1. Mapping the WTP Distribution from Individual Level Parameter Estimates Matthew W. Winden University of Wisconsin - Whitewater WEA 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, 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 WEA November 10th, 2012 2 Matthew Winden, UW - Whitewater

3. Previous Work  Louviere et al. (2008) estimate individual level parameters using conditional logit estimator (no welfare analysis)  Convergence issue 1: Collinearity of 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” 3 WEA November 10th, 2012 Matthew Winden, UW - Whitewater

4. Top-Down Versus Bottom-Up 4 WEA November 10th, 2012 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 Demonstrate Potential Bias Resulting from Distributional Assumptions in Traditional Models 5 WEA November 10th, 2012 Matthew Winden, UW - Whitewater

6. Traditional Mixed Logit 6 WEA November 10th, 2012 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 7 WEA November 10th, 2012 Matthew Winden, UW - Whitewater

8.  Results:  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 8 Individual Level Model Simulation SimulationML LLML+I LLML X3 βML+I X3 βTrue X3 β A -1282.69-1194.944.4584.5993.945 B -1597.3-1302.812.7014.5843.826 C -1864.74-1545.424.2734.8784.004 WEA November 10th, 2012 Matthew Winden, UW - Whitewater

9.  Results: Table 34: Willingness-To-Pay Estimates ($/Gal) 9 Traditional and Individual Model Comparisons Conditional LogitMixed Logit 1Mixed Logit 2Individual AttributeMP (S.E.) MP ED 0.029 (0.002) 0.031 (0.003)0.086 NR 0.023 (0.002)0.022 (0.002)0.024 (0.002)0.065 HH 0.036 (0.002)0.034 (0.003)0.035 (0.003)0.094 ScenarioConditional LogitMixed Logit 1Mixed Logit 2Individual 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 WEA November 10th, 2012 Matthew Winden, UW - Whitewater

10. 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 10 WEA November 10th, 2012 Matthew Winden, UW - Whitewater

11. 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 11 WEA November 10th, 2012 Matthew Winden, UW - Whitewater

12. Thank You All For Your Time and Attention