J Popul Econ (2010) 23:1351–1370 DOI 10.1007/s00148-008-0238-z ORIGINAL PAPER
Trade, population growth, and the environment in developing countries Ulla Lehmijoki · Tapio Palokangas
Received: 24 July 2007 / Accepted: 19 November 2008 / Published online: 16 January 2009 © Springer-Verlag 2009
Abstract We examine pollution in a developing country where fertility is endogenous and wealth increases welfare through status. When the country has defective environmental laws, it has a comparative advantage in capitalintensive “dirty” goods. Gains from trade due to trade liberalization then increase income and boost population growth. With strong incentives to save, they also stimulate investment, which hampers population growth. Because population growth crowds out labor supply, production of capital-intensive dirty goods first increases and then decreases. This yields a typical environmental Kuznets path: pollution increases at the earlier stages but decreases at the later stages of development. Keywords International trade · Population growth · EKC JEL Classification Q56 · O41 · J13
Responsible editor: Alessandro Cigno U. Lehmijoki · T. Palokangas (B) University of Helsinki and HECER, P.O. Box 17, (Arkadiankatu 7), 00014, Finland e-mail:
[email protected] T. Palokangas IZA, Bonn, Germany
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1 Introduction Does the liberalization of trade affect pollution in developing countries? Is there any environmental Kuznets curve (EKC) in poor countries? The “pessimists” argue that free trade transfers pollution-intensive production from rich countries to poor. In contrast, the “optimists” claim that gains from trade help the poor countries to reach their EKC peak, after which pollution decreases. In this paper, we show that both perspectives are in some respects correct, but insufficient alone to explain the complicated dynamics after the liberalization of trade in developing countries. Free trade changes labor supply through population growth. Together with capital accumulation, this first increases but then decreases environmental degradation. Arrow et al. (1995) suggest that the EKC path arises because people in poor countries “cannot afford environmental amenities over material well-being but . . . in richer countries people give more attention to environmental quality.” Selden and Song (1994) and Grossman and Krueger (1995) argue that the EKC may result from the interaction of the scale, composition, and technology effects as forces leading to cleaner composition of goods and techniques outweigh the adverse effects of growing economic activity. Pasche (2002) and Kelly (2003) claim that, since the latest vintages of capital are less pollutionintensive, capital accumulation and gradual technical progress together may decrease emissions. John and Pecchenino (1994) argue that poor economies do not engage in environmental investment but free-ride at the cost of future generations, whereas Stokey (1998) shows that intergenerational conflict calls for governmental activity for the EKC to arise. In contrast to this literature, we construct a mechanism by which the liberalization of trade generates the EKC through changes in fertility and labor supply. We ignore technological progress and public policy, which are only marginally important in developing countries. Our theory derives from three elements: comparative advantage, endogenous fertility, and the Rybczynski effect. We now consider these one by one. Comparative advantage. Because dirty goods are usually capital-intensive, with uniform environmental regulations, the capital-rich industrial countries would have the comparative advantage in them (Cole and Elliot 2003, 2005). According to the Pollution Haven hypothesis, poor countries have taken over this comparative advantage by implementing inferior environmental regulations (Antweiler et al. 2001; Copeland and Taylor 2004).1 Consequently, poor countries specialize in the capital-intensive dirty goods (Suri and Chapman 1998; Cole and Elliot 2003; Mani and Jha 2006). We take this reversed specialization as a starting point in this study. Endogenous fertility (Becker 1981). The demand for children depends on income, the opportunity cost of children and the incentive to invest in child
1 Several
articles on Pollution Havens have been collected and reprinted in Fullerton (2006).
