Economic Impacts of Marine Reserves:
The Importance of Spatial Behavior
Martin D. Smith
Assistant Professor of Environmental Economics
Nicholas School of the Environment and Earth Sciences
Duke University
Box 90328
Durham, NC 27708
(919) 613-8028
marsmith@duke.edu
and
James E. Wilen
Professor
Department of Agricultural and Resource Economics
University of California, Davis
One Shields Avenue
Davis, CA 95616
(530) 752-6093
wilen@primal.ucdavis.edu
JEL Codes: Q22
Short Abstract
Marine biologists have shown virtually unqualified support for managing fisheries with
marine reserves, signifying a new resource management paradigm that recognizes the
importance of spatial processes in exploited systems. Most modeling of reserves
employs simplifying assumptions about the behavior of fishermen in response to spatial
closures. We show that realistic depiction of the behavior of fishermen matters
dramatically to the conclusions about reserves. We develop, estimate, and calibrate an
integrated bioeconomic model of the sea urchin fishery in northern California and use it
to simulate reserve policies, but with behavioral response via reallocation of effort over
space. Our behavioral models show how economic incentives determine both
participation and location choices of fishermen. We compare our results with biological
modeling that presumes effort is uniformly distributed and unresponsive to economic
incentives. The modeling shows that the optimistic conclusions about reserves may be an
artifact of simplifying assumptions that ignore economic behavior.
February 5, 2002
Economic Impacts of Marine Reserves:
The Importance of Spatial Behavior
Long Abstract
Resource scientists have recently shown virtually unqualified support for
managing fisheries with marine reserves, signifying a new resource management
paradigm that recognizes the importance of spatial processes in both untouched and
exploited systems. Biologists promoting reserves have based such support on simplifying
assumptions about harvester behavior. This paper shows that these naïve assumptions
about the spatial distribution of fishing effort before and after reserve creation severely
bias predicted outcomes, generally overstating the beneficial effects of reserves.
The paper presents a fully integrated, spatial bioeconomic model of the northern
California red sea urchin fishery. The model is the first attempt to marry a spatially
explicit metapopulation model of a fishery with an empirical economic model of
harvester behavior. The biological model is calibrated with parameters representing best
available knowledge of natality, growth, mortality, and oceanographic dispersal
mechanisms. The model of spatial behavior is estimated using a large panel data set of
urchin harvester decisions, which are recorded in logbooks and on landings tickets.
The economic model tracks repeated decisions that take place on different time
and spatial scales. Harvesters make daily decisions about whether to fish and where to
fish, conditioned on home ports. On longer time scales, harvesters select home ports,
choose between northern and southern California regions, and decide whether to drop out
of the fishery.
Combining a Random Utility Model with Seemingly Unrelated
Regressions, the model predicts the aggregate supply response of fishing effort and the
1
spatial allocation of effort as a function of relative economic payoffs. The economic
model is integrated with the biological model to endogenize effort, harvest, biomass
levels, and reproductive performance of the population.
The integrated model is used to explore the efficacy of marine reserve formation
under realistic assumptions about the determinants of total effort and its spatial
distribution. Contrary to the dominant biological modeling conclusions based on naïve
assumptions, realistic behavioral assumptions lead mostly to pessimistic conclusions
about the potential of marine reserves. The results ultimately cast doubt on many of the
arguments made by those who advocate
2
Economic Impacts of Marine Reserves:
the Importance of Spatial Behavior
I.
Introduction
There is an important paradigm shift underway in the marine policy arena that is
likely to change the way in which coastal resources are managed in the future. The shift
is toward the use of spatial zoning measures that will effectively carve the ocean up into a
system of mixed areas of regulated exploitation and areas protected with marine
reserves.1 The underpinnings of this new vision are based on a mix of emerging science
and political interest in marine protected areas. On the science side, there is growing
consensus among marine ecologists, biologists, and many fisheries managers that
conventional season length and gear restriction management methods have failed and are
bound to fail in the future, and that a new approach is therefore needed. On the political
side, there is a growing view among NGOs and influential environmental lobbying
groups that long term biodiversity and conservation goals would be best served by a
network of protected areas similar to our terrestrial park systems.
Up to this point, the case for this new spatial zoning view has mainly been
promoted by biologists, with little input solicited from economists and other policy
analysts. But as real proposals emerge for specific systems of protected areas, there will
be increasing calls for economic analysis of impacts of actual policy options. Economists
are only beginning to think about how space might be introduced into conventional
models of renewable resources and how spatially differentiated policies might compare
with second best undifferentiated policies. In this paper, we present a comprehensive
empirical investigation of the implications of marine reserves, as they might be applied in
a case study of the northern California red sea urchin fishery. We focus particularly on
modeling spatial behavior of the harvesters, and we assess the degree to which
accounting for economically-driven behavior matters to the conclusions coming out of
recent biological investigations of marine reserves. We find, a bit to our surprise, that the
many and varied simplifying modeling assumptions made by biologists to handle
harvester behavior do not actually “cancel out” in the final analysis. Instead, virtually
every simplification made in biological modeling about economic behavior biases the
case in favor of the use of reserves as a fisheries management instrument. Our results
thus call into question whether the optimism displayed for reserves as a fisheries
management tool is warranted.
In the next section we review what is known about reserves, from both the
biological and economic literature. We then describe the sea urchin case study fishery,
focusing particularly on its spatial character and its short- and long-term dynamics. In
the fourth section we discuss and estimate some models of spatial behavior and then use
those, in the fifth section, to simulate the impacts of marine reserves with an integrated
1
The emerging literature on marine reserves uses a variety of terms that are sometimes synonymous and
sometimes not. We will use marine protected areas, marine reserves, and no-take zones as interchangeably
referring to areas in which no exploitation is permitted, including especially commercial and recreational
fisheries exploitation.
3
bioeconomic model. In the final section we draw some broad conclusions for both
research and policy analysis of marine protected areas.
II.
Related Biological and Economic Work
The notion of using closed areas as a marine management tool emerged a little over a
decade ago among marine ecologists and conservation biologists. The first proposals
were modest, calling for small areas off coastal research institutes in which ecologists
could study unexploited systems in order to gauge the ecological impacts of exploitation.
By the early 1990s, the idea was beginning to morph into a grander vision that called for
significant areas to be set aside, often on the order of 20-30% of the coastline. The
transformation in the scale of the proposals coincided with several important papers on
fisheries management, most of which concluded: a) that the world’s fisheries were in a
state of crisis; and b) that conventional methods were to blame and that a new approach
to management was needed. 2 Early modeling papers thus focused on the impact that
permanent closures might have on exploited fisheries.
The first modeling work on marine reserves is by Polacheck, who used a
Beverton/Holt yield per recruit model to examine how a purposeful closure might affect
an exploited fishery. Beverton/Holt developed the yield per recruit model in the 1940s to
describe fisheries in which the relationship between the spawning stock and the resultant
recruitment of juveniles is highly uncertain or unknown. Yield per recruit models
assume larval recruitment is constant and exogenous and then the equilibrium is
expressed in terms of two policy variables of interest, spawning stock biomass per recruit
(SSB/R) and yield per recruit (Y/R). In comparing management policies, options that
involve more Y/R are generally judged as desirable in terms of fishery objectives, as are
options that increase SSB/R.3 Choices that increase one and decrease the other are
problematic, however. In Polacheck’s first simulations of reserves, SSB/R always
increases over the whole system with a reserve, but Y/R generally decreases in most
simulations.4
Polacheck’s and other similar yield per recruit modeling exercises were an
important first step in understanding how marine reserves might work as a management
tool. Most of these “first generation” models assume: a) a homogeneous area that is
subdivided by a reserve into two areas; b) a constant amount of effort redistributes to the
remaining open area, thus increasing fishing mortality in the open area; c) simple
2
See for example the oft-cited paper by Ludwig and Walters (1993), which argues that reductionist
approaches cannot overcome the natural variation and irreducible uncertainty inherent in natural systems in
order to guide us toward anything like sustainable yield.
3
With a fixed or unknown stock/recruitment relationship, it is obvious why having more fisheries yield per
recruit is desirable. A caveat is that the B/H models are equilibrium models and, from a dynamic
perspective it might not be worth the sacrifice to restore a fishery to the point that squeezed the last
equilibrium levels of yield out of the system. Having more SSB/R is judged desirable because if there is
any positive relationship between spawning stocks and recruitment, a higher SSB/R would increase
recruitment and yield. Moreover, many fisheries scientists point to the “safety” provided by higher levels
of SSB in the face of perturbations and environmental shocks.
4
Polacheck concludes “in some cases the yield per recruit with a refuge can exceed the yield per recruit
without one, but the net increases are usually small”. He also concludes that “a closed area can lead to
substantial increases in spawnng stock biomass. . .and, as such, could be a viable short term management
option to reduce overall fishing mortality on an overexploited stock.”
4
dispersal assumptions such as proportional diffusion of adults; d) equilibrium analyses
that ignore transitional effects; e) no explicit relationship between spawning stock
biomass and recruitment of larvae in the system. Despite simplifying assumptions
embedded in these modeling efforts, compilation of empirical data on closed areas
around the world has confirmed most of the modeling predictions, at least of effects
within the closed areas. A recent metapopulation analysis of 89 papers with empirical
data on reserves confirms the virtually universal increase in spawning stock biomass
produced within reserves that was first predicted by Polacheck and by other similar yield
per recruit models.5
One does not need a voluminous amount of empirical work to believe that
removing fisheries exploitation from an ecosystem will increase biomass, broaden the age
distribution by providing protection for larger and more fecund fish, and perhaps increase
biodiversity and alter species composition within the protected area. What is less certain,
however, is whether the increase in spawning stock biomass and its composition within a
reserve can provide a net increase to the fishery outside the reserve.6 The first generation
modeling work identifies some mechanisms that can be important to this question,
namely the mobility of adults and the level of pre- and post-reserve exploitation in the
fishery. The first generation papers show that reserves are most likely to increase yield in
the open area when adult mobility is not too low or too high. The intuition is that, for a
given size reserve, adults must not move so widely that they are not afforded protection
by the reserve, but some adults (and juveniles) must move widely enough so as to
increase the fishable abundance available to the fishery.
