Tim Harford The Undercover Economist

Articles published in March, 2016

Trump, trade and ‘the China shock’

‘Freer trade has inflicted a more grievous toll than economists, myself included, had expected’

It hasn’t escaped the notice of pundits that the political iconoclasts Bernie Sanders and Donald Trump have something in common: they’re sceptical about trade. Trump, for example, has riffed expansively: “We don’t win any more. We don’t beat China in trade. We don’t beat Japan . . . We can’t beat Mexico, at the border or in trade.” Sanders expressed his concerns with a little more precision: “While bad trade agreements are not the only reason why manufacturing jobs in the US have declined, they are an important factor.”

Both men have vastly outperformed expectations in the primary campaigns. There are many reasons for that but perhaps the simplest explanation is that freer trade has inflicted a more grievous toll than economists, myself included, had expected.

Fifteen years ago, the conventional economic wisdom was that free trade was almost unambiguously a good idea. Here’s the basic logic. There are two ways for the British to get hold of wine. We can grow and press our own grapes, or we can make something that the French want and trade with them. If we’re good at making, say, computer games and the French are good at making wine, then trading is the better way to get what we want.

The idea that we might, Trumpishly, “beat the French in trade” sounds appealing but is incoherent. And while a British Sanders might point to the loss of jobs in the UK wine industry, that would miss the gains in the software industry. There is little economic difference between a tariff on the import of French wine and a tariff on the export of British software.

Here’s a parable beloved of economists. An entrepreneur announces a technological breakthrough: he has a machine that can disintegrate computer game discs and reconstitute the atoms into fine wine. He sets up a factory on the coast of Kent with the machine inside. Computer games go in, and cases of wine emerge. But then an investigative reporter from the Financial Times gains access to the factory and finds that there is no machine — just a dock where a forklift truck operator busily unloads French wine from a boat, replacing it with computer games for export to the French market. Should we care? From the point of view of the British, isn’t France merely a technology for converting computer games into wine?

With formal models to back up this sort of story, most economists took the view that when countries lower their trade barriers, even unilaterally, they prosper. What the British wine industry loses, the UK computer games industry gains. Meanwhile, consumers get better and cheaper wine into the bargain.

It was always clear that, despite the win-win nature of trade at the national level, freer trade could create losers — such as British vineyards and French computer game studios. But the conventional wisdom was that these losses were both small and fixable with the right policies of retraining or redistribution. Most importantly, people who lost their jobs could find new ones in booming export industries.

Admittedly, it was evident even 20 years ago that median household incomes were stagnating in the US, inequality was rising in anglophone countries, and manufacturing employment was steadily falling. But these trends seemed to owe more to technological change than to globalisation.

I’ve been phrasing all this “conventional wisdom” in the past tense but, for the most part, it stands up. However, it is acquiring an important and depressing footnote. A new research paper, “The China Shock”, from David Autor, David Dorn and Gordon Hanson, is part of a rethink under way in the economics profession.

Autor and his colleagues try to zoom in on the impact of China’s emergence as a trading power. China’s rise has been dramatic, driven almost entirely by internal policy changes inside China, and has had a differential effect on different regions and industries. For example, Tennessee and Alabama are both US manufacturing centres exposed to global competition. But Tennessee’s furniture manufacturing industry is much more exposed to China in particular than is Alabama’s heavier manufacturing industries. This helps the researchers to figure out with more confidence what the impact of the China shock has been.

Autor, Dorn and Hanson conclude that the American workers who have been hurt by competition with China have been hurt more deeply, and for a longer period, than many economists predicted. Employment has fallen in industries exposed to trade competition, as expected. But it has not shown much signs of rising in export-oriented sectors.

The US labour market is less flexible than we thought, it seems. In a simplified economic model, workers move smoothly to a new home, a new industry, even a new level of education. In practice, Autor and his colleagues find that communities hit by Chinese competition often do not adapt; they wither. It may take a generation or two, rather than a few years, to adjust.

In the long run, of course, that adjustment will happen — just as we have adjusted to the decline of agricultural labour or the need for typewriter repairs. But the long run is longer than many economists feared. It is easy to see why supporters of Trump and Sanders have run out of patience.

Written for and first published at ft.com.

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Capital ideas in a time of inequality

‘The wealthy do not simply wallow in bank vaults like Scrooge McDuck. They spend their money’

In January 1963, Warren Buffett included the following impish observation in his letter to his investment partners. “I have it from unreliable sources that the cost of the voyage Isabella underwrote for Columbus was approximately $30,000.”

