A comparison of approaches to estimating confidence intervals for willingness to pay measures

This paper describes three approaches to estimating confidence intervals for willingness to pay measures, the delta, Krinsky and Robb and bootstrap methods. The accuracy of the various methods is compared using a number of simulated datasets. In the majority of the scenarios considered all three methods are found to be reasonably accurate as well as yielding similar results. The delta method is the most accurate when the data is well-conditioned, while the bootstrap is more robust to noisy data and misspecification of the model. These conclusions are illustrated by empirical data from a study of willingness to pay for a reduction in waiting time for a general practitioner appointment in which all the methods produce fairly similar confidence intervals.willingness to pay, confidence interval, delta method, boot-strap

Modelling Heterogeneity in Patients' Preferences for the Attributes of a General Practitioner Appointment

This paper examines the distribution of preferences in a sample of patients who responded to a discrete choice experiment on the choice of general practitioner appointments. In addition to standard logit, mixed and latent class logit models are used to analyse the data from the choice experiment. It is found that there is significant preference heterogeneity for all the attributes in the experiment and that both the mixed and latent class models lead to significant improvements in fit compared to the standard logit model. Moreover, the distribution of preferences implied by the preferred mixed and latent class models is similar for many attributes.discrete choice experiment; mixed logit; latent class logit

Forecasting the demand for an employee Park and Ride service using commuters’ stated choices.

This paper uses Stated Choice (SC) data to forecast the demand for an employee Park and Ride service. Since it is well known that SC data contain sources of variation not present in Revealed Preference (RP) data we pay special attention to the scaling of the SC model. The results show that the modal shift away from parking-on site will be small unless the new service is accompanied by measures aimed at making parking on-site less attractive such as introducing parking charges.Travel plan, Stated choice, Forecasting, Scale factor

Small-sample properties of tests for heteroscedasticity in the conditional logit model

This paper compares the small-sample properties of several asymptotically equivalent tests for heteroscedasticity in the conditional logit model. While no test outperforms the others in all of the experiments conducted, the likelihood ratio test and a particular variety of the Wald test are found to have good properties in moderate samples as well as being relatively powerful.

Mixed logit estimation of willingness to pay distributions: a comparison of models in preference and WTP space using data from a health-related choice experiment.

Different approaches to modelling the distribution of WTP are compared using stated preference data on Tanzanian Clinical Officers’ job choices and mixed logit models. The standard approach of specifying the distributions of the coefficients and deriving WTP as the ratio of two coefficients estimation in preference space) is compared to specifying the distributions for WTP directly at the estimation stage (estimation in WTP space). The models in preference space fit the data better than the corresponding models in WTP space although the difference between the best fitting models in the two estimation regimes is minimal. Moreover, the willingness to pay estimates derived from the preference space models turn out to be unrealistically high for many of the job attributes. The results suggest that sensitivity testing using a variety of model specifications, including estimation in WTP space, is recommended when using mixed logit models to estimate willingness to pay distributions.WTP space; Stated preference methods; Discrete choice; Mixed logit; Willingness to pay*

Measuring and testing for gender discrimination in physician pay: English family doctors

In 2008 the income of female GPs was 70%, and their wages (income per hour) were 89%, of those of male GPs. We estimate Oaxaca decompositions using OLS models of wages (income/hours) and 2SLS models of income. The elasticity of income with respect to hours is 0.91 for female GPs and 0.29 for male GPs, so that log wage models are misspecified. The conventional discrimination measure (the unexplained difference in mean log income) is sensitive to the counterfactual (30% using male returns vs 11% using female returns), to the use of OLS vs. 2SLS (19% vs 11%, female counterfactual), but not to dropping insignificant female interactions. The unexplained pro-male difference arises because the pro male difference in regression constants offsets the pro-female difference in the effect of hours on income. We propose a set of new direct tests for within workplace gender discrimination based on a comparison of the differences in income of female and male GPs in practices with varying proportions of female GPs and with female or male senior partners. The direct tests produce mixed results. An indirect test, comparing GPs actual income with the income they report as an acceptable reward for their job, shows that female GPs are not more likely than male GPs to report that their actual income is less than acceptable income, whereas GPs from ethnic minorities and overseas qualified GPs are significantly more likely to do so.Gender discrimination. Family doctors. General practitioners. Income. Wages.

Tests for the consistency of three-level nested logit models with utility maximization.

This paper provides necessary conditions for testing the local consistency of three-level nested logit models with random utility maximization. We find that for a model with two sub-nests per nest the conditions can lead to a substantial increase in the range of acceptable dissimilarity parameters, irrespective of the number of alternatives per sub-nest.Nested logit, Discrete choice, Random utility maximization

Modelling commuters' mode choice in Scotland

This thesis contributes to the literature on the choice of transport mode for commuting trips, with special focus on the difference between urban and rural commuting in Scotland. The thesis begins by giving an overview of discrete choice theory and some empirical models consistent with this theory, before reviewing the literature on empirical applications of mode choice models for commuting trips. In the following, multinomial, nested and mixed logit models using data from a survey of commuters in the University of St Andrews are developed. The models are used to estimate aggregate mode-choice elasticities that can assist the development of efficient car reduction policies in St Andrews and other small towns in rural areas. The direct elasticities of the car mode are found to be comparable to estimates reported in studies of urban commuting, while the demand for public transport is found to be considerably more elastic. The value of in-vehicle travel time is found to be lower than in most studies of urban commuting, reflecting that the roads in the St Andrews area are relatively uncongested. Subsequently, current car drivers' willingness to use a Park and Ride service prior to the implementation of such a service are examined. The results show that the modal shift away from parking on-site will be small unless the new service is accompanied by measures aimed at making parking on-site less attractive such as introducing parking charges. Finally, the effect of the 'compact city' on modal split and congestion are examined. As well as making urban transport more sustainable as a result of an increase in the use of public transport, making cities more compact is found to contribute to lower levels of congestion in urban areas through a reduction in complex trip chains

Mixed logit estimation of willingness to pay distributions : a comparison of models in preference and WTP space using data from a health-related choice experiment

Different approaches to modelling the distribution of WTP are compared using stated preference data on Tanzanian Clinical Officers’ job choices and mixed logit models. The standard approach of specifying the distributions of the coefficients and deriving WTP as the ratio of two coefficients (estimation in preference space) is compared to specifying the distributions for WTP directly at the estimation stage (estimation in WTP space). The models in preference space fit the data better than the corresponding models in WTP space although the difference between the best fitting models in the two estimation regimes is minimal. Moreover, the willingness to pay estimates derived from the preference space models turn out to be very high for many of the job attributes. The results suggest that sensitivity testing using a variety of model specifications, including estimation in WTP space, is recommended when using mixed logit models to estimate willingness to pay distributions