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Estimating values of travel time savings for toll roads: Avoiding a common error
Transport Policy 24 (2012) 60–66
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Transport Policy journal homepage: www.elsevier.com/locate/tranpol
Estimating values of travel time savings for toll roads: Avoiding a common error Zheng Li, David A. Hensher n Institute of Transport and Logistics Studies, The University of Sydney Business School, The University of Sydney, NSW 2006, Australia
a r t i c l e i n f o
a b s t r a c t
Available online 21 August 2012
Traditionally, the empirical valuation of travel time savings (VTTS) is obtained from a linear utility specification in a discrete choice model, which implicitly assumes a risk-neutral attitude. This paper draws on recent contributions by the authors that accommodate the attitude towards risk within a non-linear utility specification as a preferred framework within which to value travel time savings. The interest in the non-linear form is motivated by the evidence in Hensher et al. (2011) that mean estimates of VTTS in a proposed toll road context are significantly lower when account is taken of risk attitude. The percentage reduction in the estimate of mean VTTS is approximately (coincidentally) equal to the actual percentage error in traffic forecasts associated with the new tollroad two years after opening. If we could show that this evidence of a lower mean estimate under the non-linear treatment is found in other data settings, then we gain confidence in suggesting that the linear-utility assumption to valuing travel time savings might be a potential contributor to over-predicted tollroad traffic forecasts. The non-linear model is applied herein to two other tollroad choice data sets and we find that sampled car commuters tend to be risk taking when decision making is subject to risk (due to the presence of variability in travel times). The model produces lower mean VTTS estimates than the traditional (linear) model, providing additional evidence of a systematic over-prediction of VTTS under the linear assumption. This paper suggests that future empirical studies on valuing time savings (and variability) should address the attitude towards risk. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Toll roads Demand forecasting Optimism bias Stated choice approach Attitude towards risk Non-linear mixed logit
1. Introduction Road tolling is growing in popularity as an attractive option to finance the construction and maintenance of roads, bridges and tunnels throughout the world. With the shortage of government funding and the desire of some governments to take the debt off the public balance sheet, the idea of tollroads being financed, constructed and operated by the private sector under a public-private partnership (PPP) has grown in appeal. The use of PPPs for new roads is growing, particularly in Europe (e.g., Spain and the UK), Latin America (e.g., Chile) and Australia. Spain has involved the private sector in toll road concessions since 1967, while the UK embraced PPPs for delivering roads in the late 1980s. Most of currently operating toll roads in Australia are under a range of PPPs with concessions, and some strictly public, over a typical period of 30 years. In Sydney, seven out of eight currently operating toll roads were delivered by PPPs, with the exception of the Sydney Harbour Bridge.1
n
Corresponding author. Fax: þ61 2 93510088. E-mail addresses: [email protected] (Z. Li), [email protected] (D.A. Hensher). 1 Sydney’s M4 Western Motorway was also delivered by PPP; however the NSW Government removed the M4 Western Motorway toll on 16 February 2010. 0967-070X/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.tranpol.2012.06.015
The toll road PPP concessions in place are typically operated by the private sector from a consortia bidding process (with three bidders in most situations), with the key players in each consortium being a construction company and a financial institution. The number of toll transactions is critical to the feasibility of toll road projects. Whether or not a privately operated toll road is able to generate sufficient revenues over the concession period determines its financial capability to recover its costs, including operations, maintenance, debt and equity. Should actual traffic be lower than forecast, the toll road will incur difficulties in delivering the expected returns to its shareholders. Hence, traffic demand forecasting is a crucial input into the financial and economic appraisal of toll road projects. In most traffic forecasting packages, the value of travel time savings (VTTS) is a critical input. In traditional four-step models, trip assignment (or route choice) is at the lowest level, which is determined by evaluating and comparing the generalised cost (i.e., the sum of time and money costs) among a number of alternative routes, where the time cost is the product of travel time and the estimated VTTS. If the generalised cost of using the toll road is lower than the generalised cost of using a free road, the traveller will be assigned to use the toll road. This concept lies at the heart of most toll road traffic forecasting models.
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Table 1 A Summary of two tollroad studies. Study
Number of sampled car commutersa
Year of data
Country
Recent toll used in reference trip (proportion of sample) (%)
Age
Gender (proportion female)b
Annual Personal Income (thousands)
Hours worked per week
1 2
243 115
2004 2007
Australia New Zealand
75.3 0
41.70 (11.26) 48.02 (12.26)
0.36 0.63
Au $87.46 (33.41) NZ $c48.10 (24.57)
41.91 (11.60) 41.92 (13.83)
The standard deviation is given in parenthesis. a
Model estimation has a multiple of 16 times the number of observations. For both locations, the gender proportions are not exactly 50/50. We could not source statistics for the year when each survey was conducted (2007 for New Zealand; 2004 for Australian; noting these are not census years), and the closest year that we were able to find is the 2006 census year for both locations. For the New Zealand location (source: Census of Population and Dwellings 2006, New Zealand), females outnumbered males when Age 419. Given that this paper focuses on car commuters (with Age419), a higher proportion of sampled female car commuters (i.e., 0.63) is in line with the population distribution. For the Australian location, at the population level, the female proportion was 0.47 (source: Australian Bureau of Statistics, Population by Age and Sex, Australia, 2006), lower than the male proportion. Based on the Australian sample, the female proportion was 0.36, which is also lower. The difference between the gender proportions at the population and sample levels may be attributed to a low response rate of 3.5 per cent for the Australian study. Given the geographical areas sampled for the two studies were a subset of the metropolitan areas where the population profile differs from the entire metropolitan area, we have been unable to source population data that is relevant to the specific locations and the age range above 19 years old. c One New Zealand dollar (NZ$) was equivalent to 0.88 Australian dollar (Au$) in 2007. b
Given the importance of VTTS to toll roads, Hensher and Goodwin (2004) claimed that the VTTS values must be properly used; otherwise ‘‘incorrect use of VTTS may cause serious distortion of investment priorities, and potentially financial stress serious enough to call the viability of a company, or the sustainability of a risk-sharing agreement, into question’’ (p.172). They also identified some common errors in using VTTS for toll roads, and suggested approaches to avoiding those errors. This paper is a follow-up of Hensher and Goodwin (2004). The aim of this paper is to reveal a further common error in the form of risk attitude associated with the estimation of VTTS. The paper is motivated by the evidence in Hensher et al. (2011) that mean estimates of VTTS in a proposed toll road context are significantly lower when account is taken of risk attitude. Evidence from a number of countries shows that traffic demand for toll roads tends to be over-predicted (see TRB, 2006 for American evidence; Vassallo, 2007 for Spanish evidence; Li and Hensher, 2010a for Australian evidence; Welde, 2011 for Norwegian evidence Bain, 2009 for evidence throughout the world). The World Bank (2008) emphasised that most tollroad failures2 are attributed to overestimated forecasts, often referred to as ‘optimism bias’ (see also Bain, 2009). The contribution of this paper to transport policy is to identify whether the traditional modelling framework to estimating VTTS might contribute to this over-prediction, and to suggest an improvement in the modelling framework that might contribute to closing the gap in forecast errors of traffic. The remaining sections are organised as follows. The next section introduces two stated choice (SC) data sets, as the empirical setting for incorporating risk attitude in order to test for VTTS over-estimates. This is followed by a discussion on the traditional modelling framework for valuing travel time savings and time variability, highlighting its major behavioural limitation, and then using an improved model that addresses both preferences and risk attitudes (two important components of decision making). We then present the empirical evidence which shows systematically higher mean VTTS estimates from the traditional (risk neutral) model, compared to the values from a model that
2 The Mexican PPP toll roads might be the best well known examples. Between 1987 and 1995, 52 toll roads were awarded under PPPs in Mexico, where 23 toll road projects failed, mainly due to overestimated traffic forecasts and cost overruns, and were rescued by the Mexican government’s bailout programme (about US$5 billion was paid to the banks and about US$ 2.6 billion was paid to the construction companies).
