Disentangling the effects of policy reform and environmental changes in the Norwegian coastal fishery for cod‡
Florian Diekert§ and Tore Schweder¶
May 13, 2015
Abstract
Understanding the effect of introducing property rights to natural resources is central
in economics, but empirical analysis is frustrated by the complexity of socio-ecological
systems. We construct a detailed bio-economic model of the Norwegian coastal fishery
for cod, which has traditionally been open-access, but was closed after 1989. To answer
whether the observed increase in both cod stock and average profits was due to good luck,
or good management, we isolate the effect of environmental variability. We project stock
and harvest forward in the counterfactual scenario of no intervention, showing that the
policy had only a small positive impact on stock biomass, but a pronounced positive effect
on profits. The main drivers of the profit gains are increases in productivity and savings
in labor costs.
(125 words)
Key words: Open access, Property rights, Quasi-experiment, Counterfactual control,
Bio-economic modeling, Productivity, North-East Arctic cod
JEL codes: C43, D23, Q22, Q28
‡
We would like to thank Kristen Lund for invaluable input and effort. Furthermore, we would like to
thank Chris Anderson, Claire Armstrong, Frank Asche, Chris Costello, Arne Eide, Linda Nøstbakken, Andries
Richter, Jim Wilen, and seminar participants in Tromsø, Kiel, Oslo, Seattle, Davis, and at the 20th EAERE
conference in Toulouse for fruitful discussions and comments.
§
Corresponding author. Department of Economics and CEES, Dept. of Biosciences, University of Oslo,
Norway. E-mail: f.k.diekert@ibv.uio.no F Diekert is funded by NorMER, a Nordic Centre of Excellence for
Research on Marine Ecosystems and Resources under Climate Change.
¶
Department of Economics and CEES, Dept. of Biosciences, University of Oslo, Norway. E-mail:
tore.schweder@econ.uio.no.
1
1
Introduction
The North-East-Arctic cod (NEA cod, gadus morhua) fishery in the Barents Sea is currently
the most valuable whitefish fishery in the world. Dried cod from Lofoten has been a highly
priced export commodity since the Viking Ages. Today, Russia and Norway agree on the annual total allowable catch (TAC) quota and its distribution. While the Russian and European
fleets (obtaining roughly 50-60% of the total TAC) predominantly consist of trawlers, this is
not the case for the Norwegian fleet. Here the main part are conventional boats that exploit
the cod’s impressive spawning migration to the coastal areas around Lofoten. Access to this
coastal fishery was basically open and the international TAC was not enforced on coastal
vessels up to 1989. At that time the cod stock had reached a record low and the Norwegian
authorities pulled the emergency break: they closed the coastal fishery, allocated individual
quotas, and enforced the TAC to a much larger degree. Subsequently, the cod stock has recovered and profits have gone up. In a nutshell, we ask: were these increases in biomass and
profits due to good luck or good management?
Individual quota systems in various forms have now been used for more than thirty years,
and their use has increased in scope and scale in the recent decade. Simultaneously, there has
been a lively debate around this type of fisheries management, in particular when individual quotas are tradable (ITQs), see e.g. Bromley (2009) and the subsequent commentaries.
Many studies have pointed to the positive economic effects of ITQ management (see for example Grafton et al., 2000; Fox et al., 2003; Dupont et al., 2005; Arnason, 2005; Schnier and
Felthoven, 2013; Reimer et al., 2014), whereas ecological effects appear to be more mixed
(Branch, 2009; Chu, 2009).1
In general, all case studies that attempt to test empirically whether the privatization of
common property has indeed improved profits by studying time series face the same fundamental problem, namely to correctly identify the causal effect of policy change: There are
neither controlled nor natural experiments for large fisheries. First of all, spillover effects
make it impossible to identify a treatment effect by randomization. Second, there is so much
specific natural and social context to a given fishery that it is virtually impossible to find
1
Most studies consider only a rather short time horizon of a few years before and after the policy change.
A notable exception is Walden et al. (2012) who study the Mid-Atlantic clam fishery over a period of 28 years.
Here we are able to use data from 1985 up to 1997 (as the sampling methodology changed in 1998), i.e. we
have 5 pre-event years and 8 post-event years.
2
an adequate control among the set of other fisheries. Last, but not least, slow environmental changes obstruct even the comparison of economic units before and after the regulatory
change.
It is this last aspect which we attack in this paper: Fish stocks, and consequently profits, might have risen due to the policy change, but also due to more favorable environmental
conditions. Therefore, we build an age-structured bio-economic model to simulate the counterfactual development of the fish stock and economic outcomes, assuming that the relationship
between stock and harvest did not change. The idea is to utilize the estimated recruitment to
the factual population after the intervention. We assume that the counterfactual recruitment
in a year would have been the observed factual recruitment, adjusted by the stock-recruitment
curve according to the counterfactual spawning stock. The counterfactual stock is then projected forward, subject to observed natural mortality and counterfactual fishing mortality.
Methodologically, our approach is related to the “synthetic control” analysis that has been
pioneered by Abadie and Gardeazabal (2003) and applied to non-renewable natural resources
by Mideksa (2013) and to fisheries by Scheld et al. (2012). In contrast to these papers, we
do not construct the counterfactual control by propensity matching, but by simulating a bioeconomic model.2 Material and methods are explained in more detail in section 2 and 3. The
first objective of our study is to analyze the effect of the 1989/1990 policy change on cod
biomass. We present our results in section 4.1. The second objective is to analyze the effect
on profits. We do so by taking a structural model of a profit function to an extended dataset
of boat-owner combinations in the Norwegian coastal cod fishery. After demonstrating that
introducing individual quotas has indeed had a positive and significant effect on profits, we
investigate how abolishing the open-access regime has lead to increased profits. Results are
presented in section 4.2.
The 1989/1990 policy change has been referred to as the “closing [of] the commons”
(Hersoug, 2005). At this point, it is important to emphasize that it is the fact that overall
harvest is being constrained (and not the introduction of individual quotas as such) that has
an effect on the stock development. However, the issuing of individual quotas was an integral
2
Scheld et al. (2012) can use the synthetic control method because in their case, there were indeed some
boats in the fishery that participated in the program while others did not, and they can convincingly make the
case that the other boats had no incentive, and indeed did not, change their behavior. Moreover, they focus
on within-season dynamics and hence abstract from the biological aspects. In our case, all boats were directly
or indirectly affected by the policy, and the biological dynamics are a key aspect of our study.
3
part of a general policy change, which allowed the authorities to enforce the TAC also for
coastal vessels. It is the stricter enforcement of the TAC that we pick up in the first part
of our analysis and it is the combined effect of stricter quota enforcement and more secure
harvesting rights that we analyze in the second part of our study.
In a recent contribution, Kjesbu et al. (2014) analyze a later management change, namely
the introduction of a “harvest-control rule” (HCR). They give an excellent introduction to
the natural environment and the current status of the NEA cod and argue that the reduction
of fishing mortality was – in part – responsible for the high stock values in recent years. To
answer how the cod stock would have evolved were it not for the HCR, or were the HCR
introduced earlier, they simulate a biological model. In contrast to Kjesbu et al. (2014), we
predict counterfactual recruitment by using counterfactual spawning stock as input in the
estimated recruitment relationship, and we take into account that the aggregate harvest rate
changes with the level of biomass. Moreover, our emphasis is on the economic dynamics of this
cod fishery. Arguably, the policy change in 1989/1990, which combined a stricter enforcement
of the TAC with the introduction of individual quotas, had a much more profound effect in
this respect.
