ScienceDirect
ReviewofDevelopmentFinance7(2017)157–168
Full
length
article
Inflation
Forecasts’
Performance
in
Latin
America
夽
João
Tovar
Jalles
a,b,∗aCentreforGlobalizationandGovernance,NovaSchoolofBusinessandEconomics,CampusCampolide,Lisbon1099-032,Portugal bUECE—ResearchUnitonComplexityandEconomics,TechnicalUniversityofLisbon,Portugal
Availableonline10October2017
Abstract
ThispaperprovidesafullcharacterizationofinflationrateforecastsusingthemeanvaluesfromConsensusEconomicsforasampleof14 LatinAmericancountriesbetween1989and2014.Italsoassessestheperformanceofinflationrateforecastsaroundbusinesscycles’turning points.Resultsshowthatinflationforecastsintheregiondisplaythestandardpropertythatastheforecasthorizonshortensaccuracyimproves. Onaverage,forecastersunderpredictinflation,butthismasksverydifferentcountryexperiences.Wefindevidencepointtobiasednessofinflation forecastsforyear-aheadforecastsbutnotforcurrentyear.Tests’resultspointtoforecastinefficiencywhichisalsoevidencedbyatendencyto smooththembetweenrevisions.Focusingonbusinesscycleturningpoints,forecasterstendtoslightlyunderpredicttheinflationrateandthe extentofunderpredictionincreasesduringrecessions.Thehypothesisofforecastefficiencyisoverwhelminglyrejectedbothduringrecessionsand recoveries.
© 2017 Africagrowth Institute. Production and hosting by Elsevier B.V.This is an open access article underthe CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
JELclassifications: C53;E27;E37;E62;D8
Keywords:Forecastcomparison;Bias;Efficiency;Informationrigidity;Recession;Recovery
1. Introduction
LatinAmericahasbeenknownforitsdisplayofhighinflation
ratesandevenepisodes of hyperinflation,particularlyshortly
afteritspoliticaltransitiontodemocracyinthe1980sandearly
1990s.1Morerecently,theimportantcurrencydepreciationsthat
affectedmanyLatinAmericancountrieshaveplacedrenewed
upwardpressureoninflation,eveniftheirimpacthasbeenmilder
thaninthepast.2Vigilanceisinanycasewarrantedineconomies
wheresecond-roundeffects are potentially big,sincethereis
quietvariabilityastohowwell-anchoredinflationexpectations
areindifferentcountries.Thisisimportantsinceseveralpapers
夽 Theusualdisclaimerapplies.Allremaining errorsaretheauthor’ssole responsibility.
∗Correspondenceto:CentreforGlobalizationandGovernance,NovaSchool ofBusinessandEconomics,CampusCampolide,Lisbon1099-032,Portugal.
E-mailaddress:joaojalles@gmail.com
1 ForseminalworksoninflationinLatinAmericarefertothestudiesbyBaer
(1967)andCole(1987).
2 Notethatimprovementsinmonetaryframeworksoverthepasttwodecades haveledtosubstantialandgeneralizeddeclinesinexchangeratepass-through toconsumerprices.
typicallypointtothenegativeeffectsofinflationoneconomic
growth.3
Theseverityandpersistenceofthefallinoutputduringthe
GlobalFinancialCrisis(GFC)ledtosignificantdeclinesin
infla-tionratesaroundtheworld.Sincethen,inflationonaveragehas
increasedandsomecentralbanksintheLatinAmericanregion
currentlyfaceatrade-off.On theonehand,domesticdemand
isweak,withsomeuncertaintyaroundoutputgaps,andfiscal
policyspaceislimitedornonexistent.Ontheotherhand,
head-line inflationisabovetargetandexpectedtoremain sointhe
nearterm.4 Such conjuncturetriggeredarevival of the
inter-estinunderstandingthe deepcauses,costsandconsequences
3 Forinstance,Fisher(1993)presentedsomeinternationalcross-sectionaland paneldataevidencetosuggestthatinflationoutweighedtheMundell–Tobin effect.Barro(1995)makinguseofcross-sectionalanalysis,suggestedthatthe high-inflationcountriesinhissampledrovethenegativeeffectsofinflationon outputgrowth.DeGregorio(1993)providedsomeearlyevidenceusingapanel oftwelveLatinAmericancountriesduringthe1950–1985period,andsuggested thatinflationwasindeeddetrimentaltoeconomicgrowth.
4 Forarecentsurveyontheregion’seconomicoutlookseeIMF(2016a).
http://dx.doi.org/10.1016/j.rdf.2017.09.002
1879-9337/© 2017 Africagrowth Institute. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
ofinflationdynamics.5 Understandinginflationdynamicsisa
very important as well as a timely and timeless issue.
