On Applied Fisheries Economics, EAFE, Salerno (April 2001)

Ragnar Arnason* On Applied Fisheries Economics A paper given at the XIII EAFE Conference Salerno April 18-20 2001 FIRST ROUGH DRAFT Not to be quoted without consulting the author * University of Iceland ragnara@hi.is Introduction In this lead-off talk, the organizers of this conference have asked me to talk about “research in applied fisheries economics” or alternatively “economic theory as applied to fisheries economics” Clearly these topics are far to broad to any kind of justice in the time that has been allotted Therefore, I will be forced to be quite selective in my address More precisely, what I propose to is to restrict my talk to certain sub-topics: First I would like to consider briefly what we mean when we are talking about applied fisheries economics models This will inevitably take us into the field of the philosophy of science My contention is that virtually all fisheries economics models are applied The difference is only the degree of applicability Then, in place of model classification based on applicability, I will propose a classification based on the content of the models In particular I will divide all fisheries models into either theoretical or empirical models acknowledging, of course, that the dividing line between the two may often be quite unclear The third class of fisheries models, numerical fisheries models may be either empirical or theoretical although most empirical models are numerical In the third section of the paper, I will briefly recount the essential history of applied fisheries economics modelling since the early 1950s This I will within the framework for classification presented in the previous section, discussing in turn theoretical, management, empirical and numerical models Following this in the fourth section of the paper, I would discuss specifically a particular type of applied fisheries economics models that I have given some thought in recent years, namely endogenous optimization fisheries models My contention there is that this type of models constitutes a theoretical advance on the more traditional type of models and, with recent advances in computer technology, perfectly feasible Finally, in the last section of the paper, I will say a few words about the future of empirical fisheries modelling as I see it? What is Applied Fisheries Economics It seems useful to begin by briefly reviewing some fundamental concepts of the philosophy of science Positive vs normative science The philosophy of science distinguishes between positive and normative science Positive science is the science that is concerned with describing and explaining phenomena It is in a sense passive It does not, or at least it does not intend to, change anything Normative science, on the other hand, is concerned with achieving or, more precisely, describing how to achieve objectives Normative science, by its very nature, is not passive It explicitly aims at a change 2 It is illuminating to note that normative science needs description and explanation of the phenomenon in question to be effective Normative science, in other words needs positive science It is not the other way around Positive science can be conducted perfectly well without normative science Hence positive science is more fundamental than normative science Normative science as applied science Normative science is concerned with describing ways to change the conditions of the physical and social world, in accordance with some specified objectives It is, moreover, based on positive science Thus, normative science seems very close to what we often call applied science It applies positive science to achieve objectives Fisheries economics as a normative science Fisheries economics, since its inception in the 1950s1, has always been motivated by the desire to solve what is generally called the fisheries problem, i.e the severe economic inefficiency characterizing traditional fisheries The bulk of accumulated work in fisheries economics is of this nature, i.e descriptions and prescriptions as to how to solve the fisheries problem Hence, one would not be far off by saying that fisheries economics is essentially a normative science One might even say that fisheries economics as a whole is one of the normative appendages of economic science Fisheries economics as applied economics If fisheries economics is essentially a normative science then it also follows that fisheries economics as a whole may be regarded as applied science From this perspective it is merely the application of economic and biological science to the particular problems arising in the area of fisheries This, of course, does not mean that there are no positive elements in fisheries economics As already stated, any normative science has to be based on positive science, i.e a careful description and analysis of the facts of the matter Hence the same applies to fisheries economics Applied fisheries economics must be based on (a) positive economic and biological theory and (b) a positive description and analysis of the situation at hand So where we stand? We have concluded that fisheries economics is essentially an applied branch of positive economics However, to be effective, it needs not only the general economic theory It also needs positive description and analysis, i.e positive fisheries economics Thus, as in any other area of normative or applied science, the normative results are found to be based on a positive scientific description and inseparable from the normative elements There is a general consensus that the papers by Gordon (1954) and Scott (1955) mark the beginning of modern fisheries economics Some would like to trace the origins of fisheries economics further back to the two papers of J Warming in 1911 and 1931 These, however, were written in Danish and had little impact 3 This of course raises the question whether it is actually useful in practice to attempt to separate applied economics from the other parts of economics Isn’t all economics in the end normative and applied? Isn’t the ultimate purpose of all science to change the world for the better? A practical definition? These considerations suggest the need for a practical definition of applied fisheries economics There are many possibilities Here is one: Applied fisheries economics is any fisheries economics designed to improve the operation of actual fisheries It will be immediately noted that this is a very wide definition At first glance, it seems to include virtually all that currently passes for fisheries economics After all, isn’t all fisheries economics concerned with improving the performance of actual fisheries directly and indirectly? That may be the case However, it is clear that some areas of fisheries economics are less concerned with the improvement of actual fisheries than others Consider for instance