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The Signs of the Times: Imposing a Globally Signed Condition on Willingness to Pay Distributions

Listed author(s):
  • David Hensher


A feature of recent developments in choice models that enable estimation of the distribution of willingness to pay (WTP) is that the sign of the distribution can change over the range. Behaviourally this often makes little sense for attributes such as travel time on non-discretionary travel, despite a growing recognition of positive utility over some travel time ranges. This can in part be attributed to the analytical distribution that is selected (except the cumbersome lognormal), many of which are unconstrained over the full range. Although a number of analysts have imposed constraints on various distributions for random parameters that can satisfy the single-sign condition, these restrictions are, with rare exception, only satisfied for the mean and the standard deviation estimates of a random parameter. When heterogeneity around the mean and/or heteroscedasticity around the standard deviation is allowed for, however, the constraint condition is often not satisfied. Given the popularity of distributions other than the lognormal, in order to satisfy the sign condition under the most general form of parameterisation, we need to impose a global sign condition. In this paper we show how this might be achieved in the context of the valuation of travel time savings for car commuters choosing amongst an offered set of route-specific travel times and costs. We illustrate the impact of the constraint under a globally constrained Rayleigh distribution for total travel time parameterisation, contrasting the evidence with a multinomial logit model and a range of other distributional assumptions within the mixed logit framework. Copyright Springer 2006

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Article provided by Springer in its journal Transportation.

Volume (Year): 33 (2006)
Issue (Month): 3 (May)
Pages: 205-222

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Handle: RePEc:kap:transp:v:33:y:2006:i:3:p:205-222
DOI: 10.1007/s11116-005-2302-9
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  1. David Revelt and Kenneth Train., 2000. "Customer-Specific Taste Parameters and Mixed Logit: Households' Choice of Electricity Supplier," Economics Working Papers E00-274, University of California at Berkeley.
  2. Erik Meijer & Jan Rouwendal, 2006. "Measuring welfare effects in models with random coefficients," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(2), pages 227-244.
  3. Small, Kenneth A & Winston, Clifford & Yan, Jia, 2002. "Uncovering the Distribution of Motorists' Preferences for Travel Time and Reliability: Implications for Road Pricing," University of California Transportation Center, Working Papers qt8zd2r34k, University of California Transportation Center.
  4. Fosgerau, Mogens, 2006. "Investigating the distribution of the value of travel time savings," Transportation Research Part B: Methodological, Elsevier, vol. 40(8), pages 688-707, September.
  5. Kenneth A. Small & Clifford Winston & Jia Yan, 2005. "Uncovering the Distribution of Motorists' Preferences for Travel Time and Reliability," Econometrica, Econometric Society, vol. 73(4), pages 1367-1382, July.
  6. repec:dgr:rugsom:00f25 is not listed on IDEAS
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