EMPIRICAL MODELS OF THE FISHERY PRODUCTION PROCESS:
CONFLATING TECHNOLOGY WITH INCENTIVES?
Matthew N. Reimera*, Joshua K. Abbottb, and Alan C. Hayniec
a
Assistant Professor, Institute of Social and Economic Research, Department of Economics,
University of Alaska Anchorage, 3211 Providence Drive, Anchorage, AK 99508,
[email protected]
b
Associate Professor, School of Sustainability, Global Institute of Sustainability, and Center
for Environmental Economics and Sustainability Policy, Arizona State University, P.O. Box
875502, Tempe, AZ, 85287, [email protected]
c
Resource Ecology and Fisheries Management Division, Alaska Fisheries Science Center,
National Marine Fisheries Service, NOAA, 7600 Sand Point Way NE, Bldg. 4, Seattle, WA
98115, [email protected]
* Corresponding Author
Running Title: CONFLATING TECHNOLOGY WITH INCENTIVES?
Abstract
Conventional empirical models of the fishing production process inadequately capture the
primary margins of behavior along which fishermen act, rendering them ineffective for policy
evaluation.
We estimate a conventional production model for a fishery undergoing a
transition to rights-based management and show that ex ante production data alone arrives at
misleading conclusions regarding post-rationalization production possibilities—even though
the technologies available to fishermen before and after rationalization were effectively
unchanged. Our results emphasize the difficulty of assessing the potential impacts of a policy
change on the basis of ex ante data alone. Since such data are generated under a different
incentive structure than the prospective system, a purely empirical approach imposed upon a
flexible functional form is likely to reflect far more about the incentives under status-quo
management than the actual technological possibilities under a new policy regime.
Keywords: policy evaluation, production function, fisheries, policy invariance, hyperbolic
distance function, targeting ability, bycatch.
JEL classification: D24, Q22
Introduction
Empirical models of the fishery production process play an important role in
informing fisheries policy. Both primal and dual models are used to assess technical
efficiency (e.g., Kirkley, Squires and Strand, 1995; Flores-Lagunes, Horrace and Schnier,
2007), measure excess capacity in limited entry regimes (e.g., Felthoven, 2002; Felthoven,
Horrace and Schnier, 2009; Horrace and Schnier, 2010), and assess evidence of technical
change (e.g., Squires and Vestergaard, 2013a, b) and skipper skill (e.g., Kirkley and Squires,
1998; Squires and Kirkley, 1999; Alvarez and Schmidt, 2006). They are also extensively
used prospectively to predict the effects of input controls (e.g., Squires, 1987a; Dupont,
1991) and examine the potential for consolidation (e.g., Weninger and Waters, 2003;
Weninger, 2008; Lian, Singh and Weninger, 2010) and substitution across multiple species
(e.g., Squires, 1987b; Squires and Kirkley, 1991; Squires, Alauddin and Kirkley, 1994;
Squires and Kirkley, 1996; Pascoe, Koundouri and Bjørndal, 2007; Pascoe, Punt and
Dichmont, 2010) in the wake of output controls or multi-species ITQs.
The dominant empirical approach to fisheries production modeling has been to adapt
production models used in other industries to a fisheries setting. For example, as agricultural
economists have modeled agricultural yield as a function of water, soil type, fertilizer, and
other inputs, fisheries economists have hypothesized catch to be a function of inputs such as
vessel length, horsepower, crew size, and fishing time. However, the production process of
fishing differs in potentially important ways from agriculture—most notably in that the firm
must accommodate its activities to the spatiotemporal dynamics of a fugitive resource. The
production process of fishing thus involves the strategic deployment of quasi-fixed inputs
over space and time as primary decision variables. The result is that many of the traditional
seasonal ‘inputs’ in conventional production models of fishing are not direct choice variables
for fishermen. Instead, they are indirect outcomes of deeper structural decisions. Most
1
conventional production models are therefore reduced form representations of the actual
underlying fishing production process, whose structural parameters pertain to the elementary
decision variables over space and time. Using a structural simulation model, Reimer, Abbott
and Wilen (2015) demonstrate that if fish catch is influenced by neglected decision variables,
and these variables are influenced by the institutional or market contexts of a fishery, then
empirically-revealed production relationships will not be policy invariant. By implication
these models will likely prove inadequate for informing policy makers of the effects of
significant policy changes (Lucas, 1976).
In this paper, we empirically investigate the institutional dependence of a
conventional model of fishing production for a fishery undergoing a transition to rights-based
management. Using catch data from before and after rationalization, we show that ex ante
production data alone arrives at grossly misleading conclusions regarding the parameters of
post-rationalization fishing production technology. We focus on one aspect of a fishing
production technology—the ability to substitute between species, as reflected in the shape of
the production possibilities frontier. This aspect is critical to many questions in fisheries
management as it summarizes the extent to which fishermen can “target” a particular species.
This in turn determines the degree to which fishermen may be able to accommodate their
catch to quota holdings in a multispecies ITQ system or respond to incentives to avoid
bycatch (Copes, 1986; Squires, Campbell and Cunningham, 1998; Holland, 2013). Previous
ex ante examinations of multispecies production technologies predict that rights-based
systems may face serious challenges due to weak targeting ability (Squires, 1987b; Squires
and Kirkley, 1991;
Squires, Alauddin and Kirkley, 1994;
Squires and Kirkley, 1996;
Pascoe, Koundouri and Bjørndal, 2007; Pascoe, Punt and Dichmont, 2010). Using data prior
to a policy intervention, these studies estimate multi-output production technologies using
conventional fishing inputs and measure targeting ability as the curvature of the production
2
possibilities frontier. Findings of widespread complementarity among outputs suggest that
fishermen are limited in their ability to substitute between species. In contrast, ex post
evidence from multi-species ITQ fisheries suggests that far greater flexibility in outputs is
possible than previously thought (Sanchirico et al., 2006; Branch and Hilborn, 2008; Abbott,
Haynie and Reimer, 2015). These disparate findings suggest that the ex ante production
technology revealed through empirical work may say just as much (or more) about the
institutions and incentives facing fishermen as about the range of available production
possibilities.
Reimer, Abbott and Wilen (2015) investigate the institutional dependence of the
conventional production possibilities frontier using simulated data from a structural model of
spatiotemporal fishing behavior. They show how the output production set in a fishery can be
assembled from the combinations of all possible fishing location choices and the joint
distribution of species over space, while holding traditional fishing inputs (e.g., fishing time)
constant. The resulting frontier for this “global” production set can exhibit the full spectrum
of relationships between strong substitutability and complementarity between species,
depending on the relative spatial distribution of species abundance. The authors then show
that location choices generated by utility maximizing fishers effectively sample output
bundles from only a subset of the global production set, resulting in an “empiricallyrevealed” production set that is drastically different from the global production set.
Depending on the institutional setting of the fishery, it is possible for the empirically-revealed
production frontier to exhibit strong complementarity between species, even though the
underlying global (i.e., policy-invariant) production set exhibits strong substitutability.
Reimer, Abbott and Wilen (2015) provide at least two important lessons for using
empirically-revealed conventional production frontiers for ex ante policy evaluation. First,
empirically-revealed production sets generated by the utility-maximizing behavior of fishers
3
reflect only a portion of all production possibilities—namely those that were most profitable
when fishing was observed. Second, the empirically-revealed production set is highly
dependent on the institutional, economic, and biological setting that existed when fishing was
observed. Therefore, while localized measures of the ‘shape’ of the production possibilities
frontier provide reasonable measures of targeting ability for a given institutional/biological
regime, there is no reason to believe that such ex ante values will provide a useful measure of
targeting ability after implementing a policy that changes fishers’ incentives.
