Mervyn King: What fates impose - facing up to uncertainty
Speech by Mr Mervyn King, Governor of the Bank of England, at the Eighth British Academy Annual
Lecture 2004, London, 1 December 2004.
The references can be found on the Bank of England's website.
I am indebted to David Aikman, Gertjan Vlieghe and Tony Yates who worked closely with me on the subject of this lecture over
a long period. They should truly be regarded as co-authors. I am also very grateful to John Campbell, Gerd Gigerenzer, Robert
May, Jim Poterba and many colleagues at the Bank for helpful comments and discussions. I would like to thank Tony Leandro
(Actuarial Profession), the Met Office, Helen Bray and Adrian Gallup (both of the Government Actuary's Department) for help in
gathering and interpreting data used in this lecture. Kath Begley provided excellent research assistance.
* * *
"What fates impose, that men must needs abide;
It boots not to resist both wind and tide".
(William Shakespeare, Henry VI part 3, Act IV Scene 3)
1. Introduction
My subject tonight is risk: how we think about, how we talk about, and how we manage risk. So let me
start by thanking all of you for coming and taking the risk of spending an hour with a central banker.
Few writers have put central bankers in their place, but one of them was Nancy Mitford, whose
centenary we celebrated last Sunday. In The Pursuit of Love and Love in a Cold Climate she
describes the marriage of Linda, the heroine, to the son of the Governor of the Bank of England. The
marriage between Linda and the incredibly boring Tony is doomed from the outset. As Lady Montdore
explained, "Bankers don't seem to be much to look at - so extraordinarily unsuitable having to know
them at all, poor things, let alone marry them".
I don't suppose Lady Montdore would have come to this lecture, but if she had I would point out to her
that life is full of surprises. Risk, luck, fate, uncertainty, probability theory - we all have names for the
game of chance. Most decisions in life involve risk. Sometimes we embrace it, as when we enjoy a bet
on the Grand National, and sometimes we avoid it, as when we insure our houses against fire. The
playing of the hand we are dealt may be a pleasure in bridge but a burden in life. We accept that Lady
Luck has her part to play in our personal lives. But in our collective life - public policy - the role of
probabilities rarely takes centre stage. An informed discussion of public policy issues, however,
requires an analysis of the risks and uncertainties involved. Whether in policies for health or transport,
matters monetary or meteorological, in times of war and peace, decisions should reflect a balance of
risks. Yet policy debates continue to be permeated by the "illusion of certainty".1
The reluctance to give adequate prominence to risks may reflect the fact that many of us feel
uncomfortable with formal statements of probabilities. Probability theory is relatively recent in our
intellectual history, dating back to a flowering of ideas around 1660 from Pascal, Leibniz, Huygens and
others.2 Despite advances since then, statistical thinking remains prone to confusion and is often
avoided. Television weather forecasts in Britain rarely employ the language of probabilities used by
the meteorologists themselves. Professor Gigerenzer of the Max Planck Institute in Berlin has
demonstrated in a series of studies how poorly doctors, lawyers, and other professionals understand
probabilities. And despite Seneca's maxim that "luck never made a man wise", airport bookshops
stock titles on how to become rich by successful investors and entrepreneurs who are confident that
their success is the result of outstanding business acumen rather than good fortune.
Many of these misunderstandings stem from a failure to grasp basic statistical concepts. Juries are not
informed that, in a country of our size, multiple cot deaths are likely to occur several times a year, that
several people will have DNA that matches the incriminating sample, and that in themselves these
coincidences are not evidence of guilt. Bookshops do not stock such titles as "I would have been a
billionaire if only Lady Luck had been faithful".3
In my lecture tonight I want to illustrate two propositions. First, in a wide range of collective decisions it
is vital to think in terms of probabilities. We cannot avoid taking decisions, so we must accept the need
to analyse the uncertainty that inevitably surrounds them. H.G. Wells is often reported as saying that,
"Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and
write". And that is even more true today when we are inundated with statistics from every quarter.
Second, in order that public discussion can be framed in terms of risks, the public needs to receive
accurate and objective information about the risks. Transparency and honesty about risks should be
an essential part of both the decision-making process and the explanation of decisions.
