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

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.

[1]  David F. Layton,et al.  Heterogeneous Preferences Regarding Global Climate Change , 2000, Review of Economics and Statistics.

[2]  Andrew Daly,et al.  Assuring finite moments for willingness to pay in random coefficient models , 2009 .

[3]  Juan de Dios Ortúzar,et al.  Confidence Interval for Willingness to Pay Measures in Mode Choice Models , 2006 .

[4]  David A. Hensher,et al.  The Mixed Logit Model: the State of Practice and Warnings for the Unwary , 2001 .

[5]  M. Bierlaire,et al.  ESTIMATION OF VALUE OF TRAVEL-TIME SAVINGS USING MIXED LOGIT MODELS , 2005 .

[6]  Danny Campbell,et al.  Willingness to Pay for Rural Landscape Improvements: Combining Mixed Logit and Random-Effects Models , 2007 .

[7]  I. Krinsky,et al.  On Approximating the Statistical Properties of Elasticities , 1986 .

[8]  Michel Bierlaire,et al.  A practical test for the choice of mixing distribution in discrete choice models , 2005 .

[9]  D. McFadden,et al.  MIXED MNL MODELS FOR DISCRETE RESPONSE , 2000 .

[10]  Juan de Dios Ortúzar,et al.  Preference Heterogeneity and Willingness to Pay for Travel Time Savings , 2004 .

[11]  Andrew Daly,et al.  Calculating Errors for Measures Derived from Choice Modeling Estimates , 2012 .

[12]  Dan Rigby,et al.  Mixed Logit Model Performance and Distributional Assumptions: Preferences and GM foods , 2009 .

[13]  Juan de Dios Ortúzar,et al.  Confidence intervals to bound the value of time , 2001 .

[14]  Kenneth Train,et al.  Customers' Choice Among Retail Energy Suppliers: The Willingness-to-Pay for Service Attributes , 2000 .

[15]  K. Train,et al.  Mixed Logit with Repeated Choices: Households' Choices of Appliance Efficiency Level , 1998, Review of Economics and Statistics.

[16]  K. Train,et al.  Utility in WTP Space: A Tool to Address Confounding Random Scale Effects in Destination Choice to the Alps , 2006 .

[17]  Cinzia Cirillo,et al.  Continuous Random Coefficient Logit Models: A Comparison of Parametric and Non-parametric Methods to Estimate Individual Preferences over Cybernetic Transportation Systems , 2010 .

[18]  G. Oehlert.  A note on the delta method , 1992 .

[19]  L. Masiero,et al.  Accounting for WTP/WTA discrepancy in discrete choice models , 2010 .

[20]  M. Bliemer,et al.  Approximation of bayesian efficiency in experimental choice designs , 2008 .

[21]  D. McFadden.  Conditional logit analysis of qualitative choice behavior , 1972 .

[22]  Kenneth Train,et al.  Utility in Willingness to Pay Space: A Tool to Address Confounding Random Scale Effects in Destination Choice to the Alps , 2008 .

[23]  John M. Rose,et al.  Design Efficiency for Non-Market Valuation with Choice Modelling: How to Measure it, What to Report and Why , 2008 .

[24]  C. Michaud,et al.  Willingness to pay for environmental attributes of non-food agricultural products: a real choice experiment , 2013 .

[25]  Juan de Dios Ortúzar,et al.  Willingness-to-Pay Estimation with Mixed Logit Models: Some New Evidence , 2005 .

[26]  Zsolt Sándor,et al.  Quasi-random simulation of discrete choice models , 2004 .

[27]  C. Bhat.  Quasi-random maximum simulated likelihood estimation of the mixed multinomial logit model , 2001 .

[28]  D Ettema,et al.  A SIMULATION METHOD FOR DETERMINING THE CONFIDENCE INTERVAL OF A WEIGHTED GROUP AVERAGE VALUE OF TIME , 1997 .

[29]  Mogens Fosgerau,et al.  Investigating the distribution of the value of travel time savings , 2006 .

[30]  Kenneth Train,et al.  Discrete Choice Models in Preference Space and Willingness-to Pay Space , 2005 .

[31]  Michel Bierlaire,et al.  BIOGEME: a free package for the estimation of discrete choice models , 2003 .

[32]  Timothy C. Haab,et al.  Valuing Environmental and Natural Resources: The Econometrics of Non-Market Valuation , 2002 .

[33]  I. Krinsky,et al.  On Approximating the Statistical Properties of Elasticities: A Correction , 1990 .