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Rights-based management is prevalent in today's developed-world fisheries, yet spatiotemporal models of fishing behavior do not reflect such institutional settings. We develop a model of spatiotemporal fishing behavior that incorporates the dynamic and general equilibrium elements of catch-share fisheries. We propose an estimation strategy that is able to recover structural behavioral parameters through a nested fixed-point maximum likelihood procedure. We illustrate our modeling approach through a Monte Carlo analysis and demonstrate its importance for predicting out-of-sample counterfactual policies.
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Structural Behavioral Models for Rights-Based FisheriesI
Matthew N. Reimer
Department of Agricultural & Resource Economics, University of California, Davis, One Shields Ave,
Davis, CA 95616 USA
Joshua K. Abbott
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 USA
Alan Haynie
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 USA
Abstract
Rights-based management is prevalent in many fisheries, yet spatiotemporal models of fish-
ing behavior do not reflect such institutional settings. We develop a model of spatiotemporal
fishing behavior that incorporates the dynamic and general equilibrium elements of catch-
share fisheries. We propose an estimation strategy that is able to recover structural behav-
ioral parameters through a nested fixed-point maximum likelihood procedure. We illustrate
our modeling approach through a Monte Carlo analysis and demonstrate its importance for
predicting out-of-sample counterfactual policies.
Keywords: structural econometrics, rights-based fisheries, discrete choice models
IWe thank several individuals for helpful comments, including Corbett Grainger, Ling Huang, Linda
Nøstbakken, Kathleen Segerson, and Brett Watson; seminar participants at Arizona State University, Uni-
versity of Alaska Anchorage, University of Connecticut, and the Norwegian School of Economics; and session
participants at the IIFET 2018, NAAFE 2019, AERE 2019, and ASSA 2020 meetings. Funding for this
research was provided by the North Pacific Research Board (NPRB-1607). The scientific results and con-
clusions, as well as any views or opinions expressed herein, are those of the authors and do not necessarily
reflect those of the authors’ affiliate or funding organizations. We declare no conflicts of interest and that
we have no relevant or material financial interests that relate to the research in this paper.
Corresponding author
Email addresses: mnreimer@ucdavis.edu (Matthew N. Reimer), Joshua.K.Abbott@asu.edu (Joshua
K. Abbott), Alan.Haynie@noaa.gov (Alan Haynie)
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1. Introduction
Economists are often called upon to inform policy makers of the potential consequences of
proposed environmental and natural resource regulations. For economists to offer reliable ad-
vice, their models must adequately capture individual decision-making processes, contextual
variables, and institutional settings to provide externally valid predictions across the range
of policy scenarios of interest to decision-makers (Lucas,1976;Heckman,2010). If the range
of these counterfactuals deviates markedly from in-sample conditions, then purely empirical,
reduced-form descriptions of behavior will likely be unsatisfactory. Instead, structural mod-
els that explicitly model individuals’ decision-making process in terms of objective-seeking
(e.g., profit or utility-maximizing) behavior under the salient economic, environmental, and
institutional constraints are needed (Wolpin,2007;Keane,2010).
In this paper, we develop a structural approach for estimating individual commercial-
fishing behavior under rights-based management institutions that provides consistent esti-
mates of behavioral parameters and is capable of predicting out-of-sample counterfactual
policies. Despite the prevalence of rights-based management in today’s developed-world
fisheries, most empirical models of commercial fishing behavior—those intended to inform
management decision making—do not explicitly reflect the incentives and constraints un-
derlying rights-based institutions. Instead, they reflect the implicit theoretical assumptions
of regulated open or limited access fisheries. As such, even if these models are calibrated on
behavior under rights-based management, they do not capture the theoretical mechanisms
by which incentives under rights-based management affect fishers’ behavior. The result, as
we demonstrate, is that the predictions of these models could be highly misleading.
To address this deficiency, we extend random utility maximization (RUM) models of
spatiotemporal fishing behavior (e.g., Eales and Wilen,1986;Holland and Sutinen,2000;
Smith,2005;Haynie et al.,2009;Abbott and Wilen,2011), which are the dominant form
of management models used to predict the consequences of proposed fishery policies, such
as spatial regulations (Smith and Wilen,2003;Berman,2006;Haynie and Layton,2010;
Hicks and Schnier,2010). Conventional RUM models of fishing behavior do not consider the
implications of individualized (and often transferable) quotas of catch entitlements within a
season, which create a shadow value reflecting the opportunity cost of quota. We incorporate
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the dynamic and general equilibrium elements of fisheries with tradable short-term rights
of annual catch entitlements by introducing a lease-market for quota, which we model as a
pure exchange economy. Fishers are assumed to be forward-looking within the fishing season
and form expectations over future quota usage when considering contemporaneous quota
supply and demand decisions. Under the assumption of rational expectations, each fisher’s
stochastic dynamic programming problem reduces to a period-by-period static maximization
problem given a set of equilibrium quota prices. Critically, expectations are updated in each
period, leading to a new set of equilibrium quota prices to reflect the changing relative
scarcity of quota in a stochastic production environment.
We demonstrate the utility of our estimation strategy—dubbed the rational expectations
RUM (RERUM)—for both parameter estimation and out-of-sample prediction through nu-
merical simulations and Monte Carlo analyses. We first show that the omitted nature of
quota lease prices in the conventional RUM approach leads to a form of omitted variable
bias (or, alternatively, non-classical measurement error). These biases could jeopardize the
estimation of shadow values or welfare estimates (e.g., Abbott and Wilen,2011;Haynie
et al.,2009;Hicks and Schnier,2006). We demonstrate that substitution of high-resolution
lease prices as data into the conventional RUM is able to eliminate estimation bias of behav-
ioral parameters. Unfortunately, thin markets combined with confidentiality concerns rarely
allow for such an approach. Imputing annual average prices—which are more commonly
available—offers only a partial mitigation of the bias, since it fails to capture dynamic ad-
justments of behavior within the fishing season. Furthermore, even if high-resolution lease
prices are available, prediction for out-of-sample policy scenarios requires the imputation of
counterfactual lease prices that are consistent with the stochastic production environment
and the changes in market, ecological, or policy conditions embodied in the scenario.
Our estimation approach imputes quota-lease prices via a market simulator at the core
of the estimation procedure, whereby a fixed-point problem is solved to determine state-
contingent equilibrium lease prices in every period. Thus, the RERUM estimator does not
rely on the availability of high-resolution lease-price data and can produce counterfactual
lease prices that are consistent with the structure of fishers’ dynamic decision problem and
observed fisher behavior. Moreover, our approach does not suffer from the curse of dimen-
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sionality because the dimensions of the fixed-point problem increase linearly, as opposed to
exponentially, with the number of quota-constrained species. Thus, we are able to solve the
behavioral model exactly and recover the structural parameters through a nested fixed-point
(NFXP) maximum likelihood procedure (Rust,1987).
We conduct numerical simulations to demonstrate how our model can be used for ex
ante evaluation of fishery policies, such as spatial closures or reductions in the total allow-
able catch. We illustrate this point through a Monte Carlo analysis and investigate data-
generating environments for which our approach matters most for out-of-sample predictions.
We find that our approach matters more as counterfactual policy changes lie increasingly
out-of-sample, as measured by the degree to which lease prices are responsive to the counter-
factual policy. For counterfactuals that have only a marginal influence on quota-lease prices,
reduced-form approaches that approximate the state-contingent equilibrium lease prices can
be sufficient for out-of-sample predictions.
Finally, we note that while our estimator is tailored specifically to the production process
and institutions of modern-day fisheries, our work has broader relevance for other industrial
and institutional settings—particularly for industries characterized by stochastic produc-
tion processes and managed under quotas (or quantity controls) with transferable property
rights. For example, cap-and-trade systems for controlling greenhouse gas emissions are
typically comprised of firms that make dynamic production decisions under uncertainty of
future abatement costs while balancing emissions and permits over a fixed regulatory horizon
(Rubin,1996;Kling and Rubin,1997;Fell,2016;Kollenberg and Taschini,2016). As in our
setting, binding quota allocations create shadow values that reflect the opportunity cost of
such constraints, and these shadow values are harmonized through the coordinating mecha-
nism of the quota market. Any proposed policy that influences these shadow values will thus
be reflected in the equilibrium quota prices. Thus, quota prices are not policy invariant, and
therefore, models of endogenous quota prices are likely required for counterfactual policy
evaluations.
The course of the paper is as follows. Section 2discusses the relevant literature and
the institutional background of rights-based management of commercial fisheries. Sections
3and 4present the structural behavioral model and the estimation strategy of the RERUM
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estimator. Section 5demonstrates the utility of the RERUM model for predicting realistic
policy changes, such as quota reductions and spatial closures, and provides Monte Carlo
simulation evidence of the estimation performance and predictive utility of the RERUM
model in comparison to alternative RUM model specifications. Section 6concludes the
paper.
2. Background and Related Literature
The governance of many nation states’ fisheries has been transformed in recent decades—
from the “tragedies” of open access and input regulation to a range of governance structures
based upon individual or collective extractive rights. By one estimate, approximately 20%
of global catch comes from fisheries managed under individual transferable quotas (Costello
and Ovando,2019)—a number that only partially accounts for the full spectrum of rights-
based management approaches, including fishing cooperatives (Deacon,2012) or TURFs
(Wilen et al.,2012). Rights-based management (RBM) is particularly common in the Global
North where it is facilitated by strong scientific input and adequate governance. RBM, in
combination with scientifically-based quotas and sound enforcement, has played a prominent
role in reversing overfishing and improving economic efficiency in many fisheries (Worm et al.,
2009;Grafton et al.,2006;Hilborn et al.,2005).
Despite these successes, RBM has not reduced the role of fisheries managers to merely
conducting stock assessments and setting seasonal quotas. Catch shares, especially individual
quotas, may leave significant in-season externalities unaddressed (Boyce,1992;Costello and
Deacon,2007), forcing managers to deploy additional management measures to address
concerns such as growth overfishing or in-season rent dissipation. Furthermore, many of the
concerns of ecosystem-based management—e.g., protection of spawning stocks or vulnerable
life stages, reducing external impacts on unfished stocks or species of conservation concern,
and habitat protection—are outside the scope of most RBM systems (Holland,2018).
