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Environmental Crises:

Past, Present and Future

M. Scott Taylor, Department of Economics, University of Calgary 1 Forthcoming as the Innis Lecture,Canadian Journal of Economics, Nov. 2009.

Abstract

Environmental crises are distinguished by rapid and largely unexpected changes in envi- ronmental quality that are di¢ cult if not impossible to reverse. Examples would be major extinctions and signi...cant degradations of an ecosystem. I argue there are three precondi- tions for crisis: failures in governance, an ecological system exhibiting a tipping point, and an economy/environment interaction with positive feedbacks. I develop a simple model to illustrate how a crisis may arise, and draw on our knowledge of past and present crises to highlight the mechanisms involved. I then speculate as to whether climate change is indeed

a crisis in the making.1I am grateful for excellent research assistance from Jevan Cherniwchan and Juan Moreno Cruz. I re-

ceived helpful comments from too many colleagues to thank, as well as seminar participants at the University

of Basel, the 2009 Canadian Economics Association Meeting in Toronto, and the 2009 European Association

of Environmental and Resource Economists Conference in Amsterdam. A version of this paper will appear

as the Innis Lecture in the November 2009 issue of the Canadian Journal of Economics. I am also a¢ li-

ated with the NBER. Funding for this research was provided by the SSHRC. Email: mstaylor@ucalgary.ca.

Phone: 403-220-8912

1

1 Introduction

The current ...nancial crisis has given many economists pause. Do we have a good under- standing of the likelihood of crises, their cause or their cure; or is the economics of crises little guidance to policymakers today? While I am not a macroeconomist, even a layman"s read of the business press suggests that something unique has transpired over the last two years, something largely unexpected by most economists, and something that has proven di¢ cult and very costly to reverse. With the ...nancial crisis in the news everyday, it is hard to think about anything else. And as the crisis dragged on, I started to think about the likelihood of a similar environ- mental crisis. Even though I have studied some very destructive environmental events, I have always viewed the probability of any future crisis as very close to zero. This view was more an article of faith than a reasoned position, and I found myself questioning it. Since environmental economics does not have a standard theory of crises to guide my thoughts or help me organize data and history in a coherent manner, perhaps a future crisis was possible. This paper describes my attempt to develop a theory of environmental crises as a means to answering this question. A recent exchange between William Nordhaus and Martin Weitzman over catastrophic climate change has brought "environmental crises" to the fore of environmental economics, so perhaps the time is ripe for a simple model that helps us understand the mechanics of crises more fully.

1Macroeconomics has, after all, well-known

models of banking and foreign exchange crises, but at present there is no similar work in environmental economics. My goal is to provide a ...rst step by identifying a set of preconditions for a crisis. By doing so I hope to provide an answer to my own question, but more importantly to spur others to investigate further. My method is deliberately simple. First, I provide a de...nition of an environmental

crisis that is both narrow enough to be useful for theory, and broad enough to include1I am refering to the recent fat tailed versus thin tailed exchange between William Nordhaus and Martin

Weitzman. See Weitzman (2009a), a comment by Nordhaus (2009) and two replies by Weitzman (2009b,c). 2 several real world examples. Second, I revisit the classic Gordon-Schaefer model of resource use (hereafter the GS model) to understand why crises are so di¢ cult to generate in this framework.

2The GS model is the simplest dynamic model we use to think about many

of the most pressing resource issues of the day - over ...shing, biodiversity loss, and global warming. The model, however, admits little room for crisis. Fortunately, it does provide us with clues as to why it is crisis resistant, and by making three simple changes I construct a far less resistant variety I refer to as the Crisis Model. The changes I introduce allow for imperfect regulation in resource industries, a tip- economic activity and the environment. These are the preconditions for crisis. I then examine the mechanics of crises using a combination of phase-plane techniques and com- parative steady state analysis. I provide analytical results, and highlight these results by simulating the model"s distribution of outputs given a distribution of input shocks. These simulations are neither calibrations nor tests of the model; they are just useful ways to illus- trate the possibilities the model presents. Throughout I draw on well known environmental crises in the very distant and not so distant past in the hope of convincing the reader that the mechanisms I identify are more than just theoretical constructs. Finally, using the theory developed, I ask whether a future crisis is possible. While there are perhaps many candidates for future crises, I consider climate change. To investigate the role played by each of the preconditions, I examine them in isolation. I eliminate one or more of the preconditions and focus on the remaining force. I adopt assumptions to ensure that in the absence of feedbacks or tipping points, the model would be well behaved; i.e. it generates a stable, interior, steady state. With this method I am able to identify the novel features introduced by each precondition, and to show how they combine to deliver a theory of environmental crises. I ...rst revisit the Brander and Taylor (1998) analysis of Easter Island but now in- troduce governance that limits overharvesting and a tipping point that generates a truly

