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Industrialization and environmental externalities in a Solow-type model
Journal of Economic Dynamics & Control 47 (2014) 211–224
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Journal of Economic Dynamics & Control journal homepage: www.elsevier.com/locate/jedc
Industrialization and environmental externalities in a Solow-type model Angelo Antoci a, Paolo Russu a, Serena Sordi b,n, Elisa Ticci b a b
Dipartimento di Scienze Economiche e Aziendali, Università di Sassari, Via Muroni 25, 07100 Sassari, Italy Dipartimento di Economia Politica e Statistica, Università di Siena, Piazza San Francesco 7, 53100 Siena, Italy
a r t i c l e i n f o
abstract
Article history: Received 29 April 2014 Received in revised form 31 July 2014 Accepted 10 August 2014 Available online 15 August 2014
In this paper we examine the role played by environmental externalities in shaping the dynamics of an economy with two sectors (a farming sector and an industrial one), free inter-sectoral labor mobility and heterogeneous agents (workers/farmers and industrial entrepreneurs). We find that, in the presence of the environmental pressure of the economic activity of the industrial sector, the stability properties of the equilibria and their features in terms of environmental preservation, welfare outcomes and sectoral allocation of labor are sensitive to the level of carrying capacity. We show that an endogenous process of industrialization associated with a reduction in farmers/workers' welfare can emerge. & 2014 Elsevier B.V. All rights reserved.
JEL classification: D62 O11 O13 O15 O41 Q20 Keywords: Environmental negative externalities Industrialization Economic growth with heterogeneous agents
1. Introduction Industrialization is usually considered a necessary, albeit not a sufficient, condition for poverty reduction. The expansion of the industrial sector is indeed a key feature of the growth processes of those countries which have been successful in combating poverty and in ensuring satisfactory living conditions for vast sections of the population. The fact that several countries have experienced higher labor productivity and industrialization without poverty reduction is often traced back to low absorption of labor in higher productivity sectors and to a lack of labor transfer from rural subsistence to modern activities with the consequent expansion of the urban informal sector (Easterly, 2003; Ocampo et al., 2009). Within this conceptual framework, less attention has been paid to the role that environmental externalities may have for economic growth and poverty reduction during the industrialization processes. This paper attempts to make a contribution towards filling this gap. To this end, in order to concentrate on the effects of industrial pollution on capital accumulation and welfare, we adjust the framework proposed by Matsuyama (1992). In this seminal work, he suggests that the link between labor productivity in farming and manufacturing growth changes according
n
Corresponding author. Tel.: +390577232644. E-mail addresses: [email protected] (A. Antoci), [email protected] (P. Russu), [email protected] (S. Sordi), [email protected] (E. Ticci).
http://dx.doi.org/10.1016/j.jedc.2014.08.009 0165-1889/& 2014 Elsevier B.V. All rights reserved.
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to the degree of trade openness. In small open economies, if productivity in the agricultural sector is low, then the industrial sector could benefit from a large supply of labor at low cost and, in this way, the economy could gain a comparative advantage in manufacturing production. The opposite relation holds for closed economies. In our paper, by focussing on the study of an open economy, we also find that low productivity in the farming sector can be an engine of the industrialization process. However, in our model the industrialization process generates environmental degradation and, consequently, a reduction in labor productivity in the farming sector. In other words, industrialization may be associated with a decrease in workers' welfare. This extension appears to be important since, in recent decades, the growth of industrial activities has expanded the industrial frontier in many poor and middle income countries. Positive and negative interactions between small producers in resourcedependent activities and industrial firms have therefore increased. A few figures are enough to describe this trend. First of all, between 1990 and 2010 the share of world industrial value added accounted for by low and middle income countries almost doubled from 17.5 to 33.5 percent, while their rural population share declined more slowly from 65 to 55 percent.1 Moreover, in the same period, it has been estimated that the domestic footprint of sulphur dioxide (SO2) for low and middle income countries climbed from about 52,000 to more than 93,000 gigagrams (Gg) compared to a decline from 54,000 to about 18,000 Gg in high income countries.2 An emblematic example of the possible effects of pollution when natural resources are used as productive inputs by small producers is reported in Reddy and Behera (2006, pp. 530–534). By analyzing the impact of industrial water pollution in a village of Andhra Pradesh, they find that the “majority of the cattle is becoming sick over the years […]. The amount of land under cultivation has declined substantially (88%) due to the incidence of pollution […]. Most of the people who were depending on agriculture before pollution have shifted to industry, business and other sources. The majority of them have become daily laborers.” The extension and severity of air, water and soil contamination of industrial activities, such as textile and leather industry, are also well documented in China (Economy, 2004; Greenpeace International, 2012) and in Bangladesh (Human Rights Watch, 2012) and recently acknowledged also by their governments.3 In what follows we analyze the interactions between economic development, sectoral output composition and the environment by modeling an economy where environmental degradation affects workers' incentive to move out of the environmentally sensitive sector. This reduces workers' dependence on natural resources, but it can also fuel a self-reinforcing process of growth in industrial production and pollution. In doing this, we contribute to a growing body of literature which studies how, in multisectoral economies where natural resources are used as productive inputs, structural change processes and reallocation of labor across sectors can emerge as endogenous adjustments to a reduction in natural capital affecting economic growth and social welfare (see López et al., 2007; López, 2010; Bretschger and Smulders, 2012; Peretto, 2012; López and Schiff, 2013). Most of these models are concerned with the role of both the substitution between natural resources and man-made inputs (or labor) and the change in natural resource prices in driving the economy towards a sectoral shift which allows sustainable growth. These models, however, abstract from the distributional implications associated with such processes and, with the exception of López (2010), identify resource-using and resource-impacting activities. We build on this literature by taking a broader distributional perspective. More precisely, we analyze a two-sector model with free access to renewable natural resources as factors of production. The physical capital is specific to the industrial sector whereas the natural capital is specific to farming. Both sectors employ labor, but only the industrial sector produces environmental externalities which, in turn, affect labor costs and labor productivity. There are no constraints to inter-sectoral labor mobility and, as a consequence, labor productivity gains in the economy are equally shared among workers and there is no risk that possible benefits of industrialization are offset by a low absorption of labor in higher productivity sectors. Moreover, we exclude the impact of domestic food supply and domestic demand on the prices of the goods produced by the two sectors. In this way, we concentrate on the role of resource-based activities in setting the basic opportunity cost for labor in the whole economy. Our model is complementary to that proposed by López and Schiff (2013). We analyze a similar setting (i.e., one with a resource-dependent sector, a manufacturing sector which is more capital intensive, exogenous prices and open access environmental resources) but with a crucial difference. In our model the polluting sector is the man-made capital intensive sector and not the resource-dependent sector. We consider a poor economy where the resource-dependent sector is represented by small producers engaged in primary activities as in López and Schiff (2013), but the main environmental threat is posed by the capital intensive sector. In other words, we concentrate on welfare and environmental dynamics generated by the pollution of non-primary activities instead of on the problem of over-harvesting and over-exploitation by primary and commodity activities which do not internalize the environmental impact. We confirm that a decline in labor share employed in the natural resource-intensive sector can arise in the absence of biased technological progress and can be an endogenous response to low labor
1
Data from World Development Indicators accessed in December 2013. The largest sources of SO2 emissions are from fossil fuel combustion in the energy and industrial sectors. These emissions are a primary cause of acid rain and have a negative impact on forest and agriculture crops and on aquatic ecosystems in addition to adverse effects on human health (World Bank, 1999). The figures given in the text are our own elaboration from the Eora MRIO dataset (Lenzen et al., 2012, 2013), accessed in November 2013. If SO2 embedded in imports are subtracted and those embedded in exports are added to domestic SO2, the total SO2 emissions at home for low and middle income countries are 56,864 Gg in 1990 and 107,747 Gg in 2011. 3 In February 2012, Chinese premier Wen Jiabao said that “Water pollution is mainly resulting from industrial and sewage waste water and is now in very serious situation.” (reported in Greenpeace International, 2012). Li Yang, Vice-President of the Chinese Academy of Social Sciences, in February 2013, said that “China's real economic growth rate would only be around 5%, if economic losses caused by ecological degradation and environmental damage are subtracted from the overall GDP,” (http://English.news.cn/, 2013-02-28). Finally, in November 2013, Bangladesh's governments planned to relocate the leather industry from central Dhaka to another area where there are several centralized waste-treatment facilities (http://asiafoundation.org/in-asia/, November 13, 2013). 2
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productivity in this sector. However, we obtain that a structural change can emerge even in the absence of a change in the relative prices of goods produced in the economy. Moreover, we find that the role of physical capital accumulation is much more ambivalent and less univocal. A development path associated with increasing physical and natural capital, and with an increase in workers' welfare, is possible only under specific conditions, namely, an intermediate level of carrying capacity and a sufficiently preserved initial environment. We follow the basic set-up proposed by Antoci et al. (2010, 2012), but with two main differences. First, we consider a stronger differentiation of the two sectors, while they analyze an economy where the production activities of both sectors depend on natural resources and generate negative environmental impacts. As a result, we obtain rather different dynamics and more clear-cut results about the welfare implications of the dynamic regimes that can be observed. Second, due to their assumption that the accumulation process of physical capital is driven by entrepreneurs' intertemporal optimization choices, the analysis in Antoci et al. (2010, 2012) does not go beyond the local stability of the equilibrium points. In contrast, we describe the investment in physical capital as a Solow-type accumulation process. Consequently, the formalization is much simpler and makes it possible to analyze the global dynamics of the model. Despite these crucial differences in the modeling of the capital accumulation process, the results are substantially confirmed, indicating that they do not critically depend on the hypotheses about agents' rationality. Our main findings seem, rather, to hinge on the inability of natural resource-dependent agents to coordinate and internalize the externalities of economic activities. We find that regimes with multiple attractive equilibria are possible and that capital accumulation can lead to an increase in inequality between the two population groups.4 The analysis of the model explains how welfare, distributive and environmental outcomes of industrialization depend on two main factors: the initial endowment of natural capital and the level of environmental carrying capacity. Industrialization is hampered in economies starting from a relatively preserved natural capital and high level of carrying capacity. On the contrary, economies with very low carrying capacity or with poor initial environmental conditions tend to undertake a process of complete industrialization with negative impacts on the environment and social equity. In other words, an immiserizing and unsustainable complete industrialization occurs. Finally, for intermediate levels of carrying capacity and sufficiently high values of initial natural capital, this type of negative industrialization can be avoided and the transition from an agrarian economy to a more diversified economy allows an increase in workers' welfare. The rest of the paper is organized as follows. The model is presented in Section 2, where the equilibrium points of its dynamic system are also derived. Section 3 contains an analysis of both the local/global stability and welfare properties of the equilibrium points, whereas Section 4 offers a characterization of the different dynamic regimes that can emerge. Section 5 concludes. All proofs and lengthy computations are contained in the Appendix at the end of the paper. 2. The model We model an economy in which economic agents belong to two different communities, one consisting of ‘farmers’, the other of ‘industrial entrepreneurs’. The former are endowed with their own working capacity only, which they use partly in their fields for the production of farming goods with the use of a natural resource and partly as employees of the industrial entrepreneurs.5 The latter produce industrial goods with the physical capital they own and the labor force they hire. Accordingly, economic activity is divided into two sectors which we define as the ‘F-sector’ (Farming) and the ‘I-sector’ (Industry). 2.1. Production in the two sectors and economic agents' choices The productivity of labor in the F-sector depends on the stock of the natural renewable resource E. On the other hand, production in the I-sector depends on the stock of the capital K owned by industrial entrepreneurs and on the labor force L provided by farmers. For simplicity, we assume that industrial entrepreneurs do not invest in the F-sector and that the latter is only composed of small firms run by farmers. Moreover, we focus on the behavior of two representative agents, one for each sector. The production function of the firm run by the representative farmer (F-agent) is given by Y F ¼ Lα Eβ
α; β 4 0;
α þ β r1
ð1Þ 6
where 1 Z L Z0 is her/his labor input and E the stock of a natural renewable resource. On the other hand, that faced by the representative industrial entrepreneur (I-agent) has constant returns to scale and is such that Y I ¼ ð1 LÞα K 1 α For simplicity, both the elasticities of YF and YI with respect to L and 1 L, respectively, are assumed to be equal to α. Thus, possible differences in the productivity of labor employed in the two sectors depend on the levels of the stocks E and K only. 4 In light of this possible negative correlation between farmers' and entrepreneurs' welfare, we do not study the social optimum. In this case, indeed, the benevolent social planner's decisions would be strictly linked to the ‘weights’ she/he assigns to the two types of agents. 5 Empirical evidence (see, e.g., Barbier, 2010) suggests that in developing countries farmers are not able to sensibly modify their physical capital endowment in the short/medium run. To simplify, we therefore assume that farmers cannot accumulate physical capital. 6 In the case in which the F-agent also owns a fixed amount T of land or other forms of capital, an equation of the same type as (1) could be obtained by writing the production function as Y F ¼ Lα T 1 α Eβ and then normalizing to one the fixed amount T.