We explore the institutional dependence of the conventional output production
frontier using the Bering Sea/Aleutian Island (BSAI) non-pollock groundfish fishery—a
multispecies fishery using bottom trawl gear and with thorny bycatch issues. Historically, the
North Pacific Fishery Management Council (NPFMC) managed the bycatch of Pacific
halibut through a fleet-wide common-pool total allowable catch (TAC). Due to the joint
production of halibut and targeted species, the bycatch limit for halibut frequently closed the
target fisheries prematurely, leaving millions of dollars of unharvested target species quota on
the table. In 2008, the NPFMC implemented Amendment 80 (A80), under which shares of
the TACs for several target and bycatch species are allocated to individual fishermen that are
vested in either a cooperative formed by participating members or in a limited access
common pool fishery. This management change potentially address the public good nature of
bycatch avoidance (Abbott and Wilen, 2009) by providing fishermen with an individual
incentive to avoid halibut bycatch.
We use an unusually detailed panel dataset of vessels from before and after
rationalization of the fishery to estimate econometric models characterizing the multi-output
production technologies of vessels before and after the policy change, all while thoroughly
controlling for observable and unobservable exogenous time-varying aspects of production.
Previous work has found that fishermen in the BSAI groundfish fishery are remarkably
4
capable of adjusting their behavior to match their desired catch compositions (Abbott, Haynie
and Reimer, 2015). However, our estimates indicate that measuring targeting ability using
only ex ante data arrives at grossly misleading conclusions—namely that fishermen were
limited in their ability to avoid halibut bycatch. Our results emphasize the difficulty in
assessing the potential for cross-species substitution in fisheries on the basis of ex ante data
alone. Since such data are generated under a different incentive structure than the prospective
system, a purely empirical approach imposed upon a flexible functional form for the
production technology is likely to reflect far more about the incentives for substitutability
under the status-quo regime than the actual technological possibilities under a new
management regime. Our findings suggest that accurate assessment of the impacts of policy
changes requires a description of the fishing production process that is sufficiently structural
so as to be invariant to changes in management institutions.
Background
Productivity relationships for technology with multiple outputs are typically represented by a
production set, which, under certain regularity assumptions (McFadden, 1978; Färe et al.,
2005), can be expressed as
P(x) = {( y,b ) :T (x, y,b) ≤ 0} ,
(1)
where x represents a vector of inputs, y represents a vector of “good” (desirable) outputs, b
represents a vector of “bad” (undesirable) outputs, and the set P represents the set of good
and bad outputs that can be jointly produced from the input vector x. For fishery productivity
analysis, the output vectors y and b typically consist of annual or seasonal measures of catch
or production for key species in the fishery. Outputs included in the bad output vector b can
be thought of as non-targeted species whose bycatch is considered a necessary byproduct of
desirable targeted catch. The vector of traditional inputs x includes fixed factors, such as
5
vessel length and tonnage, and aggregate measures of variable inputs, such as fishing time
and/or the number of gear retrievals.
The transformation function T is used to define the production possibilities frontier
(PPF) through the implicit relationship
(
)
T x,y,b ! = !0.
!
(2)
The PPF defined by (2) provides a functional representation of the set of all efficient output
combinations and allows for the derivation of standard productivity and substitution measures
(McFadden, 1978). However, the implicit definition of the transformation function is
analytically inconvenient. Furthermore, it lacks a natural scale and origin, and therefore
cannot be identified empirically without imposing some form of normalization (Hall, 1973).
To facilitate analyses of multispecies fisheries, early models of productivity
circumvented the difficulties associated with the multi-output transformation function by
making simplifying assumptions in order to “isolate” the production outputs y on one side of
equation (2), either by combining the catch of all species into a single aggregate catch index
(assuming input-output separability) or by estimating separate production functions for each
species (assuming nonjointness in inputs). Recognizing the limitations of imposing a priori
input-output separability and nonjointness in inputs on the fishing production process,
Squires (1987a, b) and Kirkley and Strand (1988) proposed examining fishing technology
indirectly by a dual formulation (Shephard, 1970; Diewert, 1974; McFadden, 1978). A dual
formulation employs the envelope theorem with assumptions regarding a firm’s profit
maximization or cost minimization behavior to enable an indirect examination of output
substitution possibilities. The dual formulation has the advantage of being able to make use
of flexible single valued cost or profit functions, thereby avoiding the more difficult endeavor
of incorporating multiple inputs and outputs into a primal representation of technology
through the transformation function in (2) (Jensen, 2002).
6
In recent years, a primal approach for characterizing multi-species fisheries has
emerged, relaxing the need for behavioral assumptions such as cost minimization or profit
maximization (e.g., Weninger and Waters, 2003;
Felthoven and Morrison Paul, 2004;
Pascoe, Koundouri and Bjørndal, 2007; Weninger, 2008; Pascoe, Punt and Dichmont,
2010). Primal representations of fishing technology take on various forms, depending on the
normalization employed for identifying the PPF. For instance, distance functions measure the
distance to the PPF following an approach path from a point within the interior of the
production set (Färe and Grosskopf, 2000). The approach path—sometimes referred to as the
mapping rule—provides the normalization required to identify the PPF, and effectively
determines the functional form that can be used to estimate the distance function and imposes
parameter constraints on the functional form (Vardanyan and Noh, 2006).
The importance of accounting for joint production became clear to economists as
many multispecies fisheries began implementing portfolios of total allowable catches
(TACs), often enforced by fleet-wide or individual output quotas. Lack of output
substitutability can lead to an imbalance of individual-species TACs with the actual catch
composition of the fleet, potentially resulting in premature fishery closures due to insufficient
quota for “choke'” species, a collapse in the markets for “slack” species or poorly functioning
markets for choke species (Holland, 2013), rampant illegal discarding, data fouling, and
subverted quota markets (Copes, 1986). Perhaps the first analysis of the effects of output
controls on a multi-species fishery was conducted by Squires (1987b), who investigated the
reasons underlying the failed attempt to manage multiple species through output controls in
the New England trawl fisheries. Squires (1987b) characterized output substitutability (i.e.
targeting ability) by estimating the elasticity of substitution between outputs in a multi-output
production process. He found widespread complementarity among outputs, concluding that
output controls had ultimately failed because individual species quotas were not set in
7
balance with natural output mixes and fishermen were limited in their ability to substitute
between species. This analysis sparked a number of ex ante evaluations attempting to predict
the likelihood of success for output controls in multispecies fisheries, with many resulting in
similar conclusions: output controls for multispecies fisheries may be in jeopardy due to
weak substitution potential between species (e.g., Squires and Kirkley, 1991, 1995, 1996;
Pascoe, Koundouri and Bjørndal, 2007; Pascoe, Punt and Dichmont, 2010).
Contrary to the warnings conveyed by ex ante evaluations, recent evidence from
multispecies fisheries with output controls—particularly those with individual or cooperative
harvesting rights—have found that fishermen are far more capable of adjusting their output
compositions than previously thought (Sanchirico et al., 2006; Branch and Hilborn, 2008;
Abbott, Haynie and Reimer, 2015). Consistent with Reimer, Abbott and Wilen (2015), these
disparate findings suggest that the ex ante production technology revealed through empirical
work is likely influenced by the incentives facing fishermen through markets and
management institutions. In particular, if important margins of production, such as the
deployment of gear in space and time, are both influenced by the institutional setting of a
fishery yet omitted from the model of fishing production, then ex ante evaluations are
unlikely to present an accurate picture of targeting ability after the introduction of individual
or cooperative harvesting rights.
