Transcript B. Mapping the WTP Distribution from Individual Level Parameter Estimation

Mapping the WTP Distribution from Individual Level
Parameter Estimates
Matthew W. Winden
University of Wisconsin - Whitewater
WEA Conference – November 2012
Motivation

Heterogeneity exists in respondents’ preferences, WTP, and
error variances within the population (Lanscar and Louviere 2008)
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Traditional Models Used in Non-Market Valuation Impose
Distributional Assumptions About Preference Heterogeneity in
the Population (Train 2009, Revelt and Train 1999)
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Top-Down Modeling (Mixed Logit, Latent Class Logit)
Misspecification May Lead to Bias in Parameter, Marginal
Price (MP), and Willingness-To-Pay (WTP) Estimates
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Leads to inefficient policy analysis and recommendations
Matthew Winden, UW - Whitewater
WEA November 10th, 2012
2
Previous Work
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Louviere et al. (2008) estimate individual level parameters
using conditional logit estimator (no welfare analysis)
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Louviere et al. (2010)
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Convergence issue 1: Collinearity of attributes
Convergence issue 2: Perfect Predictability
Cognitive Burden (Number of Questions/Attributes)
Best-Worst Scaling As Solution
Individual Models = “Bottom-Up Modeling Approach”
Matthew Winden, UW - Whitewater
WEA November 10th, 2012
3
Top-Down Versus Bottom-Up
“Top-Down”
(µ, σ)
“Bottom-Up”
Assume
Estimate Derive
β𝟏 β2 β3 Derive
Matthew Winden, UW - Whitewater
β
Estimate β𝟏 … β2 … β𝟑
WEA November 10th, 2012
4
Contributions

Objective 1: Use Monte-Carlo Simulation to Provide Evidence
of the Validity of Individual Level Estimation Techniques
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Objective 2a: Estimate Traditional and Individual Level
Models on a Stated Preference Dataset
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Eliminates Collinearity as a Convergence Problem
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Objective 2b: Estimate Traditional and Individual Level
Models on a Revealed Preference Dataset
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Objective 3: Use Individual Level Estimates to Demonstrate
Potential Bias Resulting from Distributional Assumptions in
Traditional Models
Matthew Winden, UW - Whitewater
WEA November 10th, 2012
5
Traditional Mixed Logit
P(j|vi) = exp(Uji)/Σexp(Uji)
Utility of choice j for respondent i:
U𝑗𝑖 = αji + ΒjΧ𝑖 + ΦjZji + ΘjiWji
where:
αji = alternative-specific constant
Βj = vector of fixed coefficients
Χi = fixed individual characteristics
Φj = vector of fixed coefficients
Θj = vector of varying coefficients
Zji & Wji = choice-varying attributes of choices
Matthew Winden, UW - Whitewater
WEA November 10th, 2012
6
Individual Level Simulation & Estimation Strategy
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3 Datasets (A, B, C)
 Known parameter, attribute, and error distributions
 100 respondents, 100 choice scenarios
 Face 3 attributes (X1 & X2 - Uniform, X3 – Zero, Status Quo)
 Face 3 alternatives (Respondent Specific Error Term to Each Alternative)
 Have 3 individual specific betas for each of the three attributes
Simulation A
 Beta 1 = Normal, Beta 2 = Normal, Beta 3 = Normal
Simulation B
 Beta 1 = Normal, Beta 2 = Normal, Beta 3 = Uniform
Simulation C
 Beta 1 = Normal, Beta 2 = Normal, Beta 3 = Exponential
Matthew Winden, UW - Whitewater
WEA November 10th, 2012
7
Individual Level Model Simulation

Results:
Simulation
ML LL
ML+I LL
ML X3 β
ML+I X3 β
True X3 β
A
-1282.69 -1194.94
4.458
4.599
3.945
B
-1597.3 -1302.81
2.701
4.584
3.826
C
-1864.74 -1545.42
4.273
4.878
4.004
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LL for Individual Level Models Indicates Better Fit than
Correctly Specified Mixed Logits
Comparing True X3 β Values, the Individual Level Model
Performs Well Under All Distributional Specifications for the
X3 Attribute
Matthew Winden, UW - Whitewater
WEA November 10th, 2012
8
Traditional and Individual Model Comparisons
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Results:
Attribute
ED
Conditional Logit
Mixed Logit 1
Mixed Logit 2
Individual
MP (S.E.)
MP (S.E.)
MP (S.E.)
MP
0.029 (0.002)
0.029 (0.002)
0.031 (0.003)
0.086
(0.002)
0.065
0.034 (0.003)
0.035 (0.003)
0.094
Conditional Logit
Mixed Logit 1
Mixed Logit 2
Individual
10%
Reduction
0.393 (0.024)
0.423 (0.025)
0.449 (0.037)
1.22
25%
Reduction
0.982 (0.060)
1.057 (0.062)
1.12 (0.093)
3.06
NR
HH
Scenario
(0.002)
0.022
(0.002)
0.024
Table0.023
34: Willingness-To-Pay
Estimates
($/Gal)
0.036 (0.002)
Matthew Winden, UW - Whitewater
WEA November 10th, 2012
9
Conclusions? (So-Far)
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Result 1: Validity of Individual Estimation Demonstrated
through Simulation  Kind Of...
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Result 2: Individual Level Model Distributions, MPs, & WTPs
Differ Significantly from Outcomes Using Traditional Models
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Role of Including or Excluding Individuals with Statistically
Significant (but possibly Lexicographic) Preferences on Estimates
Role of Including or Excluding Individuals with Statistically
Insignificant values (Round to Zero?)
Result 3: Without knowing underlying distribution, may
inadvertently choose incorrect mixing distribution based on LL
Matthew Winden, UW - Whitewater
WEA November 10th, 2012 10
Extensions
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E1: True (Full) Monte-Carlo Simulation For Individual Level
Specifcations
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Vary Over Number Respondents, Number Choice Occasions, Number
Attributes, Types of Distributions
E2: Comparison using Revealed Preference Dataset (Beach)
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Introduced Potential Collinearity as a Convergence Issue
More Realistic Situation Under Which Heterogenity May Matter
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E3: Develop Appropriate Significance Tests for Individual
Level Models
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E4: Scale Issues in Aggregation of Individual Respondents
Matthew Winden, UW - Whitewater
WEA November 10th, 2012 11
Thank You All For Your Time and Attention