Tim Harford The Undercover Economist

Articles published in February, 2014

Testing times for Sochi drug cheats

‘The most famous game of all is the prisoner’s dilemma, and it’s a natural explanation for why athletes take drugs despite the risks’

Testing for performance-enhancing drugs was first introduced by the International Olympic Committee not at a summer games but at the 1968 Winter Olympics. That might seem odd – the winter games aren’t normally associated with performance-enhancing drugs. Yet a dispassionate economic analysis suggests that this disconnection between testing regime and drug prevalence can hardly be a surprise.

The ideal economic tool for thinking about performance-enhancing drugs is game theory, a mathematical approach to understanding co-operation and competition. The most famous game of all is the prisoner’s dilemma, and it’s a natural explanation for why athletes take drugs despite the risks.

The essence of the prisoner’s dilemma in doping is that, regardless of what other competitors do, each individual competitor stands to benefit from taking the drugs – either by ensuring an advantage over a clean field or avoiding disadvantage compared with cheating rivals. And so everyone takes performance-enhancing drugs, even though everyone would prefer a situation where the entire field was honest.

Naturally, sporting authorities wish to change the incentives and so they test athletes and hand out bans to those who break the rules. One might think that such tests largely resolve the prisoner’s dilemma. But an analysis published last year by three economists, Berno Buechel, Eike Emrich and Stefanie Pohlkamp, suggests otherwise.

Game theory is a clever tool but the risk is that the theorist misses some bigger game. Buechel and colleagues argue that the bigger game in this case isn’t just between the athletes and the sporting authorities, but involves sports fans. The sad truth is that sports fans aren’t necessarily providing the right incentives.

Fans, understandably, do not like drug scandals: news that another sprinter has been caught taking steroids or another cyclist has been found using the blood-enhancer EPO does nothing to enhance the reputation of these sports. That typically means lower box-office takings, smaller broadcast revenues and less money from sponsors.

But what constitutes a drug “scandal”? It’s not the doping itself: that’s the offence, not the scandal. The scandal doesn’t break until the offence becomes public knowledge – that is, when the drug-taking coincides with an effective drug test. What, then, is the incentive for sports administrators to beef up their drug tests? The immediate impact will be more scandals, fewer spectators and fewer sponsors.

Of course, a totally foolproof drug-testing regime would solve this problem because nobody would cheat if detection and punishment were guaranteed. But even if such a regime were possible on some plausible budget, the costs of getting there might be prohibitive. Only after a huge scandal such as the discovery of industrialised cheating in the Tour de France do the authorities have an opportunity to improve their testing programmes.

This is a problem that may never be fully resolved. But the drug-testing regime at the Sochi Olympics has had two clever features. First, samples are being kept for 10 years. The usual reason given for this is that it may allow new and improved detection methods to catch cheats after the event, but there is nice side benefit: sporting authorities have more incentive to catch historical cheats than current cheats, because doing so presents an attractive image of a sport that is making progress.

Second, the IOC took great pains to describe the increased numbers of drug tests that would be conducted during the games – up by more than 14 per cent from the tests during the Vancouver Winter Olympics. We’re invited not to think of the failed drugs tests but all the tests that have passed. The real target for such announcements is not the athlete. It’s the sports fan.

Also published at ft.com.

Low inflation can be a disease not a cure

Deflation seems unlikely – but even a low risk is worth losing sleep over, writes Tim Harford

‘UK consumer inflation has fallen below the Bank of England’s 2 per cent target for the first time in four years.’ Financial Times, February 19


Well, perhaps.

Why are you so grumpy again? What wrong with low inflation?

Nothing, so far – but you can have too much of a good thing. Inflation is also low and edging downwards in the US, Japan and the eurozone. Correction: Inflation is also low in Japan, and low and edging downwards in the US and the eurozone. Yet in all these places, interest rates are low and central bankers have printed enough money to get the tinfoil hat brigade screaming about hyperinflation. Such low inflation might be an indication of trouble ahead.

