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

• New method for determining confidence intervals for WTP for mixed logit models.
• Using the Delta method, which requires less simulation than the current method.
• Applies to both estimations in preference space and WTP space.
• Applies to combinations of distributions, such as (log) normal, triangular, uniform, and exponential.

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.