A LONG TERM MODEL FOR LONG DISTANCE TRAVEL IN FRANCE. Isabelle CABANNE Laboratoire d'economie des Transports ENTPE, Université Lumière Lyon 2, CNRS

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1 A LONG TERM MODEL FOR LONG DISTANCE TRAVEL IN FRANCE Isabelle CABANNE Laboratoire d'economie des Transports ENTPE, Université Lumière Lyon 2, CNRS 1. INTRODUCTION This paper models the evolution of long distance traffic in France by 2020 under different hypotheses on GDP growth and transport policies (level of extension of the high speed rail network and of the motorway network, change in gas prices, motorway tolls, rail and air fares). Long distance traffic in France has increased sharply over the last twenty years. Air traffic increased by 200%. Traffic on motorways increased by 150% (not taking into account the transfer of vehicles from the old trunk roads to the motorway network when a new motorway opens up). On the other hand rail traffic increased by 10% only, despite massive investments (1200 km of high speed rail track were built). This rapid growth of long distance travel, especially of the modes that pollute most, raises problems as far as the environment, infrastructure congestion and investment costs are concerned. It is thus important to model the evolution of interurban traffic and assess the long term impact of economic growth and transport policies on the national interurban traffic volume and its modal split. To do this, we estimate a time series model with data from the last 20 years. The explanatory variables are GDP, the average price per passenger.kilometre for each mode of transport and indicators of accessibility by rail and by motorway. Time series models have already been estimated for France. However these models are not fully satisfactory, at least those for rail traffic. The variable relative to train speed or to the length of high speed rail track was found to be insignificant, which is not realistic, and traffic changes obtained from the model do not always fit observed traffic variations very well. Time series models are often used for long term planning because long distance travel is well correlated with GDP growth and time series models enable to show this trend whereas models based on a single year survey lack dynamic information. However time series models also have some drawbacks. Explanatory variables are often trended and correlated which is a problem for calibrating coefficients. Only a few variables can be used and these variables are highly aggregated. In time series models for long distance travel the variable which describes the rail network is often a route length or an average train speed. But these variables are not necessarily appropriate. A certain amount of variation in the average train speed may correspond to very different variations of rail network performance. Reducing travel time by rail from 4 hours to 2 hours for an origin - destination has an important impact on rail/plane modal share. Reducing an origin destination travel time from 2 hours to 1 hour has less impact. Yet the average national rail speed and the total route length may vary in the same way in both cases. The same problem applies with rail and air transport fares. A change in pricing policy may induce a change in traffic that the change in the average fare and a constant

2 elasticity to average fare over the years may not show. In the models that we fit, we try and improve the models by using an accessibility indicator instead of an average train speed to take into account the change in rail network better and we introduce a dummy variable to try and take into account the changes in pricing policies (since we lack the necessary data to calculate a price indicator as in the train speed case). Apart from the problem of aggregated variables, the form of the models may be questioned. Should direct demand models or generation and modal split models be applied at this nationally aggregate level? Generation and modal split models are often used on Origin-Destinations but rarely at a national level. We test both model forms. First we present the background, the changes that occurred in long distance explanatory factors especially as far as transport networks and pricing policies are concerned. We then discuss the models and their results. 2. The explanatory factors for long distance and their evolution Before modelling long distance travel we must see what the main explanatory factors for long distance travel are. We must then see how these factors varied during the period used for calibrating the models (that is ) Long distance travel main explanatory factors The main explanatory factors for long distance are economic growth and transport supply (speed and prices). The yearly variations in national traffic volumes for each mode of transport, the variations of rail / air share from one origin destination to another and an analysis of the French 1993 Long Distance National Surveys where explanatory factors were decorrelated show these factors (economic growth / income level and transport supply) are the most important factors in explaining level of travel and modal share Changes in explanatory factors for long distance travel We present changes in economic growth and transport supply (networks expansion and prices). a. Economic growth Graph 1 shows the variations in GDP over the last twenty years.

