I drafted this paper for the forthcoming Beijing Forum at Peking University. Preliminary. Comments very welcome.
Climate Policy Decisions Under Uncertainty
Honorary Visiting Fellow, Department of Economics, University of Melbourne, Parkville, Vic, 3052.
Abstract: The economics of climate mitigation decisions is discussed when there is imperfect knowledge of likely future climatic changes, of policy effectiveness and of the policy responses of other countries. Simple frameworks recognizing the role of pure uncertainty are derived from heuristics based on classical decision rules. These frameworks are analytically imprecise but offer plausible decision rules that are not informationally demanding.
- Background. Mitigating climate change means making long-term investments in technologies whose effectiveness is highly uncertain. Policy makers will be partly ignorant of the consequences of their policy choices. They will not know what future emissions will be, how these are linked to climate change and what future abatement and damage costs, will be. They might take unnecessary mitigation actions or take inadequate measures. They may get it wrong.
Section 2 discusses various uncertainties that impinge on national climate policies. Sections 3 and 4 discuss planning under risk and uncertainty respectively. Section 5 makes final remarks.
- Climate risks and uncertainties. There are scientific uncertainties about the expected extent of climate change associated with accumulating greenhouse gases in the atmosphere – the climate sensitivity issue. There are also uncertainties about the likely extent of emissions that will occur. This depends on the uncertain climate policies of major emitters and on uncertain climate feedback effects. The extent of mitigation is part driven by uncertainties associated with costs of mitigation. There are uncertainties about the prospects for catastrophic events linked to climate change. Finally, there are uncertainties even about calibrating the character of climate change induced damages. Climate change has the potential to alter the way all human and non-human life relates to its biophysical environments. It is with bold (and perhaps unwarranted) confidence that such effects are indexed using GDP (or other) changes.
What do we know about such imponderables? Clearly the policy problem of addressing climate change must explicitly involve uncertainty. It is not adequate to assume particular climate scenarios and then devise what are conceived to be appropriate policies that fit these various scenarios. Uncertainty is intrinsic and must be accounted for in policy design. For example, decisions have to be undertaken in the expectation that they may turn out to be incorrect.
We do have substantive scientific argument on likely climate change effects and with potentially catastrophic effects. We also suspect that costs of addressing climate change, although substantive, are not prohibitive.
We also know that actions to address climate change may have come too late: The long half-lives of greenhouse gases in the atmosphere raise prospects of irreversible changes already having occurred forcing catastrophe either directly or via reliance on risky “last ditch” solutions such as geo-engineering.
- Planning Under Risk. One starting point for the economic analysis of climate mitigation is the use of expected cost-benefit analysis adapted to account for the effects of irreversible climate effects, investment irreversibilities under risk when there is the prospect of learning about risk. This is “real option” theory: See Dixit and Pindyck (1991).
The main analytical insights of the real options approach involve a risk-neutral policy-maker contemplating large irreversible investments with the data determining the productivity of the investments evolving as stochastic processes. Policy-makers know the parameters of these processes but only observe the values of key evaluative variables as the future unfolds.
The conjunction of risk-neutrality, investment irreversibility, risk and the prospect of learning create incentives to delay initiation of investments beyond the times they would be initiated if outcomes were evaluated by replacing random variables by their expected values. Thus a case for caution in initiating projects emerges. Expected benefits must exceed expected costs by a positive quasi-option value reflecting the gains from waiting to get improved information.
Such insight is important but the precise extent of caution depends on the specific numerical parameters of the stochastic processes considered – their growth rates, their variances and, when there are several processes, their covariances. These data are almost never known so analysis is often conducted using simulated (= “invented”) data.
There are obvious difficulties in operationalizing these procedures and it can be questioned whether using simulation does more than verify standard qualitative properties of lower-order analytical models. These qualitative insights are well known so relying on simulations may not contribute much new.
There are also problems with assuming risk-neutrality. The motivation for assuming this is that public decision makers are often selecting a large number of diversifiable investment projects with risky returns so it makes sense to look at expected outcomes across projects in accord with the Arrow and Lind (1970) theorem. This theorem, however, is inapplicable to climate-sensitive investments since risks here are non-diversifiable and pervasively experienced.