Fishery setting and data
The BSAI non-pollock groundfish trawl fishery is a fleet of 22 catcher processors that use
bottom trawl gear to catch a variety of groundfish. The fishery can be divided into two broad
sub-fisheries: (i) the Aleutian Islands, dominated by trawling for Atka mackerel, Pacific cod,
and Pacific ocean perch; and (ii) the Bering Sea fishery, a highly mixed fishery on the
relatively shallow shelf area of the Eastern Bering Sea, where the dominant target species
8
consist of a range of flatfish species (e.g., yellowfin sole, rock sole, flathead sole, and
arrowtooth flounder) and Pacific cod.
Targeting behavior, and the resulting spatial-temporal allocation of effort over the
course of a year, is largely determined by a combination of natural and regulatory factors.
Prior to 2008, the fishery operated as a limited license program with fleet-wide TACs
allocated to each target species. Regulators monitored the in-season progress of fleet-wide
catch against the TACs using data collected by onboard observers and weekly production
reports. If regulators anticipated that a species' TAC would be exceeded, the fishery was
closed to “directed fishing”, resulting in a substantial reduction in the proportion of that
particular species which could be retained. Management also restricts the catch and retention
of certain prohibited species—species that cannot be retained by the fleet. Prohibited species
are valuable targets to fishermen outside of the BSAI groundfish fleet and include species
such as Pacific halibut, king and tanner crab, salmon, and herring.
The most problematic prohibited species in recent years for this fleet has been Pacific
halibut, which co-exists in relatively small numbers with the groundfish target species.
Given the limitations on the selectivity of trawl gear, bycatch of this species by the BSAI
groundfish fleet is, to some extent, unavoidable.
Prohibited species quotas are strictly
limited, and prior to 2008, were allocated to the BSAI groundfish fleet as a common property
TAC, subdivided between various target sub-fisheries based on their anticipated usage of the
quota. Given the common property nature of the Pacific halibut allocations, there was
limited effort to avoid halibut bycatch (Haynie, Hicks and Schnier, 2009; Abbott and Wilen,
2010, 2011), resulting in many subfisheries—particularly rock sole and yellowfin sole—
closing prematurely due to a binding halibut TAC, leaving millions of dollars of target
species quota unharvested.
9
In 2008, Amendment 80 (A80) was implemented to the BSAI Fishery Management
Plan, making at least two significant changes to the state of fishery regulations at the time.
First, A80 granted a defined share of the total A80 TAC for the six target species (yellowfin
sole, rock sole, flathead sole, Pacific cod, Atka mackerel, and Pacific Ocean perch) to each
vessel according to their catch history. Second, vessels could vest their shares in either a
cooperative formed by participating members or in a limited access common pool fishery.
Cooperatives are given considerable flexibility as to how catch entitlements are internally
allocated. Vessels that join the limited access fishery vest their shares to a common pool that
is available to all limited access vessels, similar to pre-A80 management. In addition,
cooperatives are allocated shares of prohibited species TACs according to their holding of
target quota shares. Initially, 16 vessels (from 7 different companies) formed a single
cooperative known as the Alaska Seafood Company (ASC) while the remaining 6 vessels (5
from a single company) elected to stay in the limited access sector.
Recent work by Abbott, Haynie and Reimer (2015) demonstrates that fishermen in the
BSAI groundfish fishery were remarkably capable of adjusting their behavior to match their
desired catch compositions and avoid halibut bycatch after implementation of A80. Bycatch
of halibut fell by approximately 50% in the year following A80 implementation. The authors
find that large-scale shifts in fishing grounds, larger and more immediate movements from
fishing grounds after high halibut encounters, and reduced fishing at night have all
contributed significantly to the observed changes in catch compositions. Importantly, these
margins of change were all available to fishermen before the institutional change and yet
were not practiced on a regular basis. This suggests that a conventional production model
estimated using only ex ante data is unlikely to find significant potential for substitution away
from halibut—not because the technological potential didn’t exist before A80, but rather
because fishermen had no incentive to operate in a manner that revealed this potential.
10
Our analysis relies upon a detailed confidential panel dataset of vessels from before
and after implementation of A80 collected by the North Pacific Groundfish Observer
Program (NPGOP). Data collected by on-board observers include haul-level data on spatial
location of gear deployment and retrieval (to the minute of latitude and longitude), the
duration and depth of each tow, the weight of the total catch. On-board observers also
conduct species-composition sampling whereby observers utilize rigorous methods of subsampling to obtain estimates of the species composition of the hauls. We use the haul-level
data collected by on-board observers to form temporally aggregated measures of
conventional outputs and inputs, such as daily catch (for each species) and fishing time, to be
used in our model of fishing production.1
A close examination of the cooperative and non-cooperative vessels in our sample
reveals very different participation patterns between the two groups. In particular, the noncooperative vessels primarily participate in the Aleutian Islands fisheries for Atka mackerel
and Pacific ocean perch, for which halibut bycatch is not a large concern. In contrast, the
cooperative vessels primarily participate (with some exceptions) in the Bering Sea fisheries
for flatfish and cod. Given our interest in targeting behavior with respect to halibut
avoidance, we limit our analysis to only those vessels that immediately joined a cooperative
post-A80.
Methods
1
While the NPGOP dataset is extremely detailed, it is not exhaustive in the sense that it does not contain a
species composition survey for every trawl made prior to A80 implementation. Prior to A80, all vessels over
124ft were required to maintain an observer presence on 100% of all fishing days while smaller vessels were
only required to carry an observer on 30% of days and had discretion over when to satisfy these coverage
restrictions. In addition, pre-A80 observer coverage managed to sample only approximately half of all hauls for
species composition. Aggregate measure of production will therefore only account for a fraction of the actual
catch. In contrast, all vessels after A80 are required to have two observers on-board for every trip, resulting in
nearly all hauls receiving a species composition survey. We are mindful of the different sampling schemes preand post-A80 in the analysis that follows, and conduct several robustness checks for our final model
specification of the fishing production function to ensure that are conclusions are not sensitive to this feature of
the data (see Appendix for a discussion).
11
We follow a multi-output primal approach to model the multi-species production technology
of the BSAI groundfish trawl fishery and characterize changes in targeting ability (i.e., output
substitutability) by measuring the slope and curvature of the PPF before and after A80, all
while controlling for observable and unobservable exogenous time-varying aspects of
production. We model production technology to be a function of traditionally included inputs,
such as fishing time and vessel length, while omitting unconventional decision variables,
such as spatiotemporal gear deployment, diurnal fishing patterns, and gear adaptations that
previous research has shown influence output composition (e.g., Abbott, Haynie and Reimer,
2015). Differences in the production technology before and after 2008 are therefore
attributable to the behavioral response to A80 along these latent, unconventional decision
margins of fishermen.2
The hyperbolic distance function
The most commonly used approach path for normalizing the PPF is Shephard (1970)’s output
distance function, which is based on the maximum proportional expansion of all outputs onto
the boundary of the production set, given the input vector x. The output distance function
therefore measures an output bundle’s radial distance from the frontier in the direction of the
output vector. More recent empirical studies of production technology point out that
Shephard’s output distance function is not well suited for estimating technology with bad
outputs because it does not discriminate between desirable outputs (target species) and their
undesirable byproducts (bycatch species) (Vardanyan and Noh, 2006; Cuesta, Knox Lovell
and Zofío, 2009). In contrast, (Färe et al., 1989)’s hyperbolic distance function treats good
and bad outputs asymmetrically by measuring distance to the PPF while simultaneously
expanding desirable outputs and contracting undesirable outputs. The advantage of
2
The sensitivity of the production technology to changes in behavioral patterns will ultimately depend on the
behavioral margins that are omitted from the production model. Importantly, all primary decision variables
omitted in our representation of production technology were available to fishermen both before and after the
introduction of A80.
