Decision-making under scientific uncertainty : The economics of the Precautionary Principle

Christian GOLLIER, Nicolas TREICH,

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LEERNA LABORATOIRE D'ECONOMIE DE L'ENVIRONNEMENT ET DES RESSOURCES NATURELLES Unité Mixte de Recherche de l'Institut National de la Recherche Agronomique (INRA) Et de l'Université des Sciences Sociales de Toulouse (UT1)

LEERNA INRA-UT1 21 Allée de Brienne - 31000 TOULOUSE - FRANCE Tél. : 33 (0)5 61 12 86 21 - Fax : 33 (0)5 61 12 85 20 E-Mail : mercusot@toulouse.inra.fr

Decision-making under scientific uncertainty:The economics of the Precautionary Principle

Christian GollierLEERNA and IDEI, University of Toulouse

Nicolas TreichLEERNA-INRA, University of Toulouse

First Draft

May 29, 2001

1 IntroductionAs recently illustrated by the beef crisis or by the debates on genetic manip-ulations, the Precautionary Principle (PP) is becoming increasingly promi-nent in the environmental protection and health safety debate. At the rootof these problems is a question of the management of risks evolving overtime. In spite of its economic nature, the debate on the PP has been mostlydriven by philosophers and engineers. Our aim in this paper is to survey thecontribution that economic theory may bring to this debate.In crude terms, the main idea of the PP is to encourage the prevention

of a risk before that full scientific information is available about it. Anactive decision must thus be made before scientific evidence, conversely tothe usual timing of decisions. Indeed, postponing an irreversible decision toafter getting more information allows the decision maker to take advantageof the option value, if there is some flexibility in the project. This meansthat the dynamic aspect of the decision process is central to the problem.For the sake of illustration, research on policies for limiting climate change

due to greenhouse gases emissions have emphasized the need to develop sucha sequential approach to decision-making. The choice between a moderateor an aggressive emissions reduction is determined today by the future im-provement of scientific understanding of climate change and by our abilityto switch to other sources of energy in the future.Taking into account these primary considerations, the purpose of the

paper is to develop a coherent view of the problem of risk management underscientific uncertainty. Given the prominent literature on the PP in socialsciences in general, this paper provides an economic approach to the PP basedonly on decision theory and on the economics of information. It summarizesrecent research on those matters and points out the strengths of the economicapproach as well as its limits in order to raise some promising research trends.We organize this literature survey as follows. In the section 2, we shall

begin by stressing some typical characteristics of new technological or en-vironmental risks. We argue that the interplay among those characteristicssuggest to develop sequential regulatory policies. This will permit to adaptfuture decisions to scientific progress. We then introduce the PP as a newguideline appeared in international treaties in the early 90s.In section 3, we present through a simple example the theory of sequential

investment (Dixit and Pindyck, 1994) in order to bring closer the notion ofoption value (McDonald and Siegle, 1986) to that of precaution. We then

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introduce the general model and define the notions of information structuresand that of irreversibility.In section 4, we examine the interplay between information and flexibil-

ity. In doing so, this paper presents in a summary fashion the literatureon the ’irreversibility effect’ (Arrow and Fisher, 1974, Epstein, 1980) in or-der to integrate the most recent developments in investment theory and itsinteractions with environment policy (Kolstad, 1996). Typically, when long-term effects of risks are scientifically unknown, it may be optimal to be moreprudent at the initial stage of the risk management process. This allows usto put forward a normative economic basis for the PP (Gollier, Jullien andTreich, 2000).In section 5, we show that the results derived from the literature on

option values may not carry over to a world when several actors act non-cooperatively. When decision-making is decentralized, actors may find non-optimal to develop sequential policies and to use the scientific information tocome. We give three simple illustrations of such situations. We discuss thestrength of competition in innovative markets (Weeds, 1999), the effect ofinternational coordination (Ulph and Maddison, 1997) and that of dynamicinconsistencies (Carrillo and Mariotti, 2000).In section 6, we conclude the paper by a broader discussion on regulatory

policy under conditions of large scientific uncertainty. The point is thatscientific uncertainty introduces considerable room for discretion and self-interested biases through the process of regulatory decision-making. Theissue is then to design the PP to reduce the opportunism of some agents insituation of incomplete information or incomplete monitoring.

2 A new guideline for regulating new risksThe perception of risks that society faces has profoundly changed in the lastthree decades. As illustrated by the development of cancers from abestos, bythe drama of contaminated blood transmitting AIDS, or by the recent ’madcow affair’, damages generated by decisions taken under scientific uncertaintymay affect millions of people with wide regional variations. Examples aboundof risks sharing those characteristics: hazardous wastes, species extinction,global warming, electromagnetic fields, cellular phones, transgenic food; andthe list could go on. Analysis of regulatory policies to deal with those newrisks is complicated by several features.

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First, the consequences may arise in a time-span of several decades to cen-turies. Typically damages are generated by the stock of pollutants presentin the environment, rather than by its flow which can be controlled moreeasily. The concentration of the pollutant can respond only slowly to thechange in the annual rate of emission. As a result, one cannot readily reverseor mitigate physical degradation other than letting the natural rate of decayoperate. The Montréal protocol, establishing a schedule to reduce the con-sumption of CFCs and halons, was signed as of March 1987. Yet, one willhave to wait until the end of the next century for the rate of chlorine to belower than its level of 1970. In this sense, past decisions to emit pollutantshas an irreversible effect on the risk borne by future generations.In addition to this irreversibility linked to physical processes, there ex-

ist more radical types of irreversibility. For instance the brain disease thatmay result from eating ’mad cows’ is irreversible. The loss of some animalspecies due to climate change or the diffusion of some genetically modifiedspecies may also be readily irreversible. Another kind of irreversibility comesfrom the inertia linked to the socio-economic system. Rapid changes in theturnover of capital imply higher costs than a smooth adaptation, as the timenecessary for developing low-cost substitutes of the pollutants. This timelag will involve further complications related to technical changes as well aspopulation and consumption patterns.Also, there is typically a large degree of uncertainty in predicting the

severity of such catastrophic events. For instance, scientists do not know how’mad cows’ became infectious and how long humans incubate the disease. Asa result current estimates of human victims in the U.K. over the next twodecades vary from 100 to more than 100,000. In the current debates on globalwarming or on El Nino phenomenon, complexity is a dominant characteristicof the problem. The interactions between atmosphere, clouds, oceans andpolar ice sheets are still not well understood. IPCC (1995) estimated thatfor a doubling atmospheric concentration of carbon dioxide the increase inthe temperature may lie between +1.8◦C and +5.4◦C. This represents aconsiderable scientific uncertainty.However, while at first uncertainty may loom very large, there is high

potential for rapid resolution of uncertainty. There is ongoing research onthose new risks. Recall that in the 1960s, ozone alarms began with an attackagainst supersonic flights, wrongly suspected by some US scientists to depleteozone layer. In 1974, Molina and Rowland published their famous theory inNature. Then, in the fall 1985, two teams of scientists discovered the ozone

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hole over the antarctic.To sum up, decision-making related to new environmental or technological

risks must take into account those important characteristics of the problem:long time horizon, stock externalities, possible irreversibilities (physical andsocio-economic), large uncertainties and future scientific progress.As opposed to various forms of regular risks commonly addressed by stan-

dard prevention or insurance activities, the interplay among those character-istics has emphasized the need to develop dynamic approaches to regulationstrategies. Timing is a key issue, the key issue. The cost of being wrong ineither direction is high and there are large potential gains from flexibility inprevention efforts.This underlies the need to identify optimal short-term strategies in the

face of long-term uncertainties. These strategies should permit to respondto new information with midcourse corrections. As a result, ”[preventing]measures should be periodically reviewed in the light of scientific progress, andamended as necessary” (CEC, 2000). The advantages of a so-called sequentialapproach has been often advocated as a strategy for abating climate change(see e.g. Hammitt, Lempert and Schlesinger, 1992). For instance, IPCC(1995) states that ”the challenge is not to find the best policy today for thenext 100 years, but to select a prudent and flexible strategy and to adjust itover time”.The economic approach may then be of significant help. Considerable

work has been done in economic theory on the question of uncertainty andlearning. The economic criteria of decision-making under uncertainty poten-tially permit to select among the various scientific experts’ scenarios. As anillustration, Manne and Richels (1992) or Nordhaus (1994) combined Ramseygrowth economic models together with elaborated climatic modules. Those”integrated assessment” models have identified optimal climate policies givenclimate scientific uncertainties.One of the difficulty to implement a sequential approach comes from the

danger to take decisions with a limited confidence on the underlying mech-anism generating the risk faced by the population. The costs of developingearly preventive actions is often very high compared to the do-nothing strat-egy, just waiting for better scientific evidence. Uncertainty and irreversibilitymay precisely be used as an argument in favor of the statu quo. For in-stance, in the early 1980s the American Chemistry Society complained thatany restriction on CFCs reduction would constitute ”the first regulation to bebased entirely on an unverified scientific prediction”. A DuPont spokesperson

