Where should governments spend your money? The impossible maths of political and moral decisions

Whenever the UK government decides to spend public money on a new project, it needs to weigh up the costs against the value of the benefits it hopes to achieve. And it’s rarely a simple calculation.

This is why Chancellor Rachel Reeves is changing the Treasury’s “green book”^[1] of rules which dictate how investment plans are made. Those rules, and the calculations they support, do not always work.

At one point for example, the benefit-cost ratio of HS2, the controversial high speed railway link between London and the north of England, was quite favourable – estimated as having a value of two^[2]. That meant the economic benefits were expected to end up being twice as high as the cost of building it.

That ratio then gradually decreased, until it was much closer to one (that is, the economic benefits would end up being roughly the same as the costs). The northern part of the project was later cancelled^[3].

Get your news from actual experts, straight to your inbox. Sign up to our daily newsletter^[4] to receive all The Conversation UK’s latest coverage of news and research, from politics and business to the arts and sciences. One reason for the ratio changing so dramatically was rising costs. But another factor was the way the benefits of the railway were totted up – using estimates of saved time on journeys. So how do you work out the monetary value of time saved? The standard way^[5] for something like railway infrastructure is to count one hour saved on a worker’s train journey as worth an hour of their salary. But if average salaries in a particular part of the country are low, all of the hours saved might not add up to a big enough sum to justify the cost. And this creates something of a vicious economic circle^[6]. Poorer regions end up struggling to justify major investment because the potential economic benefits appear lower. But without that investment, they remain poor^[7]. And transformative change takes more than a single project anyway. More reliable trains^[8] will not be enough to make northern England richer. Nor, individually, will a better phone signal^[9], an opera house^[10] or relocating the House of Lords^[11]. Doing all of these things at the same time could bring change, but they won’t appear in any of the separate cost-benefit analysis. One way of bypassing this problem is to do what former prime minister Rishi Sunak did in 2022: decrease the importance of the benefit-cost ratio^[12], and create special rules to emphasise^[13] the impact of a project on a chosen part of the country. Rachel Reeve’s promised changes^[14] go further in that direction, promising to put more emphasis on “transformational schemes” and specific local needs. Another option is EU-style funding^[15] that targets poorer regions exclusively. Cost-benefit analysis have other problems too. Local governments arguably spend too much money^[16] in seemingly endless competition for public funds. Supporters of a project are often way too optimistic about their costs^[17], and future benefits are very hard to predict. For instance, Crossrail in London had an initial modest benefit-cost ratio of 1.9^[18]. But when it opened, the number of passengers was much higher^[19] than even the most optimistic forecast. Regardless of the way rules are modified, the need for such rules reminds us of an inconvenient truth behind all public choices. Either we put a number on everything, or we make arbitrary decisions. Among the long list of cost overruns^[20] of HS2 was the choice to spend more than £100 million^[21] on building a barrier to protect rare bats in Buckinghamshire from the noise of the trains – the kind of thing the chancellor thinks gets in the way of much-needed development^[22]. But should society spend £100m to protect bats? Perhaps, in the context of animal conservation^[23], the answer is yes^[24]. But if the answer is no, then the cost of HS2 was increased unnecessarily. Either way, a part of nature is being allocated a certain value.

Putting a value on human lives^[26] is even harder. Many would argue that it’s impossible, or even that human lives are priceless^[27].

But that’s not very helpful when it comes to decision-making. And the same people who claim that human life is of infinite value might also object to a lower speed limit on roads for example, despite evidence that it leads to fewer fatalities^[28].

For most policy decisions in the UK, increasing someone’s life by one year in good health (a “quality-adjusted life year”^[29]) is valued at £86,416 (£70,000 in 2021 prices^[30]). And this sum is what comes into play when plans are made about things like tackling pollution or transport safety.

But it does not mean governments always have to follow their own analysis. The cost of new anti-terrorism security measures for large events is, according to the UK government’s own analysis^[31], around 90 times higher than the benefits from the small expected decrease in victims.

Yet it was decided^[32] that reducing the number of victims of terrorism was important enough to bypass the usual cost-benefit calculation.

These discussions can be morally fraught. Rich countries are able to value human^[33] life more because they have more money to spend. And although you do not hear politicians debating how much they value future generations, the answer is clearly written in official documents^[34].

The numbers we put on time savings, nature and human lives (today and in the future) are neither correct nor incorrect. Every investment decision involves impossible choices. Every pound the government spends could have been used differently.

A tool like the green book is an attempt to put some consistency in those political and moral choices. We might even benefit from using such tools more openly when discussing emotional subjects such as terrorism, climate change or migration, and at least force ourselves to acknowledge the trade-offs we are making, rather than pretending they don’t exist.

References

1. ^{^} “green book” (assets.publishing.service.gov.uk)
2. ^{^} estimated as having a value of two (www.instituteforgovernment.org.uk)
3. ^{^} later cancelled (commonslibrary.parliament.uk)
4. ^{^} Sign up to our daily newsletter (theconversation.com)
5. ^{^} standard way (assets.publishing.service.gov.uk)
6. ^{^} vicious economic circle (www.sciencedirect.com)
7. ^{^} remain poor (www.nber.org)
8. ^{^} More reliable trains (www.economist.com)
9. ^{^} better phone signal (www.telegraph.co.uk)
10. ^{^} an opera house (www.bbc.co.uk)
11. ^{^} House of Lords (www.instituteforgovernment.org.uk)
12. ^{^} benefit-cost ratio (townsfund.org.uk)
13. ^{^} special rules to emphasise (lpiphub.bham.ac.uk)
14. ^{^} promised changes (assets.publishing.service.gov.uk)
15. ^{^} EU-style funding (commission.europa.eu)
16. ^{^} too much money (theconversation.com)
17. ^{^} often way too optimistic about their costs (www.tandfonline.com)
18. ^{^} modest benefit-cost ratio of 1.9 (learninglegacy.crossrail.co.uk)
19. ^{^} much higher (tfl.gov.uk)
20. ^{^} the long list of cost overruns (www.bbc.co.uk)
21. ^{^} more than £100 million (www.bbc.co.uk)
22. ^{^} way of much-needed development (www.independent.co.uk)
23. ^{^} animal conservation (onlinelibrary.wiley.com)
24. ^{^} is yes (theconversation.com)
25. ^{^} Rudmer Zwerver/Shutterstock (www.shutterstock.com)
26. ^{^} value on human lives (www.sciencedirect.com)
27. ^{^} are priceless (theconversation.com)
28. ^{^} fewer fatalities (www.bbc.co.uk)
29. ^{^} “quality-adjusted life year” (www.nice.org.uk)
30. ^{^} £70,000 in 2021 prices (www.gov.uk)
31. ^{^} according to the UK government’s own analysis (www.gov.uk)
32. ^{^} it was decided (homeofficemedia.blog.gov.uk)
33. ^{^} value human (www.jstor.org)
34. ^{^} written in official documents (www.gov.uk)