ARTICLE IN PRESS

0308-597X/$ - s

doi:10.1016/j.m

�CorrespondE-mail addr

ngonzalez@sern

(H. Salgado).1Tel.: +56 412At present,

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property rights

Marine Policy 32 (2008) 570–579

www.elsevier.com/locate/marpol

ITQs under illegal fishing: An application to the red shrimpfishery in Chile

Carlos Chaveza,�, Nuria Gonzalezb,1, Hugo Salgadoa

aDepartamento de Economıa, Universidad de Concepcion, Casilla 1987, Concepcion, ChilebPrograma Magıster en Economıa de Recursos Naturales y del Medio Ambiente, Universidad de Conception, Chile

Received 27 August 2007; received in revised form 19 October 2007; accepted 21 October 2007

Abstract

We study an individual transferable quota system with imperfect enforcement. We apply a model of individual fisherman behavior to

the red shrimp (Pleuroncodes monodon) fishery in central-southern Chile. Simulation results suggest that illegal fishing could generate a

21% increase in fishing effort, resulting in a 13% increase in catch and a 2% lower quota price in comparison with the results of a system

that operates under perfect compliance. The results are sensitive to changes in the level of fish abundance, total allowable catch, and the

design of enforcement to induce compliance.

r 2007 Elsevier Ltd. All rights reserved.

Keywords: Individual transferable quotas; Illegal fishing; Enforcement; Quota market

1. Introduction

The use of individual transferable quotas (ITQ) as a toolfor fishery regulation is one of the most importantinnovations in natural resource management. Thesesystems are receiving more attention not only from theacademic community, but also from those interested inimproving fishery administration practice in a variety ofcountries around the world.2 Its implementation producesa series of positive effects. The ITQ system can generateincentives encouraging fisherman to avoid overexploitationand to protect the resource in the long term. The system ofindividual property rights can generate incentives to thefirms to operate more efficiently, eliminating benefitsdissipation due to the common property characteristic,

ee front matter r 2007 Elsevier Ltd. All rights reserved.

arpol.2007.10.004

ing author. Tel.: +5641 2203 067; fax: +56 41 2231 131.

esses: cchavez@udec.cl (C. Chavez),

apesca.cl (N. Gonzalez), salgado@berkeley.edu

2500 842.

there are more than 60 fisheries managed using programs

rty rights in around 15 countries. The objective of these

achieve greater efficiency by creating and assigning fishing

[1].

which usually generates excess investment in fleet andequipment.3

The ITQ system was originally proposed by Moloneyand Pearse [4]. Since then, its theoretical and empiricalproperties have been widely studied in the literature (for areview of practical experiences with ITQs, see Arnason [1]).Economic analysis of this regulatory system is based on theassumption of perfect enforcement and agent compliancewith the established rules, although recent theoreticalresearch suggests that non-compliance could affect thefunctioning of an ITQ system [5,6].In this work, we analyze the performance of an ITQ

system, considering the possibility of quota transgression.Specifically, we study the functioning of an ITQ systemwhere enforcement is insufficient to guarantee perfectcompliance.

3From an economic perspective, the ITQ system presents two desirable

characteristics. First, the possibility to transfer quotas facilitates industry’s

adjustment when there is the option to sell or buy all or part of the

allocated quota [2]. Secondly, the right to a given quantity of the resource

over time favors better planning of extractive and productive process

during the fishing season [3].

ARTICLE IN PRESSC. Chavez et al. / Marine Policy 32 (2008) 570–579 571

Our work presents two main innovations with respect tothe existing empirical literature. First, our analysisconsiders quota transgressions in a model of individualfishermen behavior which is calibrated with data from thered shrimp (Pleuroncodes monodon) fishery in central-southern Chile. Second, we measure the extent of theenforcement problems in the ITQ system and its implica-tions for quota market functioning. This allows us topresent an order of magnitude of the potential conse-quences associated to illegal fishing in a fishery regulatedwith individual property rights.

ITQ systems require the participation of a regulatoryagency responsible for establishing and controlling aggre-gate and individual fishing levels as well as enforcingcompliance of the established rules. Enforcement is one ofthe central aspects in ITQ program design. Whenimplementing it, the regulating agency should considerthat there are different incentives encouraging fishermen tocapture more than their allocated share. Consequently,each fisherman’s catch should be monitored and mechan-isms to sanction transgressions should be implemented.The successful operation of an ITQ system requiresmonitoring activities that can detect and sanction quotatransgressions.

Economic literature studying ITQ systems for fishingresources has placed little emphasis on the consequences oftransgressions in individual catch rights.4 In general, thistype of systems has been studied assuming that fishermencomply with their quotas. One exception is Chavez andSalgado [5] who studied the theoretical relevance oftransgressions in individual catch rights by examining theeffect of non-compliance behavior on an ITQ-basedsystem. The authors adapt existing literature in the contextof transferable emission permits system [15,16] to examinethe effects produced by enforcement problems on fishingquota market functioning. The study concludes that non-compliance with quotas can generate discrepancies in theequilibrium quota price and in fishermen behavior incomparison with a perfect compliance situation. Addition-ally, the authors conceptually analyze the impact ofchanges in fishing resource abundance, and total allowablecatch (TAC) levels on the functioning of the quota marketunder non-compliance.5

4The theoretical and practical relevance of transgressions in the context

of regulation of natural resource management and environmental

protection has been previously documented. A literature review is provided

by Cohen [7]. In the specific case of fishing regulation enforcement and

transgressions, see for example Sutinen and Andersen [8], Anderson and

Lee [9], Millman [10], Anderson [11], Charles [12], and more recently

Eggert and Lokina [13], and Viteri and Chavez [14]. Additionally, the

presence of transgressions of fishing quotas in a ITQ system context has

been considered as one of the critical aspects for adequate functioning of a

property rights systems in the fishing environment [2].5A recent related study that considers the effect of individual quota

infractions on the fishing quota price is Hatcher [6]. In contrast with

Chavez and Salgado [5], the former work examines the role of ‘‘subjective’’

enforcement, that is, the effect of the regulated agents’ perception of

enforcement actions on individual decisions.

