interest and inflation rates through the lens of the...

– 5 –

sveriges riksbank economic review 2015:2

* WewouldliketothankClaesBerg,PaoloBonomolo,DavidKjellberg,HannaKöhler,EricM.Leeper,JesperLindé,MarianneSterner,DavidVestinandAndersVredinforvaluablediscussionsandsuggestions.Theopinionsexpressedinthisarticlerepresenttheauthors’personalopinionsandcannotberegardedasanexpressionoftheRiksbank’sview.

InterestandinflationratesthroughthelensofthetheoryofIrvingFisherMagnus Jonsson and andré reslow*MagnusJonssonhasaPhDinEconomicsandAndréReslowhasaMaster’sDegreeinEconomics.BothworkintheMonetaryPolicyDepartmentattheRiksbank.

The nominal interest rate and inflation are positively correlated with each other in the

short run and in the long run, in Sweden as well as in other countries. In this article, we

show that the positive correlation can be understood through Irving Fisher’s theory of the

relationship between the nominal interest rate, the inflation rate and the real interest rate.

In our analysis, the short run correlation can be explained by supply and demand shocks in

a standard macroeconomic model, where Fisher’s theory is a key factor. If we assume long

run monetary neutrality, Fisher’s theory implies that the correlation between the nominal

interest rate and inflation is positive also in the long run. Finally, we show that if the real

interest rate is equated to the GDP growth rate per capita, the long run implications of

Fisher’s theory fit the data in Sweden and several other countries. This provides empirical

support to the idea that a low policy rate over the long run could lead to low inflation, as

has been proposed by Narayana Kocherlakota, among others.

AlmostsevenyearshavepassedsincetheinvestmentbankLehmanBrothersdeclared

bankruptcyintheautumnof2008andtheglobalfinancialcrisisbrokeoutwithfullforce.The

crisisbroughtwithitthelargestfallinGDPsincetheGreatDepressionofthe1930s.Moreover,

therecoveryafterthecrisishasbeenunusuallyslowinmanycountries,seeFigure1(a).In

theeuroareaandJapan,GDPisataboutthesamelevelaswhenthecrisisbrokeout,while

inSweden,theUS,theUKandCanadathelevelisfivetotenpercenthigher.Additionally,

GDPpercapitaisatthepre-crisislevelinallthesecountries,seeFigure1(b).Swedenonlyjust

reachesthepre-crisislevelandboththeeuroareaandtheUKarebelowthatlevel.

Thecentralbanksreactedpromptlyandcutthepolicyratestonearzeropercentatthe

outsetofthefinancialcrisisinordertoavoidafurtherdeepeningofthecrisis,seeFigure2(a).

However,thepolicyrateshaveremainedattheselowlevels.InSweden,thepolicyrateis

currentlyslightlynegativeandinseveralothercountriesitisclosetozeropercent.

Inflationfellrapidlyatthebeginningofthefinancialcrisis,eventhoughitrecovered

relativelyquickly,seeFigure2(b).Forexample,inSwedeninflationwasabovetwopercent

around2011,butsincethenithasbeenfallingagainandremainedatlowlevels.Thelow

inflationratesintherecentyearsare,however,notjustaSwedishphenomenon,butare

beingexperiencedbyseveralothercountries.

– 6 –


WHyISInFLATIonnoTRISInG?

Monetarypolicyhasthusbeencharacterisedbypolicyratesnearzeropercentsincethe

beginningofthecrisis.Inaddition,severalcentralbankshavepurchasedgovernmentbonds

andadoptedotherso-calledunconventionalmeasurestomakemonetarypolicyevenmore

expansionary.Atthesametime,inflationhasbeenlowandbelowtheinflationtargetin

80

85

90

95

100

105

110

115

00 02 04 06 08 10 12 14

(a) GDP

Sweden United States Euro area Japan United Kingdom Canada

80

85

90

95

100

105

110

115

00 02 04 06 08 10 12 14

(b) GDP per capita

Figure 1. GDP and GDP per capita in Sweden, the US, the euro area, Japan, the UK and Canada Index, 2007 = 100

Sources: Eurostat, Japanese Cabinet Office, Official Statistics of Japan, Statistics Sweden, Statistics Canada, UK Office for National Statistics, US Bureau of Economic Analysis and US Census Bureau

00 02 04 06 08 10 12 14

(b) Inflation rate

-4

-2

0

2

4

6

00 02 04 06 08 10 12 14

(a) Nominal interest rate

-2

0

2

4

6

8

Sweden United States Euro area Japan United Kingdom Canada

Figure 2. Nominal interest and inflation rates in Sweden, the US, the euro area, Japan, the UK and CanadaPer cent

Note. The nominal interest rates are measured by three-month treasury bills, except in the euro area where the nominal interest rate is measured by EONIA. Inflation is measured by CPI inflation in all countries, except in the US where it is measured by PCE inflation, and the euro area where it is measured by HICP inflation. Note that the high rates of inflation in Japan in 2014 were mostly, 2 percentage points, due to temporary effects from increased taxation on consumption (the calculations in the article is adjusted for this).

Sources: ECB, Eurostat, Macrobond, OECD, Statistics Sweden and the US Bureau of Economic Analysis

– 7 –


manycountries.Whatiscausingtheselowinflationrates?Whyhasmonetarypolicy,which

hasbeenexceptionallyexpansionaryinahistoricalperspective,notledtohigherratesof

inflation?

Acommonexplanationisthatmonetarypolicyhasbeenconstrainedbythezerolower

bound,i.e.thepolicyratecannotbesubstantiallybelowzeropercent.Proponentsofthis

viewarguethatdemandisstillbelownormalandisthereforenotcreatinganyupward

pressureoninflation.Inotherwords,monetarypolicyhasnotbeenexpansionaryenough.1

Anotherexplanationthathasbeenputforwardisthatincreasingcompetition,entailed

byglobalisationanddigitalisation,hasmadeitmoredifficultforfirmstoraiseprices

withoutlosingcustomers.2

CAnLoWPoLICyRATESoVERTHELonGRUnLEADToLoWInFLATIon?

Perhapsamorechallengingexplanationisthatlowpolicyratesoverthelongruncouldlead

tolowinflation.Thismaysoundcontradictory,aspolicyratecutsaccordingtostandard

theoryshouldleadtorisinginflation.nevertheless,narayanaKocherlakota,presidentofthe

FederalReserveBankofMinneapolis,exploredthisideainaspeech2010,seeKocherlakota

(2010):

Long run monetary neutrality is an uncontroversial, simple, but nonetheless

profound proposition. In particular, it implies that if the FOMC maintains

the fed funds rate at its current level of 0-25 basis points for too long,

both anticipated and actual inflation have to become negative. Why? It’s

simple arithmetic. Let’s say that the real rate of return on safe investments

is 1 percent and we need to add an amount of anticipated inflation that will

result in a fed funds rate of 0.25 percent. The only way to get that is to add a

negative number, in this case, −0.75 percent. To sum up, over the long run, a

low fed funds rate must lead to consistent, but low, levels of deflation.

Kocherlakota’sclaimisbasedontwowell-knowneconomictheories.Thefirstisthetheory

oflongrunmonetaryneutrality,whichsaysthatachangeinthepolicyratedoesnotaffect

longrunvaluesofrealinterestratesandotherrealvariables.ThesecondisIrvingFisher’s

theoryofthelongrunrelationshipbetweenthenominalinterestrate,theinflationrate

andtherealinterestrate.3Fisher’stheoryissimpleandintuitive:inthelongrun,inflation

hastocorrespondtothedifferencebetweenthelongrunlevelsofthenominalandthe

realinterestrates.Takentogether,thesetwotheoriesimplythatalong-livedchangeinthe

nominalinterestratecorrespondstoanequalchangeininflation.

1 SeeHall(2014).2 SeeApeletal.(2014).SeealsoJonsson(2007)whoquantifiestheeffectsofincreasedcompetitiononinflationin

theRiksbank’smacroeconomicmodelRamses.3 SeeFisher(1977).

