David Miles: Monetary policy and financial stability
Speech by Mr David Miles, Member of the Monetary Policy Committee of the Bank of
England, at the Bristol Business Forum, Bristol, 14 July 2010.
* * *
I would like to thank Conall MacCoille and Gilberto Marcheggiano for research assistance and I am also grateful
for helpful comments from other colleagues. The views expressed are my own and do not necessarily reflect
those of the Bank of England or other members of the Monetary Policy Committee.
Monetary Policy in the UK has never been as expansionary as it is today. Just over
15 months ago the level of Bank Rate was reduced to what is - to all intents and purposes -
its floor. As Chart 1 rather starkly shows, this is the lowest level to which Bank Rate has
fallen since the Bank of England was established at the end of the seventeenth century.
Bank Rate has not been changed for 16 consecutive meetings of the MPC. That is not so
unusual. In fact, as the Chart reveals, between 1720 and 1820 Bank Rate did not move from
5%. Had a Monetary Policy Committee then met each month, as it does now, it would have
decided at 1200 consecutive meetings not to change the level of interest rates. So it is far
from unusual for the interest rate set by the Bank to remain constant for over a year. And for
much of the period since rates fell to the floor, policy has been actively changed - asset
purchases have built up to now stand at around £200 billion.
Chart 1
Bank rate from 1694
%
18
16
14
12
10
8
6
4
2
0
1700 2000
1800 1900
So it is the level to which interest rates have fallen that is unprecedented. I believe it has
been right to loosen aggressively the stance of monetary policy because of the scale of the
deflationary and recessionary forces unleashed by the remarkably rapid downturn that
followed the crisis in the banking sector. This crisis intensified dramatically in the autumn of
2008 when the banking system came close to total collapse. That would have been an
outcome comparable in its impact to the failure of the system for electricity supply. Many now
argue that monetary policy should be set in a different way so as to reduce the chances of
this sort of banking crisis. That is one of the issues I want to discuss today. The argument
that the aims of monetary policy need to be broadened beyond a focus on inflation is one
that deserves to be taken seriously because the damage done by extreme financial instability
is great. If there were no tools better suited to help preserve financial stability than varying
interest rates then the case for broadening the goals of monetary policy would be strong. But
I believe there are tools better suited to make the financial system more robust and I want to
consider one of them - capital requirements - and how they might in future interact with
monetary policy.
More immediately, problems and fragilities in the banking sector remain and pose risks that
the recovery in demand and activity we have seen across Europe - including in the UK -
falters. But in the UK we have also seen CPI inflation rise to a level that is significantly above
the inflation target. In recent months CPI inflation has begun to fall, but remains well above
the 2% target level and that makes setting monetary policy difficult. We continue to face the
problem of balancing risks: risks that inflation of 1.0pp-1.5pp above target lasts long enough
to become ingrained in expectations and affect behaviour so that it is hard to bring down,
versus risks that the recovery in output becomes weaker and then disappears, leaving
inflation pressures lower than is consistent with the target further ahead.
Since the financial crisis towards the end of 2008 economic policy has been unusually hard
to manage. Both monetary and fiscal policy have been exceptionally expansionary. There
has been an extremely large fiscal deficit. Fiscal policy is now being tightened. I look forward
to the day when it will be appropriate to tighten monetary policy since a return to more
normal levels of interest rates would be a welcome sign that economic conditions were also
more normal. But I do not think that is where we are today.
So since I joined the MPC just over a year ago I have not voted to increase interest rates -
despite the fact that inflation has more often than not been above the target. But even though
price rises over the past year have been running at relatively high levels, the underlying
domestic inflationary pressures are not strong. Wage rises - despite a move up in household
inflation expectations - remain low. Without a pick up in wage inflation I find it hard to think it
at all likely that inflation being significantly above target is sustainable. Of course wage
pressures may build significantly over the next year or so, though I do not believe this is the
most likely outcome. And risks of an extended period of low growth - which would further
weaken those pressures - are real.
In talking about the possibility of an extended period of low, or no, growth I may sound blasé
about inflation risks. But the point about risks is that more than one can exist. There are risks
that inflation stays well above the target level; there are also risks that demand in the
economy falls even more below supply capacity so that inflation further ahead drifts below
the target. In considering how to balance these risks there is a need to look through short run
and potentially transitory factors. Reacting to today's inflation rate (which reflects where the
level of prices is now relative to 12 months ago), rather than where inflation will be looking
ahead, is not the right thing to do. The inflation rate can move a lot in a short period. Inflation
was barely 1% less than a year ago.