estimates risk attitude. The paper concludes with key findings and recommendation.
2. Data sources Two stated choice data sets from Australian and New Zealand tollroad studies conducted in 2004 and 2007 are used in this paper. The choice experiments involved each sampled commuter3 answering 16 choice scenario questions. In each choice question, the respondent was required to make a choice among three alternatives, one described by a recent trip and two alternatives defined by attribute levels pivoted off of the recent (or reference) trip profile. Pivoting offers more realism in the stated choice experiment since hypothetical alternatives are defined relative to the reference alternative (status quo), giving better specificity in the context of the choice task (Train and Wilson, 2008). The two surveys (summarised in Table 1) were conducted as computer aided personal interviews (CAPI), where a D-efficient choice experiment design was used. In these two studies, the trip time variability attribute was defined as plus or minus a level of time (see Fig. 1 for an example). In addition to trip time variability, free flow time (described to respondents as ‘can change lanes without restriction and drive freely at the speed limit’) and slowed down time (described as ‘changing lanes is noticeably restricted and your freedom to travel at the speed limit is periodically inhibited. Queues will form behind any lane blockage such as a broken down car’) are also provided in the choice tasks. The reported travel times are explained as typical times. For both studies, the trip cost is disaggregated into the running cost and the toll cost. The sample size for car commuters is 1154 in Study 2 and 243 in Study 1. 3 In both data sets, both car commuters and non-commuters were sampled. This paper focuses on car commuters. 4 A potential limitation of the New Zealand data set in particular is that the sample may not be representative; however one referee commented that: ‘‘The advantage of disaggregate models is that they can explain behaviour at an individual level, [and] so as far as we have sufficient heterogeneity in the data to explain these differences, they would account for different behaviour of different individuals’’. Although the sample size in this data set seems to preclude identification of statistically significant differences in respect of socioeconomic influences, a behavioural strength of the mixed multinomial logit model used in this paper, is that the random parameters attached to the attributes of the alternatives enables us to reveal sufficient (randomly distributed) heterogeneity in the data to explain differences in the behaviour of individuals.
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Fig. 1. Choice example used in other two studies.
variability was defined in line with the mean-variance approach. The mean-variance model assumes that travel time variability leads to the loss of utility by itself; while the scheduling model considers that disutility is incurred when not arriving at the preferred arrival time (PAT), either earlier or later than the PAT. Both models are specified as linear in sources of utility (i.e., linear in attributes and parameters). For example, a traditional meanvariance model is shown in Eq. (1). U ¼ bT T þ bV ar Var þ bCost Cost
Fig. 2. Asymptotic standard error as a function of the sample size. Source: Rose and Bliemer (2008).
The sample sizes when expanded out by the number of choice sets are large even for the New Zealand study (i.e., 115 by 16). Given that we are using optimal design theory and have a D-efficient design, we can refer to the contribution of Rose and Bliemer (2008) which shows that spending (much) more money on collecting data using a larger sample size does in the end not lead to significantly better parameter estimates for the design attributes of interest, indicated by (*) in Fig. 2. As the figure also suggests, it pays off much more to determine a design with a higher efficiency (design with attribute levels X II instead of X I Þ, in which the standard error can decrease significantly, indicated by (**) in Fig. 2.
3. Empirical models and results For travel time and time variability research in the context of passenger travel, the mean-variance model and the scheduling model are two state-of-practice frameworks (see Li et al., 2010b for a review). The two SC experiments in this paper addressed both travel time and travel time variability in which travel time
ð1Þ
bT , bVar and bCost are the test parameters associated respectively with a typical (or ‘normal’) one-way trip travel time (the sum of free flow time and slowed down time in both data sets used in this study), trip time variability (defined as plus or minus a number of minutes in two data sets)5 , and cost (e.g., the sum of fuel cost and toll cost).6 The values of travel time saving and reliability (or variability reduction) derived from Eq. (1) are obtained as bT =bCost , and bVar =bCost respectively. This linear utility specification assumes ‘risk neutrality’, in that the levels of an attribute are assumed to be riskless. However, with the presence of trip time variability (perceived and/or actual), the travel time attribute is associated with risk. For example, the first alternative in Fig. 1 has a typical travel time of 60 min ( ¼30 (free flow) þ30 (slowed down)). Given its trip time variability ( þ/ 10 min), the travel time might also be 50 min ( ¼60 10) or 70 min ( ¼60 þ10). Evidence from psychology and behavioural (experimental) economics suggests that individuals may be risk averse or risk taking (or seeking) when decision making is under risk. To incorporate the attitude towards 5 In the transport literature, the extent and frequency of delay relative to ‘normal’ travel time (e.g., a 5-min delay a week) is more often used to represent travel time variability in choice experiments (see e.g., Jackson and Jucker, 1982; Small et al., 2005). 6 The supplementary questions show that for the Australian data set, over 90 per cent added travel times and over 80 per cent added travel costs; for the New Zealand sample, the respective percentages are 70 and 90 plus. Therefore, a total time attribute and a total cost attribute are used in the models, instead of the components of time and cost.