catastrophic outcome. I show that the tipping point divides the state space into two2For the original contributions see Gordon (1954) and Schaefer (1957). For a thorough treatment see

Clark (1990).

3 basins of attraction: one basin leads to an interior steady state; the other to a catastrophic moves the economy"s interior steady state away from the catastrophe, and shrinks its basin naught. When the interior steady state occurs at a resource stock which is below a critical threshold (related to, but far above, the tipping point) then the steady state is unstable, and all trajectories (save one) lead to the catastrophic outcome. Tipping points therefore introduce dramatic changes in the system"s dynamics. While a tipping point plus poor governance can generate a crisis, these two forces alone are unlikely to be the whole story. In the Easter Island case in particular, the catastrophic outcome is only guaranteed if the tipping point is approximately 30% of carrying capacity. While this is possible, it is in some sense unsatisfactory to develop a theory where crises are always and everywhere a function of large tipping points. Consequently, I proceed to out any government intervention. Under these assumptions positive feedbacks arise quite naturally in a variety of circumstances that we often discuss in environmental economics. the American bison and the Passenger pigeon, and link my discussion to recent work on catastrophic climate change. I show how positive feedbacks magnify shocks to the system, but are, in an important sense, self-limiting. As a result, I am forced to conclude that positive feedbacks cannot be the whole story either. The ...nal section puts the three preconditions together. I demonstrate how a relatively small tipping point, weak governance, and positive feedbacks can produce a crisis. The mechanism I propose is simple. A shock hits the system (the precipitating event), and it is allowed to propagate because of weak governance. It is magni...ed by positive feedbacks, and by doing so it crosses a boundary related to the tipping point. The dynamics of the system change irrevocably, environmental quality is driven to its lowest possible level, and tipping points are complements in crisis creation. The tipping point can be very small 4 because of this complementarity (for example in my simulation the tipping point is only

4% of the carrying capacity); and positive feedbacks can be self-limiting because they are

not required to carry the day. Together these two forces provide a more nuanced theory of crises creation than either could alone. To illustrate these results I simulate the model by drawing 100,000 endowment shocks from a simple symmetric distribution and generate the resulting histogram (or sample probability density function) of steady state outcomes for the environment. The resulting mass is shifted toward extreme outcomes as feedbacks grow in strength. Once I introduce a tipping point, the probability mass bifurcates and the resulting probability density is neither fat tailed nor thin tailed. The density is instead discontinuous with the majority of the mass centered on "normal interior outcomes" with the remaining probability mass concentrated on just one point - the catastrophic outcome. This depiction of a crisis has many attractive features. The crisis is a truly unique event: it is surrounded by a sea of zero probability with no neighboring outcomes ever realized. The crisis is extremely di¢ cult to reverse. This is because the local dynamics at the crisis point are decidedly unfriendly since we are past the tipping point. And ...nally,

the crisis is di¢ cult to learn about and di¢ cult to learn from. Crises are di¢ cult to learn

about because they are by de...nition infrequent, low probability, events. They are di¢ cult to learn from because much of the useful variation in the forcing variable, that we would With at least a rudimentary theory of environmental crises in hand, I turn to assess the likelihood of a future climate crisis. I ask whether the preconditions for a crisis are met in this case, and argue that the run up in carbon dioxide (CO

2) concentrations since

the industrial revolution could be the precipitating event. Since the preconditions are met and a precipitating event is in place, I am forced to conclude that a future climate crisis is regard to climate change does satisfy the requirements for crisis.

