TRANSPORT WELFARE BENEFITS IN THE PRESENCE OF AN INCOME EFFECT

Transcription

1 TRANSPORT WELARE BENEITS IN THE PRESENCE O AN INCOME EECT James Laird Senior Researh ellow Institute for Transport Studies University of Leeds Leeds LS2 9JT J.J.Laird@its.leeds.a.u Tel: ACKNOWLEDGEMENTS The researh presented in this paper is drawn from the author s PhD thesis at the University of Leeds. I am grateful to my supervisors Peter Maie and Rihard Batley for omments, support and advie during the researh and preparation of this paper. I am also grateful to the EPSRC studentship that funded my studies and to Transport Sotland for funding the surveys. None of the above, however, is in any way responsible for the results desribed and views expressed in this paper. 1 INTRODUCTION Central to the appraisal of transport interventions is the alulation of welfare hanges. Disrete hoie models an assist this proess in two ways: firstly in the development of demand foreasts and seondly through the derivation of marginal values for poliy variables (e.g. the value of travel time savings). This paper fouses on the latter appliation and the irumstanes in whih the marginal values derived from the models, when used in a transport appraisal, an lead to a serious bias in the welfare benefit estimate of a transport intervention. In the transportation field it is normal to alulate the welfare benefits of an intervention through the hange in Marshallian onsumer surplus in ombination with the assumption of a linear demand urve. The latter assumption is usually referred to as the Rule of Half onvention. The two main inputs to the alulation are the prie of and demand for the transport good before and after the intervention. The prie of a trip is taen to be given by the generalised ost of that trip, whilst the demand (by time period) before and after the intervention an be derived through a variety of different analytial methods depending on the partiular ontext of the poliy intervention. Abstrating from the merits of the different methods available to foreast demand a good demand model would give an aurate predition of the demand in any future year with and without the intervention. The demand for transport post-intervention in a good appraisal should therefore inlude both a substitution effet from a lowering/raising of the prie (or generalised ost (GC)) of the transport good and an inome effet. A good transport appraisal therefore aurately measures Area GC 0 a b GC 1 in igure 1(b) when estimating the welfare benefit of a transport intervention. That is it will measure the area under a linear approximation to the Marshallian demand urve between the prie before (GC 0 ) and after (GC 1 )the transport intervention. The exat welfare benefit of a transport intervention is in fat given by either of the Hisian measures of ompensating or equivalent variation. With its referene point of pre-intervention utility levels ompensating variation is generally aepted as the 1

2 igure 1: Compensating variation and the hange in onsumer surplus (a) Indifferene urve analysis of hange in generalised ost Demand for omposite good (Y) G b I U 1 J a H U 0 K X 0 X X 1 Demand for transport (X) (b) Demand urve analysis of hange in generalised ost Generalised Cost (GC) GC 0 a Hisian demand urve (utility ompensated) GC 1 b Marshallian demand urve X 0 X X 1 Demand for transport (X) 2

3 appropriate Hisian measure for a transport ost-benefit analysis of hanges in transport quality (see for example Boardman et al., 2001 pp.59-64). The ompensating variation represents the inome equivalent of a prie hange. In a transport ontext it is the maximum a transport user will pay for a transport intervention. It is illustrated in igure 1(a) as the differene between points G and J, and in igure 1(b) by the Area GC 0 a GC 1. With transport ating as a normal good and a redution in generalised ost, as in igure 1(b), the ompensating variation is always less than the onsumer surplus. The differene between the two measures stems from the need to exlude the inome effet when alulating the willingness to pay for a transport intervention. With referene to igure 1(a) the initial bundle of goods omprises a omposite good (Y) and a transport good (X) and is given by point a on indifferene urve U 0. The pre-intervention budget onstraint is given by line GH. A redution in the generalised ost of transport redues the slope of the budget onstraint post intervention to that depited by line GI. This results in an optimum post intervention bundle of goods at point b on indifferene urve U 1. The resulting hange in demand for transport (X 1 - X 0 ) an be deomposed into a substitution effet (X C -X 0 ) and an inome effet (X 1 -X C ). This is beause at the postintervention pries but at the initial utility level (U 0 ) the budget onstraint would be JK and the optimum bundle of goods would be at point with a demand for transport of X C. The maximum willingness to pay for the transport intervention therefore is given by the differene in the interepts on the y-axis of the budget onstraints GI and JK. That is the maximum willingness to pay is given by the differene between G and J. This is equivalent to the area under the Hisian utility ompensated demand urve between the pre- and post-intervention generalised osts and, as mentioned above, is illustrated in igure 1(b) by Area GC 0 a GC 1. Willig (1976) argues that in almost all irumstanes, and ertainly where the hange in onsumer surplus is less than 5% of inome, onsumer surplus is a good approximation to the exat ompensating variation measure. or example, with an inome elastiity of 0.8 and a onsumer surplus that is 5% of inome the ompensating variation is within 2% of the hange in onsumer surplus. It is beause of arguments suh as Willig s that the hange in onsumer surplus as a measure of the hange in welfare has beome de rigueur in transport ost benefit analysis. A further argument espoused in support of onsumer surplus is that the inome effet an only be estimated impreisely. By attempting to orret for the inome effet an additional error is introdued into the welfare benefit alulation and this an prove more ostly in terms of preision than just using the onsumer surplus estimate with no orretion (Alston and Larson, 1993). As transport an form a large proportion of total household expenditure (14% on average in the ase of the UK (ONS, 2007 Table 1.1)) and household s use of time (about 1 hour on average per day (Metz, 2005)) a poliy intervention that signifiantly affets the generalised ost of transport ould potentially generate hanges in onsumer surplus that are large in relation to inome. Suh hanges ould for example be generated by a poliy that has a large impat on frequently made ommuting trips rather than oasional disretionary trips. In suh situations, and for the reasons disussed above, the hange in onsumer surplus may not be a good approximation to ompensating variation. Whilst anowledging this limitation, there has been little development to date in the transport eonomi literature to addressing the problem. The earliest wor is that by Jara-Díaz and Videla (1990) who found that for medium inome Chilean households the hange in Marshallian onsumer surplus is 12% higher than the ompensating variation. In more reent wor Cherhi and Pola (2007) found for a low inome Italian sample (transport expenditure omprises 50% of total expenditure) the hange in onsumer surplus is 30% larger than the ompensating variation. or high inome people (transport expenditure omprises 3

