A cityscape of Manchester at night.

Pushing the limits of the possible.

Tom Forth, .

How much do cancelled trains cost North England?

TransPennine Express (TPE) run the trains that connect North England’s major cities with themselves and with Scotland. For decades their trains have been too small and very unreliable. In January 2023 they cancelled nearly a quarter of the trains on their timetable.

I’ve been asked often if this matters and how much it costs the economy. I always answer with “yes, but it completely depends on your assumptions”, “yes, but any answer you get will be hugely uncertain”, and “yes, but I’m not sure I’ll add much value by calculating it”.

This is good economics. It is also very boring.

So recently I decided to be a bit less boring. It was after someone convinced me it was selfish not to share some of the methods that consultants use to make these estimates, discuss why they’re wrong, and discuss why they’re right. And of course, admit that they are only slightly better than guessing, which I do.

So here goes,

1. Time is money.

TPE provide about30 million journeys per year. The gap between their trains is probably about half an hour. So cancelling a quarter of trains causes 0.5 * 30 million * 0.25 = 3.75 million hours of delays. Mean hourly pay in the UK is about £16, so the total cost of those delays is £60m.

North England’s GDP is about £400bn of value per year, meaning that delays on TPE cost about 0.015% of the economy of North England. Close to nothing.

There are lots of ways to add complexity to these calculations. Was £16 the right value to use per hour or should we have used the GDP per hour worked? It’s closer to £35/hour worked in a Northern city. Should we count the lost time of everyone in the meeting they missed or the event that they were late to? Ten people in a meeting, £350/hour for delays. And was the half an hour delay we guessed at right? Maybe a train delay on average causes an hour of delay so we can double our number. What if the commuter gives up taking the train, starts driving, and causes congestion? What’s the cost of that? But there’s a flip side to that. Now we can run fewer trains, which saves money. What percentage of people lose their jobs or quit their jobs because of unreliable transport? We can go on forever. Indeed the UK government transport evaluation guidance is 1400 pages long because we do.

Making long lists of complexities and nuances is a great way to earn more money as a consultant or a civil servant. It’s a great way to reduce criticism from people without less experience or resources, often at smaller consultancies or lower tiers of government, to create a list quite as long.

The longer the list the better right? There are no good rules about what assumptions you should make, or importantly shouldn’t make. Consultants and civil servants with enough money can create very long reports, with very complex and nuanced calculations that find numbers as large or as small as required by their client or Minister. I’ll leave you to read the many HS2 business cases if you like.

The method I’ve just described for valuing delays is probably the most widely used. It’s theoretically simple but becomes complicated when dozens of simple reasonings are combined. It can be useful. But it’s usually a waste of everyone’s time.

Need an estimate of the cost of TPE delays that’s fifteen times bigger? Let’s say everyone commuting is going to work as part of a team of five, the value of a person’s time is £35/hour, and the average cancellation causes 45 minutes of delay. Now we get a cost of £1bn. That’s 0.25% of the economy. Need it to be 1%? I could probably get there if you really want.

2. Agglomeration is money.

When it comes to public transport I prefer to think about agglomeration. Sorry fans of rural transport but public transport’s largest economic purpose is to allow the existence of cities. Cities are more productive than disperse living because of efficiencies of scale, more consumer choice, deeper labour markets, faster development of new ideas through collaboration and institutions, and much more.

Cities lose much of their advantages of density when they are reliant on cars since private cars require large roads and large car parks that necessarily spread out cities and thus cost them many of their benefits. So it’s no surprise that the most prosperous large cities in the world, places like Paris, London, New York, Tokyo, Singapore, and Hong Kong, have excellent public transport. Sprawling car-based cities are of course possible and often very productive. Atlanta and Houston are two good examples. Since they will never be allowed within the UK’s planning system and public preference to save the greenbelt, ancient woodlands, and farmland, I’ll ignore them.

I’ve just described the theory of agglomeration benefits and argued that they rely on public transport in the UK. Now we need to estimate how big these benefits are.

Quite a lot of people think that agglomeration benefits are zero. So that’s easy. They think that the elasticity of agglomeration is 0%. This means that doubling the size of a city increases the strength of its economy (GDP/person) by nothing.

There have been dozens of analyses by economists to try and estimate the elasticity of agglomeration in various places and by various methods. The average result is 3%. Doubling the size of a city increases the strength of its economy by 3%.

In a recent twitter thread I explained why I think that we should use a elasticity of 12%, because we should ignore displacement concerns since we only care about North England and we will train, attract, and retain more highly skilled people from outside North England if we have better public transport. Maybe this is only half true and we should use an elasticity closer to 8%. I reckon any number between 0% and 15% is justifiable, which makes this whole exercise a bit pointless. Though I did warn you about that at the start.

Actually doing the calculations.

That’s the economics out of the way, now I’m going to do the calculations.

I take the GTFS format rail timetable for September 2022 (it doesn’t change much, so this is fine) and I randomly delete 23.7% of TPE (TP) services, 3.8% of Northern (NT) services, 4.0% of LNER (GR) services, and 7.9% of CrossCountry (XC) as per the ORR’s most recent datato create a new timetable.

Then I load these two timetables into Open Trip Planner 2.2 and calculate how far I can get in 70 minutes (people actually walk faster and change onto trains quicker than in transport models if they travel regularly, so this is equivalent to an hour journey).

I repeat this for ten weekdays using both timetables and take the area where at least nine of ten isochrones overlap. This reflects the idea that people may be able to get away with being late for work or late to pick their kids up from school or late to a doctor’s appointment once per week. I think that’s overly generous, but it’s my assumption.

Then we sum up the populations within each to show the sacrificed effective population from the typical rate of rail cancellations.

Here’s the answer.

The effective population of Leeds by rail would be 44% larger if TPE weren’t cancelling a quarter of their trains.

So the population of Leeds by rail would be 44% larger if TPE weren’t cancelling a quarter of their trains. And that would make its economy about 5.5% stronger. Which is about the same as one of the good higher estimates of the cost of Brexit to the UK . And higher than other estimates of around 4% from the OBR .

A note on further complexity and nuance.

If you like the answer I’ve got, you’ll like my method. You’ll probably find my argument thatGreater Manchester has outgrown West Yorkshire by about 6% since 2007, coincident which its tram system growing and having an effect economically, convincing. You’ll accept that if Leeds is affected by this much then so is Manchester, Liverpool, Newcastle, Sheffield, and Hull. And that’s most of the North’s population and economic output accounted for.

But if you don’t like the answer I’ve got, you’ll start picking holes in my method. You’ll talk about how I’m not looking at anything except rail. Most people drive anyway. I’m not looking at delays, just cancellations. I’m assuming that any cancellation is a complete cancellation. And I’m assuming that cancellations are random. It was ludicrous of me to dismiss displacement effects of skills. Have I done any robustness testing? Have I modelled the time periods over which this economic impact would occur? You can go on forever. I can go on forever. I’ve already said that all these methods are very uncertain so we won’t achieve much.

The extremely common desire in British economics and politics is to focus on the complexity and nuance of the problem rather than concede that the underlying large uncertainties make that an arrogant waste of time. It’s like worrying about unscrewing the broken light bulbs before you blow up a whole block of flats.

All of these assumptions are big, but they’re tiny compared to the fact that I can pick an elasticity of agglomeration between 0% and 15%.

I think that the poor performance of trains in North England costs our economy about the same as Brexit. I don’t think it very confidently. I hope that you’re similarly unconfident that I’m wrong.


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