhood

Let us consider the life of agents born in period t. In the first period of their life, which
we call childhood, agents are endowed with one unit of time and choose whether or not
to attend school. Education is assumed to be indivisible; agents can become educatedin their adulthood if and only if they finish schooling in their childhood.
If an agent decides not to go to school, she spend all the disposable time in working.
Children can work only in the traditional sector, where the productivity is low butneither education nor skill is necessary. Let z > 0 denote the marginal productivity oflabor per unit time in the traditional sector. Then, her income in the childhood is z.
If an agent wants to become educated in the adulthood, she must spend a certain
time in schooling. Although their parents do not leave financial wealth as bequests,5parents’ acquired skill has a favorable influence on their ability to learn.4 If one’s
parent is skilled (educated or obtained a skill through his job, as discussed later), atime of e ∈ (0, 1) is required to finish school. For the remaining time in her childhood,she works in the traditional sector and earns (1 − e)z. If one’s parent is not skilled, atime of e > e is required to finish school. Note that this agent needs a longer time tofinish school since she cannot rely on her parents’ knowledge. For the remaining time,
she works and earns (1 − e)z.

2.2

Adulthood

In what follows, we consider an agent’s behavior in the adulthood. Adult agents canwork either in the modern sector or in the traditional sector. Both educated anduneducated adult workers seek to find a job in the modern sector, since the expected
income there is higher than elsewhere. However, the labor market in the modern
sector is frictional. A worker must meet a vacant job in order to produce output. For
simplicity, we do not consider separate labor markets for educated and uneducatedworkers–they search for a job in the same pooled market and find one with the sameprobability.5 Let qt+1 ∈ [0, 1] denote the probability for a worker to successfully matchwith a job. Although the value of qt+1 is endogenous, each worker takes it as given.
If a worker fails to match with any vacancy in the modern sector, which occurs
with probability 1 − qt+1 , she works in the traditional sector where job is easy to findat no friction (e.g., workers can be self-employed). In that case, she earns z, regardlessof her education level.
If an adult agent successfully matches with a vacant job in the modern sector, which
occurs with probability qt+1 . her income depends on whether she is educated or not
4This can be interpreted as a particular form of intergenerational transfer of human capital, as isoften assumed in the literature; e.g., De la Croix and Michel (2002).
5

This assumption can be justified if firms cannot distinguish educated and uneducated workers

until they match with an worker. In other words, this search process is ‘undirected.’

6

(i.e., whether she has finished schooling in her childhood). When an educated worker
matches with a vacancy of a firm, this pair can produce an output of yb > z. Before

the production process starts, the worker and the firm negotiates the division of theoutput. If the worker and the firm fail to agree on the division of the output, theycannot match with other agents within the period. After the breakdown, the worker
can work in the traditional sector, where she can earn z, whereas the firm cannot
produce output and its income is zero. Let y ≡ (by − z)/2 > 0 denote the half of thesurplus from the match. Through negotiations, we assume that the pair reaches the
Nash bargaining solution with the equal bargaining powers. Then, the income of theworker is y + z, whereas that of the firm is y.
When an uneducated worker matches with a vacancy, she tries to acquire the required skill through self-training, or learning by doing in the modern sector. She
successfully obtains the skill with a small probability p ∈ (0, 1), and for this case thematch produces z + 2y. The division of the surplus is y + z and y as above. However,with probability (1 − p), she fails and the match produces only z–i.e., the surplus iszero. Then, the worker earns z and the vacancy gets nothing.

2.3

Schooling Decisions

Agents determine whether or not to attend school in order to maximize the present
value of their lifetime income. If an agent born in period t decides not to attend school,ee(y + z) + (1 − pqt+1)z], where
the present value of expected lifetime income is z + β[pqt+1eis the expected value of qt+1 as of period t. Likewise, if an agent born in period t
qt+1e(y + z) +decides to finish school, her present value of lifetime income is (1 − e)z + β[qt+1e)z], where e = e if one’s parent is skilled whereas e = e if not so. Therefore,(1 − qt+1

the net benefit of schooling ise(1 − p)y,−ez + βqt+17

where e = e or e.