As a result of these concerns, managers use a wide range of tools, including input restric-
tions, protected areas, time-area closures, and dynamic ocean management (Maxwell et al.,
2015), in addition to RBM systems. Economists have informed managers of the potential
consequences of these actions by developing positive bioeconomic models (e.g., Smith and
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Wilen,2003;Hutniczak,2015;Lee et al.,2017;Holland,2011;Huang and Smith,2014) that
predict how changes to policy design may change catch, effort, profits, employment, or eco-
logical impacts. However, the continued adoption of RBM presents a significant challenge
to fisheries policy modeling in that the overwhelming majority of empirical models used to
inform in-season management measures fail to consider the implications of individualized
(and often transferable) catch rights within a season. Catch share fisheries define individu-
alized (or sometimes cooperative-based) quota constraints, and the shadow values that arise
from such constraints are coordinated through within-season quota trading in a shared lease
market. Experience has demonstrated that in-season behavior is often drastically altered by
catch shares. This is particularly likely in terms of the allocation of fishing “effort” in both
space and time (Reimer et al.,2014;Abbott et al.,2015;Birkenbach et al.,2017;Miller and
Deacon,2017). Fishers may spread their effort temporally and reallocate where they fish
to enhance revenues or reduce costs. More complex patterns may emerge in multispecies
catch-share fisheries as vessels utilize space and time to maximize the profit associated with
their quota portfolios (Birkenbach et al.,2020). However, models of commercial fisheries
often do not capture the behavioral mechanisms that arise under RBM institutions, with
the result that their predictions could be highly misleading (Reimer et al.,2017b).
Our econometric estimation approach is not the first to include dynamic or stochastic
elements of within-season fishing behavior. Models of within-trip behavior have been ex-
tended to consider the logistical problem of the optimal trajectory of fishing decisions within
a trip. Optimal within-trip behavior is therefore cast as a dynamic programming problem,
with estimation of model parameters coinciding with the solution (Hicks and Schnier,2006,
2008) or approximation (Curtis and Hicks,2000;Curtis and McConnell,2004;Abe and An-
derson,2020) of the dynamic programming problem. Such models, however, do not capture
the overriding dynamic concern that we would expect to emerge under catch shares—the
management of a portfolio of quotas over the course of an entire season, where the state vari-
ables that provide the information set for fishermens decisions (i.e., expected catch, quota
balances) evolve in a partially stochastic manner.
A handful of papers have tackled seasonal fishing supply decisions dynamically (Provencher
and Bishop,1997;Smith and Provencher,2003;Huang and Smith,2014). However, the
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stochastic evolution of the state variables coupled with the need to solve a fisher’s seasonal
optimization repeatedly in the estimation process through stochastic dynamic programming
has resulted in the imposition of very strong assumptions on the models to maintain com-
putational tractability. This has usually taken the form of severely limiting the number of
spatial locations available to fishermen and curtailing the horizon of decision making in order
to reduce the “curse of dimensionality.” Indeed, while notable advances have been made in
reducing these computational burdens, the dimensionality of most applied dynamic discrete
choice models remains quite small (Aguirregabiria and Mira,2010). As we explain below, the
coordinating mechanism of the quota lease market allows us to specify production decisions
over a realistic spatial and temporal scale and number of state variables (species).
3. A Model of a Catch-Share Fishery
Our objective is to build a model of within-season fishing behavior that generates exter-
nally valid ex ante predictions of fishery policies in a catch-share fishery. This prospective
model must be structural or mechanistic, in the sense that it identifies policy-invariant pa-
rameters that can be safely transported into “out-of-sample” environments, facilitating the
job of ex ante prediction (Heckman and Vytlacil,2007;Heckman,2010). Structural mod-
els achieve this flexibility through explicitly modeling the hypothesized decision process of
agents in response to their decision context, usually through a constrained optimization ap-
proach. This differs from estimating a reduced-form decision rule in that the latter runs
the risk of fragility since underlying ecological, economic, or policy state variables may be
subsumed into the estimated reduced form parameters (Fenichel et al.,2013).
Our model must satisfy several criteria. First, it must capture the primary within-
season mechanisms fishermen use to shape economic returns and catch compositions. While
some aspects of input usage (e.g., bait or crew staffing) may be somewhat variable within a
season, the primary short-run mechanisms influencing vessel output are where and when to
fish (Abbott et al.,2015;Reimer et al.,2017a;Scheld and Walden,2018). Second, the model
must be both dynamic and stochastic. Dynamic models consider that fishermen allocate
their portfolio to maximize seasonal returns so that current fishing decisions depend on
expectations of fishery conditions later in the season. Stochasticity implies that planning
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will not be perfect—catch, and hence quota balances, will not exactly match expectations.
Third, the model must easily accommodate realistic changes to management policies—such
as catch limits and time/area closures. Finally, estimation and simulation of the model must
be achievable from available data with reasonable technology and computing time.
Structural models face a trade-off between realism and computational tractability, re-
quiring that modeling decisions preserve realism where it is fundamental to the nature of
agents’ decision problem and predicted outcomes while sacrificing it elsewhere. In our case,
the most fundamental decision concerns the modeling of the quota lease-market, for which
we make two simplifying assumptions. First, we assume that fishers must have enough quota
at the end of the fishing season to cover their cumulative catch. Accordingly, the market
for leasing quota clears at the end of the season, and fishers’ expectations regarding end-
of-season quota demand and supply form the basis for within-season quota prices. Second,
we assume the market for quota is competitive. That is, fishers’ treat their expectations of
quota-lease prices as given, even though prices are endogenously determined by the aggregate
behavior of all fishers. Given the incentives embodied in these expected prices, fishers carry
out individually optimal “on-the-water” plans by allocating their effort over a discrete num-
ber of fishing sites and time periods. We close the model under the assumption of rational
expectations so that equilibrium quota prices are consistent with fishers’ beliefs.
3.1. A fisher’s dynamic programming problem
Consider agent (i.e., the fisher) i, who has preferences defined over a sequence of states
of the world zi,t from period t= 1 until period t=T+ 1. In periods tT, agents choose
a fishing location aA={0,1, ..., J }, where a= 0 represents the option of not fishing. In
the final period t=T+ 1, the agent incurs costs or receives revenues from buying or selling
quota in the leasing market according to their cumulative quota usage. In any given time
period, fishers must account for the opportunity cost of using quota—whether it is best to
use quota today for the profits it generates or preserve it for sale in the competitive quota
market. The problem is stochastic because fishers do not know exactly what they (or others)
will catch at each location and time period, and thus, they form expectations over fleet-wide
catch realizations and the resulting end-of-season excess demand for quota. We assume that
8
the number of fishers is large enough that any single fisher perceives their effect on aggregate
harvest and the quota lease price as negligible. Therefore, fishers’ expectations of quota
prices are formed exogenously to their own decisions.
We make a number of simplifying assumptions for the sake of tractability. First, the state
of the world at period tfor agent iis assumed to consist of two components: zi,t = (xi,t , εi,t).
The subvector εi,t is private information known only by agent iat the time of decision, and is
assumed to be exogenous. The subvector xi,t is an endogenous and stochastic state variable
representing an agent’s S-dimensional vector of cumulative catch prior to making a decision
in period t:xi,t =fx(xi,t1) = Pt1
k=1 yi,k =xi,t1+yi,t1, where yi,t =Y(ai,t, ξi,t ) represents
fisher i’s S-dimensional vector of catch in period t.1The term ξi,t represents the stochastic
component of catch, which we assume to be serially uncorrelated and unknown to any fisher
at the time a decision is made in period t. We denote xt=Pixi,t as the vector of fleet-wide
cumulative catch at the beginning of period tfor all species, which we assume to be common
knowledge to all fishers.
Second, we assume that an agent’s contemporaneous utility function for location ai,t is
additively separable in the observable and unobservable components:
U(ai,t, zi,t ) =
u(ai,t, p0yi,t ) + εi,t (ai,t) if t∈ {1, ..., T }
u(0, w0(ωixi,T +1)) if t=T+ 1,
(1)
where ωidenotes a vector of quota endowments possessed by fisher iat the beginning of the
season, wdenotes a vector of quota-lease prices, and pdenotes a vector of ex-vessel prices.
An agent’s utility in the final period T+ 1 is evaluated at port (a= 0) with revenue equal
to the value of their remaining endowment of quota.2
Third, we assume that the unobserved state variables εi,t are independently and identi-
cally distributed (iid) across agents, time, and locations, and have an extreme-value type 1
1Note that the time index tshould also be a component of the state vector, but we omit it here for the
sake of keeping notation as simple as possible.
2It can be shown that the indirect utility function in period T+ 1 follows from an agent choosing con-
sumption and an amount of quota to maximize utility, subject to a budget constraint (see section Appendix
Bfor details).
9
distribution that is common knowledge across fishers.
Fourth, we assume that catch yis independent of the unobserved state variables εand the
observed endogenous state variables x, conditional on the location choice a. This assumption
implies that the stochastic component of catch ξis conditionally independent of past, present,
and future values of εand x, so that: E(yi,t |ai,t , xi,t, εi,t) = E(yi,t |ai,t ).Practically speaking,
this assumption has several implications. First, a fisher’s private information about a location
choice does not affect catch (or expectations of catch) once the fisher’s choice has been
made—i.e., private information only influences catch by influencing a fisher’s choice. Second,
cumulative catch, as reflected in xi,t, does not influence the distribution of contemporaneous
catch—i.e., within-season spatiotemporal stock dynamics are exogenous to fishing behavior.
Finally, this assumption also implies that the next-period cumulative catch xj,t+1 of any
fisher jis independent of fisher i’s current period unobserved state variable εi,t, conditional
on the values of the decision ai,t and state variable xi,t. Together, these assumptions define
what is often referred to as the dynamic programming conditional logit model (Rust,1987).
In periods tT, an agent observes the vector of state variables zi,t and chooses an action
ai,t Ato maximize expected utility
E T+1t
X
j=0
U(ai,t+j, zi,t+j)ai,t, zi,t !.(2)
The decision at period taffects the evolution of future values of the state variables xi,t, but
the agent faces uncertainty about these future values due to the unknown nature of future
catch. The agent forms beliefs about future states, which are objective beliefs in the sense
that they are the true transition probabilities of the state variables. By Bellman’s principle
of optimality, the value function during the fishing periods tTcan be obtained using the
recursive expression:
V(zi,t) = max
aAU(a, zi,t) + EzV(zi,t+1)a, zi,t,(3)
where Ezdenotes the expectations operator with respect to the state vector z.3
3Note that we do not include a discount factor.