3 1,60 Graph 1. GDP variations 1,40 1,20 1,00 0, Source : INSEE b. The development of the motorway and high speed rail networks Between 1979 and 1999, 3000 km of motorways were built expanding the network from 4000 km to 7000 km. In 1980, there were no high speed trains in France. Between 1981 and 2001 over 2000 km of high speed rail tracks were built, reducing travel times dramatically (Table 1). Table 1 : Travel time by rail from Paris to France main cities Population in (millions) Lyon h45 2h 2h 2h 2h Marseille h40 4h40 4h40 4h20 3h Lille h 2h 2h 1h 1h Bordeaux h 4h 3h 3h 3h Toulouse h 6h 5h05 5h05 5h05 Nantes h15 3h15 2h 2h 2h Nice h10 7h15 7h15 6h30 5h40 Strasbourg h50 3h50 3h50 3h50 3h50 Grenoble h20 3h10 3h10 2h50 2h50 Rennes h55 2h55 2h 2h 2h Source : SNCF Further expansion of the rail network is planned so as to reduce travel times towards the East of France (Strasbourg will be 2h20 from Paris in a few years time), and towards the South-West (-40 minutes between Paris and Bordeaux and Toulouse). c. Prices Prices are considered without inflation. Road travel costs decreased sharply between 1979 and Gas prices decreased dramatically (-20% in 1986). The share of diesel cars increased during the period. Diesel being cheaper than regular gas that helped bring down road travel costs. Car consumption was reduced between 1979 and 1999 (which may not be the same in future years since the increase in average car weight may balance technology

4 improvements). INRETS (Institut National de Recherche sur les Transports et leur Sécurité) calculated a gas price per car.km taking all three trends into account. That indicator fell by 28% over the period (not taking inflation into account). Tolls remained relatively stable (not taking inflation into account). Gas prices per car.km + tolls thus decreased. Gas prices and tolls per car.km are about the same all over the country. The average rail fare per passenger.km remained about constant (without inflation) except for two changes : there was an increase in the average rail fare in the early 1990s (+10% between 1989 and 1993) before a fall in 1994 (-5%) and there was another increase in the late 1990s (+5% between ) (calculated from data from [SNCF, annual]). The average rail fare varied but its structure varied even more. Within the last twenty years, SNCF (the French Railways Company) increased fares on short distance trips but decreased them on long distance trips. During the last decade SNCF has tended to increase fares on origin-destinations where rail is the most efficient mode of transport but decrease them on origin-destinations where there is harsh competition between rail and air or between rail and road. For example when high speed trains were introduced between Paris and the West and South West of France in 1989/1990, SNCF first increased its fares on all origin-destinations before bringing them down for Paris - Bordeaux (where travel time by rail is still 3 hours so plane is still quicker), keeping them stable for Paris - Le Mans (which is only 200 km away from Paris and that makes travelling by motorway still an option even for one-day to and back trips) but increased them a lit bit more for Paris - Nantes (which is 380 km and 2 hours away from Paris by rail; plane and road are not competitive) [SNCF, 1998]. Apart from adapting its pricing policy to origindestinations, SNCF has introduced yield management during the 1990s. Air fares decreased dramatically over the period (-25% between 1979 and 1999). The sharp drop took place mostly during the 1980s. However even if the average fare varied less during the last decade, there were changes in pricing policy with more yield management. 3. THE MODELS AND THEIR RESULTS To model long distance travel we must first define the traffics used and then the variables. We then present the models and their results Definition of the traffics taken into account : measuring road traffic "at stable network" Air traffic is measured by the number of air passenger.kilometres and rail traffic by the number of rail passenger.kilometres but the increase in car traffic on motorways is measured in a different way. The number of car.kilometres on motorways is not a good indicator because in 1980 the motorway network was small therefore the increase in the number of vehicles on motorways mostly shows the transfer of cars from old trunk roads to new motorways and not a real increase in the use of car for long distance trips. Instead we use an indicator of traffic variation at stable network : each year the percentage of traffic growth is calculated at stable network length on

5 the network that existed 2 years before. Graph 1 shows changes in these traffics between 1979 and Graph 1. Traffics on motorways, trains and planes (passenger.kilometres or car.kilometres) motorways (stable network) rail air Definition of the aggregated variables In the model we take into account economic growth and transport supply (improvements in the motorway and rail networks and car, rail and air prices). Economic growth is modelled with GDP. The real problem is with the definition of the transport supply variables. Expansion of the motorway and rail networks are often modelled with a total route length or an average train speed. Prices are taken into account as an average price per passenger.kilometre. If these indicators vary "homogeneously" there is no problem. If not it is necessary to try and take into account changes in the structure of speeds or prices (if the necessary data is available). a. The motorway network The motorway network is usually modelled as a network length. When improvement in a network is modelled with a total route length it is assumed that lengths of network are built from the most useful to the less useful and that the decrease in utility is of the type : L a (with L the network length and a a constant) since network lengths are usually introduced in model formulae by a term of the L b type. But a "break" may happen : the first few thousand kilometres are main trunk roads and have a high utility, the next few kilometres are of much less utility and there may be a "break" in utility between the two. To see whether we can model the motorway network by its route length we check that there is no break in motorway utility. The number of cars per motorway kilometre is an indicator of the utility of the section. The French motorway network is divided up into sections. We have the number of car.kilometres for each section for the year We also know the year when the section opened up and the length of the section. We are thus able to see the variation in the number of cars per motorway kilometre on a base year (1999) according to the length of the motorway network that was already built when that kilometre opened up. This shows the change in the utility of the sections according to the length of motorway already built. The number of cars per kilometre decreases with the length of motorway network already built, which is

