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
Mar 27, 2015
COBECOS Fisheries Enforcement Theory:
Basic Elements
A Presentation at the Special Workshopfor 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 biomassEnforcement 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*)
qq*
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:Bq(q,x)-(e)fq(q-q*)=0
Key relationship!
Private maximization
$
qq*
Marginal benefits of fishing, Bq
Marginal penalty costs, (e)fq
qenf q°
q
e
q*
[lower f][higher f]
Free access
q
Enforcement response function
Optimal enforcement
Social optimality problem
eMax B(q,x)+(G(x)-q)-C(e).
subject to: q=Q(e,x,q*), e0, q* & penalty structure fixed.
Necessary condition:
( ( , , ), ) ( ) ( , , )q e eB Q e f x x C e Q e f x
Optimal enforcement
$
q
Bq-
qcost
Bq
q°q*
Ce/Qe=Cq
qcostless
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 uncertaintyExample
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
0{ }
( ( , , *), ) ( ) r t
eMax B Q e x q x C e e dt
( ) ( , , *)x G x Q e x q S.t.
Essentials
( , , * )e x q r
) ( ,e x r , if is also a control*q
Optimal Fisheries Dynamics with costly enforcement: An illustration
0x
Ce>0
Ce=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 (Bq=)
2. Costly enforcement i. The real target harvest has to be modified
(....upwards, Bq<)ii. Optimal enforcement becomes crucial iii. The control variable is enforcement not “harvest”!iv. The announced target harvest is for show onlyv. Non-compliance is the desired outcome
3. Ignoring enforcement costs can be very costlyi. 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 qq*
(q;e,f,q*) = 0 , if q<q*
Social optimality: Illustration
e
$
e*
( )q eB Q eC
eC
e°