Demographic Trends and the Real Interest Rate

Demographic Trends and the Real Interest Rate Noëmie Lisack Rana Sajedi Gregory Thwaites Bank of England November 2017 This does not represent the views of the Bank of England 1 / 43

Disclaimer This does not represent the views of the Bank of England 2 / 43

Key points Unprecedented rise in life expectancy in recent decades in advanced economies Understand the macroeconomic impact of this change in the composition of the population A key implication: fall in the neutral interest rate OLG model to quantify the effect of population ageing Across all advanced-countries, ageing can explain: About 160bp of fall in interest rates since 1980, with a further 40bp still to come More than 75% of the rise in house prices and private credit to GDP Some of the labour productivity slow down since the 2000s Just under 30% of the variation in net foreign asset positions 3 / 43

Plan for today Key facts - Interest rates and demographics in recent decades Intuition - The neutral rate in the neoclassical model Methodology - Outline of our model and calibration Results - Macroeconomic implications of population ageing Sensitivities - Robustness and Extensions Conclusions - Summary and some caveats 4 / 43

Unprecedented population ageing Old Age Dependency Ratio (%) 0 20 40 60 80 1800 1850 1900 1950 2000 2050 2100 OECD OECD low variant OECD high variant France Belgium UK Denmark Netherlands Switzerland Source: UN Population Statistics, Human Mortality Database 5 / 43

Population growth Growth rate of 20-24 year old cohort 6 / 43

Population growth Growth rate of 20-24 year old cohort 7 / 43

Baby boomers are not the main factor Source: UN Population Statistics, own calculations 8 / 43

Life expectancy at 60 93 91 89 87 85 83 81 79 77 75 1950 1970 1990 2010 2030 2050 2070 2090 Source: UN Population Statistics 9 / 43

Natural interest rate in advanced economies since 1960 7 per cent 6 5 4 3 2 1 0-1 1961 1966 1971 1976 1981 1986 1991 1996 2001 2006 2011 2016 US Canada Euro Area UK Source: Holston, Laubach and Williams (2017) 10 / 43

Intuition: How demographics affect interest rates 12 / 43

Intuition: Age-wealth profile in the US Thousand USD 600 500 400 300 200 100 0 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 Age Source: Survey of Consumer Finances, Average Net Worth excl. Housing, 1989-2013 13 / 43

Related literature Closed economy: Carvalho et al (2016), Eggertsson et al (2017), Gagnon et al (2016), Marx et al (2016) Open economy: Backus et al (2014), Domeij and Floden (2006), Krueger and Ludwig (2007) 14 / 43

Model: overview Calibrated neoclassical overlapping generations model Households value consumption, housing and bequests They face a given life-cycle profile of labour earnings Net savings of households invested by firms Demographic change: variable birth rates and life expectancy Solved assuming perfect foresight 16 / 43

Model: Household s Problem The household born at time t maximises: max {c τ,t, a τ,t, h τ,t} T τ=1 T β τ ψ τ,t (ln c τ,t + θ τ ln h τ,t ) + β T ψ T,t φ ln a T,t τ=1 subject to, for τ = 1,..., T : c τ,t +a τ,t +p h t+τ 1(h τ,t h τ 1,t ) w t+τ 1 ɛ τ l τ,t +(1+r t+τ 1 )a τ 1,t +π τ,t τ: age ; t: birth year ψ τ,t : survival probability up to age τ Inelastic labor supply Fixed number of periods when the household is able to move ; otherwise, we impose h τ,t = h τ 1,t. 17 / 43

Model: Firm s Problem At each period t, the firm maximises: max L t, K t F (K t, L t ) w t L t (r t + δ)k t F (K, L) = A [(1 α)l σ 1 σ ] + αk σ 1 σ σ 1 σ 18 / 43

Model: Market Clearing X t : value of X t per aggregate capita. Market Clearing at every period t: Capital/Asset Market Labour Market Housing Market Ã t 1 = K t ρ ɛl t = L t H t = H Goods Market Ỹ t = C t + Ĩ t Steady state exists in per capita terms. Housing supply exogenously increases with total population size. 19 / 43

Calibration Average aggregate values for advanced economies in the 1970s World interest rate: 3.7% Housing wealth/gdp ratio: 145% Credit/GDP ratio: 45% Life-cycle patterns from the US Survey of Consumer Finances, from 1989 to 2013 Labour productivity Net wealth (excluding housing) Housing wealth Demographics data for advanced economies: Western Europe, North America, Japan, Australia, New Zealand details 20 / 43

Calibration: Labour productivity Source: Survey of Consumer Finances, Labour income, 1989-2013 21 / 43

