Why Does TGV Ridership Overperform Models?
I’ve found some TGV ridership data with which I can check the model I use for high-speed rail ridership projection. The model is trained on Japanese data and has flaws in Japan too, but I’ve wanted to see how well it ports to Europe, where I don’t have as complete a dataset of ridership between pairs of metropolitan areas. Thankfully, I have just found a short Omnil report from 2015 about intercity rail ridership at the Parisian terminals, from which we can extract some information. The TGV overperforms the model substantially; this can be explained with fudge factors, but those fudge factors only work if we assume that the aspects of the TGV that seasoned rail advocates hate don’t matter much.
The model
As a reminder, the model posits that the annual ridership in millions between two metropolitan areas with populations and
in millions, of distance d kilometers, is,
The model is very accurate for ridership between Tokyo and other cities on Honshu; it overpredicts inter-island ridership, but becomes correct if we replace the Japanese air/rail modal splits with European ones, where taking the train over five hours is more normal than in Japan. I would expect that in isolation, European ridership should overperform it, because fares here are much lower, about 0.10-0.11€/kilometer compared with about $0.23/kilometer on the Shinkansen. French ridership significantly overperforms, beyond what the fares alone can explain, as we will see.
We will need to modify the model as written above for the French case anyway. TGV ridership relies on direct through-service from Paris to every city in France, including many that are not on the network of dedicated high-speed lines (called LGVs); trains serve those by diverting from the LGVs to classical lines, on which they travel more slowly. Therefore, while we can apply the model as above for connections that entirely use LGVs, like Paris-Lyon or Paris-Marseille, we need to consider the slower speeds for connections that use classical lines. For those, we assume that trains average 220-225 km/h; this is the rough average speed of the express Shinkansen trains as well as that of the TGVs to Lyon and Marseille. Thus, the model, at travel time t, is,
The floor of 500 km, or in this case a trip time of hours, is empirical in Japan. But then it is clear, from Italian data, that speeding up the trip has a roughly square-law effect on ridership, even within the limit – the growth in ridership on Bologna-Florence is consistent with an even higher elasticity of ridership with respect to average speed. The best way to reconcile these two observations is that in the presence of high-speed rail, the effect of distance cancels out the effect of better competition with the car up to about 500 km, but if the trains are slower, the car is more competitive and this is seen as a square law at all speeds. This is not too relevant to France, but is useful context for medium-distance, medium-speed lines in Germany.
TGV ridership
I have never been able to find city-to-city or station-to-station ridership figures in France. The Omnil report is no exception: it reports ridership at the Paris stations and breaks down where people are going by region of France in the geography of 2015, before the merger of some regions.
The total ridership at the Paris stations, including TGVs, low-speed intercity trains, and other regions’ regional trains (TERs) but not Paris-area regional trains (Transilien), is 443,000/day; of those, the TGVs comprise 239,000 and the slow trains 204,000. The four Parisian terminals with TGVs – Gare de Lyon, Gare du Nord, Gare Montparnasse, Gare de l’Est – have 92% of the TGV ridership in the region, while the other 8% are at suburban stations on bypasses around the city, like CDG Airport. Ridership is asymmetric: two-thirds of those 443,000 daily riders don’t live in Ile-de-France, which is what we should expect of a commuter-heavy ridership profile. Within Ile-de-France, 63% of passengers originate or are destined to Paris itself and another 21% for the Petite Couronne suburbs, showcasing destination centralization – Paris is only 17% of regional population and about 33% of regional employment, but 63% of those interregional and intercity trips go there and not to the suburbs.
There is also a breakdown of where passengers are connecting, by region of France or country. Picardie is increasingly an exurb of Paris, to the point that as France was debating the merger of regions in the early 2010s, one proposal was to detach its southernmost department, Oise, and attach it to Ile-de-France; 19% of the non-Francilien passengers originate there and 10% of Franciliens go there, for a ratio of nearly 4:1. More relevantly to high-speed rail, Rhône-Alpes is 9% of both non-Francilien and Francilien ridership, for a ratio of about 2:1, and a total of about 40,000/day, or around 13 million/year. PACA is 5% of non-Francilien and 7% of Francilien ridership, for a ratio of about 1.4:1 and a total of 25,000/day or around 8 million/year.
