Practical Issues in Integrating Choice Models into Dynamic Policy Models Tools Development for...

Practical Issues in Integrating Choice Models into Dynamic Policy Models

Tools Development for Bioeconomic Modeling of Spatial Fisheries

Martin D. Smith

Nicholas School of the Environment

Duke University

Thanks to U.S. EPA and Resources for the Future for Thanks to U.S. EPA and Resources for the Future for funding.funding.

Part A

A Dynamic Spatial Bioeconomic Model of the Fishery

Lessons from simulation

Why study this model?

• Predicting short- and long-run consequences of marine reserve formation

• Predicting consequences of other fishery management alternatives (seasonal closures, vessel buyouts, gear restrictions, etc.)

• Trade off commercial fishing costs/benefits with ecosystem services

Data Generating ProcessThe Biology

3

11

1 jtjt jt j jt jt jk kt

kj

NN N r N H d N

K

j = 1,2,3

Logistic Growth

Harvest

Dispersal

A discrete-time version of Sanchirico and Wilen JEEM 1999

Data Generating ProcessThe Economics (1)

Individual fishermen in a limited entry fishery make discrete choices in each period to maximize random profits or utility (Smith Land Econ 2002)

Stay Home

Go Fishing

Zone 1

Zone 3

Zone 2


Revenue

Opportunity Cost

ijt itj ijtU v

, 0

, 1,2,3,itjt ijt ij

for jv

p h c l for j

TravelCost

Quasi-fixed Trip Cost

Random Profits

Deterministic Portion

Revenue TravelCost



Production FunctionEveryone faces the same stock

ijt ijt ijt ijt jt ijth h qE N

IndividualHarvest

Effort

“catchability”

, 0

, 1,2,3,

ijt

ijtt jt ij ijt

for jU

p qN c l for j

Assume degenerate for now

1 1

n n

jt ijt jt ijti i

H h qN E

Total Harvest

Data Generating ProcessThe Randomness

u F

exp exp

aF

b

ln lnb u a

~ 0,1u UDraw Uniform Random Variables

Note connection to CDF

Type I Extreme Value CDF

Invert to get Type I Draws

Assume a = 0, b controls the variance of the draws (scale coef.)

Data Generating ProcessSimulating Individual Choices

0 1 2 31, max , , ,

0,

ijt i t i t i t i tijt

if U U U U UE

otherwise

Example

A Slow-growing Sink-source Fishery

Parameter ValuesBase Economic Parameters Biological/Oceanographic

alpha 0.01 opportunity cost r1 0.4 intrinsic growthc 0.05 fixed cost of fishin r2 0.4 intrinsic growthalpha + c 0.06 r3 0.4 intrinsic growthq 0.015 catchability k1 1 carrying capacityphi 0.025 cost of travel distance k2 1 carrying capacitydelta 0.07 discount rate (only used for policy)k3 1 carrying capacityp 100 mean price d11 -0.2 dispersal

d12 0 dispersaldist1 1 mean distance of patch 1 d13 0 dispersaldist2 2 mean distance of patch 2 d21 0.15 dispersaldist3 3 mean distance of patch 3 d22 0 dispersal

d23 0 dispersalSources of Variability d31 0.05 dispersal

d32 0 dispersalsigmap 10 standard dev of price d33 0 dispersalsigmatT (b) 1 scale coefficient

Initital Conditions

distj(i)~U(0,2*dist(j)) X1(0) 0.4 initial stock patch1vardist1 0.083333 variance of dist1 X2(0) 1 initial stock patch2vardist2 0.333333 variance of dist2 X3(0) 0.9 initial stock patch3vardist3 0.75 variance of dist3

Assumptions about T and n

T = 50 (fishing periods)

n = 100 (licensed vessels)

Bioeconomic Outcomes By Patch

0 10 20 30 40 500

0.5

1

t

Sto

ck3-Patch Stock Dynamics

Patch 1 (source)Patch 2 (sink)Patch 3 (sink)