Given non-diversifiable risks and the prospect that climate change itself might lead to irreversible catastrophic environmental effects, it is natural to suppose risk-aversion rather than risk-neutrality with respect to climate outcomes.
Risk-aversion, does not necessarily imply positive quasi-option values indicating caution towards mitigation policy. Instead it can promote an anticipatory case for investing even when expected benefits fall short of costs. Policy makers will insure to protect communities from severe irreversible climate change.
This creates a tug-of-war between approaches that rely on risk neutrality and those assuming risk aversion. Risk-neutrality suggests a case for caution and delay in project initiation while risk aversion seeks an earlier anticipatory response. Without detailed knowledge of both the risks and the extent of risk aversion it is difficult to determine qualitatively, the character of appropriate responses to climatic risk.
- Planning Under Uncertainty. Pure uncertainty describes situations where possible future states of the world are known – here future possible climate states – but where not even subjective probabilities can be assigned to these states. While climate change is real, measures of climate sensitivity, because they imperfectly capture feedback effects, are too rough to provide useful probability density information (Pindyck, 2013)
When policy decisions are taken under pure uncertainty about the future there is the prospect of taking inappropriate decisions. This prospect makes policy designers uncomfortable but it is unsatisfactory – and unethical – to choose the best possible decision only for a preferred state of the world – a maxi-max policy: Nozick (1974, p. 298). The consequences of being wrong must be assessed. There are useful classical decision rule heuristics for doing this.
4.1 All-or-nothing mitigation efforts. Initially take a global perspective on mitigation with the world playing a game against nature. Suppose global efforts costs a known amount C but global benefits depend on an uncertain future state of the world. In state S1 mitigation yields large positive benefits by avoiding severe climate change effects and consequent large economic losses L. In state S2 mitigation fails to yield benefits because climate change does not occur, so L=0. In this state the cost C is incurred but no benefits arise. Finally, in S3 mitigation is implemented and climate change occurs but the mitigation efforts fail to address these problems. Both the project cost C and the losses L arise giving total costs C+L. This information is summarized in Table 1.
Table 1: Costs of mitigation outcomes
If probability information is available then this policy problem can be posed as one of minimizing expected costs. Assign probabilities p1, p2 and p3 = 1-p1-p2 to the likelihood of states S1, S2 and S3. The expected cost from mitigating is C+p3L while that of not mitigating is (p1+p2)L. Then there is a case for mitigating when C < p1L so the cost of taking action is less than the expected climate damage cost effectively avoided by taking action. This is a standard cost-benefit rule.
There are two issues involved in implementing this rule:
(i) Evaluating expected damages from not undertaking effective policy involves computing the multiplicative product of quantities that are themselves highly uncertain. First, there is the highly uncertain (though potentially “large”) expression for losses (L). Second, there is the poorly understood (though possibly extremely “small”) probabilities of successful and necessary policy action (p1). It is difficult to make sensible judgments about the size of products of the form p1L even to an order of magnitude yet this is essential for testing the standard cost-benefit rule.
(ii) With large enough losses L, irrespective of how small the probability of successful policy (p1) is, there will be an expected value case for undertaking policy action. This is a variant of “Pascal’s Wager” problem: See Green (2012). Pascal asked whether it was sensible to believe in God or not. Pascal argued that since we can’t prove or disprove God’s existence we should wager that he exists, because there is much to gain if it he does and not much lost if he doesn’t. The same argument can be applied in climate policy contexts: Given sufficiently high possible losses (the world might end!) it always makes sense to take action if costs are bounded. Indeed this argument for climate activism makes greater sense than Pascal’s case since, while we cannot use science to throw light on God’s existence, science does confirm the likelihood of at some damage from unmitigated climate change. Standard cost-benefit analysis will be irrelevant in advancing what policy should be adopted given large enough losses.
An alternative approach to this policy problem, and one that eschews use of probability information, is to choose an action that minimizes the maximum loss than could ever occur. This minimax policy is a version of what is called the Precautionary Principle: See Chisholm and Clarke (1993), Clarke (2008). This posits infinite risk-aversion and focuses on avoiding extreme very bad outcomes rather than good average outcomes.