studies of the impacts of fisheries management systems on the income distribution, geographical habitation or social structures, and the study of quota prices to find out whether exhibit random walk behaviour over time Of course these kinds of studies have a potential application to the improvement of real fisheries The point, however is that these applications are somewhat remote from the actual studies Hence, it seems that this definition excludes some research within what would normally be regarded as fisheries economics What then about theoretical papers For instance, Scott Gordon´s famous 1954 paper was clearly concerned with improving the operation of actual fisheries Yet it did not deal with any particular fishery Neither did it produce much recommendations as to how to improve the operation of fisheries in general Was that an applied piece of fisheries economics research or not? Another adaptation of a common definition of applied scientific research to fisheries economics can be phrased as follows: Applied fisheries economics consists of the application of theory to real world situations This definition however does not help much With this definition, it is for instance still unclear whether Gordon´s (1954) paper is applied research or not After all it is the application of economic and biological theory to the problem of fisheries On the other hand it the theory (in the definition) is fisheries economic theory, the paper, since it develops that theory, seems to be non-applied The above-mentioned types of studies  the impacts of fisheries management systems on the various economic and social variables and the random walk behaviour of quota prices  would however, clearly be applied research according to this definition A continuum of applied research As the foregoing discussion indicates, it is difficult to provide a precise definition for applied fisheries economics or, for that matter applied science in general Theoretical (or basic) and applied research bare simply too interwoven One blends into the other almost seamlessly Moreover, it is difficult to think of any research that does not have any practical application This suggests that the whole thing may be more usefully regarded as a continuum from the least applied to the most with no clear demarcation point where basic research turns into applied research Figure Continuum of applied research Less More This, of course, applies to fisheries research also It ranges from the least applied to the most applied Whether we characterize a particular piece of research as applied or not is largely a matter of perspective and of little practical consequence We have already stated that most fisheries research can be regarded as applied Of course funding agencies may want to encourage research in some particular area of this spectrum It is not uncommon for them to seek strongly applied research In so doing they should, however, be mindful that heavily applied research must be founded on basic research, so an excessive emphasis on practical, applicable results may ultimately reduce the supply and quality of such results Fisheries Model Classification Rather than attempt to classify research according to applicability which, as we have seen, is a somewhat pointless exercise, it may be more useful to consider another dimension for research classification This is the dimension of theoretical research vs empirical research and the corresponding classification of fisheries models into theoretical models and empirical models This will help us to locate particular models that we may come across in the general landscape of all fisheries models Remember that fisheries models are in our parlance synonymous with fisheries research Broadly speaking we may divide all fisheries models into two main classes; (i) theoretical models and (ii) empirical models The difference between these two types of models is that the former does not have any particular empirical content, i.e it does not contain a description of any particular fisheryonly fisheries in general, while the latter contains a specific empirical description  often (but not always) in a numerical form  of the features of one or more particular fishery While this classification of fisheries models into theoretical and empirical models is analytically useful, the distinction is often blurred in reality Of course, theoretical models must have some empirical content Otherwise, they would not be of much interest Similarly, many empirical models, for instance the so-called stylized models, have little specific empirical content Thus, we should recognize that there are cases where it is actually difficult to classify a model as either theoretical or empirical To emphasize this, we have, in Figure 2, where we have divided the set of economic fisheries models into theoretical and empirical models, drawn a broad grey dividing line between the two Figure Classification of Fisheries Models Empirical Theoretical Numerical There is a third category of fisheries models of considerable importance This is the class of numerical models Numerical models contain numerical descriptions of the subject and, as a result, are capable of produce numerical outcomes Most empirical models are numerical But this is not logically necessary It is easy to think of empirical models as consisting only of a qualitative description Thus, generally speaking, there are empirical models that are non-numerical Theoretical models are usually not numerical Theoretical models generally consist of analytical relationships of a fairly general nature However, in some cases, the analytical relationships are too intractable and theoretical analysis also resorts to numerical methods, but not necessarily empirically based, to obtain results Thus a relatively small part of theoretical models is also numerical This is illustrated in Figure 3, where the set of numerical models intersects both the theoretical and empirical sets of models 6 It is, of course, fairly obvious why numerical models are needed as a part of empirical modelling After all numbers are a standard way of representing empirical reality On the other hand on may wonder why numerics are useful for theoretical modelling as well .The main reason is that the analytical methods, by which theoretical models are examined, are only able to deal with simplest of fisheries models As soon as the theoretical models reach the degree of complexity necessary describe all but the simplest of fisheries situations, the analytical methods no longer suffice to derive the outcomes Under those circumstances numerical models and numerical simulations are needed to complement the theoretical analysis Applied Fisheries Models: A Brief History Let us now briefly look at the evolution of applied fisheries models during the about 50 year history of the science To assist us in reviewing this history the