0 10 20 30 40 500

20

40

t

Eff

ort

3-Patch Effort Dynamics

0 10 20 30 40 500

0.5

1

t

Har

vest

3-Patch Harvest Dynamics

Combined Bioeconomic Outcomes

0 10 20 30 40 500

2

4

t

Sto

ckStock Dynamics - Total Across Patches

0 10 20 30 40 50

60

80

100

t

Eff

ort

Effort Dynamics - Total Across Patches

0 10 20 30 40 500

1

2

t

Har

vest

Harvest Dynamics - Total Across Patches

Rent Dissipation

0 10 20 30 40 50-20

0

20

40

60

t

Ren

t3-Patch Rent Dynamics


0 10 20 30 40 50-50

0

50

100

t

Ren

t

Nominal Rent Dynamics - Total Across Patches

Model Estimation Conditional Logit

4

41 1 1

1

ln lnijt

ikt

vT n

ijtvt j i

k

eL E

e

TOGGLE TO MATLAB

m_smith_space_frontier_data_indiv_var.m

m_smith1_parm_recover_ind.m

cond_logit_ind.m

Results of 100 RunsAssumes We Can Observe Stocks (X)

alpha + c phi q

b=1True Value 0.060 0.025 0.015Mean 0.0585 0.025 0.015Standard Dev. 0.0464 0.012 0.002Significant at 5% level 31% 48% 100%

b=0.5True Value 0.060 0.025 0.015Mean 0.127 0.049 0.030Standard Dev. 0.047 0.012 0.003Re-scaled Mean 0.063 0.025 0.015Re-scaled St. Dev. 0.023 0.006 0.001

Significant at 5% level 80% 98% 100%

Structure of the bioeconomic system limits our ability to learn

about behavior!

Specifics

• q more easily recovered because N varies over time and choice– Distance varies over space and not time– No variation in the data for resolving other costs

• We observe N over much (most) of its theoretical range

• Scale of error (b) limits ability to resolve cost parameters– Too big means too much noise– Too small and the system crashes

Serial Depletion with Small Scale Termb = 0.1

1 1.5 2 2.5 3 3.5 4 4.5 50

0.5

1

t

Sto

ck3-Patch Stock Dynamics Patch 1 (source)

Patch 2 (sink)Patch 3 (sink)

1 1.5 2 2.5 3 3.5 4 4.5 50

50

100

t

Eff

ort


1 1.5 2 2.5 3 3.5 4 4.5 5-2

0

2

t

Har

vest


Part B

“True” and “Proxy” Models

Real Fisheries Problems

• Generally do not observe X directly• Typically use a proxy, i.e. backward-looking

revenues per trip• Similar situation in recreation demand models• Is the proxy adequate?• What if we do not observe the bioeconomic

draw-down period?• Does “fast-” versus “slow-growing” matter?

“Slow-” versus “Fast-” Growing

• Biologically, increase intrinsic growth

• Economically, increase costs– Prevent overreaction of the harvest sector

Example of Fast-Growing System

0 10 20 30 40 500

0.5

1

t

Sto

ck

3-Patch Stock Dynamics


0 10 20 30 40 500

20

40

t

Eff

ort


0 10 20 30 40 500

0.5

1

t

Har

vest


Monte Carlo Experimental Design

• 6 model types– True, full T– True 1st half T– True 2nd half T– Proxy (T-1)– Proxy 1st (T-2)/2– Proxy 2nd (T-2)/2

• 5 values for scale coefficient b

• 2 sets of bioeconomic parameters (fast-growing and slow-growing)

• 100 runs each

6,000 total conditional logit models

TOGGLE TO MATLAB

m_smith2_parm_recover_split.m

cond_logit_ind.m

Full Results

Summary of Conditional Logit Numerical Experiments

True Model Proxy ModelStandard Dev. of Type I Error sig=.25 sig=.5 sig=1 sig=2 sig=4 sig=.25 sig=.5 sig=1 sig=2 sig=4

Slow-Growing Bioeconomic System

Number of Crashes(Destabilized Bioecon System) 6 0 0 0 0 6 0 0 0 0catchability% q (or proxy) significant all periods 100% 100% 100% 99% 73% 100% 100% 100% 93% 44%% q (or proxy) significant 1st Half 100% 100% 100% 99% 53% 100% 100% 100% 87% 36%% q (or proxy) significant 2nd Half 100% 100% 58% 26% 16% 100% 100% 54% 29% 13%