Are you saying that low inflation is a bad thing, or are you saying that low inflation is merely a harbinger of doom?

A bit of both – but mostly I am concerned that low inflation is a bad thing in itself. One issue is that unexpectedly low inflation redistributes from borrowers to creditors.

About time too, most savers will be thinking.

I hear you. Still, borrowers are more likely to be cash-constrained (that’s why they are borrowers) and are more at risk of bankruptcy. That means lower-than-expected inflation may damage the economy as a whole rather than just moving money from one person’s pocket to another’s. And there’s another problem with deflation: the “lower-bound” problem.

What’s that?

It’s a fancy way of saying that nominal interest rates can’t fall below zero. If inflation is, say, 4 per cent then a central bank can give an economy a shot of adrenalin by cutting interest rates after inflation to minus 3 or minus 4 per cent. If inflation is 0.7 per cent – as it’s currently estimated to be in the eurozone – then that’s impossible.

Why would anyone want real interest rates of minus 4 per cent?

Usually we wouldn’t. But, against the backdrop of a slack economy, such rates would be a strong incentive to spend. And if outright deflation took hold, effective interest rates would rise: people would earn money simply by sitting on their cash and waiting for prices to fall. Sounds great but for an economy it’s a disaster. If nobody buys anything there will be a recession and more deflation – a vicious spiral.

But that isn’t going to happen. Is it?

Don’t ask me, I’m an economist. We never know what’s going to happen to the economy. But it is a serious enough problem that even a low risk is worth losing sleep over.

Is there a constructive response?

In the case of the US and the UK, there’s always “hope for the best”. Both economies have been growing in a more-or-less encouraging fashion. One could try cutting taxes and raising government spending but it may be too late.

What about this forward guidance business?

Yes, an awkward affair. In principle forward guidance makes sense: the idea is to promise to keep interest rates very low until some condition is met, even if the economy might benefit from higher rates down the track.

Why make such a promise?

Because promising low rates for a long time is the next best thing to cutting rates below zero. Imagine buying a house: a mortgage rate of minus 3 per cent might be nice; but a promise that interest rates will be held artificially low for a while is almost as good, if you believe the promise.

That all makes sense.

Yes, but recent experiments with forward guidance haven’t been a huge success. Bank of England governor Mark Carney tied his forward guidance to unemployment rates, and unemployment rates promptly plummeted, so his attempt to commit to low interest rates ended up meaning very little. Still, it was worth a try.

This all seems flimsy. Are there any other approaches?

Most of these central banks are targeting inflation of 2 per cent, or something along those lines. But four years ago IMF chief economist Olivier Blanchard proposed a sharp break with that tradition. He floated the idea of a 4 per cent inflation target next time round. The thinking makes some sense: as long as interest rates and salaries tend to adjust, a higher target should cause little harm in good times and provide a great deal more room for manoeuvre in severe recessions.

That sounds radical.

Agreed. It’s never going to happen, which is a shame. But from the standpoint of today’s sluggish growth all Mr Blanchard’s advice would amount to is: “Next time let’s start from somewhere else.”

Also published at ft.com.

The seductive appeal of cultural stereotypes

Is it obvious that Jewish or Chinese Americans have superior willpower? asks Tim Harford

‘It may be taboo to say it, but some cultural groups starkly outperform others.’ Jacket blurb of ‘The Triple Package’ by Amy Chua and Jed Rubenfeld

Which cultural groups are they talking about? I vote for the baby boomers. They run the world and retire early on fat pensions; the rest of us are still listening to their idea of good music. They are outperforming the stuffing out of the rest of us.

I don’t think the boomers are a cultural group as far as this new book is concerned.

Why not?

I’m not sure. The authors take it as obvious that the logical way to divide up the US is on ethnic and religious lines: Nigerians, Iranians, Jews, Mormons and others. Hipsters don’t seem to count. Neither do punks, lesbians, hackers or hippies.