I want to illustrate those two propositions by considering as an example public policy about pensions -
an issue, you might think, of particular interest to many of us in the Academy. When the Pensions
Commission reported in October, it highlighted the financing gap in our present system. But we must
not lose sight of the equally important question of what are the risks incurred in pension provision and
how should they be shared among us? It is not my intention to make any recommendations. That is for
the Pensions Commission next year, and the Government in its turn. But I do want to show that risk is
at the heart of the issue.
2. The nature of risk
"In this world nothing can be said to be certain, except death and taxes" wrote Benjamin Franklin in
1789. Great man though Franklin was, it is clear that there is indeed substantial uncertainty both about
death, or at least its timing, and the contributions or taxes required to pay for our pensions.
When thinking of how much to save for retirement, there are three main risks to consider. First, how
much will we be earning in the future? Second, what will be the rate of return on our savings? Third,
how long are we likely to live? Tonight I shall focus exclusively on longevity risk - the uncertainty about
how long we shall live - in order to focus on my two propositions about probabilistic thinking and public
policy.4
None of us know how long we shall live. But we can assess our chances by looking at the experience
of others. A key distinction is between individual and collective risk. Chart 1 plots the observed
mortality rates at different ages for women in England and Wales in 2002, the most recent year for
which detailed data are available. (A similar story can be told for men). The most common age of
death for women was 87, but many died at very different ages. Mortality among individuals varies
greatly - individual risk.
But there is also significant uncertainty about the average length of life of a generation as a whole -
collective risk. Longevity has changed markedly over time. Chart 2 shows female mortality in England
and Wales in both 1902 and 2002. It shows the remarkable reduction in infant mortality during the
twentieth century as well as the fall in mortality in middle age.
Of particular relevance to decisions on pensions is the expectation of life conditional on reaching
retirement age. That is directly relevant to the purchase of an annuity on retirement. Over the past
century the normal retirement age in public service in this country has been constant at age 60.
Chart 3 shows the distribution of deaths by age conditional on having reached the age of 60 in
England and Wales in both 1902 and 2002. A woman who was 60 in 1902, and subject to the mortality
rates of that year, would have expected to live for another 141⁄2 years. By 2002 that expectation had
increased to 231⁄2 years.
Individual risk - that we die either earlier or later than the average for our cohort - can be insured by
taking out life insurance against early death or by purchasing an annuity to insure against a later
death.5 Collective risk - that average expectation of life will rise or fall in the future - cannot, by
definition, be shared among members of the same generation. The principle of insuring individual
longevity risk is that those who live longer than average can be paid using the contributions of those
who die earlier than average. But if the average itself rises all contributions must increase - there is no
possibility for insuring changes in the average from within the cohort. Can we quantify this risk? The
expectation of life has risen significantly over the past century. But how will it change in the future? To
answer that question we need to model and quantify longevity risk.
3. Modelling and quantifying risks
Quantitative modelling has been one of the great advances of the social sciences over the past fifty
years. But forecasts, whether of longevity or any other economic or social variable, inevitably require a
judgment about how far the past can inform us about the future. Projecting longevity is fraught with
First Essay on
difficulty. In his Population, Malthus wrote in 1798 that "with regard to the duration of
human life, there does not appear to have existed, from the earliest ages of the world, to the present
moment, the smallest permanent symptom, or indication, of increasing prolongation". We know now
that in 1798 life expectancy in Britain was around 40. Today it is nearly 80.
There is no agreed method of forecasting life expectancy. The most widespread approach is to
assume that life expectancy will gradually approach some limit determined by medical knowledge and
our choice of lifestyle. A key uncertainty is what the limit to life is, and demographers have pursued
many ways of estimating it.6 But successive forecasts of the limit to life have been disproved as actual
life expectancy data surpassed the supposed limit. Chart 4 plots the forecast limits to female life
against the life expectancy achieved by the longest lived female population. As life spans have
increased, forecasts of the limit to life have been revised up.
The fact is that we simply do not know how life expectancy will change in the future. Unforeseen,
indeed unimagined, developments in medical science could change the prospects for life expectancy
radically. In the end we have to face up to our ignorance. Providing insurance against longevity,
whether as private annuities or public pensions, rests on an ability to calculate the risks involved. But
our present degree of knowledge means that, in the terminology of Frank Knight (1921), there is both
risk, which can be quantified, and uncertainty, which cannot.