So we need to evaluate our model against an observed ridership of 13 million between Paris and Rhône-Alpes, and 8 million between Paris and PACA. Both sets of numbers involve multiple city pairs, with fairly long tails: France is a country of small metro areas, the median person living in a metro area of 330,000, whereas half of Japan lives in the metro areas of Tokyo (37 million), Osaka (18 million), and Nagoya (9 million).
French metro areas and the model
France recently changed its definition of metro areas. The old one, the aire urbaine, was similar in definition to the American metropolitan statistical area; the new one, the EU-wide functional area, generally spits out slightly larger numbers, though it still seems tighter than the Japanese definition. The functional area of Paris, comprising Ile-de-France, about half of Oise, and surrounding communes, has 13.2 million people. The new definition splits Nice and Cannes apart, which is good, since both have TGV service to France.
| Metro city | Population | Trip time | Prediction |
| Lyon | 2.29 | 1:58 | 4.586 |
| Grenoble | 0.72 | 3:01 | 0.999 |
| Saint-Etienne | 0.5 | 2:58 | 0.771 |
| Geneva (French part)* | 0.44 | 3:13 | 0.485 |
| Annecy | 0.3 | 3:45 | 0.321 |
| Chambéry | 0.26 | 2:52 | 0.49 |
| Valence | 0.26 | 2:12 | 0.805 |
| Bourg-en-Bresse | 0.14 | 1:50 | 0.49 |
| Marseille | 1.88 | 3:07 | 2.02 |
| Nice | 0.62 | 5:48 | 0.24 |
| Toulon | 0.58 | 4:02 | 0.47 |
| Cannes | 0.39 | 5:18 | 0.199 |
| Avignon | 0.34 | 2:40 | 0.701 |
The Rhône-Alpes metro regions combine to a predicted ridership of 8.95 million; actual ridership is higher by about 50%. The PACA metro regions combine to a prediction of 3.63 million; actual ridership is higher by a factor of maybe 2.2.
Note that the prediction is already based on some optimistic assumptions. The trip time is the best that can be sustained multiple times a day; the issue of frequency is ignored, so the effective trip time on connections from Paris to cities like Annecy with a train every three hours gets no malus, even though the Japanese city pairs that the model is trained on get multiple express trains per hour. This is relevant, because as we examine fudge factors below to rescue the model, we need to keep ignoring or at best minimizing the malus due to poor frequency and lack of trip spontaneity in the ticketing system.
Fudge factors explaining the overperformance
We need to explain why Rhône-Alpes overperforms by 50%, and PACA by more than 100%.
Fares
The average JR East Shinkansen fare revenue in 2020-1 was ¥23.8/passenger-km (source, PDF-p. 50), and has risen little in the last 10 years. The average TGV fare revenue in 2019 was 0.10€/passenger-km (source, pp. 16 and 20) and has likewise little changed in nominal terms. These differ by a factor of 1.6. The elasticity of high-speed ridership with respect to price varies widely by study; the Italian study linked above says -0.37, one Spanish study says -0.59, and Börjesson’s lit review says -0.59 for non-business trips and -0.72 for business trips. A value of -0.5 explains a factor of 1.27 overperformance by itself; a value of -0.6 explains a factor of 1.33.
In fact, Germany, charging similar average intercity rail fares to France, seems to overperform the Shinkansen model too. I have little data here, only line-wide Berlin-Hamburg and Berlin-Munich, both of which look like they overperform by about 20%. This can result from a 30% overperformance mitigated by the issue of lower speed: the modeled prediction is based on trip times, but when trips are shorter than about 2:15, the model stops seeing the impact of slowdowns – Berlin-Hamburg is 1:44 and Berlin-Leipzig is 1:13, where at Shinkansen or TGV speeds they’d be 1:17 and 0:45 respectively.