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Let us now analyze agents' choices. To simplify, we assume that the prices of both the agricultural and industrial goods are constant and equal to unity and that both the I-agent and the F-agent take the wage rate w, expressed in terms of the industrial output, as exogenously given. In each instant of time t, the I-agent maximizes with respect to 1 L her/his revenue, given by RI ¼ ð1 LÞα K 1 α wð1 LÞ
ð2Þ
which gives rise to the following first order condition:
αð1 LÞα 1 K 1 α ¼ w
ð3Þ
Analogously, the F-agent maximizes with respect to L her/his revenues, measured by the function RF ¼ Lα Eβ þ wð1 LÞ
ð4Þ
such that the corresponding first order condition is
αLα 1 Eβ ¼ w
ð5Þ
Finally, by equalizing the left-hand sides of (3) and (5), we obtain the following equilibrium value of the variable L: Eβ=ð1 αÞ L ¼ β=ð1 αÞ E þK
ð6Þ
2.2. The dynamic system With regard to the dynamics of K and E, the accumulation process of the former is built on the assumption of a constant propensity to save, as in Solow's (1956) growth model. Thus, indicating with a dot over a variable its first derivative with respect to time, we have K_ ¼ sRI dK
ð7Þ
where the parameters s, d A ð0; 1Þ represent the marginal propensity to save and the depreciation rate of the capital stock, respectively. The time evolution of the stock of natural renewable resource E, on the other hand, is assumed to be given by ( _E ¼ EðE EÞ εY I for E 4 0 ð8Þ 0 for E ¼ 0 where the parameter ε 4 0 measures the environmental impact of production in the I-sector, the parameter E 4 0 represents the carrying capacity of the natural resource and Y I is the economy-wide average value of YI, taken as exogenously given by the two representative agents. Consequently, the I-sector produces negative environmental externalities that agents are not able to internalize due to coordination problems. As will soon be evident, this assumption plays a crucial role in shaping the results of our model, much more than the assumption about the mechanism for the accumulation process of physical capital. It is meant to take account of the fact that environmental externalities have a strong impact on economic activities, especially in developing countries, where property rights tend to be ill-defined and ill-protected, environmental institutions and regulations are weak and natural resources are more fragile than in developed countries (see, e.g., López, 2007). Finally, by substituting (6) into Eqs. (7) and (8), and taking account also of Eqs. (3) and (5), we obtain the following nonlinear dynamic system in the two variables E and K: 8 εK > < E E E for E 4 0 E_ ¼ ð9Þ ðEβ=ð1 αÞ þ KÞα > : 0 for E ¼ 0 " K_ ¼
sð1 αÞ
ðEβ=ð1 αÞ þ KÞα
# d K
ð10Þ
which, clearly, is not defined for E¼K ¼0. 3. Basic mathematical results and dynamic properties of the model In this section, we describe the basic mathematical results, while all proofs are deferred to the Appendix at the end of the paper.
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3.1. Isoclines We first turn to the problem of the determination and characterization of the equilibrium points of our model. First of all notice that, from (10), it follows that K_ ¼ 0 holds if either K ¼0 or K ¼ θ Eβ=ð1 αÞ
ð11Þ
where θ ≔ ½sð1 αÞ=d1=α 4 0 and 1 4 β=ð1 αÞ 4 0. According to (11), K is a strictly decreasing function of E, the graph of ð1 αÞ=β which intersects the E-axis at ðθ ; 0Þ and the K-axis at ð0; θÞ; moreover, K_ o 0 ðK_ 4 0Þ holds above (respectively, below) it. Analogously, E_ ¼ 0 holds if either E ¼0 or E E E
εK
ðEβ=ð1 αÞ þ KÞα
¼0
ð12Þ
which implicitly defines an inverted-U function K ¼ Γ ðEÞ such that Γ ðEÞ ¼ 0 and Γ ðEÞ-0 for E-0 (see Section A.1 of the Appendix). 3.2. Equilibrium points Equilibrium points with either E ¼0 or K¼0: The intersection point between the branch of the K_ ¼ 0isocline, defined by (11), and the K-axis (along which E_ ¼ 0), i.e. ð0; K 0 Þ ¼ ð0; θÞ and the intersection point between the branch of the E_ ¼ 0isocline, defined by (12), and the E-axis (along which K_ ¼ 0), i.e. ðE0 ; 0Þ ¼ ðE; 0Þ are always equilibrium points of the dynamic system (9)–(10). Internal equilibrium points: By substituting K as defined in Eq. (11) into Eq. (9), we obtain that the time evolution of E, for E 4 0, is described by the equation E_ ¼ f 1 ðEÞ f 2 ðEÞ where 1α f 1 ðEÞ ≔ E E E εθ
ε θ
f 2 ðEÞ ≔ α Eβ=ð1 αÞ
Internal equilibrium points are therefore defined by the intersections between the graphs of the two functions f 1 ðEÞ and f 2 ðEÞ. As it is easy to check (see Fig. 1), the graphs of f 1 ðEÞ and f 2 ðEÞ can have at most two intersections and consequently at most two internal equilibrium points can exist. We shall indicate by A (respectively, by B) the intersection point in 0 0 0 0 correspondence of which f 1 ðEÞ 4 f 2 ðEÞ (respectively, f 1 ðEÞ of 2 ðEÞ). Only intersections which are associated with strictly positive values of K and E are admissible internal equilibrium points. More specifically, a value E ¼ En 4 0 identifies an equilibrium point with E; K 4 0 if f 1 ðEn Þ ¼ f 2 ðEn Þ and if, when substituted in (11), gives a value of K which is strictly positive, i.e. if En o EM ≔ θ
ð1 αÞ=β
where EM – which is independent of E – is the value of E at which the K_ ¼ 0isocline intersects the E-axis. Fig. 1 illustrates the complete taxonomy of possible cases in which at least one internal equilibrium point exists. They are obtained by varying only the value of the carrying capacity E, which is increasing from E 0:4982 in Fig. 1(a) to E ¼ 1:1 in Fig. 1(d).7 The case of tangency between f 1 ðEÞ and f 2 ðEÞ is shown in Fig. 1(a). For values of E less than the value we have used to generate this figure, clearly, the two curves do not intersect in the first quadrant and, therefore, the system does not admit internal equilibrium points. When the value of E increases, the curve f 2 ðEÞ does not move, whereas the curve f 1 ðEÞ ‘expands’ itself in such a way that two points of intersection between the two curves emerge (one of type A and another of type B, as shown in Fig. 1(b)). However, the intersection points of the two curves correspond to internal equilibrium points only if they are located on the left of the vertical line E ¼ EM . Thus, when E is further increased beyond the value used to generate the ‘critical’ case of Fig. 1(c), there exists only one internal equilibrium of type A, as in Fig. 1(d). The following proposition summarizes the cases just described. 7 In this figure and in all others that follow, when not otherwise stated, we fix the parameters of the production function, the depreciation rate, the propensity to save and the environmental impact of the production in the I-sector at α ¼ 0:6, β ¼ 0:3, d ¼0.1, s ¼0.25 and ε ¼ 0:1, respectively.
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0.3
0.3
f 1 (E) 0
A ,B
A
0
f 2 (E)
B f 2 (E)
f 1 (E) −0.2
0
E
EA = EB
M
1.4
−0.2
0
E
A
B
E
1.4
EM
1.4
M
E
E 0.3
0.3
f 1 (E)
f 1 (E)
A
0
A
0
B
f 2 ( E)
f 2 (E) −0.2
E
0
EA
E =E B
E
M
1.4
−0.2
0
EA
E
Fig. 1. A taxonomy of the number of internal equilibrium points for different values of the carrying capacity of environment: (a) E 0:4982, (b) E ¼ 0:7, (c) E ¼ 1 and (d) E ¼ 1:1.
Proposition 1. A necessary and sufficient condition for the existence of a unique internal equilibrium point (which is always of type A) is E 4θ
ð1 αÞ=β
¼ EM
ð13Þ
When condition (13) is not satisfied, the dynamic system (9)–(10) generically admits either zero or two internal equilibrium points.8 In this case, a sufficient condition for the non-existence of internal equilibrium points is !2 E α β=ð1 αÞ 1α þ εθ E o εθ ð14Þ 2 while a sufficient condition for the existence of two internal equilibrium points (one of type A and the other of type B) is9 !2 !β=ð1 αÞ E α E 1α þ εθ 4 εθ 2 2
8 9
Also the case of a unique internal equilibrium point is again possible, but only in the critical case in which f 1 ðEÞ and f 2 ðEÞ are tangent. Necessary and sufficient conditions for this case could also be indicated. They are however rather complicated and not easily interpretable.
ð15Þ
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Proof. See Section A.2 of the Appendix
217
&
3.3. Local/global stability properties and welfare ranking of stationary states To go deeper into the understanding of the dynamics generated by our model, and in the attempt to identify and characterize the dynamic regimes that can emerge, we now turn to the problem of the stability properties of the equilibrium points, which are described by the following proposition. Proposition 2. The equilibrium point of type A, ðEA ; K A Þ, is always a saddle point while that of type B, ðEB ; K B Þ, is always locally attractive. The equilibrium ðE0 ; 0Þ ¼ ðE; 0Þ is a saddle point (with stable manifold lying in the E-axis) if E o EM while it is locally attractive if E 4 EM . The equilibrium point ð0; K 0 Þ ¼ ð0; θÞ is always locally attractive. Proof. See Section A.3 of the Appendix
&
In turn, the global stability properties of the dynamics generated by system (9)–(10) are illustrated by the following proposition. Proposition 3. The set Q ¼ fðE; KÞ: 0 r E r E and 0 rK r θg is positively invariant under the dynamic system (9)–(10); furthermore, every trajectory starting outside it either enters it in finite time or approaches the equilibrium point ð0; K 0 Þ ¼ ð0; θÞ lying on the boundary of Q. Proof. See Section A.4 of the Appendix
&
In order to discuss the economic and distributive implications of all possible scenarios generated by the model, it is useful to compare the various stable equilibrium points of the dynamic system of our model, in terms of the revenues of the two representative agents. As we have seen, the F-agent uses a natural resource which is available at zero cost but is exposed to negative externalities. The I-agent, on the other hand, does not use free environmental resources, but has to save in order to accumulate physical capital. Her/his advantage is that, unlike the F-agent, she/he can hire wage labor and expand her/his physical capital over time, not harmed by environmental externalities. The F-agent is indirectly affected by physical capital accumulation through two different channels: on one hand, a rise in labor productivity in the I-sector due to an increase in K has a positive effect on the equilibrium wage rate; on the other hand, the resulting net environmental impact, due to the combination of scale and labor sectoral composition effects, influences the productivity of agricultural labor and consequently the opportunity cost of wage labor. To analyze the welfare properties associated with each equilibrium point, we should remember that the revenues of the F-agent are measured by Eq. (4). By substituting in it the equilibrium values of w and L given by (3) and (6), respectively, Eq. (4) becomes RF ¼
Eβ=ð1 αÞ þ αK
ðEβ=ð1 αÞ þ KÞα
such that ∂RF =∂E 40 and ∂RF =∂K 4 0. Furthermore, since from (11) it follows that along the decreasing branch of the K_ ¼ 0isocline the condition Eβ=ð1 αÞ þK ¼ θ holds, the value of RF evaluated along it can be expressed as a function of E only, i.e. RF ðEÞ ¼
1 α β=ð1 αÞ 1α þ αθ α E
ð16Þ
θ
Let us now consider the I-agent revenues, which, given Eq. (2), can be expressed as RI ¼
ð1 αÞK
ð17Þ
ðEβ=ð1 αÞ þ KÞα
such that ∂RI =∂E o 0 and ∂RI =∂K 4 0. By substituting in (17) the equilibrium condition (11), it follows that, along the K_ ¼ 0isocline, the value of RI can be expressed as a function of K only, i.e. RI ðK Þ ¼
ð1 αÞK
ð18Þ
θα
Finally, notice that aggregated revenues, evaluated along the decreasing branch of the K_ ¼ 0isocline (where Eβ=ð1 αÞ þ K ¼ θ holds), can be written as RI ðK Þ þ RF ðEÞ ¼
1 α β=ð1 αÞ ð1 αÞK 1α þ αθ þ α E α
θ
θ
1 α sð1 αÞ ð1 αÞ=α 1α 1α ¼ α Eβ=ð1 αÞ þ K þ αθ ¼θ ¼ d θ
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1.6
K0
K
.