The extent of past uncertainty about life expectancy can be seen in the revisions to its forecasts made
over the past 20 years by the Government Actuary's Department. Nor has the financial sector itself
proved better at forecasting. Chart 5 shows successive forecasts of expected length of life for men
aged 60 published by the Actuarial Profession, a body of life assurance companies and annuity
providers. It shows how reductions in mortality were expected by the industry to lead to rises in length
of life. For example, the pink line shows the Actuarial Profession forecast made in 1980 that a man
who was 60 in that year could expect to live another 20 years. At that time, it was thought that
someone who reached 60 in 1999 would live a further 21 years. But by 1999 the forecast was that a
man of 60 would live another 26 years. Over a twenty year period, expected length of life was revised
up by 5 years. Length of life has risen faster than the industry anticipated, as can be seen by the
5
The first estimates of mortality rates using bills of mortality from the City of London were published by John Graunt in 1662.
But the widespread use of such data to price annuities began only with the calculations of Richard Price in 1780 and the
Institute of Actuaries in 1869. In Holland more accurate calculations of the prices of annuities date back to de Witt in 1671.
See Poterba (2004).
6
Manton et al (1991) and Caselli and Vallin (2001) describe alternative approaches to inferring the limit to human life. Some
estimates assume that life expectancy will converge to that of the longest-lived population; for example, that life expectancy
in the West will rise to that in Japan, the country with the highest life expectancy. But the level in Japan has itself increased
significantly over the past century. So what determines Japan's life expectancy? Another approach is to examine how life
expectancy might change if everyone adopted lifestyle patterns that increase longevity. Mormons and Seventh Day
Adventists seem to live longer than the rest of us, but exactly which aspects of their lifestyle we should adopt is not entirely
clear. See, for example, Enstrom (1989). Yet another approach is to work out the contributions that different human
diseases make to premature death, and calculate the hypothetical life expectancy that would result if medical science were
to be able to eliminate these diseases. This 'cause elimination' approach was adopted in the 1950s by Pichat. The number
derived was 75. This is the number that the UN used until the early 1980s in their population projections. The number used
from then on has been about 85, based on a similar approach by Benjamin (1982) and Olshansky et.al. (1990). And the
evidence on a limit to increases in the human lifespan is mixed; see for example, Kannisto et.a.l. (1994) and Wilmoth and
Horiuchi (1999).
BIS Review 73/2004
upward shifts over time both in the forecasts of expected life and in the rate at which it was expected
to increase.7
That there are large and unavoidable uncertainties in forecasting longevity is clear. The key unknowns
are evolutions in lifestyle, diseases and the ability of medical science to combat them. No amount of
complex demographic modelling can substitute for good judgements about those unknowns. The
danger of relying on computer modelling is well illustrated by the World Health Organisation's early
estimates of the future spread of AIDS, which, at the time, was a significant unknown in forecasting life
expectancy even in developed countries. AIDS was first recognised in 1981. The virus responsible for
AIDS, which we now call HIV, was identified in 1984. To date, around 20 million people are thought to
have died from the disease worldwide. The proportion of those who are infected with HIV who go on to
develop AIDS is now thought to be close to 100%. But the spread of HIV, and hence AIDS, has been
very uneven. At the end of last year the percentage of adults infected with HIV was estimated at 0.2%
in the United Kingdom, 21.5% in South Africa, 37.3% in Botswana, yet only 3.9% in Angola.
Why do infection rates differ so much between countries? In the 1980s the World Health Organization
and associated researchers made rather optimistic projections of the impact of AIDS on populations in
Africa using extremely detailed computer models of population structure. Complex demographic
models were combined with strong simplifying assumptions about sexual behaviour. Unfortunately,
this led the modellers to ignore those factors most critical to the spread of AIDS. They assumed that
the probability of transmitting the HIV infection was a function of the number of sexual acts, not the
number of partners of infected persons. But it is crucial to distinguish between the two.8 Ten acts with
one partner have a smaller impact on transmission of the infection than one act with each of ten
different partners. As Professor (now Lord) May, President of the Royal Society, pointed out, ignoring
this simple and crucial distinction led to a serious underestimate of the rate at which AIDS was likely to
spread.9 By building elaborate models of demographic variables for which a great deal of information
was available and making simple assumptions for behaviour about which little was known, the large
models used by the World Health Organisation produced misleading results. The fact that few data on
sexual behaviour were available was not a good reason for focusing on demographic variables - the
researchers were looking for the key under the lamp-post rather than where it fell.