So by ‘cultural groups’ they mean ‘racial groups’?

Draw your own conclusions. We find it very tempting to carve the human race at those particular joints. Such generalisations have a seductive power: they have tempted otherwise humane and sophisticated individuals into the grossest racism.

You don’t think Chua and Rubenfeld are guilty of the grossest racism, do you?

No, I do not. And it must be legitimate to ask questions about ethnic and cultural differences – with care. The Triple Package is sold alongside titles claiming the secret to success is focus, or salesmanship, or psychoanalysis, or finding your own element, or being a psychopath. Or even that the secret is luck and we’re all being fooled by random patterns we interpret as causal. The book should be held to a higher standard of evidence, though: it says the secret to success is being raised by Jewish, Chinese, Indian or Nigerian parents. Chua and Rubenfeld don’t meet that higher standard. They offer heaps of anecdote with carefully selected academic evidence.

Everyone argues by anecdote. Is it really a particular problem here?

Yes. In a rare instance where they cite research from experimental psychology, they describe studies about the power of “stereotype threat”. For example, you can put women off their chess game by reminding them that the top players are all men. White kids struggle with a mathematics test if told it is research into the mathematical prowess of Asians. These stereotypes can cause real psychological, social and political damage. They should not be casually slung about to sell books. Insisting on care isn’t mere political correctness.

Are the authors careful?

They’re tactful but that’s not the same thing. One part of their “triple package” of cultural traits, for instance, is that insecurity breeds success. We are told this flouts the entire orthodoxy of contemporary psychology; then, in contrast, that it is supported by “a well substantiated and relatively uncontroversial body of empirical evidence”. If they cited any of that evidence I missed it in a flood of references to biographies, cultural histories, pop science and newspaper articles.

And the other claims?

They do cite scholarly research linking willpower to success in life but that doesn’t seal the deal. Is it so obvious Jewish or Chinese Americans have superior willpower? It’s far from clear that pushy parenting builds willpower, and I can cherry-pick my own research suggesting the opposite.

The third part of the triple package is?

A sense of cultural superiority. But is that particularly Indian or Iranian? Russians are proud to be Russian; Ethiopians to be Ethiopian. It didn’t seem to occur to the authors to look for disconfirmation by examining less successful religious or immigrant groups.

The whole story still sounds plausible to me.

We always find stereotyping plausible. That is why it is treacherous. But there are three big holes. The first is selection bias. If Indian doctors and engineers are given US visas, and they and their children are successful, is that because of Indian culture, or because the children of doctors and engineers also do well? The second is social networks. Chua and Rubenfeld may not emphasise psychological research but their worldview is ultimately about psychology rather than the contacts an immigrant network might bring. Most fundamentally, they fail to justify their basic premise: that the way to understand success is as a phenomenon that applies to religious or ethnic groups. They say that if we couldn’t generalise about Jews or Chinese Americans, “we wouldn’t be able to understand the world we live in”. Treating people as individuals is, apparently, just too much like hard work.

Also published at ft.com.

The murkier side of transparency

‘Publishing clear information is often a way to make the world a better place – but not always. Sometimes it pays to be selective’

On a recent visit to Toronto, I was able to admire the city’s rather fashionable pedestrian traffic signals, which clearly show you how long you have before the lights change. Crossing the street to a flashing “3 – 2 – 1 – 0” is like experiencing your own little rocket launch.

Toronto isn’t the only city with such signals: Manhattan has them, Washington DC has had them for many years, and London is beginning to introduce them. But it’s Toronto that provides the stage for a fascinating new study in unintended consequences.

From late 2006 through 2008, countdown signals were gradually installed across the city. It is important to understand that from the point of view of safety, the order in which they were introduced was arbitrary. (Some accident black-spots are temporary, the result of bad luck. Had the signals been installed at junctions with a history of accidents, they would have looked like brilliant safety measures simply because the run of bad luck ended.)

