Abstract
Economic theory predicts that the least-efficient vessels are more likely to exit a fishery following the transition to an individual transferable quota (ITQ) management regime. Tools are needed to help analysts predict the likely degree and distribution of consolidation prior to implementing ITQ programs. This research utilizes a one-stage estimation procedure to determine the degree to which one’s technical inefficiency preceding an ITQ regime influences the likelihood of exiting. Our results indicate that a vessel’s measure of technical inefficiency is a significant and positive factor in explaining whether it exits the fishery following the implementation of ITQs. (JEL Q22)
I. Introduction
Economic theory predicts that open-access resource management results in rent dissipation, overcapitalization, and a lack of resource stewardship (Gordon 1954; Cheung 1970). To address these inefficiencies economists have argued that secure property rights and markets can rectify these problems and enhance the efficient utilization of our resources (Costello, Gains, and Lynham 2008; Grafton, Squires, and Fox 2000). Such a transition will in turn reduce excess capacity through consolidation among the most efficient and productive resource users. Although a number of researchers have investigated the economic benefits of switching to a rights-based management regime in fisheries, as well as whether fleet- wide measures of production efficiency and capacity utilization have increased following the implementation of such regimes (Wenin- ger 1998; Grafton, Squires, and Fox 2000; Felthoven 2002; Brandt 2007), little research has been conducted to determine whether agents’ preregime levels of technical efficiency are adequate measures to predict which vessels are more likely to remain in the fishery following the management change.1 Although retrospective analyses of efficiency changes following the introduction of individual transferable quotas (ITQs) help economists and fishery managers better understand the actual implications of such programs, predictive tools about the nature of, and degree to which, consolidation is likely to occur also have considerable value in policy formation and program design.
Although it may seem obvious that those vessels that exit a fishery following the transition to an ITQ program should be less efficient that those that remain in the fishery, it is extremely difficult to infer whether a vessel’s relative level of efficiency prior to a regime change directly maps over in the post-regime- change period, the latter being a better predictor of success following the regulatory change. This is because the incentive structures within the two environments are different, and the most efficient operating practices during a derby-style fishery may be less efficient under an ITQ regime and vice versa. Therefore, it is important that we endeavor to determine whether a vessel’s relative efficiency level prior to the regime change influences that vessel’s decision to remain active within a fishery. Failure to verify this would indicate that using measures of efficiency prior to a regime change to predict fleet restructuring is erroneous.2 This research will address this question using data on fishermen participating in the Bering Sea and Aleutian Island (BSAI) crab fisheries, prior to the enactment of an ITQ management regime, utilizing an empirical model that jointly estimates a vessel’s measure of technical inefficiency, as well as the vessel owner’s decision to exit or not following the inception of ITQs. Using this joint estimation procedure, our results indicate that a vessel’s measure of technical inefficiency prior to the introduction of ITQs is a statistically significant and positive factor in predicting whether it exited following the implementation of ITQs within these fisheries. Therefore, the assumptions made by other researchers who have been challenged with predicting how ITQs will restructure the fleet, as well as the resulting distributional impacts on regional communities and participants within the fishery, appear to be valid.
Previous research in the fishery economics literature has illustrated that sizeable efficiency gains are attainable via the implementation of ITQs and that considerable cost savings can be achieved. Using a trans-log variable cost function for fishermen operating within the Mid-Atlantic surf clam and ocean quahog fishery, Weninger (1998) conducted an ex-ante analysis that predicted that the 128- vessel fleet could be reduced to between 21 and 25 vessels as a result of the efficiency gains from consolidation. This would generate costs savings between $11.1 million and $12.8 million annually. Utilizing a similar empirical framework and cost data on 99 unique vessels within the northern Gulf of Mexico, Weninger and Waters (2003) predicted that within the northern Gulf of Mexico reef fishery the number of vessels could be reduced to between 29 and 70 vessels from 387 vessels, if they were fully utilized. These benefits would come from increased capacity utilization and efficiency, with a total cost savings between $7.86 million and $8.15 million. Expanding this analysis to the grouper fishery within the Gulf Mexico, Weninger (2008) estimated that the costs savings from implementing a rights-based management regime would be between 12% and 30%, as fewer vessels would be fishing, generating economies of scale, and fleet-wide efficiency measures would increase as the inefficient vessels leave the fishery.
The economic benefits estimated in the research conducted by Weninger (1998, 2008) and Weninger and Waters (2003) provided an a priori prediction of the expected gains that would result from a rights-based management regime. Although this research has concretely illustrated the cost savings and efficiency gains that could result from implementing a rights-based fishery management policy, the predicted degree of consolidation in the fishery is predicated upon the assumption that the most technically efficient vessels will remain in the fishery and operate at full capacity.3 This assumption is theoretically valid, but little research has been conducted to determine whether this actually happens following the transition to a rights-based fishery management regime. This said, it is important to highlight that economic theory predicts that those vessels with the highest level of overall efficiency will remain in the fishery. Although overall efficiency can be decomposed into technical, allocative, and scale components (Fried, Lovell, and Schmidt 2008), researchers rarely possess the requisite information to investigate the role that all three layers of efficiency have in fisheries, due to a lack of data. Therefore, another important contribution of this paper is to directly investigate whether technical efficiency is a useful reduced form measure of overall efficiency, when data are limited, in predicting which vessels are likely to exit following the transition to an ITQ management regime.4
We have elected to estimate technical efficiency with a primal rather than dual production model for two reasons: (1) we do not possess sufficient data (as is common in many fisheries) to estimate a dual model; and (2) a primal model more consistently reflects the incentive structure present during the time period analyzed. Within this research we focus exclusively on the time period preceding the regime change to an ITQ fishery. As has been pointed out by other researchers, derby fisheries are characterized by short-run maximization of catch and not direct cost minimization behavior (Grafton, Squires, and Fox 2000; Orea, Alvarea, and Morrison Paul 2005; Pascoe and Coglan 2002; Pascoe 2007; Wilen 2007). As such, the primal approach is a more appropriate framework in which to conduct our analysis.
