Intermodal competition in the London–Paris passenger market: High-Speed Rail and air transport

Journal of Urban Economics 71 (2012) 278–288

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Intermodal competition in the London–Paris passenger market: High-Speed Rail and air transport Christiaan Behrens, Eric Pels ⇑ Department of Spatial Economics, VU University, De Boelelaan 1105, 1081HV Amsterdam, The Netherlands

a r t i c l e

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Article history: Received 11 March 2010 Available online 29 December 2011 Keywords: Inter- and intramodal competition Mixed logit Aviation Rail Passenger behaviour

a b s t r a c t This paper studies inter- and intramodal competition in the London–Paris passenger market during the period 2003–2009. We identify the degree to and conditions under which High-Speed Rail is a viable substitute for airline travel. Using pooled cross-sectional data we estimate multinomial and mixed logit models to examine actual travel behaviour. Our model allows us to analyse the reaction of passenger behaviour on the withdrawal of aviation alternatives and the completion of the High-Speed Rail link between the two cities in November 2007. The results show that travel time and frequency are the main determinants of travel behaviour. The valuation of total travel times changes over the years following the opening of the High-Speed Rail link. Furthermore, we show that the direct elasticity of market share with respect to frequency for a number of aviation alternatives is above 1, indicating that these alternatives are not able to maximise profits. These alternatives subsequently left the market in our sample period. For the remaining aviation alternatives, except for easyJet, we find elasticities of market share with respect to frequency close to 1. Therefore, we conjecture that competition in this market will decline in the long run. Ó 2011 Elsevier Inc. All rights reserved.

1. Introduction In medium-haul passenger markets, High-Speed Rail (HSR) and airlines are increasingly competing for passengers. In this paper we study the degree to and conditions under which HSR is a viable or even a dominating substitute for airline travel using the London– Paris passenger market as the prime example. In Europe and Asia HSR plays a significant role in the medium- to long-haul markets. Examples of such markets are Frankfurt–Cologne, Madrid–Barcelona, Beijing–Tianjin and Tokyo–Osaka. Furthermore, there are ongoing projects to develop HSR networks in the United States. The California High-Speed Rail Authority proposes to connect Los Angeles with San Francisco and its international airports via HSR, while the Midwest High-Speed Rail Association is studying the possibility of connecting Chicago O’Hare airport with downtown Chicago, Milwaukee, Detroit and Indianapolis.1 The expansion of HSR around the world and its observed dominance, particularly in the direct city-to-city markets, calls for an analysis of intermodal competition and the extent to which HSR is a viable substitute for air travel. ⇑ Corresponding author. E-mail addresses: [email protected] (C. Behrens), [email protected] (E. Pels). 1 For more detailed information about the projects, see http://www. cahighspeedrail.ca.gov and http://www.midwesthsr.org. 0094-1190/$ - see front matter Ó 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.jue.2011.12.005

The authors are aware of just a few studies that have analysed intermodal competition and the role of HSR. Two studies for the European Commission (Transport and Energy Directorate General), IATA (2003) and Steer Davies Gleave (2006), explore HSR in Europe and briefly address the London–Paris market. IATA (2003) concludes that connectivity and access time are the most important determinants of the competition between HSR and aviation. Steer Davies Gleave (2006) discusses travel time improvements of the HSR and concludes that service frequency and fare levels will not be affected in this market. Adler et al. (2010) develop a network competition model including HSR, low cost airlines and conventional airlines for Europe. They show that investment in HSR, despite the massive fixed costs, is favourable from a social welfare perspective. Both Bhat (1997) and Koppelman and Wen (2000) conclude that, using discrete choice modelling, travel time is the most important mode choice determinant in the by car, train and airline served Toronto–Montreal passenger market. González-Savignat (2004) studies the viability of the (at that time) developing HSR between Madrid and Barcelona. She mentions fares, travel time, frequency, and trip purpose as the main mode choice determinants; furthermore she speculates about a dominant position of HSR in this market. Park and Ha (2006) study the projected HSR in the Seoul–Daejon market. They mention fare as the most important mode choice determinant and predict a decline in aviation demand by approximately 85% after the introduction of HSR. Finally, Ortúzar and Simonetti (2008) study the effect of a hypothetical

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HSR in the Santiago–Concepción market and conclude that travel time, fare and service delay are the most important mode choice determinants. Our paper also deals with airport airline competition in multiairport markets and therefore combines these fields in the economics literature. In the airport airline competition literature most of the contributions focuses on the San Francisco Bay multi-airport area.2 Pels et al. (2003), Basar and Bhat (2004), and Ishii et al. (2009) all use discrete choice modelling to analyse travel behaviour in this market. Both Pels et al. (2003) and Basar and Bhat (2004) find that access time and service frequency are main determinants of the airline airport choice. In contrast to the above two studies, Ishii et al. (2009) do not focus on all routes in this market but focus on specific origin–destination pairs. They conclude that non-price characteristics of airport–airline combinations are the main determinants. Empirical studies regarding HSR and intermodal competition are ex ante studies using stated preference data and discrete choice modelling. We extend the existing literature by combining intermodal and airport airline competition in a specific market using revealed preference data. Furthermore, our study is the first to examine intermodal competition over time using cross sectional data over the years 2003–2009. We follow the literature regarding the econometric methods, the set of explanatory variables and the distinction between trip purpose (see e.g. Pels et al. (2003) and González-Savignat (2004)). Like Ishii et al. (2009), we focus on a specific market and non-price characteristics. In this paper we study how the introduction of a new alternative (HSR) affects passenger preferences and market shares of travel alternatives in the London–Paris market. The analysis explains how developments in HSR in the London–Paris market changes the competitive environment and the subsequent reaction of airlines in this market. The purpose of our analysis is to use the estimation results to define the degree of competition using the measure of elasticity of market share and to define the conditions, in travel time and geographical distance, under which HSR is a viable alternative for air travel. The authors conjecture that the analysis and results may be valid for medium- to long-haul passenger markets in general, so that the paper can be used as input in policy making concerning the Los Angeles – San Francisco HSR market. The structure of the paper is as follows. Section 2 describes the market, data, model, and primary estimation results. Section 3 analyses the change in behaviour over time in this market, by discussing the elasticities of market share with respect to total travel time, weekly frequency and fare. This section also discusses the withdrawal of airlines in this market and its consequences. Section 4 provides a discussion and conclusion.