Trade, population growth, and environment in developing countries
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quality. With liberalization, gains from trade raise fertility through income, generating a “population explosion” in developing countries. Galor and Mountford (2006) show that, when a developing country specializes in goods that use unskilled labor intensively, households invest in quantity rather than the quality of children. In that case, gains from trade generate prolonged population growth. Lehmijoki and Palokangas (2009) show the following. Without sufficient incentive for investment, gains from trade lead to a highfertility and low-capital poverty trap. When there are enough such incentives, however, labor supply falls initially when women “migrate” to child-rearing, but then rises as both the grown-up children and their mothers enter the labor force.2 In this study, we incorporate these patterns of population growth into a model of environmental economics. The Rybczynski effect (Rybczynski 1955). Given full employment of capital and labor, the initial decrease in labor supply curbs the labor-intensive clean sector but expands the capital-intensive dirty one. In the long run, capital accumulation increases wages and attracts women from home to production; the labor-intensive clean sector expands and crowds out the capital-intensive dirty sector. This generates a typical EKC path, with pollution increasing at the earlier stages of development but decreasing at the later stages. The post-war liberalization of world trade increased trade volumes by an annual average of about ten percent initially and somewhat less after the oil crises (Maddison 2001). There is, however, controversial empirical evidence on trade and pollution. Suri and Chapman (1998) support the pessimists by showing that richer countries import energy-intensive goods from poorer countries, which has increased pollution in these countries. Mani and Jha (2006) document a considerable shift in Vietnamese exports toward pollutionintensive manufacturing goods (leather and textiles) since the liberalization of trade. On the other hand, Jha et al. (2006) show, by case studies in poor countries, that gains from trade provide enough resources for environmental protection. In this study, we provide some anecdotal evidence on the following. The post-war population growth (1) first accelerated and peaked around the 1970s, and (2) was then followed by a similar peak in per capita pollution. This pattern seems to support our theory. This study is organized as follows: Section 2 constructs a two-sector model of production and Section 3 a family-optimization model for a small open developing economy. The liberalization of trade is characterized by an increase in the price of the exported dirty good. Section 4 constructs the dynamics of the model. Sections 5 and 6 analyze long-run and short-run effects of the liberalization, showing that pollution first increases and then decreases after liberalization. The results are given in terms of both per capita and total pollution. Section 7 discusses the anecdotal evidence and Section 8 closes the paper.
2 See
also Bloom and Williamson (1998).
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2 The production sectors Let L be total population. The population growth rate is given by ˙ L/L = n − m,
(1)
where n is the birth rate, m the adult mortality rate,3 and (˙) the derivative with respect to time t. We assume that rearing each newborn requires a fixed amount q of labor. The number of newborns is then nL and the total labor in child rearing qnL. The labor supply (1 − qn)L is population L minus labor in child rearing, qnL. Because only women take care of children in a developing country, at most half of the population work in child-rearing:4 qnL ≤ L/2,
qn ≤ 1/2.
(2)
The economy consists of two sectors: the dirty sector, which produces the dirty good A, and the clean sector, which produces the clean good B. The economy is so small that the (relative) price of the dirty good, p, is determined from abroad. Because of lax environmental legislation, the developing economy exports the dirty good and imports the clean. We assume for simplicity that the output A of the dirty sector is produced only for exports. The domestic consumption of this good would complicate the analysis without adding any essential results. Kelly (2003) defines three different measures of pollution: the stock of pollutants, the intensity of control policy, and emissions. We use emissions because they can easily be incorporated into a model of population growth and international trade. Because emissions must be an increasing function of the output A of the dirty sector, we use A as an index of emissions. Capital K and labor in production, (1 − qn)L, are freely transferrable between the dirty sector (subscript a) and the clean sector (subscript b ): K ≥ Ka + Kb ,
(1 − qn)L ≥ La + Lb ,
(3)
where Li (Ki ) is labor (capital) input in sector i ∈ {a, b }. Outputs are produced according to the neoclassical linearly homogeneous functions A = F a (Ka , La ), B = F b (Kb , Lb ), . . F1i = ∂ F i /∂ Ki > 0 and F2i = ∂ F i /∂ Li > 0 for i = a, b .
(4)
We assume that the clean sector is always more labor intensive. This yields . . a = La /Ka < (1 − qn)L/K < Lb /Kb = b . (5)
3 The
child mortality rate is included in the parameter q, which characterizes the productivity of child rearing. Adult mortality is assumed to be exogenous to environmental degradation. 4 In other words, the labor force participation rate is over 50%. According to World Bank (2007), it is typically between 55% and 65% in low- and middle-income countries.
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The producers allocate their resources (La , Lb , Ka , Kb ) to maximize national income Y = pA + B, taking the capital–labor ratio k, the birth rate n, and the relative price p as given. In Appendix A, we show that the per capita national income y and the per capita outputs of the sectors a and b are then determined by . y(k, n, p) = pa + b , k = K/L, yk ( p) > 0, yn ( p) < 0, y p = a, . A/L = a = a(k, n, p), ak > 0, an > 0, a p > 0, ak / an = b ( p)/q, a/ an = n + (kb − 1)/q,
(6)
where the subscripts k, n, and p stand for the partial derivatives with respect to k, n, and p. By duality, the partial derivative of per capita national income y with respect to the relative price of the dirty good, p, equals the per capita supply of the dirty good, a. Because both sectors are subject to constant returns to scale, per capita national income y is linear with respect to the capital–labor ratio k, the per capita supply of labor 1 − qn, and the birth rate n: ∂ 2 y/(∂k2 ) = ∂ 2 y/(∂k∂n) = ∂ 2 y/(∂n2 ) = 0.