6 rational. The decrease is rather even, with no obvious break (apart from the first 1000 or 2000 km where the number of cars per kilometre varies erratically). The number of cars per motorway.kilometre may be modelled by : If L<1000km : E(L) = C with C = cars/day If L>1000km : E(L) = a * L -b with a = ln(14.50) et b = 0.59 L is the length of the motorway network and E(L) is the number of cars per motorway kilometre on the L th kilometre. (R² = 0.57 which is OK for a regression on spatial data). The utility of the motorway network (Nm) can then be defined as : N m (L) = L 0 E(L) dl If L<1000km : Nm = C'L with C' = 1 If L>1000km : Nm = C'' + a"l b'' with C"=-1429; a"=141.5 et b" = This indicator Nm is used in the models instead of the usual L variable. b. The rail network Change in the rail network is often modelled by an average train speed indicator. We have 1992 data about traffics between zones (in a 22 zoning system) for each mode. We can calculate an average speed indicator for each year by averaging rail speeds for the various origine-destinations with traffics between zones as weights. We do not take all origin-destinations into account; origin-destinations between adjoining regions are not taken into account since they are virtually unaffected by high speed rail and average speeds are not very precise; we then keep main traffics only. However this indicator may be questioned since this average speed does not take into account the impact of speed structure over space. If rail speed varied homogeneously over space an average rail speed indicator would do. However this is not the case. Speed variations are heterogeneous and the impact of a reduction in average speed very much depends on whether it is applied on a 4 hour origindestination or a 2 hour origin-destination. High speed rail takes much traffic away from the plane but the change in rail / plane modal share very much depends on the starting travel time on the origin-destination [Claisse, Klein, 1997]. When rail travel time is 5 hours or more, rail modal share is about 20% and does not vary much whether it is 5h or 7h, when rail travel time is about 4 hours rail modal share is about 40%, for 3 hours it is 60%, for 2 hours it is 90% to 95% and for 1 hour it is 100%. Calculating an average speed gives too much importance to reductions in travel time that take place in origin-destinations of over 5 hours or in origin-destinations below 2 hours. To take this into account we calculate an accessibility indicator that represents not an average speed but an average impact of travel time. For this we use a simple indicator denoted Nt that averages "lopped" speeds between origin-destinations : Nt = Σ ij (T ij / T) * s ij ij are the origin-destinations T ij are the traffics by air or by rail between i and j in the year 1992