In practice, the incidence of non-compliance has notgenerated too much attention in ITQ-based programs, evenwhen quota non-compliance could explain reduced stocklevel. An example of this situation is the red shrimp fisheryin central-southern Chile, which is administered by ITQsince 1992. According to resource stock evaluations, duringthe first 4 years of the ITQ system, an increase in stockabundance was observed; however, this level has reducedsince 1996 and it is currently prohibited to catch thisresource. Quota non-compliance emerges as one of theprincipal elements that explain stock level reduction [17].The paper is organized as follows. Section 2 presents the

conceptual framework that provides the basis for thenumerical analysis, including a literature review as well asthe theoretical model and its analytical solution. Section 3describes red shrimp fishing in central-southern Chile anddetails model calibration in the base scenario. Section 4presents the results of the base scenario simulation and acomparative static analysis of ITQ system functioningwhen incorporating the effects produced by changes inresource abundance levels, total catch, and enforcementparameters. Section 5 concludes.

2. Compliance model under an individual transferable quota

system

This section presents the conceptual framework thatserves as a base for the numerical simulations. The basicelements of the individual fisherman behavior model arebriefly described and the analytical solution of theproposed model is presented.

2.1. Individual behavior

The following model is based in Chavez and Salgado [5].This model considers a risk-neutral fisherman who operatesin a perfectly competitive ITQ system. The fisherman’sbenefits are determined by the difference between revenueand the total cost of fishing activity. The catch h is afunction of fishing effort e and resource abundance B. Thecatch is strictly increasing and concave in fishing effort e

(he40 and heeo0). Harvesting costs c(e) are strictlyincreasing and convex in fishing effort e (c0(e)40 andc00(e)40). Let q0 be the initially assigned fishing quota andq the quota that the fishermen maintains after transactions.The annual total allowable catch Q is fixed, the quotas aretraded at a competitive price w and the catches trade at acompetitive price p. Finally, there are n fishermenparticipating in the fishery.If a fisherman’s catch exceeds his/her quota q, then s/he

is non-compliant in the amount v ¼ h(e,B)�q. There is aprobability y that the fisherman will be inspected and apenalty will be applied. If a quota transgression is detected,the fisherman receives a sanction that is a function of thesize of the violation f(h(e,B)�q). The sanction level is zerowhen the violation is zero [f(0) ¼ 0], and the marginalsanction for a zero violation is greater than zero [f0(0)40].

ARTICLE IN PRESS

Table 1

Equilibrium conditions under perfect compliance and non-compliance

Perfect

compliance

Non-compliance

Effort level (e*) wc¼ p�ce(e

c)/

he(ec,B)

wnc¼ p�ce(e

nc)/

he(enc,B)

Quota demand (q*) qc¼ h(ec,B) wnc

¼ y f0(h(enc,B)�qnc).

Illegal dishing (v*) vc¼ 0 vnc

¼ v(y, wnc)40

defined implicitly by

wnc¼ yf0(vnc)

Source: Chavez and Salgado [5].

Table 2

Comparative results of the quota market

Variable Comparison

Effort level enc4ec

Quota holdings qncoqc

Quota price wncowc

Effect of quota on equilibrium price dwnc/dQo0, dwc/dQo0,

|(dwc/dQ)|4|(dwnc/dQ)|

Effect of stock abundance on

equilibrium price

dwnc/dB40, dwc/dB40,

|(dwc/dB)|4|(dwnc/dB)|

Source: Chavez and Salgado [5].

C. Chavez et al. / Marine Policy 32 (2008) 570–579572

For a positive violation, the sanction function is strictlyincreasing and convex [f00(v)40 for v40].

As usual in the related literature, we assume that theregulatory agency announces its enforcement strategy inorder to induce compliance. Additionally, we assume thatin equilibrium, each fisherman selects positive fishing effortand quota levels. An individual fishermen will select aneffort level e and a quota demand q, which maximizes theexpected benefit level considering as exogenous the catchprice, quota price, the probability of detection, and thepenalty function.

The agent solves the following static optimizationproblem:

maxe;q

phðe;BÞ � cðeÞ � w½q� q0� � yf ðhðe;BÞ � qÞ

s:t: hðe;BÞ � qX0 ð1Þ

The solution to this problem determines the individualfisherman choice of effort level and quota demand, whichin turn determines the level of quota violation (illegalfishing). Specifically, assuming that enforcement is notsufficient to guarantee perfect compliance of catch quotas,analysis of individual fisherman behavior suggests thefollowing results (for a formal proof, see Ref. [5]).