3 The dynastic family Following Razin and Ben-Zion (1975) and Becker (1981), we consider a representative family that derives the temporary utility log c + θ log n from per capita consumption c and the number of children proxied by the birth rate n. In addition to this, we assume that the family benefits from its status in society. Because capital is the only asset in the model, the family’s total wealth is equal . to capital K and per capita wealth to k = K/L. The family’s status can then . be proxied by the per capita wealth of the family itself, k = K/L, over and above the average per capita wealth of the other families in the economy, κ. Following Kurz (1968), Corneo and Jeanne (1997, 2001), Chang et al. (2000), Pham (2005), Fisher (2005), and Fisher and Hof (2005), we augment temporary utility at time t by an increasing function v(k − κ) of the status k − κ as follows: (7) u(t) = log c(t)+θ log n(t)+εv k(t)−κ(t) , v > 0, v < 0, v (0) = 1, where θ > 0 and ε > 0 are the constant weights for children and status. The saving incentives are stronger the bigger the multiplier ε is. Let the constant ρ be an adult’s rate of time preference given that he/she could live forever. We assume that the probability of an adult dying in a short time dt is equal to m dt, where m is the adult mortality rate. In that case, e−mt is the probability that the adult will survive beyond the period [0, t], and e−mt u(t) is the adult’s expected utility at time t. The representative family’s expected utility at time t = 0 is then given by ∞ ∞ −mt −ρt U= ue e dt = log c + θ log n + εv(k − κ) e−(ρ+m)t dt. (8) 0
0
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In this study, we consider a single dynastic family, which has only a negligible effect on the environment. Although environmental externalities between families may arise, the model does not contain any macroeconomic policymaker who could internalize these externalities. For these reasons, we can omit emissions A (or any environmental amenities) from the arguments of the utility function without losing any generality. On the assumption that capital is the only asset in the economy, the family budget constraint can be written in terms of capital accumulation as ˙ = Y − cL, K
(9)
where K˙ is savings (= capital accumulation), Y is income, and cL is the total consumption of the family. Noting Eqs. 1 and 6, the budget constraint Eq. 9 can be expressed in per capita terms as follows: ˙ K˙ KL k˙ = − = y(k, n, p) − c + (m − n)k. L LL
(10)
The representative family maximizes its utility (Eq. 8) by per capita consumption c and the number of children, n, subject to its budget constraint (Eq. 10). The Hamiltonian corresponding to this maximization is given by H = log c + θ log n + εv(k − κ) + λ y(k, n, p) − c + (m − n)k , where, noting Eq. 6, the costate variable λ evolves according to λ˙ = (ρ +m)λ−
∂H = [ρ +n− yk ( p)]λ−εv (k−κ), ∂k
lim λke−ρt = 0.
t→∞
(11)
Noting Eq. 6, the first-order conditions of this maximization are given by ∂H 1 = − λ = 0, ∂c c
∂H θ = + [yn ( p) − k]λ = 0. ∂n n
(12)
4 Dynamics Given a country’s comparative advantage for the capital-intensive dirty good A, the liberalization of trade is equivalent to an exogenous increase in the relative export price p. To construct the patterns of the capital–labor ratio k and per capita emissions a after the liberalization, we replace λ by a as the costate variable of the model for convenience. Differentiating the function a in Eq. 6, we obtain the equilibrium birth rate n as the function of (k, a, p): . n(k, a, p), nk = ∂n/∂k = − ak / an = −b /q < 0, . . an > 0, n p = ∂n/∂ p = − a p / na = ∂n/∂a = 1/ an < 0,
(13)
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where nk < 0 refers to the decrease in demand for births induced by the increase in wages, which follows from capital deepening (as in Galor and Weil 1996). Noting Eqs. 6, 12, and 13, we obtain the per capita consumption c = 1/λ = n(k, a, p)[k − yn ( p)]/θ.
(14)
Inserting functions (6), (13), and (14) into Eq. 10, we obtain capital accumulation as a function of (k, a, p) as follows: k˙ = y(k, n(k, a, p), p)+ θ1 n(k, a, p)yn ( p)+ m− 1+ θ1 n(k, a, p) k, (15) ⎛ ⎞ ˙ ∂k = 1 + θ1 ⎝ yn −k⎠ na < 0, (16) ∂a
∂ k˙ ∂p
+
−
1
= 1 + θ (yn − k) n p + y p + ⎛ ⎞
n ∂2 y θ ∂n∂ p
= (1 + 1/θ) ⎝ yn −k⎠ n p + y p +(n/θ ) an > (n/θ ) an > 0,
∂ k˙ ∂k
= 1+
−
−
θ
y n nk + y k
1
−
−
+
(17)
+
+m − 1 + θ1 (n + knk ).
