The Environmental Kuznets Curve When the Environment Exhibits Hysteresis

Transcription

1 Macquarie University, Australia From the SelecteWorks of Ram Ranjan April, 2007 The Environmental Kuznets Curve When the Environment Exhibits Hysteresis Ram Ranjan, University of Floria James Shortle, Penn State University Available at:

2 The Environmental Kuznets Curve When the Environment Exhibits Hysteresis 1 Ram Ranjan Postoctoral Associate International Agricultural Trae an Policy Center, Foo an Resource Economics Department, University of Floria. Phone: FAX: rranjan@ifas.ufl.eu an James Shortle (Professor) The Pennsylvania State University 112-C Armsby, University Park, PA Phone: FAX: jshortle@psu.eu Abstract The relevance an implications of the environmental Kuznets hypothesis are examine in the presence of stock effects an non-linearities associate with pollution generation. Stock effects lea to hysteresis an irreversibilities in environmental quality that are overlooke when emphasis is place on the flow effects of pollutants only. It is emonstrate here that an optimal growth plan in the presence of stock effects shifts the focus away from prescribing economic growth as a panacea for environmental ills. Implications for currently inustrializing economies are iscusse. (JEL: Q20, Q01, O13) 1 The authors wish to acknowlege valuable inputs from Liz Marshall on previous versions of this paper. Any remaining errors are of the authors alone.

3 Introuction The environmental Kuznets curve (EKC) escribes an inverte U-shape relationship between environmental pollution an income, which, if it is a vali escription of the true relationship between environmental pollution an economic evelopment, suggests that beyon a threshol level of evelopment, continue economic growth is goo for the environment. The policy implication rawn by some, an ispute by others, is that environmental protection will come about more or less autonomously as a result of strong pro-growth policies (see Arrow et al for a nice iscussion of such issues). Such analyses often focus on pollution as a flow phenomenon; greater levels of evelopment may lea to stricter environmental regulations an a reuction in the generation of new pollution. However, the environmental amage generate by many pollutants may be more a function of the existing stock of pollutant than of its flow; stock effects may trigger loss of system resilience or irreversibilities in the evolution of environmental quality that influence the options available to future generations (Arrow et al. 1995). Irreversibility is the more extreme of the threshol effects in environmental quality change. An example of irreversible change from the atmospheric stock of carbon ioxie an other greenhouse gasses, for instance, woul be a rise in sea level or a breakown of the thermohaline circulation belt (see Gjere et al an Keller et al. 2000). Hysteresis, on the other han, refers to an intermeiate stock effect, where eclines in environmental quality are potentially reversible, but at a much higher cost than woul have been associate with prevention of the quality ecline in the first place. This phenomenon occurs when the level of pollution stock associate with the system flipping 2

4 into a egrae state is much higher than that require for the system to return to a pristine state 2. Therefore, the stock of pollutants nees to be lowere to a level beyon its flipping threshol in orer to enable it to return to a pristine state. Though the problem of hysteresis has been wiely analyze in ecological sciences (Luwig et al. 1978), the economics of it has been taken up only recently (Maler et al. 2000). Elaborating on the concept of stock effects in the presence of an EKC, Munasinghe (1995) emphasizes the nee to explore alternative paths that allow one to attain high levels of consumption an income without generating large stocks of pollution an severely egraing the environment. He proposes that in the presence of stock effects, a more esirable transition towar higher income levels may be through a tunnel in the inverte U-shape curve (presente as a metaphorical hill) such that the irreversibilities associate with the threshol levels of stock pollution coul be avoie. In this paper we construct a moel aroun the ieas iscusse in Arrow et al. (1995) an Munasinghe (1999) to explore the implications for optimal rates an levels of capital accumulation when pollution relate stock externalities are taken into consieration. We expan the existing theoretical moels in the literature on EKC to incorporate the irreversibilities an hysteresis effects that may exist between flow of pollution an environmental quality. In our moel the incorporation of hysteresis between environmental quality an the flow of pollution implies that it may not be optimal to increase the pollution all the way up to the threshol level implie by a conventional EKC relationship. This is primarily ue to the fact that once the stock of pollution level crosses a threshol beyon which hysteresis sets in, the cost of reversing the impacts of 2 Throughout the paper, we use the term egrae an pristine to characterize the states of an ecological system that are clearly istinguishable in terms of their pollutant contents an ecological services renere. Similar terminology can be foun in the existing literature. For example, Maler et al. (2000) while looking at nutrient loaings in a lake characterize the states as clear (or oligotrophic) an turbi (eutrophic). 3

