Managing Permit Markets to Stabilize Prices

Managing Permit Markets to Stabilize Prices

Richard Newell, William Pizer, and Jiangfeng Zhang


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Managing Permit Markets to Stabilize Prices
Richard Newell, William Pizer, and Jiangfeng Zhang
© 2003 Resources for the Future. All rights reserved. No portion of this paper may be reproduced without
permission of the authors.
Discussion papers are research materials circulated by their authors for purposes of information and
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Managing Permit Markets to Stabilize Prices
Richard Newell, William Pizer, and Jiangfeng Zhang
The political economy of environmental policy favors the use of quantity-based instruments over price-based instruments (e.g., tradable permits over green taxes), at least in the United States. With cost uncertainty, however, there are clear efficiency advantages to prices in many cases, especially for stock pollutants such as greenhouse gases. The question arises, therefore, of whether one can design flexible quantity policies that mimic the behavior of price policies, namely stable permit prices and abatement costs. We explore a number of “quantity-plus” policies that replicate the behavior of a price policy through rules that adjust the effective permit cap for unexpectedly low or high costs. They do so without necessitating any monetary exchanges between the government and the regulated firms, which can be a significant political barrier to the use of price instruments.
Key Words: tradable permit market, prices, quantities, banking, borrowing, uncertainty
JEL Classification Numbers: Q28, Q48, D8, L51
1. Introduction……………………………………………………………………………………………………….1
2. Permit Banking and Borrowing…………………………………………………………………………..5
2.1. Previous Literature……………………………………………………………………………………..5
2.2. Modeling Permit Markets with Banking and Borrowing…………………………………7
2.3. Intertemporal Arbitrage by Firms…………………………………………………………………9
3. Managing Permit Markets to Fix the Price Path………………………………………………..11
3.1. Fixing Prices by Adjusting Allocations to Offset the Bank…………………………….12
3.2. Fixing Prices by Adjusting Allocations Based on Past Abatement and Prices…..14
3.3. Time Consistency and Commitment……………………………………………………………18
3.4. Contemporaneous Instruments for Fixing Prices…………………………………………..19
4. Concluding Remarks…………………………………………………………………………………………22 iii
Managing Permit Markets to Stabilize Prices
Richard Newell, William Pizer, and Jiangfeng Zhang∗
1. Introduction
Frequently in the course of designing new regulation, policymakers have incomplete information about the cost of compliance. Such circumstances lead to a dichotomy between otherwise equivalent price-based market mechanisms, such as taxes, and quantity-based market mechanisms, such as tradable permits. Price-based mechanisms fix the price and leave output uncertain, while quantity-based mechanisms fix the output level and leave prices uncertain. Seminal work by Weitzman (1974) establishes the conditions under which prices are preferred to quantities.
Weitzman’s analysis and many that followed (Roberts and Spence 1976; Weitzman 1978; Yohe 1978) are set in a single-period, static framework. In reality, most regulations exist in a multi-period, dynamic framework, which gives rise to a feature unique to a permit mechanism over time: the potential to bank and borrow permits between periods. A limited amount of work has explored the consequences of banking (Rubin and Kling 1993; Cronshaw and Kruse 1996; Rubin 1996; Kling and Rubin 1997; Schennach 2000; Leiby and Rubin 2001), and only recently has such work explored its implications for policy instrument choice due to the effect of cost uncertainty (Yates and Cronshaw 2001; Williams 2001). This is true despite the widespread
∗ Newell and Pizer are Fellows at Resources for the Future, Washington, DC. Zhang is an Economist at the Asian Development Bank, Manila. The opinions expressed in this paper do not necessarily reflect the views of the Asian Development Bank.
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allowance of banking within permit systems.1 Borrowing has been allowed to a much lesser extent to date, but is often raised in the context of potential climate change policy.2
We demonstrate that a bankable permit system in a multi-period setting can be used to create the same outcomes as a price-based system. Unlike a typical permit system where the number of permits available over time is fixed, we consider a system where the number of new permits issued each period varies based on the previous period’s emissions and price levels. By allowing the permit level to vary with past cost shocks, this bankable permit system exhibits the same cost flexibility as a price-based system.
This has important implications for environmental policy. When market-based instruments have been used, the political economy of environmental regulation in the United States has overwhelmingly favored tradable permit systems, with initial allocations given to existing firms, or “grandfathered.” Keohane et al. (1998) suggest several explanations for this revealed preference, including that tradable permits create rents, and grandfathering distributes those rents to existing firms while also erecting barriers to entry. They also point out how direct allocation of grandfathered permits offers a degree of political control over the distributional effects of regulation, enabling the formation of majority coalitions. Taxes, on the other hand, offer none of these advantages. Rather, they transfer resources from the private sector to
1 Examples of U.S. permit programs that have allowed banking include ones to curb criteria pollutants under the Clean Air Act, phase down lead in the 1980s, trade sulfur dioxide emissions under Title IV of the Clean Air Act Amendments of 1990 (Schennach 2000), trade nitrogen oxide emissions in the northeast states, and reduce NOx and particulate emissions from heavy-duty truck and bus engines.