Calibration: Net worth (excl. housing) Source: Survey of Consumer Finances, Average Net Worth excl. Housing, 1989-2013 22 / 43

Calibration: Housing wealth Source: Survey of Consumer Finances, Housing wealth, 1989-2013 23 / 43

Using the model Incorporate both the baby boom and the increase in life expectancy in our model Compute the transition from the 1950s to the 2100s according to the UN population predictions Match the data in the 1970s Let the model speak before and after these dates 25 / 43

Calibration: Demographic change Blue: model, Red: data (UN Population Statistics) 26 / 43

Results overview Savings, debt and the interest rate House prices and the role of housing Labour productivity Open economy implications 27 / 43

Model outcome: Natural interest rate 5.00 4.50 4.00 3.50 3.00 2.50 2.00 1.50 1.00 0.50-1.4 1.2 1 0.8 0.6 0.4 0.2 0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 1960 1980 2000 2020 2040 2060 2080 2100 Model Data (HLW avg) Blue: model, Red: data (Holston-Laubach-Williams Average) 28 / 43

Model outcome: capital-output ratio 29 / 43

Model outcome: Decomposing the drivers of savings Blue: full simulation Red: changing only the population age structure Yellow: changing only the household s optimal behaviour 30 / 43

Model outcome: Housing and credit Blue: model, Red: data (BIS, Private credit, House price index) 31 / 43

Model outcome: Decomposing the drivers of debt Blue: full simulation Red: changing only the population age structure Yellow: changing only the household s optimal behaviour 32 / 43

Model outcome: Labour productivity Deviation from trend, annualised growth 33 / 43

Open economy: OADR across countries 70% 60% 50% 40% Advanced Countries Japan Germany USA Australia UK 30% 20% 10% 0% 1950 1970 1990 2010 2030 2050 2070 2090 Source: UN Population Statistics 34 / 43

Open economy: Model vs data 200% 150% Switzerland 100% 50% 0% -50% Belgium Netherlands Denmark Austria US UK Canada Australia Germany France Italy R² = 0.2809 Japan -100% Ireland New Zealand Portugal Spain -150% -200% -200% -150% -100% -50% 0% 50% 100% 150% 200% Model on x-axis and Data on y-axis, grey line is the 45 degree line. 35 / 43

Open economy: model predictions Demographic Changes and NFA accumulation 190% 140% 90% 40% -10% -60% -110% R² = 0.2451 R² = 0.7497 R² = 0.8319 Ireland Australia Australia US Spain UK Switzerland Switzerland Germany Portugal UK Australia US Spain Portugal Italy Germany Italy US Ireland Japan Switzerland Japan UK Spain Germany Data 2010 Italy Portugal Model 2010 Model 2030-160% Ireland 55% 75% 95% 115% 135% 155% Japan Note: HWR on x-axis and NFA/GDP on y-axis. 36 / 43

Sensitivities and extensions Housing Monopoly profits Retirement age 38 / 43

Sensitivities and extensions: housing Housing facilitates life-cycle saving, somewhat attenuating effects of demographics Prevents negative interest rates Figure: Simulations With and Without Housing 39 / 43

Sensitivities and extensions: monopoly profits Add monopolistic competition and supernormal profits to the corporate sector. In partial equilibrium, this pushes down on the interest rate r t = 1 µ Tradable claims constitute an additional store of value, again attenuating fall and Figure: Simulations With and Without Monopoly Power Y t K t 40 / 43

Sensitivities and extensions: retirement age Simulations varying retirement age by 5 years Effects of retirement age increase surprisingly small 41 / 43

Conclusions and some caveats Conclusions: Population ageing mostly due to persistent rise in longevity Explain around half the fall in real interest rates since the 1980s, most of the rise in house prices and household debt and about 30% of cross-sectional variation in NFA positions. Potentially permanent implications Caveats: We have assumed perfect foresight, but not everyone plans ahead Not all the pressure of demographic change will fall on private savings Retirees can instead consume less (no evidence so far) Households will work more, or retire later (already some evidence) Governments will provide part of the old-age pensions through contemporaneous transfers This is not a forecast that rates will remain low - many other factors at play 43 / 43

Country list Country list for UN population data: Australia, Austria, Belgium, Canada, Denmark, France, Germany, Ireland, Italy, Japan, Netherlands, New Zealand, Portugal, Spain, Switzerland, United Kingdom, United States of America Population approximation before 1950: Belgium, Canada, Denmark, France, Italy, Netherlands, Spain, Switzerland, UK, USA Back 0 / 0