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Table 2 Modelling results for Study 1. Attribute
Linear (Eq. (1))
Non-linear (Eq. (2a))
Parameter
t-Ratio
Parameter
t-Ratio
Non-random parameters: Cost ($)
0.4599
49.72
0.4166
51.88
Means for random parameters: Alpha (a) Typical travel time (min) Trip time variability (min)
^ 0.1397 0.0122
^ 29.51 1.74
0.1347 0.1536 0.0737
2.66 5.07 6.84
Standard deviations for random parameters: Alpha (a) Typical travel time (min) Trip time variability (min)
^ 0.1397 0.0122
^ 29.51 1.74
0.0594 0.1536 0.0737
3.74 5.07 6.84
Error Components Route A and Route B (two SC alternatives)
2.0494
18.50
0.5615
7.02
Model fit No. of observations Rho-squared Log-likelihood
3,888 0.41 2517.20
0.37 2696.96
^: a is set to be ‘0’ in the linear model.
risk, non-linear utility specifications are used. Constant absolute risk aversion (CARA) and constant relative risk aversion (CRRA) are two popular mechanisms for constructing non-linear utility, where the CARA model form postulates an exponential specification for the utility function, and the CRRA form is a power specification. For the non-linear utility specification herein, the CRRA form (i.e., U ¼ ðx1a =1aÞ) rather than CARA is used to extend the linear mean-variance model into a non-linear form, given that CARA is usually a less plausible description of the attitude towards risk than CRRA (see Blanchard and Fischer, 1989). The CARA form has been adopted in alternative behavioural theories such as Expected Utility Theory and Prospect Theory. The non-linear mean-variance model is compliant with both Random Utility Maximisation (RUM) and Expected Utility Theory (EUT) (e.g., multiple attributes of the former and non-linear utility specification of the latter). For the attributes associated with risk, we embed a functional form that accounts for attribute risk (through a risk attitude parameter for the travel time and trip time variability variables), as well as preference (through the attribute-associated parameters). Hensher et al. (2011) called this model the Attribute-Specific Extended EUT (ASEEUT) model. The remaining non-risky attributes (with 100 per cent chance of occurrence for an alternative within a choice set, e.g., cost) maintain a linear-additive form under RUM. The overall utility expression for the improved mean-variance (MV) model is given in Eq. (2b) with the ASEEUT component defined in Eq. (2a). ASEEUT_MV ¼ bT
T 1a Var 1a þ bVar 1a 1a
U ¼ ASEEUT_MV þ bCost Cost
ð2aÞ ð2bÞ
Compared to model (1), a is an additional parameter to be estimated, with the value of (1 a) indicating the attitude towards risk (risk averse, neutral or taking)7. The model is reduced to a mean-variance model (see Eq. (1)) when ð1aÞ ¼ 1. 7
A risk-averse attitude: a sure alternative is preferred to a risky alternative (i.e., with multiple possible outcomes) of equal expected value; a risk-taking attitude: a risky alternative is preferred to a sure alternative of equal expected value; a risk-neutral attitude: two alternatives of equal expected value is indifferent.
Hence, the traditional scheduling model is a particular case of model (2), namely risk neutrality8 . Within a non-linear utility specification, the WTP values are no longer the ratio between the time or variability parameter and the cost parameter as per a linear utility model. The willingness to pay formulae for travel time savings and reduction in trip time variability are given in Eqs. (3) and (4) respectively. @ðUÞ @ðUÞ ¼ ð1aÞbT T ð1aÞ1 =ð1aÞ=bCost ¼ bT T a =bCost ð3Þ @ðTÞ @ðCostÞ @ðUÞ @ðVarÞ
@ðUÞ ¼ ð1aÞbVar Var ð1aÞ1 =ð1aÞ=bCost ¼ bVar Vara =bCost @ðCostÞ ð4Þ
The linear and non-linear models are estimated within a mixed multinomial logit (MMNL) framework with error components (EC) for each tollroad data set. This modelling framework is capable of addressing the panel nature of data (i.e., multiple choice tasks per respondent) and analysing unobserved betweenindividual heterogeneity in preferences and risk attitudes. Constrained triangular distributions are used to ensure that all travel time and time variability across the sample of respondents are negative9 whereas an unconstrained triangular distribution is applied to represent individual risk attitudes. The two models (linear and non-linear) for Study 1 and Study 2 are given in Tables 2 and 3 respectively. We investigated the possible role of socio-demographic variables, namely gender, age and income, but could not find statistically significant influences on risk attitudes, and when added into the model as separate potential influences, we found no significant impact on VTTS or model fit compared to the models given in the paper. We focus on the difference between the non-linear and linear models. Under the non-linear utility specification with embedded risk attitudes, both Study 1 and Study 2 deliver statistically significant parameter estimates of Alpha with positive mean 8 Fosgerau and Karlstrom (2010) analytically derived the equivalence between mean-variance and scheduling approaches to travel time variability models. 9 Although a normal distribution can also be constrained and a lognormal distribution can produce all positive or negative individual parameters, they have some serious problems when estimating models (see Cherchi, 2009 for a review).
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Table 3 Modelling results for Study 2. Attribute
Linear (Eq. (1))
Non-linear (Eq. (2b))
Parameter
t-Ratio
Parameter
t-Ratio
Non-random parameters: Cost
0.6759
33.71
0.6065
28.96
Means for random parameters: Alpha (a) ‘Typical’ travel time (min) Trip time variability (min)
^ 0.1449 0.3900
^ 21.33 18.40
0.2892 0.3157 0.0222
2.72 2.45 1.90
Standard deviations for random parameters: Alpha (a) Typical travel time (min) Trip time variability (min)
^ 0.1450 0.3900
^ 21.33 18.40
0.1084 0.3157 0.0222
2.80 2.45 1.90
Error Components Route A and Route B (two SC alternatives)
1.3603
22.22
0.3986
16.17
Model fit No. of observations Rho-squared Log-likelihood
1,840 0.33 1346.72
0.27 1484.47
^: a is set to be ‘0’ in the linear model.
10 These 243 estimates are based on the individual-specific conditional parameter distributions, and not the unconditional distribution reported in Table 2. The conditioning occurs at the individual level based on the respondent’s choices and attribute levels. 11 Given the focus of this paper, we only present the VTTS values. The values of variability are not reported and are available on request from the authors.