Unreliable indeed; there was no dollar in 1492. But we get the gist. Buffett goes on to observe that while the voyage could be considered “at least a moderately successful utilisation of venture capital”, if Queen Isabella had instead invested the $30,000 in something yielding 4 per cent compound interest, the invested sum would have risen to $2tn by 1962. For her inheritors’ sake, perhaps Isabella should have said no to Columbus and simply found the 15th-century equivalent of a passive index fund instead.

Buffett’s thought experiment returned to me as I browsed through the latest list of billionaires from Forbes. None of the leading players had achieved their position by the simple accumulation of family wealth over generations. The top five — Bill Gates, Amancio Ortega, Buffett, Carlos Slim and Jeff Bezos — are all entrepreneurs of one form or another. According to economists Caroline Freund and Sarah Oliver, the proportion of billionaires who inherited their fortunes has fallen from 55 per cent two decades ago to 30 per cent today.

Is this absence of old-money trillionaires because Buffett’s 4 per cent compound interest was unavailable to the wealthy and powerful of pre-industrial Europe? Hardly. If anything, 4 per cent is conservative. According to Thomas Piketty’s bestselling book Capital in the Twenty-First Century (2013), the real rate of return on capital, after taxes and capital losses, was 4.5 per cent in the 16th and 17th centuries, then 5 per cent until 1913. Although it fell sharply between the wars, the effective average rate of return was very nearly 4.3 per cent across the five centuries. At that rate, $30,000 invested in 1492 would be worth $110tn today.

Not to get too technical, but $110tn is a lot of money. It’s more than 1,000 times the wealth of the richest man in the world, Bill Gates. It’s 17 times the total wealth of the 1,810 billionaires on the Forbes list — or, alternatively, nearly half the household wealth of every citizen on the planet. (According to Credit Suisse’s Global Wealth Report, total global household wealth is $250tn.) Queen Isabella’s investment advisers apparently let her down. Patient, conservative investments would have left her heir today with a fortune to tower over every modern plutocrat.

All this brought to mind Piketty’s “r>g”, a mathematical expression so celebrated that people started putting it on T-shirts. It describes a situation where “r” (the rate of return on capital) exceeds “g” (the growth rate of the economy as a whole). That is a situation that described most of human history, but notably not the 20th century, when growth rates soared while capital had a tendency to be nationalised, confiscated or reduced to rubble.

“r>g” is significant because if capital is reinvested and grows faster than the economy, it will tend to loom larger in economic activity. And since capital is more unequally distributed than labour income, “r>g” may describe a society of increasingly entrenched privilege, where wealth and power steadily accrue in the hands of heirs.

This is a fascinating, and worrying, possibility. But it is a poor description of the modern world. For one thing, when billionaires divide their inheritance, mere procreation can be a social equaliser. Historically, the great houses of Europe intermarried and concentrated wealth in the hands of a single heir. (No wonder: one of Queen Isabella’s grandsons, Ferdinand I, had 15 children.) But these days, disinheriting daughters and second sons is out of fashion. (That said, “assortative mating”, the tendency of educated people to marry each other, is back and may explain more about rising income inequality than we tend to realise.)

Another thing: the rich do not simply wallow in money vaults like Scrooge McDuck. They spend. According to Harvard economist Greg Mankiw: “A plausible estimate of the marginal propensity to consume out of wealth, based on both theory and empirical evidence, is about 3 per cent.” Instead of 4.3 per cent, then, wealth compounds at 1.3 per cent after allowing for this spending. Five centuries of compound interest at 1.3 per cent turns $30,000 into about $25m, a fine inheritance indeed but not the kind of money that will get you near the Forbes list.

Of course, inherited privilege shapes our societies not only among the plutocracy but down in the rolling foothills of English middle-class wealth. There, economic destiny is increasingly governed by whether your parents bought a house in the right place at the right time — and by the UK government’s astonishing abolition of inheritance tax on family homes.

But whether mega-wealth in the 21st century will be driven by the patient accumulation of rents on capital, rather than the disruptive entrepreneurship of the late 20th century, remains to be seen. After all, long-term real interest rates in advanced economies have fallen fairly steadily from 4 to 5 per cent three decades ago to nothing at all today. You don’t need to be Warren Buffett to figure out that if you want to get rich by accumulating compound interest of zero, you’ll be waiting a long time.