12
approaching the PPF in this asymmetric direction is that the slope of the PPF can be
interpreted as the opportunity cost of reducing undesirable outputs in terms of foregone
desirable outputs (Cuesta, Knox Lovell and Zofío, 2009). For our application, this
opportunity cost measures the target species harvest that must be foregone for a marginal
reduction in the bycatch of Pacific halibut.3
Following the literature on production technology with good and bad outputs, we
estimate a hyperbolic distance function (HDF), which is defined as (Färe et al., 1989):
D H ( x, y,b ) = min {θ > 0 : ( y θ ,bθ ) ∈P(x)} .
(3)
θ
The HDF thus treats good and bad outputs asymmetrically by expanding good outputs and
contracting bad outputs in a hyperbolic approach path to the PPF. The HDF takes on values
in the interval (0,1], where DH close to one implies that an output bundle is near the PPF, and
satisfies the following properties under customary assumptions (Cuesta, Knox Lovell and
Zofío, 2009): (i) it is almost homogeneous of degrees (0,1,-1,1) (Lau, 1972);4 (ii) nondecreasing in desirable outputs; (iii) non-increasing in undesirable outputs; and (iv) nonincreasing in inputs.
In a stochastic framework, observed output bundles that do not lie on the PPF are the
result of unobserved factors v that are out of the control of an individual harvester, such as
weather or biological events and a harvester’s inherent inefficiency u ≥ 0. Let (y*,b*) be an
output bundle on the PPF for a given input vector x. The HDF implicitly assumes that the
realization of both idiosyncratic shocks and inefficiency affect the production of all good
3
There are an infinitude of possible mapping rules that treat good and bad outputs asymmetrically (for example,
the directional distance function, Färe et al., 2005), and the choice of mapping rule can have serious
consequences for modeling technology. In addition to determining the functional form and parameter constraints
for the distance function, it also determines how stochasticity and inefficiency enter the model (Vardanyan and
Noh, 2006). Furthermore, by requiring that the production frontier be approached in a particular direction, a
given mapping rule will tend to produce measures of shadow prices, substitution, and inefficiency that are
inherently “local” to a region of the production frontier.
4
k1
k2
k3
k4
A function F(x,y,b) is almost homogeneous of degrees (k1,k2,k3,k4) if F( µ x, µ y, µ b) = µ F(x, y,b) , µ > 0.
13
production equally and all bad production equally, so that for any observed output bundle
(y,b) we have y = y*e(v-u) and b = b*e(u-v). Recalling that the HDF is almost homogeneous and
recognizing that DH(x,y*,b*) = 1, it follows that
D H (x, ye(u−v) ,be(v−u ) ) = e(u−v) D H (x, y,b) = 1.
The natural log of the HDF can thus be expressed as
ln D H (x, y,b) = v − u.
(4)
Cuesta, Knox Lovell and Zofío (2009) show that under certain parameter restrictions, the
translog function satisfies almost homogeneity; thus, the translog function is a natural
candidate for a functional representation of the HDF. One particularly useful way for
imposing the almost homogeneous property for estimation purposes is by recognizing that
almost homogeneity implies
D H ( x, y,b ) = γ D H ( x, γ −1y, γ b )
(5)
for γ > 0 . Using the right-hand side of equation (5) and letting γ = y1 (or any other good
output) means that y1 will fall out of the right-hand side (since the log of one is zero). Taking
the natural log of both sides of equation (5), using (4), and letting γ = y1 , we have after some
rearranging
− ln y1 = ln D H ( x, y1−1y, y1b ) + u − v.
(6)
Model Specification
We modify Greene (2005)’s “true” fixed-effects panel data model for single output stochastic
production frontier estimation to represent a HDF that captures unobserved and technological
heterogeneity across harvesters and seasons. Greene’s “true” fixed-effects model allows for
time-varying inefficiency and a time-invariant individual-specific fixed-effect that can be
correlated with any input or output in the model. We model the log of the HDF using the
translog function and specify the HDF to include season-specific distance function
14
parameters and individual-season fixed-effects. Letting ln x, ln y, and ln b represent the
natural logs of the input, good output, and bad output vectors, respectively, the RHS of
equation (6) for harvester i during day t of season s is represented by
− ln y1its = α 0is + ln x 'itsα xs + ln ŷ 'itsα ys + ln b̂ 'itsα bs
1
1
1
s
s
+ ln x 'its A xx
ln x its + ln ŷ 'its A syy ln ŷ its + ln b̂ 'its A bb
ln b̂ its
2
2
2
s
s
+ ln ŷ 'its A syb ln b̂ its + ln x 'its A xy
ln ŷ its + ln x 'its A xb
ln b̂ its + ε its
(7)
where ŷ = y1−1y , b̂ = y1b , ε ist = uist − vist is a two-component error term comprised of an
s
s
inefficiency term and a stochastic shock, and A xx
, A syy , and A bb
are symmetric matrices for
each season s. We include the daily catch of rock sole, yellowfin sole, cod, and all other
species (labelled as “other”) in the good output vector y and the daily catch of halibut as the
lone element in the bad output vector b. Daily catch of yellowfin sole is used as the
normalizing variable y1. We include vessel length in the input vector x as the lone fixed factor
and daily trawling hours as the only variable input.5
Capturing heterogeneity across seasons and harvesters is necessary for identifying
changes in technology and substitution patterns over time. Uncontrolled technological and
harvester-specific heterogeneity will enter the model through the two-component error term,
resulting in a distance function that is measured relative to a PPF that is common over
seasons and harvesters. Thus, any differences in technology between seasons and harvesters
are incorrectly interpreted as differences in inefficiency or as heteroskedasticity (Felthoven,
Horrace and Schnier, 2009). Since we are primarily concerned with changes in technology
and substitution patterns on the frontier—as opposed to changes in inefficiency—we define
distance relative to a PPF that is harvester- and season-specific and control for both observed
and unobserved heterogeneity in the hyperbolic distance function.
5
Including both trawling hours and number of trawls was problematic due to their highly collinear relationship
(corr=0.82).
15
Observed harvester heterogeneity is accounted for by including vessel length as a
fixed input.6 Unobserved harvester heterogeneity, such as a skipper's skill in gathering and
utilizing information for finding and catching fish, is included as a harvester-specific fixedeffect α 0is (Kirkley and Squires, 1998; Squires and Kirkley, 1999) that is allowed to vary
over seasons.