Metro area size
French metro area definitions, even with the new functional areas, are somewhat tighter than Japanese ones. The functional area of Berlin has 5 million people, but reckoned the Japanese way (1.5% of the age 15+ population commuting to the central city), practically all of Brandenburg would count, a population of 5.7 million in total. This is likely more significant in PACA, where the above-listed metro area are 80% of the total population, than in Rhône-Alpes, where they are 90%. It’s possible even Paris is a bit bigger than 13.2 million – but only a bit, since Ile-de-France and Oise together only have 13.1 million. This factor can scrounge some extra ridership, but probably no more than 10%, maybe a bit more in PACA.
Leisure travel
Provence is renowned for its tourism, which generates extra trips out of Paris beyond what we should expect from population alone. This should disproportionately affect Nice and Cannes; for what it’s worth, I’m seeing seven weekday trains from those cities and Toulon to Paris, I believe all skipping Marseille, and 14 trains from Marseille; if we take ridership as proportional to the offer, this does show some Riviera overperformance relative to Marseille, though not by much.
Of course, the majority of Paris-PACA ridership comprises Provençals, not Franciliens. But perhaps the 1.4:1 ratio of Provençals to Franciliens is atypically low, and the 2:1 ratio in Rhône-Alpes is more normal of capital-province relations; I have no Japanese numbers on this, and would overall expect to see similar asymmetries in both countries, given their similar level of economic capital-centricity. If 2:1 is typical, then the extra leisure ridership from the capital to make it 1.4:1 adds a total of 14%, which is far less than PACA’s overperformance relative to Rhône-Alpes.
Metro area coverage
The PACA cities have multiple stops. The population distribution in the Riviera is linear, and multiple cities with extensive leisure (like Saint-Tropez) are served by the TGV. Marseille likwise has a second stop at Aix-en-Provence, close by car to its northern suburbs to the point that I’ve heard it called Marseille-bis. If we split metro Marseille’s population 2:1 between Marseille and Aix, then the 0.8 exponent in the model produces a 14% increase in ridership. 14% and another 14% from leisure combine to 31%, which explains the majority of the PACA overperformance relative to Rhône-Alpes.
Competition with air in small cities
The TGV competes with cars and planes; domestic buses are almost a non-factor, and were entirely a non-factor in 2015 (they’re called Macron buses because it was Macron, as minister of economics in 2014-6, who passed the reform that allowed them). In Rhône-Alpes, competition is entirely with the car: Lyon is just close enough to Paris that air travel can’t compete; in PACA, competition is mostly with the plane, especially beyond Marseille.
The population distribution in both Rhône-Alpes and PACA may favor the train. The issue is that the secondary cities of Rhône-Alpes are around three hours from Paris, at which point the train is strongly favored but planes normally still exist, as in Marseille. However, those cities are scattered all over the region, and so there is no single airport that could serve them, except Lyon – and if the choice is to take the train for three hour or to drive an hour to Lyon-Saint-Exupéry, then the train can just demolish air competition.
In PACA, the same is true for the secondary cities. Nice has a strong airport with many flights to Paris, buoyed by the leisure market, but Toulon and Avignon don’t; on the eve of corona, Toulon-Hyères had 500,000 passengers a year, most not bound for Paris.
I believe this effect on air-rail competition is more significant in Rhône-Alpes than PACA. However, air competition is overall more significant in PACA than in Rhône-Alpes, and thus it likely effects a similar boost to TGV ridership in both regions, or perhaps is more significant in PACA, explaining the remainder of its overperformance.
Some conclusions
I don’t think the TGV’s overperformance of the model invalidates the model. Most of the overperformance in Rhône-Alpes can be explained by fares alone, and I think the rest can be explained by the modal split versus air being more favorable than in Japan given the small size of Annecy, Saint-Etienne, and so on. Most of the overperformance in PACA relative to Rhône-Alpes can then be explained by leisure travel and the good metro area coverage of the TGV thanks to Aix and the linear population distribution of the Riviera. However, these fudge factors have implications for rail planning in France, Europe, and beyond.
Connections to smaller cities
The modeled prediction is that Lyon and Marseille comprise little more than half the ridership to Paris from their respective regions. Moreover, the overperformance of TGV riderhip relative to the hinkanssen model likely comes disproportionately from smaller cities, due to their lack of good air connections. This underscores the importance of good service not just to million-plus metro areas but also to the tail of metro areas of half a million, give or take. Those metro areas are less important in rich Asia or the US, but are important throughout Europe.
