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Fisheries Enforcement Theory Contributions of WP-3 A summary Ragnar Arnason COBECOS Project meeting 2 London September

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Introduction Task of WP-3 : Develop fisheries management theory – To understand the process better – To support the empirical work – To support the programming work

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I. Basic 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

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

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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

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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)

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Private behaviour Maximization problem: Max B(q,x)- (e) f (q-q*) Enforcement response function: q=Q(e,f,x)q=Q(e,f,x) Necessary condition: B q (q,x)- (e) f=0 Can show: Q 1, Q 2 0

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

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Optimal enforcement Social optimality problem B(q,x)- q-C(e). subject to: q=Q(e,f,x), e 0, f fixed. Necessary conditions, if q=Q(e,f,x)>q* Q(e*,f,x)=q*, otherwise

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

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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 3.Ignoring enforcement costs can be very costly i.Wrong target harvest ii.Inefficient enforcement

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Practical guidance Seek to determine e* (and q*) For that (i)Set q* low enough (ii)Find e* that solves Need to know B(q,x), C(e), π(e) and f

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Empirical data needs B(q,x): bioeconomic model C(e): Enforcement cost function. Need data on enforcement costs and enforcement effort. Standard econometrics π(e): Probabilty of paying a penalty function. Estimate somehow! Non-standard f: The penalty structure (expressed in monetary terms)

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Extension I Several management measures and enforcement tools Vector of fishing actions; s Vector of management measures s * – ss*, quite unrestrictive! –If s(i) unrestricted, just set s*(i) very high –If s(i)s*(i), just redefine s(i)=-s(i), s*(i)=-s*(i). Harvesting function: q=Q(s,x) Vector of enforcement tools; e Probability function: (e)

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Fishers:

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Enforcers j=1,2…J all e j >0.

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Basically the same theory applies! Conclusion

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Extension II Uncertain fishers response function Why? 1.Many fishers with different risk attitudes 2.Fishers seeking ways to bypass enforcement 3.Erratic enforcement personnel

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Distribution of actual harvest: An example (Given e,f and x; u =0.2; 1000 replications)

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Optimal stochastic enforcement Compare to the non-stochastic optimum condition: Necessary condition: Complicated function of the random varaible, u !

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Two important results Result 1 If and only if will optimal enforcement be characterized by the non- stochastic condition. Result 2 If then e*>e° and vice versa.

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e e1*e1* $ e2*e2* CeCe The effect of a high random term

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A numerical example Private fishing benefits: Cost of enforcement: Probability of penalty: Shadow value of biomass: (assumed known) (can calculate on the basis of bioeconomic model)

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Numerical assumptions

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Example (cont.) Enforcement response function: f=2p f=pf=p f=0.5p

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Social benefits Enforcement effort Nonstochastic benefits, u=0 Expected benefit function Expected stochastic and non-stochastic benefit functions

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Optimal and sub-optimal enforcement effort Table 2Optimal and suboptimal enforcement effort(1000 replications) Enforcement effortLevelExpected harvestExpected social benefitsVariance of social benefitse* %e° %

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e° policy e* policy Histograms for benefits under the optimal and sub-optimal (non-stochastic) policies

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Extension III Fully dynamic context In the basic enforcement theory, is taken to be exogenous At a given point of time (and in continuous time) it is However, for the optimal dynamic enforcement policy we need to include

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Essential model Q(e,x,f) is fishers behaviour

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Maximization Hamiltonian Some necessary conditions (1) is the basic social enforcement rule!! (2) describes the optimal evolution of

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How to calculate ? Generally not easy to obtain the path of Jointly determined with e and x With a bioeconomic-enforcement model can work out (t), all t, (in principle) For optimal enforcement need to solve the dynamic model at each point of time.

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Optimal equilibrium Costly enforcement No or costless enforcement

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So, enforcement modifies the marginal stock effect In traditional fisheries models, marginal stock effect, >0 Under costly enforcement it may be of any sign Likely that Thus likely that (enforcement) < (costless enforcement)

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Optimal approach paths (conjectures) C e >0 C e =0 Biomass, x Harvest, q

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Numerical example Parameters

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Approximately optimal paths

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Approximately optimal paths of biomass, harvest and enforcement

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Extension IV Avoidance activities Avoidance possible Another control for the fishers (e,u) probability becomes endogenous Behaviour: Q(e,f,x) U(e,f,x) Q e and Q f may be positive! The theory becomes substantially more complicated

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Empirical considerations Application to case studies Data and estimation: Dynamics and the shadow value of biomass Deal with uncertainty

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Data & estimation Observations (cross-section, time-series) on s: Management controls e: Enforcement efforts C: Enforcement costs : Probablity of penalty (if violate) Estimate the probability and cost functions –Best procedures available

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Dynamics Basically should solve the dynamic maximization problem for enforcement controls This is generally a major undertaking Short-cuts are desirable

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Approximating the shadow value of biomass Theory: Approximation: Error:

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Biomass, x(0) Economically minimum biomass Optimal equilibrium Theoretical

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Biomass, x(0) Optimal equilibrium Approximation

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Dealing with uncertainty –Guess or estimate the uncertainty: –Solve by simulations

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