Demography, Capital Flows and International Portfolio Choice over the Life-cycle

Demography, Capital Flows and International Portfolio Choice over the Life-cycle Margaret Davenport (University of Lausanne) Katja Mann (University of Bonn) EEA-ESEM Annual Congress 23 August 2017

Imbalances in debt and equity position of US vis-à-vis EU 6 Bilateral Positions: US vs EU 4 Net External Positions (ratio to GDP) 2 0-2 -4-6 Net Bilateral Position (portfolio + other investment) Net Risky Position (portfolio equity) Net Safe Position (portfolio debt + net claims banking sector) -8 1980 1985 1990 1995 2000 2005 2010 2015 Year sources: IMF Coordinated Portfolio Investment Survey, Treasury International Capital System. EU refers to the 15 EU countries of pre-2004. shares importance 2 / 22

Faster population aging in EU than US Old-age dependency Life expectancy at age 60 0.2.4.6 old age dependency ratio 1950 2000 2050 2100 year 15 20 25 30 35 life expectancy at age 60 1950 2000 2050 2100 year EU US EU US source: United Nations Population Division. EU refers to the 15 EU countries of pre-2004. 3 / 22

Research Question What is the effect of population aging on international portfolio choice? Facts on Savings and Portfolio Choice details definitions hump-shaped savings pattern over the life-cycle portfolio share of risky assets declines with age Implications: Demography and Capital Flows aggregate safe and risky asset demands reflect population s age structure autarky: demographics should affect asset prices and returns financial integration of regions with different demographics: asset trades world market-clearing asset returns reflect world demographics 4 / 22

Research Question What is the effect of population aging on international portfolio choice? Facts on Savings and Portfolio Choice details definitions hump-shaped savings pattern over the life-cycle portfolio share of risky assets declines with age Implications: Demography and Capital Flows aggregate safe and risky asset demands reflect population s age structure autarky: demographics should affect asset prices and returns financial integration of regions with different demographics: asset trades world market-clearing asset returns reflect world demographics 4 / 22

Research Question What is the effect of population aging on international portfolio choice? Facts on Savings and Portfolio Choice details definitions hump-shaped savings pattern over the life-cycle portfolio share of risky assets declines with age Implications: Demography and Capital Flows aggregate safe and risky asset demands reflect population s age structure autarky: demographics should affect asset prices and returns financial integration of regions with different demographics: asset trades world market-clearing asset returns reflect world demographics 4 / 22

Methodology 1 Structural general equilibrium model with multi-period overlapping generations with stochastic survival portfolio choice between a safe and a risky asset two fully integrated world regions with different demography asset supply modeled through Lucas trees 2 Calibration and simulation demographic transitions for US and EU between 1950 and 2095 full financial integration from 1990 details 5 / 22

Findings and contribution Findings: demographics can explain a large share of bilateral asset positions and return rate movements in 1990-2015 we predict asset returns to decrease persistently while external positions fluctuate, continuing to be sizable Contribution: imbalances and high risk-content of US position arise naturally from demographic differences and likely represent a long-run phenomenon demography as novel demand-side explanation for low interest rates and safe asset shortage, complementing e.g. Bernanke (2005), Gourinchas and Jeanne (2012), Eggertson and Mehrotra (2014), Caballero and Fahri (2017) literature 6 / 22

Demographics New cohorts born at N b start working immediately, and retire at age N r (fixed). Maximum lifetime is N d. Cohort size L n,t and population size L t = N d n=n L b n,t are determined by two demographic parameters: Birth rate γ t : L N b,t+1 = (1 + γ t+1 ) L N b,t Survival probability δ n,t L n,t = ( n 1 l=n b δ l,t n+l ) L N b,t n Regions e, u differ in terms of demographics - region e ages faster than u: δ e t > δ u t, γ e t < γ u t 7 / 22

Financial assets Two types of assets: safe bonds B t and risky stocks S t. asset prices are normalized to 1 bond pays return R t = 1 + d t, where d t is the dividend stock pays return R t = 1 + d t + risk premium t + ε t, where ε t N (0, σ ε ) asset returns are perfectly correlated internationally and the exchange rate is fixed domestic and foreign assets are identical to agents demographics affect net flows in debt and equity 8 / 22