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protested that ”we are going a very long way into the regulatory process be-fore scientists know what’s really going on” (Morone and Woodhouse, 1986,p. 82).The key point here is that there is a tension between the rapid resolu-

tion of uncertainty and the slow entropy of the system, e.g. climate evolvesslowly compared to rate of the resolution of spatio-temporal climate models.As stated for instance by the IPCC (1995): ”The choice of abatement pathsinvolves balancing the economic risks of rapid abatement now (that prematurecapital stock retirement will later proved unnecessary) against the correspond-ing risk of delay (that more rapid reduction will then be required, necessitatingpremature retirement of future capital stock)”.In this context, the PP takes a committed stand against ”learn-then-act”,

”wait-and-see” or ”business-as-usual” strategies and in favor of prematurepreventive actions. The PP first appeared as a clause in international treaties,as in the Maastricht Treaty, or at the Conference of Rio. Principle 15 of the1992 Rio Declaration states ”Where there are threats of serious or irreversibledamage, lack of full scientific certainty shall not be used as a reason forpostponing cost-effective measures to prevent environmental degradation”.1

Although devoid of practical content, the PP is formulated in such amanner as to provide the basis for regulatory policies. Considering thatthe absence of evidence is not the evidence of absence, the main message ofthe PP is conceptually clear: scientific progress do not justify the delay ofmeasures preventing environmental degradation. The PP is the most notableanticipatory principle existing in the national and international law withspecial relevance for human-induced environmental problems. In practice,its scope is even much wider and there are reasonable grounds for applyingit to regulate the protection of human, animal and plant health issues (CEC,2000). Nowadays this principle is often said to be the solid foundation onwhich to base decision-making under conditions of large uncertainty (e.g.Godard, 1997).Yet, the PP cannot stand out through decrees or discussions only. Our

1Equivalent definitions have been enacted in several international conventions such asrecently for the Cartagena Protocol on Biosafety to the Convention on Biological Diversityadopted in january 2000 . In national law, similar definitions exist too. For instance, in thefrench law, the PP is defined as a clause of the Loi Barnier in 1995 on the reinforcementof the protection of the environment. It states that ”the absence of certainty, given ourcurrent scientific knowledge, should not delay the use of measures preventing a risk of largeand irreversible damages to the environment, at an accptable cost”.

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objective is to examine whether the PP is an efficient economic guideline.Hence we will investigate in the next section a sequential decision problem.As time passes, information about the true scientific theory comes. We willexamine optimal sequential policies, i.e. policies that are robust to the timingof the resolution of scientific uncertainty. We will check whether those policiesinduce a bias towards premature investments in prevention, as suggested bythe PP.

3 Presentation of the modelThe previous section has presented the historical context in which the PP hasemerged. We have seen that since the first environmental threats developedin the mid-70s the concept of precaution has become increasingly prominentin environmental or health safety protection debates.Interestingly, during the same period, economists have performed a new

theoretical approach to cost-benefit analysis, stressing the irreversibility ofinvestment decisions and the ongoing uncertainty of the economic environ-ment. This new approach has recognized in particular the option value ofwaiting for better information. We shall now investigate the implications ofoption value theory for the regulation of the risks mentioned above.We will proceed as follows. We will first introduce the notion of option

value through a simple example. We will then introduce the general modeland define the notions of irreversibility and that of information structure.

3.1 Option values: Introductory example

The classical approach to public and private investment decisions is basedon the cost-benefit analysis. In short, an investment should be undertakenonly if the expected net present value of the project is positive. Quiterecently, the theory on investment under uncertainty and on modern financehave recognized the need to develop instead a sequential approach, realizingthat at each point of time in the decision-making process one is basicallybuying an option to reconsider the decision in the next step of the process.To introduce this new approach, we begin with an example which is similarto the one presented by Dixit and Pindyck (1994, chapter 2).A risk neutral population is considering the possibility to introduce an

innovation in the production process. This can be for example a genetic

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manipulation or a new drug. There is a once for all sunk cost I to introducethe innovation. Given the current scientific uncertainty, the expected benefitfor the Society per period is P . In fact, there are two competing theorieswhich can be true with equal probabilities given our current beliefs. But oneexpects scientific progress to be made over the first period which will revealthe true theory and the corresponding true added value of the innovation.2

With equal probability it may rise to 1.5P or fall to 0.5P . The discountfactor is β ∈]0, 1[. The problem is to determine the optimal timing of theintroduction of the innovation.If one introduces it immediately, the expected net present value of the

innovation is

NPV1 =P

1− β − I, (1)

since the project costs I in the current period and it generates value P inexpectation in each period forever. The classical method consists in intro-ducing the innovation immediately if NPV1 is positive. This, however, maynot be optimal. An alternative decision rule would be to decide whetheror not to introduce the innovation after the scientific uncertainty has beenresolved. To make the problem interesting, let us assume that

0.5P

1− β ≤ I ≤1.5P

1− β , (2)

so that the innovation is socially valuable only if the good theory is true.As a consequence, conditionally on the fact that the innovation is delayedin the first period, the innovation is introduced in the second period if and

2We assume that the revelation of the true theory comes from pure scientific research,not from experimentation. This is due to the long delay occuring between consumption ordevelopment and the observation of the adverse effects. This may be unrealistic in somecases. For instance early phasing out of ozone depleting substances has certainly slow downthe knowledge of the destructive effects of CFCs. It has also boosted chemical research.The reader may find in Fisher and Hanneman (1987), Orphanides and Zervos (1995)and Datta, Mirman and Schlee (1998) some insights on this so-called experimentationeffect. Note that there is no discussion either on the way the choice is made amongvarious scientific experiments. In our model, information is free and we do not directlypay attention to the process that drives the production of information. As a consequence,our framework does not permit either to explore the interplay between the PP and theeconomics of invention and research (see e.g. Hirshleifer and Riley, 1992).

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only if the good theory is revealed to be the true one. This implies that theexpected present value of this alternative strategy is

NPV2 = 0.5β(1.5P

1− β − I). (3)

Obviously, the risk neutral Society will find it optimal to delay the in-troduction of the innovation until period 2 if and only if NPV2 ≥ NPV1.There is a negative and a positive effect of delaying the innovation. The neg-ative effect comes from the loss of the initial expected value P. The benefitcomes from the opportunity to abandon the project if the bad theory hap-pens to be the true one. This is only when this benefit is larger than theloss of the first period cash-flow that the option is valuable. The quantitymax(0, NPV2−NPV1) is called the option value of delaying the investment,which can be positive or zero. Thus, the decision of whether it is optimal toinvest in the first period or to remain uncommitted depends upon the relativevalues of the three parameters: P, I and β. Specifically, suppose as in Dixitand Pindyck (1994) that these parameters take respectively 200, 1600 and1/1.1. Then the option value is equal to 173.This positive option value reflects the cost of an irreversible decision:

investing with no possibility of ”dis-investing”. Note that if the installationcost I was fully recoverable, then it would be always optimal to invest inthe first period and then to recover this cost if one learns that the projectis not socially valuable. But introducing an innovation is often very costlyto reverse. This choice makes the future position inflexible. Yet since theopportunity to introduce this innovation is not a take-it-or-leave-it option,one may choose to do nothing first. By doing so, one keeps the option ofintroducing the innovation later. This flexibility in the decision process makespossible for the investor to use the information to come, which is valuable.There is thus a trade-off between receiving the current period cash-flow of

the innovation and waiting for the future scientific information arrival. This isthe irreversible nature of investment decisions together with the informationvalue that is at the origin of the option value as first recognized by Arrowand Fisher (1974) and Henry (1974).3 This option value provides a strongargument in favor of the PP, if it is interpreted as the idea that scientificuncertainty should induce us to preserve flexibility for the future.

3See also more recently Bernanke (1983), McDonald and Siegel (1986), Graham-Tomasi(1995) and Drazen and Sakellaris (1996).

