Living with Low for Long
Charles Bean
London School of Economics
Royal Economic Society Presidential Address
University of Manchester, 1 April 2015
Chart 1: 300 years of the BoE policy and consol rates
Source: Bank of England Historical database
(http://www.bankofengland.co.uk/research/Pages/onebank/datasets.aspx#4)
Chart 2: Yield on 3-month and 10-year US Treasuries
Source: Hartnett & Leung (2015) “The Longest Pictures”, Bank of America/Merrill Lynch
Chart 3: “World” real interest rate, 1985-2013
(Spot yields on 10-year indexed bonds, G7 ex Italy)
Source: King and Low (2014) “Measuring the World Real Interest Rate”
Chart 4: UK real interest rate, 1700-2004
Source: Miles, Baker and Pillonca (2005)
Chart 5: Estimates of US short-term and
long-run “World” real interest rates
Source: Hamilton, Harris, Hatzius and West (2015) “The Equilibrium Real
Funds Rate: Past, Present and Future”
Growth and the interest rate
Assume an additively separable iso-elastic utility function with
𝐶 1−𝛼
intra-period utility: 𝑈 𝐶 =
1−𝛼
The Euler equation is:
𝐸𝑡 [∆𝑐𝑡+1 ] = (𝑟𝑡 + 𝛼 2 𝜎 2 /2 − 𝛿)/𝛼
where 𝑐𝑡 = logarithm of consumption at date 𝑡;
𝑟𝑡 = real interest rate between 𝑡 and 𝑡 + 1;
𝛿 = household discount rate;
𝜎 2 = variance of the growth rate of consumption.
Chart 6: Global capital market
Real
interest
rate
S
I
I’
S’
O
O’
S
S’
I
I’
Investment,
Savings
It is not so easy to foresee the future…
• “Heavier-than-air flying machines are impossible.” (Lord
Kelvin, President of the Royal Society, 1895)
• “Everything that can be invented has been invented.”
(Charles Duell, Commissioner, US Office of Patents, 1899)
• “The wireless music box has no imaginable commercial
value. Who would pay for a message sent to nobody in
particular?” (David Sarnoff Associates, 1920s)
• “Who the hell wants to hear actors talk?” (Head of Warner
Brothers, 1927)
• “I think there is a world market for maybe five computers.”
(Thomas Watson, Chairman of IBM, 1943)
• “There is no reason anyone would want a computer in their
home.” (Ken Olsen, Chairman of DEC, 1977)
Chart 7: Savings and investment shares (% of GDP)
Source: IMF WEO database
Table 1: Longevity and change in required savings
Life expectancy (years)
Change in required
savings* (share of GDP)
1970
1990
2010
1970-90
1990-2010
US
70.9
75.3
78.6
2.08
0.72
China
62.9
69.5
74.9
-0.08
1.34
Japan
72.0
78.9
82.9
1.49
1.46
Germany
70.6
75.3
80.5
0.60
0.76
*The required-savings calculation assumes complete consumptionsmoothing from the age of ten until expected death, taking into account
years of education, normal retirement age and population growth.
Source: Teulings and Baldwin (2014), Secular Stagnation: Facts, Causes
and Cures
Chart 8: Savings rates by household type(a)
Source: Living Costs and Food (LCF) survey.
(a) Saving ratios calculated using the average consumption and disposable
income levels for each group of households. Numbers in parentheses
show their share of total income in 2007.
(b) High-debt mortgagors are defined as having outstanding mortgage debt
of more than twice their annual disposable income. All other mortgagors
are low debt.
Chart 9: Safe and risky yields
*Leverage-adjusted inverted Price-Earnings ratio.
Source: Bank of England, following Broadbent (2014) “Monetary policy,
asset prices and distribution”.
A loanable funds model with safe and risky assets
Risky assets:
Safe assets:
𝑓 𝜌 𝑆𝑃𝑟𝑖𝑣𝑎𝑡𝑒 𝑟, 𝑟 + 𝜌; … = 𝐼(𝑟 + 𝜌; … )
(+)
(+) (+)
(-)
1 − 𝑓 𝜌 𝑆𝑃𝑟𝑖𝑣𝑎𝑡𝑒 𝑟, 𝑟 + 𝜌; … + 𝑆𝑃𝑢𝑏𝑙𝑖𝑐 = 0
where: 𝑟 = yield on safe assets and 𝜌 = spread between the expected
return on risky capital assets and the safe return.
The sum gives the usual loanable funds relationship:
Loanable funds: 𝑆𝑃𝑟𝑖𝑣𝑎𝑡𝑒 𝑟, 𝑟 + 𝜌; … + 𝑆𝑃𝑢𝑏𝑙𝑖𝑐 = 𝐼(𝑟 + 𝜌; … )
The ratio gives an allocational relationship determining the spread:
Funds allocation: 𝜑 𝜌 ≡ 𝑓 𝜌
1−𝑓 𝜌
= −𝐼(𝑟 + 𝜌; … )/𝑆𝑃𝑢𝑏𝑙𝑖𝑐
Chart 10: Equilibrium with safe and risky assets
IS
Spread, 𝜌
ISʹ
Oʹ
O
Oʺ
FF
FFʹ
Safe rate, 𝑟
Table 2: Decline in supply of “safe” assets
US$ trn
% of World GDP
2007
2011
2007
2011
US sovereign debt
5.1
10.7
9.2
15.8
German & French sovereign debt
2.4
3.3
4.5
4.8
Italian & Spanish sovereign debt
2.4
3.1
4.3
4.7
US MBS and ABS
11.3
9.6
20.2
14.2
“Safe” assets
20.5
12.3
36.9
18.1
Source: Caballero and Farhi (2014) “On the role of safe asset shortages
in secular stagnation”.
Chart 11: Sterling liquid assets of UK banking sector(a)
Broad ratio
(b)
Percentage of
total assets
(all currencies)
(c)
Reserve ratio
(d)
Narrow ratio
35
30
25
20
15
10
5
0
1968
73
78
83
88
93
98
2003
08
13
Source: Bank of England.
(a) Data for building societies are included from 2010 onwards. Prior to this, data are for UK banks only. Data are end-year
except for 2013 where end-November data are used.
(b) Broad ratio: Cash + Bank of England balances + money at call + eligible bills + UK gilts.
(c) Reserve ratio proxied by Bank of England balances + money at call + eligible bills.
(d) Narrow ratio: Cash + Bank of England balances + eligible bills.
Chart 12: Spot and forward yields on UK indexed gilts
Source: Bank of England
Chart 13: Forward Guidance - a calibrated example
Source: Bean “Nominal income targets: A new wine in an old bottle?”
(2013).
Chart 14: Bank of England consolidated balance sheet
Source: Bank of England
Living with Low for Long
The End