To the best of our knowledge, our study is the first to combine the assessment of an
introduction of individual quotas with an explicit simulation of the counterfactual resource
base, thereby disentangling the effects of policy reform and environmental changes. That
said, we are of course well aware of the gulf between the power of a randomized controlled
experiment and the evidence that our study might bring. Nevertheless, we take an important
step towards better understanding the effect of changing the property rights regime in our
case-study fishery. Given the central role of institutions for economic performance, we argue
that the case-study of the Norwegian coastal fishery is of substantial general interest. In
particular, we hope that our methodological approach, simple as it is, will come to be a useful
contribution to the literature.
2
Background and Data
At first sight, the stock development of the North-East Arctic (NEA) cod (Figure 1) could
serve as a textbook example of open-access and fisheries management. Biomass has declined
from more than 4 million tons after WWII to less than one million ton in the 1980s. At
4
the same time, the stock’s age structure has been severely truncated, making the stock more
susceptible to climatic variations (Rouyer et al., 2011). The aggregate stock biomass has
reached values above 3 million tons again (although the age structure remains truncated).
3000
2000
1000
0
Volume (in 1000 tons)
4000
Stock Biomass
Landings
1950
1960
1970
1980
1990
2000
2010
Figure 1: Observed stock biomass and total landings of NEA cod
Two boat groups are distinguished in the Norwegian cod fishery: Trawlers and conventional vessels. The latter group is the backbone of the Norwegian fishing fleet, landing around
70% of the cod harvest. Trawlers have always been subjected to a licensing scheme, while
access for conventional boats has traditionally been open.
Although the Joint Russian-
Norwegian Fisheries Commission agrees upon a Total Allowable Catch (TAC) quota since
1977, the quota was de facto not enforced for conventional vessels (Christensen and Hallenstvedt, 2005). This situation changed radically when the resource stock was in such a dire
state that the Norwegian authorities closed the fishery on April 18, 1989. After this shock,
the unanimous slogan was “Never again April 18th!” (Hersoug, 2005). In the fall of the same
year, the authorities issued individual vessel quotas. Although the vessel quotas were initially
not meant to be transferable, they were so in practice: Boats have been sold with a quota
and then bought back without the quota (Holm and Nielsen, 2007).
We take the biological data and the numbers for aggregate annual landings from the
2012-ICES report.3 The economic data comes from the Norwegian Directorate of Fisheries’
3
At this point, we should highlight that when we talk about “observed” stock size here, we refer to biomass
values that are derived from virtual-population analysis, a model-based technique that back-calculates the
stock numbers from fishery-dependent (landing statistics) and fishery-independent (research surveys) data.
Although the true error will always remain unknown (as the true size of the fish stock in the ocean is in fact
unobservable), it is clear that the error diminishes through time as more and more information, in particular
on the fish stock’s age-structure, becomes available. For an excellent introduction to the ICES data and VPA
5
profitability surveys, forming an unbalanced panel with information on vessel characteristics,
economic variables, the harvested amount and the harvested value. In addition, we were able
to obtain information on the boat owners from the vessel registry (through the Directorate
of Fisheries) and we could match these datasets to create boat-specific histories of ownership.
This allows us to control for vessel- and owner specific attributes and – importantly – we can
distinguish the fate of those that have entered or left the fishery.
The Norwegian cod fishery has generally been a popular study object, from the early work
on productivity (Hannesson, 1983) to its latest advances (Kumbhakar et al., 2013). It has
served as example for calibrated simulations of e.g. the effect of cannibalism (Armstrong and
Sumaila, 2001), the importance of age-differentiated management (Diekert et al., 2010), multispecies aspects (Kvamsdal and Sandal, 2012), or climate change effects (Eide, 2007). Asche
and coauthors (Asche et al., 2009; Asche, 2009) study the trawler segment of the fishery
to estimate the size of the resource rent (using data from 1997 and 1998) and to test for
adjustment cost (using data from 1986-1994). Data from 1995-2007 for the entire demersal
fleet has been used by Guttormsen and Roll (2011) to investigate technical inefficiencies.
McWhinnie (2006) uses data for the coastal fleet from 1985-2000 to investigate productivity
changes by means of index-number decomposition.
Here, we use data from 1985-1997. As the sampling methodology changed fundamentally
in 1998 it is not advisable to extend a dataset that covers the 1989/1990 policy change further
than 1997. However, we were able to pool the data from all Norwegian coastal vessels: The
directorate classifies a boat as belonging to the “demersal fleet” only when more than 50%
of its harvest is from demersal species. As the harvest composition varies substantially from
year to year, it is important to obtain data from all boats, regardless of classification. This
allows us to study the fate of a boat even if, for example, 52% of its catch are demersal
species in 1994 (when it would show up in the Directorate’s demersal dataset) and 48% of
its catch are demersal species in 1995 (when it would show up in the Directorate’s pelagic
dataset). We have removed all observations where the share of cod in total harvest is less than
5% to exclude those that catch cod only as undirected bycatch. The final selection contains
668 unique vessel-owner combinations over 13 years (in total, we have 1818 observations, on
average 140 observations per year).
Table 1 shows the main variables of the economic dataset (where the capital letter N refers
method, see Ekerhovd and Gordon (2013).
6
Table 1: Summary statistics, selected variables
Statistic
N (n)
Mean
St. Dev.
Min
Max
27.80
Length (meter)
1 818 (668)
17.20
3.53
13.00
Boat-age (in years)
1 817 (667)
22.03
15.91
0
90
Labor (Man-years)
1 818 (668)
4.27
1.61
1.00
12.06
Operating days per year
1 818 (668)
278.65
44.71
62
364
796 (388)
183.53
55.57
44
345
1 818 (668)
368.54
413.76
5.18
3 306.44
Days at Sea
Harvest (in metric tons)
Share of cod in harvest
1 818 (668)
0.46
0.24
0.05
0.99
Revenue (1000 NOK)
1 818 (668)
1 970.99
1 439.69
97.08
10 843.85
Total cost (1000 NOK)
1 818 (668)
1 834.23
1 292.16
180.08
10 075.68
Variable cost (1000 NOK)
1 818 (668)
1 151.04
812.71
59.41
7 349.87
to the total number of observations and the small case letter n refers to the number of distinct
boat-owner combinations). Our key measure of economic performance are short-run profits,
defined as the total revenue minus variable costs.4 In the following, we will use the word
profits to mean short-run profits. Figure 2 shows a box-plot of profits from 1985 to 1997 (the
thick lines within the boxes show the median and the black dots show the mean profit in the
respective year). The plot highlights the immense variation: The average value of profits in
the dataset is 819 thousand Norwegian Kroner (NOK) with a standard deviation (s.d.) of
660 thousand NOK. The variation between different vessels-owner combinations (s.d. of 654
thousand NOK) is much larger than the variation within a vessel-owner combination (s.d. of
1000
1500
2000
mean profits, observed
median profits, observed
0
500
Profits (in 1000 NOK)
2500
197 thousand NOK).