(18)
+
Because all families in the economy are similar, in equilibrium, they have the same per capita wealth, κ = k. Given κ = k, Eqs. 7, 13, and 14, we can transform the differential equation (Eq. 11) into −
1 nk + n k − yn
na nk na k˙ k˙ n˙ λ˙ k˙ − a˙ = − k˙ − a˙ − =− − = n n n k − yn n k − yn λ = ρ + n − yk ( p) − εv (0)/λ = ρ + n − yk ( p) − ε/λ = ρ + n − yk ( p) − εn k − yn ( p) /θ = ρ − yk ( p) + 1 − ε k − yn ( p) /θ n(k, a, p).
Rearranging the terms in this equation, we obtain the change in per capita emissions, a˙ , as a function of the variables (n, k, p) as follows: 1 n a˙ = yk ( p)+ ε[k − yn ( p)]/θ − 1 n(k, a, p)−ρ − na na
n nk + k− yn
˙ (19) k.
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In the neighborhood of the steady state k˙ = a˙ = 0, noting Eqs. 6, 13, and 16, this equation has the properties (cf. Appendix B): ˙ np ∂ a˙ 1 ∂k n ε n (ρ − y − n = ) − n a + a + , (20) k n k k ∂ p k=˙ na n θ na k − yn ∂ p ˙ a=0 ˙ 1 n ∂ a˙ ∂k = ρ − y − + n , k k ∂a k=˙ na k − yn ∂a ˙ a=0
(21)
˙ 1 nk n2 ε n ∂ a˙ ∂k − . = (ρ − yk ) + nk + ∂k k=˙ n n θ n k − y ∂k ˙ a=0 a a a n
(22)
5 Long-run effects of the liberalization of trade We now linearize the system Eqs. 15 and 19 in the neighborhood of the steady state k˙ = a˙ = 0: ˙ ˙ ˙ p dk ∂ k/∂k ∂ k/∂a ∂ k/∂ + dp = 0. (23) da ∂ a˙ /∂k ∂ a˙ /∂a ∂ a˙ /∂ p Because the families have perfect foresight, there is a unique development path if and only if a saddle point solution holds; i.e., the Jacobian has a negative determinant J : ∂ k˙ ∂ a˙ . ∂ k˙ ∂ a˙ J = − < 0. ∂k ∂a ∂a ∂k
(24)
If this saddle point condition does not hold, then the response of the economy is highly unstable in terms of investment and population growth. As this kind of development has not been observed, condition (24) is plausible. Noting this, Eqs. 2, 6, 13, 17, 18, 20, 22, and 23, we prove the following result (cf. Appendix C): Proposition 1 The liberalization of trade (i.e., an increase in p) decreases per capita emissions a in the long run, da/dp < 0, if and only if household incentives to save relative to those to have children, ε/θ, are high enough for 1 1 ε 1 > 1+ (yn − k)nk + yk + m − 1 + n θ n θ θ 1 × (ρ − yk ) (n p + nk an ) + ak n ×
1+
−1 nk 1 (yn − k)(n p + nk an ) + a + (yk + m − n) an + (yk − ρ) 2 . θ n
Trade, population growth, and environment in developing countries
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Trade liberalization increases gains from trade and income. When a strong desire for status generates sufficient savings incentives, households spend these gains on wealth rather than children. The birth rate then falls and labor supply increases. In that case, by the Rybczynski theorem, capital and labor will flow from the capital-intensive dirty sector to the labor-intensive clean one and per capita emissions will fall. For the remainder of the paper, we focus on the case where da/dp < 0. Consider then total emissions, A = aL. Because ∂n/∂a > 0 by Eq. 13, Proposition 1 implies that, after the liberalization of trade, population growth ˙ L/L = n − m slows down in the long run. In a steady state, a is constant, so ˙ ˙ that A/A = L/L. Hence, if the increase in the relative price p is large enough ˙ to reduce the birth rate n below the mortality rate m, then L/L < 0 holds true and total emissions A = aL fall. We summarize this result as follows: Proposition 2 If the effect of the liberalization of trade is extensive enough, then total emissions A fall in the long run as well.
6 Short-run effects of the liberalization of trade Although the long-run effects of the liberalization of trade are given by Proposition 1, the short-run pattern of development is still ambiguous. To specify this pattern, we make the following assumption: Assumption 1 Holding per capita export a and the relative price p constant, ˙ an increase in per capita wealth k decreases saving and capital deepening k, ˙ ∂ k/∂k < 0. When per capita export revenue pa is kept constant, capital accumulation diminishes. Given Assumption 1 and Eqs. 13, 18, 19, and 22, we obtain −1 1 ∂ k˙ n + k − yn yk + > 0, (25) nk = 1 + m −
θ ∂k
+ − − + −
+
˙ ∂ a˙ nk n2 ε 1 n ∂k = (ρ − y ) + − n + k k ∂k k=˙ na na θ na k − yn ∂k ˙ a=0
+
+
⎧ ⎨ε
−
⎫ ⎬ n nk n2 ε n2 ε k > (ρ − yk ) + = k − yn ( p) −1 n + ⎩θ ⎭ na na θ na na θ
− −
=
ε n nk (k − yn )nk + n − n > 0.
