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This paper examines how enforcement affects the structure and performance of emissions trading programs with price controls under uncertainty about firms' abatement costs. The analysis highlights how an enforcement strategy can cause abatement-cost risk to be transmitted to enforcement costs via the price of permits. When this occurs, accommodating the effect of abatement-cost risk with an optimal policy results in higher expected emissions and lower expected permit price than their second-best optimal values. However, it is possible to design an enforcement strategy that shields enforcement costs from abatement-cost risk by tying sanctions directly to permit prices. This enforcement strategy stabilizes enforcement effort, the optimal permit supply and price controls are independent of enforcement costs, and the policy produces the second-best optimal outcome.

Much attention has been devoted recently to adding price controls (i.e., permit price ceilings and floors) to cap-and-trade policies to control uncertainty in aggregate abatement costs. The theoretical motivation for placing price controls on emissions markets originated with Roberts and Spence (1976) . Following Weitzman's (1974) seminal analysis of the comparative optimality of price-based and quantity-based regulations, Roberts and Spence showed that policies that combine price and quantity controls, so-called hybrid policies, cannot be less efficient than either a pure price or a pure trading scheme. The reason is that pure tax and trading policies are special cases of hybrid programs. Price controls for emissions trading policies limit the risk associated with uncertain abatement costs in exchange for additional variation in aggregate emissions. The current debate about hybrid emissions control policies has been driven by their proposed use in cap-and-trade policies to contain the highly uncertain costs of controlling greenhouse gases. Some analyses of price controls only involve price ceilings, so-called safety valves ( Pizer, 2002 ; Jacoby and Ellerman, 2004 ), but several simulation studies havedemonstrated the cost-effectiveness of combining price ceilings and price floors ( Burtraw et al., 2010 ; Fell and Morgenstern, 2010 ; Philibert, 2008 ). In addition, a very recent theoretical literature has emerged that examines cap-and-trade policies with price controls and other cost-containment measures ( Weber and Neuhoff, 2010 ; Webster et al., 2010 ; Grull and Taschini, 2011 ). 1 At the same time, several emissions trading programs with various forms of price control have been proposed, and some implemented, to control greenhouse gas emissions ( Hood, 2010 ; U.S. Congressional Budget Office, 2010 ). We contribute to the theoretical literature on price controls for emissions trading by adding the enforcement component to the determination of optimal hybrid policies. 2 All regulations have to be enforced and it is well-known that enforcement costs can have important impacts on the design of environmental policies. This is demonstrated in the design of emissions markets by Malik (1992) , Stranlund (2007) , and Caffera and Chávez (2011) . Understanding the joint determination of the supply of emissions permits, permit price controls, and enforcement is a new contribution to the theoretical literature on designing market-based policies. The problem is particularly intriguing because the permit price in a competitive permit market is the marginal benefit of failing to hold enough permits to cover emissions. Higher permit prices produce a higher incentive toward noncompliance, causing regulators to respond with more vigorous monitoring or higher sanctions to maintain compliance. Thus, abatement-cost risk can be transmitted to enforcement costs via the permit price, and the optimal hybrid policy must account for this. 3 Economic analyses of enforcement of emissions markets and pri ce controls have been limited to suggestions that imperfect enforcement can be used to provide a price ceiling in emission markets to limit high-side abatement-cost risk. Imperfect enforcement in this context means that the expected marginal pe nalty for permit violations is set below the level that would guarantee full compliance under all circumstances. (We use p erfect enforcement to refer to cases in which the enforcement strategy guarantees full compliance.) If m arginal abatement costs turn out to be high enough, the permit price rises to the expected marginal penalty and firms escape a fixed permit suppl y by violating their permits. Some view the relatively high penalties in the U.S. SO 2 Allowance Trading and the E.U. Emissions Trading Scheme as safety valves because they place a ceiling on the price of permits ( Jacoby and Ellerman, 2004 ; Stavins, 2008 ). More rigorously, Montero (2002) reexamined the prices vs. quantities debate to analyze the effect of imperfect enforceme nt on the choice between an emissi ons tax and emissions trading. He found that imperfect enforcement tends to favor emissions t rading over emissions taxes precisely because the expected marginal penalty can