Journal of International Fisheries▶ Article ◀

vol.13，2014

Methodology and Application of a Model to Estimate Fishery Resource Trends
by Effort and Catch Data
Taro OISHI†, Nobuyuki YAGI＊, Masahiko ARIJI＊＊ and Yutaro SAKAI＊＊＊（Fukuoka Institute of Technology／＊The University of Tokyo, Graduate School／＊＊

Kinki University／＊＊＊University of Calgary, Graduate School）
E-mail：†t-oishi@fit.ac.jp【abstract】
In this study, we first established a resource economic model to estimate fish biomass
using Schaefer’s bioeconomic model under the assumption that fish biomass is not at
equilibrium. Second, we developed a model capable of estimating country-specificcatchability coefficients. Third, we applied OECD fishery data to the model on a trialbase. The results indicated that the Schaefer model, which has been applied to assessfishery resources for single species, can comfortably fit the macro data from OECD
countries. Next, we simulated annual trends in fish stock levels, called relative
biomass, and is defined as the ratio of fish stocks to carrying capacity. Our result
showed that from 1998 to 2007, relative biomass stably fluctuated in a large sense. Ourmodel requires only secondary fishery data and has the potential to supplement
information on resource statuses in non-OECD developing countries, where original
surveys are costly or otherwise not viable options.
【keywords】
Schaefer model, OECD fishery data, relative biomass

1．Introduction
In the field of resource economics, a famous theoretical model called the Schaefer
model(1), enables capture of the mechanisms behind resource fluctuations using only
essential variables, i.e., fish catches and fishing effort. Therefore, it has been applied toassess many types of fish stocks in local fisheries (e.g., Haddon (2011), pp. 299-300, forEastern Pacific yellowfin tuna; Tanaka (2012), p.65, for Hippoglossus stenolepis on the
North American west coast).
In the past, the Schaefer model has not been applied for cross-country macro (ormulti-species aggregate) data because the theory aims to capture resource fluctuations-1-

Taro OISHI, Nobuyuki YAGI, Masahiko ARIJI and Yutaro SAKAIof specific species in local areas. However, Tanaka (2001), p.133 indicated that while
the fish catch of individual species significantly changes that of total species tends tobalance. Introduction in Iwasaki (2009) also indicates that global fish biomass
basically remains static because, while some species may be decreasing, others are
increasing.
The Schaefer model is a type of surplus production model that pools the overall
effects of recruitment, growth, and mortality (all aspects of production) into a single
production function (Haddon (2011), p.285). Other examples of such models include theFox model and the Pella and Tomlinson model (Nose et al. (1998), pp.73-82). The Fox
model, famous in the demographic research field, postulates that intrinsic growthfollows the Gompertz curve. This is in contrast to the Schaefer model, which uses thelogistic curve popular in the field of ecological studies (Tanaka (2012), p.55). Pella’s
and Tomlinson’s model is a generalized form of Schaefer’s and Fox’s models, but it iscomplex relative to Schaefer’s model, especially under the assumption that fishbiomass is not at equilibrium. Currently, applying the Pella and Tomlinson model inthe estimation is difficult. Taking the above into consideration, we have adopted the
Schaefer model(2)(3).
The academic contribution of this paper is threefold. First, we constructed a resource
economic model to estimate fish biomass using Schaefer’s bioeconomic model, under
the assumption that fish biomass is not at equilibrium. Second, we demonstrated thatthe model can estimate country-specific catchability coefficients (𝑞𝑖 )(4). Third, we
indicated that the conventional Schaefer model can be well suited to macro fisherydata in OECD countries. Finally, we simulated an index of stock levels, called relative
biomass, which represents the ratio of fish stock to carrying capacity (𝑑/𝐾), under theabove two scenario (i.e., the conventional constant 𝑞 model and country specific 𝑞𝑖
model), as a trial simulation.

Ideally, a natural scientific approach is necessary to rigorously analyze fish biomass

including species alternations. Our models, in constant, need only secondary fisheryeconomic data, which has potential to provide approximate information on the statusof resources in countries where original surveys are not readily available.