Two previous studies have endeavored to answer the question of whether technical efficiency is a useful proxy for overall efficiency in predicting vessel exit (Felthoven 2002; Brandt 2007). However, these studies use a two-stage estimation routine that is subject to limitations (described in more detail below). Felthoven (2002) utilized data envelope analysis (Fare et al. 1992) and the stochastic production frontier (Aigner, Lovell, and Schmidt 1977; Meeusen and van den Broeck 1977) models to investigate how the American Fisheries Act (AFA) impacted the pollock fleet operating in the BSAI. Fel- thoven’s results indicate that fishing capacity fell by 30% and that technical efficiency as well as capacity utilization increased following rationalization. He also found that vessels that were "active" following the AFA possessed technical efficiency scores that were approximately 0.12 points higher and that they caught 15% more than idled vessels. To assess the explanatory power of technical efficiency (and capacity utilization) scores in predicting vessel activity, Felthoven (2002) utilized a logit model to determine whether one’s prerationalization technical efficiency and capacity utilization increased the probability of being active following rationalization. His results indicated that one’s technical efficiency and capacity utilization were positively correlated with one’s decision to be idle or not.
Brandt (2007) estimated a stochastic production frontier model that spanned across both the pre- and post-ITQ time periods in the Mid-Atlantic surf clam fishery. Her results indicate that the technical efficiency of vessels that remained in the fishery following the regulatory change was greater than that of the vessels that exited. Furthermore, she illustrated that the most inefficient vessels were those vessels that strategically became active during the quota grandfathering period (called reentrants in her model). Brandt’s second stage differs from that of Felthoven (2002) in that she first estimates the probability that a vessel exits the fishery and then uses this information as a determinant of vessel inefficiency. Brandt uncovers that vessels with a higher number of processor contracts (evidence of disloyalty to any one processor) as well as vertically integrated vessels were more likely to exit the fishery, whereas the most profitable vessels were not. Instrumenting these probabilities in the determinant of vessel-specific inefficiency, Brandt finds that the most inefficient vessels were also the ones most likely to exit the fishery, a result consistent with the findings of Felthoven (2002).
Tsionas and Papadogonas (2006) outline the problems with conducting a two-stage estimation algorithm. The two stages would consist of first estimating the production frontier using a standard production frontier model to uncover an estimate of an individual’s measure of technical inefficiency (Jon- drow et al. 1982). Using this estimate in the second stage to estimate the probability that a firm exits an industry will subject the estimates to the classic errors-in-variables problem, because the measurement error in the first stage will be transferred over to the second stage. Econometrically, this leads to inconsistent parameter estimates even with sufficiently large samples (Hausman 2001).Furthermore, our initial estimates of technical efficiency from the first stage will be inefficient because they ignore the information contained in the second stage of the decision process. This is why a one-step estimation algorithm more accurately tests whether the most efficient vessels within the fleet are the vessels that remain active following the inception of a rights-based management regime. This analysis jointly estimates vessels’ technical efficiency scores along with the decision to exit the fishery following the implementation of an ITQ management regime in a one- step empirical model. We also compare our results to those that would arise under a two- step approach to illustrate the implications for our application.
Recent advancements in the production literature have developed empirical models that allow one to jointly estimate production efficiency with one’s decision to exit an industry (Tsionas and Papadogonas 2006) or one’s selection of a given production practice (Kumbhakar, Tsionas, and Sipilainen 2009). Tsionas and Papadogonas (2006) use a one- step estimator to investigate whether a firm’s technical efficiency impacts the likelihood of a firm to exit the manufacturing sector within Greece. Their results indicate that the higher a firm’s technical inefficiency, the greater the probability that it will exit the industry. Expanding this framework further, Kumbhakar, Tsionas, and Sipilainen (2009) utilize the model to investigate how a firm’s technology-specific measure of technical efficiency influences its technology choice in organic Finnish dairy farms. Their results indicate that a firm’s technology-specific measure of technical efficiency positively influences its selection of a given technology.
