Mapping the wtp distribution from individual level parameter estimates
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Mapping the WTP Distribution from Individual Level Parameter Estimates. Matthew W. Winden University of Wisconsin - Whitewater WEA Conference – November 2012. Motivation.

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Mapping the WTP Distribution from Individual Level Parameter Estimates

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Mapping the wtp distribution from individual level parameter estimates

Mapping the WTP Distribution from Individual Level Parameter Estimates

Matthew W. Winden

University of Wisconsin - Whitewater

WEA Conference – November 2012


Motivation

Motivation

  • Heterogeneity exists in respondents’ preferences, WTP, and error variances within the population (Lanscar and Louviere 2008)

  • Traditional Models Used in Non-Market Valuation Impose Distributional Assumptions About Preference Heterogeneity in the Population (Train 2009, Revelt and Train 1999)

    • Top-Down Modeling (Mixed Logit, Latent Class Logit)

  • Misspecification May Lead to Bias in Parameter, Marginal Price (MP), and Willingness-To-Pay (WTP) Estimates

    • Leads to inefficient policy analysis and recommendations

Matthew Winden, UW - Whitewater


Previous work

Previous Work

  • Louviere et al. (2008) estimate individual level parameters using conditional logit estimator (no welfare analysis)

    • Convergence issue 1: Collinearityof attributes

    • Convergence issue 2: Perfect Predictability

    • Cognitive Burden (Number of Questions/Attributes)

  • Louviere et al. (2010)

    • Best-Worst Scaling As Solution

  • Individual Models = “Bottom-Up Modeling Approach”

Matthew Winden, UW - Whitewater


Top down versus bottom up

Top-Down Versus Bottom-Up

“Top-Down” “Bottom-Up”

Assume

(, ) EstimateDerive

DeriveEstimate

Matthew Winden, UW - Whitewater


Contributions

Contributions

  • Objective 1: Use Monte-Carlo Simulation to Provide Evidence of the Validity of Individual Level Estimation Techniques

  • Objective 2a: Estimate Traditional and Individual Level Models on a Stated Preference Dataset

    • Eliminates Collinearity as a Convergence Problem

  • Objective 2b: Estimate Traditional and Individual Level Models on a Revealed Preference Dataset

  • Objective 3: Use Individual Level Estimates to Demonstrate Potential Bias Resulting from Distributional Assumptions in Traditional Models

Matthew Winden, UW - Whitewater


Traditional mixed logit

Traditional Mixed Logit

P(j|vi) = exp(Uji)/Σexp(Uji)

Utility of choice j for respondent i:

= αji + Βj+ 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


Individual level simulation estimation strategy

Individual Level Simulation & Estimation Strategy

  • 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


Mapping the wtp distribution from individual level parameter estimates

  • Individual Level Model Simulation

  • Results:

    • LL for Individual Level Models Indicates Better Fit than Correctly Specified Mixed Logits

    • Comparing True X3βValues, the Individual Level Model Performs Well Under All Distributional Specifications for the X3 Attribute

Matthew Winden, UW - Whitewater


Mapping the wtp distribution from individual level parameter estimates

  • Traditional and Individual Model Comparisons

  • Results:

    Table 34: Willingness-To-Pay Estimates ($/Gal)

Matthew Winden, UW - Whitewater


Conclusions so far

Conclusions? (So-Far)

  • Result 1: Validity of Individual Estimation Demonstrated through Simulation  Kind Of...

  • Result 2: Individual Level Model Distributions, MPs, & WTPs Differ Significantly from Outcomes Using Traditional Models

    • 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


Extensions

Extensions

  • E1: True (Full) Monte-Carlo Simulation For Individual Level Specifcations

    • Vary Over Number Respondents, Number Choice Occasions, Number Attributes, Types of Distributions

  • E2: Comparison using Revealed Preference Dataset (Beach)

    • Introduced Potential Collinearity as a Convergence Issue

    • More Realistic Situation Under Which Heterogenity May Matter

  • E3: Develop Appropriate Significance Tests for Individual Level Models

  • E4: Scale Issues in Aggregation of Individual Respondents

Matthew Winden, UW - Whitewater


Thank you all for your time and attention

Thank You All For Your Time and Attention


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