Why are real interest rates so low? Secular stagnation and the relative price of capital goods

The facts Why are real interest rates so low? Secular stagnation and the relative price of capital goods Bank of England and LSE June 2015

The facts This does not reflect the views of the Bank of England

Overview The facts Over the past 30 years, the nominal investment rate and real interest rate have fallen around the industrialised world, while house prices and household debt have increased.

Overview The facts Over the past 30 years, the nominal investment rate and real interest rate have fallen around the industrialised world, while house prices and household debt have increased. I explain these four trends with a fifth - the widespread fall in the relative price of capital goods

Overview The facts Over the past 30 years, the nominal investment rate and real interest rate have fallen around the industrialised world, while house prices and household debt have increased. I explain these four trends with a fifth - the widespread fall in the relative price of capital goods A fall in the price of capital goods reduces the resources needed for investment So interest rates fall, and the money that previously went into capital investment now goes into mortgages and housing

The facts Overview Over the past 30 years, the nominal investment rate and real interest rate have fallen around the industrialised world, while house prices and household debt have increased. I explain these four trends with a fifth - the widespread fall in the relative price of capital goods A fall in the price of capital goods reduces the resources needed for investment So interest rates fall, and the money that previously went into capital investment now goes into mortgages and housing Real interest rates will stay low even if capital goods prices have stopped falling

The facts Overview Over the past 30 years, the nominal investment rate and real interest rate have fallen around the industrialised world, while house prices and household debt have increased. I explain these four trends with a fifth - the widespread fall in the relative price of capital goods A fall in the price of capital goods reduces the resources needed for investment So interest rates fall, and the money that previously went into capital investment now goes into mortgages and housing Real interest rates will stay low even if capital goods prices have stopped falling And preventing the accumulation of household debt would make interest rates fall further

Plan for today The facts Stylised facts Simplest possible heuristic model Results & econometric evidence

The facts World real interest rate 6.000 Spot Yields on 10 Year Bonds 5.000 4.000 3.000 2.000 Weighted Unweighted 1.000 0.000 Equity market measures spreads

Household debt The facts % of GDP 90 80 70 60 50 All countries 40 30 11 countries 20 10 0 1970 1975 1980 1985 1990 1995 2000 2005 2010 presentation

The facts Nominal investment-gdp ratio 30% 25% Full sample 11 countries 20% 15% 1970 1975 1980 1985 1990 1995 2000 2005 2010 Capital stocks presentation

The facts Nominal and real capital-gdp ratios Multiple of GDP 4.5 4 3.5 3 Nominal 2.5 Real (1995 prices) 2 1.5 1 0.5 0 1970 1975 1980 1985 1990 1995 2000 2005 investment presentation

The facts Price of investment relative to consumption 1.5 1.4 1.3 1.2 1.1 1 0.9 us KN sample 0.8 0.7 11 countries 0.6 1850 1870 1890 1910 1930 1950 1970 1990 2010 presentation

The facts Stylised facts - industrialised world before the crisis Real interest rates were falling for two decades before the crisis rates Household debt levels rose, and remain high Nominal investment rates and capital-output ratios fell investment The relative price of investment fell relative price debt

The facts Explanations for low real rates in industrialised countries Demographics Inequality Emerging markets surplus savings

The facts Savings and investment 101 r S 1 S 2 S,I ΔS (or ΔCA), ΔI

The facts Savings and investment 101 r I 1 I 2 S,I ΔS (or ΔCA), ΔI

The facts Savings and investment 101 r S 1 S 2 I 1 I 2 S,I ΔS (or ΔCA), ΔI

The facts Effect of a fall in capital goods prices Real interest rate σ<1 σ>1 Nominal investment rate

The facts Investment schedule, capital goods prices and σ The price of capital goods p has two opposing effects on the demand for investment and thus the real interest rate r = 1 Y p K δ

The facts Investment schedule, capital goods prices and σ The price of capital goods p has two opposing effects on the demand for investment and thus the real interest rate r = 1 Y p K δ Cheaper capital goods means you get more of them for each unit of consumption foregone Increased volume of capital goods lowers the marginal product of each one