provide the price ceiling that improves the efficiency of emissions trading. While the link between enforcement and price controls in emissions trading has been reco gnized, we believe that the discussion thus far is incomplete. In fact, using the expected marginal penalty to provide a price ceiling is inefficient if explicit price controls are available. Relative to a trading program with imperfect enforcement (i.e., Montero's model and the suggestion of others), adopting a perfectly enforced tax that sources can pay to emit beyond their permit holdings can eliminate the expected costs of sanctioning noncompliant firms without changing the expected emissions and price of the policy. An additional efficiency gain can be obtained if a perfectly enforced subsidy for unused permits is available to provide a price floor that motivates additional emissions control when abatement costs turn out to be significantly lower than expected. Using imperfect enforcement to provide a price ceiling cannot address the possibility that abatement costs may be lower than expected. In this paper we examine the optimal trading policy with explicit price controls that is enforced so that firms are always compliant, because this policy will always be more efficient than one that uses imperfect compliance to provide a price ceiling. 4 Given the goal of achieving full compliance, we determine optimal hybrid policies under two enforcement strategies that vary according to how penalties are set. Under one strategy the unit penalty is a fixed value that is high enough to allow the achievement of full compliance with imperfect monitoring. To achieve full compliance and conserve monitoring effort, monitoring is chosen so that the resulting expected marginal penalty is slightly above the going permit price. A problematic feature of this strategy is that abatement-cost risk can be transmitted to enforcement costs, because it makes monitoring effort an increasing function of the permit price. An alternative enforcement strategy is to make the penalty a constant multiple of the going permit price. This makes the required monitoring effort independent of price variation, which is absorbed by the penalty. There are examples of both kinds of penalties in actual and proposed emissions trading schemes. 5 In the U.S. SO 2 Allowance Trading program the penalty for failing to hold enough permits is a fixed penalty that was set at $2,000 per ton of excess emissions in 1990, and is adjusted for inflation every year ( U.S. EPA 2010 ). Similarly, the E.U. Emissions Trading Schemeset a permit violation penalty of 40 Euro per ton of excess CO 2 -equivalent emissions during the program's trial period (2005 – 2007), which increased to 100 Euro per ton in the second phase, 2008 – 2012 ( European Commission, 2003, Article 16 ). 6 In contrast, the recently proposed American Clean Energy and Security Act of 2009 ( U.S. Congress, 2009 ) includes a permit violation penalty that is set at twice the clearing price in the most recent auction of permits (Section 723). Similarly, the George W. Bush Administration's proposed Clear Skies Initiative ( U.S. EPA 2003 ) included a permit violation penalty that was to be one to three times the clearing price in a recent permit auction. With the standard linear-quadratic model of uncertain aggregate abatement costs and pollution damage, we show that the choice of enforcement strategy has important effects on the design and performance of an emissions trading program with price controls. We judge the performance of hybrid policies in terms of how their expected emissions and permit prices compare to the emissions and the permit price that minimize expected aggregate abatement costs and damage ex ante, and refer to this latter outcome as the second-best optimal outcome. We find that if enforcement costs increase with the permit price then the supply of permits and the price ceiling and floor of a hybrid policy are chosen so that expected aggregate emissions are higher and the expected permit price is lower than their second-best optimal values. Thus, allowing abatement-cost risk to affect enforcement costs is associated with reduced expected pollution control. On the other hand, choosing an enforcement strategy that shields enforcement costs from abatement-cost risk stabilizes enforcement effort; it makes the optimal hybrid policy independent of enforcement costs, and the policy produces the second-best optimal outcome. In addition, expected enforcement costs may be lower if allowing price variation to affect enforcement costs also makes these costs a strictly convex function of the permit price. We also reexamine the problem of designing an emissions trading program without the aid of price controls. As noted before, Montero (2002) addressed this problem, suggesting that imperfect enforcement can be used to limit abatement-cost risk. Like many others, Montero ignored the expected costs of sanctioning noncompliance firms in his analysis. We include these costs for a trading program in which imperfect enforcement is used to deal with high-side abatement-cost risk instead of an explicit price