1985
1987
1989
1991
1993
1995
1997
Figure 2: Boxplots of profits from 1985 to 1997
4
To be precise, we group ARBEIDSGODTGJORELSE (engl: Work compensation), PROVIANT (engl: provisions),
SOSIALE KOSTNADER (engl: social cost), PENSJONSTREKK (engl: retirement contributions) DRIVSTOFF (engl: fuel
cost), AGN IS SALT EMB (engl: Bait, salt, and packaging) and PRODUKTAVGIFT (engl: product tax) as variable
cost, whereas depreciation of vessel and quota, maintenance of gear and vessel as well as “other cost” (such
as for external accounting services etc.) are grouped as fixed costs. All prices have been deflated using the
consumer price index (1998=100) from Statistics Norway.
7
3
Methods
3.1
Counterfactual simulation of cod stock
Simulating how stock biomass would have developed if the 1990 regulatory change had not
taken place requires three steps: 1.) a function predicting the aggregate harvest for a given
stock biomass, 2.) a biological model predicting the size of each cohort the next year, accounting for harvest and natural mortality, and 3.) a procedure calculating the number of
new fish entering the exploited stock as a function of the reproductive part of the stock, while
accounting for the historical environmental conditions.
Harvest
The function which predicts aggregate harvest for a given stock is given by equation (1), where
Ht refers to the harvest during year t and Bt refers to the stock biomass at the beginning of
year t.
Ht = α + βBt + εt
(1)
Note that we simply search for the most parsimonious empirical relationship with the highest
explanatory power. Our interest is in the equation’s ability to forecast, and we therefore see
(1) as a reduced form of a model of open-access in the cod fishery. Key is that we presume that
the relationship between stock and harvest would have been the same also after 1989, were
it not for the policy change. Details on the selection of the functional form, its estimation,
and the parameter values are placed in Appendix A.1. Here we note that the straightforward
linear specification is able to explain almost 90% of the variation in the data.
Stock dynamics
The aggregate stock biomass at time t + 1 is the number of fish at age a at time t + 1 times
P
their average individual weight, summed over all ages: Bt+1 = A
a wa,t+1 Na,t+1 . The firstage-at-recruitment is 3 years for NEA cod, and the oldest age-group A (a so-called “plus
group”, collecting all individuals of age A and above) is 13 years.
In order to project the stock biomass to the next period for a given stock and harvest in
the current period, we first need to convert the aggregate harvest at time t to the harvested
8
biomass of age-class a that is caught at time t. To this end, we assume that the selectivity
pattern for a given year does not change with the regulatory regime.5 Denote the observed
aggregate fishing mortality by Ft (which is given by the ratio of aggregate harvest to aggregate
biomass Ft =
Ht
Bt )
then the age-specific selectivity can be inferred from Ha,t = sa Ft Ba,t . Thus,
the harvested biomass at age is given by:
Ĥa,t = sa F̂t B̂a,t .
(2)
The values for Ht , Ha,t , Bt , and Ba,t are taken from Table 3.7. (catch weights) and Table 3.5
(catch numbers), as well as from Table 3.8. (stock weights) and Table 3.16 (Stock numbers)
of the 2012 ICES report.
The counterfactual Stock-Numbers-at-age N̂a,t are calculated according to equation (3),
which means that we assume that fishing occurs instantaneously in the middle of the year, and
natural mortality Ma,t occurs evenly throughout the year. The values for natural mortality
are taken from the ICES report (2012, Table 3.17; Ma,t = 0.2 for most a, t). To translate the
counterfactual harvested biomass into catch-numbers-at-age, we have to divide the harvestat-age by the average individual weight-at-age wa,t , where we impose that the individual
weight-at-age does not change with the regulatory shift. Although it seems intuitive that
growth is slower at high stock levels and weight-at-age is indeed negatively correlated with
abundance for NEA cod, the causal mechanism is far from clear: Evaluating biotic and abiotic
determinants of cod growth, Ottersen et al. (2002) find that environmental conditions that
are correlated with strong recruitment also displace the new year classes farther east into
colder water masses, where prey abundance is low and growing conditions are adverse. As
environmental conditions have not changed due to the policy change, we employ the yearly
values as they are given in Table 3.7 in ICES (2012).
N̂a+1,t+1 =
Na,t e
M
− 2a,t
Ĥa,t
−
wa,t
!
e−
Ma,t
2
(3)
N̂A,t+1 =
NA−1,t e
M
− A−1,t
2
−
ĤA−1,t
wA−1,t
!
e
M
− A−1,t
2
+
M
− A,t
2
NA,t e
−
ĤA,t
wA,t
!
e
M
− A,t
2
5
Indeed, the data shows no signs of systematic changes in the selectivity pattern. Diekert (2012) gives a
theoretical argument that aggregate ITQs per se do not influence the incentives for changing gear selectivity.
9
Recruitment
Finally, the number of newly recruited fish has to be determined. Importantly, we need
to isolate the influence of the (endogenous) spawning stock biomass from the (exogenous)
environmental forces determining recruitment. The link between biomass and recruitment is
assumed to follow the Beverton-Holt form (Ohlberger et al., 2014):
N3,t =
ea SSB t−3
· eεt
1 + eb SSB t−3
(4)
where the parameters a and b are obtained from a non-linear regression of the number of
recruits on the spawning stock biomass (SSB ). Regression estimates are given in Appendix
A.2. Since NEA cod is considered to recruit at age 3 to the fishery, the relevant spawning stock
biomass is the one three years earlier.6 The projected spawning stock biomass will differ from
the observed values, and will hence drive a wedge between the projected and the predicted
recruitment values. However, we add the time-specific residual from the regression to the
log of the recruitment values. The residuals are – by assumption – independent of the stock
size and capture random environmental fluctuations (climatic or oceanographic conditions,
predator and prey abundance etc).7
We use a multiplicative lognormal error structure, which can be justified for several reasons. First, from a technical perspective, the explained variable can only take on positive
values. This is particularly important for the simulation, where negative recruitment values
could occur if an additive model structure were applied. Second, from a statistical perspective, the multiplicative model gives the better fit (see Appendix A.2, where we also show the
regression results for the additive model). Third, from a mechanistic perspective, when the
total survival from egg to recruit is viewed as the product of many smaller survival events
(Quinn and Deriso, 1999).
Figure 3 illustrates the simulation procedure. The left panel shows the observed scatter
of SSB versus abundance at age 3 three years later. The fitted Beverton-Holt function is
6
P
The spawning stock biomass is calculated as SSB t = a mat a,t wa,t Na,t where mat a,t is the proportion of
mature individuals in a given cohort (obtained from Table 3.10 in ICES, 2012).
7
Note that the residual would also pick up changes in recruitment that are due to other policy changes that
aimed at protecting juvenile fish but had no impact on harvest (such as stricter bycatch regulations in a related
fishery). However, no such policy changes took place around 1989/1990. In their review of the management
of this fishery, Aglen et al. (2005) mention the following changes: In 1984 efforts were undertaken to limit the
by-catch of juvenile Gadidae in the shrimp fishery. In 1992, efforts were undertaken to limit the by-catch in
the capelin fishery and in 1993, a sorting grid was introduced in the shrimp fishery.
10
1500
sim.R
500
1000
obs.R
0
500
1000
Recruits in million indiv
1500
Illustration
0
Recruits in million indiv
Data and fitted function
0
200
400
600
800
1000 1200
0
Spawning stock biomass in 1000 tons
sim.SSB
obs.SSB
200
600
400
800
1000 1200
Spawning stock biomass in 1000 tons
Figure 3: Stock-recruitment relationship. In the panel on the right, sim.SSB is the simulated counterfactual spawning stock while obs.SSB is the factual; similarly for the number of recruits.
given by the blue line. The right panel shows one hypothetical simulation step: Suppose the
observed SSB at time t − 3 was at 650 thousand tons. The stock-recruitment function predicts
that there would be around 700 million recruits, while – due to environmental conditions –
the actually observed recruitment was 1300 million individuals. If now the simulated SSB at
time t − 3 were at 250 thousand tons, the stock-recruitment function would predict around
462 million recruits, but multiplying the observed residual, we end up with a counterfactual
recruitment of 925 million individuals.