33What should we do? Emission reductions plus investment in geoengineering options seem to be the

obvious answer. Emission reductions will move us back from any potential tipping point in the climate

system; geoengineering needs to be explored because we may need a means to lower temperatures rapidly in

5

1.1 Environmental Crisis: A De...nition.

I de...ne an Environmental Crisis as a dramatic, unexpected, and irreversible worsening of the environment leading to signi...cant welfare losses. This de...nition includes and precludes several things. First, the change has to be dramatic and rapid in its pace. Therefore, the slow reduction in species numbers worldwide, or the gradual reduction in a ...sh stock does not constitute an environmental crisis under this de...nition. The environmental change has to be "unexpected" and by this I mean it is a low probability event. Dramatic changes and an element of unexpectedness distinguish crises from what I would refer to as resource tragedies. Resource tragedies are situations where resource overuse has been long-standing These situations are also worthy of study, but they are not true crises.

4An element of

irreversibility is also important. If resources or nature are quick healing then it is di¢ cult to see how any change in the environment should be of much concern, but if recovery would must produce a signi...cant welfare loss; therefore the scale of the damage cannot be small. If a crisis is ever to emerge I have to either limit the ability of agents to forecast the future, or reduce the government"s ability to enforce ...rst best outcomes. In what follows, I will assume governments are less than perfect while agents are trapped in a system where self-interested actions produce aggregate welfare losses.

1.2 The World According to Gordon-Schaefer

The Gordon-Schaefer model is comprised of one de...nition plus three assumptions. The

for harvesting, the biology of natural growth, and an objective function that values thethe unlikely event that a crisis occurs. For some interesting recent work in the economics of geoengineering

see Moreno-Cruz (2009). A useful introduction is Keith (2000).

4For example the collapse of the cod ...shery did create a political crisis, but most resource economists

fully expected the cod ...shery to collapse, it was just a question as to when. 6 resource by the discounted sum of rents it can provide. A typical representation would be: dS=dt=R(S)H H=LhS

R(S) =rS(1S=K)

W=1 Z 0 [pHwLh]ed(1) whereR(S)is natural growth taken to be logistic,ris the intrinsic rate of resource growth, andKis the carrying capacity of the environment.His harvesting,Lhis labor employed in harvesting,pandware prices for the harvest and labor input respectively, whileand are parameters re‡ecting the state of technology and the strength of time preference. The narrow interpretation ofSis that it represents a commercial species subject to har- vest such as ...sh or wildlife, but the model is commonly employed to examine the economics of deforestation, air pollution, water quantity and quality, soil erosion, antibiotic resistance, and issues related to long run growth. The only limit to the model"s applicability is that the "resource" in question be renewable while "harvesting" is di¢ cult to control because it To make the model operational we add an assumption on the success or failure of government policy in regulating the harvest (typically policy is either ...rst best or entirely absent); an assumption on how the opportunity costs of labor in the harvesting sector is determined (the wagewis typically taken as given), and some method of price determination (often the pricepis ...xed or a partial equilibrium demand function is speci...ed). Under standard conditions, this model cannot produce a crisis. If policy is absent, open access produces rent dissipation but rent dissipation alone does not constitute a crisis. Alternatively if policy is present and perfect, a most rapid approach path is sometimes optimal but this rapid depletion path produces no welfare losses. Under even tighter conditions, extinction of the resource can be optimal but this too does not constitute a crisis under my de...nition. Similarly, shocks to prices, wages, technologies and other parameters never produce a crisis; and this is in fact why the model and its many variants 7 have proven to be so useful.5

2 Three Steps to a Crisis

2.1 Governance

The ...rst step in generating a crisis is to limit the omniscience of government. While the ...rst best is a useful theoretical construct, in industries that draw on common pool resources that are hard to de...ne and control, governments face severe monitoring problems. Therefore, the ...rst best policy derived under the assumption of perfect information and costless enforcement may bear little resemblance to those that could be implemented in practice. Accordingly, I assume the best governments can do is scale back harvesting De...ne the strength of governance,G, as the extent to which policymakers can constrain harvesting below the unconstrained open access outcome. LetLOhdenote the labor alloca- tion in theHsector under open access and letLFhdenote the ...rst best allocation of labor, thenGis de...ned by: L h=GLOhwhere G2[LFh=LOh;1](2) WhenGis at its minimum, it implements the ...rst best withLh=LFh; when it is at its maximum, it implements open access withLh=LOh.6 While capturing governance in this simple way is ad hoc, in recent work Brian Copeland and I develop a theory of resource management where the implementation of the ...rst best is constrained by the government"s inability to monitor harvests perfectly. In Copeland and Taylor (2009) we combine a simple moral hazard model with a general equilibrium version of the GS model I developed earlier with James Brander.