The second generation of papers generalized the yield per recruit models by
closing the relationship between spawning biomass and recruits to the fishery. This is an
important addition to understanding, because protected areas may also produce eggs and
larvae that are subsequently distributed to exploitable populations in the remaining open
areas. In particular, a small number of papers from the late 1990s assume that adults
produce larvae, which disperse in some manner and then recruit into both the fishery and
the reproductive population. One of the most significant second generation papers is the
paper by Holland and Brazee, two economists. The Holland/Brazee paper is
sophisticated from a biological modeling point of view, incorporating density dependent
stock/recruitment relationships in both the reserve and open area, and uniform larval
dispersal mechanisms in a detailed age-structured population model. In addition, their
model incorporates economic variables and is fully dynamic so that the present value of
transition paths can be examined. The Holland/Brazee analysis confirms the Polacheck
results that spawning stock biomass will increase with reserves. They also find that
whether this spills over sufficiently to produce a net economic gain depends upon the
discount rate and the pre-reserve exploitation level. At high discount rates it never pays
to endure the sacrifice necessary to rebuild sustainable harvests to higher levels. In
contrast, at high pre-reserve exploitation rates, since the overall harvest is driven so far
5
Halpern, B. (2002)
Some of the fisheries literature does not seem to understand that it is a net increase and not just a gross
increase in yield that is needed in the remaining open areas. That is, from the fishing industry perspective,
it is not enough that a reserve increases harvest outside the reserve, but rather that the increase be large
enough to compensate for the area removed from fishing. As the reserve size gets larger, of course, this
hurdle rises.
6
5
below MSY, it is more likely to be worth an investment in rebuilding the overall biomass
by using a reserve.7
One important simplifying assumption made by Holland/Brazee and virtually all
of the analysis of reserves that has been done by biologists is that effort is fixed both
before and after reserve formation. Under a closure, it is presumed that the effort that is
transferred to the remaining open area increases fishing mortality there, and in the most
sophisticated analysis there are further ramifications on harvest, biomass, and
reproduction as a result. In this paper we consider how incorporating more realistic
depictions of harvester behavior affects the potential implications of marine spatial
closures. A priori, economically motivated harvester behavior ought to matter in several
ways. First, since the pre-reserve status quo is important to the net effect of a policy
change, it should be of interest to know how economic variables condition the initial
circumstances in a spatial bioeconomic system. Second, since a spatial closure will affect
the subsequent spatial distribution of relative economic returns, we would expect that
effort redistribution would have complicated spatial and intertemporal effects, both in the
short run and in the long run. Third, since most real spatial systems embody complicated
heterogeneities that affect profit differentials over space, we would expect to be able to
capture some of these as profit differentials. For all of these reasons, simplified
assumptions about effort distribution and its determinants are likely to confound and
possibly mislead policy makers considering these new forms of marine policy
instruments.
III.
Case Study: the Northern California Sea Urchin Fishery
The Northern California sea urchin fishery is an ideal case study with which to
examine empirically marine reserves and the dynamics of spatial behavior of harvesters.
Sea urchin are found along the Pacific Coast in rocky inter-tidal areas kelp forest areas
from Southern California to Alaska. Urchin have hard spiny shells and they are
harvested for the gonads (roe) found inside the shells. Urchin are harvested by divers
who make day trips to fishing grounds on vessels built especially to travel fast to the dive
location. Once on a site, a diver begins harvesting while a tender aboard the vessel
watches the scuba gear. Harvesters use rakes to remove urchins from the rocky bottom,
filling mesh toat bags which are then offloaded onto the vessel by the tender. Weather
conditions are a critical determinant of when and where divers choose to dive,
particularly in Northern California where a trip is typically made only 14% of available
open days.
At the end of a fishing day, harvesters deliver the whole urchins to processors. At
the processing plant, workers split the shells, scoop out the gonads, and then wash and
bath the gonads in alum solutions to firm the roe. Roe skeins are then carefully packed in
special wooden trays holding 250g. and the product is shipped overnight to Japan. In
7
At the same time, what this shows is that it can be a sound investment to rebuild an overexploited stock
by reducing effort. Closing a fraction of a fishery’s area is one way to reduce overall fishing mortality (as
Polacheck concluded), but another way is to simply crank down conventional methods of effort and fishing
mortality control. Hastings and Botsford have established that area controls are equivalent to conventional
effort controls under certain reasonable circumstances. Some fisheries observers point out, however, that
closed areas may be easier to enforce than conventional effort control measures such as mesh size, days at
sea, etc.
6
Japan, the roe is sold mainly at the Tokyo Central Wholesale Market, in competition with
roe from Japan and other North American fisheries. The roe is relatively high valued,
with current Tokyo Wholesale prices in the range of $25 per pound, translating into a
markdown to divers of approximately one dollar per pound of whole urchin.8 A typical
day trip brings in 750 pounds of urchin, grossing $750 per trip for the diver/tender team.
Urchin have been harvested in Southern California since the early 1970s and in
Northern California since 1988.9 They are regulated with a combination of closed
seasons, minimum size regulations, and a limited entry program. Current regulations
require that Northern California urchin be at least 3.5 inches in diameter, a size reached at
an age of approximately – years. A full closure is in effect throughout all of July, and
one week closures are operative from May to September. Within each open week, threeday per week openings are in force in June and August, and four-day openings prevail in
April and October. In total, the number of potential open days per year is approximately
– in Northern California. The limited entry program was introduced into the Californiawide fishery in 1989, grandfathering all existing permit holders (roughly 850) into the
fishery. The program has been tightened up over the intervening years in order to steer
participation to a long term goal of 300 divers. Each diver must now land 300 pounds per
trip for a minimum of 20 trips during either the current or preceding year in order to be
granted a license.10 Licenses must be fished by the holder, and licenses may not be
leased or sold.
Biological characteristics of urchin mimic those identified by biological modelers
as holding the most promise for successful use of reserves. First, urchin are “patchy” in
that they are found in several distinct and discrete areas in Northern California where
substrate and habitat characteristics are suitable for the species. Second, adult movement
within each patch is relatively low, an average of 7-15 cm. per day. Third, closed areas
promise protection of a substantial amount of productive spawning biomass. Urchin
reach sexual maturity approximately at age six, and egg production increases with age at
an exponential rate. Fourth, larvae are redistributed considerable distances from
spawning areas by currents, winds, and sea surface changes.
In addition to favorable biological characteristics, the urchin fishery is also an
ideal case study for examining spatial behavior of harvesters. Most importantly, there are
multiple dimensions to the spatial choices divers face. Among the limited set of licensed
divers allowed to participate, divers each make seasonal decisions about whether to fish
in Southern California or Northern California. These large scale spatial decisions are
made infrequently, perhaps averaging once or twice per diver over the whole period we
examine. Additionally, for those divers choosing Northern California, each diver must
make a port choice decision, essentially a decision about where to deliver (and where to
live) during the fishing season. This is an intermediate scale spatial decision, and it
8
Note that the recovery of roe from whole urchin is about 10%. Hence ten pounds of whole urchin are
needed to generate a pound of roe, mostly explaining the markdown.
9
Ironically, urchin were considered pests by abalone divers in the 1960s because they competed for the
lucrative abalone for habitat and food. Abalone divers often poured quicklime on urchin in order to remove
them and open up habitat for the commercially valuable abalone. In the 1970s, a market for California
urchin developed as the Japanese stocks were overharvested. The fishery was harvested mainly in
Southern California by ex-abalone divers after the abalone fishery collapsed. The continued growth in the
Japanese market led to the Northern California fishery being opened up in the late 1980s.
10
Provisions are also made to allow one new entrant for each ten licenses retired.
7
determines the reach and the nature of patches available for day trips taken from each
respective port. Finally, each diver leaving from a particular port on a daily basis
chooses which patch to visit from among those feasible within a day trip’s distance.
These kinds of decisions obviously cover the smallest geographic scale and over a most
frequent time scale.
The data set we use to examine spatial harvester behavior in the Northern
California sea urchin fishery is unusually rich. It consists of 57,000 individual dives
made by up to 358 divers over the period between 1988 and 1997, recorded in mandatory
logbooks and landings ticket records. Each landings ticket record records port of landing,
processor code, quantity landed, price paid, and diver code. Each logbook record reports
dive location (latitude), dive duration, average depth, and divers per vessel. We also
collected daily weather data on wind speed, wave height, and wave period from weather
buoy records, averaged it over the period preceding a typical trip decision, and keyed it to
potential dive trip decision. The fact that each trip is a day trip is also convenient since
we can model decisions as repeated nested discrete choices.11 The models we report here
estimate parameters of a repeated choice structure for several hundred divers making
decisions over a total of over 400,000 choice occasions.12 During this period, the urchin
fishery was harvested from a virgin fishery to the present level approaching a steady state
at average profit levels. Prices vary over the period as a result of exchange rate changes,
quality changes, and landings variability. Weather conditions vary on a daily basis and
with some inter-annual variation as well.
As a first step in our analysis of the urchin fishery, we examined the nature of
spatial behavior by divers taking day trips in Northern California between 1988 and 1997.
We first identified six ports that handled urchin and then keyed latitude-based diving
locations to those ports. Table 1 shows some of the raw data and it reveals that diver
activity off each port is concentrated in nearby locations, some of which overlap for
several ports. For example, most of the urchin landed in the southern- and northern-most
ports of Half Moon Bay and Crescent City are taken in patches located directly offshore
of the port location latitude. In contrast, urchin landed at Fort Bragg are harvested mostly
from four nearby patches, two of which are also major sources for Albion, an adjacent
port. Ports of Bodega and Point Arena land urchin from several nearby locations,
although with relatively little overlap. What these show is that the spatial choice set as
revealed by actual behavior varies with port location, with landings fanning out in a
Laplacian fashion that declines exponentially from distance off the port. Some of these
spatial landings patterns also reflect a pushing out of the Ricardian margins, in that early
exploitation was shallow and near ports whereas later exploitation has been deeper and at
more distant patches.
Using these effort data and knowledge of breaks in suitable habitat types, we
partitioned the entire data set into one characterized by eleven patches along the coast of
Northern California. Figures 1 and 2 are a histogram and map over the whole period with
11
A repeated decision structure is more tractable than trying to model situations with a fixed end point. In
addition, fisheries in which multi-day and multi-area trips are made must contend with the complications
introduced by decisions that are essentially searching decisions made along the journey to a targeted
destination.
12
Total choice occasions are days for which the urchin fishery is open to harvesting. Because weather
conditions so frequently keep fishermen ashore, the actual number of trips is only a fraction of total choice
occasions, about 14% of open days.
8
diving activity characterized by “patch” number.13 This shows the large concentrations
of effort located near the four ports with highest landings, together with breaks between
patches associated with substrate and habitat variation. Tables 2 and 3 show the extent of
spatial mobility across patches in Northern California, and between Southern and
Northern California on an annual basis over the whole sample period. Several interesting
facts can be gleaned from these tables. One can see the open access implications of
opening up the previously unexploited Northern California fishery starting in 1988.
From zero activity in 1987, harvesters from the pool of divers in the Southern California
fishery and elsewhere were drawn rapidly into the new fishery, with over 100 new divers
participating in 1988. The Northern California part of the fishery peaked in 1992 with
358 total divers, of which 108 fished in both regions during the year. During the peak
period, some divers fished in as many as 6-8 Northern California patches during the year,
although the majority concentrated on one or two patches from a single port. As the
Northern California fishery matured and as the unexploited stocks were drawn down and
profitability reduced, fishermen exited, some returning to the Southern California fishery
and other dropping out entirely in response to the stringent limited entry requirements.
