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CHAPTER 3

DID POT LIMITS ELONGATE SEASON LENGTH? A SIMULATION MODEL

OF THE BRISTOL BAY RED KING CRAB FISHERY

Introduction

Fishery managers often confront the dilemma of how to arrest collapsing stocks. This problem escapes few open access fisheries, including those that are license-limited. Biological causes contributing to depressed stocks are rarely controllable and fundamental changes in management to a market-based quota system are politically difficult or impossible to implement—certainly never with the expedience required to protect collapsing stocks. Management naturally defaults to familiar command and control policies designed to attack the inimical effects of excessive fishing power. There are few or no other tools at the manager’s disposal.

The efficacy of command and control fisheries management is necessarily premised on two implicit beliefs. The controls are assumed to be effective. They also are implicitly assumed to yield social benefits from stock protection that exceed any policy-induced efficiency losses, though it is not uncommon for the management imperative to preempt any economic considerations. This paper examines the efficacy of one such effort to control fishing power in the Bristol Bay, Alaska red king crab fishery.

Concerned about the inability to manage the Bristol Bay red king crab fishery, in particular, to use in-season fishery performance to protect the stock by closing the fishery at or near the pre-season guideline harvest level (GHL), the Alaska Department of Fish and Game (ADFG), with approval from the Alaska Board of Fisheries (BOF), initiated a series of increasingly stringent pot limit policies designed to elongate the collapsing seasons by constraining the fishing power of the fleet. A uniform pot limit of 250 pots was first implemented in 1992. A court ruled this policy discriminatory against large vessels. The policy was changed to a two-tiered pot limit in 1993; vessels less than or equal 38.10 meters in length were allowed to fish 200 pots, while vessels over 38.10 meters were limited to 250 pots. More stringent limits were implemented in 1997, following the 1996 season when the GHL was exceeded by two-thirds in just four days. This new and on-going regulation adjusts the pot limit depending upon the GHL and fleet size. Notably, it reduces pot limits from 200-250 to 100-125 whenever the GHL falls between six and nine million pounds. The complete regulation is given in 5AAC 34.825 (h) (ADFG 1998). The alternative pot limits that applied during the 1991-1997 period are hereafter simply referred to as "none, 250, 200-250, and 100-125".

Concerns over the effectiveness of pot limits in elongating the season were raised as soon as they were first implemented. Greenberg and Herrmann (1994) provided an econometric analysis of potential impacts of pot limits considered by the BOF. Although the authors concentrated on the allocative consequences of pot limits, they found that pot limits were “only moderately effective” in elongating the season because they provided incentives for changes in individual vessel fishing strategy. They noted that such changes alter overall fleet fishing power, though a better understanding of fishing strategies and practices is necessary to achieve the desired fleet fishing power reduction and season length elongation.

Using observer data from a small sample of the 1997 and 1998 fleet, Tracy, Byrne and Pengilly (1999) concluded that pot limits did not help managers predict season length or target GHL because little is known about the effect of pot limits on individual fishing strategies and fleet fishing power.

Briand, Matulich and Mittelhammer (2001) addressed the issue from an entirely different perspective, one based on empirical estimation of year-specific individual catch per unit effort (CPUE) functions for the 1991-1993 and 1996-1997 Bristol Bay red king crab fisheries.[1] Using a flexible functional form, they found that CPUE is an asymptotic function of soak time. Since pot limits surely impact soak time decisions, they speculated that the pot limit policy might have been counter-productive.

Behavioral response from the crabbers may have defeated the policy intent [of season elongation] and exacerbated the in-season management problem. Ironically, the pot limit policy may have educated fishers that short soaks are effective ways to increase seasonal catch during short-season, open access fishing derbies like that of Bristol Bay red king crab (p.340-341).

The objective of this paper is to examine the speculation posited by Briand, Matulich and Mittelhammer that the pot limit policy failed to elongate the season. In particular, we construct a behavioral model to simulate how catcher vessels would operate in order to maximize quasi rents (revenues in excess of variable costs) subject to alternative pot limit constraints. Year-specific CPUE functions from Briand, Matulich and Mittelhammer are embedded in the quasi rent maximization problem. The analysis abstracts from the diversity of fishing practices and highlights relevant characteristics that distinguish representative small vessels from large ones, assuming both fish around the clock. This approach allows a clear exposition of the relationship between vessel fishing strategy and its economic performance under year-specific catch and policy conditions. Additionally, it permits insight into aggregate fleet fishing performance, season length and distributional impacts of the policy.

The next section of this paper describes the method employed to simulate optimal behavior for the individual vessel and then for the fleet. Particular attention is given to model formation and implementation. Simulation results are reported in the third section. Conclusions are presented in the final section.

Methods

The model of fishing behavior, with and without pot limits, is constructed around a complete description of the fishing process and the incentives harvesters have to adjust that process to year-specific circumstances. This model is conceptualized in a rational expectations context (Varian, 1992; Henderson and Quandt, 1980). A vessel operator is assumed to form a season length expectation prior to the start of the season in order to plan the fishing strategy, e.g., the number of pots to be fished during the fishing season or length of time the pots will soak. In reality, the season length expectation is based on a variety of factors including the pre-season GHL, fleet composition and size, and institutional constraints, like pot limits and market structure. If the expectations are correct, it is rational for the operator to follow the pre-season plan. It is not essential that the vessel operator actually knows season length in advance. The operator simply needs to behave as if it is known.