5 the pollution stock may become excessively high. Consequently, even though a conventional EKC may exist between pollution flow an income, there may not exist a similar relationship between certain other inicators of environmental quality an income. In aition to an analysis of the optimal transition path, we look at the case of an imperfectly competitive economy in which capital accumulation ecisions are mae without ever consiering the externalities associate with pollution emissions. Though imperfect, for sake of simplicity, this economy will be referre to as the competitive economy in this paper. The implications for steay state levels of pollution an capital are characterize an compare to the socially optimal case when stock effects are taken into consieration. We show that multiple steay states exist, an that achievable steay states are history-epenent; since ifferent countries exhibit ifferent initial combinations of environmental quality an capital, they may en up on ifferent stable paths. One important fining from the above analysis is that the rates an levels of capital accumulation are significantly ifferent for the competitive an the socially optimal cases. We then look at the possibility of switching from the competitive path to the socially optimal path mistream, an explore how the timing of the switch influences which steay states remain achievable. While the paper is focuse aroun the implication of stock effects associate with environmental pollution on the EKC, the finings have significance in a much larger context of growth an sustainability literature. For instance, inclusion of environmental hysteresis in sustainable growth moels may help guie the choice of policies relate to environment, inustrialization an globalization in a meta-analysis framework as has been echoe in the book by Munasinghe et al. (2001). 4

6 In the following sections a theoretical moel is esigne that incorporates the hysteresis effects associate with stock accumulations. Introuction of hysteresis makes the moel non-linear an reners most analytical exposition intractable. We, therefore, perform numerical simulations in orer to explore the issues raise above. Moel Two main lines of arguments exist to explain the existence of an EKC 3. One hinges on the assumption that people have a preference for environmental quality that increases isproportionately as income rises. This is a simple case of non-homothetic preferences. The secon explanation is base upon an assumption of pollution-reucing technological progress that causes pollution levels to fall as income rises 4. Since our focus is on optimal transition paths in the presence of an EKC an not on theoretically exploring the merits of each theory, we incorporate both these aspects into the moel. The relative importance of either aspect is then merely a matter of parameter specification. The outline of the moel is escribe below. The prouction of output (or income) m exhibits ecreasing returns to scale in capital (k) given by 5 : (1) α m = k where < 1 α. 3 However, the theoretical literature on EKC has evolve extensively in the past to incorporate several versions within an beyon these two main branches (for instance see Lieb (2003) an Anreoni an Levinson 2001 an the references therein). 4 This argument makes the assumption that a threshol level of income exists beyon which less polluting technologies coul be use efficiently. 5 The role of population as another factor of prouction is ignore here to keep the analysis tractable. However, population may have implications on the existence of the EKC itself an also on the environmental egraation associate with growth. For example, with increasing population, per capita income may still remain lower than is require to trigger a shift in the environmental preferences. Also, increasing emographic pressures may make the environment more susceptible to irreversible change. 5

7 In equation (1) α is the elasticity of output with respect to capital. Pollution p rises with output, but at a ecreasing rate. This allows for pollution-reucing technological progress with capital. In equation (2) below γ is an exogenously etermine parameter that associates technological progress in emissions reuctions with capital accumulation 6. (2) p = βk α γ This specification oes not allow for the pollution level to be reuce through contemporaneous abatement expenitures. While this specification limits the generality of the moel, it greatly facilitates our exploration of the nonlinear ynamics that are the subject of this paper, an the subsequent numerical analysis. Further, the moel retains essential features. Contemporaneous abatement woul entail costs as resources are iverte either from consumption or investment, reucing future consumption. In general, there woul be a combination of both. Thus, as in this moel, reucing pollution will entail a lower level of capital accumulation. While the traeoff between contemporaneous abatement an reuce investment is an issue of interest, the results of our analysis woul emerge in a more complex moel. Capital accumulation is etermine by: (3) k& α = k c δk where c is consumption an δ is the rate of epreciation of capital. It is also possible to take irect measures in orer to influence the rate of progress in abatement technologies. This woul make the parameter γ an enogenous function of abatement measures. Another way to achieve lower emissions per unit of output is through pollution restricting legislations. Such legislation, it may be argue, woul lea to technological avances 6 See Beltratti (1996) for similar formulations. 6

8 over time, thus leaing to lower emission in the long run 7. It is also possible to have exogenous avancements in pollution reucing technologies that woul lower γ, thus leaing to lower emissions per unit of output over time. This woul certainly have an influence over the shape an possibility of the environmental Kuznets curve. Environmental quality egraation evolves as: n (4) & = θp + η ρ n + 0 In the above equation the change in environmental quality is sensitive to both pollution flow an stock. θ captures the aition to the stock of pollution from a marginal increase in pollution. Since, the focus of this paper is on pointing out the implications for EKC when non-linearities associate with environmental systems are consiere, we incorporate the hysteresis phenomenon explicitly in the equation above. Ecological systems are often characterize by hysteresis in which the system flips from a pristine state to a egrae state with the crossing of a threshol level of the stock of pollutant. This flipping is unique in the sense that costs of bringing the system back into pristine state may be far greater than the costs associate with preventing the pristine state from falling into the egrae state. The secon term on the right han sie introuces the hysteresis effect. η is the maximum rate at which environmental quality egraes, n affects the sharpness with which the egraation flips at the point of inflection an 0 is 7 Moeling enogenous technical change in an of itself is a tricky issue, an the subject of an unsettle research. While we unerstan the importance of enogenous technical change, aressing it in a satisfactory way in this moel woul greatly etract from our ability to obtain substantive results on the issues that are the focus of this paper. 7

