Discussion Papers In Economics
And Business

From Physical to Human Capital Accumulation with
Pollution
Takumi Motoyama
Discussion Paper 16-03

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANFrom Physical to Human Capital Accumulation with
Pollution
Takumi Motoyama
Discussion Paper 16-03

March 2016

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANFrom Physical to Human Capital Accumulation with
Pollution∗
Takumi Motoyama †Graduate School of Economics, Osaka University
March 22, 2016

Abstract
This study examines the process of economic development in an overlapping generations model
where higher physical capital involves pollution and deteriorates the productivity of education. In thissetting, households may not invest into education and multiple steady states of the physical/humancapital ratio can arise, leading long-run production with low initial endowment (physical capital) tobe higher than that with high initial endowment. This occurs because, owing to the low productivity of education caused by pollution, only physical capital accumulation occurs with high initialendowment, while physical and human capital accumulation occur with low initial endowment. This
result is consistent with the resource curse. We also show that higher abatement technology can solve
the resource curse problem since it helps households redirect physical capital accumulation toward
human capital accumulation.
Keywords: Human capital, Pollution, Resource curse
JEL Classification Numbers: I15, O13, Q52∗

I am grateful to Masako Ikefuji, participants in the 2015 Japanese Economic Association Spring Meeting held at
Niigata University in Japan, and participants in the 12th Western Economic Association International held at Nanyang
Technological University in Singapore, for their helpful comments on this study. I especially thank Tatsuro Iwaisako for
his invaluable suggestions concerning this research. Needless to say, all remaining errors are my responsibility.
†
Graduate School of Economics, Osaka University, 1-7 Machikaneyama, Toyonaka, Osaka 560-0043, Japan. E-mail:pge028mt@student.econ.osaka-u.ac.jp.

1

Introduction
The phenomenon of the resource curse, the stylized fact that richer natural resources decrease

output and economic growth , often in developing countries, has been empirically studied by Sachs
and Warner (2001), Gylfason (2001), Mehlum et al. (2006), and Van der Ploeg (2011) among others.
Gylfason (2001) categorized four reasons for the resource curse: (1) the Dutch disease, (2) rent
seeking, (3) a reduction in the quality of government, and (4) neglect of education.
In this study, we focus on the fourth reason of Gylfason (2001), namely the neglect of education. 1 To examine why richer natural resources crowd out education, we assume that they entail
pollution, which deteriorates the productivity of education. If we regard natural resources as oil, coal,and natural gases, richer natural resources release poisonous substances and greenhouse gas emissions; intuitively, a higher level of pollution decreases human capital such as education and health.
Empirically, there is a negative relationship between human capital accumulation, especially healthand education, and pollution intensity (e.g., Carrie et al. (2009), Graﬀ and Niedell (2012), Beatty andShimshack (2014)). More pollution increases the risk of health and disasters, which negatively aﬀects
the productivity of educational expenditure.
Based on the foregoing, in this study we construct an overlapping generations model that contains
pollution and human capital accumulation, and that admits zero educational expenditure in equilibrium by employing a linear human capital production function with a positive intercept. Such a humancapital production function used, for example, by Galor and Moav (2004) and Moav (2005), is characterized by the existence of two properties: (i) basic skills and (ii) a finite marginal productivity ofeducational expenditure (even at zero educational expenditure). By using this function, we examine
the relationship between human capital accumulation and pollution and obtain an entire dynamic pathof the physical/human capital ratio and human capital investment.
Based on this model, we show that three patterns of dynamics of the physical/human capitalratio exist, while two steady states occur in one of these cases. In Regime 1, only physical capital
accumulates with high initial physical capital, whereas in Regime 2, both physical and human capital
1

From the view of the Dutch disease, Sachs and Warner (1995) studied the resource curse theoretically. Mehlum et al.
(2005) did so from the view of rent seeking and Robinson et al. (2006, 2014) did so from the view of overconfidence (areduction in the quality of government).

1

accumulate with low initial physical capital. Furthermore, we show that there is a parameter region inwhich the production of the latter case exceeds that of the former case. Thus, an economy with highinitial endowment attains lower long-run production than one with low initial endowment, which isindeed a resource curse because high initial endowment results in lower long-run production. Since
the resource curse problem is a poverty trap, it should be addressed by implementing policy. From thisperspective, we show that higher abatement technology, which implies a lower marginal reduction in
the productivity of education caused by pollution, with no cost can solve the resource curse problem.
The implementation of such technology not only increases long-run production in Regime 2, butalso makes a regime shift likely to occur. This is because higher abatement technology increases the
productivity of education and helps households redirect physical capital accumulation toward humancapital accumulation, which in turn shifts the regime and increases the long-run production.
Some models treat human capital accumulation and pollution at the same time in order to analyze
these relationships (Gradus and Smulders (1993), Bovenverg and Smulders (1995), Schou (2000),
Ikefuji and Horii (2012), Sapci (2013). In these models, Ramsey model is used, and (at least asymptotically) endogenous growth generates. These analyze how the parameters of pollution and policies
aﬀect the growth rate of production. In such models, however dirty the economy is, positive humancapital investment is required in equilibrium. As these models are an extension of the Uzawa–Lucasmodel and the economy is on the balanced growth path in the long run, educational expenditure must
be positive in order not to lead to a zero growth rate, which means that multiple steady states do notoccur. Thus, we cannot use such models to analyze an environmental trap such as the resource curse.
By contrast, the presented model can admit zero educational expenditure with multiple steady states.
This is one of the contributions of this study. Although Raﬃn (2012) constructed a model similar
to the one we construct, her model considered an endogenous mitigation policy instead of physicalcapital accumulation and concentrated on the environmental Kuznets curve (EKC), 2 which we alsomention in Section 3.
The remainder of this paper is organized as follows. Section 2 presents the model and obtains
dynamic equations that describe the equilibrium of this economy. Section 3 shows the comparative
2

The EKC is an inverse U-shaped relationship between production (or economic growth) and pollution, as pointed by
Grossman and Kruger (1995) and others. That is, an economy with low production grows with higher production andpollution, while an economy with high production grows with higher production and lower pollution.

2

statics with respect to abatement technology and discusses the problem of the resource curse and, atthe same time, briefly the EKC. Section 4 summarizes the findings and concludes.

2

The Model

The model is described by discrete time and closed economy. There exist a household and a firm. We
employ two-period overlapping generations model with altruism. The initial population is one andthe population does not grow. Two types of capital exist, namely physical and human capital, both ofwhich depreciate completely after one period. Physical capital accumulation accompanies pollution,
which decreases the productivity of human capital investment.