To the best of our knowledge the aforementioned are the only papers to utilize this joint estimation framework, which has yet to be used in the fishery economics literature to address this endogeneity problem. Therefore, this research will fill this void and provide a more rigorous empirical framework to investigate these decisions, while providing analysts with a practical and useful tool to analyze and predict consolidation prior to the introduction of ITQ programs.5 The following section illustrates the empirical model utilized following the work of Tsionas and Papado- gonas (2006) and Kumbhakar, Tsionas, and Sipilainen (2009).6
II. Empirical Model
Following convention in the stochastic production frontier literature (Aigner, Lovell, and Schmidt 1977; Meeusen and van den Broeck 1977; Khumbhakar and Lovell 2000), we define
[1]where Cit is vessel i’s catch in time period t, Xit is a (K × 1) vector of production inputs (i.e., vessel length, horsepower, pots lifted, days fished, and crew), β is a (K × 1) vector of production parameters, Vit is a normally distributed random error, 
, and ui is a measure of technical inefficiency drawn from the distribution 
.7 This latter distributional assumption implies that the modal value of technical inefficiency, ui, is zero and that increasing values become increasing less likely to be observed within the population (Kumbhakar and Lovell 2000). In addition to vessel i’s catch Cit, we observe whether it exited the fishery following rationalization under the BCRP. Defining Ii as a binary variable that takes on a value of 1 if vessel i exited the fishery and zero otherwise, the probability that we observe an active vessel can be modeled as
[2]Note that ui is a measure of the vessel’s technical inefficiency depicted in equation [1]. Zi is a (S × 1) vector of data that help to explain a vessel owner’s decision to exit following rationalization that is independent of his measure of technical inefficiency ui γ is a (S × 1) vector of parameters thatquantify the influenceof a range of factors about the vessel, the vessel owner’s residence, and the proportion of revenue the owner receives from that particular crab fishery. δ is the marginal effect that the vessel’s technical inefficiency has on his decision to exit the fishery.
It is important to note that the focus of our research is only on fishing that occurred prior to the introduction of the ITQ program; the production model estimated in equation [1] utilizes data prior to rationalization in these fisheries, whereas the variable Ii merely indicates whether a vessel was active in the fishery following rationalization. The time periods that are used to construct the production model and the decision to exit do not overlap. The model does not estimate the probability that a vessel will exit the fishery at any point in time prior to rationalization, but only at the point where the fishery becomes rationalized. Given the stability of vessel participation across the years included in our data, we believe it is reasonable to attribute exit behavior to the rationalization of the fishery.
Given the reasons for modeling the process as a single-stage estimation procedure outlined earlier, equations [1] and [2] can be defined as the following system of simultaneous equations to be estimated:
where the distributions of vit and ui are independent. Denoting Ti as the number of observations for vessel i and utilizing the panel estimator outlined by Khumbhakar and Lovell (2000) to expand on work by Tsoinas and Papadogonas (2006), the joint distribution of the Cit and Ii has the following density:
Where
Defining
the integral of 
and does not possess a closed-form expression. Therefore Gaussian quadrature is required to estimate
which can be specified as
where 
and 
are the weights and base points for the numerical Gaussian quadrature conducted over J distinct points.8 To solve this numerical integration problem, the Gauss- Legendre routine in GAUSS (intquad1) was used with 40 basis points. The log-likelihood function maximized is
Following estimation of the one-stage model, the technical efficiency of the individual fishermen can be calculated using
where both integrals can be estimated using numerical Gaussian quadrature (Tsionas and Papadogonas 2006).9 Having defined the estimation algorithm, the following section outlines the fishery studied and data utilized in the analysis.
III. Fishery and Data Description
The two most abundant crab species targeted within the BSAI crab fisheries are red king crab (Paralithodes camtschaticus) and snow crab (Chionoecetes opilio). Fishing for red king crab dates back to the early 1930s, during which time the fishery was primarily dominated by foreign vessels (Barnard et al.2008). In the 1970s the fishery began to transition to a domestic fishery and catch rates increased, peaking in 1980 at 129.9 million pounds (Barnard et al. 2008). However, catch levels have substantially decreased to between 15 and 20 million pounds annually in recent years. Fishing for snow crab began much later than in the red king crab fishery, dating back to 1970. Catch levels for snow crab peaked in the early 1990s, exceeding 300 million pounds. However, these catch levels fell dramatically in 2000 when the stock was declared overfished, and recent catch levels have been between the mid-20 and mid-30 million pounds range.
Starting in 2000 the North Pacific crab fisheries were subject to a license limitation program that eliminated additional entry in the fishery. Although this put an upper bound on the number of vessels that could be used in the fishery, those who participated still operated in a common-pool environment. Therefore, the fishery was still essentially subject to the rent dissipation one would expect to observe in an open-access fishery (Homans and Wilen 1997). In 2005 the Bering Sea Crab Rationalization Program (BCRP) began and these fisheries were "rationalized."10 The BCRP created a rights-based management regime with crab quota allocated to eligible harvesters, processors, captains, and local communities. Eligible harvesters and captains received ITQs (defined as a fraction of the annual quota share pool), processors received an individual processor quota (IPQ), and local communities received a community development quota (CDQ). The allocation of both ITQs and IPQs was enacted in an attempt to address concerns over the market power that either the processors or harvesters might possess if all the quota were allocated to only one of the these groups (Anderson 1991; Clark and Munro 1980; Matulich, Mittlehammer, and Reberte 1996; Matulich and Sever 1999).