10
Unfortunately, there is typically no analytical form for the expected value function, and
computationally expensive numerical and recursive methods are often needed to solve the
Bellman equation instead. The restrictions these methods place on the dimensionality of
the state space have often limited the empirical relevance of dynamic programming models
of fisher behavior. Thankfully, the assumptions underlying the dynamic programming con-
ditional logit model, combined with the additional assumption that fishers are risk-neutral,
imply that fisher i’s optimal decision rule in each period is dramatically simplified. The ex-
pected quota-lease price win period tacts as a shadow price of quota, which is harmonized
across fishers given the transferability of quota.4Conditional on expected lease prices w, the
solution of Eq. (3) takes on a simple, static form:5
α(zi,t |w) = argmax
aAua, (pw)0Eyi,t a+εi,t (a).(4)
Notably, the policy function has a simple analytical form that does not depend on the endoge-
nous state variable xi,t. Rather, it depends only on the fisher’s current private information
εi,t and the expected quota-lease price w, both of which are exogenous. Intuitively, the
quota-lease price embeds all relevant information regarding expected future quota scarcity
needed to inform the present-day decision.6Functionally, this means that, given a perceived
quota-lease price, the location-choice problem in equation (2) reduces to a tractable period-
by-period static maximization problem that does not require recursively solving the Bellman
equation.
3.2. Rational Expectations Equilibrium Quota Prices
Eq. (4) presents a fisher’s optimal decision rule for a given expected quota-lease price w.
Fishers determine their current and future optimal location choices given perceived quota
prices was specified by the policy function α(zi,t |w) in equation (4). In this sense, quota
4The assumption of risk neutrality has the practical implication that revenue enters utility linearly and
is additively separable from the rest of utility.
5See Appendix C for a formal derivation.
6The policy function in equation (4) takes on a similar form to the utility function used by Miller and
Deacon (2017).
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prices determine fisher behavior. At the same time, given fishers’ decision rules α(zi,t |w),
the quota market determines expected quota prices in each period so that aggregate fisher
behavior determines the equilibrium quota prices. Rational expectations states that the
market-clearing quota prices implied by fisher behavior are the same as the quota prices on
which fishers’ decisions are based. That is, the market-clearing equilibrium quota prices are
consistent with fishers’ quota-price expectations.
The expected quota-price vector wis the equilibrium price that clears a seasonal compet-
itive market for quota leasing, which is assumed to be frictionless and without transaction
costs. Let Ω = Piωidenote the vector of fleet-wide quota endowments for all species.
Then the seasonal excess demand for quota for species scan be written as es=xs,T +1 s.
In any given period tT, a fisher does not know with certainty what the demand for quota
will be at the end of the season; thus, forward-looking fishers form expectations over excess
demand given a perceived wand the state of the world in period t:
E(es|w, xt) = E(xs,T +1 |w, xt)s
=T
P
k=tP
iP
aA
f(a|w)E(yi,s,k |a)+xs,t s,(5)
where f(·) denotes the probability mass function for the discrete location-choice variable a
and the bracketed term represents the expected catch for all fishers in the remaining periods.7
Given the assumption that fishers know the distribution of private information for all agents,
f(·) can be derived by integrating the policy function (4) over the unobserved state variable:
f(a|w) = ZI[α(z|w) = a]g(ε)dε,
where I[·] is an indicator function and g(·) is the probability density function of ε. The
expected equilibrium quota-lease prices in period tcan then be defined as those that satisfy
7For simplicity, we have implicitly assumed that a fisher forms their expectation of excess demand before
they observe their private information ε. For a large number of fishers, as we’ve assumed here, this has
a negligible influence on our results; it is, however, trivial to relax this assumption at the cost of model
presentation.
12
the following market-clearing conditions:
E(es|w, xt) = 0 for ws>0
E(es|w, xt)0 for ws= 0.
(6)
That is, in equilibrium, prices will adjust so that positive prices achieve zero expected excess
quota demand for scarce species, while prices fall to zero for species in excess supply (i.e.,
“free goods”). The equilibrium quota prices that solve the market-clearing conditions in the
system of equations (6) are state-contingent—i.e., they are a function of the observed (and
common knowledge) state of the world in period t. We denote the equilibrium quota-lease
price vector as ˜w(xt).
Under the assumption of rational expectations, fishers’ beliefs are consistent with the
market-clearing conditions in (6). Thus, to close the rational expectations model, we sub-
stitute the equilibrium quota prices ˜w(xt) into a fisher’s optimal decision rule:
α(zi,t) = argmax
aAua, (p˜w(xt))0Eyi,t a+εi,t (a),(7)
Eq. (7) serves as the basis for our rational-expectations RUM (or RERUM) model.
We emphasize here that the state-contingent equilibrium prices ˜w(xt) reflect the scarcity
of quota that exists in time tgiven expectations regarding optimal future behavior and
harvesting conditions. Thus, while the equilibrium quota prices are determined by a market-
clearing condition at the end of the season, ˜w(xt) are the equilibrium prices that emerge in
period tas quota is exchanged. We further note that since equilibrium quota prices are
determined by common knowledge of aggregate cumulative catch xt, and not knowledge of
individual catch xi,t, it is not necessary to track quota within-season quota exchanges.
4. Estimation
We wish to estimate a vector of structural parameters in the utility function θutilizing
panel data for Nindividuals who behave according to the decision model described in Section
3. For every observation (i, t) in this panel dataset, we observe the individual’s action ai,t,
the payoff variable yi,t, and the subvector xi,t of the state vector zi,t = (xi,t, εi,t). Because the
subvector εi,t is observed by the agent but not by the researcher, εi,t is a source of variation
13
in the decisions of agents conditional on the variables observed by the researcher. It is the
model’s econometric error, which is given a structural interpretation as an unobserved state
variable.
Assuming that the data are a random sample over individuals, the log-likelihood function
is PN
ili(θ), where li(θ) is the contribution to the log-likelihood function of i’s individual
history:8
li(θ) = log Pr ai,t :t= 1, ..., T yi,t, xt, θ
= log Pr ai,t =α(xi,t, εi,t, θ) : t= 1, ..., T yi,t, xt, θ(8)
=
T
X
t=1
log f(ai,t |xt, θ).
Closed-form expressions for f(·) follow from the iid extreme value type 1 distribution we’ve
assumed for εi,t, which produces the conventional logit probabilities:
f(a|xt, θ) = eu(a,(pw(xt))0E(y|a))
Pkeu(k,(pw(xt))0E(y|k)).(9)
This expression is predicated on knowledge of the quota price rules w(xt). Therefore, we
need to either observe the state-contingent quota prices or come up with a strategy for
determining the implied quota prices within the estimation process. In the former case,
observed quota prices can simply be inserted into the choice probabilities in equation (9)
and maximum likelihood estimation can proceed as usual. However, in many cases, these
lease prices are not observed due to limitations on data disclosure or because only average
prices are reported, as opposed to state-contingent prices. Given this missing data problem,
we propose solving for the rational expectations equilibrium prices for each trial value of θ.
The nested fixed-point algorithm (NFXP) pioneered by Rust (1987) is a search method
for obtaining maximum likelihood estimates of the structural parameters, which combines
8Note that we are estimating the structural parameters θtaking the harvest variable yi,t and state variable
xtas given. Thus, we are taking a partial MLE approach here. In theory, it is possible to jointly estimate
the structural parameters of both the harvesting and utility functions in a full MLE approach; however, for
the sake of simplicity, we leave that for future research.
14
an “outer” algorithm that searches for the root of the likelihood equations with an “inner”
algorithm that solves for the fixed-point of the rational expectations equilibrium for each
trial value of the structural parameters. Specifically, consider an arbitrary value of θ, say ˆ
θ0.
Conditional on ˆ
θ0, the inner algorithm solves for the wtthat solves the fixed-point problem
in equation (6) given optimal fisher behavior described in equation (5). This produces an
equilibrium vector of quota prices ˜w(xt) for each observation in our data, which can be
substituted into equation (9) to form the choice probabilities fai,t |xt,ˆ
θ0. Next, the
outer algorithm uses the gradient of the log-likelihood function with the choice probabilities
in equation (9) to start a new iteration with a new structural parameter ˆ
θ1.This process
continues until either ˆ
θor the log-likelihood converges based on a pre-specified convergence
tolerance.9
5. The RERUM Estimator: Demonstration and Evaluation
In this section, we demonstrate how the RERUM can be used for predicting counterfac-
tual fishery policies, and evaluate the estimation and predictive performance of the RERUM
estimator. We first simulate the structural model with known parameter values to demon-
strate the utility of the RERUM model for predicting realistic policy changes, such as quota
reductions and spatial closures. We then evaluate the estimation and predictive perfor-
mance of the RERUM through a Monte Carlo analysis, where we estimate the RERUM
model over several draws from a data generating process with a random parameter space.
Finally, we evaluate the in- and out-of-sample predictive performance of the RERUM model
and alternative RUM models to investigate the biological and regulatory conditions under
which alternative RUM models may provide adequate predictions of fishing behavior under
rights-based management.
5.1. Fishery setting and the data-generating process
We consider a fishery in which fishers receive individual quotas for two species that are
jointly harvested, but only one of these species (Species 1) has an ex-vessel value to a fisher—
i.e., Species 2 can be considered a bycatch species. We simulate two forms of hypothetical
9For more details on the the NFXP algorithm, see Appendix D.
15
policies designed to reduce bycatch: (1) reductions to the quota for the bycatch species, and
(2) bycatch hot-spot area closures.