0.059
D ensity
0.047 0.035 0.024 0.012 0.000 0.00
7.56
15.11
22.67
30.22
37.78
<- X i -> V TTS _L
V TTS _N
0.072 0.058 D ensity
estimates, suggesting that risk neutrality assumed under the linear model is inappropriate for these two data sets with variability in trip time, as well as significant standard deviations of Alpha, indicating unobserved heterogeneity in risk attitudes at the individual level. At the individual level, all 243 sampled commuters in Study 1 have positive estimates of mean Alpha10 , and hence all individuals’ risk attitude parameters (i.e., (1 a)) are less than one. For decision making related to travel time, a risk attitude parameter (1 a) less than one suggests risk-taking attitudes; and a risk attitude parameter greater than one suggests risk-averse attitudes (see Senna, 1994). Therefore, the non-linear model not only estimated preferences (i.e., negative taste parameters with respect to travel time, time variability and costs) which also can be identified in the linear model, but also revealed that all car commuters sampled in Study 1 tend to be risk-taking when making travel choices when the risk is associated with travel time. The implied behaviour revealed by risk attitudes can be explained using the following example. Given an equivalent expected travel time of 60 min, sampled car commuters would prefer a trip which has a 50 per cent chance of taking 50 min and a 50 per cent chance of taking 70 min, in contrast to a 100 per cent (sure) chance of taking 60 min. For Study 2, all 115 sampled commuters have a positive mean Alpha estimate, showing risktaking behaviours, which is in line with the finding of Study 1. Based on the estimated taste parameters and risk attitudes, we can calculate the value of travel time savings; for the linear case, the VTTS value is the ratio between the time parameter and the cost parameters; for the non-linear case, the VTTS is derived using Eq. (3).11 The estimated distributions for VTTS (per 60 min) under the linear model (VTTS_L) and the non-linear model (VTTS_N) are given in Fig. 3a and b for Study 1 and Study 2 respectively. With regard to the VTTS estimates, the non-linear models for both studies deliver lower mean values than the corresponding linear models, by 26.9 per cent and 18.9 per cent respectively. This finding is in line with Li et al. (2012), where a linear scheduling
0.043 0.029 0.014 0.000 0.00
6.11
12.22 18.33 <- X i ->
V TTS _L
24.44
30.55
V TTS _N
Fig. 3. (a): VTTS distributions for Study 1. (b): VTTS distributions for Study 1.
model and a non-linear scheduling are applied to a stated choice data for a proposed tollroad undertaken in Australia in 2008, which also found a lower VTTS (by 10.3 per cent) from the non-linear model, as well as risk-taking car commuters. The toll road that opened in early 2010, has to date actual patronage which is below the forecast. On the reasonable assumption that VTTS is a key input into such forecasts, a lower mean VTTS estimate carries substantial merit. This evidence in turn suggests that the non-linear model is a preferred model, from a forecasting point of view.
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Table 4 Comparison between mean VTTS (per 60 min) from the non-linear and linear models for three studies. Study 1 (Year: 2004) (Location: Australia) Mean-variance model Au$2004 Non-linear 13.37 (6.60)
Study 2 (Year: 2007) (Location: New Zealand) Mean-variance model
Linear 18.30 (7.48)
Au$2008 Non-linear Linear 15.18 (7.49) 20.77 (8.49) Non-linear: 26.9 per cent lower
NZ$2007 Non-linear 10.45 (5.89)
Li et al. 2012 (Year: 2008) (Location: Australia) Scheduling model
Linear 12.89 (5.23)
Non-linear Linear 9.07 (5.11) 11.19 (4.54) Non-linear: 18.9 per cent lower
Au$2008 Non-linear 21.85 (11.55)
Linear 24.35 (9.84)
Non-linear Linear Same as above Same as above Non-linear: 10.3 per cent lower
Standard deviations of the VTTS distributions under MMNL models are given in parentheses.
The common finding from this study and Li et al. (2012) is that the non-linear model which empirically addresses the attitude towards risk delivers a lower mean VTTS than the corresponding linear model, when decision making is subject to risk (i.e., the trip time is not fixed but varies, due to the existence of trip time variability). The estimates of value of travel time savings from three studies are summarised in Table 4 for the study year and location, as well as in a common currency and period ($Au2008). The two Australian studies deliver higher VTTS values than the New Zealand study, under both linear and non-linear conditions. This may be attributed to higher income of the Australian sample, given that the VTTS would increase with income (see Hensher and Goodwin, 2004). The VTTS values estimated from the three nonlinear models are systematically lower than the values from the linear models, by 10.3–26.9 per cent.
4. Conclusions The valuation of travel time savings is a key input in toll road project demand forecasting. A number of tollroad evaluation studies have found that predicted traffic volumes are higher than the actual traffic in the early days after opening and often as far out as 10 years of operations. The lack of such traffic, even after controlling for other sources of possible contributors to forecast error (such as problems associated with land use forecasts and strategic misrepresentation), can be traced back to the application of too high a VTTS in route choice assignment. The traditional linear-utility approach to the valuation of time savings (and variability reduction) overlooks the real attitude towards risk and implicitly assumes risk neutrality. This study proposes a modelling framework that is capable of empirically addressing the attitude towards risk, an important component of decision making, by equipping a non-linear utility form associated with the time-related attributes. It is found that the improved (nonlinear) model delivers lower mean VTTS estimates than the traditional (linear) model for two choice data sets with embedded risk. Given the consistent evidence in most actual tollroad settings of over-predicted demand, the lower VTTS may offer a more realistic estimate of the worth of time savings to tollroad users. The paper reveals that the linear-utility specification to valuing travel time savings may be a source of ‘optimism bias’ in toll road traffic forecasts. Hensher et al. (2011) found in another tollroad context a lower VTTS after accounting for risk attitudes (and some other considerations) that approximated the error in forecasts if time-cost tradeoffs are the primary driver. Given the evidence that the nonlinear utility model allowing for risk attitudes delivers a lower mean VTTS across multiple choice data sets for toll road projects, we suggest that future empirical studies on valuing time savings, as well as valuation of travel time variability, should consider
incorporating the attitude towards risk in their models. Despite the findings, we exercise caution in suggesting we have a generalisable result. Our findings have to be qualified since they are based on two data sets herein and the additional one used in Hensher et al. (2011). One challenge if our evidence turns out to be more accurate, is how to convince the private consortium in a PPP that the travel time benefits are valued considerably lower than current studies assume, making the raising of equity and possibly debt more of a challenge. If, however, investors start to see the risks associated with relatively higher VTTS that they have become accustomed to, with consequent significant over-prediction of traffic levels, they may start to adjust their expectations and recognise the benefits of a lower mean VTTS in terms of their true return on investment. Time will tell, since turning back the realism clock may prove extremely difficult.
