Assuring Finite Moments for Willingness to Pay in Random Coefficient Models

Random coefficient models such as mixed logit are increasingly being used to allow for random heterogeneity in willingness to pay (WTP) measures. In the most commonly used specifications, the distribution of WTP for an attribute is derived from the distribution of the ratio of individual coefficients. Since the cost coefficient enters the denominator, values of the cost coefficient that are close to zero induce large values of WTP, with unboundedly large values of WTP resulting from cost coefficients arbitrarily close to zero. In this paper, the authors identify a criterion to determine whether the distribution of WTP has finite moments. Using this criterion, the authors show that some popular distributions used for the cost coefficient in random coefficient models, including normal, truncated normal, uniform and triangular, imply infinite moments for the distribution of WTP, even if truncated or bounded at zero. The authors also point out that relying on simulation approaches to obtain moments of WTP from the estimated distribution of the cost and attribute coefficients can mask the problem by giving finite moments when the true ones are infinite. The authors identify several approaches that analysts can utilize to assure that the distribution of WTP has finite moments.

• Record URL:
  • https://aetransport.org/past-etc-papers/conference-papers-pre-2009/conference-papers-2009
• Corporate Authors:

  Association for European Transport (AET)

  1 Vernon Mews, Vernon Street, West Kensington
  London W14 0RL,    
• Authors:
  • Daly, Andrew
  • Hess, Stephane
  • Train, Kenneth E
• Conference:
  • European Transport Conference, 2009
  • Location: Leiden Leeuwenhorst Conference Centre , Netherlands
  • Date: 2009-10-5 to 2009-10-7
• Publication Date: 2009

Language

• English

Media Info

• Media Type: Web
• Features: Appendices; References; Tables;
• Pagination: 11p
• Monograph Title: European Transport Conference, 2009 Proceedings

Subject/Index Terms

• TRT Terms: Coefficients; Economic factors; Finite element method; Heterogeneity; Random variables; Simulation
• Uncontrolled Terms: Mixed logit models; Willingness to pay
• Subject Areas: Economics; Highways; Planning and Forecasting; I72: Traffic and Transport Planning;

Filing Info

• Accession Number: 01345423
• Record Type: Publication
• Files: TRIS
• Created Date: Jul 21 2011 2:25PM