Total California-wide numbers dropped from 826 in 1994 to 440 in 1998, whereas in
Northern California, numbers dropped from 358 to about 125 in recent years.
Table 4 shows intra-port mobility over the whole sample period. The mobility
rate can be computed by noting that there are 57,550 dives reported in Northern
California ports for which the diver previously landed in a Northern California port. Of
these, 2,796 were occasions in which the diver landed in another Northern California
port, or about 5% of the occasions. Correspondingly, there were a total of 167,042 total
dives made in both Southern and Northern California in the sample period, including
1682 switches across regions, or about 1%. In the last couple of years, there has been a
slight reduction in average mobility across Northern California ports, and a marked
reduction in large scale mobility between Southern and Northern California regions
compared with the peak period. The Northern California fishery appears to have settled
into a pattern approximating a bioeconomic equilibrium, with harvesters fishing more
intensively to maintain a living under reduced abundance conditions. The average
number of trips per year has increased from about 26 per year in 1992/93 to a current
level of about 34 trips per year. Average depth per dive (mean 35.45 feet over all
years/locations) has similarly increased at a rate of about one foot per year as the
extensive margins have been pushed out from all port locations.
IV.
Modeling Spatial Behavior
In this section, we report results using the logbook/landings ticket-based data set
on divers’ daily spatial behavior to estimate several models of individual choice. It is
convenient to begin with the hypothesis that individual divers make daily choices that
maximize some random utility function:
Uijt = vijt + εijt
13
We do not show the eleventh and southern-most area, which is off the Farallon Island off San Francisco
Bay.
9
= f(Xit, Zi1t, Zi2t, ... , ZiMt; θ) + εijt ,
(1)
where Xit includes harvester-specific and time-specific characteristics that are constant
across choices, Zimt includes choice-specific characteristics such as travel costs and
resource abundance, θ is a parameter vector, and εijt is a random component that is
unobservable to the analyst. The random utility model posits that, given M possible dive
locations, diver i in period t will choose location k if the utility of choice k is higher
than that of the other M-1 choices as well as the choice of not to dive in period t . There
are numerous discrete formulations that capture the essence of spatial decision-making
and are consistent with the random utility formulation. General approaches fall into the
following categories: Multinomial (and Conditional) Logit (MNL), Discrete Choice
Dynamic Programming (DCDP), Random Parameters Logit (RPL), Multinomial Probit
(MNP) and Nested Logit. We use a Repeated Nested Logit (RNL) approach in this
analysis for various reasons.14 First, it can be argued that the structure of the RNL
mimics the decision problem faced by fishermen in this industry reasonably well. In
particular, fishermen actually do make repeated decisions as if there is no time horizon
and without the need to make complicated dynamic decisions. Essentially what changes
from day to day are variables that determine short term expected revenues and variables
that determine weather-related risks associated with participation. Second, the RNL is
relatively easy to estimate with the large size data set we have. Third, we need an
estimation scheme with a closed form solution in order to embed the estimated behavioral
choice model into the bioeconomic simulation model discussed in the next section. The
RNL also has well-known properties that are desirable in general, including the flexibility
to admit different variances at different decision nodes.15
We follow McFadden (1978) by assuming that the εijt is independently and
identically distributed Generalized Extreme Value, and that the utility is linear in
individual- and choice-specific variables so that the following model characterizes
individual choices:

 z jt ' γ
exp
+ x t ' β + (1 − σ)I 

 (1 − σ)
Pr(Go to j ) =
10 

 z kt ' γ
 z kt ' γ 
+ x'β + (1 − σ)I 
 + exp
exp
∑
k =0 

 (1 − σ)
 (1 − σ)
(2)
and
14
On the surface, the choice structure is the same as the RNL proposed by Morey et al. (1993), which deals
with repeated participation and site choice in recreation demand.
15
The drawbacks of RNL are equally well known and include inflexible incorporation of the possibility of
heterogeneity across individuals, and assumptions of independence across time.
10
10
Pr (Do not go ) = 1 − ∑ Pr (Go to k )
k =0
1
=
1 + exp[x t ' β + (1 − σ )I ]
 10
 z ' γ 
where I = ln ∑ exp  kt  .
 (1 − σ ) 
 k =0
(3)
(4)
In the above equations, the i subscripts for the individuals are suppressed since the form
of the model is the same for each individual in the data set. Some characteristics
X could, in principle, vary across individuals. Here β denotes the parameter vector for
characteristics that vary across individuals and or choice occassions but not across
choices, γ is the parameter vector for choices that vary across choices, and (1 - σ) is the
coefficient on the nested logit Inclusive Value.
The nesting structure for the model of daily choices is straightforward and
depicted in Figure 3. On any given open day, divers choose to go or not go fishing. If
they choose to go fishing, they choose among the set of locations. For identification, we
normalize the utility of not going to zero. Note, however, that the utility of not diving
captures the utility of leisure, work opportunities outside of fishing, and the value of
being avoiding exposure to unsafe diving conditions.
Our strategy for estimating the model involved first drawing a random sample of
30 divers followed over the entire period. This relatively smaller sample of 27,000
choice occasion observations was used for preliminary specification testing. We used the
smaller subset to determine the effects of using different backward lags for our
expectations variables, different averaging methods for prices, and the impacts of various
diver-specific variables computed from the data set. We also estimated several
alternative specifications, including RPL models of just the location choice branch, that
are ultimately not usable in our simulation exercise.
In the final analysis, we estimated a parsimonious model, using the entire 401,151
observation data set, containing just the most important explanatory variables. The
estimated parameters are shown in Table 5. Included among variables that are not
presumed choice-specific are three coast-wide weather variables and a day of the week
dummy variable. The weather variables include: WP (wave period), WS (wind speed),
and WH (wave height), all computed as averages over the weather buoy data for the
twelve hour period preceding noon of the day in question. The day of the week dummy
(DWEEK) is one on Friday, Saturday, and Sunday, reflecting reduced propensity to dive
on weekends and on days that precede the Monday closure of the Tokyo Central
Wholesale Market. Variables that are location-specific are distance to the center of the
patch in question (DISTANCE), expected revenue (ER) in each patch, and the Inclusive
Value, computed from the lower level utility branch.16 As Table 5 shows, all variables
16
Some of the methodological issues associated with computing expected revenues are explored in Smith
(2000). Expected revenues reported here are calculated as the product of expected price and expected catch
per trip. The former is a rolling one-month backward looking average across the entire northern California
11
have signs as expected and all are highly significant as one would expect. Since σ is
significantly different from zero, the inclusive value coefficient is less than one. This has
two implications. First, it suggests that the model is consistent with stochastic utility
maximization.17 Second, it suggests that variance of utility for participation and for
location choices are different. This implies that choices across branches of the decision
tree are less similar than choices within each branch of the tree. For example, choosing
between patches 7 and 8 on a given day is more similar than choosing between 8 and not
going fishing on that day.
These estimated nested logit equations may be used to generate simulated short
term effects of changes in economic variables, essentially assuming a time period short
enough so that there is no induced movement of fishermen between ports or between
Southern and Northern California. A short term increase in expected revenues
anticipated in a particular patch k will have a spatial substitution effect as effort is drawn
from other patches. However, the increase in expected revenues in patch k will also have
a participation effect because fishing urchin becomes a more attractive use of time
overall. This participation effect will cause more effort to be distributed over all possible
patches. The upshot is that the own effect of an increase in expected revenues will be
positive. The cross effects may be positive or negative, depending upon whether the
participation effect outweighs the substitution effect. In general, the signs of cross effects
will hinge on all of the variable values, and the substitution effect will be larger for
patches that are visited more frequently (because Pr(k) is higher). Table 6 shows some of
the computed short term elasticities of patch choice with respect to revenues. A 10%
change in expected revenues off patch 8, for example, will result in a short term increase
in total participation of 11.03%. This increase in effort will be distributed mostly to
patch 8 which will experience a 6.2% increase, and in small amount averaging 0.5% to
the other patches.
In order to examine how a permanent or long-term closure might affect a fishery,
it is important to understand that there would be a more elastic response than those
computed for the daily port-specific nested logit model. The long term response would
be larger as fishermen relocated to other Northern California ports that were adjacent to
more open areas, or even to another region such as Southern California if similar closures
were not in effect there. In order to examine port switching activity, we estimate some
port-switching models that aggregate up both geographically and in the time scale of
choices modeled. Since the urchin fishery is a licensed limited entry fishery, we express
the models in term so shares of total licensed divers. In general, port switching and
region switching entail different lumpy costs that will be viewed differently by different
individuals. Divers with families or other attachments to regional infrastructure will view
larger scale move opportunities differently than other more mobile individuals.
Similarly, individual divers may differ in alternative income earning opportunities and
earnings potential in urchin diving in each potential location. For all of these reasons, we
would expect port shares to respond sluggishly to differences in expected earnings
fishery, so that for each day the expected price is based on the average price for the previous 30.4 days.
Expected catch is a patch-specific rolling one-month backward looking average. These proved to be bet fit
in our preliminary specification tests. In addition, one-month averages are convenient for simulating the
model in the next section.
17
McFadden (1979), Daly and Zachary (1979).
12
opportunities across ports and regions. A contemporaneous rent differential may not be
enough to induce individuals to switch ports but if the differential widens or persists, we
might expect switching response.
A convenient way to model sluggish adjustment is with a partial adjustment
framework. Let there be a long term equilibrium share of divers in each port that is a
function of relative opportunities across all options. Then we can write:
s *mt = f
m
(Π t , ..., Π t ; θ m1 ,...,θ mM ),
m = 1 ,..., M ,
(5)
as the equilibrium shares. We posit that actual shares adjust to differences between the
equilibrium shares and last period’s actual shares. With an additive error term, this leads
to:
s mt = λs mt −1 + (1 − λ ) f
m
(Π t , ..., Π t ; θ m1 ,...,θ mM ) + ε mt
(6)
We estimate versions of this model under the assumption that the forcing equations are
linear in expected monthly revenues.18 All alternative specifications involve some ad hoc
assumptions; we choose this one because it allows us to impose sensible restrictions. For
instance, this formulation allows us to impose a sensible restriction that long-run shares
sum to one when there are no expected revenue differentials across ports. One can also
impose symmetry restrictions such as that the increase in shares in one port due to own
port expected revenue increases are balanced exactly by reductions in other ports due to
that revenue change. Finally, a linear formulation is easiest to estimate and most
tractable for our simulations.
