Trading kidneys, repugnant markets and stable marriages win the Nobel Prize in Economics

Roth and Shapley charted a course for economists to go beyond simply arguing for markets in everything.

The 2012 Nobel Prize in Economics - technically the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel, but nobody cares - has been awarded to two American Economists, Alvin Roth and Lloyd Shapley "for the theory of stable allocations and the practice of market design". The Nobel Committee explains what that means:

This year's Prize concerns a central economic problem: how to match different agents as well as possible. For example, students have to be matched with schools, and donors of human organs with patients in need of a transplant. How can such matching be accomplished as efficiently as possible? What methods are beneficial to what groups? The prize rewards two scholars who have answered these questions on a journey from abstract theory on stable allocations to practical design of market institutions.

Lloyd Shapley used so-called cooperative game theory to study and compare different matching methods. A key issue is to ensure that a matching is stable in the sense that two agents cannot be found who would prefer each other over their current counterparts. Shapley and his colleagues derived specific methods – in particular, the so-called Gale-Shapley algorithm – that always ensure a stable matching. These methods also limit agents' motives for manipulating the matching process. Shapley was able to show how the specific design of a method may systematically benefit one or the other side of the market.

Alvin Roth recognized that Shapley's theoretical results could clarify the functioning of important markets in practice. In a series of empirical studies, Roth and his colleagues demonstrated that stability is the key to understanding the success of particular market institutions. Roth was later able to substantiate this conclusion in systematic laboratory experiments. He also helped redesign existing institutions for matching new doctors with hospitals, students with schools, and organ donors with patients. These reforms are all based on the Gale-Shapley algorithm, along with modifications that take into account specific circumstances and ethical restrictions, such as the preclusion of side payments.

Even though these two researchers worked independently of one another, the combination of Shapley's basic theory and Roth's empirical investigations, experiments and practical design has generated a flourishing field of research and improved the performance of many markets. This year's prize is awarded for an outstanding example of economic engineering.

The committee have yet again reaffirmed the old adage that the most important thing to do when trying for a nobel prize is to live long enough that your achievements are recognised. The Gale-Shapley algorithm, for instance, was devised in 1962, when Lloyd Shapley was 34. It concerns a maths problem known as the stable marriage problem: if you have an even number of men and women, can you always come up with a set of marriages where there are no two people of opposite sex who would both rather have each other than their current partners? (1960s maths problems: usually heteronormative.) If you can, then the marriage is "stable".

The Gale-Shapley algorithm is a way of always ensuring stable matches; and much of Shapley's work covers the same areas, straddling the boundaries between economics, mathematics, and computer science.

Roth is the younger of the two winners, and works in a far more empirical sphere. As the committee points out, although the two men never actually collaberated, Roth took Shapley's theoretical work and applied it to actually existing markets. For instance, Roth used the Gale-Shapley agorithm to ease the kidney shortage in the US. David Wessel explains (£):

As of noon yesterday, 58,470 people in the U.S. were waiting for a kidney transplant. Most won't get one this year. There aren't enough donated kidneys to go around. Surgeons transplanted just 15,129 kidneys last year. Now a band of transplant surgeons and economists are trying to fix that by creating a moneyless market for exchanging kidneys. Most transplanted kidneys come from a person who has died, a supply that grows slowly because of ignorance about the need for donations or grieving relatives' reluctance. But a kidney taken from a live donor works better, and almost everyone has a spare. As techniques improve for removing healthy kidneys and for suppressing the body's tendency to reject a transplant, doctors increasingly turn to kidneys from living donors, usually relatives. Last year, 43% of kidneys transplanted in the U.S. came from living donors, up from 28% a decade ago. But a biological barrier often blocks a transplant from a relative. In about a third of all would-be pairs, blood types are incompatible. In others, the sick person has antibodies that can initiate a rejection of the donated organ. It's heartbreaking "to have the treasure of the live donor and then have that not go forward because of a biological obstacle," says Massachusetts General Hospital transplant surgeon Francis DelMonico.

Occasionally, transplant centers spot a way out: One New England father with blood type A couldn't donate a kidney to his daughter with blood type B. So he gave a kidney to a teenager with blood type A, and the teenager's sister gave a kidney for the man's daughter. New England's transplant centers have done six such exchanges. Baltimore's Johns Hopkins University has done seven.

The crucial thing about Roth's work, from an economic point of view, is that it involves finding stable allocations using market-like situations without involving money. The kidney swaps in the New England situation are market-like, trading kidneys for kidneys in a way that makes all parties better-off, but they don't actually require kidneys to be bought and sold.

We can see the importance of this by looking at another paper of Roth's, not cited by the committee, on repugnance in markets (pdf). Roth demonstrates that some markets are limited because the very existance of a market in some goods is considered repugnant. He argues, for instance, that the trade in horse meat being banned in California is not done through fears that eating horse meat is unsafe; nor is it done for animal welfare reasons, since it is still legal to farm and kill horses. But banned it is, and Roth argues that the natural response of economists to situations of this type - to argue for freer markets - is wrong, since it ignores the very strong feelings involved in the situation. Instead:

Being aware of the sources of repugnance can only help make such discussions more productive, not least because it can help separate the issues that are fundamentally empirical—like the degree of crowding out of altruistic donations that might result from different incentive schemes compared to how much new supply might be produced—from areas of disagreement that are not primarily empirical.

Hopefully his new Nobel Prize should give that argument greater weight in the years ahead.

