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Global demographic trends and social security reform Orazio Attanasio, University College London Sagiri Kitao, University of Southern California Gianluca Violante, New York University June 28, 2007 The University of Tokyo Tokyo, June 28, 2007

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SLIDE 1

Global demographic trends and social security reform

Orazio Attanasio, University College London Sagiri Kitao, University of Southern California Gianluca Violante, New York University June 28, 2007 The University of Tokyo

Tokyo, June 28, 2007 – p. 1

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SLIDE 2

Introduction

Demographic trends significant increase in longevity decline in fertility the retirement of the ‘baby boom’ generations Global demographic trends are not completely synchronized across countries

Tokyo, June 28, 2007 – p. 2

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Introduction

1950 2000 2050 2100 2150 2200 1 2 3 4 5 6 7 Years Total fertility rates Demographic Transition: total fertility rates South: UN (data/projection) South: model North: UN (data/projection) North: model 1950 2000 2050 2100 2150 2200 10 20 30 40 50 60 Years Median age Demographic Transition: median age North: UN (data/projection) North: model South: UN (data/projection) South: model 1950 2000 2050 2100 2150 2200 0.1 0.2 0.3 0.4 0.5 Years Dependency ratio Demographic Transition: old dependency ratio (60 or above) North: UN (data/projection) North: model South: UN (data/projection) South: model 1950 2000 2050 2100 2150 2200 −1 1 2 3 4 Years Population growth Demographic Transition: population growth North: UN (data/projection) North: model South: UN (data/projection) South: model

Tokyo, June 28, 2007 – p. 3

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Introduction

Economic implications of the demographic trends large changes in factor prices and welfare sustainability of PAYG pension systems Question: when thinking about how to reform the social security system in the developed world, does the distinction

  • pen vs closed economy matter for

factor prices welfare fiscal policy variables? Contribution: offer an alternative benchmark for policy evaluation.

Tokyo, June 28, 2007 – p. 4

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SLIDE 5

Introduction

Social security in closed economy

Conesa and Krueger (1999), De Nardi, Imrohoroglu and Sargent (1999), Huggett and Ventura (1999), Abel (2003), Bohn (2003), and many more small open economy: Huang, Imorohoroglu and Sargent (1997), Kotlikoff, Smetters and Walliser (1999)

Global demographic trends and current account dynamics

Brooks (2003), Domeij and Floden (2004), Attanasio, Kitao and Violante (2006), Krueger and Ludwig (2007) and many more

Labor flow across regions

Storesletten (2000), Fehr, Jokisch and Kotlikoff (2004)

Tokyo, June 28, 2007 – p. 5

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Overview

OLG model calibrated on observed and projected demographic trends two regions: North and South Different ways to finance the social security system in the North PAYGO system is maintained The system is privatized to a fully-funded system Open and closed economy versions of the model

Tokyo, June 28, 2007 – p. 6

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MODEL

Tokyo, June 28, 2007 – p. 7

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SLIDE 8

Model

Two regions: r = n, s

Tokyo, June 28, 2007 – p. 8

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SLIDE 9

Model

Two regions: r = n, s Technology

CRS production function F(Zr

t , Kr t , Lr t)

TFP Zr

t grows exogenously at rate λr t

Tokyo, June 28, 2007 – p. 8

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Model

Two regions: r = n, s Technology

CRS production function F(Zr

t , Kr t , Lr t)

TFP Zr

t grows exogenously at rate λr t

Demographics

OLG of pairs of individuals, indexed by age i = 1, 2, ...I dependent for Id periods, become adults and start working at Id + 1, and retire from work at IR surviving probability sr

i,t, Sr i,t

fertility rate φr

i,t

number of dependent children dr

i,t = i k=i−Id+1 φr k,t−(i−k)Sr i−k+1,t

Tokyo, June 28, 2007 – p. 8

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Model: evolution of population

At time t, population shares µr

t evolve according to the transition

matrix

Γr

t

=         φr

1,t

φr

2,t

... ... φr

¯ I,t

sr

2,t+1

... ... sr

3,t+1

...

... ...