following diagram in Figure may be useful Figure The Evolution of Fisheries Modelling Theory Empirical models 1950 1960 Numerical Models 1970 1980 1990 2000 Fisheries Fisheries Economics Management A Theoretical Models The first theoretical models of consequence emerged in 1950s These were the standard static fisheries economics models of the type developed by Gordon (1954) and Scott (1955) although the latter attempted to indirectly account for dynamic considerations With little modification these models are still with us today forming the core of Of course, as already mentioned J Warming had already developed similar models in the early 1900 (Warming 1911 and 1931) undergraduate teaching in fisheries economics and, indeed, renewable natural resource economics They also continue to form the basis of simple policy thinking in the area These models may be regarded applied models for at least three reasons First they were developed in order to improve the economic operation of fisheries Gordon, for instance was commissioned to study the fisheries problem by the Canadian government Second, by explaining the root cause of the fisheries problem and providing a model structure to describe it, they suggested various ways to overcome the problem Thus, the Gordon type of analysis suggested the curtailing of fishing effort and the reduction of fisheries profitability by the imposition of taxes The Scott type of analysis focussed attention on the number of owners and, consequently, the property rights structure Third, these simple models provided a structural form description of the fishery that could be estimated by real data and thus turned into an numerical, empirical model The 1960s saw further advances in the applied static modelling Thus, e.g Turvey (1964) extended the Gordon-Scott model to indirectly take account of multi-cohort fisheries with the help of the so-called eumetric yield curve His analysis generated the policy advice to seek ways to increase fish gear selectivity (by area closures and mesh size adjustments) More importantly, however, the 1960s and early 1970s saw the emergence of explicitly dynamic models and the application of control theory to the problem of fisheries The first step of note in this respect was the Crutchfield-Zellner empirical study of the Pacific halibut fishery in 1962 In that study, which was otherwise based on the static Gordon-Scott type of anlaysis, Arnold Zellner, then a young research assistant, set out in an appendix the essential equations of the dynamic fisheries model that was to be extensively studied for the next two decades In the late 1960s, Vernon Smith, completed this analysis by developing, in a number of papers (Smith 1968, 1969), explicit models describing the dynamic evolution of competitive fisheries (and other renewable natural resource extraction) Ultimately, in collaboration with Quirk (Quirk and Smith 1970) Vernon Smith managed to derive equations describing the dynamics of an optimally managed fishery The 1970s and was the period of the development of optimal dynamic analysis in theoretical fisheries modelling Several pathbreaking papers emerged Papers by Quirk and Smith (1970) and Plourde (1970) set out the essential equations describing the optimal dynamics of fisheries Clark and Munro (1975) explicity solved the linear type of fisheries model employing control theory In so doing they managed to explain completely the capital theoretic nature of the fisheries problem and to highlight the importance of the rate of discount for the optimal equilibrium solution Finally, Colin Clark summarized the state of the theoretical modelling in his book in 1976 Following these works there was a flurry of papers deriving optimal solutions to the various specifications of the dynamic fisheries model One may say that this path of research came to an end with the paper by Clarke, Clark and Munro (1979) which derived the optimal solution paths to the standard dynamic fisheries model with two stock variables, i.e the fish stock and stock of fishing capital The extreme analytical complexity of this paper, demonstrated to the profession that this was as far as it was possible to progress in analytical optimal dynamic The application aspect of these dynamic models was very similar that of the Static models First, the motivation for the studies was the same as before, namely to improve the operation of real fisheries Second, the outcomes of the dynamic models alerted fisheries managers to certain complicating aspects of real fisheries, i.e their inherent cycles and the possibility of stock collapses along dynamic adjustment paths Thirdly, these models suggested a more appropriate functional structure for empirical models describing the fisheries than the Gordon-Scott type of analysis Consequently, from the 1980s to the end of the century, theoretical analysis has not sought to probe much deeper into the nature of optimal dynamics It has been primarily concerned with various extensions and elaboration of the existing simple models Among these we may mention (i) simple multispecies models, (ii) stochastic fisheries models and optimal stochastic control, (iii) migratory fish stocks, (iv) transboundary and high seas fisheries, (v) heterogeneous fishermen and (vi) the downstream implication of the fisheries problem on the fish markets and the processing industry Various authors have contributed to these theoretical refinements Again the applications are obvious B Management Theory The theoretical fisheries model of the 1950-1980 were primarily concerned with describing the nature and extent of the economic inefficiency of common property fisheries and to derive and to compare them with the optimal harvesting paths These models were not particularly concerned with the fisheries management problem The implicit assumption seems to have been that it would be a relatively simple matter, primarily a question of political will, to implement the optimal harvesting paths Towards the end of the 1970s, as the main tenets of fisheries economics theory had become fairly well understood and accepted and more fishing nations were seriously trying to improve their fisheries, it became increasingly clear that effective fisheries management was no easy matter It turned out to be easier said than done to generate and maintain economic rents from the fisheries During the 1960 and 70s a number of countries including Canada, the USA, Iceland, Norway, Denmark and some European countries tried various methods to improve the biological and economic outcome of some of their common property fisheries Several methods were tried, mesh size adjustments, limitations on the application of fishing capital, the imposition of total allowable catches, closed areas, closed seasons and fishing licences Although many of these measures were broadly in conformance with the simple fisheries economic