% 1st Half > 2nd Half for t-ratio on q 100% 100% 100% 98% 80% 100% 100% 97% 88% 71%other parameters% 1st Half > 2nd Half for t-ratio on c+alpha 33% 40% 54% 48% 49% 34% 38% 49% 45% 47%% 1st Half > 2nd Half for t-ratio on phi 74% 54% 57% 46% 40% 71% 53% 60% 42% 41%

Fast-Growing Bioeconomic System Number of Crashes(Destabilized Bioecon System) 15 0 0 0 0 15 0 0 0 0catchability% q (or proxy) significant all periods 100% 100% 100% 100% 91% 100% 100% 100% 100% 86%% q (or proxy) significant 1st Half 100% 100% 100% 99% 69% 100% 100% 100% 96% 59%% q (or proxy) significant 2nd Half 100% 100% 100% 98% 57% 100% 100% 100% 98% 58%

% 1st Half > 2nd Half for t-ratio on q 95% 96% 71% 61% 61% 67% 48% 39% 47% 51%other parameters% 1st Half > 2nd Half for t-ratio on c+alpha 93% 81% 49% 43% 55% 74% 42% 36% 41% 53%% 1st Half > 2nd Half for t-ratio on phi 54% 49% 42% 41% 53% 47% 46% 45% 41% 51%

Summary

True Model Proxy ModelStandard Dev. of Type I Error sig=.25 sig=.5 sig=1 sig=2 sig=4 sig=.25 sig=.5 sig=1 sig=2 sig=4

Slow-Growing Bioeconomic System Number of Crashes 6 0 0 0 0 6 0 0 0 0

catchability% q (or proxy) significant 2nd Half 100% 100% 58% 26% 16% 100% 100% 54% 29% 13%% 1st Half > 2nd Half for t-ratio on q 100% 100% 100% 98% 80% 100% 100% 97% 88% 71%

Fast-Growing Bioeconomic System

catchability% q (or proxy) significant 2nd Half 100% 100% 100% 98% 57% 100% 100% 100% 98% 58%% 1st Half > 2nd Half for t-ratio on q 95% 96% 71% 61% 61% 67% 48% 39% 47% 51%

Lessons from the “true” and “proxy” models

• not observing the draw-down phase erodes our ability to resolve the parameter on biomass

• the relative performance of estimating on the first half is stronger for the true model

• adding noise is less consequential for a fast-growing system

• observing the draw-down phase is more important in a slow-growing bioeconomic system

Brief caution on globals

If they change within a program, re-declare them each time they are used.

'First Half'global z n dist_out y_indz=zall(1:25,:);y_ind=y_indall(:,:,1:25);[betahat2,fval2,exitflag,output,grad,hessian2] = fminunc(@cond_logit_ind,parms0);

'Second Half'global z n dist_out y_indz=zall(26:50,:);y_ind=y_indall(:,:,26:50);[betahat3,fval3,exitflag,output,grad,hessian3] = fminunc(@cond_logit_ind,parms0);

Extras

Part C

State Dependence and Heterogeneity

Motivation

• Small share of the fleet catches most of the fish– 25% of Gulf of Mexico reef-fish fleet lands 75% of fish– Similar patterns in other fisheries

Lorenz Curve For Urchins

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Cumulative Percent of Divers

Cu

mu

lati

ve P

erce

nt

of H

arve

st

1996

1994

1992

1990

1988

Smith AJAE 2004

Motivation


• Heterogeneous behavioral outcomes from seemingly homogenous agents– Fishery choice (Bockstael and Opaluch JEEM 1983)– Location choices (Eales and Wilen MRE 1986; Dupont MRE

1993; Curtis and Hicks AJAE 2000– Participation and location choice (Berman et al. MRE 1997;

Smith Land Econ 2002)– Gear choices (Eggert and Tveteras AJAE 2004)

Motivation


• Heterogeneous behavioral outcomes from seemingly homogenous agents– Fishery Choice– Location choices– Participation – Gear choices

• Predicting policy outcomes

Why individual choices are correlated over time

State Dependence• Past choices cause

current/future

Heterogeneity• Heterogeneous

preferences or productive abilities induce temporal correlation in unobservables

Heterogeneity and Fishery Economics

• Infra-marginal rents (Johnson and Libecap AER 1982)