Written for and first published at ft.com.

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A modest proposal – let’s just abolish the Budget

Once upon a time, it made sense to have an annual Budget speech. When the central economic fact of the year was whether the harvest had failed or not, it behoved the Chancellor to declare how he planned to spend whatever he happened to have in his coffers. But a vital institution for the pre-industrial age has mutated into a mere circus for the post-industrial one. The central question that this Budget provoked in my mind was this: why on earth do we still have a Budget?

Skim through the transcript of yesterday’s speech — if you can bear to — and you’ll find that the items fall into a few categories: (1) trivial; (2) responses to silly self-imposed rules; (3) economic forecasts that will later be wrong; (4) pure rhetoric; (5) worse than useless; (6) irrelevant.

Mr Osborne opened with a list of all the ways in which the UK economy is strong, skimmed over all the ways in which it is weak, and blamed the Labour party or foreigners for everything. (Rhetoric.)

Then he ran through the latest outlook from the Office for Budget Responsibility, an institution that represents all that is best about rigorous independent economic forecasting — and is therefore bound to be wrong. (Bad forecasts.)

He admitted that he had broken his own rather odd rule about the ratio of debt to gross domestic product, before announcing that according to a different, nonsensical metric, he looked rather good. (Silly self-imposed rules.)

Mr Osborne threw the usual glitter-bomb of little presents. (Trivial.)

Consider the £19m for “community-led housing schemes” in the south-west of England. Very nice, but if every £1m of spending earned one word from the chancellor, his Budget speech would be considerably longer than War and Peace. Then there’s the donation of tampon VAT revenues to charity, the halving of the Severn Bridge toll, and a tax break for touring museum exhibitions. Isn’t it strange how the treats are emphasised and the multibillion pound cuts and tax rises are always relegated to the appendices?

Then there’s the Chancellor’s odd tradition of pencilling in an increase to fuel duty year after year and, regardless of circumstances, coming up with an excuse to cancel the increase one more time. (Worse than useless.)

We also have major reforms to the school system. (Nothing to do with the Budget.)

What are we left with? The bodged introduction of a sugar tax and yet another wheeze to reform pension saving, the Lifetime Isa. Both policies would have been far better separated from the rabbit-out-of-hat Budget show, and considered on their merits.

There have been more dramatic Budgets than this, of course, but even then the drama has too often fallen into the “worse than useless” category.

Would the country’s economic policy really be harmed if the chancellor set out his fiscal direction at the beginning of the parliament and left it unchanged unless extraordinary circumstances intervened?

We should abolish 100 per cent of Autumn Statements and 80 per cent of Budgets — that’s a fiscal rule that I could really get behind.

Written for and first published in the Financial Times.

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17th of March, 2016Other WritingComments off

Why Osborne’s sugar tax is half baked

I’m all in favour of a sugar tax, as I wrote in the FT Magazine on Saturday. It’s a shame, then, that — despite the headlines to the contrary — George Osborne hasn’t introduced one.

His proposal instead is to tax the manufacturers and importers of a particular variety of sugary drink. I am no dentist or dietitian, but it seems strange to take the view that sugar in general poses no risk to the nation’s teeth or waistline, unless it comes in a soft drink.

Coke and Pepsi are a problem, apparently. But it seems that sugar lumps in tea or coffee are not. Neither are cartons of chocolate milk. Nor syrupy concoctions from Starbucks and Costa. Nor soft drinks produced by boutique producers. Mars bars are fine. So are cakes. So are Coco Pops and Frosties, and for that matter the remarkable quantities of sugar that infuse cereals such as Bran Flakes, or are buried in the recipes of many ready meals. All these forms of sugar will continue to reach our taste buds free of a sugar tax.

Mr Osborne’s proposal will work, after a fashion. There is abundant evidence that people adjust their behaviour in response to financial incentives, whether through the window tax-avoiding architecture of 18th-century Britain or the inheritance tax-avoiding feat of Australians in postponing the date of their deaths to a more tax-efficient time.

So yes, as Mr Osborne expects, large companies will try to put less sugar in their soft drinks, or raise the prices of those drinks, or both. Sugar consumption from those sources will fall. But they may well rise elsewhere. For many people, a chocolate bar and a fizzy drink are substitutes. If the fizzy drink gets more expensive, the chocolate bar is a tasty alternative for the sweet-toothed consumer. It has more fat in it, too.