Quantitative models are obviously essential to explain empirical evidence. But the idea of a single
comprehensive model, whether of a population or an economy, which can capture all the relevant
features to explain all phenomena is an illusion.10 There is no substitute for thinking about the
and Abuses of
underlying process which is generating the data. Robert May's article "Uses
Mathematics in Biology", published earlier this year, should be compulsory reading for anyone
involved in public policy. In pointing to the dangers of models so complex that intuition is impossible,
he writes, "It makes no sense to convey a beguiling sense of 'reality' with irrelevant detail, when other
equally important factors can only be guessed at. ... Remember Einstein's dictum: 'models should be
as simple as possible, but not more so'" (May, 2004).
In many areas, successful public policy depends on a quantitative analysis of risks by experts and
researchers. It is important that the general public understand that such assessments are only
judgments. To enhance confidence in those judgments experts need to engage in a debate among
themselves about what they know and what they do not know. On the Bank of England's Monetary
Policy Committee the nine members debate among themselves our current state of knowledge of the
7
The data in Chart 5 are for occupational pension holders of Actuarial Profession member institutions. These individuals are
typically wealthier than the rest of the population, and for that reason tend to live longer.
8
Peterman et. al. (1988) found that the probability of infecting a partner was unrelated to the number of sexual acts with that
partner.
9
The large models made the further simplifying assumption that the rate took one of only two values. In fact, it varies widely
among the population. Robert May, and his colleague Roy Anderson, showed that a key driver of the proportion of the
population eventually infected was the "variance of the rate of acquisition of new sexual partners". Simulations of the
proportion of the population ultimately infected with AIDS are sensitive to that variance, and plausible differences in the
number of their partners among different people changed the estimate of the proportion likely to be infected from 25% to
90%.
10
Many non-economists believe that economists use a single "model" to explain all economic phenomena. Hence the interest
of many commentators in "the model" that is alleged to generate the forecasts of inflation and economic growth published by
the Bank of England. But, as we never cease pointing out, the Bank uses not one but many models to help us understand
particular aspects of economic behaviour. The relevant models change from one forecast to another.
BIS Review 73/2004
behaviour of the economy. The results of that discussion are published once a month, and the
Committee, as it did yesterday, appears regularly in front of Parliamentary committees. So I turn now
to the question of how information and judgments of risks can be communicated to the general public.
4. Communicating about risks with the public
Although it is often impossible to be precise about the risks surrounding a decision, it is vital that
policymakers resist the temptation to communicate a false sense of certainty. Two key principles
should govern the communication of risks to the public. First, information must be provided objectively
and placed in context so that risks can be assessed and understood. Second, experts and
policymakers must be open about the extent of our knowledge and our ignorance. Transparency about what
we know and what we don't know, far from undermining their credibility, helps to build trust and
confidence in policy-makers.
(a) (Mis)understanding probabilities
The first principle states that information about probabilities should be placed in context. A simple
example illustrates the difficulty we all have in interpreting probabilities when the context is unclear.
The stock market is volatile and difficult, if not impossible, to predict over short periods. At the
beginning of the week the chance of the market rising over the following week is roughly the same as
the chance of its falling. So if I were to predict the direction of the market movement correctly for five
successive weeks you might think that I knew something you didn't. Indeed, you might be willing to
subscribe to an investment service with that sort of track record. So let me explain to you how one
might create the illusion of clairvoyance. Select around 6000 or so names and addresses from the
London telephone directory. Divide the names into two groups. To the first write predicting that the
market will rise over the coming week. To the second write predicting a fall in the market. At the end of
the week keep the 3000 or so names who were given the correct prediction and discard the others.
Divide those names in turn into two groups. To the first predict a rise in the market and to the second a
fall. Repeat this process for five weeks, at which point there will be around 200 people to whom we
could write the following letter. "You may well have been sceptical when you received our first letter,
but by now you will know that we have worked out the secret of predicting successfully the direction of
movement of the stock market. You know that our method really works. To subscribe to our
investment service please send £5000 by return".