2.1.1. Individual choice of fishing effort e

A fisherman will choose a level of fishing effort so thatthe quota price equals the marginal net benefits per unit ofharvest, w ¼ p�ce(e)/he(e,B). This condition suggests thatthe individual fishing effort is a function of the extractedresource price (p), the quota price (w) and the resourceabundance level (B), that is e* ¼ e(p,w,B). Given strictconvexity of the harvesting and cost functions, fishingeffort increases in p, decreases in w, and increases in B. It isinteresting to note that the effort e does not directly dependon the parameters associated to enforcement, but ratheronly indirectly through the effect that enforcement has onthe equilibrium price w.

2.1.2. Individual choice of quota demand

Assuming an optimal fishing effort choice, any non-compliance fisherman will demand quota up to the point inwhich the marginal benefit of non-compliance (given by thequota price whose use is avoided) equals the marginal costof non-compliance (given by the expected marginalpenalty): w ¼ yf0(h(e(p,w,B),B)�q*).

Consequently, the quota demand by a non-compliantagent is a function of relevant prices, w and p, monitoringeffort y, and the level of fish abundance B; that is q*

¼ qnc

(w, p, y, B), where this choice decreases in w and increasesin y, p and B.

2.1.3. Individual equilibrium level of quota violation

The optimal choice of effort and quota levels determinesthe extent of the violation v* ¼ h(e(p,w,B),B)�qnc(w,p,y,B).At the equilibrium, this level is such that w ¼ yf0(v*). Theequilibrium level of individual quota violation is an

increasing function of quota price w and a decreasingfunction of the inspection probability y, which we denotev* ¼ v(w, y).Based on the analysis of individual fisherman behavior,

quota market functioning in the situation of non-compli-ance can be studied. The referred analysis suggests severalresults that are interesting for the numerical simulation: (i)quota demand in presence of quota non-compliance (qnc) islower than under perfect compliance (qc), that is qncoqc;(ii) the equilibrium quota price in presence of quota non-compliance is lower than under perfect compliance, that iswncowc; (iii) an increase in the total allowable catch (Q)reduces the equilibrium quota price, increases the catch,increases the quota demand, and reduces the magnitude ofequilibrium quota non-compliance; and (iv) an increase inthe abundance level (B) increases the equilibrium quotaprice and increases the magnitude of quota non-compli-ance. For a rigorous analysis of these results, see Chavezand Salgado [5]. Tables 1 and 2 summarize these results.

3. Description of the red shrimp fishery and model

calibration

In order to implement the numerical simulations of ourmodel described in Section 2, we choose the red shrimpfishery in central-southern Chile. In this fishery, an ITQsystem has been used since 1992. We use a detailed datasetthat contains information on individual vessel operationsto estimate harvest functions which are used later tosimulate optimal choices of effort, quota holdings and

ARTICLE IN PRESS

6Since some vessels operate only sporadically, the harvest function is

estimated for those that have operated in at least 10 out of 48 months of

the studied period. A total of eight boats satisfied this requirement, where

these boats captured 64% of the fleet’s total harvests in the period

analyzed. The remaining simulation analysis considers only these eight

vessels.

C. Chavez et al. / Marine Policy 32 (2008) 570–579 573

violation for individual firms. These results are thenaggregated to analyze market behavior.

3.1. General information and characteristics of fishing

regulation

The Red shrimp fishery in central-southern Chile beganmid-20th century due to the reorientation of fishing effortsfrom other overexploited fisheries [18]. The declaredcatches for the 1982–1989 period fluctuate around 6.8thousand tons. After closing the fishery in 1990–1991, itwas reopened in 1992 with catches increasing from 4.0thousand tons in 1992 to almost 12 thousand tons in 1999.Following the moratorium in 1992, the fishery was declaredto be in recovery [19], and interested parties were allowedto participate in the exploitation of this species. Participa-tion was controlled by individual fishing rights to extract apercentage of the annual TAC determined by the fishingauthority. These rights could be obtained through publicauctions. This new administrative system placed the redshrimp fishery under new regulatory measures thatincluded fixing of annual TAC quotas, definition of anauthorized fishing period, and granting of individualtransferable quotas, legally called ‘‘Permisos Extraordinar-

ios de Pesca’’ (PEP) [20]. This regulation measure wascomplemented with a minimum extraction size of 20 cm oflength (head–thorax) and with a reproductive moratoriumbetween January 1 and March 31 every year.

After several years of decreasing stocks, in 2001 theUnder-Secretary of Fisheries decreed a new extractionprohibition that continues until now. Some informationindicates that the principal reason was illegal fishing [17].These authors indicated that the total catch could havereached between 2.2 and 3.0 times the official TAC levelsestablished in the regulation for the 1996–1998 period.

In summary, the previous description suggests that theITQ system does not necessarily provide a fishing manage-ment solution if there is illegal fishing. In southern Chile,there are indications of illegal fishing, an underdevelopedITQ market, and a notable drop in stock abundance levels.In the next part, we calibrate an ITQ model to numericallyexamine the impact of imperfect enforcement on the ITQsystem functioning.

3.2. Functional specification and model calibration

The theoretical model is analytically developed inAppendix A using the functional specifications with whichthe quota market is simulated. These results are used tocalibrate the simulation model. Implementation of themodel, requires estimation of the parameters for individualcatch functions (h) in order to determine the individual andaggregate levels of illegal fishing (v and V), the individualdemand for catch rights (q), and the aggregate demand forcatch rights (Qd). We now turn to present the informationused for model calibration, which includes harvest func-tions per vessel, net processing benefits, extraction costs,

detection probability, penalty, resource abundance levels,and annual TAC.

