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

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  • David Hensher

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    Abstract

    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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    File URL: http://hdl.handle.net/10.1007/s11116-005-2302-9
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    Bibliographic Info

    Article provided by Springer in its journal Transportation.

    Volume (Year): 33 (2006)
    Issue (Month): 3 (05)
    Pages: 205-222

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    Handle: RePEc:kap:transp:v:33:y:2006:i:3:p:205-222

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    Web page: http://www.springerlink.com/link.asp?id=103007

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    Keywords: mixed logit; random parameter distributions; willingness to pay distributions;

    References

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    1. Mogens Fosgerau, 2004. "Investigating the distribution of the value of travel time savings," Urban/Regional 0410005, EconWPA, revised 25 Nov 2004.
    2. D Rigby & M Burton, 2003. "Modeling Indifference and Dislike: A Bounded Bayesian Mixed Logit Model of the UK Market for GM Food," The School of Economics Discussion Paper Series 0327, Economics, The University of Manchester.
    3. 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, 07.
    4. Meijer, E. & Rouwendal, J., 2000. "Measuring welfare effects in models with random coefficients," Research Report 00F25, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    5. 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.
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    Cited by:
    1. Hoyos, David & Mariel, Petr & Fernández-Macho, Javier, 2009. "The influence of cultural identity on the WTP to protect natural resources: Some empirical evidence," Ecological Economics, Elsevier, vol. 68(8-9), pages 2372-2381, June.
    2. Kjaer, Trine & Gyrd-Hansen, Dorte, 2008. "Preference heterogeneity and choice of cardiac rehabilitation program: Results from a discrete choice experiment," Health Policy, Elsevier, vol. 85(1), pages 124-132, January.
    3. Hensher, David A., 2008. "Influence of vehicle occupancy on the valuation of car driver's travel time savings: Identifying important behavioural segments," Transportation Research Part A: Policy and Practice, Elsevier, vol. 42(1), pages 67-76, January.
    4. de Lapparent, M., & Axhausen , K.W. & Frei, A., 2013. "Long distance mode choice and distributions of values of travel time savings in three European countries," European Transport \ Trasporti Europei, ISTIEE, Institute for the Study of Transport within the European Economic Integration, issue 53, pages 7.
    5. Hensher, David A. & Greene, William H. & Li, Zheng, 2011. "Embedding risk attitude and decision weights in non-linear logit to accommodate time variability in the value of expected travel time savings," Transportation Research Part B: Methodological, Elsevier, vol. 45(7), pages 954-972, August.

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