the neo-fisher e ect: econometric evidence from empirical ...mkredler/readgr/salionuribe18.pdfmartin...

The Neo-Fisher Effect: Econometric Evidence fromEmpirical and Optimizing Models

Martin Uribe

NBER Working Paper, 2018

April 23, 2019

Martin Uribe The Neo-Fisher Effect April 23, 2019 1 / 24

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 ↑ ↑


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.


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.


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


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).


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


Empirical ModelPriors


Empirical ModelImpulse Response Functions


Empirical ModelResponse of Real Interest Rate


Empirical ModelInflation and Permanent Monetary Shock


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


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


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.


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


A New Keynesian ModelCalibrated Parameters


A New Keynesian ModelEstimated Parameters


A New Keynesian ModelInflation and Permanent Monetary Shock


A New Keynesian ModelVariance Decomposition


A New Keynesian ModelImpulse Response Functions


A New Keynesian ModelResponse of Real Interest Rate


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.


the neo-fisher e ect: econometric evidence from empirical ...mkredler/readgr/salionuribe18.pdfmartin...

Documents