Once you know what the question actually is, you’ll know what the answer means.
—DEEP THOUGHT (a supercomputer in Douglas
Adams’s Hitchhiker’s Guide to the Galaxy)
It was a vital question. Across the UK, mortality rates for newborn babies varied substantially for no obvious reason. Could doctors and nurses be doing anything different to save these children? Clinicians were despatched to hospitals with better performances, instructed to think about the lessons that could be learned and to contemplate reconfiguring their own maternity services from the ground up.
But Dr Lucy Smith of the University of Leicester had a nagging doubt.1 So she looked in detail at the data from two hospital groups, one in the English Midlands and one in London. The hospitals served very similar communities, and yet the death rates of newborns were noticeably lower in London. Were the London hospitals really doing something different in their clinics, or labour wards, or neonatal intensive care units?
No, found Dr Smith. The explanation of the disparity in mortality rates was quite different.
When a pregnancy ends at, say, twelve or thirteen weeks, everyone would call that a miscarriage. When a baby is born prematurely at twenty-four weeks or later, UK law requires this to be recorded as a birth. But when a pregnancy ends just before this cut-off point – say, at twenty-two or twenty-three weeks – how it should be described is more ambiguous. A foetus born at this stage is tiny, about the size of an adult’s hand. It is unlikely to survive. Many doctors call this heartbreaking situation a ‘late miscarriage’, or a ‘late foetal loss’, even if the tiny child briefly had a heartbeat or took a few breaths. Dr Smith tells me that parents who have been through this experience often feel strongly that the word ‘miscarriage’ is inadequate. Perhaps in the hope of helping these parents to process their grief, the community of neonatal doctors in the Midlands had developed the custom of describing the same tragedy in a different way: the baby was born alive, but died shortly after.
Mercifully few pregnancies end at twenty-two or twenty-three weeks. But after doing some simple arithmetic, Lucy Smith realised that the difference in how these births were treated statistically was enough to explain the overall gap in newborn mortality between the two hospital trusts. Newborns were no more likely to survive in London after all. It wasn’t a difference in reality, but a difference in how that reality was being recorded.
The same difference affects comparisons between countries. The United States has a notoriously high infant mortality rate for a rich country – 6.1 deaths per thousand live births in 2010. In Finland, by comparison, it is just 2.3. But it turns out that physicians in America, like those in the UK’s Midlands, seem to be far more likely to record a pregnancy that ends at twenty-two weeks as a live birth, followed by an early death, than as a late miscarriage. Perhaps this is for cultural reasons, or perhaps it reflects different legal or financial considerations. Whatever the reason, some – by no means all – of the high infant mortality rate in the United States seems to be the result of recording births before twenty-four weeks as live when in other countries they would be recorded as miscarried pregnancies. Looking only at babies born after twenty-four weeks, the US infant mortality rate falls from 6.1 to 4.2 deaths per thousand live births. The rate in Finland barely shifts, from 2.3 to 2.1.2
The issue also arises when comparing trends over time in the same country. When the infant mortality rate rose between 2015 and 2016 in England and Wales, against a history of steadily falling rates, the press understandably raised the alarm. ‘Obesity, poverty, smoking and a shortage of midwives could all be factors, say health professionals,’ said the Guardian newspaper.3
Indeed they could. But a group of doctors, writing to the British Medical Journal, pointed out that official statistics were also recording a dramatic rise in the number of live births at twenty-two weeks of gestation, or even earlier.4 More and more doctors, it seems, were following the Midlands trend of changing their recording practices to record live births and early deaths, rather than late miscarriages. And this was sufficient to explain the increase in the infant mortality statistics.
There is an important lesson here. Often, looking for an explanation really means looking for someone to blame. The infant mortality rate is rising – are politicians not providing enough money for the health service, or is the problem caused by mothers smoking or getting fat? The infant mortality rate is lower in London than in the Midlands – what are hospitals in the Midlands doing wrong? In truth, there may never have been anything to blame anybody for at all.