2. Empirical analysis 2.1. Data The HSR between the United Kingdom and continental Europe serves the London–Paris and the London–Brussels market. The HSR, i.e. Eurostar, started its services in these markets on 14 November 1994, introducing intermodal competition between two multi-airport areas. Fig. 1 shows the aviation and rail passenger numbers in the London–Paris and London–Brussels market.3 HSR is experiencing, contrary to the aviation business, an increasing market share and number of passengers. Total passenger numbers in 2

The first seminal contributions were by Skinner (1976) and Harvey (1987). The Eurostar figures are taken from annual Revenue and Traffic press releases published by the Eurotunnel Group (2011). Only figures concerning the combined London-Paris London-Brussels market are published. Aviation statistics are compiled using annual UK airport statistics published by the Civil Aviation Authority, accessible from http://www.caa.co.uk/airportstatistics. 3

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these markets have increased from approximately 5 million in 1994 to 11.5 million in 2009. Fig. 1 suggests that the development of HSR has a considerable effect on the aviation sector in these markets, but more advanced analysis is needed to test this hypothesis. As indicated earlier, such empirical analyses of passenger behaviour in the London–Paris passenger market are not available. We consider the lack of data regarding the HSR alternative as the primary reason for the dearth of empirical research relating to this specific market. As far as we know we are the first to explore a cross-sectional data set, including actual travel behaviour, over the years 2003–2009 to study this market. The data allows us to study in depth the effects on travel behaviour of developments related to the HSR, in particular the withdrawal of two airline alternatives and the opening of the total High Speed 1 track. The data set used for the analysis is constructed from various sources. Our primary source is the International Passenger Survey (IPS). The IPS is a survey of a random sample of passengers entering or leaving the United Kingdom by air, sea or the Channel Tunnel. In the current analysis we use the IPS for the years 2003–2009 provided by the Office for National Statistics. For our study, we only select observations of passengers travelling via London airports to Paris, and vice versa, thereby revealing their actual travel behaviour in this market. We observe the departure and arrival airport or station (hereafter port), carrier, class of travel, fares paid, and trip purpose. Besides trip characteristics, we also observe individual socio-economic characteristics, amongst others, age, gender and country of residence. We use three categories of passengers: UK residents leaving the UK; UK residents entering the UK; non-UK residents (i.e. visitors) leaving the UK. For all UK residents the main county of residence is available in the data. Furthermore, for all visitors leaving the UK we know the towns they visited during their stay in the UK. We determine the road distance between the main county of residence or the last town visited as a proxy for the travelling distance to the different ports in the Greater London area.4 After the removal of incomplete observations, the sample contains 9470 business and 18,356 leisure trips made during the period January 2003 until December 2009. Table 1 shows the respondents per alternative, year and trip purpose.5 Note that only the year and the month of the interview are recorded in our primary data source. As a result, for those travelling with Eurostar in November 2007 we do not know whether they use Waterloo International (before 14 November) or St. Pancras International (from 14 November onwards) as departure or arrival port. Therefore, we exclude all observations in November 2007 from the analysis. From 2007 onwards less respondents were surveyed each time period. The characteristics of the alternatives are obtained from several sources. First of all, the average fare per alternative and ticket type is determined using the above-mentioned primary IPS source. Secondly, in-vehicle travel times and service frequency are calculated using OAG Market Analysis (OAG, 2011) and the European Rail Timetable (Thomas Cook, 2011). Thirdly, the on-time performance of the aviation alternatives are compiled using the UK Punctuality Statistics published by the Civil Aviation Authority,6 whereas the on-time performance of Eurostar is provided by the Eurostar Press Office.7 Finally, the road distance between the arrival or departure port in the UK and the individual county of residence or visit is compiled using ViaMichelin travel services for road users.8 4 Non-UK residents entering the UK is another identified category. However, we exclude this group from the analysis since we cannot determine a distance measure for these passengers. 5 Sampled market shares reflect actual market shares, i.e. no intended or unintended oversampling is present. 6 Accessible from http://www.caa.co.uk/punctuality 7 Accessible from http://www.eurostar.com/UK/uk/leisure/about_eurostar/ press_release.jsp 8 Accessible from http://www.viamichelin.co.uk

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Fig. 1. Number of passengers in the London–Paris/Brussels passenger market. Source: http://www.caa.co.uk/airportstatistics; Eurotunnel Group (2011).

Table 1 Respondents per alternative, year, and trip purpose, percentages in brackets. Businessa

2003 2004 2005 2006 2007 2008 2009

Leisure

LHR-BA

LGW-BA

LHR-BD

EUR

LHR-AF

LTN-U2

LHR-BA

LGW-BA

LHR-BD

EUR

479 (30) 418 (25) 492 (28) 461 (25) 161 (15) 112 (13) 88 (12)

95 (6) 50 (3)

115 (7) 118 (7) 108 (6) 70 (4)

601 (38) 761 (45) 832 (48) 1020 (55) 698 (66) 598 (71) 485 (71)

238 (15) 242 (14) 253 (15) 234 (12) 152 (15) 88 (11) 47 (7)

69 (4) 103 (6) 56 (3) 74 (4) 44 (4) 42 (5) 66 (10)

332 (12) 286 (10) 297 (10) 309 (11) 240 (10) 83 (4) 110 (5)

117 (4) 54 (2)

117 118 106 103

1772 1954 2116 2035 1993 2142 1868

(4) (4) (4) (4)

(63) (70) (74) (73) (80) (88) (83)

LHR-AF

LTN-U2

201 (7) 155 (6) 157 (6) 188 (7) 156 (6) 95 (4) 75 (3)

271 (10) 206 (8) 161 (6) 150 (5) 92 (4) 104 (4) 193 (9)

a For all tables please note: LHR = London Heathrow, LGW = London Gatwick, LTN = London Luton, AF = Air France, BA = British Airways, BD = BMI British Midland, U2 = easyJet, EUR = Eurostar, ASC = Alternative Specific Constant.

Combining the aforementioned sources, for each individual we define a choice set containing at least three and a maximum of six alternatives. If we observe that a person travelled first class, the alternative of travelling with easyJet is excluded, since easyJet does not offer first-class fare types. Although we assume that each individual traveller in the same period faces the same choice set, variation of the attribute levels over time is present. The definition and construction of the variables is explained in Appendix A. Table 2 shows the average on time arrival, total travel time, and weekly frequency per alternative and year. A large variation in the on-time arrival, i.e. public performance, measure between the aviation alternatives and Eurostar is observable. For no particular reason observed in our dataset, the percentage of delayed (more than 15 min late) flights declined in 2009. Although both British Airways and AirFrance have services from London Heathrow, variation in the number of on-time arrivals is present between the two airlines. So, on-time performance is based on both airport and airline performance. The average total travel time, including in-vehicle travel, check-in time and expected delay, is quite constant over the years for the aviation alternatives, whereas for Eurostar the earlier-mentioned improvements in the High Speed 1 track clearly result in a reduction of average total travel time. Finally, the weekly frequency figures partly reveal the development of HSR relative to aviation in this particular market. Two aviation alternatives exited the market and both British Airways and AirFrance reduced their frequency dramatically in 2009 and 2008, respectively, whereas the frequency of easyJet has remained stable over the whole period and, in contrast to aviation, Eurostar has increased its frequency.

Table 2 Average on-time arrival, travel time and weekly frequency per alternative and year. LHR-BA

LGW-BA

Average on time arrival in % (PPM) 2003 75 75 2004 69 69 2005 63 2006 63 2007 65 2008 67 2009 84 Average travel time in minutes 2003 136 137 2004 137 138 2005 140 2006 142 2007 141 2008 142 2009 140 Average weekly frequency 2003 73 36 2004 73 33 2005 71 2006 71 2007 71 2008 68 2009 59 Note: See footnote ‘a’ in Table 1.