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3.2 The model

We now introduce the general model. A decision-maker (DM) lives for twoperiods:

• At the beginning of period one, he must choose α1 within an opportu-nity set D that affects his first period utility u(α1);

• After decision α1 is made, he receives a message ey = y. He revises hisbeliefs according to the Bayes’rule;

• At the beginning of period 2, he takes another decision α2 within anopportunity set D(α1);

• Finally the true state of the world eθ = θ is revealed and the DM enjoysa discounted felicity v(α1,α2, θ).

The DM maximizes his lifetime expected utility:

maxα1∈D

u(α1) + βEey maxα2∈D(α1)

Eeθ/eyv(α1,α2,eθ). (4)

We assume that solutions of (4) exist and are unique.4 This model includesthe introductory example above. To see that, just take

u(α1) = α1(P

1− β − I), (5)

v(α1,α2, θ) = α2(θP

1− β − I), (6)

and assume that θ may take 0.5 or 1.5 with equal probability.How can we characterize the concept of irreversibility in this model? In

the example presented in the previous section, irreversibility may be rep-resented as a diminution of the future opportunity set implied by the firstperiod decision,

D(α1) = {0, 1− α1}. (7)

In words, taking action ”1” in the first period means ”investing”. Then, thefuture opportunity set would become D(1) = {0}, so that there is only one

4Even if the utility functions u and v are concave in the choice variables, unicity ofsolutions is not guaranteed for any set D(α1).

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possible choice let for the future, ”no investing”. As a consequence, investingnow kills the option of investing in the future. This represents the fact thatintroducing the innovation is ’irreversible’. More generally, we will say thatdecision α1 is more irreversible than α01 when

D(α1) ⊆ D(α01). (8)

This definition captures the notion of choice irreversibility. Undertaking anirreversible action, such as the the development of a wildland area results in amore inflexible position than leaving the area undeveloped today and havingthe choice of the development or preservation tomorrow. In our framework,this choice is irreversible since it will reduce the set of choicesD(α1) availablelater on.5 For instance, when the opportunity takes the form of a constrainton period 2 decision, i.e. so that f1(α1) ≤ α2 ≤ f2(α1), larger α1 is moreirreversible only if f 01(.) ≥ 0 and f 02(.) ≤ 0.Let us now turn to another crucial question. As explained earlier, our aim

is to determine the impact of scientific uncertainty on the optimal timing ofrisk-taking. Scientific uncertainty differs from natural risks by the fact thatthe first is subject to be resolved over time, at least partially. We will examinethe effect of an increase in the scientific uncertainty. The problem is thus tocharacterize more scientific uncertainty.We will say that there is more scientific uncertainty today if we expect

scientific research to be more informative in the future, i.e. if we face abetter information structure. We hereafter present the concept of a betterinformation structure introduced by Blackwell (1951).It is convenient here to assume that eθ is discrete with m atoms of prob-

ability. We then denote πy(θi) for the probability that eθ = θi conditional toreceiving signal y and πy = (πy(θ1), ..., πy(θm)) (resp. π0y0) the probabilitydistribution conditional to the message y of ey (resp. y0 of ey0). Let us alsodefine

S = {πy ∈ Rm+ |mXi=1

πy(θi) = 1},

5It is important to notice that definition (8) implies that the cost of moving fromα1 to α2 inside the opportunity set D(α1) is zero while the cost of moving outside theopportunity set is infinite. From this point of view, one could argue that irreversibility isnot well defined economically. Jones and Ostroy (1984) relax these assumptions and referto the broader notion of adjustment cost (see also Urasategui (1990)).

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as the set of all conditional distributions on eθ.In the standard terminology of Blackwell (1951), ey in model (4) describes

an ”experiment”, but what we have in mind is scientific research in general.We will consider the following intuitive definition of a better experiment firstproposed by Bohenblust, Shapley and Sherman (1949). We say that theexperiment ey is better than experiment y0 if and only if every DM prefers apriori observing ey than ey0:6

Eey maxα2∈D(α1)

Eeθ/eyv(α1,α2,eθ) ≥ Eey0 maxα2∈D(α1)

Eeθ/ey0v(α1,α2,eθ), (9)

or equivalently,

Eeyj(α1, πey) ≥ Eey0j(α1, π0ey0),

where j(α1, πy) is the period-2 value function conditional of observing signaley = y. It is defined as

j(α1, πy) = maxα2∈D(α1)

Eeθ/yv(α1,α2,eθ). (10)

Note that this function is convex in the vector of posterior probabilitiessince it is the maximum of linear functions of πy. Importantly, this resultholds independently of the decision problem under consideration. Indeedby (10), function j is the upper envelop of a set of functions f(α1,πy) =

Eeθ/yv(α1,α2,eθ),α1 ∈ D(α1), that are linear in πy. Therefore it is a convexfunction of πy.Reciprocally, one can prove that any convex function ρ(πy) on S can be

obtained from the operation (10) when appropriately choosing the decision-making environment. This is due to the well-known separating hyperplanetheorem which implies that, to any convex surface, there exists a set ofhyperplanes for which this surface is the upper envelope. Following Marschakand Miyasawa (1968), this leads to another equivalent definition of a better

6This definition that every DM prefers a better experiment in the sense of Blackwell istraditionnaly referred to the Blackwell’s theorem. Contrary to what is generally believed,this theorem does not hold for all single-agent problems. For instance, when the oppor-tunity set D(α1) depends on the information structure, then more information may bedisandavantageous (Sulganik and Zilcha, 1997). Also, Wakker (1988) argues that if theDM is a non-expected utility maximizer then the DM may prefer less informative signals.This finding was recently examined by Grant, Kajii and Polak (1998).

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information structure which will prove to be extremely useful in the rest ofthe paper.

Definition 1: Information structure y is better than information structurey0 if and only if:

for any ρ convex on S : Eyρ(πy) ≥ Ey0ρ(π0y0). (11)

Note that (11) implies that the two economies have the same beliefs exante

Eyπy = Ey0π0y0.

As a consequence (11) defines a mean-preserving spread of posterior beliefs.This means that the increase in scientific uncertainty is obtained withoutchanging the ex ante distribution of the real risk eθ. Suppose for instancethat there are two states of the world, m = 2 and denote π ≡ π(θ1) for theprior belief on state 1. Then any convex function ρ(π) on < is a measure ofinformation. Take for instance the inverse of the entropy function

ρ(π) = π log π + (1− π) log(1− π)

which is represented on figure 1.7 Entropy or uncertainty is maximal forπ = 0.5. Points a and b represent then the ex post uncertainty that couldlead an experiment. Ex ante the (average) uncertainty is a point located onthe straight line. Since this line is above the curve, any experiment diminishesthe uncertainty faces by the DM.

3.3 Prevention versus precaution

Since Knight (1921) it is standard to make a distinction between a risk, char-acterized by an objective probability distribution, and uncertainty, which isnot related to any precise statistical estimates. From this point of view,the previous model distinguishes the risk, tied to the realizations of eθ, fromuncertainty tied to the realizations of ey. Making this distinction leads to

7See e.g. Shannon (1948). This function has been proved to be extremely useful inseveral branches of science (see e.g. Georgescu-Roegen, 1975).

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recognizing that uncertainty is not independent of knowledge and thus is nota static concept. With the accumulation of knowledge, uncertainty resolves,at least partially, allowing for a revision of beliefs. Hence, we interpret thefact that the future probability distribution πey is unknown to the DM in theinitial period as the lack of full scientific certainty advocated by the PP. Ini-tially the DM ignores both θ and y. There are two sources of risk representedin the model. The second source of risk, tied to scientific uncertainty ey, is atthe root of the precautionary motive.What is the effect of scientific uncertainty on decision-making? Using

definition (11), we will answer this question in the sense of the comparativestatics analysis. We consider two economies ey and ey0 that are equivalentexcept for the flow of information, i.e., except for the degree of scientificuncertainty. In which economy is it optimal to be more flexible in the shortrun? The PP would get some theoretical support if it would be sociallyefficient to be more prudent in economy ey with more scientific uncertainty.This would mean that scientific uncertainty gives support to develop moreprudence. This is our interpretation of the idea of precaution.This interpretation of the PP will also allow us to make a basic economic

distinction between the words prevention and precaution. A preventive effortis aimed at reducing the risk on eθ. It is a static concept that refers to themanagement of a risk at a given time and given a stable probability distribu-tion. On the other hand precaution is tied to the notion of uncertainty. It isa dynamic concept that recognizes scientific progress. A precautionary mea-sure thus defines a prudent and temporary decision that allows for a bettermanagement of the current lack of scientific evidence.