3.2.1. Estimation of harvest functions

The individual harvest function parameters were esti-mated using monthly landing data for each vessel i, totalmonthly landing data as a proxy for monthly abundance,and fishing trips per month j for fishing effort. The catchfunction was estimated using the following Cobb–Douglasspecification

lnðhijÞ ¼ ai þ ai lnðeijÞ þ bi lnðBjÞ þ d1iD1 þ d2iD2 þ �ij,

(2)

where hij are landings in month j for the boat i, eij is effort,measured as the number of fishing trips for month j andboat i, Bj is stock abundance, measured as the aggregatelandings of all vessels in month j. Two seasonal dummyvariables where included in the estimation to control forseasonal effects on fishing activity. Specifically, D1 is adummy variable taking the value 1 in April, May and June;and 0 in all other months. D2 is a dummy variable equal to1 in October–December and 0 in all other months; ai, ai, bi,d1i and d2i are the coefficients to be estimated for eachvessel i. The estimates were performed using monthly redshrimp landing data per vessel for the 1997–2000 period.This information was obtained from the Chilean FishingService (Servicio Nacional de Pesca (SERNAPESCA)), apublic entity that, while being responsible for the enforce-ment of fishing regulations, gathers fishing information inChile. Specifically, the landing values were obtained fromthe fisherman-declared values.6

Table 3 presents the coefficients estimated for eachvessel. Effort and abundance elasticities are positive withvalues less than 1. The coefficients estimated for thedichotomous variables have positive or negative valuesdepending on the vessel and the period. With respect to theglobal fitting of the estimated model, the F-statisticsindicate that the model is significant for all vessels.Additionally, in all the cases, the individual coefficientshave the expected sign and in most of the cases theindividual coefficients are statistically significant.

3.2.2. Net processing benefits and harvesting costs

Since the fishing fleet and processing plants are verticallyintegrated, our analysis assumes that the red shrimpextraction value for each firm is determined by the netprocessing benefit that can be obtained for the processingplant, considering that the capture is completely used in theproduction of frozen shrimp.For the base scenario, the net processing benefit for the

year 2001, US$879 per ton, was used. This value

ARTICLE IN PRESS

Table 3

Estimated parameters for the harvest functions

Vessel

1a 2 3 4 5 6 7 8

A 5.687 (5.240*) 2.536 (5.250*) 2.796 (2.450*) 0.681 (2.550*) 7.533 (1.870*) 3.159 (0.930) 6.239 (1.590**) 10.58 (4.280*)

a 0.833 (2.260*) 0.922 (2.370*) 0.520 (4.260*) 0.623 (6.810*) 0.840 (5.780*) 0.757 (5.000*) 0.795 (8.960*) 0.530 (3.170*)

b 0.005 (0.014) 0.105 (0.350) 0.374 (3.270*) 0.414 (4.150*) 0.010 (0.050) 0.187 (1.090) 0.022 (0.210) 0.431 (2.140*)

d1 0.017 (0.070) 0.058 (0.880) 0.081 (1.050) �0.052 (�0.320) 0.034 (0.270) �0.111 (�0.990) �0.296 (�1.96*0)

d2 0.004 (0.010) �0.133 (�1.614**) 0.015 (0.170) �0.095 (�0.570) �0.039 (�0.270) �0.302 (�3.110*) 0.004 (0.020)

N 9 10 28 23 23 23 19 12

p-Value 0.040 0.010 0.000 0.000 0.000 0.000 0.000 0.000

F-statistics 5.860 12.420 64.778 47.917 11.900 21.000 37.047 12.107

Adjusted R2 0.58 0.89 0.90 0.87 0.66 0.79 0.89 0.80

Source: Based on data from SERNAPESCA.

Values between parenthesis correspond to the t-test for each estimated parameter. Parameters significant at 5% (*) and 10% (**) confidence level.aThe capture function estimated for boat 1 does not include dichotomous variables since D1 does not present variability (it does not operate between

April and June).

C. Chavez et al. / Marine Policy 32 (2008) 570–579574

corresponds to the last period for which there is availableinformation on industry profits.

The catch cost information was taken from Burgos [21],which was obtained with the collaboration of fishingcompanies. The harvest cost consists in fuel costs (diesel),ice, supplies, lubricants, and labor costs, which results in anextraction cost per fishing trip of US$1047.9.7 Theinformation related to industry costs is scarce, and this isconsidered the most reliable information source available.

3.2.3. Expected marginal penalty

The expected marginal penalty consists on two elements:probability of detection and imposition of a penalty in caseof detection of illegal fishing, and the level of the marginalpenalty.

3.2.3.1. Probability of detection and application of a fine

(y). To calibrate the base scenario, we assume that theprobability of detection is 0.20. This probability could behigher than what is actually perceived by fishermen,although this value was considered adequate to character-ize the base simulation scenario.8 In the exercises ofcomparative static analysis that are presented in Section 4,we test other y values and we analyze their influence on theresults.

7In Burgos [21] a cost per ton of catch is calculated. To obtain figures

for the cost per unit of effort we assume an average of 10 tons per fishing

trip.8Weak enforcement in the context of developing countries has been

characterized by detection probabilities below 0.25. The referred

probabilities have been used to calibrate models in the area of

experimental economics in the context of research on the effect of

external regulations for management of common property resources,

among other fishing resources; see for example Cardenas et al. [22]. Our

characterization of weak enforcement only requires that the expected

marginal sanction is incapable of generating perfect compliance,

considering risk-neutral fisherman. The simulation results for the base

scenario suggest that enforcement is effectively weak because the expected

marginal sanction is less than the equilibrium quota price.

