Modeling Effects of Habitat Closures in Ocean Fisheries

Theoretical and practical problems arise when Random Utility Models (RUM) of spatial choice developed for recreational fisheries are applied to model spatial closures in ocean commercial fisheries for creating marine protected areas. The RUM clearly has important advantages. To be consistent with RUM and also be relevant to actual closure decisions for open-ocean fisheries, models of habitat-driven fishery closures should avoid imposing unrealistic assumptions about spatial decision-making while incorporating detailed and flexible geographic scales. I describe an approach that satisfies these criteria and is easily estimated with the type of data commonly available to fisheries managers, and discuss an application to North Pacific groundfish closures. INTRODUCTION Resource managers are increasingly requested to make decisions to restrict commercial fishing for the benefit of protected species, with uncertainty about the value of reserved habitat to the fishing industry as well as to the species at risk. Claims of high annual losses by fisheries organizations cannot be independently evaluated in the absence of a scientifically defensible method to estimate the cost of the time and area closures around critical habitat areas. The controversy surrounding these actions suggests that there is an urgent need to develop objective methods to quantify their cost. Methods exist for estimating the costs of fishery time and area closures, based on extensions of the Random Utility Model (RUM) (McFadden, 1981). RUM has important theoretical advantages for dealing with spatial decision-making under uncertainty, as well as computational advantages for estimating welfare effects. For two decades, studies have relied on RUM to estimate non-market values for recreational fisheries, and the literature on applications to commercial fisheries is now growing rapidly. I argue, however, that theoretical and practical problems arise with traditional applications of RUM to model spatial decisions in ocean fisheries. These problems call into question the utility of the standard RUM approach to quantify the opportunity costs of decisions creating marine protected areas. In this paper, I discuss the limitations of RUM applications to commercial ocean fisheries, and propose a new approach that solves these problems. The new approach is theoretically consistent with RUM and is easily estimated with the type of data commonly available to fisheries managers. In the next section, I review the standard RUM approach to modeling spatial choice in commercial fisheries, and discuss its limitations for modeling time and area closures in ocean fisheries associated with creation of marine protected areas. I then outline a new empirical approach that extends RUM to address need for detailed and flexible geographic scales relevant to decisions regarding spatial closures in ocean fisheries. Next, I demonstrate the new approach in an application to the North Pacific groundfish fisheries. I conclude with a discussion of potential applications of the model to resource management decisions. 1 Cite as: Berman, Matthew. 2006. Modeling effects of habitat closures in ocean fisheries, p. 27-38. In: Sumaila, U. Rashid and Marsden, A. Dale (eds.) 2005 North American Association of Fisheries Economists Forum Proceedings. Fisheries Centre Research Reports 14(1). Fisheries Centre, the University of British Columbia, Vancouver, Canada. 2 Email: [email protected] Modeling effects of habitat closures, M. Berman 28 RANDOM UTILITY MODELS FOR COMMERCIAL FISHERIES RUM was initially developed to model transportation mode choice (Ben-Akiva and Lerman, 1985; Domencich and McFadden, 1975). Early applications to natural resources focused on estimating demand for recreational fisheries and associated non-market values (Bockstael et al., 1989). RUM was first extended to commercial fisheries by Bockstael and Opaluch (1983), and has increasingly been used to model spatial economic decisions in fisheries (Dupont 1993; Holland and Sutinen 2000). Its advantages include the ability to model choices among multiple spatial alternatives, straightforward computation using maximum likelihood techniques, and direct derivation of welfare estimates under a reasonable set of assumptions (Small and Rosen, 1981). RUM has a number of limitations, however, based on restrictions it imposes on modeling agents' choice structures. Most widely discussed is the problem of independence of irrelevant alternatives (IIA) embedded in the multinomial logit model characteristic of RUM (McFadden, 1981). IIA is a relatively minor issue in commercial fishery location choice, however. In essence, it says that closing or opening one fishing area has no effect on the relative attractiveness of the areas that remain open. Other RUM assumptions about the choice set, though less discussed, are much more problematic for applications RUM to ocean fisheries. Initial applications of RUM to natural resource management fit into the well-established travel-cost model, where the choice set consisted of a small set of discrete alternatives such as lakes, state parks, or boat launch sites. Extensions to spatial management of coastal commercial fisheries such as salmon and shellfish, where alternatives consist of bays and estuaries (Dupont, 1993; Berman et al., 1997), seem reasonable. But spatial choice in ocean fisheries (Holland and Sutinen, 2000; Curtis and Hicks, 2000) is clearly different. Ocean fishers pursue both resident and migratory fish in large expanses of habitat along continuous geography. The open ocean presents a potentially infinite set of choices – or at least a large number – in which alternatives may theoretically exceed the number of observations in the data set. Discrete choice models such as RUM apply best when the choice set