A patient receives a kidney in Johns Hopkins university in Baltimore. Photograph: Getty Images

Alex Hern is a technology reporter for the Guardian. He was formerly staff writer at the New Statesman. You should follow Alex on Twitter.

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Q&A: What are tax credits and how do they work?

All you need to know about the government's plan to cut tax credits.

What are tax credits?

Tax credits are payments made regularly by the state into bank accounts to support families with children, or those who are in low-paid jobs. There are two types of tax credit: the working tax credit and the child tax credit.

What are they for?

To redistribute income to those less able to get by, or to provide for their children, on what they earn.

Are they similar to tax relief?

No. They don’t have much to do with tax. They’re more of a welfare thing. You don’t need to be a taxpayer to receive tax credits. It’s just that, unlike other benefits, they are based on the tax year and paid via the tax office.

Who is eligible?

Anyone aged over 16 (for child tax credits) and over 25 (for working tax credits) who normally lives in the UK can apply for them, depending on their income, the hours they work, whether they have a disability, and whether they pay for childcare.

What are their circumstances?

The more you earn, the less you are likely to receive. Single claimants must work at least 16 hours a week. Let’s take a full-time worker: if you work at least 30 hours a week, you are generally eligible for working tax credits if you earn less than £13,253 a year (if you’re single and don’t have children), or less than £18,023 (jointly as part of a couple without children but working at least 30 hours a week).

And for families?

A family with children and an income below about £32,200 can claim child tax credit. It used to be that the more children you have, the more you are eligible to receive – but George Osborne in his most recent Budget has limited child tax credit to two children.

How much money do you receive?

Again, this depends on your circumstances. The basic payment for a single claimant, or a joint claim by a couple, of working tax credits is £1,940 for the tax year. You can then receive extra, depending on your circumstances. For example, single parents can receive up to an additional £2,010, on top of the basic £1,940 payment; people who work more than 30 hours a week can receive up to an extra £810; and disabled workers up to £2,970. The average award of tax credit is £6,340 per year. Child tax credit claimants get £545 per year as a flat payment, plus £2,780 per child.

How many people claim tax credits?

About 4.5m people – the vast majority of these people (around 4m) have children.

How much does it cost the taxpayer?

The estimation is that they will cost the government £30bn in April 2015/16. That’s around 14 per cent of the £220bn welfare budget, which the Tories have pledged to cut by £12bn.

Who introduced this system?

New Labour. Gordon Brown, when he was Chancellor, developed tax credits in his first term. The system as we know it was established in April 2003.

Why did they do this?

To lift working people out of poverty, and to remove the disincentives to work believed to have been inculcated by welfare. The tax credit system made it more attractive for people depending on benefits to work, and gave those in low-paid jobs a helping hand.

Did it work?

Yes. Tax credits’ biggest achievement was lifting a record number of children out of poverty since the war. The proportion of children living below the poverty line fell from 35 per cent in 1998/9 to 19 per cent in 2012/13.

So what’s the problem?

Well, it’s a bit of a weird system in that it lets companies pay wages that are too low to live on without the state supplementing them. Many also criticise tax credits for allowing the minimum wage – also brought in by New Labour – to stagnate (ie. not keep up with the rate of inflation). David Cameron has called the system of taxing low earners and then handing them some money back via tax credits a “ridiculous merry-go-round”.

Then it’s a good thing to scrap them?

It would be fine if all those low earners and families struggling to get by would be given support in place of tax credits – a living wage, for example.

And that’s why the Tories are introducing a living wage...

That’s what they call it. But it’s not. The Chancellor announced in his most recent Budget a new minimum wage of £7.20 an hour for over-25s, rising to £9 by 2020. He called this the “national living wage” – it’s not, because the current living wage (which is calculated by the Living Wage Foundation, and currently non-compulsory) is already £9.15 in London and £7.85 in the rest of the country.

Will people be better off?

No. Quite the reverse. The IFS has said this slightly higher national minimum wage will not compensate working families who will be subjected to tax credit cuts; it is arithmetically impossible. The IFS director, Paul Johnson, commented: “Unequivocally, tax credit recipients in work will be made worse off by the measures in the Budget on average.” It has been calculated that 3.2m low-paid workers will have their pay packets cut by an average of £1,350 a year.

Could the government change its policy to avoid this?

The Prime Minister and his frontbenchers have been pretty stubborn about pushing on with the plan. In spite of criticism from all angles – the IFS, campaigners, Labour, The Sun – Cameron has ruled out a review of the policy in the Autumn Statement, which is on 25 November. But there is an alternative. The chair of parliament’s Work & Pensions Select Committee and Labour MP Frank Field has proposed what he calls a “cost neutral” tweak to the tax credit cuts.

How would this alternative work?

Currently, if your income is less than £6,420, you will receive the maximum amount of tax credits. That threshold is called the gross income threshold. Field wants to introduce a second gross income threshold of £13,100 (what you earn if you work 35 hours a week on minimum wage). Those earning a salary between those two thresholds would have their tax credits reduced at a slower rate on whatever they earn above £6,420 up to £13,100. The percentage of what you earn above the basic threshold that is deducted from your tax credits is called the taper rate, and it is currently at 41 per cent. In contrast to this plan, the Tories want to halve the income threshold to £3,850 a year and increase the taper rate to 48 per cent once you hit that threshold, which basically means you lose more tax credits, faster, the more you earn.

When will the tax credit cuts come in?

They will be imposed from April next year, barring a u-turn.

Anoosh Chakelian is deputy web editor at the New Statesman.