Given that the purpose of this paper is to investigate how a vessel’s technical efficiency impacts the likelihood of it remaining active in the fishery following the BCRP, we utilize data from the five years preceding rationalization (2000-2004 for the red king crab fishery and 2001-2005 for the snow crab fishery) to estimate the stochastic production frontier portion of the model. The BCRP first took effect in the red king and snow crab fisheries in 2005 and 2006, respectively. The BCRP facilitated the contraction of vessel capital employed in the federally managed fisheries that had accrued under the regulated open-access management regime. Figure 1 graphically illustrates this change. Following the inception of the BCRP (post-2004 for the red king crab fishery and post-2005 for the snow crab fishery) the number of vessels (the first higher then lower curve) dramatically decreased in both fisheries, while season length increased (the first lower then higher curve). Within the red king crab fishery the number of vessels fell from 251 to 89, a 65% reduction in the fleet, in the first year following the BCRP (2005). Within the snow crab fishery the number of vessels fell from 167 to 78 vessels, a 53% reduction in the first year following the BCRP (2006).11 Likewise the season length dramatically increased from roughly 6 days to 71 days and 13 to 155 days within the red king crab and snow crab fisheries, respectively.12
Number of Vessels and Season Length by Fishery: Red King Crab (upper), Snow Crab (lower); BCRP = Year of Inception for the Bering Sea Crab Rationalization Program
Although the number of vessels dramatically decreased following the BCRP, a direct result of the cooperatives, this does not imply that the total amount of fishing effort fell. In raw numbers labor participation fell dramatically, but when controlling for the length of the season the full-time equivalence of effort remained relatively stable (Schnier, Horrace, and Felthoven 2008; Abbott, Garber-Yonts, and Wilen 2010).
To conduct this analysis we use data from a number of sources. Fish ticket data from the Alaska Department of Fish and Game cover all vessels that participated within the red king crab and snow crab fisheries during the years 2000-2005. Each fish ticket contains information on the date fishing began, the date the vessel returned to offload the catch, the processor at which the catch was landed, the amount landed, the price per pound received for the catch, the gross revenues earned on the trip, and the number of pot lifts conducted (a lift is the deployment of gear used to catch crab). To obtain information on the vessel’s physical capital structure we obtained data from the Alaska state vessel registration files. Data on the number of crew aboard the vessel were obtained from the National Marine Fisheries Service’s Economic Data Reports (EDRs).13 Data from 2005-2007 and 20062007 for the red king and snow crab fisheries, respectively, were used to determine whether a given vessel had elected to remain active following the BCRP, the discrete choice portion of the model.
Table 1 contains descriptive statistics for the two crab fisheries, broken into groups that remained active (left two columns) and those that exited (right two columns) following the BCRP. The table illustrates that in both fisheries in the pre-ITQ years, those vessels that eventually remained in the fisheries had the largest reported catches within the fleet. Within the red king crab fishery, active vessels caught on average 28% more crab in pre-ITQ years than those vessels that were inactive following the BCRP. In the snow crab fishery the same statistic is 36%. In addition to the larger observed catch for those vessels that remained active in both fisheries, the active vessels are marginally larger (as indicated by their length and horsepower) and newer (as indicated by age, calculated as 2005 minus the year the vessel was built) than those that did not remain in the fishery following the BCRP. It should be noted that the age variable represents the age of the hull of the vessel, and vessels may be refurbished and modified throughout their lives. Therefore, the age variable should be considered a proxy for the vintage of the capital. Another interesting fact illustrated in Table 1 is that within the red king crab fishery the percentage of vessels registered to Alaska residents that remained active is greater than those that exited. This phenomenon is reversed in the snow crab fishery, where the portion of exiting vessels registered to Alaskans exceeded the portion of active vessels registered to Alaskans.
Descriptive Statistics by Fishery
IV. Empirical Specification and Results
Given that we are primarily interested in rigorously examining which factors are the best predictors of vessel owners’ participation decisions in the transition to an ITQ management regime, rather than the effects of rationalization, we have elected to focus our analysis on the five years of harvests preceding the BCRP in both fisheries. This time frame was selected as it represents the time period leading up to the regime change and during which vessel owners jointly conducted their production activities and were cognizant of the fact that a regime change was in the works. Because their production activities and upcoming decision to exit following rationalization were inextricably linked, the need for a single-stage estimation procedure is particularly warranted. We do not model production over the pre- and post-regime change because, as noted by Wilen (2007) and discussed earlier, it is highly possible that the production technology itself may change when the transition occurs. Following the transition to ITQs the incentive structure changes from that of output maximization to cost minimization or profit maximization, and the parameters characterizing the marginal values of factors of production may change. However, this does not compromise our analysis, because it is impossible for a firm to accurately predict how its overall efficiency will change prior to the regime change. The firm must still base its decision to exit or not on its prior performance in the fishery, hence the focus of our analysis.
