Aging and Deflation from a Fiscal Perspective
Mitsuru Katagiri, Hideki Konishi, and Kozo Ueda
Bank of Japan and Waseda Univ

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0	  1980	  1981	  1982	  1983	  1984	  1985	  1986	  1987	  1988	  1989	  1990	  1991	  1992	  1993	  1994	  1995	  1996	  1997	  1998	  1999	  2000	  2001	  2002	  2003	  2004	  2005	  2006	  2007	  2008	  2009	  2010	  2011	  2012	  Negative Correlation bw Aging and Inflation in Japan8	  25	  6	  20	  4	  15	  2	  CPI	  Aging	  10	  -­‐2	  5	  -­‐4	  0	  FTPL
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Negative Correlation bw Aging and Inflation in OECDCountries
CPI inflation rate, average of 2000-13, %20Turkey

15Correlation ―0.53 (p-value 0.001)(excluding Turkey: ―0.51)

105MexicoGermany

0Switzerland

US-5
0

10

2030

Japan
40

Old (+65) dependency ratio (20-64), average of 2000-12, %FTPL

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Motivations

We aim to analyze
the reason for the concurrent population aging and deflation andthe impact of price changes on income distribution across generations.

FTPL

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What We Do
We extend the standard fiscal theory of the price level (FTPL).
1

We embed the FTPL into a standard overlapping generation (OLG)
modelI2

to examine political and economic impacts of demographic changes.

We consider endogenous policy making.
Succession of short-lived governments choose income tax rates andbond issues.
I Politico-economic perspective

IF

Governments are under the political influence of existing generations,taking into account the general equilibrium effects on the price level
and the real interest rate as well as the expected strategic responses offuture governments.

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Three Features in Constructing a Model

1

Nominal interest rates have been fixed at almost zero.
1

Passive monetary policy is the key to FTPL.

2

A part of Japanese population aging is an unexpected phenomenon.

3

Voter turnout rates for the young generation especially 20’s, 30’s, and40’s are declining and the gap between generations is widening.

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Revisions in the Japanese Total Fertility Rate Forcast
2.4(Total Fer!lity Rate)

2.2

Forecast in 1976

Replacement ra!o2

Forecast in 1986

Forecast in 1992

1.8

Forecast in 1997

1.6

Forecast in 2002

1.4

Forecast in 2012
Forecast in 2006

1.211965
Year1975

1985

1995

2005

2015

2025

2035

2045

2055

Source: Ministry of Health, Labour and Welfare; Na!onal Ins!tute of Popula!on and Social Security Research.

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Revisions in the Japanese Life Expectancy Forcast
91(Life Expectancy)

88
85

Female

82
Male

79
76

Actual Figure in 2012
Forecast in 1992

73

Forecast in 1997
Forecast in 2002

70

Forecast in 2006
Forecast in 2012

671965
Year1975

1985

1995

2005

2015

2025

2035

2045

2055

Source: Ministry of Health, Labour and Welfare; Na!onal Ins!tute of Popula!on and Social Security Research.

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Three Features in Constructing a Model

1

Nominal interest rates have been fixed at almost zero.
1

Passive monetary policy is the key to FTPL.

2

A part of Japanese population aging is an unexpected phenomenon.

3

Voter turnout rates for the young generation especially 20’s, 30’s, and40’s are declining and the gap between generations is widening.

FTPL

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Voter Turnout Rates by Age in Japan
100	  90	  80	  20's	  30's	  70	  40's	  50's	  60	  60's	  70's	  50	  40	  30	  31	  32	  33	  34	  35	  36	  37	  38	  39	  40	  41	  42	  43	  44	  45	  Note: The turnout rates by age in the Japanese lower house elections No.31–45 (from1967 to 2009) are depicted.

FTPL

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10 / 36What We Find

The accumulation of government debt does not become a burden on
future generations,Ibecause of price adjustments.

The effects of aging depend on its causes.
Aging is deflationary when caused by an increase in longevity
but inflationary when caused by a decline in birth rate.
I Numerical simulation shows that aging over the past 40 years in Japangenerated deflation of about 0.6 percentage points annually.