– 8 –


Centralbanksusechangesinashort-termnominalinterestrate(i.e.thepolicyrate)to

influenceinflation.4Buthowthesechangesaffectinflationdependonseveraldifferent

factors.5Kocherlakotaemphasisedthatthelengthofthechangemaybeanimportant

factor.Wethereforededicatealargepartofthearticletoexplainwhyshort-livedchanges

mayaffectinflationdifferentlythanlong-livedchanges.

oUTLInEAnDSUMMARy

Theoutlineofthearticleisasfollows:ThenextsectiondescribesIrvingFisher’stheoryof

therelationshipbetweenthenominalinterestrate,theinflationrateandtherealinterest

rate.Thissectionalsodescribestheassumptionsunderwhichtherealinterestratecanbe

equatedtotheGDPgrowthratepercapita.

Thefollowingsectionshedslightontheshortrunrelationshipbetweenthenominal

interestrateandinflation.Wefirstshowthatthecorrelationbetweenthesetwovariablesis

positiveinSwedenandothercountries.Thismayappearcontradictory,asshort-livedcuts

inthepolicyratenormallyleadtorisinginflationandincreasestofallinginflation,which

shouldimplyanegativecorrelation.However,thisfactneednotnecessarilyimplythat

thecorrelationinthedataisalsonegative.Changesinthepolicyratearegenerallynotan

importantfactorbehindthebusinesscyclefluctuations.Theseareinsteadmainlydrivenby

supplyanddemandshocks.Wethereforeconcludethissectionbyexplainingwhythese

shocksgiverisetoapositivecorrelationbetweenthenominalinterestrateandinflation.

Wethen,inthenextsection,lookatthelongrunrelationship.Alsothelongrun

correlationbetweenthenominalinterestrateandinflationispositiveinthedata.We

demonstratethatinastandardmacroeconomicmodel,whereFisher’stheoryandlong

runmonetaryneutralityarekeyassumptions,along-livedchangeinthepolicyrateleads

toanequalchangeininflation,whichexplainsthepositivecorrelationandalsoconfirms

Kocherlakota’sclaim.

Inthesubsequentsection,wemakeuseofthefactthatundercertainassumptions

therealinterestratecanbeequatedtotheGDPgrowthratepercapita.Weshowthat

theaverageinflationinSwedenandothercountriescanbeexplainedbythedifference

betweentheaveragenominalinterestrateandtheGDPgrowthratepercapita.This

suggeststhatthelongrunimplicationsofFisher’stheoryfitthedatainseveralcountries.

Furthermore,itprovidesempiricalsupporttoKocherlakota’sclaim.

Japanwasbadlyhitbyafinancialcrisisinthebeginningofthe1990s.TheJapanese

experienceinthepost-crisisperiodisofparticularinterest,sinceJapan'seconomyhas

beencharacterisedbylownominalinterestratesandinflation.Weshowthattheaverage

4 Thetermsnominalinterestrateandpolicyrateareusedinterchangeablyinthearticle.Intheempiricalanalysis,thenominalinterestrateismeasuredbytheyieldonathree-monthtreasurybill.Thedifferencebetweenthisinterestrateandthepolicyrateisnormallymarginal.

5 MiltonFriedmansaidthatmonetarypolicyworkswithlongandvariablelags,bywhichhemeantthattheeffectsoninflationofchangesinmonetarypolicytakestimeandvariesovertime,seeFriedmanandSchwartz(1963).

– 9 –


inflationinJapan,bothinthepre-crisisandpost-crisisperiods,canbeexplainedbythe

differencebetweentheaveragenominalinterestrateandtheGDPgrowthratepercapita.

Followingthis,thereisasectionthattakesamuch-debatedarticle,Bullard(2010),as

astartingpointforadiscussionoftheeffectsoflownominalinterestratesoveralonger

period.6Bullard’sarticleexplainswhyFisher’stheorytogetherwiththezerolowerbound

mayimplyasteadystatecharacterisedbynear-zeronominalinterestratesandlowor

negativeinflation.7ThedatasuggestthatitisstilltooearlytodeterminewhetherSweden

andothercountrieshavemovedintosuchasteadystatefollowingthefinancialcrisis.Seven

yearsofdataisnotenoughtodeterminethis.ontheotherhand,itappearsasifJapan,

followingthefinancialcrisisatthebeginningofthe1990s,hasmovedintoasteadystateof

lowinflation.Finally,wemakesomeconcludingremarks.

Therelationshipbetweenthenominalinterestrate,theinflationrateandtherealinterestrateaccordingtoIrvingFisher

IrvingFisher’stheoryoftherelationshipbetweenthenominalinterestrate,theinflation

rateandtherealinterestrate,theso-calledFisherrelation,isfundamentalinmonetary

theory.Thisrelationisalsoakeyfeatureinthemicro-foundedmacroeconomicmodelsthat

centralbanksuseintheirforecastingandpolicywork.TheRiksbank’smodelRamsesisan

exampleofsuchamodel.8

TheFisherrelationisformallyanarbitrageconditionbetweenarealandanominalasset

andcanbewritteninthefollowingway,

(1) 1 + Rt = (1 + Etπt + 1)(1 + rt),

whereR denotesthenominalinterestrate,π inflation,E expectations(Etπt + 1thusdenotes

expectedinflationintimet + 1thatanagenthasattimet),andr therealinterestrate.

AmathematicalderivationoftheFisherrelationcanbefoundinseveraltextbooks,see

forexampleWalsh(2003).Hereweexplaintheintuitionbehindtherelationthrougha

verbalreasoning.Supposethatwehavearealassetthatcostsoneappleinperiodt and

thatgivesthereturnof(1 + rt) applesoneperiodlater.Innominalterms,therealasset

costsPtinperiodt andPt + 1inthenextperiod.Thenominalpriceoftherealassetin

periodt + 1isthus(1 + rt)Pt + 1andthenominalreturnwillbe((1 + rt)Pt + 1 – Pt) / Pt.In

ordertoavoidarbitrageopportunities,thereturnontherealassetmustbeashighasona

nominalasset,Rt,i.e.Rt = ((1 + rt)Pt + 1 – Pt) / Pt.Thisexpressioncanbere-writteninterms

ofinflationrates,1 + Rt = (1 + πt + 1)(1 + rt). Ifwealsotakeintoaccountthatthefutureprice

levelisunknown,wegetequation(1).

6 SeeBullard(2010).7 Bullard’sarticlebuildsoninsightsfromBenhabibetal.(2001).8 SeeChristianoetal.(2011).

– 10 –


Forsmallvaluesoftheinflationandrealinterestrates,equation(1)canbeapproximated

withthefollowingexpression,

(2) Rt = Etπt + 1 + rt.

Equation(2)isthe”shortrun”Fisherrelation,sinceitisvalidateachpointintimet .In

macroeconomicmodels,atimeperiodisusuallyaquarter.TheFisherrelationisalsovalidin

thelongrun,i.e.insteadystate,whereitiswrittenas,

(3) R‾ = π‾ + r‾ ,

whereabarindicatesthatitisalongrun(steadystate)valueofavariable.Longrunvalues

areusuallycalculatedastheaverageoveralongerperiod,usuallytenyearsormore.

THEREALInTERESTRATECAnBEEqUATEDToTHEGDPGRoWTHRATEPERCAPITAUnDER

CERTAInASSUMPTIonS

Thefollowingfactorscanbeshowntodeterminethelongrunrealinterestrateunder

certainassumptionsonthehouseholds’preferencesandthefirms’production

technologies,9

(4) 1 + r = 1β

(1 + γ )σ,

whereβ denotesthehouseholds’discountfactor,γ the(real)GDPgrowthratepercapita

(workingagepopulation)and1 / σthehouseholds’intertemporalelasticityofsubstitution.