ceiling. We find that while it is possible to shield monitoring effort from abatement-cost risk, allowing imperfect compliance when abatement costs are high transmits risk to sanctioning costs. Moreover, the optimal program produces weaker expected emissions control than the second-best level. Eliminating these effects are additional reasons to favor the control of abatement-cost risk with explicit price controls rather than with imperfect enforcement. We complete our analysis by revisiting the prices vs. quantities choice between a pure trading program and a pure emissions tax. While Montero (2002) showed that imperfect enforcement tends to favor permit trading over emissions taxes, we show that the costs of perfect enforcement do not affect the choice between an emissions tax and permit trading unless these costs are strictly convex in the pollution price, in which case they favor an emission tax. The rest of the paper proceeds as follows. In the next section we lay out the components of a permit trading program with price controls, including its enforcement. In Section 3 we examine the compliance choices of firms under a hybrid policy and examine the alternative enforcement strategies. In Section 4 we characterize the optimal hybrid policy given costly enforcement and examine its performance relative to second-best optimal aggregate emissions and permit price. In Section 5 we examine the effects of sanctioning costs on a trading program without price controls, and in Section 6 we analyze the choice between a pure trading program and a pure emissions tax that are perfectly enforced. We conclude the paper in Section 7 .

We have modeled the determination of an optimal emissions trading scheme with price controls to limit risk associated with uncertain abatement costs when the costs of enforcing the policy must be considered. We have generated several new results that have important implications for the design of emissions markets under uncertainty. We have argued that it is inefficient to rely on imperfect enforcement to provide a safety valve to limit abatement-cost risk, because this policy has several costly characteristics that can be eliminated with a perfectly enforced program with explicit price controls. These characteristics include the presence of variable sanctioning costs, the transmission of abatement-cost risk to enforcement costs, weaker expected emissions control, and the fact that imperfect enforcement cannot motivate additional emissions control if abatement costs turn out to be low. Given the perfect enforcement of a hybrid policy, we have stressed the benefits of structuring enforcement strategies that shield enforcement costs from abatement-cost risk. This can be accomplished by making sanctions vary with changes in the permit price so that abatement-cost risk is absorbed by the sanctions and not transmitted to compliance incentives and enforcement costs. Our analysis suggests that designing enforcement with this feature can be attractive to policy designers and managers for several reasons. First, doing so stabilizes enforcement effort and costs. This can be a very practical benefit, because it allows regulators to choose an enforcement strategy prior to the implementation of a trading policy and not have to worry about adjusting it after the uncertainty about abatement costs and permit prices is resolved. A second benefit of shielding enforcement costs from abatement-cost risk is that it makes the fundamentals of a hybrid policy — the permit supply, the price floor and the price ceiling — independent of enforcement costs. That is not to say that regulators can completely ignore enforcement costs. As in all policy endeavors it is important to design cost-effective enforcement strategies that achieve desired goals. However, if enforcement costs are independent of abatement-cost risk then the permit supply and price controls of a hybrid policy can be chosen without consideration of enforcement costs. The third benefit of shielding enforcement costs from abatement-cost risk is that it eliminates the distortion from the second-best optimal outcome that comes with an enforcement strategy that makes enforcement costs dependent on the permit price. In particular, regulators do not have to sacrifice environmental performance to accommodate the effect of abatement- cost risk on enforcement costs. Finally, if an enforcement strategy makes enforcement costs a strictly convex function of the permit price, then shielding enforcement costs from abatement-cost risk can reduce these costs. The notion that uncertainty in the underlying costs and benefits of a policy can be transmitted to the public costs of administering the policy, and that this might have welfare consequences and be controlled, may be a fruitful area for future research. We are not aware of other work that addresses this issue in other regulatory contexts, but the transmission of risk to administrative costs must be present in other policies. Perhaps future work can be devoted to examining the transmission of risk to regulatory efforts in other contexts, and to looking for ways to limit this risk.