2．The model
In the Schaefer model, the growth of fish biomass and short-term catch function canbe shown, respectively, as follows(5):-2-Methodology and Application of a Model to Estimate Fishery Resource Trends
by Effort and Catch Data

𝑑𝑑𝑖,𝑡
𝑃𝑖,𝑡
= 𝑟 �1 −� 𝑃 − 𝑌𝑖,𝑡𝑑𝑑
𝐾𝑖 𝑖𝑖
𝑌𝑖,𝑡 = 𝑞𝑞𝑖,𝑡 𝑃𝑖,𝑡

(1)
(2)

where 𝑃𝑖,𝑡 is the fish biomass in time 𝑡 in country 𝑖; 𝑟 is the intrinsic fish stock

growth rate; 𝐾𝑖 is the environment’s carrying capacity in country 𝑖; 𝑌𝑖,𝑡 is the fish

catch in time 𝑡 in country 𝑖; 𝑞 is the catchability coefficient, defined as the fraction of
the biomass fished by an effort unit; and 𝑋𝑖,𝑡 is the fishing effort in time 𝑡 in country𝑖.

If the fish biomass 𝑃𝑖,𝑡 is not at equilibrium, i.e., if 𝑑𝑑𝑖,𝑡 /𝑑𝑑 ≠ 0, then the left-hand of

equation (1) will not equal zero; this can be described as follows:𝑑𝑑𝑖,𝑡= ∆𝑃𝑖 = 𝑃𝑖,𝑡 − 𝑃𝑖,𝑡−1
𝑑𝑑(3)

By substituting equation (3) into equation (1), we obtain equation (4) as follows:
𝑃𝑖,𝑡 − 𝑃𝑖,𝑡−1 = 𝑟𝑃𝑖,𝑡−1 − 𝑟

2
𝑃𝑖,𝑡−1− 𝑌𝑖,𝑡−1
𝐾𝑖

Dividing both sides of equation (4) by 𝑃𝑖,𝑡−1 , we arrive at the next equation
𝑃𝑖,𝑡 − 𝑃𝑖,𝑡−1
𝑃𝑖,𝑡−1 𝑌𝑖,𝑡−1=𝑟−𝑟−
𝑃𝑖,𝑡−1𝐾𝑖
𝑃𝑖,𝑡−1(4)(5)

Then, substituting equation (2) into equation (5), we obtain equation (6) as follows:
𝑌𝑖,𝑡 𝑋𝑖,𝑡−1 − 𝑌𝑖,𝑡−1 𝑋𝑖,𝑡𝑌𝑖,𝑡−1=𝑟−𝑟− 𝑞𝑋𝑖,𝑡−1
𝑌𝑖,𝑡−1 𝑋𝑖,𝑡𝐾𝑖 𝑞𝑋𝑖,𝑡−1(6)Through modification, equation (6) can be rewritten as follows:
𝑌𝑖,𝑡 = (1 + 𝑟)

2
∙ 𝑋𝑖,𝑡𝑌𝑖,𝑡−1 𝑋𝑖,𝑡𝑟 𝑌𝑖,𝑡−1−∙− 𝑞𝑋𝑖,𝑡 𝑌𝑖,𝑡−12
𝑋𝑖,𝑡−1𝑞𝐾𝑖
𝑋𝑖,𝑡−1(7)

We replaced (1 + 𝑟) by 𝛼, −𝑟/(𝑞𝐾𝑖 ) by 𝛽, and −𝑞 by 𝛾, and obtained estimation

model I as follows:

𝑌𝑖,𝑡 = 𝛼2
𝑌𝑖,𝑡−1∙ 𝑋𝑖,𝑡𝑌𝑖,𝑡−1 𝑋𝑖,𝑡+𝛽+ 𝛾𝑋𝑖,𝑡 𝑌𝑖,𝑡−12
𝑋𝑖,𝑡−1
𝑋𝑖,𝑡−1(8)

where the sign of parameter 𝛼 is positive and 𝛼 ≥ 1 (because 𝛼 = (1 + 𝑟), and 𝑟 ≥ 0),
and the signs of 𝛽 and 𝛾 are definitely negative. Here, note that we assume 𝐾𝑖 are�) (6).
identical and constant in each country (𝐾𝑖 = 𝐾

Next, we assume that the catchability coefficient 𝑞 is different for each country 𝑖:𝑞𝑖 . Then, equation (7) can be rewritten as follows:-3-

Taro OISHI, Nobuyuki YAGI, Masahiko ARIJI and Yutaro SAKAI

𝑌𝑖,𝑡 = (1 + 𝑟)