9 a constant parameter that affects the maximum rate of egraation 8. The thir term represents the regenerative capacity of the environment, in which ρ is the rate of growth environmental regeneration 9. The utility function is aitively separable in consumption an environmental quality an is given as: (5) u = alog( c) blog( ) In the above equation the parameter b affects the role environmental preferences play in the etermination of the EKC an parameter a weighs the utility from consumption. Society maximizes its utility from consumption net of isutility from environmental quality egraation over an infinite horizon, subject to a iscount rate r. The current value Hamiltonian for utility maximization is written as: n α (6) cvh = alog( c) blog( ) + λ1 ( k c δk) + λ2 ( θp + η ρ ) n + The first orer conition taken with respect to consumption is given by: 0 (7) a λ 1 = c 8 Following Carpenter et al. (1999), if 0 were raise to the power n, it woul etermine the level of egraation at which the maximum rate of egraation η woul reach half its value. For the case of eutorphying lakes, Carpenter et al. us the functional form for rate of change of phosphorus mass in lakes as: q rp p& = l sp +, where l is the input from watershe, r is the maximum rate of recycling of p, an q q q m + p affects the steepness of the sigmoi curve. The parameter s is the rate of loss of phosphorous an coul be consiere to be the regenerative capacity of the lake. For the case of lake Menota in the USA, the estimates are: s =.817, r= kg/year, m=116000kg, an q= Scope of regeneration may vary with the scale of the ecosystem. On a large scale is the case of issolution of atmospheric carbon ioxie into eep oceans. Though this process takes a long term to show noticeable effect, yearly rates coul still be erive. The oceanic uptake of atmospheric CO 2 has been estimate to be between 2 to 3 GTC/year (Scimel et al. 1995). Other example is applie to a much smaller scale such as that of lakes. Luwig et al moel regeneration potential of a eutrophic lake in orer to erive an optimal phosphorous loaing scheme. 8

10 Equation (7) above requires that the marginal utility from consumption be equate to the shaow price of capital λ 1 along its optimal path. The arbitrage conitions for evolution of capital an stock of egraation are given by equations (8) an (9) below an are erive as the first erivatives of equation (6) with respect to k an respectively: (8) & λ = λ δ + r αk λ θβ α γ k α 1 1 1( ) 2 ( ) α γ 1 Note that the growth in shaow price of capital is negatively relate to the shaow price of egraation, λ 2, as each aitional unit of capital leas to more pollution which as to the stock of egraation. The shaow price of egraation evolves as: (9) & n1 b = ( n 0 λ 2 λ2 η ρ r) n ( + ) 2 0 Consequently, the implications for rate of growth of consumption can be erive from (7) an (8) as: (10) c& c = αk α 1 θβc δ r + λ2 ( α γ ) k a α γ 1 The above set of equations woul etermine the rate of consumption an capital accumulation. These time paths are explore in later sections with the help of numerical simulations. However, we first examine the effect of hysteresis on the system ynamics an the location an characterization of system steay states. Steay State Analysis 9

11 10 At a steay state the rates of growths of all the state variables an their shaow prices are assume to be zero 10. These points are erive in the following equations: (11) ) ( = = γ α α γ α θβ δ α λ k a c r k c& (12) = 0 λ & 2 + = r n b n n ρ η λ ) ( (13) k k c k δ α = = 0 & (14) + = = p n n η ρ θ & This system--four equations an four unknowns--can be use to etermine the steay state values of capital an egraation. Substituting (13) into (11) yiels: (15) ) ( ) ( + + = γ α α α γ α δ θβ δ α λ k a k k r k Equating (15) an (12) yiels: (16) + r n b n n ρ η ) ( = 1 1 ) ( ) ( + + γ α α α γ α δ θβ δ α k a k k r k Equations (14) an (16) both express a relationship between capital (or pollution) an the level of environmental egraation. When solve simultaneously, these equations provie the steay state levels of capital an egraation. However, ue to the nonlinearities associate with the evolution of environmental egraation, it is only possible to implicitly solve for the steay state values of capital, pollution, consumption, an 10 The concept steay state is usually efine as a situation in which all enogenous variables grow at constant, possibly ifferent, rates of growth. This, of course, inclues zero growth rates.