When we are trying to understand a statistical claim – any statistical claim – we need to start by asking ourselves what the claim actually means.
Measuring infant mortality, at first glance, means doing something sad and simple: counting the babies who died. But think about it for a moment and you realise that the distinction between a baby and a foetus is anything but simple – it’s a deep ethical question that underlies one of the most acrimonious divides in US politics. The statisticians have to draw the line somewhere. If we want to understand what is going on, we need to understand where they drew it.
The coronavirus pandemic has raised similar questions. As I write these words, on 9 April 2020, the media are reporting that in the last twenty-four hours, 887 people died with Covid-19 on the British mainland – but I happen to know that number is wrong. Data detective work from the Scottish statistician Sheila Bird tells me that the true figure is more likely to be about 1500.5 Why such a huge disparity? Partly because some people died at home, and the statistics represent only those who died in a hospital. But mostly because these overstretched hospitals are reporting deaths with a delay of several days. Deaths announced today, a Thursday, probably took place on Sunday or Monday. And since the death toll has been growing exponentially, telling us about what happened three days ago understates how bad things are now.*
The whole discipline of statistics is built on measuring or counting things. Michael Blastland, co-creator of More or Less, imagines looking at two sheep in a field. How many sheep in the field? Two, of course. Except that one of the sheep isn’t a sheep, it’s a lamb. And the other sheep is heavily pregnant – in fact, she’s in labour, about to give birth at any moment. How many sheep again? One? Two? Two and a half? Counting to three just got difficult. Whether we’re talking about the number of nurses employed by a hospital (do two part-time nurses count as two nurses, or just one?) or the wealth of the super-rich (is that the wealth they declare to the taxman, or is there a way to estimate hidden assets too?) it is important to understand what is being measured or counted, and how.
It is surprising how rarely we do this. Over the years, as I found myself trying to lead people out of statistical mazes week after week, I came to realise that many of the problems I encountered were because people had taken a wrong turn right at the start. They had dived into the mathematics of a statistical claim – asking about sampling errors and margins of error, debating if the number is rising or falling, believing, doubting, analysing, dissecting – without taking the time to understand the first and most obvious fact: what is being measured, or counted? What definition is being used?
Yet while this pitfall is common, it doesn’t seem to have acquired a name. My suggestion is ‘premature enumeration’.
It’s a frequent topic of conversation with my wife. The radio that sits on top of the refrigerator will carry some statistical claim into our home over breakfast – a political soundbite, or the dramatic conclusion of some research. For example, ‘A new study shows that children who play violent video games are more likely to be violent in reality.’ Despite having known my limitations for twenty years, my wife can’t quite rid herself of the illusion that I have a huge spreadsheet in my head, full of every statistic in creation. So she will turn to me and ask, ‘Is that true?’ Very occasionally I happen to have recently researched the issue and know the answer, but far more often I can only reply, ‘It all depends on what they mean . . .’
I’m not trying to model some radical philosophical scepticism – or annoy my wife. I’m just pointing out that I don’t fully understand what the claim means, so I am hardly in a position (yet) to know whether it might be true. For example, what is meant by a ‘violent video game’? Does Pac-Man count? Pac-Man commits heinous acts, notably swallowing sentient creatures alive. Or what about Space Invaders? There’s nothing to do in Space Invaders but shoot and avoid being shot. But perhaps that is not quite what the researchers meant. Until I know what they did mean, I don’t know much.
And how about ‘play’; what does that mean? Perhaps the researchers had children* fill in questionnaires to identify those who play violent games for many hours in a typical week. Or perhaps they recruited some experimental subjects to play a game for twenty minutes in a laboratory, then did some kind of test to see if they’d become more ‘violent in reality’ – and how is that defined, anyway?