3.2.3.2. Penalty function, f(v). The specified marginalsanction function f0(v) ¼ dv+g is positive and increasingon v. The parameter g is the marginal sanction forzero violation (f0(0)40), and its value for the base scenariois US$500. This value is considered adequate sinceit is close to the real values set by the Chilean Govern-ment’s Subsecretary of Fishing as the sanction valuefor illegal fishing of red shrimp.9 During this period,the sanction’s value fluctuated between US$430 andUS$540 per ton. The parameter d is the value to whichthe marginal sanction increases when an additional ton isillegally fished, and this was set at US$70 for the basescenario.

3.2.4. Abundance

To estimate the catch demand per boat, the stockabundance level is required. Unfortunately, monthlyabundance values are not available, and thus the aggregatecatches were used as a proxy for each month in 1997.10

Appendix B presents the series for the variable thatrepresents abundance level. The year 1997 was chosento generate the monthly abundance level according toaggregate unloading because this year is considered to havestable red shrimp abundance levels.

9The Fishing Regulation (Ley General de Pesca y Acuicultura) defines

the sanction value as: the amount of money expressed in Monthly

tributary units (UTM) and in the physical weight (in tons) of the

hydrobiological species in its natural state, which will be the counting unit

to apply the legally established sanctions.10The use of total catch as a proxy for abundance could generate an

endogeneity bias in the abundance coefficient when estimated using

ordinary least squares because total catch could be correlated with the

error term. This is because there might be uncontrolled temporary factors

that affect individual harvest that also affect aggregated harvest. Still, given

that there is no available information on monthly abundance, we used this

proxy even though it could result in the mentioned bias because it is the

best manner to incorporate the abundance effect into the harvest function.

ARTICLE IN PRESS

Table 4

Simulation parameter values

Parameter Value

Catch price (p) US$879 per ton

Cost per unit of effort (c) US$1047.9 per fishing

trip

Probability of detection (y) 20%

Marginal punishment for zero violation (f0(0)) US$500

Change in marginal punishment (f00(v)) US$70 per ton

Annual total allowable catch (Q) 2560 tons

Source: Based on description in central text.

Table 5

Effort, catch demand, and quota demand levels with and without

compliance

Boat Perfect

compliance

Non-compliance

Effort

(trips)

Catch

demand

(tons)

Effort

(trips)

Catch

demand

(tons)

Quota

Demand

(tons)

Illegal

Fishing

(tons)

1 7 43 10 56 16 40

2 4 24 8 44 4 40

3 123 1207 138 1278 1238 40

4 23 185 26 202 162 40

5 40 243 56 322 282 40

6 72 481 89 568 528 40

7 8 53 10 66 25 40

8 34 324 38 344 304 40

Source: Authors’ elaboration.

Table 6

Comparison of aggregate effort, capture demand and quota price levels

with and without compliance

Perfect

compliance

Non-

compliance

Percentage

change

Aggregate effort 311 375 20.6

Aggregate catch demand 2560 2879 12.5

Aggregate illegal fishing 0 320 –

Quota price (w) 673 662 �1.6

Source: Authors’ elaboration.

C. Chavez et al. / Marine Policy 32 (2008) 570–579 575

3.2.5. Annual total allowable catch

Model calibration in the base scenario uses the annualTAC values corresponding to the 1992–1994 period. Foreach of these years, the TAC was set at 4000 tons. This baseperiod was chosen because it is considered normal forresource abundance levels. Considering that total catchesof the vessels included in the analysis correspond to 64% ofthe total catches for the period, 64% of the actual TAC,2560 tons, was used as the annual total allowable catch forsimulation purposes (Q). Table 4 summarizes the para-meter values used in the simulation.

4. Results

This section presents the results of the simulation for thebase scenario and the comparative static analysis, whichcompares the base scenario with a change (increase ordecrease) in abundance, in the TAC, and in enforcementparameters.

4.1. Base scenario simulations

The optimal effort level is obtained as the solution to theoptimization problem (1) for each fisherman. Using theestimated parameters of the harvesting function and theprice, cost and abundance data, the optimal behavior foreach boat can be simulated. Table 5 presents the results ofthe base scenario simulation for individual decisionvariables (effort, quota demand, catch demand, and illegalfishing level) and Table 6 presents the aggregate effort andcatch demand levels as well as the equilibrium quota priceunder compliance and non-compliance. Boat 3 presents thehighest effort level with an annual total of 138 fishing trips.Boat 2 obtained the lowest effort level with eight fishingtrips per year. The annual aggregate effort is 310 fishingtrips under perfect compliance and 375 fishing trips undernon-compliance, a 21% increase. The catch demandpresents an annual maximum of 1278 tons for boat 3 anda minimum annual catch demand of 44 tons for boat 2. Theaggregate level is 2560 tons under perfect compliance and2881 tons annually under non-compliance, which implies13% of illegal fishing. The level of individual quotaviolation is 40 tons, which implies an aggregate level of321 tons. The equilibrium quota price is US$673 per ton

under perfect compliance and US$662 per ton under non-compliance, which represents a 2% reduction due toimperfect enforcement.

4.2. Comparative static analysis

This section describes how the optimal effort, the catchdemand, the catch rights demand, and the illegal fishinglevels as well as the equilibrium price change when facedwith variations in red shrimp abundance levels, TAC andenforcement parameters.