θ n na a
+ +
+
−
(26)
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Fig. 1 The saddle point
a
.
k=0
S
.
a*
S
.
a=0 k
k*
From Eqs. 16, 17, 24, 26, and Assumption 1, it follows that ! ˙ ∂ k˙ ∂ k˙ ∂ a˙ ∂ a˙ ∂ k˙ ∂ a˙ ∂k ∂ k˙ < 0, > 0, < 0, > 0, > > 0. ∂a ∂p ∂k ∂k ∂a ∂a ∂k ∂k
−
+
(27)
−
Given Eq. 27, both singular curves a˙ = 0 and k˙ = 0 are decreasing, but k˙ = 0 falls more steeply ! ! ∂ a˙ ∂ a˙ ∂a ∂a ∂ k˙ ∂ k˙ <− = =− < 0. ∂k k=0 ∂k ∂a ∂k ∂a ∂k a˙ =0 ˙ Thus, Assumption 1 implies that the model has a saddle-point (cf. Fig. 1). Noting Eqs. 6, 13, 17, 20, 25, 27, and Proposition 1, we show in Appendix D that an increase in the relative export price p diminishes the evolution of per capita emissions: ∂ a˙ < 0. (28) ∂ p k=˙ ˙ a=0 The comparative dynamic properties of the system in the (k, a) plane are the following. Assume first that the system is initially in the steady state (k∗0 , a∗0 ). Once the price p increases, the steady state moves to the new steady state (k∗1 , a∗1 ) and the singular curves k˙ = 0 and a˙ = 0 shift to the right (cf. Eqs. 27 and 28): ! ˙ ∂k ∂ k˙ ∂k = − > 0, ∂ p k=0 ∂p ∂k ˙
+
−
! ∂k ∂ a˙ ∂ a˙ = − > 0. ∂ p a˙ =0 ∂ p k=˙ ∂k ˙ a=0
−
+
Trade, population growth, and environment in developing countries Fig. 2 The dynamics of the model
a
.
(k = 0) 0
1361
.
(k = 0)1
S a^ a*0
.
a*
1
. S
.
(a = 0) 1
.
(a = 0) 0 k*0
k*1
k
When p increases, a jumps upwards from a0 to aˆ (cf. Fig. 2). After this, the system evolves along the saddle path SS to the new steady state (k1 , a1 ), where per capita emissions are below the original level, a1 < a0 .5 We summarize this result as follows: Proposition 3 Given Assumption 1 above, the liberalization of trade (i.e., an increase in p) produces a typical EKC for per capita emissions. In addition, if the effect of the liberalization of trade is strong enough, there is a typical EKC for total emissions A as well. The intuitive explanation of the short-run response of the economy to trade liberalization is that gains from trade generate an initial jump in the birth rate n. By the Rybczynski theorem, the associated initial decrease in labor supply expands the capital intensive dirty sector. In the long run, n starts to decrease as investments increase wages and the opportunity cost of births. Labor supply increases as women re-enter the labor force together with their grown-up children. This curbs the dirty sector and a typical EKC path appears for both total and per capita emissions.
5 In line with Selden and Song (1994) and Grossman and Krueger (1995), we can define two effects:
the composition effect, where the relative proportion of the dirty and clean sectors changes, and the scale effect, where (per capita) capital stock and the scale of (per capita) output changes. The initial sharp increase in per capita emissions from a∗0 to aˆ is a pure composition effect (the dirty sector expands, the clean sector contracts). Along the saddle path SS, both the composition effect (the dirty sector contracts, the clean sector expands, per capita emissions a decrease) and the scale effect (capital accumulates, per capita emissions a increase) work, but because the former dominates over the latter, per capita emissions a fall.