.
E=0
0
0
K=0
E
E
EM
1.2
Fig. 2. The case of ð0; K 0 Þ globally attractive (with E ¼ 0:43 such that condition (13) is not satisfied whereas (14) holds).
i.e., aggregate revenues, evaluated at the equilibrium points with K 40, are constant: if farmers' revenues increase, then entrepreneurs' revenues decrease of the same amount. The following proposition sums up the above results. Proposition 4. Along the decreasing branch of the K_ ¼ 0isocline: (1) The revenues of the I-agent are represented by the strictly increasing function of K shown in (18), whereas those of the Fagent by the strictly increasing function of E shown in (16). 1α (2) Aggregate revenues are constant, that is RI ðKÞ þ RF ðEÞ ¼ θ . Eqs. (16) and (18) tell us something rather interesting: once we have fixed the parameters, the welfare of the F-agent is positively correlated with E and does not depend on K, even in the presence of diversification in income sources. Vice versa, the revenues of the I-agent are positively correlated with K and do not depend on E. Consequently, along the decreasing branch of the K_ ¼ 0isocline, to which the equilibrium points ð0; K 0 Þ and ðEB ; K B Þ belong, there is a trade-off between the Iagent's revenues and those of the F-agent. This implies that in ð0; K 0 Þ, the revenues of the I-agent are higher than in ðEB ; K B Þ, and vice versa for the revenues of the F-agent, being EB 4 0 and K B oK 0 . β Furthermore, notice that in the equilibrium ðE0 ; 0Þ ¼ ðE; 0Þ the revenues of the F-agent are given by E and that β 1α E 4 RF ð0Þ ¼ αθ holds if E 4 ðαθ
1 α 1=β
Þ
Condition (19) is always satisfied when the equilibrium ðE0 ; 0Þ is locally attractive, i.e., when E 4 θ following proposition can be stated.
ð19Þ ð1 αÞ=β
. Consequently, the
Proposition 5. In the bistable dynamic regimes in which the attractive equilibrium point ð0; K 0 Þ coexists with another attractive equilibrium – either ðEB ; K B Þ or ðE0 ; 0Þ – the revenues of the I-agent are higher in ð0; K 0 Þ than in ðEB ; K B Þ or ðE0 ; 0Þ, whereas the opposite holds for the revenues of the F-agent. 4. Dynamic regimes Having illustrated the main properties of the dynamics generated by our model, we can now go into detail about their economic interpretation. This section identifies and compares all possible paths that the economy under study may follow and discusses under which conditions each scenario emerges. All the possible configurations of the K_ ¼ 0 and E_ ¼ 0isoclines and dynamic regimes that can be (generically) observed are illustrated in Figs. 2–4,10 where attractive equilibrium points are marked by full dots ðÞ and saddle points by squares ð□Þ. It turns out, as shown by the arrow diagrams in the figures, that the regions of the plane (E,K) between the K_ ¼ 0 and E_ ¼ 0isoclines are positively invariant under the dynamic system (9)–(10). This implies that no closed trajectory can exist around the equilibrium point ðEB ; K B Þ and therefore, by the Poincaré–Bendixson Theorem, every trajectory approaches an 10 For the sake of simplicity, the non-robust case in which the K_ ¼ 0 and E_ ¼ 0isoclines have a tangency point is not considered in the following classification. However, it is easy to check that, in this case, the unique internal equilibrium point is a saddle-node.
A. Antoci et al. / Journal of Economic Dynamics & Control 47 (2014) 211–224
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1.6
K0
K
.
E=0
0
0
.
K=0
_ EM E 1.2
E
Fig. 3. The case of one internal equilibrium point of type A and two coexisting locally attractive points at ð0; K 0 Þ and ðE0 ; 0Þ (with E ¼ 1:1 such that condition (13) holds).
1.6
K0 (EA,KA)
K
.
E=0
0
0
(EB,KB)
E
_ E
.
K=0 EM
1.2
Fig. 4. The case of two internal equilibrium points, one of type A and one of type B, and one locally attractive equilibrium point at ð0; K 0 Þ (with E ¼ 0:7 such that neither condition (13) nor condition (14) is satisfied whereas condition (15) holds).
equilibrium point. The numerical simulations illustrated in the figures are obtained by varying (ceteris paribus) the value of the carrying capacity E of the environmental resource, starting from the parameter values we have used in Fig. 1 and taking into account the conditions given in Proposition 1. The possible dynamic regimes are the following three: 1. Regime with specialization in the I-sector (see condition (14)). In this dynamic regime – which is illustrated in Fig. 2 – the stationary state ð0; K 0 Þ is globally attractive. The economy converges towards a full industrialization accompanied by environment depletion, regardless of the initial endowments of natural and physical capital. In the stationary state ð0; K 0 Þ, the stock of physical capital reaches its (non transient) maximum level (that is, K0), which is however associated with the lowest and highest equilibrium values of workers' and entrepreneurs' revenues, respectively. Along the trajectories approaching ð0; K 0 Þ, the processes of capital accumulation and industrialization generate a growth in workers' poverty in that environmental degradation reduces both wages in the industrial sector and the productivity of labor in the farming sector.
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2.5
K
2.5
K0 1
K0
K
1
(EA , KA)
(EA , KA)
(EB , KB) 0
0
0.5
E
(EB , KB) 0
1.2
E
0
0.5
E
E
1.2
2.5
K0
K 1
(EA , KA) (EB , KB)
0
0
0.5
E
1.2
E Fig. 5. Basins of attraction of the attractive equilibrium points ð0; K 0 Þ and ðEB ; K B Þ for different values of the parameter ε, with the remaining parameters all fixed at the values of the simulation in Fig. 4. (a) ε ¼ 0.1, (b) ε ¼0.15 and (c) ε ¼ 0.22.
2. Bistable regime without coexistence of the two sectors (see condition (13)). In this case, illustrated in Fig. 3, only one internal equilibrium point exists, i.e., ðEA ; K A Þ, and there are in addition two coexisting locally attractive equilibrium points, the equilibrium ð0; K 0 Þ with full specialization in the I-sector and the equilibrium ðE0 ; 0Þ with full specialization in the F-sector. Dynamics are path-dependent: if the economy starts near enough to ð0; K 0 Þ (respectively, to ðE0 ; 0Þ), then the equilibrium point with full industrial (respectively, farming) specialization is reached. Along the trajectories belonging to the basin of attraction of ð0; K 0 Þ, environmental degradation helps industrial growth pushing labor force out of the Fsector and, consequently, exerting downward pressure on the wage rate in the industrial sector. In contrast, along the trajectories belonging to the basin of attraction of ðE0 ; 0Þ, industrialization does not take off. In the first phase, both K and E may increase, but then the return to labor in the farming sector becomes sufficiently high to reduce labor supply for the industrial sector and the economy converges to a full specialization in the natural-resource based sector. In this case, the farmers obtain higher revenues and the environment is preserved but the possibility of exploiting the benefits of physical capital accumulation is ruled out. Therefore, in the long run, also this equilibrium might represent a poverty-trap. 3. Bistable regime with coexistence of the two sectors (neither condition (13) nor condition (14) are satisfied). In this case, illustrated in Fig. 4, two internal equilibrium points exist. The stationary state ð0; K 0 Þ and the stationary state ðEB ; K B Þ are locally attractive and the stable manifold of the stationary state ðEA ; K A Þ separates their basins of attraction. Also in this case, the economy is characterized by a bistable regime. If initial values of E are very low, it will undertake a process of full industrialization and sustained physical capital accumulation, associated with environmental degradation and impoverishment of the F-agent. However, for higher initial values of E, a poor economy with low initial endowments of physical capital converges to the equilibrium ðEB ; K B Þ along a path with both growing physical and natural capital, namely along a sustainable path. In the equilibrium ðEB ; K B Þ, the welfare of the F-agents is higher compared to that in the alternative equilibrium ð0; K 0 Þ, the coexistence of the two sectors is observed in a non-transient way and the level of inequality between the two representative agents is less than in the two polar cases ð0; K 0 Þ and ðE0 ; 0Þ. Fig. 5 shows how the size of the basins of attraction of the equilibrium points ð0; K 0 Þ and ðEB ; K B Þ changes varying ε, the parameter measuring the environmental impact of the industrial sector. The basin of ð0; K 0 Þ is represented in grey and is separated from the basin of ðEB ; K B Þ by the stable manifold of the saddle point ðEA ; K A Þ. It turns out that, if the value of ε increases, the basin of ð0; K 0 Þ expands and that of ðEB ; K B Þ shrinks. In other words, economies which are exposed to an intensive rate of industrial pollution are less likely to undertake sustainable development paths and more prone to follow industrialization processes without development (i.e., with farmers' impoverishment and environmental depletion).
Notice that, ceteris paribus, conditions (13) and (14) are satisfied if the carrying capacity E is, respectively, high and low enough. Furthermore, the conditions (13) and (14) hold if the value of θ ¼ ½sð1 αÞ=d1=α is, respectively, low and high ð1 αÞ=β enough (remember that EM ¼ θ ). So, if θ is very high relatively to the carrying capacity E, the economy is more likely to specialize in the physical capital-intensive sector, the industrial one. Notice that the value of θ depends positively on the
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propensity to save s and on the elasticity 1 α of the industrial output YI with respect to physical capital K, while it is negatively related to the depreciation rate d of physical capital.11 The notion of welfare reducing industrialization can be better grasped by referring to a representative case. Haiti, for instance, provides an example of a country which is undertaking the first phases of industrial development starting from a very low level of carrying capacity or a very initial deteriorated environment. In the last two centuries, the carrying capacity of Haiti has drastically reduced due to both external and internal factors.12 In a context of fragile and very poor farming, a development model based on export zones for foreign-financed manufacturing firms has been experimented since the 1970s and recently reaffirmed as a one of the elements of a ‘realistic strategy’ for a rapid attainment of economic security (Collier, 2009). Recent trade agreements and government initiatives, indeed, have attracted foreign investors to the exportoriented apparel industry which appreciated Haiti's low-cost workforce and steady supply of labor (Nathan Associates Inc., 2009). Insufficient agriculture income and the promise of better wages have also encouraged rural–urban migration (Alscher, 2011) and increasing urban population and demand for charcoal have further stressed the environment. As a result of all these processes, Haiti is now characterized by extreme inequality, low wages, environmental crisis and growing industrialization. Countries with a relatively successful experience of exporting processing zones, such as Mauritius and Costa Rica, instead have promoted external-financed manufacturing within a broader agenda of economic diversification (Shamsie, 2010) and protection of environmental-based economic activities. In other words, they are more likely to reflect conditions for the economy to belong to the third regime with a large basin of attraction of the equilibrium characterized by the coexistence of both sectors (i.e. sufficiently high carrying capacity, sufficiently low industrial pollution rate and preserved initial environment). This is not to say that these countries represent a test of our model or that other institutional, economic and historical factors are not relevant. However, some of the dynamics of their development paths are consistent with the narratives behind the model we have proposed. Our conceptual framework, as all theoretical models, intends to highlight, analyze and disentangle consequences of specific relations, in this case the connection between environmental externalities of industrial activities, inequality and evolution of sector composition. It is also worth observing that major environmental challenges have begun to widespread at international level relatively recently and most of their consequences have not fully revealed. Past experiences of rich economies suggest that industrialization is a necessary condition for a widespread economic development, but that it might be not a sufficient condition. How long and to what extent in today's emerging economies, where the majority of population makes its living from farming, can industrialization bring equitable prosperity while destroying the environment?
