Ragnar Arnason COBECOS Fisheries Enforcement Theory Basic Elements

Ragnar Arnason COBECOS Fisheries Enforcement Theory: Basic Elements A Presentation at the Special Workshop for the EU Commission and Fisheries Control Administrations 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 theory of crime (Becker 1968)

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

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

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

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

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

Private maximization $ Marginal benefits of fishing, Bq Marginal penalty costs, (e) fq q* qenf q° q

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

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 Bq $ Bq- qcost q* qcostless q° q Ce/Qe=Cq

To apply theory: Empirical requirements 1. 2. 3. 4. 5. The private benefit function of fishing, B(q, x) The shadow value of biomass, The enforcement cost function, C(e) The penalty function, (e) The penalty structure, f(q-q*) Note: Items 1 & 2 come out of the usual bioeconomic 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=(1 x. N) vector • M enforcement tools e=(1 x. M) vector (e) =(1 x. N) vector f(s-s*) =(1 x. N) 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 Essentials S. t. , if is also a control

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

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

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

Social optimality: Illustration $ e° e* e