The maximum loss that can occur in a climate context is if mitigation is implemented but climate change damages continue to arise. This occurs when mitigation occurs and state S3 arises. It suggests never mitigating if there is any = however remote – possibility of policy failing to work, an extreme view. If the possibility of mitigation policy failure is excluded then migation should proceed if the policy cost C is less than the avoided climate change loss L, the standard cost-benefit view.
A twist on minimax is to suppose that, if mitigation policy fails, a backup policy such as geo-engineering can be employed to offset the impacts of climate change. Suppose this latter costs Cg but creates particular risks itself so that society would continue to be exposed to distinctive environmental costs Lg. Then if Cg+Lg > L it is again inappropriate to mitigate initially at all since eventual costs from mitigation (including geo-engineering costs) exceed the unmitigated costs of severe climate change. In the more plausible situation where Cg+Lg < L the policy and environmental costs of a final geo-engineering effort are less than unmitigated climate change, the case for early mitigation effort requires C+Cg <L-Lg so initial mitigation effort costs plus the costs of geo-engineering must be less than the environmental cost reduction caused by using a geo-engineering solution rather than experiencing unmitigated climate change.
Most authors make the judgment that minimax is too conservative because any possibility of policy failure destroys the case for policy. Can the prospect that mitigation options might fail be retained but still provide a sensible decision heuristic? One approach is to compute the regret experienced under various policies and to minimize the resulting maximum regret that could occur. Regret here is the difference between the costs incurred when making an investment decision (say c1) and the cost incurred once the state of the world (c2) is observed – the minimax regret decision rule. This heuristic avoids situations where large losses could have been avoided by incurring relatively low mitigation costs. Regrets for the climate problem are in Table 2.
Table 2: Policy regrets for different mitigation options
If mitigation proceeds and a substantial loss is avoided, because state of the world S1 occurs, there is zero regret so c1=c2. Similarly if mitigation does not occur and either severe climate change does not occur (S2) or it occurs but the construction is useless (S3) there is zero regret. If mitigation does not occur but climate change does eventuate then the regret is the loss incurred less the cost saved (L-C). If mitigation occurs and either climate change does not or the mitigation effort proves useless then the regret is only the wasted cost C.
The maximum regret possible with mitigation is C while the maximum without it is L-C so the maximum regret is minimized with active mitigation if L-C > C or if:
L > 2C. 1.
This is a more plausible heuristic: Once the possibility of policy failure is admitted, a decision to proceed with mitigation requires the expected benefits from action to “greatly” (here at least “doubly”) exceed costs. This same condition obtains if the state of the world S3, where policy fails, is omitted since the maximum regrets in state S2 are those in S1.
4.2 Mitigation policy as a game among nations against nature. Instead of a global game against nature consider a game played between nations involving nature as a passive side-party that helps determines the state of the world. For simplicity consider two countries – “China” and the “US”. Each has the same policy options described above but these are now individual national policies with global spillover effects. Each country can comprehensively mitigate emissions (strategy M) at cost Cc and Cu for China and the US resp[ectively. Each can, alternatively, do nothing (strategy D) and incur no costs.
As before one of three states S1, S2 and S3 eventuate. If both countries mitigate in states S1 and S2 then the only costs are policy costs. In state S3, where each country’s policies fail, China (respectively the US) experience large climate induced environmental damages LLc (respectively LLu).
In S1 if only China mitigates, then it experiences costs Cc+Lu. Lu are climate costs imposed on China because the US does not mitigate. The US also experiences climate costs Lu’ because only China mitigates. Similarly if the US alone mitigates it experiences costs Cu+Lc and China experiences costs Lc’. Here Lu, Lu’ are less than LLu and Lc, Lc’ are less than LLc. In S1, if neither country mitigates, each experiences the large losses, LLc and LLu respectively. In S2 the only costs are those of unnecessary policies. In S3 the policy costs are those in state S2 but in addition the respective damage costs are experienced. The overall matrix of costs incurred by each country given the various states that occur when the countries pursue the respect policies M and D is in Table 3.
|M||Cc, Cu||Cc+Lu, Lu’||Cc, Cu||Cc, 0||Cc+LLc, Cu+LLu||Cc+LLc, LLu|
|D||Lc’, Cu+Lc||LLc, LLu||0, Cu||0,0||LLc, Cu+LLu||LLc, LLu|
Table3: Payoffs in a game among countries and nature.