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aPopulation
bCO2 / GDP (kg / Dollar)
CO2 emissions pc, metric tons
Growth %
Emissions per capita
2.4
2.5 2.4
2.2
2.2
2
2
1.8
1.8
1.6
1.6
2 Emissions per GDP
1.5
1.4
1.4
Population Growth
1.2
1.2 1960
1970
1980
1990
2000
Year
1960
1970
1980
1990
2000
Year
Fig. 3 Population growth and per capita emissions (a) and emissions per GDP (b) in the low- and middle-income countries; emissions measured as CO2 emissions. Source: World Bank (2007)
7 Some anecdotal evidence Consider now the post-war history in developing countries.6 Panel a in Fig. 3 shows a rapid increase in population growth toward the 1970s and a rapid decline soon after. The per capita pollution peaked approximately one generation later, as was predicted by the model. Instead of per capita emissions, one can calculate emissions per GDP. These should exhibit an EKC path as well. Panel b in Fig. 3 illustrates CO2 emissions per GDP, showing a peak in the late 1990s. In the model, we show that total pollution decreases in the long run if there is a considerable fall in population growth. Figure 4 indeed suggests that, after a period of rapid increase, the increase of total emissions is now slowing. The EKC path is conditional on saving incentives. With low incentives, gains from trade may generate persistent population growth, there is no take-off of investment, and income remains low. This is the typical pattern in the least developing countries, where high population growth has continued until the 1990s, the per capita pollution has not peaked yet, and total pollution keeps rising at an accelerating rate (World Bank 2007). Panel a in Fig. 5 shows that the least developed countries have not been closed. On the contrary, their trade share was initially high (Fig. 5a) but domestic savings have been exceptionally low (Fig. 5b) and gains from trade have manifested themselves as demographic growth. The least developed countries have not yet reached the phase where population growth falls, labor supply swells, and per capita pollution decreases.
6 Low-
and middle-income countries in the World Bank classification.
Trade, population growth, and environment in developing countries Fig. 4 Total CO2 emissions in the low- and middleincome countries. Source: World Bank (2007)
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CO2 (gigatons) 14
10
Emissions, total 6
2 1960
1970
1980
1990
2000 Year
This evidence for the EKC is subject to several restrictions. First, it may be overly optimistic because Stern and Common (2001), Harbaugh et al. (2002), and Deacon and Norman (2006) show that there is no EKC for sulfur or lead. These authors emphasize that the EKC is sensitive to model specification and sample selection. Emissions depend on time-related factors, such as information and technical change, which should be controlled for
a
b
Trade (% of GDP)
Savings (% of GDP)
60
50
Low and Middle Income Countries
20 40
Least Developed Countries
30 10 20
Low and Middle Income Countries
Least Developed Countries
10
0 1960
1970
1980
1990
2000
1960 Year
1970
1980
1990
2000 Year
Fig. 5 Trade (a) and savings (b) in the low- and middle-income and least developed countries. Source: World Bank (2007)
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U. Lehmijoki, T. Palokangas
before the EKC can be explained by the liberalization of trade alone. Second, the evidence is aggregative and country-level research is needed. Mani and Jha (2006), Deacon and Norman (2006), and Jha et al. (2006) investigate the postliberalization pollution, but their research periods are too short for demographic trends to show up. In spite of these restrictions, the data do suggest that population growth and environment quality measured by CO2 emissions are positively correlated, as is indicated by the model. Furthermore, pollutants with higher abatement rates may peak earlier since higher income should induce more spending on abatement efforts.
8 Conclusions This paper uses a family-optimization model to examine pollution in a developing economy where children and wealth have positive effects on welfare. We assume that dirty goods are capital-intensive, but developing countries nevertheless have the comparative advantage in these goods because of their lax environmental regulations. Trade liberalization raises the relative price for exports and generates gains from trade. The outcome of this depends on the saving incentives. With high saving incentives, a considerable proportion of the gains from trade is invested, in which case population growth first increases but then decreases. Because population growth crowds out labor supply, the Rybczynski theorem indicates that the capital-intensive dirty sector first expands and crowds out the laborintensive clean sector, but ultimately, this pattern is reversed. This yields a typical EKC path, per capita pollution increasing at the earlier stages but decreasing at the later stages of development. When the population growth rate falls below zero, total pollution decreases as well. Acknowledgements The authors are grateful to the editor and two anonymous referees of this journal for their helpful and constructive comments.