Acknowledgements We thank two referees and the advice from Elizabeth Deakin for some very insightful comments that have contributed materially to improving this paper.
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Estimating values of travel time savings for toll roads: Avoiding a common error Zheng Li, David A. Hensher n Institute of Transport and Logistics Studies, The University of Sydney Business School, The University of Sydney, NSW 2006, Australia
a r t i c l e i n f o
a b s t r a c t
Available online 21 August 2012
Traditionally, the empirical valuation of travel time savings (VTTS) is obtained from a linear utility specification in a discrete choice model, which implicitly assumes a risk-neutral attitude. This paper draws on recent contributions by the authors that accommodate the attitude towards risk within a non-linear utility specification as a preferred framework within which to value travel time savings. The interest in the non-linear form is motivated by the evidence in Hensher et al. (2011) that mean estimates of VTTS in a proposed toll road context are significantly lower when account is taken of risk attitude. The percentage reduction in the estimate of mean VTTS is approximately (coincidentally) equal to the actual percentage error in traffic forecasts associated with the new tollroad two years after opening. If we could show that this evidence of a lower mean estimate under the non-linear treatment is found in other data settings, then we gain confidence in suggesting that the linear-utility assumption to valuing travel time savings might be a potential contributor to over-predicted tollroad traffic forecasts. The non-linear model is applied herein to two other tollroad choice data sets and we find that sampled car commuters tend to be risk taking when decision making is subject to risk (due to the presence of variability in travel times). The model produces lower mean VTTS estimates than the traditional (linear) model, providing additional evidence of a systematic over-prediction of VTTS under the linear assumption. This paper suggests that future empirical studies on valuing time savings (and variability) should address the attitude towards risk. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Toll roads Demand forecasting Optimism bias Stated choice approach Attitude towards risk Non-linear mixed logit
1. Introduction Road tolling is growing in popularity as an attractive option to finance the construction and maintenance of roads, bridges and tunnels throughout the world. With the shortage of government funding and the desire of some governments to take the debt off the public balance sheet, the idea of tollroads being financed, constructed and operated by the private sector under a public-private partnership (PPP) has grown in appeal. The use of PPPs for new roads is growing, particularly in Europe (e.g., Spain and the UK), Latin America (e.g., Chile) and Australia. Spain has involved the private sector in toll road concessions since 1967, while the UK embraced PPPs for delivering roads in the late 1980s. Most of currently operating toll roads in Australia are under a range of PPPs with concessions, and some strictly public, over a typical period of 30 years. In Sydney, seven out of eight currently operating toll roads were delivered by PPPs, with the exception of the Sydney Harbour Bridge.1
n
Corresponding author. Fax: þ61 2 93510088. E-mail addresses: [email protected] (Z. Li), [email protected] (D.A. Hensher). 1 Sydney’s M4 Western Motorway was also delivered by PPP; however the NSW Government removed the M4 Western Motorway toll on 16 February 2010. 0967-070X/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.tranpol.2012.06.015
The toll road PPP concessions in place are typically operated by the private sector from a consortia bidding process (with three bidders in most situations), with the key players in each consortium being a construction company and a financial institution. The number of toll transactions is critical to the feasibility of toll road projects. Whether or not a privately operated toll road is able to generate sufficient revenues over the concession period determines its financial capability to recover its costs, including operations, maintenance, debt and equity. Should actual traffic be lower than forecast, the toll road will incur difficulties in delivering the expected returns to its shareholders. Hence, traffic demand forecasting is a crucial input into the financial and economic appraisal of toll road projects. In most traffic forecasting packages, the value of travel time savings (VTTS) is a critical input. In traditional four-step models, trip assignment (or route choice) is at the lowest level, which is determined by evaluating and comparing the generalised cost (i.e., the sum of time and money costs) among a number of alternative routes, where the time cost is the product of travel time and the estimated VTTS. If the generalised cost of using the toll road is lower than the generalised cost of using a free road, the traveller will be assigned to use the toll road. This concept lies at the heart of most toll road traffic forecasting models.
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Table 1 A Summary of two tollroad studies. Study
Number of sampled car commutersa
Year of data
Country
Recent toll used in reference trip (proportion of sample) (%)
Age
Gender (proportion female)b
Annual Personal Income (thousands)
Hours worked per week
1 2
243 115
2004 2007
Australia New Zealand
75.3 0
41.70 (11.26) 48.02 (12.26)
0.36 0.63
Au $87.46 (33.41) NZ $c48.10 (24.57)
41.91 (11.60) 41.92 (13.83)
The standard deviation is given in parenthesis. a
Model estimation has a multiple of 16 times the number of observations. For both locations, the gender proportions are not exactly 50/50. We could not source statistics for the year when each survey was conducted (2007 for New Zealand; 2004 for Australian; noting these are not census years), and the closest year that we were able to find is the 2006 census year for both locations. For the New Zealand location (source: Census of Population and Dwellings 2006, New Zealand), females outnumbered males when Age 419. Given that this paper focuses on car commuters (with Age419), a higher proportion of sampled female car commuters (i.e., 0.63) is in line with the population distribution. For the Australian location, at the population level, the female proportion was 0.47 (source: Australian Bureau of Statistics, Population by Age and Sex, Australia, 2006), lower than the male proportion. Based on the Australian sample, the female proportion was 0.36, which is also lower. The difference between the gender proportions at the population and sample levels may be attributed to a low response rate of 3.5 per cent for the Australian study. Given the geographical areas sampled for the two studies were a subset of the metropolitan areas where the population profile differs from the entire metropolitan area, we have been unable to source population data that is relevant to the specific locations and the age range above 19 years old. c One New Zealand dollar (NZ$) was equivalent to 0.88 Australian dollar (Au$) in 2007. b
Given the importance of VTTS to toll roads, Hensher and Goodwin (2004) claimed that the VTTS values must be properly used; otherwise ‘‘incorrect use of VTTS may cause serious distortion of investment priorities, and potentially financial stress serious enough to call the viability of a company, or the sustainability of a risk-sharing agreement, into question’’ (p.172). They also identified some common errors in using VTTS for toll roads, and suggested approaches to avoiding those errors. This paper is a follow-up of Hensher and Goodwin (2004). The aim of this paper is to reveal a further common error in the form of risk attitude associated with the estimation of VTTS. The paper is motivated by the evidence in Hensher et al. (2011) that mean estimates of VTTS in a proposed toll road context are significantly lower when account is taken of risk attitude. Evidence from a number of countries shows that traffic demand for toll roads tends to be over-predicted (see TRB, 2006 for American evidence; Vassallo, 2007 for Spanish evidence; Li and Hensher, 2010a for Australian evidence; Welde, 2011 for Norwegian evidence Bain, 2009 for evidence throughout the world). The World Bank (2008) emphasised that most tollroad failures2 are attributed to overestimated forecasts, often referred to as ‘optimism bias’ (see also Bain, 2009). The contribution of this paper to transport policy is to identify whether the traditional modelling framework to estimating VTTS might contribute to this over-prediction, and to suggest an improvement in the modelling framework that might contribute to closing the gap in forecast errors of traffic. The remaining sections are organised as follows. The next section introduces two stated choice (SC) data sets, as the empirical setting for incorporating risk attitude in order to test for VTTS over-estimates. This is followed by a discussion on the traditional modelling framework for valuing travel time savings and time variability, highlighting its major behavioural limitation, and then using an improved model that addresses both preferences and risk attitudes (two important components of decision making). We then present the empirical evidence which shows systematically higher mean VTTS estimates from the traditional (risk neutral) model, compared to the values from a model that
2 The Mexican PPP toll roads might be the best well known examples. Between 1987 and 1995, 52 toll roads were awarded under PPPs in Mexico, where 23 toll road projects failed, mainly due to overestimated traffic forecasts and cost overruns, and were rescued by the Mexican government’s bailout programme (about US$5 billion was paid to the banks and about US$ 2.6 billion was paid to the construction companies).