To obtain the reduced form specification for the stochastic production frontier, we started with the full translog specification based on five different inputs of production: two fixed inputs (Lengthi and Hpi) and three variable inputs (Crewit, Potsit and Daysit).Following this construction, we eliminated all variables that had a linear correlation with one of the primary production inputs greater than 0.90,to reduce the potential for multicolinearity. Additional parameters were removed from the model using likelihood ratio statistics to obtain aset of parameters that represent the core production determinants and interaction terms. The final reduced form specification for the stochastic production frontier and the discrete choice to remain active within each respective BSAI crab fishery (red king and snow crab) is14
[3]Lengthi is the length of the vessel expressed in feet, Hpi is the vessel’s horsepower rating,15 Crewit is the average crew size utilized by the vessel on trip t, Potsit is the number of pots lifted on trip t, Daysit is the number of days a vessel fished on trip t, Yrsi are annual dummy variables used to control for year-to-year variation in the stock abundance and other time- specific unobservables,16 Agei is the vessel’s age measured as the difference between the year the vessel was built and the last year of fishing before the BCRP, Per_revi is the average percentage of a vessel’s Alaska-wide annual revenues that are derived within the respective fishery, AK_vesii is a dummy variable that takes a value of one if a vessel is registered in Alaska, and ui represents the degree of inefficiency of each vessel in each year, relative to the frontier.17 The magnitude and statistical significance of the parameter δprovides information on the degree to which vessel inefficiency impacts the likelihood of a vessel exiting the fishery after the transition to the ITQ regime.
The results from the estimation are contained in Tables 2 and 3 for the red king crab and snow crab fisheries, respectively. Three alternative specifications for 
were estimated to investigate the robustness of our findings to the error distribution assumptions latent in the discrete choice to exit or remain active following the BCRP. The first model assumes that the errors are independently and identically distributed (i.i.d.) normally distributed, which generates a probit probability function (probit column title), the second assumes the errors are i.i.d. logistically distributed generating a logistic probability function (logistic column title), and the third assumes the errors are i.i.d. generalized extreme value (GEV) (extreme value column title). We have also estimated a two-stage estimation model to compare with the different one-stage estimation results. In the first stage we estimated a stochastic production frontier model, and in the second stage we estimated a probit regression of the decision to exit the fishery or not that includes the measure of vessel technicalinefficiency obtained from the first stage.
Regression Results for the Red King Crab Fishery, by Model Specification for the Joint Estimation
Regression Results for the Snow Crab Fishery, by Model Specification for the Joint Estimation
In the red king crab fishery all the production frontier parameter estimates are statistically significant, except for the constant parameter. Furthermore, all the annual dummies are negative and statistically significant, indicating that landings per a unit of effort were lower in the years preceding the BCRP, ceteris paribus. In the snow crab fishery all of the fixed and variable inputs of production are statistically significant except for the coefficient on days fished and crew. In addition, the year-specific dummy variables are all negative and statistically significant, indicating that, ceteris paribus, catch per unit of effort was lower than that observed in the year immediately preceding the inception of the BCRP. The signs of the annual dummy variables in both models are consistent with the general trend in the stock assessments in both fisheries (Bechtol et al. 2010). However, the stock assessment data for the snow crab fishery does indicate that stocks were high in 2001 relative to 2005. Therefore, the dummy variable for 2001 in the snow crab fishery is also capturing other unobserved factors in this time period that were driving down catch rates.
To provide more detail on the production profile, elasticities were estimated using the Krinsky and Robb (1986, 1990) method with 1,000 draws from the parameter estimates var- iance-covariance matrix for both fisheries, using the one-stage estimation results.18 The results are illustrated in Table 4.19 Within the red king crab fishery all of the elasticity estimates are statistically significant except vessel horsepower. In the snow crab fishery the only statistically significant elasticity estimates are vessel length and the number of pots lifted. In both fisheries the elasticity for pots lifted is substantially larger than the other elasticity estimates, indicating that this is the most significant factor of production within both fisheries.
Elasticity Estimates for the Red King Crab and Snow Crab Fisheries
The large magnitude of the pots lifted elasticity in both fisheries illustrates that deploying more pots was particularly effective under the race-for-fish regime modeled in this paper; throughput was at a premium to maximize one’s share of the total allowable catch. The primary difference between these two fisheries is that the elasticities for days and crew are statistically significant in the red king crab fishery but not in the snow crab fishery. One possible explanation for these differences is the trip lengths induced by the seasonal constraints on these fisheries. The red king crab fishery was a much shorter fishery, whereas trip length for the snow crab fishery was on average twice as long (see Table 1). Because the trip length during this time period was twice as long in the snow crab fishery, vessels may have been able to more easily fill their holds within a season, whereas this was more difficult in the red king crab fishery. Therefore, the marginal value of an extra day fishing would be higher in the red king crab fishery than in the snow crab fishery, because the season constraint binds the trip length more within this fishery than in the snow crab fishery.
Turning to the parameter estimates for a vessel owner’s decision to exit these fisheries following the BCRP, we observe that the probability of exit increases with a vessel’s age as well as its measure of technical inefficiency, and decreases with its size, as indicated by the coefficient on length. In addition, within the snow crab fishery the percentage of a vessel’s Alaska-wide revenues that are derived from this fishery positively influences its decision to exit the fishery.20 This result is consistent with the recent findings of Lazrus et al. (2010) in their study of the postrationalization restructuring within the BSAI crab fisheries. Lazrus et al. (2010) find that vessels that were highly specialized in crab fishing, in terms of percentage of annual earnings, were more likely to exit than vessels that participated in other fisheries off Alaska. This result is more pronounced within the snow crab fishery relative to the red king crab fishery, because the red king crab vessels have been more likely to participate in other fisheries off Alaska, a trend that may explain whythe coefficient on a vessel’s percentage of annual landings obtained in the red king crab fishery is not statistically significant.