The facts Investment schedule, capital goods prices and σ The price of capital goods p has two opposing effects on the demand for investment and thus the real interest rate r = 1 Y p K δ Cheaper capital goods means you get more of them for each unit of consumption foregone Increased volume of capital goods lowers the marginal product of each one The elasticity of substitution between capital and labour determines which of these effects predominates - critical value is unity (Cobb Douglas)

The facts Investment schedule, capital goods prices and σ The price of capital goods p has two opposing effects on the demand for investment and thus the real interest rate r = 1 Y p K δ Cheaper capital goods means you get more of them for each unit of consumption foregone Increased volume of capital goods lowers the marginal product of each one The elasticity of substitution between capital and labour determines which of these effects predominates - critical value is unity (Cobb Douglas) We assume a value of 0.7 in the baseline model, above most estimates We need to talk about σ

Setup - households The facts The economy is closed. Households live for three periods and maximise a standard utility function over consumption and housing U(c 1, c 2, c 3, h) = 1 ( ) c1 1 θ + β 2 c2 1 θ + β 3 c3 1 θ + φ h1 γ 1 θ 1 γ (1)

The facts Setup - households cont. Households buy houses in the first period of life, borrowing if necessary, and sell them and consume the proceeds at the beginning of retirement. (They move in with their kids or into retirement homes). They supply a fraction η of their lifetime labour in the first period, and 1 η in the second period. So their budget constraints look like this c 1 + hp h + a 1 = ηw (2) c 2 + a 2 = (1 η)w + (1 + r)a 1 (3) c 3 = (1 + r)a 2 + hp h (4)

Setup - firms The facts Intermediate goods have a CES production function Y = [(1 α)l σ 1 σ + αk σ 1 σ σ ] σ 1 (5) Intermediates can be transformed into consumption goods at rate 1, or capital goods at rate π capital goods per intermediate c = Y c (6) So the aggregate resource constraint is I = πy I (7) Y = Y c + Y I = C + p K I (8) where p K = π 1 is the key exogenous technological parameter in the model

Market clearing The facts Supply of housing (viz land) is fixed h = h (9) Asset market clears a 1 + a 2 = p K K (10)

The facts Results - baseline setup, real interest rates Relative price of capital goods 1.2 1 0.8 Anticipated Unanticipated 0.034 0.032 0.03 0.028 Annualised ex ante interest rate 0.6 0 5 10 15 20 0.026 Time (in 20 year generations)

The facts Results - baseline setup, investment, debt and house prices 1.2 Annualised ex ante interest rate 0.034 1.2 Nominal investment GDP 0.15 1 0.032 1 0.145 0.03 0.14 0.8 0.028 0.8 0.135 0.6 0 5 10 15 20 0.026 0.6 0 5 10 15 20 0.13 1.2 Housing wealth annual GDP 3.2 1.2 Net debt of young/gdp 0.5 1 3.1 1 0.4 0.3 3 0.8 2.9 0.8 0.2 0.1 0.6 0 5 10 15 20 2.8 0.6 0 5 10 15 20 0

The facts Intuition Lower capital goods prices means each unit of savings buys more capital goods, with opposing effects on the interest rate With σ < 1, the interest rate falls, reducing the user cost of housing Housing supply is fixed, so house prices increase Housing is paid for early in life, so debt increases too Acquiring the debt claims of the young is an alternative to capital investment So aggregate savings and investment fall in relation to GDP

The facts Results - no household debt 1.2 Annualised ex ante interest rate 0.04 1.2 Nominal investment GDP 0.16 0.035 1 1 0.03 0.14 0.8 0.025 0.8 0.6 0 5 10 15 20 0.02 0.6 0 5 10 15 20 0.12 1.2 Housing wealth annual GDP 3.2 1.2 Net debt of young/gdp 0.5 1 3.1 1 0.4 0.3 3 0.8 2.9 0.8 0.2 0.1 0.6 0 5 10 15 20 2.8 0.6 0 5 10 15 20 0

The facts Results - baseline setup, the profit share 1.2 0.35 Relative price of capital goods 1 0.8 0.3 Profit share in GDP 0.6 0 2 4 6 8 10 12 14 16 18 20 0.25 Time (in 20 year generations)

The profit share The facts The labour share has fallen in most countries. In a simple two-factor model with no pure profits, this means the capital share rises

The profit share The facts The labour share has fallen in most countries. In a simple two-factor model with no pure profits, this means the capital share rises Capital share equals profit rate times the capital-output ratio Π Y = Π Kp K Kp K Y

The profit share The facts The labour share has fallen in most countries. In a simple two-factor model with no pure profits, this means the capital share rises Capital share equals profit rate times the capital-output ratio Π Y = Π Kp K Kp K Y But real rate and the capital-output ratio have fallen.