The data generating process (dgp) is purposefully simple to facilitate our understanding
of the model predictions. We assume fishers begin each period in port and choose from a
n×ngrid of fishing locations. The observable component of a fisher’s contemporaneous
expected utility function in equation (1) for location ais specified as:
E(ui,t) = θRev p0E(yi,t |a) + θDistDist(a),
where Dist(a) represents the distance from port to location a. A fisher’s optimal location
choice is determined by equation (7), which takes on the specification
α(zi,t) = argmax
aA
{θRev(p˜w(xt))0E(yi,t |a) + θDistDist(a) + εi,t (a)},
where the rational-expectations quota prices ˜w(xt) are determined by equation (6).10
We model fisher i’s catch of species s∈ {1,2}in period tand location aas ys,i,t =
Y(a, ξs,i,t) = qs,i exp {ξs,i,t (a)}, where qs,i (0,1) denotes fisher i’s catchability coefficient
and ξs,i,t(a) is a normally distributed random variable with location-specific mean param-
eters µs(a) and a common variance σ2. Catch is thus a log-normal distributed random
variable with mean E(ys,i,t |a) = qs,i exp{µs(a) + σ2/2}.11 For simplicity, µs(a) and σ2(and
thus expected catch) are assumed to remain constant over all individuals and time periods;
however, realized catch varies across all individuals and time periods due to the individual-
and time-specific nature of the idiosyncratic shock ξs,i,t(a).12
10In general, quota prices are sensitive to the data-generating parameters, as depicted in Figure A.1, and
have comparative statics that are consistent with theory: quota prices increase with ex-vessel prices, quota
scarcity, and the marginal utility of revenue. Note that the latter is only true for the target species. Quota
prices decrease with the marginal utility of revenue if a species’ net price (ex-vessel price minus quota lease
price) is negative. In this case, fishers will try to avoid catching this species, decreasing demand for it’s
quota.
11The mean parameters µs(a) vary over the grid according to distinct two-dimensional normal density
functions for both species.
12This example does not incorporate stock depletion or other spatial/temporal variability in expected catch
over the course of the season. We do so to focus attention on the dynamics generated by the opportunity
16
We consider two different biological scenarios with different spatial distributions for each
species, producing the global production sets depicted in Figure 1. In the first scenario, the
two species have minimal spatial overlap, and thus, fishers are able to substitute between
species relatively easily. In contrast, fishers are more constrained by the bycatch species in
the second scenario as there is greater spatial overlap between species and fishers must travel
further away from port to avoid bycatch.
5.2. Simulating bycatch quota reductions and hot-spot closures
We reduce the bycatch quota and the area open to fishing, respectively, by increments
of 5% to a minimum of 25% of their baseline levels. For the area closures, we emulate a
hot-spot closure policy by closing areas to fishing that experience the highest amount of
bycatch in the baseline simulations.13 Harvest and utility shocks (ξand ε) are drawn from
their respective probability distributions, and state variables are endogenously updated in
each time period. The remaining data-generating parameter values are known and remain
fixed across all policy simulations (presented in column 1 of Table 1).
Results from the policy simulations are presented in Figure 2, where we’ve simulated
200 counterfactual seasons under each policy. Under the baseline policies, the quota for
the bycatch species (s= 2) is binding in both biological scenarios, resulting in a positive
quota-lease price in all simulated seasons. In scenario 1, the lease price for the target species
(s= 1) is consistently positive as well, pointing toward the dominance of interior solutions in
the quota market. In contrast, the target species almost always has a non-positive lease price
in scenario 2, where the bycatch species consistently acts as a choke species, preventing the
full harvest of the target species quota. This difference largely stems from the higher spatial
overlap between the target and bycatch species in scenario 2, making bycatch avoidance so
costly that it is not possible to fully utilize the target species quota.
cost of quota. It is a relatively straightforward extension of our approach to include these extensions, so long
as fishers consider stock depletion and other non-stationarities to be an exogenous process in their planning
behavior.
13For example, if 75% of a 100-location grid is closed to fishing, we close the 75 cells that have the highest
amount of bycatch from a baseline simulation with no spatial closures.
17
The effect of the bycatch reduction policies differs across both biological scenarios and
policy types. Not surprisingly, the quota reductions are effective at achieving desired bycatch
reductions: bycatch falls at a 1:1 ratio with the bycatch quota as the quota remains binding
over all reductions. The lost utility from achieving a given level of bycatch reduction is
considerably higher in scenario 2 because of the higher cost of bycatch avoidance. In scenario
2, the primary cost of bycatch reduction is foregone catch of the target species, as the bycatch
quota continues to bind before the target-species quota is harvested. By contrast, the primary
cost in scenario 1 is traveling greater distances to avoid bycatch: there is minimal foregone
target species catch in scenario 1 and the target species quota price declines very slowly on
average while the price of bycatch quota rises steadily with increased scarcity.
Hot-spot closures, on the other hand, have virtually no impact on bycatch in either
scenario over the examined range of closures. In fact, hot-spot closures have the effect of
pushing fishers into areas with higher bycatch-to-target species ratios. Since fishers are
already avoiding bycatch under the baseline policy, bycatch is being generated in areas with
relatively low bycatch-to-target species ratios; hot-spot closures therefore push fishers out of
relatively cleaner areas, thereby increasing bycatch per unit of target species catch.
The key difference between the two bycatch-reduction policies is reflected in the quota-
lease prices: quota reductions signal scarcity to fishers through increased quota-lease prices,
and fishers have the incentive to reduce bycatch in the most cost-effective manner given their
information about catch rates. Hot-spot closures, on the other hand, do not signal bycatch
scarcity over a wide spectrum of policy severity when bycatch quota is already sufficiently
scarce under the baseline scenario to command a positive price. Instead, for fisheries where
bycatch species does not consistently act as a choke species (scenario 1), the closures decrease
the value of the target species quota price by pushing fishers into increasingly sub-optimal
fishing locations. In fact, quota prices for the bycatch species are only responsive to the
closures in scenario 1 once the target-species quota can no longer be harvested before the
bycatch quota binds.
Altogether, these policy simulations demonstrate the utility of modeling the spatiotem-
poral production decisions of harvesters under the dynamically evolving constraints imposed
by the seasonal quota market. The structural model can yield counterfactual policy predic-
18
tions of fisher welfare, catch rates, and lease price behavior for changes in both rights-based
management parameters (i.e., quota allocations) and “ecosystem based” policies targeting
the spatiotemporal footprint of fishing effort. The simulation results also highlight the role
that lease prices play in relaying signals of quota scarcity, and how policies that fail to influ-
ence the relative scarcity of quota in the desired direction as reflected in these relative prices
are likely to fall short of their intended objectives.
5.3. Evaluating the RERUM and alternative RUM models: A Monte Carlo analysis
We now evaluate the estimation and predictive performance of the RERUM model and
other alternative RUM model specifications through a Monte Carlo analysis. Specifically, we
evaluate the in- and out-of-sample predictive performance of the RERUM and common RUM
model specifications to investigate the biological and regulatory conditions under which these
models provide adequate in- and out-of-sample predictions of fishing behavior within a catch-
share program. We estimate the RERUM and alternative RUM models on each draw from
the data-generating process described in Section 5.1. To judge each estimator’s in-sample
predictive performance across different data-generating and sampling environments, we also
draw randomly from the data-generating parameter space (e.g., θ, µ, σ) and the sampling
parameter space (e.g., T, N, S). To evaluate out-of-sample prediction performance, we sim-
ulate the same counterfactual bycatch-reduction policies as in Section 5.2 using estimated
parameters from the RERUM and alternative RUM estimators.14
We note that the RERUM estimator is an unbiased estimator of the true parameters by
construction, so long as the NFXP maximum likelihood algorithm converges to it’s global
maximum. Thus, the Monte Carlo results for the RERUM estimator are useful for ensuring
that the NFXP algorithm works appropriately and for investigating the properties of the
estimator (e.g., precision and identification) under realistic data settings.
14Monte Carlo simulations were conducted using Matlab (Version 2019a) with parallel computing (18
workers) running on an Amazon EC2 instance (c4.8xlarge) with an Intel Xeon E5-2666 v3 proces-
sor (2.9 GHz) and 60 GiB of memory. Code for reproducing Monte Carlo results can be found at
https://github.com/mnreimer/RERUM.git.
19
5.3.1. Alternative RUM model specifications
We consider the following alternative RUM model specifications, which differ in their
treatment of the shadow cost of quota in the specification of a fisher’s optimal location
choice:
Static RUM (SRUM):
αi,t = argmax
aA
{θRevp0E(yi,t |a) + θDistDist(a) + εi,t(a)};
Quota-Price RUM (QPRUM):
αi,t = argmax
aAθRev (pwt)0E(yi,t |ai,t) + θDistDist(ai,t) + εi,t (a),
where wt= observed quota-lease prices;
Approximate Rational Expectations RUM (ARUM):
αi,t = argmax
aAθRev (pˆwt)0E(yi,t |ai,t) + θDist Dist(ai,t ) + εi,t(a),
where ˆws,t =γ0,s +γ0
1,szt+z0
tγ2,szt, z0
t= [x1,t, x2,t , t], s = 1,2,
and xs,t denotes the proportion of remaining fleet-wide quota for species sin period t. The
parameters θ= [θRev, θDist] are the structural preference parameters of interest and are
estimated alongside the vector [γ0,s, γ1,s] and symmetric matrix γ2,s .
The first specification (SRUM) is a static RUM approach that does not account for
the forward-looking thinking of fishers, and thus, estimates a policy function that does not
deduct the shadow cost of quota from expected revenues. So long as the TAC has a non-
zero probability of binding for at least one species, the SRUM model will underestimate the
expected revenue coefficient θRev. Moreover, to the extent that a location’s distance from
port is correlated with the expected catch of a species with binding quota, the estimate of
the distance coefficient θDist will also be biased (upwards or downwards, depending on the
direction of the correlation).
The second specification (QPRUM) represents the approach one would take to address
the bias of the SRUM model if quota-lease prices were observed—that is, include the observed
prices wtdirectly into the policy function. We consider two versions of this approach, one
which uses the period-specific quota-lease prices wt(QPRUM1, the best-case scenario) and
another which uses the seasonal average quota price ¯w(QPRUM2, a more likely scenario).
