“MODELLING THE EFFECT OF HEALTH RISK PERCEPTION ON
PREFERENCES AND CHOICE SET FORMATION OVER TIME:
RECREATIONAL HUNTING SITE CHOICE AND CHRONIC
WASTING DISEASE
THUY TRUONG
VIC ADAMOWICZ
PETER BOXALL
Resource and Environmental Economics
University of Alberta
OUTLINE
What is Chronic Wasting Disease?
 Random Utility Models and Choice Set
Formation
 Empirical Approach
 Data and Some Descriptive Statistics
 Model Results, Welfare Measures
 Extensions and Limitations
 Conclusions

THE PROBLEM: WHAT IS THE ECONOMIC
WELFARE IMPACT OF CWD?

Chronic Wasting Disease (CWD): prion disease
that affects deer, elk and other cervid wildlife
species

Neurodegenerative disease

BSE, Scrapie, CWD, Creutzfeldt Jakob Disease (vCJD)
No known link between the consumption of CWD
affected meat and human health, but
 Cautions were provided to hunters


CWD might affect a recreational hunter’s:
choice sets
 site choice


…and these effects might change over time
Source: "Chronic Wasting Disease Alliance (www.cwd-info.org)"
ECONOMIC IMPACTS OF CWD IN ALBERTA

Hunting



Cervid Farming Sector


Resident Hunters - Recreational Hunting
Aboriginal People – Traditional Use
Elk Farms
“Passive Use Values”


General Public View of CWD and Resource
Allocation
Risk to Threatened Species

Landowners

Wildlife Viewing / Recreation

Consumers / Food

Non-Resident Hunters
Source: Alberta SRD
http://srd.alberta.ca/BioDiversityStewardship/WildlifeDiseases/
documents/CWD-PositiveMap-Jan-21-2009.pdf
MANAGEMENT OF CWD

Government initiated CWD
control programs

Testing of deer heads


Provide extra tags/licenses


Allow more deer to be harvested by
hunters
Culling of deer


Only way to find disease
“experts” find deer, remove them, and
test for CWD
CWD may be perceived as a
health risk, or a nuisance, or
both, or neither!
CHOICE AND CHOICE SET FORMATION

Random Utility Theory
U jn = β ′X jn + ε jn
Pjn = Pr{U jn > U j 'n , ∀j '∈ Cn , j ' ≠ j} = Pr{U jn > max(U j 'n ), ∀j '∈ Cn , j ' ≠ j}
exp( µV jn )
exp( µβ ′X jn )
∴ Pjn =
=
∑ exp(µVkn ) ∑ exp(µβ ′X kn )
k∈Cn

k∈Cn
A More General Approach (Swait et al)
i ← ∆n
*
n
j∈C n
{
(
~
U = V ( X , Z n ; β ) + ε X , Z n ;θ
)}
OBJECTIVES OF THE STUDY

Identify whether changes in potential health
risks (CWD) result in


change in utility of a recreation site
change in its availability in the choice set (choice
set formation)
Analysis of effects over time
 Examine if there are scale differences over time
and data generating mechanism
 Examine specifications of choice set formation
models
 Examine if approximations to choice set
formation provide similar results to a fully
endogenous choice set formation model

LITERATURE REVIEW – CHOICE SETS



Exogenously determined choice sets
Define choice set using survey responses:

spatial boundaries, distance, familiarity

Explicit modeling
Modeling choice sets (endogenous choice sets)





Haab and Hicks’ (1997)
Manski’s approach (Swait 1984, Swait and Ben-Akiva 1987a
and Ben-Akiva and Boccara 1995)
GenL model (Swait 2001)
Hicks and Schnier (2010)
Implicit modeling




Cascetta and Papola (2001)
Martinez et al (2009)
Bierlaire et al (2010)
Kuriyama et al (2003)
EXPLICIT MODELING OF CHOICE SET

Haab and Hicks’ model:
p=
j

∑ P( j | j ∈C ) P( j ∈C )
Ck ⊆ Cm
k
Manski’s two stage decision process:
pj =

k
Disadvantage:
∑ P ( j | C ) Q (C )
Ck ⊆ Cm
k
k
Large number of possible choice sets (2J -1)
 Intractable for large choice problems

