Fisheries Enforcement:Basic Theory

Paper presented at

COBECOS Kick-off meeting

SalernoFebruary, 22-3, 2007

Ragnar Arnason

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

Social benefits of fishing: B(q,x)-·q

Shadow value of biomass

Enforcement sector:Enforcement effort: e

Cost of enforcement: C(e)

Penalty: f

Announced target: q*

Private benefits of fishing: B(q,x)

Exogenous

Model (cont.)

Probability of penalty function (if violate): (e)

(e)

e

1

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*

Model (cont.)

Private benefits under enforcement

Social benefits with costly enforcement:

B(q,x)-(e)f(q-q*), q q*

B(q,x), otherwise

B(q,x)-q-C(e)

Private behaviour

Maximization problem: Max B(q,x)-(e)f(q-q*)

Enforcement response function: q=Q(e,f,x)

Necessary condition:Bq(q,x)-(e)f=0

q

e

q*

[lower f][higher f]

Free access

q

Enforcement response function

Optimal enforcement

Social optimality problem

eMax B(q,x)-q-C(e).

subject to: q=Q(e,f,x), e0, f fixed.

Necessary conditions

( ( ( , , ), ) ) ( , , ) ( )q e eB Q e f x x Q e f x C e , if q=Q(e,f,x)>q*

Q(e*,f,x)=q*, otherwise

Social optimality: Illustration

e

$

e*

( )q eB Q eC

eC

e°

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

An example

2

( , )q

B q x p q cx

Private fishing benefits:

( ) ( )C e eCost of enforcement:

( ) 1 ee exp Probability of penalty:

Shadow value of biomass: (assumed known) (can calculate on the basis of biomeconomic model)

Example (cont.)

( ( ) )

2

p e f xq

c

Enforcement response function:

0 2 40

2

4

6

e, enforcement

q,

harvest

f=2p

f=p

f=0.5p

Example (cont.)

( ) 1

2opt

p xq

c f

Socially optimal harvest:

f, penalty

q,

harvest

0 10 202

3

4

5

q*(no enforcement cost)

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

Note: Items 1 & 2 come out of a bio-economic model of the fishery.Items 3, 4 and 5 are special enforcement data

To apply theory (cont)

• In real empirical cases, the functions will normally be more complicated– Include more variables (if only for statistical

purposes)– Vary across fisheries and management systems

• However, they must contain the basic elements of the theory

Extensions

1. Different enforcement targets (controls)– How does that affect theory– A vector of controls

2. Disaggregation (fishing units, gear, areas)

3. Alternative fishing opportunities4. Optimal mix of enforcement tools

– Vector of tools– Cost of each – Efficiency of each– Optimal mix (calculation of gains)

5. The structure (not only severity) of penalties

END