It’s clear enough why the chancellor has opted for this approach. He wants to blame large companies, not voters, and hide the fact that ultimately consumers will pay the tax. A broad-based tax on sugar itself would have been simpler, braver and far more effective. But Mr Osborne wanted his Budget to leave voters with a sweeter taste in the mouth.

Written for and first published in the Financial Times.

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17th of March, 2016Other WritingComments off

These are the sins we should be taxing

‘The UK already relies more than most rich countries on fuel, alcohol and tobacco duties’

Is it time to rethink the way we tax sin? The UK has long levied special taxes — “duties” — on products that pollute the environment, the lungs, the liver or the pocketbook: driving, flying, tobacco, alcohol and gambling. There are good reasons for these taxes. The government must raise revenue somehow, so there is much to be said for taxing products that are price-insensitive, socially harmful or, at the very least, unhealthy temptations.

But the way sin taxes are levied in practice is an incoherent muddle. Plenty of products that are bad for us (bacon, butter, sugar) get favourable tax treatment, attracting no value-added tax, although the standard VAT rate is 20 per cent. Heating and lighting our homes also attracts a concessional rate of tax, although a kilogram of carbon dioxide emitted from a power station or a gas boiler contributes to climate change just as much as a kilogram emitted from a car. Vehicle excise duty is a tax not on driving but on owning a car. And the rate of duty on alcohol varies depending on how we drink it.

It is easy to see how successive chancellors bodged their way to this point. Taxes on the pint or at the pump are eye-catching; raising them seems morally serious but cutting them is a crowd-pleaser. And so they bounce around like the political football they are.

George Osborne has an opportunity to fix the situation this Wednesday during his Budget speech. Here’s what he should do.

First, similar harms should attract similar taxes. The UK duty on 10ml of pure alcohol, roughly the amount in a shot of vodka or half a pint of beer, varies wildly. It is about 7p in strong cider, 18p in strong beer, or 28p in whisky and wine. A consistent price per millilitre would make more sense.

Second, he should broaden the sin tax base. UK duties are concentrated on tobacco, motor fuel and alcohol. As the Institute for Fiscal Studies showed in its “green budget” in February, revenue from duties has been falling for decades, from 4.1 per cent of national income in the early 1980s to 2.6 per cent last year. This drop is the net result of falling duties on fuel (back to the levels of 20 years ago in real terms), declining duties on alcohol and lower consumption of both tobacco and alcohol.

Should the chancellor, then, raise duties? Perhaps, but there are limits. The UK already relies more than most rich countries on fuel, alcohol and tobacco duties. Above a certain level, the smugglers and bootleggers take over.

A wiser approach is to tax sins that have thus far escaped attention. The most obvious is congestion: fuel taxes do not distinguish between driving along an uncongested country road and driving in rush-hour in a built-up area, which causes vastly more social harm. Congestion charges, which are now technically feasible, are fair and efficient, if the political case can be made.

Another obvious sin is sugar. While one can be too puritanical about nudging people to take care of their health and waistline, it seems strange that perfectly reasonable activities such as buying a T-shirt or earning a living attract tax, while sugar is tax-free. A sugar tax of a half-penny a gram would add about 18p to the cost of a can of Coke, more than that to a family pack of Bran Flakes, 25p to a 200ml bottle of ketchup and 45p to the price of a packet of chocolate digestives.

Third, Osborne should avoid arbitrary cut-offs where possible. In a bygone age it must have been simpler to slap a tax on an item in a particular category but this has led to the infamous “Jaffa Cake” problem. Are Jaffa Cakes — sponge discs with an orange jelly topping, partly coated in chocolate — cakes (zero VAT) or biscuits (VAT at 20 per cent)? A tribunal in 1991 mused that Jaffa Cakes are packaged much like biscuits, are sold next to biscuits, are the same size and shape as biscuits and, like biscuits, are eaten without a fork. However, it also noted that they are made of a cake-like dough, are soft and, like a cake, they go harder when stale. The tribunal eventually concluded that Jaffa Cakes are cakes, and thus they remain tax-advantaged, even as they nestle on the supermarket shelves next to their biscuitish rivals.

All of this is nonsense from any angle. In discouraging unhealthy eating, the relevant issue should not be whether food is circular or requires a fork but how much sugar, salt and saturated fat it contains. Sugar can be measured and taxed by the gram, whether it comes dissolved in oft-demonised soft drinks or added to bread, cereal, ready-meals, chocolate bars or anything else.