2 Corporate Average Fuel Economy standards allow car manufacturers to both bank and borrow fuel economy credits for up to three years. California’s Low-Emission Vehicle Program also allows vehicle manufacturers to receive debits to be made up in the following model year (Rubin and Kling 1993). International climate policy discussions have implicitly included borrowing within possible consequences for noncompliance under the Kyoto Protocol, through the payback of excess tons with a penalty (i.e., interest) (United Nations Framework Convention on Climate Change 2000).
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government and make the costs of regulation particularly visible. Plus, there is simply the stigma of being a “tax”—the “T” word.
In addition, practical and political issues arise when environmental policies require monetary exchanges with the government, as with taxes, auctioned permits, or hybrid systems involving a “safety valve” (where the government places an upper limit on permit prices through a willingness to sell extra permits at a set price). Beyond the factors mentioned above, these instruments also raise legislative and administrative difficulties because they cut across traditional institutional boundaries. Policies involving only emissions quantities may fall clearly within the historical bounds of particular environmental legislative committees and executive agencies. Policies entailing transfers to and from the federal treasury, however, may involve an entirely different set of legislative and executive actors not historically involved in environmental policymaking. In addition to the potential loss of authority for the traditional environmental policymakers, introducing new participants to the process raises real political and bureaucratic policymaking challenges that reduce the likelihood of agreement.3
Nonetheless, price-based policies are more efficient for many environmental problems. When uncertainty exists about the costs of abatement, and policies must be fixed before the uncertainty is resolved, price policies will lead to distinctly different outcomes than quantity policies. Pollution taxes, for example, encourage firms to reduce emissions until the marginal cost of reductions equals the tax. The tax leads to a range of possible emissions levels, depending on how uncertainty is resolved, but will fix marginal cost at the tax level. Conversely, a tradable permit system will fix the level of emissions, with the permit price determined by the marginal
3 At the international level, permits may avoid problems associated with international tax payments (Wiener 1998). Furthermore, if intertemporal trading supplants intratemporal trading as the main source of compliance flexibility among countries, this would weaken concerns about international capital flows and balance of payments caused by international permit trades (McKibbin et al. 1999).
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cost of meeting the emissions constraint. The permit mechanism will therefore lead to a range of possible marginal costs, depending on how uncertainty is resolved, but will lead to a fixed level of aggregate emissions. Different expected net benefits will therefore be associated with these alternate policies.
Weitzman’s (1974) insight was that, on economic efficiency grounds, a flat expected marginal benefit function (relative to marginal costs) favors prices, while a steep benefit function favors quantities. Intuitively, flat marginal benefits imply a constant benefit per unit, suggesting that a tax could best correct the externality. In contrast, steep marginal benefits imply a dangerous threshold that should be avoided—a threshold that is efficiently enforced by a quantity control.
Thus, for cases where the marginal benefits of pollution control are flat relative to the marginal costs of abatement, prices are preferred on efficiency grounds. Furthermore, if marginal benefits are not only relatively flat, but are close to being constant, the price policy is not only the better of “second-best” instruments, but can actually be the first-best solution—even if there is uncertainty about costs—because it corresponds perfectly to the externality. The marginal benefits of carbon mitigation, for example, are thought to be very flat due to the stock nature of the externality, thereby strongly favoring the use of price-based instruments (Newell and Pizer 2003; Hoel and Karp 2001).4
We are therefore interested in the potential of tradable permit systems incorporating banking and borrowing to mimic the behavior of a price-based regulatory system. In other words, we want to demonstrate that without actually selling permits or taxing emissions at a fixed price, a regulator can create a tradable permit program in a way that replicates the
4 Note this is true even with uncertainty about benefits when the benefit uncertainty is not revealed before emissions are determined. In that case, it is still first-best from the vantage point of achievable policy outcomes.
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emissions consequences of an emissions tax over time. We could imagine this interest stemming from a given political objective to match a stream of observed permit prices, pt, with a preconceived notion of the correct prices, pt*, regardless of where that notion comes from. Or we could imagine the motivation for mimicking a price-based system coming from a more fundamental desire to maximize expected net social benefits, which, for the case at hand, happens to lead to a preference for prices. In either case, the regulator will want to choose a set of rules to meet the objective of stabilizing permit prices around a particular price target or path of price targets.
In the next section, we summarize the existing literature regarding bankable permit systems and we present a simple model of firm and regulator behavior under uncertainty that allows for permit banking and borrowing. In Section 3, we demonstrate several different ways to manage a permit system so that it is equivalent to a tax on the regulated output, with some more complex than others.
2. Permit Banking and Borrowing
2.1. Previous Literature
Absent cost uncertainty and assuming competitive behavior, a system of emissions permits that allows trading, banking, and borrowing can achieve a cumulative emissions target over a fixed horizon at the least discounted cost to firms (Cronshaw and Kruse 1996; Rubin 1996). Given a constant annual permit allocation over a finite horizon and one-for-one banking and borrowing, in equilibrium firms will borrow emissions in early periods and pay them back later, with permit prices growing at the rate of discount in Hotelling fashion. This results in higher emissions in earlier periods and lower emissions in later periods. Unrestricted banking and borrowing of permits is generally not socially optimal, however, because it may increase total social damages depending on when emissions occur (Kling and Rubin 1997).