5. Conclusions This work draws on the intuition of Matsuyama's (1992) influential model which predicts a negative relationship between agricultural productivity and industrialization (and consequently economic growth) in small open economies. Our model is built on the idea that a large stock of natural capital, by ensuring high productivity in the F-sector, can squeeze out the manufacturing sector in a small open economy with a constant labor supply and free intersectoral labor mobility. However, we depart from this common starting point in that we focus on environmental externalities, agents' heterogeneity and capital accumulation and we exclude the possibility of learning-by-doing in order to concentrate on the negative externalities of growth. We find that some of the welfare implications of Matsuyama's model are reversed: industrialization is not always associated with welfare improvements. Regimes with multiple attractive equilibria are possible. The initial stocks of physical and natural capital and the carrying capacity of the economy affect the type of development path that the economy follows. The admissible alternative scenarios discussed in the paper suggest that environmental externalities and agents' heterogeneity in terms of dependence on natural resources and ability to accumulate physical capital are factors which deserve great attention. These elements significantly affect the distributive and welfare outcomes of industrialization processes and, more generally, of structural changes.
Acknowledgments We thank the three anonymous referees for their helpful comments and suggestions. We are also grateful to the participants in the 7th MDEF Workshop on Dynamic Models in Economics and Finance (September 2012, Urbino, Italy) for discussions and comments on a preliminary version. The usual disclaimers apply. 11 This result confirms that the dynamic regime without coexistence of the two sectors can lead to a poverty trap regardless of the equilibrium, either ð0; K 0 Þ or ðE0 ; 0Þ, to which the system converges. In fact, this dynamic regime occurs for values of s and d which generate a low value of θ and, consequently, a low aggregate welfare (see Proposition 4). 12 Deforestation was started in the 17th century by the colonial power which cleared forests for extracting wood and establishing the system of plantation monoculture. From 1825 to 1947 Haiti paid the debt for its independence and this debt burden induced the government to accelerate deforestation to export the tropical wood. Between 1923 and 1950, the percentage of Haiti's forested land passed from over 60 percent to 25 percent (Alscher, 2011; Library of Congress, 2006). Successively, colonial legacy, population growth and political mismanagement of natural resources have further worsened deforestation, soil erosion and environmental degradation compromising agriculture yield and productivity.
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Appendix A. Mathematical derivations A.1. Study of the isocline E_ ¼ 0 We have that E_ ¼ 0 holds if either E ¼0 or GðE; K Þ ≔ E E E
εK
ðEβ=ð1 αÞ þ KÞα
¼0
Notice that (a) GðE; KÞ ¼ EðE EÞ holds for E 40 and K ¼0; (b) given any K 4 0, GðE; KÞ o 0 holds if either E Z E or the value of E is low enough; (c) there exists a value K such that GðE; KÞ o 0 for every E 40 and K 4K . Some additional properties of the E_ ¼ 0isocline can be highlighted by evaluating the partial derivatives of GðE; KÞ with respect to K and E ∂G Eβ=ð1 αÞ þ ð1 αÞK ¼ ε β=ð1 αÞ ∂K ðE þKÞ1 þ α
αβε
K ∂G ¼ E 2E þ ð1 α βÞ=ð1 1αÞ αβ=ð1 αÞ ∂E ðE þKÞ1 þ α E Notice that ∂G=∂K o 0 always holds: an increase in K generates a shift of labor forces from the environmentally nondamaging F-sector towards the environmentally impacting I-sector. The derivative ∂G=∂E, for a given K 4 0, is strictly decreasing in E and is strictly positive (negative) for E low (respectively, high) enough. Consequently, the equation GðE; KÞ ¼ 0 defines an inverted-U function K ¼ Γ ðEÞ such that Γ ðEÞ ¼ 0 and Γ ðEÞ-0 for E-0. A.2. Proof of Proposition 1 Observe that the difference f ðEÞ ≔ f 1 ðEÞ f 2 ðEÞ is such that f ð0Þ o 0 and limE- þ 1 f ðEÞ ¼ 1 and remember that, by assumption, α þ β r 1 and consequently β =ð1 αÞ r 1. Furthermore, notice that f 1 ðEM Þ 4 f 2 ðEM Þ holds for E 4 εθ
α 1 ð1 αÞ=β
θ
þθ
ð1 αÞ=β
þ εθ
1 α ð1 αÞ=β
¼θ
ð1 αÞ=β
¼ EM
Such a condition holds if and only if f 1 ðEÞ and f 2 ðEÞ have two intersection points, one (which is clearly of type A) on the left of the vertical line E ¼ EM and the other (non-admissible) on the right of it. In other words, (13) is a necessary and sufficient condition for the existence of a unique equilibrium point with E; K 40. Two internal equilibrium points can exist only if condition (13) does not hold. When this is the case, a sufficient condition for the existence of two equilibrium points is f 1 ðE=2Þ 4 f 2 ðE=2Þ and E=2 o EM , i.e. E 2
!2 þ εθ
α
E 2
!β=ð1 αÞ 4 εθ
1α
and
E o EM 2
where E=2 is the value of E maximizing f 1 ðEÞ. Let us now prove the sufficiency of condition (14). A sufficient condition for the non-existence of internal equilibrium points can be obtained by imposing that ! E f1 of 2 E 2 that is, the maximum of the function f1 is less than the minimum of the function f 2 ðEÞ in the interval ½0; E. Such a condition is satisfied for E 2
!2 εθ
1α
o ϵθ
α
E
β=ð1 αÞ
A.3. Proof of Proposition 2 Linearizing the dynamic system (9)–(10) around the internal equilibrium points, and taking account of the fact that Eβ=ð1 αÞ þ K ¼ θ
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223
holds (see (11)) for all equilibrium points of this type, we obtain the following expressions for the elements of the Jacobian matrix J: ∂E_ αβε ¼ E 2E þ Eðα þ β 1Þ=ð1 αÞ K 1þα ∂E ð1 αÞθ
∂E_ ε ¼ αK θ o 0 ∂K θ1 þ α ∂K_ αβs ¼ 1 þ α Eðα þ β 1Þ=ð1 αÞ K o 0 ∂E θ ∂K_ αsð1 αÞ ¼ K o0 ∂K θ1 þ α
Then, by substituting K ¼ θ Eβ=ð1 αÞ , the determinant of J can be written as follows: βε Det J ¼ ð1 αÞ E 2E α Eðα þ β 1Þ=ð1 αÞ
θ
0
0
which is such that Det J⋚0 if f 1 ðEÞ⋛f 2 ðEÞ. Consequently, the equilibrium point of type A is always a saddle point. The trace of J is given by Tr J ¼ E 2E þ
αβε ð1 αÞθ
1þα
Eðα þ β 1Þ=ð1 αÞ K
αsð1 αÞ K θ1 þ α
where, given that Eβ=ð1 αÞ þ K ¼ θ, and consequently K o θ, we have
αβε ð1 αÞθ
1þα
Eðα þ β 1Þ=ð1 αÞ K o 0
βε
ð1 αÞθ
αE
ðα þ β 1Þ=ð1 αÞ
0
This implies that Tr J o 0 if f 1 ðEÞ of 2 ðEÞ; therefore the equilibrium point of type B is always locally attractive. Let us now analyze the local stability of ðE0 ; 0Þ. It is easy to check that the Jacobian matrix of the dynamic system (9)–(10), αβ=ð1 αÞ evaluated at ðE0 ; 0Þ, is a triangular matrix with eigenvalues E o 0 (in direction of the E-axis) and sð1 αÞ=E d (o0 ð1 αÞ=β for E 4 θ ). The system (9)–(10) is not differentiable at ð0; K 0 Þ; however, the local stability properties of the equilibrium point ð0; K 0 Þ can be easily detected by simply remembering that E_ o 0 holds if E 4 0 is low enough and that K_ o0 (respectively, K_ 40) holds above (respectively, below) the K_ ¼ 0isocline. As a result, the set fðE; KÞ: 0 r E r a; θ b rK r θ þ bg containing ð0; K 0 Þ is positively invariant for a 4 0 and b 40 small enough. This implies that ð0; K 0 Þ is always locally attractive. A.4. Proof of Proposition 3 To prove this proposition, remember that the equilibrium point ð0; K 0 Þ coincides with the intersection between the K_ ¼ 0isocline and the K-axis. Since K_ o 0 holds above this isocline, all trajectories crossing the side with K r θ of the rectangle Q enter Q. Analogously, since E_ o 0 for E ¼ E, all trajectories crossing the side with E ¼ E of Q enter Q. Furthermore, notice that every rectangle R containing Q is a positively invariant set. This implies, by the Poincaré–Bendixson Theorem, that every trajectory in R either enters Q in finite time or approaches the equilibrium point ð0; K 0 Þ. References Alscher, S., 2011. Environmental degradation and migration on Hispaniola Island. Int. Migr. 49 (S1), e164–e188. Antoci, A., Russu, P., Ticci, E., 2010. Structural change, economic growth and environmental dynamics with heterogeneous agents. In: Bischi, G.-I., Chiarella, C., Gardini, L. (Eds.), Nonlinear Dynamics in Economics, Finance and the Social Sciences. Essays in Honour of John Barkley Rosser Jr, Springer-Verlag, Berlin, pp. 13–38. Antoci, A., Russu, P., Ticci, E., 2012. Environmental externalities and immiserizing structural changes in an economy with heterogeneous agents. Ecol. Econ. 81, 80–91. Barbier, E.B., 2010. Poverty, development, and environment. Environ. Dev. Econ. 15, 635–660. Bretschger, L., Smulders, S., 2012. Sustainability and substitution of exhaustible natural resources: how structural change affects long-term RD-investments. J. Econ. Dyn. Control 36, 536–549. Collier, P., 2009. Haiti: From Natural Catastrophe to Economic Security. A Report for the Secretary-General of the United Nations, Oxford University, Oxford. Available at: 〈http://www.securitycouncilreport.org〉. Easterly, W., 2003. The political economy of growth without development: a case study of Pakistan. In: Rodrik, D. (Ed.), Search of Prosperity, Princeton University Press, Princeton, pp. 439–472. Economy, E.C., 2004. The River Runs Black: The Environmental Challenge to China's Future. Cornell University Press, Ithaca & London. Greenpeace International, 2012. Toxic threads: putting pollution on parade. How textile manufacturers are hiding their toxic trail. Available at: 〈http:// www.greenpeace.org/international/Global/international/publications/toxics/Water%202012/ToxicThreads02.pdf〉. Human Rights Watch, 2012. Toxic tanneries: the health repercussions of Bangladesh's Hazaribagh leather. Available at: 〈http://www.hrw.org/reports/2012/ 10/08/toxic-tanneries〉. Library of Congress, 2006. Country profile: Haiti. Library of Congress Federal Research Division, Washington, DC. Available at: 〈http://lcweb2.loc.gov/frd/cs/ profiles/Haiti.pdf〉.