In effect, Toronto accidentally arranged a randomised trial of the new signals. By examining the accident rate at each intersection and how it changed with the new signals, economists Sacha Kapoor and Arvind Magesan got a detailed picture of the effect of the countdown.

You might well anticipate that the countdowns would make junctions less dangerous, by telling pedestrians whether or not they have time to cross in safety. Toronto’s traffic planners certainly seemed to believe that would be the case. They were wrong. The new signals caused more accidents.

How could this be? Kapoor and Magesan suggest three explanations. One is that the signals cause pedestrians to take more risks – but it seemed that fewer pedestrians were involved in accidents after each signal was installed.

The other two explanations rely on the fact that it’s not only the pedestrians who see the countdown: drivers can too. If a signal is about to turn red for pedestrians crossing at a junction, then drivers who are trying to get across the junction in the same direction are also about to get a red light. Since there was more speeding and more rear-end collisions after the countdown signals were installed, Kapoor and Magesan reckon the natural explanation is that some drivers were accelerating into the junction to avoid being delayed, just as other drivers were slowing down.

It’s not the first time that economists have discovered that what looks like sensible transparency can have unintended consequences. Ten years ago, David Dranove, Daniel Kessler, Mark McClellan and Mark Satterthwaite looked at the impact of mandatory “report cards” in New York and Pennsylvania, which published data on the performance of individual doctors, hospitals or both.

One might imagine that this information would, at the very least, be convenient. At best it should spur physicians to improve their skills because patients would seek out the very best. But the researchers looked at the impact on cardiac surgery, and found a tragic side effect: once doctors and hospitals knew that their success rates would be published, they had a strong incentive to operate on the healthiest patients. The best hospitals had their pick of the sick and selected easy cases. Meanwhile patients with more complicated conditions were more likely to have surgery postponed. The net result: more money was spent, yet more people died of heart attacks.

Publishing clear information is often a way to make the world a better place – but not always. Sometimes it pays to be selective. Doctors could benefit from report cards, provided their patients never find out what they said. And Toronto’s countdown signals would work perfectly if only they could be hidden from drivers.

Also published at ft.com.

The economics of love

If you’re looking for Valentine’s Day inspiration, you could try:

“Everything I ever needed to know about Economics I learned from online dating” – Paul Oyer (Buy in UK; Buy in US) – A guide to economic ideas pegged on the author’s experience trying to get a date online. It’s fun without being revelatory.

“Marriage: A History” – Stephanie Coontz. (Buy in UK; Buy in US) – A weighty but fascinating history.

“Dear Undercover Economist” – My favourite letters from the “Dear Economist” column (Buy in UKBuy in US). Obviously this book is absolutely marvelous in every way.



Why opposites shouldn’t attract

‘While it may be natural and familiar, assortative mating also breeds inequality’

Those of you out courting next Friday, do enjoy yourselves – but with a twinge of guilt. Inequality has been rising for a generation in many places, especially the Anglophone countries. Let’s be honest: you and your romantic pursuits are part of the problem.

The issue here is something economists call “positive assortative mating”, a charming phrase that we blame on the evolutionary biologists. It describes the process of similar people pairing off with each other: beautiful people dating beautiful people, smokers dating smokers, nerds dating nerds. All perfectly natural, you might think.

While it may be natural and familiar, assortative mating also breeds inequality. Economists often look at sorting by education level, which is common and easy to measure. If the MBAs and PhDs were sprinkled randomly throughout the population that would spread the wealth around. But, of course, they tend to pair up with other MBAs and PhDs; meanwhile the high-school dropouts tend to end up with other high-school dropouts. Already prosperous people are made more prosperous yet by their marriages.

This is an interesting idea in theory but does it have any practical significance? A recent paper by Jeremy Greenwood and others looks at a large data set from the US Census Bureau through the lens of the Gini coefficient, which is a measure of inequality. It’s 63 in highly unequal South Africa, 40 in the UK and 23 in egalitarian Sweden. It’s 43 in the US Census data set; but if the couples in the data set were randomly paired off, the Gini coefficient would be a mere 34. Assortative mating increases inequality.