LHR-BD

EUR

LHR-AF

LTN-U2

61 59 70 70

78 89 86 92 92 92 95

65 67 70 64 67 63 77

72 71 71 55 65 69 77

113 113 110 111

201 193 191 188 186 172 170

107 105 105 108 106 109 106

121 120 120 127 121 123 122

40 35 32 32

99 98 98 104 109 119 119

92 88 82 80 80 59 56

30 30 21 26 26 26 25

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C. Behrens, E. Pels / Journal of Urban Economics 71 (2012) 278–288 Table 3 Average road distance (KM) per alternative, year, and trip purpose. Business LHR-BA

Leisure LGW-BA

Average road distance in KM 2003 72 95 2004 76 109 2005 82 2006 83 2007 92 2008 56 2009 105

LHR-BD

EUR

LHR-AF

LTN-U2

LHR-BA

LGW-BA

LHR-BD

EUR

LHR-AF

LTN-U2

106 96 111 68

49 45 49 41 38 44 53

68 67 71 68 63 63 36

106 100 88 85 101 117 88

94 97 89 88 95 85 124

136 175

166 148 155 99

62 62 62 58 46 56 70

77 65 72 68 74 59 61

123 158 102 126 87 85 96

Note: See footnote ‘a’ in Table 1.

Table 3 shows the average road distance in kilometres between the UK port and the county of residence or visit per alternative, year, and trip purpose. As is shown in the table, a considerable variation over the years exists per alternative and trip purpose. We observe that average road distances to the Eurostar station are shorter compared with those to the other ports.9 The average road distance per alternative differs between leisure and business trip purposes. On average, leisure passengers accept longer access times (distances), which is in line with the general belief that the value of time of leisure passengers is lower compared with that of business passengers. So, catchment areas depend on the kind of passengers the port serves. For example, we observe that both leisure and business passengers travelling with easyJet have a longer average road distance between the airport and county of residence or visit, which is in line with the general belief that passengers who choose for a low-cost carrier have lower monetary values for quality characteristics including travel time and accessibility. Table 4 shows the average fare paid per alternative (one-way), year, and fare category. Differences between the average fares of the aviation alternatives are considerably lower for second-class compared with first-class tickets. From 2007 onwards, Eurostar has offered the cheapest fares in the second-class fare category; before 2007 easyJet offered cheaper tickets. Fig. 2 shows relative prices and relative ridership figures for HSR versus air transport over time. Clearly, the relative price of HSR versus air transport remains fairly constant over time, but the relative ridership shows a large increase after the opening of the HSR link. This indicates that the price is not the most important decision variable for travellers and that accounting for other travel characteristics, such as travel time and convenience, is necessary in the empirical analysis.

ð1Þ

The specification includes an alternative specific constant which captures the non-stochastic unobserved heterogeneity between the different alternatives. This unobserved heterogeneity can be due, for example, to differences in quality and marketing. The aforementioned different locations of the ports in Paris is also part of this unobserved heterogeneity. The alternative specific constants are, via the specification of b1,i to b4,i, period- and fare-type specific. London Heathrow–British Airways is the reference category for these alternative specific constants. Furthermore, the period January 2003–October 2004 and the second class fare type serve as reference categories. In order to identify the model, these reference categories are normalised to zero. The aviation choice literature stresses that business and leisure passengers behave differently. Therefore, we estimate our model both for business and leisure passengers separately, as well as for the two groups together.10 The choice of an alternative depends on the average fare, road distance to the port, average on-time arrival (PPM), total travel time, and the logarithm of the weekly frequency. We expect fare, road distance, and total travel time to have a negative effect on utility, and therefore on the probability that a certain alternative will be chosen, whereas PPM and frequency are positive attributes of the alternatives. Ishii et al. (2009) argue that fare is endogenous when the fare is set by an airline with market power.11 Given this potential endogeneity problem, one should be careful in interpreting the results. Apart from the basic multinomial logit model, which suffers from the IIA property (see, e.g. Hensher et al., 2005), we specify and estimate a mixed multinomial logit model.12 In this specification we account for the possibility of unobserved stochastic heterogeneity over the alternatives and heterogeneity amongst individuals in their attitude towards prices. We specify a mixed logit model with a lognormal distributed fare parameter and two normally distributed error components. The first error component relates to all aviation alternatives, while the second error component relates to all aviation alternatives departing from London Heathrow. So, the first error component takes into account the randomness amongst travellers for the unobserved stochastic heterogeneity between aviation and rail alternatives: for example, the valuation of in-vehicle comfort levels, and the use of electronic devices on board. Using the mixed logit specification described above, we examine whether the development of HSR causes changes in travellers’ behaviour in this specific market. Four time periods are specified, in the first period (January 2003–October 2004) all aviation alternatives are in the market, whereas in the second period British Airways does not offer services anymore from London Gatwick. The

One could argue that respondents travelling with HSR are more likely to access the Eurostar terminal by public transport. This is due, for example, to traffic conditions and, more in particular, limited parking facilities in Inner London. As a consequence of this limitation in access modes, average distance travelled to the Eurostar terminal could be smaller compared with that to airports which rely heavily on both public and private transport access modes.

10 Because we prefer the trip purpose-specific models, we omit the results of the combined model. The results are, of course, available on request. 11 Note that the other, non-price, characteristics potentially suffer from the same endogeneity problem. 12 Mixed multinomial logit models are highly flexible models, which allow for correlation in unobserved effects, unrestricted substitution patterns, and random variation of individuals’ tastes (Train, 2003).

2.2. Model We model the choice of carrier and UK port, conditional on the chosen fare category. The choice set consists of three to six alternatives, depending on period and fare category. We assume that each respondent maximises utility, and we define the indirect utility of a specific alternative i of individual n as follows:

V ni ¼ b0;i þ b1;i ðNovember 2004 December 2006Þ þ b2;i ðJanuary 2007 October 2007Þ þ b3;i ðDecember 2007 December 2009Þ þ b4;i ðFirst classÞ þ b5 Farei þ b6 RoadDisti þ b7 PPMi þ b8 Ttimei þ b9 LnðFreqi Þ þ eni :

9

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Table 4 Average fare paid per alternative, year and fare category. First-class fare LHR-BA Average fare 2003 191 2004 210 2005 192 2006 171 2007 158 2008 185 2009 182

Second-class fare

LGW-BA

LHR-BD

EUR

LHR-AF

LTN-U2

LHR-BA

LGW-BA

LHR-BD

EUR

LHR-AF

LTN-U2

209 230

173 176 195 184

115 125 135 144 132 121 117

198 171 192 200 134 127 129

NA NA NA NA NA NA NA

83 72 73 66 58 75 69

58 56

59 52 62 68

53 57 59 59 55 54 51

74 72 62 61 56 53 62

41 43 42 47 56 63 57

Note: See footnote ‘a’ in Table 1.