Financial assets Supply: Lucas tree endowment economy with two types of trees. Aggregate supply of each asset is a linear function of the total population: B t = λl t S t = λl t with λ, λ scaling parameters. simple supply side allows focus on demand side constant risky share in line with empirical evidence (Gorton, Lewellen and Metrick, 2012) 9 / 22

Labor and pension income Labor income (ages n N r ) follows a stochastic iid process y i,n,t = P i,n,t ζ i,n,t θ i,n,t P i,n,t = G n P i,n,t 1 η i,n,t G n, age-specific component (hump shape over life-cycle) θ i,n,t, η i,n,t log-normally distributed shocks ζ i,n,t iid zero income shock Pension income (n > N r ) is a fixed share φ of last working period s deterministic income ỹ i,n,t = φp i,nr,tζ i,n,t Alternative: PAYGo details 10 / 22

Optimization problem Preferences are CRRA. Households maximize expected lifetime utility of consumption at each age n, ( N d n 1 ) U i,n,t = E β n u(c i,n,t+n ), n=t l=n b δ l,t+l subject to with x i,n,t = R tb i,n 1,t 1 + R ts i,n 1,t 1 + y i,n,t x i,n,t = R tb i,n 1,t 1 + R ts i,n 1,t 1 + ỹ i,n,t x i,n,t = c i,n,t + b i,n,t + s i,n,t }{{} a i,n,t if n N r if n > N r Natural borrowing constraint due to zero income shock: a i,n,t 0. Additional assumption: no short-sales in either asset. FOCs 11 / 22

Open economy: Market clearing and external positions Aggregate demand B t = N d Market clearing conditions: Bond market: Stock market: n=n b L n,tb n,t, S t = N d n=n b L n,ts n,t. B e t + B u t = B e t + B u t S e t + S u t = S e t + S u t Consumption aggregate clearing: C t + B e t + B u t + S e t + S u t = Y t + R t(b e t 1 + B u t 1) + R t(s e t 1 + S u t 1) Resulting external positions: NFB u t = B u t B u t = B e t B e t = NFB e t NFS u t = S u t S u t = S e t S e t = NFS e t, 12 / 22

Numerical Solution - Main parameters Demographics: Data and projections on birth rate γ t and survival probabilities δ n,t from UN Population Prospects spanning 1950 to 2095 Supply side parameters: Derive λ, λ in a partial equilibrium set-up for the US as a closed economy (1950 to 1989), using data on US 3-month government bond return and historical risk premium (Damodaran, 2016) λ = 1 40 1989 1950 1989 B t 1 S t λ = L t 40 L 1950 t where B t, S t are model-generated demands resulting from observed return rates, L t is population. 13 / 22

Numerical Solution - Additional parameters Age at birth N b 20 Maximum Age N d 100 Retirement Age N r 65 Subjective discount factor β 0.96 (Cocco et al, 2005) CRRA parameter ϑ 8 (Mehra & Prescott, 1985) Variance return shock σɛ 2 0.21 (Fama and French, 2002) Var. transitory income shock σθ 2 0.0738 (Cocco et al, 2005) Var. permanent income shock ση 2 0.0106 (Cocco et al, 2005) Probability of zero income p 0.01 (Carroll, 1992) Age-dependent income growth G n, P n (Cocco et al, 2005) Pension replacement rate φ 0.68 (Cocco et al, 2005) Safe asset supply parameter λ 147.8 estimated Risky asset supply parameter λ 77.3 estimated 14 / 22

Results (1): Return rates 0.04 Bond Returns 0.02 0-0.02 0.04 Bond Returns -0.04 0.02 1990 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 0 0.02 0.042 Risk Premium 0.04 0.04 1980 2000 2020 2040 2060 2080 2100 0.038 0.045 Risk Premium 0.036 0.04 0.034 0.035 0.032 1990 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 0.03 1980 2000 2020 bond return, model 2040 2060 real return 3-month T-bill, data 2080 2100 model data 15 / 22

Results (2): US external positions 5 Net Safe Position over Endowment 0 percent of GDP -5-10 -15-20 1990 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 6 Net Risky Position over Endowment 4 percent of GDP 2 0-2 -4 1990 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 model data life-cycle US aggregates 16 / 22