12 environmental egraation. We therefore make use of numerical simulations to characterize these values. Table 1 presents the values of parameters assume for the purpose of numerical simulations. It is ifficult to get realistic estimates of such parameters, especially at a global level; therefore their significance shoul be unerstoo only relative to each other. INSERT TABLE 1 HERE In orer to maximize the iscounte sum of inter-temporal utility for society we perform a numerical simulation using a time horizon of 200 perios. Given the base iscount rate of 5 percent, this successfully mimics an infinite time horizon problem. The results of the simulations are illustrate through figures. These simulations involve steay state analyses using MATHEMATICA an ynamic analyses using GAMS. Figure 1 presents the relationship between capital an environmental egraation along the & = 0 isocline. Notice that environmental egraation is irreversible once it excees 1.5 units an capital excees approximately 100 units. Beyon that level the system flips into a egrae state from which it is impossible to flip back into the pristine environment. This can be seen from the fact that in the egrae environment the egraation level associate with a stock of 100 units of capital is 4 units an to bring it back to a level below 2 units of egraation, capital nees to be totally eaccumulate 11. This reflects the fact that high levels of egraation may trigger irreversible changes in the quality of the environment, which may, at best, be extremely costly to revert back from. The flipping points are shown through ashe arrows in the figure below. Further, from phase-plane analysis it can be verifie that the transition 11 With a lesser hysteresis effect flipping back may be possible, though capital woul still nee to be lowere significantly in orer to flip. 11

13 region between the two flipping points is unstable. Dynamics near the & = 0 isocline is shown through the soli arrows in Figure 1. INSERT FIGURE 1 HERE Next, we look at the behavior of the shaow price of egraation. Figure 2 represents the shaow price of the stock of egraation along the isoclines representing the relationship between capital an egraation. Notice that the shaow price of egraation is negative (in most parts) as egraation is a ba commoity. This is represente by the two curves in the regions I an II, which fall to the left an right sies of the two asymptotes respectively. However, the region in between the two asymptotes (region III) shows a positive value for the shaow price of egraation that reaches infinity asymptotically. Such regions correspon to the flipping points for the system as they are unstable. Whereas, at either extremes of region III, the shaow price of the stock of egraation goes to positive infinity reflecting the tenency to cross over to either region I or II. INSERT FIGURE 2 HERE The hysteresis (irreversibility) evient in the relationship between capital accumulation an egraation arises primarily from the stock-flow ynamics of pollution as specifie in equation 4. Once the system flips into the egrae state, the flow of pollution nees to be reuce beyon the level it was at that flip point in orer for the system to return to the pristine state. Figure 3 illustrates the socially optimum steay state level of capital an egraation. At least four steay states (enote S1, U2, U3 an S4) are possible. These steay states are etermine by the intersection between the curves & = 0 & k & = 0. From the ynamics of the capital an egraation stocks it can be easily euce that the two 12

14 extreme points (S1 an S4) are the stable ones with the mile two (U2 an U3) being unstable 12. The steay state S4 is characterize by high levels of capital an environmental egraation an represents the egrae steay state; S1 represents the steay state with a pristine level of environment. A country s portfolio of environmental quality an capital stock when it enters the system woul etermine whether its optimal path is on a stable arm proceeing towar the left steay state (S1) or towar the right steay state (S4). INSERT FIGURE 3 HERE The ynamics of the system s optimal evelopment path are shown in figure 4 for a very low initial capital level of 0.5 units an an initial level of environmental egraation of 2.5 units. On the scale of values chosen, 2.5 units woul be associate with high levels of egraation, however, notice that the system still manages to return to the pristine steay state. Notice that though the pollution is high, it is not high enough to overcome the regenerative capacity of the environment. Also notice the rop in the level of environmental egraation as pollution falls an capital stabilizes. This illustrates the optimistic message of the environmental Kuznets curve the promise of achieving higher levels of capital an higher levels of environmental quality mae possible by high economic growth. The environmental Kuznets curve arising from this optimization is shown in figure 5. Note that ue to the high level of initial egraation, the rising portion of the conventional environmental Kuznets curve is not present in this optimization. However we will show that there are problems with pre-supposing such a path, especially when one consiers an economy characterize by myopic behavior of competitive agents. 12 On closer examination, it woul turn out that the k & = 0 curve intersects the = 0 curve twice aroun U3. However, since both of them are unstable, they have been consiere as one equilibrium for the present analysis. & 13