Appendix A. Functions (Eq. 6) . . . Denoting k = K/L and ki = Ki /L and li = Li /L for i ∈ {a, b }, and dividing Eqs. 3 and 4 by L, yields . A . B = F a (ka , la ), b = = F b (kb , lb ). k ≥ ka +kb , 1−qn ≥la +lb , a = L L
(29)
The inequalities (5) can be written as La L 1 − qn Lb lb . . la = < (1 − qn) = < = a = = b . ka Ka K k Kb kb
(30)
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Noting Eqs. 29, 30, and duality, the maximization of national income Y = pA + B by (la , lb , ka , kb ) leads to the per capita income functions Y 1 = L L = =
max
La ,Lb ,Ka ,Kb
max
la ,lb ,ka ,kb
max
la ,lb ,ka ,kb
pA + B (1 − qn)L ≥ La + Lb , K ≥ Ka + Kb
pF a (ka , la ) + F b (kb , lb ) 1 − qn ≥ la + lb , k ≥ ka + kb
pF a (ka , la ) + F b (kb , lb ) 1 − qn = la + lb , k = ka + kb
= max pF a (ka , la ) + F b k − ka , 1 − qn − la la ,ka
"
= pF a (ka , la ) + F b (k − ka , 1 − qn − la ) pF1a (ka , la ) = F1b (k − ka , 1 − qn − la ), # pF2a (ka , la ) = F2b (k − ka , 1 − qn − la ) " = pF a (1, a )ka + F b (1, b )(k − ka ) b = (1 − qn − la )/(k − ka ), # a = la /ka , pF1a (1, a ) = F1b (1, b ), pF2a (1, a ) = F2b (1, b ) $ =
1 − qn − kb , pF (1, a )ka + F (1, b )(k − ka ) ka = a − b a
b
% 1 − qn − ka a b a b kb = , pF1 (1, a ) = F1 (1, b ), pF2 (1, a ) = F2 (1, b ) b − a $ 1 − qn − kb 1 − qn − ka a b + F (1, b ) = pF (1, a ) a − b b − a % . a b a b pF1 (1, a ) = F1 (1, b ), pF2 (1, a ) = F2 (1, b ) = y(k, n, p). (31) Differentiating the equations pF1a (1, a ) = F1b (1, b ) and pF2a (1, a ) = in Eq. 31 totally and noting Eqs. 4 and 30, we obtain
F2b (1, b )
a ( p),
a > 0,
b ( p),
b < 0.
Noting this, function (31) can be written in the form 1−qn−kb ( p) 1−qn−ka ( p) . + F b (1, b ( p)) . (32) y(k, n, p) = pF a (1, a ( p)) a ( p)−b ( p) b ( p)−a ( p)
1366
U. Lehmijoki, T. Palokangas
Given Eqs. 30, 31, and 32, the function y(k, n, p) has the properties: . ∂y . pF a (1, a ( p))b ( p) − F b (1, b ( p))a ( p) yk ( p) = ( p) = = F1b > 0, ∂k b ( p) − a ( p) pF a (1, a ( p)) − F b (1, b ( p)) . ∂y yn ( p) = ( p) = q = −qF2b < 0, ∂n b ( p) − a ( p) a(k, n, p) =
A . ∂y = yp = = F a (ka , la ) = F a (1, a )ka L ∂p
= F a (1, a )
F a (1, a )q . ∂a > 0, an = = ∂n b − a b = y − pa,
F a (1, a )b . ∂a = ak = > 0, ∂k b − a
qn + kb − 1 , b − a ap =
ak / an = b ( p)/q,
∂a ∂2 y > 0 by duality, = ∂p ∂ p2 a/ an = n + (kb − 1)/q,
b < 0.
B. Results (Eqs. 20, 21, and 22) From Eq. 19 and k˙ = a˙ = 0, it follows that
(k − yn )ε/θ − 1
˙ a=0 k=˙
= (ρ − yk )/n.
(33)
Differentiating Eq. 19 in the neighborhood of the steady state k˙ = a˙ = 0 and noting Eqs. 6, 13, 16, and 33, we obtain the following: $ % n ε ε ∂2 y ∂ a˙ ∂2 y = ) − (k − y − 1 n n + n p ∂ p k=˙ na θ θ ∂n∂ p ∂k∂ p ˙ a=0 ˙ n ∂k 1 nk + − na k − yn ∂ p $ ˙ % np ∂k n ε ∂ a ∂ a 1 n (ρ − yk ) nk + = − n + − na n θ ∂n ∂k na k − yn ∂ p ˙ np 1 n ∂k n ε (ρ − yk ) ak − nk + = − n an + , na n θ na k − yn ∂ p
Trade, population growth, and environment in developing countries
1367
˙ ∂ a˙ ∂k n 1 n (k − yn )ε/θ − 1 na − nk + = ∂a k=˙ na na k − yn ∂a ˙ a=0 ˙ 1 n ∂k , = ρ − yk − nk + na k − yn ∂a
−
+
˙ ∂ a˙ n n2 ε 1 n ∂k = (k − y )ε/θ − 1 n + − + n n k k ∂k k=˙ na na θ na k − yn ∂k ˙ a=0 ˙ nk n2 ε 1 n ∂k − . = (ρ − yk ) + nk + na na θ na k − yn ∂k C. Proposition 1 From Eqs. 2, 5, 6, 13, 17, and 18, it follows that ⎞ ⎛ ⎞ ⎞⎛ ⎞ ⎛ ⎛ ˙ ˙ ⎟ ∂k ∂k ⎜ 1 ⎜ ⎟ an ⎠ +a+ ⎝ yk + m −n⎠ an + an = ⎜1+ ⎟ ⎝ yn −k⎠ ⎝ n p +nk
∂p ∂k ⎝ θ ⎠ ⎛
+
−
+
+
−
⎞
⎛ ⎞ ⎟ ⎜ 1 ⎟ ⎝ − k⎠ nk >⎜ an +a − n an ⎝1 + θ ⎠ yn
− + − ⎛
>1
⎞
> ⎝ yn −k⎠ nk an an +a − n
−
−
+
a b kb − 1 > −knk an = −knk + −n an = k + an an +a − n q q an ⎞ ⎛ an an an ⎜ ⎟ = 2kb −1 = 2(1−qn)−1 = ⎝1 − 2qn⎠ ≥ 0.
