LIMITED-ENTRY LICENSING: INSIGHTS
FROM A DURATION MODEL
MARTIN D. SMITH
Key words: duration, entry-exit, fleet heterogeneity, limited-entry fishery.
Although many fisheries around the world
have long required explicit licensing for fishery
participants, the use of limited-entry licensing
to control fishing effort has become a common
practice in the last two decades. In contrast
to individual transferable quotas (ITQs), limited entry is only a step toward rights-based
management. Limited entry neither directly
controls fishing effort nor controls the actual
amount of harvest for a fishing fleet. Instead,
limited entry only indirectly affects fleet capacity (National Research Council). In essence,
limited entry is a blunt policy instrument relative to ITQs, and its bluntness ultimately depends on how effectively it can control fishing
effort, albeit indirectly. As a consequence,
whether or not an ITQ system could achieve
optimal management for a particular fishery,
there generally will still be a divergence between the performance of limited entry and the
performance of the more comprehensive ITQ
approach. The magnitude of this divergence
will hinge on the input substitution prospects
of limited-entry licensees, the changing composition of the fishing fleet, and the rate of
attrition of license holders. For mostly political reasons, the movement toward ITQ and,
more generally, individual fishing quota (IFQ)
systems has slowed considerably, leaving many
Martin D. Smith is assistant professor of environmental economics,
Nicholas School of the Environment and Earth Sciences, Duke
University.
The author thanks Jim Wilen, two anonymous referees, and participants at the 2002 conference of the International Institute for
Fisheries Economics and Trade in Wellington, New Zealand, for
helpful comments and suggestions.
fisheries locked into limited entry for at least
the next several years (Smith and Wilen 2002).
Thus, whether or not more comprehensive
rights-based management emerges in the future, it is still important to improve our understanding of limited-entry fisheries in the near
term.
Economic research on limited-entry fishing points to some unanswered questions
about how best to apply this policy tool.
This literature assesses limited-entry programs (Wilen 1988; Karpoff; Dupont 1990,
1991; Townsend; Flaaten, Heen, and Salvanes),
simulates limited-entry fisheries (Yew and
Heaps), and develops insights for ITQ
management based on limited-entry systems (Copes; McCay, Gatewood, and Creed;
Weninger and Just). Most of the assessment
literature has focused on either input substitution or on whether limited-entry programs
generate rents. Townsend reviews the performance of thirty limited-entry programs and
finds that some succeed in generating rents,
though sometimes from price increases rather
than effort reductions. In spite of some existing successes, Dupont (1990) argues that regulators need to look beyond evaluating input
substitution prospects to focus on fleet composition and the number of participants as
well. However, no empirical work exists on
these topics. Using data from the California
red sea urchin fishery, which has been managed
with limited entry for the last decade, this article analyzes both of these issues empirically
with an eye toward improving limited-entry
systems.
Amer. J. Agr. Econ. 86(3) (August 2004): 605–618
Copyright 2004 American Agricultural Economics Association
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Limited entry is used to manage many fisheries. Effectiveness depends on a program’s ability to
control aggregate fishing power, which fleet size and composition both affect. This article analyzes fleet
composition and attrition in a limited-entry fishery, the California red sea urchin fishery. It explores
the dynamics of heterogeneity in catch and revenue and applies duration analysis to study individual
fisherman attrition using both individual-level and time-varying covariates. The results show that the
fleet is becoming more homogenous but also more potent and spatially mobile. Regulations such as
size limits and season restrictions tend to increase attrition.
606
August 2004
the extent of it) can be determined by the data
without doing what is typically done in discrete
choice models, namely including a function of
lagged dependent variables that could cause
inconsistent parameter estimates.
The first section of this article describes
the California red sea urchin fishery and discusses why it provides an ideal empirical setting to study the dynamics of fleet composition and attrition under limited entry. Using Gini coefficients and Lorenz curves, the
following section explores heterogeneity in
catch and revenue and how this heterogeneity evolves dynamically. Then duration models of individual behavior are developed and
estimated. These models explain the length
of time that an individual participates in the
fishery conditional on individual characteristics that are time invariant and conditions
that vary over time but that are exogenous
to the individuals. The application is the first
to apply a duration model to commercial
fisheries data. Finally, the article discusses
how fishery managers can use this information to make limited-entry licensing as effective as possible when they are unable to
implement more comprehensive rights-based
management.
Empirical Setting: The California
Sea Urchin Fishery
The California red sea urchin fishery provides an excellent empirical setting in which
to study limited entry, attrition, and individual fisher heterogeneity because the industry
structure permits many simplifying assumptions. First, urchin divers are owner-operators
so that contractual arrangements with boat
owners and crew shares are not an issue. Second, permits are tied to individuals rather
than to boats. Thus, performance changes for
a given permit cannot be attributed to a skipper change. Third, harvest technologies and
vessel characteristics in this fishery are virtually uniform, whereas typically differences
in gear and vessel characteristics would confound an analysis of individual heterogeneity
in a fishery. Finally, extensive individual-level
data exist to track particular harvesters across
time.