2.1

A firmA final good is produced by using physical capital Kt , which is also interpreted as resources, 3 andhuman capital Ht as follows.
Yt = AKtα Ht1−α = Ht f (kt ),(1)

where kt ≡ Kt /Ht is the physical/human capital ratio and f (kt ) ≡ F(Kt , Ht )/Ht is production per unitof human capital. Then, the profit maximization conditions are given by
rt = Aαktα−1 ≡ r(kt ),(2)

wt = A(1 − α)ktα ≡ w(kt ),(3)

where rt is the rental rate and wt is the wage per unit of human capital.

2.2 A household
We call the generation born in period t − 1 the t-generation. In period t − 1, t-generation does notconsume and receives education from her parent. We assume that the parent is altruistic and that she
gains utility not only from her own consumption but also from her oﬀspring’s income. Then, in periodt, the parent decides her consumption ct , educational expenditure to her oﬀspring et+1 , and transfer

3

To regard Kt as (natural) resources, let us assume that natural resources, especially fossil fuels, are openly available
but specific equipment is required to extract it. That is, Kt is like an oilrig or heavy machinery. Then, the amount of Kt is
proportional to that of resources.

3

to her oﬀspring st+1 . When we denote ht as human capital per capita, t-generation has the following
utility function. 4
ut = (1 − β) ln ct + β ln(wt+1 ht+1 + rt+1 st+1 ).

(4)

The parameter β ∈ (0, 1) is the degree of altruism; that is, higher β implies stronger altruism. The
budget constraint is given by
wt et+1 + st+1 + ct = wt ht + rt st ≡ It .

(5)

The right-hand side (RHS) is t-generation’s income, which we denote It , and the left-hand side (LHS)
is a composite of expenditure that consists of educational expenditure, the transfer for the oﬀspring,and consumption. Educational expenditure incurs an educational cost wt following Moav (2005),
Galor and Weil (2000), and De la Croix and Doepke (2003).
The human capital production function is given by
ht+1 = h(et+1 , kt ),(6)

where it is assumed that h1 > 0, h11 ≤ 0, h2 < 0, h(0, kt ) = 1, and h1 (0, kt ) ∈ (0, ∞). 5 Threepoints are worth mentioning on this production function. Firstly, we assume that the human capitalformed in the next period, h(et+1 , kt ), is decreasing in not pollution level Kt , but in the physical/humancapital ratio kt , which reflects two eﬀect. One is that more physical capital stock Kt reduces the levelof human capital. In reality, more physical capital, or resources such as oil, tends to cause morepollution, which reduces the productivity of education. The negative relationship between ht+1 andKt reflects this actual tendency. The other is that a positive knowledge spillover from the previous
knowledge, that is, Ht+1 , is increasing in Ht . In this production function, the homogeneity of degree 0
between Kt and Ht is assumed and hence Ht+1 depends directly on physical capital per unit of humancapital kt . Secondly, even if a parent does not invest into education, et+1 = 0, her oﬀspring attains abasic skill, which is normalized to 1. Here, it is assumed that a basic skill is unaﬀected by the intensity
4

We do not consider the negative direct eﬀect of pollution on utility in contrast to John and Pecchenino (1994), andPrieur and Brechet (2013). As long as a disutility from pollution is introduced in an additively separable form such as
ut + ν(Kt ), such an introduction does not aﬀect the equation stated below. If we introduce it in a non-separable form, it
can aﬀect the utility maximization condition; however this makes this model solution too complicated despite having lessinteresting implications, and hence we omit this eﬀect.
5
Such a human capital production function is also employed by Galor and Moav (2001) and Moav (2005).

4

of pollution Kt for simplicity., which is expressed by h(0, kt ) = 1. Finally, the marginal productivityof educational expenditure at zero is positive and finite for any kt ; h1 (0, kt ) ∈ (0, ∞). This fact implies
that the Inada condition is not satisfied and that a household may decide zero educational expenditure
optimally. In equation (9), we specify the form of human capital production function.
The utility maximization problem for t-generation is given bymax (4){ct ,et+1 ,st+1 }

s,t, (5), (6), et+1 ≥ 0 and st+1 > 0, given st > 0, et ≥ 0.
Before solving this model, note that st+1 must be an interior solution since, otherwise, production
per unit of human capital becomes zero and at that time, the interest rate becomes infinity and thehousehold should save, which contradicts st+1 = 0. Then, from the first-order conditions in et+1 andst+1 and the profit maximization conditions, we have 6
if w(kt )r(kt+1 ) > w(kt+1 )h1 (0, kt )0
et+1 = > 0 if w(kt )r(kt+1 ) = w(kt+1 )h1 (0, kt ).

(7)This equation is easy to understand. One unit of educational expenditure from zero increases theincome of the oﬀspring by wt+1 h1 (0, kt ). At the same time, since one unit of educational expenditure
costs a parent an educational cost wt , the resultant marginal benefit for a parent to invest educational
expenditure from zero is given by wt+1 h1 (0, kt )/wt . On the contrary, since more educational expenditure crowds out transfers for the oﬀspring, the child’s income decreases by rt+1 . If the former
dominates the latter, educational expenditure arises and vice versa.
From the first-order conditions of consumption and transfers, each of which holds with equality,and from the budget constraint, ct = It − wt et+1 − st+1 we obtainst+1 = β(It − wt et+1 ) − (1 − β)wt+1h(et+1 , kt ).
rt+1

(8)

Hereafter, the human capital production function is specified as follows.
h(et+1 , kt ) = 1 +1
et+1 .
γ−1 + vkt

(9)

6
The case that wt rt+1 < wt+1 h1 (0, kt ) cannot occur since then the Kuhn–Tucker multiplier for educational expenditure
would become negative, which would contradict one of the optimality conditions. Indeed, st+1 > 0 excludes this case, forunder wt rt+1 < wt+1 h1 (0, kt ), even at et+1 = 0, the marginal benefit from education dominates that from a transfer, and hence,st+1 becomes zero.

5In the above specification, γ denotes the marginal productivity of educational expenditure without pollution h1 |v=0 = γ. Moreover, v denotes the vulnerability to damage from pollution. A higher v
implies more severe damage given the same physical/human capital ratio kt .Conversely, higher abatement technology, which decreases the damage caused by pollution, is represented by a decrease in v.
From (9) and the profit maximizing conditions, the condition under which educational expenditure ispositive, et+1 > 0, becomes
kt+1 ≥ α(γ−1 + vkt ) f (kt ) ≡ θ(kt ).

