The main purpose of economic valuation for a non-market service is estimation of the change in consumer surplus. This change in consumer surplus represents WTP to obtain the service. The change in consumer surplus is generally measured by a change in utility caused from using the service. Thus, the economic valuation starts from
estimating a utility function of the service that can estimate the utilities of all individuals who use the service.
Our methodologies to estimate the option value of the MLs begin with estimation of the option users’ utility function of each choice (ML and GPL choices) as defined in the previous section. To estimate utility functions, it is necessary to model the choice each traveler makes between the MLs and the GPLs. Thus, this research first determined attributes of each alternative or individual who made the choice that needed to be
included in the lane-choice behavior model. The most fundamental attribute that affects the choice of lanes could be the monetary cost of using each alternative, especially the amount of toll paid. Travelers generally place value on their time. Thus, the other crucial attribute could be the travel time of each alternative. Both attributes (cost and time) are generally included in most lane-choice behavior models. This research identified some
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potential attributes, such as trip length and the standard deviation of travel time (a measure of travel time reliability). But, in general, trip length is significantly correlated with travel time. In addition, inclusion of travel time reliability in the model caused counter-intuitive results. Since the travel time reliability was measured by the standard deviation of travel time in this research, an increase in the standard deviation of travel time (decrease in the reliability) should lead to a decrease in utility. However, in the model, an increase in the standard deviation of travel time caused an increase in utility because the estimate of the standard deviation coefficient was positive. This research also examined additional attributes, including: direction, the time of day (peak, shoulder, and off-peak hours), and day of week. These attributes were also tested in the lane choice model, but no meaningful result was obtained. The direction attribute was significant but produced counter-intuitive results. Since the direction attribute has only two values, west and east directions, two values should have an opposite effect on utility; hence, if a westbound trip leads to a decrease in utility, an eastbound trip should lead to an increase in utility. However, both directions lead to a decrease in utility. The time of day improved explanatory power of the model but the time of day is already partially reflected in the travel time attribute and the effect of the time of day attribute on utility was much larger than the effect of the travel time attribute. For example, when this research included both travel time and time of day attributes in the model, their
coefficient estimates were −0.1185 and −1.2019, respectively. This seemed far too great an impact for time of day since toll and travel time were already in the model and accounted for those shifts. Finally, day of week was correlated with time of day because
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weekends were included in off-peak hours. Except for the random ID, no information about each traveler, such as income, gender, and purpose of trip, was available. For these reasons, the lane choice model only included the amount of toll paid and travel time in the utility functions of ML and GPL choices. The utility functions were estimated using a standard logit model. The logit model inherently assumes that travelers have
information about the attributes of each alternative, which is the amount of toll paid and travel time. The toll rate was provided in advance and could also be found online. Travelers could obtain travel time information through several sources including their own experience, media reports, roadside electronic message signs, and the Houston Transtar website. Thus, it could be reasonable to expect that travelers had a reasonable estimate of their expected travel time for their alternatives. Utility functions of ML and GPL choices are shown in Equation 7:
𝑉𝑀𝐿𝑠 = 𝛽𝑇𝑇∙ 𝑇𝑟𝑎𝑣𝑒𝑙 𝑇𝑖𝑚𝑒𝑀𝐿𝑠+ 𝛽𝑇𝑜𝑙𝑙 ∙ 𝑇𝑜𝑙𝑙𝑀𝐿𝑠 (7)
𝑉𝐺𝑃𝐿𝑠 = 𝛽𝑇𝑇∙ 𝑇𝑟𝑎𝑣𝑒𝑙 𝑇𝑖𝑚𝑒𝐺𝑃𝐿𝑠+ 𝛽𝑇𝑜𝑙𝑙∙ 𝑇𝑜𝑙𝑙𝐺𝑃𝐿𝑠 where:
𝑉𝑖 = utility derived by choosing lanes i, i = MLs or GPLs,
𝛽𝑗 = coefficients to be estimated, j = TT (travel time) or toll,
𝑇𝑟𝑎𝑣𝑒𝑙 𝑇𝑖𝑚𝑒𝑖 = travel time on lanes i, 𝑇𝑜𝑙𝑙𝑖 = the amount of toll paid on lanes i.
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The Statistical Analysis System (SAS) was used to estimate the coefficients in the utility functions. For Case 1, revealed preferences of the option users were used to estimate the utility functions and these were 13,503,494 choices (trips). For Case 2, revealed preferences of the option users were used to estimate the utility functions with 33,016,185 choices. Table 20 provides the coefficient estimates for the utility functions in each case. Intuitively, decreases in travel time and the amount of toll paid should lead to increases in utility. In both cases, the coefficients of both travel time and the amount of toll paid attributes were negative as expected and were significant based on t-statistics. The results suggest the value of travel time of $14/hour for the option users in Case 1 and the value of travel time of $5.97/hour for the option users in Case 2. This appears reasonable as Case 1 includes only travelers who have used the MLs while Case 2
includes many travelers who have not used the MLs in 2012. The correlation coefficients between travel time and the amount of toll paid are provided in Table 21. Based on the correlation coefficients, the attributes are not correlated and independence between the attributes is well maintained in the utility functions in both cases. The rest of this chapter details the methodologies that were used to estimate the option value of MLs partially based on these utility functions.
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Table 20 Coefficient Estimates for the Utility Functions of ML and GPL Choices
Variables a) Coefficient Estimates
in Case 1 b) Coefficient Estimates in Case 2 Travel Time ***-0.2489 ***-0.2394 t-statistics -729.07 -778.12 Toll ***-1.0667 ***-2.4061 t-statistics -1401.8 -2865.7 Log-likelihood at Zero -9359909 -22885076 Log-likelihood at Convergence -7857854 -14207810 ρ2 w.r.t. Zero* 0.1605 0.3792
PCP for All Trips** (%) 84.84 93.94
PCP for ML Trips (%) 7.08 0.97
PCP for GPL Trips (%) 96.66 99.25
Value of Travel Time ($/hour) 14.00 5.97
*: McFadden’s Likelihood Ratio Index.
**: PCP represents a percentage of correct predictions.
***: Statistically significant at 0.01 significance level (p<0.01).
Table 21 Correlation Coefficient between Travel Time and the Amount of Toll Paid
Case 1 Case 2
Correlation Coefficient
between Travel Time and Toll 0.1695 0.1202