(1)Note that, since e < e, the net benefit of education is higher for agents with skilledparents (i.e., parents who have finished schooling or obtained skill through working in
the modern sector).
A young agent receives education if and only if expression (1) is positive or zero.6
More specifically, a young agent whose parent is skilled receives education if and only
if the expected probability of finding a job is reasonably high:e
qt+1≥ ez/(β(1 − p)y) ≡ q ∗ .

(2)

A young agent whose parent is not skilled receives education if and only if the expected
probability of finding a job is even higher:e
qt+1≥ ez/(β(1 − p)y) ≡ q > q ∗ .

(3)

We focus on the case in which the time cost of education for children of unskilledparents, e, is fairly high so that the threshold level q exceed one.7 This means thatchildren of unskilled parents never receive education–the only way for them of acquiring skill is by learning by doing. In later sections, we show that this limitation inintergenerational mobility constitutes one factor in generating a poverty trap. Before
that, however, it must be described how jobs are created.

3

Matching Technology and Job Creation

In the modern sector, a worker must meet a vacant job in order to produce output.
Vacant jobs are created by firms through free entry. Let the cost of creating a vacant
job be denoted by k > 0, and let vt+1 represent the number of vacancies created byfirms in period t + 1. Any job, filled or not, deteriorates in one period.
There exists a search-matching friction as mentioned before. Specifically, we assume
that the number of match in a period is determined by a standard symmetric Cobb6

It is assumed that agents receive education when they are indiﬀerent to do so.

7Specifically, it is assumed that e > β(1 − p)y/z.

8

1/2 1/2

Douglas matching function, M (`t+1 , vt+1 ) = A`t+1 vt+1 , where A > 0 is a parameterof matching technology and `t+1 denotes the number of workers who search for a job.
Recall that all adult workers (with population one) search for a job in the modern
sector, which means `t+1 = 1. Therefore, the number of match in period t + 1 is√
M (1, vt+1 ) = A vt+1 . The probability for a worker to match with a vacant job is√
qt+1 = M (1, vt+1 )/1 = A vt+1 .

(4)

In a similar way, the probability for a vacant job to match with a worker can be√
expressed as M (1, vt+1 )/vt+1 = A/ vt+1 .
Let us calculate the profitability of creating a job. Let Et+1 denote the number ofeducated among the adult agents in period t + 1. When a vacant job is created, it√
meets with a worker with probability A/ vt+1 . Conditional upon this, the matchedworker turns out to be educated with probability Et+1 /`t+1 = Et+1 , and in that casethe firm earns y. With probability (1 − Et+1 ), the matched worker is uneducated. The
uneducated worker successfully train himself with probability p, for which case the firm
earns y, but if she fails to acquire the skill the firms earns 0. Therefore, the expected
profit of creating a vacancy is written by,√(A/ vt+1 ) [Et+1 + (1 − Et+1 )p] y − k.

(5)In equilibrium, the number of vacant jobs, vt+1 , is determined so that expression (5)becomes zero; i.e., vt+1 = A2 [Et+1 + (1 − Et+1 )p]2 /k 2 . Substituting it into (4) showsthat the equilibrium probability for a worker of finding a job is8
qt+1 = m0 + m1 Et+1 ,(6)where m0 ≡ pA2 y/k and m1 ≡ (1 − p)A2 y/k are positive constants. Equation (6)implies that if firms observe that there are greater number of educated worker among
8

Since qt+1 is a probability, it must be between 0 and 1. Therefore, it may be more appropriate

to write (6) as qt+1 = min[m0 + m1 Et+1 , 1], or to write the matching function as M (`t+1 , vt+1 ) =1/2 1/2

max[A`t+1 vt+1 , `t+1 , vt+1 ]. If k > A2 y, the right hand side of (6) does not exceed 1 for any Et+1 ∈[0, 1], and therefore such a consideration is unnecessary. In what follows we assume k > A2 y.

9adults, they create more jobs in the modern sector, leading to an increase in qt+1 .
We also have shown in the previous section that, if young agents expects that qt+1 ishigher, they are more willing to take education, leading to an increase in Et+1 . In thenext section, we show that the mutual dependence between qt+1 and Et+1 give rise tomultiple equilibria, which is another factor of a poverty trap.