mimics real decisions. Computational limits of algorithms for maximum likelihood estimates of coefficients of nonlinear equations effectively constrain the number of alternatives that can be considered in an empirical application. Even with advances in computing power, multicollinearity makes it increasingly difficult to invert the matrix of partial derivatives (required for estimates of standard errors) as the number of alternatives rises beyond 40 or 50. This effectively limits evaluations of ocean fisheries to large geographic units, whose boundaries are necessarily arbitrary. Attempting to match choice set boundaries to the boundaries of proposed marine reserves highlights the contradiction with the standard RUM approach. How can fishers decide whether or not to fish within an area of the ocean whose boundaries have not been identified when they make their choices? Yet to be consistent with theory, the choice set must be known in advance, with alternatives considered by the fleet as independent options. The lack of conformity to realistic decision sets casts doubt on the validity of all empirical research addressing fishery time and area closures that do not conform to established regulatory jurisdictions, especially those whose boundaries were identified after the time interval represented in the data. A recent paper by Haynie and Layton (2004) illustrates the limits of what can be done with RUM models of habitat closures in ocean fisheries. Haynie and Layton estimated a spatial choice model for pollock trawl fishing in the Bering Sea, assuming a choice set consisting of the 18 statistical reporting areas that accounted for most of the harvest between 1995 and 1998. The Bering Sea groundfish fisheries operate across a region spanning several hundred thousand square kilometers, with a complex coastal and subsurface geography; a realistic choice set for the trawl fleet would contain a much larger set of locations. Haynie and Layton (2004), despite its flaws, provides a framework from which to estimate a cost for closures of large areas, such as the Steller Sea Lion Conservation Area designated north of Unimak Pass, using the established RUM methods. However, this and other standard RUM applications lack the ability to address costs for the irregular spatial boundaries of designated Steller sea lion critical habitat closures now in effect across the North Pacific, as well as for proposed new marine reserves. Furthermore, existing methods lack the flexibility to be useful in evaluating how adjustments to closure boundaries might affect the fishing industry: decisions resource managers often have to make. To be useful to managers making 2005 NAAFE Forum Proceedings, U.R. Sumaila and A.D. Marsden 29 decisions that include spatial ecological data, a method of valuing habitat-driven fishery closures should be able to model differences at much finer resolution over a large geographic space than current RUM models allow. A DISCRETE CHOICE MODEL WITH A LARGE CHOICE SET I start with the assumptions of a Random Utility Model for spatial choice in commercial fisheries. Suppose nk identical fishers seek operating profit Vjk from a set of geographic areas Jk available at choice occasion k. The probability πjk that a vessel chooses area j ∈ Jk is given by: (1) logπjk = αVjk − γk, where α = 1/σ is a scaling parameter, Σj∈Jk = nk, and (2) γk = logΣj∈Jk eαVjk The probabilistic choice model given by equations (1) and (2) is simply a logarithmic parameterization of the standard RUM model. The motivation for the somewhat unusual specification will become clear in a moment. As specified, the scale factor γk represents the "inclusive value" in the RUM context. It varies across choice occasions, k, but is constant across areas during any given choice occasion. Now suppose that the choice set, Jk, contains a very large number of choices, so that the probability that a fisher selects any particular alternative j at choice occasion k approaches zero. Also suppose that we observe a large number of vessels, nk, so that it is reasonable to anticipate observing at least one vessel selecting area j during at least one occasion k within the scope of the empirical investigation. Under these assumptions, the number of vessels yjk observed harvesting in area j during occasion k may be approximated by a poisson distribution. That is, if λk = nkπjk, (3) prob(yjk = y) = λk exp(−λk)/y! The model summarized above extends RUM in a manner not yet attempted for commercial fisheries. It is analogous, though, to the approach proposed by Guimaraes et al. (2003) to model decisions to locate industrial facilities among a large set of geographic choices. As Guimaraes et al. originally proposed it, the scale factor, γ, was a constant, corresponding to a single choice occasion. In this case, estimating the parameters of equation (3) is a straightforward application of poisson regression. In most RUM applications to natural resources, however, resource abundance may vary over time, and agents based in different locations may have different travel costs. The inclusive value may vary over time and place, and may even vary among individuals if agents have individual-specific preferences or cost differences (such as different opportunity costs of time). In this case, γk, would differ for every case in the dataset. It is still possible to estimate equation (3) with standard maximum likelihood techniques, preserving the necessary parameter restrictions embedded in equations (1) and (2). But if the number of choice occasions is not too large -for example, if the inclusive value varies only over time and place -then the estimation may be dramatically simplified. Suppose one specifies αVjk as a linear function of a vector of variables xjk and associated parameters β, and hypothesizes a poisson probability with a mean of μk = nkexp(xjkβ + gk),