Equation(4)showsthatthelongrunrealinterestratedependsontwofundamentalfactors.

Thefirstishowhouseholdsvalueconsumptiontodayversusconsumptiontomorrow,β,and

thesecondistheGDPgrowthratepercapita,γ .10

Explainingwhytherealinterestratedependsonβ isbestdonethroughanexample.

Assumethathouseholdsareimpatient,i.e.,theypreferconsumingtodayasopposedto

consumingtomorrow.Ifhouseholdsaretovalueconsumptiontomorrowashighlyas

consumptiontoday,theymustbecompensatedfordeferringtheirconsumption.11Thatisto

say,iftheysaveandpostponesomeoftoday’sconsumptionuntiltomorrow,theremustbe

apositiverealinterestrateonthissaving.

Inaddition,therealinterestratedependsonthegrowthrate.Themarginalutility

ofconsumptionisnormallydiminishing,i.e.asmallincreaseofconsumptionincreases

households’utilitybutatadiminishingrate.or,toputitdifferently,theutilityofeleven

applesisgreaterthanthatoften,butthemarginalutilityoftheeleventhappleisless

thanthatofthetenth.Inagrowingeconomy,theconsumptionleveltodayislowerthan

9 SeeJonsson(2002).10 ”TheGDPgrowthratepercapita”willhereafterbecalled”thegrowthrate”.11 Utilitymaximisationimpliesthathouseholdsareindifferentaboutconsumingtodayortomorrow.

– 11 –


futurelevels,whichimpliesthatthemarginalutilityofconsumingtodayisgreaterthanthe

marginalutilityofconsuminginthefuture.Therealinterestratemustthereforebepositive

ifhouseholdsaretobeindifferentbetweenconsumingtodayandinthefuture.Howhigh

theinterestratehastobedependsontheintertemporalelasticityofsubstitutionofthe

households.Ifthewillingnessofsubstitutingconsumptionbetweenperiodsisrelativelylow,

i.e.ifσisrelativelyhigh,therealinterestrateneedstoberelativelyhigh.

notethataccordingtoequation(4),ifβ = σ = 1therealinterestrateequalsthegrowth

rate.Ifβ = 1thentoday’sgenerationwillvalueitsownconsumptionashighlyasfuture

generations’consumption,whichcouldbeareasonableassumptionfromtheperspective

ofjustice.Itmaybemoredifficulttojustifyacertainvalueforσ.Ithasalsoprovedtobe

difficulttoestimatethisparameterwithanycertainty.However,acommonvalueforthis

parameterinmanymacroeconomicmodelsis1,which,forexample,isthecaseinthe

Riksbank’smacroeconomicmodelRamses.Ifweassumethatβ = σ = 1thelongrunFisher

relationcanbedefinedasfollows,

(5) R‾ = π‾ + γ.

Thenominalinterestrateandinflationarepositivelycorrelatedintheshortrun

ThenominalinterestrateintheFisherrelationshouldaccordingtotheorybemeasuredby

ashort-termrisk-freenominalinterestrate.Giventhat,weusetheyieldonathree-month

treasurybillasameasureofthenominalinterestrateinSweden,theUS,Japan,theUKand

Canada.Fortheeuroarea,wheretherearenotreasurybillsissuedjointlybythemember

states,weuseEonIA(EuroovernightIndexAverage),whichisareferencerateforloans

betweenbankswithamaturityofonebankingday.Regardinginflation,thereareseveral

differentmeasurestochoosefrom.Althoughthereisnoindisputablemeasure,whichis

reflectedinthatcentralbanksusuallyreportseveralmeasuresintheirreports.Wefollow

thispracticeandreporttwomeasures.Thefirstisinflationaccordingtotheconsumerprice

index,i.e.CPIinflation.12Thesecondisameasureofso-calledcoreinflation.13

Figure3showsthecorrelationbetweenthenominalinterestrateandinflationinsix

countries:Sweden,theUS,theeuroarea,Japan,theUKandCanada.Thetimeperiodis

1961-2014forallcountries,excepttheeuroarea,whereitis1999-2014.Ascanbeseen,

thecorrelationispositivethroughout.ItisstrongestinJapan,withacorrelationcoefficient

of0.80,andweakestintheeuroarea,wherethecorrelationcoefficientis0.48.

12 However,fortheUS,weusePCEinflation(theconsumptiondeflator),whichisthepreferredmeasurebytheFederalReserve.

13 CoreinflationismeasuredbyCPIexcludingfoodandenergy,exceptinSweden,whereitismeasuredbyCPIFexcludingfoodandenergy,theUS,whereitismeasuredbyPCEinflationexcludingfoodandenergy,andtheeuroarea,whereitismeasuredbyHICPexcludingfood,energy,alcoholandtobacco.notethatmeasuresofcoreinflationarenotavailableforthe1960sand1970s.

– 12 –


MonETARyPoLICySHoCKSRESULTInAnEGATIVECoRRELATIonBETWEEnTHE

noMInALInTERESTRATEAnDInFLATIon

Thepositivecorrelationbetweenthenominalinterestrateandinflationmayappear

contradictoryatfirstglance.Policyratecutsnormallyleadtorisinginflation,whileincreases

leadtofallinginflation,whichshouldimplyanegativecorrelation.However,thisdoesnot

necessarilyimplythatthecorrelationindataalsohastobenegative.Wecanexplainwhy

thisisthecasewiththehelpofasimplemacroeconomicmodel,inwhichtheFisherrelation

isakeyfeature.14

Thecentralbankfollowsasimple,linearruleàlaTaylor(1993)withthefollowing

parameterisation,15

(6) Rt = 0.8 Rt – 1 + (1 – 0.8) [R‾ + 1.5 (πt – π‾ ) + 0.1 (yt – y‾ )] + εt ,

whereRdenotesthepolicyrate,R‾ thepolicyrate’slongrunlevel,π inflation,π‾ inflation’s

longrunlevel(i.e.theinflationtarget),youtput,y‾ thelongrunoutputlevel,andεa

monetarypolicyshock.Thedifferences,πt – π‾andyt – y‾,arethusinflation’sdeviationfrom

theinflationtargetandtheoutputgap,respectively.

14 SeeMehandMoran(2010)andJonssonandMoran(2014)foradescriptionofthemodel.15 TheTaylorruleisasimplerecommendationforhowmonetarypolicyshouldbeconductedundernormal

circumstances.Therulehasalsobeenshowntoworkwellinmanydifferenttypesofmacroeconomicmodels,seePlosser(2008).

-2

0

2

4

6

8

10

12

14

16

-2 0 2 4 6 8 10 12 14 16

Nom

inal

inte

rest

rat

e

Inflation rate

Sweden, ρ = 0.67 United States, ρ = 0.71

Euro area, ρ = 0.48

-3

0

3

6

9

12

15

18

21

-3 0 3 6 9 12 15 18 21 24 27

Inflation rate

Japan, ρ = 0.80 United Kingdom, ρ = 0.60

Canada, ρ = 0.73

Figure 3. Correlation between the nominal interest rate and inflation in Sweden, the US, the euro area, Japan, the UK and CanadaPer cent

Note. ρ denotes the correlation coefficient. Quarterly data 1961-2014 for all countries, except the euro area, which is based on quarterly data 1999-2014. The nominal interest rates are measured by three-month treasury bills, except in the euro area where the nominal interest rate is measured by EONIA. Inflation is measured by CPI inflation in all countries, except in the US where it is measured by PCE inflation, and the euro area, where it is measured by HICP inflation.

Sources: ECB, Eurostat, Federal Reserve, Macrobond, OECD, Statistics Sweden and US Bureau of Economic Analysis

– 13 –


Businesscyclefluctuationsareduetodifferenttypesofshockshittingtheeconomy,

towhichpricesandquantitiesadjust.Thisimpliesthatthecorrelationbetweendifferent

variableswilldependontheseshocks.Hence,inordertoexplain,forexample,the

correlationbetweenthenominalinterestrateandinflationitisnecessarytoknowwhich

shocksthathavecreatedthefluctuations.

