Derivation of Shadow Price of Sea Turtle Derivation of Shadow Price of Sea Turtle Bycatch in Hawaii-based Longline Fisheries: Bycatch in Hawaii-based Longline Fisheries:

An Input Distance Function ApproachAn Input Distance Function Approach

Hui Huang & PingSun LeungHui Huang & PingSun LeungUniversity of Hawaii at ManoaUniversity of Hawaii at Manoa

Interaction Between Hawaii-basedInteraction Between Hawaii-based Longline Gear and Sea Turtles Longline Gear and Sea Turtles

Sea turtle conservation: one of the most important issues Sea turtle conservation: one of the most important issues facing Hawaii-based longline fisheries facing Hawaii-based longline fisheries

Swordfish and Mixed-target fishing: Swordfish and Mixed-target fishing: shallow sets; high rate of turtle captureshallow sets; high rate of turtle capture

Tuna-target fishing:Tuna-target fishing: deep sets; relatively less interactionsdeep sets; relatively less interactions

Turtle Catches by Trip Types, 1991-1999Turtle Catches by Trip Types, 1991-1999

92.43%482113751991-1999

92.11%658121999

89.80%1054341998

91.30%430121997

89.66%940381996

85.71%98461995

96.92%22611994

96.10%33711993

96.92%26571992

94.74%310441991

% of Swordfish and MixedTunaMixedSwordfishLand Year

Source: Observer’s Report, Honolulu Laboratory, NMFS (1991-1999)

Longline Fishing Restricted AreasLongline Fishing Restricted AreasArea A: 44 N-28N, 168 W-150 W

No Fishing allowed

Area B: 44 N-28 N, 173 E-168 W

& 150 W-137 W

Restricted longline fishing

100% observer coverage

Area C: 28 N-Equator, 173 E-137 W

Only tuna-trip is allowed

Area A : Closed throughout the year

Area B & C: Closed from March 15,

until May 31

Swordfish Ban and ResumptionSwordfish Ban and Resumption

2001, NMFS’ preferred alternative:2001, NMFS’ preferred alternative: swordfish-style fishing is prohibited; an area (15-0 North, 145-180 swordfish-style fishing is prohibited; an area (15-0 North, 145-180

W) is closed for April and MayW) is closed for April and May. .

April 2004, Swordfish-style fishing return:April 2004, Swordfish-style fishing return:

fewer fishing days; observers on board at all times; strict limits on fewer fishing days; observers on board at all times; strict limits on the number of turtles (16 leather-back turtles, 17 loggerhead the number of turtles (16 leather-back turtles, 17 loggerhead turtles)turtles)

Research Objectives:Research Objectives: To Introduce an alternative method of calculating cost of sea turtle To Introduce an alternative method of calculating cost of sea turtle

protectionprotection To deduce trip-specific shadow price of sea turtle bycatchTo deduce trip-specific shadow price of sea turtle bycatch To compare shadow prices of sea turtle bycatch of various To compare shadow prices of sea turtle bycatch of various

periods, locations, and trip typesperiods, locations, and trip types

General idea of the methodology:General idea of the methodology: Distance function: used in deducing shadow prices for pollutants Distance function: used in deducing shadow prices for pollutants

(e.g. Fare & Grosskopf, 1993; Cogins and Swinton, 1996)(e.g. Fare & Grosskopf, 1993; Cogins and Swinton, 1996) General idea: Dual Shephard’s lemma yields cost-related shadow General idea: Dual Shephard’s lemma yields cost-related shadow

prices of undesirable output (prices of undesirable output (seasea turtle bycatchturtle bycatch) from the input ) from the input distance functiondistance function

Previous StudiesPrevious Studies Curtis and Hicks (2000)Curtis and Hicks (2000) Chakravorty and Nemoto (2000)Chakravorty and Nemoto (2000) implicit prices of sea turtle bycatch ; implicit prices of sea turtle bycatch ; overall welfare foregone from regulatory policiesoverall welfare foregone from regulatory policies