2
∙ 𝑋𝑖,𝑡𝑌𝑖,𝑡−1 𝑋𝑖,𝑡𝑟 𝑌𝑖,𝑡−1−∙− 𝑞𝑖 𝑋𝑖,𝑡 𝑌𝑖,𝑡−12
𝑋𝑖,𝑡−1𝑞𝑖 𝐾𝑖
𝑋𝑖,𝑡−1(9)

We again replace (1 + 𝑟) by 𝛼, −𝑟/(𝑞𝑖 𝐾𝑖 ) by 𝛽𝑖 , and −𝑞𝑖 by 𝛾𝑖 to obtain equation(10):

𝑌𝑖,𝑡 = 𝛼2
𝑌𝑖,𝑡−1∙ 𝑋𝑖,𝑡𝑌𝑖,𝑡−1 𝑋𝑖,𝑡
+ 𝛽𝑖
+ 𝛾𝑖 𝑋𝑖,𝑡 𝑌𝑖,𝑡−12
𝑋𝑖,𝑡−1
𝑋𝑖,𝑡−1(10)

Definitely, 𝛽𝑖 and 𝛽𝑗 equal −𝑟/(𝑞𝑖 𝐾𝑖 ) and −𝑟/(𝑞𝑗 𝐾𝑗 ), respectively and we assume

�, therefore 𝛽𝑖 can be substituted by 𝛽𝑗 as follows:
𝐾𝑖 = 𝐾𝑗 = 𝐾𝛽𝑖 =𝑞𝑖 − 𝑞𝑗 −1−𝑟/(𝑞𝑖 𝐾𝑖 )𝑞𝑖𝛽𝑗 = ( )−1𝛽𝑗 = (1 +) 𝛽𝑗 = (1 + 𝑑𝑖 )−1 𝛽𝑗−𝑟/(𝑞𝑗 𝐾𝑗 )
𝑞𝑗
𝑞𝑗

(11)

where 𝑑𝑖 is (𝑞𝑖 − 𝑞𝑗 )/𝑞𝑗 .

Similarly, 𝛾𝑖 and 𝛾𝑗 equal −𝑞𝑖 , and −𝑞𝑗 , respectively; therefore, 𝛾𝑖 can besubstituted by 𝛾𝑗 , as follows:
𝛾𝑖 =𝑞𝑖 − 𝑞𝑗−𝑞𝑖𝑞𝑖
𝛾𝑗 = ( )𝛾𝑗 = (1 +)𝛾𝑗 = (1 + 𝑑𝑖 )𝛾𝑗
−𝑞𝑗
𝑞𝑗
𝑞𝑗

(12)

By substituting equation (11) and (12) into (10), we get

𝑌 2 ∙ 𝑋𝑖,𝑡𝑌𝑖,𝑡−1 𝑋𝑖,𝑡
−1 𝑖,𝑡−1
𝑌𝑖,𝑡 = 𝛼+ 𝛽𝑗 (1 + 𝑑𝑖 )+ 𝛾𝑗 (1 + 𝑑𝑖 )𝑋𝑖,𝑡 𝑌𝑖,𝑡−12
𝑋𝑖,𝑡−1
𝑋𝑖,𝑡−1(13)

Therefore, we obtain estimation model II (enabling us to estimate the effects of eachcountry’s catchability coefficient) using a dummy variable as follows:
𝑌2 𝑋
𝑌𝑖,𝑡−1 𝑋𝑖,𝑡
−1 𝑖,𝑡−1 𝑖,𝑡
𝑌𝑖,𝑡 = 𝛼+ 𝛽𝑗 (1 + � 𝑑𝑖 ∙ 𝑑𝑑𝑑𝑑𝑑𝑖 )2𝑋𝑖,𝑡−1
𝑋𝑖,𝑡−1𝑖+ 𝛾𝑗 (1 + � 𝑑𝑖 ∙ 𝑑𝑑𝑑𝑑𝑑𝑖 )𝑋𝑖,𝑡 𝑌𝑖,𝑡−1

(14)

𝑖

where the sign of parameter 𝛼 is positive and 𝛼 ≥ 1 (because 𝛼 = (1 + 𝑟) and 𝑟 ≥ 0),
and the signs of 𝛽𝑗 (1 + ∑𝑖 𝑑𝑖 ∙ 𝑑𝑑𝑑𝑑𝑑𝑖 )−1 and 𝛾𝑗 (1 + ∑𝑖 𝑑𝑖 ∙ 𝑑𝑑𝑑𝑑𝑑𝑖 ) are negative forall 𝑖.