There are at several of thinking about the policy task here.
Simultaneous moves game solution. If either (or both) countries believe states S2 or S3 will eventuate with certainty then neither should mitigate. If on the other hand state S1 is believed to occur with certainty then China has a dominant strategy to mitigate if:
Cc < Lc’ (2A)
Cc+ Lu < LLc (2B)
(2A) requires that China’s mitigation costs be less than the environmental costs it would face if the US alone mitigated and severe climate change occurred. (2B) requires that China’s mitigation costs, plus its environmental costs from climate change assuming it alone mitigated, must be less than the costs it would experience if neither country mitigated.
If both inequalities (2A), (2B) are reversed then China has dominant strategies not to mitigate even given the likelihood of severe climate change.
These arguments suppress risk by assuming known states eventuate. To incorporate risk again assign probabilities p1, p2 and p3=1-p1-p2 to S1, S2 and S3. It is then straightforward to seek Nash equilibria that maximize expected returns to each country. The expected payoff matrix is Table 4:
|M||Cc+p3LLc , Cu+p3LLu||p1Lu +Cc + p3LLc , p1Lu’ + p3LLu|
|D||p1Lc’+p3LLc , p1Lc +Cu + p3LLu||(1-p2)LLc, (1-p2)LLu|
Table 4: Expected payoffs in the game among nations and nature
Conditions for China to now have dominant strategies to mitigate are analogous to those for the case where S1 was assumed to occur with certainty but where climate losses are now replaced by their expected values. Instead of (2A), (2B):
Cc+p3LLc < p1Lc’+p3LLc ó Cc < p1Lc’ (3A)
p1Lu +Cc + p3LLc < (1-p2)LLc ó Cc + p1Lu < p1LLc. (3B)
Now China’s costs of mitigating must be less than the expected damages it would experience if it didn’t act and the US acted alone on climate. Chinese mitigation must be less than the expected costs it would experience if it “free rode” by relying on US efforts. In addition Chinese mitigation costs must be less than the expected extra damages it faces from unmitigated climate change when it acts to address climate change but the US did not. It must be cost effective to mitigate even if the US does not.
The quantities that determine the efficacy of this action are crucially the probability, p1, that severe climate change will occur and can be usefully addressed, the scale of the losses associated with climate change when, in turn, China and the US free ride on the efforts of the other country, and the losses accruing to China when neither country mitigates, respectively Lc’, LLc and Lu.
As in assessing the standard cost-benefit rule of Section 4.1 there are a highly indeterminate set of cross product terms that must be evaluated in carrying out these evaluations. There are again highly uncertain expressions for losses (Lc’, LLc, Lu) and poorly understood (though possibly extremely “small”) probabilities of successful and necessary policy action (p1) so again there are “Pascal Wager” issues: With large enough losses (Lc’, LLc, Lu), irrespective of how small the probability of successful policy (p1) is, there is an expected value case for undertaking policy.
Finally, strategic issues between national climate policies are characterized as market failure/Prisoners Dilemma (PD) situations where individual national incentives do not imply cooperative beneficial outcomes – where both countries have dominant strategies not to mitigate even though they would both be better off if they mitigated: See Clarke (2010). Here a PD requires that each of the two inequalities (3A), (3B) be reversed so there are dominant strategies not to mitigate. In addition, there is the requirement that each country must be better off mitigating if both did.
For China this last condition is:
Cc+p3LLc < (1-p2)LLc ó p1LLc > Cc. (4)
Therefore, expected payoffs to China from mitigating must be less than known mitigation costs – a generalization of the standard cost-benefit rule now adapted specifically for China. A symmetric condition holds for the US. Now neither country will mitigate even given the standard cost-benefit case for doing so.
It is also of interest to determine how the nations will select policies if they are each extremely risk-averse.
Minimax solutions. If China mitigates then the maximum cost it can incur is in S3 when its costly policy fails. It then incurs costs Cc +LLc. If China plays D then the maximum cost it can incur is either in S1 when neither it nor the US mitigate or when climate change occurs but both policies fail. This cost is LLc. Since Cc +LLc > LLc it is always more costly, comparing worst outcomes, to mitigate than not to, so China should not mitigate. A comparable analysis applies to the US.
