Reformulating the Support Ratio to Reflect Asset Income and Transfers - - PowerPoint PPT Presentation

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

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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

• n consumption.
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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!
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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.

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Here is the standard model Y= Labor x av product of labor Cons = (1‐s)Y Divide by N, effective consumers. Consump per effective consumer = Support ratio x proportion not saved x av product of labor

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( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

, 1 1 , 1 , 1 , Y LAf k hk C s Y C s LAf k hk C L s Af k hk N N L c s Af k hk N = = − = − = − = −

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?

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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.

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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)

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Illustration of accumulation of assets by elderly (age pattern is relevant; motive is not)

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200 400 600 800 1000 1200 0‐19 20‐34 35–44 45–54 55–64 65–74 75+ Net Worth ($000s) Age

Net Worth by Age of Household Head in US, 2007, from Survey

• f Consumer Finance

Source: Survey of Consumer Finance

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.

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Accounting

• Lifecycle deficit: Two methods of funding

– Public and private net transfers – Asset‐based reallocations

• Asset income (rA(x))
• Dissaving (‐S(x))

Lifecycle Deficit Net Transfers Asset-based Reallocations Age Reallocations

( ) ( ) ( ) ( ) ( ) ( )

l

C x Y x x x rA x S x τ τ

+ −

− = − + − 14 4 24 4 3 14 4 244 3 14243 1444442444443

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Funding the lifecycle deficit, US 2003

‐1 ‐0.5 0.5 1 1.5 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90

Units of Average Labor Income 30‐49 Age Public Transfers Asset‐based Reallocations Private Transfers

For US children, deficit funded almost entirely by transfers For US elderly, asset‐based reallocations more important than transfers.

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AT ES SE 1/3 1/3

2/3

2/3 Assets Public transfers Family transfers

TH JP

KR

TW PH

CL 1/3 2/3

MX US SI BR DE CR CN IN HU UY

Shares of net consumption of elderly funded by Family Transfers, Public Transfers and Asset income (part not saved)

Above line, elderly rely more than 50% on assets, less on transfers. Support ratio misleads. On this side of line, elderly rely almost entirely on public transfers. Support ratio is good.

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The Solution – take asset based reallocation into account

• Generalized support ratio

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

, , ,

l

N x t y x dx N x t rA x s x dx GSR t N x t c x dx

ω ω ω

+ − ⎡ ⎤ ⎣ ⎦ = ∫

∫ ∫

( , ): population age x in year t Base year profiles held constant ( ) : labor income profile ( ) ( ) : asset-based reallocation profile ( ) : consumption profile N x t yl x rA x s x c x −

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The Solution

• General Support Ratio

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

, , ,

l

N x t y x dx N x t rA x s x dx GSR t N x t c x dx

ω ω ω

+ − ⎡ ⎤ ⎣ ⎦ = ∫

∫ ∫

Standard support ratio: share of consumption funded through work.

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The Solution

• General Support Ratio
• 1‐GSR(t): Share of consumption funded by

relying on public and private transfers.

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

, , ,

l

N x t y x dx N x t rA x s x dx GSR t N x t c x dx

ω ω ω

+ − ⎡ ⎤ ⎣ ⎦ = ∫

∫ ∫

Share of consumption funded by relying on assets.

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Age profiles of consumption, labor income and asset‐based reallocations, US 2003

‐10 10 20 30 40 50 60 70 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90

Thousands of 2003 US Dollars Age Consumption (C) Asset‐based Reallocations (ABR) Labor Income (Y)

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Standard support ratio and general support ratio, US (2011=1.0)

0.6 0.8 1.0 1.2 1950 2000 2050 2100

Support ratio (2011=1) Year Y/C (Y+ABR)/C

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Standard support ratios (blue) and general support ratio (red)

0.7 0.8 0.9 1.0 1.1 1.2 1950 1975 2000 2025 2050 Support ratio (2011=1)

• a. United States

Y/C (Y+ABR)/C

0.7 0.8 0.9 1.0 1.1 1.2 1950 1975 2000 2025 2050

• b. Sweden

0.7 0.8 0.9 1.0 1.1 1.2 1950 1975 2000 2025 2050

• c. Finland

0.7 0.8 0.9 1.0 1.1 1.2 1950 1975 2000 2025 2050

• d. Austria

0.7 0.8 0.9 1.0 1.1 1.2 1950 1975 2000 2025 2050 Support ratio (2011=1)

• e. Japan

0.7 0.8 0.9 1.0 1.1 1.2 1950 1975 2000 2025 2050

• f. Germany

0.7 0.8 0.9 1.0 1.1 1.2 1950 1975 2000 2025 2050

• g. Slovenia

0.7 0.8 0.9 1.0 1.1 1.2 1950 1975 2000 2025 2050

• h. Mexico

0.7 0.8 0.9 1.0 1.1 1.2 1950 1975 2000 2025 2050 Support ratio (2011=1) Year

• i. Chile

0.7 0.8 0.9 1.0 1.1 1.2 1950 1975 2000 2025 2050 Year

• j. Costa Rica

0.7 0.8 0.9 1.0 1.1 1.2 1950 1975 2000 2025 2050 Year

• k. South Africa

0.7 0.8 0.9 1.0 1.1 1.2 1950 1975 2000 2025 2050 Year

• l. Philippines

Vertical lines at year 2011 represent first year of projection. All SR scaled to equal 1 in 2011.

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Change in support ratios from 2010 to 2050

‐30% ‐20% ‐10% 0% 10% 20% 30%

Percent Change in Ratio, 2010‐2050 Standard Support Ratio, YL/C General Support Ratio, (YL+ABR)/C

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Proportion of C financed by ABR vs. difference between the change in the two support ratios, 2010‐2050

US SE FI AT JP DE SI MX CL CR SA PH 0.2 0.4 0.6 0.8 1 1.2 ‐0.12 ‐0.1 ‐0.08 ‐0.06 ‐0.04 ‐0.02 0.02

Asset‐Based Reallocations/Consumption, Age 65+ Difference in Change in Support Ratios, 2010‐2050, (SR ‐ GSR)

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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?

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Conclusion for General Support Ratio

• Describes the economic dependency structure

better than the support ratio.

• Avoids unduly pessimistic view of population

aging by incorporating second dividend effects that arise from capital accumulation.

• Reflects cost of heavy reliance on transfers.
• Implications relative to traditional ratio

– Dividend period is extended – Effects of population aging are smaller.

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