The positive and statistically significant coefficient on technical inefficiency (δ) in both fisheries illustrates that our use of technical efficiency, a component of overall efficiency, is a good predictor of a vessel owner’s exit decision following the transition to an ITQ fishery. This confirms the conventional assumptions made in the fisheries literature, albeit using a more rigorous empirical specification that has not been used to investigate this decision in the fisheries literature. Furthermore, these results are consistent regardless of the empirical specification used to estimate the probability of exiting following rationalization.
Comparing the one-stage estimation results to those obtained using a two-stage estimation algorithm, we see that for both fisheries the two-stage estimation results are consistent with those obtained in the one-stage model. Although the models are consistent according to the sign and statistical significance of the coefficients, the magnitudes differ from those observed in one-stage model. In addition, the estimated variance of technical inefficiency, 
for both models is substantially smaller than that observed in the one-stage estimation procedure. These differences will result in different technical efficiency distributions relative to the one-stage estimator. This will be discussed in more detail in the upcoming section, as will the stability in the resulting technical efficiency measures and comparisons across those that exit and remain active within the fishery.
Technical Efficiency
The distributions of technical efficiency estimates are consistent across the three different specifications utilized in our analysis: probit, logistic, and GEV.21 Figures 2 and 3 graphically illustrate the technical efficiency distributions for the red king crab and snow crab fisheries, respectively, using the results from the one-stage estimation routine. The results are illustrated using the estimates for all vessel types (intrafleet comparisons are discussed in the upcoming paragraphs). The technical efficiency estimates within the red kingcrab fishery are more right-skewed than those within the snow crab fishery. A majority of the distributional mass within the red king crab fishery is above 0.70, whereas a sizeable portion of the distributional mass within the snow crab fishery lies below 0.70, and the overall distribution is flatter than within the red king crab fishery.22
Technical Efficiency Distribution for the Red King Crab Fishery Broken Down by Error Assumptions in the Regression Model
Technical Efficiency Distribution for the Snow Crab Fishery Broken Down by Error Assumptions in the Regression Model
The one-step estimator for both the red king crab and snow crab fisheries indicates that those vessels that were more inefficient were more likely to exit the fishery following the BCRP. Table 5 illustrates the differences in the vessel-specific technical efficiency estimates for all three model specifications (i.e., probit, logit, and GEV) and both fisheries. Within the red king crab fishery the average technical efficiency scores for vessels that exited the fishery are 0.8311,0.8317, and 0.8296 for the probit, logistic, and GEV specifications, respectively. The average technical efficiency scores for vessels that remained active within the fishery are 0.9417,0.9432, and 0.9421 for the probit, logistic, and GEV specifications, respectively. To graphically demonstrate the distributional differences between those vessels that exited and remained active in the red king crab fishery, Figure 4 illustrates the cumulative density function (CDF) of the technical efficiency estimates for these two subsets of the fleet. This figure illustrates that the technical efficiency scores begin at around 0.38 for vessels that exited the fishery, and begin at around 0.82 for vessels that remained active. Therefore, the technical efficiency distribution for vessels that remained active is centered around the most efficient vessels within the fleet.
Technical Efficiency Descriptive Statistics for the Red King Crab and Snow Crab Fisheries
Cumulative Density of Technical Efficiency Estimates within the Red King Crab Fishery Broken Down by Exited and Active Vessels
To test whether the mean technical efficiency of vessels that remained active was greater than that of those vessels that exited the fishery we used the convolution method (Poe, Giraud, and Loomis 2005). Using each of the 1,000 draws from our Krinsky and Robb (1986, 1990) elasticity estimates, we estimated the mean technical efficiency for those who exited the fishery as well as those who remained active. Following this we convoluted all possible combinations of differences (one million in total) to simulate the empirical distribution of the mean differences. The results are illustrated in Table 6. These results support the hypothesis that the mean technical efficiency of those who remained active within the fishery was greater than that of those who exited. On average (averaged across the three model specifications) the technical efficiency score for those who remained active was 0.1068 higher than for those who exited the fishery.
Confidence Intervals (95%) for the Hypothesis Test That the Mean Technical Efficiency for Active Vessels Exceeds That of Those Who Exit the Fishery
The results for the snow crab fishery are similar to those observed within the red king crab fishery. The mean technical efficiency scores of vessels that exited the fishery were 0.7638, 0.7625, and 0.7670 for the probit, logistic, and GEV specifications, respectively, whereas the corresponding estimates for those that remained active were 0.8626, 0.8634, and 0.8677. The distributional differences across these two subfleets within the snow crab fishery are not as pronounced as within the red king crab fishery. To illustrate this, Figure 5 plots the CDF of the technical efficiency estimates for the two subfleets within the snow crab fishery. Both of the CDFs—for those who exited and for those who remained ac- tive—begin at around a technical efficiency score of 0.36, but the primary difference is that the distributional mass for those vessels with a higher technical efficiency score is greater for those vessels that remained active versus those that exited. This said, the most efficient vessel within the snow crab fishery prior to the BCRP (estimated within the probit and logit models—this does not hold for the GEV model) did exit the fishery. However, the second-most efficient vessel, with a technical efficiency score exceeding 0.99, remained within the snow crab fishery. This further illustrates that the distributional differences across these two subfleets is not nearly as stark as within the red king crab fishery.
