Demographic Structure and Macroeconomic Trends
Yunus Aksoy (Birkbeck, London) Henrique S. Basso (Banco de España)
Tobias Grasl (Birkbeck, London) Ron Smith (Birkbeck, London)
6th Joint BoC/ECB Conference
8th June 2015
Motivation
Medium-run outlook?
I
Slow recovery after great recession and disappointedly low growth of
productivity in the last decade have fostered a debate on medium-run
prospects of develop economies.
I
Debate (Gordon (2012, 2014)) has centred around
I
Future impact of innovation
I
Structural characteristics - demographics, education, inequality and debt
overhang
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8th June 2015
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0.20
0.15
0.10
0.05
Proportion of Population in Age Group
Motivation
1970
1980
1990
2000
2010
0−9
10−19
20−29
30−39
40−49
50−59
60−69
70+
2020
2030
Year
Figure: Demographic Structure in (sample) OECD countries
Population aged 60+ 16% in 1970 to 29% in 2030.
Working age group (20 − 59) 50% in 1970, 56% in 2003, 48% in 2030
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Motivation
Demographics, Labour Supply and Population Growth
I
Normally demographics is generally linked to lower population growth and
lower labour supply.
I
A more general view: demographic structure, defined as the proportion of the
population in each age group, may have an impact on economic performance.
Different age groups
I
may have different savings behaviour, according to the life-cycle hypothesis;
I
may have different contributions to productivity gains, following the age profile
of wages;
I
may contribute differently to the innovation process, with young and middle
age workers contributing the most;
I
may generate different investment opportunities, as firms target their different
needs.
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Motivation
This paper
Propose a framework to formally assess the impact of demographics in develop
economies both empirically and theoretically
I
Empirically: Assess the effect of changes in the demographic structure on
medium term macroeconomic dynamics.
Question 1 - Does demographic structure affect the trend of growth,
investment, saving, real rates? How about innovation (R&D)?
I
Theoretically: Build a model that incorporates both demographic
heterogeneity and endogenous productivity to account for the empirical facts
and analyse the channels through which demographics affect the
macroeconomy.
Question 2 - What does the theory has to say about the links between
demographic structure and macroeconomic trends? Can a model account for
the observed empirical patterns?
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Empirical Analysis
Methodology - Estimation
I
Estimate a Panel VAR with intercept heterogeneity but slope homogeneity
given by (we additionally control for population growth and oil prices (2 lags)
which as demographics are assumed exogenous)
Yit = ai + A1 Yi,t−1 + A2 Yi,t−2 + DWit + controls + uit ,
Wit denote the matrix with the shares of the 7 first age group minus the last
j = 1, ..8 (0 − 9, 10 − 19, . . . , 70+) in total population. Adjustment is done
to avoid collinearity thus we restrict the coefficients of age groups to sum to
0.
D is the 6 × 7 matrix of coefficients of the demographic variables.
Endogenous variables - Yit = (git , Iit , Sit , Hit , rrit , πit )0
I
Dataset covers the period 1970-2007. The twenty countries covered by the
data are: Australia, Austria, Belgium, Canada, Denmark, Finland, France,
Greece, Iceland, Ireland, Italy, Japan, Netherlands, New Zealand, Norway,
Portugal, Spain, Sweden, Switzerland, United Kingdom, United States.
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Empirical Analysis
Methodology - Impact of Demographic Structure on
Macroeconomy
I
Demographic Structure is a slow moving variable. We are looking for not
only its direct impact on each variable but the overall impact of
demographics on the system after the feedback effects are accounted for,
exploring the dynamic properties of the macroeconomic variables (system).
We thus concentrate on the long-run contribution of demographics by
looking at the demographic attractor
YitD = (I − A1 − A2 )
I
−1
DWit .
(1)
Important to distinguish between steady state effect and long-run effect.
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8th June 2015
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Empirical Analysis
Estimation - Results
Yit = ai + A1 Yi,t−1 + A2 Yi,t−2 + DWit + uit
gt−1
It−1
St−1
Ht−1
rrt−1
πt−1
δ1
-0.14
-0.58
-0.16
-1.86
-0.43
0.96
δ2
0.16
0.13
0.53
-0.13
-0.30
0.65
δ3
0.11
0.41
-0.26
0.66
0.35
-0.28
δ4
0.10
0.36
0.36
2.44
0.39
-1.01
δ5
0.11
0.06
0.39
0.47
0.17
-0.59
δ6
-0.04
0.07
0.72
0.59
0.44
-0.26
δ7
-0.32
0.26
-0.05
-1.11
0.28
0.22
δ8
0.01
-0.70
-1.53
-1.05
-0.91
0.32
Table: Long-Run Demographic Impact - Matrix - (I − A1 − A2 )−1 D
See D, A1 and A2
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Empirical Analysis
Estimation - Results
Matrix - (I − A1 − A2 )
gt−1
It−1
St−1
Ht−1
rrt−1
πt−1
δ1
-0.14
-0.58
-0.16
-1.86
-0.43
0.96
−1
D
δ2
0.16
0.13
0.53
-0.13
-0.30
0.65
δ3
0.11
0.41
-0.26
0.66
0.35
-0.28
δ4
0.10
0.36
0.36
2.44
0.39
-1.01
δ5
0.11
0.06
0.39
0.47
0.17
-0.59
δ6
-0.04
0.07
0.72
0.59
0.44
-0.26
δ7
-0.32
0.26
-0.05
-1.11
0.28
0.22
δ8
0.01
-0.70
-1.53
-1.05
-0.91
0.32
Table: Long-Run Demographic Impact
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Empirical Analysis
Estimation - Results
Matrix - (I − A1 − A2 )
gt−1
It−1
St−1
Ht−1
rrt−1
πt−1
δ1
-0.14
-0.58
-0.16
-1.86
-0.43
0.96
−1
