options in bioeconomic modelling of stocks and harvesting of tuna john kennedy department of...

Options in Bioeconomic Modelling

of Stocks and Harvesting of Tuna

John Kennedy

Department of Economics and Finance

La Trobe University

Melbourne

Sustainability of Oceanic Top Predator Species Workshop

University of California at Santa Barbara, 12-14 April 2007


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The Case of Western and Central Pacific (WPC) Migratory Tuna Stocks

The four main migratory tuna species in the WCPO are:

Yellowfin

Bigeye

Skipjack

Albacore


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Skipjack, yellowfin, and bigeye straddle the equator, throughout the year migrating in response to changes in feed supply, dependent on the position of the sun relative to the equator.

Migration of the three stocks is through the EEZs of Pacific Island Nations and the High Seas.

The ability of the Pacific Island Nations to determine harvesting access to stocks in their EEZs by their nationals or by Distant Water Fishing Nations does not enable the attainment of an economically efficient outcome across the coastal states. Even if the coastal states agree to pursue nominated catches in their EEZs through time, the leakage of stock to the High Seas means that overfishing will occur there.

The United Nations Fish Stocks Agreement goes some way towards establishing a system of annual catch quotas and their allocation across all interested harvesting parties. The system is implemented by a Regional Fisheries Management Organisation. A Western and Central Pacific Fisheries Commission is now in force for the WCP.


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Characteristics of the WCP Tuna Fishery

Multifaceted:

Multi-species (Skipjack, Yellowfin, Bigeye, Albacore)

Multi-gear (Mainly Purse seine and Longline, but also Pole and Line, and Troll

Many Distant Water Fishing Nations (Asian – Japan, Taiwan, Korea, China; USA; growing EC interest)

Many disparate Pacific Island Nations – coastal states with EEZs.

Sustainability:

Yellowfin and Bigeye stocks are now viewed as over-exploited, requiring reduced targeting to ensure sustainability.


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Scope for modelling many interactions:

Physical/Biological effects

Between fleets with different gears targeting different species - e.g. Purse seiners taking young surface skipjack, yellowfin and bigeye for a low price return compared with longliners taking deeper older and much higher priced (sashimi) tuna. Increased purse seining reduces returns to longliners through lower stock in older age catergories, increasing the cost of catching additional tuna.

Price effects

As more is caught of a grade of tuna by some fleets, price of the grade falls, adversely affecting returns for other fleets taking that grade.


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The Western and Central Fisheries Commission boundary, and national EEZs


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The Forum Fisheries Agency (FFA) region defined by outline of 5 degree squares and the EEZs of FFA member countries (shaded)

20N

0

120E

20S

140E 160E 180 160W 140W

M a r sh a llI s la n d s

Fe d e r a te d Sta te s o f M ic r o n e s iaP a la u

P a p u a N e w G u in e a

So lo m o n I s la n d s

A u str a lia

N e w Z e a la n d

V a n u a tu

Fij iT o n g a

N iu eC o o kI s la n d s

K ir b a ti( L in e )

K ir ib a ti( P h o e n ix )

Sa m o aT u v a lu

N a u r u K ir ib a ti( G ilb e r t)


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Criteria for gauging the impact of policy or environmental change:

Biological/Sustainability

Economic efficiency

Socioeconomic

Equity/fairness

Who determines the criteria? A regulatory regime?


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The WCP Regulatory Regime

In the case of the WCP tuna fishery, the regional tuna stocks are now to be managed by the WCP Fisheries Commission based on an agreed Convention.

Such an economic objective can be taken to be sanctioned by:

Article 5 (a) of the Convention, which advocates “measures to ensure long-term sustainability of highly migratory fish stocks in the Convention Area and promote the objective of their optimum utilization”.

Resources are optimally utilized if the result is economically efficient. However, the article 5 (b) objective, which is the only one discussed at length, in general will not be economically efficient. It is to be subject to economic (and environmental) factors, but in what way is not spelt out.

Article 5 (b) of the Convention makes the main management objective the targeting of the stock resulting in maximum sustainable yield.

As is well known, this objective only results in outcomes which are economically efficient if the cost per unit of fishing effort and the real rate of discount are zero (both unlikely to hold in practice), or for particular combinations of positive effort costs and rates of discount.