In order to estimate the port share equations, we must first generate a proxy for
expected rents, since they are not observed across space and time. We use a structural
approach that generalizes the famous Leslie closed population model (Hilborn and
Walters, 1992). Suppose that biomass evolves over time according to the simple
equation:
X mt = X mt −1 − H mt + Rm
(7)
where X mt is unobservable biomass in patch m at time t, H mt is harvest, and Rm is
mean recruitment of new additions to the biomass. If we define revenues to be:
Rmt = pqEX mt
(8)
18
This is a compromise between consistency and tractability for our simulation modeling. Alternative
models transform the exogenous regressors into the unit interval. Examples include the logistic transform,
used by Miller and Plantinga (1999) to estimate land use shares. One could also use an inverse logistic
transformation of the right hand side with an additive error.
13
where q is a catchability scaling coefficient, p is price per unit harvest, and E is effort,
we may, by recursive substitution arrive at the following equation for catch per trip
( ymt ):
t −1


ymt = qE  X m 0 − ∑ H mτ + tRm 
τ =0


(9)
In reality, catch per trip might persist for some time beyond the decline of abundance
because divers possess information about relative abundance within larger patches. The
persistence of catch per trip might differ across ports because of differences in habitat and
size of the fishable area. A generalization of (9) that allows some persistence is then:
 t −1

ϕ(L ) y mt = β 0 + β1  ∑ H mτ  + β 2 t + ε mt
 τ=0

(10)
This specification makes catch per trip a mean value, corrected for biomass drawdown
with cumulative catch, and corrected for periodic mean recruitment with a time trend.
The auto regressive structure helps purge residual autocorrelation, an especially
important feature since the cumulative catch variable includes data that are lagged values
of the dependent variable. We aggregated data to a monthly level, and corrected for
heteroskedasticity by weighting each regression by the number of trips in each month.
Table 7 presents GLS regressions with lags of catch per trip as additional
regressors. We test for residual autocorrelation by regressing the residuals on right hand
side variables and lagged residuals and performing joint hypothesis tests that the
coefficients on the lagged residuals are zero. The test for residual autocorrelation is
constructed so that the null is no autocorrelation, and we fail to reject the null in all but
Crescent City, which has the fewest observations. The coefficients are nearly all
significant and all have the expected signs consistent with the Leslie population modeling
framework.
We use the above GLS equations to generate projections of expected revenues per
port and across Southern and Northern California ports aggregated together. Catch per
trip forecasts are combined with last month’s mean port price to generate expected
revenues. Since a good fraction of costs are determined with a share system, and since
travels costs per trip are lumped into the constant for each port, anticipated revenues are a
reasonable proxy for fishing profits or rents. These computed anticipated rents are used
in explanatory variables in two port switching share systems. The first is a specification
predicting the share of total harvesters choosing Northern and Southern California in each
month, and the second is a Seemingly Unrelated Regressions system predicting share of
Northern California fishermen in each of the six Northern California ports. We
transform the expected revenue variables by converting them into logs and we impose
restrictions on each specification to identify each model system. The main restriction
imposed is a type of adding up restriction that ensures that the share increase resulting
from a one percent rise in expected revenues in port k is identical to the sum of share
losses in other ports associated with that increase. This is imposed by requiring that:
14
M
∑γ
m =1
mk
=0
In the SUR system, we also impose the restriction that the speed of adjustment is
common within the system, suggesting that inertia against switching ports is the same for
similar decisions, but not necessarily the same as with the North/South decision. With
these restrictions, we drop one equation from each system and recover the parameters of
the dropped equation computationally.
Table 8 summarizes the results for the North/South system and Table 9
summarizes results for the Northern California ports. The North/South port share
equation works well, explaining 82% of the monthly variation in the shares of fishermen
participating in each of the large regions. The model suggests some moderate
responsiveness to revenue differentials, tempered with a fairly sluggish adjustment
process. The implied short run elasticity of shares with respect to changes in either
region’s expected revenues is about 0.10, and the long run elasticity of response is about
0.33.19 The coefficient on the lag (0.861) suggests, for example, that it would take about
a year and a half for shares to reach 90% of any new equilibrium induced by a change in
relative expected revenues. The responsiveness to revenue changes is symmetric and an
F test fails to reject the hypothesis that the coefficients are equal and opposite signed
between the North and South regions.20 The SUR regressions also work well, although
explaining much less monthly variation than the North/South model. The coefficient on
lagged shares (0.436) implies that fishermen move between ports in response to revenue
differentials within Northern California much faster than they move in response to
North/South differentials. A change in permanent expected rents between Northern
California ports would induce an adjustment that would be 90% completed in about three
months, ceteris paribus. For the most part, coefficients on expected revenues are in
accord with a priori beliefs. Three own-revenue coefficients are positive and statistically
significant, one is positive and insignificant, and the other negative and insignificant.
Many of the off-diagonals are negative and significant, but a couple have positive
significant signs. The data on revenues across ports are fairly collinear and hence we
expect that some of the aberrations are due to insufficient relative variation. In the next
section we integrate the nest logit and seemingly unrelated shares models with a dynamic
spatially explicit biological model to forecast the implications of reserve formation with
behavioral response.
V.
An Integrated Bioeconomic Model of Reserve Formation
In this section we outline a spatially explicit and dynamic bioeconomic model of the
sea urchin fishery. The model is innovative in several respects. First, the model is a true
bioeconomic model, integrating a population model of the urchin with a behavioral
model of the harvesting sector so that the equilibria generated are joint bioeconomic
19
The short run elasticity is the gamma coefficient divided by the share and the long run elasticity is the
short run elasticity divided by (1 – λ).
20
The test statistic for an F test is 0.0446, and the critical value is 3.93 at a 5% confidence level.
15
equilibria. Second, the biological model is explicitly spatial and dynamic. We depict the
sea urchin population as a metapopulation of 11 discrete patches, each with its own
natality/mortality and growth parameters. The populations are linked with a dispersal
matrix capable of characterizing any type of qualitative dispersal pattern. We
parameterize the dispersal matrix with parameters calibrated to mimic field observations
of larval settlement along the Northern California coast. Third, the economic model also
explicitly spatial and dynamic. We use the model discussed above to depict industry
behavior as an aggregation of individual choices made by divers, each of which is
presumed responsive to the relative expected profitability of participation and location.
Finally, the economic model of harvester behavior and the biological model are linked
and integrated over both time and space. This allows us to experiment with different
spatially explicit policies, change economic and biological parameters, and trace out both
short run impacts, long run steady state impacts, and the dynamic and spatial adjustments
that take place in transition to steady states.
A. The Metapopulation Model
The metapopulation model developed to examine spatial management policies in the red
sea urchin fishery consists of 11 discrete size-structured populations linked by a dispersal
matrix.21 Each separate subpopulation has a size structure described by a von Bertalanffy
equation, so that the size of an individual of age a in patch j is given by:
(
Size j,a = L∞j 1 − e
−k ja
),
(11)
where j is indexed from 0 to 10, a is indexed as a monthly time index from 1 to 360, and
L∞j and kj are patch specific growth parameters. Note that L∞j is the terminal size of an
individual organism, and this parameter dictates the maximum amount of biomass per
individual. The model begins computations with a set of initial abundance matrices for
each site. The initial abundance matrix in the first period is generally set with all zeros
except for the month zero age class, which is read from an initial distribution file.22 The
populations are then aged by advancing the abundance values for each month to the next
older month so that A i,a = A i,a-1 where A denotes the number of organisms in the cohort.
After the populations are aged, the numbers surviving in the population are computed,
along with the catch. Survival is determined by a Beverton-Holt mortality relationship,
which embeds both patch-specific natural mortality rates m j as well as fishing mortality
rates f j if the size is above the minimum size limit L limit . We link the economic model
of diver behavior to the population model by making monthly fishing mortality rates a
function of predicted diver trips. Accounting for both natural and fishing mortality,
survival of the number of individuals to age a becomes:
21
The metapopulation model is more fully described in Botsford et. al. (1999)
In the simulations performed in the next section, we generally begin with initial conditions that simulate
a non-harvested steady states, which would mimic the situation in 1988 when the northern California
resource first came under exploitation.
22
16
A j,a
 A j,a e -m j
=
-m − f
 A j,a e j j
if Size j ,a < Llim it
(12)
if Size j ,a > Llim it
and total catch (C) consists of the sum of harvests of all sizes greater than the minimum
size over all patches, which is
10 360
C = ∑∑ ( 1 − e
−fj
)w Sizeb j,a A j, a
(13)
,
j =0 a =0
where w and b are allometric parameters relating weight and length. These parameters
essentially convert number of organisms of each size to an aggregate measure of biomass.
Note that for a given organism terminal size, L∞j , there is a corresponding terminal
biomass. This, in turn, implies a maximum possible catch for a given number of
organisms. The allometric parameters give rise to the possibility of a non-convex
production technology whenever b>1, which is the common case.
The metapopulation model also computes egg production, larval dispersal,
settlement and survival. Egg production is computed after survival has been calculated
for each month. If the month is a spawning month, then egg production in patch j is
computed with:
a = 360
ej=
∑
a =0
α x β A j,a
Size j ,a
where x = 
0
if Size j ,a > Lmaturity
if Size j ,a < Lmaturity
.
(14)
This equation sums the egg production from each size class, where there is only positive
production for sizes greater than the size at reproductive maturity. The exponent on the egg
production parameter is greater than one, since egg production increases exponentially with
size.
After eggs are produced, they are distributed spatially over the system, using a
dispersal matrix which can take on a number of different qualitative forms. During the
months in which larval dispersal is assumed to take place, settlement of larva is calculated.
For each month of the egg production period, a fraction of egg production is presumed to
survive and this is distributed via the dispersal matrix from each of the patches to each
individual patch according to:
s in = pDe
(15)
This 11x1 vector gives the array of settlement associated with the array of egg production
from the system, modified by the survival probability p, and distributed by the dispersal
matrix D. If all of the patches cover all possible dispersal sites, then the rows of D sum to
one. Beyond that possible restriction, D is general and can characterize a variety of
dispersal mechanisms. One particularly important dispersal mechanism is uniform
dispersal. This refers to situations in which the production of larvae in each location
17
redistributes uniformly over the entire system, often referred to a common larval pool
assumption.
The number that actually end up settling successfully is then assumed to follow a
stock-recruitment function, namely:
s inj
out
(16)
s j = −1
a + c −1 s inj
This specification enables the model to simulate various density dependent larval survival
mechanisms in the system, all of which may be patch specific. Once the settlement is
out
calculated for any given site, the successful settlers ( s j ) become the next period’s age zero
entry and the growth process starts again. Appendix A contains baseline values of the
parameters that we used to calibrate the spatial biological model. The parameters are based
on ongoing field work being conducted off the coast of northern California by colleagues
investigating the sea urchin in a joint long-term research program.23 Raw data on growth
increments and adult size distributions have been gathered in dive transects at several
exploited and unexploited sites along the coast. These have been used to compute growth
and natural mortality coefficients using maximum liklihood techniques. We have also been
using larval counts from brush collectors that trap larvae on a continuous basis and
correlating these settlement patterns with sea surface, wind, and current patterns on a fine
time scale to understand disperal processes. The dispersal matrix used here is calibrated to
reflect our best available understanding of current patterns and their impacts on larval
settlement off the northern California coast.