... sr

¯ I,t+1

        µr

t+1

= Γr

tµr t

Tokyo, June 28, 2007 – p. 9

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Model: preferences

ur(ca

i,t, cd i,t) =

  • ca

i,t

1−θ 1 − θ + dr

i,tω

  • dr

i,t

  • cd

i,t

1−θ 1 − θ

Tokyo, June 28, 2007 – p. 10

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Model: preferences

ur(ca

i,t, cd i,t) =

  • ca

i,t

1−θ 1 − θ + dr

i,tω

  • dr

i,t

  • cd

i,t

1−θ 1 − θ

From F.O.C.

cd

i,t = ca i,tω

  • dr

i,t

1

θ

Tokyo, June 28, 2007 – p. 10

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Model: preferences

ur(ca

i,t, cd i,t) =

  • ca

i,t

1−θ 1 − θ + dr

i,tω

  • dr

i,t

  • cd

i,t

1−θ 1 − θ

From F.O.C.

cd

i,t = ca i,tω

  • dr

i,t

1

θ

Express utility as a function of household consumption ci,t = ca

i,t + di,tcd i,t

ur(ci,t) = Ωr

i,t

c

1−θ

i,t

1 − θ, Ωr

i,t =

  • 1 + ω
  • dr

i,t

1

θ dr

i,t

θ

Tokyo, June 28, 2007 – p. 10

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Model: preferences

ur(ca

i,t, cd i,t) =

  • ca

i,t

1−θ 1 − θ + dr

i,tω

  • dr

i,t

  • cd

i,t

1−θ 1 − θ

From F.O.C.

cd

i,t = ca i,tω

  • dr

i,t

1

θ

Express utility as a function of household consumption ci,t = ca

i,t + di,tcd i,t

ur(ci,t) = Ωr

i,t

c

1−θ

i,t

1 − θ, Ωr

i,t =

  • 1 + ω
  • dr

i,t

1

θ dr

i,t

θ Ur =

I

  • i=1

βi−1Sr

i,t+i−1Ωr i,t+i−1

c

1−θ

i,t+i−1

1 − θ

Tokyo, June 28, 2007 – p. 10

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Model: budget constraint

  • 1 + τr

c,t

  • cr

i,t + sr i+1,t+1ar i+1,t+1 = yr i,t +

  • 1 +
  • 1 − τr

a,t

  • rt
  • ar

i,t

Tokyo, June 28, 2007 – p. 11

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SLIDE 17

Model: budget constraint

  • 1 + τr

c,t

  • cr

i,t + sr i+1,t+1ar i+1,t+1 = yr i,t +

  • 1 +
  • 1 − τr

a,t

  • rt
  • ar

i,t

yr

i,t =

    

  • 1 − τr

w,t

  • wr

t εr i,tlr i,t =

  • 1 − τr

w,t

  • ˜

yr

i,t

if i < IR,

pr

i,t = κr t W r

i,t

IR−1

if i ≥ IR

Tokyo, June 28, 2007 – p. 11

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SLIDE 18

Model: budget constraint

  • 1 + τr

c,t

  • cr

i,t + sr i+1,t+1ar i+1,t+1 = yr i,t +

  • 1 +
  • 1 − τr

a,t

  • rt
  • ar

i,t

yr

i,t =

    

  • 1 − τr

w,t

  • wr

t εr i,tlr i,t =

  • 1 − τr

w,t

  • ˜

yr

i,t

if i < IR,

pr

i,t = κr t W r

i,t

IR−1

if i ≥ IR

W r

i,t =

             ˜ yr

1,t

if i = 1

˜ yr

i,t + W r i−1,t−1

if 1 < i < IR

W r

i−1,t−1

if i ≥ IR.

Tokyo, June 28, 2007 – p. 11

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SLIDE 19

Model: government

Gr

t + (1 + rt) Br t + I i=IR pr i,tµr i,t =

τr

w,twr t

IR−1

i=1

µr

i,tεr i,tlr i,t + I i=1 µr i,t

  • τr

a,trtar i,t + τr c,tcr i,t

  • + Br

t+1

Tokyo, June 28, 2007 – p. 12

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SLIDE 20

Equilibrium

A Competitive Equilibrium of the Two-Region Economy, for given sequences of demographic matrices {Γr

t}∞ t=1, TFP {Zr t }∞ t=1

and fiscal variables

  • Gr

t, κr t, τr a,t, τr c,t, Br t

∞

t=1, is

—————————————————————————–

  • 1. household allocations
  • 2. wage tax rates
  • 3. wage rates (in North and South)
  • 4. world interest rate
  • 5. aggregate variables
  • 6. external wealth of the North

such that:

Tokyo, June 28, 2007 – p. 13

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SLIDE 21

Equilibrium

A Competitive Equilibrium of the Two-Region Economy, for given sequences of demographic matrices {Γr

t}∞ t=1, TFP {Zr t }∞ t=1

and fiscal variables

  • Gr

t, κr t, τr a,t, τr c,t, Br t

∞

t=1, is

—————————————————————————– such that:

  • 1. households and firm maximize
  • 2. regional labor markets clear
  • 3. regional bond markets and international capital market clear
  • 4. government budget constraints are satisfied
  • 5. allocations are feasible

Tokyo, June 28, 2007 – p. 13

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CALIBRATION

Tokyo, June 28, 2007 – p. 14

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SLIDE 23

Calibration

Model period: five years

Tokyo, June 28, 2007 – p. 15

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Calibration

Model period: five years Demographics

demographic variables: UN projections (2005-2200) North “more developed regions" US, Canada, Europe, Japan, Australia and NZ South “less developed regions" Africa, Asia (ex-Japan), Latin America, and the rest Id = 3, I = ¯ I − Id = 24 − 3 = 21, IR = 11,

Tokyo, June 28, 2007 – p. 15

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Calibration

Model period: five years Demographics

demographic variables: UN projections (2005-2200) North “more developed regions" US, Canada, Europe, Japan, Australia and NZ South “less developed regions" Africa, Asia (ex-Japan), Latin America, and the rest Id = 3, I = ¯ I − Id = 24 − 3 = 21, IR = 11,

Technology

Cobb-Douglas with 0.3 share of capital growth of Zr

t : match historical growth of income per capita and

converge to the same rate in the long-run Zr

0 to match the North-South income per capita ratio of 7 in 2000

Tokyo, June 28, 2007 – p. 15

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Calibration

Preference

risk-aversion coefficient σ = 2 preference weight for children ω(dr

i,t) calibrated to match equivalence

scale (Fernandez-Villaverde and Krueger, 2006)

Tokyo, June 28, 2007 – p. 16

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SLIDE 27

Calibration

Preference

risk-aversion coefficient σ = 2 preference weight for children ω(dr

i,t) calibrated to match equivalence

scale (Fernandez-Villaverde and Krueger, 2006)

Endowment and labor supply

efficiency units calibrated using micro data for US and Mexico males assumed to work full time female participation rates calibrated as a function of fertility and trend using data for US (North) and Brazil, India, Korea and Mexico (South) P r

i,t(dr i,t) = βr 0 +(P +Ti−βr 0){1−exp[−βr 1 ∗(t−1)]}+Id j=1 ˆ

αjdr

i,j,t

Tokyo, June 28, 2007 – p. 16

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SLIDE 28

Calibration

Government

Bt/Yt Gt/Yt τc τa ρ τw

North 35.5% 26.5% 9% 38% 46.6% 26.3% South 50% 20% 15% 38% 10.1% 6.0%

Tokyo, June 28, 2007 – p. 17

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SLIDE 29

POLICY SIMULATIONS

Tokyo, June 28, 2007 – p. 18

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Policy simulations

Assume that the world economy is in the initial steady state characterized by the demographic parameters of 1950 Then, the world experiences a demographic shock and a gradual change through the actual and projected demographic transitions, eventually reaching the final steady state Agents have perfect foresight on the demographic path

Tokyo, June 28, 2007 – p. 19

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Policy simulations

Two sets of experiments

  • 1. alternative policies to sustain PAYG system in the North

wage tax (benchmark) consumption tax retirement age government debt retirement benefit ⇒ policy change is announced in 2005 and implemented in 2010

  • 2. privatization with ‘recognition bonds’

Each experiment is performed in closed and open economy

Tokyo, June 28, 2007 – p. 20

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SLIDE 32

Benchmark simulation

Interest rates in open and closed economies

2000 2020 2040 2060 2080 2100 1 2 3 4 5 6 7 8 9 10 percentage (%) OPEN CLOSED: NORTH CLOSED: SOUTH

Tokyo, June 28, 2007 – p. 21

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SLIDE 33

Benchmark simulation

Current account of the North (% of GDP)

1960 1980 2000 2020 2040 2060 2080 2100 −6 −5 −4 −3 −2 −1 1 2 3 percentage (%)

Tokyo, June 28, 2007 – p. 22

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SLIDE 34

Benchmark simulation

Current account of the North (% of GDP)

