Reformulating the Support Ratio to Reflect Asset Income and Transfers Ronald Lee and Andrew Mason NTA9 Barcelona June 3, 2013 We are grateful to country teams whose data we have used and to Gretchen Donehower for assistance. Research supported by NIA R37 AG025247 and by the Bill and Melinda Gates Foundation
What is macro ‐ economic impact of changing pop age distribution? • Support Ratio is a simple and intuitive indicator of the impact • Consumption changes in proportion to support ratio, other things equal. • Very widely used. • This discussion applies equally to the Dependency Ratio R. Lee and A. Mason, Barcelona, June 3 2
Suppose that labor is the only source of income. Then… • The LCD of young and old would be balanced completely by transfers from workers to young and old. • Output would be proportional to size of effective labor. • Standard support ratio would give correct impact of population age distribution changes on consumption. R. Lee and A. Mason, Barcelona, June 3 3
More realistically, output comes from labor and capital • Then – Output is not proportional to labor – Ownership of capital is source of income. • Suppose that individuals are completely financially independent, accumulating assets during working years for retirement. – Now population age distribution is irrelevant. – Population aging is no problem for workers. • The support ratio falls nonetheless ‐‐ misleading • Impacts arise only through transfers! R. Lee and A. Mason, Barcelona, June 3 4
The standard story is not quite right • Labor is not the only source of output or income • Consumption exceeds labor income by 22% in average NTA country. • Capital and other assets also generate income and pay for consumption. • The Life Cycle Deficit is balanced by asset income as well as transfers from workers. R. Lee and A. Mason, Barcelona, June 3 5
Here is the Y= Labor x av product of standard model labor ( ) = Y LAf k hk , Cons = (1 ‐ s)Y ( ) = − C 1 s Y ( ) ( ) = − C 1 s LAf k hk , Divide by N, effective C L ( ) ( ) = − 1 s Af k hk , consumers. N N Consump per effective L ( ) ( ) = − c 1 s Af k hk , N consumer = Support ratio x proportion not saved x av product of labor R. Lee and A. Mason, Barcelona, June 3 6
From this comes standard story: Other things equal, consumption is proportional to the support ratio. But should we expect other things to be equal when support ratio changes? R. Lee and A. Mason, Barcelona, June 3 7
Consider an increase in workers. • Add 10% more workers – Support ratio rises by 10%. • But each new worker raises output by marginal product of labor , not by average product. – Capital ‐ labor ratio declines – Output rises by only 10%* β , where β is labor share in output, or about 2/3, say 7%. • Not obvious whether consumption per EAC goes up or down. R. Lee and A. Mason, Barcelona, June 3 8
Consider an increase in elderly • Support ratio falls, consumption declines • But suppose each new elder has accumulated capital to fund own consumption? – output rises by marginal product of capital, or elasticity .3 • No one else’s consumption is reduced, and possibly it is raised (due to higher capital ‐ labor ratio) R. Lee and A. Mason, Barcelona, June 3 9
Illustration of accumulation of assets by elderly (age pattern is relevant; motive is not) Net Worth by Age of Household Head in US, 2007, from Survey of Consumer Finance Net Worth ($000s) 1200 1000 800 600 400 200 0 0 ‐ 19 20 ‐ 34 35–44 45–54 55–64 65–74 75+ Age Source: Survey of Consumer Finance R. Lee and A. Mason, Barcelona, June 3 10
Two problems with standard story • Change in output is wrong (we just saw). • Life cycle deficit may be funded by asset income rather than by transfers. • Standard story correct only when LCD is funded entirely by transfers. R. Lee and A. Mason, Barcelona, June 3 11
Accounting + − − = τ − τ + − l C x ( ) Y ( ) x ( ) x ( ) x rA x ( ) S x ( ) 14 4 24 4 3 14 4 244 3 14243 Lifecycle Deficit 1444442444443 Net Transfers Asset-based Reallocations Age Reallocations • Lifecycle deficit: Two methods of funding – Public and private net transfers – Asset ‐ based reallocations • Asset income (rA(x)) • Dissaving ( ‐ S(x)) R. Lee and A. Mason, Barcelona, June 3 12
Funding the lifecycle deficit, US 2003 1.5 For US children, deficit funded Units of Average Labor Income 30 ‐ 49 almost entirely 1 by transfers Public Transfers 0.5 Asset ‐ based Reallocations 0 Private Transfers For US elderly, ‐ 0.5 asset ‐ based reallocations ‐ 1 more important 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 than transfers. Age R. Lee and A. Mason, Barcelona, June 3 13
