Self-policing in a targeted enforcement regime

Southern Economic Journal, April, 2008 by Sarah L. Stafford

With respect to deliberate violations, the facility has two possible choices, to abate or to pollute. With respect to the probabilistic violations, the facility must make three decisions: (i) whether to audit; (ii) whether to remediate a violation is one if discovered; and (iii) whether to disclose a violation. (20) If a facility decides not to audit, it has no more decisions to make. If it does audit, it can choose to remediate but conceal the violation, remediate and disclose the violation, or to not remediate and not disclose. This is consistent with EPA's Audit Policy, as remediation is required as a part of disclosure. However, auditing without remediation or disclosure is dominated by not auditing because the facility saves the cost of auditing with no change in the probability of detection. Thus, there are three viable actions with respect to probabilistic violations: no audit; audit--remediate--conceal; or audit--remediate--disclose. (21)

Combining these actions with the actions for deliberate violations yields six possible strategy combinations:

i. Abate/no audit

ii. Pollute/no audit

iii. Abate/conceal

iv. Pollute/conceal

v. Abate/disclose

vi. Pollute/disclose

Given these strategies, one can write down the expected cost of each strategy based on whether the facility is in [G.sub.1] or [G.sub.2]. For example, a facility that undertakes a strategy of abating but not auditing (strategy 1) if it is in [G.sub.1] will have the following expected cost:

c p[[pi](F [delta][beta]) (1 - [pi]) [delta][alpha]] (1 -p) [delta][alpha] = c p[pi]F p[pi][delta][beta] (1 - p[pi])[delta][alpha],

where [alpha] is the expected present value of being in [G.sub.1] given the strategy being considered and [beta] is the expected present value of being in [G.sub.2] given the strategy being considered. Under this strategy, the facility pays c to abate. Additionally, because it does not audit, with probability p[pi] the facility is inspected and found to be in violation, fined F, and put into [G.sub.2] for the following period; with probability p(1 - [pi]) it is in violation but not inspected and thus stays in [G.sub.1]; and with probability (1 - p), there is no violation, so it also stays in [G.sub.1] regardless of whether it is inspected. Using the same logic, one can develop the expected cost of each strategy for each initial starting point as shown in Table 3. The facility then has 36 possible policies denoted by [f.sub.ij], where i describes the strategy taken in [G.sub.1] and j describes the strategy taken in [G.sub.2]. To evaluate the expected cost of each policy, one solves the system of equations formed by taking the expected cost of strategy i using [G.sub.1] as a starting point and the expected cost of strategy j using [G.sub.2] as a starting point. (22)

Some of the expected cost functions are very straightforward. For example, a facility that chooses a policy of abatement and disclosure in both groups ([f.sub.55]) is always in full compliance and has an expected present value cost of