Present WorkPresent Work No need to specify regulatory constraintsNo need to specify regulatory constraints Modest data requirementModest data requirement Flexibility for comparing shadow prices by trip Flexibility for comparing shadow prices by trip

characteristics: time; areas; trip typescharacteristics: time; areas; trip types

Input Distance FunctionInput Distance Function

xo/Di(uo,xo )

x1

x2

xo

L(uo)

}),,()(:{max),,( RtuLxtxuD

Maximum amount of the input vector can be Maximum amount of the input vector can be

deflated, keeping the output vector in the deflated, keeping the output vector in the technology settechnology set

Dual to cost function according to Shephard’s Dual to cost function according to Shephard’s LemmaLemma

FOC: how many units of desirable output FOC: how many units of desirable output (swordfish) would be willing to forego to reduce (swordfish) would be willing to forego to reduce one sea turtle bycatchone sea turtle bycatch

Swordfish observed price= shadow price Swordfish observed price= shadow price derive shadow price for sea turtlederive shadow price for sea turtle

j

iji utxuD

utxuDrr

/),,(/).,(.**

Functional form to derive value of distance functionFunctional form to derive value of distance function

Translog functional formTranslog functional form

n=1,2: trip length (days, weighted by net tons), hooks in that trip (1,000) n=1,2: trip length (days, weighted by net tons), hooks in that trip (1,000) m=1,2,3: swordfish catch, tuna catch, catch of other species (1,000 m=1,2,3: swordfish catch, tuna catch, catch of other species (1,000

pounds)pounds) m=4: number of sea turtlem=4: number of sea turtle

m

M

mmtn

N

nntttt

m

N

n

M

mnnmmm

M

m

M

mmm

n

N

nn

M

nnnm

M

mm

N

nnn

utxttt

uxuu

xxuxtxuLnD

lnln21.

lnln21lnln

21

lnln21lnln),,(

11

2

1 1'

1 1''

'1 1'

'11

0

Estimation of ParametersEstimation of Parameters

Subject toSubject to C1C1

C2C2

C3C3

C4C4

C5aC5a

C5bC5b

C5cC5c

C5dC5d

C6aC6a C6bC6b

212

1),,( ),,(lnk

txuDMinimize

,0),,(ln txuD

0),,(ln

nxtxuD

0),,(ln

mutxuD

0),,(ln

mutxuD

12

1

n

n

02

1'

nnn

02

1

n

nm

02

1

n

nt

nnnn ''

mmmm ''

C1: value of input distance function >=1

C2: non-decreasing in inputs

C3: non-increasing in desirable outputs

C4:non-decreasing in undesirable output

C5: linear homogeneity in inputs

C6: parameter symmetry conditions for translog function

Descriptive statistics of variables included in the analysisDescriptive statistics of variables included in the analysis (54 vessels, 212 obs., 1991-1999) (54 vessels, 212 obs., 1991-1999)

1011.411.84Turtle (number)

Undesirable Outputs

9.4601.401.18Other (thousand pounds)16.0903.454.13Tuna (thousand pounds)66.390.6212.2920.42Swordfish (thousand pounds)

Desirable Outputs

25.400.755.1012.63Hooks (thousands)

55.740.4112.9521.63Trip Length (days standardized by net tons)

Inputs

MaxMinStd. Dev.MeanVariable (units) |

Fish Abundance Effects on OutputsFish Abundance Effects on Outputs

Catch of different species is sensitive to harvestable Catch of different species is sensitive to harvestable stocksstocks

Abundance indices for the species in different periods Abundance indices for the species in different periods and areas are indicators of resource conditions and areas are indicators of resource conditions

Weigh each output of every trip by abundance indicesWeigh each output of every trip by abundance indices

Abundance Indices DerivationAbundance Indices Derivation

Seemingly Unrelated Regression (SUR); analyze catch rates with Seemingly Unrelated Regression (SUR); analyze catch rates with assumption of lognormal error distributionsassumption of lognormal error distributions

Explanation variables: Year, Month, Vessel classes, Regions, Trip Explanation variables: Year, Month, Vessel classes, Regions, Trip typestypes

: expected catch rate for vessel length c in month s of year y in region a by trip type q.