D
δ2
0.16
0.13
0.53
-0.13
-0.30
0.65
δ3
0.11
0.41
-0.26
0.66
0.35
-0.28
δ4
0.10
0.36
0.36
2.44
0.39
-1.01
δ5
0.11
0.06
0.39
0.47
0.17
-0.59
δ6
-0.04
0.07
0.72
0.59
0.44
-0.26
δ7
-0.32
0.26
-0.05
-1.11
0.28
0.22
δ8
0.01
-0.70
-1.53
-1.05
-0.91
0.32
Table: Long-Run Demographic Impact
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Empirical Analysis
Estimation - Results
Matrix - (I − A1 − A2 )
gt−1
It−1
St−1
Ht−1
rrt−1
πt−1
δ1
-0.14
-0.58
-0.16
-1.86
-0.43
0.96
−1
D
δ2
0.16
0.13
0.53
-0.13
-0.30
0.65
δ3
0.11
0.41
-0.26
0.66
0.35
-0.28
δ4
0.10
0.36
0.36
2.44
0.39
-1.01
δ5
0.11
0.06
0.39
0.47
0.17
-0.59
δ6
-0.04
0.07
0.72
0.59
0.44
-0.26
δ7
-0.32
0.26
-0.05
-1.11
0.28
0.22
δ8
0.01
-0.70
-1.53
-1.05
-0.91
0.32
Table: Long-Run Demographic Impact
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Empirical Analysis
Estimation - Results
Matrix - (I − A1 − A2 )
gt−1
It−1
St−1
Ht−1
rrt−1
πt−1
δ1
-0.14
-0.58
-0.16
-1.86
-0.43
0.96
−1
D
δ2
0.16
0.13
0.53
-0.13
-0.30
0.65
δ3
0.11
0.41
-0.26
0.66
0.35
-0.28
δ4
0.10
0.36
0.36
2.44
0.39
-1.01
δ5
0.11
0.06
0.39
0.47
0.17
-0.59
δ6
-0.04
0.07
0.72
0.59
0.44
-0.26
δ7
-0.32
0.26
-0.05
-1.11
0.28
0.22
δ8
0.01
-0.70
-1.53
-1.05
-0.91
0.32
Table: Long-Run Demographic Impact
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Empirical Analysis
Estimation - Results
Matrix - (I − A1 − A2 )
gt−1
It−1
St−1
Ht−1
rrt−1
πt−1
δ1
-0.14
-0.58
-0.16
-1.86
-0.43
0.96
−1
D
δ2
0.16
0.13
0.53
-0.13
-0.30
0.65
δ3
0.11
0.41
-0.26
0.66
0.35
-0.28
δ4
0.10
0.36
0.36
2.44
0.39
-1.01
δ5
0.11
0.06
0.39
0.47
0.17
-0.59
δ6
-0.04
0.07
0.72
0.59
0.44
-0.26
δ7
-0.32
0.26
-0.05
-1.11
0.28
0.22
δ8
0.01
-0.70
-1.53
-1.05
-0.91
0.32
Table: Long-Run Demographic Impact
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8th June 2015
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Empirical Analysis
Estimation - 3 Generations Case
gt−1
It−1
St−1
Ht−1
rrt−1
πt−1
β1
0.02
0.03
0.28
-0.64
-0.11
0.68
β2
0.12
0.17
0.31
1.53
0.32
-0.85
β3
-0.14
-0.20
-0.59
-0.89
-0.20
0.17
Table: Long-Run Demographic Impact
Robustness
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2020
2025
2020
2025
2030
2000
2020
2025
(d) US Real Rates
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2030
2020
2025
2030
2025
2030
0.03
0.02
D Impact:Core Europe Real R
0.02
2015
Year
−0.08 −0.06 −0.04 −0.02 0.00
D Impact: Japan Real R
2010
2015
(c) Core Europe GDP
0.04
0.03
0.02
0.01
0.00
−0.01
2005
2010
Year
(b) Japan GDP
−0.02
2000
2005
Year
(a) US GDP
D Impact: United States Real R
2015
0.005
0.010
2010
0.000
D Impact: Core Europe GDP
2005
−0.010 −0.005
0.002
2000
2030
2000
2005
2010
2015
2020
Year
(e) Japan Real Rates
2025
2030
0.01
2015
Year
−0.03 −0.02 −0.01 0.00
2010
0.004
0.006
2005
0.000
D Impact: Japan GDP
2000
−0.006 −0.004 −0.002
0.020
0.015
0.010
0.005
D Impact: United States GDP
0.025
Empirical Analysis
2000
2005
2010
2015
2020
Year
(f) Core Europe Real Rates
8th June 2015
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2005
2010
2020
2025
2020
2025
2030
0.020
2025
ABGS (6th Joint BoC/ECB Conference)
2010
2015
0.010
2030
2000
2005
2010
2020
Year
(f) Japan Real Rates
2025
2030
2015
2020
2025
2030
2020
2025
2030
Year
0.04
(d) Spain GDP
0.01
(e) US Real Rates
2005
0.005
D Impact: Spain GDP
−0.005
2020
0.03
D Impact: Spain Real R
0.00
−0.04
2000
Year
0.000
0.010
0.008
2015
0.00
D Impact: Sweden Real R
0.00
0.02
2015
2010
(c) Sweden GDP
−0.08 −0.06 −0.04 −0.02
D Impact: Japan Real R
2010
2005
Year
0.04
0.03
0.02
0.01
0.00
−0.01
2005
2000
2030
(b) Japan GDP
−0.02
D Impact: United States Real R
2015
Year
(a) US GDP
2000
0.015
0.012
2000
2030
0.02
2025
0.01
2020
−0.01
2015
Year
−0.02
2010
−0.03
2005
0.006
D Impact: Sweden GDP
0.002
−0.006
2000
0.004
0.006
0.004
0.002
0.000
D Impact: Japan GDP
−0.004
−0.002
0.020
0.015
0.010
0.005
D Impact: United States GDP
0.025
Empirical Analysis
2000
2005
2010
2015
2020
Year
(g) Sweden Real Rates
2025
2030
2000
2005
2010
2015
Year
(h) Spain Real Rates
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2005
2010
2015
2020
2025
2030
2015
2020
2025
2030
D Impact: Italy GDP
2020
2025
2030
ABGS (6th Joint BoC/ECB Conference)
2010
2015
2005
2010
2020
Year
(f) France Real Rates
2025
2030
2015
2020
2025
2030
2020
2025
2030
(d) Italy GDP
0.03
0.04
0.02
D Impact: Italy Real R
D Impact: Greece Real R
(e) Canada Real Rates
2005
2000
Year
−0.01
2000
Year
−0.005
−0.010
2015
0.03
0.01
−0.01
−0.02
D Impact: France Real R
−0.03
−0.04
2010
2010
(c) Greece GDP
0.00
0.04
0.03
0.02
0.01
−0.02 −0.01 0.00
2005
2005
Year
(b) France GDP
0.05
(a) Canada GDP
2000
2000
Year
2000
2005
2010
2015
2020
Year
(g) Greece Real Rates
2025
2030
0.01
2000
2030
0.00
2025
−0.03 −0.02 −0.01
2020
0.000
0.005
0.010
0.015
0.010
0.005
D Impact: Greece GDP
−0.005
2015
Year
0.02
2010
0.01
2005
0.00
2000
D Impact: Canada Real R
0.000
0.010
D Impact: France GDP
0.005
0.015
0.010
0.005
0.000
D Impact: Canada GDP
0.020
0.015
0.025
Empirical Analysis
2000
2005
2010
2015
Year
(h) Italy Real Rates
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Empirical Analysis
Link between demographics and innovation - Great
Inventions
F
1.—A D
G
I
nnovators in the
IEW OF ECONOMICS AND STATISTICS
ISTRIBUTION OF
REAT
NNOVATION
.01
Frequency
.02
.03
.04
.05
GE
0
ons and locates
I find substanny demographic
upward trend in
ve careers. The
at minds of the
active at age 23
at age 31 at the
while, there has
ty of innovators
IGURE
o further under20
30
40
50
60
70
80
show that PhD
Age
h century. I next
Nobel Prize Winners
Great Inventors
riments, testing
Note: Data are pooled across time.
