Willingness-to-Pay Estimation with Mixed Logit Models: Some New Evidence

Abstract

IntroductionSince the dawn of discrete-choice modelling in the 1960s, when binary logit and probit models became useful tools to derive values of time, we have come a long wayöand increasingly faster in the last few years. We have seen almost three decades of unchecked rule by the multinomial (MNL) and nested logit (NL) models, with the more powerful and flexible multinomial probit (MNP) being left aside because of the difficulties involved with its use in real-life problems. Today, when computing power and better numerical techniques have made possible its use in practical applications, MNP has been overshadowed again by the equally flexible and/or powerful but less unyielding, mixed logit (ML) model. Both approaches have the ability to treat correlated and heteroscedastic alternatives, as well as random taste variations through the estimation of random rather than fixed parameters.In this paper we discuss a number of issues related to the interpretation of results and the use of this exciting model in real-life applications. In particular, we dig deeper into the use of the model to estimate measures of willingness to pay (WTP), such as the value of time or the value of a statistical life (Rizzi and Ortu¨zar, 2003).The WTP for a unit change in a certain attribute can be computed as the marginal rate of substitution (MRS) between income and the quantity expressed by the attribute, at constant utility levels (Gaudry et al, 1989). The concept is equivalent to computing the compensated variation (Small and Rosen, 1981), as one usually works with a linear approximation of the indirect utility function. Thus, point estimates of the MRS represent the slope of the utility function for the range where this approximation holds. Furthermore, as income does not enter in the truncated indirect utility function, the MRS is calculated with respect to minus the cost variable (Jara-D|¨az, 1990). In this way, the WTP in a linear utility function simply equals the ratio between the parameters of the variable of interest (that is, time in the case of the subjective value of time, SVT) and the cost variable (that is, the marginal utility of income, which itself has to follow certain properties in a well-specified model).Abstract. Mixed-logit models are currently the state of the art in discrete-choice modelling, and their estimation in various forms (in particular, mixing revealed-preference and stated-preference data) is becoming increasingly popular. Although the theory behind these models is fairly simple, the practical problems associated with their estimation with empirical data are still relatively unknown and certainly not solved to everybody's satisfaction. In this paper we use a stated-preference datasetö previously used to derive willingness to pay for reduction in atmospheric pollution and subjective values of timeöto estimate random parameter mixed logit models with different estimation methods. We use our results to discuss in some depth the problems associated with the derivation of willingness to pay with this class o...

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