1960 1980 2000 2020 2040 2060 2080 2100 −6 −5 −4 −3 −2 −1 1 2 3 percentage (%)

Reversal of capital flow

Tokyo, June 28, 2007 – p. 22

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SLIDE 35

Benchmark simulation

Current account of the North (% of GDP)

1960 1980 2000 2020 2040 2060 2080 2100 −6 −5 −4 −3 −2 −1 1 2 3 percentage (%)

External assets of the South (% of total wealth) 1970−90 Model: −40% Data: −10% (Kraay, et al)

Tokyo, June 28, 2007 – p. 22

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SLIDE 36

Benchmark simulation

2010 2020 2030 2040 2050 2060 2070 1 1.05 1.1 1.15 1.2 1.25 1.3 Wage rate 2010 2020 2030 2040 2050 2060 2070 2 4 6 8 Interest rate (%) 2010 2020 2030 2040 2050 2060 2070 1 1.25 1.5 1.75 2 2.25 2.5 Capital per capita 2010 2020 2030 2040 2050 2060 2070 0.85 0.9 0.95 1 1.05 1.1 1.15 Output per capita 2010 2020 2030 2040 2050 2060 2070 20 25 30 35 40 Wage tax (%) 2010 2020 2030 2040 2050 2060 2070 −6 −4 −2 2 Current account (% of GDP)

Solid lines represent closed economy and dotted lines represent open economy.

Tokyo, June 28, 2007 – p. 23

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SLIDE 37

Benchmark simulation

Demographic transition induces higher capital accumulation and lower interest rates Capital flows first North to South and then South to North Factor prices in open and closed economies differ substantially, but the paths of wage tax are similar increase in wage (and the wage tax revenue) is offset by the decline in interest rates (and the capital tax revenue)

Tokyo, June 28, 2007 – p. 24

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SLIDE 38

Consumption tax

2010 2020 2030 2040 2050 2060 2070 1 1.05 1.1 1.15 1.2 1.25 1.3 Wage rate 2010 2020 2030 2040 2050 2060 2070 2 4 6 8 Interest rate (%) 2010 2020 2030 2040 2050 2060 2070 1 1.25 1.5 1.75 2 2.25 2.5 Capital per capita 2010 2020 2030 2040 2050 2060 2070 0.85 0.9 0.95 1 1.05 1.1 1.15 Output per capita 2010 2020 2030 2040 2050 2060 2070 5 10 15 20 25

Consumption tax (%)

2010 2020 2030 2040 2050 2060 2070 −6 −4 −2 2 Current account (% of GDP)

Solid lines represent closed economy and dotted lines represent open economy.

Tokyo, June 28, 2007 – p. 25

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SLIDE 39

Retirement age

The government announces in 2005 that the retirement age is raised by one period (=5 years) starting in 2020 The transition is financed by the adjustment of wage tax

Tokyo, June 28, 2007 – p. 26

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SLIDE 40

Retirement age

2010 2020 2030 2040 2050 2060 2070 1 1.05 1.1 1.15 1.2 1.25 1.3 Wage rate 2010 2020 2030 2040 2050 2060 2070 2 4 6 8 Interest rate (%) 2010 2020 2030 2040 2050 2060 2070 1 1.25 1.5 1.75 2 2.25 2.5 Capital per capita 2010 2020 2030 2040 2050 2060 2070 0.85 0.9 0.95 1 1.05 1.1 1.15 Output per capita 2010 2020 2030 2040 2050 2060 2070 24 26 28 30 32 34 Wage tax (%) 2010 2020 2030 2040 2050 2060 2070 −6 −4 −2 2 Current account (% of GDP)

Solid lines represent closed economy and dotted lines represent open economy.

Tokyo, June 28, 2007 – p. 27

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SLIDE 41

Government debt

2010 2020 2030 2040 2050 2060 2070 1 1.05 1.1 1.15 1.2 1.25 1.3 Wage rate 2010 2020 2030 2040 2050 2060 2070 2 4 6 8 Interest rate (%) 2010 2020 2030 2040 2050 2060 2070 1 1.25 1.5 1.75 2 2.25 2.5 Capital per capita 2010 2020 2030 2040 2050 2060 2070 0.85 0.9 0.95 1 1.05 1.1 1.15 Output per capita 2010 2020 2030 2040 2050 2060 2070 30 40 50 60 70 80 Govt debt ratio (%) 2010 2020 2030 2040 2050 2060 2070 25 30 35 40 45 Wage tax (%)

Solid lines represent closed economy and dotted lines represent open economy.

