Aging and Deflation: A Politico-Economic Perspective Ippei Fujiwara Shunsuke Hori DSGE conference @ Matsuyama

Dec 17, 2016

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Brief Summary ▶

▶

▶

Question: ▶

What is optimal inflation rate in NK OLG model?

▶

Is low inflation a consequence of gray democracy?

Method: ▶

Construct an OLG model with price stickiness

▶

Find optimal inflation rate

▶

Socially optimal inflation rate with varying weighting

Results: ▶

Non-zero optimal inflation rate

▶

Not population composition, but life expectancy

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Introduction

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Declining inflation rate/deflation in Japan Change in GDP deflator in Japan 6 5 4 3

Inflation rate

▶

2 1 0 −1 −2 −3 1980

1985

1990

1995

2000

2005

2010

2015

Year

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Is it optimal? Consequence of optimal policy? ▶

Gray democracy: older people prefer low inflation? 110 100 90

Population (million)

▶

80 70 60 50 40

Total Population Worker’s Population Retiree’s Population

30 20 10 1985

1990

1995

2000

2005

2010

year 5 / 37

Another perspective of societal aging ▶

Longer life expectancy at age 20 65

Life Expectancy at age 20

64 63 62 61 60 59 58 1985

1990

1995

2000

2005

2010

2015

year

▶

Affect decision making of HHs

▶

Which effect explains low inflation/deflation? 6 / 37

Literature review

▶

Aging and monetary policy ▶

Fujiwara and Teranishi [2008], Imam [2015], Wong [2015]

▶

Optimal inflation rate in OLG model ▶

Bullard et al. [2012], Oda [2016]

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The model

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Model overview ▶

Based on Gertler [1999] ▶ ▶ ▶

Extension of Blanchard–Yaari OLG model “Worker → retiree” with common prob. “Retiree → die” with common prob. ▶

▶

Epstein–Zin preference ▶ ▶

▶

Labor productivity: retiree
Add price stickiness a´ la Rotemberg

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UMP for retiree: set up

▶

Objective function (ρ = r Vj,k ,t =

▶

[{(

r Cj,k,t

)v (

σ−1 ) σ

1 − Lrj,k ,t

)1−v }ρ

{ r }ρ ] ρ1 + βγ Vj,k . ,t+1

Budget constraint FArj,k,t Rt−1 FArj,k ,t−1 Wt r r = + ξLj,k ,t − Cj,k,t + Dtr . Pt γ Pt Pt

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UMP for retiree: solution ▶

Labor supply Lrj,k,t = 1 −

▶

Consumption function

1 − v Pt r C . v ξWt j,k ,t

[(

) ] Rt FArj,k,t r = ϵj,k ,t θj,k,t + Hj,k,t . γ Pt Present value of human wealth Wt r Γ γπt+1 r r Dj,t + Hj,k,t ξLj,k,t + H = . Pt 1+Γ Rt+1 j,k,,t+1 MPC for retiree r Cj,k,t

▶

▶

(ϵj,k,t θj,k,t )ρ−1 = βγ (ϵj,k,t+1 θj,k,t+1 (1 − ϵj,k,t θj,k,t ))ρ−1 ( )ρ(1−v ) ( )ρ Wt Rt × . Wt+1 γπt+1

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UMP for retiree: solution

▶

Value function for retiree [ − ρ1

r Vj,k ,t = (ϵj,k,t θj,k,t )

r Cj,k,t

(

1 − v Pt v ξWt

)1−v ] .

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UMP for worker: set up ▶

Objective function (ρ =  Vj,tw

▶

 =

{(

w Cj,t

σ−1 ) σ

)v (

1 − Lwj,t

)1−v }ρ

 ρ1

 }ρ  . { w r +β ωVj,t+1 + (1 − ω) Vj,t+1

Constraint FAwj,t FAwj,t−1 Wt w w w . + Dj,t = Rt + L − Cj,t Pt Pt Pt j,t

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UMP for worker: solution ▶

Labor supply Lwj,t = 1 −

1 − v Pt w C . v Wt j,t

▶

Consumption function [ ] FAwj,t w w w Cj,t = θj,t Rt + Hj,t + PDj,t . Pt

▶

Present value of human wealth Wt w 1 Lj,t + Dj,t Pt 1+Γ ( )1−v w r ρ−1 πt+1 Hj,t+1 1 πt+1 Hj,t+1 ρ +ω +(1 − ω) (ϵj,t+1 ) . Rt Ωt+1 ξ Rt Ωt+1 w = Hj,t

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UMP for worker: solution ▶

MPC for worker [ θj,t = 1− βRtρ (πt+1 )−ρ Ωρt+1

▶

Wt+1 Pt Pt Wt

1 )ρ(v −1) ] 1−ρ

θj,t θj,t+1

.