4

Equilibrium

In the model presented above, the current state of the economy is suﬃciently describedby the number of educated among the adult agents, Et . Given Et , the first subsection
investigates the equilibrium of the economy in a particular period. Then, the second
subsection considers the evolution of the economy over generations and explains why
a poverty trap emerges.

4.1

Stage Equilibria

Let us consider the behavior of generation t agents (those born in period t), given thenumber of educated among the previous generation’s adults, Et . To this end, we firstneed to know how many generation t agents have skilled parents. Similarly to (6),firms in period t creates vacant jobs so that the probability for an generation t − 1
adult of finding job is qt = m0 + m1 Et . Therefore, qt (1 − Et ) uneducated workers findjobs in the modern sector, and pqt (1 − Et ) of them successfully obtain the required
skills by themselves. The number of skilled workers among generation t − 1 is the sumof educated and self-trained workers, which can be written as a function of Et :S(Et ) ≡ Et + pqt (1 − Et ) = Et + p(m0 + m1 Et )(1 − Et ).

(7)

Observe that function S(Et ) is increasing and concave for all Et ∈ [0, 1].99

By straightforward calculations, S 0 (Et ) = 1 +p(m1 − m0 )− 2pm1 Et and S 00 (Et ) = −2pm1 < 0. In

addition, since it it is assumed that k > A2 y (see footnote 8), S 0 (1) = 1−p(m0 +m1 ) = 1−pA2 y/k > 0.

10

Among the young agents in period t, S(Et ) of them are with skilled parents and
1 − S(Et ) of them are with unskilled parents. Recall that children of skilled parents
receive education if and only if they expect that they will find a job in the modern
sector in the next period with probability higher than or equal to q ∗ (see equation 2).
Recall also that children of unskilled parents never receive education. Therefore, thenumber of young agents who obtain education is



e
0
if qt+1
< q∗,
=
Et+1


e
S(Et ) if qt+1
≥ q∗.

(8)

Equation (8) determines the number of educated in period t + 1, Et+1 , as a functione. Then, as a function of Et+1 , the actualof the expected matching probability, qt+1

matching matching probability qt+1 is determined according to (6). As long as agentsemust coincide with the actual
are rational, the expected matching probability qt+1

probability qt+1 .10 Therefore, rational expectations equilibrium for this period is given
by a pair of q t+1 and Et+1 that simultaneously satisfy (6) and (8).
Figure 1 displays job creation (6) and schooling decisions (8) in (q t+1 , Et+1 ) space.
Throughout the analysis, we assume that the probability of obtaining skill without
education is low so that m0 ≡ pA2 y/k < q ∗ holds. Observe that if S(Et ) ≥ (q ∗ −m0 )/m1 ≡ S ∗ , there are two rational expectations (stage) equilibria:(m0 , 0)· · · thin market eq.
e(qt+1 , Et+1 ) =(m0 + m1 S(Et ), S(Et )) · · · thick market eq.

(9)

If young agents in period t expect that the matching probability in period t + 1 islow, they do not receive education. Then, in period t + 1, firms observing few educated worker are not willing to create many jobs in the modern sector. Thus, the low
Therefore S 0 (Et ) > 0 for all Et ∈ [0, 1] follows.
10

Note that, for simplicity, we rule out mixed strategies. If agents are allowed to choose schoolingdecisions probabilistically, (q ∗ , S ∗ ) can be another equilibrium. However, equilibria such as (q ∗ , S ∗ )are often ruled out in the literature since they seem ‘unstable.’11

Figure 1: Reaction functions and stage equilibria

matching probability realizes, which we call the thin market equilibrium. Conversely,
young agents with skilled parents receive education in period t if they expect that thematching probability in period t + 1 is high. Then, in period t + 1, firms observing
many educated workers create suﬃciently many jobs that the matching probability is
actually high, which we call the thick market equilibrium.
If S(Et ) < S ∗ , only the thin market equilibrium exists:e, Et+1 ) = (m0 , 0).
(qt+1

(10)

In this case, the young agents who have skilled parents correctly know that, even when
all of them choose to receive education, firms will not create enough jobs such that
their devoted time is legitimized.11

11

From (1) and (6), the net benefit of education when all of the fortunate young agents who haveskilled parents receive education is −ez + β(m0 + m1 S(Et ))(1 − p)y. This expression is negative if
S(Et ) < S ∗ .