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Lenzen, M., Kanemoto, K., Moran, D., Geschke, A., 2012. Mapping the structure of the world economy. Environ. Sci. Technol. 46 (15), 8374–8381. Lenzen, M., Moran, D., Kanemoto, K., Geschke, A., 2013. Building Eora: a global multi-regional input–output database at high country and sector resolution. Econ. Syst. Res. 25 (1), 20–49. López, R.E., 2007. Structural change, poverty and natural resource degradation. In: Atkinson, G., Dietz, S., Neumayer, E. (Eds.), Handbook of Sustainable Development, Edward Elgar, Cheltenham, UK, pp. 220–239. López, R.E., 2010. Sustainable economic development: on the coexistence of resource-dependent and resource-impacting industries. Environ. Dev. Econ. 15, 687–705. López, R.E., Anríquez, G., Gulati, S., 2007. Structural change and sustainable development. J. Environ. Econ. Manag. 53, 307–322. López, R.E., Schiff, M., 2013. Interactive dynamics between natural and man-made assets: the impact of external shocks. J. Dev. Econ. 104, 1–15. Matsuyama, K., 1992. Agricultural productivity, comparative advantage, and economic growth. J. Econ. Theory 58, 317–334. Nathan Associates Inc., 2009. Bringing HOPE to Haiti's Apparel Industry. Improving Competitiveness through Factory-level Value-chain Analysis. Report Number 53316, World Bank, Washington, DC. Ocampo, J.A., Rada, C., Taylor, L., 2009. Growth and Policy in Developing Countries. Columbia University Press, New York. Peretto, P., 2012. Resource abundance, growth and welfare: a Schumpeterian perspective. J. Dev. Econ. 97, 142–155. Reddy, R.V., Behera, B., 2006. Impact of water pollution on rural communities: an economic analysis. Ecol. Econ. 58, 520–537. Shamsie, Y., 2010. Time for a “High-Road” approach to EPZ development in Haiti. Paper prepared for the Conflict Prevention and Peace Forum, Social Science Research Council, New York. Available at: 〈http://www.ssrc.org/publications/view/03C92980-9E49-E011-9A1B-001CC477EC84/〉. Solow, R.M., 1956. A contribution to the theory of economic growth. Q. J. Econ. 70, 65–94. World Bank, 1999. Pollution Prevention and Abatement Handbook 1998: Toward Cleaner Production. World Bank, Washington, DC.
Contents lists available at ScienceDirect
Journal of Economic Dynamics & Control journal homepage: www.elsevier.com/locate/jedc
Industrialization and environmental externalities in a Solow-type model Angelo Antoci a, Paolo Russu a, Serena Sordi b,n, Elisa Ticci b a b
Dipartimento di Scienze Economiche e Aziendali, Università di Sassari, Via Muroni 25, 07100 Sassari, Italy Dipartimento di Economia Politica e Statistica, Università di Siena, Piazza San Francesco 7, 53100 Siena, Italy
a r t i c l e i n f o
abstract
Article history: Received 29 April 2014 Received in revised form 31 July 2014 Accepted 10 August 2014 Available online 15 August 2014
In this paper we examine the role played by environmental externalities in shaping the dynamics of an economy with two sectors (a farming sector and an industrial one), free inter-sectoral labor mobility and heterogeneous agents (workers/farmers and industrial entrepreneurs). We find that, in the presence of the environmental pressure of the economic activity of the industrial sector, the stability properties of the equilibria and their features in terms of environmental preservation, welfare outcomes and sectoral allocation of labor are sensitive to the level of carrying capacity. We show that an endogenous process of industrialization associated with a reduction in farmers/workers' welfare can emerge. & 2014 Elsevier B.V. All rights reserved.
JEL classification: D62 O11 O13 O15 O41 Q20 Keywords: Environmental negative externalities Industrialization Economic growth with heterogeneous agents
1. Introduction Industrialization is usually considered a necessary, albeit not a sufficient, condition for poverty reduction. The expansion of the industrial sector is indeed a key feature of the growth processes of those countries which have been successful in combating poverty and in ensuring satisfactory living conditions for vast sections of the population. The fact that several countries have experienced higher labor productivity and industrialization without poverty reduction is often traced back to low absorption of labor in higher productivity sectors and to a lack of labor transfer from rural subsistence to modern activities with the consequent expansion of the urban informal sector (Easterly, 2003; Ocampo et al., 2009). Within this conceptual framework, less attention has been paid to the role that environmental externalities may have for economic growth and poverty reduction during the industrialization processes. This paper attempts to make a contribution towards filling this gap. To this end, in order to concentrate on the effects of industrial pollution on capital accumulation and welfare, we adjust the framework proposed by Matsuyama (1992). In this seminal work, he suggests that the link between labor productivity in farming and manufacturing growth changes according
n
Corresponding author. Tel.: +390577232644. E-mail addresses: [email protected] (A. Antoci), [email protected] (P. Russu), [email protected] (S. Sordi), [email protected] (E. Ticci).
http://dx.doi.org/10.1016/j.jedc.2014.08.009 0165-1889/& 2014 Elsevier B.V. All rights reserved.
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to the degree of trade openness. In small open economies, if productivity in the agricultural sector is low, then the industrial sector could benefit from a large supply of labor at low cost and, in this way, the economy could gain a comparative advantage in manufacturing production. The opposite relation holds for closed economies. In our paper, by focussing on the study of an open economy, we also find that low productivity in the farming sector can be an engine of the industrialization process. However, in our model the industrialization process generates environmental degradation and, consequently, a reduction in labor productivity in the farming sector. In other words, industrialization may be associated with a decrease in workers' welfare. This extension appears to be important since, in recent decades, the growth of industrial activities has expanded the industrial frontier in many poor and middle income countries. Positive and negative interactions between small producers in resourcedependent activities and industrial firms have therefore increased. A few figures are enough to describe this trend. First of all, between 1990 and 2010 the share of world industrial value added accounted for by low and middle income countries almost doubled from 17.5 to 33.5 percent, while their rural population share declined more slowly from 65 to 55 percent.1 Moreover, in the same period, it has been estimated that the domestic footprint of sulphur dioxide (SO2) for low and middle income countries climbed from about 52,000 to more than 93,000 gigagrams (Gg) compared to a decline from 54,000 to about 18,000 Gg in high income countries.2 An emblematic example of the possible effects of pollution when natural resources are used as productive inputs by small producers is reported in Reddy and Behera (2006, pp. 530–534). By analyzing the impact of industrial water pollution in a village of Andhra Pradesh, they find that the “majority of the cattle is becoming sick over the years […]. The amount of land under cultivation has declined substantially (88%) due to the incidence of pollution […]. Most of the people who were depending on agriculture before pollution have shifted to industry, business and other sources. The majority of them have become daily laborers.” The extension and severity of air, water and soil contamination of industrial activities, such as textile and leather industry, are also well documented in China (Economy, 2004; Greenpeace International, 2012) and in Bangladesh (Human Rights Watch, 2012) and recently acknowledged also by their governments.3 In what follows we analyze the interactions between economic development, sectoral output composition and the environment by modeling an economy where environmental degradation affects workers' incentive to move out of the environmentally sensitive sector. This reduces workers' dependence on natural resources, but it can also fuel a self-reinforcing process of growth in industrial production and pollution. In doing this, we contribute to a growing body of literature which studies how, in multisectoral economies where natural resources are used as productive inputs, structural change processes and reallocation of labor across sectors can emerge as endogenous adjustments to a reduction in natural capital affecting economic growth and social welfare (see López et al., 2007; López, 2010; Bretschger and Smulders, 2012; Peretto, 2012; López and Schiff, 2013). Most of these models are concerned with the role of both the substitution between natural resources and man-made inputs (or labor) and the change in natural resource prices in driving the economy towards a sectoral shift which allows sustainable growth. These models, however, abstract from the distributional implications associated with such processes and, with the exception of López (2010), identify resource-using and resource-impacting activities. We build on this literature by taking a broader distributional perspective. More precisely, we analyze a two-sector model with free access to renewable natural resources as factors of production. The physical capital is specific to the industrial sector whereas the natural capital is specific to farming. Both sectors employ labor, but only the industrial sector produces environmental externalities which, in turn, affect labor costs and labor productivity. There are no constraints to inter-sectoral labor mobility and, as a consequence, labor productivity gains in the economy are equally shared among workers and there is no risk that possible benefits of industrialization are offset by a low absorption of labor in higher productivity sectors. Moreover, we exclude the impact of domestic food supply and domestic demand on the prices of the goods produced by the two sectors. In this way, we concentrate on the role of resource-based activities in setting the basic opportunity cost for labor in the whole economy. Our model is complementary to that proposed by López and Schiff (2013). We analyze a similar setting (i.e., one with a resource-dependent sector, a manufacturing sector which is more capital intensive, exogenous prices and open access environmental resources) but with a crucial difference. In our model the polluting sector is the man-made capital intensive sector and not the resource-dependent sector. We consider a poor economy where the resource-dependent sector is represented by small producers engaged in primary activities as in López and Schiff (2013), but the main environmental threat is posed by the capital intensive sector. In other words, we concentrate on welfare and environmental dynamics generated by the pollution of non-primary activities instead of on the problem of over-harvesting and over-exploitation by primary and commodity activities which do not internalize the environmental impact. We confirm that a decline in labor share employed in the natural resource-intensive sector can arise in the absence of biased technological progress and can be an endogenous response to low labor
1
Data from World Development Indicators accessed in December 2013. The largest sources of SO2 emissions are from fossil fuel combustion in the energy and industrial sectors. These emissions are a primary cause of acid rain and have a negative impact on forest and agriculture crops and on aquatic ecosystems in addition to adverse effects on human health (World Bank, 1999). The figures given in the text are our own elaboration from the Eora MRIO dataset (Lenzen et al., 2012, 2013), accessed in November 2013. If SO2 embedded in imports are subtracted and those embedded in exports are added to domestic SO2, the total SO2 emissions at home for low and middle income countries are 56,864 Gg in 1990 and 107,747 Gg in 2011. 3 In February 2012, Chinese premier Wen Jiabao said that “Water pollution is mainly resulting from industrial and sewage waste water and is now in very serious situation.” (reported in Greenpeace International, 2012). Li Yang, Vice-President of the Chinese Academy of Social Sciences, in February 2013, said that “China's real economic growth rate would only be around 5%, if economic losses caused by ecological degradation and environmental damage are subtracted from the overall GDP,” (http://English.news.cn/, 2013-02-28). Finally, in November 2013, Bangladesh's governments planned to relocate the leather industry from central Dhaka to another area where there are several centralized waste-treatment facilities (http://asiafoundation.org/in-asia/, November 13, 2013). 2
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productivity in this sector. However, we obtain that a structural change can emerge even in the absence of a change in the relative prices of goods produced in the economy. Moreover, we find that the role of physical capital accumulation is much more ambivalent and less univocal. A development path associated with increasing physical and natural capital, and with an increase in workers' welfare, is possible only under specific conditions, namely, an intermediate level of carrying capacity and a sufficiently preserved initial environment. We follow the basic set-up proposed by Antoci et al. (2010, 2012), but with two main differences. First, we consider a stronger differentiation of the two sectors, while they analyze an economy where the production activities of both sectors depend on natural resources and generate negative environmental impacts. As a result, we obtain rather different dynamics and more clear-cut results about the welfare implications of the dynamic regimes that can be observed. Second, due to their assumption that the accumulation process of physical capital is driven by entrepreneurs' intertemporal optimization choices, the analysis in Antoci et al. (2010, 2012) does not go beyond the local stability of the equilibrium points. In contrast, we describe the investment in physical capital as a Solow-type accumulation process. Consequently, the formalization is much simpler and makes it possible to analyze the global dynamics of the model. Despite these crucial differences in the modeling of the capital accumulation process, the results are substantially confirmed, indicating that they do not critically depend on the hypotheses about agents' rationality. Our main findings seem, rather, to hinge on the inability of natural resource-dependent agents to coordinate and internalize the externalities of economic activities. We find that regimes with multiple attractive equilibria are possible and that capital accumulation can lead to an increase in inequality between the two population groups.4 The analysis of the model explains how welfare, distributive and environmental outcomes of industrialization depend on two main factors: the initial endowment of natural capital and the level of environmental carrying capacity. Industrialization is hampered in economies starting from a relatively preserved natural capital and high level of carrying capacity. On the contrary, economies with very low carrying capacity or with poor initial environmental conditions tend to undertake a process of complete industrialization with negative impacts on the environment and social equity. In other words, an immiserizing and unsustainable complete industrialization occurs. Finally, for intermediate levels of carrying capacity and sufficiently high values of initial natural capital, this type of negative industrialization can be avoided and the transition from an agrarian economy to a more diversified economy allows an increase in workers' welfare. The rest of the paper is organized as follows. The model is presented in Section 2, where the equilibrium points of its dynamic system are also derived. Section 3 contains an analysis of both the local/global stability and welfare properties of the equilibrium points, whereas Section 4 offers a characterization of the different dynamic regimes that can emerge. Section 5 concludes. All proofs and lengthy computations are contained in the Appendix at the end of the paper. 2. The model We model an economy in which economic agents belong to two different communities, one consisting of ‘farmers’, the other of ‘industrial entrepreneurs’. The former are endowed with their own working capacity only, which they use partly in their fields for the production of farming goods with the use of a natural resource and partly as employees of the industrial entrepreneurs.5 The latter produce industrial goods with the physical capital they own and the labor force they hire. Accordingly, economic activity is divided into two sectors which we define as the ‘F-sector’ (Farming) and the ‘I-sector’ (Industry). 2.1. Production in the two sectors and economic agents' choices The productivity of labor in the F-sector depends on the stock of the natural renewable resource E. On the other hand, production in the I-sector depends on the stock of the capital K owned by industrial entrepreneurs and on the labor force L provided by farmers. For simplicity, we assume that industrial entrepreneurs do not invest in the F-sector and that the latter is only composed of small firms run by farmers. Moreover, we focus on the behavior of two representative agents, one for each sector. The production function of the firm run by the representative farmer (F-agent) is given by Y F ¼ Lα Eβ
α; β 4 0;
α þ β r1
ð1Þ 6
where 1 Z L Z0 is her/his labor input and E the stock of a natural renewable resource. On the other hand, that faced by the representative industrial entrepreneur (I-agent) has constant returns to scale and is such that Y I ¼ ð1 LÞα K 1 α For simplicity, both the elasticities of YF and YI with respect to L and 1 L, respectively, are assumed to be equal to α. Thus, possible differences in the productivity of labor employed in the two sectors depend on the levels of the stocks E and K only. 4 In light of this possible negative correlation between farmers' and entrepreneurs' welfare, we do not study the social optimum. In this case, indeed, the benevolent social planner's decisions would be strictly linked to the ‘weights’ she/he assigns to the two types of agents. 5 Empirical evidence (see, e.g., Barbier, 2010) suggests that in developing countries farmers are not able to sensibly modify their physical capital endowment in the short/medium run. To simplify, we therefore assume that farmers cannot accumulate physical capital. 6 In the case in which the F-agent also owns a fixed amount T of land or other forms of capital, an equation of the same type as (1) could be obtained by writing the production function as Y F ¼ Lα T 1 α Eβ and then normalizing to one the fixed amount T.