4 13% of total expenditure) the error is muh smaller (<5%) as it is for a mixed sample of high and low inome people. Daly et al. (2008) using the Duth national model system estimate that the ompensating variation of a poliy to introdue national road priing with a very high per m harge is 34% lower than the hange in onsumer surplus (i.e. the hange in onsumer surplus overestimates the exat welfare benefit by just over 50%). Clearly the limited evidene that exists suggests that the impat of inluding inome effets in the alulation of the welfare benefit from a transport intervention is quite varied. In some instanes the impat an be tolerated at a pratial level but in others it seems very large. urthermore eah of these studies uses analytial methods to inlude and exlude inome effets from the demand funtion to obtain either the estimate of the hange in onsumer surplus or the estimate of ompensating variation. Errors in the estimation of the Marshallian and Hisian demand funtions may dominate any omparison between the two measures of welfare benefit and this may loud the findings available in the literature. The assumption of a linear demand urve also introdues an error into the appraisal. or small ost hanges this error is not an issue, but for large hanges a signifiant overestimation in the hange in onsumer surplus an our. Nellthorp and Hyman (2001) for example argue that the error assoiated with a linear approximation to the demand urve is more than 10% when ost hanges exeed 33%. Two potential errors therefore exist in a typial transport appraisal. irstly that assoiated with assuming the hange in onsumer surplus is a good approximation to the ompensating variation, and seondly assuming the Rule of Half onvention gives a good approximation to the hange in onsumer surplus. This paper is distint from the existing literature in that it omes at the problem of from a different angle. Instead of estimating different demand shedules and omparing the benefit measures as Jara-Díaz and Videla, Cherhi and Pola, Daly et al. and Nellthorp and Hyman have done, the researh presented here uses two different stated hoie designs to separately estimate marginal values of headway and operating hours for ferry servies. The marginal values from the first design are used to alulate the hange in onsumer surplus of a transport intervention using the Rule of Half onvention, whilst the marginal values from the seond design represent the ompensating variation. A omparison between the two benefit measures identifies the error assoiated with using the Rule of Half onvention to approximate welfare benefits in the presene of an inome effet. The remainder of the paper is strutured as follows. The next setion of the paper presents the empirial analysis. It provides baground information on the stated hoie survey, and desribes the eonometri models estimated. The third setion utilises the marginal valuations from the eonometri models to derive estimates of the hange in onsumer surplus and the ompensating variation. The fourth and final setion presents the onlusions and suggests avenues for further researh. 2 Empirial analysis 2.1 Data The data used in this analysis were olleted in the Outer Hebrides in 2005 as part of a wider study to obtain estimates of the marginal values of ferry headways and operating hours, as well as the differene in ris premium between a ferry and a fixed lin (a bridge or a auseway) (Laird, 2008 Chapters 4, 5 and 6). or this paper only the data from the household survey is utilised. 4