4 An economic interpretation of the Precau-tionary Principle

In section 3.2, we have introduced the notions of irreversibility and that ofinformation value. We will now examine the interplay between these twonotions leading us to propose our own interpretation of the PP based on the’irreversibility effect’.We proceed as follows. In our general model, we will now focus on the

effect of information on ex ante decision. In doing so, we examine how thestructure of information about future risk is expected to affect the optimal

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timing of decisions. We then develop that comparative static analysis in amodel of stock externality.

4.1 The ’irreversibility effect’

Consider model (4). Assume that the unique solutions of the first periodproblem in economy ey and ey0, respectively denoted α∗1 and α∗01 , are the uniquesolutions to the respective equations

Eyj1(α∗1, πey) = 0 and (12)

Ey0j1(α∗01 , π0ey0) = 0,

where j is the value function as defined in (10), and j1 denotes its partialderivative with respect to α1. It can then easily be checked that

α∗1 ≥ α∗01 ⇐⇒ Ey0j(α∗1, π

0ey0) ≤ 0.

So using (12) it is obvious that a better information structure increases op-timal α1 if and only if

Eyj1(α∗1, πey) ≥ Ey0j1(α∗1,π

0ey0),for every α∗1 ∈ D. Inequality (11) gives then the following lemma due toEpstein (1980). This lemma is very general since it imposes no restrictionon the decision problem nor on the random variables eθ and ey.Lemma 1 Consider the general problem (4). The optimal level of the ex antedecision variable α∗1 is increased (resp. decreased) by any better informationstructure if and only if j1(α∗1,πy) is convex (resp. concave) in πy.

We will now use this lemma to examine the interplay between informationand irreversibility. Let us recall again the Dixit and Pindyck’s example. Weshowed a situation where no information led to investing in the first periodα∗01 = 1 while perfect information led to delay the investment decision α∗1 = 0.The basic insight of that example is that the prospect to receive informationin the future leads to adopt a more flexible position. The intuitive reasoningis clear: choosing an inflexible position undermines the value of information.Hence, as the informativeness increases, the incentive to remain flexible andtake advantage of it also increases.

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Let us now generalize the Dixit and Pindyck’s example to derive a formalstatement of this so-called ’irreversibility effect’ that has first been formalizedby Arrow and Fisher (1974) and Henry (1974a, 1974b). To keep the modelsimple, we assume that

D = [0, 1] and (13)

D(α1) = [0, 1− α1].

Unambiguously, lowering α1 increases flexibility for the future. A simpleapplication of this model is for a non-renewable resource of size 1 that canbe consumed over two period.Future profits are assumed to be uncertain in the future, due to the social

cost it generates in terms of biodiversity for instance. Although we gener-alize the Dixit and Pindyck’s model to introduce risk aversion and partialresolution of uncertainty, we still assume that future utility do not dependdirectly on previous actions (recall eq. (6)) :

v(α1,α2, θ) ≡ v(α2, θ). (14)

Yet, current actions may affect future utility indirectly through the impacton the future opportunity set.Let us solve this problem. Let α∗2(y) the solution when the constraint

α2 ≤ 1− α1 is not binding, i.e.

Eeθ/yv2(α∗2(y),eθ) = 0.

Hence, we have that

j(α1, πy) =

(Eeθ/yv(α∗2(y),eθ) if Eeθ/yv2(1− α1,eθ) ≤ 0

Eeθ/yv(1− α1,eθ) otherwise.From definition 1, we know that this function is convex in πy. Let us nowdifferentiate with respect to α1 so that we get

j1(α1, πy) =

(0 if Eeθ/yv2(1− α1,eθ) ≤ 0

−Eeθ/yv2(1− α1,eθ) otherwise,or, equivalently,

j1(α1, πy) = −max(0, Eeθ/yv2(1− α1,eθ)).15

Since Eeθ/yv2(1 − α1,eθ) is linear in πy, j1(α1,πy) is concave in πy. Lemma1 implies that the optimal α1 decreases with better information. Since de-creasing α1 leads to a larger opportunity set in the future D(α1), an increasein the degree of informativeness biases ex ante decisions in favor of more flex-ibility. This is in the spirit of the PP. The prospect to receive information isan argument to reduce irreversibility. In the following Proposition, scientificuncertainty means a more informative structure.

Proposition 1 Take the problem (4) with (14) and (13). Scientific uncer-tainty induces the DM to preserve more flexibility for the future.

We conclude that the notion of option value that sustained the PP in theexample of section 3.1 can be generalized in several directions: partial resolu-tion of uncertainty, relative flexibility, continuous decision variables and riskaversion. However, several authors have pointed out that the ’irreversibilityeffect’ holds in rather special models (see e.g. Freixas and Laffont (1984)and Graham-Tomasi (1995)). For example models such as growth modelsdo not satisfy restriction (14) since today’s output realization affect directlyfuture welfare. In most cases, future utility v(α1,α2, θ) do depend on α1.The next section examines whether the ’irreversibility effect’ carry over toa broader class models. An important question is to determine the optimaltiming of prevention efforts when current actions affect the risk borne byfuture generations.

4.2 Stock externalities

There is an important literature since Keeler, Spence and Zeckhauser (1971)on the optimal growth in the presence of environmental externalities, particu-larly stock externalities. Consumption accumulates in some medium (water,soil, air, body...) and may have harmful effects in the future. We now will ex-amine the effect of better information in a very simple model of consumptionexternality.The model work as follows. We assume that the only source of utility

comes from the consumption αt of a good in each period t. The good is freebut its consumption may turn out to be toxic in the future. The damagerepresenting this toxicity is measured in terms of final consumption and issupported only in the second period. This damage is proportional to the

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quantity of the good already consumed C ≡ δα1 + α2 so that we get

v(α1,α2, θ) ≡ v(α2 − θ(δα1 + α2)). (15)

Parameter δ denotes the fraction of the good consumed in the first periodwhich remains toxic in the second period. This parameter depicts the stockexternality. When δ = 0, restriction (14) applies.The extent of the damage is unknown at the beginning of the first period.

This is represented by the random variable eθ. Experiments ey will allow theconsumer to revise the distribution of eθ according to the Bayes’ rule. Thedecision problem (4) may thus be written as

maxα1

u(α1) + Ey {maxα2

Eeθ|y v(α2 − eθ(δα1 + α2))}. (16)

As before, our aim is to examine the effect of scientific uncertainty onthe initial efficient decision. To keep this analysis simple, we assume that uis increasing and concave and that the v belongs to the well-known class ofHyperbolic Absolute Risk Aversion (HARA) functions such that

v(x) =γ

1− γ·η +

x

γ

¸1−γ. (17)

Some restrictions on the parameters are required to make v(.) increasing andconcave in its domain {x ∈ R | η + x/γ > 0}. 8Let us now solve this problem. It is easy to check that if v(.) is defined as

in (17), then the optimal stock of consumption C∗ = δα1 +α∗2 is proportionalto η − δα1

γ. More precisely, we obtain C∗(α1, πy) = c∗(πy)(η − δα1

γ), with

c∗(πy) defined by Ez(1 + c∗(πy)zγ

)−γ = 0. As a result future consumption islinear in η − δα1

γ. It yields

j(α1, πy) =γ

1− γ (η − δα1

γ)1−γg(πy) (18)

8HARA utility functions corresponds to the set of functions whose absolute risk tol-erance is linear in x. Indeed, we can easily verify that −v0(x)/v00(x) = η + x

γ . If η = 0,we get the standard Constant Relative Risk Aversion (CRRA) functions, with constantrelative risk aversion γ. We get Constant Absolute Risk Aversion (CARA) functions if γtends to infinity.

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with g(πy) = E(1 + c∗(πy)zγ

)1−γ. By definition 1, we know that j is convex inπy. Thus, g is convex in πy if and only if γ is less than 1 and larger than 0.But we have also

j1(α1,πy) = − δγ

(η − δα1

γ)−γg(πy). (19)

We conclude that j1 is concave in πy only if γ is strictly positive and less thanunity. Lemma 1 then concludes the comparative statics analysis. We thusderive the following proposition due to Gollier, Jullien and Treich (2000) inwhich more precaution means less early consumption of the polluting good.

Proposition 2 Take the problem (16) with (17). Scientific uncertainty in-creases the efficient level of precaution in period 1 if and only if 0 < γ < 1.In the case with γ → 1, i.e. v(x) = ln(η + x), scientific uncertainty has noeffect on the efficient level of precaution.