By applying estimation model I [equation (8)] or II [equation (14)] to the OECD

cross-country data, we can determine whether or not the Schaefer model can beapplied to macro data.
Additionally, we can estimate relative biomass (𝑃𝑡 /𝐾) using the estimatedparameters (𝛼, 𝛽 and 𝛾) of the above two models. In estimation model I, we calculate
relative biomass (𝑃𝑡 /𝐾) using-4-

Methodology and Application of a Model to Estimate Fishery Resource Trends
by Effort and Catch Data𝑌𝑖,𝑡𝑃𝑡 = � 𝑃𝑖,𝑡 = � ��𝑞𝑋𝑖,𝑡gained from equation (2) and𝑖

𝐾 = � 𝐾𝑖 = � �−
𝑖

(15)

𝑖

𝑖

𝑟
𝑟
∙𝑖
� =−
𝑞𝑞
𝑞𝑞

(16)

gained from equation (8). Here 𝑞 is given as – 𝛾 and the 𝛾 is estimated in equation(8).

In estimation model II, we calculate relative biomass (𝑃𝑡 /𝐾) using 𝑃𝑡 obtained

fromand 𝐾 obtained fromgained from equation (10).

𝑌𝑖,𝑡𝑃𝑡 = � 𝑃𝑖,𝑡 = � ��𝑞𝑖 𝑋𝑖,𝑡𝑖

𝐾 = � 𝐾𝑖 = � �−
𝑖

(17)

𝑖

𝑖

𝑟
�
𝑞𝑖 𝛽𝑖

(18)

In the following, we estimate above two relative biomass indicators and weigh theconsequences.

3．The data
To check the feasibility of the model, data from developed countries were used due totheir availability. Data were obtained primarily from “Fishstat” (FAO) and “Review ofFisheries in OECD Countries” (OECD). Table 1 shows the descriptive statistics of therelevant variables. Fish catch is denoted as 𝑌, and the root of the product of thenumber of vessels and the number of labors as 𝑋(8). Data from 22 OECD countries

between 1998 and 2007 are available, but some values are missing. As a result, thenumber of observations totaled 155.

4．Results
4-1．Estimation results
Table 2 shows the results for estimation models I and II. We used the statisticalsoftware

TSP version 4.5 for the estimation. The estimation method used for

estimation model I was ordinary least squares (OLS) and that for estimation model II-5-Taro OISHI, Nobuyuki YAGI, Masahiko ARIJI and Yutaro SAKAI

Table 1 Descriptive statistics

Average
S. D.
Min.
Max.
No. of obs.

Fish catch[Y ]<1,000 tonnes>
1,008
1,223
20
5,315
155

Fishing effort[X ]<->102,414
144,996
3,104
654,890
155

Source

FAO "Fishstat"(Vessels x Labors)

Vessels[-]<GRT/GT>273,121343,334
15,425
1,548,071
155

1/2

Labors[-]<Number>
45,567
72,798481
277,042
155

OECD "Review of OECD "Review ofFisheries in OECD Fisheries in OECDCountries"
Countries"

Notes:
1) [ ] and < > indicate variables and units, respectively.
2) We supplemented the missing Japanese data from other available sources: The
Ministry of Agriculture, Forestry and Fisheries (MAFF) “Survey on Marine
Fishery Production”(8) for fish catches; Fisheries Agency “Statistic Tables ofFishing Vessels (General Reports No.59, as of the end of 2006)”(9) for vessels;
Ministry of Agriculture, and Forestry and Fisheries (MAFF) “Survey of Persons
Engaged in Fishery”(10) for labors. However, this supplement had little impact
on the estimation results.

was non-linear least squares (NLS).
According to estimation model I, which is a simpler form, the estimate of 𝛼 ispositive and 𝛼 ≥ 1, estimates of 𝛽 and 𝛾 are negative. All are statistically significant

at the 1% level. Thus, the result satisfies the theoretically expected sign conditions.
From the perspective of goodness of fit, 𝑅 2 is 0.952 and 𝑎𝑎𝑎. 𝑅 2 is 0.951, making themodel’s overall fit sufficiently large. These results suggest that our model can perform
well using cross-country OECD fisheries data.