IIFTPL

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Literature Review 1
FTPL
Leeper (1991), Sims (1994), Woodford (1995), and Cochrane (2005),
among others.
I FTPL framework into an OLG model (e.g., Cushing [1999] and Braunand Nakajima [2012], Sims [2013])
I Although not dealing with the FTPL, Bullard et al. (2012) is alsosimilar to our analysis in that it focuses on income redistribution to theolder generation through deflation.

IThese studies do not endogenize political decisions on fiscal policy
variables.
To the best of our knowledge, our study is the first to analyze thepublic choice of fiscal policy variables such as income tax rates andbond issues in the FTPL framework.

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Literature Review 2
Fiscal burden
Bowen et al. (1960) and Barro (1974)
Strategic debt accumulation: Tabellini and Alesina (1990) and Persson
and Svensson (1989)
I Rohrs (2010), Song, Storesletten, and Zilibotti (2012), and Ono (2013)
incorporated national debt into a political economy framework like ours.

II

All these previous studies, however, assume that government debts are
specified in real terms and therefore adjustments in the price level do
not change the intertemporal budget constraint of the public sector.
In the FTPL framework, irrespective of the amount of nominal debt
accumulated, each government can pursue a fiscal policy in its own
interest, thanks to the adjustments in the price level.

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13 / 36ModelFTPL

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Recap: Fiscal Theory of Price Level (FTPL)
Assumptions of FTPL
Nominal debts: govt has liabilities predetermined in nominal terms.
Passive monetary policy: CB keeps a nominal interest rate constantover time.
I Active govt policy: govt is not constrained by its budget balance eqn.
I Price adjustment: Intertemporal budget is balanced only in equilibrium
through current price adjustment.

II

Today’s price level Pt is determined to balance govt’s intertemporalbudget in real terms [Leeper (’91), Woodford (’01) etc.] .
∞RBt −1= Tt − Gt + ∑Pts =t +1FTPLs∏ rk! −1(Ts − Gs )k =t +1

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15 / 36What does the Standard FTPL Predict?

Price level in Japan should rise sooner or later.
IFiscal surplus is expected to deteriorate due to aging.

The standard FTPL takes account of no political factors.
Policy choice will also respond to demographic aging throughintergenerational politics.
I Need to incorporate intergenerational politics and endogenize policy
choice into FTPL.

IFTPL

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16 / 36Model Features

Endowment economy. No physical capital.
OLG model. The economy consists of the young Nt and the oldθ t Nt − 1 .
Each individual will live at most for two periods with a survival
probability θtj . No aggregate uncertainty.
I nt = Nt /Nt −1 represents a birth rate.
I

Monetary policy is passive.
Govt remains in power only for one period.
II

Income tax only, which is imposed on the young.
Govt determines bond issues and tax rates. Expenditure is fixed.

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Household

Each young household in period t maximizes the expected utility:log cty + βθt +1 log cto+1(1)θ t +1 oc= 1 − τt ,rt +1 t +1(2)stcty +

where rt +1 ≡ Rt Pt /Pt +1 is the real interest rate a young household faces
in period t.
Behind this, we assume insurance firms faced with perfect competition.

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A young household’s utility maximization yields its demand for goods andnominal annuities as follows:
1 − τt,1 + βθt +1βrt +1 (1 − τt )cto+1 =
1 + βθt +1cty =(3)(4)

andAt =Pt βθt +1 (1 − τt ).
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Fiscal balance:
Rt −1 Bt −1 = Bt + Pt Nt τt .

(6)

Market clearing for government bonds:
Nt At = Bt .

FTPL

(7)

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Economic Equilibrium with Exogenous Fiscal
PolicyTax rates are exogeneous.

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Real Interest Rate

The fiscal balance equation together with market clearing forgovernment bonds yields the equilibrium real interest realized inperiod t + 1 :rt +11 + βθt +1 βθt +2 + τt +1=.
nt +1βθt +1 (1 − τt ) 1 + βθt +2II

(8)

rt +1 depends on τ, n, and θ.
In the model of an infinitely lived representative household, rt +1 isconstant at 1/β irrespective of the stream of tax rates.

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PriceThe fiscal balance equation together with market clearing forgovernment bonds yields the equilibrium price level in period t:
Rt −1 Bt −1 1nt (τt + βθt +1 )=.
Nt − 1Pt
1 + βθt +1(9)A higher τt and a higher θt +1 deflate Pt , but a lower nt inflates it.