15 INSERT FIGURES 4 an 5 HERE Next, we look at an economy with low initial capital an low environmental egraation. Such economies may be characterize by a heavy emphasis on capital accumulation with little or no consieration given to isutility from environmental egraation. Therefore we moel such an economy by neglecting the isutility from environmental egraation in their welfare functions. Because, in such an economy capital accumulation ecisions are mae without consiering the externalities associate with pollution emissions, we will refer to this economy as the (imperfectly) competitive economy. The rest of the ynamics remain the same as the socially optimum case. The steay state level of capital (rawn as a straight line) is compare to the socially optimal case in figure 6. Notice the steay state level of capital is now unaffecte by the level of environmental egraation. A high level of esire capital woul obviously lea to hysteretic shifts in environmental egraation. INSERT FIGURE 6 HERE In orer to compare the long term welfare for an economy following a socially optimum path with the one following an imperfectly competitive path, we look at the iscounte sum of utilities for the two economies. The total iscounte sum of utility for an economy following a socially optimal path but starting levels of capital of 0.5 an a egraation level of 2.5 is 3.6. If a similar utility preference for environmental quality is assume for an economy following an imperfectly competitive path (an thus not consiering environmental egraation in its optimization plan), the total utility is slightly lower at Notice that uner the socially optimal plan, a high level of initial 14

16 egraation penalizes the current generation, as the benefits from improve environmental quality accrue to generations too far away in future, thereby, iscounting its value. However, in the figure below we see that the ifferences in utilities between the two economies become inee much higher as the initial level of environmental egraation is lowere only marginally to Clearly, the ifferences in the utilities between the socially optimal paths an the imperfectly competitive paths increase as the initial environmental quality enowment is higher. INSERT FIGURE 7 HERE Summary of results: The possibility of an environmental Kuznets curve uner stock effects is heavily influence by the nature of the economic growth plan aopte. An imperfectly competitive regime is more likely to fall into the hysteretic or irreversible state of environmental egraation than a socially optimal one. Initial levels of environmental egraation an capital play a crucial role in etermining the extent of total possible welfare uner the two regimes. Implications for Currently Inustrializing Economies So what are the lessons for the currently inustrializing economies? If high levels of capital accumulation are linke with hysteresis in the evolution of environmental quality, what shoul be the optimal level an rate of such accumulation? An o initial enowments matter? In this section we explore these issues. Figure 8 shows the ynamics of pollution, capital accumulation an egraation along the competitive economy path for an economy enowe with low levels of capital 15

17 but high levels of environmental egraation. In this case the economy settles into the egrae state in the long run. Clearly, the combination of initial levels of capital an environmental egraation is crucial in etermining whether an economy along the competitive path woul be able to retain its pristine environmental state an still maintain high levels of capital accumulation or woul flip into a egrae state as it inustrializes. INSERT FIGURE 8 HERE We explore this issue by looking at the threshol level of initial environmental egraation for a given level of initial capital beyon which the economy settles into the egrae state. For the values of the parameters presente in Table 1, we fin that for an initial level of capital of 0.5 units, this threshol is achieve at a level of egraation of units. If an economy starts with a higher level of egraation, it woul shift into a egrae state, whereas if it starte with a level lower than the above threshol, it woul settle into the pristine state. This is shown in figure 9 below. INSERT FIGURE 9 HERE Are economies that are characterize by levels of egraation above the threshol oome? A possible solution in the competitive case woul be to restrict the initial capital enowment an thus affect the rate at which capital grows. This fact is reflecte in figure 9 where, when the initial level of capital has been halve to 0.25, the pristine levels of environment coul be achieve while still maintaining high levels of consumption. Such austerity measures allow the environment to recover an ultimately return the country to a point where passage to the pristine steay state represents its optimal evelopment path. This oes show a tunnel out of the hysteresis an 16

18 irreversibilities associate with the turning point levels of egraation as propose by Munasinghe (1999). However, the above result also coul vary with the environmental characteristics of a region uner consieration. These characteristics can best be efine by the various parameters in our moel an hence it is crucial to unerstan the sensitivity of results to such parameters. Summary of results: It is possible for imperfectly competitive economies to attain the environmental Kuznets curve if they start with a sufficiently low level of environmental egraation. In case the threshol level of egraation for reaching the pristine state in the long run has been crosse, it may still be possible to tunnel out for some economies that start with a low level of initial capital. Parameter Sensitivity Certain key parameters coul make all the ifference in terms of whether an economy is lucky enough to fin a tunnel or not. For instance, two countries both of which start with the same level of initial egraation may en up on two extremes of environmental quality, epening upon whether they start with a low or high level of capital. As shown above starting with a slightly lower level of capital (.25) leas to a pristine state in the long run. In the above example, parameters such as the initial levels of egraation an available capital are crucial as they etermine the kin of equilibrium attaine in the long run. This ifference arises primarily from the fact that initial level of environmental quality allows for the possibility of reaching either of the two stable equilibriums S1 an S4 as shown in figure 4. Consequently, a marginal ifference in pollution emissions in the early stages of capital accumulation ecies whether the hysteresis effect of 17