Tokyo, June 28, 2007 – p. 28

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SLIDE 42

Pension benefits

2010 2020 2030 2040 2050 2060 2070 1 1.05 1.1 1.15 1.2 1.25 1.3 Wage rate 2010 2020 2030 2040 2050 2060 2070 2 4 6 8 Interest rate (%) 2010 2020 2030 2040 2050 2060 2070 1 1.25 1.5 1.75 2 2.25 2.5 Capital per capita 2010 2020 2030 2040 2050 2060 2070 0.85 0.9 0.95 1 1.05 1.1 1.15 Output per capita 2010 2020 2030 2040 2050 2060 2070 10 20 30 40 50

Replacement rate (%)

2010 2020 2030 2040 2050 2060 2070 −6 −4 −2 2 Current account (% of GDP)

Solid lines represent closed economy and dotted lines represent open economy.

Tokyo, June 28, 2007 – p. 29

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SLIDE 43

Welfare comparison: PAYG system

1900 1920 1940 1960 1980 2000 2020 2040 2060 2080 2100 −6 −4 −2 2 4 6 8 Cohort birth year Consumption equivalent variation (%) consumption tax government debt replacement ratio

Tokyo, June 28, 2007 – p. 30

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SLIDE 44

Welfare comparison: PAYG system

1900 1920 1940 1960 1980 2000 2020 2040 2060 2080 2100 −4 −2 2 4 6 Cohort birth year Consumption equivalent variation (%) consumption tax government debt replacement ratio 1900 1920 1940 1960 1980 2000 2020 2040 2060 2080 2100 −4 −2 2 4 6 Cohort birth year Consumption equivalent variation (%) consumption tax government debt replacement ratio

Closed Economy Open Economy

Tokyo, June 28, 2007 – p. 30

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SLIDE 45

Privatizing social security

Privatization of the pension system as an alternative policy Issue of how to finance the transition Reform is announced in 2005 and implemented in 2015 retired: honor payments under PAYG in labor force but not retired: issue "recognition bond" for accumulated pension rights (Chile) not yet in labor force in 2015: no PAYG

Tokyo, June 28, 2007 – p. 31

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SLIDE 46

Privatizing social security

Every year t > t∗ = 2015, a ‘recognition bond’ Ωt is paid to the retiring cohort that was age i∗ at time t∗

Ωt =

  • κold Wi∗,t∗

IR − 1  1 +

I−IR

  • i=1

i

  • j=1
  • sIR+j,t+j

Rold

t+j

  Wi∗,t∗: wage accumulated up to age i∗ and time t∗ κold Wi∗,t∗

IR−1 : benefit they would have been entitled to under the

previous system

Ωt: PDV of such stream of payment at retirement

Tokyo, June 28, 2007 – p. 32

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SLIDE 47

Privatizing social security

The transition is financed by: wage tax consumption tax government debt

Tokyo, June 28, 2007 – p. 33

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SLIDE 48

Privatization: wage tax

2010 2020 2030 2040 2050 2060 2070 1 1.05 1.1 1.15 1.2 1.25 1.3 Wage rate 2010 2020 2030 2040 2050 2060 2070 2 4 6 8 Interest rate (%) 2010 2020 2030 2040 2050 2060 2070 1 1.25 1.5 1.75 2 2.25 2.5 Capital per capita 2010 2020 2030 2040 2050 2060 2070 0.85 0.9 0.95 1 1.05 1.1 1.15 Output per capita 2010 2020 2030 2040 2050 2060 2070 10 20 30 40 50 Wage tax (%) 2010 2020 2030 2040 2050 2060 2070 −6 −4 −2 2 Current account (% of GDP)

Solid lines represent closed economy and dotted lines represent open economy.

Tokyo, June 28, 2007 – p. 34

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SLIDE 49

Privatization: wage tax

The North accumulates capital faster The paths of prices in closed and open economy are similar capital flow from the South is replaced by an increase in domestic life-cycle savings The paths of policy variables are similar in closed and open (again, but for different reasons)

Tokyo, June 28, 2007 – p. 35

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SLIDE 50

Privatization: consumption tax

2010 2020 2030 2040 2050 2060 2070 1 1.05 1.1 1.15 1.2 1.25 1.3 Wage rate 2010 2020 2030 2040 2050 2060 2070 2 4 6 8 Interest rate (%) 2010 2020 2030 2040 2050 2060 2070 1 1.25 1.5 1.75 2 2.25 2.5 Capital per capita 2010 2020 2030 2040 2050 2060 2070 0.85 0.9 0.95 1 1.05 1.1 1.15 Output per capita 2010 2020 2030 2040 2050 2060 2070 −10 10 20 30

Consumption tax (%)

2010 2020 2030 2040 2050 2060 2070 −6 −4 −2 2 Current account (% of GDP)

Solid lines represent closed economy and dotted lines represent open economy.