For the result of estimation model II, which considers the effect of each country’s
catchability coefficient as the dummy variables, the estimate of 𝛼 is positive andα ≥ 1 , and the estimates of 𝛽 and 𝛾 are negative. 𝛼 and 𝛾 are statisticallysignificant at the 1% level, but 𝛽 is not significant at the 10% level (further datacollection may be needed to improve the significance of 𝛽, because we use relatively
large numbers of dummy variables). These signs are consistent with the theoreticalrationale. With regards to the dummy variable coefficients, 18 out of 21 are significant,and the 18 coefficients are larger than − 1 ; this is desirable from the theoretical signcondition [see, equation (14)]. The determination coefficient, 𝑅 2, is 0.915 and 𝑎𝑎𝑎. 𝑅 2

is 0.900, and the model’s indicator of fitness is sufficiently large.
-6-

Methodology and Application of a Model to Estimate Fishery Resource Trends
by Effort and Catch Data

Table 2 Estimation results
Estimation model I
Parameter

Estimate(t-value)
1.21 ***(25.16)-6.75 ***(-8.02)-7 ***(-3.54)-2.82 × 10

αβγ

Estimation model II
Estimate
1.74 ***-1.82-5.58 × 10-6 ***(t-value)(14.82)(-0.55)(-3.58)-0.98 ***(-22.13)-0.99 ***(-17.64)-0.82 ***(-2.71)-0.97 ***(-16.16)-0.98 ***(-26.24)-0.96 ***(-13.82)

1.46(0.64)-0.97 ***(-18.88)0.30(0.62)

d 1 [Australia]
d 2 [Belgium]d 3 [Denmark]d 4 [Finland]d 5 [France]d 6 [Germany]d 7 [Greece]d 8 [Ireland]d 9 [Italy]

d 10 [Netherlands]
d 11 [Poland]d 12 [Portugal]
d 13 [Spain]d 14 [Sweden]d 15 [United Kingdom]d 16 [Iceland]d 17 [Japan]

d 18 [Korea, Rep.]
d 19 [Mexico]

d 20 [New Zealand]d 21 [Norway]

-0.97

***

(-16.33)

-0.98

***

(-27.47)

-0.99

***

(-61.99)-0.14(-0.59)-0.93 ***(-7.69)-0.97 ***(-17.76)-0.86 ***(-3.46)-0.98 ***(-23.46)-0.98 ***(-33.76)-0.59 ***(-5.41)-0.92 ***(-7.12)-0.91 ***(-5.55)

0.952

0.915

Adj. R 2

0.951

0.900

Number of observation

155

155

R

2

MethodOrdinary least squares (OLS) Nonlinear least squares (NLS)

Notes:
1) *𝑃 < 0.10, ** 𝑃 < 0.05, *** 𝑃 < 0.01.

2) The benchmark of 𝑑𝑗 (𝑗 = 1, … ,21) is Turkey.

3) 𝑅2 values are calculated as the square of the correlation coefficient between
the observation value and the estimation value of fish catch (𝑌). The valuesof 𝑎𝑎𝑎. 𝑅 2 are calculated as 1 − (1 − 𝑅2 ) × (𝑛 − 1)/(𝑛 − 𝑘), where 𝑛 is thenumber of observations and 𝑘 is the number of independent variables. For
further details, see Minotani and Maki (2010), p.205.

-7-

Taro OISHI, Nobuyuki YAGI, Masahiko ARIJI and Yutaro SAKAI

20,00018,000100.0

16,00014,00080.0

12,00060.0

10,000
8,000

40.0
20.0

Pt/K [Estimation model I] (left)

6,000

Pt/K [Estimation model II] (left)

4,000

Y (right)

2,000

0.0

Fish catch [ Y ]< 1,000 tonnes >Relative biomass [ Pt /K ]
<%>

120.0

0
2007

2006

2005

2004

2003

2002

2001

2000

1999

1998

Year
Figure 1 Relative biomass
4-2．Relative biomass
Figure 1 shows the result of the simulation of relative biomass (𝑃𝑡 /𝐾). Relative

biomass simulated from estimation model I has a value close to 0.5. Relative biomass
simulated from estimation model II goes around 0.75 in a large sense. This difference
could be explained by the fact that the value of 𝛽, as estimated by estimation model II

in Table 2, is not significant. Therefore, estimation model II requires further data to
conduct a more rigorous simulation despite the existence of the favorable feature thatit bases on country specific catchability coefficient 𝑞𝑖 .

