aging and pension reform in a two-region world: the role...

Aging and Pension Reform in a Two-RegionWorld: The Role of Human Capital

Edgar Vogel, Alexander Ludwig, Axel Borsch-Supan

University of Mannheim, University of Cologne, Munich Center for the Economicsof Aging

13th Annual Joint Conference of the RRCWashington D.C., August 4 – 5, 2011

Edgar Vogel, Alexander Ludwig, Axel Borsch-Supan Pension Reform and Human Capital

Questions & General Setup

Effects of population aging on

Factor pricesWelfare

How do answers change

1. With endogenous human capital2. Under different social security regimes / pension reforms3. More interesting: interaction of 1.) and 2.)

Two-region open economy OLG model with endogenous

Consumption/saving decisionLabor supplyHuman capital accumulation


Household Setup

Agents start making decisions at age 16, retire at age 65(benchmark) and live at most until age 90

They choose each period

Consumption/savingLabor supplyTime investment into human capital

. . . and like consumption and leisure

Receive labor income or pensions

Linear contribution rate τ to social securityPensions are a fraction ρ of current net wages

Formal Representation


Macroeconomic Setup & Government

Aggregate production with physical capital and effective labor

Effective labor Lt =∑jr−1

j=0 `t,jNt,jht,j

Factors earn marginal products

Regional labor markets, international capital markets,exogenous technical progress

Balanced budget PAYGO social security with two scenarios

1. Benchmark Retirement: replacement rate ρ or contributionrate τ fixed

2. Pension Reform: increase retirement age given τ/ρ – regime


Pension Reform & Calibration

Increasing the Retirement Age

Simple rule: for additional 1.5 years of life expectancy at age65 retirement increases by one yearRetirement age of 71 years

U.S. Life Expectancy at Age 65

CalibrationDemographics: United Nations

“Old”: basically OECD“Young”: rest of the world

Targets: K/Y , avg. labor supply, I/Y , region-specific wageprofiles, and region-specific growth of GDP/Capita

Retirement Age & Wage Profiles

WAPR


Thought Experiment & Results

Thought experiment

Exogenous demographics induces economic transitionTwo human capital specifications

Exogenous human capitalEndogenous human capital

⇒ during calibration identical, then diverging

ResultsMacroeconomic variables

Rate of returnDetrended GDP per capita

Welfare of households alive in 2010Effects of pension reform

Focus on

Endogenous vs. exogenous human capitalResults for “old” countries, open economy


Benchmark Retirement Age: Rate of Return

Figure: Rate of Return

2010 2015 2020 2025 2030 2035 2040 2045 20506.5

7

7.5

8

Year

r in

%

Rate of Return

EndogenousExogenous

Constant Replacement Rate

2010 2015 2020 2025 2030 2035 2040 2045 20506.5

7

7.5

8

Yearr

in %

Rate of Return

EndogenousExogenous

Constant Contribution Rate

Open vs. Closed


Benchmark Retirement Age: Detrended GDP per Capita

Figure: Detrended GDP per Capita

2010 2015 2020 2025 2030 2035 2040 2045 205090

92

94

96

98

100

102

104

106

108

110

Year

Det

ren

ded

GD

P p

er C

apit

a

Detrended GDP per Capita

Endogenous, BMExogenous, BM


2010 2015 2020 2025 2030 2035 2040 2045 205090

92

94

96

98

100

102

104

106

108

110

YearD

etre

nd

ed G

DP

per

Cap

ita


Endogenous, BMExogenous, BM


Open vs. Closed


Pension Reform: Detrended GDP per Capita (1)


2010 2015 2020 2025 2030 2035 2040 2045 205095

100

105

110

115

Year

Det

ren

ded

GD

P p

er C

apit

a


Endogenous, BMEndogenous, PR


2010 2015 2020 2025 2030 2035 2040 2045 205095

100

105

110

115

YearD

etre

nd

ed G

DP

per

Cap

ita




Rate of Return


Pension Reform: Decomposition of Effects

Effects of increasing retirement age on GDP/Capita

Exogenous human capital

1. “Mechanical” effect ⇒ more working people2. Higher labor supply if τ ↓

Endogenous human capital

1. “Mechanical” effect ⇒ more working people2. Higher investment into human capital3. Higher labor supply (to make use of 2.)4. Higher labor supply and human capital if τ ↓⇒ effects are not additive