theory of the time, the results were uniformly disappointing Although, in some cases, the measures managed to prevent a serious stock decline, in no case did they manage to generate significant economic rents Clearly, something was wrong We could say that there was a problem with the application of fisheries economic theory to real life fisheries In response to this, since the early 1980s until now, a specific fisheries management theory has been under development Several papers and conferences mark this development One may for instance mention three major conferences which as luck would have it were held with an interval of roughly a decade The first was the Powell River conference on fisheries management in 1979, which reviewed the management experience so far and found most of the usual measures severely wanting The second was the Reykjavik conference on rights-based fishing in 1988 (Neher et al 1979) which firmly put fisheries property rights and ITQs forward as theoretically and empirically effective fisheries management systems The third was the Fremantle conference, Fishrights99 (Shotton 2000), which confirmed the general superiority of property-rights based fisheries management but also opened the door to the exploration of further variants of property rights in fisheries including community property rights as well as the possibility of fisheries self-management on the basis of private property rights Broadly, one may say that in modern fisheries management theory, sociology and political science are combined with the traditional fisheries economics in order to produce an economically efficient and socially workable framework for fisheries management Thus, under this new fisheries management, the main tools of analysis are game theory, property rights and incentive theory and the theory of social groups and socio-political behaviour The current results of fisheries management theory may be summarized thus: (i) Private property rights, provided they can be enforced, are extremely conducive to efficient fisheries management (ii) These property rights, however, may be of various kinds including TURFS, ITQs, community rights and so on (iii) There are sever problems with governments as a fisheries manager (government failure) (iv) Well defined private property rights provide a basis for effective government-industry co-management and even industry self-management Current research areas of substantial intensity concern (i) fisheries management on the basis of community rights, (ii) the conditions for effective fisheries self management, (iii) management under uncertainty and (iv) the cost of fisheries management A major drawback of the theoretical models is that they are not capable of representing the complex nature of real fisheries Typical real fisheries consist of (i) several species, (ii) composed of various cohorts, (iii) contained in an ecosystem, (iv) interacting in various manners, (v) migrating from one area to another, (vi) being harvested by several vessel types (vii) employing various types of gear and (viii) operating in different areas Neither is the theory capable of dealing with the complex social conditions controlling the harvesting process and the various marketing and outlet conditions for the harvest This is one reason why empirical and numerical modelling is required C Empirical models The initial empirical models were simple application of the static fisheries theory of the 1950s, consisting of estimates of the aggregate biomass growth function, the fisheries cost functions and the price of the output On this basis it was possible to calculate the optimal (static) fishing effort corresponding to the optimal sustainable yield (OSY), the optimal sustainable levels of other input variables of note as well as the sustainable harvest and economic rents This kind of a simple empirical fisheries model actually requires considerable research effort to construct, estimate and operate To this very day there are empirical fisheries models being constructed on this basis 10 More advanced empirical models started to emerge in the 1960s The famous Crutchfield-Zellner (1962) study of the Pacific halibut fishery constitutes a case in point However, it was not until the 1970s that fully fledged dynamic empirical fisheries models came into being A major reason for this was that in the dynamic context, the optimal solution consists of harvesting paths over time that may or may not converge to a sustainable equilibrium Such paths can generally not be calculated analytically Therefore, to solve for the optimal solution to dynamic fisheries models required substantial computational power that simply was not available to fisheries economists (although it was to the armed services and space exploration) until the 1970s Indeed, more advanced dynamic fisheries models started to appear in the 1970s one of the very first was by the European, Hannesson, in his doctoral thesis published in 1974 Hannesson´s model involved cohort disaggregated stocks of the Beverton-Holt type and fully fledged stock dynamics Hannesson even managed to solve for the optimal (profit maximizing) paths discovering bang-bang type of solutions, referred to as pulse fishing, that was to confound the profession for a number of years One of the reasons for Hannesson´s pulse fishing results was the linearity of his control model.3 The effect disappeared when later in the 1970s and the 1980s more realistic nonlinear models were constructed by e.g Mitchell (1979), Arnason (1984) and others A summary of many such models can be found in Rodrigues (1990) The more advanced empirical fisheries models of the 1980s and later are typically large scale cohort-disaggregated, multi-stock and multi-fleet models The more elegant of these models moreover involve various stochastic parameters giving rise to uncertain outcomes There are currently many examples of these kinds of models in existence They are typically used for three main purposes; (a) predicting the future of the fishery, (b) studying the impact of management measures and changes in other exogenous variables on the fishery and (c) calculating optimal (in some sense) harvesting paths The first two are accomplished by simulation, often stochastic simulation, of the model so the outcomes will have an associated probability distribution The third, the calculation of optimal harvesting paths, requires extensive numerical search which, even with modern computers is often very difficult to complete Most fishing nations have developed empirical fisheries economics models for their fisheries The construction, estimation and operation of these kinds of models is a major undertaking, typically requiring several man-years It is therefore pleasing to be able to report that within the European Union a number of these empirical models have actually been developed with funding