But this is a difficult situation to have to deal with. I dislike clichés so will resist the temptation to
talk about the ship having being blown near to the rocks and now having to steer a difficult
course in treacherous waters with rather out of date maps that have not been updated since
noone expected we would be in such a place. But it is a temptation since it is not a bad analogy.
How we came to be in this difficult situation is something on which many books have already
been written. At the heart of the problems has been a banking system which proved
catastrophically fragile. That fragility reflected the fact that many banks had come to have
very high leverage - a lot of debt relative to capital - which made them vulnerable to
concerns about losses on their assets.
This poses a big and obvious question: how do we reduce the fragility of the banking system
in a way that does not come at too high price - a price may come in the form of a lower level
of overall economic activity? And should we change the goal of monetary policy to include a
wider range of objectives that include maintaining the stability of the banking sector?
Why were banks so fragile?
On the eve of the crisis we had come to be in a situation where the capital of UK banks,
relative to their assets, was around half the level that was typical fifty years earlier and
probably around one third the level that was usual one hundred years ago (Chart 2). In the
US the decline in bank capital over the past one hundred years is quite probably even larger.
Chart 2 Chart 3
Capital levels relative to total Liquidity ratio of the UK banking sector
holdings for UK banks
Per cent
45
40
35
30
25
20
15
10
5
0
1921 1931 1941 1951 1961 1971 1981 1991 2001
Sources: Bank of England, Financial Stability Report
Sources: United Kingdom: Sheppard, D (1971), The
June 2009 and "The British Economy, Key Statistics
growth and role of UK financial institutions 1880-1962,
1900-1970", published for the London & Cambridge
Methuen, London; Billings, M and Capie, F (2007),
Economic Service. From 1968 the liquidity ratio is:
"Capital in British banking", 1920-1970, Business
Cash + Bank of England balances + money at call +
History, Vol 49(2), pages 139-162; BBA, published
eligible bills + UK gilts as a percentage of banks' total
accounts and Bank calculations. (a) US data show
asset holdings. Prior to 1968 the ratio is calculated as
equity as a percentage of assets (ratio of aggregate
the liquid assets of the London Clearing Banks as a
dollar value of bank book equity to aggregate dollar
percentage of gross deposits, as defined in "The
value of bank book assets). (b) UK data on the capital
British Economy, Key Statistics 1900-1970".
ratio show equity and reserves over total assets on a
time-varying sample of banks, representing the
majority of the UK banking system, in terms of assets.
Prior to 1970 published accounts understated the true
level of banks' capital because they did not include
hidden reserves. The solid line adjusts for this. 2009
observation is from H1. (c) Change in UK accounting
standards. (d) International Financial Reporting
Standards (IFRS) were adopted for the end-2005
accounts. The end-2004 accounts were also restated
on an IFRS basis. The switch from UK GAAP to IFRS
reduced the capital ratio of the UK banks in the sample
by approximately 1 percentage point in 2004.
Furthermore, in recent years the quality of banks' capital deteriorated as banks exploited the
availability of new hybrid capital instruments which often had the tax advantages of debt. In
practice hybrid capital did not absorb banks' losses despite being treated for regulatory
purposes as if it was like equity.
The liquidity of banks, as measured by the ratio of their most liquid assets (central bank
reserves, gilts and Treasury bills) relative to total assets, was a fraction of what had been
normal twenty years earlier and a tiny fraction of what had been normal before the 1970's
(Chart 3). And banks had also become larger. Their assets, relative to the size of the
economy, had grown very sharply. Relative to GDP, they had roughly doubled in the
10 years up to 2007 (Chart 4).
The UK banking sector had low capital, illiquid assets and was very large when fears about
the value of its assets increased. The combination of those things accounts for the scale of
the damage that ensued.
Chart 4
UK monetary and financial institutions,
assets as % of nominal GDP
600
500
400
300
200
100
0
1987 1990 1993 1996 1999 2002 2005 2008
Note: Monetary and financial institutions do not include insurance companies,
pension funds and other financial intermediaries.
Source: Bank of England, Monetary and Financial Statistics.