ThemonetarypolicyshockintheTaylorrulemaybeinterpretedasachangeinthe

policyratethatisduetoneitherdeviationsofinflationfromthetargetnordeviationsof

outputfromitsnormallevel.Wecanthusillustratehowshort-livedchangesinthepolicy

rateaffectinflationbyallowingmonetarypolicyshockstodrivethebusinesscycle.Figure

4(a)showsthecorrelationbetweenthenominalinterestrateandinflationinthiscase.As

expected,thecorrelationisnegativeandthecorrelationcoefficientis–0.36.

0

2

4

6

8

0 1 2 3 4

(a) Monetary policy shocks, ρ = – 0.36

Nom

inal

inte

rest

rat

e

3.5

3.8

4.1

4.4

4.7

1.4 1.7 2.0 2.3 2.6

(d) Bank capital shocks, ρ = 0.68

3.0

3.5

4.0

4.5

5.0

1.0 1.5 2.0 2.5 3.0

Nom

inal

inte

rest

rat

e

(b) Supply shocks, ρ = 0.90

0

2

4

6

8

0 1 2 3 4

Inflation rate Inflation rate

(c) Demand shocks, ρ = 0.95

Figure 4. Correlation between the nominal interest rate and inflation after monetary policy shocks, supply shocks, demand shocks and bank capital shocksPer cent

Note. ρ denotes the correlation coefficient.

Source: Own calculations

– 14 –


Animportantassumptioninthemodelisthatpricesarestickyintheshortrun,i.e.some

firmsarenotchangingtheirsellingpricesalongwithchangesindemand.Assumea

short-livedcutinthepolicyrateandthatthepricesaresostickythattheyinitiallyremain

unchanged.Thismeansthatthecut,Rt ↓,mustbematchedbyanequallylargefallinthe

realinterestrate,rt ↓,i.e.,

(7) Rt ↓= π‾ + rt ↓ ,

whereπ‾ indicatesthatinflationinitiallyremainsonthelongrunlevel.However,astime

passes,thefallingrealinterestratetendstoincreasehouseholds’consumptionandfirms’

investment.Thisboostsdemand,whichpushesupinflationwhenfirmseventuallystart

tochangetheirprices.Short-livedpolicyratecutsarethusassociatedwithrisinginflation

and,conversely,increasesareassociatedwithfallinginflation.Thisexplainsthenegative

correlationaftermonetarypolicyshocksinFigure4(a).

Buthowcanitthenbethatthenominalinterestrateandinflationarepositively

correlatedinthedatawhenmonetarypolicyshocksgiverisetoanegativecorrelation?This

issimplybecausemonetarypolicyshocksareingeneralnotanimportantcauseofbusiness

cyclefluctuations.Theseareusuallyduetoothershocks.

BUTSUPPLyAnDDEMAnDSHoCKSRESULTInAPoSITIVECoRRELATIon

Supplyanddemandshocksareoftenthemaindriversofthebusinesscycleand,hence,the

correlationsinthedata.Thesupplyshockismodelledasashocktothefirms’production

technology.Thisshockaffectstheproductionpossibilitiesofthefirmsandthereforehas

adirecteffectonthesupplyofgoodsandservices.Animprovementoftheproduction

technologymeansthatthefirms’productionpossibilitiesincrease,butitalsomeansthat

thecostofproductiondecreasesandthatthefirmscanlowertheirprices.Apositivesupply

shockthusleadstofallingprices.Thecentralbankreactstothisbycuttingthepolicyrate

tobringinflationbacktothetarget.Hence,thecorrelationbetweenthenominalinterest

rateandinflationbecomespositive.Thecorrelationcoefficientis0.90,seeFigure4(b).

Thedemandshockequalspublicconsumptioninthemodel,sincechangesinpublic

consumptionhavedirecteffectsonaggregatedemand.Anincreaseinpublicconsumption

pushesdemandupandthereforealsoincreasesinflationarypressures.Tokeepinflation

ontargetthecentralbankraisesthepolicyrate.Thisgivesrisetoapositivecorrelation

betweenthenominalinterestrateandinflation,seeFigure4(c),andacorrelation

coefficientof0.95.

Wehaveclaimedthatsupplyanddemandshocksarethemostcommonshocks,but

othershocksdoalsooccur.Thecreditcrunchassociatedwiththefinancialcrisisof2008is

anexampleofafinancialshock(aso-calledbankcapitalshock)wheretheeffectsspread

rapidlytootherpartsoftheeconomy.Thistypeofshockisunusualand,likethemonetary

policyshock,doesnotprovideanimportantexplanationofthecorrelationsindataover

– 15 –


longerperiods.nevertheless,themacroeconomicmodelshowsthatthecorrelation

betweenthenominalinterestrateandinflationispositive,asinthedata,andmeasures

0.68whenthebanks’lendingisexposedtobankcapitalshocks,seeFigure4(d).

Thenominalinterestrateandinflationarepositivelycorrelatedalsointhelongrun

Figure5showsthelongruncorrelationbetweenthenominalinterestrateandinflation

infivecountries:Sweden,theUS,Japan,theUKandCanada.Thelongrunvalueshave

beencalculatedasten-yearaverages.Thetimeperiodcovers1965to2014,meaningfive

observationsforeachcountryandatotalof25observations.Aswecansee,thecorrelation

ispositivethroughoutandthecorrelationcoefficientis0.83.

ThebluelineinthefigureshowsthetheoreticalFisherrelation,inwhichwehave

calculatedthelongrunrealinterestrateastheaveragedifferencebetweenthenominal

interestrateandinflationforallcountriesovertheentireperiod.Thisgivesavalueof

1.56percent.TheredlineshowsanestimateoftheFisherrelation.Theestimatedslope

coefficientis0.86,whichisrelativelyclosetothetheoreticalvalueof1.Also,astatistical

testdoesnotrejectthenullhypothesisthattheslopeis1.16

0

2

4

6

8

10

12

14

16

-4 -2 0 2 4 6 8 10 12 14

Nom

inal

inte

rest

rat

e

Inflation rate

ρ = 0.83 Estimated Fisher relation Theoretical Fisher relation

Figure 5. Long run correlation between the nominal interest rate and inflation in Sweden, the US, Japan, the UK and Canada, ten-year averages, 1965-2014Per cent

Note. ρ denotes the correlation coefficient. The nominal interest rates are measured by three-month treasury bills. Inflation is measured by CPI inflation in all countries, except in the US where it is measured by PCE inflation. The blue line shows R–

t =1.56 + π– t. while the red line

shows R– t = 2.16 + 0.86π–

t.

Sources: Federal Reserve, Macrobond, OECD, Statistics Sweden, US Bureau of Economic Analysis and the Riksbank

16 AnF-testwiththenullhypothesisthattheslopeisoneintheestimatedFisherrelationgivesap-valueequalto0.06(F-value=3.79,covariance=0.01anddegreesoffreedom(1,23)).

– 16 –


WecanseeinthefigurethattheestimatedFisherrelationliesrelativelyclosetothe

theoreticalrelation,butseveralisolatedpointsneverthelessliesomedistanceaway.This

canbeduetoseveralthings.Thelongrunrealinterestratemaynothavebeenthesame

inallcountriesovertheentireperiod.Itisalsolikelythatthelongrunrealinterestratehas

variedbetweentheten-yearperiodswithinthedifferentcountries.

ALonG-LIVEDPoLICyRATECUTIMPLIESTHATInFLATIonWILLBELoWERoVERTHE

LonGRUn

Wecanunderstandthelongruncorrelationbetweenthenominalinterestrateandinflation

throughtheimplicationsofthelongrunFisherrelation.Assume,likeKocherlakota,thatthe

realinterestrateisindependentofmonetarypolicyinthelongrun(monetaryneutrality)

andthatthecentralbankdeterminesthepolicyrate.Thissecondassumptionmeansthat

thecausalitybetweenthepolicyrateandinflationrunsfromthepolicyratetoinflation.