Fig. 2. Relative first- and second-class fares and degree of ridership for HSR versus air travel over time.

alternative London Heathrow–British Midland is no longer available from the third period onwards, while the relocation of Eurostar services to St. Pancras International station marks the start of the last period. 2.3. Results Table 5 shows the coefficient estimates and robust standard errors of the multinomial logit model, as specified in Eq. (1), for business and leisure passengers separately.13 The estimation results of the mixed logit model are depicted in table 6.14 The coefficients of fare, road distance, and weekly frequency are significant for both trip purposes in both the multinomial and mixed logit model.15 In contrast, the estimated coefficient for on-time arrival for business trips is not significant in both models. Remarkably, the effect of total travel time for leisure trips turns out to be not significant as well. The qualitative interpretation of the estimation results is the same for both models. Our findings in terms of the signs of fare, road distance, on time arrival, travel time, and frequency are both in line with intuition and results of previous transport mode choice studies. The alternative specific constants and the interactions with the period dummies show mixed results. In the period November 2004–December 2006 no alternative specific interactions term is found to be significant16, whereas for the periods January 2007– October 2007 and December 2007–December 2009 significant 13

We use the software package Biogeme to estimate the models (Bierlaire, 2003). The number of Halton draws is maximized given the computational restrictions: 20,000 and 10,000 draws for the business and leisure sample, respectively. The results are robust for different numbers of draws and starting values. 15 Note that the mean of the estimated fare parameter in the mixed logit model equals: exp(m + s/2), where m is the obtained point estimate and s the obtained standard deviation. So, the mean of the estimated fare parameter equals 0.0037 and 0.0151 for the business and leisure segments respectively. 16 An exception is the London Heathrow-British Midland interaction effect for the business segment in the multinomial logit specification. 14

estimates are found. This indicates that the non-observed characteristics of the alternatives as perceived by the consumers remain constant over the period January 2003–December 2006 but they change after this period. The significant estimates of the alternative specific constants for the Eurostar, including period interactions, are all positive. This suggests that the Eurostar alternative has valuable nonobserved characteristics, for example: in-vehicle comfort and the use of electronic devices on board. Due to the non-linear nature of the applied models, we cannot directly compare the magnitude of each of the estimated parameters. Therefore, we calculate elasticities of market share in the next section in order to make such comparisons. Because the multinomial and mixed logit models produce similar qualitative results, we use the log-likelihood (LL) ratio-test statistic, following a Chi-squared distribution with degrees of freedom equal to the number of extra estimated parameters, to test overall model significance (see e.g. Hensher et al., 2005). We reject the hypothesis that the mixed logit model is not better than the multinomial logit model.17 The additional insights from the mixed logit model are related to the lognormal specified fare parameter and the two variance error components. The estimated standard deviation of the fare parameter is highly significant for the leisure trips, but insignificant for the business trips. This is an indication that leisure passengers are more heterogeneous as a group regarding the valuation of the average fare compared to business passengers. Differences between business and leisure passengers are also found in the unobserved stochastic utility of the alternatives. The mixed logit model detects that unobserved heterogeneity – for example, the final destination within France or the use of electronic devices on

17 This test statistic, 2(LLlogit model  LLmixed model), equals 10 for the business model. For the leisure model, the test statistic equals 98. Using the critical values of 7.81 (three extra parameters) and 11.07 (five extra parameters) for the business and leisure segments respectively, we reject the null hypothesis that the mixed logit is not better than the multinomial logit model for both segments.

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C. Behrens, E. Pels / Journal of Urban Economics 71 (2012) 278–288 Table 5 Estimation results for multinomial logit model estimation. Business

ASC LGW-BA ASC LHR-BD ASC EUROSTAR ASC LHR-AF ASC LTN-U2 November 2004–December 2006 * LHR-BD November 2004–December 2006 * EUR November 2004–December 2006 * LHR-AF November 2004–December 2006 * LTN-U2 January 2007–October 2007 * EUR January 2007–October 2007 * LHR-AF January 2007–October 2007 * LTN-U2 December 2007–December 2009 * EUR December 2007–December 2009 * LHR-AF December 2007–December 2009 * LTN-U2 First class * LGW-BA First class * LHR-BD First class * EUR First class * LHR-AF Fare Road distance in KM On time arrival in % (PPM) Travel time in minutes Ln (weekly frequency) Observations Null log-likelihood Final log-likelihood

Leisure

Parameter

Robust S.E.

Parameter

Robust S.E.

0.1266 0.8880* 0.1897 1.4050* 0.3991 0.2294*** 0.0404 0.0276 0.0325 0.2733** 0.5002* 1.0696* 0.0967 0.3763** 1.5397* 0.3871*** 0.1764 0.8025* 0.3338* 0.0035* 0.0303* 0.0058 0.0138*** 1.1958* 9470 14,310 10,464

0.2381 0.3564 0.5503 0.2479 0.3359 0.1321 0.0953 0.0896 0.1487 0.1381 0.1417 0.2344 0.2232 0.1587 0.1691 0.2129 0.1443 0.0702 0.0812 0.0010 0.0008 0.0050 0.0078 0.2834

0.1312 0.6087** 1.0999* 0.9500* 0.3206 0.0025 0.0069 0.0975 0 0.2239** 0.1807 0 0.6799* 0.5779* 0.9685* 0.2077 0.0213 0.4671* 0.1230 0.0132* 0.0182* 0.0126* 0.0058 0.9847* 18,356 28,522 15,108

0.1870 0.2741 0.3935 0.1933 0.2586 0.1166 0.0752 0.0940 NA 0.0950 0.1223 NA 0.1758 0.1407 0.1062 0.4716 0.2463 0.1248 0.1840 0.0015 0.0006 0.0040 0.0057 0.2004

Note: See footnote ‘a’ in Table 1. * Significant at 1. ** Significant at 5. *** Significant at 10.

board – between aviation alternatives and Eurostar plays a significant role for business trips. By including variance error components we can capture unobserved heterogeneity caused by not observing final destinations in Paris. Furthermore, mixed logit allows for more flexible substitution patterns, and the log-likelihood ratio tests indicate that the model outperforms the standard logit model. Hence, we will analyse consumer behaviour over time using the more sophisticated mixed logit model estimates in Section 3. As mentioned in the introduction, our results, and in particularly the method of analysis, may be used to study other potential HSR markets. One prime example of such a market is the earlier mentioned San Francisco – Los Angeles passenger market. Here we are interested under which set of travel times HSR in the San Francisco – Los Angeles passenger market may be a viable alternative for air transport. For this purpose, we use our mixed logit estimation results of the London–Paris passenger market and plot the expected market shares against the set of travel times. Although we use strong simplifying assumptions, such as equal passenger behaviour in both markets, our market share forecasts are in line with the official forecasts published by the California High-Speed Rail Authority.18 In addition, we assume that the fare level of HSR is about 80% of the airline fare, which is equal to 65 lb (in 1995 British pounds). This relative fare level is rather constant over time in the London–Paris passenger market (see Fig. 2) and is also used by the California High-Speed Rail Authority. Furthermore, following the business plan, we use 650 direct HSR connections a week and the current supply of 595 flights a week between the two cities (including San Francisco International Airport, Oakland International Airport, Los Angeles International Airport, Ontario International Airport and Bob Hope Airport). 18 See http://www.cahighspeedrail.ca.gov/Business_Plan_reports.aspx, Source Document 5: Ridership and Revenue.