5 Householders on the islands of Salpay, Berneray, Erisay and Vatersay were surveyed (see loation maps in igure 2 and igure 3). These islands are part of the Outer Hebridean group and lie approximately 80 ilometres from the mainland of Sotland. They are lined to the ten other populated islands in the group, by a series of fixed lins and ferries, and to the mainland by ferries. Eah of the surveyed small islands had reently had its lifeline ferry servie to the main islands replaed by a fixed lin. Of the small islands the largest is Salpay, with a population of just over 300 (GROS, 2008 Table UV51), and as with the other parts of the Outer Hebrides is poor relative to the rest of the UK. Average GDP/apita in the Outer Hebrides was 66% of the UK average in 2003 (Roberts, 2005 p.1). The ferry servies that used to serve the islands operated over a 12 hour day at average headways of about 75 minutes, though there was variation between islands and between winter and summer. Suh timetables, ombined with small island populations, meant households had limited aess to the types of failities, servies, and employment opportunities their mainland ounterparts tae for granted. One of the purposes of the household survey therefore was to eliit the willingness to pay for the alleviation of restritive ferry timetables. rom the perspetive of this paper what maes the sample interesting is that on average households are not wealthy and the benefits of the transport intervention per household are large. This is due to the frequeny of off-island trips by residents and the potential large benefits per trip that an be derived from improving restritive ferry timetables. As part of the survey respondents faed three tass of partiular relevane to the interest of this paper. They were ased to hoose between two types of ferry servie in what is referred to hereafter as the loal ferry stated preferene game, and they were ased to hoose between a ferry and a fixed lin in what is referred to hereafter as the fixed lin stated preferene game and they were ased a ontingent valuation question to eliit the annual willingness to pay to replae to inrease the operating day of a ferry from 12 hours to 24 hours. Eah of the tass was framed within the ontext of the old ferry servie to the island and/or the fixed lin that replaed it. Example senario ards and the question that supported the ards are given below in igure 4 and igure 5. In the loal ferry SP game the ferry servies were desribed by headway (H), operating hours (OH) and fare (P). or the fixed lin SP game the ferry servie was desribed by the same attributes, whilst the fixed lin option was desribed by a ounil tax premium and relative journey time ompared to the ferry servie. In both SP games there were no vehile restritions on the ferry. Additionally, for the fixed lin SP game only operating hours varied between senarios for the ferry and only the ounil tax premium varied between senarios for the fixed lin. In this game the ferry was also free at the point of use. Householders were interviewed fae-to-fae, and ompleted questionnaires were returned from 149 households. This represents just under 50% of the population over the four islands. This gave a maximum number of ases of 596 for the loal ferry SP game and 745 for the fixed lin SP game. After data leaning this redues down to 404 and 517 ases respetively. urther details of the survey design and data leaning proess are desribed in Laird (2008, Chapters 4 and 6). An important distinguishing feature between the two stated preferene games, from the perspetive of this paper, is that the payment vehile for the loal ferry game is a fare per trip, whilst that for the fixed lin game is an annual premium on the household s ounil tax (a loal tax used to fund amongst other things loal transport servies). It is this differene that allows the omparison of the results from the eonometri models fitted to the two SP datasets to be used as a basis for omparing the hange in onsumer surplus and ompensating variation of a transport intervention. 5

6 igure 2: Case study loation with respet to the rest of Sotland Outer Hebrides fixed lin ase studies (see igure 3) Inverness Aberdeen Dundee Edinburgh Glasgow Soure: Sottish Exeutive Urban Rural Classifiation [aessed 4th January 2008] 6

7 igure 3: Loation of Salpay, Berneray, Erisay and Vatersay within the Outer Hebrides Salpay Berneray Erisay Vatersay igure 4: Loal ferry stated preferene game senario framing and presentation I am now going to show you some more HYPOTHETICAL situations. This time I would lie you to imagine that this island was still only onneted to Harris 1 by ferry. I will show you two types of ferry servie, whih differ in fares, frequeny and hours of operation. In eah situation I would be grateful if you ould hoose the ferry servie that YOUR HOUSEHOLD would most prefer. OPTION A Vehile erry OPTION B Vehile erry Vehile size No restritions No restritions ares (vehile and passengers) (return) (return) requeny (average) Every 4 hours Every hour Opening Hours irst ferry: Last ferry: 9am to 5pm irst ferry: Last ferry: 7am to 7pm 1 Wording varied with island surveyed to reflet whether a bridge or auseway lined it to the neighbouring island and what that neighbouring island was. 7

8 Example Sailing times 0900, 1300, , 0830, 0900, 1000, et., 1700, 1800, 1900 Choose one only A B igure 5: ixed lin stated preferene game senario framing and presentation I am now going to show you a number of HYPOTHETICAL situations. I would lie you to imagine the situation before the bridge was onstruted but YOUR HOUSEHOLD ould hoose whether this island was to be onneted to Harris with a REE ferry or with a bridge 1. However, as the bridge has to be onstruted by the loal ounil, ounil tax must go up to pay for it. In eah situation I would be grateful if you ould hoose the transport and ounil tax option that YOUR HOUSEHOLD would most prefer. unding OPTION A (Vehile erry) ully subsidised through ounil tax OPTION B (Bridge Error! Boomar not defined. ) Construted by the ounil Vehile size No restritions No restritions Journey time 15 minutes quier than ferry ares/tolls No fares No tolls requeny Half Hourly Opening Hours irst ferry: Last ferry: 7am 7pm 24 hrs Counil Tax As existing Existing per wee ( 800 per year) Choose one only A B 2.2 Estimation results The eonometri model The modelling approah adopted within this paper essentially follows industry pratie for the analysis of stated hoie data (e.g. Bateman et al., 2002 hapters 7 and 8; Hensher and Greene, 2003). Multinomial logit (MNL) and mixed logit (MXL) models are estimated to the data. The added value the MXL model form has over the MNL model form is that it overomes the problem of repeated hoies and taste variation between individuals (Train, 2003 Chapter 6). or the ferry alternatives in the stated preferene games the following eonometri speifiation for utility is adopted. 8