‘Many studies won’t measure violence,’ says Rebecca Goldin, a mathematician and director of the statistical literacy project STATS.6 ‘They’ll measure something else such as aggressive behaviour.’ And aggressive behaviour itself is not easy to measure because it is not easy to define. One influential study of video games – I promise I’m not making this up – measured aggressive behaviour by inviting people to add hot sauce to a drink that someone else would consume. This ‘hot sauce paradigm’ was described as a ‘direct and unambiguous’ assessment of aggression.7 I am not a social psychologist, so perhaps that’s reasonable. Perhaps. But clearly, like ‘baby’ or ‘sheep’ or ‘nurse’, apparently common-sense words such as ‘violent’ and ‘play’ can hide a lot of wiggle room.
We should apply the same scrutiny to policy proposals as we do to factual claims about the world. We all know that politicians like to be strategically vague. They will often trumpet the merits of ‘fairness’ or ‘progress’ or ‘opportunity’, or say, in the most infuriating tic of all, ‘we’re proposing this policy because we think it’s the right thing to do’. But even specific-sounding policies can end up meaning very little if we don’t understand the claim. You’d like to increase funding for schools? Great! Is that a funding increase per pupil, after inflation – or not?
For example, a policy paper published in the UK in 2017 by the Brexit lobby group Leave Means Leave called for a ‘five-year freeze on unskilled immigration’.8 Is that a good idea? Hard to say until we know what the idea really is: by now, we should know to ask, ‘What do you mean by “unskilled”?’ The answer, on closer inspection, is that you’re unskilled if you don’t have a job offer on a salary of at least £35,000 – a level that would rule out the majority of nurses, primary school teachers, technicians, paralegals and chemists. Now that might be a good policy or it might be a bad policy, but most people would be surprised to hear that this freeze on ‘unskilled immigration’ is a policy that proposes excluding people coming to work as teachers and intensive care nurses.9 This wasn’t just a policy paper, either: in February 2020, the UK government announced new immigration restrictions using a lower cut-off (a salary of £25,600) but similar language about ‘skilled’ and ‘unskilled’.10
Premature enumeration is an equal-opportunity blunder: the most numerate among us may be just as much at risk as those who find their heads spinning at the first mention of a fraction. Indeed, if you’re confident with numbers you may be more prone than most to slicing and dicing, correlating and regressing, normalising and rebasing, effortlessly manipulating the numbers on the spreadsheet or in the statistical package – without ever realising that you don’t fully understand what these abstract quantities refer to. Arguably this temptation lay at the root of the last financial crisis: the sophistication of mathematical risk models obscured the question of how, exactly, risks were being measured, and whether those measurements were something you’d really want to bet your global banking system on.
Working on More or Less, I found the problem everywhere. After working with a particular definition for years, the experts we talked to could easily forget that the ordinary listener might have something very different in mind when they heard the term. What the psychologist Steven Pinker calls the ‘curse of knowledge’ is a constant obstacle to clear communication: once you know a subject fairly well, it is enormously difficult to put yourself in the position of someone who doesn’t know it. My colleagues and I weren’t immune. When we started researching some statistical confusion, we’d habitually start by pinning down the definitions – but as we quickly took them for granted, we always had to remind ourselves to explain them to our listeners, too.
Darrell Huff would be quick to point to the fact that an easy way to ‘lie with statistics’ is to use a misleading definition. But we can often mislead ourselves.
Consider the number 39,773. That was the number of gun deaths in the United States in 2017 (this number is from the National Safety Council and is the most recent available from that source). This number, or something very like it, is repeated every time a mass shooting makes the headlines, even though the vast majority of these deaths are nothing to do with these grim spectacles.* (Not every mass shooting is headline news, of course. Using the common definition of four people killed or injured in a single incident, there is a mass shooting almost every day in the United States, and many of them would be well down the news editor’s order of priorities.)
‘Gun death’ doesn’t sound like a complicated concept: a gun is a gun and dead is dead. Then again, nor does ‘sheep’, so we should pause to check our intuitions. Even the year of death, 2017, isn’t as straightforward as you might think. For example, in the UK in 2016, the homicide rate rose sharply. This was because an official inquest finally ruled that ninety-six people who died in a crush at the Hillsborough football stadium in 1989 had been unlawfully killed. Initially seen as accidental, those deaths officially became homicides in 2016. This is an extreme example, but there are often delays between when somebody died and when the cause of death was officially registered.