Cumulative Density of Technical Efficiency Estimates within the Snow Crab Fishery Broken Down by Exited and Active Vessels
To test whether the mean technical efficiency of those vessels that remained active was greater than that of those who exited the fishery, the convolution method (Poe, Giraud, and Loomis 2005) discussed earlier was repeated using the snow crab fishery results.The results indicate that the average technical efficiency of those vessels that remained active exceeded that of those who exited the fishery. The average difference (across the three different models estimated) between these two subfleets was 0.1020, which is very similar to that observed within the red king crab fishery. Therefore, although the intrafleet difference in the distribution of technical efficiency is not as stark as with the red king crab fishery (see Figure 5 vs.Figure 4), the average differences are strikingly similar.
The two-stage estimation procedure generates a different profile of technical efficiency for vessels within the red king crab and snow crab fisheries than the one-stage estimator. In both fisheries the average technical efficiency estimate is greater in the two-stage model than in the one-stage model; the average two-step technical efficiency estimate within the red king crab fishery is 0.9586, and it is 0.9181 in the snow crab fishery. Comparing those fishermen who exit the fishery and those that remain fishing generates similar results to those observed in the one-stage model, but the magnitudes of the differences are much smaller. Within the red king crab fishery the average technical efficiency for those that remained in the fishery was 0.9676, whereas it was 0.9417 for those that exited. Within the snow crab fishery the differences are slightly larger. The average technical efficiency for those that remained was 0.9477, whereas it was 0.8626 for those that exited. The most striking difference is illustrated in the convolution results used to determine whether the two distributions—the technical efficiency for those who remain fishing versus exit the fishery—are statistically significant. The results for the red king crab fishery indicate that the technical efficiency scores are not statistically different, whereas those in the snow crab fishery indicate that they are statistically significant. Although, the snow crab results are similar to the one-stage estimates, it is also important to note that magnitude is less than a third of what it is in within the one- stage model.
In summary, all of these results are in accordance with our a priori predictions that the average technical efficiency estimates for those vessels that remained active within the fishery were greater than those that exited. Our results provide support for the hypothesis that technical efficiency can serve as a good proxy for overall efficiency in predicting the exit behavior of fishermen prior to the transition to an ITQ program. This suggests that using efficiency analysis to forecast compositional changes in fisheries can be instructive, and that ceteris paribus, more technically efficient vessels are likely to comprise the post- ITQ fishery when such regimes are instituted. Furthermore, our results highlight the differences that may arise when using a one-stage versus a two-stage estimation procedure, due to the statistical issues discussed by both Tsionas and Papadogonas (2006) and Hausman (2001). However, it is important to note that the observed differences in this research may not transfer to other fisheries.
V. Conclusion
Utilizing a one-step econometric model to investigate a vessel’s decision to remain active or exit following the transition to a rights- based management regime, we illustrate that the more inefficient a vessel is relative to others within the fleet, the more likely it is that it will exit the fishery when consolidation occurs. This result is similar to that found in other research efforts utilizing a two-stage estimation process (Felthoven 2002; Brandt 2007) but avoids the shortcomings of the two- stage approach pointed out by Tsionas and Pa- padogonas (2006). Furthermore, our empirical results indicate that those vessel owners that remained active in both fisheries possessed a higher mean technical efficiency score than those that were inactive.
From a policy perspective this analysis generates two important results. First, the conventional assumptions made by researchers to facilitate ex-ante policy analysis were valid in our study; using measures of technical efficiency to proxy for measures of overall efficiency provided a good metric to predict fleet restructuring prior to the inception of an ITQ management regime. This said, it is important to note these results are specific to the fishery studied and further research is necessary to generalize these findings to fisheries at large. However, given that the incentive structure present prior to the enactment of an ITQ regime is consistent with output maximization versus cost minimization (Grafton, Squires, and Fox 2000; Orea, Alvarez, and Morrison Paul 2005; Pascoe and Coglan 2002; Pascoe 2007; Wilen 2007), constructing measures of technical efficiency may in fact be the better approach for modeling production practices prior to the ITQ regime. Our second and related policy-relevant result is that the transition from a derby fishery to an ITQ fishery does appear to lead less efficient vessels to exit and more efficient vessels to remain, which is consistent with economic theory. Because our efficiency measures were based upon the derby-based performance, this suggests that those vessel owners who were most efficient in the derby may be more inclined or better positioned to successfully transition into the rationalized fishery, even though their capital structure and fishing platform were likely optimized for derby conditions. In future research we plan to analyze the performance of the remaining vessels and the way in which vessel owners exploit efficiency arbitrage opportunities within harvesting cooperatives to maximize economic gains by using the most efficient set of vessels to land their quota.
Acknowledgments
We would like to acknowledge Efthymios Tsionas and Theodore Papadogonas for providing us with the GAUSS code used in our estimation as well as the thoughtful referee reports we received from two anonymous referees who helped to improve the quality of this research. All errors and omissions are the sole responsibility of the authors. We would like to acknowledge the funding support from NOAA Fisheries Office of Science and Technology. Schnier would also like to acknowledge the funding provided by the NSF (Award #0719105) that facilitated the execution of this research.
Footnotes
The authors are, respectively, associate professor, Department of Economics, Andrew Young School of Policy Studies, Georgia State University, Atlanta; and economist and program manager, Alaska Fisheries Science Center, U.S. National Marine Fisheries Service, Seattle, Washington.