Finally, we should not worry too much about the distributional consequences of sin taxes. This isn’t because distribution doesn’t matter — it does. But, by some measures at least, alcohol and fuel duties hit the middle classes harder than they hit the poor. In any case, there are better ways to deal with inequality than by cutting sin taxes. People on low incomes need support but that help is better provided through tax credits, child benefit or good public services rather than cheap booze, sweets and tobacco. We are all free to buy vodka and cigarettes. Yet trying to make them cheaper would be a strange way to address social injustice.

Written for and first published at ft.com.

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The lost leisure time of our lives

‘Keynes was right to predict that we would be working less but overestimated for how long that trend would continue’

Three hours a day is quite enough,” wrote John Maynard Keynes in his 1930 essay Economic Possibilities for our Grandchildren. The essay continues to tantalise its readers today, thanks in part to a forecast that is looking magnificently right — that in advanced economies people could be up to eight times better off in 2030 than in 1930 — coupled with a forecast that is looking spectacularly wrong, that we would be working 15-hour weeks.

In 2008, economists Lorenzo Pecchi and Gustavo Piga edited a book in which celebrated economists pondered Keynes’s essay. One contributor, Benjamin Friedman of Harvard University, has recently revisited the question of what Keynes got wrong, and produced a thought-provoking answer.

First, it is worth teasing out the nature and extent of Keynes’s error. He was right to predict that we would be working less. We enter the workforce later, after long and not-always-arduous courses of study. We enjoy longer retirements. The work week itself is getting shorter. In non-agricultural employment in the US, the week was 69 hours in 1830 — the equivalent of working 11 hours a day but only three hours on Sundays. By 1930, a full-time work week was 47 hours; each decade, American workers were working two hours less every week.

But Keynes overestimated how rapidly and for how long that trend would continue. By 1970 the work week was down to 39 hours. If the work week had continued to shrink, we would be working 30-hour weeks by now, and perhaps 25-hour weeks by 2030. But by around 1970, the slacking-off stopped. Why?

One natural response is that people are never satisfied: perhaps their desire to consume can be inflamed by advertisers; perhaps it is just that one must always have a better car, a sharper suit, and a more tasteful kitchen than the neighbours. Since the neighbours are also getting richer, nothing about this process allows anyone to take time off.

No doubt there is much in this. But Friedman takes a different angle. Rather than asking how Keynes could have been so right about income but so wrong about leisure, Friedman points out that Keynes might not have been quite so on the mark about income as we usually assume. For while the US economy grew briskly until the crisis of 2007, median household incomes started stagnating long before then — around 1970, in fact.

The gap between the growth of the economy and the growth of median household incomes is explained by a patchwork of factors, including a change in the nature of households themselves, with more income being diverted to healthcare costs, and an increasing share of income accruing to the highest earners. In short, perhaps progress towards the 15-hour work week has stalled because the typical US household’s income has stalled too. Household incomes started to stagnate at the same time as the work week stopped shrinking.

This idea makes good sense but it does not explain what is happening to higher earners. Since their incomes have not stagnated — far from it — one might expect them to be taking some of the benefits of very high hourly earnings in the form of shorter days and longer weekends. Not so. According to research published by economists Mark Aguiar and Erik Hurst in 2006 — a nice snapshot of life before the great recession — higher earners were enjoying less leisure.

So the puzzle has taken a different shape. Ordinary people have been enjoying some measure of both the income gains and the leisure gains that Keynes predicted — but rather less of both than we might have hoped.

The economic elites, meanwhile, continue to embody a paradox: all the income gains that Keynes expected and more, but limited leisure.

The likely reason for that is that, in many careers, it’s hard to break through to the top echelons without putting in long hours. It is not easy to make it to the C-suite on a 20-hour week, no matter how talented one is. And because the income distribution is highly skewed, the stakes are high: working 70 hours a week like it’s 1830 all over again may put you on track for a six-figure bonus, while working 35 hours a week may put you on track for the scrapheap.

The consequences of all this can emerge in unexpected places. As a recent research paper by economists Lena Edlund, Cecilia Machado and Maria Micaela Sviatschi points out, urban centres in the US were undesirable places to live in the late 1970s and early 1980s. People paid a premium to live in the suburbs and commuted in to the city centres to work. The situation is now reversed. Why? The answer, suggest Edlund and her colleagues, is that affluent people don’t have time to commute any more. They’ll pay more for cramped city-centre apartments if by doing so they can save time.