But the big question here is about the connotations of ‘death’. True, it’s not an ambiguous concept. But we hear the number ‘39,773’ at the very moment we are watching news footage showing lines of ambulances and police cars at the sight of some vivid and horrifying slaughter. So we naturally associate it with murder, or even mass murder. In fact, about 60 per cent of gun deaths in the United States are suicides, not homicides or rare accidents. Nobody set out to mislead us into thinking gun-related homicides are two and a half times more common than they actually are. It’s just an assumption we understandably make from the context in which we are usually presented with the number.
Having noticed our error, what conclusions we should draw from it is another question. It’s possible to spin it to support various political outlooks. Gun rights advocates will claim that it shows the fear of mass shootings is overblown. Gun control advocates will counter-claim that it weakens a common argument of the gun rights lobby – that people should be able to arm themselves to defend against an armed attacker, which is no help if the bigger risk is that people will turn their guns against themselves.
As thoughtful readers of statistics, we don’t need to rush to judgement either way. Clarity should come first; advocacy can come once we understand the facts.
We should also remember that behind every one of those 39,773 gun deaths is a tragic human story. There’s little evidence that Stalin ever said ‘The death of one man is a tragedy, the death of millions is just a statistic’, but the aphorism has echoed down the years in part because it speaks to our profound lack of curiosity at the human stories behind the numbers. Premature enumeration is not just an intellectual failure. Not asking what a statistic actually means is a failure of empathy, too.
Staying with the grim subject of suicide, this time in the UK: ‘A Fifth of 17- to 19-year-old Girls Self-harm or Attempt Suicide’ blares a headline in the Guardian. The article goes on to speculate that this may be because of social media, pressure to look good, sexual violence, pressure to do well in exams, difficulty finding work, moving to a new area, cuts in central government services, or iPads.11 But while the piece is long on scapegoats, it’s short on detail about what is meant by self-harm.
So let’s turn to the original study, funded by the UK government and conducted by some respected research organisations.12 It doesn’t take long to realise that an error has slipped into the headline, as errors often do. It’s not true that a fifth of seventeen- to nineteen-year-old girls self-harm or attempt suicide. What is true is that a fifth of them say that they have done so at some stage – not necessarily recently. But . . . ‘done so’. What exactly have they done? The study itself is no more illuminating than the Guardian report on it.
The National Health Service website lists a variety of self-harming behaviours, including cutting or burning your skin, punching or slapping yourself, eating or drinking poisons, taking drugs, misusing alcohol, eating disorders such as anorexia and bulimia, pulling out your hair, or even excessive exercise.13 Is this what these young women were thinking of when they answered ‘yes’ to the question? We don’t know. I asked the researchers what their question meant; they told me they wanted ‘to capture the entire spectrum of self harm’ and so did not provide a definition of self-harm to the young women they interviewed. Self-harm means whatever the interviewees thought it means.14
That’s fine; there is nothing necessarily wrong with aiming to capture the broadest possible range of behaviour. It might be useful to know that a fifth of seventeen- to nineteen-year-old girls have at some point behaved in a way they subjectively consider to be self-harm. But those of us interpreting the statistic will want to bear in mind that nobody else can know precisely what they meant. All forms of self-harm are disturbing, but you may find some of them a great deal more disturbing than others. Binge drinking seems very different from anorexia.
Bearing this in mind, the headline lumping together self-harm and suicide, which at first glance seemed natural, starts to look irresponsible. There is an enormous gulf between excessive exercise and killing yourself. And while this survey suggests that self-harm is worryingly common among young women, suicide is thankfully quite rare. Out of every 100,000 girls in the UK aged between fifteen and nineteen, 3.5 kill themselves each year; that’s about seventy across the entire country.15
(By now I hope you are wondering what exactly the authorities mean by ‘suicide’. It is not always clear whether someone intended to kill themselves; sometimes people intended only to hurt themselves but died by accident. In the UK, the Office for National Statistics draws a clear line: if the child is fifteen or over, the death is assumed to be deliberate; under the age of fifteen, it is assumed to be an accident. Evidently, those assumptions will not always reflect the truth, which is sometimes impossible to know.)