Site choice utility
Choice set
INDEPENDENT AVAILABILITY MODEL
Swait (1984)
 Probability of Ck being the ”true” choice set

Q ( Ck ) =
∏ A ∏ (1 − A )
j∈Ck
j
l∉Ck
l
1 − ∏ (1 − Ah )
h∈Cm
1
Aj =
− γ Zij
1+ e
IMPLICIT MODELING OF CHOICE SET

Implicit Availability and Perception model
(Cascetta and Papola 2001)
pij =

Availability function:
Aj e
µVij
J
µVik
A
e
∑ k
k =1
1
Aij =
−α Z
1+ e
IMPLICATIONS
Long history of concern over choice set
misspecification, but little done...
 Applies to a large class of models / applications

Transportation
 Food Choices (health risks?)
 Housing Demand
 Stated Preference Data Sets



SP Data with multiple alternatives, etc.
Marketing
Little theory or understanding of the impact of
misspecifed choice sets
 Behavioral Econ – ”too much choice”?

DATA AND ESTIMATION

Data:
2 years, stated and revealed preference data
 Attributes: cwd prevalence, tags, culling and travel
cost
 11 sites (wildlife management units )
 Demographics


Estimation
Utility function: alternative specific constants,
attributes and relevant interactions
 Scale function: dummy for SP/RP data, time dummy
in exponential function
 Availability function: cwd and its interaction with
time dummy, age, urban and hunting years

ESTIMATION CONTINUED
Examine probability of site choice, and choice set
formation, in random utility framework
 Evaluate impact of CWD (and other features)
over time

Differences in utility, choice set formation, and scale
 Examine welfare measures

Contribution from utility function
 Contribution from choice set formation

MODELS
MNL model (utility function only)
 MNL model with scale function
 MNL model with scale and availability (CP)
 RPL (random parameter logit) versions of the
models above
 IAL model (fully endogenous choice set
formation) with scale
 MNL model using a ”thresholds” specification of
the availability function

EXAMPLE OF CONTINGENT BEHAVIOUR / SP QUESTION
Do you feel CWD is a threat to human
health?
Do you feel CWD is a threat to wildlife?
I no longer consume deer meat
because of CWD
CWD has affected my enjoyment of
hunting deer
I eat or give away deer meat before I get
testing results back from Fish and Wildlife
RESULTS: ESTIMATED MODELS
Fixed parameter
models
Model
Random parameter
models
Loglikelihood
Rhosquared
Loglikelihood
Rhosquared
Base MNL
-7,583.41
0.275
-5,067.19
0.516
With scale
-7,500.26
0.283
-4,960.53
0.526
With scale
and
availability
-7,375.68
0.295
-4,937.84
0.528
RESULTS: FIXED PARAMETER MODEL
Utility function
Availability function
Travel cost
-23.2 (1.08)
CWD
0.627 (0.087) CWD
Tags
0.572 (0.105) CWD x year 2 -0.116 (0.054) Year2 x SP
Cull
-0.961 (0.129) Age
Tc x urban
11.1 (0.776)
Tags x urban
-0.265 (0.136) Hunting years
CWD x urban
-0.655 (0.083)
Cull x hunt
years
0.014 (0.005)
CWD x year 2 -0.054 (0.027)
Constant
Urban
4.59 (0.594)
Scale function
Year 2
-0.768 (0.062) SP
-0.305 (0.068)
-0.468 (0.045)
0.3 (0.09)
-0.077 (0.015)
10 (2.31)
0.12 (0.012)
Loglikelihood
Rho-square
-7,375.68
0.295
WELFARE CHANGE OF MOVING TO THE
WORST SCENARIO – CWD SPREAD
MNL
Base MNL
MNL with
scale
Year 1
Year 2
Rural
Urban
Rural
Urban
15.37
(3.75)
-4.24
(4.38)
-11.23
(3.66)
-40.67
(4.74)
15.00
(5.18)
-18.35
(4.73)
-23.07
(6.28)
-49.93
(15.78)
CP MNL
Year 1
Year 2
Rural
Urban
Rural
Urban
Utility function
248.49
(30.51)
-7.26
(3.41)
248.98
(0.63)
-28.45
(8.39)
Availability
factor
-81.41
(32.7)
-0.35
(1.03)
-116.05
(3.4)
-0.69
(2.82)
Total
68.33
(21.17)
-7.69
(2.71)
-38.36
(1.98)
-29.04
(8.52)
COMPARISON WITH THE IAL MODEL
(ENDOGENOUS CHOICE SETS)
Scale components similar
 Utility components similar



But CWD has a negative effect for all hunters, in all
years.
Availability component – somewhat different
Urban residents do not consider all sites available
(although they still have high probabilities relative to
rural individuals)
 CWD effect positive in year 1, negative year 2
interaction.


