Go north or don't go at all

The recent news that the UK government has cancelled the extension of its planned high speed rail line (HS2) to cities in the north of England should not really surprise anyone. Expanding what is essentially nineteenth century technology at great expense in the twenty first century was always a controversial policy option. Naturally there was a political angle to this and called into question the government’s commitment to levelling up regional inequalities. But whilst the UK clearly does suffer from significant regional inequality issues, a bigger question is whether investment in railways is a good way to address them.

A historical perspective on British railways

The railway network has been at the centre of the political debate on transport for decades. In the wake of WW2 the government nationalised the dilapidated network as a prelude to a significant investment programme to phase out steam. In the 1960s, the (in)famous Beeching Report advocated slashing the network to eliminate the least profitable lines in the face of rising competition from road transport. This was duly acted upon and the UK rail network today is less than half the length of 60 years ago (incidentally, the cuts did nothing to restore the network to profitability). The UK is not alone, of course, in slashing its rail network: The track length in Germany, France and Italy is currently between 60% and 70% of its historical peak. Arguably, however, the UK went too far.

I have long believed that the Beeching approach to managing the rail network was a huge forecasting mistake since it assumed that then-current trends would continue indefinitely (before anyone wants to talk about the shortcomings of economic forecasting I should point out that Beeching was a physicist not an economist). To illustrate the folly of extrapolation, by 2019 the annual number of UK railway passenger journeys had surged to its highest level since 1923, representing a figure almost three times the modern-day low recorded in 1982 (chart 1). Anyone who regularly travelled by train prior to March 2020 will be aware of the extent to which trains were frequently overcrowded. On an international comparative basis the UK rail network is the most intensely used in Europe. Although the total number of passengers carried on German railways in 2019 was 60% higher than that of the UK, the German network is more than twice the size. On a passenger miles per km basis the UK figure is 78% higher (chart 2).

Assessing the pros and cons of extending the network

The consensus of academic opinion is that railways contribute considerable benefits to the economy’s productive potential, including alleviating congestion on the road network and facilitating the development of clusters of economic activity. They also cut CO₂ emissions and reduce the number of casualties on the transport network relative to what would happen were the journeys to be made by road. Congestion reduces the efficiency of the network which has an associated economic cost and there are studies which attempt to put a price on it (see this study, which looks at London). Whilst we can be sceptical of the exact numbers, inefficient networks undoubtedly have an impact at the margin by adversely affecting productivity and business location decisions.

When making the case for HS2 it is therefore important to assess the costs of the investment against the benefits. To get a handle on the financial costs, it was initially suggested in 2010 that to build a high-speed line between the cities of London and Birmingham (a distance of 215 km) would cost around £20bn. More than a decade on, and after considerable political and economic wrangling, the cost of this phase is estimated to have doubled to around £45bn. It was further proposed to extend the network northwards in two phases: one running a further 114km north-west to Manchester and the other an additional 190km towards Leeds (this is the part that has been shelved). Costs have spiralled accordingly. 

The previous estimate put the cost of building the network at £55.7bn: the latest official estimate is a cost between £72bn and £98bn. Even after allowing for inflation, that represents an increase of up to 60%. The cost-benefit ratio has already halved to around 1.2 - a figure that classifies the project as low value for money on the Treasury's classification scale - implying that a 20% rise in costs will make this a marginal project at best. The benefits of HS2 are dominated by time savings. Around half of the transport benefits (and over 40% of the total network benefits) are derived from time savings. It is expected that HS2 will cut the journey time between London and Birmingham from 81 to around 52 minutes when (if) the line opens between 2029 and 2033 (as projected) and reduce the London to Manchester journey time from 127 to 67 minutes. In the view of many laypeople, these are relatively small time savings compared to the costs.

The respected transport economist Stephen Glaister, who I first heard dismiss the economics of HS2 in a lecture almost a decade ago, recently wrote a report which sounded a sceptical note. He wrote that “it will inevitably be a financial loss-making enterprise, with the taxpayer filling the funding gap, with those resources having to forgo alternative uses.” That is not necessarily a reason for not undertaking the investment but he further noted that “an appraisal of the likely effects of the Covid-19 pandemic on the demands for travel and hence on the finances or economic benefits of the scheme has not been published.” In addition, he was a lot more cautious regarding the assumptions on carbon emissions than the project’s proponents. Glaister also referenced the 2006 Eddington Transport Study which concluded that economic returns from high-speed rail in the UK are unlikely to be as large as for investment in some alternative projects. In Glaister’s words, “in England, unlike in some parts of the European mainland or China, the revenue and other benefits of high speed are limited because the major cities are relatively close to one another and … there has been strong competition from established, medium speed and high frequency railways.”

With the costs of the first stage of the project having spiralled, it is hardly surprising that the government has suddenly got cold feet about further extending HS2. It is equally unsurprising that political leaders in the north feel that they have been short-changed by a government that promised not to ignore the provinces. Indeed, if the government had been serious about levelling up in the first place, it should have followed the recommendation of the National Infrastructure Commission which suggested that connectivity between the northern cities was a higher priority than HS2.

High-speed can work - the Italian example

It is sometimes hard to escape the view that British politicians want a high-speed network because other countries have successfully introduced them and the French TGV system is often cited as a model for Britain to copy. But Italy provides a better role model where last month Alitalia ceased flight operations after years of financial underperformance, driven in large part by the fact that its domestic business was being undercut by the rail network. According to a 2019 report by Trenitalia, passenger numbers on its high-speed trains soared from 6.5 million in 2008 to 40 million in 2018. On the lucrative route between Rome and Milan, 69% of those travelling between the two cities went by train whilst the share of those travelling by air fell from 26% in 2015 to below 20% in 2018.