Individual divers harvest sea urchins for
their roe, which is a high-value sushi item
in Japanese cuisine called uni. In California,
sea urchin is a relatively new fishery in
which owner-operators take single-day trips on
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The literature on entry and exit in commercial fisheries mainly analyzes open access settings. In the first empirical work, Wilen (1976)
focuses on the aggregate fleet size, assumes
homogeneous fishing vessels, and models the
economic dynamics with a single speed-ofadjustment parameter. He empirically estimates a Vernon Smith (1968, 1969) open access
model with historical data on the north Pacific
fur seal fishery in which all vessels are treated
the same. Bjorndal and Conrad follow a similar approach for the North Sea herring fishery. In both cases, the aggregate fishing power
of a fleet for a given number of vessels is invariant to the composition of the fishing fleet.
In contrast, empirical studies of disaggregated
entry-exit behavior model discrete choices of
fishing alternatives that are conditional on vessel characteristics and performance. Hence, aggregate fishing power results from integrating
or adding up over heterogeneous vessel types.
Bockstael and Opaluch analyze switching behavior among different target fisheries, though
implicitly a switch from one fishery to another
is both an exit and an entry event. Ward and
Sutinen explicitly address vessel entry and exit
behavior at the individual level in the Gulf
of Mexico shrimp fishery. Like Bockstael and
Opaluch, Ward and Sutinen use repeated discrete choices. With a similar model structure,
Ikiara and Odink use survey data to study exit
in Kenya’s Lake Victoria fishery and find that
fisherman characteristics are determinants of
exit inertia.
The current article uses duration analysis
rather than discrete choice to model disaggregated exit behavior in a limited-entry fishery.
For policy purposes, duration modeling is a
natural empirical strategy because it directly
addresses the question of how long a vessel
(or participant) of a given type will remain in
the fishery. This permits an analyst to forecast
the overall size and fishing power of a fleet
at future dates under a limited-entry program
by integrating over individual conditional survival functions. There are also two econometric advantages of a duration approach over the
standard discrete choice approach. First, a duration model allows for a continuous length of
participation. In the discrete choice approach
for which the time step is seasonal, a vessel
that exits after 1.1 seasons would be treated
the same as a vessel that exits after 1.9 seasons.
Second, a resistance to exit (or an acceleration
of exit) can be incorporated with a parametric
assumption about the hazard function in a duration model. Whether there is exit inertia (and
Amer. J. Agr. Econ.
Smith
607
Table 1.
Number of Active Divers
Year
Permit Holders
(Total)
Permit Holders
(Minimum of 10
Total Dives)
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
186
398
621
698
718
720
674
591
553
532
168
351
537
587
607
607
585
550
519
498
ports the number of active divers in the fishery for each year.1 The second column (total)
shows substantial entry during a boom phase
in the late 1980s followed by considerable
attrition after 1993. This trend follows the
rapid rise of the urchin fishery to become one
of California’s largest fisheries (measured in
dockside revenues) by 1992. The peak diver
count occurs in 1993, the first year in which
the limited-entry program actually binds. The
third column (minimum of ten total dives) concentrates on a subset of total divers. It shows
that many permit holders had very little activity in the fishery and were likely trying out
urchin diving. This may reflect several phenomena, including a low cost of entry, the fact
that commercial urchin diving is relatively new
in the state, and the potential for hobbyists to
cross over into the commercial sector before
requirements for permit renewal existed. Nevertheless, the same pattern of a boom phase
followed by attrition persists.
Performance Heterogeneity
To understand a fishery’s aggregate catching
power requires characterizing the heterogeneity of a fleet. As the number of participants
built up in the early years of the urchin fishery, peaked in 1993, and then began a steady
decline, how did fleet composition evolve? A
large literature in fisheries economics examines performance heterogeneity by focusing on
1
The data in this table are not based on permit records but instead are based on landings records. To infer the number of permit
holders, we take all unique license codes that have landings in the
landings ticket database, compute active windows for each diver by
recording minimum and maximum landings dates, and then count
the number of open windows for each calendar year.
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10–15 meter vessels that are equipped with
air compressors. The fishery emerged in the
1970s in southern California, spreading to
northern California in the late 1980s. By the
early 1990s, sea urchin was among the top
revenue-producing fisheries in the state of
California. While connected to the surface with
an air hose, an individual diver scrapes sea
urchins into baskets from rocky inter-tidal areas. This simple harvest technology does not
vary across the fleet, so differences in catch
are attributable to differences in lengths of
time spent diving, physical abilities of divers,
and skills in locating concentrations of urchins.
Divers sell raw urchins dockside to processors
in northern and southern California ports. Because the harvest technology is uniform across
the fleet, individual diver heterogeneity in participation and skill are the determinants of the
fleet’s total catching power.
In response to declines in catch per unit effort, regulators have implemented size limits,
seasonal closures, and beginning in the early
1990s, a limited-entry program. In 1988, the
California Department of Fish and Game began requiring divers to have a permit in order
to harvest urchins but did not limit the number of permits issued. When the limited-entry
program took shape in 1992, it grandfathered
all existing permit holders and only allowed
new entrants as a function of attrition. The permits are strictly nontransferable. As such, the
program provides some degree of excludability but does not implement a more comprehensive form of rights-based management such as
an ITQ system.