12Figure 2: Dynamics and multiple steady states

4.2

Poverty Trap

In what follows, we consider the long-term dynamics of the economy in terms of thenumber of educated, Et . From (9) and (10), Et evolves over generations according to0if S(Et ) < S ∗ ,Et+1 =either 0 or S(Et ) if S(Et ) ≥ S ∗ ,as illustrated in Figure 2. We find that there exist two steady state values of Et : one isa good steady state in which all agents receive education (Et = 1), whereas the otheris a poverty trap in which no agent receives education (Et = 0).
Figure 2 also shows an example path converging to the good steady state. Observe
that, for the economy to converge to the good steady state, two distinct conditions
must be satisfied. First, for every generation, young agents must expect that theprobability of finding a job in the modern sector is high so that the thick market
equilibrium realizes for all periods. Second, the number of skilled agents in the initial
adult generation, S(E0 ), must be larger than the threshold level, S ∗ , since otherwise
13

the thick market equilibrium does not exist. If either of the above two conditions isviolated the economy falls to the poverty trap, as we now describe in detail.
Observe that, regardless of the initial state E0 , the thin market equilibrium is always
feasible. Therefore, if the initial young agents happens to have a pessimistic expectationthat firms in the modern sector do not create many jobs (which is one of the rational
expectations), they do not receive education, and the thin market equilibrium realizes
in the next period (i.e., E1 = 0). Obviously, this is a worse outcome than the thickmarket equilibrium in which many of them obtain jobs in the modern sector. Then,
why each of them does not change his or her mind and have a optimistic expectation?
The reason is that each agent cannot rationally change one’s expectation given that ofothers: if other agents have a pessimistic expectation, one can rationally expect that
other agents do not receive education and that, in the next period, firms observing it
do not create enough jobs. Therefore, this bad outcome cannot be escaped unless all
young agents somehow coordinate their expectations: i.e., a coordination trap emerges.
The selection of equilibrium depends not only on expectation but also on the previous generation’s educational attainments. Suppose that the threshold level S ∗ islarger than pm0 , or equivalently that the time cost of education, e, is higher thane. Then, young agents cannot hold an optimistic expecβ(1 − p)(1 + pm1 )m0 y/z ≡ btation about the probability of finding a job in the modern sector, unless suﬃciently
many (E ∗ ≡ S −1 (S ∗ )) agents in the previous generation have obtained education. If

the economy starts from E 0 < E ∗ , then the initial young agents necessarily hold apessimistic expectation since the thin market equilibrium is the only possible equilibrium in the next period, and therefore they choose not to receive education. Thismeans E1 = 0 < E ∗ , which induces the young agents in period 1 to choose again not
to receive education. Such a bad linkage continues over generations, which we call anintergenerational trap.
The coordination trap and the intergenerational trap emerge for distinct reasons,but they fortify each other. Suppose that, in some period t, the young agents fails

14

to coordinate on the optimistic expectation and therefore Et+1 realizes. Then, fromperiod t + 1 on, the only possible equilibrium is the thin market equilibrium. That is, acoordination trap in a certain period triggers the intergenerational trap that persists.
Conversely, suppose that the economy has been in the intergenerational trap and then,for some period t, the thick market becomes feasible (e.g., if e suddenly falls belowe). This means that the economy is no longer in the intergenerational trap. However,bsince young agents in period t know that the probability of finding a job in the modern
sector has been low for a number of generations before them, they are likely to thinkthat the thin market equilibrium realizes again in the next period (more precisely, they
are likely to think that other young agents will hold a pessimistic expectation). Thatis, even when the economy can escape from the intergenerational trap, the history that
it was in that trap increases the likelihood of the coordination trap in this period, andalso in the future.12

5

Economic Policies

The previous section has shown that if Et = 0 < E ∗ , the economy is dually trappedin the sense that both the intergenerational and coordination issues must be resolved
before it can archive economic development. This section considers policy prescriptions
for escaping from this dual poverty trap.