B. Simulating Spatial Policies: Spatial Response Elasticities
To simulate the implications of spatial closures, we combined the spatially explicit
biological model with the model of spatial behavior estimated with the logbook/landings
ticket data base. The key link in the integrated model is the connection between monthly
fishing mortality in each patch f jt and monthly trips, or:
4
f jt = (Trips jt )hq = (ot ∑ d p p pjt )hq )
p =1
where h is diving hours per trip, q is the scaling or catchability coefficient, ot is the number
of choice occasions in that month24 , d p is the number of divers in port p , and p pjt is the
probability of a trip from port p to patch j in month t. We presume h is fixed across all
ports and time periods, and we use q to calibrate model forecasts to actual aggregate
harvests. For short run projections, we fix the number of divers in each port and project
23
This work is reported in various sources, including Botsford et. al (1994), Morgan (1997), Smith et. al.
(1998), Botsford et. al. (1999), Morgan et. al. (2000), and Wilen et. al. (2002).
24
Choice occasions are determined by the season closure regulations, generally the same across all northern
California ports.
18
diver participation and spatial choices for each port using probabilities from the nested logit
model. For long run projections, we allow the number of divers per port to be endogenous,
using the SUR port share and North/South share results. In all simulations, since expected
revenues are rolling one month backward averages, we use actual lagged catch per trip
multiplied by an exogenous price to predict trips and shares of divers in each location. In
the simulations reported here, we use a stylized and reduced-dimension model that focuses
on four ports.25
Table 10 shows the implication of short and long term adjustments of effort to
changes in revenues in terms of elasticities. Columns one and two take patch choice
probabilities as given, and assume that there is no adjustment at the intra-port level. All
elasticities are inelastic, not surprising given the infrequency of port switches. Column one
shows, for example, that a 10% revenue increase in patch 8 would induce a 0.9% increase in
trips to patch 8 in the very short run. Without further changes in divers in ports off patch 8,
there would be an intermediate run adjustment involving patch switching toward patch 8 as
well as some increase in participation, shown in column 2. The combined effects of these
inter patch substitutions would raise the responsiveness to 1.78% Over the long run, a
persistent increase in patch specific revenues would draw divers to nearby ports, as well as
divers from southern California. Columns 3 through 5 show the increase in response
elasticities associated with allowing inter-port and inter-region movement. With both port
adjustment and full adjustment within and across patches in each port, elasticities rise to
multiples of the short run elasticities. Long run elasticities with full adjustment are mostly
in the unitary to elastic ranges, with differences reflecting the number of divers and trips in
each patch. For example, the heavily fished areas in patches 7 and 8 show response
elasticities of 1.014 and 0.876 respectively, whereas lightly fished patches 3 and 4 have
elasticities of 1.588 and 1.784 respectively.
C. The Importance of Behavior
To understand how economic behavior matters to the forecasts of impacts of
marine reserve formation, we compare simulations of the integrated bioeconomic model
(the ECON model) with a standard biology only model that we dub the NOECON model.
To keep things simple, we start with the less elastic model that forecasts patch choice and
participation with the nested logit specification only, and not the port switching model.
These models are closer to being identical, except that fishing mortality is made
endogenous and dependent upon economic conditions in the ECON model. The
NOECON model assumes constant total fishing effort before and after reserve formation
and it is assumed (as typical in biological modeling) that effort is distributed uniformly.
We incorporate a dispersal pattern that mirrors our current thinking about coastal
oceanography off northern California. In particular, correlations of larval settlement in
our collectors with weather events suggest that there are two gyres, one off Point Reyes
(just south of Bodega) and one west of Point Arena. During upwelling events, larvae are
swept south into the gyres and then are swept back and redistributed in weather relaxation
25
The two northern- and southern-most ports of Half Moon Bay and Crescent City are excluded, leaving
Bodega, Point Arena, Fort Bragg, and Albion. Both excluded ports handle smaller amount of urchin. The
reduced dimension port share system uses the estimated adjustment parameter for North/South choices, and
incorporates symmetric off-diagonal coefficients for the substitute ports.
19
events. This combined advection/upwelling mechanism appears to collect larvae in the
two pools and then deposit them non-uniformly, with more deposited close to the gyres
and less deposited as distance increases.
Figure 4 shows how the integrated model calibrates with the actual harvest path
during the drawdown of the northern California urchin population over the past decade.
We adjust the catchability coefficient to mimic actual harvests and then simulate the
integrated model out to a steady state. We incorporate assumptions that mirror
regulations in place, including seasonal and weekly closures and a minimum size limit of
3.5 inches. Table 11 shows the results of the simulations, including simulations of
closures of patch 8, the heavily fished area off Fort Bragg.26 There are several important
points to glean from this table about how incorporating behavior matters. First, the
NOECON model dramatically overstates the extent of decline when calibrated to the
drawdown phase of early fishery exploitation. The intuition for this is obvious once
stated. Early in a fishery’s development, abundance is high and revenues are high,
drawing large amounts of effort into the fishery. This results in a drawdown phase that
ultimately overpredicts the amount of effort and fishing mortality that will remain after a
steady state is approached. For example, the NOECON model predicts a steady state
harvest of only 386 thousand pounds and a dramatically reduced egg production
reflecting the assumed low reproductive potential of the overexploited biomass. In
contrast, the ECON model continuously adjusts effort to profitability. As the fishery is
drawn down, effort exits and fishing mortality falls, generating an ultimate steady state
that is much larger. Under the ECON scenario, the steady state harvest is more than
double the NOECON prediction, at 830 thousand pounds. Perhaps more importantly, the
predicted egg production is almost five times that predicted with the NOECON model.
The higher egg production emerges from two sources. First, since overall exploitation is
lower, total reproductive biomass and egg production are larger. But second, the ECON
model predicts a spatial distribution of effort that depends upon relative spatial profits.
Areas that are high cost (eg. more distant) will be lightly exploited and hence will serve
as de facto “reserves”, even without closures.27
Table 11 also shows how misleading biological models without behavior may be
about the impacts of reserve formation. For example, the NOECON model calibrated to
the approach path predicts that a closure of patch 8 will produce a 40% increase in steady
state harvest, coupled with a 48% increase in system wide egg production. In the
NOECON model, it is assumed that displaced effort adjusts immediately an in full
numbers to the remaining open areas. Thus total harvest falls to zero in the closed area
but increases in the open areas. Whether the loss over the whole adjustment period is
made up by the corresponding gain depends on initial conditions and adjustment speeds.
In this simulation, regardless of whether there is an initial net loss, it is compensated over
the whole transition path because the present value of a closure is positive. Contrast
26
We use patch 8 to demonstrate the impacts of closures mainly because most literature suggests that
reserves are likely to be beneficial to fisheries production in two instances: a) either when the closed patch
is heavily exploited; or b) when the closed patch operates as a source rather than a sink. The gyre pattern
and north-south pattern of larval flow makes patch 8 a type of source, although the definition is not always
clear in the literature.
27
The steady-state spatial coefficient of variation for NOECON is 0.28 whereas for ECON it is 0.43. We
know that spatial variation in the NOECON model must be due to net larval dispersal differences. In the
ECON model, spatial variation is also due to differential fishing effort responding to differential rents.
20
these results with the ECON case, which makes the transition and ultimate steady state
dependent upon relative profits. In the ECON simulation, a closure of patch 8 results in a
10% loss in steady state harvests, in addition to the transition losses associated with the
closure. The result is that discounted revenues fall by 14%, rather than rise as predicted
by the NOECON model. The importance of incorporating economic behavior into
models intended to forecast the implications of reserves is thus profound. Importantly,
the assumptions of uniformly distributed and unresponsive effort used in virtually all of
the biological literature bias predictions toward overly pessimistic status quo harvest and
egg production predictions, and overly optimistic predictions of harvest gains and the net
economic costs of reserve formation.
While calibrating a biological model incorrectly during the drawdown phase is
one source of difference between NOECON and ECON predictions, it is not the only
source. Suppose, in contrast, that a fishery that has adjusted to a steady state is modeled
and calibrated to (lower) steady state effort levels. The third section of Table 11 shows
what the NOECON model calibrated to steady state harvests would predict as response to
closures. In this case, the NOECON model still predicts a steady state harvest gain,
although much smaller than the approach path calibrated model. The smaller ultimate
harvest gains are not enough to compensate for initial harvesting losses in the closed
patch, however, and hence the system-wide present value of revenues falls. A more
important difference may be in predicted egg production from the system. Because the
NOECON model assumes uniform effort distribution, the whole system’s reproductive
biomass is drawn down relatively uniformly to establish the status quo. In contrast, the
ECON model predicts a heterogeneous distribution of effort reflecting distance from
ports and other costs of remote patches. These act as defacto sources, hence contributing
to predictions of overall egg production that are larger than the NOECON model.
Figures 5 and 6 make clear how this arises. These figures show the steady state size
distributions and egg production from a heavily exploited patch and from a closed patch.
The closed patch has a wider age distribution with more larger individuals that
exponentially produce more eggs in total. These depict how the de facto closures
associated with relatively uneconomic patches can contribute in important ways to a
system’s egg production.
Table 12 shows that siting decisions may also look different, depending upon
whether economic behavior is accounted for or not. This table shows the implications of
siting reserves in various different patches in order to achieve different objectives such as
harvest gains and system reproductive capacity gains. The NOECON model is calibrated
to the same steady state harvest level as the ECON model, but with uniform effort
distribution. Again, the ECON model predicts a drop in steady state harvests whereas
the NOECON model predicts increases with certain patch closures. Decreases in
harvests are predicted in the NOECON model from closures of the southern-most patches
and in patches in the southern gyre around Point Arena. In contrast, in the ECON model,
closing those patches is least costly in term of harvest lost, because they are most lightly
exploited before the reserve. In terms of total system-wide egg production, the gains
predicted by the ECON model are not as large proportionately as those predicted with the
NOECON model. The NOECON model predicts relatively large egg production gains in
patches 1 and 2, but mainly because the model overpredicts harvest pressure in those
relatively unprofitable patches. The ECON model predicts relatively large egg
21
production gains from closing patch 2, but because it is lightly exploited and a large
contributor to the first gyre. Large egg production gains are also predicted from closing
patches 6, 7, and 8, but for different reasons. Patch 8 production gains come from closing
a heavily exploited area, but patch 6 gains come from its critical role as a source feeding
the second gyre. Overall, then, the rankings of best sites appears to depend upon both
economic and biological dispersal. Ignoring economic dispersal seems to have critical
effects on site choices, often missing the true configuration of the pre-reserve status quo,
or mis-predicting eventual larval dispersal and harvest adjustments by failing to
anticipate the behavioral response to closures.
