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STANDARDS AND THE REGULATION OF ENVIRONMENTAL RISK BRENT HUETH AND TIGRAN MELKONYAN A BSTRACT. We study regulatory design for a pollution-generating firm who is better informed than the regulator regarding pollution mitigation possibilities, and who chooses an unobservable action when employing a particular mitigation plan. We distinguish among performance, process, and design standards, and study the relative merit of each type of regulatory instrument. Relative to previous work on standards design, we emphasize technology and process verification. An optimal performance standard is relatively strict when regulator and firm preferences are congruent, but the regulator may prefer no performance standard at all if verification costs are sufficiently high. A process standard unambiguously increases expected surplus (relative to no regulation) in some environments, and otherwise improves welfare only when it is unlikely to generate a “bad” technology choice by the firm. A design standard can improve welfare if the regulator is sufficiently well informed about the technological possibilities for pollution control, but only when the firm’s private benefits from technology choice are sufficiently small.
I NTRODUCTION The regulation of environmental risk is dominated by the use of standards. Although performance incentives (e.g., Pigouvian taxes and emissions-trading programs) are sometimes employed, standards remain the core component of environmental and safety regulatory design across issues ranging from worker safety and hazardous materials control to water and air pollution mitigation (Viscusi et al., 2000; Harrington et al., 2004). This is despite advocacy by economists regarding the potential benefit—resulting fundamentally from firm-level technological heterogeneity—of “market-based” solutions to environmental regulation.1 Moreover, the “command-and-control” standards that are employed often go well beyond specifying the level of a scalar pollution level or input Date: October 3, 2007. 1 A large literature has studied political-economy considerations supporting this apparent gap between the theory and practice of environmental policy design (e.g., Keohane et al., 1998). 1
use (as in, e.g., Weitzman, 1974; Shavell, 1984; Kolstad et al., 1990), and include features such as technology requirements, mandated information collection and reporting, and on-going process monitoring. What role, if any, do such features play in efficient standards design? We suggest a partial answer to this question with a model of standards design where uncertainty and private information play a key role. We assume that firms have better information than regulators regarding the relative cost and efficacy of alternative mitigation technologies, and that, for a given technology or “mitigation plan,” there is moral hazard in its implementation. These informational asymmetries lead to a formal distinction among process, performance, and design standards, and generate results regarding the relative merit of each form of regulatory control. Briefly, we model a setting where a regulator is restricted in the level of monetary penalty that can be imposed for the occurrence of an “accident.”2 If the regulator is unconstrained in the level of penalty that can be assessed, the first-best outcome can be achieved and there is no need for standards. In practice, however, it is often costly to impose the full social cost of an adverse outcome. For example, it may be difficult to trace responsibility to an individual source, as with food contamination or non-point source pollution. Alternatively, firms may be risk averse or “judgment proof” in the sense that potential monetary damages associated with an accident exceed the value of firms’ assets (Shavell, 1986). Even for simple regulatory control of end-of-pipe emissions, Harrington et al. (2004, pg. 8) note how political issues in policy implementation often lead to emissions charges being set too low to induce efficient emissions abatement.3 For simplicity, we model these potential frictions by assuming that the first-best outcome is unattainable with monetary incentives alone. 2
We treat the externality in our model as a stochastic event with a binary outcome so that our results are most naturally interpreted in the context of safety regulation. However, if there is a monotonic relationship between pollution and the harm caused by pollution, our analytic framework can also be viewed as a simple (perhaps overly simple) way of modeling uncertainty in more general kinds of pollution control processes. Thus, depending on the context, we will sometimes use the term “accident,” and other times “pollution,” in referring to the externality in our model. We will also sometimes make generic reference to the externality by using the term “adverse outcome.” 3 Moreover, the textbook treatment of “end-of-pipe” emissions control is a stylized representation of most real-world pollution production processes. In practice, there is rarely a single pollutant that is emitted, or even a single emissions point for a given source, and pollution at each emissions point is measured imperfectly. 2
The regulator cares about the probability of an adverse outcome and corresponding mitigation costs. There are two channels through which the firm’s sequential actions affect the probability of an adverse outcome. The firm chooses a discrete technology, or “mitigation plan,” and then chooses an effort level, or “action,” for the given plan. We study three types of regulatory standards. A design standard imposes a particular mitigation plan, while a process standard specifies (and enforces) the efficient action for a given plan. Thus, these two standards differ in the timing of the regulator’s intervention. Both standards have direct and indirect effects on the probability of an adverse outcome. A design standard imposes a plan choice, which indirectly affects the firm’s action choice, while a process standard enforces a particular action, which in turn affects the firm’s ex ante plan choice. The magnitude and direction of these indirect effects determine, among other things, comparative advantage of these second-best instruments. In certain circumstances, these indirect effects lower social welfare to a degree that renders no regulation preferred to the optimally chosen design or process standard. A performance standard allows the firm to select its preferred technology and action, subject to meeting a specified level of performance. We assume that performance can only be verified ex ante via inspection of the chosen plan and action, and that verification is costly. Performance verification costs increase with lower levels of accident probability. This assumption captures the idea that relatively stringent standards are costly to enforce. For example, in the case of an accident probability, the regulator must require a relatively large quantity of ex ante testing to ensure that the chosen plan and action meet a relatively stringent performance target. In this context, a use of a performance standard is optimal only when verification costs are sufficiently low, or when accident damages are sufficiently high. These standards capture qualitative features of regulatory standards that are commonly employed. We discuss a particular example in detail later in our paper, but briefly we have in mind regulatory instruments such as “best available control technologies” used in the regulation of air pollution (design and performance standards), process and performance monitoring associated with “Hazard Analysis and Critical Control Point” regimes used in food-safety regulation (process and performance standards), and maximum acceptable risk criteria used in toxic substances control (performance standard). In all 3
cases, firms inform the regulator about the relevant production environment and mitigation possibilities, and regulators expend considerable resources verifying the expected performance of firms’ mitigation plans, and ensuring their proper implementation. We show how each type of standard in our model can increase welfare, relative to no regulatory control.4 This is in contrast to the traditional notion of a technology standard as an inefficient way to achieve a target level of environmental performance, or as a suboptimal alternative to first-best incentives (e.g., an optimal Pigouvian tax). While the standards we model do constrain a firm’s technology and action choices, they do so by limiting its ability to make socially inefficient decisions. As we describe in more detail in the next section, the main contribution of our analysis is to compare standards in an informational environment where the verification, monitoring, and information reporting activities that make up actual regulatory design have merit. The practical import of our contribution is to emphasize the need for efficient standards design—something about which there has been little research—in controlling environmental risk. R ELATED L ITERATURE Weitzman (1974) shows how a quantity instrument, which can be interpreted as a performance standard,5 can dominate performance incentives (a “price instrument”) when there is uncertainty and asymmetric information in policy design. A number of authors have extended Weitzman’s analysis by comparing price and quantity instruments in different technological or regulatory-control environments (e.g., Stavins, 1996; Jung et al., 1996). In contrast to this work, we assume from the outset that the regulatory authority is restricted in the way it can use performance incentives, but we consider an informational and production environment where alternative forms of standards can be defined and compared. Besanko (1987) and Helfand (1991) both consider the merits of standards in a full information setting. In Besanko (1987), a polluting firm operates in an oligopoly market, so that two kinds of distortions are present. In this setting, a design standard (defined 4
Our “no regulatory control” regime can also be interpreted as a system of charges or ex post penalties for harm, but where in each case the first-best is unattainable. 5 When regulating a single firm the interpretation is straightforward. With multiple firms, Weitzman (1974) demonstrates how a “cap-and-trade” program—incentives cum aggregate performance standard— can dominate performance incentives alone. 4
