Motivation
Theoretical Framework
The Fishery
Empirical Analysis
The Role of Fixed and
Non-Discretionary Variables in
Fisheries
A Theoretical and Empirical Examination
Stephanie F. McWhinnie and Kofi Otumawu-Apreku
IIFET - July 2014 - Australia
.
Conclusion
Motivation
Theoretical Framework
The Fishery
Empirical Analysis
Conclusion
Motivation
Understanding profit efficiency is important in fisheries:
It identifies sources of inefficiency which is important to
owners & policy makers
Addresses firm survival concerns and is vital to ensure industry
and stock sustainability
Vessels are a key, firm-level input and are fixed with a heavy
initial outlay (Clark et al 1979; Smith 1969)
Efficiency studies underscore the need to separate fixed cost in
the analysis (Anderson et al 2000; Anderson 2000; Grafton et
al 2006)
Additional non-discretionary variables (biomass, exchange
rates) should not be ignored when investigating profit
efficiency (Dupont et al 2005; Fox et al 2003)
Motivation
Theoretical Framework
The Fishery
Empirical Analysis
Conclusion
Our Paper
We develop a theoretical basis for considering the importance
of vessel capital when evaluating profit efficiency
We allow firms to make long-run decisions about optimal level
of variable effort, choosing vessel size accordingly and
subsequently to make an alternative short-run decisions
Examine the impact of fixed (sunk) input on fish biomass
Generate testable empirical predictions of exogenous changes
in biomass, price, and vessel size on profits
We use a semi-parametric approach to empirically identify
fixed and non-discretionary factors that affect profit efficiency
in the South Australian Rock Lobster Fishery
Calculate DEA efficiency scores
Conduct a truncated regression with bootstrap on these scores
Motivation
Theoretical Framework
The Fishery
Empirical Analysis
Conclusion
Long-Run Decision
Standard Gordon-Schaefer model but with two inputs, Eit and
Vit . Thus the profit-maximisation decision is:




ˆ∞


−δt
(pqBt − c)Eit − γVit )
e
dt
max
{z
}
| {z } 

Eit , Vit
|

0
s.t.
variable profit
Bt = F (Bt ) − qEit Bt −
| {z } | {z }
growth
i 0 s harvest
vessel cost
X
qEjt Bt
j6=i
|
{z
}
others 0 harvest
Motivation
Theoretical Framework
The Fishery
Empirical Analysis
Conclusion
Long-Run Equilibrium
In the long-run, both vessel and effort are variable and so vessel
size will be chosen to minimise costs at the optimal effort level
The associated symmetric steady-state is implicitly defined by
the Modified Golden Rule:
!
r B̃
r
B̃
pq B̃
+
1−
δ=−
K
n
K pq B̃ − (c + γ)
From which we define optimal biomass (B̃), effort (Ẽ ) and
vessel size (Ṽ )
Motivation
Theoretical Framework
The Fishery
Empirical Analysis
Conclusion
Short-Run Decision
Now consider the decision for a fisherman who has already
purchased a vessel of size Ṽ and the cost of doing so is sunk
If there are no inefficiencies associated with using the ’wrong’
size of vessel, the short-run decision would be defined as above
but with γ = 0.
Suppose, however, that to use vessel of size Ṽ with E 6= Ẽ
involves additional cost such that the short-run profit
maximisation is now (with usual constraint):