Decomposing the effect Demographic change can affect aggregate asset demand in three ways: distribution channel: changes in relative size of age groups due to decreased fertility and increased longevity life-cycle channel: changes in agents savings and portfolio choice due to increased life expectancy valuation channel: changes in market-clearing return rates Decompose these in counterfactual exercise: holding either or both of returns and life-cycle responses of individuals fixed 17 / 22

Channels over time age groups 18 / 22

Conclusion In a structural general equilibrium model with life-cycle portfolio choice, we show that demographic change in the EU and US increases the demand for financial assets, evidenced by a decrease in return rates the faster-aging EU will export risky and import safe assets, explaining the observed bilateral external positions effects result from a shift in population structure towards the elderly rather than from change in life-cycle behavior or return rate responses 19 / 22

Appendix 20 / 22

Robustness checks and extensions EU is poorer than US (70 percent of US labor income) US position slightly more negative, but similar variation retirement at age 62 similar external positions more more PAYGo pension system with constant and common tax rate of 12.4 percent, varying replacement rate (US data, OECD 2016) more similar external positions until around 2030 once most US baby boomers are dead (but those in EU still alive), extreme external positions emerge implausibly low equilibrium safe return rates from 2040 PAYGo pension system with different tax rates, in line with US and EU data (OECD 2016) more implausibly high positive US external positions 20 / 22

Related Literature Demographic change and portfolio choice in a closed economy: Auerbach & Kotlikoff (1987), Abel (2001, 2003), Brooks (2000, 2006), Kuhle, Ludwig & Börsch-Supan (2007) Demographic change and portfolio choice in an open economy: De Santis & Lührmann (2009) Demographic change and (aggregate) international capital flows: Börsch-Supan, Ludwig & Winter (2006), Krueger & Ludwig (2007), Backus, Cooley & Henriksen (2014), Bárány, Coeurdacier & Guibaud (2015) Asymmetries in international positions: Gourinchas and Rey (2007), Gourinchas, Rey and Govillot (2010); Caballero, Farhi and Gourinchas (2008), Mendoza, Quadrini and Rios-Rull (2009) back 21 / 22

Estimated Life-cycle Savings and Portfolio Shares financial assets (thsd. 2013 $) conditional risky share Total financial assets, US Conditional risky share of financial assets, US 400 0.4 350 300 250 200 150 100 50 0 20 40 60 80 0.39 0.38 0.37 0.36 0.35 0.34 0.33 0.32 0.31 0.3 20 40 60 80 estimation based on Survey of Consumer Finances, 1989 to 2013; following Deaton & Paxson (1994): controlling for time- and cohort-fixed effects and for endogenous participation details declining risky share with age is also found by Poterba and Samwick (2001), Guiso, Haliassos & Japelli (2002), Fagereng, Gottlieb & Guiso (2017), among others back 21 / 22

Estimation of Life-cycle Asset Holdings and Risky Share Deaton & Paxson (1994) method to estimate cohort-, time- and age-fixed effects simultaneously Heckman estimation of risky share first stage: probit estimation of participation in stockmarket P iact prob(p iact = 1 x) = prob(δ aa a + δ cc c + δ td t + δ 0Trend+ υz iact + υ 2L iact + η iact > 0) second stage: estimation of the risky share conditional on participation; Deaton & Paxson (1994) method: ω iact = β aa a + β cc c + β td t + β 0Trend + δz iact + δ 2λ iact + ε iact. estimation of life-cycle financial asset holdings: z iact = γ a A a + γg c + γ t D t + ψz iact + ν iact back 21 / 22

Definition of safe and risky assets Source Risky assets Safe assets SCF stocks; stock mutual funds; IRAs/Keoghs invested in stock; other managed assets with equity interest (annuities, trusts, managed investment accounts) if invested in stocks; thrift-type retirement accounts invested in stocks; savings accounts classified as 529 or other accounts that may be invested in stocks CPIS and TIC short- and long-term debt instruments, e.g. bonds, debentures, treasury bills, negotiable certificates of deposit, commercial papers, bankers acceptances transaction accounts; certificates of deposit; bonds (except mortgagebacked); mutual funds invested in bonds; quasi-liquid retirement accounts (IRAs and thrift-type accounts) and individual retirement accounts/keoghs if invested in bonds; savings bonds; cash value of life insurance; other managed assets (trusts, annuities, managed investment accounts) if invested in bonds equity and investment fund shares, e.g. shares, stocks, participations or similar documents back 21 / 22