The limited-entry program targets 300
licenses in the long run. Whenever the number exceeds 300, one new license can be issued for each ten that are retired. Neither the
target number nor the rate of new license issues depend on the catching power composition of harvester attrition. When the number
of licenses falls below 300, the regulator issues
licenses to bring the total back to 300. To maintain a license, divers must harvest 300 pounds
of urchin at least twenty times over a two-year
period.
Starting in 1988, the California Department
of Fish and Game started collecting an extensive data set of logbook and landings tickets that includes prices, quantities harvested,
and geographic information about harvest locations. The data set in this article uses unique
license and boat codes to combine logbook
and landings tickets over the period 1988–1997
and track individual urchin divers. Table 1 re-
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August 2004
Amer. J. Agr. Econ.
1
0.8
0.7
0.6
0.5
1996
0.4
1988
1994
0.3
1990
0.2
1992
0.1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Cumulative Percent of Divers
Figure 1. Lorenz curves for diver catch
capacity utilization and technical efficiency.2 In
the urchin fishery, there is essentially no variation in physical capital nor in harvest technology. The only variation in inputs across
divers, i.e., across vessels, comes from differences in skipper decisions—location choices3
as well as dive lengths, frequencies, and timing. Thus, all efficiency differences would be
attributable to individual skippers. To understand catching power, the essential issue for
regulators then is who stays in the fishery and
who leaves. As such, in contrast to the capacity
utilization literature, the analysis in this article
looks at dynamic aspects of fleet heterogeneity
and how patterns of attrition contribute to this
heterogeneity.
As a starting point, consider whether the
fleet of harvesters is becoming more or less
2
A comprehensive review is beyond the scope of this paper, but
several examples include Kirkley, Squires, and Strand, which estimates technical efficiency for the mid-Atlantic sea scallop fishery;
Weninger, which estimates cost functions to examine efficiency
gains from ITQs in the mid-Atlantic surf clam and ocean quahog
fishery; Kirkley, Paul, and Squires, which provides an overview
of the various techniques and their application to fisheries; and
Pascoe and Coglan, which specifically examines skipper skill and
finds that skill accounts for most of the variation in efficiency.
3
Location choices may indicate search behavior. Active
searchers may be engaging themselves in some form of spatial arbitraging (Sanchirico and Wilen). More active searchers may also
have lower opportunity costs of time or simply lower costs of movement due to personal circumstances. See Smith (2000) for a review
of the empirical literature on search in fisheries.
heterogeneous. In other words, is performance
inequality among urchin divers increasing or
decreasing? One way to look at this issue is
to calculate Gini coefficients and plot Lorenz
curves across time. A Gini coefficient is the
area between the 45◦ line (perfect equality)
and the Lorenz curve, divided by the total
area under the Lorenz curve. In contrast to
the usual comparison of cumulative percent
of individuals with cumulative income, this
Lorenz-curve analysis compares cumulative
percent of individuals to cumulative percent
of harvest. For purposes of sustainability, it
is the harvest potential of the fleet that is
critical. Figure 1 plots these Lorenz curves
for even years beginning in 1988. All curves
are severely bowed outward, suggesting that
there is considerable heterogeneity in the composition of aggregate harvest. Even in the
most egalitarian year, 1996, 50% of the divers
catch less than 20% of the total sea urchin
harvest.
The Lorenz curves also hint at dynamic
changes in fleet composition. In particular,
they flatten over time such that the distribution of catch in the harvester population becomes more uniform over the sample period.
This trend is likely attributable to either the
changing pool of sea urchin harvesters, the evolution of the underlying sea urchin stocks, or
both. Both of these structural explanations are
consistent with a more stable fishery in which
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Cumulative Percent of Harvest
0.9
Smith
Limited-Entry Licensing
609
Table 2. Diver Gini Coefficients
Year
Catch Gini
All Divers
Catch Gini
Exclude < 2 Dives
Revenue Gini
All Divers
Revenue Gini
Exclude < 2 Dives
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
0.708
0.646
0.653
0.631
0.631
0.618
0.637
0.522
0.501
0.513
0.680
0.609
0.600
0.561
0.568
0.555
0.528
0.500
0.478
0.489
0.703
0.704
0.657
0.645
0.656
0.632
0.633
0.529
0.502
0.523
0.685
0.682
0.613
0.592
0.606
0.589
0.524
0.507
0.488
0.503
the heterogeneity in number of trips across
divers. As the coefficients of variation suggest, there is considerable variation across individuals in participation rates. This variation
decreases over time, while average participation increases. In fact, the correlation between mean participation and the coefficient
of variation is –0.97.
The increase in mean participation reflects
an increase in average intensity of exploitation. Inevitably, part of this change reflects
the constraints of the limited-entry program
(minimum of twenty landings over two years)
binding for divers with low participation rates.
Nevertheless, this trend is striking given that
additional partial season closures took effect
in 1992 and reduced the number of potential
fishing days by eighty six per year compared to
1991. The decline in the coefficient of variation
reflects a decrease in the variability of exploitation intensity. Taken together these trends suggest that the fleet is more potent but also potentially more predictable.
Duration Models of Harvester Exit Decisions
The level of commercial exploitation of sea
urchin, and hence the sustainability of the fishery, depends critically on the number of active fishers and their characteristics. An individual’s potential harvest is limited not just by
the abundance of urchin but also by the individual’s skill, weather conditions, the physical stress of diving time, and regulations
such as size limits and season closures (Smith
2001). Because licenses are nontransferable
and there are few opportunities for input substitution in the urchin fishery, there is a natural limit to the potential aggregate harvest
statewide. This potential harvest is a function
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there is less fluctuation from year to year as
time passes.