This proposition describes the circumstances where the prospect to re-ceive information in the future induces the consumer to reduce the consump-tion of the toxic product. This in turn gives a normative support to the PPin the presence of stock externalities.Two opposite effects take place in the analysis. On the one hand, a

better information structure leads the DM to behave in a more efficient wayin the future because of the better knowledge of the risk. If we associate animprovement in efficiency to a sure increase in future incomes, this impliesthat the agent will want to consume more today, as he wants to smoothconsumption over time. This effect goes the opposite direction of the onesuggested by the PP. On the other hand, better information leads to morerisk ex ante since the posterior probability distribution is more risky. Aprudent consumer may then reduce initial consumption for a precautionarymotive. For the special case of HARA utility functions, we have shown thatthis last effect dominates when 0 < γ < 1.9

9This result may sound strange at first since larger risk aversion γ should rather leadto reduce risk-exposure. However Gollier, Jullien and Treich (2000) proved that the resultdepends in fact on an imbricated relation between the coefficient of prudence (Kimball,1990) and the coefficient of risk aversion. This is only for the special class of HARA utilityfunctions that this condition implies that more risk-averse agents take more risk in theinitial period.

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This shows that the PP cannot be justified independently of the pref-erences of the DM when the important aspect of the question is a stockexternality rather than irreversibility. This raises the issue of the choice ofthe preference and of the type of DM which is considered. This also leads toinquire about the importance of specification (15) in the previous analysis.Basically this specification meant that damages could be evaluated in mon-etary terms. Assume now instead that damages are intangible and take thefollowing form

v(α1,α2, θ) ≡ v(α2)− θS(δα1 + α2), (20)

where S(C) denotes the impact on future utility of previous consumption C.Using specification (20), Ulph and Ulph (1997) showed that it is not easy totell whether the irreversibility effect applies to that model of global warming.They so derived sufficient conditions where the PP is always justified.Another important specification in model (16) is that we have implicitly

assumed D = D(α1) = <. What would happen if we extend model (16) byincorporating an irreversibility constraint? Ulph and Ulph (1997) and Gol-lier, Jullien and Treich (2000) examined the interplay between irreversibilityand the stock effect. They considered a constraint of type α2 ≥ kα1. E.g., ina model of global warming, when k = 0, this means that emissions in period2 cannot be negative. It is not possible to remove greenhouse gases fromthe atmosphere. Those two papers showed that such an irreversibility con-straint always require lower current consumption. The ’irreversibility effect’combines with the ’stock effect’ towards precaution.Interestingly Kolstad (1996) introduced the symmetrical constraint, i.e.

a constraint of type α2 ≤ mα1. In his model of global warming, this con-straint means that next-period controlled emissions should be at least aslarge as current-period controlled emissions (up to a factor m). This rep-resents irreversibility of capital investment in control measures: emissionscannot go too high because of previous investment in capital abatement.Kolstad (1996) showed that this type of constraint may make precautionarypolicies non-optimal. Irreversibility of capital may dominate environmentalirreversibility.10

In summary, we have mentioned three sources of inertia in our model ofpollution externality. First, stock externality, δ > 0: pollution accumulates

10The model of Dixit and Pindyck (1994) presented above could easily be reinterpretedas a model of investment in pollution control, leading immediately to that conclusion.

19

and it is not possible to reduce this stock more than the natural rate of de-cay δ. Second, environmental irreversibility, α2 ≥ kα1: if one emits pollutionone cannot retrieve the initial state of the environment. Third, capital irre-versibility, α2 ≤ mα1: if one invests in pollution control, one cannot reducethe abatement capital stock.An interesting question is which is the dominant ”irreversibility effect”?

We have shown that the first effect, due to stock externality, may be brokendown into two basic effects of opposite sign. The global sign depends uponthe specification of the DM’s preferences. We have also said that the secondand third ones have clear-cut but opposite directions. As a result, there isno theoretical consensus on which is the dominant irreversibility. At leastfour different effects play in opposite directions. This ambiguity has alsobeen demonstrated in empirical works, as in Nordhaus (1994) and Ha-Duong(1998).

5 Decentralized decision-making under scien-tific uncertainty

In the previous section, we analyzed the changes that scientific uncertaintybrings to the optimal timing of prevention efforts. We have shown that, un-der certain circumstances, it may support the adoption of the PrecautionaryPrinciple (PP) as a socially efficient guideline. Instrumental to the reasoningis that information has a positive value and that it increases the incentive toremain flexible (proposition 1) and to reduce current risk-exposure (proposi-tion 2).To derive those results, we have followed the tradition of public economics,

i.e. we considered a class of problems where there is one DM who decidesthe level of risk that should be supported by the society as a whole. In manysituations though, there is not only one DM but multiple DMs that act in adecentralized way.We will show in this section that the policies that result from a decentral-

ization process may be not robust to the resolution of uncertainty over time.In other words, we will show that even when precautionary policies shouldbe adopted in the global economy, the competing forces among the severalDMs may be such that sequential policies do not emerge at the equilibrium.The PP may then be viewed as an incentive or constraint for the DMs to

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select even so those policies.

5.1 Competition and preemption

A typical difficulty of a decentralization process comes from the incentiveof competitive firms to introduce an innovation too early, as explained forexample by Weeds (1999). To keep the argument simple, let us use the simpletwo-period model presented in section 3.1. We hereafter assume that n riskneutral firms compete for the introduction of a new good whose expectedvalue for consumers is P per period. Because of the fixed sunk cost I toinitiate production, there is increasing return to scale and only one firmwill invest at equilibrium. The natural monopoly extracts all the surplus atequilibrium.As before, at the end of the first period, everybody will learn whether

the value of the new good is P/2 or 3P/2 for the future. We have seen insection 3.1 that it is socially efficient to wait for this information to comebefore deciding whether to introduce the new good or not if NPV2 is largerthan NPV1. It is interesting to see whether competitive firms follow this ruleor not.To answer this question, let us solve this problem by backward induction.

Suppose that all firms decide to delay the introduction of their investmentup to the date where the scientific uncertainty is resolved. When a lowvalue of the innovation is revealed by scientific progress, no firm is willing tointroduce the good, under condition (2). Suppose alternatively that a highvalue of the innovation is revealed. In that case, the monopoly discountedprofit 1.5P (1−β)−1−I is positive, and each firm is willing to take the marketbefore the other firms. Suppose that each firm has an equal probability toact first and to get the monopoly rent. This lottery can come from theuncertainty about which firm will get the information about the quality ofthe innovation first. As seen from the first period, the net present expectedprofit for each firm is NPV2/n. This is the value of a firm in the first periodif they all decide to delay the introduction of the innovation.Let us now look at the decision of the firms in the first period. Under

which condition is it an equilibrium for the firms to postpone their invest-ment? Because the net present expected value of the investment is NPV1 forthe firm which gets the market, the decision not to introduce the good in theinitial period if no other firm did introduce it before is an optimal decision ifNPV1 is smaller than NPV2/n. Thus, delaying the introduction of the new

21

good in the first period is an equilibrium only when NPV1 is smaller thanNPV2/n, which tends to zero has n tends to infinity. This means that ina competitive economy, all innovations are introduced as soon as their netpresent expected value is nonnegative. Competitive firms do not use theoption value to wait, because the risk would be too large to be preemptedby other firms. This implies that innovations are introduced too early incompetitive economies.The PP can thus be interpreted as a constraint for firms to include the

value of future information generated by scientific progress in their decisionprocess.

5.2 Coordination under uncertainty

Another typical problem is the global aspects of some externalities. Whenpollution is a public good, no one would want to pay the cost of reducingpollution alone. This raises the familiar free-rider issue. In this section, weexplore the effect of scientific progress when this issue is present.Consider the following simple model of global warming. There are two

DMs, say two countries i = A,B, and two periods t = 1, 2. Each country ichooses the level of emission in each period αit. Damages occur only in period2. Importantly, they depend on the total emissions of both DMs. Felicity ofeach country is of form (20), i.e. so that

vi ≡ v(αi1,αi2, θi, C) ≡ u(αi2)− θiS(C),

where C = δαA1 + δαB1 + αA2 + αB2 denote total consumption.Damages are unknown in period 1. The structure of uncertainty is the

following:

• With probability π, damages only occur in country A: (eθA,eθB) = (θ, 0)where θ > 0.

• With probability 1−π, they only occur in country B: (eθA,eθB) = (0, θ).