as a minimum level of a pollution control activity) can result in higher social surplus than optimally designed performance incentives. Helfand (1991) compares the relative merit of various kinds of standards in a full-information competitive environment under the assumption that first-best policies are nonimplementable. We explicitly model informational frictions that can support such an assumption. Shavell (1984) studies an environment where multiple instruments emerge as an optimal regulatory response to accident risk. In particular, regulators are uncertain about the level of harm each firm in an industry might cause, and firm wealth is lower than the maximum potential harm. In such a setting, it is not possible to mandate an efficient level of care for each firm, nor will ex post liability for harm induce efficient behavior. Given the imperfections associated with each instrument, using both instruments can increase expected welfare, relative to using either instrument in isolation. In a related analysis, Innes (1998) shows how ex ante safety standards can be welfare reducing when optimal liability rules can be implemented, and when there is firm heterogeneity and uncertainty in the level of harm caused by an accident. Kolstad et al. (1990) provides a different rationale for the joint use of regulation with ex post liability for harm by noting that specification of a minimum level of care can influence firms’ perceptions of the negligence standard that will be enforced by a court of law. Our analysis is complementary to these papers in that we identify an alternative informational setting (firms have private information about their respective production environment) where standards can improve welfare. Also, to the best of our knowledge, there has been little formal recognition of the distinction between design (specifying technology) and process (monitoring implementation) standards in the environmental and safety regulation literature. Similarly, process verification requirements and on-going information reporting from firms to the regulator are not part of existing regulatory design analyses, though such requirements are observed in many actual standards. The recent work of Coglianese and Lazer (2003) is a notable exception. These authors describe and analyze the increasing use of “management-based regulation,” which is conceptually akin to our process standard.6
6
See also Office of Technology Assessment (1995) and Coglianese et al. (2003) for useful description of various types of standards currently employed by U.S. regulatory agencies. 5
Finally, at a purely formal level, our analysis is related to moral hazard models with multitasking. Holmström and Milgrom (1991) show how an efficient contract between a principal and an agent might involve the simultaneous use of output-based performance incentives and restrictions on the set of activities in which an agent can engage. Similarly, Prendergast (2002) shows that output-based incentives are preferable to input-based incentives when there is uncertainty regarding the appropriate technology for a given task. Our analysis differs from that of Holmström and Milgrom (1991) in that the multitasking that occurs in our model is sequential (firms first choose a technology, and then choose an implementation strategy), and our model incorporates hidden information and hidden actions. Our model is most closely related to Prendergast (2002), but extends his analysis by considering two different forms of input monitoring (technology selection, and implementation), and by focusing on technology choice and implementation, rather than on the stochastic structure of the agent’s signal generation technology. In the next section, we present and analyze our model. We characterize settings where some form of standard is efficient. The subsequent section discusses our results in the context of a specific example.
M ODEL Technology. A single risk neutral firm selects a process to control the probability of an adverse outcome. There are two feasible control processes, which for concreteness we call “prevention” and “treatment” plans.7 Firms can reorganize the production process to reduce the probability of contamination (prevention), or they can detoxify emissions (treatment). The probability of an adverse outcome under each plan depends on how it is employed. Thus, we let the firm choose an action a ∈ R+ that, together with the plan, influences the probability of an adverse outcome. For one of the plans, the probability of an adverse outcome is given by a twice-differentiable and strictly convex8 function p1 (a) ∈ (0, 1], while for the other plan there is an analogous function p2 (a) ∈ (0, 1]. We 7
At the cost of additional notational and expositional complexity, all of our results can be generalized to deal with an arbitrary number of discrete plans. 8 In contrast to convexity of probability functions, differentiability is not required to establish our results. Since convexity of a function implies differentiability almost everywhere, we would not gain much generality by abandoning the differentiability assumption. 6
spell out the details of the assignment of the probability functions to the two plans in the next subsection. We interpret a as an “effort” variable measured in monetary units, and suppose that higher effort leads to a lower probability of an adverse outcome, p′i (a) < 0 for all i = 1, 2 and all a ∈ R+ . To avoid uninteresting corner solutions, we assume that no effort can completely eliminate the possibility of an adverse outcome, and that it is always efficient to choose strictly positive effort: lim pi (a) > 0, and lim p′i (a) = −∞, for i = 1, 2. We a→∞
a→0+
assume that for a given level of action a, the plan with function p1 (a) results in a lower probability of an adverse outcome, and is more responsive to effort than the plan with function p2 (a): p1 (a) < p2 (a) and p′1 (a) ≤ p′2 (a) for all a ∈ R+ . Thus, for a plan with function p1 (a), a marginal increase in action a results in a relatively large (in absolute value) decrease in the probability of an adverse outcome. Mathematically, pi (a) exhibits complementarity in index i and action a. The plan with probability function p1 (a) is naturally interpreted as more efficient. Information. We model two types of informational problems faced by the regulator. First, action a can be observed by the regulator only by incurring some strictly positive exogenous cost. When a is not monitored, the firm will choose its level to maximize private payoffs. Second, the firm is better informed than the regulator concerning the relative cost and efficacy of alternative mitigation strategies. We model this information asymmetry by supposing the regulator knows only that there are two plans, prevention and treatment, and that one of these plans has probability function p1 (a) while the other has p2 (a). The regulator assigns probability q ∈ (0, 1) to the event that the treatment plan is characterized by function p1 (a). In contrast, the firm is perfectly informed about the mapping of probability functions onto plans. That is, the firm knows if the treatment plan is characterized by probability function p1 (a) or p2 (a). To this point, we have said nothing about the cost associated with alternative mitigation plans (other than effort cost). In practice, the plan with the lowest probability of an adverse outcome is not necessarily the least costly from the perspective of the firm. Suppose that each technology has some associated fixed cost, that the level of these costs varies across mitigation plans, and that the exact magnitude of the relevant cost is private information to the firm. Then, depending on the incentives and the regulatory design the 7
firm faces, the firm may prefer to exchange an increase in the probability of an adverse outcome for a lower fixed cost. Thus, we suppose that a single plan, either the treatment or the prevention plan, offers a cost reduction b > 0 compared to the other plan. Moreover, the firm knows the identity of the plan that yields a cost reduction, while the regulator does not.9 From the regulator’s perspective, the treatment plan has probability r of yielding the private benefit. Assuming statistical independence of the event that a plan has a specific probability function and the event that the plan has the private benefit, the possible outcomes (assignments of the probability functions and the private benefit to the two plans) and their probabilities are summarized as follows for the treatment plan: TABLE 1. Regulator beliefs regarding cost reduction and probability assignment to “treatment” plan. cost reduction (b) no cost reduction p1 (a) qr q(1 − r) p2 (a) (1 − q)r (1 − q)(1 − r) For future reference, we note that the likelihood that the plan with probability function p1 (a) has the private benefit is equal to the sum of the probability that the treatment plan has probability function p1 (a) and the private benefit, and the probability that the prevention plan has probability function p1 (a) and the private benefit. From Table 1, this likelihood is equal to ρ ≡ 1 − q − r + 2qr. A simple analytical example may help to further clarify the structure of this informational environment. The regulator knows that there are two options for controlling pollution, treatment and prevention. It also knows that, for given a, one of these tech√ nologies results in probability of adverse outcome 1 − 7 a, while the other technology √ results in probability of adverse outcome 1 − 3 a.10 However, it cannot match each probability function to a specific mitigation plan, prevention and treatment. Moreover, the regulator does not know which of the technologies has lower private cost (or higher “private benefit”) for the firm. In contrast, the firm can match each mitigation plan with its true probability function and knows which of the plans generates the private benefit. We elaborate on this example further below. This type of informational asymmetry is 9
Because compliance with regulation is mandatory, it is not important whether the firm learns the identity of this project before or after the regulatory design is established. 10 For a sufficiently small, these probability functions satisfy all of the assumptions imposed in this section. 8
formally analogous to that in Aghion and Tirole (1997) and Prendergast (2002), and is a simple way of representing the idea that, although the regulator may have a reasonable sense of what is technologically feasible in terms of accident prevention possibilities, it does not know how to adapt its knowledge into workable recommendations for reorganizing the firm’s production process.