Table 2 reports four different sets of Gini
coefficients. Following the Lorenz curves, the
first two report Gini coefficients for catch. The
second two report Gini coefficients for revenues. Within each series pair, the distinction
is whether all license codes are considered or
license codes that have just one landing over
the entire sample period are excluded. Singletrip individuals are excluded to check the robustness of trends to license code errors. All
series exhibit the same patterns as the Lorenz
curves. Inequality decreases over time. The
catch and revenue Ginis are remarkably similar at the beginning and end of the sample period. In between, however, there appears to be
slightly more inequality in the revenue terms.
This may be due to the evolution of qualitybased pricing. In the late 1980s, processors had
just begun to introduce quality premia on raw
product purchases. Eventually, all processors
began to offer quality premia, and perhaps
more skilled divers responded by harvesting
higher quality product. This would concentrate
a larger share of revenues with the high-skilled
divers. After several years of the limitedentry program, some low-skilled divers may
have exited the fishery, possibly dissipating the
inequality differences between revenue and
catch.
Much of the inequality across the urchin
fleet is attributable to heterogeneity in participation rates. Full-time divers simply harvest more than part-time divers. Within each
year, the correlation between a diver’s pounds
harvested and number of trips is 0.69. For every year in the sample, there are always some
divers who make only one landing and others who make the minimum landings necessary
to renew their licenses. Figure 2 summarizes
Amer. J. Agr. Econ.
40.00
1.60
35.00
1.40
30.00
1.20
25.00
1.00
20.00
0.80
15.00
Coef. of Variation
August 2004
0.60
correlation = -0.97
10.00
0.40
5.00
0.20
0.00
0.00
1988
1989
1990
1991
1992
Mean Rate
1993
1994
1995
1996
1997
Coef. of Variation
Figure 2. Diver participation: average trips per year and variability
of total licenses, the characteristics of license
holders, other regulations, and characteristics
of the bio-physical system beyond the regulator’s control such as weather and reproductive characteristics of urchins. In a system with
few input substitution prospects, fishing effort
more readily becomes a binding constraint on
harvest. As such, when fishing effort is determined by number of fishable days, number
of participants, and harvester skill, a limitedentry program may very well turn out to be
effective.4 Given that the limited-entry program for sea urchins allows one new license
for each ten that are retired, understanding the
process of attrition and changing fleet composition is the key to understanding maximum
harvest potential for the fishery.5
Although the requirements to renew a license in the urchin fishery are moderate, many
divers exited the fishery altogether after the
4
Arguably, when input substitution opportunities abound, limiting licenses would not appear to limit total harvest because the
fishing effort constraint does not bind.
5
Predicting actual harvest and biomass is beyond the scope of
this article, but the results here could be linked to a more comprehensive bioeconomic model like the one in Smith and Wilen
(2003) to add one more dimension of behavioral complexity.
boom phase in northern California ended. The
recent trend in attrition raises several important management questions, including what
drives the rate of attrition, how many harvesters will remain in the future, and what
types of individuals are likely to remain active in the fishery? The first two questions are
related. With a sound model of attrition, one
can forecast how many divers will remain active in the fishery and hence the maximum harvest potential. However, it is also important to
recognize that diver heterogeneity could have
substantial impacts on the health of the fishery. Consider two different stylized scenarios
for the future urchin fishery that have the same
number of harvesters. In the first scenario, harvesters that remain in the fishery are parttime urchin divers. They are also involved in
other fisheries and work seasonally as diving
instructors. When conditions are good, they
dive for urchins, but sea urchin fishing is not
their primary source of income. In the second scenario, divers who stay in the fishery
are full-time. The divers who exited the industry took full-time jobs in other areas and do
not have time and do not maintain equipment
to continue diving commercially for urchins.
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(1)
F(t) =
t
f (s) ds = Pr(T ≤ t)
0
where f(t) is the underlying probability density
function. This gives rise to a survival function,
S(t), where
(2)
6
S(t) = 1 − F(t).
Some papers look at spells of employment, which is more similar to the current context. See, for example, Taylor.
The rate at which spells come to an end conditional on surviving to t is the hazard rate,
(3)
(t) =
f (t)
.
S(t)
A higher hazard rate, ceteris paribus, suggests that spells end more rapidly. In the case
of the fishery, a higher hazard rate thus indicates a higher rate of attrition.
One can add generality to the basic duration model by allowing the hazard rate to vary
across individuals. If individual fishers are in
fact different from one another in ways that can
be measured, then their dropout rates should
vary in some deterministic ways. Paramaterizing the hazard function parameter is a way to
account for this heterogeneity. Let
(4)
i = e− xi
where i indexes individuals, xi contains exogenous variables, and is a parameter vector.
This form can be used to estimate a Weibull
model, which also nests the exponential model.