We determine the indirect utility based on these three characteristics and our mixed logit estimation results and determine the market shares for travel times of HSR varying from 120 to 200 min. As depicted in Fig. 3, the HSR is expected to capture a market share of 50% if travel time equals around 145 min in the leisure segment, and the same market share if travel time equals around 160 min in the business segment. According to the official business plans of the California High-Speed Rail Authority, average travel time between the two cities equals 180 min. These travel times will result in a market share of around 30% in the business segment and 40% in the leisure segment. So, the HSR will be a viable alternative, in terms of market shares and travel times, for air transport in the San Francisco – Los Angeles market, but we do not expect the HSR to become a dominant alternative. 3. Elasticities of market share and market developments With our model we are able to investigate whether and how passenger behaviour or preferences change over time. These changes over time can be related to changing market circumstances, in particular the earlier-mentioned ongoing improvement of the HSR alternative. However, different, unobserved, factors can also play a role. More interestingly, we show here that passenger preferences can be used as an explanation for market developments, in particular the withdrawal of aviation alternatives. The measure of passenger behaviour that we apply here is what is called the elasticity of market share with respect to a particular attribute. The direct elasticity of market share measures the effect of a 1% change in the attribute of an alternative on the total probability of choosing the specific alternative. Besides the direct elasticities of market share discussed in this section, Appendix B deals with the cross-elasticities of market share and the insights these provide for intermodal competition.

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Table 6 Estimation results for mixed multinomial logit model estimation. Business

Leisure

Parameter ASC LGW-BA ASC LHR-BD ASC EUROSTAR ASC LHR-AF ASC LTN-U2 November 2004–December 2006 * LHR-BD November 2004–December 2006 * EUR November 2004–December 2006 * LHR-AF November 2004–December 2006 * LTN-U2 January 2007–October 2007 * EUR January 2007–October 2007 * LHR-AF January 2007–October 2007 * LTN-U2 December 2007–December 2009 * EUR December 2007–December 2009 * LHR-AF December 2007–December 2009 * LTN-U2 First class * LGW-BA First class * LHR-BD First class * EUR First class * LHR-AF Mean of ln (Fare) Std. dev. of ln (Fare) Road distance in KM On time arrival in % (PPM) Travel time in minutes Ln (weekly frequency) Variance error component Mean of aviation alternative Std. dev. of aviation alternative Mean of LHR alternative Std. dev. of LHR alternative Observations Number of Halton Draws Null log-likelihood Final log-likelihood

Robust S.E.

0.0420 0.9630* 0.2830 1.5700* 0.4460 0.2200 0.0945 0.0335 0.0226 0.3700** 0.4990* 1.1600* 0.1740 0.3750** 1.6800* 0.4320*** 0.1700 1.0100* 0.3310* 5.5900* 0.0079 0.0345* 0.0043 0.0182** 1.2800* 0 0.9940* 0 0.5800 9470 20,000 14,310 10,459

Parameter

Robust S.E.

0.2540 0.3930 0.6250 0.2910 0.3650 0.1390 0.1140 0.0921 0.1590 0.1670 0.1430 0.2550 0.2690 0.1650 0.1970 0.2340 0.1450 0.1110 0.0817 0.3030 0.0078 0.0019 0.0058 0.0091 0.3030

1.1200 0.7690*** 2.9300* 1.2500* 1.3200 0.0403 0.0065 0.1440 0.0271 0.4630* 0.0619 0.0308 1.4700* 0.5520* 1.9100* 0.0798 0.0596 1.3900* 0.0881 4.6700* 0.9490* 0.0248* 0.0110** 0.0156 1.1100*

0.7650 0.4100 0.6660 0.3940 0.9350 0.1410 0.1340 0.1070 0.1910 0.1840 0.1360 0.3950 0.3970 0.1630 0.4740 0.8490 0.2500 0.3040 0.1900 0.2570 0.1970 0.0053 0.0058 0.0120 0.3090

Fixed 0.2190 Fixed 0.3720

0 1.2700 0 2.8300*** 18,356 10,000 28,522 15,059

Fixed 1.5100 Fixed 0.8150

Note: See footnote ‘a’ in Table 1. * Significant at 1. ** Significant at 5. *** Significant at 10.

Fig. 3. Projected market share for HSR in the San Francisco – Los Angeles passenger market.

In the case of the mixed multinomial logit specification of our model, the individual direct elasticity of market share is as follows:

@Pni X ni X ni n n ¼ n @X i Pi Pi

Z

bð1  Lni ðbÞÞLni ðbÞf ðbÞdb;

ð2Þ

where Lni ðbÞ is the logit probability Pni evaluated at parameters b, the parameters in Eq. (1); and f(b) is a density function. The elasticity as defined in Eq. (2) is an individual point elasticity of market share, and needs to be evaluated by aggregating the individual elasticities using the individual choice probabilities as weights (Hensher et al., 2005). The resulting elasticity, like the model itself, has no closed

form. Therefore, we use Halton draws to calculate the elasticity. For each draw we calculate the resulting elasticity, and then take the average. If the attribute X ni is stated in logarithmic form, as is the case with weekly frequency, Eq. (2) is multiplied by 1=X ni . The above-defined elasticity of market share depends on preferences changing over time, which are incorporated via the specification of the period interaction dummies in the indirect utility function, and by changing the attribute levels of the alternatives. The attribute levels play a role via the indirect utility function, and, in the case of total travel time, the attribute levels appear directly in the definition of the elasticity of market share. Table 7

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C. Behrens, E. Pels / Journal of Urban Economics 71 (2012) 278–288 Table 7 Direct elasticities of market share with respect to travel time, frequency, and fare per alternative, year, and trip purpose for the mixed multinomial logit model. Business LHR-BA Travel time in minutes 2003 1.59 2004 1.62 2005 1.65 2006 1.69 2007 1.95 2008 1.97 2009 1.94 Weekly frequency 2003 0.82 2004 0.83 2005 0.83 2006 0.83 2007 0.97 2008 0.96 2009 0.97 Fare 2003 2004 2005 2006 2007 2008 2009

0.26 0.24 0.23 0.22 0.33 0.38 0.37

Leisure LGW-BA

LHR-BD

EUR

LHR-AF

LTN-U2

LHR-BA

LGW-BA

LHR-BD

EUR

LHR-AF

LTN-U2

1.98 2.11

2.24 2.29 2.36 2.41

1.09 0.99 0.91 0.85 0.59 0.51 0.51

2.04 2.04 2.06 2.14 1.99 2.18 2.14

1.86 1.85 2.06 2.11 1.74 1.39 1.39

1.42 1.44 1.41 1.44 1.37 1.63 1.61

1.82 1.91

1.71 1.52 1.53 1.86

0.44 0.42 0.38 0.34 0.24 0.17 0.17

1.74 1.75 1.65 1.81 1.65 1.44 1.70

0.80 0.75 0.66 0.79 1.34 1.73 1.65

1.02 1.08

1.15 1.17 1.19 1.19

0.56 0.51 0.45 0.42 0.30 0.25 0.25

1.05 1.04 1.03 1.05 0.99 1.07 1.07

0.96 0.95 1.03 1.04 0.87 0.68 0.70

0.74 0.75 0.72 0.72 0.69 0.81 0.81

0.95 1.00

0.89 0.79 0.78 0.93

0.23 0.22 0.19 0.17 0.12 0.09 0.09

0.91 0.91 0.84 0.91 0.83 0.72 0.86

0.42 0.39 0.33 0.39 0.68 0.86 0.84

0.28 0.28

0.27 0.24 0.29 0.30

0.12 0.11 0.11 0.10 0.09 0.07 0.07

0.32 0.30 0.28 0.29 0.35 0.32 0.33

0.12 0.12 0.13 0.14 0.14 0.13 0.11

0.61 0.99 0.88 1.73 2.52 1.09 0.89

1.28 2.18

2.30 3.72 3.02 3.64

0.94 0.77 0.66 0.92 0.58 0.39 0.15

0.92 0.92 1.95 3.12 3.37 5.77 1.54

2.29 1.96 1.63 3.05 4.18 1.26 1.89

Note: See footnote ‘a’ in Table 1.