9 U ferry hj ferry ferry ferry ferry ( H) + χ g( OH) + φ h P ε hj = α + β f ( ) + (1) where ferry U qj is the utility that household h (belonging to population segment ) reeives from the ferry servie j. ( H) f is a funtion in headway, ( OH ) in operating hours and h ( P) is a funtion in prie (fares). g is a funtion ferry α is the population segment speifi interept for the ferry servie, arising from its unobserved attributes. In this model speifiation this inludes journey time and omfort. β, χ and φ are population segment parameters assoiated with headway, operating hours and prie and density funtions n( β ), r ( χ ) and s( φ ) respetively. By assuming that ε hj is an unobserved term that is independently and identially distributed (IID) with a type I extreme value (Weibull) distribution. or the fixed lin alternative in the fixed lin stated preferene game the following utility speifiation is used. U ixedlin h ixedlin ixedlin h = α + φ h( P) + ε (2) ixedlin where α is the population segment speifi interept for the fixed lin, arising from its unobserved attributes, inluding journey time, onveniene and availability (reliability). In appliation equations 1 and 2 are not fully identified. This means that for the loal ferry stated preferene game α is not estimated. or the fixed lin stated ferry preferene game only the differene between the respetive alternative speifi ixedlin ferry ixedlin ferry onstants an be estimated α ( = α α ) rather than the two separate onstants. This onstant also inludes differenes in attributes that do not vary between the SP senarios (e.g. journey time). Loal ferry stated preferene game In the first instane multinomial logit (MNL) models were estimated. An unsegmented model linear in headway, operating hours and ost is presented in the first olumn of Table 1 (model L-MNL1). Experimentation with segmentation by H g OH and soio-eonomi harateristis and different forms for the funtions f ( ), ( ) ( P) h gave rise to model L-MNL5 as the best performing MNL model (seond olumn of Table 1). This model is linear in ost and is a step funtion in headway and operating hours. The model ats as the starting point for the estimation of the MXL models. Model L-MXL3 uses a normal distribution funtion to apture taste variation, model L-MXL4 uses triangular distribution funtion with no onstraints on the spread, and model L-MXL5 a triangular distribution funtion with the spread onstrained to the mean. The log-normal distribution is not used as it results in unrealistially high estimates of the mean willingness to pay (see e.g. Laird, 2008 Chapter 5). As an be seen from the log-lielihood values introduing taste variation into the model improves the level of fit signifiantly for the models fitted with the normal (L-MXL3) and the unonstrained triangular (L-MXL4) distributions. The improvement in fit over the MNL model of the onstrained triangular distribution (L- MXL5) is marginal. In the models presented only some of the variables are treated as random. This is beause some of the spread parameters are not signifiantly different from zero. It an also be seen that the introdution of taste variation 9

10 Table 1: Loal ferry SP game estimation results Cost All trips Headway oeffiient (Headways 30 mins) Inrement on headway oeffiient for: Headways 60 mins Headways 240 mins Households maing 5 or more trips per wee over fixed lin L-MNL1 L-MNL5 L-MXL3 L-MXL4 L-MXL5 b (-6.26) (-6.49) (-5.48) (-5.58) (-5.79) b (-6.29) (-3.53) (-3.22) (-3.29) (3.25) TC (4.11) b (3.14) (3.07) (3.14) N TU (-3.70) (3.92) b (1.85) b (-3.17) (-3.22) (-3.20) (-3.41) Operating hours oeffiient (no. of b (-7.80) hours losed) Inrement on operating hours oeffiient for: Hours losed 12 hours Households maing 3 or more trips per wee over fixed lin Households maing 17 or more trips per wee over fixed lin b (-3.27) (-2.64) (-2.66) (-2.29) N TU TC (-3.56) (-3.85) (-2.29) b (-4.18) (-3.77) (-3.71) (-4.03) TU (-3.46) b (-2.13) (-2.47) (-2.68) (-2.43) No. of observations Log-lielihood Adjusted rho-squared Notes:, N, and TU and TC indiate distribution funtion for parameters. means fixed (i.e. no distribution funtion), N is the normal, and TU is the triangular where the spread is not onstrained in estimation and TC is the triangular with spread onstrained equal to the mean. or eah random parameter two oeffiients are estimated (b and ). or the normal distribution the mean=b and st.dev.=; and for the triangular mean=b and spread=. T-statistis in parentheses. Parameter is signifiant at 99% level if the t-statisti>2.33; at the 95% level if the t-statisti>1.96 and at the 90% level if the t-statisti>1.65. T-statistis for MXL models alulated using robust standard. MNL models estimated with ALOGIT v4.2, MXL models with Train s Gauss ode using 500 Halton draws. 10

