December Organization of the Petroleum Exporting Countries 287

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1 The hybrid permit cum price ceiling policy proposal: intuition from the prices versus quantities literature Gary W. Yohe Abstract The social value of choosing a marketable permit cum price ceiling mechanism over an unencumbered marketable permit scheme to limit the emission of greenhouse gases is explored. Insight from the prices versus quantities literature instructs that this relative valuation weighs the benefit of increased variability in emissions as economic conditions warrant against an increase in the expected cost of climate change. The value of the hybrid scheme is high and carries a low price ceiling when, ceteris paribus, the marginal benefit of emissions reduction is not very sensitive to changes in the regulatory environment, when the marginal cost of reducing emissions is sensitive to that environment, when the variance in marginal cost is high and/or when the distortion created by the initial allocation of permits is large. The value is correspondingly low and the ceiling high when the opposite conditions hold. December Organization of the Petroleum Exporting Countries 287

2 The author is from the Department of Economics, Wesleyan University, Middletown, Connecticut, and the Centre for Integrated Study of the Human Dimensions of Global Change, Carnegie Mellon University, Pittsburgh, Pennsylvania, USA. This research was funded by the National Science Foundation, through its support of the Centre, under SBR Organization of the Petroleum Exporting Countries OPEC Review

3 T HE DEBATE BETWEEN optimists, who believe that carbon emissions can be dramatically reduced in response to the potential threat of greenhouse warming at little cost, and pessimists, who claim that significant reductions in emissions would certainly cause serious economic dislocation, has turned recently to focus attention on the issue of policy design. Admitting that marketable permits for carbon emissions hold the greatest promise of reducing the cost associated with any reduction target, some scholars have proposed a hybrid control mechanism that would simply set a limit, above which the price of those permits could not climb. Indeed, Pizer (1997) has proposed an alternative that would allow a specific number of tradable emissions permits for specific time periods to be auctioned or distributed, but would require that the government stand ready, willing and able to sell as many permits as might be demanded over any period at some predetermined price. In this way, a meaningful reduction target could be announced, but the marginal cost of emissions reduction would be capped. If the optimists are right, then the government will never sell a single permit and everyone goes away happy. If the pessimists are right, though, then the government effectively limits the economic damage of its greenhouse mitigation policy and the advocates of stringent control are disappointed. The hybrid permit cum price ceiling proposal has it intuitive appeal, but the devil is in the details. It is not enough to assert that the price of emissions permits will be capped. To make the hybrid work, its advocates must articulate exactly how the permit price ceiling might be determined. The problem of greenhouse warming has more than a cost side, and so the ceiling should weigh some sort of hedge against the potential damage that exorbitantly high emissions might cause against the expected harm of excessively restrictive constraints. Given this interpretation, though, the question of how to set the price ceiling can easily be cast in the classical prices versus quantities framework offered by Weitzman (1974). This framework was explored more fully by Yohe (1977 and 1978), Roberts and Spence (1996) and Weitzman (1978). It has been applied to sudden supply shortfalls by Yohe (1979) and to carbon emissions in Yohe (1992 and 1997). The framework applied here examines how a regulatory authority might choose a price ceiling for an arbitrary allocation of permits without complete knowledge of how the marginal cost of emissions reduction might vary, but with the full understanding that variability in emissions can increase the expected damage associated with greenhouse warming. The prices versus quantities structure is, of course, so stylized that precise numerical answers cannot be expected from its application. Its simplicity and the intuition that it supports can, nonetheless, be used to explore the sensitivity of a permit ceiling price that minimizes the deadweight loss of not specifying the right price and the right quantity to changes in the fundamental parameters that frame the issue. It can, thereby, offer some qualitative descriptions of the circumstances under which the hybrid might be most beneficial and when it might not be worth the effort. It can highlight some December Organization of the Petroleum Exporting Countries 289