7The resulting theory shows

how the constrained ...rst best outcome lies somewhere between the unconstrained ...rst best

(without the monitoring problem) and the open access result, and links the extent of policy5If we add uncertainty to resource growth then further possibilities present themselves some of which are

"crisis-like". See for example Pindyck (1984).

6Open access refers to a situation where withdrawls from the resource are free. Zero pollution regulation

implies open access to the atmosphere; no harvesting limits implies open access to wildlife, to forest stocks,

or to an acquifer.

7See Brander and Taylor (1997).

8 failure to country characteristics such as enforcement power, the extent of overcapacity in the resource sector, and what we refer to as the incentive to extinguish the resource. What I am assuming here is more than a short cut to the Copeland-Taylor analysis, as it makes two further restrictions. First, I takeGas constant both in and out of steady state whereas the Copeland and Taylor (2009) analysis is concerned almost exclusively with steady states. Second, I varyGfreely rather than link it to primitives of the economic system.

2.2 Positive Feedbacks

model exhibits a strong negative feedback from stock reduction to harvesting productivity and this negative feedback insulates the economy from extreme outcomes. To generate a positive feedback, I introduce an explicit general equilibrium structure where harvestingHcompetes with another sectorMfor labor. Activity in theMsector will not help or harm the environment, but its productivity may be sensitive to changes in the environment. Speci...cally, I write the production functions in the two sectors as follows:

H=h(Lh;S)

M=m(Lm;S)(3)

wherehandmare homogenous of degree one in labor and increasing in the measure of the environment"s health,S: Mwill be the numeraire, and I choose units so that one unit of labor produces one unit ofM(whenSis at its carrying capacity). These assumptions ensure the model is "Ricardian" with a linear production possibility frontier at every point in time. A positive feedback is created when productivity changes brought about by a worsening of the environment feed back through labor or product reduction inSis to lower harvesting for a given labor allocation; but if relative prices or productivity in theMsector change, then the resulting general equilibrium adjustment may shift labor into harvesting. If the general equilibrium reallocation of labor is towards (away 9 For example, suppose each unit ofHproduction emitted pollution, and this pollution loweredS. Suppose further thatMis an agricultural industry whose productivity is Then a small expansion of the harming industryHcould, by loweringS, lead to a further expansion because the general equilibrium adjustment will shift labor towards the polluting my de...nition. 8 To be precise, in the Crisis Model the extent of feedbacks,F, is given by:

F[1][mh](4)

wheremandhare the partial elasticities ofmandhto a change inS(and are assumed to be constant); andis the representative consumer"s elasticity of substitution between can be positive, negative or zero. 9 The standard GS model assumesh= 1, and has only one sector som= 0. It often takes product prices as given which is equivalent to letting! 1. As a result the GS model exhibits a very strong negative feedback under my de...nition.

2.3 Tipping Point

The ...nal step in generating a crisis is to alter the natural growth assumptions of the GS model. The standard GS model adopts the speci...c logistic formR(S) =rS(1S=K). More generally we could assumeR(S)is strictly concave withR(0) =R(K) = 0and R

0(S)>0forSlow andR0(S)<0forShigh. Either assumption amounts to much the

same thing - the natural growth of the environment is modeled as purely compensatory;

that is, the percentage rate of growth of the environment,R(S)=S, is higher the lower is8See Section 4 for more examples and for the precise requirements for this case to exhibit positive