estimates risk attitude. The paper concludes with key findings and recommendation.
2. Data sources Two stated choice data sets from Australian and New Zealand tollroad studies conducted in 2004 and 2007 are used in this paper. The choice experiments involved each sampled commuter3 answering 16 choice scenario questions. In each choice question, the respondent was required to make a choice among three alternatives, one described by a recent trip and two alternatives defined by attribute levels pivoted off of the recent (or reference) trip profile. Pivoting offers more realism in the stated choice experiment since hypothetical alternatives are defined relative to the reference alternative (status quo), giving better specificity in the context of the choice task (Train and Wilson, 2008). The two surveys (summarised in Table 1) were conducted as computer aided personal interviews (CAPI), where a D-efficient choice experiment design was used. In these two studies, the trip time variability attribute was defined as plus or minus a level of time (see Fig. 1 for an example). In addition to trip time variability, free flow time (described to respondents as ‘can change lanes without restriction and drive freely at the speed limit’) and slowed down time (described as ‘changing lanes is noticeably restricted and your freedom to travel at the speed limit is periodically inhibited. Queues will form behind any lane blockage such as a broken down car’) are also provided in the choice tasks. The reported travel times are explained as typical times. For both studies, the trip cost is disaggregated into the running cost and the toll cost. The sample size for car commuters is 1154 in Study 2 and 243 in Study 1. 3 In both data sets, both car commuters and non-commuters were sampled. This paper focuses on car commuters. 4 A potential limitation of the New Zealand data set in particular is that the sample may not be representative; however one referee commented that: ‘‘The advantage of disaggregate models is that they can explain behaviour at an individual level, [and] so as far as we have sufficient heterogeneity in the data to explain these differences, they would account for different behaviour of different individuals’’. Although the sample size in this data set seems to preclude identification of statistically significant differences in respect of socioeconomic influences, a behavioural strength of the mixed multinomial logit model used in this paper, is that the random parameters attached to the attributes of the alternatives enables us to reveal sufficient (randomly distributed) heterogeneity in the data to explain differences in the behaviour of individuals.
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Fig. 1. Choice example used in other two studies.
variability was defined in line with the mean-variance approach. The mean-variance model assumes that travel time variability leads to the loss of utility by itself; while the scheduling model considers that disutility is incurred when not arriving at the preferred arrival time (PAT), either earlier or later than the PAT. Both models are specified as linear in sources of utility (i.e., linear in attributes and parameters). For example, a traditional meanvariance model is shown in Eq. (1). U ¼ bT T þ bV ar Var þ bCost Cost
Fig. 2. Asymptotic standard error as a function of the sample size. Source: Rose and Bliemer (2008).
The sample sizes when expanded out by the number of choice sets are large even for the New Zealand study (i.e., 115 by 16). Given that we are using optimal design theory and have a D-efficient design, we can refer to the contribution of Rose and Bliemer (2008) which shows that spending (much) more money on collecting data using a larger sample size does in the end not lead to significantly better parameter estimates for the design attributes of interest, indicated by (*) in Fig. 2. As the figure also suggests, it pays off much more to determine a design with a higher efficiency (design with attribute levels X II instead of X I Þ, in which the standard error can decrease significantly, indicated by (**) in Fig. 2.
3. Empirical models and results For travel time and time variability research in the context of passenger travel, the mean-variance model and the scheduling model are two state-of-practice frameworks (see Li et al., 2010b for a review). The two SC experiments in this paper addressed both travel time and travel time variability in which travel time
ð1Þ
bT , bVar and bCost are the test parameters associated respectively with a typical (or ‘normal’) one-way trip travel time (the sum of free flow time and slowed down time in both data sets used in this study), trip time variability (defined as plus or minus a number of minutes in two data sets)5 , and cost (e.g., the sum of fuel cost and toll cost).6 The values of travel time saving and reliability (or variability reduction) derived from Eq. (1) are obtained as bT =bCost , and bVar =bCost respectively. This linear utility specification assumes ‘risk neutrality’, in that the levels of an attribute are assumed to be riskless. However, with the presence of trip time variability (perceived and/or actual), the travel time attribute is associated with risk. For example, the first alternative in Fig. 1 has a typical travel time of 60 min ( ¼30 (free flow) þ30 (slowed down)). Given its trip time variability ( þ/ 10 min), the travel time might also be 50 min ( ¼60 10) or 70 min ( ¼60 þ10). Evidence from psychology and behavioural (experimental) economics suggests that individuals may be risk averse or risk taking (or seeking) when decision making is under risk. To incorporate the attitude towards 5 In the transport literature, the extent and frequency of delay relative to ‘normal’ travel time (e.g., a 5-min delay a week) is more often used to represent travel time variability in choice experiments (see e.g., Jackson and Jucker, 1982; Small et al., 2005). 6 The supplementary questions show that for the Australian data set, over 90 per cent added travel times and over 80 per cent added travel costs; for the New Zealand sample, the respective percentages are 70 and 90 plus. Therefore, a total time attribute and a total cost attribute are used in the models, instead of the components of time and cost.