4 pitfalls and opportunities and it can examine the effect of stipulating that the target, that initially fixes emissions, might not match the expected marginal cost with expected marginal benefit. This paper reports the results of exploring these questions. The structure, modified appropriately to reflect the hybrid greenhouse policy context, will be described in Section I and some modest conclusions will be advanced in Sections II and III, before returning to a stylized version of the optimist/pessimist debate in Section IV. I. The prices versus quantities structure applied to the hybrid greenhouse gas policy context Figure 1 displays the usual prices versus quantities structure. Let Z 0 be the maximum amount of emissions reduction that is possible (100 per cent or some large proportion dictated by technological feasibility). The marginal cost and marginal benefit of emissions reduction [represented notationally MC(Z) and MB(Z), respectively] are taken to be linear of the form: and: MC(Z) = c 0 + c 1 (Z Z*) + q MB(Z) = b 0 + b 1 (Z Z*) where, without loss of generality, c 0 = b 0 > 0, c 1 > 0 and b 1 < 0 and q represents uncertainty in the regulator s knowledge of marginal costs. The expected value of q is taken to be zero, so that: and: E{MC(Z)} = c 0 + c 1 (Z Z*) E{MB(Z)} = b 0 + b 1 (Z Z*) As a result, Z* represents the second-best level of emissions reduction, from the perspective of a regulator who cannot observe q prior to announcing either a quantity or a price control, because: E{MC(Z*)} = E{MB(Z*)} Clearly, then, P* = E{MC(Z*)} = E{MB(Z*)} is the expected value of the market-clearing price of permits, if (Z 0 Z*) were allocated; and it is also the certainty equivalent emissions tax that would achieve Z on average across the range of possible q. Indeed, given an emissions tax of P*, cost-minimizing emitters would set actual marginal cost equal to that tax and they would produce emissions streams with an expected value of Z*. The socially optimal level of emissions for any q sets actual marginal cost equal to expected marginal benefit, i.e. Z*(q) solves: Organization of the Petroleum Exporting Countries OPEC Review

5 MC(Z*(q),q) = E{MB(Z*(q))} so: Z*(q) = Z* [q/(c 1 + b 1 )] Note that neither P* nor Z* can elicit the socially optimal emission for any value of q other than zero, and therein lies the crux of the prices/quantities comparison which option produces the smaller deadweight loss from being wrong and what does the difference depend upon? The reader may wonder why uncertainty is not modelled in the marginal benefit schedule. The key here is to remember that the regulator must consider only uncertainty that will be resolved for the emitters after the announcement of a regulatory strategy. Emitters will read q every year, know marginal cost and decide how much to produce and emit, given q and the announced regulatory structure. Potential damage, that might be associated with climate change, is perhaps more uncertain to us all, but its resolution will proceed over decades. The regulatory authority need not anticipate, therefore, that anyone will react to changes in the perception of MB(Z) on a yearly basis. Finally, it needs to be emphasized that MC(Z) reflects the horizontal sum of the marginal cost curves of many potential greenhouse gas-emitters. They collectively achieve any emissions reduction target at least cost, when the last ton of emissions removed from the effluent is independent of its source. Either a tax or a permit scheme achieves this least-cost condition; but, again, total emissions are fixed under the permit scheme, while they can vary widely in response to changes in marginal cost under the certainty equivalent tax. Figure 2 adds the complication of the proposed hybrid scheme to the discussion. A marginal cost schedule for some q > 0 is drawn there, to assist in the discussion; it lies everywhere above E{MC(Z)}. Faced with a strict permit mechanism that reduced emissions to Z*, emitters would fix emissions at Z*, and the market clearing price of the permits would be [P* + q]; the resulting deadweight loss associated with this outcome is: DWL(Z*) = [q 2 /2(c 1 + b 1 )] Suppose, instead, that a permit ceiling, equal to [P*+A], had been imposed, with, as drawn, A < q. Emissions reductions would then decline to: Z A (q) = Z* + [(P* + A q c 0 )/ c 1 ] = Z* + [(A q)/ c 1 ] Notice that Z A (q) < Z*(q) < Z*; and the associated deadweight loss would be: DWL(Z*; P*+A) = [P*(c 1 + b 1 ) b 1 q]/2[(c 1 + b 1 )c 1 ] December Organization of the Petroleum Exporting Countries 291