Payoffs. In the absence of regulation, the firm’s payoff when there is no adverse outcome is normalized to 0. The total social cost of an adverse outcome is equal to s > 0, and the firm internalizes a fraction 0 < λ < 1 of the total social cost. Assuming λ < 1 is the simplest possible way of introducing the idea that regulatory control of the firm is socially desirable. There are many possible motivations for this assumption, one being that the set of incentives provided by ex post liability for harm, and possible damage to the firm’s reputation, are inadequate for the firm to engage in efficient mitigation (which includes both technology selection and abatement effort a). We assume λ > 0 because firms typically bear some cost when an accident occurs or pollution is emitted. The ex ante expected private cost (net of the private benefit) for a firm using the plan with probability function pi (a) is given by pi (a)λs + a. The regulator is concerned with expected social cost which is given by pi (a)s + a when the firm uses the plan with probability function pi (a). For arbitrary ex post cost x, we let ai (x) denote the costminimizing abatement effort, so that ai (x) is the solution to −p′i (a)x = 1. For the same level of ex post cost x, effort is higher under the plan with probability function p1 (a): a1 (x) ≥ a2 (x). Further, we have a′i (x) = −p′i (ai (x))/p′′i (ai (x)) = 1/xp′′i (ai (x)) > 0 for all x > 0 and all i = 1, 2. That is, the firm’s effort under both plans is increasing in cost x. To simplify the presentation of certain results and their proofs we assume that a′1 (x) ≥ a′2 (x). Finally, for notational simplicity, we define ci (ai (x), y) ≡ pi (ai (x))y + ai (x). When x = s the action choice is socially optimal given a plan choice, while for x = λs the action choice is privately optimal given a plan choice. When y = s, ci (ai (x), y) represents expected social cost conditional on the firm choosing the plan with probability function pi (a), while for y = λs, ci (ai (x), y) represents expected private cost conditional on the firm choosing the plan with probability function pi (a). We assume that the magnitudes of the private benefit and other parameters in our model are such that, given the socially optimal action choice under both plans, the plan 9
with probability function p1 (a) is the full-information first-best plan for the regulator even if it does not yield private benefit to the firm: Assumption 1. Conditional on the first-best action choice under both plans, the regulator prefers the plan with probability function p1 (a) : c2 (a2 (s), s) − c1 (a1 (s), s) ≥ b. Denoting L(x) ≡ c2 (a2 (x), x) − c1 (a1 (x), x), Assumption 1 can be written as b ≤ L(s). For x ≥ 0, L(x) is strictly positive and increasing (since L′ (x) = p2 (a2 (x)) − p1 (a1 (x)) ≥ p2 (a1 (x))−p1 (a1 (x)) ≥ 0). Hence, Assumption 1 is satisfied for relatively large values of s and relatively small values of b. The firm may prefer the plan with probability function p2 (a), because it does not internalize the full social benefit from its plan choice. As will become clear below, this divergence of preferences over plan choice arises for relatively large values of b. In what follows, we restrict our analysis to parameter values satisfying Assumption 1 in order to ensure a potential divergence of interests between the firm and the regulator even if the first-best actions are implemented. The analysis can be easily carried out for parameter values that violate Assumption 1. We impose Assumption 1 to focus on the more interesting case where the preferences of the regulator and the firm are not perfectly aligned. It is straightforward to demonstrate that for all λ ∈ (0, 1), and all values of s satisfying Assumption 1, c2 (a2 (λs), λs) − c1 (a1 (λs), λs) > 0: expected accident costs that would be born by the firm under privately optimal actions are lower under plan 1 than plan 2. Of course, if it is plan 2 that has the private benefit, an unregulated firm will choose this plan over plan 1 if the private benefit is sufficiently large. More generally, cost differences for plans with probability functions p1 (a) and p2 (a) are ranked as follows when evaluated at privately and socially optimal action choices and at private and social costs: Lemma 1. For all λ ∈ (0, 1) and all values of s satisfying Assumption 1: b1 ≡ c2 (a2 (s), λs) − c1 (a1 (s), λs) < b2 ≡ c2 (a2 (λs), λs) − c1 (a1 (λs), λs) < b3 ≡ c2 (a2 (λs), s) − c1 (a1 (λs), s) < b4 ≡ c2 (a2 (s), s) − c1 (a1 (s), s).
Proof. All proofs are in the Appendix.
The plan with probability function p1 (a) results in a larger reduction in the expected private costs when evaluated at the privately optimal actions than at the socially optimal 10
actions (first inequality in the Lemma). In contrast, the reduction in expected social costs is larger at the socially optimal actions (last inequality in the Lemma). The second inequality states that when the privately optimal actions are chosen, probability function p1 (a) reduces expected social costs more than expected private costs. These relationships are of course due to the assumed complementarity between plan index and action choice. We can use Lemma 1 to define a set of mutually exclusive intervals for the private benefit that cover the full range of potential reductions in expected social and private costs: A ≡ [0, b1 ], B ≡ (b1 , b2 ], C ≡ (b2 , b3 ], D ≡ (b3 , b4 ). Under Assumption 1, the regulator always prefers the plan with probability function p1 (a) given that the socially optimal action will be chosen. However, preferences of the firm over different plans depend on which of these intervals contains the private benefit. Thus, b measures the degree of noncongruence of the firm’s and regulator’s preferences over plan choice. For future reference, we note that expected social welfare is maximized when the plan with probability function p1 (a) and action a1 (s) are chosen. The corresponding expression for ex ante expected social surplus is given by ρb − c1 (a1 (s), s).
The Unregulated Firm. The unregulated firm chooses a plan and an action that maximize its expected private payoff. Formally, conditional on the privately optimal action choice aj = aj (λs) for a plan with probability function pj (a) for each j = 1, 2, the firm selects the plan that yields the highest private payoff. First, note that the firm will choose the plan with probability function p1 (a) when that plan yields the private benefit. When the plan with probability function p2 (a) yields the private benefit, the firm will choose the plan with probability function p2 (a) when the private benefit is relatively large (c2 (a2 (λs), λs)−c1 (a1 (λs), λs) < b), while it will choose the plan with probability function p1 (a) otherwise (c2 (a2 (λs), λs) − c1 (a1 (λs), λs) ≥ b.) Ex ante expected social surplus in the absence of regulation then depends on the magnitude of b. For relatively small b (b ∈ A ∪ B), expected social surplus is given by ρb − c1 (a1 (λs), s), while for relatively large b (b ∈ C ∪ D), expected social surplus is given by b − [ρc1 (a1 (λs), s) + (1 − ρ)c2 (a2 (λs), s)] . 11
We now turn to description of various regulatory possibilities in this environment and assess regulatory performance in relation to no regulation and in relation to the first best. Regulatory Design. The firm has better information about the relative efficacy of alternative mitigation plans than does the regulator, and the firm chooses a private action. We consider three types of regulatory instruments that can be used to address these informational problems. The regulator does not know the probability functions for the treatment and the prevention plans and does not know which of these plans yields the private benefit. The regulator may wish to mandate the firm to use the treatment or the prevention plan when it believes such a choice would improve expected social welfare. When it does so, we say that the regulator uses a design standard. When the regulator chooses to specify and verify a particular a, we say that the regulator uses a process standard. Under such a standard, the firm chooses a plan. The regulator observes the plan, verifies its probability function, and specifies and verifies the socially efficient action. Thus, under a process standard, the firm is free to choose any of the two plans, but the regulator specifies and enforces the socially efficient level of effort contingent on this choice. We also assume the regulator is able to fully commit to its regulatory strategy. Upon observing the firm’s chosen plan, the regulator cannot force the firm to use instead the other plan.11 This characterization of a process standard captures situations where ex ante verification of the technology is essential, and where, for a given technology, ongoing production activities and regulatory compliance must be closely monitored.12 We model the use of a performance standard by supposing the regulator can specify a maximum probability of an adverse outcome for the firm. For example, the regulator might choose to specify that the firm achieve the level of performance (i.e., probability 11If