Quite what our President, as the former Deputy Chairman of the Financial Services Authority, would
make of this scheme I do not know. But it illustrates vividly that the interpretation of ex post outcomes
ex ante
depends critically on understanding the process which generated those outturns.
Another example shows that it is not just lay people who find statistical inference difficult. Experts of all
kinds do too. The advent of DNA profiling in the 1980s led to the use of match probabilities in criminal
cases. The jury is told that the probability of finding a match between the sample taken from the scene
of the crime and the DNA of the defendant is, for example, only 1 in 500,000. That is sometimes taken
as evidence that the probability of the defendant being innocent is also only 1 in 500,000. Such an
inference is incorrect. In a city such as London where there might be about 5 million people who could
have committed the crime, around ten people would have DNA that matched the relevant sample.
Hence, in the absence of any other evidence, the probability that the defendant is guilty, far from being
overwhelming, is only one in 10. Of course, in practice other evidence is usually available. But this
incorrect statistical reasoning has swayed enough cases to be given its own name - the prosecutor's
fallacy.11
The cases of Sally Clark and Angela Cannings, both convicted and imprisoned for the alleged murder
of their own children, show the desperate consequences of the false use of statistics to create a
presumption of guilt to resolve the cause of apparently inexplicable events. Both women were
convicted by juries which had in all likelihood been influenced by the assertion that the probability of
two cot deaths in the same family was extraordinarily low. That assertion was based on the
assumption that cot deaths in the same family were independent events, a view for which there was
no scientific evidence and which is a priori implausible.12 The assumption of independence was crucial
to the prosecution evidence against Sally Clark that the odds of two cot deaths in a family such as
hers were 1 in 73 million and so would be expected only once a century. Given the complex and
conflicting medical evidence, it would not be surprising if that striking and simple statistic had played a
role in helping the jury come to its conclusion. In fact, as pointed out by Professor Ray Hill, the
statistical evidence on cot deaths suggests that in England and Wales we should expect several cases
a year.13 Thankfully, both women were eventually released after winning their appeals, albeit largely
on other grounds.
Why then do probabilities cause us so much difficulty? Our understanding of probabilities evolved
through counting the frequencies of various events, whether the number of days in summer on which it
rains or the outcomes of tossing a coin. All this was part of our evolutionary experience long before the
Reckoning with
concept of probability was invented in the seventeenth century. In his book Risk,
Gigerenzer argued forcefully that risks should be presented not as probabilities but in terms of natural
frequencies, which correspond to our experience in counting events. Although people do understand
probabilities in familiar contexts, such as betting on horse races or tossing a coin, it is not easy to
calculate odds when the context is unfamiliar.
(b) Explaining probabilities
How then can we best present information about risks to the public? Both the Monetary Policy
Committee and the Met Office face this problem almost every day: the former in explaining the outlook
for inflation and the latter in forecasting the weather. Both have independently developed similar visual
representations of forecasts that avoid the use of the word "probability".
Chart 6 shows the forecast for inflation over the next three years published by the Bank of England in
its latest Inflation Report on 10 November 2004. It is in the form of a 'fan chart'. We do not say that in
our view inflation will be 2%, or any other number. Such a statement is incoherent because a forecast
is inherently probabilistic. So we represent the uncertainties by the coloured bands in Chart 6.14 Their
interpretation is as follows. If we found ourselves in economic circumstances identical to today's on
100 occasions, we would expect that inflation would lie within the darkest central band on only 10 of
those occasions. As we increase the width of the coloured section by moving from the dark central
band to the lighter shades of red further out, the number of outturns that we think will lie within the
section increases. The bands are drawn so that the number of outturns increases by 10 for each
change of colour intensity. The inflation outturn would be expected to lie somewhere within the entire
coloured area on 90 out of 100 occasions.
On the same day that the Bank of England produced its forecast for inflation, the Met Office produced
a forecast for the temperature in various towns over the following ten days. Chart 7 shows this 'plume
chart', as the Met Office refers to its fan charts, for the town of Reading. I will leave a detailed
explanation to meteorologists, but the interpretation of the temperature plume chart parallels that of
the inflation fan chart closely. The width of the plume chart indicates the degree of uncertainty about
future temperatures, and different colours suggest different probability bands. And the probability of
the central temperature projection - in this case the solid blue line - is extremely small. I am not
suggesting that the BBC use such charts in its forecasts, but surely it might give a little more freedom
to the meteorologists to use probabilistic thinking in describing the outlook.