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Let us now analyze agents' choices. To simplify, we assume that the prices of both the agricultural and industrial goods are constant and equal to unity and that both the I-agent and the F-agent take the wage rate w, expressed in terms of the industrial output, as exogenously given. In each instant of time t, the I-agent maximizes with respect to 1 L her/his revenue, given by RI ¼ ð1 LÞα K 1 α wð1 LÞ
ð2Þ
which gives rise to the following first order condition:
αð1 LÞα 1 K 1 α ¼ w
ð3Þ
Analogously, the F-agent maximizes with respect to L her/his revenues, measured by the function RF ¼ Lα Eβ þ wð1 LÞ
ð4Þ
such that the corresponding first order condition is
αLα 1 Eβ ¼ w
ð5Þ
Finally, by equalizing the left-hand sides of (3) and (5), we obtain the following equilibrium value of the variable L: Eβ=ð1 αÞ L ¼ β=ð1 αÞ E þK
ð6Þ
2.2. The dynamic system With regard to the dynamics of K and E, the accumulation process of the former is built on the assumption of a constant propensity to save, as in Solow's (1956) growth model. Thus, indicating with a dot over a variable its first derivative with respect to time, we have K_ ¼ sRI dK
ð7Þ
where the parameters s, d A ð0; 1Þ represent the marginal propensity to save and the depreciation rate of the capital stock, respectively. The time evolution of the stock of natural renewable resource E, on the other hand, is assumed to be given by ( _E ¼ EðE EÞ εY I for E 4 0 ð8Þ 0 for E ¼ 0 where the parameter ε 4 0 measures the environmental impact of production in the I-sector, the parameter E 4 0 represents the carrying capacity of the natural resource and Y I is the economy-wide average value of YI, taken as exogenously given by the two representative agents. Consequently, the I-sector produces negative environmental externalities that agents are not able to internalize due to coordination problems. As will soon be evident, this assumption plays a crucial role in shaping the results of our model, much more than the assumption about the mechanism for the accumulation process of physical capital. It is meant to take account of the fact that environmental externalities have a strong impact on economic activities, especially in developing countries, where property rights tend to be ill-defined and ill-protected, environmental institutions and regulations are weak and natural resources are more fragile than in developed countries (see, e.g., López, 2007). Finally, by substituting (6) into Eqs. (7) and (8), and taking account also of Eqs. (3) and (5), we obtain the following nonlinear dynamic system in the two variables E and K: 8 εK > < E E E for E 4 0 E_ ¼ ð9Þ ðEβ=ð1 αÞ þ KÞα > : 0 for E ¼ 0 " K_ ¼
sð1 αÞ
ðEβ=ð1 αÞ þ KÞα
# d K
ð10Þ
which, clearly, is not defined for E¼K ¼0. 3. Basic mathematical results and dynamic properties of the model In this section, we describe the basic mathematical results, while all proofs are deferred to the Appendix at the end of the paper.
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3.1. Isoclines We first turn to the problem of the determination and characterization of the equilibrium points of our model. First of all notice that, from (10), it follows that K_ ¼ 0 holds if either K ¼0 or K ¼ θ Eβ=ð1 αÞ
ð11Þ
where θ ≔ ½sð1 αÞ=d1=α 4 0 and 1 4 β=ð1 αÞ 4 0. According to (11), K is a strictly decreasing function of E, the graph of ð1 αÞ=β which intersects the E-axis at ðθ ; 0Þ and the K-axis at ð0; θÞ; moreover, K_ o 0 ðK_ 4 0Þ holds above (respectively, below) it. Analogously, E_ ¼ 0 holds if either E ¼0 or E E E
εK
ðEβ=ð1 αÞ þ KÞα
¼0
ð12Þ
which implicitly defines an inverted-U function K ¼ Γ ðEÞ such that Γ ðEÞ ¼ 0 and Γ ðEÞ-0 for E-0 (see Section A.1 of the Appendix). 3.2. Equilibrium points Equilibrium points with either E ¼0 or K¼0: The intersection point between the branch of the K_ ¼ 0isocline, defined by (11), and the K-axis (along which E_ ¼ 0), i.e. ð0; K 0 Þ ¼ ð0; θÞ and the intersection point between the branch of the E_ ¼ 0isocline, defined by (12), and the E-axis (along which K_ ¼ 0), i.e. ðE0 ; 0Þ ¼ ðE; 0Þ are always equilibrium points of the dynamic system (9)–(10). Internal equilibrium points: By substituting K as defined in Eq. (11) into Eq. (9), we obtain that the time evolution of E, for E 4 0, is described by the equation E_ ¼ f 1 ðEÞ f 2 ðEÞ where 1α f 1 ðEÞ ≔ E E E εθ
ε θ
f 2 ðEÞ ≔ α Eβ=ð1 αÞ
Internal equilibrium points are therefore defined by the intersections between the graphs of the two functions f 1 ðEÞ and f 2 ðEÞ. As it is easy to check (see Fig. 1), the graphs of f 1 ðEÞ and f 2 ðEÞ can have at most two intersections and consequently at most two internal equilibrium points can exist. We shall indicate by A (respectively, by B) the intersection point in 0 0 0 0 correspondence of which f 1 ðEÞ 4 f 2 ðEÞ (respectively, f 1 ðEÞ of 2 ðEÞ). Only intersections which are associated with strictly positive values of K and E are admissible internal equilibrium points. More specifically, a value E ¼ En 4 0 identifies an equilibrium point with E; K 4 0 if f 1 ðEn Þ ¼ f 2 ðEn Þ and if, when substituted in (11), gives a value of K which is strictly positive, i.e. if En o EM ≔ θ
ð1 αÞ=β
where EM – which is independent of E – is the value of E at which the K_ ¼ 0isocline intersects the E-axis. Fig. 1 illustrates the complete taxonomy of possible cases in which at least one internal equilibrium point exists. They are obtained by varying only the value of the carrying capacity E, which is increasing from E 0:4982 in Fig. 1(a) to E ¼ 1:1 in Fig. 1(d).7 The case of tangency between f 1 ðEÞ and f 2 ðEÞ is shown in Fig. 1(a). For values of E less than the value we have used to generate this figure, clearly, the two curves do not intersect in the first quadrant and, therefore, the system does not admit internal equilibrium points. When the value of E increases, the curve f 2 ðEÞ does not move, whereas the curve f 1 ðEÞ ‘expands’ itself in such a way that two points of intersection between the two curves emerge (one of type A and another of type B, as shown in Fig. 1(b)). However, the intersection points of the two curves correspond to internal equilibrium points only if they are located on the left of the vertical line E ¼ EM . Thus, when E is further increased beyond the value used to generate the ‘critical’ case of Fig. 1(c), there exists only one internal equilibrium of type A, as in Fig. 1(d). The following proposition summarizes the cases just described. 7 In this figure and in all others that follow, when not otherwise stated, we fix the parameters of the production function, the depreciation rate, the propensity to save and the environmental impact of the production in the I-sector at α ¼ 0:6, β ¼ 0:3, d ¼0.1, s ¼0.25 and ε ¼ 0:1, respectively.
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0.3
0.3
f 1 (E) 0
A ,B
A
0
f 2 (E)
B f 2 (E)
f 1 (E) −0.2
0
E
EA = EB
M
1.4
−0.2
0
E
A
B
E
1.4
EM
1.4
M
E
E 0.3
0.3
f 1 (E)
f 1 (E)
A
0
A
0
B
f 2 ( E)
f 2 (E) −0.2
E
0
EA
E =E B
E
M
1.4
−0.2
0
EA
E
Fig. 1. A taxonomy of the number of internal equilibrium points for different values of the carrying capacity of environment: (a) E 0:4982, (b) E ¼ 0:7, (c) E ¼ 1 and (d) E ¼ 1:1.
Proposition 1. A necessary and sufficient condition for the existence of a unique internal equilibrium point (which is always of type A) is E 4θ
ð1 αÞ=β
¼ EM
ð13Þ
When condition (13) is not satisfied, the dynamic system (9)–(10) generically admits either zero or two internal equilibrium points.8 In this case, a sufficient condition for the non-existence of internal equilibrium points is !2 E α β=ð1 αÞ 1α þ εθ E o εθ ð14Þ 2 while a sufficient condition for the existence of two internal equilibrium points (one of type A and the other of type B) is9 !2 !β=ð1 αÞ E α E 1α þ εθ 4 εθ 2 2
8 9
Also the case of a unique internal equilibrium point is again possible, but only in the critical case in which f 1 ðEÞ and f 2 ðEÞ are tangent. Necessary and sufficient conditions for this case could also be indicated. They are however rather complicated and not easily interpretable.