The simulation have been implemented in R 3.1.1 (2014). In order to quantify the uncertainty surrounding our simulations, we run a thousand simulations where we, for each time
step, add an error to the harvest and to the residual of the recruitment function. The former is a randomly drawn residual from the harvest regression and the latter is taken from a
normal distribution with a standard deviation corresponding to the estimates of the 0-group
abundances obtained from the Barents Sea ecosystem survey (Anon., 2011).
3.2
Estimation of policy effect on profits
The second objective of our study is to estimate the effect of introducing individual quotas on
profits. In order to do so, we fit a profit function to the data with help of a linear fixed-effect
regression. We include dummy variables to distinguish the period before the policy change
for the period after 1989. We then predict profits for the period 1990 to 1997 when setting
the dummies to 0 and using counterfactual instead of observed biomass values as co-variates.
11
In other words, we fit:
ln πi,t = f (αi , pi,t , Li,t , Bt , D) + εi,t ;
D = 1 for t ∈ [1990, 1997];
εi,t ∼ iid(0, σ 2 )
(5)
and we project:
ln π̂i,t = f (αi , pi,t , Li,t , B̂t , D);
D = 0 for all t ∈ [1985, 1997]
(6)
Here αi is an individual effect (at the level of boat-owner combination; a Hausman test
clearly rejected the use of a random-effects model), pl,i,t is a vector of output prices (cod,
haddock, and a composite of other species), indexed by l, observed by individual i at time t,
Li,t is the amount of labour (assumed to be fixed in the short run). Bt is the observed stock
biomass and B̂t is the counterfactual biomass used in the projection. D is the dummy variable
representing the management regime. It is set to 0 in the period 1985-1989 and to 1 in the
period 1990-1997 in the estimation. Throughout the projection of counterfactual profits, D
is set to 0.
We exploit duality to avoid the endogeneity problem that arises when using labour and
capital as proxy for effort (Gordon, 2013). An important maintained assumption is therefore
that prices are indeed exogenous and that the individual firm adjusts in- and outputs. As
the products from the demersal fish species are either a small part of the larger world-market
for white fish, or go to the specialized market for dried fish where the final price depends
much on the idiosyncratic characteristics of the individual fish and the weather during the
drying period, this assumption is likely to hold for the output prices. The assumption that
the amount of employed labour is fixed in the short run is maybe more problematic. However,
wages are directly linked to harvest due to the share system, while the decision how many
men to employ has to be taken before the fishing trip.8
To obtain a better understanding of how the policy change has lead to gains in profits,
we calculate elasticities, Eπ,y =
d ln π
d ln y ,
where y = pcod , phaddock , potherspecies or labor L. This
8
The expert reader will have observed that we do not use fuel prices as explanatory variable in our regression.
The reason is that only fuel expenditure, but not fuel prices are available. As pointed out by Gordon (2013),
constructing a fuel price proxy by dividing fuel expenditures by e.g. some measure of boat size does not help, as
it would just let the endogeneity problem slip in through the backdoor (as fuel use is directly related to the effort
used in catching fish). Using available fuel prices on the national level cannot help us either, unfortunately, as
we would then be unable to identify the effect of biomass, our key variable of interest. Being stuck between a
rock and a hard place, we accept a potential omitted variable bias.
12
tells us roughly how a 1% increase in output prices or the use of the input labor would have
resulted in changes in profits.
We choose a simple Cobb-Douglas function as our main specification. This function provides sufficient flexibility and has the advantage that the elasticities are directly obtained from
the estimates of the regression coefficients. In addition, we fit a more detailed “transcendental
logarithmic (translog) function” (Lau, 1978; Squires, 1987) to the data, which allows us to
account for second-order interaction effects. However, multi-collinearity prevents us from interacting the dummy variable with the full set of co-variates and we therefore confine ourselves
with a dummy variable on the intersect in the translog specification. Equation (7) spells out
the Cobb-Douglas specification:
f (α, p, L, B, D) = αi +
X
βl ln pl,i,t + βL ln Li,t + βB ln Bt
l
!
+ D βD +
X
βlD ln pl,i,t + βLD ln Li,t + βBD ln Bt
(7)
l
Equation (8) spells out the translog specification:
f (α, p, L, B, D) = αi + βD D +
X
βl ln pl,i,t + βL ln Li,t + βB ln Bt
l
X
1
1 XX
βlm ln pl,i,t ln pm,i,t +
βlL ln pl,i,t ln Li,t + βLL (ln Li, t)2
2
2
m
l
l
X
1
+
βlB ln pl,i,t ln Bt + βLB ln Li,t ln Bt + βBB (ln Bt )2
(8)
2
+
l
4
4.1
Results
Counterfactual simulation of cod stock
Was the increase of the cod stock due to good luck or due to good management? In order
to answer this question, we have projected how stock biomass would have developed if the
relationship between stock and harvest after 1990 had been the same as before 1990: The
black line with solid points in Figure 4 gives the actual observed stock development, while
the blue line with open circles shows the counterfactual cod stock. The dashed lines plot the
95% simultaneous confidence bands (Schweder and Hjort, 2015). A sample of hundred paths
13
used to generate these confidence bands are in the background. These grey lines show how
1000
1500
2000
observed
counterfactual
0
500
Biomass (in 1000 tons)
2500
the uncertainty surrounding our simulation compounds as the projection interval increases.
1986
1988
1990
1992
1994
1996
Figure 4: Observed values (black line) and counterfactual simulation of cod stock (blue line, open
circles). The grey lines are re-sampled paths used to gauge the uncertainty of the simulation.
The policy has had a positive effect on stock biomass: The observed stock is significantly
larger than our counterfactual projection of the stock biomass in the case of intervention.
Nevertheless, it appears that the main part of the post 1990 increase in the stock size was
independent of the policy change. Three drivers are identified in the literature (see e.g.
Godø, 2003; Hjermann et al., 2007): First a recovered capelin stock (the main prey of cod)
significantly improved the feeding conditions and consequently reduced cannibalism. Second,
warmer temperatures generally benefited cod (which lives on its Northernmost boundary in
the Barents Sea). Third, oceanographic conditions were favorable in this period as they
predominantly transported cod larvæ into nutrient rich waters.
Note that the effect is not as crystal clear as one may have hoped; the observed stock
development overlaps with the 95% simultaneous confidence band in some years (in particular
in the beginning, which is expected because of the filtering effect of the fish stock’s age
structure). We find that the counterfactual biomass is significantly smaller than the observed
biomass in all years at a level of 6% (one-sided test).
Our simulation of the counterfactual cod stock relies on aggregate data from the ICES
reports. Hence the estimated impact of the policy could have nothing to do with the fact
that the commons in the Norwegian coastal fishery for cod have been closed, but only be a
factor of an overall change in the setting and enforcement of the global TAC-quotas or that,
14
for example, the Russian harvest has significantly decreases after 1990. To show that neither
of these is the case, we plot the total harvest and its relative distribution and juxtapose it
to the level of the agreed TAC (blue cross-marks; Figure 5). Total harvest (including Illegal,
Unreported, and Unregulated (IUU) catch) has exceeded the agreed-upon TAC in almost all
years, before and after 1989/1990. Similarly, the distribution of harvest between Russia and
800
200
400
600
Other+IUU
Russia
Norway
0
Harvest and TAC (blue crosses) in 1000 tons
Norway has roughly stayed the same throughout the period.