innovation and
be “made up”
Age Distribution of Great Inventions - Source Jones (2010)
eld, cross-timeFigure:
this is simply the year in which the achievement is listed.
D ageABGStypically
(6th Joint BoC/ECB
ForConference)
the Nobel Prize, the year of achievement was deter- 8th June 2015
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Empirical Analysis
90
AGE STRUCTURE
AND
PRODUCTIVITY
Link between demographics and innovation - Patents
FIGURE 4 Distribution by single years of age of US inventors granted
patents, 1975–95
1975
1980
.04
1985
.04
.04
.03
.03
.03
.02
.02
.02
.01
.01
.01
0
0
0
20
40
Age
60
0
0
80
1990
20
40
Age
60
80
20
40
Age
60
80
0
20
40
Age
60
80
1995
.04
.04
.03
.03
.02
.02
.01
.01
0
0
0
20
40
Age
60
80
0
SOURCE: Jones (2005).
Figure: Distribution by single years of age of US inventors granted patents, 1975-95 Idea adoption
Source Jones (2005)
ABGS
While creative output is one potential channel through which age may affect
productivity, it may not be the most relevant for cross-country comparisons.
For most of the countries in the world, idea creation matters less than idea
(6th Joint BoC/ECB Conference)
adoption. Organizations (or countries) that increase productivity by produc-8th June 2015
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Empirical Analysis
Estimation - Including Patent Applications
y
I
S
H
rr
PA
π
δ1
-0.13
-0.59
-0.24
-1.60
-0.38
0.50
0.87
δ2
0.15
0.09
0.58
-0.20
-0.57
-0.56
0.80
δ3
0.08
0.40
-0.22
0.43
0.54
0.02
-0.35
Benchmark
δ4
δ5
0.12
0.08
0.42
0.03
0.36
0.42
2.43
0.63
0.34
0.20
0.05
0.70
-0.95
-0.66
δ6
-0.06
0.03
0.78
0.48
0.52
-1.32
-0.27
δ7
-0.30
0.34
-0.11
-0.88
0.41
0.17
0.11
δ8
0.06
-0.72
-1.57
-1.29
-1.05
0.44
0.45
Three Generations
β1
β2
β3
0.02
0.11
-0.13
0.01
0.17
-0.18
0.27
0.34
-0.61
-0.58
1.55
-0.97
-0.16
0.34
-0.19
-0.16
0.22
-0.06
0.68
-0.87
0.20
Table: Long-Run Demographic Impact
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Empirical Analysis
Summary - Empirical Results
I
Demographic Structure, after controlling for population growth, has
significant effects on macroeconomic variables
I
Savings, investment, hours worked, interest rate and output are negatively
impacted when dependent group shares (young and old) increase and are
positively affected when middle aged shares increase.
I
When a measure of innovation is included, we confirm the asymmetry
between young/mature workers and workers close to retirement, and that
economies with higher share of workers innovate more.
I
Using population predictions for the next 20 years we show that demographic
changes are a strong force in reducing trend growth and real rates in most
OECD economies. Particularly problematic for Southern European countries.
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Theoretical Model
Overview
Two key features:
I
demographic heterogeneity - closest framework is Gertler (1999) who
develops a model a la Blanchard (1985) and Yaari (1965). We modify it to
include young dependents and introduce human capital accumulation.
I
endogenous productivity - closest framework is Comin and Gertler (2006)
who develops a real business cycle model adding invention of new varieties a
la Romer (1990). We simplify the framework to consider only a one sector
economy.
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Theoretical Model
Economic Environment
I
The economy consists of three sectors: a production sector, an innovation
sector and households.
I
The production sector comprises a final good producer and input producers.
I
Innovation sector consists of two joint processes. Product creation
(prototypes) or R&D and product adoption, in which prototypes are made
ready to be used in the production process.
I
Individuals, who supply labour, accumulate assets and consume, exhibit
life-cycle behaviour, albeit of a simple form. Individuals face three stages of
life: young/dependant, worker and retiree.
I
A financial intermediary is used to aggregate assets (capital and lending) of
households to simplify exposition.