Lumping together self-harm and suicide is all the more irresponsible because the headline singles out girls. The study did indeed find that seventeen- to nineteen-year-old girls are much more likely than seventeen- to nineteen-year-old boys to say they had harmed themselves, yet it is the boys who are the bigger suicide risk. Boys of this age are twice as likely as girls to kill themselves.
Awful tragedies lie behind each of these numbers. Pinning down the definitions is vital if we want to understand what is happening and, perhaps, how we might make life better. That is, after all, why we’re collecting the numbers.
I’d like to devote the rest of the chapter to a more detailed example, which I hope will illustrate how we might try to think through a complex problem – first by clarifying what’s being measured, and only then by breaking out the mathematics. It’s an important issue, but also an issue about which many people have very strong beliefs, yet a weak grasp of the definitions involved. That issue is inequality. Let’s start with perhaps the most famous soundbite on the topic.
‘Oxfam: 85 Richest People as Wealthy as Poorest Half of the World’. That was a Guardian headline in January 2014.16 The Independent picked up on the same research published by the development charity Oxfam, as did many other media outlets. It’s an astonishing claim. But what does it tell us?
Oxfam’s aim was publicity. They wanted to generate heat; if they shed any light on the subject, that was a secondary consideration. This isn’t just my opinion: the report’s lead author, Ricardo Fuentes, said as much when interviewed for an Oxfam blog post titled ‘Anatomy of a Killer Fact’, which celebrated the ‘biggest-ever traffic day on the Oxfam International website’.17 The blog post focuses on all the attention the claim received. But was the ‘Killer Fact’ informative, or even true? Mr Fuentes later told the BBC that his research ‘has shortcomings but it was as good as it gets’.
I’m not so sure about that. Three years later, Oxfam had revised its analysis so comprehensively that the headline number had changed from eighty-five billionaires to eight billionaires. Had the inequality really become ten times worse, the billionaires ten times richer – or perhaps the poor of the world had lost nine tenths of their wealth somehow? No, there was no such economic cataclysm. Oxfam’s measure was just a very noisy and uninformative way to think about inequality in the first place.
The dramatic change in the headline claim is one indication that this may not be a terribly educational way to think about inequality. The excited bewilderment of some of the media reporting is another sign of just how baffling the number really was. While the Guardian accurately repeated Oxfam’s headline – eighty-five people among them have as much wealth as the poorest half of the world – the Independent published an infographic declaring that the eighty-five richest people had as much wealth as the rest of the world put together. (A trailer for a BBC documentary about the super-rich repeated the error.) That’s not even close to being the same claim, although you might have to think twice about why.
If thinking twice didn’t help: almost all global wealth is held neither by the poorest half of the world, who have little or nothing, nor by the richest eighty-five (or eight?) ultra-billionaires. It lies with a few hundred million prosperous people in the middle. You may very well be one of them. The Independent and the BBC had mixed up ‘the wealth of the poorest half’ and ‘the wealth of everyone who isn’t a zillionaire’. This apparently minor confusion turns out to be between a sum of less than $2 trillion and a sum of more than $200 trillion. Not thinking hard enough about the exact claim being made introduced a hundred-fold error.
In a magnificent display of statistical befuddlement, the Independent also declared ‘The 85 richest people – 1%’ to have the same wealth as ‘Rest of the world – 99%’. This implies that the population of the world is 8500. If the previous claim was a hundred-fold error, this one is nearly a million times too small.