But does this pairing-off process matter more than it used to? Does it explain any part of the rise in inequality we’ve seen since the 1970s? The answer, again, is yes – but a guarded yes. Marriage patterns have little or nothing to do with the concentration of earning power in the hands of the richest 1 per cent and 0.1 per cent: women are major breadwinners in the top quarter of the distribution but less so right at the very top – not yet, at any rate.

But assortative mating is having an impact on inequality more broadly. It’s not so much that well-educated people are more likely to pair off – although they are – but that educated women are more likely to earn serious money than a generation ago.

Consider my own mother: she was well on the way to a PhD in biochemistry when I arrived on the scene in the early 1970s. She then dropped out of education and spent most of her time looking after her children. Her academic qualifications had no impact on our household income. Assortative mating has always been with us but it’s only in a world of two-income households that it increases income inequality.

The sociologist Christine Schwartz showed in 2010 that the incomes of husbands and wives in the US are far more closely correlated than they were in the 1960s, and that this explained about one-third of the increase in income inequality between married couples. John Ermisch and colleagues have shown other consequences: in both the UK and Germany, assortative mating substantially explains low social mobility because the children of prosperous parents marry each other.

We should not place too much emphasis on all this. Assortative mating explains only part of the rise of inequality, and perhaps very little at the top of the income scale. The usual remedies for inequality – unionisation, redistributive taxes, minimum wages – still have the same advantages and limitations as ever, even if they need to reflect the reality of the two-income household. It’s a reminder that the most welcome social trends can have unwelcome side-effects.

Happy Valentine’s day.

Also published at ft.com.

Don’t bet the house on price rises persisting

Supply constraints are not the only cause of the UK’s property inflation, writes Tim Harford

‘George Osborne has admitted that UK housing supply will struggle to keep up with demand for the next decade . . . ’, Financial Times, February 5

I saw the headlines: George Osborne predicts that house prices will keep rising for the next 10 years.

That’s the erroneous conclusion that seems to have emerged but it’s not what Mr Osborne said when giving evidence to the House of Lords economic affairs select committee. His only gesture towards a house-price forecast was to mention the view of the Office for Budget Responsibility. The OBR does forecast price rises but not with nearly the same gusto of private sector forecasters – often estate agents. So it’s strange to see the chancellor of the exchequer being linked with a bullish view on the price of houses.

But Mr Osborne predicts a continued shortfall of supply – and that can only mean that prices go up.

That rather assumes that the key reason for high house prices is a shortage of new homes. It’s far from clear that this is true.

Are you repealing the laws of supply and demand? Didn’t a Financial Times poll of economists say that the best response to high housing prices was to build more houses? What sort of economist are you anyway?

I quite agree that the UK needs more housebuilding – it would help provide jobs and cheaper, more environmentally friendly and more comfortable homes. And it’s true that all other things being equal, house prices will be lower in a scenario where lots of homes are built than in one where very few are built. But none of that means the chief cause of high house prices now is constrained supply – nor that continued supply constraints mean that the high prices will continue too.

I’m still confused.

OK. What is the single most reliable indicator that housing is scarce?

High house prices.

I disagree. It’s high rents. Rents can change more quickly, are affected less by the state of the UK mortgage market and don’t have a speculative component. People sometimes buy houses simply in the hope of reselling at a profit; not many people rent a house in the hope of a profitable sublet.

But aren’t rents high too?

Yes. But not nearly as high as house prices are, which is the point. A government review of the rental market in 2010 found that rents had increased by 40 per cent in the decade running up to the 2008 recession, almost exactly tracking the increase in what people earned. House prices, in contrast, had increased by more than 100 per cent.

A report last spring from the OECD also used rents as a benchmark to assess UK house prices and concluded that they were overvalued. Buy-to-let investment looks like an expensive proposition in many parts of the country unless rents rise sharply.

So you think it’s a bubble rather than supply and demand.