Tokyo, June 28, 2007 – p. 36

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SLIDE 51

Privatization: government debt

2010 2020 2030 2040 2050 2060 2070 1 1.05 1.1 1.15 1.2 1.25 1.3 Wage rate 2010 2020 2030 2040 2050 2060 2070 2 4 6 8 Interest rate (%) 2010 2020 2030 2040 2050 2060 2070 1 1.25 1.5 1.75 2 2.25 2.5 Capital per capita 2010 2020 2030 2040 2050 2060 2070 0.85 0.9 0.95 1 1.05 1.1 1.15 Output per capita 2010 2020 2030 2040 2050 2060 2070 100 200 300 400 500 Govt debt ratio (%) 2010 2020 2030 2040 2050 2060 2070 −6 −4 −2 2 Current account (% of GDP)

Solid lines represent closed economy and dotted lines represent open economy.

Tokyo, June 28, 2007 – p. 37

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SLIDE 52

Welfare comparison: privatization

1900 1920 1940 1960 1980 2000 2020 2040 2060 2080 2100 −14 −12 −10 −8 −6 −4 −2 2 4 6 Cohort birth year Consumption equivalent variation (%) wage tax consumption tax government debt

Tokyo, June 28, 2007 – p. 38

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SLIDE 53

Welfare comparison: privatization

1900 1920 1940 1960 1980 2000 2020 2040 2060 2080 2100 −14 −10 −6 −2 2 6 Cohort birth year Consumption equivalent variation (%) wage tax consumption tax government debt 1900 1920 1940 1960 1980 2000 2020 2040 2060 2080 2100 −14 −10 −6 −2 2 6 Cohort birth year Consumption equivalent variation (%) wage tax consumption tax government debt

Closed Economy Open Economy

Tokyo, June 28, 2007 – p. 38

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SLIDE 54

Conclusions

Does the distinction open vs closed economy matter? NO, in terms of the evolution of fiscal variables YES, in terms of factor prices during the transition YES, if concerned about welfare effects

Tokyo, June 28, 2007 – p. 39

slide-55
SLIDE 55

Tokyo, June 28, 2007 – p. 40

slide-56
SLIDE 56

Benchmark simulation

External assets of the South (% of total wealth)

1960 1980 2000 2020 2040 2060 2080 2100 −70 −60 −50 −40 −30 −20 −10 10 20 30

Tokyo, June 28, 2007 – p. 1

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SLIDE 57

Benchmark simulation

External assets of the South (% of total wealth)

1960 1980 2000 2020 2040 2060 2080 2100 −70 −60 −50 −40 −30 −20 −10 10 20 30 percentage (%) Data from Kraay, et al (2004)

Tokyo, June 28, 2007 – p. 1

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SLIDE 58

Benchmark simulation

External assets of the South (% of total wealth)

1960 1980 2000 2020 2040 2060 2080 2100 −50 −40 −30 −20 −10 10 20 30

Reversal of external wealth

Tokyo, June 28, 2007 – p. 1

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SLIDE 59

Robustness analysis (1)

Endogenous labor supply Development process and TFP growth

immediate catch up of the TFP in the South with the North full convergence of per-capita GDP in the South to the North

Risk aversion

alternative values of CRRA

The role of China and India

findings of Fehr, Jokisch and Kotlikoff (2006)

Tokyo, June 28, 2007 – p. 2

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SLIDE 60

Robustness analysis (2)

Frictional capital markets

transaction cost of capital invested by the North

Population projection Capital income tax in the South

Tokyo, June 28, 2007 – p. 3

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SLIDE 61

Robustness analysis: endogenous labor supply

preference over consumption and leisure

u (cit, lit) =

  • cη

it

¯ Lit − lit 1−η1−θ 1 − θ

pension benefit

pk,t = κt IR − 1

IR−1

  • j=1

wt−k+jεj,t−k+jφ¯ Lj,t−k+j

calibrate β and η capital-output ratio of 2.5 average work hours 40% (also set φ = 0.4) implied Frisch elasticity of 0.8 and IES of 0.45