• Heterogeneous responses to policy – Responsiveness to economic opportunities over space – Attractiveness of exit (spatial closures, vessel buyouts, …)

• Examples– Location choice: Mistiaen and Strand AJAE 2000; Smith

JEEM 2005– Gear choice: Eggert and Tveteras AJAE 2004

State Dependence and Fishery Economics

• Sluggish adjustment at the intensive margin • Double-edged sword

– Takes time to exploit new opportunities– Inertia of fishing pressure on degraded stocks

• Examples– Bockstael and Opaluch JEEM 1983 fishery choice– Holland and Sutinen LandEcon 2000 New England

fishing ground choice - “old habits die hard”– Smith JEEM 2005 location choice

, 0

, 1, 2,3,

i ijt

ijtt i jt i i ij ijt

for jU

p q N c l for j

Data Generating ProcessEconomic Heterogeneity

(No True State Dependence)

TravelCost

Opportunity Cost

ProductivityQuasi-fixedCost

2 1 0.5

1 2 1

i i

i

i

u if u

u else

Triangular Distributions(see Train 2003)

Support space of behavioral parameter distribution has bioeconomic consequences

• Negative “catchability” meaningless

• Infinite positive support (e.g. log-normal) can destabilize the system

• Can estimate infinite support models but bio-physical relationships limit potential applicability

Example of Parameter Heterogeneity

0 0.02 0.04 0.06 0.08 0.1 0.120

2

4

6

8

10

12

14

16

18

20Travel Cost Heterogeneity

0 0.2 0.4 0.6 0.8 1 1.2 1.40

2

4

6

8

10

12

14

16

18

20Opportunity Cost Heterogeneity

0 0.005 0.01 0.015 0.02 0.025 0.030

2

4

6

8

10

12

14

16

18

20Catchability Heterogeneity

0 10 20 30 40 500

2

4

t

Sto

ck

Stock Dynamics - Total Across Patches

0 10 20 30 40 500

50

100

t

Eff

ort

Effort Dynamics - Total Across Patches

0 10 20 30 40 500

1

2

t

Har

vest

Harvest Dynamics - Total Across Patches

Rent Dynamics

0 10 20 30 40 50-20

0

20

40

60

t

Ren

t

3-Patch Rent Dynamics


0 10 20 30 40 50-50

0

50

100

t

Ren

t

Nominal Rent Dynamics - Total Across Patches

Modeling State Dependence

1

1

, 0

, 1,2,3,

i ijt ijt

ijtt i jt i i ij ijt ijt

E for jU

p q X c z E for j

Estimation

• Use 250 (3 x 1) Halton draw vectors

• Multiply by Cholesky matrix

• Add to mean parameters

• Form simulated likelihoods

• Maximize sum of average simulated log-likelihoods

General Observations

• Conditional on scale coefficient, more variability in individual catch and effort

• Key tradeoff in designing the bioeconomic experiment – If scale coefficient too low, system crashes– If scale too high, random parameters are not jointly

significant (only 1 out of 8 when b = 0.5)

• System crashes could represent something real: serial depletion and search in fisheries

Bioeconomic limits on simulation, using simulation as a tool to

explore econometric estimators, and the performance of

simulation-based estimation are all interacting!

Results from a Single RunTrue heterogeneity but not state dependence

True Proxy Proxy + SD Proxy + HetProxy + SD

+ Het True w/ Het

alpha + c 2.7837 2.4528 2.3742 2.1935 2.3737 2.7061(26.04) (26.37) (25.18) (13.22) (25.15) (20.82)

phi 0.2374 0.2398 0.2235 0.2694 0.2237 0.2857(15.12) (14.99) (13.80) (14.33) (13.81) (15.36)

q 0.059 3.0134 3.0124 2.8653 3.0123 0.0625(22.69) (23.49) (23.23) (13.08) (23.21) (20.16)

State Dependence 0.5407 0.5407(17.27) (17.27)

st dev (alpha + c) 0.7849 0.0349 0.5426(1.69) (0.23) (1.48)

st dev phi -0.0019 -0.0057 -0.0147(0.03) (0.14) (0.24)

st dev q 1.1373 0.0464 0.029(2.37) (0.19) (5.47)

n 5000 4900 4900 4900 4900 5000log-lik per observation 1.247 1.250 1.221 1.248 1.221 1.241Asymp t's in parentheses