4.2.1. Changes in abundance and annual total catch

A change in abundance level induces a change in fishingeffort, catch demand, illegal fishing, quota demand levelsas well as the equilibrium price.The impact of effort level changes caused by a 20%

abundance increase is presented in Table 7. The aggregateeffort decreased in 30 fishing trips per year. Individual effort ismodified in different magnitudes for the different boats. Forexample, boat 5 reduces its effort in 17 fishing trips yearly andboat 3 increases its effort in 3 fishing trips per year.The change in individual effort in response to change in

the resource’s abundance level can be negative or positive.This is because the sum of two opposite effects that are presentwhen abundance changes. First, there is abundance’s direct

ARTICLE IN PRESS

Table 7

Effect on effort (e) and harvest (h) under non-compliance when faced with a 20% increase in abundance and TAC

Nave e0 Change in B Change in TAC h0 Change in B Change in TAC

E1 D (%) E1 D (%) h1 D (%) h1 D (%)

1 10 7 �24.0 14 48.7 56 42 �14.3 79 39.2

2 8 5 �34.0 20 133.9 44 28 �16.3 96 118.9

3 138 140 2.8 158 14.8 1278 1381 102.6 1374 7.5

4 26 27 1.5 31 19.2 202 224 21.6 226 11.6

5 56 39 �20.5 85 51.3 322 238 �84.1 456 41.6

6 89 80 �10.6 117 31.4 568 542 �25.5 698 22.9

7 10 8 �10.0 14 38.2 66 53 �12.8 85 29.3

8 38 39 3.8 44 15.2 344 381 36.1 371 7.8

Total 375 345 �7.9 483 28.7 2879 2888 7.3 3385 17.5

Source: Authors’ elaboration.

Table 8

Effect on harvest demand, aggregate illegal fishing, and quota price due to

a change in abundance, TAC, and enforcement parameters

Simulation Percent

change

in E*

Percent

change

in H*

Percent

change

in V*

Percent

change

in w*

Base scenario 375 2881 321 662

+20% Stock abundance �7.9 0.2 2.2 1.9

�20% Stock abundance 9.5 �0.3 �2.5 �2.1

+20% TAC 28.7 17.5 �2.6 �2.2

�20% TAC �26.5 �17.4 3.3 2.8

+20% y1 �2.9 �2.2 �19.3 0.3

+20% g1 �0.6 �0.4 �3.5 0.1

+20% d1 �2.9 �1.8 �16.4 0.3

Source: Authors’ elaboration.

C. Chavez et al. / Marine Policy 32 (2008) 570–579576

effect on effort: increases in abundance result in increases ineffort because the trips are more productive. Secondly, there isan indirect effect due to changes in the equilibrium quota price:increases in abundance result in increases in the equilibriumquota price, reducing the equilibrium effort. The relative size ofthese distinct contrasting effects results in increased effort insome cases and decreased effort in others. For example, forboat 1 in April (see Appendix C), the change in the effortlevel is �0.3, which is De1 ¼ �0.3, where the indirect effectis (De/Dw)� (Dw/DB) ¼ �0.37 and the direct effect is(De/DB) ¼ 0.01. In the case of boat 8, De8 ¼ 0.1 with anindirect effect of (De/Dw)� (Dw/DB) ¼ �0.21 and a directeffect of (De/DB) ¼ 0.31.

Table 7 shows that an aggregate demand of 2888 tons isgenerated with an increase of 7.2 tons in comparison withthe base scenario. However, even when the aggregate catchdemand is higher, individual demands are lower than in thebase scenario in five of eight boats. Individual catchchanges are explained by the change in the effort level andthe abundance effect on catch per effort unit.

In Table 7, the impact of changes on the effort level isobserved to be caused by a 20% increase in the TAC.Individual effort is modified in different magnitudes fordifferent vessels: for example, boat 5 presents the greatestchange, increasing its effort in 29 fishing trips. We can alsoobserve that when increasing TAC, the demand for catchesalso increases in both aggregate and individual terms.

Table 8 presents the changed values of the aggregatevariables when faced with a 20% increase in abundanceand TAC. Faced with a change in stock abundance,aggregate effort (E*) decreases in 7.9%, catch demand (H*)increases 0.25%, fishing violations (V*) increase in 2.2%,and the equilibrium price (w*) increases in 1.9%.

When stock abundance diminishes in 20%, the equili-brium price drops 2.1%, aggregate effort increases 9.5%,the catch demand increases 0.28% and aggregate violationsdecrease 2.5%.11

11The simulation results developed in the framework of static

comparative exercises for the levels and changes in individual effort and

catch demand are available from the authors upon request.

In Table 8, a change in individual and aggregate effort isobserved when TAC increases 20%. The associatedoptimal aggregate effort is 483 fishing trips, 108 trips morethan in the base scenario. Individually, there is a positivechange in the effort realized by entire fleet.When there is a 20% increase in TAC, the aggregate

catch demand reaches 3385 tons, increasing in 503 tonswith respect to the base scenario, corresponding to a 17.5%catch increase. It is important to note that since illegalfishing decreases, the catch level increases to a lesser extentthan the increase in TAC.Table 8 presents the change in aggregate effort,

aggregate quota demand, aggregate illegal fishing, andequilibrium quota price when faced with a 20% increase inTAC. Both the illegal fishing level and the equilibrium pricedecrease in more than 2%. Our results also indicate that a20% drop in TAC produces a 26.5% reduction inaggregate fishing effort, with 99 fishing trips less than inthe base scenario. The aggregate catch demand diminishedin 17%, capturing 501 tons less than in the base scenario.The new quota price is US$680.4 per ton, a 2.8% increase,and is associated to a 3.3% increase in illegal fishing,reaching a value of 331.7 tons.