If there is a limited supply of city-centre apartments, and your affluent colleagues are snapping them up, what on earth can you do? Work harder. Homes such as Keynes’s elegant town house in Bloomsbury now cost millions of pounds. Three hours a day is not remotely enough.

Written for and first published at ft.com.

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How to make good guesses

‘Would you say that someone reading the FT is more likely to have a PhD or to have no college degree at all?’

What’s the likelihood that the British economy will fall into recession this year? Well, I’ve no idea — but I have a new way to guess.

Before I reveal what this is, here’s a totally different question. Imagine that you see someone reading the Financial Times. Would you say that this individual, clearly a person of discernment, is more likely to have a PhD or to have no college degree at all?

The obvious response is that the FT reader has a PhD. Surely people with PhDs better exemplify the FT reader than people with no degree at all, at least on average — they tend to read more and to be more prosperous.

But the obvious response is too hasty. First, we should ask how many people have PhDs and how many people have no college degree at all? In the UK, more than 75 per cent of adults have no degree but the chance that a randomly chosen person has a PhD is probably less than 1 per cent.

It only takes a small proportion of non-graduates to read the FT before they’ll outnumber the PhD readers. This fact should loom large in our guess, but it does not.

Logically, one should combine the two pieces of information, the fact that PhDs are rare with the fact that FT readers tend to be well educated. There is a mathematical rule for doing this perfectly (it’s called Bayes’ rule) but numerous psychological experiments suggest that it never occurs to most of us to try. It’s not that we combine the two pieces of information imperfectly; it’s that we ignore one of them completely.

The number that gets ignored (in this example, the rarity of PhDs) is called the “base rate”, and the fallacy I’ve described, base rate neglect, has been known to psychologists since the 1950s.

Why does it happen? The fathers of behavioural economics, Daniel Kahneman and Amos Tversky, argued that people judge such questions by their representativeness: the FT reader seems more representative of PhDs than of non-graduates. Tversky’s student, Maya Bar-Hillel, hypothesised that people seize on the most relevant piece of information: the sighting of the FT seems relevant, the base rate does not. Social psychologists Richard Nisbett and Eugene Borgida have suggested that the base rate seems “pallid and abstract”, and is discarded in favour of the vivid image of a person reading the pink ’un. But whether the explanation is representativeness, relevance, vividness or something else, we often ignore base rates, and we shouldn’t.

At a recent Financial Times event, psychologist and forecasting expert Philip Tetlock explained that good forecasters pay close attention to base rates. Whether one is forecasting whether a marriage will last, or a dictator will be toppled, or a company will go bankrupt, Tetlock argues that it’s a good idea to start with the base rate. How many marriages last? How many dictators are toppled? How many companies go bankrupt? Of course, one may have excellent reasons to depart from the base rate as a forecast but the base rate should be the beginning of the journey.

On this basis, my guess is that there is a 10 per cent chance that the UK will begin a recession in 2016. How so? Simple: in the past 70 years there have been seven recessions, so the base rate is 10 per cent.

Base rates are not just a forecasting aid. They’re vital in clearly understanding and communicating all manner of risks. We routinely hear claims of the form that eating two rashers of bacon a day raises the risk of bowel cancer by 18 per cent. But without a base rate (how common is bowel cancer?) this information is not very useful. As it happens, in the UK, bowel cancer affects six out of 100 people; a bacon-rich diet would cause one additional case of bowel cancer per 100 people.

Thinking about base rates is particularly important when we’re considering screening programmes or other diagnostic tests, including DNA tests for criminal cases.

Imagine a blood test for a dangerous disease that is 75 per cent accurate: if an infected person takes the test, it will detect the infection 75 per cent of the time but it will also give a false positive 25 per cent of the time for an uninfected person. Now, let’s say that a random person takes the test and seems to be infected. What is the chance that he really does have the disease? The intuitive answer is 75 per cent. But the correct answer is: we don’t know, because we don’t know the base rate.

Once we know the base rate we can express the problem intuitively and solve it. Let’s say 100 people are tested and four of them are actually infected. Then three will have a (correct) positive test, but of the 96 uninfected people, 24 (25 per cent) will have a false positive test. Most of the positive test results, then, are false.

It’s easy to leap to conclusions about probability, but we should all form the habit of taking a step back instead. We should try to find out the base rate, or at least to guess what it might be. Without it, we’re building our analysis on empty foundations.

Written for and first published at ft.com.

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