(10)

The function θ(kt ) is an increasing function, and is concave for small kt and convex for large kt . 7 Since
we specify the human capital production function as a linear function of educational expenditure as(9), the term et+1 no longer exists in (10). The inequality (10) must hold if educational expenditureis positive for the following reasons. The current capital stock per unit of human capital kt has
two negative eﬀects on the incentive to spend on education. One is that more current capital stock
accompanies more pollution, which reduces the marginal eﬃciency of educational expenditure. The
other is that more capital stock increases the opportunity cost for educational expenditure given byw(kt ). Only when the next capital stock is suﬃciently high such that the next wage w(kt+1 ) dominates
these two negative eﬀects from the current capital stock, can positive educational expenditure arise.
When kt+1 < θ(kt ), there exists no educational expenditure. That is, et+1 = 0. Given that t − 1
generation has educational expenditure et ≥ 0, from (8), the transfer is given by
st+1 = βIt − (1 − β)

wt+1
wt+1
= β[wt h(et , kt−1 ) + rt st ] − (1 − β)
.
rt+1
rt+1

The physical capital market-clearing condition is
kt =

st+1
st
, kt+1 == st+1 .
h(et , kt−1 )h(0, kt )Therefore, by using profit maximization conditions, the dynamics of kt under zero educational expen-

7

The second derivative of θ(kt ) is given by
θ′′ (kt ) = Aα2 ktα−2 [(1 + α)vkt − (1 − α)γ−1 ].

Hence, the inflection point is given by kt = (1 − α)/[(1 + α)vγ] > 0.

6

diture are
kt+1 = β[w(kt ) + r(kt )kt ]h(et , kt−1 ) − (1 − β)= β f (kt )h(et , kt−1 ) − (1 − β)w(kt+1 )r(kt+1 )1−αkt+1 .
α

By solving the above expression for kt+1 , the dynamics of the physical/human capital ratio become
kt+1 =αβf (kt )h(et , kt−1 ) ≡ ϕ(kt )h(et , kt−1 ),α + (1 − β)(1 − α)(11)where ϕ(kt ) ≡ αβ f (kt )/[α + (1 − β)(1 − α)] is an increasing and concave function. Furthermore, if theprevious educational expenditure is 0, that is et = 0, (11) can be simplified to
kt+1 = ϕ(kt ).

(12)

On the contrary, if et > 0, then as shown later, kt = θ(kt−1 ) must be satisfied in the previous period,and (11) becomes
kt+1 = h(et , θ−1 (kt ))ϕ(kt ),, where θ−1 (•) is an inverse function of θ(•). 8
Once kt+1 ≥ θ(kt ) is realized, positive educational expenditure arises, that is, et+1 > 0. In sucha case, the optimal transfer must satisfy kt+1 = θ(kt ). Otherwise, that is, if kt+1 > θ(kt ) holds, themarginal utility from educational expenditure dominates that of the transfer, and hence, st+1 becomes
0. However, since st+1 must be an interior solution as mentioned before, it is contradictory. In thiscase, from (8) and the profit maximization conditions, the transfer is given by
st+1 = β[w(kt )h(et , kt−1 ) + r(kt )st − w(kt )et+1 ] − (1 − β)w(kt+1 )h(et+1 , kt ).
r(kt+1 )If educational expenditure is positive in the previous period, et > 0, then kt = θ(kt−1 ), equivalently
kt−1 = θ−1 (kt ), andst+1 = β[w(kt )h(et , θ−1 (kt )) + r(kt )st − w(kt )et+1 ] − (1 − β)w(kt+1 )h(et+1 , kt ).
r(kt+1 )The physical capital market-clearing condition is
kt+1 =

st+1⇔ st+1 = kt+1 h(et+1 , kt ).
h(et+1 , kt )The inverse function θ−1 (kt ) can be derived by solving kt = θ(kt−1 ) for kt−1 . Although we cannot obtain an explicit formof θ (kt−1 ), since θ(kt ) is monotonically increasing, the inverse function exists.
8

−1

7

Hence,θ(kt )h(et+1 , kt ) = β[w(kt )h(et , θ−1 (kt )) + r(kt )kt h(et , θ−1 (kt )) − w(kt )et+1 ] − (1 − β)w(kt+1 )h(et+1 , kt ).
r(kt+1 )Substituting the profit maximization conditions, and the definition of θ(kt ) and h(et+1 , kt ), and thensolving the resultant expression for et+1 lead toet+1 = βh(et , θ−1 (kt )) − [α + (1 − β)(1 − α)](γ−1 + vkt ).

(13)This equation is a dynamic equation of educational expenditure et+1 when et , 0, and the case where
no educational expenditure is in the previous period, et = 0, is the same equation as (13) with et = 0.
To simplify the dynamics of the physical/human capital ratio, we impose the following assumption.
Assumption 1 The economy starts with zero educational expenditure; e0 = 0 and positive physicalcapital stock K0 > 0.
This assumption also implies that the initial physical/human capital ratio is positive since k0 =K0 /H0 = K0 > 0 given that H0 = h(0, k−1 ) = 1 irrespective of k−1 .
We can divide the regime based on whether educational expenditure is positive or zero. We callthe regime where t-generation receives no education (et = 0) Regime 1 in period t. By contrast, whent-generation receives an education (et > 0), we call this regime Regime 2. Since we assume e0 = 0,
the economy is in Regime 1 in the initial period. When t-generation with no educational expenditureinvests in educational expenditure for her oﬀspring, et+1 > 0, the economy shifts from Regime 1 toRegime 2. Once the economy moves to Regime 2, it follows kt+1 = θ(kt ) and stays in Regime 2 until
et+1 = 0 is optimal.
In Regime 1, the dynamics are described by kt+1 = h(et , kt−1 )ϕ(kt ) and et+1 = 0. In particular, if
the parent has no education, et = 0, the economy follows kt+1 = ϕ(kt ). Since ϕ(kt ) is increasing andconcave with ϕ(0) = 0, this economy monotonically converges to its steady state k1∗ , which is given
by
k1∗ =

(

Aαβ
α + (1 − β)(1 − α))1/(1−α).