D.
Port Switching and Long-run Behavior
The simulations and comparisons between ECON and NOECON models reported
above are mostly computed from steady states calibrated using a simple model of spatial
behavior without port switching. In the long term, this fishery will tend toward an
equilibrium reflecting balancing of economic opportunities across patches, across ports,
and between northern and southern California. To understand how these more flexible
opportunities to adjust in response to closures matter, we now examine a more
comprehensive bioeconomic model that allows port switching behavior. The long run
model is calibrated to reflect the long run regulatory goal of having 300 divers in the
fishery. There is currently in place a limited entry program that induces attrition through
minimum landings requirements and license fees. Our port choice models distribute a
fixed number of total divers across the two northern and southern regions, and then
across the ports in the northern region. We calibrate to a steady state that begins with
about 130 divers making about 30 trips per year. The remainder of the 300 divers are
assumed to locate in southern California.
Table 13 shows how increases in mobility affect the steady state and changes
associated with a closure of patch 8, with the first two rows repeating results from the
previous section. By introducing port switching, the long run steady state begins with a
smaller exploitation rate on the northern California stocks. The number of divers falls,
although diving intensity is predicted to rise so that divers fish more days per season.
Since the model without port switching is calibrated to current conditions including diver
numbers close to 400, part of the difference in predictions arises out of the hypothesized
long run reduction in number of about 25%. The remainder of the predicted reduction
comes from divers rearranging their numbers to arbitrage opportunities across northern
California ports, as well as switches to southern California. The model probably
overpredicts switches to southern California because we have not endogenized the urchin
population model to incorporate southern California biology. We thus parameterize
returns in southern California to predict north/south shares. If divers actually did shift in
large numbers, we would expect returns in southern California to fall, mitigating the
profit differentials. In the third group of results in Table 13 we show how steady states in
the northern California system would adjust with port switching. These are probably
more realistic ranges, given the parameters of both the biological and economic models.
Can reserves ever pay off in this system? The results of our simulations with and
without port switching suggest that it is unlikely that reserves pay in this system from the
perspective of the fishing industry. Adding more layers of spatial mobility does not
22
change the fundamental structure of the problem, either in the steady state or in transition.
Our results confirm the analytical results of Sanchricio and Wilen (2002), namely that
reserves are unlikely to increase aggregate harvests unless the fishery begins with a
dramatically overexploited status quo. As they argue, there are two forces in play in
those circumstances. First, with a highly overexploited reserve designate patch, the
opportunity costs of closure are low. Second, as an overexploited population is rebuilt, it
is more likely to have large payoffs in some dispersal systems (eg. density dependent
migration). To further test these conclusions we experimented with two other situations
designed to produce initial overexploitation. The fourth and fifth groupings in Table 13
show these simulations. In the fourth, we double ex-vessel prices and arbitrarily alter the
participation equation of the nested logit almost four fold. This results in an
overexploited system in the initial steady state, and as a result, a closure in patch 8
actually increases steady state harvests. However, the approach to the new steady state is
slow, and the present value of revenues still drops as a closure is instituted. In the fifth
set of results, we open movement up to port switching and region switching and perturb
the southern California returns to generate high exploitation rates in the north. This
scenario again fails to make reserves produce an economic return.
VI.
Summary and Conclusions
This paper discusses the economic impacts of marine reserve creation, with
particular attention to the role that economically motivated behavior plays in determining
outcomes. We address a potentially important shortcoming of the vast marine reserves
literature, namely the assumption that effort is fixed and uniformly distributed. Instead,
we presume that effort in complex and realistic settings responds to economic incentives,
particularly differential profit opportunities that are dynamic and spatial. To address the
importance of behavior, we construct and estimate a series of spatial choice models using
a comprehensive data base from logbooks and landings tickets. It is important to point
out that these data are collected by fisheries scientists to guide regulatory decisions rather
to aid economic research per se. Nevertheless, we show how this kind of data can also be
used to examine economic choices in informative ways. Our spatial models address
behavior across a range of time and spatial scales and at different levels of aggregation.
We characterize the most important of these as short- and long-run models, the former
taking place on fine (daily) scale and the latter taking place on longer (monthly and
yearly) scales.
The spatial models confirm what we would expect, namely that divers respond to
differences in returns expected in different patches. The nested logit models show that
fishermen respond negatively to weather risk and travel distance, and positively to
expected returns, affected by both relative abundance and expected price. Although
divers actually choose to participate only about 11% of the time, even a parsimonious
model successfully explains a reasonable fraction of the variance in behavior. We link
compliment the nested logit daily choice models with two systems of share equations
designed to predict the share of total effort by port in northern California, and the share of
divers locating in northern and southern California. Effort elasticities are reasonable and
exhibit inelastic response in the short run to patch-specific expected revenue changes, and
more elastic long run response allowing for port and region switching.
23
We link the spatial models of choice behavior to a biological model intended to
capture the most important features of our case study. The biological model is cutting
edge, and is one of the first to depict a multi-patch system with explicit hypotheses about
larval dispersal. Most existing literature uses two patch models; ours is an eleven patch
system calibrated with parameters derived from field data. A unique feature of the
biological model is it incorporation of the “dual gyre” nature of coastal circulation in
northern California. This feature represents the most current thinking about dispersal
processes affecting urchin larvae and it adds detail and complexity that generate new
hypotheses about reserve impacts and reserve siting questions. We simulate the model on
a monthly time scale and the output from the model consists of aggregates such as
system-wide egg production, total harvest, and current and present values of revenues, as
well as patch specific system characteristics. Only a handful of papers consider the role
of larval dispersal analytically; this paper is among the first to calibrate it empirically.
Our results confirm that economic behavior is a critical determinant of the
predicted impacts of reserves. Moreover, we show that the typical assumptions made by
biologists for analytical tractability consistently bias the predicted impacts in a manner
that makes reserves look more favorable than they actually might be. For example, a
model that calibrates fishing mortality during a drawdown phase will consistently
overpredict the extent of overexploitation compared with an economically based model
that incorporates the natural decline in profitability as the steady state is approached.
Since aggregate harvest is more likely to be increased in overexploited fisheries, results
based on mis-calibrated fishing mortality are likely to be favorable. However, we also
show that even without drawdown phase mis-calibration, the assumptions of uniform
effort rather than economically motivated effort are likely to produce mistaken
characterizations of reserve siting in realistic settings. We show, for example, that some
remote or high cost or high risk areas are naturally less profitable and hence exploited
less by fishermen. These patches form de facto reserves and hence contribute to overall
egg production in ways not revealed by simpler uniform effort distribution models. The
manner in which they contribute to both harvest and system reproduction is complicated,
however, because their role depends upon economic, biological, and oceanographic
factors. And the remoteness of particular patches is relative and dependent upon fishery
independent factors such as port location and roadways.
Our overall conclusions about the usefulness of reserves as a marine policy tool
are at variance with the received wisdom in the biological literature for reasons discussed
above. Our conclusions are more in accord with the very small amount of economic
analysis that has been devoted to the topic. We find, as did Holland and Brazee in an
early analysis, that reserves are more likely to produce harvest gains in an age structured
model when the biomass is severely overexploited. We also find, as Holland and Brazee
did, that even when steady state harvests are increased with a closure, the discounted
returns are often negative reflecting slow biological recovery relative to the discount rate.
We find results that confirm the Sanchirico and Wilen analytical work that show that
easily exploited (low bioeconomic ratio) patches are most likely to be the best sites to
produce both harvest and reproductive potential gains. Sanchirico and Wilen also have
results pertaining to dispersal processes, but in a model in which (implicitly) only adults
and juveniles migrate. The model used in this paper depicts a much richer and more
realistic scenario in which dispersal is driven by oceanographic transport of larvae. Most
24
marine biologists believe that larval transport mechanisms are likely to be more important
and more realistic determinants of dispersal in marine spatial systems than adult
migration. We show that some of the notions about site selection currently in vogue
appear to be based on naïve views of spatial dynamics that fail to incorporate fisher
behavior. In particular, whether a particular patch is a source or sink depends very much
on its relative level of exploitation as well as its physical placement in an oceanographic
system. Patches with high intrinsic productivity in an unexploited system or a lightly
exploited system may be less productive to the system as a whole when differential
harvesting pressure (driven by relative economic opportunities) affects the spatial
distribution of abundance and hence larval production. These results suggest, in contrast
to the tone of recent dialogue among marine scientists about reserves, that there are still
unanswered questions about whether they can deliver what is promised by simple
modeling. At the very least, our integrated bioeconomic modeling efforts raise some new
questions about whether oceanographic dispersal is the key driver of closure impacts, or
whether harvester dispersal may be equally important.
References
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Marine Resource Economics 13, 159-170.
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Hastings, Alan and L. Botsford (1999). “Equivalence in Yield from Marine Reserves and
Traditional Fisheries Management”. Science, 284.
Hilborn, Ray and Carl J. Walters (1992), Quantitative Fisheries Stock Assessments:
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Holland, Daniel S. and Richard J. Brazee (1996), “Marine Reserves for Fisheries
Management,” Marine Resource Economics 11, 157-171.
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Stongylocentrotus franciscanus, Fishery: Catch, Effort, and Management Trends,"
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Marine Fisheries Review 47:3, 1-20.
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Convservation: Lessons from History”, Science, 260: 17-18.
McFadden, Daniel (1978), “Modeling the Choice of Residential Location,” in Spatial
Interaction Theory and Residential Location, Amsterdam: North-Holland.
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Behavioral Travel Modeling, London: Croom Helm, 279-318.
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Journal of Agricultural Economics, 81, 180-194.
Morey, Edward R., Robert D. Rowe, and Michael Watson (1993), "A Repeated NestedLogit Model of Atlantic Salmon Fishing," American Journal of Agricultural
Economics 75, 578-592.
Morgan, Lance. (1997). Spatial Variability in Growth, Mortality and Recruitment in the
Northern California Red Sea Urchin Fishery, Ph.D. Dissertation, University of
California, Davis.
Morgan, Lance, Stephen Wing, Louis Botsford, Carolyn Lundquist, and Jennifer Diehl
(2000). “Spatial Variability in Red Sea Urchin Recruitment in Northern California”,
Fisheries Oceanography, 9(1), 83-98.
Polacheck, Tom (1990). “Year Around Closed Areas as a Management Tool”, Natural
Resource Modeling, 4(3), 327-353.
26
Quinn, James F., Stephen R. Wing, and Louis W. Botsford (1993), “Harvest Refugia in
Marine Invertebrate Fisheries: Models and Applications to the Red Sea Urchin,
Strongylocentrotus franciscanus,” American Zoologist 33, 537-550.
Sanchirico, James N. and James E. Wilen (1999), "Bioeconomics of Spatial Exploitation
in a Patchy Environment,” Journal of Environmental Economics and Management,
37: 129-150.
