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 intra-period utility: 𝑈 𝐶 = 𝐶 1−𝛼 1−𝛼 The Euler equation is: 𝐸 𝑡 [∆ 𝑐 𝑡+1 ]=( 𝑟 𝑡 + 𝛼 2 𝜎 2 /2−𝛿)/𝛼 where 𝑐 𝑡 = logarithm of consumption at date 𝑡; 𝑟 𝑡 = 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 S’ I’ O S O’ I S’ 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 80.5 0.60 0.76 *The required-savings calculation assumes complete consumption- smoothing 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. 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. 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: 𝑓 𝜌 𝑆 𝑃𝑟𝑖𝑣𝑎𝑡𝑒 𝑟,𝑟+𝜌;… =𝐼(𝑟+𝜌;…) (+) (+) (+) (-) Safe assets: 1−𝑓 𝜌 𝑆 𝑃𝑟𝑖𝑣𝑎𝑡𝑒 𝑟,𝑟+𝜌;… + 𝑆 𝑃𝑢𝑏𝑙𝑖𝑐 =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: 𝑆 𝑃𝑟𝑖𝑣𝑎𝑡𝑒 𝑟,𝑟+𝜌;… + 𝑆 𝑃𝑢𝑏𝑙𝑖𝑐 =𝐼(𝑟+𝜌;…) The ratio gives an allocational relationship determining the spread: Funds allocation: 𝜑 𝜌 ≡ 𝑓 𝜌 1−𝑓 𝜌 =−𝐼(𝑟+𝜌;…)/ 𝑆 𝑃𝑢𝑏𝑙𝑖𝑐

Chart 10: Equilibrium with safe and risky assets 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 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 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) Source: Bank of England. 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. Broad ratio: Cash + Bank of England balances + money at call + eligible bills + UK gilts. Reserve ratio proxied by Bank of England balances + money at call + eligible bills. 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