For the economy to shift from Regime 1 to Regime 2, the parent with no education must have an
incentive to invest into education for her oﬀspring. Then, how does the parent decide to invest into8

Figure 1: ϕ(kt ) and θ(kt ) when k̄ > 0

Figure 2: Two positive steady–state values of k2∗

education ? To answer this, we define k̄ as follows:
(
)
1
β
−1
ϕ(k̄) = θ(k̄) ⇔ k̄ =−γ .
v α + (1 − β)(1 − α)(14)The threshold k̄ is uniquely determined, which implies that if ϕ(kt ) and θ(kt ) intersect, only one point
arises. Therefore, by considering the curvature of θ(kt ), if k̄ > 0, the positional relationship shown in
Figure 1 is realized. Hereafter, we focus on the parameter values such that k̄ > 0. Hence, we assume
the following.
Assumption 2 Assume that k̄ > 0. That is,β> γ−1 .
α + (1 − β)(1 − α)(A.1)

This assumption guarantees that ϕ(kt ) and θ(kt ) must intersect at k̄ > 0. In other words, thepositional relationship in Figure 1 holds. Then, we show the following lemma corresponding to theshift from Regime 1 to Regime 2.
Lemma 1 If the economy is in Regime 1 in period t, that is, et = 0, the economy with Kt > k̄ has
no educational expenditure (stays in Regime 1), while the one with Kt ≤ k̄ has positive educational
expenditure (shifts to Regime 2).

9Proof.
Since we assume that et = 0, if educational expenditure is paid, from (13), et+1 = β − [α + (1 −β)(1 − α)](γ−1 + vkt ) holds. Hence, at kt = k̄, et+1 = 0, that is, educational expenditure becomeszero. Further, since et+1 is decreasing in kt , when kt > k̄, et+1 becomes negative. However, negativeeducational expenditure is not admitted and et+1 is zero. On the contrary, when kt < k̄, et+1 becomes
positive. 
Lemma 1 states that when the level of physical capital is low in Regime 1, the economy is likely
to shift to Regime 2 because it has less pollution with low physical capital, which induces humancapital accumulation due to a lower decrease in the marginal productivity of education. Next, weconsider the shift from Regime 2 to Regime 1. To show the regime shift, we again use (13) and obtainthe following lemma.
Lemma 2 If the economy is in Regime 2 in period t, that is, et > 0, when h(et , θ−1 (kt ))ϕ(kt ) ≥θ(kt ) is satisfied, positive educational expenditure arises (stays in Regime 2). On the contrary, whenh(et , θ−1 (kt ))ϕ(kt ) < θ(kt ) is satisfied, educational expenditure becomes zero (shifts to Regime 1).
Proof.
From (13), if et > 0, et+1 becomes as follows.
et+1 = βh(et , θ−1 (kt )) − [α + (1 − β)(1 − α)](γ−1 + βkt )()α + (1 − β)(1 − α)
αβ
−1
−1
=
h(et , θ (kt ))f (kt ) − α(γ + βkt ) f (kt )α f (kt )α + (1 − β)(1 − α)=)
α + (1 − β)(1 − α) (h(et , θ−1 (kt ))ϕ(kt ) − θ(kt ) .
α f (kt )Since k0 > 0 and kt do not converge to zero, f (kt ) must be positive for all t, and hence if h(et , θ−1 (kt ))ϕ(kt ) >θ(kt ) is satisfied, positive educational expenditure is realized, while if h(et , θ−1 (kt ))ϕ(kt ) < θ(kt ) is satisfied, zero or negative educational expenditure arises. However, since educational expenditure cannot
be negative, educational expenditure becomes zero, and hence, when h(et , θ−1 (kt ))ϕ(kt ) < θ(kt ), theoptimal educational expenditure is zero. As shown in Figure 3, the condition that h(et , θ−1 (kt ))ϕ(kt ) ≥ θ(kt ) implies that a relatively low
physical/human capital ratio kt is realized when the economy is in Regime 2. Similar to the logic ofLemma 1, since the economy is not as polluted in this case, it can invest into education. Note that10

even when kt = k̄, educational expenditure is positive, that is, if the economy is in Regime 2, there ispositive education and the economy stays in Regime 2 at kt = k̄ in contrast to Lemma 1. 9
In Regime 2, the physical/human capital ratio is determined by kt+1 = θ(kt ). The steady–statelevel of the physical/human capital ratio in Regime 2 is given byk2∗ = θ(k2∗ ), ⇔ k2∗ 1−α = Aα(γ−1 + vk2∗ ).

(15)

From Figure 2, we can obtain at most two fixed points of θ(kt ). We do not ignore the case of no fixed
points, and if any, we label two fixed points as k2∗ and k2∗+ , where k2∗+ > k2∗ . 10 From Figure 2, we
confirm that higher vulnerability v leads to an increase in k2∗ and a decrease in k2∗+ since a higher v
shifts θ(kt ) downward.

2.3 Dynamics of kt
There exist three patterns of dynamics of the physical/human capital kt , and we focus on the casewhere multiple steady states are generated. Let us assume that θ(kt ) has two distinct fixed points,
namely k2∗ and k2+∗ exist, and that k̄ < k1∗ . 11 The phase diagram of kt in this case is depicted in Figure
3. Depending on the initial capital stock K0 = k0 , we can classify the following three patterns oftransitional dynamics.
1. k0 > k̄: In this case, θ(k0 ) > ϕ(k0 ) and the economy stays in Regime 1 according to Lemma 1.
Since in the transition, θ(kt ) > ϕ(kt ) holds, the economy follows the dynamics that kt+1 = ϕ(kt )and monotonically converges to k1∗ .
9Under kt = k̄, educational expenditure is positive for any et > 0 since)
1 (( ) h(et , θ−1 (k̄))ϕ(k̄) − θ(k̄)
f k̄
( )
)
ϕ k̄ (αβet( ) > 0,= ( ) h(et , θ−1 (k̄)) − 1 =
α + (1 − β)(1 − α) γ−1 + vθ−1 k̄
f k̄

et+1 =

where the second equality holds since ϕ(k̄) = θ(k̄) from the definition of k̄. This fact implies that when the economy is in
Regime 2, the economy does not shift into Regime 1 and stays in Regime 2 even under kt = k̄.
10Strictly speaking, we ignore the case of only one fixed point. This case arises only when the derivative of θ(kt ) is equal
to 1 at the fixed point. Such a condition is knife-edge, and hence we do not consider this case. However, by using a similar
procedure to that stated below, we can treat this case.
11
The cases in which θ(kt ) has two distinct fixed points but k̄ > k1∗ , and in which θ(kt ) has no fixed points are analyzed inAppendix 1. There, it is shown that for any k0 , the economy eventually converges to k2∗ in the former case, and it converges
to k1∗ in the latter case.