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As Kling and Rubin (1997) note, the regulator can identify a permit trading ratio that is not one-for-one to induce firms to behave more in accordance with a social optimum. The permit trading ratio acts like a rate of interest, providing a return to banking and a penalty for borrowing. For flow pollutants, if marginal damages are constant and unchanging, the ideal trading ratio over time simply equals the inverse of the discount factor, e.g., one permit for 1/β permits next year, thereby exactly offsetting firms’ desire to borrow emissions due to discounting. Note that in a setting with constant costs and constant allocations, firms will be indifferent to banking, borrowing, or doing neither if the trading ratio equals the inverse of the discount factor. Banking and borrowing have no value in that setting. Leiby and Rubin (2001) generalize these results to handle the case of stock pollutants and nonconstant marginal damages, finding that the optimal trading rate between periods (i.e., the trading ratio minus one) is equal to the discount rate minus the desired rate of change in permit prices.
The above studies assume full information on future abatement costs and production technology. In such a scenario, the instrument choice decision does not arise because the regulator can achieve the first-best solution through either a price or quantity policy. If there is cost uncertainty, however, Yates and Cronshaw (2001) and Williams (2001) find that outcomes differ and the choice of whether to allow banking or borrowing of permits depends, as one might expect, on the relative slopes of marginal benefits and marginal costs.5 They find that in cases where marginal damages are less steep than marginal costs, intertemporal trading raises net benefits.6
5 Also see Requate (2002) and Phaneuf and Requate (2002) on the influence of cost uncertainty on the level and welfare effects of permit banking.
6 Yates and Cronshaw (2001) also solve for the optimal intertemporal trading ratio in a two-period model, finding that, in addition to the discount rate, the ideal trading ratio is a function of the parameters of the cost and benefit functions, including the degree of cost uncertainty.
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Newell and Pizer (2003) take this one step further, suggesting that in the absence of permanent cost shocks, full banking and borrowing across all periods would in fact make a quantity control behave much like a price control since quantities rather than marginal costs and prices would fluctuate in response to cost shocks. They draw an analogy to how the marginal utility of consumption fluctuates only slightly in response to transient income shocks under the permanent income hypothesis. The purpose of our paper is to test this suggestion by laying out policy tools whereby the regulator can use quantity instruments to mimic a price policy.
2.2. Modeling Permit Markets with Banking and Borrowing
There are two necessary elements to our policy design: (i) the mechanism governing banking and borrowing, and (ii) a rule for setting policy stringency, that is, the (aggregate) annual permit allocation. Banking and borrowing reduce—and can even eliminate—price shocks by converting them to quantity shocks, which are shifted across time through intertemporal arbitrage. The stringency-setting rule is necessary to anchor the price path at the desired level and to adapt to unexpected shocks. We entertain only design elements that do not involve money transfers between the government and the regulated firms.7
We consider a world with competitive markets for permits in every period where firms take prices as given. At the beginning of each period, the regulatory authority decides on the number of new permits to issue, determining supply.8 Each individual firm chooses its emissions level and end-of-period bank of permits. The aggregate market demand for permits is determined
7 The direct buying and selling of permits at fixed prices by the government would be the most straightforward way to implement an arbitrary price policy—a point we revisit a bit later.
8 The allocation need not be for the immediately subsequent period; for example, business interests typically advocate allocation in blocks of five to 10 years. Our results are easily extended in this case, although it might suggest additional interest in the contemporaneous interventions noted later.
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by adding the total current period emissions to the desired bank at the end of the period, then subtracting any banked permits from the previous period.
Permits represent the right to emit a fixed amount of pollution within a particular period of time: for example, one ton of sulfur dioxide in the year 2003. Banking occurs when firms present an unused permit for emissions in the current year and, in exchange, get permit(s) for the subsequent year from the regulatory authority. For each period, there exists a trading ratio (Rt) that defines the number of permits received: n permits in period t can be traded for Rt × n permits in period t + 1. Market equilibrium in period t can therefore be written as:
, (1) ( ) ( ) 1 t t t t t t y e a B B R + = − − +
t y
where is the new aggregate supply of period t permits provided by the regulatory authority and the right-hand side of the equation reflects aggregate demand described above. The term indicates the net aggregate emissions level (and use of permits) in the current period, where is aggregate baseline emissions and at is aggregate abatement. Bt is the volume of banked permits at the beginning of period t, and equals the aggregate amount of permits that firms bank at the end of period t. ( ) t t e −a
t e
t1 t B R +
( ) , , i it t
Borrowing occurs when firms get n permits in the current period in exchange for the obligation to return Rt × n permits in the subsequent period. Note that the same trading ratio that applies to banking also applies to borrowing. Also, note that while the banking transaction can be completed immediately—a trade of period t permits for period t + 1 permits—the borrowing transaction requires some type of contract because it is not complete until the firm returns the borrowed permits, with interest, in the next period. Borrowing appears in Equation (1) as a negative value for Bt. Apart from the general rules for trading among periods, described above, the remaining elements of the permit system are an allocation or allocation rule for the supply of new permits, yt, and specification of the trading ratios, Rt.