from EU scientific programme In spite of the very substantial effort that has been put into empirical fisheries models and their relative success in some respects, they have generally proved disappointing as a tool for evaluating fisheries management proposals The problem seems to be that for that purpose, these models are too mechanical Their relationships are based on observed behaviour in the past and, consequently, cannot account for fishermen´s responses to new management tools Thus, when it comes to the question of fisheries management regimes, these models not represent the true situation For that need we More precisely, it was linear in the control variables 11 need an entirely different kind of empirical models, that based on endogenous optimization (Arnason 2000) D Numerical models Greatly assisted by advances in computer technology I remember when I was taking my first steps in numerical models in the 1970s We had to write our programs on punch cards And the computers were charcterized by (a) immense size  special rooms had to be prepared for them, (b) very little memory  all programs had to specially designed to economize on memory, (c) computationally very slow  simple regression runs took many minutes, fairly simple optimization runs could take days Finally, the quality of the numerical software available was poor As a result, running a numerical fisheries model of any reasonable size was a major task  not lightly undertaken Therefore, the reliance in applied modelling was much more on (a) theoretical models and (b) very simple numerical models than has since been found to be healthy Consequently, before the 1990s, there were few numerical fisheries economics models in existence (Rodrigues 1990), and those that existed were generally fairly unsophisticated and cumbersome in operation models Nowadays, of course this has all changed Computers of many times the power of the mainframes of the 1960s are now on everyone’s desk and through computer linkages it is now possible to inexpensively obtain the computing power one needs for almost any reasonable fisheries model As a result we have seen a substantial increase in the construction and operation of fairly complex numerical fisheries models However, I for one think that there is still a lot to be done in this area and that we in fisheries economics have far from fully exploiting the new potential offered by the computational revolution The problem seems to be of several types (i) lack of programming and numerical training, (ii) lack of facilities and funds, (iii) lack of publicational outlet for these kinds of studies It is a fact that few fisheries economics journals are designed to publish these kinds of studies As a result, an up and coming researcher in fisheries economics is not well advised to try to make his mark in the numerical fisheries modelling field He would normally be much better off in either theory or smaller empirical problems Hopefully, we will see a change in this in the future 4 Endogenous Optimization Fisheries Models4 Much of the research on which this section is based was conducted as a part of the EU funded project FAIR-CT95-0561 (see e.g Arnason et al 1997 and Arnason 2000) which is hereby gratefully acknowledged The content of this section nevertheless, does not necessarily reflect the views of the Commission of the European Communities and in no case anticipates the Commission’s position in this domain 12 Let us start by briefly reviewing the essential structure of conventional fisheries models These models consist of two fundamental components: (i) a biomass growth function and (ii) an economic performance function Their two basic components may be represented by the following three sets of equations5: ∫ ∞ π(e,x;z)⋅ exp(-r⋅ t) dt, (1) Π= (2) π(e,x;z) = p⋅ Y(e;x,z) - C(e;x,z), (3) x = G(x) - Y(e;x,z), In this formulation Π is the ultimate performance measure of the fishery π(e,x,z) represents the instantaneous flow of benefits from the fishery with the vectors e, x, and z representing the use of economic inputs, biological stock size measures, and exogenous variables, respectively Thus the expression ∫ ∞ π(e,x;z)⋅ exp(-r⋅ t) dt, with r as the rate of time discount, represents the present value of the flow of benefits from the fishery forever Y(e;x,z) represents a vector of harvesting functions, p the corresponding vector of output prices and C(e,x,z) the total cost function Finally, the third equation represents the evolution of the biological stock sizes with G(x) as the vector of stock size growth functions It should be noted that biological fisheries models, i.e those without an economic module, would only contain equations (3) above Thus, such models, typically developed by marine research institutes, constitute but a subset of bioeconomic fisheries models A major objective of bio-economic fisheries models is to find the time path of the control variables, e, that maximizes the performance measure, Π In other words, it is typically attempted to solve the problem: (4) Max Π {e} Subject to x = G(x) - Y(e;x,z), The solution to this problem yields the optimal time paths of the control variables {e*}, say This represents the optimal fisheries policy For later reference it should be noticed that the optimal fishing effort at a point of time, e*, generally represents a multidimensional vector Plugging the optimal fisheries policy into equations (1) to (3) yields the maximum performance as a function of the fisheries policy , the biological and physical capital stock levels and the time path of exogenous variables as follows: Π({e*}; x(0); {z}) It will be recognized that this representation omits several important aspects of advanced bioeconomic fisheries models such as the use and accumulation of fishing capital that normally significantly modifies the overall dynamics of the system 13 Thus we see that the conventional fisheries models are, at least in principle, capable of identifying the optimal fisheries policy (in the sense of performance maximizing levels of fisheries inputs), calculate the corresponding course of the fishery over time as measured by the state variables, x and to calculate the maximized level of the performance indicator, Π In more advanced, stochastic versions of the models these outcomes would receive a probabilistic representation Limitations The above procedure, while most informative, is generally not of much practical use The reason is that fisheries authorities normally cannot control the vector of fishing effort, e, at least not directly Therefore, although conventional bio-economic fisheries models may provide the fisheries authorities with much improved estimates of the optimal path of fishing effort, they give very little indication as to how to put these paths into effect What national and regional fisheries authorities can is to set and operate fisheries management