∞


ˆ


m
−δt
2
max e
(pqBt − c)Eit −
(Eit − Ṽi )
dt
|
{z
} |2


Eit


{z
}
 variable profit

0
suboptimal use cost
Motivation
Theoretical Framework
The Fishery
Empirical Analysis
Conclusion
Short-Run Equilibrium
This associated symmetric steady-state is implicitly defined by
the Modified Golden Rule:
!
r
B̂
pq B̂
r B̂
+
1−
δ=−
K
n
K pq B̂ − c − m r 1 − B̂ − Ṽ
nq
Thus, if the suboptimal use cost is
positive but less than the fixed cost:
Biomass (B̂) will be lower
Effort (Ê ) will be higher
Leading to lower than anticipated
profits
K
Motivation
Theoretical Framework
The Fishery
Empirical Analysis
Conclusion
Empirical Predictions
Simple comparative statics of the MGRs give:
Profit is (in the relevant range) increasing in biomass but at a
decreasing rate. This result is stronger for larger firms
Profit is increasing in price through a direct short-run effect,
but decreasing indirectly via the long-run impact on biomass
Profit is increasing (decreasing) in vessel size if the vessel is
being under(over)-used, ie, it depends on whether the increase
diminishes or exacerbates any suboptimal vessel use
Motivation
Theoretical Framework
The Fishery
Empirical Analysis
Conclusion
South Australian Rock Lobster Fishery
Most valuable commercial fishery in SA: 41% of SA fisheries
share of gross state product in ’08/09
Northern (NZ) and Southern (SZ) zones have different:
geography, biomass, costs, management
Cross-sectional, confidential, firm-level data on this fishery
were obtained from EconSearch for four seasons
Data grouped into discretionary & non-discretionary variables
– direct variable and quasi-fixed
costs
– biomass, boat length, boat age,
engine age and electrical
equipment age
Motivation
Theoretical Framework
The Fishery
Empirical Analysis
Conclusion
Empirical Specification
First we calculated profit efficiency scores using DEA and
using only the variable inputs
We then invert these to get a measure of inefficiency for each
observation: θ̃ ≥ 1
We take these scores and apply a truncated bootstrap
regression:
Profit Inefficiencyizt
2
= ψ(Biomasszt , Biomasszt
, Boat Ageizt ,
Boat Lengthizt , NZ Dummyzt ,
ITQ Dummy zt , Period Dummy ,
Engine Ageizt , Electrical Equipt.
Ageizt , AUD/HKDt ) + εi
Motivation
Theoretical Framework
The Fishery
Empirical Analysis
Conclusion
DEA Inefficiency Score and Explanatory
Variable Means
Year
Zone
Obs
Ineff. BioBoat
Boat
Eng.
Elect. HKD
Mse
mass
Age
Lgth
Age
Eqpt
/
(θ̃)
Age
AUD
97-98
NZ
18
1.32
2912 11.78 10.27
6.56
4.47
5.28
SZ
26
1.30
2912 12.82 11.94
7.28
4.54
00-01
NZ
24
1.42
2351 10.38 10.24
5.13
5.25
4.20
SZ
26
1.42
4511 14.42 11.89
5.22
4.62
04-05
NZ
22
1.83
1716 19.50 10.19 10.19
5.95
5.86
SZ
82
2.07
4466 14.17 11.77
5.79
6.13
07-08
NZ
19
1.53
1475 21.83 10.16
6.26
3.09
6.99
SZ
55
1.73
2534 16.67 11.83
6.73
4.04
Notes: Biomass is in tonnes; Boat Age, Engine Age, and Electrical Equipment
Age are all in years; and Boat Length in metres. The Inefficiency Measure (θ̃)
refers to period-zone specific profit inefficiency measures.
Data sources: EconSearch (2011), SARDI (2012) and Reserve Bank of
Australia (2013)
Motivation
Theoretical Framework
The Fishery
Empirical Analysis
Truncated Bootstrap Regression Results
Biomass
Biomass2
Boat Age
Boat Length
NZ Dummy
ITQ Dummy
’04-05 Dummy
Engine Age
Elect. Age
AUD/HKD
Dependent Variable: Inefficiency Score
-7.720*
-7.705*
-7.462*
-7.447*
(-4.55)
(-4.64)
(-4.49)
(-4.28)
1.069*
1.067
1.082*
1.080*
(-0.65)
(-0.65)
(-0.66)
(-0.63)
-0.240
-0.268
-0.239
-0.267
(-0.22)
(-0.22)
(-0.22)
(-0.21)
2.776*
2.699*
2.708*
2.634
(-1.67)
(-1.59)
(-1.60)
(-1.62)
-3.791*
-3.777*
-3.154*
-3.139*
(-2.04)
(-2.13)
(-1.90)
(-1.80)
-2.977*
-2.968
-3.261
-3.252*
(-1.78)
(-1.82)
(-2.06)
(-1.93)
3.027**
3.024**
2.700**
2.696***
(-1.17)
(-1.21)
(-1.10)
(-1.02)
0.091
0.092
(-0.27)
(-0.25)
-0.010
-0.010
(-0.24)
(-0.24)
0.508
0.509
(-0.46)
(-0.44)
Notes: 269 observations.
Bootstrap standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.10
Conclusion
Motivation
Theoretical Framework
The Fishery
Empirical Analysis
Results
Larger vessels impact profit efficiency
negatively suggesting that existing boat
lengths are not commensurate with
biomass
Increases in biomass have a positive effect
on efficiency but at a decreasing rate
ITQ management has a positive impact on
profit efficiency
The Northern Zone has higher efficiency
despite being less profitable
Conclusion
Motivation
Theoretical Framework
The Fishery
Empirical Analysis
Conclusion
Conclusion
We have examined the importance of factors such as vessel
size when evaluating profit maximization in fisheries
In an industry with important non-malleable inputs, the
investigation provides insight into the significance of such
costs in profit analysis in both the short- and long-run
In the context of fisheries our empirical methods are new and
provide further evidence on important policy characteristics for
economic and biological sustainability of the SA Rock Lobster
Fishery
Motivation
Theoretical Framework
Thank you
The Fishery
Empirical Analysis
Conclusion