The decision about αi2 is taken before observing which country incurs thedamage, but after observing some signal correlated to π. To solve the model,we follow Ulph and Maddison (1997). The functional forms are assumed tobe quadratic: the utility function u(x) is HARA (see eq. (17)) with γ = −1,i.e. u(x) = −0.5(η − x)2, and S(C) = 0.5C2. These assumptions will enable

22

us to get closed-form solutions for the Nash equilibrium of this game. Moreprecisely, it is easy to derive the optimal level of emissions in period 2 as afunction of π. It yields

αA2 (π) =η(1 + θ − 2πθ)− πcθ

1 + θ

αB2 (π) =η(1− θ + 2πθ)− (1− π)cθ

1 + θ,

where c = δαA1 + δαB1 . Using those solutions, it is then straightforward tocompute the value functions in period 2 as a function of π. Using obviousnotation, we obtain

jA(π) = −π(2η + c)2θ(1 + πθ)

2(1 + θ)2

jB(π) = −(1− π)(2η + c)2θ(1 + (1− π)θ)

2(1 + θ)2.

Observe that j0A(π) < 0 and that j0B(π) > 0. It is intuitive that an increasein the probability to have its own country incurring the loss reduces one’sown expected utility at equilibrium.Consider now an utilitarian welfare of that economy, j(π) = 0.5jA(π) +

0.5jB(π). Using the two last equalities, it is then easy to get that

j00(π) = −(2η + c)2θ2

(1 + θ)2< 0.

The social value function is thus a concave function in posterior beliefs. Thepoint here is that, according to definition 1, the value of information is alwaysnegative in this game.11 Hence, it will be optimal for those countries toignore future information opportunities. This in turn makes non-optimal thesequential approach described previously. Countries should be committed toa prevention policy before scientific uncertainty be resolved.To get an intuition let us compare the no-information to the perfect-

information cases. Suppose so that there is no opportunity for mid-termlearning and assume π = 0.5. Then each country will emit in period 2 thesame quantity αi2(0.5) = (η − 0.5cθ)/(1 + θ), i = A,B. This corresponds to

11The result that information may have negative value in non-cooperative games is notnew (see e.g. Vives (1985), Hirshleifer and Riley (1992)).

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the optimal level of emissions in the cooperative equilibrium of that economy.Now suppose that there is a possibility to get perfect information in thiseconomy. Then the country facing no damage will emit as much as theoptimal level in autarchy i.e. η, while the other country will emit (η − θη −cθ)/(1 + θ). Importantly note that this leads to a mean-preserving spread ofex post emissions with respect to the no-learning case since

0.5αi2(0) + 0.5αi2(1) = 0.5η + 0.5(η − θη − cθ)/(1 + θ)

= αi2(0.5).

Hence, since vi as defined above is concave in period 2 emissions in bothcountries, it is direct that the non-cooperative responses by the two countriesincrease the variability of the welfare for each country ji. As a result, thenon-cooperative equilibrium under no-information leads to a larger welfarethan under perfect-information.This simple illustration shows that when scientific progress reveals the

asymmetric consequences of a global risk, it makes a latent conflict an actualone, rendering problematic the coordination among the several DMs. Thisis why learning may then be a source of a loss of welfare in this game. Thisresembles an ”Hirshleifer effect” (see e.g. Hirshleifer and Riley, 1992). Whenone ignores which country will be affected, the two countries may find amutual advantage in cooperating. Yet if information is revealed early, it maydestroy risk-sharing opportunities.12

The PP may then be seen as a device to favor ex ante coordination andso to reach the welfare of the cooperative equilibrium.

5.3 Time inconsistencies

In the previous model, we have shown that non-cooperation among DMscould induce a paradoxical situation where it may be optimal to ignore infor-mation to come. Let us now consider another form of non-cooperation, basedon the conflict between the current DM and the future DMs, the so-calledtime-inconsistency problem.Time-inconsistencies may occur for instance when a government is tempted

to pass the burden of its successors. Take the climate policy negotiations.12Moreover it is noticeable that Ulph and Ulph (1996) examined numerically in this

game the effect of learning on first period global emissions. They showed that, due to thefree-rider issue, this effect can go either way.

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In the absence of the credibility of important sanctions at the internationallevel, there may be a divergence between actual government commitmentsand future governments decisions.Basically, time-inconsistency means that an optimal plan from the per-

spective of the current DMmay no longer be optimal for future DMs. Thanksto the dynamic optimization principle, such a behavior could not arise in theprevious framework: an optimal plan is an optimal plan whether looked fromtoday or tomorrow. However, there exists a representation of preferences ini-tiated by Strotz (1956) that makes such a situation possible. It is based onthe fact that preferences may change from one period to the other.This kind of preferences is traditionally associated to the process of pro-

crastination (Akerlof, 1991). This process is well-known: from my point ofview it may be optimal to ”smoke today” and to ”stop smoking” tomorrow.But when tomorrow comes, the trade-off is the same as today and I decideto continue to ”smoke today”, delaying one day further the decision to ”stopsmoking”.With this daily life example in mind, it surely requires no algebra to

understand why time-inconsistencies may affect the analysis developed above.Simply replace in the sentence above ”smoke” by ”invest”. Then the sentencewould mean that even if it is optimal to delay investment until tomorrow, thetomorrow’s DM may also find optimal to delay it as well. As a result, eachDM may decide to put off the project an additional day and the project isnever undertaken. When preferences change - and if one cannot precommitfuture decisions - the option value is ill-defined.13

Dynamic inconsistencies may also have troubling consequences as to thebehavior with respect to the information acquisition. Indeed, even if acquir-ing information permits to take a better optimal action for the current period,this information will be shared with all future conflicting DMs. Learning isirreversible! As a consequence, the subsequent DMs will take the optimal

13One can also easily imagine that the optimal response of the current DM is to investas soon as today even if in a first-best world it would be optimal for him to delay theinvestment decision. This strategy allows him to grab today’s immediate cash-flows, whileif he waits he runs the risk of missing indefinitely any rewards of the project. We referhere to the attitude of a sophisticated procrastinator, i.e. someone who foresees futureself-control problems. In a model where agents have to perform an activity exactly once,O’Donoghue and Rabin (1999) distinguish naive versus sophisticated DMs. They show thata sophisticated person always perform the activity sooner than a naive person (proposition2). They also show that a sophiscated person may do it sooner than time-consistent agent(example 2).

25

action from their perspective. If the agent anticipates the deviations of itssuccessors, there may be a situation where the current DM may steadilyprefer to ignore information.As a benchmark, consider the following simple model of consumption

externality on three periods. In the first three periods, the consumer mayconsume αt of a good which yields current utility u(αt) but may have anegative externality with probability π. This externality depends linearly ontotal consumption C = α1 +α2 +α3. The problem of the consumer in period2 writes as follows

j(α1, π) = maxα2∈D

u(α2) + β{maxα3∈D

u(α3)− πθ(α1 + α2 + α3)}. (21)

To solve it, we follow Carrillo and Mariotti (2000), i.e. we assume thatconsumption is indivisible D = {0, 1} and that preferences are linear u(α) =α. Let also suppose θ > 1/β.Then three different cases may arise. First, if π ∈ [0, 1/θ], then the

consumer would choose to consume both in periods 2 and 3, i.e. α∗2 = α∗3 = 1.Second, if π ∈ [1/θ, 1/θβ], then the consumer would choose to consume inperiod 2 and to abstain in period 3, i.e. α∗2 = 1 and α∗3 = 0. Finally ifthe probability of negative externality is sufficiently large, π ∈ [1/θβ, 1], theconsumer would choose to never consume, i.e. α∗2 = α∗3 = 0.Assume now that the consumer is inconsistent in the following sense.

When he arrives at date 3, i.e. when he has to decide α3, he underestimatesthe risk of a negative externality πθC. To make things simple, let us assumethat this externality is deflated by a factor β with respect to what he thoughtbefore. As a result the consumer behaves as

maxα3∈D

u(α3)− βπθ(α1 + α2 + α3),

so that, when arriving in period 3, the optimal choice will be to set α∗∗3 = 1only when π ∈ [0, 1/θβ]. The key point here is that this does not correspondto the strategy planned in the previous period for the future consumptionstrategy, i.e. α∗3. Combining optimal choices, i.e. α

∗2 and α

∗∗3 , defines the

optimal strategy of the inconsistent consumer in period 2 and 3. This leadsto the following value function

bj(α1,π) = 1 + β − βπθα1 − 2βπθ if π < 1/θβ

= −βπθα1 otherwise.

26

Importantly bj is then no more continuous (and nor convex) around 1/θβ,as represented on figure 2 by the plain line. As a consequence, informationvalue is not necessarily positive in this problem. This is true for instanceif it is optimal for the DM not to consume (take π just above 1/θβ) beforeinformation arrival. In other words, this means that one possible device toreduce future self-control problems for the current DM is to stop the flow oflearning.As a result, when preferences change over time, current DMs may pro-

crastinate - wait when they should act - or preproperate - act when theyshould wait - or restrict access to information - strategic ignorance -. ThePP could then be interpreted as a safe-guard against such time-inconsistentbehaviors.