↵1 The "rights" we are referring to throughout this paper are, more precisely, limited access privileges because they are revocable privileges awarded by the federal government.
↵2 Efficiency-based data envelopment analysis or stochastic production frontier models have been applied to fisheries more frequently than cost- or profit-based analyses due to the lack of cost data available for most fisheries (Weninger 1998; Felthoven 2002; Pascoe and Coglan 2002; Orea, Alvarea, and Morrison Paul 2005; Grafton, Squires, and Fox 2000; Brandt 2007). However, because the frontier models do not fully characterize the economic decision-making process, there is some question as to whether these models canadequately predict economic behavior (specifically, exit decisions).
↵3 Wilen (2007) notes that it also possible that the technology selected following a change to an ITQ fishery may change as well and warns that determining the optimal size of the fleet in a post-ITQ period using pre-ITQ data may be problematic.
↵4 Grafton, Squires, and Fox (2000) in their analysis of the British Columbia halibut fishery do conduct a pre- and post-regime change analysis of overall efficiency and discovered that smaller vessels increased their technical and allocative efficiency, whereas larger vessels increased their cost efficiency following the transition.
↵5 The National Marine Fisheries Service has made it a priority to introduce more of these "catch share" programs throughout U.S. waters.
↵6 We would like to thank Efthymios Tsionas and Theodore Papadogonas for providing us with the GAUSS code used in our estimation.
↵7 The specification of our model follows the work of Tsionas and Papadogonas (2006) as well as Kumbhakar, Tsionas, and Sipilainen (2008). The notation and econometric theory follows Tsionas and Papadogonas (2006).
↵8 Alternatively simulated maximum likelihood could be utilized. However, as pointed out by Tsionas and Papadogonas (2006), because the integral is univariate, Gaussian quadrature is more precise than maximum simulated likelihood methods.
↵9 As was conducted by Tsionas and Papadogonas (2006), to facilitate the numerical Gaussian quadrature, technical efficiency, TEi = exp(− ui),, was used to transform the numerical integrations to the 0,1 domain because TE is bound between 0 and 1 via the following property: ui = − ln(TEi). Therefore, a vessel’s technical efficiency is directly incorporated into the likelihood function via this transformation.
↵10 The term "rationalization" is used commonly in fisheries to refer to programs that convey access privilegesto individuals, often in the form of a quota linked to a given amount or share of fish, providing rational incentives to harvest the fish in a more cost-effective manner than under a derby-style fishery.
↵11 Statistics are based on the reported non-CDQ landings. The data set used in our analysis contains the entire non-CDQ fleet with a few vessels removed from the analysis due to data limitations.
↵12 In the pre-BCRP era the maximum season length was determined by adding two days prior to the announced season opening, because vessels were allowed to leave port at this time, and two days after the announced closure to allow for travel to port foroffloading. All reported season lengths are obtained by truncating the reported start and land dates using these assumptions and then calculating the trip length within this window of time. The most binding truncation of the potential season length is the reported landing date, as many vessels have reported landing dates that often reflect them waiting at port for over a week to offload their landings. Given that this wasnot active fishing time, we elected to employ this season truncation based on the estimated time it takes for a vessel to get into port from the fishing grounds.
↵13 The EDR data was recorded in 1998, 2001, and 2004 2007. For the years in which no EDR data were collected, we used vessel-specific averages from other pre-BCRP years to impute crew size.
↵14 The subscripts on β6 indicate whether the parameter β6 was active for the red king crab fishery (subscript rkc) versus the snow crab fishery (subscript snw).
↵15 In the discrete choice model, length was divided by 100 and horsepower was divided by 1,000.
↵16 We explored using stock information in the regression model directly, but the variable generated substantial multicolinearity in our model (with the annual dummy variables). Therefore, we elected to retain the annual dummies as controls to capture the suite of potential environmental variables affecting mean annual catch levels.
↵17 In the case that any of the abovementioned observations were missing, we used propensity score nearest-neighbor matching to impute the missing values (Rosenbaum and Rubin 1983; King et al. 2001). The variable that was most influenced by the imputation method was the crew variable. We imputed roughly 14% and 28% of the crew observations within the red king crab and snow crab fisheries, respectively.
↵18 The elasticities for the two-stage estimators generated qualitatively similar results to those observed in the one- stage estimator. However, the magnitude of a few of the elasticities were marginally different. We have elected to not illustrate these results and to instead focus on the implications of the different model specifications on the technical efficiency estimates.
↵19 Within the two fisheries the regularity conditions were nearly always met at the observation level. The only exception to this is that approximately 17% of the vessel-specific observations did not meet the implied regularity conditions for vessel horsepower in both fisheries.
↵20 Being an Alaska registered vessel is statistically significant at the 90% level for one of the specifications in the snow crab fishery (probit). However, given that it is not statistically significant in the other models, logit and extreme value, we have elected to remove it from the general discussion.
↵21 For all of the models we scaled the technical efficiency measures so that the highest observed technical efficiency in the model was one to facilitate relative comparisons across models.
↵22 Since the models are estimated separately and allow for different fishery-specific technologies, the efficient frontier in each model is relative to each technology and thus does not allow for efficiency comparisons of the vessels across models (fisheries).