11 redues the number of variables in the models. That is the distribution funtions apture some of the variation in marginal utility that previously required an additional variable. The advantage of using the onstrained triangular distribution over the normal or unonstrained triangular distributions is that no part of the distribution of willingness to pay values has the wrong sign (negative). The fit, however, of the models with the unonstrained normal or triangular distributions is better (L-MXL3 and L-MXL4). These models result in a proportion of the population being attributed a negative willingness to pay between 0% and 14% depending on the model estimated, the attribute in question and the attribute s level. or a pratial appliation suh proportions, whilst undesirable, are onsidered aeptable. Of the two models L- MXL3 and L-MXL4, model L-MXL4 (triangular unonstrained) has a marginally higher log-lielihood and the fitted distribution is also bounded whih the normal distribution (model L-MXL3) is not. This is more appealing as it is unrealisti to expet the marginal utility of headway and operating hours to tend to infinity for some members of the population. On these grounds L-MXL4 is taen as the preferred model. The seond olumn of Table 2 shows the marginal values from the preferred model are, depending on headway length, 2.0 and 11.3 pene per headway minute and, depending on the length of the operating day, 19.7 and 34.7 pene per operating hour. These marginal valuations are within design range of the stated preferene questions and this gives onfidene in the validity of the results. Using average oupanies from the Berneray ferry suggests that a headway minute is valued between 0.07 and 0.42 of a ar-ivt minute (depending on headway length), whilst an operating hour is valued between 0.73 and 1.28 ar-ivt minutes (see Table 3). No onfidene intervals are available for these results whih derive from the preferred mixed logit model. The ase for these results being robust therefore entres on how well the parameters of the distribution funtions for the different marginal utilities have been estimated. As an be seen from Table 1 they are all signifiant at the 99% level. Some onfidene in the robustness of the results an also be gained from the preliminary MNL model (L-MNL1) where the 95% onfidene intervals for the marginal value of headway and operating hours are +/-25% or below. The validity of these results is important for the omparison that will be made in Setion 3. The uniqueness of this researh however maes it diffiult to mae omparisons with other empirial evidene. The only empirial evidene in the literature to whih it is diretly omparable is that by Bråthen and Hervi (1997) whih has sine been adapted into Norwegian appraisal guidane (Bråthen and Lyhe, 2004). The latter give values for inonveniene osts (i.e. the osts imposed by headway and operating hour restritions). The impliation of the Norwegian guidane is that inonveniene osts for replaing a lifeline ferry, that operated from 0530 to 2400 and with pea headways of less than 30 mins, with a fixed lin is equivalent to a 21 minute time saving. The estimation results presented here would give a marginal value per vehile of 17 ar-ivt minutes. The results are omparable and give onfidene in the validity and believability of the marginal values per single household trip. Additionally the results for the marginal value of headways (< 60 minutes) are onsistent with, though slightly lower than those found by Wardman (2004 Table 12) for other forms of publi transport. 11

12 Table 2: Properties of willingness to pay distributions for headway and operating hours (loal ferry SP game MXL models) Marginal value of a headway minute (pene/headway minute/household trip) When 30 mins headway < 60 mins L-MXL3 L-MXL4 L-MXL5 Mean Standard deviation Proportion with negative WTP 0% 0% When 60mins headway 240 mins As for headways between 60 and 240 mins Mean Standard deviation Proportion with negative WTP 13% 14% 0% Marginal value of an operating hour (pene/operating hour/household trip) Between 7pm and 7am (i.e. late evening and night) Mean Standard deviation Proportion with negative WTP 0% 0% 0% After 7am and before 7pm (i.e. during day) Mean Standard deviation Proportion with negative WTP 11% 11% 0% Notes: Mean and standard deviation values estimated using a monte-arlo simulation based on a population of 10,000 (split into the statistially relevant soio-eonomi groups from the model using sample proportions). Lowest and highest 2.5% are exluded from alulation of mean and standard deviation for the unbounded normal distribution (L-MXL3) (Hensher and Greene, 2003; Cirillo and Axhausen, 2006). ixed ost oeffiients and bounded distributions mean that all 10,000 simulations are used for L-MXL4 and L-MXL5. 12

13 Table 3: Loal ferry SP game preferred willingness to pay values as a proportion of ar in-vehile-time (2005 pereived pries and values) (a) Headway When headways are between: Marginal value of a headway minute (per household per single trip) 30 and 59 mins 11.3 p/min (678 p/hr) 60 and 240 mins 2.0 p/min (120 p/hr) Equivalent ar in-vehile time minutes (assumes average vehile oupany of 3.2) 0.42 ar-ivt mins per headway min (25.2 ar-ivt mins per headway hour) 0.07 ar-ivt mins per headway min (4.2 ar-ivt mins per headway hour) (b) Operating hours When operating day is: 8 hours (9am to 5pm) 12 hours (7am to 7pm) 17 hours (6am to midnight) Marginal value of an operating hour (per household per single trip) Equivalent ar/lgv in-vehile time minutes (assumes average vehile oupany of 3.2) 34.7 p/hr 1.28 ar-ivt mins per hour 19.7 p/hr 0.73 ar-ivt mins per hour 19.7 p/hr 0.73 ar-ivt mins per hour 24 hours 19.7 p/hr 0.73 ar-ivt mins per hour Notes: Marginal values derived from model L-MXL4. Average vehile oupany of 3.2 for an island residents trip on a ferry - derived from analysis of Berneray Causeway ex-ante and ex-post studies (Halrow ox, 1996 and SQW, 2004 respetively). Average ar oupant value of time is 5.07 per hour (i.e. 8.5 p/min) (2005 pereived pries and values). Derived from standard value of travel time savings per passenger (DfT, 2007) using non-wor other value of time. ixed lin stated preferene game The same estimation strategy to that used for the loal ferry stated preferene game was used for the estimation of a model to the fixed lin stated preferene game data. An unsegmented model linear in operating hours and ost is presented in the first olumn of Table 4. Experimentation with segmentation by soio-eonomi harateristis and different forms for the funtion g ( OH ) gave rise to model L- MNL2 as the best performing MNL model (seond olumn of Table 4). This model is linear in ost and is a step funtion in operating hours. It was not possible to fit estimate a mixed logit model with anything but a onstrained triangular distribution assumed for the poliy variables. The estimation proess did not onverge if a normal distribution funtion was used (with or without onstraints on the standard deviation) or an unonstrained triangular distribution was used. The best performing mixed logit model is L-MXL4 and is presented in the third olumn of Table 4. This model is taen to be the preferred mixed logit model on the grounds of fit and ability to reprodue the observed willingness to pay distribution funtion (see Laird, 2008 pp ). 13