Again minimax makes no sense unless policy failures (state S3) can be ruled out since when S3 is possible neither country should mitigate. If S3 can be ruled out then the maximum cost China can face if it mitigates occurs when the US doesn’t is Cc+Lu. If China does not mitigate the maximum cost it can ever face is when the US also does not mitigate and is LLc.
Thus if policy failure is ruled out China will minimise the maximum cost it can face by mitigating whenever LLc > Cc+Lu so the costs it experiences when no country mitigates exceeds the costs it faces if it mitigates but the US does not.
Minimax regret options. A regret matrix for each country experiences is now computed. In S1, if the countries spend Cc, Cu respectively and there is no regret. If they mitigate but either S2 or S3 occur then the regret is the respective wasted expenditure. Likewise if they do not make mitigate and S2 or S3 arise there is no regret. If they do not make these expenditures but S1 occurs then the regret is the respective climate loss less the saved policy cost. In S2 and S3 when one country mitigates and the other does not, only the country mitigating experiences regret equal to the respective cost.
In S1 if one country mitigates and the other does not then the country not mitigating experiences excessive climate losses net of saved mitigation costs. What is the regret experienced by a country, say China, which mitigated while the other country (the US) did not? Perhaps it could have acted unilaterally in this situation to offset all losses it faced because the US did not. It would then experience still higher mitigation costs CCc > Cc which would be unwise if LLc < CCc. For simplicity assume neither country has the option to scale up mitigation in this way, perhaps because this is too expensive. Thus each will experience no regrets if it mitigates inadequately when the other country does not.
If China plays M its maximum regret is Cc. If China Plays D its maximum regret is LLc-Cc so the case for mitigation requires LLc-Cc>Cc or LLc> 2Cc, a generalization of (1) for each country. Provided costs to each country of mitigating are “small” (less than ½) costs of unmitigated climate change, each should mitigate.
|M||0,0||0, LLu-Lu’-Cu||Cc, Cu||Cc, 0||Cc, Cu||Cc, 0|
|D||LLc-Lc’-Cc, 0||LLc-Cc, LLu-Cu||0, Cu||0,0||0, Cu||0, 0|
Table 5: Regrets in the game among nations and nature
This is again a more plausible heuristic than minimax suggesting that, once the possibility of policy failure is admitted, a decision to proceed with mitigation requires expected Chinese benefits from mitigation to greatly exceed Chinese policy costs. Again, this same outcome obtains even if the state S3, where policy fails, is omitted. By symmetry the same holds for US mitigation decisions given its mitigation costs and potential maximum climate change damages.
4.3 Mitigating a lot or a little. We return to consider global issues but change the structure of the damages the world faces and its policy options. Suppose a global decision-maker is thinking of either making a substantial mitigation effort to cover severe climate change (e.g. 6oC of warming) or a more modest effort to meet less damage ( 2oC warming).
As above, large-scale mitigation effort involves cost C and is warranted only with severe climate change. In the absence of such efforts large-scale climate change would impose substantial economic costs L > C. If only moderate climate change occurred only a more moderate mitigation effort costing c < C would be sought. The absence of any mitigation effort in this latter situation of mild climate change creates damage costs ell < L. Mistakes here can also be made with respect to deciding on the appropriate scale of effort. If moderate effort is exerted when severe climate change eventuates the cost is el < L
C, L, c, el and ell are deterministic. There are three policy options – undertake substantial effort, moderate effort or do nothing. There are also three possible states. Two states involve the moderate or severe climate change mentioned above when mitigation efforts work as planned. A third state arises where severe climate change occurs but where both possible mitigation efforts (large and small scale) fail completely to address social losses because, for example, environmental irreversibilities have set in. Redefine the states of the world as::
- S1 where severe climate change occurs that is most successfully met by a substantial mitigation effort costing C,
- S2 where moderate climate change occurs that can be offset by low mitigation effort costing c or, at greater cost C, by substantial effort.
- S3 where severe climate change occurs but mitigation effort fails..