6 Figure 1 ( ) Figure Organization of the Petroleum Exporting Countries OPEC Review

7 It is clear, then, that neither option achieves the optimum in this case; and figure 2 displays the associated deadweight losses. 1 Following Weitzman, then, the hybrid permit cum price ceiling mechanism should be preferred to the straight permit scheme, only if the expected value of the deadweight loss associated with the hybrid is less than the deadweight loss imposed by the permits. II. The comparative advantage of the hybrid mechanism over the straight marketable permit scheme Computing and comparing the deadweight losses just identified gets tedious and there is no reason to grind through the calculations here. Some simple simulations, combined with the intuition that has grown from the prices/quantities literature, are sufficient to support some remarkably robust insights. Assuming that the q are normally distributed, for example, it is possible to track the difference between the expected value of the deadweight loss associated with the hybrid policy and the expected value of the deadweight loss associated with the fixed permit mechanism. Call that difference in expected values D the comparative advantage of the hybrid permit cum price ceiling mechanism over the marketable permit scheme. It is also possible to use that difference to highlight the value of A (the difference between the designated ceiling price and the expected price in an unfettered permit market) that maximizes D; and, finally, it is possible to track the sensitivity of this maximum D and its associated A to changes in the variance of q, changes in the slope of the marginal cost curve and changes in the slope of the marginal benefit curve. The various panels of figure 3 display some results. Panel A, for example, shows loci that plot comparative advantage estimates (i.e. values for D) against values for A the degree to which the designated price ceiling should lie above P*. Maximum values for D fall as the slope of the marginal benefit curve (parameter b 1 ) increases in magnitude; and the associated values for A climb. Indeed, there are values for b 1 for which the comparative advantage of the hybrid scheme approaches zero, as the ceiling price climbs beyond the range of q. Why should this be the case? The hybrid scheme allows emissions to vary as the emitters observe q, and so it generates an efficiency gain on the expected cost side of the calculus. Variable emissions do, however, diminish the expected benefit of emissions control; and they do so to a degree that is proportional to the slope of the marginal benefit curve. Find that environmental conditions cannot tolerate variability in emissions (i.e. increase that slope too much), and it follows immediately that allowing emitters anything but a fixed and inflexible limit would be foolish. Panel B shows the same sort of comparison with various slopes in the marginal cost schedule. Note that the maximum comparative advantage rises and then falls as c 1 climbs, even though the associate ceiling price falls towards P*. The key here is that the slope of the marginal cost curve dictates the degree to which variation in cost is translated into variation in emissions. Steeper marginal costs portend less efficient variation in emissions, more specifically until, in the limit, there is no efficiency incentive to try to move emissions at all. This, in the extreme, is the case where the outcomes of a straight marketable permit scheme, a hybrid permit cum price ceiling mechanism and a tax all produce the same outcome, regardless of the value assumed by q. December Organization of the Petroleum Exporting Countries 293

8 Organization of the Petroleum Exporting Countries OPEC Review Comparative advantage of the hybrid mechanism Figure 3, panel A Sensitivity of the comparative advantage of the hybrid mechanism to the slope of the marginal benefit of emissions reduction Price limit above certainty equivalent permit price Base case B1 at 50% of base B1 at 150% of base B1 at 250% of base

9 December Organization of the Petroleum Exporting Countries 295 Comparative advantage of the hybrid mechanism Figure 3, panel B Sensitivity of the comparative advantage of the hybrid mechanism to the slope of the marginal cost of emissions reduction Price limit above certainty equivalent permit price Base case C1 at 50% of base C1 at 150% of base C1 at 250% of base