The hopeless confusions of the Independent are worth dwelling on for a moment. They remind us how easy it is for our emotions to run away with us. There are some people out there with extraordinary, imagination-boggling fortunes. There are other people out there with nothing. It’s not fair. And as we start to seethe at the unfairness, the risk is that we stop thinking. The Independent confused nearly 8 billion people with 8500 people. It confused the wealth of the poorest half of the world with the wealth of everyone except the richest eighty-five people. These are ludicrous errors – but as Abraham Bredius showed us, when we stop thinking and start feeling, ludicrous errors show up very promptly.
It’s a nice little reminder to all of us to stop and think for a moment. It should not be too complicated a calculation to realise that whoever ‘the 1%’ might be, there are more than eighty-five of them.
I can’t blame Oxfam, an organisation devoted to campaigning and fundraising, for seeking the most sensational headlines possible. Nor do I hold them responsible for the fact that the claim prompted all kinds of screw-ups from the media.
The rest of us, however, might prefer some clarity. So – back to the drawing board, and that starts with being clear about what’s being measured, and how.
What’s being measured is net wealth – that is, assets such as houses, shares and cash in the bank, less any debts. If you have a house worth $250,000 with a $100,000 mortgage on it, that’s $150,000 of net wealth.
The Oxfam calculations on which the headline was based took the best available estimate of the total net wealth of the poorest half of the world (accumulated by researchers paid by a bank, Credit Suisse)18 and compared it to the best available estimate of the total wealth of the top multi-billionaires (as reported by newspaper rich lists). They found that you only had to total up the wealth of the eighty-five richest billionaires before you exceeded the total wealth of the poorest half of the world, about 2.4 billion adults (Credit Suisse’s researchers ignored children).
But does net wealth really tell us much? Let’s say you buy a nice $50,000 sports car with a $50,000 loan. The moment you drive it off the lot, the sports car has lost a few thousand dollars in value, and your net wealth has just fallen. If you’ve just finished an MBA, or law school, or medical school, and you’ve picked up a few hundred thousand dollars of debt, your net wealth is way below zero. But financially, a young doctor is likely to feel much more comfortable than a young subsistence farmer, even if the doctor is up to her chin in debt and the farmer owns a scrawny cow and a rusty bike for a net worth of $100.*
Net wealth is a great way to measure riches, but not such a good way to measure poverty. Lots of people have zero, or less than zero. Some of them are destitute; others, like the junior doctor, are going to be fine.
A further problem is that when you add up all those zeros and negative numbers, you’re never going to get a positive number. As a result, my young son’s piggy bank is worth more than the assets of the poorest billion people in the world put together, because a billion zeros and negative numbers never get you above the £12.73 he had in there when we last counted it all up. Does that suggest that my son is rich? No. Does it demonstrate that grinding poverty is endemic? Well, no, not directly. The fact that more than a billion people have no wealth is striking, but it’s not clear that trying to add up all those zeros tells us much more. I’m not sure that it tells us anything, except that a billion times zero is zero.
Now that we’ve avoided premature enumeration – rushing to work with the numbers before we really understand what those numbers are supposed to mean – it’s the perfect time for a little light mathematics, which can be wonderfully clarifying.
Looking at the Global Wealth Report from Credit Suisse, the source of Oxfam’s claims, we can play with some of those numbers to shed more light on the topic.*
• 42 million people have more than a million dollars each, collectively owning about $142 trillion. A few of them are billionaires, but most are not. If you have a nice house with no mortgage, in a place such as London, New York or Tokyo, that might easily be enough to put you in this group. So would the right to a good private pension.†19 Nearly 1 per cent of the world’s adult population are in this group.
• 436 million people, with more than $100,000 but less than a million, collectively own another $125 trillion. Nearly 10 per cent of the world’s adult population are in this second group.
• Those two groups, collectively, have most of the cash.
• Another billion people have more than $10,000 but fewer than $100,000; they own about $4 trillion among them.
• The remaining 3.2 billion adults have only $6.2 trillion, less than $2000 each on average. Many of them have much less than that average.