Specifically, α 0is = α 0s + α 0ip , where the superscript p indicates whether the
season s is pre- or post-A80. In other words, harvesters share a seasonal fixed effect but have
vessel-specific effects that are allowed to vary before and after implementation of A80. The
use of additive fixed-effects in the HDF model assumes that harvester heterogeneity scales
good and bad outputs along an asymmetric hyperbolic approach path from any observed
input/output bundle.7
We model A80-induced technological change as a latent variable that is captured in
the season-specific technological parameters in equation (7). Previous studies of policyinduced technological changes (e.g., Morrison Paul, Johnston and Frengley, 2000) treat
regulatory change as an input to the production process and include it as a dummy variable in
the input vector x. While this approach allows first-order effects of inputs and outputs on
overall productivity to be regulatory-dependent, it assumes that second-order and cross-term
effects between inputs and outputs are invariant to regulatory changes. Since these effects
shape technological substitution patterns, we follow Färe et al. (2005) and allow all
technological parameters to vary over time so that measures of substitutability and the
curvature of the PPF have maximum flexibility.
6
Other fixed vessel characteristics, such as gross tonnage and horsepower, are highly correlated with vessel
length and each other, and are thus excluded. Information on crew size for the Bering Sea groundfish fishery is
not available for all years. However, vessel length was found to be highly correlated with crew size in other
Bering Sea fisheries (Reimer, Abbott and Wilen, 2014) and is likely an acceptable proxy.
7
Since vessel length does not vary across years, it is not possible to separately identify harvester-specific fixed
effects and first- and second-order effects of vessel length in the HDF. We therefore exclude vessel length from
the parameter vector α xs and matrix A sxx . We do however interact vessel length with all other inputs and
outputs in the model to allow for observed heterogeneity in the cross-effect matrices A sxy and A sxb .
16
One potential problem with this approach is that changes in regulations between
seasons may be confounded with changes in exogenous seasonal variables such as the size
and distribution of the latent fish stock. While it is possible to include fishery-independent
measures of biomass in the distance function (e.g., Pascoe, Koundouri and Bjørndal, 2007),
stock assessments in the Bering Sea are performed annually and do not have sufficient
independent variation for identification once seasonal fixed effects are included.8 Instead, we
omit measures of the latent fish stock and interpret the estimation results in light of the stock
assessments in Figure 3. In addition, we limit our analysis to the years 2005 to 2010—three
years before and after implementation of A80. This relatively small window controls for
changes in long-term species abundance growth, but leaves short-term volatility in species
abundance and distribution uncontrolled.
Finally, we limit our analysis to the early-season rock sole fishery to control for
changes in production technology that could arise from movement between subfisheries.
Each subfishery within the BSAI groundfish fishery operates within a fairly distinct spatial
and temporal context tied to the seasonal distribution of fish populations, so that each
subfishery likely possesses a distinct production technology. Since annual estimates of stock
abundance do not provide information pertaining to seasonal or spatial abundance patterns, it
is important to insulate our estimates from the effects of this substitution.9
Characterizing targeting ability
8
Furthermore, fish populations in the Bering Sea interact with sea ice during the winter and spring, and
therefore, annual stock assessments are not necessarily representative of stock abundance at any particular point
of time in the year (Haynie and Pfeiffer, 2013).
9
The winter rock sole fishery is relatively well-defined both before and after A80 due to a consistent annual
opening date (January 20), clear bycatch-driven closures in the pre-A80 period, the spatial separation of the
fishery from the other contemporaneous subfishery (the Atka mackerel fishery in the Aleutian Islands), and the
fact that the fishery is mostly driven by the spawning of rock sole females and the value of its roe-in product in
Japan—factors that remained unchanged with A80. The end of the rock sole fishery is not particularly welldefined post-A80, however, since there is no longer an official closing date. To remedy this, we chose a postA80 “closing date” equal to the latest date observed in the pre-A80 years (March 1), where it is clear from the
weekly production data presented in Appendix Figure 1 that vessels continue to target rock sole up until this
date.
17
Prior to A80 implementation, harvesters were overwhelmingly constrained by their bycatch
of halibut in the rock sole fishery, resulting in rock sole quota being left unharvested due to
premature bycatch closures (Abbott, Haynie and Reimer, 2015). Given that one of the
primary goals of A80 was to reduce the bycatch of halibut, we focus on vessels’ ability to
target rock sole and avoid halibut before and after A80.
Squires (1987b), Squires and Kirkley (1991), and Pascoe, Koundouri and Bjørndal
(2007, 2010), among many others, use the slope and curvature of the PPF to measure
substitutability between species in a multispecies fishing production process. In similar
fashion, we use the HDF to derive two primary measures of substitutability. First, we
estimate the marginal rate of transformation (MRT), which measures the opportunity cost of
reducing halibut bycatch in terms of the foregone harvest of rock sole. As shown in the
Appendix, the MRT can be expressed as a ratio of the first derivatives of the HDF with
respect to halibut (b) and rock sole (y),
MRT = −
∂D H (x,y,b) ∂b
.
∂D H (x,y,b) ∂ y
Second, following Pascoe, Koundouri and Bjørndal (2007, 2010), we estimate the
Morishima elasticity of substitution (MES) between rock sole and halibut (Blackorby and
Russell, 1989). The MES provides a unitless measure of the curvature along the PPF,
quantifying the rate at which the MRT increases as the rock sole to halibut ratio increases.
The MES measures the responsiveness of the MRT as the good to bad output ratio (y/b)
increases, and can be derived directly from the HDF:10
MESby =
⎡ ∂ 2 D H (⋅) ∂ y ∂b ∂ 2 D H (⋅) ∂b2 ⎤
∂ln MRT
= b⎢
−
⎥.
H
∂ln( y / b)
∂D H (⋅) ∂b ⎦
⎣ ∂D (⋅) ∂ y
10
The MES measures the rate at which the MRT changes as one of the outputs in the ratio (y/b) changes. The
formula used for MES therefore depends on which output in the (y/b) ratio is being held fixed. We follow
Pascoe, Koundouri and Bjørndal (2007) and use the term MESby to indicate that we are varying the bad output b
(halibut) while holding the good output y (rock sole), along with all other outputs and inputs, constant. The
derivation of MESby is shown in the Appendix.
18
MES will take on a negative value if the outputs are substitutes and a positive value if the
outputs are complements. We thus expect MES to be positive between rock sole and halibut.
The absolute size of the MES reflects the rate at which the opportunity cost of reducing
halibut in terms of foregone rock sole changes with the ratio of these outputs. Small (large)
positive values of the MES therefore reflect fairly stable (unstable) complementarity
relationships so that relatively small (large) changes in the shadow prices of outputs will
induce large (small) changes in the ratios of outputs.
As a final measure, we also examine how changes in the overall position of the
production frontier over time translate into non-marginal changes in targeting ability. For
example, an upward shift in the PPF indicates that fishermen are capable of catching more
target species for any given value of bycatch. Given the parameter estimates for equation (7),
we estimate a representative deterministic PPF in rock sole-halibut space by solving for the
values of rock sole, given a range of values of halibut, such that ln D H (⋅) = 0 , all while
holding the values of all remaining inputs and outputs constant at their mean values.
Likelihood function and error distribution
Ordinary least squares (OLS) estimation of equation (7) will consistently estimate the slope
parameters of the HDF. However, OLS will not provide consistent estimates of the constant
terms if E(ε ist ) ≠ 0 (Greene, 2008), which is necessarily the case with inefficiency. While
only the slope parameters are necessary to provide information on output substitutability, we
are also concerned with the location of the production frontier, which is affected by the
constant terms. Accordingly, estimation of the parameter matrices in equation (7) is achieved
through maximum likelihood estimation (MLE) once distributional assumptions are made for
each component of ε.