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Theoretical Model
Economic Environment
Educaon (ξ)
Young
Workers
Retirees
Assets
Households
Consumpon
F. Intermediary
Γ yw
Final Good
Production
Funding
Innovators
K
Prototypes (Z)
ξL
Inputs
Adopters
Innovation Sector
Variees (A)
Input
Production
Production Sector
Demographic Flows
Γ yw = Share of Workers contribung to Innovaon
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Theoretical Model
Model - Key Features
Model Detail
I
Ztp be the stock of invented goods (prototypes) and Γyw
t = share of workers
that contribute to innovation. Thus,
p
ρyw
Zt+1
= ϕt Stp + φZtp = (Γyw
χ[(Ψ̃t )ρ (St )1−ρ ]−1 Zt Stp + φZtp
t )
I
Value of an Adopted Product (Vt ) is given by
Vt = Πm,t + (Rt+1 )−1 φEt Vt+1
I
Aggregate consumption functions are:
w
w
w
Ctw = ςt [Rt FAw
t + Ht + D t − Tt ]
Ctr = εt ςt [Rt FArt + Dtr ]
I
I
Population (Nt ) grows at rate nt
Young (Nty ) becomes worker with probability 1 − ωy
Workers (Ntw ) retire with probability 1 − ωr
Once retired (Ntr ) individual survives with probability γ
Share of Retirees over Workers, ζtr = Ntr /Ntw , and Share of young dependants
over workers, ζty = Nty /Ntw .
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Theoretical Model
Equilibrium
The symmetric equilibrium is a sequence of allocations and prices obtained such
that:
a. Workers and retirees, maximize utility subject to their budget
constraint and investment in education is such that society’s
marginal cost and benefit is equated;
b. Input and final firms maximize profits, and firm entry occurs until
profits are equal to operating costs;
c. Innovators and adopters maximise their gains;
d. The financial intermediary selects assets to maximize profits, and
their profits are shared amongst retirees and workers according to
their share of assets;
e. Consumption goods, capital, labour and asset markets clear;
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Theoretical Model
Simulation
Use the parameters of Gertler (1999) (for households and population dynamics)
and Comin and Gertler (2006) (firms and innovation) Parameters . Show results for
different ρyw (importance of workers for innovation) and λy (persistency of stock
of workers/age for innovation).
Perform three simulation exercises (perfect foresight)
I
titled baby-boomers analyses the effect of increasing fertility holding longevity
constant.
I
titled aging looks at the effects of increasing longevity by increasing γ
permanently.
I
titled prediction, attempt to match the change in the demographic structure
predicted for a selected number of countries in our sample during the next
two decades and measure their impact on growth and real interest rates.
ABGS (6th Joint BoC/ECB Conference)
8th June 2015
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Theoretical Model
y
n
−3
ζ
g
x 10
3.5
2
0.02
1.5
1
3
2.5
−1
2
−1.5
1.5
−2
1
−2.5
0.5
0.01
0.5
0
10
20
30
40
50
60
0
70
A
−3
0
10
20
−3
g
x 10
30
40
50
60
70
−3
10
20
30
40
50
60
70
0
ξ
−3
g
x 10
0
10
20
8
0
6
−0.2
4
−0.4
6
2
−0.6
4
0
−0.8
30
40
50
60
70
40
50
60
70
40
50
60
70
R
x 10
8
12
10
8
6
4
2
2
0
0
10
20
30
40
50
60
70
−2
0
10
20
−3
investment
5
0.01
4
30
40
50
60
70
−1
0
0
10
20
MPC workers
x 10
0.015
30
c
40
50
60
70
30
40
50
60
70
−1
r
c
−1
0
−2
−3
0
20
30
0
−0.005
10
20
1
1
0
10
x 10
0.01
2
−0.005
0
−3
3
0
−2
w
0.005
0.005
−0.01
0
−3
g
x 10
10
−2
yw
Γ
−3
x 10
0
−0.5
0.03
2.5
0
r
ζ
−3
x 10
0.04
3
0
10
20
30
40
50
60
70
−0.01
0
10
20
30
40
50
60
70
−4
0
10
20
30
Figure: Simulation: baby-boomers
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8th June 2015
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Theoretical Model
gA
−3
x 10
−3
x 10
8
0
8
6
−0.2
4
−0.4
2
−0.6
6
gξ
−3
g
x 10
10
4
2
0
0
−2
0
20
−3
40
60
80
−2
−0.8
0
20
R
x 10
40
60
80
10
5
0.01
4
8
0.005
4
0
20
40
60
80
60
80
MPC workers
x 10
0.015
6
0
−3
investment
12
3
2
1
2
−0.005
0
−2
−1
0
20
40
60
80
−0.01
w
0
0
20
c
60
40
60
80
−1
0
20
40
r
−3
c
x 10
0.01
40
1
0
0.005
−1
0
−2
−0.005
−0.01
−3
0
20
40
60
80
−4
0
20
Baby boomers − Benchamrk
80
Baby boomers − ρyw=0.5
Figure: Simulation: benchmark Baby-boomers versus ρyw = 0.5
ABGS (6th Joint BoC/ECB Conference)
8th June 2015
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Theoretical Model
ζy
n
−3
g
x 10
ζr
2.5
0
2
1.5
−0.01
1
Γyw
−3
x 10
0.1
0
0.08
−1
0.06
−2
0.04
−3
−0.02
0.5
0
0.02
0
20
40
60
80
100
−0.03
0
gA
−3
x 10
20
−3
0
60
80
100
0
−4
0
20
40
60
80
100
−5
gξ
−4
g
x 10
5
40
x 10
20
−3
8
2
6
0
4
−5
2
−10
0
0
40
60
80
100
60
80
100
60
80
100
R
x 10
4
5
−2
−5
−4
0
−6
−10
0
20
40
60
80
100
−8
0
20
investment
40
60
80
100
−2
−15
0
20
MPC workers
0.01
−0.004
0.005
−0.006
0
−0.008
−0.005
−0.01
40
c
60
80
100
−20
w
0
20
40
cr
−3
x 10
0
15
10
−0.01
−0.012
−0.015
−0.014
−0.02
−0.016
−0.005
5
−0.01
0
0
20
40
60
80
100
0
20
40
60
80
100
−0.015
Aging holding population growth constant
0
20
40
60
80
100
−5
0
20
40
Aging holding fertility constant