Letusassumethatthecentralbankcarriesoutalong-lived(inthisscenariopermanent)

cuttothepolicyrate,R‾ ↓,seeequation(8).Monetaryneutralityimpliesthatthereal

interestrateremainsunchangedatthelongrunlevel,r‾.Hence,thepolicyratecutonly

affectslongruninflation(i.e.theinflationtarget),whichisadjusteddownwards,π‾ ↓.Itis

adjusteddownwardsasmuchasthepolicyrateinordertoavoidarbitrageopportunities

betweennominalandrealassets.Along-livedpolicyratecutthusleadstolowerlongrun

inflationinaccordancewithKocherlakota’sclaim.Thisalsoexplainsthelongrunpositive

correlation,

(8) R‾ ↓ = π‾ ↓ + r‾.

notethedifferencetoashort-livedchangeinthepolicyrate.Aswehaveseen,inthiscase

thereisachangeintherealinterestrate,sincepricesinthemodelaresticky.Thismeans

thatthenominalinterestrateandinflation,intheshortrun,neednotnecessarilymovein

thesamedirection.

Themacroeconomicmodelcanbeusedtoillustratehowtherealinterestrateand

inflationmayadjustafteralong-livedpolicyratecut.Assumethatthelongrunlevelsofthe

policyandrealinterestratesareinitiallyfourandtwopercent,respectively.Inflationisthus

twopercent.Thecentralbankcutsthepolicyratesuccessivelytotwopercent,whereit

remains,seeFigure(6).Therealinterestrateinitiallyrisesslightly,butthenfallsbacktothe

longrunleveloftwopercent.Inflationfallssuccessivelyoverthewholeperiodtoitsnew

longrunvalue,whichaccordingtotheFisherrelationmustbezeropercent.

Anotablefeatureofthisscenarioisthatinflationsuccessivelyadjustsdownwardsto

itsnewlongrunlevel.Themainreasonforthisisthatagentsintheeconomyhavewhat

isknownasrationalexpectations.Thismeansthatthehouseholdsandthefirmsdonot

makeanysystematicerrorswhentheyformexpectationsoffuturemonetarypolicy.They

understandthatthepolicyratecutwillbelong-lived.Theyalsounderstandthatalong-

– 17 –


livedcutisassociatedwithalowerinflationrateoverthelongrun.Thefirmsthereforestart

adjustingtheirpricesdownwardsatthemomentofthepolicyratecut.

-1

0

1

2

3

4

5

0 4 8 12 16 20 24 28

Quarter

Policy rate Inflation rate Real interest rate

Figure 6. The policy rate, the inflation rate and the real interest rate after a long-lived (in this scenario permanent) cut in the policy rate with two percentage pointsPer cent

Source: Own calculations

AccordingtothelongrunFisherrelationthereisonlyonelevelofthepolicyratethat

isconsistentwithaspecificinflationtarget,giventhelongrunrealinterestrate.Ifthe

policyratedeviatesfromthislevelduringalongerperiod,thereisariskthatagentsinthe

economymayinterpretthisasachangeintheinflationtarget.Theagentsmaytherefore

haveinterpretedthelong-livedcutinthepolicyrateasanintentiontolowertheinflation

targetfromtwotozeropercentinthisscenario.Inotherwords,ifthecentralbankhasan

inflationtargetoftwopercentandthelongrunrealinterestrateistwopercent,thepolicy

ratemustonaveragebefourpercentiftheinflationtargetistobeattained.Ifthepolicy

rateinsteadaveragestwopercent,theinflationrate,aswehaveseeninFigure(6),willon

averagebetwopercentagepointslower,i.e.zeropercent.

Thisscenarioalsoillustrateswhytheleveloflongrunrealinterestrateisimportant

tothecentralbank.Itmustbeawareofthislevelinordertosetapolicyratelevelthatis

consistentwiththeinflationtarget.Inthewakeofthefinancialcrisis,LarrySummersand

othereconomistshaveadvancedathesisofsecularstagnation.17Amongotherthings,they

arguethatthelongrunleveloftherealinterestratemayhavefallen.Ifthisiscorrect,the

longrunlevelofthepolicyratemustbeadjusteddownwardsinproportiontothefallinthe

realinterestrate,otherwiseinflationwillbetoohigh.

17 SeeSummers(2014).

– 18 –


ThelongrunFisherrelationfitsthedatainSwedenandothercountries

Kocherlakota’sclaimthatlowpolicyratesoverthelongruncanleadtolowinflationrelies

onthelongrunFisherrelation.Inthissection,wecarryoutanempiricaltestofthisrelation.

Todoso,wecalculatetheinflationimpliedbythelongrunFisherrelationandcompareitto

theobservedaverageinflation.Inthesecalculationswemakeuseofthefactthatthereal

interestrateundercertainassumptionscanbeequatedtothegrowthrate,seeequation

(4).Hence,wecalculateinflationfromtheFisherrelationasthedifferencebetweenthe

averagelevelsofthenominalinterestrateandthegrowthrate.18Thisinflationrateiscalled

theFisherinflation,andisthusdefinedas,

(9) π‾ F = R‾ – γ.

TodeterminewhetherthelongrunFisherrelationfitsthedata,weshowthedifference

betweentheFisherinflationandtheobservedinflationfromdifferentcountriesinbar

chartsaswellasresultsfromastatisticaltest.notethattherealinterestrateinthis

test,whichisequatedtothegrowthrate,mayvaryfromcountrytocountry,unlikethe

calculationsinFigure5.

Totestlongrunrelationshipsthetimeperiodexaminedshouldbeaslongaspossible,at

thesametimeasthedatashouldnotdisplayanycleartrends.Itmayalsobeanadvantage

ifthemonetarypolicyregimeisthesameovertheentireperiod.Totakethisintoaccount,

wepresentresultsfromtwodifferentperiods.Thefirstlongerperiodislimitedbyaccessto

dataandstretchesfrom1961to2014.Forthisperiod,wehavedataforSweden,theUS,

Japan,theUKandCanada.

Thesecondshorterperiodis,totheextentpossible,characterisedbyastablemonetary

policyregimeandnocleartrendsinthedata.AlanGreenspanwasappointedChairmanof

theFederalReservein1987.TheperiodpriortoGreenspanwascharacterisedbybothhigh

nominalinterestratesandhighinflation.WethereforestartthesecondperiodfortheUSin

1987.FortheUK,CanadaandSweden,thesecondperiodstartsoneyearaftertheinflation

targetswereannouncedineachcountry,i.e.1992forCanada,1993fortheUKand1994

forSweden.Startingtheyearaftertheannouncementofinflationtargetingallowsusto

avoidincludingtheeffectsoftheeconomicandfinancialcrisisthathitthesecountriesat

thestartofthe1990s.Duringthe1960sand1970s,Japanunderwentatransitionfrom

relativelylowGDPlevelstolevelsinparitywiththoseofthedevelopedindustrialcountries.

TheshorterperiodforJapanthereforestartsin1981.Thisperiodalsoincludestheeuro

area.Theeurowasofficiallyintroducedon1January1999,whichiswhytheperiodstarts

in1999fortheeuroarea.

18 Hence,theempiricaltestdoesnotjustincludetheFisherrelationbutalsohowwellthelongrunrealinterestratecanbeapproximatedbythegrowthrate.Thereasonwemakethisapproximationisbecausethelongrunleveloftherealinterestrateisnotobservable.

– 19 –


ThenominalinterestrateinSwedenaveragedjustoversixpercentbetween1961

and2014,whilethegrowthratewasjustovertwopercent,seeTable1.Thismeansthat

theFisherinflationwasaroundfourpercent,whichwasonlyslightlylowerthantheCPI

inflation,seeFigure7(a).FortheshorterperiodwecanseethattheFisherinflationwasin

linewiththeobservedinflation,i.e.boththeCPIandcoreinflation,seeFigure7(b).