ð15Þ
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Proof. See Section A.2 of the Appendix
217
&
3.3. Local/global stability properties and welfare ranking of stationary states To go deeper into the understanding of the dynamics generated by our model, and in the attempt to identify and characterize the dynamic regimes that can emerge, we now turn to the problem of the stability properties of the equilibrium points, which are described by the following proposition. Proposition 2. The equilibrium point of type A, ðEA ; K A Þ, is always a saddle point while that of type B, ðEB ; K B Þ, is always locally attractive. The equilibrium ðE0 ; 0Þ ¼ ðE; 0Þ is a saddle point (with stable manifold lying in the E-axis) if E o EM while it is locally attractive if E 4 EM . The equilibrium point ð0; K 0 Þ ¼ ð0; θÞ is always locally attractive. Proof. See Section A.3 of the Appendix
&
In turn, the global stability properties of the dynamics generated by system (9)–(10) are illustrated by the following proposition. Proposition 3. The set Q ¼ fðE; KÞ: 0 r E r E and 0 rK r θg is positively invariant under the dynamic system (9)–(10); furthermore, every trajectory starting outside it either enters it in finite time or approaches the equilibrium point ð0; K 0 Þ ¼ ð0; θÞ lying on the boundary of Q. Proof. See Section A.4 of the Appendix
&
In order to discuss the economic and distributive implications of all possible scenarios generated by the model, it is useful to compare the various stable equilibrium points of the dynamic system of our model, in terms of the revenues of the two representative agents. As we have seen, the F-agent uses a natural resource which is available at zero cost but is exposed to negative externalities. The I-agent, on the other hand, does not use free environmental resources, but has to save in order to accumulate physical capital. Her/his advantage is that, unlike the F-agent, she/he can hire wage labor and expand her/his physical capital over time, not harmed by environmental externalities. The F-agent is indirectly affected by physical capital accumulation through two different channels: on one hand, a rise in labor productivity in the I-sector due to an increase in K has a positive effect on the equilibrium wage rate; on the other hand, the resulting net environmental impact, due to the combination of scale and labor sectoral composition effects, influences the productivity of agricultural labor and consequently the opportunity cost of wage labor. To analyze the welfare properties associated with each equilibrium point, we should remember that the revenues of the F-agent are measured by Eq. (4). By substituting in it the equilibrium values of w and L given by (3) and (6), respectively, Eq. (4) becomes RF ¼
Eβ=ð1 αÞ þ αK
ðEβ=ð1 αÞ þ KÞα
such that ∂RF =∂E 40 and ∂RF =∂K 4 0. Furthermore, since from (11) it follows that along the decreasing branch of the K_ ¼ 0isocline the condition Eβ=ð1 αÞ þK ¼ θ holds, the value of RF evaluated along it can be expressed as a function of E only, i.e. RF ðEÞ ¼
1 α β=ð1 αÞ 1α þ αθ α E
ð16Þ
θ
Let us now consider the I-agent revenues, which, given Eq. (2), can be expressed as RI ¼
ð1 αÞK
ð17Þ
ðEβ=ð1 αÞ þ KÞα
such that ∂RI =∂E o 0 and ∂RI =∂K 4 0. By substituting in (17) the equilibrium condition (11), it follows that, along the K_ ¼ 0isocline, the value of RI can be expressed as a function of K only, i.e. RI ðK Þ ¼
ð1 αÞK
ð18Þ
θα
Finally, notice that aggregated revenues, evaluated along the decreasing branch of the K_ ¼ 0isocline (where Eβ=ð1 αÞ þ K ¼ θ holds), can be written as RI ðK Þ þ RF ðEÞ ¼
1 α β=ð1 αÞ ð1 αÞK 1α þ αθ þ α E α
θ
θ
1 α sð1 αÞ ð1 αÞ=α 1α 1α ¼ α Eβ=ð1 αÞ þ K þ αθ ¼θ ¼ d θ
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1.6
K0
K
.
.
E=0
0
0
K=0
E
E
EM
1.2
Fig. 2. The case of ð0; K 0 Þ globally attractive (with E ¼ 0:43 such that condition (13) is not satisfied whereas (14) holds).
i.e., aggregate revenues, evaluated at the equilibrium points with K 40, are constant: if farmers' revenues increase, then entrepreneurs' revenues decrease of the same amount. The following proposition sums up the above results. Proposition 4. Along the decreasing branch of the K_ ¼ 0isocline: (1) The revenues of the I-agent are represented by the strictly increasing function of K shown in (18), whereas those of the Fagent by the strictly increasing function of E shown in (16). 1α (2) Aggregate revenues are constant, that is RI ðKÞ þ RF ðEÞ ¼ θ . Eqs. (16) and (18) tell us something rather interesting: once we have fixed the parameters, the welfare of the F-agent is positively correlated with E and does not depend on K, even in the presence of diversification in income sources. Vice versa, the revenues of the I-agent are positively correlated with K and do not depend on E. Consequently, along the decreasing branch of the K_ ¼ 0isocline, to which the equilibrium points ð0; K 0 Þ and ðEB ; K B Þ belong, there is a trade-off between the Iagent's revenues and those of the F-agent. This implies that in ð0; K 0 Þ, the revenues of the I-agent are higher than in ðEB ; K B Þ, and vice versa for the revenues of the F-agent, being EB 4 0 and K B oK 0 . β Furthermore, notice that in the equilibrium ðE0 ; 0Þ ¼ ðE; 0Þ the revenues of the F-agent are given by E and that β 1α E 4 RF ð0Þ ¼ αθ holds if E 4 ðαθ
1 α 1=β
Þ
Condition (19) is always satisfied when the equilibrium ðE0 ; 0Þ is locally attractive, i.e., when E 4 θ following proposition can be stated.
ð19Þ ð1 αÞ=β
. Consequently, the
Proposition 5. In the bistable dynamic regimes in which the attractive equilibrium point ð0; K 0 Þ coexists with another attractive equilibrium – either ðEB ; K B Þ or ðE0 ; 0Þ – the revenues of the I-agent are higher in ð0; K 0 Þ than in ðEB ; K B Þ or ðE0 ; 0Þ, whereas the opposite holds for the revenues of the F-agent. 4. Dynamic regimes Having illustrated the main properties of the dynamics generated by our model, we can now go into detail about their economic interpretation. This section identifies and compares all possible paths that the economy under study may follow and discusses under which conditions each scenario emerges. All the possible configurations of the K_ ¼ 0 and E_ ¼ 0isoclines and dynamic regimes that can be (generically) observed are illustrated in Figs. 2–4,10 where attractive equilibrium points are marked by full dots ðÞ and saddle points by squares ð□Þ. It turns out, as shown by the arrow diagrams in the figures, that the regions of the plane (E,K) between the K_ ¼ 0 and E_ ¼ 0isoclines are positively invariant under the dynamic system (9)–(10). This implies that no closed trajectory can exist around the equilibrium point ðEB ; K B Þ and therefore, by the Poincaré–Bendixson Theorem, every trajectory approaches an 10 For the sake of simplicity, the non-robust case in which the K_ ¼ 0 and E_ ¼ 0isoclines have a tangency point is not considered in the following classification. However, it is easy to check that, in this case, the unique internal equilibrium point is a saddle-node.
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219
1.6
K0
K
.
E=0
0
0
.
K=0
_ EM E 1.2
E
Fig. 3. The case of one internal equilibrium point of type A and two coexisting locally attractive points at ð0; K 0 Þ and ðE0 ; 0Þ (with E ¼ 1:1 such that condition (13) holds).
1.6
K0 (EA,KA)
K
.
E=0
0
0
(EB,KB)
E
_ E
.
K=0 EM
1.2
Fig. 4. The case of two internal equilibrium points, one of type A and one of type B, and one locally attractive equilibrium point at ð0; K 0 Þ (with E ¼ 0:7 such that neither condition (13) nor condition (14) is satisfied whereas condition (15) holds).
equilibrium point. The numerical simulations illustrated in the figures are obtained by varying (ceteris paribus) the value of the carrying capacity E of the environmental resource, starting from the parameter values we have used in Fig. 1 and taking into account the conditions given in Proposition 1. The possible dynamic regimes are the following three: 1. Regime with specialization in the I-sector (see condition (14)). In this dynamic regime – which is illustrated in Fig. 2 – the stationary state ð0; K 0 Þ is globally attractive. The economy converges towards a full industrialization accompanied by environment depletion, regardless of the initial endowments of natural and physical capital. In the stationary state ð0; K 0 Þ, the stock of physical capital reaches its (non transient) maximum level (that is, K0), which is however associated with the lowest and highest equilibrium values of workers' and entrepreneurs' revenues, respectively. Along the trajectories approaching ð0; K 0 Þ, the processes of capital accumulation and industrialization generate a growth in workers' poverty in that environmental degradation reduces both wages in the industrial sector and the productivity of labor in the farming sector.
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2.5
K
2.5
K0 1
K0
K
1
(EA , KA)
(EA , KA)
(EB , KB) 0
0
0.5
E
(EB , KB) 0
1.2
E
0
0.5
E
E
1.2
2.5
K0
K 1
(EA , KA) (EB , KB)
0
0
0.5
E
1.2
E Fig. 5. Basins of attraction of the attractive equilibrium points ð0; K 0 Þ and ðEB ; K B Þ for different values of the parameter ε, with the remaining parameters all fixed at the values of the simulation in Fig. 4. (a) ε ¼ 0.1, (b) ε ¼0.15 and (c) ε ¼ 0.22.
2. Bistable regime without coexistence of the two sectors (see condition (13)). In this case, illustrated in Fig. 3, only one internal equilibrium point exists, i.e., ðEA ; K A Þ, and there are in addition two coexisting locally attractive equilibrium points, the equilibrium ð0; K 0 Þ with full specialization in the I-sector and the equilibrium ðE0 ; 0Þ with full specialization in the F-sector. Dynamics are path-dependent: if the economy starts near enough to ð0; K 0 Þ (respectively, to ðE0 ; 0Þ), then the equilibrium point with full industrial (respectively, farming) specialization is reached. Along the trajectories belonging to the basin of attraction of ð0; K 0 Þ, environmental degradation helps industrial growth pushing labor force out of the Fsector and, consequently, exerting downward pressure on the wage rate in the industrial sector. In contrast, along the trajectories belonging to the basin of attraction of ðE0 ; 0Þ, industrialization does not take off. In the first phase, both K and E may increase, but then the return to labor in the farming sector becomes sufficiently high to reduce labor supply for the industrial sector and the economy converges to a full specialization in the natural-resource based sector. In this case, the farmers obtain higher revenues and the environment is preserved but the possibility of exploiting the benefits of physical capital accumulation is ruled out. Therefore, in the long run, also this equilibrium might represent a poverty-trap. 3. Bistable regime with coexistence of the two sectors (neither condition (13) nor condition (14) are satisfied). In this case, illustrated in Fig. 4, two internal equilibrium points exist. The stationary state ð0; K 0 Þ and the stationary state ðEB ; K B Þ are locally attractive and the stable manifold of the stationary state ðEA ; K A Þ separates their basins of attraction. Also in this case, the economy is characterized by a bistable regime. If initial values of E are very low, it will undertake a process of full industrialization and sustained physical capital accumulation, associated with environmental degradation and impoverishment of the F-agent. However, for higher initial values of E, a poor economy with low initial endowments of physical capital converges to the equilibrium ðEB ; K B Þ along a path with both growing physical and natural capital, namely along a sustainable path. In the equilibrium ðEB ; K B Þ, the welfare of the F-agents is higher compared to that in the alternative equilibrium ð0; K 0 Þ, the coexistence of the two sectors is observed in a non-transient way and the level of inequality between the two representative agents is less than in the two polar cases ð0; K 0 Þ and ðE0 ; 0Þ. Fig. 5 shows how the size of the basins of attraction of the equilibrium points ð0; K 0 Þ and ðEB ; K B Þ changes varying ε, the parameter measuring the environmental impact of the industrial sector. The basin of ð0; K 0 Þ is represented in grey and is separated from the basin of ðEB ; K B Þ by the stable manifold of the saddle point ðEA ; K A Þ. It turns out that, if the value of ε increases, the basin of ð0; K 0 Þ expands and that of ðEB ; K B Þ shrinks. In other words, economies which are exposed to an intensive rate of industrial pollution are less likely to undertake sustainable development paths and more prone to follow industrialization processes without development (i.e., with farmers' impoverishment and environmental depletion).
Notice that, ceteris paribus, conditions (13) and (14) are satisfied if the carrying capacity E is, respectively, high and low enough. Furthermore, the conditions (13) and (14) hold if the value of θ ¼ ½sð1 αÞ=d1=α is, respectively, low and high ð1 αÞ=β enough (remember that EM ¼ θ ). So, if θ is very high relatively to the carrying capacity E, the economy is more likely to specialize in the physical capital-intensive sector, the industrial one. Notice that the value of θ depends positively on the
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propensity to save s and on the elasticity 1 α of the industrial output YI with respect to physical capital K, while it is negatively related to the depreciation rate d of physical capital.11 The notion of welfare reducing industrialization can be better grasped by referring to a representative case. Haiti, for instance, provides an example of a country which is undertaking the first phases of industrial development starting from a very low level of carrying capacity or a very initial deteriorated environment. In the last two centuries, the carrying capacity of Haiti has drastically reduced due to both external and internal factors.12 In a context of fragile and very poor farming, a development model based on export zones for foreign-financed manufacturing firms has been experimented since the 1970s and recently reaffirmed as a one of the elements of a ‘realistic strategy’ for a rapid attainment of economic security (Collier, 2009). Recent trade agreements and government initiatives, indeed, have attracted foreign investors to the exportoriented apparel industry which appreciated Haiti's low-cost workforce and steady supply of labor (Nathan Associates Inc., 2009). Insufficient agriculture income and the promise of better wages have also encouraged rural–urban migration (Alscher, 2011) and increasing urban population and demand for charcoal have further stressed the environment. As a result of all these processes, Haiti is now characterized by extreme inequality, low wages, environmental crisis and growing industrialization. Countries with a relatively successful experience of exporting processing zones, such as Mauritius and Costa Rica, instead have promoted external-financed manufacturing within a broader agenda of economic diversification (Shamsie, 2010) and protection of environmental-based economic activities. In other words, they are more likely to reflect conditions for the economy to belong to the third regime with a large basin of attraction of the equilibrium characterized by the coexistence of both sectors (i.e. sufficiently high carrying capacity, sufficiently low industrial pollution rate and preserved initial environment). This is not to say that these countries represent a test of our model or that other institutional, economic and historical factors are not relevant. However, some of the dynamics of their development paths are consistent with the narratives behind the model we have proposed. Our conceptual framework, as all theoretical models, intends to highlight, analyze and disentangle consequences of specific relations, in this case the connection between environmental externalities of industrial activities, inequality and evolution of sector composition. It is also worth observing that major environmental challenges have begun to widespread at international level relatively recently and most of their consequences have not fully revealed. Past experiences of rich economies suggest that industrialization is a necessary condition for a widespread economic development, but that it might be not a sufficient condition. How long and to what extent in today's emerging economies, where the majority of population makes its living from farming, can industrialization bring equitable prosperity while destroying the environment?
