Markets, Pooling and Insurance
for Managing Bycatch in Fisheries
Daniel S. Holland,
Northwest Fisheries Science Center
Another Perspective on Bycatch
Canary rockfish Canary rockfish
Individual bycatch quotas NORTH of 40'10'N SOUTH of 40'10'N
strengthen individual Perce
incentives to avoid bycatch 97%
94.1%
0.7%
2.2%
When bycatch is highly
5%
uncertain individual quotas
markets may be subject to Widow rockfish Widow rockfish
high price variability
NORTH of 40'10'N SOUTH of 40'10'N
(creating substantial financial Perce
risk for fishermen) and may 98.3%
1.2%
97.6%
fail to allocate quota
1.3%
efficiently.
I explore how pooling Yelloweye rockfish
NORTH of 40'10'N
Yelloweye rockfish
SOUTH of 40'10'N
approaches and possibly Perce
market insurance can be
used to reduce financial risk 99.7% 0.3% 99.8% 0.2%
for fishermen in these cases
Model Assumptions
Fishing events and bycatch are discrete homogeneous events.
Each fishing event yields one unit of target catch with certainty
and has a constant probability of catching one unit of bycatch.
For simplicity, the bycatch is assumed to have no value and the
target catch has a unit net value after harvest costs.
Bycatch is purely random modeled as a Bernoulli process
where bycatch events are independent over time and across
fishermen
With this specification the expected value of an individual bycatch
quota allocation is equal to the sum of negative binomial probabilities
of exactly reaching period k before exhausting IBQ holdings, j,
summed over periods (ITQ use) k<=t and IBQ holdings j
probability of reaching the final period without exhausting IBQ times
the profit associated with harvesting in all possible periods.
t 1 (k 1)!
E q, t , p t
k q
* p (1 p) *(k t )
q
k q ( q 1)! k q !
Expected Value of IBQ and ITQ with discrete bycatch
probabilities of 0.01 and 0.05
Maximum value of unit of IBQ=1/p
(a) (b)
Marginal IBQ Value 1.0
Marginal ITQ Value
100
1st Unit IBQ
0.9
90 2nd Unit IBQ
3rd Unit IBQ 0.8
80
Incremental Value of ITQ
Incremental Value of IBQ
4th Unit IBQ 0.7
70
5th Unit IBQ
60 0.6
0.5
P=0.01
50 P=0.01
40 0.4
0.3 Holds 1 Unit IBQ
30 Holds 2 Units IBQ
20 0.2 Holds 3 Units IBQ
0.1 Holds 4 Units IBQ
10
Holds 5 Units IBQ
0 0.0
1 26 51 76 101 126 151 176 201 226 251 276 1 26 51 76 101 126 151 176 201 226 251 276
ITQ Units Already Held
(c) ITQ Units Left (d)
20 1.0
18 1st Unit IBQ 0.9
5th Unit IBQ
16 10th Unit IBQ 0.8
Incremental Value of IBQ
Incremental Value of ITQ
14 15th Unit IBQ 0.7
20th Unit IBQ
12 0.6
10 0.5
8
P=0.05
0.4
Holds 1 Unit IBQ
P=0.05
6 0.3 Holds 5 Units IBQ
4 0.2 Holds 10 Units IBQ
Holds 15 Units IBQ
2 0.1 Holds 20 Units IBQ
0 0.0
1 26 51 76 101 126 151 176 201 226 251 276 1 26 51 76 101 126 151 176 201 226 251 276
ITQ Units Left ITQ Units Already Held
The distribution of ITQ units used (with a maximum of 300) before for (a)
one, (b) two, (c) three units of IBQ is exhausted with p=0.01.
(a) (b) (c)
25% 25% 50%
Probability of Occurence
20%
Probability of Occurence
40%
Probability of Occurence
20%
15% 15% 30%
10% 10% 20%
5% 5% 10%
0% 0% 0%
20-40
40-60
60-80
100-120
120-140
140-160
160-180
180-200
200-220
220-240
240-260
260-280
280-300
0-20
80-100
20-40
40-60
60-80
100-120
120-140
140-160
160-180
180-200
200-220
220-240
240-260
260-280
280-300
0-20
80-100
00
0
0
0
0
0
20
0
14
18
22
26
30
-6
-1
0-
40
0-
0-
0-
0-
0-
80
12
16
20
24
28
Profit Range Profit Range Profit Range
With only one unit of IBQ the distribution of possible outcomes
50%
40% is skewed to the right but with three units it is skewed to the left
Probability of Occurence
30% Thus trading away a unit of quota always increases downside
risk, in terms of increased right skew of the new distribution of
outcomes, and may either increase or decrease standard risk
20%
10%
as measured by the standard deviation of expected revenue.