IntheUS,thenominalinterestrateaveragedfivepercentandthegrowthrateaveraged

almosttwopercentovertheperiod1961-2014,seeTable1.TheFisherinflationwas

thereforeabout3.2percent.Thiswasjustafewtenthsofapercentagepointlowerthan

thePCEinflation,seeFigure7(a).TheFisherinflationalsocorrespondedwellwithboththe

PCEandcoreinflationfortheshorterperiod,seeFigure7(b).

IntheUK,theFisherinflationunderestimatedtheobservedinflationslightlyforthe

longerperiod,whileitoverestimatedtheCPIandcoreinflationslightlyfortheshorter

period,seeFigures7(a)and7(b).InCanada,theFisherinflationwasinlinewiththe

observedinflationinboththeshorterandthelongerperiods,seeFigures7(a)and7(b).

TheFisherinflationintheeuroareawaslowerthanboththeCPIandthecoreinflation,

althoughitwasnotthatfarfromthecoreinflation,seeFigure7(b).nevertheless,theresult

indicatesthattheFisherrelationseemstofitsomewhatlesswellintheeuroareathanin

theothercountries.Thiscouldbeduetoanumberoffactors.Thetimeperiodisrelatively

short,15years,andalmosthalfoftheseyearshavebeencharacterisedbythefinancial

crisis.Anotherproblemcouldbethatitdoesnotexisttreasurybondsissuedjointlybythe

memberstates,i.e.theEonIAratemayhavebeenapoorapproximationofashort-term

risk-freerateinseveralofthecountriesintheeuroarea.

Table 1. The nominal interest rate and the GDP growth rate per capita in different countries and time periodsPercentandannualpercentagechangerespectively,averages

CoUnTRy PERIoD THEnoMInALInTERESTRATE THEGDPGRoWTHRATEPERCAPITA

Sweden 1961-20141994-2014

6.33.3

2.22.0

UnitedStates 1961-20141987-2014

5.03.6

1.81.5

Euroarea 1999-2014 2.2 1.2

Japan 1961-19801981-19901981-20141991-2014

8.56.12.51.0

5.43.71.70.9

UnitedKingdom 1961-20141993-2014

7.04.1

2.01.7

Canada 1961-20141992-2014

6.03.4

1.81.5

Russia 1999-2013 9.4 4.9

India 1994-2013 7.4 4.8

China 1998-2013 3.4 8.3

Sources:ECB,Eurostat,FederalReserve,JapaneseCabinetoffice,Macrobond,oECD,ReserveBankofIndia,StatisticsCanada,StatisticsSweden,theWorldBank,UKofficefornationalStatisticsandUSBureauofEconomicAnalysis

– 20 –

SVERIGESRIKSBAnKEConoMICREVIEW 2015:2

THELonGRUnFISHERRELATIonDoESnoTFITTHEDATAInJAPAnInTHE1960sAnD

1970s–AnDFoRGooDREASonS

InJapan,theFisherinflationwasalmost1.5percentagepointslowerthantheobserved

inflationfortheperiod1961-2014,seeFigure7(a).ontheotherhand,fortheshorter

period,1981-2014,theFisherinflationwasentirelyinlinewiththeobservedinflation,

measuredbyboththeCPIandcoreinflation,seeFigure7(b).

InorderforthelongrunFisherrelationtofitthedatatheeconomyneedstobeina

steadystatewithnocleartrendsinthedata.TheJapaneseeconomygrewrapidlyfollowing

theendoftheSecondWorldWar,withgrowthratesofabout10percentperyear.These

highgrowthrateslasteduntilthebeginningofthe1970s,whentheeconomysuffered

fromtheeffectsofrisingoilprices.Hence,theJapaneseeconomyinthe1960sand1970s

wasinatransitionalphase,asitmovedfromrelativelylowGDPlevelstolevelsinparity

withthoseofthedevelopedindustrialcountries.Consequently,weshouldnotexpectthe

longrunFisherrelationtofitthedataduringthisperiod.

Japanesegrowthratesinthe1960sand1970saveraged5.5percentandthenominal

interestratewasjustover8.5percent,seeTable1.ThismeansthattheFisherinflationwas

around3percent.TheCPIinflationwasaround7.5percentduringthisperiod,seeFigure

8(a).Hence,theFisherinflationunderestimatedtheCPIinflationbymorethanfourper

cent.

0

2

4

6

8

Sweden1961-2014

the US1961-2014

Japan1961-2014

the UK1961-2014

Canada1961-2014

(a)

0

1

2

3

4 (b)

Sweden1994-2014

the US1987-2014

Euro area1999-2014

Japan1981-2014

the UK1993-2014

Canada1992-2014

Figure 7. Inflation according to the Fisher relation and observed inflation in Sweden, the US, the euro area, Japan, the UK and CanadaPer cent

Note. Core inflation is measured by CPI excluding food and energy, except in Sweden, where it is measured by CPIF excluding food and energy, the United States where it is measured by PCE inflation excluding food and energy, and the euro area where it is measured by HICP excluding food, energy, alcohol and tobacco.

Sources: ECB, Eurostat, Federal Reserve, Japanese Cabinet Office, Macrobond, OECD, Statistics Sweden, Statistics Canada, the World Bank, UK Office for National Statistics, US Bureau of Economic Analysis and the Riksbank

CPI-inflation Inflation according to the Fisher relationCore inflation

– 21 –


Wecanobserveasimilarpattern,asinJapan’stransitionphase,incountriessuchasRussia,

IndiaandChina,wherethegrowthrateshavebeenhighinthelast15-20years.InRussia

andIndia,thegrowthrateshavebeenjustbelowfivepercentand,inChina,justover

eightpercent,seeTable1.Inotherwords,growthratesinparitywiththoseduringJapan’s

transitionphase.However,itisnotlikelythatthesegrowthrateswillbesustainableover

thelongrun–thoseofJapanwerenot.

Figure8(a)showsthattheFisherinflationinRussia,IndiaandChinawasclearlybelow

theobservedinflation,justastheFisherinflationwasinJapan’stransitionphase.Inline

withthetheory,thisconfirmsthatlongrunrelationsdonotapplytotransitionalphases.In

addition,andalsoinlinewiththetheory,itislikelythatthegrowthrateisapoormeasure

oftherealinterestrateintransitionalphaseswithhighgrowthrates.

ASTATISTICALTESTConFIRMSTHATTHELonGRUnFISHERRELATIonFITSTHEDATA

Byusingsimple”eyeballeconometrics”,wehaveshownthattheFisherinflationisinline

withtheobservedinflationinSwedenandseveralothercountries.Thisconclusioncanbe

confirmedbyat-testwiththenullhypothesisthattheFisherinflationcorrespondstothe

observedinflationineachcountry.TheaveragedifferencebetweentheFisherinflationand

thecoreinflationis−0.06,withap-valueof0.73,whilethedifferencebetweentheFisher

inflationandtheCPIinflationis−0.20,withap-valueof0.28,seeTable2.Forthelonger

period,1961-2014,wehaveonly4observations.Inthiscase,thedifferencebetweenthe

FisherinflationandtheCPIinflationis−0.34,withap-valueof0.17,seeTable2.

-1

0

1

2

3

4

Japan1981-1990

Japan1991-2014

Japan1961-1980

Russia1999-2013

India1994-2013

China1998-2013

-6

0

6

12

18

24 (a) (b)

Figure 8. Inflation according to the Fisher relation and observed inflation in Japan, Russia, India and ChinaPer cent

Note. Core inflation is measured by CPI excluding food and energy.