Payoffs from the various investments are summarized in Table 6.
|Large scale mitigation||C||C||C+L|
|No mitigation effort||L||ell||L|
Table 6: Costs of mitigation and climate change
If large-scale efforts are initiated then the maximum cost that can ever eventuate is their costs plus the losses experienced because these efforts fail, namely C+L, under S3. Similarly, given the decision to proceed with more limited effort, maximum possible losses are at c+L. Finally if no action at all is undertaken maximum losses are L.
Choosing the policy that minimizes the maximum loss – the minimax policy – involves not mitigating at all when losses are bounded above at L which must be less than C+L and c+L. If either a large scale or moderate mitigation efforts are envisaged then the worst that can happen is that actions are taken at some cost but fail. These costs always exceed L. If projects can fail to achieve their objective entirely then the minimax policy in this type of setting is, as above, to do nothing.
A more confident policy-maker might rule out state S3 and assume investments are never unsuccessful. Payoffs then become.
|Large scale mitigation||C||C|
|No mitigation effort||L||ell|
Table 7: Costs of mitigation and climate change without policy failure
Now the highest cost of undertaking large-scale mitigation is C, of limited effort c+el and from doing nothing L. The minimax policy involves choosing the policy minimizes these three maximum costs. Since L > C it can now never be optimal to not mitigate at all. The choice then is between mitigating comprehensively or on a more limited basis.
The minimax decision is to mitigate comprehensively if C < c+el and on a more limited scale if C > c+el. The extra costs incurred in making a substantial rather than a limited effort, (C-c), need to be compared with the social and economic losses, el, of making limited efforts when more substantial efforts were required (el). This rule leads policy makers who know relative costs to focus on only the social losses associated with limited effort when climate change could be severe.
Minimax regret measures are now discussed when policy failure can occur.
If substantial (limited) mitigation efforts occur and there is severe (moderate) climate change then there is zero regret. Policy was chosen appropriate to the climate change that occurred. If nothing is done and there is severe (moderate) climate change then the regret is the corresponding environmental loss less the policy cost that was saved by not addressing it (L-C and ell-c, respectively). If large-scale mitigation efforts are undertaken when lower scale efforts would have sufficed the regret is the unnecessary extra cost (C-c).
If only low level mitigation effort is undertaken when severe climate change occurs and the policy is effective then the regret equals the net gain that would have been obtained from large scale policy less the net gain that was obtained by utilizing the lower cost option. This is L-C – max(0, el-c) = L-C-el+c if the low level effort does, at least, reduce losses when climate change is severe. Take el > c so this assumption is always met.
In assessing prospects for policy failure two cases are distinguished:
Case 1. Both low and high-level mitigation efforts fail completely to provide an economic outcome because (for example) both encountered the same difficulty that they were implemented too late. Then the regrets are C and c respectively. If policy was not undertaken there is no regret since each would have failed. The matrix of payoffs is set out in Table 8A.
Case 2. The high-level mitigation action can fail (e.g. because it was left too late to be implemented) but the low level policy does not (e.g. it relies on effective adaptation option). To sharpen the analysis suppose the low level policy retains its effectiveness and yields net returns el-c. Then the regret in undertaking the high level policy is its wasted cost C plus the regret from not undertaking a more effective low level adaptation strategy, el-c. Implementing the low-level adaptation strategy involves no regret since it works as effectively as the alternative policies. If there is no policy action at all the regret is the foregone gains ell-c. Payoffs are set out in Table 8B.
These cases can also be interpreted as corresponding to two new states of the world that correspond to the situation where, respectively, the large scale policy alone fails and where both active policies fail.
|Large scale mitigation||0||C-c||C|
|Small scale climate policy||L-C- el+c
Table 8A: Policy regret in Case 1.
|Large scale mitigation||0||C-c||C+el-c|
|Small scale mitigation||L-C-el+c||0||0|
Table 8B: Policy regret in Case 2.
From Table 8A the maximum regret that can be experienced with large-scale mitigation is C if it proves ineffectual. With lower level mitigation maximum regret arises in state S1 if L-C-el +c > c or if L-C > el. Without any active climate policy the maximum regret arises if state S1 eventuates assuming that L-C > ell-c as is plausible. Then minimum regret arises with the low level policy.
