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Assuring finite moments for willingness to pay in random coefficients models

Daly, AJ, Hess, S and Train, KE (2012) Assuring finite moments for willingness to pay in random coefficients models. Transportation, 39 (1). 19 - 31 . ISSN 0049-4488


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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, its distribution plays a major role in the distribution of WTP. Depending on the choice of distribution for the cost coefficient, and its implied range, the distribution of WTP may or may not have finite moments. In this paper, we identify a criterion to determine whether, with a given distribution for the cost coefficient, the distribution of WTP has finite moments. Using this criterion, we 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. We 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 issue by giving finite moments when the true ones are infinite.

Item Type: Article
Copyright, Publisher and Additional Information: © 2012, Springer. This is an author produced version of a paper published in Transportation. Uploaded in accordance with the publisher's self-archiving policy. The original publication is available at www.springerlink.com.
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Environment (Leeds) > Institute for Transport Studies (Leeds)
Depositing User: Symplectic Publications
Date Deposited: 12 Apr 2012 14:52
Last Modified: 19 Sep 2014 07:25
Published Version: http://dx.doi.org/10.1007/s11116-011-9331-3
Status: Published
Publisher: Springer Verlag
Identification Number: 10.1007/s11116-011-9331-3
URI: http://eprints.whiterose.ac.uk/id/eprint/43622

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