TOGGLE TO MATLAB

m_smith3_space_frontier_data_indiv_var.mm_smith3_parm_recover_ind.m

cond_logit_sd.mhalton.m

halton_write.mmixed_logit_ind.mmixed_logit_sd.m

Summary of 20 Sets of Runs

Out of 20Random Parameters Jointly Significant (True) 20Random Parameters Jointly Significant (Proxy) 14Random Parameters Jointly Significant (Proxy + SD) 1Coefficient on SD significant (SD only) 20Coefficient on SD significant (SD + Het) 20Log-lik per observation highest a model with SD 20

Why State Dependence Performs Well

• Scale of heterogeneity limited by bioeconomic sensitivity (particularly q)

• Lagged revenue a noisy signal– Price assumed not to be autocorrelated– After draw-down phase, autocorrelation of last

period’s stock and this period’s stock is lower– Aggregate revenue per trip not the true expected

revenue for the individual• 1st order Markov is parsimonious• Simulation noise

Section III Part D

Bioeconomic Calibration

Calibration and Policy

• We do not know the scale coefficient in the real world

• Example: forming a marine reserve

Can use biological information to recover scale coefficient

follows Smith and Wilen JEEM 2003; MRE 2004

ˆˆ ˆ ˆ, ,c c and q q

31 1

1

ˆˆˆ ˆexpˆ

ˆˆˆ ˆ1 exp

n nt jt ijTOT

jt jti i

t kt ikk

p qN c lE E

p qN c l

Find to make estimated bioeconomic system consistent with observed system in-sample

0 10 20 30 40 500

0.2

0.4

t

Sto

ck

Patch 1 Stock Dynamics

SimulatedTrue Stock

0 10 20 30 40 500

0.5

1

t

Sto

ck


SimulatedTrue Stock

0 10 20 30 40 500

0.5

1

t

Sto

ck


SimulatedTrue Stock

Calibration Exampleb= 0.5

.4916

Limits to Effort Calibration

0 10 20 30 40 500

20

40

t

Eff

ort

Patch 1 Effort Dynamics

SimulatedTrue Effort

0 10 20 30 40 500

50

100

t

Eff

ort



0 10 20 30 40 500

20

40

t

Eff

ort



Present Value Rents

3

1 1

1

ˆ ˆˆˆ ˆ

1

n

t kt ik iktTi k

tt

p qN c l E

PV

Baseline Rents 223Marine Reserve Patch 1 302Marine Reserve Patch 2 36Marine Reserve Patch 3 63

End of Section III3 themes

1. Simulation can be a tool for understanding the economic problem, the econometric problem, and for estimation

2. A bio-physical system can limit our ability to learn about economic behavior

3. Disentangling state dependence and heterogeneity is important but difficult

Section IV

Recovering Bio-physical Parameters from Economic Data

in Spatial Fisheries

Old Paradigm Canonical Fishery Model

0

0

max

1

0

te pH t cE t dt

N tsubject to N t rN t H tK

H t qE t N t

N N

Given p, N0 and , if we can estimate:

we can derive the optimal policy!

, , , ,r K c and q

Example: In Steady State (Clark 1990):2

* 81 1

4

K c c cN

pqK r pqK r pqKr

1 0

0

max

1

0

Jt

j j jj

jj j j

j

jj j jk k jk j

j j j j

j j

e pH t c E t dt

N tsubject to N t r N t K

d N t d N t H t

H t q E t N t

N N

New ParadigmDiscrete Space Version

Note the j’s!

11 1

1

J

J JJ

d d

d d

D

1

J

r

r

r 1

J

K

K

K

Given p, , and a vector of initial conditions N0j , j=1, …, J

we need to estimate:

1

J

q

q

q 1

J

c

c

c

Dispersal Parameters

Can we recover spatial bio-physical parameters from

economic data ?

In principle, yes!

