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The Neo-Fisher Effect: Econometric Evidence fromEmpirical and Optimizing Models
Martin Uribe
NBER Working Paper, 2018
April 23, 2019
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Introduction
What is the effect of interest rate increase on inflation?
Fisher equation is built in most of modern dynamic macroeconomicmodels
it = rt + Etπt+1
Depending on time horizon and type of increase, response of inflationvaries
Short RunEffect on π
Long RunEffect on π
Transitory increase in i ↓ 0
Permanent increase in i ↑ ↑
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Introduction
The paper estimates an empirical and a New-Keynesian model drivenby temporary and permanent monetary and real shocks by using USpostwar data.
Results:
Dynamics of empirical and New-Keynesian model are similar.Permanent monetary shocks are main drivers of inflation fluctuationswhile temporary monetary shocks play a moderate role.Permanent increase in nominal interest rate generates an increase ininflation in the short run (less than a year) with no output loss.Response of output and inflation to temporary monetary policy shocksare in line with conventional wisdom.
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Evidence on Fisher Effect
Evaluating Fisher equation on average and assuming that on averageexpected inflation equals to actual inflation
i = r + π
Furthermore assuming that the average real interest rate isdetermined solely by real factors, we expect one-to-one relationshipbetween inflation and nominal interest rate.
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Evidence on Fisher Effect
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Evidence on Fisher Effect
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Empirical Model
Model aims to capture dynamics of the logarithm of real output percapita, yt , the inflation rate, πt , and the nominal interest rate, it .
yt , πt , and it are driven by four exogenous shocks:
1) a nonstationary (or permanent) monetary shock Xmt
2) a stationary (or temporary) monetary shock zmt3) a nonstationary nonmonetary shock X n
t4) a stationary nonmonetary shock znt
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Empirical Model
ytπt
it
=L
∑i=1
Bi
yt−iπt−iit−i
+ C
∆Xm
t
zmt∆X n
t
znt
where yt
πt
it
≡ yt − X n
t
πt − Xmt
it − Xmt
and
4Xm
t
4X nt
zmtznt
= ρ
4Xm
t−1
4X nt−1
zmt−1
znt−1
+ Γ
ε1t
ε2t
ε3t
ε4t
yt is detrended output per capita, it and πt are cyclical components of thenominal interest rate and inflation. ρ and Γ are 4× 4 diagonal matrices.εit are i.i.d disturbances N(0, 1).
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Empirical ModelIdentification Restrictions
Output, yt is cointegrated with permanent nonmonetary shock, X nt .
Inflation, πt is cointegrated with permanent monetary shock, Xmt .
The nominal interest rate, it is cointegrated with permanentmonetary shock, Xm
t .
Nonpositive impact effect of transitory increase in the nominalinterest rate on inflation: C22 ≤ 0
Nonpositive impact effect of transitory increase in the nominalinterest rate on output: C12 ≤ 0
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Empirical ModelPriors
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Empirical ModelImpulse Response Functions
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Empirical ModelResponse of Real Interest Rate
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Empirical ModelInflation and Permanent Monetary Shock
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Empirical ModelVariance Decomposition
∆yt ∆πt ∆itPermanent Monetary Shock, ∆Xm
t 9.1 44.6 21.9
Transitory Monetary Shock, zmt 2.1 6.2 10.9
Permanent Nonmonetary Shock, ∆X nt 49.8 27.9 13.5
Transitory Nonmonetary Shock, znt 39.1 21.4 53.7
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A New Keynesian ModelHouseholds
maxE0
∞
∑t=0
βteξt
[(
Ct − δCt−1
) (1− eθtht
)χ]1−σ
− 1
1− σ
subject to ∫ 1
0 PitCitdi +Bt+1
1+It+ Tt = Bt +W n
t ht + Φt
Ct =[∫ 1
0 C1−1/ηit di
] 11−1/η
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A New Keynesian ModelFirms
maxE0
∞
∑t=0
qt
[Pit
PtCit −
W nt
Pthit −
φ
2X nt
(Pit
Xmt Pit−1
− 1
)2]
subject toYit ≥ Cit
Cit = Ct
(PitPt
)−η
Yit = eztX nt h
αit
where Xmt = (Xm
t )γm(Xmt )1−γm is indexation factor and Xm
t is permanentcomponent of nominal interest rate and inflation.
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A New Keynesian ModelMonetary and Fiscal Policy
Taylor type interest-rate rule
1 + It =
[A
(1 + Πt
Xmt
)απ(Yt
X nt
)αy
Xmt
]1−γI
(1 + It−1)γI ez
mt
where zmt is transitory monetary shock and Xmt is permanent
monetary shock.
Ricardian (or no government expenditure) fiscal policy
Tt +Bt+1
1 + It= Bt
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A New Keynesian ModelCalibrated Parameters
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A New Keynesian ModelEstimated Parameters
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A New Keynesian ModelInflation and Permanent Monetary Shock
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A New Keynesian ModelVariance Decomposition
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A New Keynesian ModelImpulse Response Functions
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A New Keynesian ModelResponse of Real Interest Rate
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Conclusion
Policy implication of this paper: The monetary authority keeps theinterest rate low because inflation is below target and inflation is lowbecause interest rate has been low for a long period of time. FromNeo-Fisher effect, they should increase the interest rate!
Comments on this conclusion:
Shock to nominal interest rate can be shock to inflation expectationsNominal interest rate pegging for a long period of timeIf Neo-Fisher effect exists and you don’t increase the rates, economysuffers from low growth rates with low inflation. If Neo-Fisher effectdoesn’t exist and you do increase the rates, economy suffers fromrecession.
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