Such charts can also be used to illustrate uncertainty about longevity. Chart 8 constructs a fan chart
for female life expectancy at birth in the United Kingdom derived from the latest forecast published by
the Government Actuary's Department. The width of the fan chart shows how forecasts of life
expectancy are likely to change in the future, as new information and ideas about mortality evolve,
causing forecasts to be revised - assuming that news about life expectancy arrives in the future at
about the same rate as in the past. The colour shading depicts the same probability bands as used in
the fan chart for inflation that I showed earlier. Chart 8 illustrates the uncertainty about longevity.
Of course, statistics and their visual representation can be both used and abused. The design of
charts has gone backwards since that (shown as Chart 9) of Napoleon's march to Moscow and
subsequent retreat constructed in 1861 by Charles Joseph Minard, Inspecteur-Général des Ponts et
Chaussées and, appropriately given tonight's theme, en retraite. Brilliant in conception and the
quantity of information which it conveys, the chart shows the devastating losses suffered in Napoleon's
fateful Russian campaign of 1812. So I do not underestimate the difficulties of promoting the better
understanding of statistics in discussions of public policy.15 Too often figures are bandied about
without a careful description of where they came from and what they might tell us. As we learn from
the Rime of the Ancient Statistician (with apologies to Samuel Taylor Coleridge):
Figures, figures, everywhere
Enough to make us sink
Figures, figures, everywhere
But none to help us think.
The second key principle governing the explanation of risk to the public is the open recognition of the
limits of our present knowledge. The failure to do that is damaging to public confidence in
policymakers. The BSE affair showed the danger of claiming greater certainty than the science warranted.
And in the Angela Cannings case, the Court of Appeal observed that, "not so long ago, experts were
suggesting that newborn babies should lie on their tummies. That was advice based on the
bestinformed analysis. Nowadays, the advice and exhortation is that babies should sleep on their backs -
Back to Sleep. This advice is equally drawn from the best possible known sources". As the Court of
Appeal pointedly continued, "It is obvious that these two views cannot both, simultaneously, be right".
Expert advice is invaluable, but it is not infallible. As Robert May said recently, "open contention of
opinion is exactly what has served science so well over the centuries, and I believe we simply must
learn to extend this openness to all forms of science advice in policy-making. Such open publication of
advice, and frank admission of areas of uncertainty, ultimately engenders confidence" (May, 2003).
That is the spirit in which the Monetary Policy Committee was created and continues to function. The
challenge is to extend that spirit to other areas of policy.16
Effective communication of the relevant risks is vital. Thinking about how to present information may
seem to be the role of a spin doctor. But whereas a spin doctor wishes to claim certainty for the
correctness of his master's decision, presenting accurate information about risks to the electorate at
large is essential to democratic accountability. As one of the more illustrious members of the
profession might have said, "spin doctors don't do doubt". That is the trouble with much debate on
public policy. As Voltaire put it, "Doubt is not a pleasant condition, but certainty is an absurd one".17
5. Managing risks
Managing risks is about sharing risks with others. By finding ways of pooling risks we share both the
upside and downside with others. This is beneficial because typically we dislike extremes. In the
language of economics, we are 'risk averse'.
A key part of managing risk is the design of institutions that determine the ultimate incidence of risk.
The Pensions Commission performed a valuable service in making us aware of the size of the shortfall
in our current savings to finance future pension provision. It will report next year on various ways of
closing this funding gap. But there is an additional and fundamental question of how to design a
pension system which shares risk optimally among individuals and generations.
Longevity risks are both individual and collective in nature. Collective risks raise difficult issues of
fairness between generations. Individual risks are easier to handle.
In theory, individual longevity risks can be pooled through private annuity markets. As long as the
provider of the annuity, typically an insurance company, knows how long we will live on average, then
additional payments to the long-lived will be exactly offset by fewer payments to the short-lived. By
pooling risks, annuity providers can offer insurance against longevity. But to offer a single annuity is
risky. In Sense and Sensibility, Fanny Dashwood explains to her husband the drawbacks of providing
an annuity to his family: "if you observe, people always live forever when there is any annuity to be
paid them. An ann