There are many different proposals to build a more robust banking sector. Some of these
involve using conventional monetary policy, that is interest rates. But most proposals are
about changes to the way banks do business. These range from those requiring banks to
hold somewhat higher capital and liquidity ratios to much stricter capital and liquidity
requirements; but they also include more fundamental changes to the financial architecture
that would preclude banks from undertaking many types of business. It may seem
inappropriate to present these alternative proposals on a continuous spectrum. Some are
about altering balance sheet structure (capital and liquidity requirements) and others focus
on limits on the activities banks can pursue. But in practice I think many of the proposals can
be seen to lie on a continuous spectrum. This is because stopping a bank from undertaking
an activity and insisting that it be (in the limit) completely equity financed are quite close. One
can think of a bank as an entity that finances its acquisition of assets with substantial use of
debt finance. By setting capital standards on a type of business high enough one prevents it
being financed with much debt; that comes close to making it an activity banks cannot do.
Amongst the most radical proposals for creating a less fragile financial structure are those of
Laurence Kotlikoff1. The Kotlikoff proposal is - in essence - to turn the funding of the vast
majority of what are now assets on bank balance sheets (largely loans) into equity claims.
This could be seen as equivalent to imposing 100% capital ratios. It would mean that banks
would, to the extent they continued to hold the loans that they make, be more like unit trusts
with an origination arm rather than banks.
So many - in fact almost all - of the proposals to make banks less fragile will mean they
would come to hold more equity capital. I think this is right. And I believe it is the most
fundamental response to banking fragility because it directly deals with solvency problems -
risks that people who have lent money don't get it back. I believe that those risks - real or
perceived - have been the fundamental drivers of the financial disasters of the past few
years. Other problems, which are sometimes described as funding or liquidity problems,
often arise because of fears about solvency.
I do not want to imply that other measures to make the financial sector more stable
- including liquidity requirements and changes to the way asset values are assessed and
reported - are not important. But I want to consider whether changes in capital are a
powerful tool to make the banking sector robust and whether it is right to see them, rather
than monetary policy, as a more natural means to that end.
Some are sceptical that higher capital requirements can work because banks may be able to
avoid (or evade) them. If capital requirements are increased significantly, but only on some
activities, banks may re-classify assets to switch their business into forms where the capital
requirements are no higher than today. To me that is an argument for thinking about very
substantial rises in required bank capital pretty much across the full range of their activities.
Of course if this is very costly it will create two problems: it would create big incentives to
avoid them and potentially big costs to the wider economy, because of the impact on the
price and availability of bank loans.
Two issues are important. First, the scale of the impact on bank funding costs from higher
capital requirements. Higher funding costs would push up on the cost of bank loans to
households and non-financial companies and affect lending and investment, which in turn
could require a monetary policy response; those costs will also affect the incentives to avoid
(or evade) capital requirements. The second issue is how much more robust the financial
sector, and banks in particular, become with different amounts of extra capital.
Several estimates of the cost of higher bank capital exist. The Institute for International
Finance (IIF) suggest that proposed regulatory reform which could be part of the Basle III
system could reduce the path of average annual GDP growth in the US, euro area and
Japan by 0.3pp for the next ten
years2. This implies that the level of GDP would ultimately be
around 3% lower. If we use a real discount rate of 2.5% a year, the present value of a
permanent fall in output of 3% is in excess of 100% of current annual GDP. This is at the
high end of estimates of the cost of higher capital requirements. Recent analysis by
economists from the National Institute of Economic and Social Research (NIESR),
commissioned by the FSA, puts the present value of the costs of permanently raising capital
requirements by 1% at approximately 2.7% of current GDP3. And illustrative estimates in the
most recent Bank of England Financial Stability Report (FSR) indicate, under certain
conservative assumptions, that the long run costs could amount to 4% of current annual
GDP in present value terms, though it also finds that the GDP benefits from increasing
capital requirements from their current level substantially outweigh these costs4.
The NIESR and FSR estimates look much lower than the IIF figure. But the IIF estimate is for
the impact of a range of adjustments which include a more than 1% rise in bank capital.
Nonetheless that estimate looks likely to be higher than the illustrative calculation in the FSR.
But rather than seeing the FSR calculations as generating a very low estimate of the cost of
higher capital requirements, I think they are more likely to be a conservative assessment that
reflects the care taken not to underestimate the cost of higher bank capital.
The costs of extra bank capital
Many assessments from commentators and practitioners, though often not precisely
quantified, suggest that the costs of significantly higher capital requirements for banks are
very substantial. I am rather sceptical about the claims that substantially higher capital
requirements must mean significantly higher costs of funds for those who borrow to invest
and that total investment and output in the economy will be significantly lower.
There are two reasons for my scepticism.