In any case, the ratio of global fish biomass to carrying capacity approximately

ranges from 0.5 to 0.75 in our study. These results are consistent with those of theexisting study targeting Hippoglossus stenolepis on the North American west coast(Tanaka (2012), p. 67), in which relative biomass was estimated as having a value close
to 0.5 between 0.25 and 1.

5．Conclusion
In this study, we developed a model to estimate global fish biomass using theconventional Schaefer model (where catchability coefficient 𝑞 is constant) and is used
to estimate country-specific catchability coefficients (𝑞𝑖 ) as well as annual changes inrelative biomass, which represents the ratio of fish stocks to carrying capacity. The

results indicated that the Schaefer model can comfortably fit the macro data from-8-

Methodology and Application of a Model to Estimate Fishery Resource Trends
by Effort and Catch Data

OECD countries. Our results also revealed that relative biomass approximately
fluctuated from 0.5 to 0.75 between 1998 and 2007. These results are consistent withthe existing study targeting a single species (Tanaka (2012), p.67).
Simultaneously, several limitations on the outcomes of this study must be
highlighted. First, this study is not based upon a species-by-species approach, butrather showed annual macro-level changes of biomass for aggregated fish stocks
subject to commercial fishing. In this sense, this study’s methodology can only be used
as a tool to provide supplemental information on the status of fish stocks rather thansubstitute it for scientific works engaged in collecting species-by-species scientific data.
Second, although the catchability coefficient can be understood as the relative
efficiency of a given country’s fishery operations, it may include factors such as
distance between fishing grounds and home ports or fishing vessels average size. The
catchability coefficient, therefore, should not necessarily be considered to represent theefficiencies of a country’s fishing industry. Third, this study assumes that intrinsic fishstock growth rate and environment’s carrying capacity are constant among eachcountry. These theoretical constraints should be relaxed in future challenges, forexample by assigning specific values exogenously. Forth, this study only used datafrom OECD countries. In addition, some data were unavailable for some OECD
countries in certain years, and the number of countries varies. Considering the factthat non-OECD countries and economies make significant contributions to global
fishery production, future studies using more complete data, including non-OECD
members, would be desirable.
Notes(1) For the explanation on the Schaefer or the surplus production model based on thelogistic growth function from the viewpoint of resource economics, see Clark (2010),
pp.14-22 and Conrad (2010), pp.75-131.
(2) Nose et al. (1988), p.82 indicate that an estimation result of Pella and Tomlinson model
are relatively similar to those of the Schaefer model under the equilibrium
assumption.
(3) Richer model in reproduction theory is similar to the Schaefer model, but this model istypically used for species with non-overlapping generations, such as the various
Pacific salmon species (Clark (2006), p.32). This model follows theoretically different
assumptions against surplus production models such as the Schaefer model, whichassume overlapping generation by considering both recruitment and growth. On-9-Taro OISHI, Nobuyuki YAGI, Masahiko ARIJI and Yutaro SAKAI
reproduction theory, see also Nose et al. (1988), pp.185-194.
(4) Takarada (2009) theoretically analyzes the effects of country specific catchability
coefficients under a two-country model. Here our contribution is to develop an
econometric model to estimate country specific catchability coefficients and use it
under an empirical approach.
(5) We referred to Ariji (2004), p.143 with regard to the Schaefer model under theassumption that fish biomass is not at equilibrium. See also Nose et al. (1988),
pp.72-73. We referred Tanaka (2012), pp.61-62 for the notation of each variable.
(6) Some previous studies argue that 𝛾 and 𝐾 differ according to each country (e.g., Rus(2012), see also Brander and Taylor (1998), Dong and Takarada (2010)). On the other

hand, Tanaka (2012), p.70 indicates that the habitat density of fishery resources isbasically non-uniformly-distributed even in a specific area. The assumption ofidentical and constant 𝛾 and 𝐾 among each country is a restriction in this study, but
the remediation is challenges for future. See also McWhinnie (2009) which assumes
constant 𝛾 and 𝐾 for the whole earth.