6 Concluding discussionThe PP has defined a new standard of risk management when the very exis-tence of the risk is subject to scientific controversies. It provides the founda-tions for building a new risk regulatory pattern under conditions of scientificuncertainty. However the common formulation of the Precautionary Prin-ciple (PP) has no practical content and offers little guidance for conceivingregulatory policies. It was said recently that ”no general agreement exists onwhat the PP means in different socioeconomic and cultural systems” (Reportof the Conference on Science and The Precautionary Principle, 2000).In this paper, our interpretation of the PP has been limited to its crude

definition in national law or international treaties (Rio Conference, Maas-tricht Treaty, Loi Barnier, Protocol on Biosafety...). The PP encourages theprevention of a risk before that full scientific information is available. Hencewe have emphasized in section 2 that the PP implies that a decision should betaken in advance, even if it may be revised later on. The process of decision-making is sequential. In such a context, the objective is not only to find theoptimal level of risk exposition at a given time and given stable probabilitydistribution. The objective should be to define a dynamic strategy which isrobust to the resolution of uncertainty over time.In section 3, we have set up the standard economic approach to the prob-

lem of dynamic risk management. In particular we have characterized thenotions of irreversibility and information structure within a sequential frame-work. We also made a basic distinction between prevention versus precaution.

27

Prevention is a static concept that refers to the management of a pure risk,i.e. represented by a given probability distribution. Precaution is a dynamicconcept that recognizes the evolution of scientific knowledge; A precaution-ary measure has thus been defined as a prudent and flexible decision thatpermits to manage the current lack of scientific informationIn section 4, we have showed that risk management is different if we ex-

pect new scientific knowledge to arrive over time. A simple reason for that isirreversibility. Undertaking an irreversible action, such as the developmentof a wildland area, is less valuable if one expects to obtain better informationover time. Indeed, keeping a flexible position would permit to take advan-tage of the information to come (Dixit and Pindyck, 1994). There is thusan option value to leave the area undeveloped. Basically, the prospect toinformation over time biases decisions in favor of more flexibility. This well-known ”irreversibility effect” (Henry, 1974) justifies the PP when preservingthe environment leaves more flexibility for future choices.However, in many situations the irreversible nature of our decisions is

only one element entering the picture of risks regulation. Generally, to-day’s actions affect future welfare not only through a reduction of the futureset of choices but also directly by changing the risk borne by future genera-tions. This problem is considered by Gollier, Jullien and Treich (2000). Theyshowed that scientific uncertainty leads to increase current prevention whencumulative externalities and risk aversion are present. This effect takes placeunder a restrictive but plausible condition on the utility function of the so-cial planner. Thus, together with the pure ”irreversibility effect”, this effectprovides a strong normative basis to the PP.Finally, in section 5, we have showed that when decision-making is de-

centralized, the impetus of the market may be such that optimal policiesmay be not robust to the resolution of uncertainties over time. Precaution-ary policies may not spontaneously emerge in competitive industries wherehigh profits are promised for the industries able to preempt the market. Asa result, competitive firms may not use the option value to wait and mayintroduce innovations too early. The PP may then be viewed as an incentiveor a constraint to include the value of information generated by future scien-tific progress on the optimal decision process. Other issues such free-ridingor time-inconsistencies have been also discussed.Our interpretation of the PP has been of course marred by our own biases

and interests. In particular, we have emphasized above all the role played byscientific progress within the process of decision-making. This is because we

28

consider that the concept of precaution only refers to situations where theknowledge of the risk evolves over time. In such a situation, it is necessaryto adapt the course of action to the nature and to the severity of the risks.According to us, this idea is really the novel idea that brought the PP intoregulatory decision-making.As an illustration of our interpretation of the PP, take the Kyoto Protocol.

In the global warming issue, uncertainty are pervasive and implicit in theproblem about controlling emissions is how fast this uncertainty will resolveover time. In relation to that question, the response of the Kyoto Protocolhas been to set near-term reduction objectives together with introducing alarge degree of flexibility for the implementation of future commitments. TheProtocol specifies limiting emission levels rather than specifying long-termconcentration targets. This will permit to adapt the strength of abatement toevolving scientific knowledge. In addition, the Protocol incorporates severaldimensions of flexibility, e.g. the Protocol is defined in terms of a basket ofseveral greenhouse gases and it allows several regulatory instruments: jointimplementation, clean development mechanism and emission trading (see e.g.Grubb, 2000).Of course, there are many reasons why the timing of the climate policy

may not account appropriately for the dynamics of uncertainty resolution.For instance, several economists have stressed the lack of institutional de-signs and policy architectures to help the enforcement of abatement policies(Shmalensee, 1998). The PP may be then be interpreted as a step towardsthat objective.More generally, the presence of scientific uncertainty may favor, through

the multiple channels of decision-making, opportunistic behaviors. Indeed,scientific uncertainty opens a considerable room for discretion and for self-interested biases. Several social actors may use the argument of the lackof scientific evidence to push the final decision toward their own interest.For example, experts may provide biased policy recommendations becausethey have been sensitive to some incentives from the parties involved in thematter. The problem is then of determining the right mechanism to forcethe various social actors to participate efficiently to the process of regulatorydecision-making. Hence, the PP, by increasing the liability of these actors,may be viewed as a safe-guard against opportunitic behaviors in situations ofasymmetric information or imperfect monitoring (see e.g. Laffont and Tirole,1993).Typically, regulatory policies are determined in fine by government rep-

29

resentatives and are thus somehow dependent on some political aspects. Thepoint is that the outcomes of short run regulatory policy often do not matchthe political agenda of the government. Take for instance the story of ’madcow disease’. In the mid-80s, even under high scientific uncertainties, the En-glish government delayed the decision to ban flour made from the carcassesof sick animals. One may suspect that this decision has something to do withthe political consequences that would have followed a crisis in the breedingsector.Scientific uncertainty may also generate a typical phenomenon of politi-

cal demagogy. Indeed, it makes sense to think that the public is in generalless informed than politicians about some particular danger. Then, politi-cians with strong career concerns may prefer to select the risk policy thatthe public believes is good rather than the one which is actually good for thepublic. As a result, the influence of politics together with imperfect knowl-edge of the risk by the public will cause the regulator to depart from socialwelfare maximization. Remember that it was only after the discovery of the”ozone hole” that shocked public opinion that the Montreal Protocol waseventually signed. Before that discovery, the risk of ozone degradation wasnearly unknown to the public and so partly ignored by politicians, except incountries with the highest environmental concerns (Germany, Scandinaviancountries...).How to reduce political opportunism? One may investigate ways to mod-

ify the Constitution in order to generate better incentives in risk regulatorydecision-making. From this point of view, it is often said that the PP maychange the rule of the game in risk politics. Indeed, it may help to makepoliticians aware of their responsibilities in decisions taken under large con-ditions of uncertainty. In France for instance, in april 1993, the Conseild’Etat gave a warning of caution to politicians: ”In a situation of risk, onenon-validated hypothesis should be taken as temporary true, even if it is notformally demonstrated” (french translated). A few years after this caution,several french ministers have been judged for their respective liabilities in thecontaminated blood affair.In the same vein, the PP by increasing the liability under conditions

of uncertainty may lead firms to better internalize for the damages theygenerate to society. For example, the PP, by imposing a no-fault system, isan incentive for firms to acquire the scientific knowledge before delivering anew product to the market. But this may not be enough to guarantee thatfirms implement an efficient level of precaution. Indeed the damages may

30

occur far in the future so that the firm may no longer exist at that date, as itwas the case in the abestos industry for example. Also, it raises the issue ofthe potential bankruptcy of the firms, which gives rise to an ex post problemof vistim compensation and to an ex ante problem of under prevention byinjurers.As a final word, it is maybe opportune to mention also that the PP may

have many drawbacks. First, if it is interpreted in a too extreme way, thePP may inhibit economic development in our society (Gollier, 2001). It maylead to delay innovations that are safe and effective. It may be used to setup high safety domestic standards in order to develop protective measures.A broad discussion on the PP should also account for the Viscusi (1998)’sfinding that too much effort are spent on newly discovered risks comparedwith familiar risks policies. Also, risk policies designed by experts and pol-icy makers should recognize the cognitive limitations by individuals. To thisend, risk policies may be the product of mixing the ubuquitous rational cost-benefit approach with a process of social coordination in order to make thosepolicies acceptable by the public. Another important concern is that thelegal or bureaucratic incentives are generally more stringent for people whocause unfavorable outcomes by acting than for people who cause unfavor-able outcomes by not acting. Can we punish English ministers because theyhave not banned flours? Can we blame an entrepreneur because he has notsufficiently tested a product that turned out to be toxic?Obviously, examining those implications and trade-offs needs a broader

reflection on the channels and on the institutions of risk management. Thiswas not the purpose of the present paper. This leaves open an interestingdomain for future research in information economics and law and politicaleconomy.