We follow the convention of assuming the stochastic error component is normally,
independently and identically distributed vits ~ N[0,σ v ] and independent of all future,
19
contemporaneous, and past inefficiencies. We assume the inefficiency component u follows a
one-sided distribution that is discussed in more detail below. Assuming that the inefficiency
component is independently distributed within and across seasons, we can write the loglikelihood function for our model in equation (7) as
(
)
(
)
ln L Θ,σ u ,σ v | ε ,x, ŷ, b̂ = ∑ ∑ ∑ ln f ε its | x ist , ŷ ist , b̂ ist ;Θ s ,σ us ,σ v ,
s
i
t
(8)
where ε represents a vector containing all ε its , σ u is a vector containing season- and
individual-specific parameters σ us relating to the one-sided inefficiency term, Θ represents
all distance function parameters in equation (7), and f (⋅) is the conditional distribution of ε its .
Due to persistence in the HDF arising from the inclusion of season-specific parameters, we
allow the distribution of uits to follow a season-specific distribution (Hadri, Guermat and
Whittaker, 2003).
Results and Discussion
We considered multiple versions of our final model to examine the sensitivity of our
estimates. We estimated both an “annual model”, where season s in equations (7) and (8) is
defined as the year in which fishing took place, and a “before-and-after model” (henceforth
B&A model), where season is defined as either before or after implementation of A80.11 In
addition, we considered alternative distributional assumptions for the two-component error
term ε , including normal (i.e., no inefficiency), normal-half normal, and normalexponential.12 Finally, we estimated both fixed effect and pooled models (i.e., one overall
11
The annual model permits the most flexibility for capturing annual patterns in fishing technology but suffers
from drawing heavily upon limited degrees of freedom (184 parameters estimated using 2323 observations). In
contrast, the B&A model has more degrees of freedom for parameter estimation (80 parameters estimated using
2323 observations), but suffers from aggregating annual patterns and imposing the structural break of A80 a
priori. The B&A model also has the advantage of “averaging out” the influence of annual fluctuations in
relative biomass for each species.
12
We attempted to estimate the normal-truncated normal model but encountered numerical instabilities and nonconvergence. Estimation of the normal-gamma model was not attempted.
20
intercept for a season) for both the annual and B&A models.13 Overall, variations in our
model specification resulted in little volatility in parameter estimates and yielded consistent
general patterns and conclusions.
Table 1 contains diagnostics for the annual and B&A models.14 Both the AIC and
BIC prefer the normal-exponential model over the alternatives and the fixed-effects model
over the pooled model for each of the annual and B&A models. The normal-exponential
specification tends to attribute more variation in ε to the random component relative to the
normal-half normal model, as witnessed by the larger estimates of both σ v and Jondrow et al.
(
(1982)’s estimate of technical efficiency Ê e−u | ε
)
for the normal-exponential model. As
expected, technical efficiency is higher and random variation is smaller for the annual models
since there is more flexibility in the distance function for the annual specification. Overall,
general conclusions are consistent across different specifications of the model. Based on the
AIC and BIC, we utilize the normal-exponential model with fixed-effects for both the annual
and B&A models for the remainder of this analysis.
Parameters for the translog HDF in equation (7) are not easily interpretable, and are
thus relegated to the Appendix. Estimates of the average distance elasticities—i.e., the
percentage change in the distance to the PPF associated with a marginal percentage change in
a single output or input (Grosskopf, Margaritis and Valdmanis, 1995;
Morrison Paul,
Johnston and Frengley, 2000)—as well as the average of Jondrow et al. (1982)’s estimate of
(
)
technical efficiency, are reported in Table 2. The values of Ê e−u | ε provide some evidence
of improved technical efficiency after A80; however, unlike most analyses, inefficiency here
13
Other robustness checks—such as varying the temporal horizon for aggregation of inputs and outputs (e.g.
day or week), changing the normalizing output variable, varying the inputs and outputs in the model, and
investigating parameter sensitivity to the variation in observer coverage prior to A80—were also conducted.
The details of these robustness checks are included in the Appendix.
14
Estimation was conducted using Stata SE 12.0 (StataCorp LP, College Station, Texas). For numerical stability
in the estimation process, all variables were standardized by their sample means.
21
is not measured relative to the same baseline frontier across seasons. The signs of the
distance elasticities verify that the maximum likelihood estimated HDF is consistent (on
average) with its theoretical monotonicity properties (Cuesta, Knox Lovell and Zofío,
2009).15 Both halibut and fishing duration impact the HDF negatively as an increase in either
argument increases the distance to the PPF, all else equal, thereby decreasing DH towards
zero. Using similar logic, the good outputs rock sole, cod, and “other” impact the HDF
positively as an increase in any output decreases the distance to the PPF, thereby increasing
DH towards one.
The HDF can be used to derive all the classical properties of the production
technology, including the characteristics of the bilateral output and input spaces—i.e. the
shape of the production functions, isoquants, and production possibility frontiers (Morrison
Paul, Johnston and Frengley, 2000; Cuesta, Knox Lovell and Zofío, 2009). Given our focus
on targeting ability in a multispecies context, we focus our analysis on output substitutability
along the PPF (in terms of the MRT and MES), particularly between rock sole and halibut
bycatch. Previous work by Abbott, Haynie and Reimer (2015) showed that vessels were
incredibly successful at adjusting their catch compositions with the altered incentives under
A80, as evidenced by the raw daily catches of rock sole relative to halibut in Figures 1 and 2.
We therefore focus our discussion on the extent to which ex ante measures of the
complementarity between rock sole and halibut serve as a useful characterization of targeting
ability after the implementation of A80.
15
Previous applications of the output distance function interpret the distance elasticity as a measure of an input
or output’s “contribution” to overall production (e.g., Grosskopf, Margaritis and Valdmanis, 1995; Morrison
Paul, Johnston and Frengley, 2000). This is motivated by the fact that the output distance function is
homogeneous of degree one, and therefore the distance elasticity measures the expansion of the normalizing
output with respect to an input or output while keeping all output ratios fixed. In contrast, the HDF does not
share this same interpretation due to the fact that it is almost homogeneous of degree one. The distance elasticity
for the HDF therefore measures the expansion of the normalizing output while keeping only the good output
ratios fixed, but leaving the bad outputs to vary freely in order to keep the product y1b constant (see equation 6).
22
In general, we expect that the introduction of A80 would compel harvesters to
internalize the cost of halibut bycatch, thus raising the shadow cost of halibut relative to
target species and causing production to occur along a steeper portion of the PPF (a higher
MRT). The mean estimated MRT are both economically and statistically larger after the
implementation of A80 (Figure 4). Note that pre-A80 MRT are nonetheless positive,
indicating that there was some value to avoiding halibut prior to A80 (Abbott and Wilen,
2011). Wald tests of the null hypothesis of equal MRT before and after A80 are easily
rejected for both models at significance levels of 0.01. Overall, both the annual and B&A
models indicate that the average shadow value of halibut increased approximately three to
four times its pre-A80 level.
We expect MES to be positive between rock sole and halibut, with larger positive
values of the MES indicating that incremental reductions in halibut bycatch come at an
increasingly higher opportunity cost. Estimated mean values of the MES between rock sole
and halibut, as measured along the HDF, are presented in Figure 5. As expected, MES is
positive for all seasons—indicating that rock sole and halibut are complements in
production—lying between 0.8 and 1, with the exception of 2005. Using ex ante data alone,
therefore, the complementarity implied by the estimated MES suggests that A80 may not be
successful given harvesters’ difficulty in substituting away from halibut bycatch.