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Equity considerationsThe Convention does refer to many economic and social issues which should be taken into account in deciding regulatory measures, but with no indication of weighting. For example:

Recognizing the ecological and geographical vulnerability of the small island developing States, territories and possessions in the region, their economic and social dependence on highly migratory fish stocks, and their need for specific assistance, including financial, scientific and technological assistance, to allow them to participate effectively in the conservation, management and sustainable use of the highly migratory fish stocks,Further recognizing that smaller island developing States have unique needs which require special attention and consideration in the provision of financial, scientific and technological assistance, …

Because the management of migratory and high seas fish stocks typically results in returns to more than one nation, the question arises as to whether returns should be differentially weighted by nation in determining joint returns. Should returns to the PINs be weighted more highly than returns to DWFNs? Should the PINs as a bloc be encouraged to develop strategies to maximise their total access-fee income, on grounds of equity, or of evening the bargaining power between the PINs and the DWFNs?


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Simulation or Optimisation mode?

Simulation

Ideal for conducting ‘What If?’ analysis (Policy or Environmental change)

Few constraints in formulating the problem

Large search for policy settings which result in a ‘good’ outcome.

Optimisation

May be used normatively for finding the best catch levels, or predictively (positively) for predicting the catch levels of rent maximising fishers.


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A Simulation Example:

WESTERN AND CENTRAL PACIFIC OCEAN BIOECONOMIC TUNA MODELThe spatially disaggregated bioeconomic model described by Bertignac et al. (2000) for investigating optimal reductions in fishing effort by fleets across tuna species in the western and central Pacific Ocean has been updated for further explorations of policy relevant in the Commission era. Cost and price parameters have been updated (Reid et al. 2003); and fleet coverage has been expanded, effort and stock exponents in Schaefer harvest functions have been estimated empirically and are not necessarily set to 1, and fishing effort is now split between effort within the FFA region and outside

the FFA region (Reid et al. 2006).

Effect of effort reduction across all fisheries on economic rents A paper was prepared by the Scientific Committee of the WCPFC in response to a resolution passed by the Commission requesting estimation of potential consequences of alternative management options for bigeye and yellowfin tuna based on projections from population models (Hampton et al. 2005). One of the options considered was a 30 per cent reduction in fishing effort of all fisheries from levels in 2003.

By way of complementary analysis, the results for economic rents from running the updated model for a 30 per cent reduction in effort are briefly reported below. Fuller details are given in Reid et al.

(2006).


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Change in fishery rent under a 30 per cent effort reduction


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Optimisation

A common approach:

Determine the optimal outcome (maximum present value of rents generated by all participants across some time period; if rents, is this all rents – producer, consumer and government?)

What regulatory mechanisms or incentive systems might bring this about?

e.g. ITQs, ITEs – for economically efficient outcomes? But are the markets competitive?

- but these options are very likely to have impacts on the objective function, which when taken into account will change what outcome is optimal.


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An WCP Optimisation Example

Species Purse seine Longline Reference Rent max Reference Rent max f Change (%) f Change (%)

Bigeye 0.06081 0.00028 -99.5 0.01627 0.01715 5.4 Yellowfin 0.02478 0.00042 -98.3 0.00461 0.00877 90.3 Skipjack 0.03138 0.00072 -97.7 0 0 Catch Change (%) Catch Change (%) Bigeye 29.0 0.2 -99.4 87.7 119.8 36.6 Yellowfin 199.8 4.0 -98.0 88.9 203.3 128.7 Skipjack 1251.7 33.4 -97.3 0 0 Rent Change (%) Rent Change (%) All 123.0 7.7 -94.1 114.7 562.5 390.3 Rent as % of revenue Rent as % of revenue All 10 23.0 10 27.0

Fleets active Fleets active All Taiwan All Taiwan, Others

Comparison of rent-maximizing and reference solution. Catch is in thousand tonnes and rent in million US$.

Hannesson and Kennedy (2007)


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Time dimension

Static or steady state

Comparative statics – Change of equilibrium catch and stocks from a base equilibrium resulting from a new management policy or from environmental change.

DynamicLength of planning horizon (finite or infinite?)Rate of discount (real rate? market or normative?)


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Spatial dimension

One fishing ground or many?

Important in modelling migratory stock passing through the EEZs of coastal states and the High Seas if the EEZs are the control areas.

• Then modelling of diffusion and advection of stock between say 5 degree squares of ocean likely to be important.

But from an overall control point of view, these may be artificial.

May be more reasonable to have TACs set across the whole region, allocating the TAC equitably across coastal and distant water states, and allowing the quotas to be traded.