Very roughly speaking, the richest half a billion people have most of the money in the world, and the next billion have the rest. The handful of eighty-five staggeringly wealthy super-billionaires are still just a handful, so they own less than 1 per cent of this total. All this, it seems to me, tells us a great deal more about the distribution of assets than a widely repeated ‘killer fact’ that talks about wealth inequality while ignoring almost all the wealth in the world. And while Oxfam’s aim, understandably, is to produce such ‘killer facts’ to win attention and raise money, my aim is to understand our planet and our society. Those facts were easily accessible online; it was a matter of an extra click or two. To find them, all it took was a couple of minutes, and a curiosity about the world.
At least Oxfam was clear that it was talking about inequality of wealth. Often we hear someone make a vague assertion like ‘inequality has risen’ and we can’t even guess that much: inequality of what, between whom, and measured how?
Perhaps they’re talking about wealth inequality, having read Oxfam’s stat updating the eighty-five billionaires to just eight. Or perhaps they mean inequality of income. If you want to understand how people live and what they are able to consume from day to day, inequality of income is a more natural thing to examine. What we eat, what we wear and how we live tends to be related not to our wealth but to regular income from a salary, a pension, payments from the state, or the profits from a small business. Very few people have enough wealth to fund their lifestyle purely out of interest payments, and so if we want to understand how inequality manifests itself in everyday life, it makes sense to look at income rather than wealth. The other advantage of looking at income is that we do not need to confront the absurdity of suggesting that an ordinary schoolboy and his piggy bank are richer than a billion people put together.
If we look at inequality of income, inequality between whom? The obvious answer: between the rich and the poor. But there are other possibilities: one could look at inequality between countries, or between ethnic groups, or between men and women, or between the old and the young, or between different regions within a country.
But even once we’ve settled on looking at inequality of income, and between high earners and low earners, the question remains: measured how?
Here are a couple of possibilities. You could compare the median income (the income of a person right in the middle of the distribution) to the tenth percentile income (the income of someone near the bottom of the income distribution). This is called the 50/10 ratio, and it’s an indication of how the poor are doing relative to the middle class.
Alternatively, you could look at the income share of the highest-earning 1 per cent – a decent indicator not just of how the billionaires are faring, but the millionaires too. You don’t need to do this yourself: think tanks and academics have done these calculations and they are usually easy to find online.20
Both of these measures seem to tell us something important. But what if they conflict? Imagine a country where the income of the highest-earning 1 per cent surged, while at the same time there was a reduction in inequality further down the income scale, as the 50/10 ratio shrank and poorer households caught up with the comfortably off. If the rich grow richer but the poor grow richer too, relative to the median, has inequality risen? Or fallen? Or a bit of both?
This might seem like a cute hypothetical question, but as it happens it describes the situation in the United Kingdom between 1990 and 2017. After taxes, the top 1 per cent saw their share of income rise, but inequality among lower-earning households fell as poorer households tended to catch up on those with middling incomes. It’s an awkward story for anyone who wants an easy answer, but in a complicated world we shouldn’t expect that the statistics will always come out neatly.
A few years ago I was invited to be the resident data geek on a TV debate about inequality in the UK. The show was an ambitious hour-long special in front of a studio audience during which various worthies would discuss why inequality in the UK mattered. In early discussions with the programme’s production team, I pointed them towards the World Inequality Database, a resource that was originally put together by the economists Sir Tony Atkinson and Thomas Piketty. Piketty, of course, was the superstar author of Capital in the Twenty-First Century; Sir Tony, who died in 2017, was one of his academic mentors. The two of them favoured stiff redistributive taxes and wide-ranging government intervention in the economy. Like many economists, I’m quite wary of that sort of policy, but I recommended their database anyway. They were simply the world’s leading experts.