ARTICLE IN PRESSC. Chavez et al. / Marine Policy 32 (2008) 570–579 577

4.2.2. Change in enforcement parameters

As indicated in Section 2, the optimal level of illegalfishing depends on the quota price w and the marginalexpected sanction function, which is defined by theprobability of being detected and fined for fishing illegally(y) and by the marginal fine, defined by the parameters dand g. A change in one of these parameters will directlyaffect the violations and the quota demand, changing theequilibrium price and impacting on the fishing effort andthe catch.

A 20% increase in one of these parameters produces adifferent magnitude of reduction in illegal fishing. If theincreasing parameter is the probability of detection andfining, then illegal fishing decreases in almost 20%,increasing the quota price in 0.3%. With this increase inw*, the fishing effort and catch demand decrease. The sameeffect increases in 20% the parameters of the sanctionfunction, where the percentage change in aggregate illegalfishing is lower when increasing y. In Table 8, theequilibrium values and percentage change (with respect tothe base scenario) for illegal fishing, price, effort and catchdemand are presented when the enforcement parameterschange in 20%.

From an enforcement perspective, to reduce quotaviolations, the regulator should orient its effort to increasethe perception that the fishing agent that she/he will becaught when illegally fishing (increase y) since a change inthis parameter appears to cause the greatest dissuasiveeffect.

5. Conclusions

The functioning of the individual transferable quotamarket is perturbed when individual quota compliance isnot well enforced. The numerical simulations indicate thatan ITQ system with non-compliance triggers a 2% lowerprice, 13% higher catches and 21% higher effort than if theITQ system were in perfect compliance.

Changes in exogenous variables, such as abundance andthe TAC, induce changes in the ITQ market. An increase inabundance availability decreases the aggregate effort,increases the aggregate catch demand, increases theaggregate level of illegal fishing, and increases theequilibrium quota price. An important result emergeswhen exploring the effect on individual fishing effort whenchanging the resource’s abundance level. The change inindividual effort can be positive or negative since anincrease in abundance increases effort because fishing tripsare more productive. Additionally, an increase in abun-dance increases the equilibrium quota price, whichresults in a drop in effort. Whether the final result will bepositive or negative depends on each boat’s catch function,and specifically on the parameters associated to abundanceand effort.

A change in the TAC can also produce changes in theITQ market. If the regulating body restricts the TAC, thereis a drop in fishing effort and in the catch demand,

increasing the equilibrium quota price as well illegalfishing.When the effects of changes in the exogenous variables

abundance and TAC are considered separately, we observethat a change in the total allowable catch (TAC) has agreater effect on the ITQ market. Even when both variablesproduce changes in the equilibrium quota price, themagnitudes of these changes are not proportional tothe change in the exogenous variables (a 20% change inthe variables produces changes between 2% and 3.5% inthe equilibrium quota price).A possible extension of the present simulations would be

to consider the effect of market power in the quota market.On the one hand, the theoretical literature suggests that thepresence of market power does not guarantee maximiza-tion of fishing income (see Ref. [23]), while on the otherhand environmental economic analysis suggests that thepresence of market power in an ITQ system generatesdifferent incentives to violate the quotas; see for exampleVillegas and Chavez [24]. We suggest that with theincorporation of market power in the simulations, theresults should change significantly.

Acknowledgements

The authors are especially grateful to Rosa Aguilera whoprovided helpful comments and suggestions on early stagesof this research and an anonymous referee for helpfulsuggestions. We are fully responsible for any remainingerrors. We gratefully acknowledges the financial supportfor this research provided by the Direccion de Investiga-cion, Universidad de Concepcion, under Project P.I. No202.042.013-1.3.

Appendix A. Analytical model solution

In this section, the theoretical model used to simulate thequota market is analytically developed using functionalspecifications.

A.1. Harvest function

To obtain the analytical solutions of the theoreticalmodel, a Cobb–Douglas-type individual catch functionwas used. The catch function for vessel i in month j is of thetype:

hij ¼ hiðeij ;BjÞ ¼ aieai

ij Bbi

j , (A.1)

where eij is the fishing effort of boat i in month j and Bj isthe stock abundance in month j.

A.2. Optimal effort and harvest demand

From the analysis results of the individual choiceproblem in Eq. (1), optimal effort e* can be obtained; seeChavez and Salgado [5]. The following condition should be

ARTICLE IN PRESSC. Chavez et al. / Marine Policy 32 (2008) 570–579578

satisfied:

w ¼ p�ceðeÞ

heðe;BÞ

� �, (A.2)

where ce is the marginal cost of effort and p is the resourceprice. To obtain an expression for marginal productivity ofeffort he, the derivative of the capture function should bemade in Eq. (A.1) with respect to effort (subindices havebeen omitted to simplify notation).