regimes Each fisheries management regime contains a set of parameters.6 The operation of any fisheries management regime consists of adjusting these parameters Those adjustments are conveniently referred to as fisheries management measures Thus, the fisheries management tools at the disposal of the fisheries authorities consist of selecting the fisheries management regime and setting its parameters Faced with this, the fishing firms will correspondingly adjust their behaviour including the relevant components of fishing effort Thus, with the help of the fisheries management regime, the fisheries authorities can affect fishing effort indirectly This brings us to the principal limitation of conventional bio-economic fisheries models as practical tools for fisheries management They generally not model the relationship between fisheries management regimes and fishing effort As a result, they not provide the fisheries authorities with a link between their actual control variables, namely the fisheries management regime and its parameters, and the outcomes of the fishery It is important to recognise that this shortcoming of conventional bio-economic models is not simply one of modelling omission The problem has to with the fundamental structure of conventional bio-economic models As a result, its resolution requires a major restructuring of these models Conventional bio-economic fisheries models consist of technical relationships such as biomass growth functions, harvesting functions and cost functions These functions essentially represent production possibility frontiers that are insensitive to economic variables, fisheries management regimes and controls Hence these frontiers can be estimated on the basis of observed fisheries and fishing industry data, more or less irrespective of the fisheries management regime in place Thus, in an effort control fisheries management regime, the number of allowed fishing days would constitute an example of such parameters 14 The relationship between the fisheries management regime and the vector of fishing effort is an entirely different matter The fisheries management regime directly affects the choice set of the economic agents, i.e fishing firms, that select fishing effort components Hence the actual vector of fishing effort chosen by the fishing firms depends on the fisheries management regime and its parameters (as well as a range of market prices and other variables) It follows immediately that the empirical estimation of this relationship requires data on the choice of fishing effort components under all relevant fisheries management regimes and parameters These data, however, are usually unavailable precisely because improvement in fisheries management normally requires the introduction of new and untested fisheries management regimes.7 Thus, it emerges that there are fundamental obstacles to simply including fishing effort response functions to fisheries management regimes in bio-economic fisheries models What seems to be required is a modification in the modelling strategy An alternative modelling strategy: Endogenous optimization fisheries models A seemingly promising alternative is to drop the idea of specifying a fishing effort response function in favour of modelling the fishing firm decision process This represents a very different modelling approach Instead of specifying an explicit behavioural relationship, presumably estimated on the basis of empirical data, between fisheries management regimes and the vector of fishing effort, the decision process giving rise to that relationship is modelled In this sense, the resulting model generates behaviour endogenously It may be helpful to try to express these ideas more formally: Let R represent the fisheries management regime and its parameters Thus, R is a collection of functional constraints and variables that define the fisheries management regime Presumably, it may be taken for granted that fishing firms maximize their objective function subject to this fisheries management regime A somewhat more questionable assumption is that this objective function is profits In any case the maximization procedure results in a mapping from the fisheries management regime, R, to the vector of fishing effort, e Let the expression ψ represent this mapping Thus, more formally we may define this mapping by the expression: ψ: R → e such that {e = Σe(i) e(i) maximize π(i) subject to R}, where the index i refers to firm i and π(i) represent firm i's profit function or, more generally, its objective function Adding this component to the conventional bio-economic fisheries model defined by (1) - (3) above we obtain an alternative modelling structure as follows: (5) ψ: R→e such that {e = Σe(i) e(i) maximize π(i) subject to R}, Even if the fishery had experienced a range of fisheries management regimes, the necessary data would be hard to come by since data on many of the components of the fishing effort vector are not routinely collected and many are in fact difficult to observe 15 ∫ ∞ (6) Π= (7) π(e,x;z) = p⋅ Y(e;x,z) - C(e;x,z), (8) x = G(x) - Y(e;x,z), π(e,x;z)⋅ exp(-r⋅ t) dt, Expressions (5)-(8) represent what may be referred to as the endogenous optimization bio-economic fisheries model The endogenous optimization is represented by expression (5) According to this expression, the fishing firms maximize profits or more generally their objective functions within the confines of the model This maximization procedure gives rise to fishing behaviour in the form of vectors of fishing effort Thus, this type of fisheries models may also be referred to as endogenous behaviour models It should be mentioned that endogenous optimization fisheries models, in addition to presenting a superior modelling approach, have certain very useful attributes First, they can be used to generate data on effort responses to fisheries management regimes This can be accomplished with the help of model simulations over different fisheries management regimes In this way, endogenous optimization models can be used essentially as laboratories to generate data and even to carry our controlled experiments Second, endogenous optimization models offer a way to test for loopholes in management regimes that are being prepared Fisheries management systems consist of fairly complex set of restrictions imposed on a even more complex and varied fishing industry Experience has shown that parts of the fishing industry frequently manage to discover and exploit loopholes in the system unforeseen by the system designers By virtue of their endogenous optimization features, endogenous optimization fisheries models offer a systematic method to test (at least partially) for loopholes of this kind All that is needed is to carry out extensive runs the model and observe the behaviour of the profit maximizing fishing firms Obviously, the more detailed the