7 T is the sum of the T ij s ij are the lopped speeds; we lop travel times at 2h and 5h (if travel time is between 2h and 5h we keep it as it is, if it is below 2h it becomes 2h, if it is above 5h it becomes 5h); the lopped speed s ij is the inverse of this lopped travel time. Notes : - It is possible to calculate slightly more elaborate indicators but they have proven to be equivalent to Nt when introduced in the models. - T ij is the traffic by either air or rail and not just rail so that the weight of the ij origin-destination does not depend on whether high speed rail was already introduced in 1992 or not. c. Prices Gas prices vary homogeneously over France and tolls per car.km are also about the same and have varied homogeneously. Modelling travel price by motorway by an average price per car.km is thus all right (there is no need to worry about a structure problem). To model car travel price we use the INRETS gas price per car.km described above and the average toll price from ASFA (Association Française des Sociétés d'autoroutes). Total travel price by motorway is obtained by adding the average gas price and the average toll price. An average rail fare per passenger.kilometre can be estimated by dividing SNCF annual revenue from ticket sales by the number of passenger.kilometers. However this indicator may be questioned since price structure strongly varies over time. According to the MATISSE model [INRETS, 1997] average rail fares increased by 0.1% per year between 1980 and 1992, and yet induced an increase in rail travel of 0.4% per year, because fares increased on short distance trips but decreased on long distance trips. It would be interesting to be able to calculate a price structure indicator that would model the impact of a change in pricing policy but we do not have access to the necessary data. However we know that a change in the SNCF pricing policy took place in 1997/1998. To take that effect into account we introduce a dummy variable P, which is 0 before 1997, 0.5 in 1997 and 1 from 1998 on. Up to 1997 (when Air France and Air Inter merged) average air fare per passenger.kilometre can be estimated by dividing Air Inter annual revenue from ticket sales by the number of passenger.kilometers. For the variations from 1997 on we use an air price indicator calculated by INSEE (Institut National de la Statistique et des Etudes Economiques); however this indicator is calculated under a different basis and does not take very well into account special offers. The P indicator presented above may take some of the effect of the change in the estimation method of average air fares The models, their calibration and their results Two types of models are tested: direct demand models and a generation and modal split model. The explanatory variables in both models are the variables we have just described : GDP, the average price per passenger.kilometre for each mode of transport, the indicator for pricing policy change P, the indicator of accessibility by rail

8 Nt, the indicator of accessibility by motorway Nm. We first test direct demand models, which are the most commonly used models for modelling traffic at a national aggregate level. We then model the traffics with a generation and modal split model. This type of models is very often used on origin-destinations but not very often at a nationally aggregate level. Using them at a national level is difficult because there is an aggregation problem. However they correspond better to the way the economic market works : economic growth and change in transport supply explain total demand and change in transport supply and change in the value of time (linked to economic growth) explain market share. a. The direct demand models Traffics at a national level are usually modelled thanks to direct demand equations. T i = K * V 1 a1 * V n an with T i traffic of mode i, V 1 V n the n explanatory variables and a 1 a n the elasticities. Several models were tested. All coefficients must have the right sign and be significantly different from 0, otherwise the variable is rejected. The R² and the Durbin-Watson must be all right. We present the final equations for the direct demand models. Tm : traffic on motorways Ta : traffic by air Tt : traffic by train Pm : travel price by road per car.kilometre Pa : average air fare per passenger.kilometre Pt : average rail fare per passenger.kilometre Nm : accessibility indicator for the motorway network Nt : accessibility indicator for the rail network P : the variable for policy change in 1997 described above D : trend variable that takes into account the expansion of air travel in the 1980s (it is ln(1) in 1980, ln(2) in 1981 ln(11) from 1990 to 1999 and after). Equation for motorway traffic ln(tm) = -9,55 + 1,30 ln(gdp) 0,59 ln(pm) + 0,74 ln(nm) (7,3) (5,7) (5,0) (3,5) R² = 0.99; DW = 1,51; no autocorrelation Equation for air traffic ln(ta) = -9,10 + 1,48 ln(gdp) + 0,12 D 0,77 ln(pa) + 0,99 ln(pt) 0,026 P 0,16 ln(nt) (16,3) (20,9) (14,5) (9,3) (6,2) (4,2) (3,0) R² = 0.99; DW = 1,80; no autocorrelation Equation for rail traffic ln(tt) = 5,88 + 0,21 ln(gdp) 2,00 ln(pt) + 0,055 P + 0,45 lnnt (10,4) (1,6) (6,4) (2,9) (4,9) R² = 0.88; DW = 0,62; autocorrelation For motorway traffic, only variables relative to road travel prove to be significant. That was to be expected. Cross elasticities depend on the modal shares of the other modes and rail and air modal shares are small. (The fact that other modes have little