Figure: Simulation: aging
ABGS (6th Joint BoC/ECB Conference)
8th June 2015
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Theoretical Model
gA
−3
x 10
−3
0
gξ
−4
g
x 10
5
x 10
4
8
2
6
0
4
−2
−5
2
−4
0
−6
−10
0
50
−3
100
−8
150
0
50
R
x 10
100
150
−2
0.01
−0.004
0
0.005
−0.006
0
−0.008
−5
−0.005
−0.01
−0.01
−0.012
−10
−15
−0.015
0
50
100
150
−0.02
cw
100
150
−0.014
0
50
100
150
100
150
−0.016
0
50
100
150
cr
−3
x 10
0
50
MPC workers
5
−20
0
investment
15
10
−0.005
5
−0.01
0
−0.015
0
50
100
150
Aging holding population growth constant ρyw=0.9
−5
0
50
Aging holding population growth constant ρyw=0
Aging holding population growth constant ρyw=0.5
Figure: Simulation: benchmark aging versus different ρyw
ABGS (6th Joint BoC/ECB Conference)
8th June 2015
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Theoretical Model
gA
−3
x 10
−3
gξ
−4
g
x 10
5
x 10
4
8
2
6
0
0
−2
−5
4
−4
2
−6
−10
0
50
100
150
−8
0
50
R
100
150
0
0
investment
0
50
100
150
MPC workers
0.01
−0.004
0.005
−0.006
0
−0.008
−0.005
−0.01
−0.005
−0.01
−0.01
−0.012
−0.015
−0.015
−0.02
0
50
100
150
−0.02
cw
−0.014
0
50
150
−0.016
0
50
100
150
cr
−3
x 10
0
100
15
10
−0.005
5
−0.01
0
−0.015
0
50
100
150
−5
0
50
Aging holding population growth constant λy = 1/3
100
150
Aging holding population growth constant λy=1/10
Figure: Simulation: benchmark aging versus different λy = 1/10
ABGS (6th Joint BoC/ECB Conference)
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Theoretical Model
A
−3
−3
g
x 10
gξ
−4
g
x 10
5
x 10
4
8
2
6
0
0
−2
−5
4
−4
2
−6
−10
0
50
−3
100
150
−8
0
50
R
x 10
100
150
0
0.01
−0.004
0
0.005
−0.006
0
−0.008
−5
−10
−15
−0.005
−0.01
−0.01
−0.012
−0.015
0
50
100
150
−0.02
cw
15
10
−0.01
5
−0.015
0
−0.02
−5
0
50
50
100
150
150
0
100
150
100
150
−0.016
0
50
100
150
cr
x 10
0
100
−0.014
0
−3
−0.005
50
MPC workers
5
−20
0
investment
50
Aging holding population growth constant − Benchamrk
Aging holding population growth constant − Mature Inventors
Figure: Simulation: benchmark aging versus Delayed flow of inventors
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Theoretical Model
Simulation - Prediction
Period
2000-2005
2005-2011
2011-2016
2016-2021
2021-2026
2026-2031
∆sw
0.5%
-1.3%
-1.4%
-2.1%
-1.3%
-0.3%
∆sr
0.5%
2.0%
1.9%
2.2%
1.7%
0.8%
gn
1.053
1.056
1.043
1.040
1.037
1.033
Table: Prediction Data Input: United States
I
I
We match three measures {g n , ∆sw , ∆sr }, namely, population growth, the
share of workers and the share of retirees.
Recall the share of workers in the population is given by 1+ζ1y +ζr and the
share of retirees is given by 1+ζζyr+ζr , thus by setting those shares we are
essentially selecting ζy and ζr , the young and retirees dependency ratios.
I
By implicitly select three structural parameters, the fertility rate ñ, the
longevity parameter γ and the probability a dependent become a worker ωy .
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Theoretical Model
US
Japan
0.05
Sweden
Spain
0.01
0.02
0.07
0
0.015
0.06
−0.01
0.01
0.05
−0.02
0.005
0.04
−0.03
0
0.03
0.02
0.01
0
−0.04
−0.05
Output Growth
Output Growth
Output Growth
0.03
Output Growth
0.04
−0.005
−0.01
0.02
0.01
−0.06
−0.015
0
−0.07
−0.02
−0.01
−0.01
−0.08
−0.02
2000
2005
2010
2015
2020
2025
−0.09
2000
2030
0.03
−0.025
2005
2010
2015
2020
2025
−0.03
2000
2030
0.04
2010
2015
2020
2025
−0.03
2000
2030
0.01
0.02
0.02
−0.02
2005
2005
2010
2015
2020
2025
2030
2005
2010
2015
Years
2020
2025
2030
0.1
0
0.08
0
0.01
−0.01
0.06
−0.02
−0.04
−0.06
−0.08
−0.02
Real Interest Rate
−0.01
Real Interest Rate
Real Interest Rate
Real Interest Rate
−0.02
0
−0.03
−0.04
−0.1
0.04
0.02
0
−0.03
−0.05
−0.12
−0.04
−0.05
2000
−0.14
2005
2010
2015
Years
2020
2025
2030
−0.16
2000
−0.02
−0.06
2005
2010
2015
Years
2020
2025
2030
−0.07
2000
2005
2010
2015
Years
2020
2025
2030
−0.04
2000
Figure: Simulation: prediction
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2005
2010
2020
2025
2020
2025
2030
0.020
2025
ABGS (6th Joint BoC/ECB Conference)
2010
2015
0.010
2030
2000
2005
2010
2020
Year
(f) Japan Real Rates
2025
2030
2015
2020
2025
2030
2020
2025
2030
Year
0.04
(d) Spain GDP
0.01
(e) US Real Rates
2005
0.005
D Impact: Spain GDP
−0.005
2020
0.03
D Impact: Spain Real R
0.00
−0.04
2000
Year
0.000
0.010
0.008
2015
0.00
D Impact: Sweden Real R
0.00
0.02
2015
2010
(c) Sweden GDP
−0.08 −0.06 −0.04 −0.02
D Impact: Japan Real R
2010
2005
Year
0.04
0.03
0.02
0.01
0.00
−0.01
2005
2000
2030
(b) Japan GDP
−0.02
D Impact: United States Real R
2015
Year
(a) US GDP
2000
0.015
0.012
2000
2030
0.02
2025
0.01
2020
−0.01
2015
Year
−0.02
2010
−0.03
2005
0.006
D Impact: Sweden GDP
0.002
−0.006
2000
0.004
0.006
0.004
0.002
0.000
D Impact: Japan GDP
−0.004
−0.002
0.020
0.015
0.010
0.005
D Impact: United States GDP
0.025
Theoretical Model
2000
2005
2010
2015
2020
Year
(g) Sweden Real Rates
2025
2030
2000
2005
2010
2015
Year
(h) Spain Real Rates
8th June 2015
24 / 40
Theoretical Model
Canada
France
0.07
Greece
0.03
0.06
0.02
Italy
0.03