20
The third specification (ARUM) attempts to address the bias of the SRUM model with-
out the luxury of having quota-lease prices. Specifically, the ARUM model introduces a
reduced-form quadratic approximation of quota-lease prices by interacting expected catch
with observed state variables meant to reflect the scarcity of quota, including the proportion
of remaining quota xs,t and time period t.15 Similar approaches have been followed previ-
ously, for example, to estimate the implicit cost of fleet-wide bycatch quotas (Abbott and
Wilen,2011) and to estimate the extent of cooperation in a common-pool fishery (Haynie
et al.,2009). The ARUM model approximates the shadow value of quota using both species’
cumulative catch information. Note that without temporal variation in the ex-vessel price p,
it is not possible to identify the constant γ0,s in the ARUM model. In practice, it is rare to
observe within-season variation in prices; thus, we omit γ0,s from the ARUM specification,
and note that only the differences in quota prices wacross the state space are identified, as
opposed to the absolute level of quota prices. As we discuss below, this has implications for
identifying the structural parameter θRev, but has no implications for prediction.
5.3.2. Estimation and in-sample performance
For each of 200 independent Monte Carlo draws, we estimate the parameters of the
RERUM and the alternative RUM models, and calculate parameter bias and the root-mean-
squared-error (RMSE) of predicted location-choice probabilities, relative to the true model.
Column 2 of Table 1provides the range of parameter values for the random parameter space
that we sample from (uniformly).
As expected, both the RERUM and QPRUM1 estimators are able to recover the struc-
tural parameters θdue to explicitly accounting for the evolving shadow-cost of quota (either
imputed or observed, respectively) in the estimation process (Figure 3). The QPRUM2
estimator, which accounts for only the seasonal average quota price, also provides a rela-
tively unbiased estimator θRev. In contrast, the SRUM specification underestimates θRev , as
predicted for situations in which the shadow cost of quota is strictly positive. The ARUM
specification does not improve the estimation performance of θRev over the SRUM because
15We also considered fleet-wide cumulative catch as a state variable, but the proportion of remaining quota
was selected for the ARUM model due to it’s superior predictive performance.
21
it is unable to identify the absolute level of the quota prices (γ0) due to the time-invariant
nature of prices p. Instead, γ0is subsumed into the estimate of θRev, resulting in a underes-
timation of θRev. Moreover, including an approximation of the shadow cost of quota creates
challenges for precision, as reflected in the wide distributions of ˆ
θRev for the ARUM specifica-
tion. All five models have relatively good estimation performance for θDist , which is expected
when the distance from port to areas with high expected catch is symmetric across species.16
Altogether, despite having trouble using variation in observed state variables to identify θRev,
the ARUM model offers an improvement over the SRUM model for in-sample predictions
according to the RMSE of choice probabilities. By contrast, the QPRUM2 estimator does
not provide much improvement over the SRUM estimator for in-sample predictions because,
despite incorporating quota price information into the estimation process, it does not account
for the within-season evolution of the quota shadow costs.
In Figure 4, we investigate whether there are any particular areas of the data-generating
and sampling parameter space in which the RERUM estimator performance is worse at
recovering estimates of θRev. The median bias of θRev for the RERUM estimator is unsur-
prisingly zero across the parameters space; however, heterogeneity in the spread between
the 10th and 90th percentiles indicates that there are some areas of the parameter space
in which the sampling distribution of the RERUM estimator is more diffuse. Most notably,
the RERUM estimator tends to perform better when there are a larger number of species S
and a larger level of harvest variance σ2. With more species, there is potential for greater
spatiotemporal variation in “net revenue”—i.e., (p˜wt)0E(yi,t)—that can be used to iden-
tify θRev, especially if quota prices vary asynchronously over time across species.17 A similar
argument can be made regarding σ2: with low σ2, quota prices tend to be relatively stable
over time, providing less spatiotemporal variation for identifying θRev. In general, Monte
16This symmetry is exhibited, on average, in our Monte Carlo sample since we allow for the spatial overlap
of species to be randomly determined when drawing from the data-generating parameter space.
17As an example, in the extreme case with S= 1, the relative fishing payoffs over space do not change over
time because the quota price affects all locations the same, regardless of how much the quota price changes
over time. With more species, the relative payoffs do change over time, so long as the quota prices for each
species do not vary synchronously over time.
22
Carlo draws that have small Sand/or small σ2tend to have a flatter log-likelihood function,
resulting in less precise estimates.
We also consider practical issues regarding estimation of the RERUM model. To investi-
gate the potential for convergence issues of the NFXP algorithm, we estimate the RERUM
parameter vector multiple times for each Monte Carlo draw starting from different initial
values.18 While the algorithm displays occasional convergence issues, the RERUM estimator
behaves reasonably well, with approximately 90% of the Monte Carlo draws appearing to
converge to a global maximum.19 Convergence issues generally occur under the same con-
ditions that produce a flat log-likelihood function—i.e., when the number of species (S) or
the variance of the stochastic harvesting component (σ2) are small. Measures of estimation
time demonstrate that while the computational burden of the RERUM estimator increases
with the number of observations per year (N×T) and the number of species (S), it does so
at a rate that is more-or-less linear in Sand slightly convex in N×T(Figure A.3).20 Alto-
gether, the computational costs of the RERUM estimator do not appear to be prohibitively
burdensome within the range of sample sizes and numbers of quotas/species encountered by
practitioners on a regular basis.
5.3.3. Out-of-sample Performance
For both forms of policy counterfactuals considered in Section 5.2, we simulate an entire
fishing season with stochastic harvest and state variables that are endogenously updated in
each time period. Fishers make location choices according to their policy-function specifica-
tion (i.e., SRUM, QPRUM, ARUM, or RERUM). For both the ARUM and RERUM models,
18Specifically, for each Monte Carlo draw, we estimate the RERUM model starting from nine different
initial guesses arranged in a grid centered on the true data-generating parameter values. The parameter
vector(s) associated with the largest log-likelihood value is the RERUM estimate.
19The proportion of estimates that converged to the same maximum log-likelihood value is presented in
Figure A.2
20In theory, the computational burden of the RERUM estimator (above that for a static RUM) is a function
of the number of rational-expectations equilibrium quota prices that need to be computed. Let time(T, N , J)
represent the time it takes to solve for a single quota price, which is increasing linearly in the number of
individuals (N), time periods (T), and locations (J) (see equation 5). Then the computation time devoted
to solving for quota prices is equal to time(T, N, J )×T×S×Y rs.
23
the quota-lease price is updated in each period using each model’s respective quota-price
rule. For example, the ARUM model inserts the observed state variables into the quadratic
quota-price approximation function, while the RERUM model updates the quota-lease price
using the observed state variables and solving for the rational-expectations equilibrium quota
prices in equation (6). In contrast, the SRUM and QPRUM models are static, and do not
update each period to reflect the evolving shadow cost of quota. The SRUM model uses no
quota prices while the QPRUM models use the observed quota prices from the estimation
sample, essentially considering them exogenous to the counterfactual policies under consid-
eration. For each counterfactual policy, we generate 200 independent draws from the dgp.
Process error is introduced through harvest and utility shocks (ξand ε), which are drawn
from their respective probability distributions. Sampling error is introduced by drawing
utility parameters from simulated sampling distributions, which are generated by estimating
the parameters of the RERUM and the alternative models using 500 independent draws
from the dgp under the baseline policy. More details concerning the process for generating
out-of-sample simulations is contained in Appendix E.
In general, the alternative RUM models perform well in predicting changes in expected
utility for small changes from the baseline policy, but get progressively worse as counter-
factual policies move farther away from the baseline (Figure 5).21 In both scenarios, the
alternative RUM models tend to overestimate the cost of reducing the bycatch TAC. The
SRUM and QPRUM models have no method of accounting for increased shadow prices from
TAC reductions; thus, fishers are predicted to fish business-as-usual until the season ends
from a binding TAC. As a result, predicted changes in expected utility under the SRUM
and QPRUM models are proportional to bycatch TAC reductions. The ARUM model does
account for changes in bycatch quota scarcity through the approximated quota-lease prices,
and in turn, fishers are predicted to fish in different locations with less expected bycatch.
As a result, early-season endings from hitting the bycatch TAC are avoided and predicted
changes in expected utility are relatively close to the truth, at least for small reductions in
21Given the similarity in the out-of-sample predictions for the QPRUM1 and QPRUM2 models, we only
present the results for QPRUM1.
24
the TAC.
The alternative RUM models tend to do better predicting changes in expected utility
from the hot-spot closures. The performance of the SRUM and QPRUM models tend to
be inferior to the ARUM model, although they are still capable of producing reasonable
predictions for a small number of closures. Predictions from the ARUM model are quite
good for the hot-spot closures, particularly for scenario 2; ARUM predictions are close to
the true model, on average, even for large changes from the baseline. However, sampling
error in the lease-price parameters leads to considerably more variation in the ARUM model’s
prediction error, demonstrating a potential drawback of using the reduced-form approach to
approximate the quota-lease prices.
The out-of-sample predictions we consider here produce two important insights. First,
despite being able to recover structural parameters reasonably well, static RUM models that
incorporate observed quota-lease prices in the estimation process do not produce good out-
of-sample predictions if quota-prices are not allowed to adjust to the market, ecological, or
regulatory conditions of the counterfactual policy. This is true even for policies such as the
bycatch hot-spot-closure policy for scenario 2, which does not induce large changes in quota
prices, on average (Figure 2). The reason lies in the stochastic realizations of production,
which are embodied in the observed quota prices but are not expected to be the same as
those observed in the estimation sample. Thus, quota prices that do not update to reflect
the prevailing state-of-the-world under counterfactual policies will not accurately predict
behavior.
Second, RUM models that incorporate a state-contingent, reduced-form approximation
of the quota-price, such as the ARUM, are capable of improving out-of-sample predictions
over static RUM models. However, this improvement is limited to only certain situations.
The reason largely lies in the quota-price responses to the policy change (Figure 2): as quota
prices move further away from those observed in the estimation sample, predictions from
the reduced-form models tend to move further away from the truth. For example, hot-spot
closures in scenario 2 have almost no effect on quota prices. Accordingly, the ARUM model
does very well at predicting out-of-sample in this case since the lease-price parameters of
the ARUM are calibrated to replicate the in-sample behavior under economically equivalent
25
scenarios. In contrast, TAC reductions in scenario 1 have the largest influence on quota
prices, and in turn, predictions from the ARUM model are only acceptable for small changes
in the TAC.