Sanchirico, James N. and James E. Wilen (2002), "Bioeconomics of Marine Reserve
Creation”, Journal of Environmental Economics and Management, 42(3).
Smith, Barry, Louis W. Botsford, Stephen Wing. (1998). “Estimation of Growth and
Mortality Parameters from Size Frequency Distributions Lacking Age Patterns: the
Red Sea Urchin (Strongylocentrotus franciscanus) as an Example”, Canadian Journal
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Challenges of Empirical Modeling," American Journal of Agricultural Economics
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Avoiding Surprises: Incorporating Fishermen Behavior into Management Models”,
Bulletin of Marine Science (forthcoming).
27
Table 1
Number of Diving Trips by Northern California Port
1988-1997
Latitude
Bin
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
18
21
25
Total
HMB
3
572
18
45
28
2
3
BOD
32
1
32
62
748
596
6,055
752
39
9
16
19
1
PTA
ALB
CRC
Total
% of Trips from
Port in Bin
3
282
3
604
19
77
93
750
599
6,475
5,920
7,877
6,674
13,172
6,705
2,643
217
113
39
18
291
0%
95%
0%
0%
0%
0%
0%
94%
0%
96%
0%
36%
98%
0%
0%
0%
0%
0%
97%
285
52,289
49%
3
2
394
5,002
7,556
333
104
41
30
1
10
47
151
5,416
4,692
56
19
2
671
FTB
8
1
8,370
13,466
10,394
13
119
131
914
8,360
6,589
2,593
217
111
39
15
19,101
Notes:
The boxed numbers indicate that the port is located in that bin.
There is no activity in bins 17, 19, 20, 22, 23, and 24.
28
Table 2
Diver Spatial Mobility Across Patches
Number of Active Divers
# of Patches
Active In
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
50
44
20
10
4
1
0
0
0
0
0
60
51
19
8
0
0
0
0
0
0
0
146
72
59
36
20
6
2
0
1
0
0
139
72
60
32
23
12
8
4
3
0
0
139
62
52
36
38
13
15
3
0
0
0
99
65
46
32
18
15
9
0
0
0
0
107
67
45
25
13
13
2
0
0
0
0
49
48
30
21
15
3
1
1
0
0
0
37
44
25
21
0
4
0
0
0
0
0
36
45
33
22
7
3
0
0
0
0
0
43
33
27
18
5
3
1
0
0
0
0
43
39
24
9
9
1
0
0
0
0
0
Total Divers
129
138
342
353
358
284
272
168
131
146
130
125
Weighted Average
# Patches
2.05
1.82
2.25
2.53
2.68
2.60
2.33
2.54
2.35
2.51
2.40
2.24
1
2
3
4
5
6
7
8
9
10
11
Table 3
Diver Spatial Mobility Across
Northern and Southern Regions
Number of Active Divers
Year
Total
Divers
Just S. Cal.
Divers
Just N. Cal.
Divers
Just One
Region Divers
Both Regions
Divers
Share in
Both Regions
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
210
387
684
735
714
738
826
539
524
525
440
465
81
249
342
382
356
454
554
371
393
374
306
336
117
113
272
260
250
186
191
106
77
95
109
108
198
362
614
642
606
640
745
477
470
469
415
444
12
25
70
93
108
98
81
62
54
56
25
21
0.06
0.06
0.10
0.13
0.15
0.13
0.10
0.12
0.10
0.11
0.06
0.05
29
Table 4
Port Switches
To
ALB BOD CRC FTB HMB PTA SOC
From
ALB
BOD
CRC
FTB
HMB
PTA
SOC
24
3
328
14
194
129
26
3
1
324
60
10
3
68
31
175
233
11
6
Total
692
536
29 1206
19
32
8
6
9
525
278
6
9
193
182
7
527
7
Total
121
208
6
247
9
203
686
507
29
1184
70
1114
888
794
4478
233
72 1149
Table 5
Nested Logit Estimates
Not Location-Specific
Variable
Coefficient
Standard
Error
Z - statistic
Constant
WP
WS
WH
DWEEK
1.06
-0.18
-0.11
-0.74
-0.74
0.048
0.005
0.003
0.011
0.012
22.21
-34.69
-36.69
-70.36
-60.02
Coefficient
Standard Error
Z - statistic
-7.27
0.08
0.22
0.036
0.001
0.027
-203.72
65.17
8.34
Location-Specific
Variable
DISTANCE
ER
σ
Log-likelihood
Observations
Pseudo R2 (1)
2
Pseudo R (2)
-189,878
401151
0.21
0.81
Pseudo R2 (1) is based on the log-likelihood in a Conditional Logit Model with choice-specific constants.
Pseudo R2 (2) is based on the log-likelihood of n*ln(1/J), where J = 12 possible choices.
30
Table 6
Nested Logit Cross-Revenue Elasticities
Mid-week distance adjusted
1% Change in ERj
j
0
%
Change
in Pk
k
0
1
2
3
4
5
6
7
8
9
10
Net Change in PGO
1
2
3
4
5
6
7
8
9
10
1.515
0.130
0.117
0.119
0.117
0.124
0.126
0.129
0.130
0.126
0.104
0.042
0.598
0.045
0.046
0.045
0.048
0.049
0.050
0.050
0.049
0.041
0.085
0.093
1.212
0.094
0.093
0.098
0.100
0.102
0.103
0.100
0.083
0.080
0.097
0.088
1.145
0.088
0.093
0.094
0.097
0.097
0.094
0.078
0.086
0.104
0.094
0.095
1.221
0.099
0.101
0.103
0.104
0.101
0.084
0.065
0.080
0.072
0.073
0.071
0.938
0.077
0.079
0.079
0.077
0.064
0.058
0.071
0.064
0.065
0.064
0.067
0.836
0.070
0.071
0.069
0.057
0.047
0.057
0.051
0.052
0.051
0.054
0.055
0.672
0.057
0.055
0.046
0.043
0.052
0.047
0.048
0.047
0.050
0.051
0.052
0.620
0.051
0.042
0.058
0.071
0.064
0.065
0.064
0.067
0.069
0.070
0.071
0.837
0.057
0.112
0.136
0.122
0.124
0.122
0.129
0.131
0.134
0.135
0.131
1.580
2.736
1.063
2.163
2.051
2.190
1.675
1.491
1.196
1.103
1.492
2.857
Table 7
GLS Structural Model of Expected Catch Per Trip
Coefficient
SOC
HMB
BOD
PTA
ALB
FTB
CRC
Intercept
96.82
(1.06)
3607.34
(8.7)**
2455.42
(7.55)**
913.60
(3.57)**
426.29
(2.55)**
1021.66
(4.52)**
1869.89
(2.14)**
Cumulative Catch
-9.07E-06 -0.006142 -0.000213 -9.32E-05
(-1.99)** (-3.81)** (-6.31)** ('2.78)**
Time Trend
7.72
(1.86)*
ymt-1
15.27
(1.49)
-8.05E-05 -0.000073 -0.010859
(-2.09)** (-4.92)**
(-1.72)*
12.90
(3.84)**
9.03
(2.21)**
4.71
(1.84)*
8.26
(4.67)**
28.32
(1.28)
0.61
(7.51)**
0.62
(7.85)**
0.66
(6.63)**
0.65
(10.91)**
0.87
(10.99)**
0.52
(4.16)**
ymt-2
0.21
(2.24)**
-0.23
(-2.97)**
0.04
(0.35)
0.09
(1.73)*
-0.11
(-1.51)
ymt-3
0.09
(1.05)
Observations
R-Square
143
0.916
71
0.414
123
0.871
116
0.888
116
0.856
122
0.943
34
0.838
F (for residual autocorrelation)
F Critical
2.01
2.44
0.97
2.52
1.46
2.45
1.07
2.46
0.90
2.46
1.60
2.45
2.75
2.74
t-statistics are in parentheses under the coefficients.
* indicates significant at the 10% level and ** at the 5% level.
31
Table 8
South/North Switching OLS Model of Port Shares
Variable
Parameter
Coefficient
t-statistic
Constant
α
0.028061
Lagged SOC Share
λ
0.861212
17.242 **
ln(RSOC)
γ SOC
0.056192
1.6678 *
ln(RNOC)
γ NOC
-0.050767
-1.908 *
0.151
R2
0.8231
n
111
** indicates significant at the 5% level and * indicates the 10% level.
Table 9
SUR Results for Northern California Port Switching
V a ria b le
P a ra m eter
C o efficien t
t-sta tistic
D iv er sh a re fo r:
H a lf M o o n B a y
α
C o nstant
HMB
0 .0 3 6 0 0 8
λ
0 .4 3 6 3 8 5
0 .7 1
1 0 .3 7 **
L agge d H M B S hare
ln(R H M B )
γ
H M B ,H M B
0 .0 0 9 2 9 5
ln(R B O D )
γ
H M B ,B O D
-0 .0 1 1 4 1 8
-1 .1 3
-0 .2 4
2 .2 9 **
ln(R P T A )
γ
H M B ,P T A
-0 .0 0 1 9 8 3
ln(R A L B )
γ
H M B ,A L B
0 .0 0 2 1 1
0 .1 6
ln(R F T B )
γ
H M B ,F T B
-0 .0 0 6 5 7 3
-0 .5 7
ln(R C R C )
γ
H M B ,C R C
0 .0 0 6 4 4 1
1 .4 0
B o d eg a
α
C o nstant
-0 .5 8 8 0 5 8
HMB
λ
0 .4 3 6 3 8 5
-4 .3 8 **
L agge d B O D S hare
ln(R H M B )
γ
B O D ,H M B
0 .0 0 5 3 9 2
0 .5 0
ln(R B O D )
γ
B O D ,B O D
0 .0 2 0 2 2 6
0 .7 6
ln(R P T A )
γ
B O D ,P T A
0 .0 3 8 5 6 2
1 .7 9 *
ln(R A L B )
γ
B O D ,A L B
-0 .0 9 3 3 0 1
-2 .7 1 **
ln(R F T B )
γ
B O D ,F T B
0 .1 4 3 5 6 9
ln(R C R C )
γ
B O D ,C R C
-0 .0 0 8 3 3
-- restric ted --
4 .6 9 **
-0 .6 9
P o in t A ren a
α
C o nstant
PTA
0 .5 2 4 7 7 7
λ
0 .4 3 6 3 8 5
2 .6 0 **
L agge d P T A S hare
ln(R H M B )
-- restric ted --
γ
P T A ,H M B
-0 .0 1 8 3
-1 .1 5
ln(R B O D )
γ
P T A ,B O D
-0 .0 0 1 5 6 6
-0 .0 4
ln(R P T A )
γ
P T A ,P T A
0 .0 6 8 0 6 4
ln(R A L B )
γ
P T A ,A L B
-0 .0 6 5 8 8 8
-1 .2 9
2 .1 3 **
ln(R F T B )
γ
P T A ,F T B
-0 .0 5 2 1 6
-1 .1 4
ln(R C R C )
γ
P T A ,C R C
0 .0 0 0 8 5 1
0 .0 5
32
Table 9
SUR Results for Northern California Port Switching (cont’d)
Variable
Parameter
Coefficient
t-statistic
Albion
Constant
α ALB
0.424906
2.99 **
Lagged ALB Share
ln(RHMB)
λ
0.436385
γ ALB,HMB
-0.013528
-1.19
ln(RBOD)
γ ALB,BOD
-0.056048
-2.00 **
ln(RPTA)
γ ALB,PTA
-0.043831
-1.93 *
ln(RALB)
γ ALB,ALB
0.103488
2.86 **
ln(RFTB)
γ ALB,FTB
-0.067638
-2.10 **
ln(RCRC)
γ ALB,CRC
0.033086
2.56 **
α FTB
0.15705
Lagged FTB Share
ln(RHMB)
λ
0.436385
γ FTB,HMB
0.019082
1.17
ln(RBOD)
γ FTB,BOD
0.048374
1.17
ln(RPTA)
γ FTB,PTA
-0.064931
ln(RALB)
γ FTB,ALB
0.047362
0.90
ln(RFTB)
γ FTB,FTB
-0.011484
-0.25
ln(RCRC)
γ FTB,CRC
-0.027462
-1.48
α CRC
-- restricted --
Fort Bragg
Constant
0.77
-- restricted --
-1.99 **
Crescent City
Constant
0.008932
-- recovered --
Lagged CRC Share
ln(RHMB)
λ
0.436385
-- recovered --
γ CRC,HMB
-0.001941
-- recovered --
ln(RBOD)
γ CRC,BOD
0.000432
-- recovered --
ln(RPTA)
γ CRC,PTA
0.004119
-- recovered --
ln(RALB)
γ CRC,ALB
0.006229
-- recovered --
ln(RFTB)
γ CRC,FTB
-0.005714
-- recovered --
ln(RCRC)
γ CRC,CRC
-0.004586
-- recovered --
R2 (System Weighted)