Value function for worker Vj,tw

▶

(

− ρ1

= (θj,t )

( w Cj,t

1 − v Pt v Wt

)1−v .

where Ωt+1 = ω + (1 − ω) (ϵt+1 )

ρ−1 ρ

( )1−v 1 . ξ 15 / 37

Firms: production

▶

Final goods production function: κ [´ ] κ−1 κ−1 1 κ . Yt = 0 (Yi,t ) di

▶

Intermediate good production function: α . Yi,t = (exp (Zt ) Li,t )1−α Ki,t−1 Wt Pt

α = (1 − α) ψt (exp (Zt ))1−α (Li,t )−α Ki,t−1 .

▶

Real wage:

▶

α−1 Capital rental rate: rtK = αψt (exp (Zt ) Li,t )1−α Ki,t−1 .

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Firms: price determination

▶

F Firm’s profit: Di,t =

▶

NKPC

Pi,t Yi,t Pt

− ψt Yi,t −

ϕ 2

(

Pi,t Pi,t−1

−1

)2 Yt .

(−κ + 1) Yt + ψt κYt − ϕ (πt − 1) Yt πt m0,t+1 + Et ϕ (πt+1 − 1) πt+1 Yt+1 = 0. m0,t ▶

Set τ =

1 : κ−1

eliminate distortion

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Investment funds: set up

▶

Profit: ΠKt =

▶

FAt FAt−1 K − Rt−1 + rt−1 Kt−1 − It . Pt Pt

Capital law of motion [ Kt = (1 − δ) Kt−1 + 1 − S

(

It It−1

)] It .

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Investment funds: solution ▶

FOC w.r.t. capital Qt =

] m0,t+1 [ Qt+1 (1 − δ) + rtK . m0,t

▶

FOC w.r.t. investment [ ( ) ) ] ( It It It ′ Qt 1 − S −S It−1 It−1 It−1 ( )( )2 m0,t+1 It+1 It+1 ′ + Qt+1 S = 1. m0,t It It

▶

FOC w.r.t. financial asset Rt m0,t = . m0,t+1 πt+1 19 / 37

Set up: Population ▶

Population dynamics w Nt+1 = ωNtw + (1 − ω) Ntw , r Nt+1 = γNtr + (1 − ω) Ntw .

▶

Stationary population N w = 1 and N r =

▶

1−ω ≡ Γ. 1−γ

Assumption about bequest: ▶

equal distribution to retirees

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Aggregation ▶

Retiree

1 − v Pt r Lrt = Γ − C. v ξWt t [ ] FArt r r r Ct = ϵt θt Rt + Ht + PDt . Pt [ ( )1−v ] 1 1 − v P t − Vtr = (ϵt θt ) ρ Ctr . v ξWt Htr =

Wt r Γ γπt+1 r ξLt + Dt + H . Pt 1+Γ Rt+1 t+1

FAr FArt Wt r Γ = Rt−1 t−1 + ξLt − Ctr + Dt Pt Pt Pt 1+Γ ( ) FAwt−1 Wt w 1 w + L − Ct + + (1 − ω) Rt Dt . Pt Pt t 1+Γ 21 / 37

Aggregation ▶

Worker

1 − v Pt w C . v Wt t ( )1−v 1 − v Pt − ρ1 w w Vt = (θt ) Ct . v Wt [ ] FAwt w w w Ct = θt Rt + Ht + PDt . Pt Lwt = 1 −

Htw =

w Wt w πt+1 Ht+1 Lt + ω Pt Rt Ωt+1

+ (1 − ω) (ϵt+1 )

ρ−1 ρ

( )1−v r 1 πt+1 Ht+1 , ξ Rt Ωt+1 22 / 37

Aggregation ▶

Aggregate profit Dt = DtF + ΠKt .