Unlike the MRT, there does not appear to be a distinct shift in the MES with A80,
despite the obvious reduction in the relative bycatch of halibut after 2007, as demonstrated in
Figures 1 and 2. With the exception of a small increase between 2005 and 2006, MES
remains fairly stable across all seasons.16 This temporal stability of the MES can be explained
by the radically different pre- and post-A80 rock sole-halibut frontiers presented in Figure
16
Wald tests of the null hypothesis of equal MES before and after A80 for the B&A model cannot be rejected at
significance levels of 0.05.
23
6.17 As demonstrated by Reimer, Abbott and Wilen (2015) production sets revealed by ex
ante data alone reflect only a portion of all production possibilities—namely those that were
most profitable when fishing was observed, conditional on the constraints imposed by
management institutions. The fact that post-A80 frontiers sit considerably higher than preA80 frontiers suggests that fishers under A80 were able to sample from an area of the
“global” production set in which larger amounts of rock sole catches exist for a given amount
of halibut, as evidenced by the significant spatial and temporal shift in effort post-A80
(Abbott, Haynie and Reimer, 2015).18 The MES therefore measures fundamentally different
production frontiers pre- and post-A80, with no clear theoretical reason for the curvature of
the frontier to change in any particular direction. Altogether, our estimates suggest that while
the MES can be useful for measuring the potential for additional substitution across outputs
along an empirically-revealed frontier (i.e., in a given economic/institutional/biological
regime), it completely fails to capture the aspects of substitutability induced by institutional
change.
Conclusion
We conduct an empirical investigation of a multi-species fishery that experienced a major
policy change in the form of a rights-based cooperative to examine whether the estimated
production relationships in the fishery tell a consistent story about technological possibilities,
or, alternatively, are fragile to the changes in incentives and resulting fishing behaviors. We
specifically focus on measures of substitution between good and bad outputs (bycatch), given
that A80 implemented a form of management that fully internalized the cost of bycatch to
individual vessels. Production frontiers estimated before the policy change seem to confirm
17
The description of the methods used to estimate the rock sole-halibut frontiers, in addition to figures that
include confidence intervals for the frontiers, are contained in the Appendix.
18
While the frontier in 2009 crosses the pre-A80 frontiers when halibut is roughly equal to 1.5mt, the majority
of the data points lie near the steeper portions of the post-A80 frontiers, indicating greater identification of the
frontier as halibut approaches zero (Figure 1).
24
the intuition reflected in descriptive summaries of catch compositions (Figures 1 and 2) as
well as a common colloquial judgment of multispecies trawls—that fishermen are limited in
their ability to target rock sole and avoid halibut due to a strong complementary production
relationship. Pre-A80 production frontiers indicate that a considerable reduction in harvested
rock sole would be needed in order to reduce halibut bycatch to post-A80 levels.
Despite these ex ante findings, an identical empirical strategy pursued immediately
after A80 finds a substantially different production possibilities frontier between rock sole
and halibut. The quantity of rock sole that can be caught for a given quantity of halibut
bycatch and fishing time actually increased over much of the active range of production—
shifting out the estimated frontier (Figure 6). Increased incentives on the part of fishermen to
avoid halibut caused fishermen to predominately operate in a region of the PPF with a higher
MRT. The result is a dramatic reduction in the bycatch/target ratio (Figure 2); yet the upward
shift in the PPF is such that this conservation occurs without erosion of rock sole catch rates.
Importantly, these striking instabilities in estimated production technologies occur despite the
fact that fishermen possessed fundamentally the same technology in 2007 as in 2008. The
changes in individual incentives did not lead to an immediate, discrete change in the vessels
or gear employed by fishermen. Rather, as we demonstrate in previous work (Abbott, Haynie
and Reimer, 2015), the altered incentives encouraged fishermen to shift the manner in which
they deployed their gear in space and time—proactively avoiding bycatch hot spots, quickly
changing locations in response to “dirty trawls”, and significantly curtailing fishing in nighttime hours. These spatiotemporal decisions call attention to the “multiple margins” available
to fishermen (Smith, 2012)—margins that are often aggregated or ignored altogether in most
empirical production models.
It is possible that the substantial shifts in the production frontiers witnessed in the
previous sections are partially driven by trends in omitted seasonal variables such as changes
25
in relative biomass of species, due to our inability to parse the changes in estimated biomass
from the temporal fixed effects. Estimates of the biomass for rock sole (Figure 3) do indicate
some growth in 2008, while halibut biomass perhaps shrank slightly—movements that could
contribute to the dramatic upward shift in the frontier in 2008. However, trends in 2009-2010
are less friendly to this hypothesis. Halibut biomass soared in these years even as rock sole
biomass moderated; yet the estimated production frontiers in these years (Figure 6) remain
well above historical levels, with dramatic and stable reductions in the mean and variance of
halibut/rock sole catch rates (Figure 2). Altogether, it seems unlikely that biomass changes
over such a short horizon are likely to be the main drivers of the patterns revealed in our
study.
Our empirical results confirm the intuition revealed in the simulations conducted by
Reimer, Abbott and Wilen (2015). Shifts in the estimated production frontiers are consistent
with the idea that empirically revealed frontiers identify the border of behavioral production
sets that lie within the “true” production set. Upward shifts in the production frontiers
indicate that fishermen may have faced significant institutionally-exacerbated inefficiencies
before A80 as race-to-fish conditions distorted the “virtual price” of traveling between
locations (Abbott and Wilen, 2011) or using halibut excluders. Furthermore, as shown in
Reimer, Abbott and Wilen (2015), changes in market prices and management institutions
alter the virtual prices attached to different species—altering the spatiotemporal sampling of
the fishing grounds, and therefore the sampling of the production set. This institutionally
driven sample selection can have dramatic, and potentially deceptive, effects. In the present
case, the increased accountability for halibut bycatch led to fishermen exploring regions of
production space with a far higher MRT than in the past—revealing substitution possibilities
for which there was little identification in earlier years.
26
Our analysis shows that the technological capacity to alter the composition of catch in
the BSAI groundfish fishery was far more developed than ex ante production analysis alone
would suggest. ‘Technology’—the intersection of the physical gear with the spatiotemporal
fishing environment—presented ample margins for selectivity. What was missing was the
incentive to exploit these opportunities. Clearly there are limits to substitution, and not all
concerns about the ability to balance catch with quota under multispecies catch shares are
overblown. Settings where quotas of certain rare species are set at very low levels can choke
an entire fishery – particularly if the catch of these species is ‘fat tailed’ and highly random,
with little discernable pattern to inform avoidance (Holland, 2010; Holland and Jannot,
2012). Nevertheless, our study suggests that estimates of substitution potential based on ex
ante data from policy regimes with weak incentives for selective fishing will inevitably be
biased in a pessimistic direction.
Using ex ante production models to extrapolate outcomes after a non-marginal policy
shock requires that the estimated model be “structural” with respect to that shock (Lucas,
1976)—that its parameters not change as a function of the policy. Unfortunately, both theory
(Reimer, Abbott and Wilen, 2015) and our empirical demonstration suggest that most
estimated production technologies are instead reduced-form in nature.