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Sum Sum %Group WCPO FFA FFA/WCPOalb_mt 1,197,347 258,106 22 bet_mt 2,292,563 919,079 40 skj_mt 11,591,580 8,856,799 76 yft_mt 4,821,425 3,383,454 70

CES Data to 5 degree squares map


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Column 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 50 N 110 E 115 120 125 130 135 140 145 150 155 160 165 170 175 180 175 170 165 160 155 150 145 140 135 130 125

45

40

35

30

25 11,978 16,697 14,470 9,929 8,047 7,705 6,410 8,089 6,774 6,739 591 1,936 2,904 3,710 4,573 6,459 4,285 1,885 1,336 577 344 54 5,656 4,950 7,672 2,242 2,616 3,530 3,294 4,185 4,594 8,858 5,435 4,143 4,303 4,325 4,628 4,472 5,666 6,451 10,549 11,481 10,235 2,864

51,212 44,035 75,459 6,270 727 1,198 1,124 360 1,696 4,888 16,633 9,279 271 7 13 28 6 11 4 0 0 0 16,134 6,722 14,326 2,612 821 937 759 890 959 2,203 3,007 1,477 774 1,050 1,319 971 673 570 921 818 924 191

20 1,326 1,397 967 1,893 3,230 3,834 3,180 1,509 1,156 704 519 486 799 863 1,154 1,086 778 566 519 160 53 12 1,440 986 1,216 1,638 2,455 2,905 2,045 1,173 988 1,977 973 2,005 3,029 3,761 3,165 3,777 5,708 7,227 9,936 12,862 6,816 175

13,378 17,336 48,183 16,022 11,441 16,024 12,573 8,550 6,631 4,582 5,931 7,509 8,766 2,042 45 47 12 12 9 6 2 0 5,963 2,273 5,407 2,202 3,030 2,370 1,273 464 424 574 183 574 1,105 1,351 1,178 753 811 683 1,108 1,768 1,267 57

15 1,822 2,330 474 287 1,188 1,207 1,033 1,129 1,016 395 201 326 595 2,038 667 133 21 29 38 10 1 0 1,196 1,063 392 244 565 680 654 286 1,002 2,758 832 797 1,109 5,142 10,845 5,377 2,104 2,267 2,618 2,252 281 41

30,476 45,958 31,880 46,234 25,382 21,872 25,931 30,144 14,693 7,381 7,146 4,652 384 416 483 27 4 2 3 2 0 - 4,926 3,710 2,497 1,386 1,336 1,307 901 498 862 1,066 285 375 514 1,620 2,508 460 225 251 237 196 52 40

10 1,093 730 463 378 754 958 1,000 803 1,161 2,043 965 1,060 957 715 241 51 50 17 1 3 3 6 9,826 6,281 5,916 6,832 9,971 10,784 7,009 4,768 15,073 37,355 14,807 23,183 25,824 28,734 19,905 7,112 3,247 1,131 157 42 93 106

52,863 42,420 23,225 28,030 30,556 29,956 20,017 23,593 14,665 8,993 2,504 815 391 94 22 1 2 0 0 - - - 27,436 18,576 13,442 12,323 15,351 13,957 6,479 4,065 8,961 18,053 4,825 6,150 5,228 4,448 2,060 797 437 258 81 284 1,227 147

5 1,268 1,109 164 127 169 198 160 186 170 360 168 149 57 79 49 81 78 13 12 17 8 7 13,335 25,581 17,210 12,705 16,712 25,606 15,603 14,028 12,476 28,909 13,013 14,857 12,444 9,996 20,444 23,249 23,266 16,942 18,037 18,618 13,878 12,071 28,653 147,799 144,867 157,424 132,931 74,696 71,384 85,767 77,342 65,178 42,122 23,421 13,546 7,272 288 409 6 1 1 0 1 2 41,027 83,575 44,337 37,820 40,671 35,082 19,961 20,217 13,085 21,854 10,494 10,379 6,314 5,478 8,862 9,501 8,853 6,573 5,420 5,322 4,318 3,109

0 758 470 296 98 156 157 229 333 178 430 114 209 121 209 77 76 34 20 12 15 14 4 13,930 22,584 36,252 37,727 39,047 34,830 32,702 27,291 17,426 34,526 10,890 17,244 15,672 10,969 13,380 24,899 24,068 21,812 21,472 18,338 12,299 12,106 92,352 296,024 870,353 798,218 607,673 487,614 328,606 219,178 220,251 213,779 130,031 93,395 29,547 10,700 4,175 602 12 5 3 1 3 1 86,926 116,350 243,931 251,491 228,386 197,117 152,034 111,318 60,462 101,423 40,739 32,691 21,772 18,675 17,312 18,760 13,510 10,461 8,223 5,840 3,323 2,466