5.1

Ineﬃcacy of Separate Implementation

When economy is in the intergenerational trap, only a few young agent has skilledparents (S(Et ) < S ∗ ). Then the majority of the young agents, with unskilled parents,

12

Rostow (1990) calls such a phenomenon “long run fatalism,” whereas Hoﬀ and Pandey (2004)

named it behaviors “historically created social identities.” Chamley (2002) shows that a similarequilibrium will be chosen again and again if there is small uncertainty about the structure of theeconomy.

15

face a high time cost of education, and therefore do not receive education. This, inturn, lower the number jobs created by firms in the next period, and therefore deters
even the fortunate young agents with skilled parents from receiving education. To
resolve this trap, one can imagine two types of policy. One is to subsidize education sothat the fortunate young agents with skilled parents receive education even when they
expect that the probability of finding a job is not very high. Another is to provide
free education for some of unfortunate young agents; then firms in the next period will
create more jobs, which can induce the fortunate young agents to choose to receive
education.
Both types of policy will be eﬀective if the only problem is intergenerational issues.
However, in a dually trapped economy, such policies cannot help the economy escapeee, does not change: i.e., qt+1=
from poverty as long as expectation of the agents, qt+1

pm0 and therefore Et+1 = 0 are always rational expectations equilibrium. Therefore,
subsidy or free provision of education should be combined with appropriate policies
that convince young agents that their life can be diﬀerent from their parents’ generation(e.g., public awareness campaigns).
Note also that any public awareness campaign never changes the expectation ofrational agents unless it is combined with subsidy or free provision of education–thethin market equilibrium is only the feasible equilibrium in the dual poverty trap andthe only rational expectation is a pessimistic one.
Therefore, the remedies for the intergenerational issue and the coordination issue
must be implemented simultaneously–if they are implemented separately or sequentially, they are most likely to fail. The following discusses the combined policy package
in more detail.

5.2

Uniform Subsidy for SchoolingConsider a subsidy program in which any young agent who completes schooling receives σt z, where σt > 0. The expenditure for this program is covered by foreign aids16

(the result do not change if it is covered by a non-distortionary tax). Adding σt z toexpression (1) shows that this subsidy in eﬀect lowers the time cost of education, e
and e, by σt . Unless σt is very large, it does not change the behavior of young agents
who face the high cost e − σt of schooling.13 Therefore, the uniform subsidy is virtually
directed to privileged agents who have skilled parents.
How much should the size of subsidy σt be? By replacing e by e − σt in (2), it
turns out that subsidy σt lowers the threshold number of skilled adults from S ∗ ≡(q ∗ − m0 )/m1 to S ∗ − λσt , where λ ≡ z/(β(1 − p)m1 y) is a constant. As shown in
Figure 3, the thick market equilibrium becomes possible if
S(Et ) ≥ S ∗ − λσt ⇔ σt ≥ (S ∗ − S(Et ))/λ.
Suppose that the economy is initially in the dual poverty trap: Et = 0 < E ∗ . Since thenumber of skilled adults is S(Et ) = pm0 , the subsidy is eﬀective only if σt ≥ e − eb.14

eWith subsidy σt ≥ e − eb, an optimistic expectation qt+1
= m0 (1 + pm1 ) as well as thee=pessimistic (or conservative in the sense that it is the same as qt ) expectation qt+1

m0 are rational. Therefore, combining a suﬃcient amount of subsidy and a policy
instrument that coordinate expectation, the number of agents receiving education canbe increased: Et+1 = S(Et ) > Et .
How long education should be subsided in this case? Since S(Et ) is increasing in
Et , the required amount of subsidy (S ∗ − S(Et ))/λ falls periods by periods. S(Et )eventually exceeds S ∗ , and thereafter subsidy is unnecessary. Even after this take-oﬀ
periods are finished, young agents must coordinate upon the thick market equilibrium
for all periods. This is typically not diﬃcult given that they observe that firms are
creating enough jobs for their parents when they form expectations. Over generations,the economy approaches the good steady state, Et = 1.
13

If σt is that large, all agents go to school and economic development is completed in one period.