7 References

Akerlof, G., 1991, Procrastination and obedience, American EconomicReview Papers and Proceedings, 81.Arrow, K.J. and A.C. Fischer, 1974, Environmental preservation, uncer-

tainty and irreversibility, Quarterly Journal of Economics, 88.Bernanke, B., 1983, Irreversibility, uncertainty and cyclical investment,

Quarterly Journal of Economics, 98.

31

Blackwell, D., 1951, Comparison of Experiments, in J. Neyman (ed.),Proceedings of the Second Berkeley Symposium on Mathematical Statisticsand Probability, University of California Press, Berkeley.Bohenblust, H., Shapley, L. and S. Sherman, 1949, Reconnaissance in

Game Theory, 208, Rand Corporation.Carrillo, J.D. and T. Mariotti, 2000, Strategic ignorance as a self-disciplining

device, Review of Economic Studies, 67.CEC (Commission of the European Communities), 2000, Communication

from the commission on the Precautionary Principle, available at www.europa.eu.int.Datta, M., Mirman, L. and E. Schlee, 1998, Optimal experimentation in

signal dependent decision problems, mimeo, Arizona State University.Dixit, A.K. and R.S. Pindyck, 1994, Investment under Uncertainty, Prince-

ton University Press.Drazen, A. and P. Sakellaris, 1996, News about news: Information arrival

and irreversible investment, mimeo, University of Maryland, paper presentedat ESEM 1997 in Toulouse.Epstein, L.S., 1980, Decision-making and the temporal resolution of un-

certainty, International Economic Review, 21.Fisher, A.C. and W.M. Hanneman, (1987), Quasi-option value: some

misconceptions dispelled, Journal of Environmental Economics and Man-agement, 14.Freixas, X. and J.-J. Laffont, 1984, On the irreversibility effect, inBayesian

Models in Economic Theory, M. Boyer and R. Khilstrom editors, Amsterdam:elsevier.Georgescu-Roegen, N., 1975, The Entropy Law and the Economic Process,

Harvard University Press, Cambridge, Massachussetts.Godard, O., 1997, Social decision-making under conditions of scientific

controversy, expertise and the Precautionary Principle, in Integrating Scien-tific Expertise into Regulatory Decision-Making, C. Joerges, K.-H. LadeurandE. Vos editors, Nomos Verl.-Ges., Baden-Baden.Gollier, C., 2001, Should we beware of the Precautionary Principle?, Eco-

nomic Policy, forthcoming.Gollier C., Jullien B. and N. Treich, 2000, Scientific progress and irre-

versibility: An economic interpretation of the Precautionary Principle, Jour-nal of Public Economics, 75.Graham-Tomasi, T.,1995, Quasi-option value, in The Handbook of Envi-

ronmental Economics, Broomley (ed), Blackwell, 26.

32

Grant, S., Kajii, A. and B. Polak, 1998, Intrinsic preference for informa-tion, Journal of Economic Theory, 83.Grubb, M., 2000, The Kyoto Protocol: An economic appraisal, mimeo,

Royal Insitute of International Affairs, London.Ha-Duong, M., 1998, Quasi-option value and climate policy choices, En-

ergy Economics, 20.Hammitt, J.K., Lempert R.J. and M.E. Schlesinger, 1992, A sequential-

decision strategy for abating climate change, Nature, 357.Henry, C., 1974a, Investment decisions under uncertainty: The ’irre-

versibility effect’, American Economic Review, 64.Henry, C., 1974b, Option values in the economics of irreplaceable assets,

Review of Economic Studies Symposium, 196.Hirshleifer, J. and J.G. Riley, 1992, The Analytics of Uncertainty and

Information, Cambridge University Press.IPCC, Intergovernmental Panel on Climate Change, 1995, Working Group

3, Economic and Social Dimensions of Climate Change, Cambridge Univer-sity Press.Jones, J.M. and R.A. Ostroy, 1984, Flexibility and uncertainty, Review

of Economic Studies, 6.Keeler, E., Spence M. and R. Zeckhauser, 1971, The optimal control of

pollution, Journal of Economic Theory, 4.Kimball, M.S., 1990, Precautionary savings in the small and in the large,

Econometrica, 61.Knight, F.H., 1921, Risk, Uncertainty and Profit, Augustus, M. Kelley,

New York.Kolstad, C.D., 1996, Fundamental irreversibility in stock externalities,

Journal of Public Economics, 60.Laffont, J.-J. and J. Tirole, 1993, A Theory of Incentives in Procurement

and Regulation, The MIT Press, Cambridge, Massachusetts.Manne, A.S., and R. Richels, 1992, Buying Greenhouse Insurance: The

Economic Cost of CO2 Emissions Limits, The MIT Press, Cambridge.Marschak, J., and K. Miyasawa, 1968, Economic comparability of infor-

mation systems, International Economic Review.McDonald, R. and D. Siegel, 1986, The value of waiting to invest, Quar-

terly Journal of Economics, 101.Molina, M.J. and Rowland F.S., 1974, Stratospheric sink for chlorofluo-

romethanes: Chlorine atom catalysed destruction of ozone, Nature, 249.

33

Morone, J.G. and E.J. Woodhouse, 1986, Averting catastrophe: Strategiesfor regulating risky technologies, University of California Press.Morgan, G. and M. Henrion, 1990, Uncertainty: A Guide to Dealing with

Uncertainty in Quantitative Risk and Policy Analysis, Cambridge UniversityPress.Nordhaus, W.D., 1994, Managing the Global Commons, The MIT Press,

Cambridge.O’Donoghue, T. and M. Rabbin, 1999, Doing it now or later, American

Economic Review, 89.Orphanides A. and D. Zervos, 1995, Rational addiction with learning and

regret, Journal of Political Economy, 4.Report of the Conference on Science and The Precautionary Principle,

2000, International Conference on Biotechnology in the Global Economy,Sustainable Developments, www.iisd.ca/sd/biotech/.Rothschild, M.J., and J. Stiglitz, 1970, Increasing risk I: A definition,

Journal of Economic Theory, 2.Shannon, C., 1948, A mathematical theory of communication, Bell Sys-

tem Technical Journal, 27.Shmalensee, R., 1998, Greenhouse policy, architectures and institutions,

Economics and Policy Issues in Climate Change, W. Nordhaus editor, Re-source for the Future.Strotz, R.H., 1956, Myopia and inconsitency in dynamic utility maxi-

mization, Review of Economic Studies, 23.Sulganik, E., and I. Zilcha, 1997, The value of information: The case

of signal-dependent opportunity sets, Journal of Economic Dynamics andControl, 21.Treich, N., 2001, What is the economic meaning of the Precautionary

Principle?, Geneva Papers on Risk and Insurance - Issues and Practice,forthcoming.Ulph, A. and D. Maddison, 1997, Uncertainty, learning and international

environmental policy coordination, Environmental and Resource Economics,9.Ulph, A. and D. Ulph, 1996, Who gains from learning about global warm-

ing?, Economics of Atmospheric Pollution, E. van Ierland and K. Gorka eds,NATO ASI series.Ulph, A. and D. Ulph, 1997, Global warming, irreversibility and learning,

The Economic Journal, 107.

34

Urasategui, J., 1990, Uncertain irreversibility, information and transfor-mation costs, Journal of Environmental Economics and Management.Viscusi, W.K., 1998, Rational Risk Policy, The Arne Ryde Memorial

Lecture Series, Clarendon Press, Oxford.Vives, X, 1986, Duopoly information equilibria: Cournot and Bertrand,

Journal of Economic Theory, 34.Wakker, P., 1988, Non-expected utility as aversion of information, Journal

of Behavioral Decision Making, 1.Weeds, H., (1999), Strategic delay in a real options model of R&D com-

petition, mimeo, Cambridge, UK.

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é

ê (é )

0 1

a

b

Figure 1:

The inverse of the entropy function ρ(π) = π log π + (1− π) log(1− π) isa convex function of posterior belief π.

36

1+Ä

1/èÄ é

J(~1, é )

0

- ~1

- ~1 + 1 - Ä

Figure 2:

Period 2 value function when the DM is time-inconsistent: informationvalue is negative around 1/θβ.

37