1985
1990
1995
Figure 5: Annual harvest from Norway, Russia, and other countries (includes IUU catch), compared
to agreed TAC (blue cross) Data is from (Aglen et al., 2005) and (Joint Commission, 2014)
Evidently, it is not possible to test the validity of our predictions from within the model.
What we can do is to point to the validation exercise of the biological model that shows that
we are able to reproduce past stock development for the period before the intervention (see
Appendix A.3). Similarly, we have subjected our model to two placebo tests as a falsification
strategy. That is, by applying the model to units that – so to say – have actually not been
treated, we learn whether the reported results are maybe simply driven by the model’s inability
to replicate the true data. In other words, if our method of constructing a counterfactual
cod stock is correct, we should not see a large deviation between projected and actual stock
estimates when assuming that the policy change would have happened in 1980 or 1985. Indeed,
no significant difference between the actual stock biomass and the counterfactual projections
is discernible in Figure 6 when the treatment is fictitiously applies in 1980 (left panel) and
1985 (right panel). Although our approach of augmenting the before/after comparison of
individuals with help of a bio-economic model does, by its very nature, not adhere to the
standards in other fields such as labor- or development economics, we do think that this sort
of structural modeling is very fruitful in natural resource economics (see e.g. Smith and Wilen,
2003; Weninger and Waters, 2003).
All in all, we conclude that the improvement in the fisheries management is likely to have
15
1000 1500 2000 2500
observed
counterfactual
0
500
Biomass (in 1000 tons)
1000 1500 2000 2500
500
0
Biomass (in 1000 tons)
observed
counterfactual
1975
1980
1985
1990
1980
1985
1990
1995
Figure 6: Placebo test: Applying the treatment to 1980 (left panel) and 1985 (right panel)
had a positive effect on the stock development, but that the fluctuations in the stock are
primarily driven by environmental factors.9 This somewhat ambiguous finding is in line with
previous difficulties to establish clear positive ecosystem effects of ITQ management (Branch,
2009; Chu, 2009). It also reflects the recent work of Rouyer et al. (2011), who argue that the
qualitative changes of the stock’s properties, in particular its age-truncation, has increased
the importance of climatic conditions for stock dynamics. Further, a “both...and” answer to
the question of good luck or good management is also supported by the study of Kjesbu et al.
(2014). Investigating the introduction of the harvest-control-rule they find, in their words,
“synergies between climate and management”.
4.2
Estimation of policy effect on profitability
Did the introduction of individual quotas have a significant positive effect on profits? In
order to answer this question, we fit a Cobb-Douglas and translog profit function to the
data and predict counterfactual profits by setting the dummy-variable to zero and using the
counterfactual cod stock as a co-variate. Figure 7 shows the actual observed development of
average annual profits (black line), the fit of the estimated profit functions (gray lines) and
the projected counterfactual profit development (blue line). The results of the underlying
regressions are given in Table 2, column (1) for the Cobb-Douglas profit function and in
Appendix A.4 for the translog function (as tabulating the interaction effects take up a lot of
space). Clearly, the policy change has had a significant positive effect on profits.10
9
This is at least the case in the period that we have observed. The quota system might have a much stronger
effect in less favorable periods, e.g. by preventing depletion.
10
Variable profits are not to be confused with rents; they are positive also under open-access as they relate
to the returns to fixed inputs to production such as capital and the renumeration of the vessel owner.
16
800
600
400
200
Profits (in 1000 NOK)
800
600
400
observed
predicted
counterfactual
0
observed
predicted
counterfactual
0
200
Profits (in 1000 NOK)
1000
(b) Projection of translog Profit function
1000
(a) Projection of Cobb-Douglas Profit function
1986 1988 1990 1992 1994 1996
1986 1988 1990 1992 1994 1996
Figure 7: Time series of average profits: observed (black line), predicted (gray line) and counterfactual
(blue line). They gray area represents the 95% confidence band.
According to the estimation of the Cobb-Douglas function, the average difference between
the observed and counterfactual annual profits per boat is 120 thousand NOK (in 1998 value,
with the 95% confidence interval being 68 and 170 thousand NOK). According to the estimation of the translog function, the average difference between the observed and counterfactual
annual profits per boat is 142 thousand NOK (in 1998 value, with the 95% confidence interval
being 92 and 192 thousand NOK). Moving from open access to individual quotas raised profits
on average between 16% (Cobb-Douglas projection) and 19% (translog projection). As there
are roughly 1800 boats in the relevant population, the total estimated gain for society from
this policy over the period 1990 to 1997 amounts to 1.7 billion NOK (in 1998 value) based
on the more conservative Cobb-Douglas projection. This corresponds to 2.9 billion Euro (in
2015 value) or 3.1 billion US-Dollar (in 2015 value).
Analyzing the elasticities (which – for a Cobb-Douglas profit function – are conveniently
given by the regression estimates), we see first of all that general productivity has increased.
Furthermore, we see that the contribution of labor costs has fallen. The changes in the codprices and the prices of other species are not significant. The effect of haddock prices is
negative, which is probably due to the fact that haddock serves as a (weak) substitute for
cod in the whitefish market, and the unexpected sign is caused by an interaction effect that
the simple Cobb-Douglas function fails to pick up.11 Furthermore, the effect of the biomass
is smaller after the introduction of individual quotas. The explanation is twofold: First, more
11
This is indeed confirmed when inspecting the regression results of the translog function in Appendix A.4.
17
Table 2: Regression Results for Cobb-Douglas Profit Function (Equation 7). Column 1 presents
results for the full sample and column 2 for the restricted sample of boat-owner combinations that
are both observed before and after the policy change, column 3 presents results for the sample of
boat-owner combinations that are observed before and after the policy change and that have stayed
throughout the sample period and column 4 are boat-owner combinations that have quit before 1997.
Dependent variable: log π
policyD
cp
(1)
(2)
(3)
(4)
Full sample
Restricted sample
Boats that stayed
Boats that left
3.612∗∗∗
(1.044)
2.880∗∗
(1.451)
3.253
(1.966)
1.591
(3.006)
0.0185
(0.0981)
-0.000660
(0.114)
0.215
(0.165)
-0.0386
(0.153)
(0.533)
0.170
(0.145)
0.424∗∗
(0.199)
0.0393
(0.209)
1.049∗
hp
0.00378
(0.0748)
0.0322
(0.0839)
0.0499
(0.0964)
0.00596
(0.140)
D hp
-0.229∗∗
(0.101)
-0.351∗∗
(0.141)
-0.219
(0.145)
-0.652∗
(0.329)
0.0992
(0.0654)
0.104
(0.0863)
-0.0365
(0.128)
0.200∗
(0.104)
D cp
op
D op
-0.0973
(0.0595)
-0.124
(0.0751)
-0.0172
(0.0951)
-0.167
(0.120)
0.748∗∗∗
(0.111)
0.808∗∗∗
(0.148)
0.886∗∗∗
(0.211)
0.762∗∗∗
(0.200)
-0.165∗
(0.0841)
-0.244∗∗
(0.0971)
-0.326∗∗∗
(0.104)
-0.168
(0.173)
0.100
(0.125)
0.126
(0.148)
0.0859
(0.232)
0.213
(0.186)
D bio
-0.408∗∗∗
(0.148)
-0.340∗
(0.198)
-0.310
(0.291)
-0.295
(0.338)
cons
4.365∗∗∗
(0.805)
4.100∗∗∗
(0.973)
4.088∗∗∗
(1.372)
3.432∗∗
(1.339)
lab
D lab
bio
N(n)
adj.R2
1818 (668)
691 (123)
367 (53)
324 (70)
0.62
0.60
0.61
0.55
∗
∗∗
∗∗∗
Fixed-effect within regression; p < 0.10,
p < 0.05,
p < 0.01
(Standard errors in parentheses, clustered at the level of boat-owner combination)
secure harvesting rights meant that profits were less dependent on the availability of the stock
as under a “race to fish”. Moreover, the specifics of the Norwegian quota allocation key (the
so-called “trawl-ladder”) imply that the coastal vessels obtain a proportionally larger share
of the total quota when the TAC is low. This means that small boats in fact benefit from a
low TAC (which is closely related to a low stock): while they do not get to harvest much less,
they enjoy increased prices.