shows the aggregated direct elasticities of market share with respect to total travel time, weekly frequency and fare on an annual basis. Suppose that the total travel time of the Eurostar alternative decreases by 1% in 2003. This decrease in total travel time would lead to an increase in market share of 1.09% and 0.44% in the business and leisure market, respectively. We observe that, except for easyJet in the years 2008 and 2009, business travellers are more sensitive to total travel time compared with leisure travellers. In general, the differences between the direct elasticities of the related parameters for business and leisure trip passengers are in line with expectations. Business passengers are more affected by lower total travel times, and higher weekly frequencies, but are less affected by fare. In contrast, for leisure passengers fares seem important, whereas frequency, and total travel time seem to be of less importance.19 Furthermore, for both groups, the sensitivities to total travel time are considerably lower for the Eurostar and easyJet alternatives compared with the other alternatives. In addition, we observe that, after the completion of High Speed 1, the sensitivities towards total travel time decline for Eurostar, and for other alternatives, in particular LHR-BA and LTN-U2 (leisure), the sensitivities increase compared with the years before. So, the improvement of the HSR alternative would result in favourable changes in passenger valuation for the HSR at the cost of mainly LHR-BA, in the business market, and LTN-U2, in the leisure market. The withdrawal of London Gatwick–British Airways and London Heathrow–British Midland from the market is interesting from a theoretical perspective. Pels et al. (2000) indicate that, in order to be able to maximise profits, the frequency elasticity of market share may not exceed a certain upper limit. They show that, when market share is determined in a nested logit model and there are constant marginal costs per flight, profit can be maximised only if the frequency elasticity of market share does not exceed 1.20

19

The latter is speculative since the parameter estimate is not significant. If this condition is not met, an increase in the number of flights results in a more than proportional increase in demand.

Appendix C shows that this finding holds in the more general case of (mixed) multinomial logit models. In our case, Table 8 shows that the sample-based aggregated elasticity with respect to frequency exceeds 1 for the alternatives London Gatwick–British Airways and London Heathrow–British Midland in the last year they were in the market, indicating profits could not be maximised in these markets. A possible explanation for the high elasticities of market share with respect to frequency is the fact that airport capacity is

Table 8 Sample-based aggregated direct elasticities of market share with respect to travel time, frequency, and fare per alternative and year for mixed multinomial logit model. Business + Leisure LHR-BA

LGW-BA

LHR-BD

EUR

LHR-AF

LTN-U2

1.90 1.81 1.85 2.08

0.68 0.64 0.58 0.54 0.34 0.26 0.25

1.85 1.86 1.81 1.94 1.75 1.63 1.80

1.18 1.17 1.19 1.32 1.46 1.64 1.59

0.98 1.03

0.98 0.93 0.94 1.03

0.35 0.33 0.29 0.27 0.17 0.13 0.13

0.96 0.96 0.91 0.97 0.88 0.81 0.91

0.62 0.60 0.60 0.65 0.74 0.81 0.81

0.92 1.46

1.56 2.40 1.98 2.30

0.64 0.52 0.45 0.59 0.43 0.31 0.13

0.70 0.69 1.31 1.99 2.47 4.37 1.26

1.50 1.26 1.06 1.89 2.97 0.97 1.47

Travel time in minutes 2003 1.48 1.88 2004 1.51 1.99 2005 1.50 2006 1.54 2007 1.54 2008 1.72 2009 1.69 Weekly frequency 2003 0.77 2004 0.78 2005 0.76 2006 0.76 2007 0.77 2008 0.85 2009 0.85 Fare 2003 2004 2005 2006 2007 2008 2009

0.48 0.71 0.63 1.13 1.87 0.91 0.77

20

Note: See footnote ‘a’ in Table 1.

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Table 9 Cross-elasticities of market share with respect to travel time and frequency per alternative, year, and trip purpose for mixed multinomial logit model. Business LHR-BA Travel time in minutes 2003 0.68 2004 0.76 2005 0.89 2006 0.96 2007 1.27 2008 1.36 2009 1.32 Weekly frequency 2003 0.35 2004 0.39 2005 0.44 2006 0.48 2007 0.63 2008 0.67 2009 0.66

Leisure LGW-BA

LHR-BD

LHR-AF

LTN-U2

LHR-BA

LGW-BA

LHR-BD

LHR-AF

LTN-U2

0.78 0.87

0.66 0.75 0.87 0.95

0.70 0.80 0.91 0.98 1.31 1.41 1.40

0.64 0.72 0.86 0.94 0.93 0.84 0.84

0.61 0.66 0.69 0.75 0.89 1.02 1.00

1.19 1.25

0.62 0.51 0.54 0.72

0.62 0.67 0.68 0.75 0.86 1.05 1.02

0.63 0.56 0.50 0.65 1.15 1.57 1.51

0.40 0.45

0.34 0.38 0.44 0.47

0.36 0.41 0.46 0.48 0.65 0.69 0.70

0.33 0.37 0.43 0.46 0.47 0.41 0.42

0.32 0.34 0.35 0.37 0.45 0.51 0.50

0.62 0.65

0.32 0.27 0.28 0.36

0.32 0.35 0.35 0.38 0.43 0.52 0.52

0.33 0.29 0.26 0.33 0.58 0.78 0.76

Note: See footnote ‘a’ in Table 1.

constrained at London airports.21 Airlines compete on the basis of price and frequency. The frequency offered by an airline in the market from London to Paris is restricted by the total capacity of the airports and the market share in earlier years due to grandfathering of slots. When demand in a specific market is larger than the capacity allocated to this market, we expect that the elasticity of market share with respect to frequency will be relatively high, because airlines cannot increase their frequency. The airlines are not able to adjust prices upwards freely, since the HSR does not face the same capacity constraints. The direct elasticities of market share with respect to fares are, as shown in Table 8, indeed high for the aviation alternatives. Adjusting the prices upwards would therefore result in a high loss of market share. Combining the above theory with our estimations shows that London Gatwick–British Airways and London Heathrow–British Midland are not capable of optimising their frequency and thereby maximising their profits, because of the competition and/or capacity restrictions. This might be a reason why these alternatives left the market. We do not observe whether the not-optimised profits are positive or negative. In the Los Angeles – San Francisco market capacity restrictions also play a role, but not to the extent we see in Europe, where slot allocation to a large extent dictates available capacity. Nevertheless, also in the case of the Los Angeles – San Francisco market we expect low market shares and high frequency elasticities of market shares to coincide.22 If airlines with high frequency elasticities of market share cannot increase their market share,23 our results suggest they will disappear from the market, at least in theory. The elasticity with respect to frequency for the HSR alternative is relatively low, so profits can be maximised, and capacity restrictions appear to be less important. As the HSR increases its market share over time (see Table 1), its frequency elasticity decreases, and this effect is even more pronounced when other alternatives leave the market. EasyJet also attracts passengers from the other airlines, resulting in a decreasing frequency elasticity. Table 8 furthermore suggests that London Heathrow–British Airways and London Heathrow–Air France most probably face difficulties in optimising profits in this particular market. However, it is expected that they stay in the market because of the feeder function this route has in their hub-and-spoke network. On the other hand, if

21 Correlation between the frequency and variables not included in the analysis may be another reason for this particular result. 22 See e.g. Pels et al. (2003). 23 Given that HSR has low relative prices this will be likely.