Rational expectations are modeled in a two-stage process. The first stage involves an optimization model in which the individual harvester is assumed to choose the optimal fishing strategy for a given expected season length, independent of all other vessels. The optimal strategies for the two vessel sizes are brought into equilibrium in the second stage by solving for aggregate vessel behavior, given the fleet-wide catch, fleet size and distribution. Each harvester is assumed to maximize quasi rents subject to three generic constraints: 1) implicit year-specific conditions that are embedded in the CPUE function; 2) relevant vessel characteristics, such as pot carrying capacity and variable cost structure; and 3) policy constraints concerning the maximum number of pots a vessel may fish under alternative policy scenarios. Individual vessel behavior that maximizes quasi rents is simulated under alternative policy scenarios by parameterizing the policy constraints. Fleet performance and fishery season length are determined in the second stage by aggregating across all vessels.

In stage one, individual decision variables include optimum amount of gear and soak time that maximizes quasi rents over an expected season length. These in turn, define the individual vessel catch for a given season length. The shortest season length required to catch the actual fleet-wide harvest, given stage one optimal individual vessel behavior, fleet size and composition, is determined in stage two.

This methods section is devoted first to individual vessel model development and then to the model implementation. An overview of the optimization model is presented next using a simplified representation of the optimization problem, which we subsequently expand to the full model. The expansion involves detailing how the red king crab fishing practices link into the catch functions and cost functions. The linkage between the year-specific CPUE functions and the catch component of the model is also addressed. Model implementation initially addresses how the individual vessel model is used to infer the corresponding aggregate fleet behavior and performance. The section concludes with a discussion of CPUE model calibration and the optimization procedure used to optimize the numerical model.

Simplified Optimization Model

A general representation of the harvesters’ constrained optimization problem is presented in equation (3.1).

(3.1) s.t.

where v denotes the vessel size, QR denotes quasi-rents (revenue in excess of variable costs) retained by the vessel. The symbol denotes the exvessel price of crab; denotes the crew share of gross revenue; CATCH is the total harvest by the vessel. Thus, the first term in the objective function is gross revenue to the vessel, net of crew share. The second term is the variable cost of fishing, which is a function of the number of pots fished (n), the intensity of the fishing activity – reflected by the number of times pots are turned over during the fishing season (m) and the time it takes the vessel operator to carry out the fishing plan (FT). SLEXP denotes the operator’s pre-season expectation of season length. The number of pots n that the operator fishes cannot exceed the lesser of the vessel size-specific pot limit, PotLimit, or the maximum number of pots that a vessel may fish, MaxPots. A large catcher (>38.10 meters in length) is assumed to fish at most its vessel carrying capacity of 300 pots, while a small catcher is assumed to fish a maximum of 250 pots—twice its vessel carrying capacity.

Expansion of the simplified model presented in (3.1) derives from a complete representation of the fishing process. In particular, the term CATCH potentially differs in each of three different fishing periods within a single season. These distinct periods are a consequence of the fishing process, which is now described.

The Fishing Process

The general fishing process involves setting and picking pots, as illustrated in Figure 3.1. After soaking a baited pot one, two or three days, the pot is picked from the seabed. Legal male crabs are retained, the pot is rebaited and the set-pick cycle is repeated for all pots, one at a time, until season closure. This process is common across the fleet, though vessel-specific behavior differs between the two vessel size classes.

Period one (P1) consists of the initial setting (set), picking (pick) and resetting all n pots. Small vessels that choose to fish pots in excess of their vessel carrying capacity (VCC) take an in-season trip (intrip) from the fishing grounds to a wet storage area, in order to retrieve (retrieve) additional pots (n - VCC). Small vessels first set all pots initially carried to the grounds before retrieving additional pots. It is assumed these vessels set all pots that were retrieved from wet storage before starting the picking process, rebaiting and resetting of the gear. In period two (P2), this pick-set process is repeated for all pots, conceivably m times (). Anticipation of season closure may require vessels at the end of P2 to reset only a subset of the pots. It follows that the end of P2 occurs when the subset of pots () are reset for final picking in period three (P3). Finally, the third and last period consists only of the final pick of all n pots.

Implications for Full Model Specification

The fishing process illustrated in Figure 3.1 implies catch differs across the three periods because soak times differ in each of the three periods. Thus, the variable CATCH in equation (3.1) is replaced by P1catch, P2catch and P3catch. Each of these three periodic catch functions is defined as the year-specific CPUE function evaluated at the period-specific soak time, summed over all pot lifts in the period. For example,

(3.2)

where i denotes the ith pot, and P1STi denotes the first period soak time for pot i. The parameter represents the year-specific asymptotic catch, and represents the year-specific rate at which the asymptotic catch is reached.

This analysis simplifies the prior findings of Briand, Matulich and Mittelhammer that the year-specific CPUE function rotates downward as the season progresses. Instead, the CPUE function is assumed to be constant throughout the season. Year-specific CPUE functions are chosen through a model calibration process described below under the implementation subsection.

CPUE differs across the three fishing periods because each is characterized by a different soak time. The initial period soak time (P1STi) differs from the mid-season soak time (P2ST) and the final soak time (P3STi). The first- and third-period terms are subscripted to reflect soak times differ from pot to pot, whereas the second-period soak times are constant across all pots.

Consider period 1. The soak time for the first pot that is set is determined by the amount of time it takes to initially set all other pots, including any time spent obtaining additional gear from wet storage. The soak time for the last pot is determined by the amount of time it takes to pick and reset all prior pots. The initial soak time of any other pot is determined by its exact position in the fishing sequence. This soak time accounting protocol is given in equation (3.3).

(3.3)

where, is an indicator function that captures the effect of obtaining additional gear from wet storage on pot i soak-time. This zero-one indicator equals one when the number of pots fished exceeds VCC and the th pot is in the closed interval [1, VCC]. When either of these two conditions is not met, the indicator function equals zero.