112. k2∗+ < k0 < k̄: In this case, since ϕ(k0 ) > θ(k0 ), and from Lemma 1, the economy shifts to
Regime 2 initially. Then, the economy follows kt+1 = θ(kt ), and since k2∗+ is unstable andthe considered region is higher than k2∗+ , the economy tends to diverge. However, as shownin the next subsection, since educational expenditure falls as kt accumulates, in finite time
the optimal educational expenditure, et becomes zero. Thus, such a divergence does not lastforever. Explicitly, when educational expenditure is positive in period T but is zero in period
T + 1, that is eT +1 = 0 with a physical/human capital ratio kT , the function h(eT +1 , kT )ϕ(kT +1 )becomes ϕ(kT +1 ); then, in period T + 1, θ(kT +1 ) > ϕ(kT +1 ) must be satisfied. This fact implies
that before period T + 1 is period T e , which satisfies θ(kt ) < h(et , kt−1 )ϕ(kt ) in period t < T e , andafter period T e , θ(kt ) > h(et , kt−1 )ϕ(kt ). Then, from Lemma 2, the economy shifts to Regime
1 in period T e , and after period T e + 1, the economy follows kt = ϕ(kt ) and monotonicallyconverges to k1∗ .
3. k0 < k2∗+ : In this case, the economy also shifts to Regime 2 initially since ϕ(k0 ) > θ(k0 ).
However, now that k0 < k2∗+ , the economy moves to the other stable steady state k2∗ . For
k0 < k2∗ , kt monotonically increases, while for k0 ∈ (k2∗ , k2∗+ ), kt monotonically decreases towardk2∗ .
Hence, if k̄ < k1∗ , that is, if the threshold at which the household decides not to invest into education is low, multiple steady state are generated. If the initial physical capital is suﬃciently low
such that k0 < k2∗+ , the economy is always (except for period 0) in Regime 2, while the economy iseventually in Regime 1 if the initial physical capital is high such that k0 > k2∗+ . This fact implies thatthe long-run physical/human capital ratio with low initial physical capital is less than the long-run
physical capital with high initial physical capital. This results in greater production per unit of humancapital f (kt ) with high k0 than with low k0 . However, this does not imply that long-run production
with low k0 is less than that with high k0 since human capital is accumulated in the case of low k0 , andthus the resultant production can be larger than that with high k0 . We analyze this point in Section 3.
In summary, we obtain the following proposition.
Proposition 1 Suppose Assumptions 1 and 2. Further, assume that θ(kt ) has two distinct fixed points,

12

Figure 3: The phase diagram of kt when θ(kt ) has two distinct fixed points and k̄ < k1∗
and k̄ < k1∗ . Then, the economy with k0 < k2∗+ converges to k2∗ , and the economy with k0 > k2∗+
converges to k1∗ .

2.4

Dynamics of et

In Regime 2, educational expenditure is positive and we must consider the dynamics of educational
expenditure et , (13). Since the physical/human capital ratio kt is predetermined independently of
educational expenditure, we can treat kt as an exogenously determined variable. When the economy
shifts to Regime 2 in initial period, kt < k̄ is realized. Hereafter, we consider the case that the two
fixed points of θ(kt ) are less than k̄, that is, k∗+ < k̄. Slightly rewriting (13) yields
et+1 =

[
]
β
−1
e
+
β
−
[α
+
(1
−
β)(1
−
α)(γ
+
vk
)
≡ et+1 (et , kt ).
tt
γ−1 + vθ−1 (kt )(16)

By regarding kt as an exogenous variable because kt is a predetermined variable, et+1 is linear in etwith intercept β − [α + (1 − β)(1 − α)](γ−1 + vkt ). Note that when kt < k̄, this intercept is positive.
Since the slope and intercept of (16) are decreasing in kt , if the economy starts with k0 < k2∗ , overtime, the intercept decreases toward β − [α + (1 − β)(1 − α)](γ−1 + vk2∗ ) and the slope becomes flat13

toward β/(γ−1 + vk2∗ ). 12 The condition that educational expenditure converges to its steady state( i.e.,the slope of (16) becomes less than 1) is given by γ−1 + vk2∗ > β. In this case, the steady–state valueof educational expenditure is obtained by substituting et = et+1 = e∗ and kt = k2∗ into (16) as
γ−1 + vk2∗e∗ = [β − [α + (1 − β)(1 − α)](γ−1 + vk2∗ )] −1.
γ + vk2∗ − β(17)From the convergence condition, γ−1 + vk2∗ > β, the denominator of (17) is positive, and since k2∗ isless than k̄, the term β − [α + (1 − β)(1 − α)](γ−1 + vk2∗ ) is also positive. Hence, e∗ is positive. The
steady-state value of human capital is given by
γ−1 + vk2∗.
h∗ = β(1 − α) −1
γ + vk2∗ − β(18)

On the contrary, when the slope of (16) at kt = k2∗ is larger than one, that is, β > γ−1 + vk2∗ , educational
expenditure diverges. In such a case, instead of the steady-state value of educational expenditure, we
can obtain the long-run growth rate of educational expenditure as follows:
lim

t→∞

β
et+1
≡ ge > 1.
= −1
et
γ + vk2∗(19)

Furthermore, human capital grows at the same rate as educational expenditure in the long run, for
γ−1 + vk2∗ + ge et
ht+1
lim= ge ,(20)= lim
t→∞ htet →∞ γ−1 + vk∗ + et2
where the second equality holds from L’Hôpital’s rule.
Note that when kt diverges beyond k̄, educational expenditure becomes zero in finite time. In the
period that kt = k̄, the intercept of (16) is zero, while the slope of (16) is positive. 13 Hence, if previous
educational expenditure is positive, in the period that kt = k̄, positive educational expenditure arises.
However, for kt > k̄, the intercept of (16) becomes negative, although the slope of (16) is still positive.
This finding implies that the optimal educational expenditure becomes zero in finite time. Since
educational expenditure cannot be negative, zero educational expenditure arises thereafter. Once theeconomy shifts to Regime 1, it follows kt = ϕ(kt ) and kt monotonically increases toward k1∗ . Hence,on the transition after the regime shift, there is no incentive for the parent to invest into education
since the level of physical/human capital is much higher than the level that she gives up investing into
education for her oﬀspring.
Note that θ−1 (k2∗ ) = k2∗ since k2∗ is a fixed point of θ(kt ).
From the definition of k̄, the slope of e(et , k̄) is given by α + (1 − β)(1 − α), which is less than one. For kt < k̄, the slopee(et , kt ) is larger than α + (1 − β)(1 − α) since k2∗ < k̄ must hold to stay in Regime 2.
12

13

14

2.5

Long-run production

Finally, we derive long-run production in Regimes 1 and 2. In the long run, the physical/humancapital ratio converges to k1∗ in Regime 1 and to k2∗ in Regime 2. Since educational expenditure is zeroin Regime 1, long-run production in Regime 1 is given by)α/(1−α)
(
Aαβ
∗
∗
∗α
.
Y1 = f (k1 ) = Ak1 = A
α + (1 − β)(1 − α)
In Regime 2, there exist two scenarios, namely et → ∞ and et → e∗ . In the former case, long-run
production grows at the same rate as human capital ge , since it is a product of human capital andproduction per unit of human capital, which is constant. In the latter case, the production per unit ofhuman capital is less than that in Regime 1, f (k2∗ ) < f (k1∗ ); however, now human capital accumulationarises as in (18). When et → e∗ , long-run production in Regime 2 is given by
Y2∗ = h∗ f (k2∗ ) =k2∗β(1 − α),αγ−1 + vk2∗ − β(21)where we use f (k2∗ ) = k2∗ /[α(γ−1 + vk2∗ )] from the steady state condition, (15).