the regulator can commit to a regulatory design in which it promises to specify some arbitrarily bad action for all technologies proposed by the firm except for the one with a specific probability function, the best the firm can do is propose the plan with that probability function. Such a policy will generally not be renegotiation proof, and we therefore rule out this possibility. 12 For example, food safety regulation requires firms to develop a plan for controlling food-borne hazards, which is then submitted for regulatory review. Proposed plans (so-called “Hazard Analysis and Critical Control Point” plans) can be rejected or amended, but implementation of the actions specified in an approved plan (e.g., storage temperature or sanitary requirements) are monitored by regulators (MacDonald and Crutchfield, 1997; Food and Drug Adminstration, 2005). We discuss another example (regulation of pulp and paper firms) in more detail later. 12
of an adverse outcome) that occurs when the first-best technology and action are chosen. Because performance in our model is measured as the probability of an adverse outcome, satisfying the performance standard requires carrying out the same ex ante technology verification and on-going process monitoring needed to implement the process standard.13 Thus, a performance standard is at least as informationally demanding, and hence potentially more costly, than a process standard. Moreover, it is reasonable to imagine that verification costs increase with standard stringency, if for no other reason than that more testing has to be done to guarantee a lower accident probability. Accordingly, we assume there is a per-unit performance verification cost. Unlike process and design standards, performance standards address neither the action, a, nor the technology choice directly, but have an indirect influence on both. The regulation of toxic substances via risk or safety-first standards (e.g., pesticides, and drugs) are examples where the regulator imposes requirements that are expressed as probabilities of an adverse outcome (e.g., maximum cancer risk). In the next subsections we formally model each regulatory instrument and characterize equilibrium behavior by the firm and optimal instrument design by the regulator . Performance Standard. Under a performance standard, the regulator chooses a particular level of performance, p¯, and the firm is allowed to produce only after the regulator verifies that the firm meets the set level of performance. The regulator collects data to verify that the firm’s technology and action choices achieve p¯. The cost of verifying that the firm meets performance level p¯ is given by γ(1 − p¯), where γ < s. Thus, the cost of verification is large for relatively stringent performance standards (relatively low p¯). Upon verification of compliance, the regulator allows the firm to proceed with production. For a given p¯, the firm chooses a plan with some probability function pi (a) and action ai such that pi (ai ) = p¯.14 It follows directly from the assumptions imposed on functions p1 (·) and p2 (·) that a¯2 ≡ p−1 p) > a ¯1 ≡ p−1 p) . That is, to meet any performance 2 (¯ 1 (¯ standard p¯ the firm has to choose a higher action and, hence, incur a higher cost when 13
Even for “end-of-pipe” pollution, performance may be difficult to measure and the regulator may want to ensure performance by verifying process and design parameters. The pulp and paper example discussed below is one such case. 14 We assume throughout our analysis that the firm can do no better than to comply with the regulator’s announced p. 13
it chooses the plan with probability function p2 (·). The firm will choose the plan with probability function p1 (·) if it yields private benefit b. In spite of the higher cost of meeting a performance standard with the plan that has probability function p2 (·), the firm may choose such a plan if it yields a sufficiently large private benefit or if the performance standard is sufficiently lax (¯ p is sufficiently large). Formally, when the plan with probability function p2 (a) offers the private benefit, the firm will choose that plan if and only if (1)
a¯2 − a ¯1 = p−1 p) − p−1 p) < b. 2 (¯ 1 (¯
Let p¯t denote the unique solution to p−1 p) − p−1 p) = b. If performance standard p¯ 2 (¯ 1 (¯ t set by the regulator is strictly greater than p¯ , then the firm will choose the plan with probability function p2 (·) when it yields the private benefit. If performance standard p¯ set by the regulator is smaller than p¯t , then the firm will choose the plan with probability function p1 (·) regardless of which plan yields the private benefit.15 Thus, the expected social welfare for performance standard p¯ is given by ( V1 (¯ p) ≡ ρb − p¯s − p−1 p) − γ(1 − p¯), if p¯ ≤ p¯t 1 (¯ V (¯ p) = V2 (¯ p) ≡ b − p¯s − ρp−1 p) − (1 − ρ)p−1 p) − γ(1 − p¯), if p¯ > p¯t 1 (¯ 2 (¯ It is straightforward to verify that both functions V1 (¯ p) and V2 (¯ p) are concave in p¯.16 The analysis of the regulator’s problem is facilitated by comparing p¯t to the unique maximizers of functions V1 (¯ p) and V2 (¯ p), denoted by p¯∗1 and p¯∗2 , and implicitly given by 15To
verify this, differentiate the left-hand-side of (1) with respect to p¯ to obtain 1 1 1 [¯ p] 1 ∂p−1 p] ∂p−1 2 [¯ − ′ ≤ ′ − ′ ≤ 0, − 1 = ′ a2 ] p1 [¯ a1 ] a2 ] p1 [¯ a2 ] ∂ p¯ ∂ p¯ p2 [¯ p2 [¯
where the first inequality follows from convexity of p1 (a) while the second inequality follows from p′1 (a) ≤ p′2 (a). 16Note also that (2)
V1 (¯ p) ≥ V2 (¯ p) if and only if p−1 p) − p−1 p) ≥ b if and only if p¯ ≤ p¯t . 2 (¯ 1 (¯
Inequality p¯ ≤ p¯t is an incentive compatibility constraint which characterizes performance standards that induce the firm to always choose the plan with probability function p1 (·). The relationships in (2) tell us that for any given performance standard, the regulator’s preferences regarding the plan and action choice are perfectly aligned with the preferences of the firm. When the regulator sets a relatively stringent performance standard (¯ p ≤ p¯t ), both the regulator and the firm ex post prefer the plan with probability function p1 (·), even if the latter does not yield the private benefit. Otherwise (¯ p > p¯t ), both the regulator and the firm ex post prefer the plan with probability function p2 (·) so long as it yields the private benefit. 14
(3) (4)
(s − γ) p′1 p−1 p∗1 ) = −1 and 1 (¯ 1−ρ ρ −1 ∗ + ′ −1 ∗ = − (s − γ) . ′ p1 p1 (¯ p2 ) p2 p2 (¯ p2 )
Trivially, p¯∗1 < p¯∗2 . The form of the regulator’s objective function V (¯ p) and the solution to t ∗ the regulator’s problem depends on the relationship between p¯ , p¯1 and p¯∗2 . The top panel of figure 1 depicts V (¯ p) for the parameter values such that p¯t < p¯∗1 . In this case, it follows from the definitions of p¯t , p¯∗1 and p¯∗2 that V1 (¯ p∗1 ) < V2 (¯ p∗2 ). The middle panel depicts V (¯ p) ∗ t ∗ for the parameter values such that p¯1 ≤ p¯ ≤ p¯2 . Note that although we have depicted the case where V1 (¯ p∗1 ) > V2 (¯ p∗2 ) there are parameter values for which the reverse inequality holds. The bottom panel corresponds to the case p¯∗2 < p¯t . Here, it follows from the definitions of p¯t , p¯∗1 , and p¯∗2 , that V1 (¯ p∗1 ) > V2 (¯ p∗2 ). Inspection of each panel in the figure, together with expressions for p¯t , p¯∗1 , and p¯∗2 , facilitates the determination of the optimal performance standard and its relationship to the parameters of the model. We start our analysis of performance standards with the case where verification is not costly: Proposition 1. Suppose verification is not costly: γ = 0. Then an optimal performance standard induces first-best behavior. The regulator sets the performance standard equal to the first-best level of performance given by p1 (a1 (s)), and the firm always chooses the plan with probability function p1 (·) and action a ¯1 = a1 (s). Thus, when it is not costly to verify that the firm meets the set standard, a performance standard weakly dominates the other two forms of standard (and strictly dominates a design standard), and unambiguously improves welfare, relative to no regulation. By requiring the firm to achieve the first-best performance, the best the firm can do is to choose the first-best plan and action. Intuitively, since the plan with probability function p1 (a) is first best, implementing the action required to achieve p1 (a1 (s)) under any plan other than the plan with probability function p1 (a) is excessively costly for the firm. Now we turn to the more interesting case where γ > 0. The regulator cannot achieve the first-best outcome in this case. It is also straightforward to verify that when γ is sufficiently large the regulator prefers no regulation to an optimally chosen performance standard. Thus, we focus on the more interesting scenarios where it is optimal for the 15
pt < p∗1
V2 (p2 )
V1 (p1 )
pt
p∗1
p∗2
p
p∗1 < pt < p∗2
V1 (p1 ) V2 (p2 )
pt
p∗1
V1 (p1 )
p∗2
p
pt > p∗2
V2 (p2 )
p∗1
p∗2
pt
p
F IGURE 1. Determination of optimal performance standard.