9 impact on motorway traffic is confirmed by other studies [INRETS, 1997]).The statistical tests are good and there is good proximity between observed and modelled traffic. A direct demand equation seems to be a good enough model for motorway traffic. Elasticity of motorway traffic to GDP is 1.30, the elasticity for motorway price (gas + tolls) is 0.60, the elasticity for motorway network utility is 0.74 and thus the elasticity for the motorway network length is There is a break in air traffic in 1990 that neither GDP nor transport supply can explain. This may be due to the fact that air transport was still relatively new in the early 1980s; there was a spreading of its use in the 1980s. The 1990 break may also be due to the fact that direct demand models may not be well suited to model the start of a mode of transport that is increasingly taking away shares from the rail. To take the break into account we had to introduce a trend variable : the D variable. After having introduced this variable the DW becomes very good. All coefficients have the right sign and are significantly different from 0. There is little interaction between road and plane so there are no variables relative to road travel. Elasticity to GDP is very high : 1.5. Elasticity to air fare is 0.77 and elasticity to rail fare is Elasticity to the rail network accessibility indicator is Observed traffics and modelled traffics are very close to each other. Rail traffic is modelled with rail variables only. There is strong competition from plane and motorways so plane and motorway variables should have been among the variables used in the equation. On the other hand we only have 21 observation points. If all expected variables are in the equation there are too many variables compared to the number of observation points. Direct demand models demand that traffics should depend on few explanatory variables. Rail travel being under harsh competition from both the plane and road, it is not the case. The average air fare is not a perfectly reliable variable (its calculation method varied over time) and air modal share is smaller than the rail's (which diminishes cross elasticity to air fare) so that may explain why it is difficult to estimate it and why it was insignificant. Expansion of the motorway network is correlated with GDP growth so that may explain why it does not appear in the equation together with GDP. Apart from these "missing" variables, the DW statistic is not very good. When comparing observed and modelled traffics we see that the problem comes from the 1993 to 1996 period where modelled traffics are higher than observed traffics. This may be due to two events not taken into account in the model : the booking system SOCRATE introduced in 1993 did not work well at first, which led passengers away, and on December 1995 there was a one month strike. We corrected traffics by adding to the 1995 rail traffic the number of passenger.kilometres the SNCF claims to have lost due to the strike, however the December strike probably had consequences on the medium term; it sometimes takes time for passengers to come back. Rail elasticity to GDP is 0.21 only, elasticity to rail fares is 2.0, elasticity to the rail network is However we must be very cautious with these elasticities. Also we must keep in mind that a direct demand model assumes that elasticities are constant, which is likely to be true for motorways or air; for rail the introduction of high speed trains may change the elasticity. Direct demand equations model well motorway and air travel. With rail travel it is not so. Direct demand equations model well modes which do not suffer too much from competition from other modes (like motorways) : elasticities are then likely to be

10 stable (no change in passenger profiles). When a mode suffers from harsh competition the form of the direct demand model does not necessarily correspond to the variations in traffic and traffic elasticities may not be stable. Also direct demand models require few variables, which is not the case in the rail case, where variables from all 3 modes should appear. To model rail better we now test generation and modal split models. c. The generation and modal split models Generation and modal split models are not very often used at a national level but they are often used for modelling traffic on origin-destination pairs. Of course using modal split models in the case of three modes (even on OD pairs) is rather difficult. Multinomial logits do not perform well because of their IIA property (introducing a high speed train would take away the same percentage of people from the plane and from the road, which is not realistic). For that reason we will not use multinomial logits. Since motorway traffic growth is little influenced by air or rail competition, we keep the direct demand equation to model motorway traffic growth. As for rail and air traffic there is competition between the two : modal share is influenced by the relative speeds of train and plane, the relative prices and change in the value of time (which is due to change in traffic growth). To model rail and air, we first model traffic by train + traffic by plane with a direct demand equation. We then model modal split with a logit model where the explanatory factors are GDP and rail and air transport supply. Competition between rail and road appears through GDP. For example, in the modal split equation GDP represents both the increase in the value of time which tends to make some people shift from train to plane but it also represents the increase in the value of time which tends to make some other people shift from the train to the motorway (and thus makes train modal share within train + plane traffic decrease). The abbreviations are the same as the ones used in the direct demand equations. We use another abbreviation : Pat : average fare per passenger.km for air and rail : Pat = (Pa*Ta+Pt*Tt)/(Ta+Tt) We tested several equations. In the modal share equation we tested variables without a logarithmic form and with a logarithmic form. The final equations are : Generation equation : ln(ta+tt)= 1,06 + 0,69 ln(ta+tt) ,23 ln(gdp) 0,61 ln(pat) + 0,073 ln(nt) + 0,023 P (14,9) (17,2) (5,9) (10,1) (2,9) (6,1) Modal split equation without a logarithmic form ln(ta+tt)= - 3,78 + 0,00034 GDP + 0,13 Pt - 0,0014 Nt 0,025 Pa 0,11 P (20,6) (8,0) (7,1) (2,4) (9,2) (8,2) DW=1,50 Modal split equation with a logarithmic form ln(ta/tt) = -11,21 + 0,90 ln(gdp) + 3,09 ln(pt) - 1,56 ln(pa) - 0,16 ln(nt) - 0,10 P (9,5) (5,5) (7,8) (8,7) (1,9) (6,8) DW = 1,6