14 Table 4: ixed Lin SP game estimation results L-MNL1 L-MNL2 L-MXL4 Cost oeffiient for all household inomes ixed lin onstant (all households) Inrement on fixed lin onstant for: b (-8.5) (-8.8) -8.8(-4.97) TC -8.8(-4.97) b 1.411(7.5) 1.421(6.4) 2,817.3 (6.33) Households on Berneray b (-3.6) -1,317.3(-2.11) Households on Vatersay b (-3.3) Households maing 5 or more trips per wee over fixed lin Households maing 17 or more trps per wee over fixed lin b 0.776(2.9) b 0.680(1.7) Operating hours oeffiient (no. of b (-2.6) hours losed) Inrement on operating hours oeffiient for: Households maing 3 or more trips per wee over fixed lin b (-4.1) (-2.09) TC (-2.09) No. of observations Log-lielihood Adjusted rho-squared Notes: and TC indiate distribution funtion for parameters. means fixed (i.e. no distribution funtion) and TC is the triangular with spread onstrained equal to the mean. or eah random parameter two oeffiients are estimated (b and ). or the triangular mean=b and spread=. T- statistis in parentheses. Parameter is signifiant at 99% level if the t-statisti>2.33; at the 95% level if the t-statisti>1.96 and at the 90% level if the t-statisti>1.65. T-statistis for MXL models alulated using robust standard. MNL models estimated with ALOGIT v4.2, MXL models with Train s Gauss ode using 500 Halton draws. As an be seen from the third olumn of Table 5 the preferred model, model L- MXL4, has a value for the fixed lin onstant of per household per annum and a marginal value for an operating hour of (per household per annum). As before no onfidene intervals are available for these results whih derive from a mixed logit model. The robustness of the results rests on the how well the different parameters of the model have been estimated. As an be seen all are signifiant at the 95% level. Confidene intervals an be alulated for the preliminary MNL model (L-MNL1) and these are +/- 27% for the fixed lin onstant and +/-70% for the marginal value of operating hours. Of relevane to this paper is the validity in the estimate of the marginal value for an operating hour. Unlie the marginal values per trip derived previously no other empirial wor exists against whih the derived value an be validated. The inlusion of a ontingent valuation question allows an internal validation to our. The data from the ontingent valuation question indiates that the mean value to move from a 12 hour operating day to a 24 hour operating day is (or per hour) with a 95% onfidene interval of +/- 32%. It an therefore be seen that the fixed lin 14

15 stated preferene data and the ontingent valuation data give similar orroborating results. Table 5: Properties of willingness to pay distributions for fixed lin onstant and operating hours (fixed lin SP game) L-MNL1 L-MNL3 L-MXL4 Value of fixed lin onstant ( per household per annum) Mean Standard deviation N/A N/A Proportion with negative WTP N/A N/A 0% Marginal value of an operating hour ( per household per annum) Mean Standard deviation N/A N/A 23.0 Proportion with negative WTP N/A N/A 0% Notes: Mean and standard deviation values estimated using a monte-arlo simulation based on a population of 10,000 (split into the statistially relevant soio-eonomi groups from the model using sample proportions). Lowest and highest 2.5% are exluded from alulation of mean and standard deviation for models L-MXL4 where the ost parameter is treated as random. 3 The hange in onsumer surplus and the ompensating variation To ompare the hange in onsumer surplus ( CS ) and the ompensating variation the findings from the analysis of the stated preferene data are applied to the ontext of an atual transport intervention the onstrution of fixed lins to the islands of Salpay, Berneray, Erisay and Vatersay. Unlie the ferries the fixed lins are free to use, i.e. there is no toll and give on average about a 15 minute journey time saving over the ferries. urthermore the fixed lins are available at all times of the day, whereas previously the ferries only operated a 12 hour day and at around a 75 minute headway on average. Change in onsumer surplus Prior to onstrution of the fixed lins an average 3.7 return person trips per household per wee were made on the ferries to the islands (Halrow, 1996; SQW, 2004). This inreases to 10.9 after onstrution of the fixed lins. With referene to igure 1 X 0 is therefore 3.7 whilst X 1 is X is unnown. As disussed previously in a transport appraisal it is normal to assume the Marshallian demand urve is linear. In whih ase the hange in onsumer surplus, Area GC 0 a b GC 1, an be estimated using equation 3. 1 CS = ( X 0 + X1) ( GC0 GC1) (3) 2 With a linearly additive expression for generalised ost in headway, operating hours and prie, as implied by equations 1 and 2, as well as time (T) and vehile operating osts (VOC) this alulation an be disaggregated into a series of mini onsumer 15