10 Organization of the Petroleum Exporting Countries OPEC Review Comparative advantage of the hybrid mechanism Figure 3, panel C Sensitivity of the comparative advantage of the hybrid mechanism to the variance in the marginal cost of emissions reduction Price limit above certainty equivalent permit price Base case B1 at 50% of base B1 at 150% of base Base case without expanded variance

11 Finally, panel C of figure 3 tracks the effect of widening the uncertainty in marginal cost. More variability in costs means, from the regulator s perspective, more potentially harmful variation in emissions around their expected value. It is reasonable to expect, as depicted here, that a higher variance in q would portend a smaller comparative advantage for the hybrid scheme, that allows it to be translated into variable emissions and a higher ceiling price for permits. III. The comparative advantage when the permit scheme is not fixed at the regulator s optimum The careful reader will have noticed that the preceding analysis proceeded under the assumption that the initial permit allocation, that summed to Z*, was taken to be the solution to the regulator s informationally constrained social optimization problem; i.e. the analysis presumed implicitly that Z* maximized expected social welfare, so that: E{MB(Z*)} = E{MC(Z*)} Most of the proposals for greenhouse gas emissions that are being discussed currently would, however, restrict emissions far beyond the economically efficient optimum. 2 Indeed, it is the debate over this over-restriction of emissions that has led to the suggestion that the hybrid permit cum price ceiling might be an attractive compromise. It is important, therefore, to examine the sensitivity of the value of the hybrid mechanism to changes in the specification of the initial allocation of permits. Figure 4 portrays the complication created by the over-restriction by setting the benchmark level of emissions reduction at Z' > Z*; i.e. figure 4 depicts a situation in which: (Z 0 Z') < (Z 0 Z*) permits are allocated. Since setting the corresponding ceiling price for emissions will be the focus of attention, it is more convenient to represent this circumstance in terms of the distortion in price (to be denoted D) that is thereby created between the marginal benefit of emissions reduction at Z' and the expected price of (Z 0 Z') permits. Since this expected price is E{MC(Z')}: D = MB(Z') E{MC(Z')} = (c 1 + b 1 )(Z 0 Z*) is linear in the degree of over-restriction. As can be deduced from the geometry in figure 4, the deadweight loss now associated with the unfettered permit scheme is: DWL(Z') = [(D + q] 2 /2c 1 This is an expanded area that increases linearly and with the square of D. December Organization of the Petroleum Exporting Countries 297

12 Equipped with this revised structure, simulation reveals some robust results. The value of adopting the permit cum price ceiling mechanism in lieu of the simple permit scheme increases with the size of the distortion (D) caused by the initial overrestriction of emissions for any combination of marginal cost and/or benefit parameters; correspondingly, the preferred price ceiling falls with increases in D. Figure 5 displays these tendencies for various specifications of the slope of marginal benefits. High sensitivity of marginal benefits to changes in emissions reduces the value of the hybrid mechanism and increases the appropriate ceiling, to be sure, but the trends hold. On the other hand, the preferred ceiling falls to P* [the expected price of the socially optimal allocation of permits (Z 0 Z*)] but no further, when b 1 is sufficiently small and the distortion (D) is sufficiently large. Figure 4 ' IV. Returning to the debate between the optimists and the pessimists The results presented here, on the basis of the basic prices versus quantities methodology, support the notion that: (i) creating a hybrid permit cum price ceiling regulatory mechanism for greenhouse gas emissions might be worth the effort; and Organization of the Petroleum Exporting Countries OPEC Review