First, a simple historical point. In the UK and in the USA economic performance was not
obviously far worse when banks held very much higher levels of capital. Investment - relative
to GDP - was not lower. This is prime facie evidence that much higher levels of bank capital
do not cripple development, and the financing of investment. Conversely, there is little
evidence that investment or the average (or potential) growth rate of the UK economy picked
up as spreads on bank lending narrowed over the past decade, and the volume of bank
credit expanded sharply (Chart 5).
Chart 5
UK GDP growth
%
GDP Growth 10 Year Rolling Average
8
6
4
2
0
-2
-4
-6
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
Source: Bank of England, Monetary and Financial Statistics.
Second, the most straightforward and logically consistent model of the overall impact of
higher equity capital (and less debt) on the total cost of finance of a company implies that the
effect is zero. The Modigliani Miller (MM) theorem implies that as more equity capital is
raised the volatility of the return on that equity falls, and the safety of the debt rises, so that
the required rate of return on both sources of funds falls. It does so in such a way that the
weighted average cost of finance is unchanged5. It is absolutely NOT self-evident that
requiring banks to hold more capital has to substantially increase their costs and must mean
that they need to charge substantially more on loans to service the providers of their funds.
There are certainly reasons why the Modigliani Miller result is unlikely to hold exactly. The
Modigliani-Miller theorem may not hold for banks because of asymmetric information
problems in financial markets. But I will argue that one of the most obvious reasons why it
does not hold (differential tax treatment of debt and equity) need not imply that there is a
wider economic cost to be paid for higher capital requirements on banks.
Indeed, recent research suggests that the Modigliani-Miller theorem might not be a bad
approximation even for banks. Kashyap et al find that the long-run steady state impact on
bank loan rates from increases in external equity finance is modest, in the range of 25-45
basis points for a ten percentage point increase in capital requirements6. They also find that
the costs of capital requirements are greater if they are phased in very quickly.
I want to briefly describe some ways of trying to calibrate the costs and benefits of higher
capital requirements - which do not assume the MM theorem holds. The method I use
follows that outlined in the recent Bank of England FSR7. The methodology followed in the
FSR seems to me very sensible. The idea is to calculate the impact of a given change in
equity capital - that is an equity for debt swap - on a typical bank's cost of funding. I
assume, as in the FSR, the higher cost of bank funding is passed on in the form of a higher
cost of bank loans. To assess what effect that has on the wider economy we then make an
educated guess at the effect of a rise in the cost of bank loans on the overall required return
on investment. That in turn will affect the stock of capital and economic activity. This impact
on economic activity is the cost of higher capital requirements.
The illustrative estimates in the FSR indicate that conservative assumptions about effects of
higher bank capital on the costs of bank funding and lending generate a marginal cost of
about 4% of annual GDP, in present value terms, for a 1% of risk-weighted assets rise in
capital. The FSR notes that by relaxing these assumptions the cost may be lower, so that the
estimates are probably an upper bound8.
The starting point for my calculations is the case presented in the FSR. This is that the cost
of a 1% rise in banks' capital relative to their risk weighted assets would reduce annual GDP
by about 0.1%. At a discount rate of 2.5% this implies that the present value of this loss in
output over all future periods is 4.25% of current annual GDP9. I illustrate that less
conservative assumptions imply a much smaller estimated cost of higher bank capital
requirements. Specifically, I sequentially take account of:
5
See Modigliani, F.; Miller, M. (1958). "The Cost of Capital, Corporation Finance and the Theory of
Investment". American Economic Review 48 (3): 261-297.
6
See Kashyap, K., Stein, J. and Hanson, S. "An Analysis of the Impact of "Substantially Heightened" Capital
Requirements on Large Financial Institutions", Working Paper.
7
See in particular box 7 in chapter 5 of Bank of England, Financial Stability Report, June 2010.
8
In particular, it notes that the costs may be over-estimated because the calculations assume that the
Modigliani-Miller theorem does not hold and because they use a Cobb-Douglas production function to
compute the reaction of output to changes in firms' cost of capital.
9
Underlying these calculations are assumptions that the cost of equity and debt are 10% and 5% respectively
and remain fixed. Our baseline calculations are similar, but slightly higher than those in the June 2010
Financial Stability Report.
BIS Review 100/2010
1. the possibility that if a bank has more equity capital the return on equity is less
variable lowering the required rate of return. (This is a partial allowance for the
mechanism underlying the Modigliani-Miller result.)