modelling of the industry, the more complete will this testing procedure be Third, endogenous optimization models offer a natural way toward a general equilibrium modelling of the fishery The maximization procedures of individual firms generate supply and demand functions for the relevant inputs and outputs including the supply of fish, the demand for fishing vessels etc These supplies and demands are in most institutional circumstances equilibrated via price adjustments in the corresponding markets These market transactions and equilibrating processes often have a large impact on the evolution of the fishery Hence, it is important to include them in the modelling effort This is relatively easily and straight-forwardly done within the framework of endogenous optimization models Computational Aspects Endogenous optimization models are much more computationally demanding than conventional bio-economic models The factors primarily responsible for this are the 16 maximization processes of individual firms especially when combined with market equilibrating processes In endogenous optimization models, the fishing industry tries to maximize its objective functions at each point of time subject to the relevant constraints including those of the fisheries management system This overall industry optimization problem is composed of sub-problems according to the level of modelling detail chosen, e.g the number of individual fishing firms (or representatives of groups of firms) explicitly featured in the model Each firm (or firm representative) in the model solves its own maximization problem subject to its own constraints and opportunities For realism, these individual optimization problems should normally be dynamic In virtually all fisheries, the fishing firms are faced with investment or disinvestment in imperfectly malleable capital such as fishing vessels, fishing gear, human capital etc not to mention the fish stocks themselves Hence, provided they are rational, they must solve their maximization problem over a certain (most properly infinite) time horizon This, of course, greatly complicates the maximization problem and hence the computational requirements Not only are dynamic problems intrinsically complex, their existence requires the formulation of expectations, presumably rational ones For computational efficiency, the numerical techniques to solve these dynamic maximization problems should preferably be designed for each particular situation To further speed up the calculations it may in many cases be advisable to deal with significant nonlinearities by linear segments or splines The solution to the firms' maximization problem yields among other things demand and supply, conveniently referred to as net demand (positive or negative), for commodities such as fish, fishing rights, fishing vessels etc by each fishing firm In virtually all economies these net demands and supplies are expressed in the corresponding markets8, i.e the markets for fish, fishing rights, fishing capital etc There they are made compatible with the net demands of all the other fishing firms by price adjustments Individual plans become compatible when all relevant markets reach equilibrium simultaneously, i.e the aggregate net demand in all markets are zero at the same time.9 This is referred to as a market equilibrium If a market equilibrium in this sense does not prevail, prices are adjusted until an equilibrium is located This market equilibrating process generally constitutes an important part of the progression of the fishery This applies not least in cases where new fisheries management regimes are imposed giving rise to significant shifts in market equilibria It follows that in order to adequately reflect reality, bioeconomic fisheries models should normally include market equilibrating processes of the sort described They should, in other words, include general equilibrium components This clearly adds a new level of computational complexity to the model During the market equilibration process, the firms solve their maximization problem repeatedly for new prices This gives rise to new net demands and so on However imperfectly these markets may operate More precisely the aggregate net demand is ≤ and the corresponding price = if the inequality sign applies 17 Hence, a crucial computational task of endogenous optimization fisheries models with general equilibrium components is to locate equilibria in all markets simultaneously This would normally be achieved with the help of numerical search algorithm However, since this search involves the solution of all firms maximization problems at each iteration, the process as a whole constitutes a significant computational task This iterative process is illustrated in Figure Figure Endogenous Optimization: Computational Flow Diagram Adjust prices Firms solve maximization problem Net demands Equilibrium? No Yes End As a general rule, endogenous optimization fisheries models require computational efforts several orders of magnitude greater than those of the usual empirical fisheries models The exact difference, of course, depends on the nature of the models in each case To throw some light on this consider the following example: An example Consider a fisheries model with the following dimensions: Number of fishing firms: Number of markets: Planning time horizon: N M T Let’s, moreover, assume that the number of search iterations to numerically locate solutions are: Fishing firm maxima: Market equilibria: L H 18 This means that NxMxTxLxH iterations are required to solve the model at the initial point of time The number of iterations during the next period would be the same or, alternatively NxMx(T-1)xLxH, depending on the needs of the model operator Clearly, the number of iterations may be very high Thus, for instance reasonable values for these variables for a fairly standard fishery might be: N M T L H 20 20 10 10 This means that at each point of time: NxMxTxLxH = 200.000 iterations have to be performed to calculate logically consistent behaviour within the endogenous optimization model framework Representing the same fisheries situation with a conventional empirical fisheries model essentially means that the individual firm maximization part can be dropped Notice, however, that for a properly specified exogenous optimization model, the market equilibrating process would still have to be included This is equivalent to setting L=T=1 in the above example while retaining the previous values for N, M and H Hence, for this example the exogenous optimization model requires LxT=200 times fewer iterations than the endogenous optimization variant Thus, for instance, if the exogenous optimization model takes minutes to run, the endogenous optimization version would take over 16 hours, ceteris paribus These very substantial computational requirements of endogenous optimization