0.357
n
555
** indicates significant at the 5% level and * indicates the 10% level.
33
Table 10
Elasticities With and Without Port Model
Trips to Patch j with Respect to Revenues in Patch j
Elast.
1
Elast.
2
Elast.
3
Elast.
4
Elast.
5
Mean Revenues
Farallons
0.251
1
0.098
2
0.207
3
0.017
4
0.126
5
0.119
6
0.057
7
0.111
8
0.090
9
0.122
10
0.233
0.508
0.197
0.457
0.068
0.301
0.271
0.127
0.239
0.178
0.241
0.461
2.076
0.807
1.607
1.520
1.483
1.066
0.974
0.775
0.699
0.983
1.895
2.328
0.904
1.814
1.537
1.608
1.186
1.031
0.886
0.788
1.104
2.127
2.584
1.004
2.064
1.588
1.784
1.337
1.101
1.014
0.876
1.223
2.355
1.5 x Mean Revenues
Farallons
0.251
1
0.098
2
0.207
3
0.017
4
0.126
5
0.119
6
0.057
7
0.111
8
0.090
9
0.122
10
0.233
0.508
0.197
0.457
0.068
0.301
0.271
0.127
0.239
0.178
0.241
0.461
3.114
1.210
2.410
2.279
2.224
1.600
1.461
1.162
1.048
1.474
2.842
3.366
1.308
2.617
2.297
2.350
1.719
1.518
1.274
1.138
1.596
3.075
3.622
1.408
2.867
2.347
2.525
1.871
1.588
1.401
1.226
1.715
3.303
0.5 x Mean Revenues
Farallons
0.251
1
0.098
2
0.207
3
0.017
4
0.126
5
0.119
6
0.057
7
0.111
8
0.090
9
0.122
10
0.233
0.508
0.197
0.457
0.068
0.301
0.271
0.127
0.239
0.178
0.241
0.461
1.038
0.403
0.803
0.760
0.741
0.533
0.487
0.387
0.349
0.491
0.947
1.290
0.501
1.011
0.777
0.867
0.653
0.544
0.499
0.439
0.613
1.180
1.546
0.601
1.260
0.828
1.042
0.804
0.614
0.626
0.527
0.732
1.408
Patch
Elasticity Definitions
1) Short-run elasticity with no discrete adjustment.
2) Long-run elasticity with no discrete adjustment.
3) Elasticity with no port adjustment (short- and long-run are the same).
4) Short-run elasticity with both port and discrete adjustment.
5) Long-run elasticity with both port and discrete adjustment.
34
Table 11
Marine Reserves and Economic Behavior
The Northern California Red Sea Urchin Fishery
Steady-State
Harvest
(1,000 pounds)
Steady-State
Egg Production
(Billions)
Discounted*
Revenues
($1000)
1,316
1,441
17,440
15,074
With Discrete Choice Behavioral Model (a=0.005)
No Closure
Close Patch 8
830
752
With No Economic Model - NOECON (a=0.005) Steady-state Calibration
No Closure
Close Patch 8
829
868
**
434
553
17,400
16,423
With No Economic Model - NOECON (a=0.005) Approach Path Calibration
No Closure
Close Patch 8
386
545
***
267
397
8,096
8,204
* Uses a 5% constant discount rate and assumes $1 per pound of sea urchin.
** Calibrated steady-state harvest to behavioral model.
*** Calibrated approach path catch to actual catch.
Table 12
Impacts of Dispersal and Spatial Behavior
System-wide Totals for the NOECON Model
System-wide Totals for the Discrete Choice Model
SS Harvest
(1,000 pounds)
SS Eggs
(Billions)
SS Harvest
(1,000 pounds)
SS Eggs
(Billions)
828.6
433.6
830.5
1316.0
Separate Patches
Close Farralons
Close Patch 1
670.6
749.4
566.5
580.3
819.1
827.1
1322.5
1317.5
First Gyre
Close Patch 2
Close Patch 3
Close Patch 4
807.5
812.4
816.3
584.1
571.3
559.3
755.2
765.3
761.2
1395.4
1382.3
1385.3
Gyre Border
Close Patch 5
911.6
559.7
755.0
1425.6
Second Gyre
Close Patch 6
Close Patch 7
Close Patch 8
Close Patch 9
Close Patch 10
868.3
869.1
868.0
862.3
839.5
594.7
572.6
553.3
522.2
470.8
743.6
746.7
752.4
787.3
829.6
1446.9
1447.5
1440.6
1374.3
1316.0
No Closure
35
Table 13
Economics of Marine Reserves with Macroeconomic Shocks
The Northern California Red Sea Urchin Fishery
Steady-State
N. California
Divers
Trips
Per Diver
Per Year
Steady-State
Steady-State Discounted*
Participation
Harvest
Egg Production Revenues
Rate
(1,000 pounds)
(Billions)
($1000)
Discrete Choice Only (a = 0.005)
No Closure
Close Patch 8
131
131
29.9
25.3
13%
11%
830
752
1,316
1,441
17,440
15,074
57.8
47.2
25%
20%
638
576
1,627
1,692
13,400
11,660
16%
13%
802
728
1,399
1,495
16,846
14,683
46%
41%
883
921
720
879
18,548
17,362
796
910
20,402
18,865
Port Choice and Discrete Choice (a = 0.005)
No Closure
Close Patch 8
33
36
Port Choice and Discrete Choice (a = 0.005) - 50% Decrease in S. Cal. Revenues
No Closure
Close Patch 8
83
89
37.9
31.2
Discrete Choice Only (a = 0.005)
Double prices and exogenous increase in participation rate
No Closure
Close Patch 8
131
131
107.1
96.5
Port Choice and Discrete Choice (a = 0.005)
75% Decrease in S. Cal. Revenues, double prices, and exogenous increase in participation rate
No Closure
Close Patch 8
56
68
174.5
143.1
75%
61%
* Uses a 5% constant discount rate and assumes $1 per pound of sea urchin.
36
972
952
Figure 1
Diving Activity Coastal Histogram
Trips in North-Central California 1988-1997
3,500
3,000
Number of Dives
2,500
2,000
1,500
1,000
500
0
37.95
Patch 1
38.10
38.25
38.40
Patch 2
38.55
Patch 3
Bodega
38.70
Patch 4
38.85
Patch 5
39.00
39.15
Patch 6
Pt. Arena
39.30
39.45
Patch 7
Patch 8
Albion
Ft. Bragg
Latitude
Figure 2
Crescent City
Northern California
Sea Urchin Ports
Ft. Bragg
Albion
Pt. Arena
Bodega
Half Moon Bay
37
39.60
Patch 9
39.75
39.90
Patch 10
40.05
Figure 3
Daily Participation and Location Choice Decision
Do Not Go
Patch 0
Patch 1
Patch 2
Patch 3
Diver i
at time t
Patch 4
Patch 5
Patch 6
Go
Patch 7
Patch 8
Patch 9
Patch 10
Figure 4
Calibration of Bioeconomic Simulation Model
14,000,000
12,000,000
Total Catch (pounds)
10,000,000
8,000,000
6,000,000
4,000,000
2,000,000
0
1991
1992
1993
1994
1995
Actual Catch
1996
1997
Simulated Catch with a=0.005
38
1998
1999
Figure 5
Steady-State Size Distribution and Egg Production
Patch 8 when Fished
450
6,000
400
5,000
350
4,000
250
3,000
200
150
Billions of Eggs
Millions of Organisms
300
2,000
100
1,000
50
14
6
13
8
13
0
12
2
11
4
10
6
98
90
82
74
66
58
50
42
34
26
18
0
10
2
0
Size Class (mm)
Organisms Below the Size Limit
Organisms Above the Size Limit
Egg Production from Size Class
Figure 6
Steady-State Size Distribution and Egg Production
Patch 8 when Closed
450
6,000
400
5,000
350
3,000
200
150
2,000
100
1,000
50
14
6
13
8
13
0
12
2
11
4
10
6
98
90
82
74
66
58
50
42
34
26
18
0
10
0
Size Class (mm)
Organisms Below the Size Limit
Organisms Above the Size Limit
39
Egg Production from Size Class
Billions of Eggs
4,000
250
2
Millions of Organisms
300
Appendix A
Baseline Parameter Values for Bioeconomic Simulations
Parameter
k
m
Linf
Llimit
Lmature
f
w
b
α
β
p
a
c
Description
Value
growth
natural mortality
terminal size (mm)
min. size limit (mm)
min. size of sexually mature organism
fishing mortality
1st allometric weighting parm.
2nd allometric weighting parm.
1st egg production parm.
2nd eggs production parm.
survival probability
resiliency settlement parm.
carrying capacity settlement parm.
40
0.24
0.09
118
89
60
0.29
0.001413
2.68
5.47E-06
3.45
1.0
0.005 - 0.05
1.2E+07 - 2.4E+07