19 environmental quality kicks in or not. However, the role of other parameters such as those that affect the extent of hysteresis an technological progress relate to abatement technology cannot be unerestimate as they might vary from country to country, thus making a straightforwar comparison ifficult. For instance, η, 0 an n, the parameters that etermine the imensions of hysteresis effect woul be ifferent for ifferent types of environments that are prone to hysteresis. Consequently, the threshols that etermine the presence or absence of the environmental Kuznets curve woul vary amongst nations. Another set of parameters that woul significantly affect the threshols for the environmental Kuznets curve are those relate with technological progress (γ ) an the amount of pollution per unit of output ( β ). These parameters influence the rate at which the environment egraes an thus pushes it towars the hysteretic stock of environmental egraation. Since these parameters too woul iffer over regions, they coul be a cause for presence or absence of the Kuznets curve amongst nations. The regenerative capacity of the environment coul also significantly etermine the possibility an extent of the environmental Kuznets curve. Point of No Return A crucial question asks how currently inustrializing countries can grow an still avoi the kin of irreversibilities (or at best high costs) associate with the transition of their natural environments into egrae states. As mentione above, an economy with a heavy emphasis on growth an little or no regar for environmental egraation woul fall into a egrae state if its initial enowments are on the wrong sie of the threshol. The literature on EKC has assume that preferences for environmental quality exist right 18

20 from the start of the inustrialization process an therefore, that an economy crossing a threshol ratio of environmental quality to egraation will experience a rop in levels of pollution. However, this stylize representation of preferences masks the complexity of the role that information plays. The process of inustrialization has often been characterize by a rapi increase in capital simultaneously with a rapi egraation of environment. Information about the health costs associate with environmental pollution an the economic an ecological amages from a stock buil-up become available only in the avance stages of a country s growth. Preference for environmental quality may in fact take iscrete jumps as more information becomes available an the uncertainty associate with the impacts of environmental egraation is remove. The recent controversy over the impacts of global warming is a goo example. The concept of iscrete changes in preferences can be incorporate into our moel by assuming that countries start with a heavy emphasis on growth (characterize by the competitive path), but as information about environmental egraation becomes available, there is a regime change after which the socially optimal growth path is aopte. This regime change may be either enogenously specifie (for example, the environmental utility parameter b becoming non-zero beyon a certain ratio of capital an egraation) or exogenously specifie base upon the observation of currently inustrialize economies. The critical element in etermining the long-term effect of a regime change is at what point it occurs; the country s portfolio of environmental egraation an capital stock at the point the optimal growth path is aopte will etermine the system s eventual settling point. We fin the threshol levels of capital an egraation for the competitive 19

21 an socially optimal growth paths an therefore, erive the point of no return for such economies. The point of no return is akin to the Skiba point in the macro economics literature. It exists when there are non-linearities associate with the state variable, (for example, a concave-convex prouction function) thus leaing to multiple historyepenent steay states (Skiba 1978, Tahvonen an Seppo 1996). The Skiba point is the point from which one coul go to either of the steay states an still get the same total welfare. However, when the number of state variables is more than one, the threshol point becomes a line, an then a plane as the imensions increase. In the moel escribe above, the point of no return woul actually be a line plotte on the capital-egraation plane. We erive this line by solving for combinations of capital an egraation in the socially optimal case, beyon which the system falls into the egrae steay state. This is represente below in figure 10. The two roughly vertical lines represent the points of no return for the competitive an the socially optimal cases, with the left one representing the competitive case. The competitive Skiba line represents the combination of initial parameters for egraation an capital, starting to the right of which there is no returning back to the pristine state uner a competitive economy. INSERT FIGURE 10 HERE Figure 11 shows the ynamics containe within the Skiba region efine by the area between two Skiba lines. A competitive economy starting in the Skiba region, when left to itself, woul eventually cross the threshol an fall into the egrae state (case a). If the regime change occurs after the social Skiba line has been crosse, the system still heas towars the egrae state (case b). On the other han, when regime change 20

22 occurs early enough that the system is still below the social Skiba line, the system heas towar the pristine steay state (case c). INSERT FIGURE 11 HERE At the point of regime shift, countries coul be characterize by several possible combinations of environmental egraation an capital enowments. The low capital an low egraation combination characterizes an agrarian economy. High initial capital an low egraation combination is highly unlikely but is possible if the country has a competitive avantage in proviing services or receives substantial capital transfers from other nations. Similarly the case of high initial capital an high egraation may represent currently inustrializing economies with low environmental preferences. Finally, the case of high initial egraation combine with low capital might characterize certain countries that ha rich mineral wealth; the mineral extraction can have an averse impact on the environment, but certain countries may have been unable to exploit the mineral wealth to buil capital (Porter s hypothesis). Summary of Results: Environmental preferences are ynamic an subject to changing information relate to the impacts of certain kins of pollutants on society. It is possible to erive points-of-no-return for economies that mark threshols levels of capital accumulation an relate environmental egraation below which it may still be feasible to revert back towars the pristine state after preference reversals. Conclusion 21