16 surplus alulations for eah omponent of generalised ost. Summing these, as in equation 4, gives the total hange in onsumer surplus of the intervention. OH H P T CS = CS + CS + CS + CS + CS (4) where OH 1 OH OH CS = ( X 0 + X1) ( C0 C1 ), 2 H 1 H H CS = ( X 0 + X1) ( C0 C1 ), 2 P 1 P P CS = ( X 0 + X1) ( C0 C1 ), 2 T 1 T T CS = ( X 0 + X1) ( C0 C1 ), 2 VOC 1 VOC VOC CS = ( X 0 + X1) ( C0 C1 ), 2 OH H P T VOC and C, C, C, C and C are the ost of operating hours, headway, prie, time and vehile operating osts in the before and after situations respetively. oussing on the user benefit arising from a hange in operating hours (i.e. CS ). As eah of the ferries operated a 12 hour day, the onstrution of the auseway inreases availability from a 12 hour day to a 24 hour day. rom Table 3(b) the marginal value of inreasing operating hours from 12 hours to 24 hours is 19.7p/hr/single vehile trip. With an average vehile oupany of 2.8 when travelling on the ferry (Halrow, 1996; SQW, 2004) this implies a marginal value of 7.04 p/hr/single person trip (i.e p/hr/return person trip). The hange in onsumer surplus arising from an inrease in operating day is therefore given by: VOC OH CS OH 1 = ( )(14.07 * 12 0) 2 = p / household / wee Over the ourse of a year this implies a hange in onsumer surplus from the inrease in operating hours of per household. User benefits from operating hours form 14.3% of the total hange in onsumer surplus of the Berneray Causeway (Laird, 2009 Chapter 9). This implies that the average hange in total onsumer surplus aross the four islands is about 4,500 per household per annum. This represents 27% of household disposable inome 2. Clearly this is large. Compensating variation With referene to igure 1 the ompensating variation is given by the maximum willingness to pay to move from indifferene urve U 0 to U 1, that is by the differene between G and J (equivalent to Area GC 0 a GC 1 ). In this study this value has been eliited indiretly through stated preferene questions ouhed in terms of willingness to pay over the ourse of a year through an inrement in ounil tax. The result was 2 Mean net household inome in the Outer Hebrides is 16,642. Soure: 2003/4 Sottish Household Survey variable annetin (MORI Sotland et al., 2005) 16

17 validated with a ontingent valuation question a diret eliitation of the willingness to pay. rom Table 5 the maximum willingness to pay per additional operating hour is per household per annum. This implies the ompensating variation of inreasing operating hours from a 12 to 24 hr operating day is per household per annum. An alternative estimate, , of the ompensating variation an be obtained diretly from the ontingent valuation question. 4 DISCUSSION A omparison between the hange in onsumer surplus estimated using the Rule of Half onvention ( CS ROH ) and the ompensating variation indiates a large disrepany. This disrepany is if omparing the CS ROH against the ompensating variation derived from the fixed lin SP game model, and if omparing against the ontingent valuation result. The CS ROH is therefore more than double either of the estimates of the ompensating variation. This error is very serious in an appraisal ontext. To be onfident that there really is a large disrepany between the CS ROH and the ompensating variation it is neessary to examine other potential explanations that may have given rise to the finding. irstly, the finding ould be an outome of omparing two impreise estimates. The robustness argument therefore hinges on the statistial signifiane of the differene between the CS ROH and the ompensating variation. Whilst no onfidene intervals for the marginal values derived from the MXL models are available, onfidene intervals are available from the MNL models. Taing these as representative of the robustness of the hange in onsumer surplus results and the ompensating variation results implies 95% onfidene intervals for the differene between the two estimates 3 as follows: +/-85% (i.e. a 95% onfidene interval of 50 to 600) for the differene based on the estimate of the ompensating variation from fixed lin SP game; and. +/-49% (i.e. a 95% onfidene interval of 190 to 550) for the differene based on the estimate of the ompensating variation based on the ontingent valuation estimate. These are quite large ranges, though both indiate that a statistially signifiant differene exists. The omparison against the ontingent valuation results also indiates that even at the lower end of the onfidene interval the error assoiated with using the hange in onsumer surplus as an approximation to the ompensating variation is about 50%. Clearly two errors exist in measuring the exat welfare benefit. With the method adopted in this paper it is not possible to separate the two exatly. However experimentation with negative exponential demand urves indiate that a linear approximation to the demand urve (i.e. the use of the Rule of Half onvention) may result in an overestimate of the hange in onsumer surplus of up to 40% (Laird, 2008 pp ). Though for suh an overestimate to our, the demand urve must be very onvex to the origin 4. This implies that with a 100% error between the 3 Standard errors and onfidene intervals for the differene between the hange in onsumer surplus and the ompensating variation were alulated following Hess and Daly (2008). 4 Demand urve D 1 =D 0 e (-β.ost^0.3), where D 1 is demand after intervention, D 0 is demand before the intervention and ost is the differene in generalised ost before 17

