The static model of compliance, shows that firms choose whether or not to comply based on whether the cost of compliance is lower than the expected cost of non-compliance. However, because the probability of inspection tends to be low due to the cost of employing more inspectors, the expected non-compliance fine tends to be low.
The Harrington paradox, is the concept that even though fines are low and the frequency of inspection is low, firm compliance to these regulations remains very high, when in theory should be low. Harrington ‘shows how an enforcement agency can enhance deterrence by dividing regulated firms into two groups according to their past compliance record’ (Friesen, 2001).
There have been multiple theories which look into this paradox, such as Heyes & Rickman’s research into regulatory dealings and Friesen’s/Harrington’s research into the two-group model.
Heyes and Rickman created a model in which an environmental protection agency deals with a given firm in multiple domains for which they could comply or not. This model shows that the agency may pursue firms in both domains in an attempt to get them to comply or they may accept non-compliance in one of the domains for compliance in another. This is because there is not perfect information and the agency only has knowledge on the distribution function of the firms cost in each domain. For the purpose of this essay it will assume that there is a uniform distribution for all the firms in every domain.
Firstly, the Full pursuit model is when the agency attempts to get firms to comply in all domains. Firms will choose whether to comply in each domain if the cost of compliance in domain a, is less than the probability of inspection in that domain*fine which is the expected noncompliance fine (cia<Λ). For example, if we set the cost of compliance (cia)=0.45 and expected noncompliance fine (Λ)=0.45 across all domains, then with the assumed uniform distribution, firms will comply in 45% of cases, in all domains.
However, with the alternative model an enforcement agency allows firms to comply in one domain for non-compliance in another. This is because the difference in compliance cost over different domains means that it may increase total compliance across both domains. For example, if cia=0.45 in Domain A and cib=0.8 in Domain B, then with full pursuit there will be non-compliance in both domains. This is because the cost of compliance in both domains is higher or equal to the expected fine of non-compliance. Therefore, firms are willing to run the risk of not complying because at worst if they’re one of the firms inspected then they need to pay the fine, which would be equal to the compliance cost in domain a, and less than the compliance cost in domain b, and if they aren’t inspected, they incur 0 cost. Now if the agency offers them a deal to comply in domain a, for non-compliance in domain b, then there will be compliance in domain a, as the firm now doesn’t have the risk of being fined in domain b, increasing the total compliance.
However, if the cost of compliance is extremely low for example cia = 0.1 and cib = 0.2, then offering a deal actually decreases total compliance because with the full pursuit method firms comply in both domains as the cost is lower than the expected fine, but with a deal they’ll only comply in the domain with the lower cost (cia).
While rare the only time a firm will reject the deal is if the lowest cost of compliance in one domain is greater than the sum of the expected fines across both domains i.e. 2Λ<cia
However, the probability of this occurring is 2.25% (0.15*0.15=.0225), so the remaining 97.75% of firms will accept the deal. As these firms are only complying in one domain there is a compliance rate of 48.875% (97.75/2), which is an increase from the full compliance rate of 45%.
Friesen’s targeted enforcement model (Cason & Gangadharan, 2004) explains that there are two hypothetical groups (One that is inspected and another that is not), and like Heyes’ model firms comply if the expected fine is lower than the cost of compliance. For example, if we have 200 firms (m), and the agency can only inspect 30 of these firms (x), where the cost of compliance is 50 (c) and the Noncompliance fine is 150 (n) with a discount factor of 0.8 ().
If the inspection of all 200 firms is done randomly then the compliance rate will be zero. This is because the expected fine is (x/m)*n = (30/200)*150 =22.5, which is less than the compliance cost 50. Therefore, all firms are willing to run the risk of being inspected.
However if the agency has a smaller sample size and for example will only potentially inspect 80 firms (group 2) then, expected fine for these 80 firms is (30/80)*150=56.25 which is greater than the compliance cost so ALL 80 of these firms will comply, while the remaining 120 firms (group 1) do not as they are not going to be inspected.
Friesen then realised that the remaining 120 firms would never comply so it was not an efficient method, so he extended this model by moving the firms that were inspected and complied into the non-inspected group, and those that failed had to pay the noncompliance cost, and remained in the inspection group (Friesen, 2001). For the equilibrium to be kept the number of firms moved out of the inspected group must be replaced by those from the non-inspected group. This increases the reward of compliance because by complying you can move from group 2 to group 1 where no inspection takes place.
In terms of expected cost, we need compliance, C1, in group 2 to be higher than the noncompliance, N1, in group 2 and vice versa with group 1.
N_1=0 + δ(x/m_1 C_2+(1-x/m_1 ) N_1 = 0.8(30/120)*C2+(1-30/120)N1 = 0.8(0.25C2+0.75N1) = 71.429
Therefore the noncompliance in group 1 =0.8((30/120)*C2+(1-(30/120)N1 = 0.8(0.25C2+0.75N1) = 71.429 , and expected noncompliance cost in group 2 is
N_2=x/m_2 *k/(1-δ) = (30/80)*(150/(1-0.8)=281.25
The compliance cost in group 2 is:
C_2=c+δ(x/m_2 C_2+(1-x/m_2 ) N_1) = 50+0.8(0.375N1+0.625C2)=142.857
As C2<N2, firms comply all the time in group 2 so the 30 firms move out of group 2 into group 1. Therefore 80+ firms should potentially be inspected to maximize the number of firms complying in group 2.
When group 2 has 120 firms N2=187.5, C2=178.571 and N1=107.143 which means that the compliance cost is not greater so all the firms comply
When group 2 has 124 firms N2=181.452, C2=181.81 and N1=111.27 which means that the compliance cost is greater so none of the firms comply
Optimally as shown, group 2 should contain 123 firms because all the compliance cost is lower so the maximum number of firms comply, as N2=182.927, C2=180.999 and N1=110.228.
Therefore, the Harrington’s model shows that when the agency splits the sample into 2 groups the total compliance level increases.
A problem with this model is that it is very difficult to apply in real life. In particular, optimal targeting will be infeasible for high desired compliance rates or large compliance costs. This is because for this to occur the agency will incur large inspection costs to increase the expected cost of non-compliance as more firms would be at risk of getting caught. Many agencies do not have the funds to put this method into action. For example, the US Environmental Protection Agency (EPA) faces constrained fiscal budgets and labor limitations, making it impossible for them to hold inspections yearly (Friesen, 2001).
Another key problem with the two-group model is that all firms pay the same compliance cost, but some firms may be polluting more than others. This could be a big problem as the relative effect of the compliance cost is then reduced. This brings into question the fairness of the model (Friesen, 2001)