Sources: Japanese Cabinet Office, Macrobond, OECD, Reserve Bank of India and the World Bank

CPI-inflation Inflation according to the Fisher relationCore inflation

– 22 –


Table 2. Matched t-test with the null hypothesis that the Fisher inflation equals the observed inflation

MEAnVALUE T-VALUESTAnDARDDEVIATIon

DEGREESoFFREEDoM P-VALUE

ΔKPI −0.34 −1.81 0.37 3 0.17ΔKPI −0.20 −1.21 0.41 5 0.28ΔUnd −0.06 −0.36 0.37 5 0.73

note.Intheempiricaltest,ΔKPI= π‾ F – π‾ KPI andΔUnd= π‾ F – π‾ Undarecalculated.At-testismadeoftheΔ-series,whichteststhenullhypothesisthatthethreeΔ-seriescomesfromanormaldistributionwithmeanzero.Row1referstoFigure7(a),excludingJapan.Rows2and3refertoFigure7(b).

DoESTHELoWPoLICyRATEInJAPAnExPLAInTHELoWInFLATIon?

ThefinancialmarketsinJapanwitnessedwidespreadderegulationinthe1980s,which

amongotherthingsledtoasteepriseinstockandpropertyprices.Thiscametoanabrupt

endatthebeginningofthe1990swhenboththestockandpropertypricesfellinthewake

ofafinancialcrisis.Sincethen,Japan’scentralbankhasheldthepolicyrateatlowlevels,

andatthesametimetheinflationhasbeenclosetozeroornegative.Thisperiod,which

beganatthebeginningofthe1990sandwhich,inallessentials,iscontinuingtoday,is

knownasJapan’s“lostdecades”.

ItmaybeofparticularinteresttoapplytheFisherrelationtoJapan'slostdecades,since

theywerecharacterisedbybothlowpolicyratesandlowinflation.Infact,wecanshow

thattheFisherinflationisentirelyinlinewiththeobservedinflationnotonlyduringthelost

decades,butalsointheprecedingperiod.

Inthepre-crisisperiod,1981-1990,theaveragenominalinterestratewasaboutsix

percentandthegrowthratealmostfourpercent,seeTable1.ThisimpliesthattheFisher

inflationwasjustovertwopercent,whichwasinlinewiththeobservedinflation,see

Figure8(b).Duringthelostdecades,boththenominalinterestrateandthegrowthratefell

toaboutonepercent.ThisimpliesaFisherinflationaroundzeropercent,whichwasalso

theleveloftheobservedinflation,seeFigure8(b).

DoesthismeanthatthelowinflationinJapan’slostdecadeswasduetothelowpolicy

rate?ourresultsareconsistentwithsuchaconclusion,butwecannotruleoutother

explanations.19nevertheless,itisworthnotingthattheaveragegrowthrateinJapan’slost

decadeswasjustbelowonepercent,whichcanbecomparedto1.4percentintheUS

and1.3percentinCanada.Inotherwords,Japanesegrowthrateswereaboutthesame

asthoseoftheUSandCanada–unlikeitsmonetarypolicy.Thenominalinterestratein

Japanwasaboutonepercent,whileintheUSitwas2.9percentandinCanadaitwas3.5

percent.Hence,theFisherinflationwas1.5percentintheUSand2.2percentinCanada,

whichcorrespondsrelativelywellwiththeactualoutcomeofabouttwopercentinboth

countries.InJapan,aswehaveseen,theinflationwasaboutzeropercentonaveragein

thedataandaccordingtotheFisherrelation.

19 Shirai(2012)discusses,forexample,theroleofdemographyineconomicdevelopmentsandshows,amongotherthings,estimatesoftheoutputgapwhichindicatethatithasbeennegativeoveralmosttheentireperiodsincethemid-1990s.However,healsonotesthatthereis,asofyet,noconsensusoverthefactorsthatcouldexplainsuchadevelopment.

– 23 –


π‾ F

JamesBullardontheeffectsoflownominalinterestratesoveralongerperiod

Inamuch-debatedarticlefrom2010,JamesBullard,presidentoftheFederalReserveBank

ofSt.Louis,discussedtheeffectsoflownominalinterestratesoveralongerperiodoftime,

seeBullard(2010).ThepurposewastoshedlightontheriskthattheUScouldbemoving

toanewsteadystatewithdeflationarytendencieslikethoseinJapan.Hisanalysiswas

basedoninsightsfromearlierworkbyBenhabibetal.(2001),inwhichtheFisherrelation

andthezerolowerboundwerekeyingredients.20

MonetarypolicyisoftendescribedbyalinearTaylorruleinstandardmacroeconomic

models.21Asaconsequence,thereexistsnozerolowerboundforthepolicyrate.

Furthermore,thereisonlyonesteadystateinflationrate,whichcoincideswiththecentral

bank’sinflationtarget.However,ifthereexistsazerolowerbound,theremaybeasecond

steadystate,inwhichthepolicyrateisclosetozeropercentandinflationislowor

negative.

InFigure9weillustratethetwosteadystates.ThesolidlineshowstheFisherrelation,

givenalongrunrealinterestrateof0.5percent.Thedashedlineshowsanon-linear

Taylorrule,wherethenon-linearityisduetothezerolowerbound.Hence,therearetwo

pointswheretheFisherrelationandthenon-linearTaylorruleintersect,markingthetwo

steadystates.Theblueareamarksthesteadystatewherethenominalinterestrateis

wellabovethezerolowerboundandinflationisontarget.Thissteadystateisknownas

the”targeted”steadystate.Theothersteadystate,markedred,mayappearwhenthere

isalowerzerobound.Asmentioned,inthissteadystate,inflationmaybeloworeven

negative,whichmeansthatitwillbebelowthecentralbanksinflationtarget.Thissteady

stateisthereforeknownasthe“unintended”steadystate.

Thearrowsinthefigureillustrateapossibletransitionalpathfromthetargetedsteady

statetotheunintendedsteadystate.notethatmonetarypolicybecomespassiveoncethe

economygetsstuckintheunintendedsteadystate,sincethepolicyratewillnotreactto

changesininflation.Ifinflationweretofall,thecentralbankwouldbeunabletocutthe

policyrateduetothezerolowerbound.If,ontheotherhand,inflationweretorise,the

policyratecannotberaisedeither,sinceinflationisfarbelowtheinflationtarget.Inflation

expectationsthereforeremainatalevelconsistentwithanominalinterestrateofzeroper

centandarealinterestrateof0.5percent,i.e.anegativeinflationrateof−0.5percent.

Whentheeconomygetsstuckintheunintendedsteadystate,itcanbedifficultto

escapefromit,sincestandardmonetarypolicyactionsareineffective.Thecentralbank

mayinsuchasituationresorttounconventionalmeasures.Bullardarguesthatquantitative

easing(purchasinggovernmentbonds)isthemeasurethathasthebestchanceoftaking

theeconomybacktothetargetedsteadystate.

20 Thelevelofthelowerboundisnotimportanttotheanalysisinthissection.Theimportantpointisthattherede factoexistsalowerbound.Forthesakeofsimplicity,thislowerlimitisassumedtobezeropercent.

21 Themonetarypolicyruleinequation(6)isanexampleofthis.

– 24 –

SVERIGESRIKSBAnKEConoMICREVIEW 2015:2

-1

1

2

3

4

5

-1 1 2 3

Nom

inal

inte

rest

rat

e

Inflation rate

Unintendedsteady state

Targetedsteady state

Figure 9. The two steady states for the nominal interest rate and inflation when monetary policy is constrained by the zero lower boundPer cent

Fisher relation Non-linear Taylor rule

Source: Own illustration

JAPAnAPPEARSToHAVEGoTSTUCKInTHEUnInTEnDEDSTEADySTATE

Japanhasbeencharacterisedbylownominalinterestratesandinflationsincetheoutbreak

ofthefinancialcrisisinthebeginningofthe1990s.DoesthissuggestthatJapanhasgot

stuckintheunintendedsteadystate?Toinvestigatethis,welookatthemovementsofthe

nominalinterestrateandinflationbeforeandafterthecrisis.