2. the likelihood that the extra tax revenue that accrues to the government as banks
are forced to switch to equity that is less favourably treated is used to offset any
resultant rise in the cost of finance for companies using bank debt. (For example the
government could use the extra revenue to increase capital allowances so that the
negative impact on investment from a higher cost of bank debt is neutralised.)
3. the likelihood that the relative importance of bank funding for investment is lower
than the baseline conservative estimate that banks account for 1/3 of private,
nonfinancial companies (PNFCs) external finance.
4. the likelihood that the sensitivity of investment and the capital stock to a rise in the
cost of funds to non-financial firms is lower than the value assumed in the baseline
(where an assumption of a unit elasticity of substitution between capital and labour
is used).
Suppose we first allow the cost of equity to fall as more capital reduces its volatility. I only
allow for a partial offset relative to what the Modigliani Miller theorem implies - in fact I
assume the offset is only 30% as great, which means that the weighted average cost of cost
of capital rises by 70% of the baseline10. Making this adjustment reduces the estimated
present value of the cost of permanently higher bank capital by about 1% of annual GDP -
from just over 4% to 3%.
The major part of this remaining cost reflects that fact that we assume that all interest paid by
banks on debt they raise is tax deductible at the corporation tax rate (of 28%) while equity
capital has to earn the required rate of return out of post tax profits. But in thinking about the
wider economic impact of a switch to less tax sheltered funding for banks we need to take
account of the extra revenue generated for the government. The government could use the
extra tax revenue it gets from banks to shelter the users of bank loans from any knock on
impact on their cost of raising finance. This seems a natural assumption to make. And it
would mean that we should reduce the estimated negative impact on economic activity.
When we allow for this the cost - in terms of the lost output of a permanent change to bank
capital of +1% of assets - almost halves from just over 3% of annual GDP to about 1.7%
Next I allow for less than 30% of investment in the economy to be financed by bank lending.
PNFCs' liabilities with banks are made up of direct loans from banks', but also banks' holding
of corporate bonds and equities, issued by PNFCs. I assume that only PNFCs' bank loans
are affected by the increase in banks' funding costs. Chart 5 illustrates that over the past
year the share of bank loans in PNFCs financial liabilities has declined from close to 20% to
close to its average over the past two decades of 16%.
Allowing for this halves again the estimated cost of higher bank capital - which falls from
around 1.7% to 0.8% of annual GDP. This estimate is based on the impact of higher cost of
bank lending feeding through to a (Cobb-Douglas) production function, and that implies a
high sensitivity of investment to the cost of funds (a unit elasticity of substitution between
capital and labour). Bank of England research11 suggests that this elasticity is probably
substantially lower. If that elasticity is 0.4, which looks a central estimate, then the cost of
higher bank capital (of 1% of assets) falls from 0.8% of GDP to around 0.3%. Table 1 shows
the estimated costs of higher bank capital under various assumptions about the economic
environment.
Chart 6
Share of MFIs in UK PNFCs financial liabilities12
%
25
20
15
10
5
0
1987 1992 1997 2002 2007
Note: Monetary and Financial Institutions do not include insurance companies,
pension funds and other financial intermediaries. Here, PNFCs financial liabilities are
measured at current market value. This measure excludes PNFCs financial liabilities
secured on dwellings which are predominately liabilities with MFIs and account for
around 1% of PNFCs total financial liabilities.
Source: Office for National Statistics, UK Economic Accounts.
Table 1
The costs of higher capital requirements
Benefits
Costs Required Marginal Extra Months in the Average
Probability Gap between Crises from 25 years
present value, present value, of 1% rise in risk weighted
% of GDP % of GDP capital ratio
55%
(1) Baseline 4.25 0.077% 5.9
(2) 30% Modigliani-Miller effect 55% 3.25 0.059% 4.5
(3) Tax offset 55% 1.67 0.030% 2.3
(4) More Substitutes to Bank Finance 55% 0.80 0.015% 1.1
(5) Less Sensitive Investment 55% 0.32 0.006% 0.4
20%
Temporary Impact on GDP from Crises 0.32 0.016% 1.2
How do these costs measure against the benefits of a more robust banking sector and a
lower frequency of banking crises? I will make the same assumptions as in the FSR, namely
that if a bank crisis occurs the initial impact is to reduce output by 10% of GDP. That is
almost exactly the amount by which UK GDP is now below the level it would have reached
had it continued on the trajectory it was on up to 2007. I assume that three quarters of this
reduction lasts for just five years, but that the other 2.5% of lost GDP is gone forever. Under
these assumptions, and using the same discount rate of 2.5%, the present value of reducing
the likelihood of a systematic crisis in any one year by one percentage point is around 55%
of current annual GDP. If we instead assumed that there are no permanent effects on GDP
from financial crises the benefits of reducing the chance of a crisis happening in a year are
lower at around 20% of GDP (Table 1, column 2).