All seemed well until, a few days before the show, I had an awkward phone call with one of the production team. I mentioned in passing that the pre-tax income share of the top 1 per cent had fallen slightly over the previous few years. As we’ve seen, that’s by no means the only way to measure inequality, but it’s a metric Piketty and Atkinson like to emphasise, and it seemed a good starting point: it was crisp, rigorous and easy to explain on TV. Alarmed, she told me that the entire programme was based on the premise that inequality had been increasing since the 2007–08 financial crisis. Why did they think this was true? The data were clear: the top 1 per cent had 12 per cent and rising of pre-tax income in 2008, but the crisis knocked that back to 10 or 11 per cent.* This was hardly astonishing: a massive financial crisis is likely to temporarily hit the income of high-earners such as bankers, lawyers and corporate executives. And this was data, remember, gathered by two left-leaning economists who would have been first in line to decry the effects of bankers’ greed or government cutbacks.
But no: the idea that inequality had risen just seemed to the TV producers like the kind of thing that should be true. Perhaps they looked at the data I’d recommended and found some flaw with it. Perhaps they found some different measure that they felt was better. But the strong impression from my conversation was that the production team simply hadn’t looked at the data I’d recommended to them. I hope that isn’t so, because it takes a special lack of curiosity to be able to produce an ambitious TV programme without taking the ninety seconds or so necessary to check whether the premise of the show is actually true.
I made my excuses and did not participate.
Statisticians are sometimes dismissed as bean-counters. The sneering term is misleading as well as unfair. Most of the concepts that matter in policy are not like beans; they are not merely difficult to count, but difficult to define. Once you’re sure what you mean by ‘bean’, the bean-counting itself may come more easily. But if we don’t understand the definition then there is little point in looking at the numbers. We have fooled ourselves before we have begun.
The solution, then: ask what is being counted, what stories lie behind the statistics. It is natural to think that the skills required to evaluate numbers are numerical – understanding how to compute a percentage, or to disentangle your millions from your billions from your zillions. It’s a question of mathematics, is it not?
What I hope we’ve learned over the past few pages is that the truth is more subtle yet in some ways easier: our confusion often lies less in numbers than in words. Before we figure out whether nurses have had a pay rise, first find out what is meant by ‘nurse’. Before lamenting the prevalence of self-harm in young people, stop to consider whether you know what ‘self-harm’ is supposed to mean. Before concluding that inequality has soared, ask ‘Inequality of what?’ Demanding a short, sharp answer to the question ‘Has inequality risen?’ is not only unfair, but strangely incurious. If we are curious, instead, and ask the right questions, deeper insight is within easy reach.
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* Then there is the question of what a Covid-19 death is: some who succumb were already terminally ill; some, indeed, died with the virus but not of it. With that in mind, perhaps 1500 deaths is an overstatement after all.
* And by ‘children’, do we mean five-year-olds? Ten-year-olds? Sixteen-year-olds?
* Even the definition of ‘mass shooting’ is slippery. The FBI keeps a record of incidents of mass murder, but their definition only includes attacks in a public place, which leaves out many drug-related incidents, as well as domestic homicides. An alternative count, maintained by the Gun Violence Archive, includes such incidents. That makes a big difference to the total count – but either way, the number of people killed in mass shooting incidents is a small fraction of the total number of gun deaths.
* And there’s an oft-repeated anecdote about Donald Trump, years before he became President and heavily indebted after some failing real-estate deals, pointing to a homeless person and telling his young daughter, ‘See that bum? He has a billion dollars more than me.’ I’ve no idea if the story is true, but the financial logic is sound.
* I’ve used the 2018 Global Wealth Report. The 2013 version – the foundation of the original ‘85 Richest People’ headlines – offers slightly different numbers but the big picture has changed only slowly.
* Credit Suisse did not include the entitlement to a state pension in its calculations. That matters, because state pensions are very valuable to those who have them. It’s unclear whether counting state pensions as assets would increase measured inequality (since many of the poorest people lack them) or reduce measured inequality (since a state pension represents a substantial asset for the poorer people in richer countries). I’m guessing that things would look less unequal if state pensions were included, but it is just a guess. I might be quite wrong. Around the world, a third of older people have no pension of any kind.
* Another popular measure of inequality – one we’ll encounter in the next chapter – is the Gini coefficient. This measure was telling the same story of falling inequality in the wake of the crisis.