(7) Ariji (2004), p.112 indicates that fishing effort can be expressed as a multiplication ofplural input variables. Here the number of vessels and that of labors are not flows but
stocks, because both of them are values at a certain point.
(8) URL: http://www.e-stat.go.jp/SG1/estat/List.do?lid=000001061498 (Accessed in April
2014)(9) URL: http://www.library.maff.go.jp/GAZO/60002481/60002481_02.pdf (Accessed in
April 2014) The data of tidal waters fishery (p.22, p.23) are used in the study.
(10) URL: http://www.e-stat.go.jp/SG1/estat/List.do?lid=000001061630 (Accessed in April
2014)

References[1] Ariji M. (2004) Economic Analysis on Sustainability of Japanese Fishery (Nippon

Gyogyo no Jizokusei ni Kansuru Keizaibunseki), Taga Shuppan (in Japanese).
[2] Brander J. A. and M. S. Taylor (1998) “Open Access Renewable Resources: Trade andTrade Policy in a Two-Country Model,” Journal of International Economics, 44,
181-209.
[3] Clark C. W. (2006) The Worldwide Crisis in Fisheries: Economic Models and Human

Behavior, Cambridge University Press.
[4] Clark C. W. (2010) Mathematical Bioeconomics: The Mathematics of Conservation, 3rdedition, John Wiley & Sons, Inc., Hoboken, New Jersey.

- 10 -

Methodology and Application of a Model to Estimate Fishery Resource Trends
by Effort and Catch Data
[5] Conrad J. M. (2010) Resource Economics, 2nd edition, Cambridge University Press.
[6] Dong W. and Takarada Y. (2010) “International Trade and Economic Theory in Fishery:
An Implication on Domestic Industry (Boueki to Suisangyou no Keizairiron:Kokunaisangyou heno Inpurikeishon),” in Y. Takarada and S. Managi (ed.) An

Invitation to Resource Economics: Fishery as a Case Study (Shigenkeizaigaku heno
Shoutai: Keisusutadi toshiteno Suisangyo), Minervashobo (in Japanese).
[7] Haddon M. (2011) Modelling and Quantitative Methods in Fisheries, 2nd edition, CRC
press.
[8] Iwasaki T. (2009) World Trend of Fishery Resources and Management (Sekai no

Suisansigen no Doko to Shigenkanri), Suisansha (in Japanese).
[9] McWhinnie S. F. (2009) “The Tragedy of the Commons in International Fisheries: An
Empirical Examination,” Journal of Environmental Economics and Management, 57,
321-333.
[10] Minotani C. and Maki A. (ed.) (2010) Handbook of Applied Econometrics(Ouyoukeiryoukeizaigaku Handobukku), Asakura Shoten (in Japanese).
[11] Nose Y., Ishii T. and Shimizu M. (1988) Fishery Resources (Suisanshigengaku),
Toukyoudaigaku Shuppankai (in Japanese).
[12] Oishi T., Yagi N., Ariji M. and Sakai Y. (2012) “Bioeconomic Modeling for the
Evaluation of Fishery Resources Based on the Schaefer Model,” International

Institute of Fisheries Economics & Trade (IIFET) International Conference inTanzania, proceedings, 1-8.
[13] Rus H. A. (2012) “Transboundary Marine Resources and Trading Neighbours,”

Environmental and Resource Economics, 53, 159-184.
[14] Takarada Y. (2009) “Transboundary Renewable Resource and International Trade,”

RIETI Discussion Paper Series, 09-E-041, 1-30.
[15] Tanaka E. (2012) Analysis of Fishery Resources (Suisan Shigen Kaisekigaku),
Seizandou Shoten (in Japanese).
[16] Tanaka S. (2001) An Essay on Fishery Resources (Suisanshigengaku wo Kataru),
Kouseisha Kouseikaku (in Japanese).
[Acknowledgements] This paper builds on previous work introduced in non-refereed
proceedings compiled for the Conference of the International Institute of Fisheries
Economics & Trade (IIFET) held in 2012 in Tanzania (Oishi et al. (2012)). This paper
includes newly calculated estimation on relative biomass and a totally revised discussionsection. The authors would like to express their sincere appreciation to the anonymous- 11 -Taro OISHI, Nobuyuki YAGI, Masahiko ARIJI and Yutaro SAKAI
referees of this journal and participants at the IIFET Conference who provided
constructive comments on the authors’ oral presentation.

- 12 -