Thenominalinterestrateinthepre-crisisperiodappearstohavevariedaroundalong

runlevelof6-8percentandinflationaroundalevelof2-3percent,seetheblueoutcomes

inFigures10(a)and10(b).outcomesinthepost-crisisperiodaremarkedred.Thenominal

interestrateappearstofluctuatearoundzeropercent.Theinflationratehasvaried,but

mostoftheobservationsarestillaroundzeropercent.ThisindicatesthatJapanmayhave

movedfromthetargetedsteadystatetotheunintendedsteadystate.22

SEVEnyEARSoFDATAISnoTEnoUGHToDETERMInEWHETHERSWEDEnAnDoTHER

CoUnTRIESHAVEMoVEDToTHEUnInTEnDEDSTEADySTATE

Swedenandseveralothercountrieshavesincetheoutbreakofthefinancialcrisisin2008

hadnominalinterestratesclosetozeroandlowinflation.Doesthissuggestthatthese

countriesareabouttomovetotheunintendedsteadystate?Sevenyearsofdataisnot

enoughtodeterminethis,butitmaybeenoughtodistinguishcertaintendencies.

22 ThisisalsoconfirmedbyAruobaetal.(2014).

– 25 –


Figures10(c)and10(d)showthenominalinterestrateandinflationinSwedenbetween

theyears1994and2014.Inthepre-crisisperiodthenominalinterestratevariedaround

3-4percentandinflationaround1-2percent.Aftertheoutbreakofthecrisis,the

nominalinterestratehasbeenfallingtoaroundzeropercent,althoughitisnotpossible

todistinguishanewsteadystate.ThisisthecaseregardlessofwhetherwelookatCPI

inflationorcoreinflation.

IntheUS,thesteadystatepriortothefinancialcrisisappearstohavebeenabout4per

centforthenominalinterestrateandabout2percentforinflation,seeFigure11(a).Inthe

post-crisisperiod,thenominalinterestratehasbeenaboutzeropercent,butinflationhas

variedagooddealandmostoftheobservationsfluctuatearound1-2percent.

-2

0

2

4

6

8

10

-3 -2 -1 0 1 2 3 4 5 6 7

Nom

inal

inte

rest

rat

e

(a) Japan, CPI (b) Japan, core

-2

0

2

4

6

8

10

-3 -2 -1 0 1 2 3 4 5 6 7

-2

0

2

4

6

8

10

Nom

inal

inte

rest

rat

e

Inflation rate Inflation rate

(c) Sweden, CPI

-3 -2 -1 0 1 2 3 4 5 6 7-2

0

2

4

6

8

10

-3 -2 -1 0 1 2 3 4 5 6 7

(d) Sweden, core

Figure 10. Nominal interest rates and inflation in Japan and SwedenPer cent

Note. The nominal interest rates are measured by three-month treasury bills. Core inflation is measured by CPI excluding food and energy in Japan and by CPIF excluding food and energy in Sweden.

Sources: Macrobond, OECD, Statistics Sweden and the Riksbank

1981-1990 1991-2014

1994-2007 2008-2014 1994-2007 2008-2014

1981-1990 1991-2014

– 26 –


Intheeuroareainflationhasbeenfluctuatingextensivelyinthepost-crisisperiod.At

lowest,itwas–0.3percentand,athighest,3percent,seeFigure11(b).Wenotethatthe

mostrecentobservationsindicatethatinflationisapproachingdeflationterritory.Butitis

hardtodistinguishanewsteadystateonthebasisofthis,eveniftheeuroareaappearsto

haveleftthesteadystateitwasinpriortothecrisis.neitherdothedevelopmentsinthe

UKandCanadainthepost-crisisperiodindicatethatthesecountrieshavebeenfallinginto

theunintendedsteadystate,seeFigures11(c)and11(d).However,liketheeuroarea,the

UKappearstohaveleftthesteadystateitwasinbeforethefinancialcrisis.

Figure 11. Nominal interest rates and inflation in the US, the euro area, the UK and CanadaPer cent

Note. The nominal interest rates are measured by three-month treasury bills, except in the euro area where the nominal interest rate is measured by EONIA.

Sources: ECB, Eurostat, Macrobond, OECD and the US Bureau of Economic Analysis

-2

0

2

4

6

8

10

-1 0 1 2 3 4 5

(a) United States, PCE

Nom

inal

inte

rest

rat

e

(b) Euro area, HICP

-2

0

2

4

6

8

10

-2

0

2

4

6

8

10

-2

0

2

4

6

8

10

-1 0 1 2 3 4 5

-1 0 1 2 3 4 5 -1 0 1 2 3 4 5

(c) United Kingdom, CPI (d) Canada, CPI

1987-2007 2008-2014 1999-2007 2008-2014

Nom

inal

inte

rest

rat

e

Inflation Inflation

1993-2007 2008-2014 1993-2007 2008-2014

– 27 –


Concludingremarks

oneoftheobjectivesofthisarticlehasbeentoexplorenarayanaKocherlakota’sclaimthat

alowpolicyrateoverthelongruncanleadtolowinflation.Theideareliesonlongrun

monetarypolicyneutralityandthelongrunFisherrelation.Undertheseassumptions,it

followsthatalong-livedcutinthepolicyrateleadstoaproportionalfallininflation.

However,evenifeconomictheorypredictslowinflationifthepolicyrateisheldatalow

leveloveralongerperiod,thisdoesnotnecessarilyimplythatthisalsowillbethecasein

reality.Economictheoriesarebasedonvarioussimplifiedassumptionsandaretherefore,by

definition,inaccurateinonewayoranother.Itisthereforeimportanttoempiricallytestto

whichextenttheeconomictheoryisconsistentwithdata.Wehaveshownthat,ifthereal

interestrateisequatedtotheGDPgrowthratepercapita,theaverageinflationinSweden

andothercountriescanbeexplainedbythedifferencebetweentheaveragenominal

interestrateandthegrowthrate.Wefindthisinteresting,sinceitindicatesthat,inseveral

countries,thelongrunFisherrelationisconsistentwiththedata.Inaddition,itprovides

empiricalsupporttoKocherlakota’sclaim.

SeveralscientificarticleshaverecentlybeenpublishedwheretheFisherrelationisoneof

thekeyfactorsbehindtheresults.Schmitt-GrohéandUribe(2013)isoneexample.They

presentascenariowhichisintendedtoresembletheexperiencesoftheUSfollowingthe

outbreakofthefinancialcrisisin2008,i.e.alongperiodofnominalinterestratesclose

tozero,inflationexpectationsbelowtheinflationtargetandslowemploymentgrowth.

TheFisherrelationplaysakeyroleinhowhouseholdsandfirmsinterpretchangesinthe

policyrateintheirmodel.Apolicyrateincreaseisasignalofhigherfutureinflation.oneof

theirconclusionsisthatanincreaseinthepolicyratepushesupinflationexpectationsand

promotesemployment.

AnotherexampleisLeeperandLeith(2015).Theypresentamodelinwhichthefiscal

theoryofthepricelevelandtheFisherrelationaretwokeyfeaturesindetermining

inflation.23Thefiscaltheoryofthepricelevelisrelevantwhenexpansionsinnominaldebt

arenotexpectedtobefundedbyhighertaxesorlowerexpenditure,i.e.whenhouseholds

andfirmsdonotexpectfiscalpolicyexpansionstobefundedbyafuturesurplus.When

thisisthecase,raisingthepolicyrateraisesthenominalinterestratereceiptsofthebond

holders(i.e.thehouseholds).Sincetheydonotexpecthigherfuturetaxestofinancethe

increasedexpenditurestheirnominalwealthalsoincrease.Theincreaseofwealthpushes

upconsumptionanddemand,whicheventuallyalsopushesupinflation.

23 SeealsoLeeperandyun(2006)foradescriptionofthefiscaltheoryofthepricelevel.

– 28 –


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