16
regulator to use a performance standard. Let ˆb denote the solution to V1 (¯ p∗1 ) = V2 (¯ p∗2 ). Solving this equation we obtain ∗ 1 ˆb ≡ (¯ p2 − p¯∗1 ) (s − γ) + ρp−1 p∗2 ) + (1 − ρ)p−1 p∗2 ) − p−1 p∗1 ) . 1 (¯ 2 (¯ 1 (¯ (1 − ρ)
Since V1 (¯ p∗1 ) > V2 (¯ p∗2 ) for b < ˆb, the regulator will set the performance standard at p¯∗1 while the firm will always choose the plan with probability function p1 (·) and action p−1 p∗1 ) when b < ˆb. When b > ˆb the regulator will set the performance standard at 1 (¯ p¯∗2 while the firm will choose the plan with the private benefit. When the plan with probability function p1 (·) yields the private benefit, the firm will choose action p−1 p∗2 ) 1 (¯ while when the plan with probability function p2 (·) yields the private benefit, the firm will choose action p−1 p∗2 ). 2 (¯ It also follows immediately from the definition of V (·) and the above derivations that there exist threshold values sˆ and γˆ such that for all s ≥ sˆ and γ ≤ γˆ , the regulator sets the performance standard equal to p¯∗1 given by (3); the firm always chooses the plan with probability function p1 (·) and action p−1 p∗1 ). That is, when the cost of performance is 1 (¯ sufficiently low, or when the cost of an adverse outcome is sufficiently high, it is optimal to induce the first-best plan choice. Finally, we turn to the characterization of situations when the optimally chosen performance standard dominates the unregulated outcome. It follows immediately from Proposition 1 and the form of the expected social welfare under a performance standard that: Proposition 2. There exist threshold values sˆ and γˆ such that for all s ≥ sˆ and γ ≤ γˆ , the optimally chosen performance standard strictly improves social welfare over the unregulated outcome. Process Standard. With a process standard, the firm is free to choose any of the two plans, but the regulator learns the probability function of the chosen plan and enforces the socially optimal action for that probability function.17 The firm will choose the
17An
ability to enforce this action might also be interpreted as “monitoring,” rather than a “process standard.” What we are modeling in this section has characteristics of both a standard and a monitoring activity. The regulator enforces a specified level of a (standard), and ensures that this level is implemented (monitoring). In any case, for expositional simplicity we refer to this regulatory instrument as a “process standard.” 17
plan with probability function p1 (a) when that plan yields the private benefit, or when c2 (a2 (s), λs)−c1 (a1 (s), λs) ≥ b. The firm will choose the plan with probability function p2 (a) whenever it yields the private benefit and c2 (a2 (s), λs) − c1 (a1 (s), λs) < b. As in the unregulated regime, expected social surplus depends on the magnitude of b. If the plan with probability function p2 (a) has the private benefit, and if b is sufficiently large, then the firm will select this plan. Formally, for relatively large b (b ∈ B ∪ C ∪ D), expected social surplus is given by b − [ρc1 (a1 (s), s) + (1 − ρ)c2 (a2 (s), s)] .
(5)
For relatively small b (b ∈ A), the firm always choose the plan with probability function p1 (a) and expected social surplus is given by ρb − c1 (a1 (s), s).
(6)
Comparison of expected social surplus under a process standard, under no regulation, and under the first-best yields: Proposition 3. (i) If b ∈ A, the optimally chosen process standard achieves the first-best; (ii) If b ∈ B, the optimally chosen process standard strictly improves social welfare if and only if the probability (1 − ρ) that the plan with probability function p2 (a) yields the private benefit is sufficiently small: 1−ρ
(1 − 2r) b.
Proposition 4. Let β ≡ b/(2 [c2 (a2 (λs), s) − c1 (a1 (λs), s)]) ≥ 0. Then, (i) If b ∈ A ∪ B ∪ D or b ∈ C and q ∈ 21 − β, 21 + β , then any design standard strictly reduces expected social welfare; (ii) If b ∈ C and q ∈ 0, 12 − β ∪ 21 + β, 1 , then an optimally chosen design standard strictly improves expected social welfare compared to the unregulated outcome. The optimal choice of plan is (a) “prevention” when q ∈ 0, 21 − β and (b) “treatment” when q ∈ 12 + β, 1 .
First note that a design standard never achieves the first best. Given the regulator’s imperfect information regarding production possibilities, it will specify the “wrong” plan with strictly positive probability. Also, for relatively small b (b ∈ A∪B), the unregulated firm always chooses the plan with probability function p1 (a). A design standard can never improve welfare in this case. 19
For relatively large b (b ∈ D), the firm always chooses the plan with the private benefit. Given that the firm is choosing the privately optimal action, and because b is large, the plan with the private benefit is socially optimal. In this case, the design standard interferes with what would otherwise be a second best plan choice (the firm’s action is not at its first best level). For intermediate values of b (b ∈ C), Lemma 1 implies that the plan with probability function p1 (a) is socially efficient given the firm’s privately optimal action. In contrast, the firm always prefers the plan with the private benefit. When the regulator is relatively well informed about the identity of the plan with probability function p1 (a) (i.e, q is sufficiently different from 1/2), the design standard improves welfare. Standards Comparison. Up to this point we have considered the optimal design of three different regulatory instruments, where each is used in isolation. In this section we consider pairwise comparisons across these three instruments, and briefly discuss the possibility of combining multiple instruments in a single regulatory regime. Using Propositions 4 and 5 we obtain the following corollary: Corollary 1. (i) If b ∈ A ∪ D, the optimally chosen process standard dominates the optimally chosen design standard; (ii) If b ∈ B and c1 (a1 (λs), s) − c1 (a1 (s), s) > 1 − ρ, c2 (a2 (s), s) − c1 (a1 (s), s) − b
the optimally chosen process standard dominates the optimally chosen design standard; (iii) If b ∈ B and c1 (a1 (λs), s) − c1 (a1 (s), s) ≤ 1 − ρ, c2 (a2 (s), s) − c1 (a1 (s), s) − b
both the optimally chosen process and the optimally chosen design standards decrease expected social welfare; (iv) If b ∈ C and q ∈ 21 − β, 21 + β , the optimally chosen process standard dominates the optimally chosen design standard; 20
(v) If b ∈ C and q ∈ 0, 12 − β ∪ 12 + β, 1 , both optimally chosen standards improve expected social welfare; (a) When q ∈ 21 + θ; 1 , the optimally chosen design standard dominates the optimally chosen process standard if and only if [ρc1 (a1 (s), s) + (1 − ρ)c2 (a2 (s), s)]−[qc1 (a1 (λs), s) + (1 − q)c2 (a2 (λs), s)] > (1−r)b. (b) When q ∈ 0; 21 − θ , the optimally chosen design standard dominates the optimally chosen process standard if and only if [ρc1 (a1 (s), s) + (1 − ρ)c2 (a2 (s), s)] − [(1 − q)c1 (a1 (λs), s) + qc2 (a2 (λs), s)] > rb. When b is relatively small or relatively large, the process standard unambiguously dominates a design standard. The process standard increases expected welfare in these cases, while the design standard reduces expected welfare. For b ∈ B, the design standard decreases expected welfare. The process standard increases expected welfare only when the likelihood that the plan with probability function p1 (a) has the private benefit is sufficiently large. For b ∈ C, the process standard dominates the design standard when the regulator is relatively uninformed. When the regulator is relatively well informed, both standards improve expected welfare, but neither achieves the first best. Intuitively, the process standard will tend to result in a larger gain in expected welfare when specifying the ex post efficient action is relatively important. In comparing performance and process standards, first note that when b ∈ A, an optimally chosen process standard achieves the first best and, hence, dominates an optimally chosen performance standard if γ > 0. For b sufficiently large the optimally chosen process standard also dominates. The firm chooses the plan with the private benefit under both standards, but uses the efficient action choice (contingent on the chosen plan) under the process standard. More formally, we have Proposition 5. If b > ˆb, the regulator (weakly) prefers the optimally chosen process standard to the optimally chosen performance standard. For intermediate values of b it is difficult to compare performance and process standards without imposing additional restrictions on the probability functions. The regulator cannot be sure which plan the firm will choose in response to either standard. For a given 21