Tokyo, June 28, 2007 – p. 4

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SLIDE 62

Robustness analysis: endogenous labor supply

2010 2020 2030 2040 2050 2060 2070 1 1.05 1.1 1.15 1.2 1.25 1.3 Wage rate 2010 2020 2030 2040 2050 2060 2070 2 4 6 8 Interest rate (%) 2010 2020 2030 2040 2050 2060 2070 1 1.25 1.5 1.75 2 2.25 2.5 Capital per capita 2010 2020 2030 2040 2050 2060 2070 0.85 0.9 0.95 1 1.05 1.1 1.15 Output per capita 2010 2020 2030 2040 2050 2060 2070 20 25 30 35 40 Wage tax (%) 2010 2020 2030 2040 2050 2060 2070 0.9 0.95 1 1.05 1.1 Average work hours

Solid lines represent the closed economy and dotted lines represent open economy.

Tokyo, June 28, 2007 – p. 5

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SLIDE 63

Robustness analysis: endogenous labor supply

little effect on equilibrium what matters is the wage net of taxes – the effects of higher wage and higher labor income tax offset each other labor supply increase only in the open economy towards 2100, when the payroll tax levels off and wage keeps rising

Tokyo, June 28, 2007 – p. 6

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SLIDE 64

Robustness analysis: TFP growth

Benchmark

TFP growth in the North higher than in the South during 1950-2000 the South catches up during 2000-2050 GDP per capita of the South 1/7 of the North to 1/5

Experiments

  • 1. TFP of the South converge to the level of the North in 2000

almost no effect

  • 2. the South grows to fully catch up with the North in terms of per-capita
  • utput, i.e. it grows much faster than in the benchmark

no significant effect on experiment results with faster growth of labor productivity, interest rates are higher in the South the South is larger and open economy interest rates are closer to South

Tokyo, June 28, 2007 – p. 7

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SLIDE 65

Robustness analysis: risk aversion

benchmark θ = 2 experiments θ = 1.5 and 2.5 higher θ implies lower IES

⇒ more saving and output, slightly lower interest rate and

higher wage. no significant effect on the policy variables.

Tokyo, June 28, 2007 – p. 8

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SLIDE 66

Robustness analysis: role of China and India

Fehr, Jokisch and Kotlikoff (2005) allowing for the capital flow between the US and China, the US wage 8% higher in 2100 Experiment: open economy with and without China and India capital flow to the North halved and wages lower by 6% in 2070

Tokyo, June 28, 2007 – p. 9

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SLIDE 67

Robustness analysis: role of China and India

2010 2020 2030 2040 2050 2060 2070 1 1.1 1.2 Wage rate 2010 2020 2030 2040 2050 2060 2070 2 4 6 8 Interest rate (%) 2010 2020 2030 2040 2050 2060 2070 1 1.2 1.4 1.6 1.8 Capital per capita 2010 2020 2030 2040 2050 2060 2070 0.95 0.975 1 1.025 1.05 Output per capita 2010 2020 2030 2040 2050 2060 2070 25 30 35 40 Wage tax (%) 2010 2020 2030 2040 2050 2060 2070 −6 −4 −2 2 Current account (% of GDP)

Solid lines represent the open economy without China and India.

Tokyo, June 28, 2007 – p. 10

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SLIDE 68

Robustness analysis: frictional capital markets

transaction cost as a function of the external wealth, reducing the return to the capital invested by the North in the South

χ (Nt) = ¯ χN0.5

t

if Nt > 0, if Nt ≤ 0. calibrate ¯

χ so that we match the fraction of external wealth in

the South as in Kraay, et al (2004) interest rate in the South is higher in the open economy no effect on the results after the capital flow reverses

Tokyo, June 28, 2007 – p. 11

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SLIDE 69

Robustness analysis: frictional capital markets

2010 2020 2030 2040 2050 2060 2070 1 1.05 1.1 1.15 1.2 1.25 Wage rate 2010 2020 2030 2040 2050 2060 2070 2 4 6 8 Interest rate (%) 2010 2020 2030 2040 2050 2060 2070 1 1.2 1.4 1.6 1.8 Capital per capita 2010 2020 2030 2040 2050 2060 2070 0.98 1 1.02 1.04 1.06 Output per capita 2010 2020 2030 2040 2050 2060 2070 20 25 30 35 40 Wage tax (%) 2010 2020 2030 2040 2050 2060 2070 −6 −4 −2 2 Capital flow (% of GDP)

Solid lines represent the open economy with transaction costs and dotted lines represent the economy with perfect international capital markets.