As a robustness check, we investigate the restricted sample of those boat-owner combinations that were observed before and after the policy change (Table 2, column 2). Also here
the coefficient for the indicator variable of the policy change is significant and positive. We
have further distinguished between those that have stayed in the fishery throughout the time
period and those that have left between 1990 and 1997 (Column 3 and 4 in Table 2). Not
surprisingly, the effect is larger for the boat-owner combinations that stay and smaller for the
units that leave.12 Looking at the elasticities confirms that the main drivers of the increase
in profits are gains in productivity and a decrease in labor costs. This particularly true for
those boats have stayed in the fishery after the introduction of individual quotas, while the
12
The coefficient are actually not statistically significant, but that is likely due to the smaller sample size.
18
drop in the labor elasticity is much smaller – and in fact not significant – for those boat-owner
combinations that have left the fishery after 1989/1990.
In contrast to the examples from North American fisheries (Grafton et al., 2000; Fox et al.,
2003; Dupont et al., 2005), we do not see that prices play a more and more important role after
the introduction of individual quotas. The reason is probably that the pre-ITQ regulations
in many North American fisheries lead to extremely short harvesting seasons, so that there
was a lot to gain from alleviating these adverse market effects. In Norway the availability of
fish has, on the one hand, always been determined by the seasonal spawning migration and,
on the other hand, the season was never that extremely short so that latent potential gains
were simply not present to the same extent.13 Furthermore, there are no signs of an increased
importance of unregulated species as the cod fishery becomes regulated (in contrast to the
Norwegian pelagic fleet; see Asche et al., 2007). Rather, ending the “race to fish” through
the introduction of individual quotas allowed the firms to reduce their fuel- and labor costs.
Moreover, the increase in productivity is likely a combination of three effects: the increase in
stock biomass, technological change, and the fact that the quotas of boats that have left the
fishery were re-distributed among the entire group, which meant that each remaining boat
obtained a larger quota share over time.
Figure 8 provides a closer look at the data to document these effects: The leftmost panel
shows the increase of cod harvest per vessel by presenting boxplots over time. Similarly, the
three panels to the right show what lies beneath the reduction in labor-cost. As Abbott et al.
(2010), we find little evidence of changes in the share of labor cost to revenue. The overall
amount of man-years (corrected for vessel length) has dropped and then stayed stable, while
the number of operating days per vessel have declined over time.14 Our empirical analysis
thus confirms anecdotes according to which boat-owners took turns in working at each other’s
boat. Such beneficial trade was only possible once harvest was secured through individual
quotas.
Note that we take the observed structure in the fleet as given. It is very likely that
more capital would have been entered or remained in the fishery under open-access, further
dissipating existing rents. Our estimate is of the profit gains is therefore a lower bound of the
13
We thank Frank Asche for discussion on this point.
Ideally, we would have used a measure of days-at-sea, but unfortunately our data has too little information
on this variable (see the summary statistics in Table 1).
14
19
laborcost/revenue
man-years/length
Days of operation
0
350
300
250
200
0.3
150
0.1
100
0.4
0.2
200
0.5
0.3
300
0.6
0.4
400
0.7
Cod harvest
1985
1988
1991
1994
1997
1985
1988
1991
1994
1997
1985
1988
1991
1994
1997
1985
1988
1991
1994
1997
Figure 8: Boxplots of selected variables over time.
full gains from rationalization.
Indeed, our analysis cannot tell to what extent the observed profit gains came about by
changes along the intensive or the extensive margin. It is beyond the scope of this study to
decompose these effects by an elaborate structural model as in Reimer et al. (2014), but we can
take a look at the numbers of total registered fishing vessels Norway and the participation
in the Lofoten fishery. Figure 9 then reveals something very interesting, namely that the
participation in the Lofoten fishery increased after the introduction of quotas, while the total
numbers of vessels steadily decreased (though one may discern a slow-down in the years
1800
1600
1400
1200
1000
800
Participation in Lofoten Fishery
2000
24000
22000
20000
18000
16000
14000
Total Number of Norwegian Fishing Vessels
immediately following the introduction of individual quota).15
1986
1988
1990
1992
1994
1996
Figure 9: Total number of registered fishing vessels (left axis, blue dots) and Number of vessels participating in the Lofoten fishery (right axis, red triangles). Data is from the Lofoten-reports (“Årsberetning
vedkommende Norges Fiskerier”) and the “Lønnsomhetsundersøkelse”, both published by the Norwegian Directorate of Fisheries.
The marked increase in participation points to the important effect of asset security.
With their individual quota in hand, more fishermen found it now worthwhile to take the
trip to Lofoten in order to join this lucrative (but previously very competitive) fishery. This
15
The fact that the participation in 1990 has increased compared to 1989 but not reached later levels can
be explained by the reportedly adverse weather in that year (see the Lofoten-report for 1990), as well as with
the fishermen’s hesitant and observant reaction towards the new quota system.
20
interpretation is corroborated by investigating the distribution of fuel expenditures (per meter
length) over time, differentiated according to geographical region (Figure 10). While fuel
expenditures increased for vessels in Southern and Western Norway, who have to travel quite
some distance to reach Lofoten, it has stayed constant, or even decreased for vessels from
Nordland and Troms (the counties that border the Lofoten archipelago).
1985 1988 1991 1994 1997
1985 1988 1991 1994 1997
15
20
Finnmark county
0
5
10
15
10
5
0
5
10
15
20
Troms county
20
Nordland county
0
0
5
10
15
20
Southern & Western Norway
1985 1988 1991 1994 1997
1985 1988 1991 1994 1997
Figure 10: Boxplots of fuel expenditures divided by length over time, for vessels in Southern and
Western Norway, Nordland county, Troms county, and Finnmark county.
5
Discussion and Conclusion
Fisheries are maybe the canonical example to highlight the importance of property rights:
Theory tells that rents are dissipated and fish stocks are depleted under open-access (Gordon,
1954), while well-defined harvesting rights give rise to considerable profits and high stock
values (Scott, 1955). Real-world processes are evidently much more complex than the theoretical dichotomy of rent-dissipation and rent-maximization. Nonetheless, cross-sectional
studies have indeed identified negative effects of open-access (McWhinnie, 2009) and positive
effects of secure rights-based management (Costello et al., 2008; Grainger and Costello, 2014).