The hazard function and survival function for
Weibull are:
(5)
i (t) = i p(i t) p−1
S(t) = e−(i t) .
p
and
Note that the exponential model results
from restricting p to equal one. With the exponential distribution, the hazard function is
constant across time, whereas the Weibull implies that the hazard function is monotonically
decreasing when p < 1 and increasing when
p > 1. A decreasing hazard function for the
fishery data implies that the instantaneous
probability of exiting the fishery decreases
over time. This may be the case, for instance, if
over time the fishery naturally selects for highliners, i.e., fishermen with high skill relative to
other participants, or simply full-time fishermen. Thus, the Weibull model naturally incorporates a tenure effect. Note also that with this
specification:
(6)
∂i
sign
∂ xik
= sign{e− xi (−k )}
= −sign{k }.
Thus, we can interpret the parameter signs as
indicating the effect of a given exogenous variable on survival.
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Under these two extreme scenarios, we might
see radically different participation levels and
impacts on the resource. A population of fulltime divers would probably put more pressure on the resource than a population of parttime divers. Thus a model of attrition that accounts for harvester characteristics helps to assess future potential exploitation of the urchin
resource.
Duration modeling is an empirical approach
that can estimate a trend of attrition and also
condition on differences across individuals.
The basic idea is that there is some underlying
stochastic process that drives survival times of
individual agents. A survival time in our case
is the length of time that an individual stays active in the fishery, i.e., the period between entry
and exit. If individuals are assumed to be the
same, survival times are typically modeled with
a one- or two-parameter probability distribution. If individuals are different, however, the
location parameter for the distribution can be
made a function of covariates that capture individual heterogeneity. Of course, we also do
not observe exit times for individuals who are
currently active in the fishery. Duration models explicitly account for this censoring effect
much in the way that a tobit model operates.
This is the first application of a duration model
to fishery participation.
To perform a basic duration analysis, we
must define the survival function, choose
a parametric distribution for duration, and
choose covariates that may affect survival
times. The treatment below follows Greene
and draws on Kiefer and Gourieroux. Much
of the economic duration literature analyzes
spells of unemployment, which is arguably the
standard motivation for duration analysis.6 In
contrast, a spell in the urchin fishery is the
length of time that a diver holds a valid permit, T. It has the following cumulative density
function:
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Amer. J. Agr. Econ.
Again following Greene, we can construct
the log-likelihood of the Weibull model with
covariates. We first make the following definitions:
1 if the individual exits
1
(7) = , i =
0 if not (i.e., is censored)
p
and
wi = p ln(i ti ) =
model can be matched to these intervals. This
may greatly simplify deriving the survival function for empirical analysis because the portion
of the hazard that involves covariates in (10)
passes through the integral. In the case of the
Weibull model, what is left to integrate has
an analytical solution. Using (5), (9), and (10),
the survival function for the Weibull model in
which the covariates vary in discrete time is:
ln ti − xi
(11)
tj
ps p−1 ds
t j−1
To obtain estimates of and p, one simply maximizes (8).
Not all conditions that influence an individual’s duration are necessarily individualspecific and time-invariant. Length of a spell
may be determined in part when an individual
is active in the fishery. Different time periods
have different prevailing conditions such as the
stringency of fishing regulations, the state of
the resource stock, and the macroeconomic environment. One can incorporate these effects
into a duration model by reparameterizing the
hazard rate such that it conditions on both
individual characteristics and time-varying covariates. Denoting the vector of time-varying
covariates as z(t) and the corresponding parameter vector as , we can rewrite (4) as
To find the survival function, following
Petersen one can break the survival duration
into k subperiods (each indexed by j). The
function for individual i surviving beyond tk ,
where t0 = 0, and for a generic hazard functionis then
Si (tk ) = exp −
k j=1
tj
= exp
− (e xi ) p
k
(e z j ) p
j=1
× (t j ) p − (t j−1 )
p
.
The likelihood function is simply the survival function for censored observations and
the product of the likelihood and the hazard for uncensored observations (Petersen,
Kiefer, Gourieroux). Thus, we can write the
log-likelihood as:
(12)
ln L =
i
−(e xi ) p
(s | xi , z(s)) ds .
t j−1
Many time-varying covariates change in discrete time, while others are continuous but can
only be measured at discrete intervals. When
the measurement intervals are the same across
the set of covaraites—for instance annual measurements of a resource stock and annually
delineated regulations—the subperiods of the
ki
e z j
p
(t j ) p − (t j−1 ) p
j=1
+ i ln( p) + p ln(tki ) − xi − z tki .
i (t) = e− xi − z(t) .
(10)
(e z j ) p
Most individual characteristics that might
affect duration of fishing participation are unobservable, so it is necessary to select plausible proxies. Diving skill is arguably the most
important characteristic that varies across individuals. Skill involves both the ability to find
large clumps of sea urchins and the ability to
find high quality urchins that can be sold for
a price premium, but these individual effects
of quality targeting and quantity targeting are
difficult to separate (Smith 2001). Opportunity
cost of participation is also potentially an important determinant of who will remain in the
industry. Average revenue per season (REV)
is used as a proxy for both skill and outside opportunities. It is an individual-specific average
and is simply the person’s total diving revenue
divided by the person’s length of participation
in the fishery. For individuals active less than
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×
i
k
j=1
The log-likelihood then reduces to
(8)
i (wi − ln ) − ewi .
ln L =
(9)
− (e xi ) p
Si (tk ) = exp
Smith
Limited-Entry Licensing
Table 3.
ple period. Other key fishery characteristics
are season length and size limit, both of which
change over the sample period. More restrictive regulations may make fishing more costly
in the short run and stimulate exit. However,
regulations may actually improve the fishery
for those who remain. Outside the fishery, the
California unemployment rate may affect survival times. When unemployment is high, the
ability to find other work is lower and urchin
divers may be more likely to stay in the fishery.