The profit share The facts The labour share has fallen in most countries. In a simple two-factor model with no pure profits, this means the capital share rises Capital share equals profit rate times the capital-output ratio Π Y = Π Kp K Kp K Y But real rate and the capital-output ratio have fallen. Profits remunerating something other than capital Mismeasured capital-output ratio - intangibles? MPK vs r in financial markets - corporate taxes, physical depreciation, marginal v average returns 3 factors

The facts Econometric evidence - approach Modelling the world economy with 20-year time periods results in few datpoints Exploit cross-country dimension But countries are (partially) open to trade in goods and assets So solve an small open economy version of the model (trade in intermediates, exogenous interest rate) to generate new predictions Estimate x it = α i + βp it + u it or x i = α + β p i + u i

The facts Econometric evidence - results Table : Coefficent on p Prediction of model Variable Closed Open Data Nominal investment rate + + + HH debt/gdp -? - Real house prices - - - Current account/gdp n/a -?

Sensitivity analysis The facts Results go through a fortiori without housing Effect stronger with inelastic utility function Results go through with bequests bequests no housing inelastic utility Heterogeneous bequest motive - increased wealth inequality heterogeneous agents Effects reversed with highly elastic production function elastic production

Policy implications The facts Low real rates here to stay Higher inflation target to avoid the ZLB Higher public debt So is high household debt Note the side effects of macroprudential tools Look for safer ways for young households to borrow

The facts Thank you

Extra charts Bequests Heterogeneous bequest motive Parameterisation Econometric results US stock market yields 0.2 0.18 0.16 Dividend yield Earnings yield 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 1871 1891 1911 1931 1951 1971 1991 2011 Back to rates

Extra charts Bequests Heterogeneous bequest motive Parameterisation Econometric results US AAA corporate yield spreads to 10 year Treasuries pp 1.80 1.60 1.40 1.20 1.00 0.80 0.60 0.40 0.20 0.00 1963 1968 1973 1978 1983 1988 1993 1998 2003 2008 2013 Back to rates

Bequests Extra charts Bequests Heterogeneous bequest motive Parameterisation Econometric results Add bequests to the utility function U = 1 ( ) c1 1 θ + β 2 c 1 θ 2 + β 3 c 1 θ 3 + φ h1 γ 1 θ 1 γ + ξ b 1 ζ 1 ζ (11) c 1 + hp h + S 1 = ηw (12) c 2 + S 2 = (1 η)w + (1 + r)s 1 + b (13) c 3 + b = (1 + r )S 2 + hp h (14)

Results - bequests Extra charts Bequests Heterogeneous bequest motive Parameterisation Econometric results Annualised interest rate 3.2 3 2.8 2.6 2.4 2.2 0.7 0.8 0.9 1 Relative price of capital Net debt of young/annual GDP 0.3 0.25 0.2 0.15 0.1 0.05 0 0.05 0.7 0.8 0.9 1 Relative price of capital Nominal investment GDP 0.16 0.15 0.14 0.13 Baseline No debt Binding debt limit 0.12 0.7 0.8 0.9 1 Relative price of capital Housing wealth annual GDP 3.2 3.1 3 2.9 2.8 0.7 0.8 0.9 1 Relative price of capital Back to presentation