HSR can be integrated in British Airways’s or Air France’s network, by substituting HSR for a London–Paris flight, both airlines could be better off. On the basis of our results, we conjecture that the presence of HSR results in the withdrawal of airlines whose network does not rely on the particular O/D route. In the case of the London–Paris passenger market, the low-cost carrier seems to survive, although it competes heavily with the HSR for leisure passengers. In less dense markets, the probabilities of low-cost carriers leaving these markets entered by HSR are high, thus increasing the dominant market position of the HSR even further. 4. Conclusion Intermodal competition, particularly including HSR, attracts more and more attention in the literature because of investments such as the High-Speed Rail. Here we studied the behaviour of travellers in the London–Paris passenger market and the conditions under which HSR becomes a viable alternative for passengers. We estimated mixed logit models using cross-sectional revealed preference data over the period 2003–2009. We analysed the relationship between passengers’ preferences and the withdrawal of airlines and completion of the High-Speed Rail link in November 2007. We find frequency, total travel time, and distance to the UK port as the main determinants of travellers’ behaviour. Business and leisure passengers behave differently regarding these main determinants. We conclude that leisure passengers are more heterogeneous regarding average fares compared with business passengers. Furthermore, we show that accounting for correlation between the alternatives in unobserved effects, while making this correlation random amongst the travellers, and allowing for a random fare coefficient, improve the discrete choice model. Regardless the improvements in the HSR alternative and the withdrawal of aviation alternatives, we conclude that the consumer preferences are fairly constant in the period 2003–2009. For example, direct elasticities of market share with respect to total travel time only change slightly after the withdrawal of two airlines and the completion of the HSR link. In particular London Heathrow–British Airways suffers from the improvement in HSR by having to confront higher direct elasticities of market share with respect to total travel time and frequency, suggesting that the competitive position of London Heathrow–British Airways has become worse. We find higher cross-elasticities of market share compared with those reported in the literature, indicating that fierce

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competition is present within this market. More precisely, within the business segment, competition between London Heathrow– British Airways and London Heathrow–Air France on the one hand, and Eurostar, on the other, is more fierce compared with competition between Eurostar and easyJet, whereas for the leisure segment the opposite is the case. So, the degree and pattern of intermodal competition in this market depends largely on trip purpose. The HSR is clearly a viable alternative for both market segments. Our analysis of the London–Paris market illustrates that a longer average travel time for HSR can be offset by frequency and fares to attract passengers in both market segments. Our findings suggest that in markets with even larger differences in average travel times, due to for example a lower average speed or a larger distance between the city pairs, HSR may also be a viable alternative compared with aviation. Applying our results of the London–Paris market we show this to be the case for the projected HSR in the San Francisco – Los Angeles market. The presence of multiple aviation alternatives in the specific market, as is the case in the London Paris market, is not a feasible entry barrier for HSR. Moreover, we show that HSR competes both with conventional as well as low cost carriers. In addition, we find that the direct elasticity of market share with respect to frequency exceeds 1 for some aviation alternatives. As a result, the conventional airlines are not able to maximise profits by optimising their frequency and may leave the market. Airlines showing these high elasticities have indeed left the market. Although, in the first instance, our findings show that competition in the London–Paris passenger market is present and rather strong compared with the findings in empirical studies in other markets, the dominant position of Eurostar in this market warrants attention. We show that airlines are not able to maximise profits regarding service frequency, and that these airlines are leaving the market. Furthermore, the remaining airlines are also experiencing the same difficulties in maximising profits. However, we conjecture that these airlines will stay in the market because of the presence of this route in their network, as long as HSR is not integrated in the airlines’ network. Transport policy needs to address the development of HSR into dominant firms in the markets they serve. Combined with our findings, the fact that most HSR routes, in contrast to air transport, are currently operated by a single consortium implies that competition in medium-haul transport markets will decline in the future. Recognising this threat, the European Commission introduced a policy to open up the international passenger services to competition within the European Union from 2010 onwards.24 In the case of the San Francisco – Los Angles passenger market the difference in travel time are such that we expect that HSR can be a viable competitor but will not end up having a dominant market position. Even though our current findings suggest that HSR in the Los Angeles – San Francisco market may not obtain a dominant position, policy makers should consider the effect of market shares and frequency elasticities on the number of competitors.

Appendix A.:. Definition and construction of the variables

Acknowledgment

Appendix B.:. Cross-elasticities of market share

We would like to thank Erik Verhoef, Mark Lijesen, Stuart Rosenthal, and two anonymous referees for their helpful comments. Christiaan Behrens gratefully acknowledges The Netherlands Organization for Scientific Research (NWO) for financial support (Grant number 400-08-012).

The cross-elasticity of market share measures the effect of a 1% change in the attribute of an alternative, i, on the probability of another, not i, alternative, and is defined as follows:

24 See Directive 2007/58/EC on the allocation of railway infrastructure capacity and the levying of charges for the use of railway infrastructure: this Directive envisages opening the market for international passenger services to competition from 1 January onwards, http://www.eea.europa.eu/policy-documents/directive-2007-58-ec.

A.1. Average on time arrival in % (PPM) The so-called Public Performance Measure (PPM) in aviation and rail transport is used to determine the percentage of on-time arrival of a certain alternative on a yearly basis. A flight is delayed if it arrives or departs 15 min later compared with the scheduled departure or arrival time. For long-haul trains in the UK a 10 min time interval is used to determine the PPM. A.2. Total travel time in minutes The total travel time in minutes is defined by the summation of three elements. The first element is the average scheduled in-vehicle travel time per alternative and period. For the aviation alternatives monthly periods are used, whereas for the rail alternative the average scheduled in-vehicle travel time is seasonally based (summer and winter). The second element is the time in minutes that passengers are advised (airline specific, otherwise airport specific) to arrive at the port before their flight or train departs. BA indicates 60, AF, BD and Eurostar 30 and U2 40 min. The last component of the total travel time is the expected delay in minutes. The expected delay in minutes is the average delay on a yearly basis multiplied by the percentage of delayed arrivals or departures (1 – PPM). For all aviation alternatives the average delays are published in the UK Punctuality Statistics, whereas Eurostar does not make public the average delays in minutes. However, given that for the aviation alternatives the average delay in minutes is close to the official 15 min boundary, we take the official rail boundary of 10 min as the proxy of the average delay in minutes of Eurostar. A.3. Weekly frequency The weekly frequency is measured as the total number of departures from London to Paris per alternative. The frequencies of the aviation alternatives are based on monthly figures whereas the number of train departures is seasonally based (summer and winter), both are translated into weekly figures. Since frequency is considered to be a measure of size of the alternative, we take the logarithmic of frequency, and include that in our model specification. A.4. Fare We calculate an average fare per alternative, ticket type and year. We exclude indicated fares lower than 15 or higher than 1000 British pounds (1995). The calculation of the average fare from 2007 onwards involves an extra step. We first use cluster analysis to categorise the fares into first- or second-class fare type, and based on this classification we calculate the average fare per alternative, ticket type, and year.