: catch rate obtained by a tuna trip of vessel 1 in January 1991 in area 1.

: vessel classes; : month; : year; : trip types; : region.

csyqaaqysccsyqa ln

Yearly Average Technical Efficiency and Shadow PricesYearly Average Technical Efficiency and Shadow Prices

Chakravorty and Nemoto (2000Chakravorty and Nemoto (2000)): $14,000 in 1995 USD ( $12,343 in 1991 dollars) per loggerhead turtle; use number (66) (Kleiber,1998)

Curtis and Hicks (2000): $41,262 per turtle from seasonal closure and $ 52, 976 per turtle; =$33,843 (seasonal) and $43,509 (full) in 1991 USD

Pradham and Leung (2004): Between $35,000-$55,000 per sea turtle

32,5610.67071991-1999

16,4960.69481999

23,0230.65501998

16,9010.60651997

24,2320.73781996

34,2440.72711995

38,1720.63291994

27,0820.56721993

33,5150.67341992

37,2430.76581991

Shadow Prices(in 1991 USD)

Technical EfficiencyLanding year

Shadow Prices by Trip TypesShadow Prices by Trip Types

17,50214,2331999

18,26232,5451998

17,87410,0841997

25,16123,5091996

31,99434,8441995

9,26539,3281994

18,61027,8301993

26,53434,5731992

20,76939,5971991

Shadow Price(in 1991 USD)

Shadow Price (in 1991 USD)Landing Year

MixedSwordfish

Shadow prices by monthShadow prices by month

26,08626,0861212

40,37340,3731111

8,4168,4161010

33,79533,79599

22,70922,70988

23,63123,63177

34,87434,87466

48,96148,96155

41,43241,43244

32,83632,83633

23,87523,87522

13,36313,36311

Shadow PricesShadow Prices(in 1991 USD)(in 1991 USD)Landing MonthLanding Month

Sea turtle catch and Shadow Price by areasSea turtle catch and Shadow Price by areas

1120,532168,931817,5021999

345,4382516,3152620,4871998

132,578421,819109,2921997

231,2001722,0821625,3161996

538,2861337,462926,7241995

320,7622633,7421847,7531994

533,3844323,5342130,3701993

1521,3571641,8382635,2821992

841,728843,1322632,7911991

NumberShadow Price(in 1991 USD)

NumberShadow Price(in 1991 USD)

NumberShadow Price(in 1991 USD)

Landing Year

Area CArea BArea A

ConclusionsConclusions $32,651 (1991 USD) per turtle, close to Curtis & Hicks $32,651 (1991 USD) per turtle, close to Curtis & Hicks

(2000) and Pradham & Leung (2004) estimates, higher (2000) and Pradham & Leung (2004) estimates, higher than Chakravorty and Nemoto (2000) estimate than Chakravorty and Nemoto (2000) estimate

Not assuming policy implementation; modest data Not assuming policy implementation; modest data requirement; information for trade-offs between incidental requirement; information for trade-offs between incidental capture and costs of bycatch abatementcapture and costs of bycatch abatement

Reveal variation pattern by trip characteristicsReveal variation pattern by trip characteristics

Shortcoming: nonstochasticShortcoming: nonstochastic

AcknowledgementsAcknowledgements

This research is funded by The Joint Institute of Marine and Atmospheric Research

of the University of Hawaii &National Oceanic and Atmospheric Administration

Thanks to

Pelagic Fishery Research ProgramHonolulu Laboratory, National Marine Fishery Services