18 CS ROH and the ompensating variation 43% of it is due to the presene of an inome effet and 57% is due to the use of the Rule of Half. Willig s (1976) rule of thumb indiates that a differene of 43% between the hange in onsumer surplus and the ompensating variation ould only be assoiated with a hange in onsumer surplus as a proportion of inome far in exess of the 27% estimated here unless a very high inome elastiity exists. This would suggest that the estimate of the error of inluding the inome effet in the welfare benefit measure is too large. However, for transport interventions suh large differenes may our beause the intervention impats on both the money budget onstraint and the time budget onstraint. Willig s analysis only onsiders the money budget onstraint. A ontrasting argument to the above is that the differene between CS ROH and the ompensating variation is in part due to the presene of respondent bias in the data the most relevant of whih is soping effet bias. This bias ours as respondents have diffiulty valuing the size of the benefit. This an result in small benefits (per trip) being valued too highly and large benefits (per annum) being valued too low. It has already been argued that the marginal values (per trip) implied by the models estimated to the data are omparable with other literature inluding that derived from revealed preferenes. The onsisteny with revealed preferene data in partiular would suggest that the marginal values per trip are of the orret order of magnitude. The interest in this bias therefore beomes one of understanding whether the annual values are too low. This unfortunately annot be answered with the existing data. Whilst there is onsisteny between the responses to the senarios posed in the fixed lin stated preferene game and the response to the ontingent valuation question it is possible that soping effet bias has had a similar effet on both sets of data. As the survey was not designed to test for soping effet bias no definitive answer an be given as to whether the phenomena has had a signifiant impat on the annual willingness to pay results. It is the author s opinion, however, that the annual willingness to pay results seem plausible when onsidered in relation to household inomes, whereas the hange in onsumer surplus values seem high. On balane therefore the differene found between the two estimates of welfare benefit (in exess of 300 per household per annum) seems realisti, though possibly at the upper end of the range, when onsidered as the potential error between the exat welfare benefit of a transport intervention and one estimated using the CS ROH. 5 CONCLUSION The main onlusion of this paper is that the inome effet and the error assoiated with assuming a linear demand urve, whilst ignored in almost all transport eonomi appraisals, an be important to the alulation of welfare benefits. or the example of the onstrution of fixed lins in small remote island ommunities a standard transport appraisal an give an estimate of the hange in onsumer surplus that is over 25% of household disposable inome. This is quite substantial. This derives from time savings, ferry fare savings and improvements in availability (frequeny and operating hours). ousing on the latter this study has estimated: marginal values per household trip of between 2.0 and 11.3 pene per headway minute, and between 19.7 and 34.7 pene per operating hour; as well as annual willingness to pay marginal values of between and per operating hour per household. By doing so it has been possible to ompare the hange in onsumer surplus as and after the intervention. 18

19 estimated in a onventional transport appraisal with the ompensating variation. There is a large disrepany between the two values. or this partiular example the estimated hange in onsumer surplus is more than double the ompensating variation the exat measure of welfare benefit of the transport intervention. Up to 57% of this differene is attributed to the pratie of assuming a linear Marshallian demand urve when estimating the hange in onsumer surplus (i.e. the Rule of Half). It is well nown that the assumption of a linear demand urve in the presene of large ost hanges an seriously overestimate the hange in onsumer surplus. Despite this the pratie of maing the assumption ontinues. This paper has therefore provided further evidene on the need to use alternative methods when estimating welfare benefits. The remaining 43% of the differene is attributed to the presene of an inome effet. Inome effets beome more important the larger the inome elastiity of demand and the larger the benefit reeived is relative to inome. urthermore as transport shemes impat on both the money budget onstraint and the time budget onstraint inome effets may be larger than would have been thought from an analysis of the money budget alone. Saying that until we have a better understanding of the impliations of using the hange in onsumer surplus as an approximation to the exat welfare benefit in a transport appraisal it is important that analysts examine the sale of benefit aruing to households/individuals in relation to their inome as a standard part of any appraisal (e.g. as suggested by Willig). The nature of the empirial wor means there is some unertainty in the estimates, and this oupled with the potential presene of soping effet bias in the data does mean the sale of the inome effet may have been overestimated. urther researh is needed. A potentially fruitful avenue ould be to extend the empirial analysis presented in this paper to other senarios with a larger relevane to national transport poliy: suh senarios ould inlude road priing, or any infrastruture or priing intervention in whih large ost hanges are experiened by frequent transport users (e.g. ommuters). urther added value ould be obtained by also olleting suffiient data to estimate the Marshallian and Hisian demand urves something that was not possible with the existing dataset. 6 REERENCES ALSTON, J.M. and D.M. LARSON Hisian vs. Marshallian Welfare Measures: Why Do We Do What We Do? Amerian Journal of Agriultural Eonomis, 75(3), pp BATEMAN, I.J., R.T. CARSON, B. DAY, M. HANEMANN, N. HANLEY, T. HETT, M.J. LEE, G. LOOMES, S. MOURATO, E. OZDEMIROGLU, D.W. PEARCE, R. SUGDEN, and J. SWANSON Eonomi valuation with Stated Preferene Tehniques: A Manual. Cheltenham/Northampton: Edward Elgar. BOARDMAN, A.E.; D.H. GREENBERG, A.R. VINING and D.L. WEIMER Cost-benefit analysis: onepts and pratie 2 nd edition. Upper Saddle River, N.J.: Prentie Hall. BRÅTHEN, S. and A. HERVIK Strait Crossings and Eonomi Development. Developing Eonomi Impat Assessment by Means of Ex Post Analyses. Transport Poliy. 4(4), pp

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