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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 S EA Conference – November 2012. Motivation.

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Mapping the WTP Distribution from Individual Level Parameter Estimates

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  1. Mapping the WTP Distribution from Individual Level Parameter Estimates Matthew W. Winden University of Wisconsin - Whitewater SEA Conference – November 2012

  2. 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 – Impose Continuous Distribution • Latent Class Logit – Impose Discrete Distribution • 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

  3. Individual Level Modeling As Solution • 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 • Why Individual Level Models? •  “Bottom-Up Modeling Approach” Matthew Winden, UW - Whitewater

  4. Top-Down Versus Bottom-Up Modeling “Top-Down” “Bottom-Up” Assume Derive (, ) Estimate Derive Estimate Matthew Winden, UW - Whitewater

  5. 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 Examine Potential Bias Resulting from Distributional Assumptions in Traditional Models Matthew Winden, UW - Whitewater

  6. 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

  7. 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

  8. Individual Level Model Simulation LL Values Indicate Stronger Fit Not Statistically Significantly Different Matthew Winden, UW - Whitewater

  9. Traditional and Individual Model Comparisons Table 34: Willingness-To-Pay Estimates ($/Gal) Matthew Winden, UW - Whitewater

  10. Individual Level Mapped Distribution • Kolmogorov-Smirnov tests reject the null hypothesis of the equivalence of normal and log-normal distributions Matthew Winden, UW - Whitewater

  11. Conclusions? (So-Far) • Result 1: Validity of Individual Estimation Demonstrated through Simulation  Kind Of... • Result 2: Individual Level Model Distributions, MPs, & WTPs Differ 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 • Although in the SP Case, the results are not statistically different Matthew Winden, UW - Whitewater

  12. Extensions • E1: True (Full) Monte-Carlo Simulation For Individual Level Specifcations • Vary Over Types of Non-Traditional Distributions and Number of Respondents, Choice Occasions, and Attributes • E2: Comparison using Revealed Preference Dataset • Introduces Potential Collinearity as a Convergence Issue • More Realistic Situation Under Which Heterogenity May Exist • E3: Significance Tests for Individual Level Models • E4: Compare Results Against Latent Class Models • E5: Scale Issues in Aggregation of Individual Respondents Matthew Winden, UW - Whitewater

  13. Thank You!

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