plan choice, the performance standard has two sources of inefficiency relative to the process standard: there is a cost γ that must be incurred to verify that the chosen plan and action meet the standard, and there is an action distortion relative to the action that is first-best for the given plan choice. However, it can be the case that the firm chooses the plan with probability function p1 (a) under the performance standard, and the plan with probability function p2 (a) under the process standard. Comparing performance and design standards, we know that for sufficiently low b, a design standard reduces expected welfare relative to an unregulated outcome. In contrast, a performance standard improves expected welfare for sufficiently low b. Thus a performance standard dominates a design standard when preferences of the regulator and the firm regarding plan choice are sufficiently congruent. As we will see in the Application and Discussion section below, actual policy can involve the combined use of all three instruments. In the context of our model there is scope for improving expected welfare by using multiple standards. For example, combining a design standard with a process standard will always improve welfare, relative to a design standard alone. Similarly, this combination can improve on a process standard alone if the process standard does not achieve the first best, and if the regulator is relatively well informed. Also, our model suggests that it is always better to couple a design standard with a process standard, rather than with a performance standard. The design standard fixes a given technology, and the process standard ensures that the technology is used efficiently; a performance standard adds cost and does not guarantee an efficient action choice. Illustrative Example. In this section we elaborate on the simple analytical example referenced earlier to further clarify the structure of our model and to demonstrate its √ results. Let pi (a) = 1 − µi a for i = 1, 2, where µ1 > µ2 > 0. It is straightforward to verify that these probability functions satisfy all of the assumptions imposed in the model with the exception of non-negativity of the probability functions for all action choices. To accommodate this characteristic of the chosen functional form we restrict our focus to parameter values for which both p1 (a) and p2 (a) are non-negative at the 2 optimal solutions. It is straightforward to verify that ai (x) = (µi4x) . Direct calculation (λ−0.5)(µ21 −µ22 )s2 λ2 (µ21 −µ22 )s2 λ(2−λ)(µ21 −µ22 )s2 (µ21 −µ22 )s2 also yields b1 = ; b = ; b = ; b = . 2 3 4 2 4 4 4 22
TABLE 2. Values for δi , θi and bc in equation (10) under each regulatory regime. Parameter No regulation δ1 ρ δ2 1 λsµ21 (2−λ) θ1 4 λs2 c1 (2−λ) θ2 4 λ2 s2 (µ21 −µ22 ) bc 4
Process ρ 1
Standard Performance ρ 1
µ21 s2 4 c1 s2 4 s2 (λ−0.5)(µ21 −µ22 ) 2
µ21 (s−γ)2 4 µ21 µ22 (s−γ)2 4c2 µ21 (µ21 −µ22 )(s−γ)2 4c2
Design r 1−r
λsc3 (2−λ) 4 λs2 c3 (2−λ) 4 λs2 (q−0.5)(2−λ)(µ21 −µ22 ) 4(0.5−r)
For each regulatory regime (including no regulation), expected social welfare takes the general form δ b − s + θ if b < bc 1 1 V = (10) δ2 b − s + θ2 otherwise,
where parameters δi , θi , and bc vary across regulatory regimes. To simplify presentation, let c1 ≡ ρµ21 + (1 − ρ)µ22 , c2 ≡ ρµ22 + (1 − ρ)µ21 , and c3 ≡ qµ21 + (1 − q)µ22 . Table 2 displays the values of δi , θi , and bc under each regulatory regime for this specification of our model. Derivation of parameter values under the performance standard are in the appendix. All other derivations are tedious, but straightforward. With the expressions in this table, it is straightforward to construct numerical examples where any given regulatory regime maximizes expected total welfare. We illustrate one set of examples in Figure 2. The left panel of Figure 2 depicts expected surplus under optimally chosen standards as a function of µ1 . Note that the relative attractiveness to the firm of the plan with probability function p1 (a) increases with µ1 . An optimally chosen process standard achieves the highest expected surplus when the plan with probability function p1 (a) is relatively unattractive to the firm (µ1 sufficiently small). This is because when µ1 is relatively small the benefits from an optimal action choice are relatively more important to the regulator than the gains from an optimal plan choice (the plan with probability function p1 (a)). As µ1 increases, expected surplus rises under the optimally chosen performance standard, and eventually exceeds expected surplus under the optimally chosen process standard. Numerically, because λ − 0.5 < 0 for this specification, b is less than bc under the process standard for all values of µ1 . Under the performance 23
-1.3
unregulated process performance design
-1.60
expected surplus
-1.4 -1.65 -1.5
-1.70 -1.6
-1.75
-1.7
-1.8 0.5
-1.80 0.7
µ1
0.9
0.1
0.5
0.9
λ
F IGURE 2. Comparison of expected surplus across each standard as functions of the parameters µ1 and λ. In both panels,γ = .2 and µ2 = .3. In the left panel, r = .2, q = .4, s = 2, b = .15, and λ = .1. In the right panel, r = .1, q = .9, s = 2.2, b = .3, and µ1 = .6. standard, bc = 0.32 > b = .2. Therefore, when calculating expected surplus, θ2 is the operative parameter under a process standard, while θ1 is the operative parameter under a performance standard. The right panel demonstrates how the design standard can be optimal when the regulator is sufficiently well informed. Here, we have depicted the expected social welfare under the optimally chosen standards as a function of the fraction λ of the social cost internalized by the firm. Expected social welfare is constant under the process and performance standards because in both cases the firm is being induced to choose the first-best action, which is independent of λ. In accord with Proposition 4 and Corollary 1, the optimally chosen design standard dominates the unregulated outcome and the other two optimally chosen standards for intermediate values of λ. A PPLICATION
AND
D ISCUSSION
Regulating environmental risk is a complex task. Although our model is a stylized representation of this task, it rationalizes features of regulatory institutions that, though 24
often observed, are largely ignored in existing regulatory design models. In this section, we illustrate the features we have in mind with a specific example—air pollution control of pulp and paper manufacturing firms.18 We begin by describing the relevant production and regulatory environment, and then discuss the relationship between observed features of this setting and our regulatory design model. Air Pollution Control in Pulp and Paper Manufacturing. A typical pulp and paper manufacturing plant is a classic “point source” of pollution.19 There are a little over 500 such plants in the United States, and roughly 200 of these produce only paper (these latter generate far less pollution than pulp, or integrated pulp and paper, manufacturing firms). According to the Environmental Protection Agency’s (EPA) toxic release inventory, the pulp and paper sector as a whole accounts for nearly 10 percent of all toxic releases to air, 7 percent to water, and slightly less than 0.5 percent to land.20 The sector is also a major contributor of ambient air pollutants classified by the EPA as “criteria pollutants” (e.g. sulfur and nitrous oxides, and particulates). There are three main potential sources of toxic air emissions from pulping plants: pulping system vents, pulping process “condensates,” and bleaching system vents. Pulping process condensates refers to the liquid condensation of toxic chemicals that volatilize during transport from the processing to treatment facilities. Within each of these emissions sources there are multiple emission points (e.g., digestor system, turpentine recovery system, evaporator system), and the relevant emissions standard (described below) applies individually to each of these points. In addition, most pulping plants generate energy from waste and hazardous materials incineration. The boilers used to generate 18
The example is in no way exceptional; we refer the interested reader to the Environmental Protection Agency’s Sector Notebook series at http://www.epa.gov/compliance/resources/publications/assistance/sectors/notebooks (last accessed, May 16, 2006), which contains detailed descriptions of the relevant production processes, pollution control possibilities, and regulatory designs, for over 30 major industrial sectors. 19 Much of the information in this section comes from the U.S. Environmental Protection Agency (1998) and the U.S. Environmental Protection Agency (2002). Our discussion is a highly abridged version of these documents (parts of which are themselves abridged versions of Smook (1992)), and for brevity focuses strictly on the “kraft” pulping technology. We do not discuss pollution or regulatory control of other types of pulping facilities, or of the paper-making process that occurs subsequent to pulping. 20 For the pulp and paper industry in particular, these include over 30 toxic substances (counting only those that are emitted by at least 10 of the nearly 200 distinct plants that report toxic emissions) emitted through all transport media (air, water, and land). 25
this energy are the main source of criteria pollutant and total reduced sulfur emissions from pulp manufacturing. Under the Clean Air Act, the EPA distinguishes between criteria air pollutants, which are subject to the National Ambient Air Quality Standards (NAAQS), and hazardous air pollutants, which are subject to the National Emissions Standards for Hazardous Air Pollutants (NESHAP). Many of the steps taken by a firm to reduce hazardous air pollutants simultaneously reduce criteria pollutants, although attainment of one standard does not imply attainment of the other. Each state must meet a set of federally mandated ambient air quality “attainment criteria” under NAAQS, with the means of aggregate attainment left to the discretion of state regulators. There are, however, process-specific operational standards (“New Source Performance Standards”) that serve as minimum requirements in state implementation plans. Under NESHAP, firms are subject to a set of maximum achievable control technology (MACT) “standards” that effectively apply a maximum allowable emissions criteria uniformly across all plants and regions. For illustrative purposes, we briefly summarize the practical implementation of one of these standards (MACT applied to a particular emission point). Detailed explanations for the standards implemented at other emissions points under NESHAP can be found in U.S. Environmental Protection Agency (1998). Further description of the standards implemented under NAAQS can be found in U.S. Environmental Protection Agency (2002) and Becker and Henderson (2000). Although MACT does impose a uniform standard on all firms, there is considerable flexibility in how firms are allowed to meet the relevant standard, and even in how the standard is defined. For emissions within the pulping system vents source, firms can: use a particular technology (“boiler, lime kiln, or recovery furnace”), use a different technology if continuously monitored with periodic reports of process parameters (“thermal oxidizer operated at a minimum temperature of 1,600o F and minimum residence time of 0.75 seconds”), or demonstrate a specific performance, measured as a percentage reduction in a proxy for hazardous air pollutants (“methanol emissions can be used as a surrogate measure of total emissions”). In each case the firm must perform monthly inspection to ensure that the relevant system is functioning properly, and maintain records of these inspections. When the firm opts for performance measurement, it must also run an initial performance test to ensure that the relevant control device (chosen by the firm) 26