6. Conclusion
We develop a model of spatiotemporal fishing behavior that incorporates the dynamic and
general equilibrium elements of catch-share fisheries. Our approach extends the traditional
RUM framework for estimating fishing location choices by incorporating a within-season
market for quota exchanges, which determines equilibrium quota-lease prices (or, equiv-
alently, quota shadow costs) endogenously. Our proposed estimation strategy is able to
recover structural behavioral parameters under reasonable sample sizes and specifications of
the data generating process, even when quota-lease prices are unobserved. We demonstrate
the use of our model for predicting behavioral responses to fishery policies, such as spatial
closures and TAC reductions, within a catch-share fishery and illustrate the importance of
allowing quota-prices to be endogenous for conducting out-of-sample policy evaluations.
Our study provides several insights. First, the inclusion of quota-prices, either observed
or imputed, in the specification of RUM models is necessary to identify structural parameters.
However, identifying the structural parameters of the RUM model is not sufficient for making
accurate out-of-sample predictions of counterfactual policy changes. Rather, sufficiency lies
in determining what quota prices would be under the counterfactual policy change. Thus,
even if practitioners observe quota prices and use them to recover the structural behav-
ioral parameters, a model of endogenous quota prices is necessary for counterfactual policy
evaluations. In other words, quota prices themselves are not policy invariant.
Second, in the absence of a structural model for quota-lease prices, a reduced-form ap-
proximation of state-contingent quota-lease prices can perform well in evaluating out-of-
sample policy changes, provided there is adequate quota-price variation in the sample, rela-
tive to the range of price variation induced by the counterfactual policy. Changes in quota
prices reflect the realized magnitude of the effect of the policy on economic incentives, and
therefore function as sufficient statistics for whether a particular policy/economic/biological
regime is sufficiently “in sample” to be evaluated using a reduced-form model. The challenge
26
is knowing ahead of time whether a policy change of interest will result in quota-prices that
lie out-of-sample. As we demonstrate in Section 5, even seemingly “marginal” policy changes
can result in large quota-price changes. Without knowing how quota prices will respond to a
policy change, it is hard to determine ex ante whether a reduced-form approach will produce
adequate policy evaluations.
In short, the layering of spatial closures and a host other policies on top of RBM systems
creates unavoidable feedbacks to seasonal quota markets. These prices, or internal shadow
prices for systems that disallow leasing, are the endogenous mechanisms by which RBM alters
the responses of fishers to these scenarios. Our model has shown the crucial importance of
drawing upon structural models of the quota-price determination process for prediction—
whether or not these models are used to estimate fishers’ underlying behavioral parameters.
Failure to do so will fundamentally limit the ability of economists to answer crucial “what
if” questions posed by fishery managers.
27
References
J. K. Abbott and J. E. Wilen. Dissecting the Tragedy: A Spatial Model of Behavior in the
Commons. Journal of Environmental Economics and Management, 62(3):386–401, 2011.
URL https://doi.org/10.1016/j.jeem.2011.07.001.
J. K. Abbott, A. C. Haynie, and M. N. Reimer. Hidden flexibility: Institutions, incentives,
and the margins of selectivity in fishing. Land Economics, 91(1):169–195, 2015. ISSN
00237639. doi: 10.3368/le.91.1.169. URL https://doi.org/10.3368/le.91.1.169.
K. Abe and C. M. Anderson. A Dynamic Model of Endogenous Fishing Duration. Working
Paper, pages 1–39, 2020.
V. Aguirregabiria and P. Mira. Dynamic discrete choice structural models: A survey. Journal
of Econometrics, 156(1):38–67, 2010. URL https://doi.org/10.1016/j.jeconom.2009.
09.007.
M. D. Berman. Modeling Spatial Choice in Ocean Fisheries. Marine Resource Economics,
21(4):375, 2006. URL https://doi.org/10.1086/mre.21.4.42629522.
A. M. Birkenbach, D. J. Kaczan, and M. D. Smith. Catch Shares Slow the Race to Fish.
Nature, 544:223–226, 2017. URL https://doi.org/10.1038/nature21728.
A. M. Birkenbach, A. L. Cojocaru, F. Asche, A. G. Guttormsen, and M. D. Smith. Seasonal
Harvest Patterns in Multispecies Fisheries. Environmental and Resource Economics, 75:
631–655, 1 2020. URL https://doi.org/10.1007/s10640-020-00402-7.
J. R. Boyce. Individual Transferable Quotas and Production Externalities In a Fishery. Natu-
ral Resource Modeling, 6:385–408, 1992. URL https://doi.org/10.1111/j.1939-7445.
1992.tb00286.x.
C. Costello and R. T. Deacon. The Efficiency Gains from Fully Delineating Rights in an
ITQ Fishery. Marine Resource Economics, 22(4):347–361, 1 2007. URL https://doi.
org/10.1086/mre.22.4.42629566.
28
C. Costello and D. Ovando. Status, Institutions, and Prospects for Global Capture Fisheries.
Annual Review of Environment and Resources, 44(1):177–200, 10 2019. URL https:
//doi.org/10.1146/annurev-environ-101718-033310.
R. E. Curtis and R. L. Hicks. The Cost of Sea Turtle Preservation: The Case of Hawaii’s
Pelagic Longliners. American Journal of Agricultural Economics, 82(5):1191–1197, 2000.
URL https://doi.org/10.1111/0002-9092.00119.
R. E. Curtis and K. E. McConnell. Incorporating Information And Expectations In Fish-
erman’s Spatial Decisions. Marine Resource Economics, 19(1):131–143, 2004. URL
https://doi.org/10.1086/mre.19.1.42629422.
R. T. Deacon. Fishery Management by Harvester Cooperatives. Review of Environmental
Economics and Policy, 6(2):258–277, 7 2012. URL https://doi.org/10.1093/reep/
res008.
J. Eales and J. E. Wilen. An Examination of Fishing Location Choice in the Pink Shrimp
Fishery. Marine Resource Economics, 2(4):331–351, 1986. URL https://doi.org/10.
1086/mre.2.4.42628909.
H. Fell. Comparing policies to confront permit over-allocation. Journal of Environmental
Economics and Management, 80:53–68, 11 2016. URL https://doi.org/10.1016/j.
jeem.2016.01.001.
E. P. Fenichel, J. K. Abbott, and B. Huang. Modelling angler behaviour as a part of the
management system: synthesizing a multi-disciplinary literature. Fish and Fisheries, 14
(2):137–157, 6 2013. URL https://doi.org/10.1111/j.1467-2979.2012.00456.x.
R. Q. Grafton, R. Arnason, T. Bjørndal, D. Campbell, H. F. Campbell, C. W. Clark, R. Con-
nor, D. P. Dupont, R. Hannesson, R. Hilborn, J. E. Kirkley, T. Kompas, D. E. Lane, G. R.
Munro, S. Pascoe, D. Squires, S. I. Steinshamn, B. R. Turris, and Q. Weninger. Incentive-
based approaches to sustainable fisheries. Canadian Journal of Fisheries and Aquatic
Sciences, 63(3):699–710, 3 2006. URL https://doi.org/10.1139/f05-247.
29
A. C. Haynie and D. F. Layton. An Expected Profit Model for Monetizing Fishing Location
Choices. Journal of Environmental Economics and Management, 59(2):165–176, 2010.
URL https://doi.org/10.1016/j.jeem.2009.11.001.
A. C. Haynie, R. L. Hicks, and K. E. Schnier. Common Property, Information, and Cooper-
ation: Commercial Fishing in the Bering Sea. Ecological Economics, 69(2):406–413, 2009.
URL https://doi.org/10.1016/j.ecolecon.2009.08.027.
J. J. Heckman. Building Bridges Between Structural and Program Evaluation Approaches
to Evaluating Policy. Journal of Economic Literature, 48(2):356–398, 2010. URL http:
//doi.org/10.1257/jel.48.2.356.
J. J. Heckman and E. J. Vytlacil. Econometric Evaluation of Social Programs, Part I:
Causal Models, Structural Models and Econometric Policy Evaluation. In J. Heckman and
E. Leamer, editors, Handbook of Econometrics, volume 6B, chapter 70, pages 4779–4874.
Elsevier, New York, 2007. URL https://doi.org/10.1016/S1573-4412(07)06070-9.
R. L. Hicks and K. E. Schnier. Dynamic Random Utility Modeling: A Monte Carlo Analysis.
American Journal of Agricultural Economics, 88(4):816, 2006. URL https://doi.org/
10.1111/j.1467-8276.2006.00900.x.
R. L. Hicks and K. E. Schnier. Eco-Labeling and Dolphin Avoidance: a Dynamic Model of
Tuna Fishing in the Eastern Tropical Pacific. Journal of Environmental Economics and
Management, 56(2):103–116, 2008. URL https://doi.org/10.1016/j.jeem.2008.01.
001.
R. L. Hicks and K. E. Schnier. Spatial Regulations and Endogenous Consideration Sets in
Fisheries. Resource and Energy Economics, 32:117–134, 2010. URL https://doi.org/
10.1016/j.reseneeco.2009.11.008.
R. Hilborn, J. M. L. Orensanz, and A. M. Parma. Institutions, incentives and the future of
fisheries. Philosophical transactions of the Royal Society of London. Series B, Biological
sciences, 360(1453):47–57, 1 2005. URL http://doi.org/10.1098/rstb.2004.1569.
30
D. S. Holland. Optimal Intra-annual Exploitation of the Maine Lobster Fishery. Land
Economics, 87(4):699–711, 11 2011. URL http://doi.org/10.3368/le.87.4.699.
D. S. Holland. Collective RightsBased Fishery Management: A Path to Ecosystem-Based
Fishery Management. Annual Review of Resource Economics, 10(1):469–485, 10 2018.
URL https://doi.org/10.1146/annurev-resource-100517-023110.
D. S. Holland and J. G. Sutinen. Location Choice in New England Trawl Fisheries: Old
Habits Die Hard. Land Economics, 76(1):133–149, 2000. URL https://doi.org/10.
2307/3147262.
L. Huang and M. D. Smith. The dynamic efficiency costs of common-pool resource ex-
ploitation. The American Economic Review, 104(12):4071–4103, 12 2014. URL http:
//doi.org/10.1257/aer.104.12.4071.
B. Hutniczak. Modeling heterogeneous fleet in an ecosystem based management context. Eco-
logical Economics, 120:203–214, 12 2015. ISSN 0921-8009. doi: 10.1016/J.ECOLECON.