This service to smaller cities can take the characteritic of TGV-style direct connections to Paris on classical lines. In Switzerland, the Netherlands, Austria, and increasingly Germany, service to smaller cities is provided through timed connections at carefully-chosen nodes; the Swiss network particularly excels at this. But the French system’s ridership is such that it not obviously inferior, and is unlikely to be inferior to the German system at all. Thus, a country like Poland or Britain can safely choose between the French and German system, or even mix them.
The issue of frequency
The low frequency of TGV services to smaller cities – trains run every two to three hours, often timed to just miss regional trains – should be visible as a serious malus to ridership. But it isn’t. Perhaps it exists and countermands the effect of lack of air competition to cities the size and distance class of Grenoble – but Grenoble is not Nice, and air competition there even under more favorable scenarios to planes would be second-order.
At the same time, there are markets where the TGV is visibly much weaker. The TGV’s modal split between provincial regions is not good. Because trains from Paris to Marseille don’t stop at Lyon, and trains from Paris to Lyon don’t continue onward to Marseille, the Lyon-Marseille city pair cannot piggyback on strong connections to the capital the way same-side pairs of provincial Japanese cities can. The dedicated Marseille-Lyon trains have an inexplicable six-hour gap, with frequent service on both sides of it, and the Toulon-Lyon trains are even worse. The modal split is evidently weaker – in 2009, nearly everyone drove betwen Lyon and Toulon (the 2023 number in the link are speculation for what if an LGV is built to Nice), even over a rail-friendly distance of about 390 km, averaging around 130-150 km/h.
So while the system that centers direct trains to Paris is not suspect, the lack of frequency on shorter connections between secondary cities is. This could be resolved with buying rolling stock that makes boarding and alighting faster, with two door pairs per car rather than just one; TGV connections not including Paris run local, and since the trains are not optimized for many stops, those connections have low average speed, which in turn discourages SNCF from providing more frequent local connections.
Liberalization
The EU is increasingly forcing national railways to allow on-rail competition. This is an idea imported from the UK, where John Major’s privatization of British Rail split up operations and infratructure, the latter eventually renationlized; in Japan, privatization broke up JNR into regional JR companies, each responsible for both infrastructure and operations as in the pre-nationalization era of rail, and in the US, the breakup of Conrail likewise restored the pre-nationalization status quo. SNCF resists the mandate for competition in increaingly spiteful ways: it makes up excuses why RENFE can’t operate on its network, and where it does operate, it won’t even let its crew use break rooms at French stations. Eurocrats, even more progressive ones, treat SNCF as public enemy #1.
And SNCF’s anti-competitive monopoly on domestic rail travel generates high rail ridership. Italy and Spain have both seen sharp increases in ridership from the competition mandate. But Madrid-Barcelona, offering worse frequency and a more broken market than the domstic TGVs (domestic TGVs are split just between lower-price OuiGo and higher-price InOui brands; Spanish high-speed trains have more classes of train on thinner markets), don’t perform nearly so well. Madrid-Barcelona riderhip in 2019 was 4.4 million; the modeled prediction is 4.1 million for this city pair alone, and 6 million including intermediate trip to Zaragoza. Riderhip ha risen since the introduction of competition in 2020, and media coverage has been laudatory, and at times depreating of France for failing to liberalize – but the 50% growth in ridership cited in most articles still leave the line barely overperforming the high-fare Shinkansen and strongly unerperforming the TGV.
European media should be less credulous of promises of private-sector efficieny and recognize that the TGV’s model of public-sector monopoly, with integration between infraatructure and service (even if this means shoving direct trains to Paris on trunk line rather than building a Swiss integrated timed transfer system), produces better outcomes than competition. Germany has the same model too and, relative to how slow its trains are, has good outcomes too; Switzerland, the undisputed leader of European rail ridership, resists privatization entirely. Private competition did not invent high-speed rail, and where it has been introduced it has so far failed to produce outcomes on a par with what the TGV has with entirely public operations.