11 Contrary to direct demand equations generation and modal split models enable elasticities to vary over time. We calculated these elasticities for the year The models with and without a logarithmic form gave about the same results. Air traffic elasticity to GDP is 1.4 to 1.7 (the same as in the direct demand equation 1.5). Air traffic elasticity to rail price is 0.70 to 0.85 (much the same as in the direct demand equation 1.0). Air traffic elasticity to air fare is much higher (-1.4 to 1.6 instead of 0.8). Air traffic elasticity to rail speed is different; it is almost nihil (0.04 to 0.10) and of a sign contrary to what it should be (it should be negative; in the direct demand equation it was 0.16). Rail traffic elasticity to GDP is higher (0.42 to 0.53) to what it was (0.21) in the direct demand equation. Rail traffic elasticity to rail network accessibility is smaller (0.3) instead of Rail traffic elasticity to rail fares is about the same (-2.2 instead of 2.0). Rail traffic elasticity to air fares is very small and of the wrong sign (-0.10 to 0.15; in the direct demand equation it was unsignificant). 4. SUMMARY AND CONCLUSION In this paper we have calibrated time series models on yearly data on long distance traffic for France. Time series models have some drawbacks. They require few explanatory variables and the variables are highly aggregated. When the explanatory factor varies homogeneously over space it does not matter to have an aggregated variable (that is the case of gas prices and motorway tolls). When the explanatory factor varies heterogeneously spatially, a same amount of variation in the average variable may correspond to various changes in the network or price structure and thus have varying impacts on traffic. To tackle the problem, instead of using an average train speed, we have calculated an accessibility indicator for the rail network that "cuts off" travel times before averaging them so as to take into account the structure of travel time between French cities and the varying impact of travel time reduction according to initial travel time. We also replaced motorway route length by an indicator estimating motorway utility from variation of traffics per kilometre on a base year (1999) according to the age of the road section. For fares it was not possible to calculate a price structure impact indicator for lack of the necessary data, but we used a dummy variable to take into account a change in pricing policy in 1997/1988. Another question about time series is the model structure that may be use : direct demand models or generation and modal split models? Direct demand models model well motorway and air traffic but they have proven not to model so well rail traffic. A generation and modal split model was then used to model air and rail traffics. The direct demand models and generation and modal split models give results not very far apart. GDP elasticity is higher than 1 for air and car traffic (1.5 for air traffic and 1.3 for traffic on motorways) but it is much smaller for rail traffic (0.3 to 0.5). Expanding the motorway network has an important impact on motorway traffic growth : the elasticity for the motorway network length is 0,30. The elasticity of motorway traffic for the price of motorway travel (gas + tolls) is 0,6. The impacts of the expansion of the high speed rail network and of the evolution of rail fares on motorway traffic growth are not significant. The elasticity of rail traffic to our railway network accessibility indicator is 0.30 to The elasticity of air traffic to railway accessibility is small and

12 not always significant. It is difficult to produce air and rail fare elasticities : SNCF improved its commercial policy, putting a yield management policy into place, which drew some traffic despite the relative stability of the average rail fare over the period; much the same problem applies with air fares. Of course one may be cautious about some elasticities (those relative to fares for example) and we may regret that we were not able to produce a reliable cross elasticity of air traffic for rail network accessibility for example. However the hierarchy in the importance of explanatory factors is the same as that obtained from other models calibrated on long distance travel in France sometimes with very different methods [INRETS, 1997]; the elasticities that we were not able to produce correspond to factors that have small impacts. Our main elasticities are of the same size (or even equal) as the ones produced by the other models. This modelling enables us to draw some conclusions about the evolution of long distance travel by Economic growth is bound to have a great impact on motorway and air traffic in future years and an expansion of the high speed rail network will not be able to change the upward trend in air traffic growth or in motorway traffic growth. We used this model to produce estimates of long distance traffic evolution in the next twenty years. Depending on the assumptions made on economic growth, the extent of rail and road networks and the evolution of gas prices and air and train fares, air traffic increases by 90% to 180%, rail traffic by 10% to 60%, motorway traffic by 60% to 130% between 2000 and The gaps between the lowest and highest evolution rates are mainly due to the gap between a low and a high GDP growth hypotheses.

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