0%
Sufficient standard risk aversion and or prudence (downside
0-20 20- 40- 60- 80- 100- 120- 140- 160- 180- 200- 220- 240- 260- 280-
risk aversion) could inhibit trading even where it would lead to
40 60 80 100 120 140 160 180 200 220 240 260 280 300
increases in total expected value.
Modeling an IBQ-ITQ Market
Assume numerous homogeneous participants
Assume that risk premiums are not large enough to
preclude trading between individuals with different
ratios of IBQ and ITQ, and markets continually
equilibrate the levels and ratios of IBQ and ITQ
across fishermen
We can model the prices of IBQ as the expected
value of an additional unit of IBQ or ITQ if all the
quota was held by one individual – what would they
pay for another unit of IBQ given their existing ITQ
allocation?
Need to approximate IBQ value with simulation
techniques since values in equation 1 approach
infinity
Marginal IBQ value for varying starting levels of aggregate IBQ when
aggregate ITQ is 5000 and p is 0.01 (panel a) or 0.05 (panel b)
(a) (b)
100 20
90
80
15
ICQ Per Unit Value
ICQ Per Unit Value
70
60
50 10
40
30
5
20
10
- 0
25 30 35 40 45 50 55 60 65 70 75 200 210 220 230 240 250 260 270 280 290 300
Starting Total ICQ Starting Total ICQ
When aggregate ITQ is large and ∑IBQ=p* ∑ ITQ, the value of
IBQ is approximately 0.5/p.
The marginal value of IBQ will asymptotically approach 1/p for
decreasing levels of aggregate IBQ, and the expected value will
asymptotically approach zero for increasing levels of aggregate
IBQ.
Simulated price paths for IBQ from simulations with p=0.01 and 50 fisher
each with allocations of 100 units (aggregate ITQ=5000) and aggregate IBQ
of (a) 45 units, (b) 50 units and (c) 55 units.
(a)
Price (b)
Cumulative Bycatch
110.0 55
100.0 50
90.0 45
80.0 40
Cumulative Bycatch
70.0 35
• Prices vary 60.0 30
Price
50.0 25
widely during the 40.0
30.0
20
15
year as actual 20.0
10.0
10
5
-
bycatch departs
-
1 11 21 31 41 51 61 71 81 91 1 11 21 31 41 51 61 71 81 91
Period Period
(c) (d)
from the 110.0
100.0
55
50
expected level 90.0 45
40
Cumulative Bycatch
80.0
70.0 35
60.0 30
Price
50.0 25
40.0 20
30.0 15
20.0
10
5
10.0
-
-
1 11 21 31 41 51 61 71 81 91
1 11 21 31 41 51 61 71 81 91
Period Period
(e) (f)
110.0 55
100.0 50
90.0 45
80.0 40
Cumulative Bycatch
70.0 35
60.0 30
Price
50.0 25
40.0 20
30.0 15
20.0 10
10.0 5
- -
1 11 21 31 41 51 61 71 81 91 1 11 21 31 41 51 61 71 81 91
Period Period
Simulated distribution of IBQ prices mid season
(a)
45%
Simulated distribution of 40% Q=45 Q=50 Q=55
IBQ prices half way through
Percentage of Price Observations
35%
the fishing year for varying 30%
bycatch probabilities (a) 25% P=0.01
1%, (b) 5% and with initial 20%
total IBQ allocations equal 15%
to 90%, 100% and 110% of 10%
the expected total bycatch. 5%
0%
With a very low bycatch 0-10 10-20 20-30 30-40 40-50 50-60
IBQ Price Interval
60-70 70-80 80-90 90-100
probability (p=0.01) the (b)
80%
likelihood of intermediate 70% Q=225 Q=250 Q=275
prices is high.
