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°