q q q
≥0
(34)
+
Given J < 0, Eqs. 13, 20, 22, 23, and 34, we obtain ˙ ˙ ∂k ∂k ∂ k˙ ∂ k˙ 1 n da 1 ∂k ∂ p ∂k ∂p =− =− dp J ∂ a˙ ∂ a˙ J na (ρ − y ) nk + n ε (ρ − y ) n p − ε n a + a k n k n n k ∂k ∂ p θ θ ∂ k˙ 1 n ∂k =− J na (ρ − y ) nk + n ε k n θ
˙ + an ∂∂kk (ρ − yk ) n1 n p + nk an + ak ∂ k˙ ∂p
1368
U. Lehmijoki, T. Palokangas −
+ ( ∂ k˙ 1 n 1 ak = − (ρ − yk ) n p + nk an + J na ∂k n
* ε, ∂ k˙ + ∂ k˙ nk + an (ρ − yk ) + n <0 − ∂p ∂k n θ )
˙ ∂k ε ∂ k˙ ρ − yk ∂ k˙ nk ⇔ + an > (n p + nk an ) + (ρ − yk ) + n ak ∂p ∂k n θ ∂k n
+
nk ε 1 1 ⇔ (ρ − yk ) + n > 1+ (yn − k)nk + yk + m − 1 + n n θ θ θ ˙ ∂ k˙ −1 1 ∂k + an an ) + × (ρ − yk ) (n p + nk ak n ∂p ∂k ⇔
ε nk 1 > (yk − ρ) 2 + θ n n
1 1 1+ (yn − k)nk + yk + m − 1 + n θ θ
1 an ) + ak × (ρ − yk ) (n p + nk n −1 1 (yn − k)(n p + nk an × 1+ an ) + a + (yk + m − n) θ .
D. Result (Eq. 28) Noting Eqs. 13 and 14, temporary utility Eq. 7 in the steady state is u = log c + θ log n + εv k − κ = (1 + θ) log n(k, a, p) + log[k − yn ( p)] − log θ + εv k − κ .
(35)
Because p is the price of an exported good that is not domestically consumed, an increase in p must increase the resources of the economy and the steady-
Trade, population growth, and environment in developing countries
1369
state temporary utility Eq. 35. Noting Eqs. 6, 7, 13, κ = k, and Proposition 1, we then obtain du dk da 1 dk dk 1+θ + na − an + εv 0< nk = + np +
dp
dp n dp k − y dp dp
n + + − +
+
−
+
1 dk θ 1+θ nk 1 ak dk + εv (0) +ε− < nk + = + n k − yn dp n k − yn n an dp n an ε θ dk = nk + + n an − ak k − yn θ θ n an dp
+
and
+
n an ε nk + + n an − ak > 0. k − yn θ θ
(36)
Noting Eqs. 13 and 27, the saddle point condition Eq. 24 can be written as ˙ ˙ ˙ ∂ k˙ ∂ k˙ ∂ k˙ ∂k ∂k ∂ k − na ∂ k˙ ∂k ∂a ∂k ∂a ∂k nk ∂a ∂a J = ∂ a˙ ∂ a˙ = = 2 2 n ε ∂k ∂a (ρ − yk ) nk + n ε ρ − yk ρ − yk na na θ na θ na ∂ k˙ n2 ε ∂ k˙ ∂ k˙ (ρ − yk ) − − < 0. = ∂k nk ∂a na θ ∂a
−
−
−
+
−
Rearranging terms, we obtain n2 ε ∂ k˙ ∂ k˙ na ∂ k˙ ρ − yk = − > 0, na θ ∂a ∂k nk ∂a
+
−
−
−
yk < ρ.
(37)
−
From Eqs. 13, 17, 20, 25, 36, and 37, it follows that ˙ np ∂ a˙ ε 1 n ∂k = (ρ − yk ) + ak − n an − nk +
∂ p k=˙ n θ n k − y ∂ p ˙ a=0 n
+ −
< ak −
+
>n an /θ
an ε n n a n − nk + < 0. θ k − yn θ
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