Percentage Observations
60%
50%
With higher bycatch 40% P=0.05
probabilities (p=0.05) prices 30%
are more predictable and 20%
tend toward the extremes 10%
0%
2
4
6
8
10
12
14
16
18
20
0-
2-
4-
6-
8-
-
-
-
-
-
10
12
14
16
18
IBQ Price Interval
(c)
120%
100%
CV of individual profit as bycatch probability and quota
vary
1.00
Short 10% Balanced Surplus 10%
0.80
CV of Individual Annual Profit
0.60
0.40
0.20
-
0.01 0.05 0.10
Bycatch Probability
Although there is little variance in total industry profit there can
be quite a bit of variance in individual profit as some gain and
some lose through transactions in the quota market to cover
bycatch
Pooling
Pooling bycatch quota can protect pool members from
variability in profit due to individual variability in bycatch and
exposure to price variability in the IBQ market
Similarly, commitment to a reciprocal trading system at a set
price could also reduce risk and bargaining inefficiencies that
arise from private information (Matouschek and Ramezzana
2007)
While larger pools decrease price variability they may also
increase problems associated with moral hazard and adverse
selection – so limited pool sizes may be preferable
Lee and Lignon (2001) show that in the presence of moral
hazard there are typically finite optimal pool sizes. They find
optimal pools sizes between 50 and 100 for a variety of loss
probabilities and utility function specifications.
CV of individual profit with different pool sizes
1.000
Q=45 Q=50 Q=55
0.800
P=0.01
CV of Individual Annual Profit
0.600
∑ITQ=5000
0.400
∑IBQ=45,50 or 55
0.200
-
1 2 5 10 25 50
Pool Size
Pooling can substantially reduce variability of individual
income even for small pool sizes and low bycatch
probabilities
Insurance
Risk could be reduced further or even eliminated with market
insurance.
Insurance might also be important if there was some concern
that a race for fish might develop (e.g., where fishermen, or
pools of fishermen, would race to use up their individual or
pooled allocations of target catch quota early before the total
bycatch quota was exhausted and the fishery shut down).
For example, the proposed regulations for the West Coast
groundfish trawl ITQ could potentially shut down the entire
fishery in the event of a large bycatch event, a “disaster tow”,
that is greater than or equal to the total remaining quota for
that species.
Market Insurance Against Insufficient IBQ
(All IBQ pooled and individual ITQ allocations insured)
IBQ=p*ITQ IBCQ=p*ITQ*0.8
25.00 25.00
80% insured 90% insured 100% insured 80% insured 90% insured 100% insured
Insurance
Insurance Premium
20.00
Insurance Premium
20.00
premiums per 15.00 15.00
vessel 10.00 10.00
5.00 5.00
- -
n=25 n=50 n=75 n=100 n=25 n=50 n=75 n=100
CV expected
Pool Size Pool Size
0.20 0.20
80% insured 90% insured 100% insured
revenue (pre-
80% insured 90% insured 100% insured
CV Revenue Per Vessel
CV Revenue Per Vessel
0.15
insurance)
0.15
per vessel
0.10 0.10
0.05 0.05
-
-
CV of
n=25 n=50 n=75 n=100
n=25 n=50 n=75 n=100
Pool Size
Pool Size
expected 0.04 0.04
80% insured 90% insured 100% insured 80% insured 90% insured 100% insured
profit (post
CV of Profit Per Vessel
CV Profit Per Vessel
0.03 0.03
insurance) 0.02 0.02
per vessel 0.01 0.01
- 0
n=25 n=50 n=75 n=100 n=25 n=50 n=75 n=100
Pool Size Pool Size
Conclusions
When bycatch is highly uncertain and rare, markets may not
work effectively or will leave individuals facing substantial
financial risk.
In such cases it is useful to think about bycatch management
as a risk management problem rather than a joint production
problem.
Risk reduction mechanisms such as pooling quotas, self
insurance and market insurance may be useful ways for
stakeholders to reduce risk and perhaps increase efficiency as
well.
There is anecdotal evidence that fishermen do form these
types of risk pools informally with reciprocal trading behavior.
The risk faced by the industry and the need for insurance might
be partly mitigated in some cases by allowing quotas to be
borrowed or carried forward across years or by setting multi-
year TACs and quota allocations.
(forthcoming in Ecological Economics)
For a copy of the paper email me at
dan.holland@noaa.gov