From Table 8B the maximum regret with a large-scale policy is in S3, with a low mitigation policy or no policy at all in S1. Regret associated with a low mitigation policy always dominates no policy at all so the minimum maximum regret choice lies between choosing either active policy. A large scale policy is preferred if:
C+el-c < L-C –el+c or:
L > 2(C-c) + 2el 5.
Justifying a large scale policy using minimax regret requires that losses from unaddressed severe climate change be large relative both to the extra costs of the policy and to the social losses inflicted by utilizing a low level response when climate change turns out to be severe.
This rule involves only one extra item of data over minimax namely the absolute level of losses in using a small-scale policy when ideally a large-scale policy was required. We can easily show that this same conclusion holds when various classes of policy failure are admitted to the analysis simultaneously – when both policies fail or when either the large or small-scale policy alone fail: See Appendix. With some work the taxonomy of policy failures could be reorganized to include states of the world where only moderate climate change eventuates.
The approaches suggested here to handling the issue of policy failure can be interpreted as ways of addressing gross uncertainty where one is unaware of some possible states of the world and where there are “unknown unknowns”. In accord with the risk-averse perspective one captures these unknown states by seeking to model the worst that can happen in these states. In many cost-benefit settings these will be expensive policy failures.
Section 5 Final remarks. Practical policy-makers might not want to use the exact formalism suggested above. The broad logic however might make some sense. States of the world are identified where policies work and where they fail.
The advantages of the heuristics used to make climate policy decisions under uncertainty over real option approaches based on risk are several. The implausible assumption that people have sensible subjective probability information on the various possible states of the world is dispensed with. In addition the use of invented data is replaced by procedures that focus on a few key costs and loss estimates.
Of course the assumption that future states of the world are known and that they can be adequately described by a few extreme situations is unattractive. The assumption that unforeseen states of the world might arise – the gross ignorance case – is part captured by admitting policy failure as a possibility. Moving too far in the direction of admitting the general possibility of totally unanticipated states of the world in general suggests a case for adaptive planning and this is difficult to model when large, lumpy, irreversible investments are being made.
The minimax heuristic only works if the possibility of policy failure is entirely excluded. In this latter case policy heuristics of the form employ comprehensive policies when the extra costs of so doing exceeds the losses you would incur by utilizing smaller scale policies when the larger scale policies were ideally required. This can be understood as reflecting the conservative minimax view.
The minimax regret heuristic works when the possibility of policy failure is admitted though it depends on the form of the failure. If again the choice lies between utilizing large and small scale responses and when failure is understood here to mean either that either both types of policy fail or that only the larger scale policy might fail.
Appendix: Minimax Regret Policies with Possible Comprehensive and Specific Policy Failures.
The two minimax regret situations examined in Section 5 can be put together so that various types of policy failure are possible. In all these failure situations severe climate change occurs but:
- S3 above occurs where both large and small scale policies fail (S3 in Table 8A);
- S3* (S3 in Table 8B) occurs so only the large scale policy fails.
- S3** occurs so only the small scale policy fails.
The associated regrets are in Table 8C.
|Large scale policy||0||C-c||C||C+el-c||0|
|Small scale policy||L-C-el+c
|No policy action||L-C||ell-c||0||el-c||0|
Table 8C: Policy regret with three classes of policy failure
The largest regret if a large scale policy is implemented arises if a small plant would have not failed and is C+el-c. The largest regret if a small scale policy had been implemented is again L-C-el+c in state S1 if L-C > el-c. Plausibly the largest regret if no policy action is taken also arises in S1. This is the regret that occurs when climate change is severe and a large scale policy would have been effective. Choosing the minimum regret involves choosing min(C+el-c, L-C-el+c, L-C) min (x,y,z). Here z > y since L-C > L-C +(c-el) if el > c as assumed – a small scale policy is cost-effective if moderate climate change occurs. Now y-x = L-C-el+c –(C+el-c) = L-2(C+el-c). Thus for a large scale policy to be regret minimizing:
L > 2(C+el-c).
So, as before, justifying a large scale policy using minimax regret requires that losses from unaddressed severe climate change be large relative both to the extra costs of a large scale policy and to the social losses inflicted by utilizing a small scale policy when climate change turns out to be severe.
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