An important assumption is that all covariates are strictly exogenous. In that sense, we
assume that the duration of activity does not
affect the value of a regressor. This is problematic in the case of individuals who only participate once (or a small number of times) because
the port variable, for instance, is necessarily
equal to one if the duration is only one day. It
also poses problems for the revenue variable
because the measure of a diver’s performance
is pinned to a point in a particular season, and
there is no interval over which this is measured.
Thus, we consider two separate samples: the
full sample of all active participants prior to
1998 and a restricted sample of participants
who fished at least one full year.
Table 3 contains summary statistics for the
duration length (DURATION) and covariates
used in the duration estimation. There are two
sets of summary statistics to highlight the differences between the full sample and the restricted sample. For duration and individual
characteristics, means and standard deviations
are computed using one observation per individual. The individual characteristics include average revenues per season (REV),
number of ports visited (PORTS), share of
Summary Statistics
All Divers
Mean
Dependent variable
DURATION
3.08
Individual characteristics
REV
9.50
PORTS
2.74
SH SC
0.64
EARLY
0.12
Time-varying covariates
STOCK
2.11
UNEMP
7.57
SEASON
260.64
SIZE LIM
85.36
At Least 1 Full Season
Min
Max
St. Dev.
Mean
Min
Max
St. Dev.
0.00
10.00
3.60
6.27
1.00
10.00
2.64
0.00
1.00
0.00
0.00
172.25
16.00
1.00
1.00
15.58
2.68
0.46
0.33
17.32
4.48
0.65
0.22
0.00
1.00
0.00
0.00
172.25
16.00
1.00
1.00
19.00
2.95
0.43
0.41
1.73
4.87
92.00
0.00
2.37
9.34
366.00
89.00
0.20
1.43
60.00
15.65
2.11
7.54
260.00
85.32
1.73
4.87
92.00
0.00
2.37
9.34
366.00
89.00
0.21
1.43
59.97
15.73
Downloaded from http://ajae.oxfordjournals.org/ at Pennsylvania State University on May 17, 2016
one full year, average revenue per season is
simply their total revenue in the fishery. High
revenues indicate a high frequency of diving
(i.e., low opportunity cost), quantity skill, quality skill, or some combination of these effects.
PORTS counts how many distinct ports at
which the diver landed urchin. This is a mobility measure that may reflect either fish finding
skill or a low opportunity cost, both of which
would increase the probability of staying in the
fishery. Share of southern California (SH SC)
is the diver’s total number of southern California diving trips divided by his total number
of diving trips. A higher southern California
share indicates that more of a diver’s activity is
concentrated in a less physically risky environment in terms of weather. EARLY is a dummy
variable that indicates whether the diver was
active in the urchin fishery prior to 1989. This
is potentially an important skill proxy because
many early participants in the fishery were previously abalone divers and thus were experienced in commercial dive fisheries.
For time-varying covariates, we choose exogenous variables that change over time and
that increase or decrease the overall attractiveness of participating in the urchin fishery.
Naturally, the sea urchin stock is changing, and
a higher stock increases the appeal of staying
in the fishery. Though there are no independent assessments of the urchin stock available,
we can use the annual empirical bioeconomic
projections from Smith and Wilen (2003) to
account for the northern California sea urchin
stock. The southern California stock is plausibly excluded because it has a relatively stable
catch per unit effort and may have locked into
a bioeconomic equilibrium prior to the sam-
613
614
August 2004
Table 4.
Amer. J. Agr. Econ.
Duration Model Maximum Likelihood Results
All Divers
At Least 1 Full Season
Model 2
Model 3
Model 4
Model 5
0.251b
(0.006)
CON
1.033b
(0.119)
Individual characteristics
REV
0.354b
(0.008)
−4.838b
(0.199)
0.342b
(0.008)
−16.633b
(1.463)
1.361b
(0.069)
2.518b
(0.049)
1.652b
(0.079)
1.145b
(0.081)
0.939b
(0.084)
33.155a
(14.840)
0.135b
(0.014)
1.732b
(0.092)
0.372a
(0.180)
0.866b
(0.316)
0.134b
(0.015)
1.732b
(0.094)
0.897b
(0.190)
−1.861b
(0.401)
0.017b
(0.004)
0.209b
(0.021)
0.268b
(0.074)
0.111
(0.085)
0.028b
(0.007)
0.365b
(0.046)
0.623b
(0.145)
−0.467a
(0.184)
PORTS
SH SC
EARLY
Time-varying covariates
STOCK
UNEMP
SEASON
SIZE LIM
LL
Obs.
Pseudo R2
−3,880
1583
−3,126
1583
0.19
8.214b
(0.542)
−0.461b
(0.070)
−0.032
(0.177)
−2.947b
(0.855)
−2,911
1583
0.25
−768
768
−615
768
0.20
Model 6
1.948
(1.079)
0.106
(0.165)
1.472a
(0.702)
−46.418a
(18.076)
−560
768
0.27
Standard errors in parentheses.
a Indicates significant at the 5% level. b Indicates significant at the 1% level.
fishing in southern California (SH SC), and
a dummy variable for early participation
(EARLY). By their nature, time-varying covariates evolve over each individual’s spell.