0.02
0.02
0.01
0.05
0
0
−0.01
0.01
0
0
−0.01
Output Growth
0.02
Output Growth
0.03
Output Growth
Output Growth
0.01
0.01
0.04
−0.01
−0.02
−0.02
−0.03
−0.03
−0.04
−0.02
−0.01
−0.03
−0.04
−0.02
−0.03
2000
2005
2010
2015
2020
2025
−0.04
2000
2030
0.07
2005
2010
2015
2020
2025
−0.05
2000
2030
0.01
0.06
0
0.05
−0.01
0.04
−0.02
−0.05
2005
2010
2015
2020
2025
−0.06
2000
2030
0.04
2005
2010
2015
2020
2025
2030
2005
2010
2015
Years
2020
2025
2030
0.04
0.02
0.02
0
0.02
0.01
−0.03
−0.04
−0.05
Real Interest Rate
0.03
Real Interest Rate
Real Interest Rate
Real Interest Rate
0
−0.02
−0.02
−0.04
−0.04
0
−0.06
−0.01
−0.07
−0.06
−0.06
−0.02
−0.03
2000
−0.08
−0.08
2005
2010
2015
Years
2020
2025
2030
−0.09
2000
2005
2010
2015
Years
2020
2025
2030
−0.08
2000
2005
2010
2015
Years
2020
2025
2030
−0.1
2000
Figure: Simulation: prediction - Additional Countries
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2005
2010
2015
2020
2025
2030
2015
2020
2025
2030
D Impact: Italy GDP
2020
2025
2030
ABGS (6th Joint BoC/ECB Conference)
2010
2015
2005
2010
2020
Year
(f) France Real Rates
2025
2030
2015
2020
2025
2030
2020
2025
2030
(d) Italy GDP
0.03
0.04
0.02
D Impact: Italy Real R
D Impact: Greece Real R
(e) Canada Real Rates
2005
2000
Year
−0.01
2000
Year
−0.005
−0.010
2015
0.03
0.01
−0.01
−0.02
D Impact: France Real R
−0.03
−0.04
2010
2010
(c) Greece GDP
0.00
0.04
0.03
0.02
0.01
−0.02 −0.01 0.00
2005
2005
Year
(b) France GDP
0.05
(a) Canada GDP
2000
2000
Year
2000
2005
2010
2015
2020
Year
(g) Greece Real Rates
2025
2030
0.01
2000
2030
0.00
2025
−0.03 −0.02 −0.01
2020
0.000
0.005
0.010
0.015
0.010
0.005
D Impact: Greece GDP
−0.005
2015
Year
0.02
2010
0.01
2005
0.00
2000
D Impact: Canada Real R
0.000
0.010
D Impact: France GDP
0.005
0.015
0.010
0.005
0.000
D Impact: Canada GDP
0.020
0.015
0.025
Conclusions
2000
2005
2010
2015
Year
(h) Italy Real Rates
8th June 2015
25 / 40
Conclusions
Conclusions
I
Utilize a new empirical methodology to measure the effect of demographic
structure on macroeconomic trends. Short-term impact on macro variables so
demographic variables can be considered exogenous. Use properties of the
dynamic system to obtain long-run impact and show age profile impacts
macroeconomic trends.
I
Build a model with demographic heterogeneity and endogenous productivity
that matches well the empirical findings. Key channel is the link between
innovation and demographics, which is supported by our evidence and
evidence in Jones (2005).
I
Population aging and reduced fertility expected in the next decades imply
strong reduction on the trend of growth and real rates across most OECD
economies, but particularly in Europe.
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8th June 2015
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Conclusions
References I
Blanchard, O. J. (1985): “Debt, Deficits, and Finite Horizons,” Journal of
Political Economy, 93(2), 223–47.
Comin, D., and M. Gertler (2006): “Medium-Term Business Cycles,”
American Economic Review, 96(3), 523–551.
Gertler, M. (1999): “Government debt and social security in a life-cycle
economy,” Carnegie-Rochester Conference Series on Public Policy, 50(1),
61–110.
Gordon, R. J. (2012): “Is U.S. Economic Growth Over? Faltering Innovation
Confronts the Six Headwinds,” Working Paper 18315, National Bureau of
Economic Research.
(2014): “The Demise of U.S. Economic Growth: Restatement, Rebuttal,
and Reflections,” Working Paper 19895, National Bureau of Economic
Research.
Jones, B. F. (2005): “Age and Great Invention,” NBER Working Paper 11359,
NBER.
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8th June 2015
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Conclusions
References II
(2010): “Age and Great Invention,” The Review of Economics and
Statistics, 92(1), 1–14.
Park, C. (2010): “How does changing age distribution impact stock prices? a
nonparametric approach,” Journal of Applied Econometrics, 25(7), 1155–1178.
Romer, P. M. (1990): “Endogenous Technological Change,” Journal of Political
Economy, 98(5), S71–102.
Yaari, M. E. (1965): “Uncertain Lifetime, Life Insurance, and the Theory of the
Consumer,” The Review of Economic Studies, 32(2), 137–150.
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Additional Material
Methodology - Demographic Structure
I
How granular should demographic structure be? Due to lack of data for all
periods for some countries we use data by 10 yrs of cohorts and thus do not
to restrict age shape effects (as in Park (2010))
I
Denote the share of age group j = 1, ..8 (0 − 9, 10 − 19, . . . , 70+) in total
population by wjit . The effect on the variable of interest, say xit , where i
denote country and t denotes year, takes the form
xit = α +
8
X
δj wji,t + uit .
j=1
P8
I
j=1 wjit = 1 ⇒ exact collinearity
To deal with this, we restrict the coefficients to sum to 0, use (wji,t − w8i,t )
as explanatory variables and recover the coefficient of the oldest age group.