Before going forward, a key feature to keep in mind is the perpetual information asymmetry that we assume exists between the regulator and firm. In particular, let Ca θ
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represent a convex abatement cost function for each firm, i, where ai,t is abatement by firm i at time t and θt represents a mean-zero random shock to the marginal cost function that is the same for all firms and that may be correlated across time.9,10 We assume the regulator knows the abatement cost function,, but never directly observes θt. However, the regulator can usually infer the value of θt in period t+1 based on the observed market price and level of abatement in period t. In contrast, the firm learns the value of θt at the beginning of period t and makes abatement decisions accordingly. (The firm does not know the value of future θ .) We therefore consider practical rules for setting yt+1 that are based on observed abatement and permit prices in period t.
( ) , , i it t C a θ
2.3. Intertemporal Arbitrage by Firms
With our competitive market assumption, individual firm i focuses on a sequence of optimal abatement (ai,t) and banking (Bi,t+1) decisions, based on the realized cost shock (θt), the market permit price (pt), the current trading ratio (Rt), and their initial banking position (Bi,t). These abatement and banking decisions also depend on future trading ratios {Rt+s} and expectations about future prices {pt+s}. Let be the vector of exogenous variables to each individual firm. Firms maximize expected profits each period, which can be formulated as negative costs plus the expected discounted value of banked permits in the next period. As long as the banking/borrowing possibility exists, this suggests a Bellman equation for each firm of the form: ( { }) , |0 | 0 , , , i t t t t ss t t ss pθ R E p + ≥ + > Ω ≡
( ) ( )
, (2) { ( ) ( ) }
, , 1
, , , , , , 1 , 1 , 1
, max , ( ) ,
i t i t
i t i t i i t t t i t i t i t t t i t i t
a B
V B C a θ p a B B R βE V B
+ + + Ω = − − − − + +  Ω 
9 Here and throughout, the absence of an i subscript indicates aggregate variables; e.g., at is aggregate abatement and ai,t is abatement by firm i (both at time t).
10 The assumption that the cost shock is the same for all firms can be relaxed without changing the basic results.
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where, for each firm i and period t, VB Ω is the value of the bank (or debt) of permits at the beginning of period t, is the expected value of the period bank of permits conditional on information known at time t (e.g., the value of θt), and β is a constant discount factor. Note again that i subscripts reflect firm-level variables, while the absence of an i subscript reflects an aggregate variable.11 Maximizing the bracketed portion of Equation (2) with respect to the levels of abatement and banking to the next period yields the necessary first-order conditions:
( ) , , , i t i t
Et[V(Bi,t+1,Ωi,t+1)] t +1
( )
, (3) ititVB(),,,1itititVB∂Ω=−
( ) , , ,
, ,
, ,
0 i t i i t t
i t
C a
a a
∂ Ω ∂ θ
= − + =
∂ ∂
and . (4) ( ) ( ) , 1 , 1
, 1
, ,
0 i t i t
t t t
i t
p R E
β + +
+ +
∂ Ω 
+   =
∂  ∂ 
That is, optimizing firms equate their marginal cost of abatement with the permit price and, in equilibrium, this price must equal the expected discounted marginal value of banking permits until the next period, after adjusting for the trading ratio. Note that application of the envelope theorem to the maximized expression (2) yields:
, (

which, when applied to (4), implies:
. (5) [ ] t t t t 1 p β R E p + =
In other words, banking and borrowing creates an arbitrage opportunity between periods. If expected prices do not satisfy the no-arbitrage condition given by Equation (5), an opportunity exists to make money by buying and selling permits in different periods. Profit-maximizing
11 We have not included the cost of permits for uncontrolled emissions, ,titpe, because it does not affect the choice of abatement or banking.
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firms will exploit this opportunity until demand and supply in these markets re-establishes the no-arbitrage condition.
Notice that the no-arbitrage condition fixes the relationship among prices over time. Any change in the current period price affects the entire path based on Equation (5). Current period price shocks are reduced or eliminated via the no-arbitrage condition, which converts them into quantity shocks that can be moved across time through banking/borrowing.12 Also note that (5) implies that for the regulator to achieve the desired price path, the trading ratio, Rt, should be set so that , as in the deterministic banking literature, with the ratio equaling the inverse of the discount rate for the case of constant prices.
* *
1 (
Rt pt βpt ) + =
We cannot stop here, however, because the no-arbitrage condition only fixes the ratio of prices between periods; it does not set the precise price level in any period. Without further policy conditions, any price path having the stipulated period-to-period price ratios, βRt, would satisfy Equation (5), including pt = 0 for all t. To complete the price-replicating quantity policy, we turn to methods for fixing the price level.13 These methods rely on setting the overall stringency of the policy—that is, the effective number of permits in the system.