Data Generating ProcessThe Biology

Logistic Growth

Harvest

Dispersal

A discrete-time version of Sanchirico and Wilen JEEM 1999

1 1 jtjt jt j jt jj jt jk kt jt jt

k jj

NN N r N d N d N H

K

ProcessError

Data Generating ProcessProduction

Harvest Functionijt ijt ijt j ijt jt ijth h q E N

IndividualHarvest

Effort

catchability

Observation Error

1 1

n n

jt ijt j jt ijt ijti i

H h q N E

Total Harvest

Note that with no observation error1

nTOT

jt jt ijt jt jti

H qN E qN E

Effort

Everyone in patch j at time t faces the same stock

Data Generating ProcessEconomic Behavior (1)

Individual fishermen in a limited entry fishery make discrete choices in each period to maximize random profits or utility (Smith Land Econ 2002)

Stay Home

Go Fishing

Zone 1

Zone 3

Zone 2

Data Generating Process Economic Behavior (2)

Revenue

Opportunity Cost

ijt itj ijtU v

, 0

, 1, 2,3,...,itjt ijt ij

for jv

p h c l for j J

TravelCost


Random Profits

Deterministic Portion

TravelCost


0 1 2 31, max , , , ,...,

0,

ijt i t i t i t i t iJtijt

if U U U U U UE

otherwise

Choice

Recovering Bio-Physical Parameters

21

2

1 j jjjt j ktjt jt jk jt jt

k jj j j j j

r dz r zz z d H

q q q K q

2 *1 1 2

1

J

jt jk kt jJ jt jJ jt jtk

z z z H

jtjt TOT

jt

Hz

E Aggregate Catch-Per-Unit-Effort in Patch j

Can Estimate with Seemingly Unrelated Regression

Other Stock Indices

Simple Example• 3 patches

• 100 time periods

• 100 individuals

• No observation error

• Sink-source dispersal

11

21 11 21 31

31

1 2 3

0 0

0 0 ,

0 0

d

D d d d d

d

q q q q

Example 100 Monte Carlo SimulationsSeemingly Unrelated Regression on Sink-Source System

True StandardParameter Value Mean Median Deviation

Form of Dispersal Matrix Is Known A Priori

q 0.015 0.0149 0.0150 0.0008d21 0.15 0.1370 0.1398 0.0485d31 0.05 0.0453 0.0506 0.0573r1 1.4 1.3755 1.3813 0.0995r2 0.5 0.5467 0.5394 0.1306r3 0.8 0.8160 0.8209 0.1409k1 3 2.9935 2.9893 0.2082k2 2 1.9986 2.0030 0.1414k3 2 2.0047 2.0050 0.1143

And we can also recover spatial economic parameters

Can recover scale coefficientbecause coefficient on revenuemust equal 1!

, 0

, 1,2,3,...,itj jtt ij

for j

v z qp c l for j J

q

Need spatially-explicit costs for optimal spatial management. It is not enough to estimate up to scale.

Spatially Explicit CostsDiscrete Choice Model

True StandardParameter Value Mean Median Deviation

Raw Estimates

c 1.000 0.5211 0.5153 0.1165 0.500 0.2491 0.2485 0.0090

Revenue 1 0.5095 0.5047 0.0519

Transformed by Estimated Scale - True Scale = 2.0

c 1.000 0.9996 0.9981 0.0704 0.500 0.5008 0.4967 0.0437

A Density-Dependent System

1 2 1 2

1 2 3

11 12 13

1 3 3121 22 23

1 2 331 32 33

3 2 32

1 2 3

a a a a

K K Kd d d

a a aad d d

K K Kd d d

a a aa

K K K

D

1 2 1 3 11 1 1 1 1 1 2 1 1

1 2 1 3 1

1 t t t t tt t t t t

N N N N NN N r N a a H

K K K K K

Empirically, restricted model is highly nonlinear in the parameters

Conclusions so far from simulated data experiments

• It is possible to recover unbiased estimates of structural spatial-dynamic parameters in a sink-source system from economic data alone!