13 (ii) the ceiling price for permits should never be below the estimated equilibrium price of permits for the dynamically efficiently allocation (i.e. the shadow price of carbon along the intertemporally optimal emissions trajectory). 3 The social value of choosing such a mechanism over an unencumbered marketable permit scheme weighs the benefit of increased variability in emissions, as economic conditions warrant, against an increase in the expected cost of climate change. The value is high, ceteris paribus, when the marginal benefit of emissions reduction is not very sensitive to changes in the regulatory environment, when the marginal cost of reducing emissions is sensitive to that environment, when the variance in marginal cost is high and when the distortion created by the initial allocation of permits is large. It is correspondingly low when the opposite conditions hold. The price ceiling that maximizes the expected value of the hybrid mechanism is, meanwhile, low, when the marginal benefit of emissions reduction is not very sensitive to changes in the regulatory environment, when the marginal cost of reducing emissions is sensitive to that environment, when the variance in marginal cost is high and when the distortion created by the initial allocation of permits is large; and it is high when the opposite conditions hold. Will the creation of a hybrid permit mechanism ease the debate between optimists and pessimists? Probably not. Pessimists probably believe that the marginal benefit of emissions reduction is not very sensitive to changes in the regulatory environment, that the marginal cost of reducing emissions is sensitive to that environment, that the variance in marginal cost is high and that the distortion created by the initial allocation of permits is large; and optimists probably believe exactly the opposite. If that is the case, then pessimists will think that the hybrid permit cum price ceiling mechanism has great value and that the price ceiling should be set relatively low; and optimists will think that the hybrid mechanism is of little use and that, if it were adopted, the ceiling price should be set relatively high. The proposal might, therefore, sharpen the debate, but it will fall short of silencing it. December Organization of the Petroleum Exporting Countries 299

14 Organization of the Petroleum Exporting Countries OPEC Review Figure 5, panel A The sensitivity of the maximum comparative advantage of the hybrid mechanism to the distortion caused by the initial allocation of permits Comparative advantage of the hybrid mechanism Base case B1 at 150% of base B1 at 250% of base Distortion D

15 December Organization of the Petroleum Exporting Countries 301 Figure 5, panel B Sensitivity of the ceiling price for permits to the distortion caused by the initial allocation Price ceiling net of the expected price of the optimal allocation of permits Base case B1 at 150% of base B1 at 250% of base Distortion in the initial allocation of permits

16 Footnotes 1. The recorded formulae for deadweight loss are simply the areas of the respective triangles highlighted in figure Weyant (1997) observed that the participants in EMF-14 (Energy Modelling Forum), who reported optimal emission trajectories, saw cumulative reductions in emissions from the baseline of perhaps 5 10 per cent through 2010 far less than the per cent required to stabilize emissions at 1990 levels by that time. 3. Weyant (1997) surveyed the EMF-14 participants who reported optimal emissions trajectories; he found that the initial shadow price of carbon ran between $5 per ton and $15 per ton. References Pizer, William (1997), Prices versus quantities revisited: the case of climate change, Resources for the Future Discussion Paper, Washington DC. Roberts, Marc, and Michael Spence (1976), Effluent changes and licenses under uncertainty, Journal of Public Economics, 5, pp Stavins, Robert (1997), Statement in Panel IV of the White House Conference on Climate Change: the Challenge of Global Warming, Washington DC, 6 October. Weitzman, Martin (1974), Prices versus quantities, Review of Economic Studies, 41, pp Weitzman, Martin (1978), Optimal rewards for economic regulation, American Economic Review, 68, pp Weyant, John (1997), Insights for integrated assessment, Intergovernmental Panel on Climate Change Asia-Pacific Workshop on Integrated Assessment Models, Tokyo, 10 March. Yohe, Gary (1977), Single valued control of a cartel under uncertainty, Bell Journal of Economics, 8, pp , Spring Yohe, Gary, (1978) Towards a general comparison of price controls and quantity controls under uncertainty, Review of Economic Studies, 45, pp Yohe, Gary (1979), Managing the demand side of a sudden supply shortage: some policy alternatives with information is costly, Resources and Energy, 2, pp Organization of the Petroleum Exporting Countries OPEC Review

17 Yohe, Gary (1992), Carbon emissions taxes: their comparative advantage under uncertainty, Annual Review of Energy and the Environment, 17, pp Yohe, Gary (1997), First principles and the economic comparison of regulatory alternatives, OPEC Review, June, pp December Organization of the Petroleum Exporting Countries 303