A New Baseline Model for Estimating Willingness to Pay from Discrete Choice Models

We show a substantive problem exists with the widely-used ratio of coefficients approach to calculating willingness to pay (WTP) from choice models. The correctly calculated standard error for WTP using this approach is shown to always be infinity. A variant of this problem has long been recognized for mixed logit models. We show it occurs even in simple models like the conditional logit used as a baseline reference specification. It occurs because the standard error for the cost parameter implies some possibility that the true parameter value is arbitrarily close to zero. We propose a simple yet elegant way to overcome this problem by reparameterizing the coefficient of the (negative) cost variable to enforce the theoretically correct (and empirically almost always found) positive coefficient using an exponential transformation of the original parameter. This reparameterization enforces the desired restriction that no-part of the confidence region for original cost parameter spans zero. With it the confidence interval for WTP is now finite and well behaved. Our proposed model is straightforward to implement using readily available software. Its log-likelihood value is the same as the usual baseline discrete choice model and we recommend its use as the new standard baseline reference model.