I
We denote the 7 element vector of (wji,t − w8i,t ) as Wit .
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Additional Material
Methodology - Dynamic System
I
Endogenous variables Yit = (git , Iit , Sit , Hit , rrit , πit )0
I
Ideal - Estimate an identified structural system allowing for expectations
Φ0 Yt = Φ1 Et (Yt+1 ) + Φ2 Yt−1 + ΓWt + εt .
I
(2)
We can only estimate reduced form, where A solves Φ1 A2 − Φ0 A + Φ2 = 0.
−1
Yt = AYt−1 + Φ−1
0 ΓWt + Φ0 εt .
I
(3)
Given we want to analyse impact of Wt , we do not need to take a stand on
link between A and Φ0 , Φ1 , Φ2 .
Back
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Additional Material
Estimation - Results I
Yit = ai + A1 Yi,t−1 + A2 Yi,t−2 + DWit + uit
g
I
S
H
rr
π
gt−1
0.24
0.17
-0.12
0.22
-0.19
0.36
It−1
-0.18
0.76
-0.10
-0.05
-0.18
0.21
St−1
0.01
0.01
0.77
0.01
-0.10
0.05
Ht−1
-0.01
0.01
-0.01
0.92
0.05
-0.02
rrt−1
-0.26
-0.10
-0.10
-0.13
0.90
-0.16
πt−1
-0.28
-0.10
-0.07
-0.11
0.24
0.55
Table: Sum of VAR coefficients A1 + A2
I
There is evidence that all our endogenous variables are Granger causal for some
other variables in the system, except in the case of savings which does not have a
significant influence on any other variable
I
Only surprising feature lagged investment has a negative effect on growth, though
there is a strong positive contemporaneous correlation between the growth and
investment residuals.
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Additional Material
Estimation - Results II
Yit = ai + A1 Yi,t−1 + A2 Yi,t−2 + DWit + uit
g
I
S
H
rr
π
δ1
-0.06
-0.03
-0.10*
-0.10*
-0.33*
0.50*
δ2
0.25*
0.04
0.17*
-0.02
-0.08
0.13
δ3
0.18*
0.08*
0.02
0.07
0.14
-0.16
δ4
-0.03
-0.03
0.11
0.14*
0.29*
-0.46*
δ5
-0.03
-0.06
0.08
-0.03
0.21*
-0.30*
δ6
0.02
0.03
0.19*
0.08
0.16
-0.07
δ7
-0.07
0.18*
0.01
0.05
0.01
0.18
δ8
-0.25*
-0.20*
-0.49*
-0.20*
-0.39*
0.19*
Table: Short-Run Demographic Impact - Matrix D
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Additional Material
Robustness - 2-way effects
I
I
I
Benchmark model is a one-way fixed effects model and includes oil prices as a
the only variable that affects all countries.
So if there are shared, cross-country factors driving the trend in dependent
variables as well as demographic variables, this trend may be wrongly
attributed to the demographic variables.
A two-way effects model avoids this issue by removing any common
cross-country factors from all variables prior to estimation.
g
I
S
H
rr
π
δ1
-0.16
-0.71
0.09
-2.13
-0.19
0.54
δ2
0.18
-0.12
0.78
-0.14
-0.08
0.28
δ3
0.09
0.27
0.01
0.50
0.41
-0.56
Benchmark
δ4
δ5
0.11
0.14
0.31
0.42
0.39
0.25
2.62
1.04
0.07
-0.12
-0.83
0.00
δ6
-0.04
0.15
0.22
0.37
0.50
-0.03
δ7
-0.29
0.42
0.12
-0.90
0.17
0.02
δ8
-0.03
-0.75
-1.87
-1.36
-0.76
0.57
Three Generations
β1
β2
β3
0.01
0.13
-0.14
-0.26
0.36
-0.10
0.63
0.20
-0.83
-0.91
1.76
-0.85
-0.02
0.15
-0.13
0.44
-0.59
0.15
Table: Long-Run Demographic Impact (2-way effects)
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Additional Material
Production
I
Final Good Producers Ntf
"Z
Yc,t =
#µt
j (1/µt )
(Yc,t
)
dj
0
I
I
I
where Ntf is the number of firms in input sectors and µt = µ(Ntf ), µ0 (·) < 0.
So variable mark-up and fact that firms must pay operating costs control
entry and exit.
Production of input firm j
h
i(1−γI ) h iγI
j
Yc,t
= (Utj Ktj )α (ξt Ljt )(1−α)
Mtj
Intermediate composite good
Mtj
"Z
=
At
#ϑ
(Mtji )(1/ϑ) di
0
where each producer i acquires the right to market the good via the creation
and adoption process. Thus At is determined by innovation sector.
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Additional Material
Innovation: R&D
I
Let Ztp be the stock of invented goods (prototypes) at the beginning of time
t. Inventor p spends Stp to add new prototypes to her stock. Productivity of
innovation spending is given by ϕt .
p
ρyw
= ϕt Stp + φZtp = (Γyw
χ[(Ψ̃t )ρ (St )1−ρ ]−1 Zt Stp + φZtp
Zt+1
t )
I
I
φ = implied product survival rate
ρ = elasticity of new technology creation
Γyw
t = share of workers that contribute to innovation
ρyw = Importance of workers for innovation process.
Innovators borrow Stp from the household. Define Jt as the value of an
invented intermediary good. Then
φE [Jt+1 ] =
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Rt+1
ϕt
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Additional Material
Innovation: Adoption
I
Let Aqt ⊂ Ztq denote the stock of converted goods marketed to firms.
Adopter q invest (intensity) Ξt to transform Ztq into Aqt .
Aqt
Conversion process is successful with probability λt = λ Ψ̃
Ξt
with λ0 > 0 Flow of converted goods
t
Aqt+1 = λt φ(Ztq − Aqt ) + φAqt
I
A converted good can be marketed at every period to firms, thus its value,
denoted Vt is given by
Vt = Πm,t + (Rt+1 )−1 φEt Vt+1
where Πm,t is the profit from selling an intermediate good to input firms.