These studies convincingly document that better property rights are associated with better
performance, but they are less able to establish the causal mechanism at work. Although the
1989/1990 policy change in the Norwegian coastal fishery for cod is far from the textbook
example of perfect ITQs,16 we argue that analyzing the results of introducing individual quotas and simultaneously enforcing the TAC – so to say – in the spirit of program evaluation
advances the current literature.
16
In fact, the individual quotas were not meant to be tradable in the beginning, and to this day the perpetuity
of the individual harvesting rights is disputed.
21
In this paper, we have taken structural models very seriously, perhaps too seriously. However, as sketched in the introduction, there are no randomized controlled experiments for large
scale socio-economic systems. This frustrates the search for a clean causal estimate of the
effect of introducing harvesting rights to resources that were formerly governed by open-access
regimes. Instead of giving up, we argue that one should turn to biological and economic modeling to obtain information on how the world might have looked like were it not for the policy
change. Taking this interdisciplinary approach, we propose a way to disentangle the effects
of policy reform and environmental changes and apply it to the Norwegian coastal fishery for
cod. Moreover, we present a detailed data-set over 13 years (5 years pre intervention and 8
years post-intervention) with information on vessel and owner characteristics. Augmenting
this quasi-experimental setting with our modeling efforts, we find that the change from openaccess to individual quotas has had a significant but comparatively small effect on the cod
stock. The main part of the observed increases in the resource base appears to have been due
to favorable environmental conditions. However, the policy did lead to a significant increase
in the average profits of about 16-19%, that is by around 130 thousand Norwegian Kroner per
boat (in 1998 value). Because fishermen had more secure harvesting rights after the policy
change, they could avoid a costly race to fish and exploits gains from specialization as well as
economize on labor inputs. The fact that cost savings are the main driver of efficiency gains is
well in line with basic theory. In contrast to the findings for many North-American fisheries,
we do not find that output prices have played a role in this.
Our analysis has been silent on one central aspect: Who gains and who loses from this
reform (Armstrong and Clark, 1997)? The main challenge is how to define a “winner” and
a “loser”: One would need to know much more about the socio-economic circumstances of
the fishers, especially about those that have left the fishery. Did they get a golden retirement
from selling their boat that now had a quota with good-looking prospects attached to it, or
did they become unemployed and had to live off public welfare?
To get a first impression, we compare, from the restricted sample of boat-owner combinations that were observed both before and after 1990, those that have experienced an increasing
trend in profits with those that have experienced a decreasing trend (Table 3).
Although the difference between these two subsamples is small, there is some indication
that the boats that enjoyed an increase in profits after 1990 are smaller, older, and more
22
Table 3: Summary statistics for units with increasing or decreasing profits. Stars indicate statistical
significant difference between the means (Welch two sample t-test)
increasing trend
Statistic
N (n)
∗∗∗
Boat-age
Length
Man-years∗∗∗
Total harvest
Share of cod
Profits∗
∗
p < 0.10,
∗∗
414
414
414
414
414
414
(71)
(71)
(71)
(71)
(71)
(71)
p < 0.05,
∗∗∗
decreasing trend
Mean
St. Dev.
23.98
17.10
4.25
314.81
0.46
782.38
14.27
3.12
1.46
358.05
0.25
738.75
N (n)
277
277
277
277
277
277
(52)
(52)
(52)
(52)
(52)
(52)
Mean
St. Dev.
19.75
17.45
4.58
329.88
0.44
865.99
13.83
3.19
1.53
271.75
0.21
568.35
p < 0.01
specialized in catching cod. That there is correlation between catching more cod and an
increasing trend after the introduction of cod quotas is not surprising at all. It is also not too
surprising that smaller and older boats gain relatively more from the avoidance of a derby
fishery.17 However, it is a little bit surprising in the Norwegian context, because a popular
theme in the political debate was that individual quotas would hurt the small independent
boat owners from the North. Similarly, an analysis of the Gini coefficient shows that the
inequality in terms of profits has declined: The average Gini-coefficient in the period 19851989 was 0.422 and in the period 1990-1997 it was 0.379. One reason for this decrease in
inequality in the sample could of course be that the poorest fishermen simply dropped out of
the sample. Limiting entry must have had effects on the extensive margin, but as said, we
do not have the data to make statements about the fate of those boat-owners that left the
fishery after 1990.
Investigating the effect of the 1989/1990 policy change on investment pattern and industry
dynamics in general (Nøstbakken, 2012; Schnier and Felthoven, 2013), as well as on the microeconomic situation of the affected firms in particular, is an important task for further research,
especially as the introduction of private rights to public resources was (and still is) a contested
political issue.
17
Of course also here, we cannot tell whether we observe the decreases in fuel and labor cost as the main
effect because smaller and older boats gain more than larger and faster boats from avoiding a “race to fish”,
or whether we observe that smaller and older boats gain more because the main effect of avoiding a “race to
fish” is to save fuel and labor.
23
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25
Appendix
A.1
The stock-harvest relationship in the biomass simulation model
Table A-1 gives the parameter values of the model we employed in the simulation (Model 1) as well
as several simple alternative models that we have considered (Model 3-4). Interestingly, the average
price of cod p̂t (instrumented by the price of the previous year∗ ) did not turn out to be significant.
Hence we use the simplest model: It has the best overall fit and soundly passes the Durbin-Watson
test (dw-statistic of 1.98).†
Table A-1: Regression results of harvest on total biomass
Model 1
Ht
(Intercept)
Bt
ln(Bt )
α + βBt
Model 2
Model 3
α + β ln(Bt )
∗∗∗
−23.98 −7756.39
(54.70)
(753.61)
0.43∗∗∗
(0.04)
592.26∗∗∗
(53.53)
α + βBt +
−116.59
(192.46)
0.57∗
(0.29)
α + βBt + γ p̂t
−243.69
(231.10)
0.46∗∗∗
(0.05)
−4.75· 10−5
9.45· 10−5
Bt2
price p̂t
N
adj. R2
Model 4
γBt2
23.79
(24.31)
20
0.88
20
0.86
20
0.87
Robust standard errors in parentheses, ∗ p < 0.10,
20
0.88
∗∗
p < 0.05,
∗∗∗
p < 0.01
The parameters are estimated on ICES-data‡ for the time from 1970 to 1989. The ICES-data
before the 1970’s are generally considered to be less reliable (Ekerhovd and Gordon, 2013, p.384).
Importantly, the chosen period also strikes a balance between obtaining sufficiently many observations
and not extending the time series too far into the past when conditions may have been different, due
to, for example, technological change. At the end of the day, the choice of 1970 as the starting year
is somewhat arbitrary. We have therefore plotted the slope coefficient and the R2 value from Model
1 when taking different starting values (Figure A-1). As one would expect, the relationship appears
to be different for the early 1960s before the sonar and the power block have been introduced and
diffused (Hannesson et al., 2010). Similarly, one can see how the precision of the estimate decreases as
the degrees of freedom decline when one moves the starting date towards 1980. For different staring
∗
The first-stage model pt = α + βpt−1 + has an R2 of 0.69 with coefficients α = 2.34(1.02) and β =
0.71(0.13). The coefficient for the lagged price is significant at the 1% level.