3. Managing Permit Markets to Fix the Price Path
As shown in Equation (5), in order to fix the price today at the desired level, p , we need to fix the future expected price, , at the desired level, . We consider several approaches, some of which are oriented to work over a finite horizon, and others that work over an infinite horizon. Generally, a deterministic permit supply rule (e.g., yt = 100) will not lead to
] t t 1 E p+
t 1 p +
12 That is, current period shocks affect current prices only to the extent that they shift the entire expected price path. This might be true, for example, in the case of a permanent shift in costs.
13 Note that we have not explicitly optimized over environmental damages. Rather, we assume that the social welfare function leads to a preference for a particular price path, and we simply try to achieve that price path. For economic optimality, prices would correspond to marginal damages.
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a deterministic price path. If costs turn out to be unexpectedly and persistently high, the entire expected price path will have to rise because supply is fixed. Similarly, if costs turn out to be unexpectedly and persistently low, the market price will have to fall given a fixed supply. In order to find a permit supply rule that leaves the price path unchanged, we must turn to supply rules that depend on observed cost shocks revealed through the market.
A sufficient condition will be to either fix at some point in the future, or to impose some other constraint that rules out alternatives to the desired price path. Fixing the expected price in some future period will fix the price path in all prior periods through intertemporal arbitrage. In the case of a finite horizon problem, where banking and borrowing will end on a particular date, T, we can fix (though the actual price in the last period will not be fixed). In the case of an infinite horizon problem, we can either intermittently establish fixed expected prices by closing the bank (as in the finite horizon problem), or create the second condition by carefully constructing a permit supply rule, yt, along with finite limits on banking and borrowing.
[ ] * , 1 t t t E p p τ τ τ + + = ≥
[ ] *
Et pT = pT
Note that an explicit target price, even absent direct government efforts to enforce it, would be a valuable policy development because it would make clear to all parties what permit price outcome is intended. This would be of obvious benefit for both short-term and long-term investment planning because it would prove a clear signal of expected incremental abatement costs.
3.1. Fixing Prices by Adjusting Allocations to Offset the Bank
For a finite horizon, or for an infinite horizon divided into discrete intervals, the regulatory authority can easily fix the expected price in the last period of the interval by declaring that permits cannot be banked or borrowed after that period and by adjusting permit
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allocations in the last period to offset the bank.14 In particular, the market equilibrium given by Equation (1) is replaced by:
, (6) T T T T y e a B = − −
T a T 1
where is aggregate abatement and where the regulator constrains to zero and chooses yT so that . That is, the regulator chooses yT to solve equilibrium condition (6) and first-order condition (3) (price equals marginal cost) for yT so that .15 Thus, the total permit allocation in the last period is equal to baseline emissions minus expected abatement at the desired price level and minus any accumulated bank (or debt) of permits. The size of the bank (debt) will depend on the history of cost shocks. If costs turned out to be unexpectedly high, on average, there would be a debt that would be offset by a higher-than-expected allocation. If costs turned out to be unexpectedly low, there would be a bank that would be offset by a lower-than-expected allocation. This implies that the actual market price in period T will be given by the solution, pT, to the system of equations:
B +
[ ] *
T1 T T E p p − =
1 ( , ) T T T T T T T y e E a p θ B − = −  −
. (7) ( ) ,
, i iT T
i T
i T T T T
C a
a e B y
∂ θ

Σ = − −
1 0 T B + =
Note that the first-order condition given by Equation (4) is eliminated by the constraint that . By choosing yT so that the expected value, the regulator can establish the desired price, on average, in period T and, more importantly, the expected price prior to period T. Having chosen to satisfy Equation (5) based on the desired price path
[ ] *
T 1 T T E p = p −
* *
1 (
) t t t R p βp+ =
14 The permit system may end in period T, banking/borrowing may simply cease, or the policy may continue with a new system of intertemporally tradable permits, lasting from T +1 to 2T, for example, that are not exchangeable with the earlier system.
15 For example, if ()()()2,01,2,iitttititCaccacaθθ=+++ , t 21tt and θρθε−=+ with independent identically distributed εt, then ()*1,211[]TiTTTEapccρθ−−=−− and ()21TTTTyecc*TiBp 1 ρθ−−−=−−Σ.
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{pt*}, the regulator establishes the desired price with certainty in all periods t < T. Note that by offsetting the bank in period T (subtracting it from the allocation in period T), it does not really matter what the regulator does in periods t < T concerning permit supply, so long as the bank is not too large (so that ; for credibility, it may be desirable to keep the bank roughly at zero). In such a “true-up” period, any accumulated bank or debt is offset by the permit allocation for that period. In this manner, quantity shocks that have accumulated in the bank are absorbed by the regulator’s allocation, yT. Thus, our “quantity-plus” policy replicates a price policy through intertemporal quantity arbitrage and banking/borrowing, and by adjusting for any cumulative abatement surplus or shortfall through a final period allocation rule that adjusts for unexpectedly low or high costs.
0 T y ≥
In effect, the regulator accepts the information asymmetry that reveals θt with a lag (the regulator must wait to observe the market price and abatement level). However, rather than fixing the permit level for many periods, the regulator uses newly revealed information to set the permit supply in each period (or at least in the very last period). The only “error” in terms of missing the desired price path, , occurs in the final period, T, where and .16 If autocorrelation in θt is high and/or the periods are short enough (e.g., quarters rather than years), this error may be very small. This approach can be applied repeatedly in the case of an infinite regulatory horizon.