@h

@e¼ aaBbea�1. (A.3)

Substituting Eq. (A.3) in Eq. (A.2) and assuming aconstant marginal cost per effort unit (c), the following isobtained:

w ¼ p�c

aaBbea�1. (A.4)

From Eq. (A.4), the optimal effort (e*) can be obtained.Solving for e:

e� ¼aaðp� wÞBb

c

� �ð1=1�aÞ: (A.5)

Eq. (A.5) suggests that the optimal effort level positivelydepends on the resource abundance level and the priceplaced on the beach; and depends negatively on the catchcosts and the quota price. Then, to obtain the catchdemand h*, the value of optimal effort, e* is substituted inthe capture function (A.1),

h�ðp;w;C;BÞað1=ð1�aÞÞBðb=ð1�aÞÞaðp� wÞ

c

� �ða=1�aÞ: (A.6)

Due to the high level of integration between the fleet andthe red shrimp processing plants, the procedure proposedby Salgado and Aliaga (2001) [3] will be used to calculatethe catch price. Since all the catch will be used for frozenshrimp, from the perspective of fleet operation decisionmaking, the real value of the resource is given by the netbenefit of processing that can be obtained from theindustry. That is

p ¼ ðpc � cpÞR, (A.7)

where pc is the price in US dollars for a ton of frozenshrimp; cp is the cost of processing a ton of frozen shrimp,and R is the technical transformation coefficient in theprocessing sector. This coefficient transforms tons of rawmaterials into the final processed product. Additionally, itis important to note that Eq. (A.6) provides the catchdemand for each fishing agent and the aggregate catchdemand is obtained by aggregating the demand of thedistinct firms.

A.3. Estimation of illegal fishing (quota violation)

To determine the illegal fishing level desired by a firm, weused the results of Chavez and Salgado [5], who showedthat the optimal level of catch right violation (v) depends

on the quota price w and the function of marginal expectedsanction yf0(v) according to

w ¼ y0f ðvÞ. (A.8)

Eq. (A.8) implicitly defines the level of violations as afunction of the quota price level and the enforcementeffort, which is v* ¼ v(w, y).

A.4. Expected marginal penalty

The expected marginal sanction consists on two ele-ments: (a) the probability of detection of illegal fishing andfine application and (b) the marginal penalty.

(a)

The probability of detection of illegal fishing and fineapplication y: To obtain this probability, fishermanperception that they will be detected and finally finedwhen committing an infraction is considered. In this case, afisherman must be detected capturing in excess of his/herquota, must be accused to the corresponding authority,and is then sanctioned and must pay a fine. Consequently,y is a probability that includes all this process.

(b)

Penalty function, f(v). Considering the structure of thesanction function in Chavez and Salgado [5], the sanctionfunction used is of the type f(v) ¼ (d/2)v2+gv. Themarginal sanction function for this case is:

f 0ðvÞ ¼ vþ g, (A.9)

where d and g are positive parameters.When substituting Eq. (A.9) in Eq. (A.8), individual

quota violation is obtained:

vðw; yÞ ¼w� ygyd

. (A.10)

Given that individual violation does not depend onindividual characteristics of fishermen, the aggregatedviolation is V ¼ nv(w,y), where n is the number ofregulated fisherman.

A.5. Demand for Catching rights

In presence of illegal fishing, Chavez and Salgado [5]have shown that the demand function for catch rights isgiven by the difference between the catch demand h* andthe optimal quota violation v*. Consequently, the demandfunction for catch rights is represented as

qðw;B; yÞ ¼ hðw;BÞ � vðw; y; d; gÞ. (A.11)

Individual demands are aggregated to obtain aggregatedemand for catch rights

Qd ¼Xn

i

qiðw;B; y; d; gÞ:

A.6. Market equilibrium quota price

The equilibrium price w* is obtained when theaggregate demand for catch rights Qd is equal to the quota

ARTICLE IN PRESSC. Chavez et al. / Marine Policy 32 (2008) 570–579 579

supply Qo, which is the total quota (TAC) relevantfor the compliance period. Finally, after determiningw*, the model is solved, obtaining the solution for

the optimal effort level, catch demand, quota violation,and quota demand at both the individual and aggregatelevels.

Appendix B. Monthly landing values (tons) for red shrimp for the year 1997. Values used as a proxy for abundance

Months

April May June July August September October November December

Biomasa

523.67 872.3 999.63 1317.69 1625.33 1244.87 809.79 166.62 161.21

Source: Based on SERNAPESCA data.

Appendix C. Change in individual and aggregate effort with a 20% increase in abundance

Esfuerzo

April May June July August September October November December Annual

De1

�0.3 �0.3 �0.3 �0.3 �0.3 �0.3 �0.3 �0.3 �0.3 �2.9 De2 �0.2 �0.4 �0.5 �0.5 �0.8 �0.5 �0.3 0.0 0.0 �3.4 De3 0.2 0.3 0.3 0.4 0.5 0.4 0.2 0.1 0.1 2.4 De4 0.1 0.1 0.1 0.2 0.2 0.2 0.1 0.0 0.0 1.1 De5 �1.8 �1.8 �1.8 �2.6 �2.6 �2.6 �1.4 �1.2 �1.2 �17.0 De6 �0.8 �1.1 �1.3 �1.4 �1.6 �1.3 �0.8 �0.2 �0.2 �8.9 De7 �0.3 �0.3 �0.3 �0.4 �0.4 �0.4 �0.1 �0.1 �0.1 �2.5 De8P 0.1 0.1 0.1 0.3 0.4 0.3 0.2 0.0 0.0 1.5

Dei

�3.0 �3.5 �3.6 �4.4 �4.7 �4.3 �2.5 �1.8 �1.8 �29.7

Source: SERNAPESCA data.

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