3Resource curse problem

3.1

Resource curse problem

The previous subsection implied that whether long-run production in Regime 1 is lower than thatin Regime 2 is ambiguous. That is, long-run production in Regime 1 could be larger less than thatin Regime 2, although the initial resources (physical capital) is higher in Regime 1 than Regime 2.
This phenomenon is known as resource curse since high initial resource allocation eventually leads
to lower production than that with low initial resource allocation. When the economy is in Regime 1
in the long run though Y2∗ > Y1∗ , the resource curse problem arises. Then, in which parameter regionis the resource curse likely to occur? Moreover, if the economy lapses into the resource curse case, is
it solvable, and if so, how? We examine these problems in this subsection.
Naturally, when et diverges, production in Regime 2 must be larger than that in Regime 1 in thelong run. Production in Regime 1 converges to a positive value, while that in Regime 2 diverges at thesame growth rate as human capital ge . In such a case, the resource curse occurs. Hereafter, we showthat even in the case of et → e∗ , there is room for the resource curse. Long-run production in Regime15

2 (21) contains not only A, β, and α, but also v and γ, which are not contained in long-run production
in Regime 1, and we concentrate on the vulnerability from pollution, v. As shown in equation (Ap.1)
in Appendix 2, we obtain the following sign or the derivatives:
∂Y2∗
< 0.
∂v

(22)

This fact implies that less vulnerability can cause the resource curse since this change increases longrun production in Regime 2 Y2∗ , while production in Regime 1 Y1∗ is unaﬀected. Hence, lower v ismore likely to cause the resource curse problem. 14 Inequality (22) is intuitive, but still somewhat
interesting. If vulnerability becomes small, the parent wants to invest into education, and hence
she increases educational expenditure and decreases the transfer. Hence, human capital increases
and physical capital decreases, making the change in long-run production ambiguous. However,according to (22), an increase in human capital must dominate a decrease in physical capital.

3.2

Comparative dynamics

In what follows, we show that higher abatement technology can not only increase production in
Regime 2 but also make the economy shift from Regime 1 to Regime 2. Higher abatement technology implies less vulnerability to pollution, leading to a decrease in v. As shown in (22), production in
Regime 2 is decreasing with respect to v. Thus, higher abatement technology can increase production
in Regime 2. Furthermore, the lower v becomes, the greater is the likelihood that educational expenditure diverges because the divergence condition of educational expenditure is given by γ−1 + vk2∗ < β,and a lower v implies lower vk2∗ , where it is verified that ∂vk2∗ /∂v > 0. Therefore, by using higher
abatement technology, this inequality is likely to be satisfied, which implies a higher possibility of
the resource curse problem arising given that the economy has remained in the same regime.
Even if we concentrate on the case that educational expenditure does not diverge, the resource
curse problem can be solved. From Figure 2, we can obtain a negative sign of the derivatives of k2∗+
14

If we calculate the condition that long-run welfare in Regime 2 is higher than that in Regime 1, we have the following:
(
)1−β
β
Y2∗ >
Y1∗ .
(γ−1 + vk2∗ )(α + (1 − α)(1 − β))Since the coeﬃcient of Y1∗ is larger than one, even when an economy has the resource curse problem, that is, Y2∗ > Y1∗ ,although the economy is in Regime 1, this does not necessarily imply that to shift the regime improve its welfare. However,higher abatement technology decreases the coeﬃcient of Y1∗ , meaning that an introduction of suﬃciently high abatement
technology can help the economy escape from the resource curse and improve its welfare.

16Figure 4: The comparative dynamics in the case of a decrease in v.
with respect to v, that is,

∂k2∗+
< 0.
∂v
The threshold at which educational expenditure occurs in the long run when the initial physical/capitalstock falls below it (see Proposition 1), k2∗+ , is decreasing in v. That is, higher abatement technology
widens makes the region in which positive educational expenditure arises and the economy is thus
likely to shift to Regime 2. A similar eﬀect arises when the marginal productivity of educational
expenditure γ increases.
The comparative dynamics are illustrated in Figure 4. Consider the dynamics of kt that has multiple steady states. Suppose, first, that the economy is in the steady state in Regime 1 with the resource
curse problem (i.e., the economy is at point E1 in Figure 4 with Y2∗ > Y1∗ ). Then higher abatement
technology (i.e., a decrease in v) is introduced. As shown before, since production in Regime 2 isdecreasing in v, higher abatement technology guarantees Y2∗ > Y1∗ . Since ∂k̄/∂τ < 0 and ϕ(kt ) do
not depend on v, the decrease in v leads to a shift of θ(kt ) downward, as shown in Figure 4 (a shift
from θ(kt ) to θ̃(kt )), while ϕ(kt ) remains unchanged. Furthermore, Figure 4 depicts the case where the17resultant k̄′ (> k̄) exceeds k1∗ . Then, after the parameter changes, now that ϕ(k1∗ ) > θ′ (k1∗ ) at point E1 ,the economy shifts to Regime 2 according to Lemma 1, and the economy monotonically converges
to k2∗ ′ (< k2∗ ) thereafter, which is point E2 in Figure 4. As for educational expenditure, the interceptof (16) shifts upward and the slope of it becomes steeper, which implies an overall increase in educational expenditure. Although the steady-state level of kt decreases in comparison with the original
point, positive educational expenditure arises, and the resultant long-run output must be higher thanthe original one.
In summary, the following proposition is derived.
Proposition 2 Suppose that Assumptions 1 and 2 hold. Then, higher abatement technology increases
long-run production in Regime 2 Y2∗ , and the resulting threshold of the physical/human capital ratiok2∗+ . That is, higher abatement technology can solve the resource curse problem.
Moreover, the comparative dynamics implies the EKC. Assume that an economy has an initial
capital stock of {k̄, k1∗ } and that the economy evolves in Regime 1 initially. Since k0 < k1∗ , the economy monotonically increases toward k1∗ , and hence production monotonically rises. By contrast, theeﬀective pollution, which is given by the ratio of pollution and human capital level vkt , also rises
since kt monotonically increases in the transition. Here assume that at some time, for example, attime τ, higher abatement technology is introduced and v decreases exogenously. As shown before,
suﬃciently higher abatement technology shifts the economy from Regime 1 to Regime 2. Then, sincek2∗ < k̄ and the resulting steady-state level of the physical/human capital ratio in Regime 2 k2∗ ′ is lessthan k2∗ , kt monotonically decreases after τ and the eﬀective pollution vkt also decreases. If the resulting long-run production in Regime 2, Y2∗ (k2∗ ′ ), is higher than production in period τ, Y1 (τ), in finite
time after τ, production must also increase. Thus, in early periods, the economy grows with higher
production and pollution, and in late periods, it grows with higher production and less pollution,
which is consistent with the EKC.
The EKC arises from the following reason. In early periods, the economy has high pollution
and a parent leaves a transfer to her oﬀspring instead of investing into education. Then, physicalcapital accumulates more and pollution increases. However, if suﬃciently high abatement technology
is introduced, the parent finds it beneficial to invest into education and redirects the transfer for her
18