* ( )
T T T p =p +f θ
( ) { } 1 1 | , , 0 T T E f θ θ θ
− =  …
3.2. Fixing Prices by Adjusting Allocations Based on Past Abatement and Prices
An alternative approach in the case of an infinite horizon, or an additional instrument within a finite horizon, is to specify a permit supply rule that periodically adjusts allocations based on observations of past prices and abatement to account for past cost shocks. We develop
16 Thus the final period looks like the traditional one-period efficiency divergence between prices and quantities.
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this rule by first laying out the regulator’s optimal permit supply rule and optimal aggregate abatement level in the absence of cost shocks. In particular,17
. (8) ( )
, * * * * *
; ; and i it
t t i t t t t
i t i
C a
p i a a y e a

= ∀ = Σ = −
In other words, at each point in time, each firm’s marginal costs equal the desired permit price, individual abatements sum to aggregate abatement, and the supply of permits equal the chosen residual level of emissions. Note that without cost shocks, banking and borrowing would not be necessary since the regulator has enough information to use quantity controls to correctly fix the price in each period.
Now imagine we are back in the world of cost shocks and the regulator wants to specify a permit supply rule that fixes prices by adjusting allocations to exactly offset realized cost shocks. We assume the regulator cannot observe θ directly, but instead must infer its value by observing and . We begin the development of this rule by constructing a linear approximation of the first-order condition that permit prices equal marginal abatement costs (3), around the optimum defined by (8):
t a t p
. (9)
( ) ,tttpp 2 * ( ) 2 ( * )
* , *
2 , ,
, ,
,0 ,0 i it i it
i t i t
i t i t t
C a C a
a a
a a
∂ ∂
− = − +
∂ ∂ ∂
Equation (9) tells us how deviations in permit prices relate to deviations in marginal costs due to deviations in the level of abatement and the size of the cost shock. Note that the units of (9) are for prices and marginal costs ($/ton, for example). To arrive at an allocation adjustment rule that is measured in emissions units, we therefore need to reexpress (9) by rearranging it in terms of quantity deviations, like tons. The result is:
17 This establishes the relationship between desired price, p*, and quantity, a*, absent a cost shock. The quantity a* will equal the expected quantity if marginal cost is linear in a and θ.
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, (10)
2 ( * ) 2 ( * )1( ) ( ) 2 ( * )1
, , * * ,
2 , , 2
, , ,
,0 ,0 ,0 i it i it i it
t i t i t t t
i t t i t i t
C a C a C a
a a p p
a a a
− − ∂ ∂  ∂ 
   = − − + −  
 ∂ ∂  ∂   ∂ 
t t a −a
where we have isolated the effect of the cost shock on the left, and reexpressed it in quantity terms. Equation (10) tells the regulator the size of each firm’s abatement deviation attributable to the cost shock, based on the observed abatement, permit price, and slope of the marginal cost function. Note that this is different from the actual deviation in abatement, , a point that we discuss below.
By aggregating (10) over all firms, the regulator can compute how much the allocation in period t+1 must be increased or decreased to exactly offset the effect of the period t cost shock, thereby stabilizing prices at p . The resulting permit supply rule is:
, t>0, (11) ( ) ( ) ( ) 2 * 1
* * * ,
1 1 2,
,0 i it
t t t t t t t
i i t
C a
y y R a a p p

+ +
= + − − + −  ∂ 
  ∂ 
*t1t1 y
where we have set the adjustment to the permit allocation () equal to the aggregate uncertainty-related quantity shock (found by summing (10) over i), adjusted by the trading ratio (Rt) to offset any interest on the shock-related bank or debt that is carried from period t to + .18 Using (11), the increase in permit supply () in one period exactly replaces the permits borrowed (banked) in the previous period to cover low (high) abatement due to unexpectedly high (low) costs. To complement (11), the expected permit supply is defined as:
+ + −
t 1
* *, t t t y =e−a
0 0 y =y *
t a
t t
and the initial period supply and given by (8).
Notice that if the regulator uses the permit supply rule and achieves the intended goal of setting , the last term in the expression (11) drops out. So what is the point of this last p = p
18 This rule is appropriate for either small deviations in price or a linear marginal cost schedule. A more complex relation can be used for arbitrary convex cost functions.
