IDEAS home Printed from https://ideas.repec.org/a/eee/transb/v58y2013icp199-214.html
   My bibliography  Save this article

Confidence intervals of willingness-to-pay for random coefficient logit models

Author

Listed:
  • Bliemer, Michiel C.J.
  • Rose, John M.

Abstract

Random coefficient logit (RCL) models containing random parameters are increasingly used for modelling travel choices. Willingness-to-pay (WTP) measures, such as the value of travel time savings (VTTS) are, in the case of RCL models estimated in preference space, ratios of random parameters. In this paper we apply the Delta method to compute the confidence intervals of such WTP measures, taking into account the variance–covariance matrix of the estimates of the distributional parameters. The same Delta method can be applied when the model is estimated in WTP space. Compared to simulation methods such as proposed by Krinsky and Robb, the Delta method is able to avoid most of the simulations by deriving partly analytical expressions for the standard errors. Examples of such computations are shown for different combinations of random distributions.

Suggested Citation

  • Bliemer, Michiel C.J. & Rose, John M., 2013. "Confidence intervals of willingness-to-pay for random coefficient logit models," Transportation Research Part B: Methodological, Elsevier, vol. 58(C), pages 199-214.
    • Handle: RePEc:eee:transb:v:58:y:2013:i:c:p:199-214
    DOI: 10.1016/j.trb.2013.09.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0191261513001707
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.trb.2013.09.010?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Sándor, Zsolt & Train, Kenneth, 2004. "Quasi-random simulation of discrete choice models," Transportation Research Part B: Methodological, Elsevier, vol. 38(4), pages 313-327, May.
    2. Raquel Espino & Juan Ortúzar & Concepción Román, 2006. "Confidence Interval for Willingness to Pay Measures in Mode Choice Models," Networks and Spatial Economics, Springer, vol. 6(2), pages 81-96, June.
    3. 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.
    4. Daly, Andrew & Hess, Stephane & de Jong, Gerard, 2012. "Calculating errors for measures derived from choice modelling estimates," Transportation Research Part B: Methodological, Elsevier, vol. 46(2), pages 333-341.
    5. David Hensher & William Greene, 2003. "The Mixed Logit model: The state of practice," Transportation, Springer, vol. 30(2), pages 133-176, May.
    6. Fosgerau, Mogens & Bierlaire, Michel, 2007. "A practical test for the choice of mixing distribution in discrete choice models," Transportation Research Part B: Methodological, Elsevier, vol. 41(7), pages 784-794, August.
    7. Bhat, Chandra R., 2001. "Quasi-random maximum simulated likelihood estimation of the mixed multinomial logit model," Transportation Research Part B: Methodological, Elsevier, vol. 35(7), pages 677-693, August.
    8. Campbell, Danny, 2007. "Combining mixed logit models and random effects models to identify the determinants of willingness to pay for rural landscape improvements," 81st Annual Conference, April 2-4, 2007, Reading University, UK 7975, Agricultural Economics Society.
    9. 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.
    10. 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.
    11. Celine Michaud & Daniel Llerena & Iragael Joly, 2013. "Willingness to pay for environmental attributes of non-food agricultural products: a real choice experiment," European Review of Agricultural Economics, Oxford University Press and the European Agricultural and Applied Economics Publications Foundation, vol. 40(2), pages 313-329, March.
    12. Riccardo Scarpa & John M. Rose, 2008. "Design efficiency for non-market valuation with choice modelling: how to measure it, what to report and why ," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 52(3), pages 253-282, September.
    13. Francisco Amador & Rosa González & Juan Ortúzar, 2005. "Preference Heterogeneity and Willingness to Pay for Travel Time Savings," Transportation, Springer, vol. 32(6), pages 627-647, November.
    14. David F. Layton & Gardner Brown, 2000. "Heterogeneous Preferences Regarding Global Climate Change," The Review of Economics and Statistics, MIT Press, vol. 82(4), pages 616-624, November.
    15. Krinsky, Itzhak & Robb, A Leslie, 1990. "On Approximating the Statistical Properties of Elasticities: A Correction," The Review of Economics and Statistics, MIT Press, vol. 72(1), pages 189-190, February.
    16. Riccardo Scarpa & Mara Thiene & Kenneth Train, 2008. "Utility in Willingness to Pay Space: A Tool to Address Confounding Random Scale Effects in Destination Choice to the Alps," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 90(4), pages 994-1010.
    17. Andrew A. Goett & Kathleen Hudson & Kenneth E. Train, 2000. "Customers' Choice Among Retail Energy Suppliers: The Willingness-to-Pay for Service Attributes," The Energy Journal, International Association for Energy Economics, vol. 0(Number 4), pages 1-28.
    18. Dan Rigby & Kelvin Balcombe & Michael Burton, 2009. "Mixed Logit Model Performance and Distributional Assumptions: Preferences and GM foods," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 42(3), pages 279-295, March.
    19. Scarpa, R. & Thiene, M. & Train, K., 2008. "Appendix to Utility in WTP space: a tool to address confounding random scale effects in destination choice to the Alps," American Journal of Agricultural Economics APPENDICES, Agricultural and Applied Economics Association, vol. 90(4), pages 1-9, January.