Results - bequests Extra charts Bequests Heterogeneous bequest motive Parameterisation Econometric results 1.2 0.035 0.5 0.15 Relative price of capital goods 1 0.8 0.03 Annualised ex ante interest rate 0.4 0.3 0.2 0.1 Net debt of young/annual GDP 0.145 0.14 0.135 Nominal investment GDP 0.6 0 5 10 15 20 0.025 Time (in 20 year generations) 0 5 10 15 20 0 Time (in 20 year generations) 0 5 10 15 20 0.13 Time (in 20 year generations) 1.2 4.5 0.35 1.3 Relative price of capital goods 1 0.8 4 Housing wealth annual GDP 0.3 Profit share in GDP C Young C Middle C Old Output 1.2 1.1 1 Consumption index 0.6 0 5 10 15 20 3.5 Time (in 20 year generations) 0 5 10 15 20 0.25 Time (in 20 year generations) 0 5 10 15 20 0.9 Time (in 20 year generations)

Extra charts Bequests Heterogeneous bequest motive Parameterisation Econometric results Heterogeneous bequest motive Inherited wealth is unequally distributed Changes in asset prices induced by p will have distributional consequences To study this, divide the population into two equally-sized dynasties, one with a bequest motive as above, one without

Extra charts Bequests Heterogeneous bequest motive Parameterisation Econometric results Results - heterogeneous bequests 1.2 1.15 1.2 1.15 Relative price of capital goods 1.14 1 1.13 1.12 0.8 p 1.11 housing wealth/gdp (index lhs) Ratio of dynastics to life cyclers 0.6 0 5 10 15 20 1.1 Time (in 20 year generations) Consumption of the young 1.14 1 1.13 1.12 0.8 p 1.11 housing wealth/gdp (index lhs) Ratio of dynastics to life cyclers 0.6 0 5 10 15 20 1.1 Time (in 20 year generations) Consumption of the middle aged 1.2 1.15 1.2 1.7 Relative price of capital goods 1.14 1 1.13 1.12 0.8 p 1.11 housing wealth/gdp (index lhs) Ratio of dynastics to life cyclers 0.6 0 5 10 15 20 1.1 Time (in 20 year generations) Consumption of the retired 1 1.6 0.8 p Total wealth/gdp (index lhs) Ratio of dynastics to life cyclers 0.6 0 5 10 15 20 1.5 Time (in 20 year generations) Total wealth

Results - σ = 1.3 Extra charts Bequests Heterogeneous bequest motive Parameterisation Econometric results Annualised interest rate 3.2 3.1 3 2.9 2.8 2.7 0.7 0.8 0.9 1 Relative price of capital Net debt of young/annual GDP 0.3 0.2 0.1 0 0.1 0.2 0.7 0.8 0.9 1 Relative price of capital Nominal investment GDP 0.16 0.15 0.14 0.13 Baseline High sigma Cobb Douglas 0.12 0.7 0.8 0.9 1 Relative price of capital Housing wealth annual GDP 3.2 3.1 3 2.9 2.8 2.7 2.6 2.5 0.7 0.8 0.9 1 Relative price of capital Back to presentation

Results - no housing Extra charts Bequests Heterogeneous bequest motive Parameterisation Econometric results 1.2 Annualised ex ante interest rate 0.036 1.2 Nominal investment GDP 0.15 0.034 1 0.032 0.03 1 0.145 0.028 0.14 0.8 0.026 0.024 0.8 0.135 0.022 0.6 0 5 10 15 20 0.02 0.6 0 5 10 15 20 0.13 1.2 Housing wealth annual GDP 5 1.2 Net debt of young/gdp 0.5 0.4 1 1 0.3 0 0.8 0.8 0.2 0.1 0.6 0 5 10 15 20 5 0.6 0 5 10 15 20 0

Extra charts Bequests Heterogeneous bequest motive Parameterisation Econometric results Results - inelastic utility 1.2 Annualised ex ante interest rate 0.04 1.2 Nominal investment GDP 0.16 0.035 1 1 0.03 0.14 0.8 0.025 0.8 0.6 0 5 10 15 20 0.02 0.6 0 5 10 15 20 0.12 1.2 Housing wealth annual GDP 4 1.2 Net debt of young/gdp 0.5 1 3 1 0.4 0.3 2 0.8 1 0.8 0.2 0.1 0.6 0 5 10 15 20 0 0.6 0 5 10 15 20 0