5 6 6 46 194 318 331 606 813 867 1,597 2,047 3,619 3,547 2,420 1,337 1,039 642 256 54 39 54 13 2,368 695 12,149 16,853 11,982 16,935 21,698 15,994 15,990 13,226 12,359 12,111 14,949 15,322 15,939 20,767 25,430 26,746 23,973 18,617 14,302 10,916

118,996 14,336 356,301 493,960 425,244 393,622 312,456 131,281 169,479 162,725 149,851 81,958 23,422 10,389 37,436 1,393 19 12 8 3 1 1 22,771 5,685 117,334 174,891 145,048 161,610 144,951 87,835 84,300 66,087 58,334 53,416 29,187 23,734 23,674 12,180 10,607 9,382 7,764 5,984 3,494 2,438

10 - 2,784 2 260 458 1,476 3,255 5,213 8,461 6,589 11,955 15,789 19,069 16,873 11,184 10,053 9,048 4,198 1,721 2,500 1,748 1,003 1,827 899 26 5,013 11,086 19,959 13,384 12,615 11,906 5,480 8,821 7,941 9,976 10,095 11,026 18,159 29,264 17,942 31,489 51,384 46,628 45,986

146,362 90 79 99,314 254,390 543,172 203,898 128,481 127,891 88,272 127,908 43,561 11,584 8,531 1,853 437 27 10 14 12 5 10 16,371 1,739 98 50,121 95,345 149,858 89,789 67,000 40,982 20,913 25,408 15,347 12,958 15,615 10,727 12,353 15,700 13,158 12,963 18,518 16,354 15,358

15 6 2 51 3,176 9,199 13,038 17,507 9,488 12,298 9,450 5,081 26,346 9,286 10,315 13,240 9,124 11,255 9,918 10,134 12,317 10,688 6,709 1 1 81 1,102 3,188 9,494 6,840 1,478 1,732 1,407 891 1,166 1,150 1,278 2,015 2,541 6,610 10,948 10,767 27,713 32,165 27,038 1 - 31 1,838 17,809 173,662 38,516 13,127 21,770 13,176 10,031 7,214 661 204 75 26 40 25 11 6 2 1 3 1 1,597 11,940 24,654 59,693 33,482 6,926 8,725 6,603 3,383 3,005 1,966 2,029 2,134 2,483 4,101 5,542 5,380 8,643 7,913 7,351

20 - 0 885 8,862 12,287 9,204 9,238 28,205 8,633 5,051 8,385 4,112 2,340 2,003 3,806 3,823 2,876 5,667 12,844 17,669 20,735 - - 2,556 1,553 801 718 563 937 1,230 797 657 396 168 195 489 473 384 989 1,442 1,885 2,368 122 0 512 161 2,791 8,943 1,415 691 39,761 27,888 973 37 26 7 18 13 4 5 18 38 21 - 3 10,519 10,171 4,653 3,918 2,444 4,504 8,431 5,042 1,865 876 381 273 738 747 451 568 1,447 1,626 2,127

25 - 1 1,465 7,800 7,496 3,360 7,439 10,587 3,082 6,883 4,387 1,748 1,256 1,217 1,199 1,854 1,612 3,388 4,543 3,954 23 91 833 1,514 426 477 343 568 345 471 310 209 155 190 200 242 302 893 1,441 1,537

- 21 61 659 1,154 1,820 43 6,431 630 41 24 4 1 3 4 5 3 9 8 4 24 74 6,272 6,185 2,062 3,160 1,255 3,121 999 1,007 532 272 197 301 256 189 249 576 804 804

30 3,285 19,451 15,640 6,297 15,132 15,020 6,246 19,761 19,657 16,424 11,758 10,715 6,275 5,900 10,555 4,419 1,783 1,279 4,810 4,232 1,554 1,186 869 1,037 979 1,225 972 783 664 489 338 329 484 229 197 160

76 218 252 6 74 30 13 62 54 27 26 19 8 3 42 2 1 - 14,649 11,744 5,376 2,100 1,458 1,530 1,239 1,786 1,630 1,402 1,148 1,032 687 568 875 479 156 116