@Pni X ni X ni n n ¼  n @X i Pi Pi

Z

bLni ðbÞLni ðbÞf ðbÞdb:

ð3Þ

To determine the effect of a change in the level of the attributes time and frequency of Eurostar on the other aviation alternatives, we calculate the cross-elasticities in the same way as for the direct

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elasticities. Table 9 shows these cross-elasticities of market share with respect to a 1% increase in, respectively, total travel time and weekly frequency of Eurostar. So, for example a 1% increase in Eurostar’s total travel time in 2009 results in a market share increase of 1.32% for London Heathrow–British Midland, 1.40% for London Heathrow–Air France, and 0.84% for London Luton-easyJet in the business market. The relative magnitudes of these cross-elasticities indicate the level of competition between aviation and HSR in this market. For both total travel time and weekly frequency we observe rather high values for the cross-elasticities compared with figures reported in the literature. Bhat (1997), Koppelman and Wen (2000), and Park and Ha (2006) report cross-elasticities of market share. Bhat (1997) reports cross-elasticities regarding daily frequency, also based on changes in the attribute level of the rail alternative, of around 0.03 for business travellers. This is considerably lower compared with our results. Koppelman and Wen (2000) report cross-elasticities of the same order of magnitude as Bhat (1997), while Park and Ha (2006) find a cross-elasticity with respect to frequency of about 0.17. In addition, our obtained cross-elasticties with respect to travel time are considerably higher compared with the figures reported by Bhat (1997). He reports a cross-elasticity of about 0.4 in the business market. We can conclude, therefore, that intermodal competition in the London–Paris passenger market is present and seems to be stronger compared with other markets studied in the literature. Furthermore, the cross-elasticities as shown in Table 9 indicate that in the business segment, competition between London Heathrow–British Airways and London Heathrow–Air France, on the one hand, and Eurostar, on the other, is more fierce compared with the competition between Eurostar and London Luton-easyJet, whereas for the leisure segment the opposite is the case: we observe high cross-elasticities of market share, both for total travel time and weekly frequency, for London Heathrow–British Airways and London Heathrow–Air France, and lower figures for London Luton-easyJet in the business segment, and the other way around in the leisure segment. Appendix C.:. Market exit and the elasticity of market share with respect to frequency Following Pels et al. (2000) but using a (mixed) multinomial logit model, we specify the profit function of an airline as follows:

pi ¼ ðpi  cÞPi  k f i ;

ð4Þ

where pi is the generalised price, c is the marginal cost per passenger, k is the constant marginal cost of frequency, and Pi is the (mixed) multinomial logit probability. The existence of an equilib2 2 2 2 @ 2 pi 2 rium is guaranteed if @@ 2pp i < 0, @@ 2pf i < 0 and @@ 2pp i @@ 2pf i  ð@p Þ > 0. @f i

i

i

i

i

i

The first condition yields bp Pi < 0 and is always met; and the secb k2 ond condition yields bp P ðbf ð1  Pi Þ  1Þ < 0, where bp and bf are the i f coefficient estimates for fare and frequency, respectively. The term outside the brackets is necessarily positive, implying that the term inside the brackets needs to be negative, and therefore that bf ð1  Pi Þ < 1. The elasticity of market share with respect to frequency is determined as bf ð1  Pi Þ. Hence, we know that, if the elasticity of market share with respect to frequency exceeds 1, no equilibrium exists, i.e. the airline cannot maximise its profits. References Adler, N., Pels, E., Nash, C., 2010. High-speed rail and air transport competition: Game engineering as tool for cost-benefit analysis. Transportation Research Part B: Methodological 44, 812–833. Basar, G., Bhat, C., 2004. A parameterized consideration set model for airport choice: An application to the San Francisco Bay Area. Transportation Research Part B: Methodological 38, 889–904. Bhat, C.R., 1997. Covariance heterogeneity in nested logit models: econometric structure and application to intercity travel. Transportation Research Part B: Methodological 31, 11–21. Bierlaire, M., 2003. Biogeme: a free package for the estimation of discrete choice models. In: 3rd Swiss Transportation Research Conference, Ascona, Switzerland. Eurotunnel Group, 2011. Annual reviews. Accessible from . González-Savignat, M., 2004. Competition in air transport – the case of the high speed train. Journal of Transport Economics and Policy 38, 77–107. Harvey, G., 1987. Airport choice in a multiple airport region. Transportation Research Part A: General 21, 439–449. Hensher, D.A., Rose, J.M., Greene, W.H., 2005. Applied Choice Analysis: A Primer. Cambridge University Press, Cambridge. IATA, International Air Transport Association, 2003. Air/Rail Intermodality Study. Air Transport Consultany Services, Hounslow, p. 212. Ishii, J., Jun, S., Van Dender, K., 2009. Air travel choices in multi-airport markets. Journal of Urban Economics 65, 216–227. Koppelman, F.S., Wen, C.H., 2000. The paired combinatorial logit model: properties, estimation and application. Transportation Research Part B: Methodological 34, 75–89. OAG, 2011. OAG Historical Schedules. OAG Aviation, Dunstable. Ortúzar, J.D., Simonetti, C., 2008. Modelling the demand for medium distance air travel with the mixed data estimation method. Journal of Air Transport Management 14, 297–303. Park, Y., Ha, H.K., 2006. Analysis of the impact of high-speed railroad service on air transport demand. Transportation Research Part E: Logistics and Transportation Review 42, 95–104. Pels, E., Nijkamp, P., Rietveld, P., 2000. Airport and airline competition for passengers departing from a large metropolitan area. Journal of Urban Economics 48, 29–45. Pels, E., Nijkamp, P., Rietveld, P., 2003. Access to and competition between airports: a case study for the San Francisco Bay Area. Transportation Research Part A: Policy and Practice 37, 71–83. Skinner, R.E., 1976. Airport choice: an empirical study. Transportation Engineering Journal 102, 871–882. Gleave, Steer Davies., 2006. Air and Rail Competition and Complementarity. Office for Official Publications of the European Communities, Luxembourg. Thomas Cook, 2011. European Rail Timetable. Winter 2002/03 – Winter 2009/10 ed. Thomas Cook Publishing, Peterborough. Train, K., 2003. Discrete Choice Methods with Simulation. Cambridge University Press, Cambridge.