Welfare measures: TBD
RESULTS: IAL MODEL
Utility function
Availability function
Scale function
Travel cost
-59.608 (4.909) Constant
-0.068 (0.267) Year 2
-1.377 (0.074)
CWD
-0.148 (0.053) CWD
1.176 (0.364) SP
-0.782 (0.104)
Tags
1.929 (0.282) CWD x year 2
-0.747 (0.254) Year2 x SP
0.676 (0.113)
Cull
-2.48 (0.260) Age
-0.001 (0.008)
Tc x urban
26.472 (2.855) Urban
0.356 (0.186)
Tags x urban
-1.676 (0.345) Hunting years
-0.004 (0.007)
CWD x urban
-0.203 (0.110)
Cull x hunt
years
0.0455 (0.012)
CWD x year 2 -0.164 (0.066)
Loglikelihood
Rho-square
-7402.643
0.292
IAL MODEL
Implied Probabilities of Choice Set Size
# alternatives
Q (probability)
1 alt
0.00
2 alts
0.00
3 alts
0.01
4 alts
0.03
5 alts
0.08
6 alts
0.15
7 alts
0.21
8 alts
0.22
9 alts
0.18
10 alts
0.10
11 alts
0.03
MODEL 3: A ”THRESHOLDS” MODEL

Many suggestions surrounding specification of
choice formation


Hauser 2010 summary – ”thresholds” / heuristics
We now model availability as a function of
CWD threshold (presence / absence)
 Travel cost threshold (above / below average)

Availability function
Constant
28.750 (17.228)
CWD Threshold
-27.949 (17.227)
CWD RP x year 2
-1.342 (0.366)
Travel Cost Threshold
-2.012
CWD SP x year 2
18.474
Utility function
CWD
0.139
Tags
0.779
Cull
-0.882
Travel Cost (TC)
-21.851
TC x urban
9.846
Tags x urban
-0.662
CWD x urban
-0.155
Cull x hunt years
0.020
CWD x year 2
-0.174
Scale function
-0.587
SP
-0.220
Year 2
0.187
Year 2 x SP
(0.264)
(13.537)
(0.027)
(0.117)
(0.139)
(0.993)
(0.747)
(0.137)
(0.023)
(0.005)
(0.033)
PARAMETERS OF A
MNL MODEL
EMPLOYING
“THRESHOLDS” IN
AVAILABILITY
(0.042)
(0.068)
(0.080)
Note: coefficients in italics are NOT significant at 10%. Standard errors are in parentheses.
Welfare Measures – from the “Thresholds”
Model (with availability and scale)
Year 1
Utility
Availability
Total
Year 2
Rural
Urban
Rural
Urban
46.82
(9.86)
-1.76
(5.73)
-27.5
(3.52)
-60.27
(22.24)
-8.38
(4.06)
-24.51
(4.00)
-32.85
(7.19)
-83.45
(13.75)
39.96
(12.92)
-25.07
(7.67)
-40.07
(3.64)
-163.62
(18.87)
Note: Welfare change $/trip of moving to the worst case scenario. Standard deviations are in parentheses.
CONCLUSION
Using the CP model, CWD is found to have an
effect on choice set formation
 The negative effect of CWD on choice set
formation increases over time


Time and habit effects? (similar to BSE research)
However, the impact of results are sensitive to
specification and model type
 Is the CP approach a tractable choice set
formation model?

LIMITATIONS AND EXTENSIONS

Limitations:
Complex behaviors, observed and unobserved
heterogeneity
 Small sample with possible selection bias


Next Steps
Checks on robustness of IAL model
 Endogeneity of CWD?
 Simulation analysis


Extensions / Future Research:

A Theory for Choice Sets?

Kreps – “options” (1978) or Sarver – “regret” (2008)
Choice sets versus “cutoffs”?
 Welfare analysis?

FUNDING SOURCES