    20. Danny Campbell, 2007. "Willingness to Pay for Rural Landscape Improvements: Combining Mixed Logit and Random‐Effects Models," Journal of Agricultural Economics, Wiley Blackwell, vol. 58(3), pages 467-483, September.
    21. Hess, Stephane & Bierlaire, Michel & Polak, John W., 2005. "Estimation of value of travel-time savings using mixed logit models," Transportation Research Part A: Policy and Practice, Elsevier, vol. 39(2-3), pages 221-236.
    22. Krinsky, Itzhak & Robb, A Leslie, 1986. "On Approximating the Statistical Properties of Elasticities," The Review of Economics and Statistics, MIT Press, vol. 68(4), pages 715-719, November.
    23. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Scaccia, Luisa & Marcucci, Edoardo & Gatta, Valerio, 2023. "Prediction and confidence intervals of willingness-to-pay for mixed logit models," Transportation Research Part B: Methodological, Elsevier, vol. 167(C), pages 54-78.
    2. Daziano, Ricardo A. & Achtnicht, Martin, 2014. "Accounting for uncertainty in willingness to pay for environmental benefits," Energy Economics, Elsevier, vol. 44(C), pages 166-177.
    3. Paleti, Rajesh, 2018. "Generalized multinomial probit Model: Accommodating constrained random parameters," Transportation Research Part B: Methodological, Elsevier, vol. 118(C), pages 248-262.
    4. De Ayala Bilbao, Amaya & Hoyos Ramos, David & Mariel Chladkova, Petr, 2012. "Landscape valuation through discrete choice experiments: Current practice and future research reflections," BILTOKI 1134-8984, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística).
    5. Caputo, Vincenzina & Scarpa, Riccardo & Nayga, Rodolfo M. & Ortega, David L., 2018. "Are preferences for food quality attributes really normally distributed? An analysis using flexible mixing distributions," Journal of choice modelling, Elsevier, vol. 28(C), pages 10-27.
    6. Stephane Hess, 2014. "Latent class structures: taste heterogeneity and beyond," Chapters, in: Stephane Hess & Andrew Daly (ed.), Handbook of Choice Modelling, chapter 14, pages 311-330, Edward Elgar Publishing.
    7. Arata, Linda & Diluiso, Francesca & Guastella, Gianni & Pareglio, Stefano & Sckokai, Paolo, 2021. "Willingness to pay for alternative features of land-use policies: the case of the lake Garda region," Land Use Policy, Elsevier, vol. 100(C).
    8. de Ayala, Amaia & Hoyos, David & Mariel, Petr, 2015. "Suitability of discrete choice experiments for landscape management under the European Landscape Convention," Journal of Forest Economics, Elsevier, vol. 21(2), pages 79-96.
    9. West, Grant H. & Snell, Heather & Kovacs, Kent & Nayga, Rodolfo M., 2020. "Estimation of the preferences for the intertemporal services from groundwater," 2020 Annual Meeting, July 26-28, Kansas City, Missouri 304220, Agricultural and Applied Economics Association.
    10. Doherty, Edel & Campbell, Danny & Hynes, Stephen, 2012. "Exploring cost heterogeneity in recreational demand," Working Papers 148832, National University of Ireland, Galway, Socio-Economic Marine Research Unit.
    11. Mariel, Petr & Artabe, Alaitz, 2020. "Interpreting correlated random parameters in choice experiments," Journal of Environmental Economics and Management, Elsevier, vol. 103(C).
    12. Edel Doherty & Danny Campbell & Stephen Hynes, 2013. "Models of Site-choice for Walks in Rural Ireland: Exploring Cost Heterogeneity," Journal of Agricultural Economics, Wiley Blackwell, vol. 64(2), pages 446-466, June.
    13. Gillespie Rob & Kragt Marit E., 2012. "Accounting for Nonmarket Impacts in a Benefit-Cost Analysis of Underground Coal Mining in New South Wales, Australia," Journal of Benefit-Cost Analysis, De Gruyter, vol. 3(2), pages 1-29, May.
    14. Abildtrup, Jens & Garcia, Serge & Olsen, Søren Bøye & Stenger, Anne, 2013. "Spatial preference heterogeneity in forest recreation," Ecological Economics, Elsevier, vol. 92(C), pages 67-77.
    15. Hoyos, David, 2010. "The state of the art of environmental valuation with discrete choice experiments," Ecological Economics, Elsevier, vol. 69(8), pages 1595-1603, June.
    16. Kemper, Nathan & Nayga, Rodolfo M. Jr. & Popp, Jennie & Bazzani, Claudia, 2016. "The Effects of Honesty Oath and Consequentiality in Choice Experiments," 2016 Annual Meeting, July 31-August 2, Boston, Massachusetts 235381, Agricultural and Applied Economics Association.
    17. Haghani, Milad & Bliemer, Michiel C.J. & Hensher, David A., 2021. "The landscape of econometric discrete choice modelling research," Journal of choice modelling, Elsevier, vol. 40(C).
    18. Stephane Hess & John Rose, 2012. "Can scale and coefficient heterogeneity be separated in random coefficients models?," Transportation, Springer, vol. 39(6), pages 1225-1239, November.
    19. Søren Olsen, 2009. "Choosing Between Internet and Mail Survey Modes for Choice Experiment Surveys Considering Non-Market Goods," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 44(4), pages 591-610, December.
    20. Benoit Chèze & Charles Collet & Anthony Paris, 2021. "Estimating discrete choice experiments : theoretical fundamentals," CIRED Working Papers hal-03262187, HAL.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:transb:v:58:y:2013:i:c:p:199-214. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/548/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.