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Table 2 Modelling results for Study 1. Attribute
Linear (Eq. (1))
Non-linear (Eq. (2a))
Parameter
t-Ratio
Parameter
t-Ratio
Non-random parameters: Cost ($)
0.4599
49.72
0.4166
51.88
Means for random parameters: Alpha (a) Typical travel time (min) Trip time variability (min)
^ 0.1397 0.0122
^ 29.51 1.74
0.1347 0.1536 0.0737
2.66 5.07 6.84
Standard deviations for random parameters: Alpha (a) Typical travel time (min) Trip time variability (min)
^ 0.1397 0.0122
^ 29.51 1.74
0.0594 0.1536 0.0737
3.74 5.07 6.84
Error Components Route A and Route B (two SC alternatives)
2.0494
18.50
0.5615
7.02
Model fit No. of observations Rho-squared Log-likelihood
3,888 0.41 2517.20
0.37 2696.96
^: a is set to be ‘0’ in the linear model.
risk, non-linear utility specifications are used. Constant absolute risk aversion (CARA) and constant relative risk aversion (CRRA) are two popular mechanisms for constructing non-linear utility, where the CARA model form postulates an exponential specification for the utility function, and the CRRA form is a power specification. For the non-linear utility specification herein, the CRRA form (i.e., U ¼ ðx1a =1aÞ) rather than CARA is used to extend the linear mean-variance model into a non-linear form, given that CARA is usually a less plausible description of the attitude towards risk than CRRA (see Blanchard and Fischer, 1989). The CARA form has been adopted in alternative behavioural theories such as Expected Utility Theory and Prospect Theory. The non-linear mean-variance model is compliant with both Random Utility Maximisation (RUM) and Expected Utility Theory (EUT) (e.g., multiple attributes of the former and non-linear utility specification of the latter). For the attributes associated with risk, we embed a functional form that accounts for attribute risk (through a risk attitude parameter for the travel time and trip time variability variables), as well as preference (through the attribute-associated parameters). Hensher et al. (2011) called this model the Attribute-Specific Extended EUT (ASEEUT) model. The remaining non-risky attributes (with 100 per cent chance of occurrence for an alternative within a choice set, e.g., cost) maintain a linear-additive form under RUM. The overall utility expression for the improved mean-variance (MV) model is given in Eq. (2b) with the ASEEUT component defined in Eq. (2a). ASEEUT_MV ¼ bT
T 1a Var 1a þ bVar 1a 1a
U ¼ ASEEUT_MV þ bCost Cost
ð2aÞ ð2bÞ
Compared to model (1), a is an additional parameter to be estimated, with the value of (1 a) indicating the attitude towards risk (risk averse, neutral or taking)7. The model is reduced to a mean-variance model (see Eq. (1)) when ð1aÞ ¼ 1. 7
A risk-averse attitude: a sure alternative is preferred to a risky alternative (i.e., with multiple possible outcomes) of equal expected value; a risk-taking attitude: a risky alternative is preferred to a sure alternative of equal expected value; a risk-neutral attitude: two alternatives of equal expected value is indifferent.
Hence, the traditional scheduling model is a particular case of model (2), namely risk neutrality8 . Within a non-linear utility specification, the WTP values are no longer the ratio between the time or variability parameter and the cost parameter as per a linear utility model. The willingness to pay formulae for travel time savings and reduction in trip time variability are given in Eqs. (3) and (4) respectively. @ðUÞ @ðUÞ ¼ ð1aÞbT T ð1aÞ1 =ð1aÞ=bCost ¼ bT T a =bCost ð3Þ @ðTÞ @ðCostÞ @ðUÞ @ðVarÞ
@ðUÞ ¼ ð1aÞbVar Var ð1aÞ1 =ð1aÞ=bCost ¼ bVar Vara =bCost @ðCostÞ ð4Þ
The linear and non-linear models are estimated within a mixed multinomial logit (MMNL) framework with error components (EC) for each tollroad data set. This modelling framework is capable of addressing the panel nature of data (i.e., multiple choice tasks per respondent) and analysing unobserved betweenindividual heterogeneity in preferences and risk attitudes. Constrained triangular distributions are used to ensure that all travel time and time variability across the sample of respondents are negative9 whereas an unconstrained triangular distribution is applied to represent individual risk attitudes. The two models (linear and non-linear) for Study 1 and Study 2 are given in Tables 2 and 3 respectively. We investigated the possible role of socio-demographic variables, namely gender, age and income, but could not find statistically significant influences on risk attitudes, and when added into the model as separate potential influences, we found no significant impact on VTTS or model fit compared to the models given in the paper. We focus on the difference between the non-linear and linear models. Under the non-linear utility specification with embedded risk attitudes, both Study 1 and Study 2 deliver statistically significant parameter estimates of Alpha with positive mean 8 Fosgerau and Karlstrom (2010) analytically derived the equivalence between mean-variance and scheduling approaches to travel time variability models. 9 Although a normal distribution can also be constrained and a lognormal distribution can produce all positive or negative individual parameters, they have some serious problems when estimating models (see Cherchi, 2009 for a review).
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Table 3 Modelling results for Study 2. Attribute
Linear (Eq. (1))
Non-linear (Eq. (2b))
Parameter
t-Ratio
Parameter
t-Ratio
Non-random parameters: Cost
0.6759
33.71
0.6065
28.96
Means for random parameters: Alpha (a) ‘Typical’ travel time (min) Trip time variability (min)
^ 0.1449 0.3900
^ 21.33 18.40
0.2892 0.3157 0.0222
2.72 2.45 1.90
Standard deviations for random parameters: Alpha (a) Typical travel time (min) Trip time variability (min)
^ 0.1450 0.3900
^ 21.33 18.40
0.1084 0.3157 0.0222
2.80 2.45 1.90
Error Components Route A and Route B (two SC alternatives)
1.3603
22.22
0.3986
16.17
Model fit No. of observations Rho-squared Log-likelihood
1,840 0.33 1346.72
0.27 1484.47
^: a is set to be ‘0’ in the linear model.
10 These 243 estimates are based on the individual-specific conditional parameter distributions, and not the unconditional distribution reported in Table 2. The conditioning occurs at the individual level based on the respondent’s choices and attribute levels. 11 Given the focus of this paper, we only present the VTTS values. The values of variability are not reported and are available on request from the authors.