Pension Reform: Detrended GDP per Capita (2)


2010 2015 2020 2025 2030 2035 2040 2045 205090

95

100

105

110

115

Year

Det

ren

ded

GD

P p

er C

apit

a


Endogenous, BMExogenous, BMEndogenous, PRExogenous, PR


2010 2015 2020 2025 2030 2035 2040 2045 205090

95

100

105

110

115

YearD

etre

nd

ed G

DP

per

Cap

ita


Endogenous, BMExogenous, BMEndogenous, PRExogenous, PR


XXX


Welfare Evaluation – Concept

Define a base year (here 2010)

Compute (remaining) lifetime utility VGE given GE prices

“Freeze” prices/transfers from base year and recompute V2010

Welfare difference expressed as Consumption EquivalentVariation (CEV)

Positive numbers are welfare gains from GE effects

Welfare Evaluation - Graph


Welfare Effects of Reform: Agents alive in 2010

Figure: Welfare: Agents alive in 2010

20 30 40 50 60 70 80 90−4

−3.5

−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

1

Age

CE

V

Consumption Equivalent Variation − Cohorts alive in 2010



20 30 40 50 60 70 80 90−7

−6

−5

−4

−3

−2

−1

0

1

2

AgeC

EV




Open vs. Closed


Welfare Effects of Reform: Agents alive in 2010

Table: Maximum Welfare Losses - Agents alive 2010

Open Economy

Pension System Constant ρ Constant τEndog. Exog. Endog. Exog.

Benchmark -3.0% -3.6% -4.4% -6.5%Pension Reform -1.9% -3.0% -3.6% -6.0%

Difference 36.7% 16.7% 18.2% 7.7%


Conclusions & Policy Implications

Investment into human capital substantially dampens

effects of aging on factor priceswelfare losses

PI: Important to keep this adjustment channel flexible

A generous pension system is more redistributive but lowerswelfare of future generations

Higher retirement age can substantially increase welfare,especially when distortions are already high

PI: Small distortions are magnified: human capital is “multiplier”⇒ effects are not additive

PI: Inequality best decreased by increasing retirement age

Warning: we assumed a frictionless world ⇒ results are onlyupper/lower bounds of “true” effects


Model Parameters

Table: Model Parameters

“Young” “Old”Preferences σ Inverse of Inter-Temporal Elasticity of Subst. 2.00

β Pure Time Discount Factor 0.985φ Weight of Consumption 0.370

Human Capital ξ Scaling Factor 0.176 0.166ψ Curvature Parameter 0.576 0.586δh Depreciation Rate of Human Capital 1.4% 0.9%h0 Initial Human Capital Endowment 1.00 1.00

Production α Share of Physical Capital in Production 0.33δ Depreciation Rate of Physical Capital 3.5%

gA Exogenous Growth RateCalibration Period 1.5% 1.9%Final Steady State 1.9% 1.9%

Notes: “Young” and “Old” refer to the region. Only one value in acolumn indicates that the parameter is identical for both regions.

Back


U.S. Life Expectancy

Figure: U.S. Life Expectancy at Age 65

1950 1960 1970 1980 1990 2000 201014

15

16

17

18

19

20

Year

Rem

ain

ing

Lif

e E

xpec

tan

cy in

Yea

rs

Remaining Life Expectancy U.S.

Sources: Human Mortality Database (2011).