23 In this paper we have presente a simplifie theoretical moel that incorporates the hysteresis effects associate with pollution accumulation into the theory of the environmental Kuznets curve. We show that the stress on rapi capital accumulation without any concern for the stock effects associate with environmental pollution may lea to costly irreversibilities an hysteresis. Incorporation of these concerns significantly lowers the esirable steay state stock of capital as well as consumption levels. The moel also inicates that a country nee not always start on the socially optimal growth path to ultimately reach the socially esirable levels of capital an environmental quality. It remains possible to reach the pristine steay state espite starting off the optimal path, as long as certain threshol combinations of capital an egraation are not crosse. Further, the amount of effort require in terms of foregone consumption (reflecte in lower rates of capital accumulation) epens upon a combination of various parameters. Significant amongst them are the initial levels of egraation an capital, the regenerative capacity of the environment, an the egree of hysteresis in the system ynamics. The propose iea of tunneling in the literature assumes that some transition path coul be esigne that woul enable high levels of capital accumulation an still preserve the environment. However, in this moel, preserving the pristine state comes only at a cost of reuce levels of capital accumulation. This is reflecte in the large ifference associate with the steay state capital levels erive with an without regar for environmental egraation. Perhaps tunneling may be feasible in the wake of significant future avances in pollution-reucing technologies or geo-engineering 22

24 avances that may help restore egrae ecosystems at reuce costs. This raises aitional questions about when to jump onto the socially optimal capital accumulation path when there may be expectations or real possibilities of such future iscoveries. Our analysis also provies insight into some of the observe iscrepancies in the literature on the environmental Kuznets curve. One reason an EKC may not be observe along certain imensions is that even though there may exist an inverte U-shape relationship between pollution levels an income, other observable inicators of environmental quality may continue to egrae ue to stock effects. A simple example is the case of iminishing bioiversity all over the worl. The existence of an observable EKC in such cases epens upon the type of environmental inicators chosen. It is important to note that when one consiers the stock effects of environmental pollution, a istinction has to be mae between national an trans-national impacts. The above analysis is more representative of pollutants with regional impacts such as eutrophication of lakes or loss of wetlans than of those with global impacts such as carbon stock accumulation. The implications of environmental egraation for optimal capital accumulation rates are much simpler to etermine when the scale of impact an jurisictional control are the same. When pollutant impacts cross national bounaries, optimization must occur at a more global level. The implications for capital accumulation at a global level are much harer to etermine ue to the complex inter-connections an regional ifferences in human conition, the global economy, an the planet s fragile ecological balance. As a consequence of such pollutants, however, the impacts of a nation s inustrialization can no longer be consiere in isolation with the rest of the worl. To the extent that national 23

25 short cuts such as tunnels through the EKC involve regional reistribution of environmental egraation, such policies must be evaluate from a global perspective. This paper suggests caution in interpreting the optimistic EKC prescription for the power of economic growth at reucing environmental egraation. Environmental egraation is increasingly measure through stock-relate variables such as bioiversity, ecosystem resilience, an lan use; such measures o not bounce back when preferences lea to policy changes. In the presence of ecological threshol effects, myopic growth prescriptions may therefore lea to irreversible or isproportionately costly eclines in environmental quality. Uner such conitions, the socially optimal path may involve a more conservative growth strategy in which capital accumulation rates are intentionally constraine. It is possible that with enogenous technological avances an avances in abatement possibilities the rate of capital accumulation coul be increase, however the extent of such possibilities woul become much clearer in future. Therefore, there is nee for further research on such possibilities. 24

26 References 1. Anreoni J. an A. Levinson (2001), The Simple Analytics of the Environmental Kuznets Curve. Journal of Public Economics, v. 80, Arrow, K., B. Bolin, R. Costanza, P. Dasgupta, C. Folke, C. S. Holling, B.O. Jansson, S. Levin, K.G. Mäler, C. Perrings an D. Pimentel (1995), Economic Growth, Carrying Capacity an the Environment. Ecological Economics, 15, Beltratti, A. (1996), Moels of Economic Growth an Environmental Assets. Kluwer Acaemic Publishers. 4. Carpenter, S.R., D. Luwig, an W. A. Brock (1999), Management of Eutrophication for Lake Subject to Potentially Irreversible Change. Ecological Applications 9: Gjere, J., S. Grepperu an S. Kvernokk (1999), Optimal Climate Policy uner the Possibility of a Catastrophe. Resource an Energy Economics, 21, Keller, K., K. Tan, F. M. M. Morel, an D. F. Brafor (2000), Preserving the Ocean Circulation: Implications for Climate Policy. Climatic Change, 47(1): Lieb, C. M. (2003), The Environmental Kuznets Curve. A Survey of the Empirical Evience an of possible Causes. University of Heielberg, Department of Economics, Discussion Paper Series no Luwig, D., D.D. Jones, C.S. Holling (1978), Qualitative Analysis of Insect Outbreak Systems: The Spruce Buworm an Forest. Journal of Animal Ecology, 47,