complies with the emission limit, and establish the operating parameters that must be monitored to ensure continuous compliance. Similar options are available for controlling emissions from the two other sources (pulping process “condensates,” and bleaching system vents). Discussion. This description reveals features of standards that are rarely discussed in economic analyses of environmental regulatory design, but that seem important in practice. First, although the set of standards in question are nominally referred to as “uniform technology standards,” in reality they allow firms considerable flexibility in specifying a mitigation plan. The overarching MACT standard is really more of a generic policy than a set of specific technology standards. The EPA interprets and tailors the objectives embedded in this policy for each specific industry it regulates. For regulation of air pollution stemming from pulp and paper manufacturing, this has resulted in a set of compliance options from which firms can choose. Firms can adopt a specific technology, adopt some other technology and provide detailed performance information, or verify a specific performance. While our model does not capture the selection feature of this policy design, it does demonstrate the potential role for each option individually. Second, to implement this regulatory strategy the EPA must expend considerable effort in learning about the relevant technological possibilities for pollution control and in verifying that a given mitigation plan, if it is not a standard design, meets the relevant performance criteria.21 Firms are required to maintain detailed records of their pollution control activities, and to make these records accessible to the EPA. These activities are consistent with the informational transmission component of our model. Firm managers are in a much better position than regulators to identify potential pollution control options. If continuous monitoring of emissions and a system of pollution charges are infeasible, designing efficient “command-and-control” measures requires access to this information. The information reporting and process verification activities described above represent precisely this kind of information transmission. 21Becker
and Henderson (2000, pp. 382-383) have an especially illuminating discussion on this point where they note that the practical implementation of standards typically involves extended negotiations between plant officials and state and federal regulators. For a large pollution source, these negotiations “make extensive use of plant engineers and outside consultants and can involve almost weekly meetings over, say, a two-year period.” 27
Contrary to the characterization of standards as uniform and inefficient restrictions on firms, the standards described here seem like carefully thought attempts to manage a difficult problem. Our model, which provides a rationale for ex ante verification and process monitoring activities, is consistent with this conclusion. A market (or some other incentive) instrument can no doubt be an efficient tool for controlling pollution. Economists have often blamed the apparent unpopularity of such tools on an unfounded disbelief among the public at large in their potential efficacy; and there is probably some merit to this complaint. However, the local nature of many pollutants,22 the difficulty in defining a comprehensive and easily monitored set of performance measures, the limited liability of firms, and so on, also seem like good places to lay the blame.23 Absent an incentive instrument of some sort, standards are a necessary tool. Our analysis, which is based on a plausible pair of informational frictions between the firm and the regulator, is consistent with prominent features of standards that are actually employed. Still, there remain obvious inefficiencies in the way some standards are set and implemented. For example, Cropper et al. (1992) document significant variation in the implicit value assigned to a statistical life in granting pesticide registrations. Similarly, Hamilton and Viscusi (1999) note how the EPA uses inconsistent and apparently politically motivated risk criteria in setting priorities for toxic waste site cleanup. Thus, although economists are perhaps best known for designing markets, there are ample opportunities to also provide analysis regarding efficient design of nonmarket instruments as in Lichtenberg and Zilberman (1988), or to offer suggestions for innovative hybrid approaches of the kind studied in Montero (2005). C ONCLUSION We study efficient regulatory design of a firm that has better information than the regulator regarding technological possibilities for controlling risk, and where some aspects of the firm’s implementation of a given technology are potentially unobservable. If effectively unlimited penalties can be imposed on regulated firms, the first-best action and 22
The most significant source of efficiency gain from market instruments come from cross-firm trades in the context of ambient pollutant control. 23 McDonald’s and other franchise firms impose strict process and design standards on their franchisees partially in an attempt to ensure name-brand integrity. Perhaps it is not surprising for the EPA to do the same in an effort to ensure the health and safety of U.S. citizens! 28
technology can be implemented. Otherwise, design, performance, and process standards can potentially improve expected social welfare, relative to no regulation. In relation to previous literature on environmental regulatory design, we emphasize information transmission from firms to the regulator, process verification, and monitoring. A process standard requires monitoring the day-to-day activities of firms; this monitoring has an indirect effect on a regulated firm’s ex ante choice of mitigation technology. If this indirect effect is positive in the sense that the firm’s chosen technology under a process standard is superior to the technology that would be chosen in the absence of regulation, then a process standard can potentially achieve the first-best outcome. Under a design standard, the regulator directly specifies the firm’s technology, and the firm chooses its preferred action contingent on this technology. Of course, whether such a standard is beneficial will depend in large part on the quality of the regulator’s information regarding the set of appropriate mitigation strategies. However, taking the quality of this information as given, a design standard potentially increases expected welfare only when preferences regarding technology choice are sufficiently noncongruent between the firm and the regulator. A performance standard simultaneously addresses technology and action choices by providing the regulated firm with a specific performance criteria to meet. However, a performance standard requires costly performance measurement, and this generally limits possibilities for achieving a first-best outcome. When measurement costs increase with the level of standard stringency, and when the optimal performance standard is highly restrictive (e.g., because accident damages are relatively large), optimally chosen design and process standards can dominate an optimally chosen performance standard. Although not part of our formal analysis, there is reason to expect the cost of administering a design standard (which only requires observation of the relevant technology) to be low in comparison with a process standard (which requires observation of the technology, knowledge of how it is implemented, and periodic compliance monitoring). Thus, even when a process standard dominates a design standard in our model, differential enforcement and compliance costs may play an important role in instrument choice (see Heyes (2000) for a recent survey of the topic). We describe a particular (though we believe representative) example of regulatory design that shares some of the qualitative features of our model. When regulating pulp and 29
paper manufacturers, the EPA expends considerable resources to observe and verify mitigation plans that are proposed by firms, subject to meeting a given set of performance criteria. Firms are also asked to monitor their pollution control processes and to periodically report to the EPA. Absent access to monetary incentives, this sort of verification and monitoring activity is precisely what one would expect from a regulator attempting to efficiently control the pollution of firms who have private information about their production environment, and who do not face the full social cost of their activities.
