A Methodology for the Estimation of Value-of-Time A Methodology for the Estimation of Value-of-Time Using State-of-the-Art Econometric Models

Value-of-time (VOT) measures are valuable in a wide range of public transport policy and planning applications. However, VOT is a latent variable that cannot be measured directly. In this research, state-of-the-art econometric models are developed within a methodological framework that allows for the estimation of the VOT. Ordered and binary discrete choice models have been developed. Furthermore, a mixed effects model that accounts for the unobserved heterogeneity across different individuals has also been specified. The models have been applied to short intercity trips between two medium-size cities (Agrinio and Patras) in Greece. The model specification combines trip-based characteristics (mode, travel time, and travel cost), with socioeconomic characteristics, such as profession, education, and car ownership. A stated-preference survey has been designed and administered to a random sample of 289 people. The estimated coefficients from the developed models have been used to estimate VOT measures and the overall performance of the ordered logit and the generalized linear mixed model has been found to be superior to the binary logit model. Journal of Public Transportation, Vol. 10, No. 3, 2007 Introduction Value-of-time (VOT) measures are valuable in a wide range of public transport policy and planning applications. Public transportation infrastructure projects can be justified through the quantification of the generalized benefits to society, including reduction of harmful emissions, conservation of energy, and recovery of productivity lost in congestion. Quantification of each of these components is a complicated process, which involves estimates of the gains in each category. To develop a single overall figure, these components need to be translated into a single unit, which is usually a monetary currency. Delay and travel time can be converted to dollar amounts through the concept of VOT. For example, Lehtonen and Kulmala ( 00 ) used VOT figures to estimate the travel time savings due to signal prioritization and real-time passenger information enhancements along two transit lines in the city of Helsinki, Finland. Grant-Muller et al. ( 00 ) review the state-of-the-art in the economic appraisal of transport projects, drawing on national practice in Western European countries. While there are substantial cultural and economic differences, one of the key commonalities is the principle of monetizing direct transport impacts. In their review of valuation studies of railway rolling stock, Wardman and Whelan ( 00 ) demonstrate the importance of VOT measures. While VOT is a very important notion in transportation planning and infrastructure management, it is a latent theoretical construct that cannot be easily quantified or measured. As a result, methodologies for the indirect assessment of the VOT have been developed. Different socioeconomic characteristics, trip purpose, and other attributes result in very heterogeneous traveler populations and therefore potentially in very different VOTs across individuals. For example, affluent travelers may be willing to pay a steep toll to save trip time, while students may not have this option. One approach to quantify VOT is to develop discrete choice models based on data collected by surveys and then use the estimated coefficients for the cost and duration of travel to compute a VOT measure. This article develops models for the estimation of VOT using state-of-the-art econometric models and demonstrates their application in a medium-size city in Greece. Ordered logit models and mixed effects models are developed, and compared with a more widely used binary logit model. The more advanced models are found to be superior to the binary logit model often used in such applications. Besides providing a resource for researchers, this research can be readily used by A Methodology for the Estimation of Value-of-Time practitioners, thus helping bridge the gap between state-of-the-art and state-ofthe-practice. The remainder of this article is structured as follows. The next section presents a review of relevant literature. Previous studies with Greek data are also shown to establish the range of VOT values available in the literature. This section is followed by an outline of the application methodology and data collection process. Model specification and estimation results for the entire data are shown next, followed by models using indicative subsets of the data. The article concludes with findings and directions for further research. Literature Review VOT is a very volatile measure that depends on several parameters and changes from country to country, industry to industry, and even from individual to individual. The objective of this literature review is to present the state-of-the-art in the modeling of VOT in terms of data collection and models used. Specific VOTs are only mentioned for the applications that refer to Greece, in order to establish the range of VOT obtained by other studies. Models developed for the estimation of VOT for other applications (such as commercial motor carriers) are also presented as they are often methodologically very similar. Kawamura ( 000) used stated-preference data from California to estimate the VOT of commercial motor carriers, using a modified logit model in which the coefficients were assumed to be distributed log-normally across the population. The questionnaire included questions about the characteristics of the motor carrier company and 0 stated-preference choices between options with tolls and without tolls. Kurri et al. ( 000) present the results of two separate studies for the estimation of freight-specific VOTs for road and rail transport, using the same methodology. Stated-preference data was used, in which hypothetical choice situations between two road or rail transport alternatives were presented to transport managers in manufacturing companies in Finland. A logit model was employed for the estimation of the coefficients that were used for the determination of the VOT. In the past decade, several VOT studies have been conducted in Europe, including The Netherlands (Gunn and Rohr 996), Norway (Ramjerdi et al. 997), Sweden (Alger et al. 996), the United Kingdom (Gunn et al., 996), and Switzerland (Axhausen et al., 004). Wardman ( 998) presents a meta-analysis of VOT derived Journal of Public Transportation, Vol. 10, No. 3, 2007 4 from 05 travel demand studies using revealed-preference and/or stated-preference methods. Kumar et al. ( 004) developed multinomial logit models for the estimation of the VOT, the service headway and the comfort levels for trip-makers traveling along rural bus routes in India. Data were collected through a statedpreference survey. While trip characteristics and socioeconomic characteristics of the respondents were collected, they were not included in the final models. Diamandis et al. ( 997) estimated the VOT for Greek drivers. The survey was based on revealed preferences made by participating travelers in choosing between alternative modes with different prices and travel times. The collected data were analyzed with the use of the multinomial logit model. Finally the evaluated VOT for nonprofessional trips range between US $ .7 /hr and US $4. /hr and for professional trips between US $5.4 /hr and US $6.4 /hr. (Dollar amounts represent original figures from the paper and have not been adjusted for inflation.) Polydoropoulou et al. ( 000) present the results of a large-scale study in Greece. The survey used stated-preference data collected via a telephone survey. The scenarios that were presented to the participants included choices between car, bus, train, ship, and airplane. The attributes that were chosen to describe each alternative were mode, time, and cost. The authors identify the incorporation of socioeconomic data into the model formulation as a useful direction for further research. The selected data were analyzed with the use of multinomial logit and mean VOTs were evaluated for each mode: US $6.6/hr, car; US $4.9 /hr, bus; US $4. /hr, train; US $5.64/hr, ship; and US $ 0.76/hr, airplane. (Dollar amounts represent original figures from the paper and have not been adjusted for inflation.) Bierlaire and Thémans ( 005) developed models for the prediction of travel decisions and consequently transportation demand with regard to different strategies of traffic management. A combination of revealed-preference and stated-preference data were analyzed using mixed logit models. The VOT was evaluated for short-distance (<50km) and medium-distance trips. The influence of several socioeconomic characteristics was evaluated. In conclusion, most of the studies aiming at the estimation of VOT for freight and passenger travel use discrete choice models. Due to practical reasons, most studies use logit models, while recent studies (such as that of Bierlaire and Thémans 005) use more advanced models such as mixed logit. In terms of data, most studies use stated-preference data, no doubt due to the difficulty of obtaining revealedpreference data. The inclusion of socioeconomic characteristics into the model A Methodology for the Estimation of Value-of-Time 5 formulation is recommended. Richardson ( 00 ) demonstrated the use of adaptive stated-preference surveys using simulated data.