2015.10.023. URL https://doi.org/10.1016/j.ecolecon.2015.10.023.
M. P. Keane. Structural vs. Atheoretic Approaches to Econometrics. Journal of Economet-
rics, 156(1):3–20, 2010. URL https://doi.org/10.1016/j.jeconom.2009.09.003.
C. Kling and J. Rubin. Bankable permits for the control of environmental pollution.
Journal of Public Economics, 64(1):101–115, 1997. URL https://doi.org/10.1016/
S0047-2727(96)01600-3.
S. Kollenberg and L. Taschini. Emissions trading systems with cap adjustments. Journal of
Environmental Economics and Management, 80:20–36, 11 2016. URL https://doi.org/
10.1016/j.jeem.2016.09.003.
M.-Y. Lee, S. Steinback, and K. Wallmo. Applying a Bioeconomic Model to Recreational
Fisheries Management: Groundfish in the Northeast United States. Marine Resource
Economics, 32(2):191–216, 4 2017. URL https://doi.org/10.1086/690676.
31
R. E. Lucas. Econometric Policy Evaluation: A Critique. In K. Brunner and A. H. Meltzer,
editors, The Phillips Curve and Labor Markets, Carnegie-Rochester Conference Series on
Public Policy, pages 19–46. North Holland, Amsterdam, 1976. URL https://doi.org/
10.1016/S0167-2231(76)80003-6.
S. M. Maxwell, E. L. Hazen, R. L. Lewison, D. C. Dunn, H. Bailey, S. J. Bograd, D. K.
Briscoe, S. Fossette, A. J. Hobday, M. Bennett, S. Benson, M. R. Caldwell, D. P. Costa,
H. Dewar, T. Eguchi, L. Hazen, S. Kohin, T. Sippel, and L. B. Crowder. Dynamic ocean
management: Defining and conceptualizing real-time management of the ocean. Marine
Policy, 58:42–50, 8 2015. URL https://doi.org/10.1016/j.marpol.2015.03.014.
S. J. Miller and R. T. Deacon. Protecting Marine Ecosystems: Regulation Versus Market
Incentives. Marine Resource Economics, 32(1):83–107, 1 2017. URL https://doi.org/
10.1086/689214.
M. Miranda and P. L. Fackler. Applied Computational Economics and Finance. The MIT
Press, Cambridge, MA, 2002. ISBN 9780262633093.
B. Provencher and R. C. Bishop. An Estimable Dynamic Model of Recreation Behavior
with an Application to Great Lakes Angling. Journal of Environmental Economics and
Management, 33(2):107–127, 1997. URL http://doi.org/10.1006/jeem.1996.0978.
M. N. Reimer, J. K. Abbott, and J. E. Wilen. Unraveling the multiple margins of rent
generation from individual transferable quotas. Land Economics, 90(3):538–559, 8 2014.
URL https://doi.org/10.3368/le.90.3.538.
M. N. Reimer, J. K. Abbott, and A. C. Haynie. Empirical Models of Fisheries Produc-
tion: Conflating Technology with Incentives? Marine Resource Economics, 32(2):169–190,
2017a. URL https://doi.org/10.1086/690677.
M. N. Reimer, J. K. Abbott, and J. E. Wilen. Fisheries Production: Management Institu-
tions, Spatial Choice, and the Quest for Policy Invariance. Marine Resource Economics,
32(2):143–168, 2017b. URL https://doi.org/10.1086/690678.
32
J. D. Rubin. A model of intertemporal emission trading, banking, and borrowing. Journal
of Environmental Economics and Management, 31(3):269–286, 1996. URL https://doi.
org/10.1006/jeem.1996.0044.
J. Rust. Optimal Replacement of GMC Bus Engines: An Empirical Model of Harold Zurcher.
Econometrica, 55(5):999, 1987. URL http://doi.org/10.2307/1911259.
A. M. Scheld and J. Walden. An Analysis of Fishing Selectivity for Northeast US Multispecies
Bottom Trawlers. Marine Resource Economics, 33(4):331–350, 10 2018. URL https:
//doi.org/10.1086/699712.
M. D. Smith. State Dependence and Heterogeneity in Fishing Location Choice. Journal
of Environmental Economics and Management, 50(2):319–340, 2005. URL https://doi.
org/10.1016/j.jeem.2005.04.001.
M. D. Smith and B. Provencher. Spatial Search in Commercial Fishing: A Discrete Choice
Dynamic Programming Approach. In American Agricultural Economics Association,
American Agricultural Economics Association, 2003.
M. D. Smith and J. E. Wilen. Economic impacts of marine reserves: the importance of
spatial behavior. Journal of Environmental Economics and Management, 46(2):183–206,
9 2003. ISSN 0095-0696. doi: 10.1016/S0095-0696(03)00024-X. URL https://www.
sciencedirect.com/science/article/abs/pii/S009506960300024X.
J. E. Wilen, J. Cancino, and H. Uchida. The Economics of Territorial Use Rights Fisheries,
or TURFs. Review of Environmental Economics and Policy, 6(2):237–257, 7 2012. URL
https://doi.org/10.1093/reep/res012.
K. I. Wolpin. Ex ante policy evaluation, structural estimation, and model selection. American
Economic Review, 97(2):48–52, 2007. URL https://doi.org/10.1257/aer.97.2.48.
B. Worm, R. Hilborn, J. K. Baum, T. A. Branch, J. S. Collie, C. Costello, M. J. Fogarty,
E. A. Fulton, J. A. Hutchings, S. Jennings, O. P. Jensen, H. K. Lotze, P. M. Mace,
T. R. McClanahan, C. Minto, S. R. Palumbi, A. M. Parma, D. Ricard, A. A. Rosenberg,
33
R. Watson, and D. Zeller. Rebuilding global fisheries. Science (New York, N.Y.), 325
(5940):578–85, 7 2009. URL http://doi.org/10.1126/science.1173146.
34
Tables
Parameter Values
Parameter KnownaRandombDescription
θRev 1 [0.5,1.5] True preference parameter for expected revenue
θDist -0.4 [-0.5,-0.1] True preference parameter for distance
J100 [36,144] Number of locations
N20 [10,40] Number of individual fishers
T50 [25,60] Number of time periods in a year
S2 [1,4] Number of species
Y rs 1 [1,5] Number of years
p(1000,0) [500,1500] Ex-vessel price vector
q103[0.15,5.8]×103Catchability coefficient
σ23 [0.1,5] Variance of random harvest component (ξ)
T AC (13,7)×103[0.8,1.5]×103Total allowable catch (proportion of abundance)
aDenotes the parameter values (species-specific, where applicable) for the data generating process with
known (and fixed) parameter values.
bDenotes the range of parameter values for the data generating process with a random parameter space.
Parameter values are drawn randomly from a uniform distribution.
Table 1: Parameter values and descriptions for the data generating process.
35
Figures
Figure 1: Spatial distribution of expected catch for species 1 (left) and 2 (center) with port located in the
upper left-hand corner in cell [1,1]; expected global production set (right) with the total allowable catch
(black dot and dashed lines).
36
Figure 2: Numerical simulation outcomes—bycatch hot-spot closures (left column) and bycatch TAC re-
ductions (right column) for two biological scenarios (blue and red). The median (solid line) and 25th-75th
percentile range (shaded area) are presented using 200 draws from the data-generating process.
37
SRUM
QPRUM1
QPRUM2
ARUM
RERUM
-160
-140
-120
-100
-80
-60
-40
-20
0
SRUM
QPRUM1
QPRUM2
ARUM
RERUM
-80
-70
-60
-50
-40
-30
-20
-10
0
SRUM
QPRUM1
QPRUM2
ARUM
RERUM
1
2
3
4
5
6
7
8
9
Figure 3: Parameter estimation and in-sample predictive performance—percent bias in utility parameter
estimates (left and center columns); root-mean-square error (RMSE) between estimated and population
choice probabilities (right column). Markers denote median values and error bars denote the 25th and 75th
percentiles. Distributions generated from 200 draws from the data-generating process with random draws
from the data-generating and sampling parameter space.
Figure 4: RERUM parameter bias for θRev across four parameter spaces: number of observations per year
(far left), number of years (mid left), number of species (mid right), and the variance of the stochastic
harvest component (far right). The lines denote quantile regression predictions for the 10th, 50th, and 90th
quantiles. Distributions generated from 200 draws from the data-generating process with random draws
from the data-generating and sampling parameter space.
38
Figure 5: Out-of-sample prediction errors: percentage change in expected utility. Top: bycatch hot-spot clo-
sures. Bottom: bycatch TAC reductions. Markers denote median values and error bars denote the 25th and
75th percentiles. QP-SRUM model uses period-specific quota-prices from estimation sample. Distributions
generated from 200 draws from the data generating process and sampling distributions of utility parameter
estimates.
39
Appendix A. Supplementary Figures
Figure A.1: Quota prices in period t= 1 as a function of ex-vessel prices (p1and p2, row 1), total allowable
catches (T AC1and T AC2, row 2), and preference parameters (θRev and θDist, row 3). Dashed lines indicate
the data-generating parameter values.
40
Figure A.2: Global convergence of the RERUM estimator—the proportion of maximum-likelihood searches,
for each draw from the data generating process, that converged to the same maximum. Distribution generated
by 200 independent draws from the data-generating process and 9 initial values for each draw.
41
Figure A.3: RERUM estimation time across four parameter spaces: number of observations per year (far
left), number of years (mid left), number of species (mid right), and the variance of the stochastic harvest
component (far right). The lines denote quantile regression predictions for the 10th, 50th, and 90th quantiles.
Distributions generated from 200 draws from the data-generating process with random draws from the data-
generating and sampling parameter space.
42
Appendix B. Deriving the Last-Period Utility Function
The indirect utility function in period T+ 1 in equation (1) can be derived as follows.
Each agent is endowed with an S×1 vector of quota ωi, which can be used to fund harvests
over the season or be leased in the competitive quota market. The agent buys a vector of
quota qiafter observing their cumulative harvest xi,T +1. The agent’s objective in period
T+ 1 is to maximize utility with respect to consumption c, subject to a budget constraint:
max
c,q u(0, c) subject to cw0(ωiq) + mi;qxi,T +1 ,
where the consumption good is the numeraire good whose price is normalized to one, w
denotes a vector of quota lease prices, u(·) is equivalent to the utility function in equation
(1) evaluated at a= 0 (i.e., port), and midenotes agent i’s exogenous component of income.