5. Conclusions This work draws on the intuition of Matsuyama's (1992) influential model which predicts a negative relationship between agricultural productivity and industrialization (and consequently economic growth) in small open economies. Our model is built on the idea that a large stock of natural capital, by ensuring high productivity in the F-sector, can squeeze out the manufacturing sector in a small open economy with a constant labor supply and free intersectoral labor mobility. However, we depart from this common starting point in that we focus on environmental externalities, agents' heterogeneity and capital accumulation and we exclude the possibility of learning-by-doing in order to concentrate on the negative externalities of growth. We find that some of the welfare implications of Matsuyama's model are reversed: industrialization is not always associated with welfare improvements. Regimes with multiple attractive equilibria are possible. The initial stocks of physical and natural capital and the carrying capacity of the economy affect the type of development path that the economy follows. The admissible alternative scenarios discussed in the paper suggest that environmental externalities and agents' heterogeneity in terms of dependence on natural resources and ability to accumulate physical capital are factors which deserve great attention. These elements significantly affect the distributive and welfare outcomes of industrialization processes and, more generally, of structural changes.
Acknowledgments We thank the three anonymous referees for their helpful comments and suggestions. We are also grateful to the participants in the 7th MDEF Workshop on Dynamic Models in Economics and Finance (September 2012, Urbino, Italy) for discussions and comments on a preliminary version. The usual disclaimers apply. 11 This result confirms that the dynamic regime without coexistence of the two sectors can lead to a poverty trap regardless of the equilibrium, either ð0; K 0 Þ or ðE0 ; 0Þ, to which the system converges. In fact, this dynamic regime occurs for values of s and d which generate a low value of θ and, consequently, a low aggregate welfare (see Proposition 4). 12 Deforestation was started in the 17th century by the colonial power which cleared forests for extracting wood and establishing the system of plantation monoculture. From 1825 to 1947 Haiti paid the debt for its independence and this debt burden induced the government to accelerate deforestation to export the tropical wood. Between 1923 and 1950, the percentage of Haiti's forested land passed from over 60 percent to 25 percent (Alscher, 2011; Library of Congress, 2006). Successively, colonial legacy, population growth and political mismanagement of natural resources have further worsened deforestation, soil erosion and environmental degradation compromising agriculture yield and productivity.
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Appendix A. Mathematical derivations A.1. Study of the isocline E_ ¼ 0 We have that E_ ¼ 0 holds if either E ¼0 or GðE; K Þ ≔ E E E
εK
ðEβ=ð1 αÞ þ KÞα
¼0
Notice that (a) GðE; KÞ ¼ EðE EÞ holds for E 40 and K ¼0; (b) given any K 4 0, GðE; KÞ o 0 holds if either E Z E or the value of E is low enough; (c) there exists a value K such that GðE; KÞ o 0 for every E 40 and K 4K . Some additional properties of the E_ ¼ 0isocline can be highlighted by evaluating the partial derivatives of GðE; KÞ with respect to K and E ∂G Eβ=ð1 αÞ þ ð1 αÞK ¼ ε β=ð1 αÞ ∂K ðE þKÞ1 þ α
αβε
K ∂G ¼ E 2E þ ð1 α βÞ=ð1 1αÞ αβ=ð1 αÞ ∂E ðE þKÞ1 þ α E Notice that ∂G=∂K o 0 always holds: an increase in K generates a shift of labor forces from the environmentally nondamaging F-sector towards the environmentally impacting I-sector. The derivative ∂G=∂E, for a given K 4 0, is strictly decreasing in E and is strictly positive (negative) for E low (respectively, high) enough. Consequently, the equation GðE; KÞ ¼ 0 defines an inverted-U function K ¼ Γ ðEÞ such that Γ ðEÞ ¼ 0 and Γ ðEÞ-0 for E-0. A.2. Proof of Proposition 1 Observe that the difference f ðEÞ ≔ f 1 ðEÞ f 2 ðEÞ is such that f ð0Þ o 0 and limE- þ 1 f ðEÞ ¼ 1 and remember that, by assumption, α þ β r 1 and consequently β =ð1 αÞ r 1. Furthermore, notice that f 1 ðEM Þ 4 f 2 ðEM Þ holds for E 4 εθ
α 1 ð1 αÞ=β
θ
þθ
ð1 αÞ=β
þ εθ
1 α ð1 αÞ=β
¼θ
ð1 αÞ=β
¼ EM
Such a condition holds if and only if f 1 ðEÞ and f 2 ðEÞ have two intersection points, one (which is clearly of type A) on the left of the vertical line E ¼ EM and the other (non-admissible) on the right of it. In other words, (13) is a necessary and sufficient condition for the existence of a unique equilibrium point with E; K 40. Two internal equilibrium points can exist only if condition (13) does not hold. When this is the case, a sufficient condition for the existence of two equilibrium points is f 1 ðE=2Þ 4 f 2 ðE=2Þ and E=2 o EM , i.e. E 2
!2 þ εθ
α
E 2
!β=ð1 αÞ 4 εθ
1α
and
E o EM 2
where E=2 is the value of E maximizing f 1 ðEÞ. Let us now prove the sufficiency of condition (14). A sufficient condition for the non-existence of internal equilibrium points can be obtained by imposing that ! E f1 of 2 E 2 that is, the maximum of the function f1 is less than the minimum of the function f 2 ðEÞ in the interval ½0; E. Such a condition is satisfied for E 2
!2 εθ
1α
o ϵθ
α
E
β=ð1 αÞ
A.3. Proof of Proposition 2 Linearizing the dynamic system (9)–(10) around the internal equilibrium points, and taking account of the fact that Eβ=ð1 αÞ þ K ¼ θ
A. Antoci et al. / Journal of Economic Dynamics & Control 47 (2014) 211–224
223
holds (see (11)) for all equilibrium points of this type, we obtain the following expressions for the elements of the Jacobian matrix J: ∂E_ αβε ¼ E 2E þ Eðα þ β 1Þ=ð1 αÞ K 1þα ∂E ð1 αÞθ
∂E_ ε ¼ αK θ o 0 ∂K θ1 þ α ∂K_ αβs ¼ 1 þ α Eðα þ β 1Þ=ð1 αÞ K o 0 ∂E θ ∂K_ αsð1 αÞ ¼ K o0 ∂K θ1 þ α
Then, by substituting K ¼ θ Eβ=ð1 αÞ , the determinant of J can be written as follows: βε Det J ¼ ð1 αÞ E 2E α Eðα þ β 1Þ=ð1 αÞ
θ
0
0
which is such that Det J⋚0 if f 1 ðEÞ⋛f 2 ðEÞ. Consequently, the equilibrium point of type A is always a saddle point. The trace of J is given by Tr J ¼ E 2E þ
αβε ð1 αÞθ
1þα
Eðα þ β 1Þ=ð1 αÞ K
αsð1 αÞ K θ1 þ α
where, given that Eβ=ð1 αÞ þ K ¼ θ, and consequently K o θ, we have
αβε ð1 αÞθ
1þα
Eðα þ β 1Þ=ð1 αÞ K o 0
βε
ð1 αÞθ
αE
ðα þ β 1Þ=ð1 αÞ
0
This implies that Tr J o 0 if f 1 ðEÞ of 2 ðEÞ; therefore the equilibrium point of type B is always locally attractive. Let us now analyze the local stability of ðE0 ; 0Þ. It is easy to check that the Jacobian matrix of the dynamic system (9)–(10), αβ=ð1 αÞ evaluated at ðE0 ; 0Þ, is a triangular matrix with eigenvalues E o 0 (in direction of the E-axis) and sð1 αÞ=E d (o0 ð1 αÞ=β for E 4 θ ). The system (9)–(10) is not differentiable at ð0; K 0 Þ; however, the local stability properties of the equilibrium point ð0; K 0 Þ can be easily detected by simply remembering that E_ o 0 holds if E 4 0 is low enough and that K_ o0 (respectively, K_ 40) holds above (respectively, below) the K_ ¼ 0isocline. As a result, the set fðE; KÞ: 0 r E r a; θ b rK r θ þ bg containing ð0; K 0 Þ is positively invariant for a 4 0 and b 40 small enough. This implies that ð0; K 0 Þ is always locally attractive. A.4. Proof of Proposition 3 To prove this proposition, remember that the equilibrium point ð0; K 0 Þ coincides with the intersection between the K_ ¼ 0isocline and the K-axis. Since K_ o 0 holds above this isocline, all trajectories crossing the side with K r θ of the rectangle Q enter Q. Analogously, since E_ o 0 for E ¼ E, all trajectories crossing the side with E ¼ E of Q enter Q. Furthermore, notice that every rectangle R containing Q is a positively invariant set. This implies, by the Poincaré–Bendixson Theorem, that every trajectory in R either enters Q in finite time or approaches the equilibrium point ð0; K 0 Þ. References Alscher, S., 2011. Environmental degradation and migration on Hispaniola Island. Int. Migr. 49 (S1), e164–e188. Antoci, A., Russu, P., Ticci, E., 2010. Structural change, economic growth and environmental dynamics with heterogeneous agents. In: Bischi, G.-I., Chiarella, C., Gardini, L. (Eds.), Nonlinear Dynamics in Economics, Finance and the Social Sciences. Essays in Honour of John Barkley Rosser Jr, Springer-Verlag, Berlin, pp. 13–38. Antoci, A., Russu, P., Ticci, E., 2012. Environmental externalities and immiserizing structural changes in an economy with heterogeneous agents. Ecol. Econ. 81, 80–91. Barbier, E.B., 2010. Poverty, development, and environment. Environ. Dev. Econ. 15, 635–660. Bretschger, L., Smulders, S., 2012. Sustainability and substitution of exhaustible natural resources: how structural change affects long-term RD-investments. J. Econ. Dyn. Control 36, 536–549. Collier, P., 2009. Haiti: From Natural Catastrophe to Economic Security. A Report for the Secretary-General of the United Nations, Oxford University, Oxford. Available at: 〈http://www.securitycouncilreport.org〉. Easterly, W., 2003. The political economy of growth without development: a case study of Pakistan. In: Rodrik, D. (Ed.), Search of Prosperity, Princeton University Press, Princeton, pp. 439–472. Economy, E.C., 2004. The River Runs Black: The Environmental Challenge to China's Future. Cornell University Press, Ithaca & London. Greenpeace International, 2012. Toxic threads: putting pollution on parade. How textile manufacturers are hiding their toxic trail. Available at: 〈http:// www.greenpeace.org/international/Global/international/publications/toxics/Water%202012/ToxicThreads02.pdf〉. Human Rights Watch, 2012. Toxic tanneries: the health repercussions of Bangladesh's Hazaribagh leather. Available at: 〈http://www.hrw.org/reports/2012/ 10/08/toxic-tanneries〉. Library of Congress, 2006. Country profile: Haiti. Library of Congress Federal Research Division, Washington, DC. Available at: 〈http://lcweb2.loc.gov/frd/cs/ profiles/Haiti.pdf〉.
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