Thus for the time-varying covariates, means
and standard deviations are weighted averages based on the number of duration intervals
for each individual—the ki ’s from (12). Timevarying covariates include the sea urchin stock
(STOCK), the California unemployment rate
(UNEMP), season length (SEASON), and a
size limit (SIZE LIM). Not surprisingly, the
mean duration for the restricted sample is
more than twice that of the full sample. This is a
result of the prevalence of single-trip divers in
the full sample, i.e., individuals who only tried
urchin fishing once and did not continue. The
summary statistics for time-varying covariates
in the two samples are virtually identical, reflecting both greater weight on the longer duration lengths, which are in both samples, and
some uniformity in the short duration length
distribution over the sample period.
Table 4 reports the results from maximum
likelihood estimation of six duration models.
Duration for each individual is their last decimal date fished minus their first decimal date
fished, so the time is measured in decimal
years. If the individual is still active as of the
beginning of 1998, the observation is considered censored and the maximum date is replaced with 98.0 for the duration calculation.7
Estimates for Models 1, 2, 4, and 5 were obtained by maximizing (8), whereas estimates
for Models 3 and 6 were obtained by maximizing (12).8 Models 1–3 use the entire sample of
urchin divers who were active prior to 1998.
7
The last term in (8) accounts for the censoring. If the individual
remains in the fishery, the term in parentheses is multiplied by zero
and only this last term affects the probability. In the event that
a diver exits and re-enters, the analysis counts the re-entry as a
distinct spell if a new license code is assigned. If the diver keeps
the original license code, presumably because the individual was
out of the fishery for less than two years, the analysis treats this
diver as if there is just one long spell.
8
All of the models were estimated using GAUSS MAXLIK.
The estimates were invariant to starting values, but convergence
was achieved only using the Berndt, Hall, Hall, and Hausman algorithm. As an additional check, the results of Models 2 and 5 were
replicated by using (12) and restricting the coefficients to zero.
Downloaded from http://ajae.oxfordjournals.org/ at Pennsylvania State University on May 17, 2016
Model 1
Weibull parameters
p
Smith
615
likely to survive than low earning divers. Similarly, the positive signs on ports visited suggest that more mobile divers are more likely to
survive. This result, that more successful fishers are ones who are willing and able to explore multiple locations, is consistent with the
findings of previous analyses of spatial choice
in fisheries. Abrahams and Healey find that
catch rates for vessels in the British Columbia
salmon troll fleet are positively correlated with
a measure of spatial mobility. Evans finds that
mobile vessels in the California salmon fishery outperform sedentary vessels in terms of
both catch per day and revenue per day. In
contrast, mobility increases the probability of
exit in Ward and Sutinen’s study of the Gulf
of Mexico shrimp fishery, though the result is
only marginally significant.
At the same time, a positive sign on mobility is consistent with a diver having lower costs
and thus surviving longer in the fishery. Specifically, movement could indicate a low opportunity cost due to limited outside opportunities
or few personal connections that tie a diver
to a particular home port. Since net revenues
arguably are what affect attrition, without controlling for mobility, the coefficient on gross average revenues would overstate the propensity
for high revenue earners to stay in the fishery.
The interpretations of the southern
California share and early entry dummy are
somewhat amorphous. The positive signs
on the share of southern California suggest
simply that southern California participants
are more likely to remain in the fishery. The
question of why this would be the case is
more complicated. Certainly, the southern
California urchin fishery has been more
stable in terms of aggregate catch than that in
northern California. In that sense, this share
measure may be related to mobility. Divers
are more likely to remain in the fishery if they
are willing to move to more productive areas,
many of which are in southern California.
Also, weather conditions in the south are
milder. Thus, individuals are more likely to
exit the fishery if they are exposed more
often to unsafe diving conditions. The sign on
the early dummy variable flips when we add
time-varying covariates. One might expect
that early participation captures a degree
of professionalization because many early
participants in the fishery were previously
engaged in the abalone dive fishery. Perhaps
a number of nonprofessionals entered for
the boom period but quickly exited because
overall profitability of urchin diving declined.
Downloaded from http://ajae.oxfordjournals.org/ at Pennsylvania State University on May 17, 2016
Models 4–6 restrict the sample to only individuals who were active for at least one full
season. This eliminates the ambiguity of how
to define revenue (particularly for individuals
who dove only once) and addresses the endogeneity problem of the port variable. However,
if individuals who were testing out the urchin
fishery really do come from the same population of interest as other divers, the restricted
sample may introduce sample selection bias.
Models 1 and 4 are duration models without any covariates such that the hazard rate
is assumed constant across individuals. However, given the Weibull distribution, the hazard
rate in these models is not necessarily constant
across time, and the distribution is described by
two parameters (p and CON). Models 2 and 5
contain covariates that are time invariant but
vary across individuals in the sample. These
estimates also demonstrate that including covariates does help to explain exit behavior. The
likelihood ratio test statistic for restricting the
covariates is –2 ∗ [ln(LR )−ln(LU )] and is distributed 2 with four degrees of freedom. The
critical value for a 95% confidence level is 9.49.