Tokyo, June 28, 2007 – p. 12

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SLIDE 70

Robustness analysis: population variants Use alternative variants of UN population projections. The low and high variants differ from the medium variants with respect to the assumption about total fertility. Medium variants (benchmark): total fertility in (almost) all countries is assumed to converge eventually toward a below-replacement level of 1.85 by 2050 and remain there for about 100 years. It will then return to the replacement level (2.1) and remain there until 2300 High variants: 0.5 (and 0.25) children above the medium variant before (and after) 2050 Low variants: 0.5 (and 0.25) children below the medium variant before (and after) 2050

Tokyo, June 28, 2007 – p. 13

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SLIDE 71

Robustness analysis: HIGH variants

2010 2020 2030 2040 2050 2060 2070 1 1.05 1.1 1.15 1.2 1.25 1.3 Wage rate 2010 2020 2030 2040 2050 2060 2070 2 4 6 8 Interest rate (%) 2010 2020 2030 2040 2050 2060 2070 0.75 1 1.25 1.5 1.75 2 2.25 2.5 Capital per capita 2010 2020 2030 2040 2050 2060 2070 0.85 0.9 0.95 1 1.05 1.1 1.15 Output per capita 2010 2020 2030 2040 2050 2060 2070 25 30 35 40 Wage tax (%) 2010 2020 2030 2040 2050 2060 2070 −6 −4 −2 2 Current account (% of GDP)

Tokyo, June 28, 2007 – p. 14

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SLIDE 72

Robustness analysis: LOW variants

2010 2020 2030 2040 2050 2060 2070 1 1.05 1.1 1.15 1.2 1.25 1.3 Wage rate 2010 2020 2030 2040 2050 2060 2070 2 4 6 8 Interest rate (%) 2010 2020 2030 2040 2050 2060 2070 1 1.25 1.5 1.75 2 2.25 2.5 Capital per capita 2010 2020 2030 2040 2050 2060 2070 0.85 0.9 0.95 1 1.05 1.1 1.15 Output per capita 2010 2020 2030 2040 2050 2060 2070 25 30 35 40 45 50 Wage tax (%) 2010 2020 2030 2040 2050 2060 2070 −6 −4 −2 2 Current account (% of GDP)

Tokyo, June 28, 2007 – p. 15

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SLIDE 73

Robustness analysis in the high variant, the demographic trends are not too severe rise in the wage tax is smaller qualitative effects are the same

Tokyo, June 28, 2007 – p. 16

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SLIDE 74

Robustness analysis: Capital tax in South Benchmark capital tax rate same as the North 38% too little capital and higher interest rate in the South? → more capital flow before the reversal? Experiment find τs

a so that we match the capital flow as in Kraay, et al

(2004) ⇒ 20%

Tokyo, June 28, 2007 – p. 17

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SLIDE 75

Robustness analysis: Capital tax in South = 20%

2010 2020 2030 2040 2050 2060 2070 1 1.05 1.1 1.15 1.2 1.25 1.3 Wage rate 2010 2020 2030 2040 2050 2060 2070 2 4 6 8 Interest rate (%) 2010 2020 2030 2040 2050 2060 2070 1 1.25 1.5 1.75 2 2.25 2.5 Capital per capita 2010 2020 2030 2040 2050 2060 2070 0.85 0.9 0.95 1 1.05 1.1 1.15 Output per capita 2010 2020 2030 2040 2050 2060 2070 25 30 35 40 Wage tax (%) 2010 2020 2030 2040 2050 2060 2070 −6 −4 −2 2 Current account (% of GDP)

Solid lines represent closed economy and dotted lines represent open economy.

Tokyo, June 28, 2007 – p. 18

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SLIDE 76

Robustness analysis: Capital tax in South = 20% External assets of the South (% of total wealth)

1960 1980 2000 2020 2040 2060 2080 2100 −50 −40 −30 −20 −10 10 20 30 percentage (%) Data from Kraay, et al (2004) South K tax=20% South K tax=38%

Tokyo, June 28, 2007 – p. 19