Scarce supply and robust demand is pushing rents up in many places, and that’s a good reason for public policy to encourage more housebuilding. But the additional house-price margin over and above what rents explain may indeed indicate a bubble.

Are there other explanations?

Certainly. It’s possible that investors have taken a far-sighted view of the prospects for future rents, and are buying houses in expectation that rents will leap in due course. Time will tell.

Or low interest rates?

I was coming to that. Real interest rates are very low and the government’s help-to-buy policies are also making it easier to buy houses. And houses are expensive because other assets are expensive, too. But real interest rates won’t stay low for ever.

Returning to the subject of building houses, has Mr Osborne done enough?

He has thrown money at banks and housebuyers and tried to liberalise the planning system but he admitted himself that the problem hasn’t been solved. There is colossal economic value to granting more planning permission – it can increase the value of agricultural land roughly a hundred times over.

So why don’t local authorities grant more permission?

Because they have little to gain but angry voters. If local authorities could reap some of the value of the planning permission they granted, they could use the cash to compensate existing residents and to provide services. That could be a vote-winner. But they can’t – so it isn’t.

Also published at ft.com.

The Royal accounts are printed in red and gold

The monarchy costs the same as the milk the nation pours on its cereal, says Tim Harford

‘Britain’s Royal Household spent more than it received last year and is doing too little to improve the management of its finances, a parliamentary watchdog says.’, Financial Times, January 28

What – parliamentarians have condemned deficit spending and poor financial management?

They are the experts on such things, I am sure. This is Margaret Hodge MP’s public accounts committee at work. It has a reputation for shaking things up but I’ve never been able to take Ms Hodge seriously since her complaints about a cap on housing benefit.

What was risible about a cap on housing benefit?

Nothing risible about that as such. But because the cap would particularly affect Londoners claiming the benefit, Ms Hodge was among those complaining that it would change the shape of London. She called it “a massive demographic and social upheaval the likes of which have never been seen before”. Since the London mayor’s office – which also opposed the policy – estimated that fewer than 0.2 per cent of the capital’s families would have to move home as a result, that suggests an alarmingly shaky grasp of the numbers for someone whose job is to oversee value for money in public spending.

You’re an unforgiving sort. In any case, Ms Hodge’s committee is concerned about the way the world’s largest housing benefit cheque is being spent.

Yes, the Royal Household receives £31m – a slice of the income from the Crown Estate.

Isn’t that the Queen’s money?

The Estate is nominally the property of the Queen but George III signed over its revenue to parliament.

Wasn’t he the mad one?

Not at the time he gave up the revenues from the Crown Estate. In any case, the current arrangement is only a couple of years old. The Royal Household gets 15 per cent of the income from the Crown Estate. That income, I might add, is sharply rising.

So all this talk of the Queen being down to her last million is nonsense?

It is obviously jolly amusing and has provoked many enormously original jokes. The Queen’s cash reserve has indeed fallen to £1m – not much relative to the scale of the spending required to run the Royal Household. But since income is rising, both from the Crown Estate and from admissions to the likes of Windsor Castle, and spending has been steadily falling, the Royal Household is about to go into surplus. That is more than you can say for the government.

But you can understand why parliament takes an interest. There’s serious money at stake. Think of the hospital beds you could provide for £31m.

Oh, absolutely. You could keep the English National Health Service running for almost three hours for that kind of money.

I’m getting the sense that you’re a monarchist.

Not particularly, but one thing I’m sure of is that the case for or against the monarchy can’t depend on £31m, which is roughly the cost of the milk the nation pours on its cornflakes each morning, plus a bit of tea and toast. This has been reported in all the papers for roughly the same reason that Kim Kardashian’s latest celebrity exploits are reported everywhere.

Why is that, by the way?

Because we’re all monkeys, and we’re fascinated by other monkeys with higher status than us.