The constraints act to restrict the agent from consuming more than their net income, while
also ensuring that the owner has enough quota to cover their annual harvests. Assuming that
u0(c)>0 for c > 0 and that miis large enough to allow for positive consumption, then the
budget constraint will be binding and the agent will choose quota such that q
i(w) = xi,T +1.
Thus, the agent’s indirect utility function can be expressed as
V(zi,T +1) = u(0, w0(ωixi,T +1)) ,
which gives us the indirect utility function for period T+ 1 in equation (1). For supplemental
derivations, it is useful to simplify this expression further as
V(zi,T +1) = u(0) + v(w0(ωixi,T +1 ))
=v(w0(ωixi,T +1)) ,(B.1)
where the first equality follows from the assumption that revenue is additively separable from
the rest of utility and the second equality follows from using location a= 0 as the baseline
choice alternative.
Appendix C. Derivation of the Policy Function
Consider the Bellman equation in (3) given the state of the world zi,t = (xi,t, εi,t), where
we substitute in the assumed utility function (1) and, since catch is not known ex ante, we
43
replace it with the expected catch:22
V(zi,t) = max
aAua, p0Eyi,t a+εi,t(a) + EzV(zi,t+1 )a, zi,t.
To see that the policy function takes the form presented in equation (4), note that the next-
period expected value function in the last fishing period Tcan be written in the following
way:
EzV(zi,T +1)ai,T , zi,T =vw0ωiExxi,T +1 ai,T , xi,T 
=v(w0(ωixi,T )) vw0Eyyi,T ai,T .
The first equality follows from substituting the indirect utility function in period T+ 1 (equa-
tion B.1) into the expectation of the last-period value function, while the second equality
follows from the transition equation, xi,T +1 =xi,T +yi,T , and the linear nature of v(·). Notice
that vw0Eyyi,T ai,T —i.e., the marginal effect of location choice on the value of remain-
ing quota used in the last period—is the only term that affects the optimal location choice in
period T. In contrast, the term v(w0(ωixi,T ))—i.e., the value of remaining quota—is sunk
and does not influence the contemporaneous location choice. Substituting the derivation of
the next-period expected value function into the Bellman equation for the last fishing period
T, we have:
V(zi,T ) = max
ai,T Auai,T , p0Eyyi,T ai,T +εi,T (ai,T )
vw0Eyyi,T ai,T +v(w0(ωixi,T ))
= max
ai,T Au(ai,T ) + vp0Eyyi,T ai,T +εi,T (ai,T )
vw0Eyyi,T ai,T +v(w0(ωixi,T ))
= max
ai,T Au(ai,T ) + v(pw)0Eyyi,T ai,T 
+εi,T (ai,T )}+v(w0(ωixi,T ))
= max
ai,T Auai,T ,(pw)0Eyyi,T ai,T +εi,T (ai,T )
+v(w0(ωixi,T )) ,
(C.1)
22This substitution is justified on the basis that revenues are assumed to be enter linearly into utility (i.e.,
risk neutrality).
44
where we’ve used the fact that utility is linear in revenue and revenues are additively separa-
ble from non-revenue aspects in utility. The optimal location choice in period Tis therefore
defined as:
α(εi,T |w) = argmax
ai,T Auai,T ,(pw)0Eyyi,T ai,T +εi,T (ai,T ).
Moving to the penultimate fishing period T1, we can write the next-period expected
value function in the Bellman equation as:
Ez(V(zi,T ai,T 1, zi,T 1=Ex,ε max
ai,T Auai,T ,(pw)0Eyyi,T ai,T 
+εi,T (ai,T )}+v(w0(ωixi,T )) ai,T 1, xi,T 1, εi,T 1.
Let Λi,T = max
ai,T Auai,T ,(pw)0Eyyi,T ai,T +εi,T (ai,T )for notational simplicity. Be-
cause wis considered exogenous by fishers and yis conditionally independent of x, Λi,T is not
influenced by the location choice ai,T 1. Thus, we can write Ex,ε i,T |ai,T 1, xi,T 1, εi,T 1) =
Eεi,T ) and simplify the next-period expected value function in the Bellman equation as:
Ez(Vzi,T ai,T 1, zi,T 1
=Ex,ε Λi,T +v(w0(ωixi,T )) ai,T 1, xi,T 1, εi,T 1
=Ex,ε Λi,T +v(w0(ωixi,T 1yi,T 1)) ai,T 1, xi,T 1, εi,T 1
=vw0Eyyi,T 1ai,T 1+v(w0(ωixi,T 1)) + Eεi,T ).
As in period T, the only component of next-period’s value function that varies with ais its
effect on the value of remaining quota in the final period: vw0Eyyi,T 1ai,T 1. Thus,
the optimal decision rule in period T1 is fully characterized by
α(εi,T 1|w)
= argmax
ai,T 1Auai,T 1,(pw)0Eyyi,T 1ai,T 1+εi,T 1(ai,T 1).
45
Repeated substitution into earlier periods generalizes this result to any decision period t,
giving us the optimal decision rule in equation (4). Ultimately, it is the conditional indepen-
dence assumption for y, the assumption that utility is linear in revenue (and therefore also
additively separable in non-revenue components in utility), and the assumption that fishers
consider their effect on the quota price wto be negligible that allow us to reduce a fishers
optimal decision rule to something tractable and easily solvable (conditional on w).
Appendix D. The Nested Fixed-Point (NFXP) algorithm
Appendix D.1. Inner algorithm: the fixed-point problem
A rational expectations equilibrium for the inner algorithm is a vector-valued function
of quota prices w(xt|θ) that solves the market clearing conditions in (6) subject to fishers
making their optimal fishery choices according to equation (4) for a given vector of structural
parameters θ. Our goal is to find ˜w(xt|θ) such that:23
F( ˜w(xt|θ)) = max {E(es|˜w(xt|θ), xt),˜w(xt|θ)}= 0 s∈ {1, ..., S },(D.1)
where esis the end-of-season excess demand function for species squota. Since we are
solving for Squota lease prices that satisfy Sequilibrium equations, the system of equations
in (D.1) is just identified.
Appendix D.1.1. Algorithm
Consider an arbitrary initial vector of quota prices w0. Then the rational equilibrium
quota prices ˜w(xt|θ), conditional on a given vector of structural parameters θ, can be
determined by the following algorithm:
1. For each time period tin the data, use the observed state variable xtto calculate the
cumulative fleet-wide catch for each species, Xs,t.
2. Calculate the choice probabilities f(ai,t |xt, w0).
23This is actually a complementarity problem, as opposed to a fixed-point problem. See page 44 in Miranda
and Fackler (2002) for more details.
46
3. Calculate the expected end-of-season excess demand E(es|w0, xt) for each species
s∈ {1, ..., S}using Xs,t from step 1 and f(ai,t |xt, w0) from step 2.
4. Given the expected excess-demand functions from step 3, compute the system of equa-
tions F(w0) in (D.1).
5. In general, F(w0) will not equal 0, as required by the equilibrium conditions in (D.1).
Generate a new value of w, say w1, using a Newton step (or some other method).
6. Repeat steps 2 to 5 until F(wk) = 0.
7. Repeat steps 2 to 6 for all time periods tin the data.
8. Use the resulting equilibrium quota-price vector ˜w(xt|θ) to calculate the rational
expectations choice probabilities (equation 9) and pass them to the outer algorithm.
Appendix D.2. Outer algorithm: maximum likelihood estimation
The goal of the outer algorithm is to find a value for the vector of parameters ˆ
θthat max-
imizes the log-likelihood function Pili(θ) while allowing the rational-expectations quota
price ˜w(xt|θ) to be endogenous to the structural parameter vector θ. Consider an arbitrary
value of θ, say ˆ
θ0. Then NFXP maximum likelihood parameter ˆ
θis determined as follows:
1. Pass ˆ
θ0to the inner algorithm, which will return the choice probabilities nfai,t |xt,ˆ
θ0oi,t .
2. Use the choice probabilites in step 1 to evaluate the log-likelihood l(ˆ
θ0) = Pili(ˆ
θ0)
and it’s gradient, where li(·) is given in equation (8).24
3. Use the gradient from step 2 to obtain a new structural parameter vector, say ˆ
θ1.
4. Repeat steps 1 through 3 until either ˆ
θkor l(ˆ
θk) converges based on a pre-specified
convergence tolerance.
Appendix E. Out-of-Sample Policy Simulations
The out-of-sample policy simulations presented in Section 5.3 are generated in the fol-
lowing way. We first generate sampling distributions for the structural parameter estimates
24While the gradient of the log-likelihood function, conditional on w, has a closed-form expression under
the DP conditional logit assumptions, the gradient of w(xt|θ) does not; thus, the gradient of the log-likelihood
function must be computed using numerical methods. This means that each time θis ‘perturbed’ to obtain
the numerical gradient, a new solution for the rational-expectations quota prices is required.
47
ˆ
θand ˆγ(where applicable) under the baseline policy scenarios using the data-generating
parameter values reported in Column 1 of Table 1. The sampling distributions are created
using 500 independent samples from the dgp, where draws differ due to harvest and util-
ity shocks (ξand ε). To simulate outcomes under the counterfactual policies, we use the
following procedure:
1. For each counterfactual policy (including the baseline) and RUM model (including
the RERUM model): draw parameter values from their respective simulated sampling
distribution, draw harvest and utility shocks from the dgp, and simulate an entire
fishing season.
2. Compare a model’s simulated outcome against its baseline counterpart to generate a
“relative impact”. For example, for the SRUM model under the 5% TAC reduction
policy, compare a fisher’s expected utility u(α(zi,t), p0E(yi,t |α(zi,t)) from draw 1 to the
expected utility predicted by the SRUM model for draw 1 under the baseline policy.
3. Compare a model’s relative impact against the relative impact from the true model to
come up with the “impact prediction error.”
4. Repeat Steps 1-3 200 times.
Note that for a given draw, the set of harvest and utility shocks are the same for each of the
counterfactual policies and RUM models, so the only differences across policies and models
are the policy and model parameters.
48
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