aging and pension reform in a two-region world: the role...
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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
Edgar Vogel, Alexander Ludwig, Axel Borsch-Supan Pension Reform and Human Capital
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
Edgar Vogel, Alexander Ludwig, Axel Borsch-Supan Pension Reform and Human Capital
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
Edgar Vogel, Alexander Ludwig, Axel Borsch-Supan Pension Reform and Human Capital
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
Edgar Vogel, Alexander Ludwig, Axel Borsch-Supan Pension Reform and Human Capital
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
Edgar Vogel, Alexander Ludwig, Axel Borsch-Supan Pension Reform and Human Capital
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
Edgar Vogel, Alexander Ludwig, Axel Borsch-Supan Pension Reform and Human Capital
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
Constant Replacement Rate
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
Detrended GDP per Capita
Endogenous, BMExogenous, BM
Constant Contribution Rate
Open vs. Closed
Edgar Vogel, Alexander Ludwig, Axel Borsch-Supan Pension Reform and Human Capital
Pension Reform: Detrended GDP per Capita (1)
Figure: Detrended GDP per Capita
2010 2015 2020 2025 2030 2035 2040 2045 205095
100
105
110
115
Year
Det
ren
ded
GD
P p
er C
apit
a
Detrended GDP per Capita
Endogenous, BMEndogenous, PR
Constant Replacement Rate
2010 2015 2020 2025 2030 2035 2040 2045 205095
100
105
110
115
YearD
etre
nd
ed G
DP
per
Cap
ita
Detrended GDP per Capita
Endogenous, BMEndogenous, PR
Constant Contribution Rate
Rate of Return
Edgar Vogel, Alexander Ludwig, Axel Borsch-Supan Pension Reform and Human Capital
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
Edgar Vogel, Alexander Ludwig, Axel Borsch-Supan Pension Reform and Human Capital
Pension Reform: Detrended GDP per Capita (2)
Figure: Detrended GDP per Capita
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
Detrended GDP per Capita
Endogenous, BMExogenous, BMEndogenous, PRExogenous, PR
Constant Replacement Rate
2010 2015 2020 2025 2030 2035 2040 2045 205090
95
100
105
110
115
YearD
etre
nd
ed G
DP
per
Cap
ita
Detrended GDP per Capita
Endogenous, BMExogenous, BMEndogenous, PRExogenous, PR
Constant Contribution Rate
XXX
Edgar Vogel, Alexander Ludwig, Axel Borsch-Supan Pension Reform and Human Capital
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
Edgar Vogel, Alexander Ludwig, Axel Borsch-Supan Pension Reform and Human Capital
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
Endogenous, BMEndogenous, PR
Constant Replacement Rate
20 30 40 50 60 70 80 90−7
−6
−5
−4
−3
−2
−1
0
1
2
AgeC
EV
Consumption Equivalent Variation − Cohorts alive in 2010
Endogenous, BMEndogenous, PR
Constant Contribution Rate
Open vs. Closed
Edgar Vogel, Alexander Ludwig, Axel Borsch-Supan Pension Reform and Human Capital
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%
Edgar Vogel, Alexander Ludwig, Axel Borsch-Supan Pension Reform and Human Capital
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%
Edgar Vogel, Alexander Ludwig, Axel Borsch-Supan Pension Reform and Human Capital
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
Edgar Vogel, Alexander Ludwig, Axel Borsch-Supan Pension Reform and Human Capital
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
Edgar Vogel, Alexander Ludwig, Axel Borsch-Supan Pension Reform and Human Capital
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
Edgar Vogel, Alexander Ludwig, Axel Borsch-Supan Pension Reform and Human Capital
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
Edgar Vogel, Alexander Ludwig, Axel Borsch-Supan Pension Reform and Human Capital
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
Constant Replacement Rate
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
Constant Contribution Rate
Back
Edgar Vogel, Alexander Ludwig, Axel Borsch-Supan Pension Reform and Human Capital
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
Constant Replacement Rate
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
Constant Contribution Rate
Back
Edgar Vogel, Alexander Ludwig, Axel Borsch-Supan Pension Reform and Human Capital
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
Constant Replacement Rate
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
Constant Contribution Rate
Back
Edgar Vogel, Alexander Ludwig, Axel Borsch-Supan Pension Reform and Human Capital
(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
Edgar Vogel, Alexander Ludwig, Axel Borsch-Supan Pension Reform and Human Capital
Benchmark Retirement Age: Rate of Return
Figure: 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
Constant Replacement Rate
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
Endogenous, ClosedExogenous, ClosedEndogenous, OpenExogenous, Open
Constant Contribution Rate
Back
Net Foreign Assets
Edgar Vogel, Alexander Ludwig, Axel Borsch-Supan Pension Reform and Human Capital
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
Edgar Vogel, Alexander Ludwig, Axel Borsch-Supan Pension Reform and Human Capital
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, ClosedExogenous, ClosedEndogenous, OpenExogenous, Open
Constant Replacement Rate
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, ClosedExogenous, ClosedEndogenous, OpenExogenous, Open
Constant Contribution Rate
Net Foreign Assets
Comparison GDP/GNP
Back
Edgar Vogel, Alexander Ludwig, Axel Borsch-Supan Pension Reform and Human Capital
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
Consumption Equivalent Variation − Cohorts alive in 2010
Endogenous, ClosedExogenous, ClosedEndogenous, OpenExogenous, Open
Constant Replacement Rate
20 30 40 50 60 70 80 90−7
−6
−5
−4
−3
−2
−1
0
1
2
AgeC
EV
Consumption Equivalent Variation − Cohorts alive in 2010
Endogenous, ClosedExogenous, ClosedEndogenous, OpenExogenous, Open
Constant Contribution Rate
Back
Edgar Vogel, Alexander Ludwig, Axel Borsch-Supan Pension Reform and Human Capital
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
Edgar Vogel, Alexander Ludwig, Axel Borsch-Supan Pension Reform and Human Capital
Pension Reform: Rate of Return
Figure: 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
Endogenous, BMEndogenous, PR
Constant Replacement Rate
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
Endogenous, BMEndogenous, PR
Constant Contribution Rate
Back
Edgar Vogel, Alexander Ludwig, Axel Borsch-Supan Pension Reform and Human Capital
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
Edgar Vogel, Alexander Ludwig, Axel Borsch-Supan Pension Reform and Human Capital
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