But the public accounts committee thinks the real monkeys are the ones in charge of maintaining Royal Household properties – that whoever is in charge of electrical repairs, repointing the bricks, that sort of thing, has been letting things fall into ruin.

Yes – the committee’s view is also that the Royal Household needs to take responsibility for itself and the Treasury needs to take responsibility for it; that it is successfully saving money but should save more; and that it is successfully raising money from tourists but should raise more from tourists. Basically, just think really hard about whatever you already believe is true about the Royal Household, and I am sure I can spare you the trouble of reading the committee’s report.

And do you agree that maintenance of Household properties is lax?

I don’t know because they’ve never invited me in to poke around the plumbing. But it wouldn’t surprise me. There isn’t much competition, and as the great economist John Hicks said: “The best of all monopoly profits is a quiet life.” That may well be how the courtiers felt – until the public accounts committee came along.

Also published at ft.com.

How to plan for your pension

‘The standard tool is the online pension calculator, of which countless variants exist. There’s only one problem: they leave out almost everything that matters’

Everyone seems to be talking about whether pensioners are vulnerable and poor or living gilded lifestyles. I decided to take a rather self-centred look at that question; I am an economist, after all. I’m 40. Retirement is more than half my working life away. Leaving aside the fate of today’s pensioners, what about my fate? How much cash will I enjoy in my golden years?

The standard tool for such crystal-gazing is the online pension calculator, of which countless variants exist. Type in the basics (age, income, retirement date, current pension contributions, current pension pot) and the calculator spits out the projected size of the eventual pension pot, along with the monthly income it is forecast to generate. More complex varieties allow for all sorts of tweaks – inflation, investment returns, and smoothly rising income and contributions over the years.

There’s only one problem: these calculators leave out almost everything that matters. It is useful, I suppose, to know what one’s income in retirement would be given a particular salary progression, rate of return on a portfolio, inflation rate, annual charges and the annuity rate available on retirement – although simply to list the variables gives a sense of just how uncertain that “knowledge” really is.

It is worth adding that, over the past 14 years the FTSE 100 index hasn’t risen, even in nominal terms; over the 14 years prior to that, the index roughly quintupled. Stick that in your pension calculator and smoke it. In some ways that’s an extreme case – after all, sensible investors rely on reinvesting dividends and will diversify.

Yet, in other ways, the FTSE’s fate over the past 14 years understates the uncertainty produced by long-term compounding. The relevant time horizon isn’t 14 years but more like 30 – over such a span, a modest 4 per cent rate of return would turn £100,000 into £310,000. A tastier 8 per cent return would compound into £930,000. And an optimistic-but-not-unheard-of 12 per cent return would deliver nearly £2.7m.

Those numbers will surprise some: we underestimate the value of a high rate of compound interest so predictably that behavioural economists even have a name for the condition: exponential growth bias. A reasonable forecast range for a £100,000 investment then, 30 years later, seems to be anything from several million pounds to less than you had when you started.

The uncertainties don’t end there – when we look away from the spreadsheet, at the real world, we realise they are barely beginning. Three big risks simply don’t figure in the tidy world of the calculator: one, that I lose my job and can’t find anything comparable; two, that my wife and I divorce, an expensive business; three, that anything from depression to a slipped disc to cancer renders me too ill to work. Ill health, unemployment and divorce are common and bad for your net worth. (They are also bad for measures of “subjective wellbeing”; more colloquially, they make you sad.)

Then there are the wilder possibilities – I might be defrauded by con artists; I could be sued for libel; my home, which is near a flood plain, may be rendered uninhabitable and unsellable by the weather.

I’m not planning on being sideswiped by any of these misfortunes but, then, who is? A common cause of a penurious old age is not a savings problem as such, but an insurance problem: people who are on track to save enough for a comfortable retirement but are then derailed by “events, dear boy, events”.

My plan for a gilded retirement still involves saving for a pension but I have reinforced it with a number of other tactics: buying disability insurance, keeping fit, being nice to my wife – and hoping that the fates are kind.

Also published at ft.com.


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