Back


Welfare Evaluation – Graph

Figure: Constant vs. Variable Prices

2010 2020 2030 2040 2050 2060 20703

3.5

4

4.5

5

5.5

6

6.5

7

Year

Rat

e o

f R

etu

rn in

\%

Rate of Return

General EquilibriumConstant Prices

Back


Benchmark Retirement Age: Net Foreign Assets

Figure: Net Foreign Assets

2010 2015 2020 2025 2030 2035 2040 2045 2050−100

−50

0

50

Year

Fo

reig

n A

sset

s / G

DP

Foreign Assets as Percentage of GDP

EndogenousExogenous


2010 2015 2020 2025 2030 2035 2040 2045 2050−60

−40

−20

0

20

40

60

YearF

ore

ign

Ass

ets

/ GD

P

Foreign Assets as Percentage of GDP

EndogenousExogenous


Back


Benchmark Retirement: Comparison GDP/GNP per Capita

Figure: Comparison GDP/GNP per Capita

2010 2015 2020 2025 2030 2035 2040 2045 205090

95

100

105

110

115

Year

GD

P/G

NP

per

Cap

ita

Detrended GDP/GNP per Capita

GDP, EndogenousGDP, ExogenousGNP, EndogenousGNP, Exogenous


2010 2015 2020 2025 2030 2035 2040 2045 205090

95

100

105

110

115

YearG

DP

/GN

P p

er C

apit

a

Detrended GDP/GNP per Capita

GDP, EndogenousGDP, ExogenousGNP, EndogenousGNP, Exogenous


Back


(Inter)National Capital Markets

Compute equilibrium transition path for closed economies

We then “surprise” agents by opening up the economy in 1975

Compute the transition to the open economy steady-state

Agents alive in 1975 re-optimize for their remaining lifetime,newborns use prices and transfers from open economy

Back


Benchmark Retirement Age: Rate of Return


2010 2015 2020 2025 2030 2035 2040 2045 20507

7.1

7.2

7.3

7.4

7.5

7.6

7.7

7.8

7.9

8

Year

r in

%

Rate of Return

Endogenous, ClosedExogenous, ClosedEndogenous, OpenExogenous, Open


2010 2015 2020 2025 2030 2035 2040 2045 20506.8

7

7.2

7.4

7.6

7.8

8

Year

r in

%

Rate of Return



Back

Net Foreign Assets


Household Setup – Formal Representation

Formally, agents maximize

maxJ∑

j=0

βjπj1

1− σ{cφj (1− `j − ej︸︷︷︸

leisure

)1−φ}1−σ

subject to

aj+1 =

{(aj + trt)(1 + rt) + wn

t,j − cj if j < jr

(aj + trt)(1 + rt) + pt − cj if j ≥ jr

wnt,j = `jhjwt(1− τt)

human capital formation using Ben-Porath (1967) technology

hj+1 = hj(1− δh) + ξ(hjej)ψ

Back


Benchmark Retirement Age: Detrended GDP per Capita


2010 2015 2020 2025 2030 2035 2040 2045 205090

92

94

96

98

100

102

104

106

108

110

Year

Det

ren

ded

GD

P p

er C

apit

a




2010 2015 2020 2025 2030 2035 2040 2045 205090

92

94

96

98

100

102

104

106

108

110

Year

Det

ren

ded

GD

P p

er C

apit

a




Net Foreign Assets

Comparison GDP/GNP

Back


Welfare Effects Benchm. Retirement: Agents alive in 2010

Figure: Welfare: Agents alive in 2010

20 30 40 50 60 70 80 90−4

−3.5

−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

1

Age

CE

V




20 30 40 50 60 70 80 90−7

−6

−5

−4

−3

−2

−1

0

1

2

AgeC

EV




Back


Retirement Age & Wage Profiles

1900 1950 2000 2050 2100 215063

64

65

66

67

68

69

70

71

72

73

Labor Market Cohort

Ret

irem

ent

Ag

e

Statutory Retirement Age

Benchmark (Constant Retirement)Pension Reform (Rising Retirment Age)

Retirement Age

20 25 30 35 40 45 50 55 601

1.1

1.2

1.3

1.4

1.5

1.6

1.7

Age

Pro

duct

ivity

Productivity Profiles

Old CountriesYoung CountriesObserved US−Profile

Life Cycle Productivity

Back


Pension Reform: Rate of Return


2010 2015 2020 2025 2030 2035 2040 2045 20507.4

7.5

7.6

7.7

7.8

7.9

8

8.1

Year

r in

%

Rate of Return



2010 2015 2020 2025 2030 2035 2040 2045 20507.4

7.5

7.6

7.7

7.8

7.9

8

8.1

Yearr

in %

Rate of Return



Back


Stylized Facts

Figure: Working Age Population Ratio

1950 2000 20500.65

0.7

0.75

0.8

0.85

0.9

0.95

1

Year

Wo

rkin

g A

ge

Po

pu

lati

on

Rat

io in

%

Working Age Population Ratio

Industrialized Countries (old)Transition Countries (young)

Sources: United Nations (2007) and own computations.“Old” includes USA, Canada, Japan, Australia, New Zealand, Switzerland, Norway and the EU15

“Young” all other countries

Back


aging and pension reform in a two-region world: the role...

Documents