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Including cost income ratio into utility function as a way of dealing with ‘exploding’ implicit prices in mixed logit models


  • Giergiczny, Marek
  • Valasiuk, Sviataslau
  • Czajkowski, Mikolaj
  • De Salvo, Maria
  • Signorello, Giovanni


The estimates of mean WTP are typically of main interest in non-market valuation studies. In the case of mixed logit models 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. A standard practice in analysing the data from choice experiments is to assume the cost coefficient is fixed, which implies that there is no heterogeneity in price sensitivity. The three most commonly given reasons for this are: (i) the distribution of the marginal willingness-to-pay for an attribute is then simply the distribution of that attribute's coefficient; (ii) in this way analysts wish to restrict the price variable to be non-positive for all individuals; and (iii) analysts avoid assuming log-normal cost because it is often found to produce behaviourally implausible estimates. Constraining a price coefficient to be fixed can however have serious consequences, i.e. a constant price coefficient implies that the standard deviations of unobserved utility is the same for all observations which can lead to biased results. Respondents are also likely to vary in price sensitivities, thus ignoring this variation can lead to erroneous interpretation and conclusions. In this paper we demonstrate a choice experiment exercise in which specifying a log-normal cost results in implausibly large WTP, however, adding into the utility function the cost income ratio prevents implicit prices from ‘exploding’.

Suggested Citation

  • Giergiczny, Marek & Valasiuk, Sviataslau & Czajkowski, Mikolaj & De Salvo, Maria & Signorello, Giovanni, 2012. "Including cost income ratio into utility function as a way of dealing with ‘exploding’ implicit prices in mixed logit models," Journal of Forest Economics, Elsevier, vol. 18(4), pages 370-380.
  • Handle: RePEc:eee:foreco:v:18:y:2012:i:4:p:370-380
    DOI: 10.1016/j.jfe.2012.07.002

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    References listed on IDEAS

    1. Scarpa Riccardo & Thiene Mara & Marangon Francesco, 2007. "The Value of Collective Reputation for Environmentally-Friendly Production Methods: The Case of Val di Gresta," Journal of Agricultural & Food Industrial Organization, De Gruyter, vol. 5(1), pages 1-28, September.
    2. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555, May.
    3. David Revelt & Kenneth Train, 1998. "Mixed Logit With Repeated Choices: Households' Choices Of Appliance Efficiency Level," The Review of Economics and Statistics, MIT Press, vol. 80(4), pages 647-657, November.
    4. Andrew Daly & Stephane Hess & Kenneth Train, 2012. "Assuring finite moments for willingness to pay in random coefficient models," Transportation, Springer, vol. 39(1), pages 19-31, January.
    5. Carlsson, Fredrik & Frykblom, Peter & Liljenstolpe, Carolina, 2003. "Valuing wetland attributes: an application of choice experiments," Ecological Economics, Elsevier, vol. 47(1), pages 95-103, November.
    6. Daniel McFadden & Kenneth Train, 2000. "Mixed MNL models for discrete response," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(5), pages 447-470.
    7. David Hensher & William Greene, 2003. "The Mixed Logit model: The state of practice," Transportation, Springer, vol. 30(2), pages 133-176, May.
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    Cited by:

    1. Piotr Ćwiakowski & Marek Giergiczny & Michał Krawczyk, 2013. "Pirates in the lab. Using incentivized choice experiments to explore preference for (un)authorized content," Working Papers 2013-25, Faculty of Economic Sciences, University of Warsaw.
    2. Wiktor Budziński, 2015. "The effects of non-constant marginal utility of cost for public goods valuation," Ekonomia journal, Faculty of Economic Sciences, University of Warsaw, vol. 43.
    3. repec:eee:appene:v:212:y:2018:i:c:p:141-150 is not listed on IDEAS
    4. Giergiczny, Marek & Czajkowski, Mikołaj & Żylicz, Tomasz & Angelstam, Per, 2015. "Choice experiment assessment of public preferences for forest structural attributes," Ecological Economics, Elsevier, vol. 119(C), pages 8-23.

    More about this item


    Choice experiments; Mixed logit models; WTP's distribution; Cost income ratio coefficient;

    JEL classification:

    • Q23 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - Forestry
    • Q51 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Valuation of Environmental Effects
    • Q57 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Ecological Economics


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