oﬀspring toward educational expenditure; hence, pollution decreases, while production still increases.
This mechanism is similar to that proposed by Raﬃn (2012), although the EKC arises endogenously
in her model since mitigation policy is determined endogenously. 15

4Conclusion

In this study, we construct a model that contains pollution from resources (physical capital) accumulation and a human capital production function that admits zero educational expenditure in equilibrium.
Unlike previous studies that treat pollution and human capital accumulation simultaneously, depending on the initial endowment k0 , one case generates multiple steady states in this model. We define
Regime 1 as the regime in which only physical capital is accumulated and Regime 2 as the regime
where both physical and human capital are accumulated. Then, an economy with low initial physicalcapital shifts to Regime 2 and that with high initial physical capital stays in Regime 1 in the longrun. Although the level of the physical/human capital ratio in Regime 1 is larger than that in Regime
2, there is positive educational expenditure in Regime 2, and long-run production in Regime 2 may
be larger than that in Regime 1. In such a case, the resource curse problem occurs because of thepollution derived from the use of physical capital.
Further, we show that higher abatement technology (and greater productivity of educational expenditure) enables the economy not only to increase long-run production in Regime 2 but also to shift
from Regime 1 to Regime 2 by raising a productivity of educational expenditure and by a household redirecting a transfer toward educational expenditure. That is, by employing higher abatement
technology, the economy can overcome the resource curse problem.
There are two limitations of this model. Firstly, we assume that the amount of physical capital isequal to that of natural resources. Hence, we cannot treat the eﬀect stemmed from a scarcity of natural
resources. Secondly, we consider an exogenous mitigation policy in this model. In fact, a parent or
the government endogenously decides it. Therefore, it is interesting to construct and analyze a model
which also contains a stock of natural resource and/or an endogenous mitigation policy. These studies
15
It is possible to introduce an endogenous mitigation policy into this model by setting vulnerability v as a decreasing
function of mitigation policy and letting the parent choose mitigation policy in parallel with her consumption, transfers,
and educational expenditure in order to maximize her utility. However, this makes the dynamics of this model somewhat
complicated and is beyond the scope of this study.

19are left to future works.

AppendicesA.1 Other dynamics of kt
In the text, we focus on the dynamics of kt , which generate multiple steady states by assuming that
θ(kt ) has two distinct fixed points and k1∗ > k̄. Here, we examine the other two dynamics of kt . The
first pattern is the case that θ(kt ) has two distinct fixed points, while k̄ > k1∗ . The second pattern is thecase that θ(kt ) has no fixed points.
The first case of the dynamics of kt is illustrated in Figure 5. In Figure 5, the line h(et , θ−1 (kt ))ϕ(kt )is not shown since we do not need to consider it. In this case for any k0 , the economy converges to k2∗ .
To show this, we divide the case depending on the value of initial capital k0 .
1. k0 ∈ [0, k̄]: In this case, since k0 ≤ k̄, ϕ(k0 ) > θ(k0 ) holds, and it is optimal to shift to Regime
2 initially. However, since k2∗+ > k̄ > k0 and the steady state of k2∗ is stable, this economy
converges to k2∗ .
2. k0 > k̄: In this case, since k0 > k̄, the economy is initially in Regime 1 and monotonicallydecreases toward k1∗ . However, k1∗ < k̄ implies that at some period, the level of capital stock
falls below k̄ before it reaches k1∗ . At that time, ϕ(kt ) > θ(kt ) is realized, and according toLemma 1, it is optimal to shift from Regime 1 to Regime 2. After that, since k̄ < k2∗+ as in
Figure 5 and k2∗ is stable, this economy converges to k2∗ .
Consequently, in the second case, the economy converges to k2∗ regardless of k0 . This fact implies that
if k̄ > k1∗ , that is, if the threshold at which the parent decides not to invest into education is high, theeconomy is in Regime 2 in the long run for any initial physical capital.
To examine the case where θ(kt ) has no fixed points, let us divide the dynamics into the cases ofk̄ < k1∗ and k̄ > k1∗ . The phase diagram of the case that k̄ < k1∗ is illustrated in Figure 6, in whichθ(kt ) does not cross the 45-degree line. For k0 < k̄, as in the previous case, the economy shifts to
Regime 2 in the initial period and follows kt+1 = θ(kt ). However, as explained in subsection 2.3, sucha divergence is feasible only at period t < T e , which is defined in the text. In period T e , the economy

20

Figure 5: The phase diagram of kt when θ(kt ) has two distinct fixed points and k̄ > k1∗
shifts from Regime 2 to Regime 1; then, after T e + 1, it follows kt+1 = ϕ(kt ) and kt monotonicallyconverges to k1∗ . For k0 > k̄, the economy stays in Regime 1 and monotonically converges to k1∗ . Thatis, for any level of initial physical capital, the economy eventually converges to k1∗ .
Next, we consider the case of k̄ > k1∗ . When k̄ > k1∗ , θ(kt ) must have fixed points. That is, thecase that θ(kt ) has no fixed points and that k̄ > k1∗ is infeasible. To show this, see Figure 4. From thedefinition of k̄, θ(kt ) must pass the coordinate (k̄, ϕ(k̄)). However, it is impossible that θ(kt ) passes thispoint without crossing the 45-degree line, and hence θ(kt ) must have two fixed points, as shown in
Figure 6. Therefore, in the case that θ(kt ) has no fixed points, it is suﬃcient only to consider the caseof k̄ < k1∗ .