27 9. Luwig D., S. Carpenter an W. Brock (2002), Optimal Phosphorous Loaing for a Potential Eutrophic Lake. Ecological Applications, 13(4): Maler, K.G., A. Xepapaaes, an A. e Zeeuw (2000), The Economics of Shallow Lakes. Working Paper No The Centre for Economic Research, Tilburg. 11. Munasinghe, M. (1995), Making Economic Growth More Sustainable. Ecological Economics, 15, Munasinghe, M. (1999), Is Environmental Degraation an Inevitable Consequence of Economic Growth: Tunneling through the Environmental Kuznets Curve. Ecological Economics, 29, Munasinghe, M., O. Sunkel, an C. e Miguel (2001), The Sustainability of Long-Term Growth: Socio-Economic an Ecological Perspectives, Ewar Elgar Publications, UK. 14. Schimel, D., I.G. Enting, M. Heimann, T.M. L. Wigley, D. Raynau, D. Alves, an U. Siegenthaler (1995), CO 2 an the Carbon Cycle in Hoghton J.T. et al. (es.) Climate Change 1994: Raiative Forcing of Climate Change an an Evaluation of IPCC IS92 Emission Scenarios, Cambrige University Press, Cambrige. 15. Skiba, A.K. (1978), Optimal Growth with Concave-Convex Prouction Function. Econometrica, 46, Tahvonen, O. an S. Seppo (1996), Non-Convexities in Optimal Pollution Accumulation. Journal of Environmental Economics an Management, 31,

28 Table 1: Parameter Definition Elasticity of output with respect to α.4 capital Maximum rate of quality egraation from hysteresis η.25 Rate of natural regenration of environmental quality ρ.08 Parameter affecting hysteresis Parameter affecting hysteresis n 6 Pollution per unit output β 15 Technological progress parameter γ.005 Rate of capital epreciation δ.01 Weight on consumption affecting utility a 1 Scalar affecting impact of pollution on θ.001 egraation Rate of iscount r.05 Weight on egraation affecting utility b.8 27

29 Figure 1: Optimal Steay State Relation between Capital an Environmental Degraation 250 k & =

30 2 Figure 2: Shaow Price of Degraation λ & = III I II 29

31 k Figure 3: Socially Optimal Equilibrium & = U2 50 S1 U3 S4 k & = Note: The contours of the k & = 0 an = 0 curves were plotte using the ContourPlot option in Mathematica. It is possible to getter better estimates of the contours that may revise the intersection points aroun the unstable steay states. However, the intersection points aroun the steay states remain unaffecte. & 30

32 Figure 4: Social Optimum Case k c Time K0=.5, 0=2.5 Note: Since pollution is irectly proportional to capital accumulation, the time path of pollution resembles that of capital accumulation, albeit at a higher scale. 31

33 Figure 5: Environmental Kuznets curve (Social Optimum Case) Degraation k 32

34 Figure 6: Comparison of Social Optimum an egraation in steay state: 250 k & = k & = 0 Competitive case capital level

35 Figure 7: Welfare Comparison uner Different Regimes Time Utility socially-optimal (k0=.5, 0=2.371) competitive economy (k0=.5, 0=2.371) -0.9 Note: The figure above represents the iscounte per perio utility over time uner the two regimes. The total utility uner the socially optimal plan is 1, whereas that uner the imperfectly competitive plan is

36 Figure 8: Competitive Case k c Time k0=.5, 0=2.5 Note: Since pollution is irectly proportional to capital accumulation, the time path of pollution resembles that of capital accumulation, albeit at a higher scale. We have use a 200 perio time horizon for our numerical simulations which mimics the infinite horizon case. Consequently, the fall in the capital as seen at the en of time horizon is ue to the capital being consume as its iscounte value approaches zero. 35

37 Figure 9: Degraation (s-o, k0=.5, 0=2.372) (c-e, k0=.5, 0=2.372) (c-e, k0=.25, 0=2.372) (c-e, k0=.5, 0=2.371) Time 36

38 Figure 10: Point of No Return in the Competitive an Socially Optimal Cases & = k 150 Competitive Skiba Line Social Skiba Line Competitive Capital Level 0 k & =

39 k Figure 11: Dynamics within the Skiba Region Social Case Skiba Line Competitive Case Skiba Line Case c Case a Case b