• Test down to true sink-source when we know which restriction to impose

• Can approximate dispersal in a density-dependent system, but we estimate too many parameters

Now Add Observation Error with 5,000 Runs

True Standard Not aParameter Value Mean Median Min Max Deviation Number*

Overidentfied Density-Dependent Model - Observation Error Sig=2.0

q 0.015 -0.0142 -0.0128 -0.3298 0.3686 0.0307 2d11 -0.250 -0.4874 -0.3686 -12.9063 1.9023 0.6196 2d12 0.083 0.1589 0.1037 -1.9886 7.5357 0.2772 2d13 0.167 0.1281 0.0842 -3.5595 6.5235 0.2586 2d21 0.083 0.2347 0.1601 -3.3590 9.7365 0.4143 2d22 -0.333 -0.3597 -0.2644 -9.0540 7.7592 0.4699 2d23 0.250 0.1478 0.0999 -4.3462 5.3882 0.2809 2d31 0.167 0.2527 0.1757 -1.6992 11.8684 0.4032 2d32 0.250 0.2008 0.1381 -8.4907 7.6496 0.3406 2d33 -0.417 -0.2759 -0.2045 -6.8424 4.1885 0.4039 2r1 1.000 0.0072 -0.0540 -6.7300 15.3708 1.1412 2r2 1.000 -0.1438 -0.1668 -6.1892 11.0015 0.9329 2r3 1.000 -0.2581 -0.2782 -5.6480 7.7297 0.8213 2k1 3.000 25.7282 9.1508 -52890 105430 2390 2k2 3.000 -16.6114 10.9632 -487770 107030 7540 2k3 3.000 -483.9056 12.0781 -398980 128510 6070 2

Conclusions with Observation Error

• As in single-equation case, errors-in-variables leads to inconsistent population parameters

• Surprisingly, dispersal parameters are still estimated reasonably

Take to Real Data and Ignore Observation Error

Zone 3

Zone 2

Zone 1

Real World Always More Complicated

0 20 40 60 80 100 120 1400

100

200

300

400

500

600

700Gulf of Mexico Reef Fish Catch Per Unit Effort

Time (Month)

Pou

nds

Per

Trip

Day

zone 1

zone 2zone 3

Raw Parameter EstimatesControlling for Seasonal Catchability

Coefficient t-stat Coefficient t-stat Coefficient t-stat

j1 0.9057 2.32 0.4497 3.589 1.3543 7.064

j2 -5.85E-04 -0.431 -1.50E-03 -3.441 -0.0032 -4.792

j3 0.542 2.24 0.7246 9.33 0.0815 2.099

j4 -0.1483 -0.687 0.0861 1.243 0.1189 1.09

j5 -1.25E-04 -1.008 -2.40E-05 -0.602 -3.98E-06 -0.097

j6 0.0002 1.237 -0.0001 -2.506 -0.0001 -1.472

j7 -0.0006 -0.478 0.0012 3.183 0.0015 1.652

Parameter Estimate Parameter Estimate

q1 1.25E-04 d11 0.2004

q2 2.40E-05 d12 0.5420

q3 3.98E-06 d13 -0.1483

r1 0.7119 d21 0.7246

r2 0.1106 d22 0.6235r3 0.2921 d23 0.0861k1 9.70E+06 d31 0.0815k2 3.07E+06 d32 0.1189k3 2.28E+07 d33 -0.0622

Recovered Structural Parameters from Point Estimates are Reasonable

Interestingly, only 3 of raw dispersal parameters are statistically significant.

A New Method for the Old Paradigm

Zhang and Smith (2007) • Exploit individual-level data to difference

away stock

• Can recover production parameters in first stage using within-period estimator

• Use simulation extrapolation (SIMEX) (Cook and Stefanski JASA 1994) to correct observation error in second stage and recover biological parameters

Policy Implications of 2-Stage Model

Naïve SIMEX

Carrying capacity 39,092 31,947Maximum sustainable yield 3,318 2,675

Carrying capacity 24,801 19,805Maximum sustainable yield 2,311 1,670

Generalized Schaefer

Schaefer

Combining Empirical Ideas

• Use two-stage approach with micro-data from Zhang and Smith 1. Allows a more realistic production function

2. Incorporates process and observation error

• Use spatially stacked model with aggregate stock indices to recover dispersal parameters

• Use micro-data to recover spatially-explicit costs

A Research Agenda

• Theoretical modeling to characterize optimal (and second-best) management of marine spatial-dynamic processes

• Empirical work to – Recover parameters of spatial-dynamic processes

from economic data– Collaborate with scientists in other fields to limit the

universe of possible spatial-dynamic structures– Analyze proposed spatial policies– Evaluate existing spatial policies

Practical Issues in Integrating Choice Models into Dynamic Policy Models Tools Development for...

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