Shares of net consumption of elderly funded by Family Transfers, Public Transfers and Asset income (part not saved) IN Assets PH MX TH US 2/3 1/3 Above line, elderly rely more than 50% on assets, UY KR less on transfers. ES Support ratio misleads. JP CR DE BR 1/3 2/3 TW CL CN AT SI HU SE Family Public 2/3 1/3 transfers transfers On this side of line, elderly rely almost entirely on public transfers. Support ratio is good. R. Lee and A. Mason, Barcelona, June 3 14
The Solution – take asset based reallocation into account • Generalized support ratio ω ω ( ) ( ) ( ) ( ) ( ) = ∫ ∫ + ⎡ − ⎤ N x t y , x dx N x t , rA x s x dx ⎣ ⎦ ( ) l 0 0 GSR t ω ( ) ( ) ∫ N x t c x dx , 0 N x t ( , ): population age x in year t Base year profiles held constant yl x ( ) : labor income profile − rA x ( ) s x ( ) : asset-based reallocation profile c x ( ) : consumption profile R. Lee and A. Mason, Barcelona, June 3 15
The Solution • General Support Ratio ω ω ( ) ( ) ( ) ( ) ( ) = ∫ ∫ + ⎡ − ⎤ N x t y , x dx N x t , rA x s x dx ⎣ ⎦ ( ) l 0 0 GSR t ω ( ) ( ) ∫ N x t c x dx , 0 Standard support ratio: share of consumption funded through work. R. Lee and A. Mason, Barcelona, June 3 16
The Solution • General Support Ratio ω ω ( ) ( ) ( ) ( ) ( ) = ∫ ∫ + ⎡ − ⎤ N x t y , x dx N x t , rA x s x dx ⎣ ⎦ ( ) l 0 0 GSR t ω ( ) ( ) ∫ N x t c x dx , 0 Share of consumption • 1 ‐ GSR(t): Share of consumption funded by funded by relying on relying on public and private transfers. assets. R. Lee and A. Mason, Barcelona, June 3 17
Age profiles of consumption, labor income and asset ‐ based reallocations, US 2003 70 Consumption 60 (C) Thousands of 2003 US Dollars 50 40 Asset ‐ based 30 Reallocations (ABR) 20 10 Labor Income 0 (Y) ‐ 10 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 R. Lee and A. Mason, Barcelona, June 3 18 Age
Standard support ratio and general support ratio, US (2011=1.0) 1.2 Support ratio (2011=1) 1.0 Y/C (Y+ABR)/C 0.8 0.6 1950 2000 2050 2100 Year R. Lee and A. Mason, Barcelona, June 3 19
Standard support ratios (blue) and general support ratio (red) a. United States b. Sweden c. Finland d. Austria 1.2 1.2 1.2 1.2 Y/C (Y+ABR)/C 1.1 1.1 1.1 1.1 Support ratio (2011=1) 1.0 1.0 1.0 1.0 0.9 0.9 0.9 0.9 0.8 0.8 0.8 0.8 0.7 0.7 0.7 0.7 1950 1975 2000 2025 2050 1950 1975 2000 2025 2050 1950 1975 2000 2025 2050 1950 1975 2000 2025 2050 e. Japan f. Germany g. Slovenia h. Mexico 1.2 1.2 1.2 1.2 Support ratio (2011=1) 1.1 1.1 1.1 1.1 1.0 1.0 1.0 1.0 0.9 0.9 0.9 0.9 0.8 0.8 0.8 0.8 0.7 0.7 0.7 0.7 1950 1975 2000 2025 2050 1950 1975 2000 2025 2050 1950 1975 2000 2025 2050 1950 1975 2000 2025 2050 i. Chile j. Costa Rica k. South Africa l. Philippines 1.2 1.2 1.2 1.2 Support ratio (2011=1) 1.1 1.1 1.1 1.1 1.0 1.0 1.0 1.0 0.9 0.9 0.9 0.9 0.8 0.8 0.8 0.8 0.7 0.7 0.7 0.7 1950 1975 2000 2025 2050 1950 1975 2000 2025 2050 1950 1975 2000 2025 2050 1950 1975 2000 2025 2050 Year Year Year Year R. Lee and A. Mason, Barcelona, June 3 20 Vertical lines at year 2011 represent first year of projection. All SR scaled to equal 1 in 2011.
Change in support ratios from 2010 to 2050 30% Standard Support Ratio, YL/C General Support Ratio, (YL+ABR)/C Percent Change in Ratio, 2010 ‐ 2050 20% 10% 0% ‐ 10% ‐ 20% ‐ 30% R. Lee and A. Mason, Barcelona, June 3 21
Proportion of C financed by ABR vs. difference between the change in the two support ratios, 2010 ‐ 2050 1.2 SA Asset ‐ Based Reallocations/Consumption, 1 0.8 MX Age 65+ 0.6 US PH 0.4 JP DE CR 0.2 SI FI CL AT SE 0 ‐ 0.12 ‐ 0.1 ‐ 0.08 ‐ 0.06 ‐ 0.04 ‐ 0.02 0 0.02 Difference in Change in Support Ratios, 2010 ‐ 2050, (SR ‐ GSR) R. Lee and A. Mason, Barcelona, June 3 22
Caveats • Assumes that new elderly have accumulated assets equal to those of previous elderly. – They might accumulate less due to public pensions and annuitization of wealth – They might accumulate even more due to fewer kids and for longer retirement. • If elder assets are land or other natural resources then their assets do not boost output. – In this case, standard support ratio story is correct. – Is this so in lower income countries with high reliance on asset income in old age? Indonesia, India, Philippines? R. Lee and A. Mason, Barcelona, June 3 23
Recommend
More recommend