The distance between Rome and Milan is 570km which means that a fast train can compete with air travel. This is double the distance between London and Birmingham which nobody in their right mind would ever want to fly. However, London to Edinburgh is a distance of 650km where a fast rail service would be competitive vis-à-vis flying. Whilst time savings will be derived on the first half of the journey to Manchester, these are insufficient to do in the UK what was achieved in Italy. The key takeaway in my view is that building a long distance high-speed network that can compete with air travel, thus leading to a reduction in carbon emissions, would have positive social benefits. However, there are better ways to spend £98bn than a relatively short stretch of high-speed rail that looks increasingly like a vanity project. These funds could provide up to 150 new hospitals, for example, or be invested in green electricity options. The message is thus extend north, or not at all.

The economics of flight overbooking (or how to avoid a beating)

The recent news that a passenger was unceremoniously hauled off a United Airlines flight because the airline was unable to persuade enough passengers to voluntarily disembark strikes me as an extreme case of market failure. It is well known that airlines routinely overbook flights in order to maximise the chances of a full aircraft, given that a certain number of passengers will not travel for one reason or another. In the event that there are more passengers than seats, the airline must offer some form of compensation to persuade passengers to voluntarily make way. At the same time, the passenger must weigh up whether the price offered is sufficient to compensate them for the inconvenience. It is a classic bargaining situation worthy of further investigation.

Obviously, the aircraft cannot take off until all passengers are seated and it must wait at the departure gate until the supply and demand for seats is in equilibrium. The airline is charged in proportion to the time elapsed over and above the scheduled departure time. According to industry estimates (here), the cost of such delay is around £70 ($87.50) per minute. The airline will know before boarding begins that they are overbooked so it is in their interests to offer compensation before passengers take their seat, although in the recent United case the airline appears to have waited until they were on board, which is a major strategic error.

We can devise a simple model to analyse the choices facing the airline, based on some arbitrary assumptions but it makes the point. If we assume that it takes 10 minutes to remove luggage and repack the hold, then the airline has an incentive to offer compensation of less than $87.50 up to 10 minutes before the scheduled departure time. Between 9 and 10 minutes prior to departure, the strike price rises to $87.50 which is the price of saving another minute of delay. With less than 10 minutes until the scheduled departure time, and no takers for the offer of compensation, the fine will continue to rise in a linear fashion because the airline cannot unload the luggage and still make the slot. The airline will thus have to raise its offer to passengers on the basis that $87.50 has not proved sufficient incentive so far. On the assumption that one of the passengers does not suddenly “crack” during this standoff, the airline will have to engage in a price discovery process in order to tempt one of them to drop their claim for a seat because otherwise the delay will continue indefinitely.

Suppose that for every minute that elapses, the airline raises its offer by $10. Thus, with 9 minutes to go, the airline will face a fine of $87.50 and offers passengers a similar amount. With eight minutes to go, the fine rises to $175 and the passenger payout to $97.50 and so on (see chart for the representation of the cost structure in this case). The total cost to the airline is the fine levied by the airport for missing the departure slot plus the customer payout (we ignore the costs of any overnight accommodation for inconvenienced passengers). If there are still no takers at the scheduled takeoff time, the airline faces costs of $1052 (a fine of $875 and compensation of $177.50). Obviously, this process could go on for a while – in theory up the point at which it becomes cheaper to refund all passengers and cancel the flight (less the cost of unused fuel and any sundry items).

As it happens, one limit to the process is the legal maximum compensation which US airlines are required to pay ($1350). In our simple model formulation, the airline would have to wait two hours before reaching this limit but by that point the airport fines would exceed $11,000. Indeed, as the chart shows, the airline has an incentive to avoid the steeply rising departure fines. A simpler option would be for the airline to decide in advance how much to offer the passenger before it has to pay any departure fines. Thus, more than 10 minutes prior to departure the airline will not be subject to fines but knows that if it waits until the scheduled departure time before finding an agreement, it will have to pay $1052. The sensible option is thus for the airline to offer the passenger an amount up to $1052 which allows it to take off on time without incurring any departure fines; gains goodwill from the affected passenger and still pay an amount which is less than the legal maximum. Note, by the way, that European airlines are less generous. Payouts per passenger depend on the distance travelled and range from a minimum of €250 for short-haul flights to €650 for longer journeys.

The simple model suffers from a number of shortcomings, none of which change the broad picture. It does not deal with multiple equilibria (i.e. if more than one passenger were to accept the offer). A workaround to this problem is to pick a passenger at random and make the offer rather than hold an auction. More problematic would be the case where the airline needs to bump more than one passenger which changes the airline payoff because different people have different preferences, thus making it harder to find a series of market clearing prices.

This raises a question of what would tempt a passenger to accept the airline’s offer of compensation? It all depends on their time preference, or the rate at which they discount the need to be at their destination on time. This will depend on factors such as income and the value they place on their time. If you are a US worker with just two weeks holiday per year and you lose one day due to flight problems, you may set a high value on the cost of delays. If, however, you earn $50,000 per year, you can earn an extra day’s pay ($200) simply by holding out for two minutes beyond the scheduled departure time.

If the model outlined above does not provide a solution, the process can be short-circuited by the drawing of lots to choose who leaves the aircraft – as apparently United did. Unfortunately, the gentleman removed from the United flight was a doctor, who presumably applied a very high discount rate to his time, so it is hardly surprising that he was not best pleased at being asked to leave the flight – let alone the manner of his departure. There are many issues involved here, but perhaps the key takeaway is that airlines are desperate to avoid departure fines so if you have the time to negotiate, chances are you can drive a hard bargain. There again, you might just be hauled off the aircraft …