While this is theoretically possible, the magnitude of expenditure required for such a policy would be
implausibly huge.
14

σt ≥ (S ∗ −S(Et ))/λ = ((q ∗ −m0 )/m1 −pm0 )·(β(1−p)m1 y)/z = e−β(1−p)(1+pm1 )m0 y/z = e−be.

17Figure 3: Dynamic eﬀects of subsidy for schooling

It should be noted that even though only agents with skilled parents receive thesubsidy, those who are not also benefit from an externality. When the agents receiving
subsidy acquire education, firms create more jobs in the modern sector, and agents
without education can enjoy more opportunity to self-train themselves when they are
hired in the modern sector. In fact, this is the immediate reason why Et increases overgenerations.

5.3

Providing free education

The previous subsection has shown that, even though the uniform subsidy for education is virtually directed only for children of skilled parents, if it and appropriate
campaigns policy can change the expectation of those fortunate agents, children of
unskilled parents also benefit from such a policy package through an externality. However, for various reasons, aid organizations often aims to support directly the mostunfortunate people. This subsection examines the eﬀectiveness of such programs.
Consider a policy of providing free education to a certain number young agents.
The recipients of ‘free education’ are compensated not only direct expenses regarding18

education (not explicitly considered in the model) but also the opportunity cost oflearning (i.e., ez or ez). Suppose that, in each period, the government or an aid
organization who implement this program can control the number of recipients, nt ,as well as the number of the children of unskilled parents among the recipients, nut .
Then, even in the thin market equilibrium, nt agents receive education freely. In the
thick market equilibrium where agents expect qt+1 to be higher than q ∗ , education isreceived by all children of skilled parents, S(Et ), and nut young agents not with skilledparents but with provision of free education. Therefore equation (8) changes to



e
n t
if qt+1< q∗,
Et+1 =
(11)


u
e
∗
S(Et ) + nt if qt+1 ≥ q .

Firms’ decision of creating job is the same as (6). From (11) and (6), we can derive

the dynamics of Et over generations:15



nt




Et+1 = either nt or S(Et ) + nut





S(E ) + nutt

if S(Et ) + nut < S ∗ ,if S(Et ) + nut ≥ S ∗ > nt ,(12)

if nt ≥ S ∗ .

Observe that, as shown by the third line of (12), there is only a thick market equilibrium
if free education is provided for more than S ∗ children (regardless of whether they arechildren of unskilled parents or not). Obviously, the problems of the dually trapped
economy can be solved all at once if the majority of people can receive education freely.
However, such a policy typically requires excessively large amount of expenditure in
one period, and thus often cannot be implemented within the limited budget (e.g.,financial aids).
In the following, we propose a two-step method in which the required budget ineach period is smaller. When nt < S ∗ , the dynamics of Et , determined by (12), can15

Since there are only S(Et ) children of skilled parents, the number of free education recipientamong them, nt − nut , cannot exceed S(Et ). Therefore, S(Et ) + nut ≥ (nt − nut ) + nut = nt .

19

Figure 4: Dynamic eﬀects of free education

be illustrated as in Figure 4. Suppose that the economy is initially in the dual poverty
trap and denote the initial period by 0: E0 = 0. If n1 young agents receive freeeducation in the initial period, they become educated and therefore E1 = n1 . Thatis, even though n1 is far smaller than S ∗ and therefore the economy stays in the thinmarket equilibrium, the new steady state level of Et is raised by n1 .
Then, in the following period, let nu2 = S ∗ − S(n1 ) children with uneducated parent
receive free education. S(E1 ) + nu2 reaches the threshold level S ∗ , and therefore, if
combined with appropriate policies that aﬀect the young agents’ expectation, sucha policy can realize the thick market equilibrium, in which E2 = S ∗ . Thereafter
the economy can trace the development path without further assistance since E3 =S(E2 ) = S(S ∗ ) > S ∗ , and so forth.
Not only this two-step method can diversify the required expenditure over two
periods, it can also reduce the total expenditure required before the full development
has been done. Let us return to the initial question of who should receive free education.
In the first step, the type of recipient does not matter. In that case, as a rule, provisionof free education for able students (in the model, those with skilled parents) may

20

be financially more reasonable.16 However, it must be noted in the second step theprovision of free education must be directed toward the unfortunate children born tounskilled parents. The activities of aid organizations in favor of unfortunate children
can be legitimized when such activities are parts of a long-running program.