0.059
D ensity
0.047 0.035 0.024 0.012 0.000 0.00
7.56
15.11
22.67
30.22
37.78
<- X i -> V TTS _L
V TTS _N
0.072 0.058 D ensity
estimates, suggesting that risk neutrality assumed under the linear model is inappropriate for these two data sets with variability in trip time, as well as significant standard deviations of Alpha, indicating unobserved heterogeneity in risk attitudes at the individual level. At the individual level, all 243 sampled commuters in Study 1 have positive estimates of mean Alpha10 , and hence all individuals’ risk attitude parameters (i.e., (1 a)) are less than one. For decision making related to travel time, a risk attitude parameter (1 a) less than one suggests risk-taking attitudes; and a risk attitude parameter greater than one suggests risk-averse attitudes (see Senna, 1994). Therefore, the non-linear model not only estimated preferences (i.e., negative taste parameters with respect to travel time, time variability and costs) which also can be identified in the linear model, but also revealed that all car commuters sampled in Study 1 tend to be risk-taking when making travel choices when the risk is associated with travel time. The implied behaviour revealed by risk attitudes can be explained using the following example. Given an equivalent expected travel time of 60 min, sampled car commuters would prefer a trip which has a 50 per cent chance of taking 50 min and a 50 per cent chance of taking 70 min, in contrast to a 100 per cent (sure) chance of taking 60 min. For Study 2, all 115 sampled commuters have a positive mean Alpha estimate, showing risktaking behaviours, which is in line with the finding of Study 1. Based on the estimated taste parameters and risk attitudes, we can calculate the value of travel time savings; for the linear case, the VTTS value is the ratio between the time parameter and the cost parameters; for the non-linear case, the VTTS is derived using Eq. (3).11 The estimated distributions for VTTS (per 60 min) under the linear model (VTTS_L) and the non-linear model (VTTS_N) are given in Fig. 3a and b for Study 1 and Study 2 respectively. With regard to the VTTS estimates, the non-linear models for both studies deliver lower mean values than the corresponding linear models, by 26.9 per cent and 18.9 per cent respectively. This finding is in line with Li et al. (2012), where a linear scheduling
0.043 0.029 0.014 0.000 0.00
6.11
12.22 18.33 <- X i ->
V TTS _L
24.44
30.55
V TTS _N
Fig. 3. (a): VTTS distributions for Study 1. (b): VTTS distributions for Study 1.
model and a non-linear scheduling are applied to a stated choice data for a proposed tollroad undertaken in Australia in 2008, which also found a lower VTTS (by 10.3 per cent) from the non-linear model, as well as risk-taking car commuters. The toll road that opened in early 2010, has to date actual patronage which is below the forecast. On the reasonable assumption that VTTS is a key input into such forecasts, a lower mean VTTS estimate carries substantial merit. This evidence in turn suggests that the non-linear model is a preferred model, from a forecasting point of view.
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Table 4 Comparison between mean VTTS (per 60 min) from the non-linear and linear models for three studies. Study 1 (Year: 2004) (Location: Australia) Mean-variance model Au$2004 Non-linear 13.37 (6.60)
Study 2 (Year: 2007) (Location: New Zealand) Mean-variance model
Linear 18.30 (7.48)
Au$2008 Non-linear Linear 15.18 (7.49) 20.77 (8.49) Non-linear: 26.9 per cent lower
NZ$2007 Non-linear 10.45 (5.89)
Li et al. 2012 (Year: 2008) (Location: Australia) Scheduling model
Linear 12.89 (5.23)
Non-linear Linear 9.07 (5.11) 11.19 (4.54) Non-linear: 18.9 per cent lower
Au$2008 Non-linear 21.85 (11.55)
Linear 24.35 (9.84)
Non-linear Linear Same as above Same as above Non-linear: 10.3 per cent lower
Standard deviations of the VTTS distributions under MMNL models are given in parentheses.
The common finding from this study and Li et al. (2012) is that the non-linear model which empirically addresses the attitude towards risk delivers a lower mean VTTS than the corresponding linear model, when decision making is subject to risk (i.e., the trip time is not fixed but varies, due to the existence of trip time variability). The estimates of value of travel time savings from three studies are summarised in Table 4 for the study year and location, as well as in a common currency and period ($Au2008). The two Australian studies deliver higher VTTS values than the New Zealand study, under both linear and non-linear conditions. This may be attributed to higher income of the Australian sample, given that the VTTS would increase with income (see Hensher and Goodwin, 2004). The VTTS values estimated from the three nonlinear models are systematically lower than the values from the linear models, by 10.3–26.9 per cent.
4. Conclusions The valuation of travel time savings is a key input in toll road project demand forecasting. A number of tollroad evaluation studies have found that predicted traffic volumes are higher than the actual traffic in the early days after opening and often as far out as 10 years of operations. The lack of such traffic, even after controlling for other sources of possible contributors to forecast error (such as problems associated with land use forecasts and strategic misrepresentation), can be traced back to the application of too high a VTTS in route choice assignment. The traditional linear-utility approach to the valuation of time savings (and variability reduction) overlooks the real attitude towards risk and implicitly assumes risk neutrality. This study proposes a modelling framework that is capable of empirically addressing the attitude towards risk, an important component of decision making, by equipping a non-linear utility form associated with the time-related attributes. It is found that the improved (nonlinear) model delivers lower mean VTTS estimates than the traditional (linear) model for two choice data sets with embedded risk. Given the consistent evidence in most actual tollroad settings of over-predicted demand, the lower VTTS may offer a more realistic estimate of the worth of time savings to tollroad users. The paper reveals that the linear-utility specification to valuing travel time savings may be a source of ‘optimism bias’ in toll road traffic forecasts. Hensher et al. (2011) found in another tollroad context a lower VTTS after accounting for risk attitudes (and some other considerations) that approximated the error in forecasts if time-cost tradeoffs are the primary driver. Given the evidence that the nonlinear utility model allowing for risk attitudes delivers a lower mean VTTS across multiple choice data sets for toll road projects, we suggest that future empirical studies on valuing time savings, as well as valuation of travel time variability, should consider
incorporating the attitude towards risk in their models. Despite the findings, we exercise caution in suggesting we have a generalisable result. Our findings have to be qualified since they are based on two data sets herein and the additional one used in Hensher et al. (2011). One challenge if our evidence turns out to be more accurate, is how to convince the private consortium in a PPP that the travel time benefits are valued considerably lower than current studies assume, making the raising of equity and possibly debt more of a challenge. If, however, investors start to see the risks associated with relatively higher VTTS that they have become accustomed to, with consequent significant over-prediction of traffic levels, they may start to adjust their expectations and recognise the benefits of a lower mean VTTS in terms of their true return on investment. Time will tell, since turning back the realism clock may prove extremely difficult.
Acknowledgements We thank two referees and the advice from Elizabeth Deakin for some very insightful comments that have contributed materially to improving this paper.
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