feedbacks. 10 the resource stock.10Under the logistic growth assumption of the GS model,R(S)=Sis linear as shown in the top right panel of Figure 1. This characteristic of natural growth implies for example that the percentage growth rate of a species, the cleansing rate of the atmosphere, or the resistance of humans to bacteria - responds more aggressively the harder it is hit by harvesting, by pollution or by infection. This feature provides a nice sort related feature is the absence of any point of no return, or tipping point where the dynamics of natural growth change for the worst. This is evident in the top left panel of Figure 1 whereR(S)is everywhere (at least weakly) positive. [Insert Figure 1 about here] My last change to the GS model removes these properties while simultaneously address- ing one other concern. Natural scientists are often alarmed when economists capture the environment in one variableS. Their concern is typically not the heroic aggregation we undertake to do so - after all they undertake equally heroic aggregations themselves - but rather that a one variable depiction of nature rules out many important and interesting our treatment of one harvestable species in isolation, without a consideration of how its competitors react when selective harvesting weakens their competition; a climatologist may be alarmed when we ignore additional physical processes such as sea ice melt or permafrost thaw in our one variable analysis of climate change; and ecologists surely ...nd it disconcert- The simplest way to address some of these concerns is to enrich the model by adding another physical process. Speci...cally, I assume this additional process,P(S)lowers natural growth available for harvesting, cleansing, etc.P(S)has the following properties:

P(S)0; P0(S)<0;P(0)>0;P(K) = 0(5)

Net (natural) growth is thenN(S) =R(S)P(S).10See Clark (1990) for a discussion of various classes of growth functions (compensatory, depensatory,

critically depensatory, etc.) 11 The interpretation ofP(S)varies with the application. For example, ifSrepresents a harvestable species thenP0(S)<0implies competitive pressure from other species is most intense when the population of the harvested species is low. This additional pressureP(S) results in lower growth. IfSmeasures the density of trees within a given area, thenP(S) could represent the impact of soil erosion. Soil erosion intensi...es as the forest is thinned, and erosion lowers forest growth. And ifSwas a measure of the climate"s health, then sea become larger contributors to climate change as temperatures rose and the climate"s health worsened. If I make the further assumption thatP(S)is linear, then net natural growth can be written as a slight variant of the standard logistic growth function: 11

N(S) =r(ST)(1S=K)(6)

whereTis a measure of the tipping point in units of the stock. This new growth function has three properties that are shown in the bottom two panels in Figure 1. In the bottom left panel it is apparent that natural growth is negative if the stock falls below the tipping pointT. Once this barrier is breached, even zero harvesting cannot restore the stock. Also noteworthy is that the rate of net growth atS= 0is strictly negative. Since a negative stock is not possible, these dynamics will imply a sudden stop to stock depletion as theS= 0barrier is crossed. This has the ‡avor of a car hitting a brick wall atS= 0and decelerating to zero instantaneously. This feature seems suitable - even desirable - in a paper focussing on catastrophic outcomes. The percentage rate of growth,N(S)=Sis graphed in the bottom right panel. As shown, nature can no longer continually compensate for stock reduction. Nature at ...rst compensates with faster percentage growth as it is diminished, but eventually delivers lower percentage growth as it is pushed too far (below pT). Growth per unit time (percentage

or absolute) is of course negative for any stockS < T. To make things a bit cleaner, I have11LetP(S)take the linear formP(S) =c[KS]wherec=rT=K, then we obtain the simple form in

the text. The critical assumptions are thatP(0)>0andP0(S)<0. To be fair, not all excluded physical processes will, once added, work in this way. For example in the case of climate change when warming increases evaporation and cloud cover this increases the world"s albedo which decreases warming. 12 chosen units such thatK= 1. Under this units choice, net natural growth,N(S), takes its maximum at(T+ 1)=2as shown. The percentage rate of (net) growth,N(S)=S, takes its maximum at pTK=pT > T. With these assumptions in hand, the Crisis Model is almost complete. To close the model I assume a representative consumer with tastes given by a symmetric CES utility function. That is u= [H1+M1]1;with>0(7) Identical tastes seems like an innocuous assumption when all agents have the same income. as the economy grows or shrinks. The complete model is described by the production functions in (3), the growth function linking growth, harvesting and stock accumulationdS=dt=N(S)H, and the preferences given in (7). Since the resource stock is held in common, and agents are atomistic they face no intertemporal problem at all, and with no other store of value in the economy, period by period optimization determines decisions. These harvesting decisions are howeverquotesdbs_dbs11.pdfusesText_17