The third column in the table shows by how much the chances of a banking crisis would
need to fall given a rise in capital of 1% of bank assets so that the benefits of that would
match the estimated cost. (Whereas before both benefit and cost are expressed as the
present value of lost or gained GDP.) This is the reduction in the probability of a banking
crisis required to justify a 1% increase in banks' risk-weighted capital - given the
assumptions made on tax, Modigliani Miller offsets and so on corresponding to that row in
the Table. Chart 7 illustrates this calculation for multiples of a 1% increase in banks' capital.
For example, on the least favourable assumptions about the cost of extra bank capital
(corresponding to row 1 in the table) the Chart shows that a 10% increase in banks' capital
ratios would require a minimum reduction in the probability of financial crises of 0.8 (the red
line) for it to pass a cost-benefit test. If we assume that financial crises would otherwise occur
once in every 25 years (an annual frequency of 4%) then a rise in banks capital by 10 of
riskweighted assets would be justified if it reduced the probability of financial crises so that they
occurred with an annual probability of 3.2%, or once every 31 years. Alternatively, taking the
most favourable assumptions on cost (full tax offsets, partial Modigliani Miller offsets, a lower
use of bank debt and lower sensitivity of investment spending) the blue line indicates a 10%
rise in capital relative to assets would be justified if it reduced the probability of financial
crises from 4% a year to 3.9%, or from once every 25 years to once every 25.4 years. (The
final column in the table shows that calculation for each case). Such a small decline in the
likelihood of a financial crisis would not appear to be overly ambitious for such a sharp rise in
the capital ratio. For typical banks the capital ratio starts out from a level under 10%, so that
a rise in capital of 10% of risk assets is more than a doubling in the amount of bank capital.
Chart 7
Banks capital and the break-even impact
on probability of financial crises
reduction in the probability of a financial
Baseline crisis per year, %
0.9
30% Modigliani-Miller Effect
0.8
Tax offset
0.7
More Substitutes to Bank Finance
0.6
Less Sensitive Investment
0.5
0.4
0.3
0.2
0.1
0
0 1 2 3 4 5 6 7 8 9 10
additional capital as % of banks' risk-weighted assets
That said, initial increases in banks' capital will probably have a much more pronounced
impact on the likelihood of financial crises than successive increases. For example, a
5 percentage point increase in banks capital from 15% to 20% would likely have considerably
less impact on the probability of banks' failing than raising capital from 10% to 15%. So it is
important to consider the rate at which the marginal benefits of banks holding more capital
will diminish. The June 2010 Financial Stability Report provides illustrative estimates that
indicate the benefits of additional capital fall to close to zero once a threshold of around 15%
of risk-weighted assets is reached.
It is difficult to predict the likely volatility of banks' assets values and the probability of
extreme events that could lead to a financial crisis. A natural starting point is to assume that
the shocks hitting the economy and banks' asset values follow a normal distribution.
However, a distribution with "fatter tails" would imply a greater likelihood of extreme events
and hence potentially larger benefits from higher capital requirements.
It seems pretty unlikely to me that the distribution of risks that affects banks follows a normal
distribution. A much better way to match the distribution of risks that end up affecting GDP is
to assume that most of the time risks - or shocks - follow a normal distribution but that once
every few decades a shock comes that is very large. The frequency of such large shocks is
very much greater than would be implied by an estimated normal distribution that most of the
time matches the GDP data well. This assumption is one made by Robert Barro in a series of
important studies of rare events that hit economies12.
A few years ago I calibrated a version of the Barro model so as to match historical
experience13. I used a very large sample of countries and data going back some 200 years.
Using data on the annual change in GDP for this sample of countries gave over 4000
observations of historical economic growth. The best fit of the data I could find - and it did fit
the data extremely well (Chart 8 see below) - implied that 95% of the time the shock to
annual GDP was well behaved and came from a normal distribution with a fairly small
volatility (a standard deviation of about 3%).
About once every 20 years, on average, a shock came along which could be either very
good or very bad; it either increased or decreased GDP by around 12%. Much less
frequently there came a very much larger - and always negative - hit to GDP. On average
this very bad shock came along about once a century; reducing