35 - 0 4,542 12,160 7,615 10,459 6,604 5,253 2,578 6,163 5,540 5,250 5,135 5,872 5,481 3,723 3,034 2,976 758 246 - - 1,219 4,424 1,536 1,605 3,321 2,720 620 532 371 278 168 132 118 140 195 153 68 63 - - 178 30 60 7 101 24 0 5 1 13 14 30 10 4 3 2 1 -

2 - 12,707 5,750 1,838 1,558 1,036 761 199 432 446 394 160 150 121 108 295 274 27 7

40 S 60 33 11,285 13,902 6,691 3,768 970 11,505 2,958 1,490 838 6,028 5,994 14,164 17,276 10,725 9,294 5,490 981 187 4 21 984 2,211 925 327 162 2,155 100 205 26 20 63 88 106 139 183 117 3 -

- 736 20,782 4,987 1,797 27 16,130 45,039 15 1 0 6 4 70 26 3 1 0 - - 17 162 7,226 1,805 834 130 137 1,415 23 550 56 9 50 115 106 275 577 464 1 -

lonc 110 E 115 120 125 130 135 140 145 150 155 160 165 170 175 180 175 170 165 160 155 150 145 140 135 130 125 lond 110 115 120 125 130 135 140 145 150 155 160 165 170 175 180 185 190 195 200 205 210 215 220 225 230 235

Sum Sum %Group WCPO FFA FFA/WCPOalb_mt 1,197,347 258,106 22 bet_mt 2,292,563 919,079 40 skj_mt 11,591,580 8,856,799 76 yft_mt 4,821,425 3,383,454 70


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Stock dimension

Stock size captured by:

total biomass of the stock?

biomass of each age cohort?


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Deterministic or stochastic

• If stochastic, how is the objective function different from that for a deterministic formulation of the model?

• Expected return? Implies the decision maker is risk neutral

•Utility functions for risky income, allowing for risk preferring or risk aversion in decision making?


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Number of decision makers

Are there one or many decision makers/governments/ regulatory bodies/stakeholders? Each with one or many objective functions? If many decision makers, game theory is relevant, at least for insights.

What if the decision makers each went their own way, harvesting through time to maximise their objective function, taking as given the harvesting of the other decision makers? The outcome of such behaviour across all decision makers is a Nash Equilibrium.


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Some Game Theory Concepts

Solution Concepts1) The core, for side payments feasible (Straffin, 1993 p. 165)2) Coalition-proof Nash equilibrium (CPNE) for side payments feasible

Allocationsi) Joint maximisation solutionii) Shapley value

Aumann (1989, p. 23) sums up the value with: “Fully characterised by a set of axioms, it may be thought of as a reasonable compromise or arbitrated outcome, given the power of the players.”

iii) The nucleolusEven if the rent maximising solution is not in the core, it can still be argued that it is the allocation most likely to be accepted by all players, because the greatest loss (or equal losses) suffered by players through not receiving coalition returns would be minimized (Straffin 1993, p. 205).


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NE Single fleet

(Defector) rent

NE Total rent for coalition of

remaining fleets

Maximum payment coalition could make to

dissuade defection, given the maximum

cooperative joint rent is 569.7

NE rent for each fleet competing against all other fleets

Japan 197.3 238.3 331.4 22.3 Korea 230.0 221.1 348.6 20.8 Taiwan 259.4 222.5 347.2 26.7 PICs 128.7 294.1 275.6 25.7 China 180.2 313.5 256.3 21.3 US 126.2 155.9 413.9 24.8 Others 223.5 272.0 297.8 12.9

Total 1345.2 154.5

Rent obtained by one defecting fleet, rent for coalition of remaining fleets , and coalition rent for dissuading defection. Million US$.

Hannesson and Kennedy (2007)

WCP Example


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Conclusions

The WCP tuna fishery presents many modelling choices. Which choices should be made obviously depends on the purpose or objectives of the modelling effort. Different objective require extensions along different dimensions.

The change in regulatory system from reliance on national autonomy over provision of access rights to tuna in EEZs to a Commission with responsibility for overall sustainability and economic returns suggests that modelling will become less spatially explicit. To obtain agreement at the Commission level on total allowable catches and their allocation will require bargaining between many disparate parties. Equity considerations will be one influence; a second and probably stronger influence will be tradeoffs and side payments in agreeing allocations. What is lost or gained by an alternative course of action to the current action can only be determined by modelling. Game theory concepts are likely to play a larger role in modelling the WCP tuna fishery to highlight the bargaining power of the participants.


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options in bioeconomic modelling of stocks and harvesting of tuna john kennedy department of...

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