Extra charts Bequests Heterogeneous bequest motive Parameterisation Econometric results We need to talk about σ Results of this model require that the elasticity of substitution between capital and labour σ < 1 When σ is low, it is hard to vary the production technology, so a rise in the quantity of capital goods depresses the marginal product more than proportionally Most estimates find σ well below unity See e.g. the survey in Chirinko (2008). Median value of estimates is.5, 85th percentile is unity Karabarbounis and Neiman (2014) find σ = 1.3 using corporate sector labour share Other tests of Karabarbounis and Neiman s model with their data suggest σ well below unity σ econometrics

σ econometrics Extra charts Bequests Heterogeneous bequest motive Parameterisation Econometric results Table : Two ways to estimate σ: labour share and investment rate Dependent variable Labour share Investment rate Robust regression OLS Robust regression OLS Relative price of investment Implied value of sigma Coefficient 0.210** -0.032 0.455*** 0.592*** standard error [0.09] [0.11] [0.16] [0.19] Observations 57 57 53 53 Central 1.21 0.97 0.55 0.41 lower bound of CI 1.03 0.75 0.23 0.03 upper bound of CI 1.39 1.19 0.87 0.79

Extra charts Bequests Heterogeneous bequest motive Parameterisation Econometric results The profit share in a nested CES function Can reconcile investment rate and labour share if we add a third factor M that is paid in profits but cannot be accumulated Y = [ [ [ µm θ 1 θ + (1 µ) (1 α) L σ 1 σ ] + αk σ 1 σ σ 1 σ ] θ 1 ] θ θ 1 θ

Extra charts Bequests Heterogeneous bequest motive Parameterisation Econometric results Labour share and investment both increasing in p 1.4 1.2 1 0.8 0.6 0.4 0.2 Lower bound on sigma for labour share upper bound on sigma for capital share 0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Investment rate Extra charts Bequests Heterogeneous bequest motive Parameterisation Econometric results Table : Estimates of the elasticity of substitution σ Dataset Panel Time trends Panel Time trends Estimator FE OLS Robust FE OLS Robust RHS source PWT WDI Log(p) 0.491*** 1.121*** 0.776*** 0.290*** 0.999*** 0.695*** [0.04] [0.21] [0.17] [0.04] [0.25] [0.16] ˆσ 0.509-0.121 0.224 0.71 0.001 0.305 σˆ H 0.589 0.299 0.564 0.79 0.501 0.625 σˆ L 0.429-0.541-0.116 0.63-0.499-0.015 N 1632 54 54 1643 52 52 no. of countries 99 100 Back to presentation

HH debt/gdp Extra charts Bequests Heterogeneous bequest motive Parameterisation Econometric results Table : Regression of household debt on relative price of capital Left-hand side variable Household debt/gdp Dataset Panel Time trends Panel Time trends Estimator FE OLS Robust FE OLS Robust RHS source PWT WDI log(p) -0.993*** 0.702-0.779*** -1.179*** 0.571-0.888*** [0.05] [0.65] [0.25] [0.07] [0.72] [0.30] N 535 18 18 551 18 18 no. of countries 21 21 Back to presentation

Real house prices Extra charts Bequests Heterogeneous bequest motive Parameterisation Econometric results Table : Regression of real house prices on relative price of capital Left-hand side variable Real house prices Dataset Panel Time trends Panel Time trends Estimator FE OLS Robust FE OLS Robust RHS source PWT WDI log(p) -1.082*** 0.121-0.672-0.976*** -0.277-1.520** [0.10] [0.89] [0.79] [0.12] [0.91] [0.65] N 535 18 18 551 18 18 no. of countries 21 21 Back to presentation

Extra charts Bequests Heterogeneous bequest motive Parameterisation Econometric results Current account balance Table : Regression of current account on relative price of capital Left-hand side variable Current account/gdp Dataset Panel Time trends Panel Time trends Estimator FE OLS Robust FE OLS Robust RHS source PWT WDI log(p) -0.055*** 0.006 0.020-0.025** 0.025 0.028 [0.01] [0.05] [0.05] [0.01] [0.05] [0.05] N 1004 35 35 992 34 34 no. of countries 50 51 Back to presentation