Resources for the Future Richard Newell, William Pizer, and Jiangfeng Zhang
term involving ()? Let’s use the following figure to show the meaning of this term first. The figure shows two marginal cost curves: in the absence of cost shocks, and with a realized cost shock. Point A corresponds to equation (3) for abatement at the market price () given the realized cost shock, and point B corresponds to equation (8) for the abatement at the desired price () in the absence of cost shocks. Point C decides a~ , an individual firm’s abatement at the desired price level under the realized cost shock. We can see:
( ) i i t t MC a ,θ ,
t p
t p i,t
( ) ( ) ( )
2 * 1
* ,
, , 2,
,0 i it
t t it it t t
i i t i
C a
pp a a a a
− ∂ 
−   = − = −
 ∂ 
Σ Σ 􀀄 􀀄
t t a a
Thus, the bracketed expression in (11) equals . * − ~
ttiiaMCθ,, ( ,0) i i,t a
p C B
A t p
i a , i t a ,
i,t a
t t a a
No matter what the market price is in period t, the adjustment the firms will receive in the next period is , the aggregate abatement at the desired price in the absence of cost shocks minus the aggregate abatement at the desired price under the realized cost shock. Firms know that when the market price falls below the desired price (< p ), the optimal abatement for each individual firm is (using the first-order condition (3)), but firms will not receive the full
* − ~
t p *
i,t a
Resources for the Future Richard Newell, William Pizer, and Jiangfeng Zhang
adjustment, , in period t+1. At time t, the firms must hold similar expectations about future periods based on the optimization condition, , namely, that , that and that the debt from borrowing will grow over time. Assuming a finite limit to borrowing, this limit will be reached almost surely at some point in the future.19 At that moment, say, time t+s, prices will necessarily rise so that . Recognizing this, firms have a financial incentive to abate more now and bank permits to sell at above-market returns in period t+s. If firms behave this way, it will bring current prices in line with .
*tta a −
[Ep[]*ttsEpp+< t s +[[][1tstRE+−ttsEp+−< ] [ ] t t s t s t t s1 βR E p + + + + =
] *
t t s t s E a a + + <
] 1 t s β p+
3.3. Time Consistency and Commitment
Both of the above proposals require commitment by the regulatory authority. In the case of the first policy, which adjusts allocations and closes the bank in the final period, the regulator will eventually want to relax the banking/borrowing constraint that BT+1 = 0 and allow banking and borrowing in the last period. Otherwise, the actual price in the last period will deviate from the desired price by some random amount. As noted earlier, this deviation may be negligible if the regulator is able to collect information up to period T and make an accurate forecast of θT.
In the case of the second policy of periodic allocation adjustments, if the price, pt, falls below the desired price, pt*, eventually a permit shortage appears, leading pt+s to exceed pt+s*.20 Yet, even if firms box themselves into this corner, the regulator should not punish them by
19 Note that with no constraints on borrowing, firms could choose to abate nothing and borrow permits each period to cover both previously borrowed permits and new emissions. This is consistent with pt = 0 for all t and satisfies (5). This behavior is possible regardless of the permit supply rule. The permit supply rule therefore needs to be coupled with limits on borrowing, with those limits tied to the size of the cost shock.
20 When borrowing hits its limit in future period t+s, []*ttstEpp s ++=, that is, the expected price will equal the desired price. However, with no capacity to borrow, the actual price will exceed the desired price as soon as an adverse shock occurs.
Resources for the Future Richard Newell, William Pizer, and Jiangfeng Zhang
allowing the price to be higher than the desired level; the optimal response is to forgive and try to avoid missing the price target in the next period.
Whether these theoretical possibilities raise a serious issue depends, of course, on the practical ability of the regulatory authority to commit to and actually implement policies that it would not want to implement ex post, at least in the short run. In reality, regulatory authorities successfully undertake such commitments all the time. Family welfare payments are stopped after specified time limits, sometimes regardless of the recipient’s current situation. Criminals are incarcerated for long periods under “three-strikes-you’re-out” policies, even if the third strike is a misdemeanor. It seems that the broader, longer-term negative effects of not carrying out a commitment carry real weight in actual policy settings. Nonetheless, the fact that each of the above policies depends on future commitments rather than current action suggests it might be more fruitful to opt for real-time policy actions that could be applied on an as-needed basis.
3.4. Contemporaneous Instruments for Fixing Prices
Each of the above approaches relies on firms properly taking into account expectations of future action, potentially leading to mistakes as well as commitment problems. In this section, we instead propose actions that take place contemporaneously with cost shocks to immediately offset their consequences and stabilize prices. Each of the methods below represents a different approach for achieving the same end—stabilizing permit prices by adjusting the permit cap in response to cost fluctuations. While we have not formalized the policies or resulting behavior, we speculate about their consequences and believe they could be fruitful areas for further analysis.
Direct government buying and selling of permits. Perhaps the most direct method to attain a particular price target would be for the regulatory authority to regularly intervene through direct buying and selling of permits at the target price, much like the Federal Open Market Committee uses market transactions of government securities to influence interest rates.
Resources for the Future Richard Newell, William Pizer, and Jiangfeng Zhang
Knowing that regulators will intervene to maintain a particular price level, firms would abate, bank, and borrow in accordance with that expectation, thereby fixing the price path. While this is a potentially attractive option to keep in mind, it compromises our original intent to entertain only methods that do not involve monetary exchanges between the regulatory authority and firms (note that combined with the finite-horizon borrowing policies noted earlier, it might be possible to limit the need for government sales to unexpected shocks in the last period).