For both Models 2 and 5, we reject the restriction that the parameters on the covariates are
zero. The 2 statistics are 1,507 and 306 respectively. Models 3 and 6 include time-varying covariates as well, but they only vary across individuals to the extent that different individuals are in the sample in different time periods.
We also reject restricting these models down
to Models 2 and 5. The 2 statistics, again with
four degrees of freedom, are 430 and 110 respectively.
In all models, the constant and the Weibull
p parameters are statistically significant. Four
of the models (1–3 and 6) have p < 1, which
indicates that the base hazard rate is decreasing over time. This finding is consistent
with Bockstael and Opaluch results of switching inertia based on a discrete choice with a
lagged dependent variable. The other models
(4 and 5) have p > 1 such that the base hazard rate is increasing over time. For Model
6, the decreasing base hazard is not significant because, though p is statistically different
from zero, it is not statistically different from
one.
For individual characteristics, the signs of
the parameters provide insight on why some
fishers remain in the fishery and others exit.
Across all models, the parameter signs are
consistent for three of the four characteristics.
The positive signs on average revenue per season indicate that high earning divers are more
Limited-Entry Licensing
616
August 2004
Discussion
This article examines fleet composition and attrition in a limited-entry fishery with a unique
data set on California sea urchin fishing and a
novel application of duration modeling. Over
the sample period (1988–1997), divers show
substantial variation in participation. While
the average number of dives increases over this
period, the heterogeneity in participation decreases based on the coefficient of variation
of individual diver trips in each year. Gini ratios show the same pattern. Over the life of
the limited-entry program, the fleet is becoming more homogenous. This motivates the need
to study attrition and particularly what diver
characteristics increase the probability of exiting the fishery.
Using a duration model to analyze conditional attrition, we find that the probability of
exiting the fishery decreases as average revenue per season and number of ports visited increase. Thus, attrition is lower for more
successful divers, and attrition is also lower
for more spatially mobile divers. Differences
across individual harvesters also appear to be
important and, in part, manifest themselves in
proclivity for spatial mobility. In light of recent emphasis on fishery management through
spatial closures and other forms of marine
protected areas, this is an important finding.
Compared to a sedentary fleet, a fleet of spatial arbitrageurs will more rapidly dissipate
any gains generated by spatial management.
As such, it is essential to link spatial management to rights-based management in order to achieve spatially explicit bioeconomic
objectives.
What can regulators do with these results?
Though it is not surprising to economists, these
results demonstrate empirically a basic tenet
of bioeconomics that is often ignored by managers; specifically, the fleet size will adjust in
response to the resource stock. Less central
to most bioeconomic studies but equally important here is fleet heterogeneity. Regulators
administering a limited-entry program need to
recognize the changing fleet composition and
the connection between performance and attrition when setting the target license count
and the rate of new license issuance. After all, if
one assumes contrary to the facts that attrition
is random, a forecast of the fleet’s aggregate
catching power would be biased downward,
and the bias would grow over time. In principle,
one could go further and use duration results to
fine-tune the limited-entry program. That is, a
regulator might consider continuously updating the license target, or at least the rate of reissue, as information about fleet composition updates in each year. Alternatively, the regulator
may adjust other instruments, e.g., the size limit
or the season length, in response to changing
catching power. Such exercises are beyond the
scope of this paper because they necessarily involve biological assessment of the resource as
well as a forecast of aggregate catching power.
The notion of continuously updating a
limited-entry program is consistent with adaptive management, an idea that is gaining popularity among fisheries scientists and managers.
First developed by Holling and in a fisheries
context by Walters, adaptive management
seeks to manage fundamental uncertainty by
allowing policy makers to adjust policies in response to changing information. This is precisely what a dynamic limited-entry program
Downloaded from http://ajae.oxfordjournals.org/ at Pennsylvania State University on May 17, 2016
However, this explanation does not hold up
when time-varying covariates are introduced.
The signs on the time-varying covariates are
mostly consistent with expectations. The sea
urchin stock has a positive and significant influence on survival though only marginally significant in Model 6. This suggests that spells tend
to last longer when the stock is larger, and the
result is consistent with the findings of Ward
and Sutinen for the Gulf of Mexico shrimp
fishery. The significant coefficients for the two
regulation variables have their expected effects. The season length coefficient in Model 6
is positive, suggesting that divers are more
likely to stay in the fishery when they have
more fishing opportunities. The size limit coefficient is negative and significant in Models 3
and 6. Thus, when regulators tighten size limits, they increase the rate of attrition. The one
inexplicable result is the negative and significant coefficient on unemployment in Model 3.
It appears that unemployment does not have
the expected effect on duration, and perhaps
the time series picks up another effect that is
not in the model. This is particularly surprising in light of the results in Smith (2002) that
show that California unemployment increases
the rate of participation based on both discrete
choice and count data models. In other words,
conditional on being in the fishery, when unemployment is high divers tend to fish more often
(presumably because they have fewer employment opportunities outside of fishing). However, this effect does not appear to transfer to
the decision to maintain one’s license.
Amer. J. Agr. Econ.
Smith
Limited-Entry Licensing
[Received November 2002;
accepted October 2003.]
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