A.2 The derivatives of long-run production in Regime 2 Y2∗ in v
Here, we derive the sign of ∂Y2∗ /∂v. By considering that k2∗ is a function of v, we obtain(])2 [ ∗∂Y2∗ β(1 − α)∂(vk2∗ ) ∗∂k2 −11∗=[γ + vk2 − β] −
k .
∂v
α
∂v
∂v 2
γ−1 + vk2∗ − β21Figure 6: The phase diagram of kt when θ(kt ) has no fixed points and k̄ < k1∗
The terms in the above bracket become∂k2∗ −1(γ − β) − k2∗ 2 .
∂v
Since the sign of ∂Y2∗ /∂v is the same as that of the above expression, we focus on this expression. By
totally diﬀerentiating (15) in k2∗ and v, we obtain
dk2∗
Aαk2∗
=
.
dv
(1 − α)k2∗ −α − Aαv
From Figure 2, we can show that dk2∗ /dv > 0, and hence, (1−α)k2∗ −α > Aαv. Recall that if et converges
to e∗ , γ−1 + vk2∗ > β holds. By using dk2∗ /dv, (1 − α)k2∗ −α > Aαv holds, and from the definition of k̄,22k2∗ and Assumption 2, we obtain the following expression.
∂Y2∗
Aαk2∗
∝
(γ−1 − β) − k2∗ 2∂v(1 − α)k2∗ −α − Aαv
1=[Aαk2∗ (γ−1 − β) − k2∗ 2 ((1 − α)k2∗ −α − Aαv)]∗(1 − α)k2 −α − Aαv
k2∗=[Aα(γ−1 + vk2∗ − β) − (1 − α)k2∗ 1−α ](1 − α)k2∗ −α − Aαv
Aαk2∗[(γ−1 + vk2∗ − β) − (1 − α)(γ−1 + vk2∗ )]=(1 − α)k2∗ −α − Aαv[()]
vAα2 k2∗
1 β 1
∗
=
k
−
−
(1 − α)k2∗ −α − Aαv 2 v α γ()][
vAα2 k2∗
β
1
1
∗
<
k −
−
(1 − α)k2∗ −α − Aαv 2 v α + (1 − α)(1 − β) γ[]vAα2 k2∗
k2∗ − k̄ ,=−α∗(1 − α)k2 − Aαv
where we use (15) in the third equality. The first inequality holds since β/α > β/[α + (1 − β)(1 − α)]and the last equality holds from the definition of k̄ in (14). Since k2∗ < k̄ from Figure 3, we conclude
that the last expression is negative. Therefore,∂Y2∗< 0. 
∂v(Ap.1)

References[1] Beatty, K.M. Timothy and Shimshack, Jay P. (2014) “Air Pollution and children’s respiratory
health: A Cohort Analysis”, Journal of Environmental Economics and Management, 67 , 39-54.
[2] Bovenverg, A Lans and Smulders, Sjak. (1995) “Environmental Quality and Pollutionaugmenting Technological Change in a Two-sector Endogenous Growth Model”, Journal of
Public Economics, 57, 369-391.
[3] Carrie Janet, Niedell Matthew and Schmieder, Johannes F. (2009) “Air Pollution and Infant
Health: Lessons from New Jersey”, Journal of Health Economics, 28, 688-703.
[4] de la Croix, David, and Matthias Doepke. (2003) ”Inequality and Growth: Why Diﬀerential
Fertility Matters.” American Economic Review, 93(4): 1091-1113.
23

[5] Galor, Oded and Moav, Omer. (2004) “From Physical to Human Capital Accumulation: Inequality and the Process of Development”, Review of Economic Studies, 71, 1001-1026.
[6] Galor, Oded and Weil, David N. (2000) “Population, Technology, and Growth: From Malthusian
Stagnation to the Demographic Transition and Beyond”, American Economic Review, 90(4),806-828.
[7] Gradus, Raymond and Smulders, Sjak. (1993) “The Trade-oﬀ Between Environmental Care andLong-term Growth - Pollution in Three Prototype Growth Models”, Journal of Economics, 58,
25-51.
[8] Graﬀ, Zivin Joshua and Niedell Matthew. (2012) “The Impact of Pollution on Worker productivity”, American Economic Review, 102 , 3652-3673.
[9] Grossman, G., and A. Krueger. (1995) “Economic Growth and the Environment”, Quarterly
Journal of Economics, 110 , 353-377.
[10] Gylfason, Thorvaldur. (2001) “Natural Resources, Education and Economic Development”, European Economic Review, 45, 847-859.
[11] Ikefuji, Masako and Ryo, Horii. (2012) “Natural Disasters in a Two-sector Model of Endogenous Growth Model”, Journal of Public Economics, 96, 784-796.
[12] John, A., and Pecchenino, R. (1994) “An Overlapping Generations Model of Growth and theEnvironment”, The Economic Journal, 20, 1393-1410.
[13] Mehlum, Halvor, Moene, Karl and Torvik Ragner. (2006) “Institutions and the Resource Curse”,
The Economic Journal, 116, 1-20.
[14] Moav, Omer. (2005) “Cheap Children and the Persistence of Poverty”, The Economic Journal,
115 , 88-110.
[15] Prieur, Fabien., and Brechet, Thierry. (2013) “Can Education Be Good for Both Growth and theEnvironment?”, Macroeconomic Dynamics, 17, 1135-1157.

24

[16] Raﬃn Natacha. (2012) “Children’s environmental health, education, and economic development”, Canadian Journal of Economics, 45, 996-1022.
[17] Robinson, A James, Torvik, Ragner, and Verider Thierry. (2006) “Political foundations of theresource curse”, Journal of Development Economics, 79, 447-468.
[18] Robinson, A James, Torvik, Ragner, and Verider Thierry. (2014) “Political foundations of theresource curse: A simplification and a comment”, Journal of Development Economics, 106,194-198.
[19] Sachs, Jeﬀrey D and Warner, Andrew M. (1995) “Natural resource abundance and economic
growth”, NBER Working Paper, 5398
[20] Sachs, Jeﬀrey D and Warner, Andrew M. (2001) “The curse of natural resources”, European
Economic Review, 45 , 827-838.
[21] Sapci, Onur. (2013) “Environment, Human Capital, and Growth”, Job Market Paper, 15 October
2013.
[22] Schou, Poul. (2000) “Polluting Non-Renewable Resources and Growth”, Environmental andResource Economics, 16 , 211-227.
[23] van der Ploeg, F. (2011) “Natural Resources, Curse or Blessing ?”, Journal of Economic Literature, 49 , 366-420.

25