Adjustable permit reserves. With this option, at least some—but not necessarily all—regulated firms would be subject to a reserve requirement to always hold a certain quantity of unused permits in their accounts. For example, the reserve requirement could be imposed on all firms receiving gratis allocations, based on a certain percentage of the allocation. Or, the requirement could be imposed on current emitters based on a certain percentage of last year’s emissions. In both cases, initial reserves could be created through a special allocation process. These reserves would be roughly analogous to the reserve requirement that the Federal Reserve places on banks, whereby they are required to always hold and not loan out a certain percentage of deposits.21 As with the Fed’s reserve requirement, firms not meeting the permit reserve requirement could be allowed to borrow from the regulatory authority in order to meet it.
Although the reserves are held by the regulated firms, the regulator maintains control over the use of the reserves. This gives the regulator an additional policy lever to stabilize permit prices by influencing the effective amount of permits in circulation, in the same manner that the Fed can adjust reserve requirements to influence the interest rate. Raising the reserve
21 Another analogy to Federal Reserve policy tools would be to influence permit prices by adjusting the intertemporal trading ratio, just as the Fed influences interest rates by changing the discount rate it charges banks for short-term loans. Increasing (decreasing) the trading ratio applied to borrowed or banked permits would tend to increase (decrease) current permit prices because the value of permits in the present is raised (lowered) relative to the future. However, this approach fails to support a desired price path {}*tpbecause there is only one trading ratio that reflects ()**1tttRppβ+=.
Resources for the Future Richard Newell, William Pizer, and Jiangfeng Zhang
requirement, for example, would lower the effective amount of permits available in the market, thereby raising the permit price. Lowering the reserve requirement would have the opposite effect. The regulator could take this action any time it saw prices deviating from the target.
As with direct government intervention, this option would encourage permit buying and selling in response to cost fluctuations, but it would effectively delegate this responsibility to permit holders through the use of permit reserves. Because firms holding reserves would know in advance that the regulator will react to prices above or below the target by adjusting the reserve requirement, these firms will have an incentive to act first. Irrespective of whether the regulator actually adjusts the reserve requirement, they will want to acquire permits when the price falls below the target in anticipation of the government requiring them to do so, potentially at a less favorable price (and the reverse if costs are high).
In effect, to avoid monetary exchanges with the regulated firms, the regulator simply places the pool of “potential permits” in the hands of the firms, and the firms themselves do all the buying and selling—under the watchful eye (and perpetual threat) of the intervening regulator. Borrowing and banking would be equivalent to holding permits below or above the reserve requirement. Here, the level of the reserve requirement acts as an effective limit on borrowing, a requirement noted earlier for the stringency adjustment rule (11).
Loans and special allocations. All of the preceding approaches allow for some form of regular borrowing above the expected cap level if costs are unexpectedly high—a policy that could be unwelcome to environmentalists who want emissions limits treated as rigid constraints. An alternative would be to allow the regulator to react to specific high-permit-price circumstances by making special allocations. That is, when the permit price reaches a particular threshold, the regulator could give away some volume of additional permits, thereby lowering permit prices. To be equitable and avoid a situation where some permits are given away shortly after others have been sold at a high price, it might be preferable to loan rather give away these permits. These loans could be distributed through a bidding process whereby firms bid the
Resources for the Future Richard Newell, William Pizer, and Jiangfeng Zhang
interest rate they would be willing to pay on these special loans, thereby providing a simple and fair distribution mechanism for the extra permits.
Splits and reverse splits. A direct means of influencing prices is to directly change the quantity of outstanding permits by announcing a split or reverse split of existing permits, as with shares in the stock market. If prices are too high, for example, the regulator can simply announce an X-for-1split so that one unit of permits is converted into X units. A reverse split of 1-for-X permits could be used if permit prices were too low.
4. Concluding Remarks
Many competing forces determine the design of environmental policy. Often, these forces lead to quantity-based regulation despite a large expected gain from price-based controls (Newell and Pizer 2003). In the case of efforts to mitigate the consequences of global climate change, this tendency toward quantity-based regulations leads to concern over the uncertain costs of particular targets, with banking and especially borrowing arising as a potential solution.22
We demonstrate that permit systems incorporating banking, borrowing, and adjustments to the quantity of outstanding permits can replicate price-based regulation. The methods do not require any monetary transfers between the government and the regulated firms, thereby avoiding a politically unattractive aspect of price-based policies. The approaches we lay out can work for both finite and infinite horizons and involve a variety of instruments ranging from adjustment of allocations based on past prices and abatement to the establishment of adjustable permit “reserves,” splits and reverse splits, loans, and special allocations. With such a wide range of potential options, opposition to overt price policies should not be viewed as an obstacle to considering other means of achieving the flexibility associated with these instruments.
22 See description of borrowing implicit within possible compliance outcomes in paragraph II.XV, United Nations Framework Convention on Climate Change (2000).
Resources for the Future Richard Newell, William Pizer, and Jiangfeng Zhang
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Resources for the Future Richard Newell, William Pizer, and Jiangfeng Zhang
Rubin, Jonathon, and Catherine Kling. 1993. An Emission Saved is an Emission Earned: An Empirical Study of Emission Banking for Light-Duty Vehicle Manufacturers. Journal of Environmental Economics and Management 25:257-274.
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