▶

Financial market FAwt + FArt = Qt Kt , Pt

▶

Goods Yt = Ctr + Ctw + It +

▶

ϕ (πt − 1)2 Yt . 2

Labor Lt = Lwt + ξLrt . 23 / 37

Benchmark calibration Parameters

Values

ω

transition probability to retiree

0.995

γ

survival rate (1 − γ)

0.9833

β

discount factor

1.04− 4

σ

IES

0.25

ρ

Curvature of Epstein-Zin preference

σ−1 σ

v

weight on consumption

0.4

ξ

relative productivity of retiree

0.6

α

capital share

0.333

κ

elasticity of substitution

10

1

= −3

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Benchmark calibration

ϕ

Rotemberg cost parameter

50

δ

capital depreciation rate

1.01− 4 − 1

s

investment adjustment cost parameter

2.48

ρz

persistency of technology shock

0.9

σz

standard deviation of technology shock 10−5

1

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Optimal inflation rate: comparative statics

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Optimal inflation rate Life expectancy and optimal inflation rate 1 Optimal for W Optimal for R

0.8

Optimal inflation rate

▶

0.6 0.4 0.2 0 −0.2 −0.4 5

10

15

20

25

Life expectancy for retiree

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Intuition ▶

Workers ▶

Avoid overaccumulation ▶

▶

−→ High MPC & Low saving

High π −→ High w and H

Retirees ▶

Want worker to save more ▶

▶

High π −→ Low

R π

−→ Low MPC & High saving

Prefer high real interest ▶

▶

R π

Prefer high wage rate ▶

▶

Low π −→ High

Low π −→ High

R π

Longer retirement life ▶

More saving ▶

stronger instrument

▶

more weight on capital income 28 / 37

Support intuition ▶

EIS=0.25 (left) and EIS=0.5 (right) 1.5

1.5 Optimal for W Optimal for R

Optimal for W Optimal for R 1

Optimal inflation rate

Optimal inflation rate

1

0.5

0

−0.5

−1 5

0

−0.5

10

15

Life expectancy for retiree

▶

0.5

20

25

−1 5

10

15

20

25

Life expectancy for retiree

Larger EIS −→ less sensitive to interest change −→ stronger instrument for saving motive

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Optimal inflation rate ▶

Working period and optimal inflation rate 1 Optimal for W Optimal for R

Optimal inflation rate

0.8 0.6 0.4 0.2 0 −0.2 −0.4 35

40

45

50

55

Expected working period

▶

Longer working life −→ less worry about retiree life −→ less saving motive 30 / 37

Analyses with Japanese data

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Demographic change in Japan ▶

Two types of changes 1. Population composition 2. Life expectancy

▶

Evaluation 1. Fix ω and γ, Use population weight 2. Fix weight, Use life expectancy data for ω and γ ▶

▶

Use population weight and life expectancy data

(Inconsistent with theory)

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Data 0.8

24

42

22

40

Weight on worker

0.76 0.74 0.72 0.7 0.68 0.66

Expected Working Year

Life Expectancy at Retirement

0.78

0.64 0.62 1985

1990

1995

2000

2005

2010

20 1985

1990

1995

year

1. Fix

1 1−γ

= 22 and

1 1−ω

2000 year

2005

2010

38 2015

= 40,

weight by population data (left panel) 2. Fix weight by W:R=0.72:0.28 (composition in 2000), use life expectancy data for γ and ω (right panel)

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Result 1. Using population weight... 0.04

Optimal inflation rate

0.02 0 −0.02 −0.04 −0.06 −0.08 −0.1 −0.12 1985

1990

1995

2000

2005

2010

2005

2010

year

2. Using life expectancy data... Optimal (annual) inflation rate

−0.065

−0.07

−0.075

−0.08

−0.085

−0.09

−0.095 1985

1990

1995

2000

Year

34 / 37

Result

Using population weight and life expectancy data... 0.04 0.02

Optimal (annual) inflation rate

▶

0 −0.02 −0.04 −0.06 −0.08 −0.1 1985

1990

1995

2000

2005

2010

Year

35 / 37

Conclusion

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Conclusion

▶

Non-zero optimal inflation rate

▶

Not population composition, but Life expectancy explains deflation as optimal

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