6

Conclusions

Using an overlapping generations model of search equilibrium, this paper demonstrated
that limited intergenerational mobility and a coordination failure mutually reinforce
each other, generating a dual poverty trap, Escaping from the dual trap requires a
combined implementation of financial assistance for schooling and policies for changing agents’ expectation. When financial assistance is given by a uniform subsidy on
education, it benefits initially able children who are born to skilled parents but subsequently trickle-down to children in less favorable families. On the other hand, whenassistance is given as a form of free education to a limited number of children, it ismore eﬀective when it is given to children in less favorable situation. In both cases,
there is a threshold level for the size of financial assistance, and the assistance must
be continued for certain periods.
We suggest from this research that a combined approach to the intergenerationaland coordination traps, not a single approach to either one, is necessary to help low
income countries escape from the persistent poverty trap.

References[1] Acemoglu, Daron. (1997) “Training and Innovation in an Imperfect Labour Market.” Review of Economic Studies, Vol. 64: p. 445-464.

16

To compensate the opportunity cost of education, provision of free education for a child of skilledparents costs ez and that for a child of unskilled parents costs ez > ez.

21[2] Azariadis, Costas and Allen Drazen. (1990) “Threshold Externalities in Economic
Development.” Quarterly Journal of Economics, Vol. 105(2):p.501-26.
[3] Behrman, Jere. R. (1997) “Mother’s Schooling and Child Education: A Survey.”
PIER Working Paper 97-025, University of Pennsylvania.
[4] Behrman, Jere. R. and Mark R. Rosezweig. (2002) “Does Increasing Women’s
Schooling Raise the Schooling of the Next Generation?” American Economic
Review. Vol. 92, May: p.323-34[5] Burdett, Kenneth and Eric Smith. (2002) “The low skill trap.” European Economic
Review, Vol. 46: p.1439-1451.
[6] Bratti, Massimiliano. (2002) “Parents’ Current Income, Long-term Family Characteristics and Children’s Educational Outcomes: Evidence from the 1970s British
Cohort Study.” Warwick Economic Research Paper No. 658.
[7] Chamley, C.P. (2004) Rational Herds, Cambridge University Press.
[8] De la Croix, David and Phillips Michel (2002) A theory of economic growth: Dynamics and policy in overlapping generations. Cambridge University Press.
[9] Grootaert, Christiaan. (1999) “Child Labor in Cote d’Ivoire.”in Grootarert, C.
and Patrinos, H. (eds), The Policy Analysis of Child Labor: A Comparative Study,
New York: St Martin’s Press.
[10] Hoﬀ and Pandey (2004) “Belief Systems and Durable Inequalities: An Experimental Investigation of Indian Caste,” World Bank Policy Research Working Paper
3551.
[11] Laing, Derek, Theodore Palivos, and Ping Wang. (1995) “Learning, Matching and
Growth.” Review of Economic Studies, Vol.62: p.115-129.

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[12] Patrinos, H.A. and G. Psacharopoulos. (1997) “Family Size, Schooling and Child
Labor in Peru - An Empirical Analysis.” Journal of Population Economics, Vol.
10(4): p. 387-405.
[13] Ray, Ranjan. (2000) “Analysis of Child Labor in Peru and Pakistan: A Comparative Study.” Journal of Population Economics, Vol. 13(1): p.3-19.
[14] Rostow, W.W. (1990) The Stages of Economic Growth: A Noncommunist Manifesto, 3rd edition, Cambridge University Press.
[15] Strauss, John and Duncan Thomas (1995) “Human Resources: Empirical Modeling of Household and Family Decisions.” eds. Behrman and Srinivasan, Handbookof Development Economics, Elsevier.
[16] World Bank (2005)World Development Indicators 2005, World Bank.

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