Table: Share of bilateral positions in total external asset positions EU US debt equity debt equity OFCs as RoW 0.45 0.44 0.45 0.42 OFCs as bilateral 0.57 0.64 0.59 0.62 Source: CPIS, using a definition of offshore financial centers (OFCs) by the IMF. Numbers are averaged over 1997-2015. back 21 / 22

First order conditions The first order conditions with respect to consumption and assets result in the Euler equation (ω = risky share) [ )] c ϑ i,n,t = β δ n,t E t c ϑ i,n+1,t+1 ((1 ω i,n,t )R t+1 + ω i,n,t R t+1 and the portfolio share optimality condition: β δ n,t E t [c i,n+1,t+1 a n,t ( R ] t+1 R t+1 ) = 0 Effect of demographic change (increase in δ n,t ): savings: reduce current consumption in Euler eq.s portfolio choice (through savings): increase the share of risky assets back 21 / 22

Simulation results: Life-cycle asset holdings 600 Life-cycle Financial Assets 1 Life-cycle Risky Share 0.9 500 0.8 thousands of 2010 US dollars 400 300 200 thousands of 2010 US dollars 0.7 0.6 0.5 0.4 0.3 100 0.2 0.1 0 0 20 20 30 40 50 60 70 80 90 100 30 40 50 60 70 80 90 100 age age Total, 1950 Total, 2010 Total, 2095 Risky Assets, 1950 Risky Assets, 2010 Risky Assets, 2095 back 21 / 22

Simulation results: US aggregates 0.12 Consumption over Total Financial Assets, Household Sector 0.26 80 Total Financial Assets, Household Sector 80 0.118 0.116 0.114 0.112 0.11 0.108 0.24 0.22 0.2 0.18 trillions of US dollars 70 60 50 40 70 60 50 40 30 20 10 0.106 1950 1960 1970 1980 1990 2000 2010 0.16 30 1950 1960 1970 1980 1990 2000 2010 0 2.8 Total Risky Assets over GDP, Household Sector 0.9 18 Aggregate Endowment (GDP) 2.75 0.8 16 2.7 0.7 14 2.65 2.6 2.55 2.5 0.6 0.5 0.4 0.3 0.2 trillions of US dollars 12 10 8 6 2.45 0.1 4 2.4 1950 1960 1970 1980 1990 2000 2010 0 2 1950 1960 1970 1980 1990 2000 2010 model data (right axis) back 21 / 22

Channels across age groups back 21 / 22

US and EU share of of world external assets assets.55.6.65.7.75 1990 1995 2000 2005 2010 2015 Year equity debt source: Lane and Milesi-Ferretti (2007) back 21 / 22

PAYGo pension system working-age individuals pay a constant tax rate τ on their labor income retirees of any age n earn a period t income Ỹ t = N r 1 n=n τy n,tl b n,t N d n=n L ; r n,t pension income is larger when the working-age population is larger or more concentrated at high-earning age groups, when the tax rate is higher, or the number of retirees smaller for now we assume that retirement age is held constant and that the government budget always balances back 22 / 22

0.05 Safe Assets 0 0.05 0.1 0.15 1980 2000 2020 2040 2060 2080 2100 0.06 Risky Assets 0.04 0.02 0 1980 2000 2020 2040 2060 2080 2100 Year back 22 / 22

0 Safe Assets 0.1 0.2 0.3 0.4 1980 2000 2020 2040 2060 2080 2100 0.08 Risky Assets 0.06 0.04 0.02 0 1980 2000 2020 2040 2060 2080 2100 Year back 22 / 22

1.5 Safe Assets 1 0.5 0 0.5 1980 2000 2020 2040 2060 2080 2100 0.4 Risky Assets 0.3 0.2 0.1 0 1980 2000 2020 2040 2060 2080 2100 Year back 22 / 22

0.2 Safe Assets 0.1 0 0.1 0.2 1980 2000 2020 2040 2060 2080 2100 0.08 Risky Assets 0.06 0.04 0.02 0 1980 2000 2020 2040 2060 2080 2100 Year back 22 / 22

de jure financial openness.4.6.8 1 1960 1980 2000 2020 year EU US source: Chinn and Ito (2008) back 22 / 22