30
A PPENDIX Proof of Lemma 1. The first inequality in (1) holds if and only if ∆(λ) ≡ [c2 (a2 (λs), λs) − c1 (a1 (λs), λs)] − [c2 (a2 (s), λs) − c1 (a1 (s), λs)] > 0. Differentiating ∆(·) twice with respect to λ and using the first-order conditions for action choice we obtain: s ∆′′ (λ) = [a′1 (λs) − a′2 (λs)] > 0. λ Thus, ∆(·) is a strictly convex function. Moreover, ∆(0) = a1 (s) − a2 (s) > 0, ∆(1) = 0 and ∆′ (1) = 0. Hence, ∆(λ) > 0 for all λ ∈ (0, 1). The second inequality in (1) holds if and only if λ [p2 (a2 (λs)) − p1 (a1 (λs))] < p2 (a2 (λs)) − p1 (a1 (λs)), which holds since λ ∈ (0, 1) and p2 (a2 (λs)) > p1 (a1 (λs)). The last inequality in (1) holds if and only if Ψ(λ) ≡ [c2 (a2 (s), s) − c1 (a1 (s), s)] − [c2 (a2 (λs), s) − c1 (a1 (λs), s)] > 0. Differentiating Ψ(·) with respect to λ and using the first-order conditions for action choice we obtain: s Ψ′ (λ) = [a′2 (λs) − a′1 (λs)] < 0. λ Since Ψ(0) = [c2 (a2 (s), s) − c1 (a1 (s), s)] > 0, Ψ(1) = 0 and Ψ(·) is strictly monotonic, Ψ(λ) > 0 for all λ ∈ (0, 1). Proof of Proposition 1. When γ = 0, p¯∗1 = p1 (a1 (s)) while p¯∗2 is given by p′1
1−ρ ρ −1 ∗ + ′ −1 ∗ = s. p1 (¯ p2 ) p2 p2 (¯ p2 )
31
We have that V1 (¯ p∗1 ) ≡ −c1 (a1 (s), s) + (ρ) b = −ρ [c1 (a1 (s), s) − b] − (1 − ρ)c1 (a1 (s), s) ∗ ≥ −ρ [c1 (a1 (s), s) − b] − (1 − ρ) p¯∗2 s + p−1 (¯ p ) − b 2 2 −1 ∗ −1 ∗ ≥ −ρ p1 p1 (¯ p2 ) s + p1 (¯ p2 ) − b − (1 − ρ) p¯∗2 s + p−1 p∗2 ) − b 2 (¯ = −ρ p¯∗2 s + p−1 p∗2 ) − b − (1 − ρ) p¯∗2 s + p−1 p∗2 ) − b 1 (¯ 2 (¯ = V2 (¯ p∗2 ),
where the first inequality follows from Assumption 1 and p¯∗2 s + p−1 p∗2 ) ≥ c2 (a2 (s), s) 2 (¯ while the second inequality follows from the definition of a1 (s). It follows directly from inspection of function V (¯ p) that p¯t ≥ p¯∗1 = p1 (a1 (s)). Thus, the regulator can achieve the first-best by setting performance standard equal to p1 (a1 (s)). The firm chooses plan with probability function p1 (·) even if it does not yield the private benefit. Proof of Proposition 4. We start with the case b ∈ A ∪ B. In this case, the unregulated firm always chooses the plan with probability function p1 (a), and the expected social surplus under the unregulated outcome is given by (11)
ρb − c1 (a1 (λs), s).
To determine optimality of using a design standard, we need to compare (11) to (7) when (9) holds and to (8) when the converse of inequality (9) holds. Under (9), the unregulated outcome strictly dominates the “treatment” plan if and only if [c2 (a2 (λs), s) − c1 (a1 (λs), s)] + (1 − 2r)b > 0. This inequality holds for all parameter values satisfying Assumption 1 since b ∈ A ∪ B implies that [c2 (a2 (λs), s) − c1 (a1 (λs), s)] > b. Similarly, one can show that the unregulated outcome dominates the “prevention” plan under the converse of (9). Now consider b ∈ C ∪ D. In this case, the unregulated firm chooses the plan with the private benefit. Again, there are two possibilities to explore; one where (9) holds and the converse case. In the former case, by comparing (7) to the expected social surplus in the
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absence of regulation we obtain that the “treatment” plan strictly dominates the unregulated outcome if and only if q > 21 + θ. Similarly, when the converse of (7) holds, the “prevention” plan strictly dominates the unregulated outcome if and only if q < 12 − θ. b ≤ 12 if and The rest of the proposition follows by noting that θ = 2[c2 (a2 (λs),s)−c 1 (a1 (λs),s)] only if b ∈ A ∪ B ∪ C. Proof of Proposition 5: In what follows we suppose without loss of generality that either form of regulation (performance or process standard) is preferred to no regulation. If b ∈ A, an optimally chosen process achieves the first best and, hence, dominates an optimally chosen performance standard. Thus, it is left to verify that this result holds for b ∈ B ∪ C ∪ D. In this case, the expected social surplus under an optimally chosen process standard is equal to F ≡ b − [ρc1 (a1 (s), s) + (1 − ρ)c2 (a2 (s), s)] . When b > ˆb, the expected social welfare under an optimally chosen performance standard is equal to V2 (¯ p∗2 ) ≡ b − ρc1 p−1 p∗2 ), s + (1 − ρ)c2 p−1 p∗2 ), s − γ(1 − p¯∗2 ). 1 (¯ 2 (¯ By definition of a1 (s) and a2 (s), c1 (a1 (s), s) ≤ c1 p−1 p∗2 ), s and c2 (a2 (s), s) ≤ 1 (¯ ∗ c2 p−1 ), s . Hence, V2 (¯ p∗2 ) ≤ F. (¯ p 2 2 Derivation of values for δi , θi , and bc under a performance standard:
2 2 1−¯ p 1−¯ p t We have that a ¯i ≡ p−1 [¯ p ] = − . Let p ¯ denote the unique solution to i µi µ2 2 √ µ1 µ2 b 1−¯ p = b. Solving, we obtain p¯t = √ . Expected social welfare for the perfor2 2 µ1 µ1 −µ2
mance standard p¯ is given by √ 2 µ1 µ2 b 1−¯ p √ V1 (¯ if p ¯ ≤ , p) ≡ ρb − γ − (s − γ)¯ p − µ1 µ21 −µ22 √ h i V (¯ p) = µ1 µ2 b 2 V2 (¯ √ if p ¯ > p) ≡ b − γ − (s − γ)¯ p − ρ2 + (1−ρ) (1 − p ¯ ) , 2 2 2 µ1
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µ2
µ1 −µ2
Solving for p¯∗1 and p¯∗2 we obtain µ21 (s − γ) 2 2 2 µ1 µ2 (s − γ) . p¯∗2 = 1 − 2 [ρµ22 + (1 − ρ)µ21 ] p¯∗1 = 1 −
Substituting for p¯∗1 and p¯∗2 into the expression for ˆb we obtain bc =
µ21 (µ21 − µ22 ) (s − γ)2 . 4 [ρµ22 + (1 − ρ)µ21 ]
Substituting into the expression for expected social welfare we obtain the values in Table 2.
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