†
For completeness, we have also estimated the model ln Ht = α + β ln Bt + ε, which yielded an intercept of
-1.19 (SE: 0.58) and a value of 1.04 (SE: 0.08) for the coefficient β. However, the R2 of this model and model
1 in Table A-1 are not directly comparable, so that we divided the dependent variable by its geometric mean
Q =1990
1
(H̃t = Ht ( Tt=1970
Ht )− 21 ) and regressed H̃t and ln H̃t on Bt and ln Bt , respectively. The modified linear
2
model (R = 0.88) is then comparable to the modified log-log model (R2 = 0.89). Since the difference between
the models’ explanatory power is negligible, we have opted for the simpler linear model.
‡
Table 3.24 on page 180 in ICES (2012).
26
years around 1970, the slope coefficient varies very little and the explanatory power of the simple linear
R-squared
0.6
0.7
0.8
0.9
0.5
0.4
0.3
0.5
0.2
0.4
0.1
Slope coefficients and 95% C.I.
1.0
model is indeed very high.
1965
1970
1975
1980
1965
1970
1975
1980
Figure A-1: Slope-coefficient (left panel) and R2 (right panel) for different starting years
A possible concern could be that we use the harvest data from all boats, instead of explaining
only the harvest from the Norwegian coastal vessels. There are two reasons for doing so. First, while
the harvest from these boats account for up to 70% of Norwegian harvest and about 32% of total
harvest, it is important to predict the entire harvest in order to simulate the development of the cod
stock. Second, there are clear signs that a more general change in the management of this fishery has
occurred in 1990. This is visualized by Figure A-2. It shows a scatterplot of biomass against harvest,
where the blue points and blue dashed line refer to the relationship before 1990 (in fact the regression
line of Model 1 in Table A-1). The red diamonds and the red dotted line refer to the relationship
after 1990. The black solid line is the regression-line from the estimation that covers the entire period
1970 to 1997. A Chow test clearly rejects that there is a common relationship between stock and
harvest before and after 1990: The test statistics is 12.91, which is larger than the relevant value at
1000
800
600
400
Harvest in year t (in 1000 tons)
1% significance F2;36;0.99 = 5.25.
500
1000
1500
2000
Biomass at the beginning of year t (in 1000 tons)
Figure A-2: A different stock-harvest relationship before and after 1990
27
Finally, one could ask why have not used an explicit theoretical model to explain the relationship
between the stock and aggregate harvest. For example we could have employed the generalized GordonSchaefer harvest function H = qE 1−α B β . The main problem here is to find an appropriate proxy for
effort E. The best available proxy for aggregate effort is the numbers of boats. But of course, the
number of participating boats is hopelessly endogenous (Gordon, 2013). Hence one would have to
explicitly model participation. This would not only add yet another layer of structural uncertainty
to our projections, it would also come close to catch 22 as one would use effort to explain the stock
development and the stock biomass to explain effort.§
A.2
The stock-recruitment relationship in the biomass simulation model
The recruitment relationship (4) is estimated by regressing equation (A-1) with help of the non-linear
least-squares routine “nls” in R 3.1.1 (2014). In addition, we have also estimated the model (A-2) with
additive error. The regression results are given in Table A-2.
ln N3,t = ln
N3,t =
ea SSB t−3
1 + eb SSB t−3
+ ln εt
ea SSB t−3
+ εt
1 + eb SSB t−3
(A-1)
(A-2)
Table A-2: Regression results for recruitment function
Model A-1
a
b
N
AIC
MSE
1.23∗∗∗ (0.29)
−5.69∗∗∗ (0.53)
Model A-2
1.97∗∗∗ (0.52)
−4.79∗∗∗ (0.69)
61
111.7
0.33
61
893.6
40.9
Standard errors in parentheses,
∗∗∗
p < 0.01
Figure A-3 plots the distribution of the sample residuals against the quantiles of the normal distribution. As one can also see from the Akaike Information Criterion (AIC) and the Mean Squared
Error (MSE) in Table A-2, the model with multiplicative errors fares better not only on theoretical
grounds, but also from a statistical point of view.
§
As a footnote in the appendix, we point out that it is possible to derive the linear harvest equation (1)
theoretically from first principles. Consider the following aggregate harvest function with decreasing returns
to total effort E(i.e. with infra-marginal rents): H = qE 1−α B β . Further, suppose costs are proportional to
effort by a factor w so that c(E) = wE. Solving harvest for effort, we can write costs as a function of harvest
1/(1−α)
and stock size: c(H, B) = w H/B β
. Under open-access, there will be zero rents at the margin, so that
1−α 1 β
p
α
pH = c(H, B), which can be re-arranged to give H = w
q α B α . This function is approximately linear in
stock biomass when β ≈ α. But again, finding out whether this is indeed the case is frustrated by the lack of
an exogenous effort variable.
28
1000
500
-500
0
Sample Quantiles
0.0 0.5 1.0 1.5
Normal Q-Q Plot, Model A-2
-1.0
Sample Quantiles
Normal Q-Q Plot, Model A-1
-2
-1
0
1
2
-2
Theoretical Quantiles
-1
0
1
2
Theoretical Quantiles
Figure A-3: Quantile-quantile plot comparing residuals from Model A-1 (left panel) and Model A-2
(left panel) to standard normal distribution
A.3
Validation of biomass simulation model
Figure A-4 shows the development of the cod stock from 1970 to 1990. The purple line plots the
result from our model (equation (1) to (4) in section 3.1) when we use the actual observed harvest
and recruitment values as inputs, showing the difference between our simulation technique and the
virtual-population analysis from ICES (black line). For the red line, we have used the harvest values
estimated according to equation (1) but still use the observed recruitment values. The blue line
incorporates both estimated harvest and a projection of the recruitment values.¶ Although the error
does increase progressively, our model succeeds in replicating the overall trend of the stock development
in the seventies and eighties. Moreover, it is almost always within the 95% confidence interval band
1500
1000
500
0
Biomass (in 1000 tons)
2000
of a simple first-order auto-regressive process.
observed
Model, obs H obs R
Model, sim H obs R
Model, sim H sim R
1970
1975
1980
1985
1990
Figure A-4: Observed and simulated stock biomass values 1970-1990
¶
Since recruitment depends on the spawning stock three years ago, the first three years of the red and blue
simulation are identical.
29
A.4
Regression results for translog profit function
Table A-3 gives the results of a fixed-effect within regression. Standard errors (clustered at the level
of boat-owner combination) are in parentheses.
Table A-3: Regression Results for Translog Profit Function (Equation 8)
Dependent variable: log π
0.231∗∗∗
-5.412∗∗
5.755∗∗∗
0.268
3.835∗∗∗
7.226∗∗∗
1.113∗
-0.799∗∗
0.190
-0.447∗∗
0.660∗∗∗
-0.0803
0.0546
-0.227∗∗
-0.516∗∗∗
-0.0511
0.104
-0.111
-0.138
-0.247∗∗
-1.009∗∗∗
-22.06∗∗
policy D
cp
hp
op
lab
bio
cp cp
cp hp
cp op
cp lab
cp bio
hp hp
hp op
hp lab
hp bio
op op
op lab
op bio
lab lab
lab bio
bio bio
Intercept
N(n)
adj.R2
∗
p < 0.10,
(0.0675)
(2.203)
(1.344)
(0.822)
(0.987)
(2.012)
(0.582)
(0.350)
(0.149)
(0.185)
(0.246)
(0.217)
(0.0987)
(0.114)
(0.158)
(0.0600)
(0.107)
(0.0822)
(0.185)
(0.120)
(0.258)
(8.552)
1818(668)
0.57
∗∗
p < 0.05,
30
∗∗∗
p < 0.01