As such, their
parameters are not purely technological; instead they reflect the intersection of technology
and the incentives embodied in economic and biological conditions and management
institutions. When incentives change, so do the parameters and the inferences erected upon
them. Generating robust ex ante predictions of fishery policy interventions is not easy. It
requires an empirically-identified characterization of the production process that is
sufficiently “deep'” so as to be invariant to a specified range of changes in management
institutions, as well as an economic model of how agents respond to novel incentives (e.g.,
Smith and Wilen, 2003; Dowling et al., 2013; Reimer, Abbott and Wilen, 2014). However,
27
achieving this synthesis is critical to ensure that the “crystal ball” of economic modeling does
more than merely reflect forward the biases wrought by the incentives of the past.
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31
Tables
Table 1: Model diagnostics
Annual Modela
Statistic
N
Pd
N
FE
N-HN
Pd
N-HN
FE
N-E
Pd
N-E
FE
ˆv
Ê(e u |")
AIC
BIC
LL
0.4206
1
2720
3617
-1203.855
0.4107
1
2634
3692
-1133.152
0.2296
0.6656
2531
3469
-1102.638
0.1925
0.6655
2373
3472
-995.615
0.2656
0.7522
2447
3384
-1060.306
0.2248
0.7429
2262
3360
-939.794
B&A Modela
Statistic
N
Pd
N
FE
N-HN
Pd
N-HN
FE
N-E
Pd
N-E
FE
ˆv
Ê(e u |")
AIC
BIC
LL
0.4589
1
3025
3324
-1460.631
0.4482
1
2942
3402
-1391.089
0.2712
0.6360
2903
3219
-1396.317
0.2306
0.6353
2768
3246
-1301.242
0.2852
0.7169
2769
3086
-1329.625
0.2422
0.7123
2583
3060
-1208.366
a
N=Normal; HN=Half-Normal; E=Exponential; Pd=Pooled; FE = Fixed E↵ects.
LL=Log Likelihood; Ê(e u |") = Jondrow et al. (1982)’s technical efficiency.
Table 1: Model diagnostics - Log Likelihood (LL) values, AIC, and BIC for the annual and B&A
fixed-e↵ects and pooled models, along with estimates of v and the average estimate of Jondrow’s [? ]
technical efficiency Ê(e u |").
Annual Model
B&A Model
Variable
2005
2006
2007
2008
2009
2010
Pre-A80
Post-A80
halibut
rsole
cod
other
duration
length
-0.153**
0.343**
0.346**
0.108**
-0.556**
-0.111
-0.143**
0.311**
0.413**
0.095**
-0.576**
-0.364**
-0.174**
0.341**
0.218**
0.343**
-0.472**
-0.109
-0.120**
0.522**
0.083**
0.258**
-0.113**
-0.007
-0.175**
0.514**
0.140**
0.129**
-0.189**
-0.323**
-0.156**
0.426**
0.154**
0.264**
-0.316**
-0.341**
-0.142**
0.338**
0.333**
0.148**
-0.587**
-0.119*
-0.156**
0.461**
0.133**
0.236**
-0.207**
-0.092
0.76
480
0.71
358
0.67
315
0.73
411
0.76
387
0.81
372
0.69
1153
0.73
1170
Ê(e
N
u
|")a
Notes: * p<0.05, ** p<0.01; a Mean efficiency.
Table 2: Distance Elasticities - MLE estimates of the mean distance elasticities @lnD(·)/@lny for the
annual and B&A fixed e↵ects HDF normal - exponential model.
32
a
N=Normal; HN=Half-Normal; E=Exponential; Pd=Pooled; FE = Fixed E↵ects.
LL=Log Likelihood; Ê(e u |") = Jondrow et al. (1982)’s technical efficiency.
Table 1: Model diagnostics - Log Likelihood (LL) values, AIC, and BIC for the annual and B&A
fixed-e↵ects and pooled models, along with estimates of v and the average estimate of Jondrow’s [? ]
technical efficiency Ê(e u |").
Table 2: Mean distance elasticities for the fixed-effects HDF normal-exponential model.
Annual Model
B&A Model
Variable
2005
2006
2007
2008
2009
2010
Pre-A80
Post-A80
halibut
rsole
cod
other
duration
length
-0.154**
0.353**
0.341**
0.076*
-0.596**
0.033
-0.116**
0.343**
0.466**
0.008
-0.565**
-0.048
-0.127**
0.366**
0.250**
0.344**
-0.547**
-0.180*
-0.147**
0.494**
0.080**
0.231**
-0.129*
0.063
-0.141**
0.511**
0.183**
0.073
-0.424**
-0.257*
-0.145**
0.411**
0.180**
0.262**
-0.255**
0.145
-0.137**
0.340**
0.351**
0.099**
-0.551**
-0.004
-0.146**
0.453**
0.145**
0.230**
-0.166**
-0.065
0.76
480
0.71
358
0.67
315
0.73
411
0.76
387
0.81
372
0.69
1153
0.73
1170
Ê(e
N
u
|")a
Notes: * p<0.05, ** p<0.01; a Mean efficiency.
Table 2: Distance Elasticities - MLE estimates of the mean distance elasticities @lnD(·)/@lny for the
annual and B&A fixed e↵ects HDF normal - exponential model.
2
33
0
10
Rock Sole (mt)
20
30
40
Figures
0
.5
2005
1
Halibut (mt)
2006
2007
2008
1.5
2009
2
2010
Figure 1: Scatter plots of daily catches of rock sole and halibut (divided by the number of
daily trawls) for a small window of average trawl duration (2.9 – 3.25 hours) during the rock
sole season. Lighter colored circles represent years prior to Amendment 80 (A80) while
darker colored diamonds represents years after A80. The grey and black curves are predicted
quadratic regressions for pre- and post-A80 years, respectively, fit through the origin for nulljointness.
34
.6
.4
.2
0
Daily catch of halibut per rock sole
2005
2006
2007
2008
2009
2010
excludes outside values
-20
-10
% difference from 2007
0
10
20
30
40
Figure 2: Halibut bycatch rates—box-and-whisker plots of daily harvests of halibut per rock
sole during rock sole season, 2005-2010.
2005
2006
2007
2008
2009
2010
Year
Cod
Yellowfin sole
Rock sole
Halibut
Figure 3: Percentage difference in stock assessment estimates of biomass, relative to 2007.
35
15
MRT
10
5
0
0
5
10
MRT
15
20
Before-and-After Model
20
Annual Model
2005
2006
2007
2008
2009
2010
Pre-A80
Post-A80
Figure 4: Average marginal rate of transformation (MRT) between halibut and rock sole.
Whiskers represent 95% confidence intervals.
.8
.6
MESby
.4
.2
0
0
.2
.4
MESby
.6
.8
1
Before-and-After Model
1
Annual Model
2005
2006
2007
2008
2009
2010
Pre-A80
Post-A80
Figure 5: Average Morishima elasticity of substitution (MES) between halibut and rock sole.
Whiskers represent 95% confidence intervals.
36
Before-and-After Model
60
Rock Sole (mt)
20
40
60
40
0
0
20
Rock Sole (mt)
80
80
100
100
Annual Model
0
.5
1
1.5
2
2.5
2005
2006
2007
2008
0
.5
1
1.5
2
2.5
Halibut (mt)
Halibut (mt)
2009
2010
Pre-A80
Post-A80
Figure 6: Median production possibilities frontiers in rock sole-halibut space for the normalexponential models.
37