# COBECOS Fisheries Enforcement Theory: Basic Elements A Presentation at the Special Workshop for the EU Commission and Fisheries Control Administrations.

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COBECOS Fisheries Enforcement Theory: Basic Elements A Presentation at the Special Workshop for the EU Commission and Fisheries Control Administrations Ragnar Arnason Bruxelles, December 3, 2008

Introduction Fisheries management needs enforcement –Without it there is no fisheries management Enforcement is expensive Enforcement is complicated Optimal fisheries policy needs to take enforcement into account Enforcement theory is fundamentally the theory of crime (Becker 1968)

Model: Key Elements Social benefits of fishing: B(q,x)+ ·(G(x)-q) Shadow value of biomass Enforcement sector: Announced target:q* Enforcement effort:e Cost of enforcement:C(e) Probability of penalty: (e) Penalty function:f(q-q*) Private benefits of fishing:B(q,x)

Model (cont.) Probability of penalty function: (e) (e) e 1

Model (cont.) Penalty function: f(q-q*) f(q-q*) q q*q* Corner

Model (cont.) Private benefits under enforcement Social benefits with costly enforcement: B(q,x)- (e) f(q-q*) B(q,x)+ (G(x)-q)-C(e)

Private behaviour Maximization problem: Max B(q,x)- (e) f(q-q*) Enforcement response function: q=Q(e,x,q*) Necessary condition: B q (q,x)- (e) f q (q-q*)=0 Key relationship!

Private maximization \$ q q* Marginal benefits of fishing, B q Marginal penalty costs, (e) f q q enf q°

q e q* [lower f] [higher f] Free access q Enforcement response function

Optimal enforcement Social optimality problem B(q,x)+ (G(x)-q)-C(e). subject to: q=Q(e,x,q*), e 0, q* & penalty structure fixed. Necessary condition:

Optimal enforcement \$ q B q - q cost BqBq q° q* C e /Q e =C q q costless

To apply theory: Empirical requirements 1.The private benefit function of fishing, B(q,x) 2.The shadow value of biomass, 3.The enforcement cost function, C(e) 4.The penalty function, (e) 5.The penalty structure, f(q-q*) Note: Items 1 & 2 come out of the usual bio- economic model of the fishery. Items 3, 4 and 5 are specific to enforcement

Extensions 1.Higher dimensions –Many fisheries actions –Discrete fisheries actions –Many enforcement tools 2.Enforcement under uncertainty 3.Enforcement when avoidance is possible 4.Optimal fisheries dynamic paths with costly enforcement

Higher dimensions N fisheries actions s=(1xN) vector M enforcement tools e=(1xM) vector (e) =(1xN) vector f(s-s*) =(1xN) vector Fishers: Select profit maximizing vector s Enforcers: Select benefit maximizing vector e More complicated, but essentially the same!

Enforcement under uncertainty All components of enforcement model are subject to uncertainty This can have an impact on best enforcement Must take account of this Some theoretical investigations Usually enforce more (to reduce risk) In practice: Monte Carlo simulations

Enforcement under uncertainty Example Compare (1) maximization of benefits ignoring stochasticity to (2) maximization of expected benefits (proper procedure)

Enforcement when avoidance is possible (e) (e,a) a is avoidance activity New social cost: C(a) Analysis becomes more complicated –compliance may be reduced when e or f increase!! The social benefits of enforcement are reduced, sometimes drastically

Optimal Fisheries Dynamics S.t. Essentials, if is also a control

Optimal Fisheries Dynamics with costly enforcement: An illustration C e >0 C e =0 Biomass, x Harvest, q

END

Discrete fisheries actions Some fisheries actions are either/or –E.g. either use dynamite or not, either enter a closed zone or not, etc. These are discrete actions Need to extend the theory to deal with that Straight-forward; But maximality conditions more complicated

The discontinuity problem Analytically merely cumbersome Practically troublesome –Stop getting responses to enforcement alterations To avoid the problem –Set q* low enough (lower than the real target) –Aim for the appropriate level of noncompliance A well chosen q* is not supposed to be reached ( Non-compliance is a good sign!)

Some observations 1.Costless enforcement traditional case (B q = ) 2.Costly enforcement i.The real target harvest has to be modified (....upwards, B q < ) ii. Optimal enforcement becomes crucial iii.The control variable is enforcement not harvest! iv.The announced target harvest is for show only v.Non-compliance is the desired outcome 3.Ignoring enforcement costs can be very costly i.Wrong target harvest ii.Inefficient enforcement

Model (cont.) q (q;e,f,q*) q* (e) f Private costs of violations: (q;e,f,q*)= (e) f (q-q*), if q q* (q;e,f,q*) = 0, if q<q*

Social optimality: Illustration e \$ e*e* e°

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