fisheries models are of course the main reasons why this type of models has not been in common use With the advances in computing technology, however, this type of empirical fisheries models has become feasible Hence, with their theoretical superiority, there is no reason to omit using them any more Conclusion: Applied Fisheries Economics Modelling in Coming Years As already indicated, the fisheries problem is fundamentally a problem of fisheries management and the appropriate management regime It follows that there is not very much point in constructing elaborate fisheries models of the traditional kind to calculate optimal harvesting programmes The contribution of such models is essentially only to demonstrate the advantages to be had, if proper management could somehow be implemented Contrary to traditional fisheries modelling, the main focus in applied fisheries research in coming years should be on the various types of fisheries management regimes and their efficiency attributes There are many areas for applied fisheries management research In terms of large scale fisheries modelling, endogenous optimization models would feature very high on that 19 list Other areas for research include the study of the properties of the various fisheries management systems, including (but not by any means exclusively) property rights-based systems The efficiency community management structures, the feasibility of fisheries selfmanagement and a complete decentralization of fisheries management are interesting subareas for research Other important areas for applied fisheries economics research include: (i) (ii) (iii) (iv) (v) The construction and study of ecosystem models including the interaction between aquaculture and traditional fisheries This is particularly important as this may warn us of dynamically problematic areas in the stock-capital state-space giving rise to possible irreversibilities, regime shifts, instability, strange dynamics and chaos The study of social structures for the appropriate resolution to the various conflicting uses of the ocean habitat for (a) fisheries, (b) communication, (c) conservation and tourism, (d) coastal habitation, (e) ocean mining etc This is clearly related to topic (i), the ecosystem approach The appropriate response to the problem posed by imperfect knowledge and consequently uncertainty and risk The inclusion of the spatial dimensions in fisheries models Most fish stocks continually alter location in three dimensions The location at each point of time and its rate of change are important variables for optimal harvesting Therefore, it is of some importance to come to grips with this in applied modelling The appropriate resolution to the problems posed by migratory and transboundary fish stocks as well as the high seas fisheries Applied fisheries research has long been hampered by the shortage of the appropriate data This applies not the least to economic data It seems that current data collection processes, extensive as they are in most developed countries, are simply not geared to the needs of fisheries research As a result, empirical model builders are usually forced to spend a large part of their resources on collecting the necessary data Sometimes more than one research projects find themselves collecting and re-collecting the same data Many promising modelling enterprises suffer from poor and inadequate data Others simply have to be abandoned because of lack of data It would probably be a very good investment for most fishing nations to allocate added resources to the systematic collection of fisheries data of particular use for applied fisheries modelling 20 References Arnason, R 1984 Efficient Harvesting of Fish Stocks: The Case of the Icelandic demersal Fisheries Ph.D dissertation University of British Columbia Vancouver Arnason, R 2000 Endogenous Optimization Fisheries Models Annals of Operations Research 94: 219-30 Arnason, R., P Coccorese, S Olafsson, V Placenti G and Rizzo 1997 Comparison of the Icelandic (UI) and Italian (IREPA) Fisheries Management Models FAIRCT95-0561, DP-1 Clark, C.W 1976 Mathematical Bioeconomic: The Optimal Management of Renewable Resources John Wiley and Sons, New York Clark, C.W and G.R Munro 1982 The Economics of Fishing and Modern Capital Theory: A Simplified Approach Journal of Environmental Economics and Management 2:92-106 Clark, C.W., F.H Clarke and G.R Munro 1979 The Optimal Exploitation of Renewable Resource Stocks: Problems of Irreversible Investment Econometrica 47:25-49 Crutchfield, J.A and A Zellner 1962 Economic Aspects of the Pacific Halibut Fishery Fisheries Industrial Research vol 1.1 U.S Department of the Interior Washington D.C Gordon, H.S 1954 The Economic Theory of a Common Property Resource: The Fishery Journal of Political Economy 62: 124-42 Hannesson, R 1974 Economics of Fisheries: Some Problems of Efficiency Ph.D dissertation Studentlitteratur Lund Mitchell, C.L 1979 Stock Adjustment Models, Canada´s East Coast Groundfish Fisheries Ph.D dissertation University of Ottawa Ottawa Neher, P.A., R Arnason and N Mollett 1989 (Eds) Rights Based Fishing Kluwer Academic Publishers, Dordrecht Plourde, C.G 1970 A Simple Model of Replenishable Resources Exploitation American Economic Review 60:518-22 Quirk, J.P and V.L Smith 1970 Dynamic Economic Models of Fishing In A.D Scott (ed.) Economics of Fisheries ManagementA Symposium University of British Columbia Institute off Animal Resource Ecology Vancouver Rodrigues, G 1990 (Editor) Operations Research and Management in Fishing Kluwer Academic Publishers Dordrecht Scott, A.D 1955 The Fishery: The Objectives of Sole Ownership Journal of Political Economy 63:727-56 Shotton, R 2000 (Ed.) Use of Property Rights in Fisheries Management FAO Fisheries Technical paper 401/1 and 401/2 Food an Agricultural Organization Rome Smith, V.L 1968 Economics of Production from Natural Resources American Economic Review 58:409-31 Smith, V.L 1969 On Models of Commercial Fishing Journal of Political Economy 77:181-98 Turvey, R 1964 Optimization and Suboptimization in Fishery Regulation American Economic Review 54:64-76 21 Warming, J 1911 Om Grundrente av Fiskegrunde Nationalokonomisk Tidskrift 499-511 Warming, J 1931 Aalegaardsretten Nationalokonomisk Tidskrift 151-62  ... definition? These considerations suggest the need for a practical definition of applied fisheries economics There are many possibilities Here is one: Applied fisheries economics is any fisheries economics... that fisheries economics is essentially a normative science One might even say that fisheries economics as a whole is one of the normative appendages of economic science Fisheries economics as applied. .. recommendations as to how to improve the operation of fisheries in general Was that an applied piece of fisheries economics research or not? Another adaptation of a common definition of applied scientific