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Indirect Utility

vty = (1 + βθt +1 ) log(1 − τt ) + βθt +1 log rt +1β+ βθt +1 log
1 + βθt +1vto = log

Rt −1 Bt −1θt Nt −1 PtFTPL(10)(11)

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Politico-Economic Equilibrium
Tax rates are endogenous.

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Optimization Problem Facing Short-lived Governments
To endogenize government policies and characterize thepolitico-economic equilibrium, we assume that tax rates and bondissues are chosen by a succession of short-lived governments.
ISong, Storesletten, and Zilibotti (2012), among others.

Each government remains in power just for one period and chooses
policies to maximize
Wt = γt vto + vty ,(12)II

following the spirit of the probabilistic voting model,
where γt represents the political bias toward the well-being of the old,and vto and vty represent the indirect utility of the old and the young,respectively.

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The policy decisions of successive governments are usually consideredintertemporally linked by the inheritance of outstanding debts.
IStrategic debt creation pioneered by Persson and Svensson (1989) andTabellini and Alesina (1990)

In our model, the previous problem is reduced toγt log(τt + βθt +1 ) + (1 + βθt +1 ) log(1 − τt ) + βθt +1 log rt +1(13)subject to (8). bt −1 does not appear here!
This suggests that government t − 1’s decision has no influence on
government t’s policy choice.
Since the governments issue nominal bonds and are in the situation of
fiscal dominance, the price level adjusts to eliminate the linkage andeach government can pursue its own optimal policy irrespective of
how much nominal debt it inherits from its predecessor.

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Markov Perfect Equilibrium
Assumeγt =ωθt,nt(14)and θt = θt +1 = θ and nt = nt +1 = n. Then, we haveτt = 1 −1 + βθ
1 + ωθ/n(15)ωrt + 1 =βRt −1 Bt −1
11Pt =+.
Nt − 1ωθ nFTPL

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(16)
(17)

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ResultsTax (τt )Bond (bt )Price (Pt )Real interest rate (rt +1 )ωt ↑+––+nt ↓+–+0θt ↑++–0

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The price level response to demographic aging depends on its causes.
If the birth rate declines, a contraction in the tax base will reduce thefiscal surplus and the government will be induced to generate inflationin order to maintain solvency at the cost of the older generation’swell-being and impose higher taxes on the younger generation tomitigate the extent of inflation, based on the strengthened politicalinfluence of the older generation.
In contrast, in case of an unexpected increase in life expectancy andthe old survive longer than expected, the government will be inclined
to favor them because of their shortage in savings for their retirement
period and their strengthened political power relative to the youngergeneration. In such a situation, the government will opt to suppress
inflation and support the older generation’s well-being with deflation.

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Quantitative Investigations Using a Generalized
ModelFTPL

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A production economy with variable labor supply.
General utility functions and employ the constant relative risk
aversion (CRRA) class.
Two types of government expenditure, government consumption andtransfer to the older generation

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Calibration

A period consists of 40 years.
σ = 1; Frisch elasticity υ = 0.5; β = 0.9940 ; government spendingg C = g T = 0.01.
In 1976, θ = 0.482; n = 1.058; ω = 0.969.
Forecasts of the National Institute of Population and Social Security
Research (IPSS)I Voter turnout rates in the election No. 34 held in 1976.
IIn 2012, θ = 0.781; n = 0.629; ω = 1.230.

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Note: The blue lines with circles represent the tax rate τ (left axis) and the green lines
the annualized real interest rate r (right axis).

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Note: t = 0 corresponds to 1974. At t = 1, unexpected demographic and politicalchanges occur, which corresponds to the year 2012. From t = 2 onward, demographicand political parameters are unchanged. The inflation rate at t = 0 is set 0.
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Cocluding Remarks: Future Work

Our study represents a first step toward embedding the FTPL in apolitico-economic framework.
Two main challenges.
Address Japan’s accumulation of government bonds over the past 40years. Our finding that aging improves fiscal balances by increasing thetax rate imposed on the young seems questionable in reality.
I Introduce foreign investors buying government bonds into the model. It
is well known that around 90% of Japanese government bonds are heldby domestic investors.

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