I
The value of a unadopted product (Jt ) is
Jt = max −Ξt + (Rt+1 )−1 φEt [λt Vt+1 + (1 − λt )Jt+1 ]
Ξt
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Additional Material
Household Sector: Population Dynamics
I
Population Nt
Young (Nty ) becomes worker with probability 1 − ωy
Workers (Ntw ) retire with probability 1 − ωr
Once retired (Ntr ) individual survives with probability γ.
y
Nt+1
= ñt,t+1 Nty + ω y Nty = (ñt,t+1 + ω y )Nty = nt,t+1 Nty ,
w
Nt+1
r
Nt+1
=
(1 − ω y )Nty + ω r Ntw ,
=
(1 − ω r )Ntw + γt,t+1 Ntr
define ζtr = Ntr /Ntw and ζty = Nty /Ntw .
I
Stock of workers that contribute to innovation
y
Γyw
t ≡ (1 − ω )
Nty
ζty
y
+ (1 − λy )Γyw
=
(1
−
ω
)
+ (1 − λy )Γyw
t−1
t−1 ,
Nt
1 + ζty + ζtr
λy < 1 augments the stock of young workers just entered work! Worker’s age
matters for innovation.
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Additional Material
Household Sector: Human Capital
I
Let ξt be the average effective units across workers at period t.
Let Ity = Wτt Nt w be the total effective expenditure society makes on the
t
education of the young, financed by transfer τt from workers.
y
Each young who becomes a worker at the end of period t will provide ξt+1
effective units.
y
ξt+1
I
χE
= ρE ξt +
2
Ity
ξt
2
ξt
The evolution of workers effective labour units
ξt+1 = ωr
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y
Ntw
y
y Nt
ξ
+
(1
−
ω
)
t
w
w ξt+1
Nt+1
Nt+1
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Additional Material
Household Sector: Consumption and Labour
I
Retirees are assumed not to work. Two key assumptions to offset impact of
risk of death (perfect annuity market) and retirement (risk neutrality) on
households decision. Gertler (1999)
I
Thus, for z = {w , r } we assume agent j selects consumption and asset
holdings to maximise
o1/ρU
n
j
z
| z]ρU )
(Et [Vt+1
Vtjz = (C jz )ρU + βt,t+1
subject to
jz
j z
jz z
z
z
Ctjz + FAjz
t+1 = Rt FAt + Wt ξt I + dt − τt I
I
Aggregate consumption functions are:
w
w
w
Ctw = ςt [Rt FAw
t + Ht + D t − Tt ]
Ctr = εt ςt [Rt FArt + Dtr ]
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Additional Material
Growth
Three drivers of growth:
a. exogenous growth of population, nt
b. endogenous growth rate of effective labour force, ξ
c. endogenous innovation/adoption of new intermediate goods, At
that affects Kt , Lt
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Additional Material
Parameters
Standard
β = 0.96
α = 0.33 δ = 0.08
U == 80% γI = 0.5 µ = 1.1
(1/ (1 − ρU )) = 0.25
Innovation
obsolescence: (1-φ)=0.03
productivity in innovation:χ = 94.42
elasticity of intermediate goods w.r.t R&D ρ = 0.9
ave. adoption time λ = 0.1
elasticity of adoption time to intensity λ = 0.9
Population
Ny
= 48%
N wr
N
(1 − ω r ) = 0.023
= 20%
Nw
10 yrs in retirement γ = 0.9
Population and Inovation
ratio of workers influencing innovation (1 − λy ) = 23
importance of worker to innovation productivity ρyw = .9
(1 − ω y ) = 0.05
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Additional Material
US
Japan
0.035
0.03
0
0.025
−0.01
Spain
Sweden
0.01
0.015
0.06
0.05
0.01
0.04
0.015
−0.02
−0.03
Output Growth
0.02
Output Growth
Output Growth
Output Growth
0.005
0
0.03
0.02
0.01
−0.005
0.01
−0.04
0.005
−0.05
0
0
2000
2005
2010
2015
2020
2025
−0.06
2000
2030
0.025
−0.01
−0.01
2005
2010
2015
2020
2025
−0.015
2000
2030
0.04
2005
2010
2015
2020
2025
−0.02
2000
2030
0.01
2010
2015
2020
2025
2030
2005
2010
2015
Years
2020
2025
2030
0.07
0.005
0.02
2005
0.06
0.02
0
0.015
0.05
−0.005
0
−0.005
−0.02
Real Interest Rate
0.005
Real Interest Rate
0
Real Interest Rate
Real Interest Rate
0.01
−0.01
−0.015
−0.02
0.04
0.03
0.02
−0.04
−0.025
0.01
−0.01
−0.03
−0.06
−0.015
−0.02
2000
0
−0.035
2005
2010
2015
Years
2020
2025
2030
−0.08
2000
2005
2010
2015
Years
2020
2025
2030
−0.04
2000
2005
2010
2015
Years
2020
2025
2030
−0.01
2000
Figure: Simulation: prediction - Lower ρyw
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Additional Material
Canada
France
0.05
Greece
Italy
0.025
0.02
0.01
0.02
0.015
0.005
0.04
0.01
0.01
0.005
0.005
0
0
Output Growth
0.02
0.015
Output Growth
Output Growth
Output Growth
0.03
0
−0.005
−0.005
−0.01
−0.015
0.01
−0.005
−0.01
−0.01
−0.015
−0.015
−0.02
−0.02
0
−0.01
2000
2005
2010
2015
2020
2025
−0.02
2000
2030
0.06
0.01
0.05
0
0.04
−0.01
2005
2010
2015
2020
2025
−0.025
2000
2030
−0.025
2005
2010
2015
2020
2025
−0.03
2000
2030
0.04
2005
2010
2015
2020
2025
2030
2005
2010
2015
Years
2020
2025
2030
0.03
0.02
0.03
0.01
0.02
−0.02
Real Interest Rate
0.03
Real Interest Rate
Real Interest Rate
Real Interest Rate
0.02
0.01
0
0
−0.01
−0.02
−0.03
−0.01
−0.03
0.01
0
2000
−0.04
2005
2010
2015
Years
2020
2025
2030
−0.05
2000
−0.02
2005
2010
2015
Years
2020
2025
2030
−0.03
2000
−0.04
2005
2010
2015
Years
2020
2025
2030
−0.05
2000
Figure: Simulation: prediction Additional Countries - Lower ρyw
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