Fore-castingitcorrectly,however,seemsanequallyimportantissue
butit hasreceivedfar lessprominence. Giventhe well
docu-mentedrelationshipbetweencyclicalfeatures ofinflationand
unemployment(PhillipsCurve)andhowstructuralpoliciescan
affectaggregatedemand(IMF,2016b)andimprovelabor
mar-ketmatching(Bovaetal.,2016),itisimportanttoassesshow
forecastershavebeenperformingwhenitcomestopredicting
inflation.Recentstudieshavealsodocumentedhowinflationrate
(professional)forecastsareconsistentwiththePhillipsCurve.6
Suchliteraturecan beviewedinthe broaderscopeof testing
whethermacroeconomicempiricalregularitiesholdtruewhen
usingforecastsinsteadofactualdata.7
Inthiscontext,andacknowledgingtherelevanceofbusiness
cycle behavior to inflation dynamics (Tatom, 1978; Oinonen
etal.,2013),thispaperaimstoassesstheperformanceof
infla-tionforecastsinasampleofLatinAmericancountriesinboth
normal times but also around business cycle turning points.
Recentforecastingassessmentexercisesaroundbusinesscycles
turningpointsforeithertheGDPgrowthorthebudget
balance-to-GDP-ratioforacross-sectionofcountriesusingConsensus
EconomicsdatawerecarriedoutbyLounganietal.(2013)and
Jallesetal.(2015),respectively.However,aperusalofthe
lit-erature findsnosuch analysis forthe caseof inflationinthis
particularregionoftheworld.Tothisend,werelyontheprivate
sector’spredictionsfortheinflationrateforasampleof14Latin
American economies between October 1989 and September
2014 brought together by Consensus Economics—which are
knowntobehardtobeat(BatchelorandDua,1992).8
The paper proposes toaddress the following, more
expo-sitional,questions:(i) Howdo inflationforecasts behaveand
performstatistically?(ii)Whatsensitivityanalysiscanbemade
atdifferentforecasthorizons,thatis,isthereamarked
differ-encebetweencurrent-yearandyear-aheadpredictions?(iii)Do
forecasters,onaverage,under-orover-predicttheinflationrate
andfor how long?iv) Are inflationforecastsaccurate during
recessionsandrecoveriesepisodes?Toanswerthesequestions,
5 See the remarks of the ECB Vice-President Mr Constancio about “Understanding Inflation Dynamics and Monetary Pol-icy in a Low Inflation Environment” (5 November 2015) —
https://www.ecb.europa.eu/press/key/date/2015/html/sp1511051.en.html. 6 Forinstance,Fendeletal.(2011)provideevidenceonthetrustof profes-sionalforecastersinalternativeexpectationalversionsofthePhillipscurvefor agroupof7advancedeconomies.Rülke(2012)assesseswhetherprofessional forecastersapplythePhillipscurveinsixAsiancountries.
7 Forinstance,Balletal.(2015)testwhetherprofessionalforecastersbelieve intheOkun’sLawwhenmakingtheiroutputandunemploymentpredictionsfor asampleof9advancedcountries.Indeed,theauthorsshowthat,consistentwith Okun’sLaw,forecastsofrealGDPgrowthandthechangeinunemployment arenegativelycorrelated.Previously,Pierdziochetal.(2009)providedsimilar evidencefortheG7countries.
8 Evenifindividualprivatesectorforecastsmaybesubjecttovarious behav-ioralbiases,manyofthesearelikelyto beeliminatedbypoolingforecasts fromseveral individualforecasters.Moreover,ZarnowitzandBraun (1993)
havedocumentedthatgroupmean(“consensus”)forecastsaremoreaccurate thanvirtuallyallindividualforecasts.
we rely on aplethora of time series methodsand regression
analyses.
Our results showthat inflation forecastsinthe region
dis-playthestandardpropertythatastheforecasthorizonshortens
accuracyimproves.Onaverage,forecastersunderpredict
infla-tion,butthismasksverydifferentcountryexperiences.Infact,
Paraguay and Argentina areexamples of countries for which
forecasts are largerthanrealizedinflation,that is,forecasters
overpredictinflation.Wefindevidencepointtobiasednessof
inflationforecastsfor year-aheadforecastsbutnotfor current
year. Asfar as efficiency is concerned,tests’results pointto
inefficiencywhichisalsoevidencedbyatendencytosmooth
forecasts. Inotherwords, informationalrigidities arepresent.
Finally, focusingonbusinesscycle turningpoints,forecasters
tendtoslightlyunderpredicttheinflationrateonaverage,and
the extent of underpredictionseemstoincreaseduring
reces-sions.Thehypothesisofforecastefficiencyisoverwhelmingly
rejectedduringrecessions.Inrecoveryperiods,thehypothesis
ofefficiencyininflationforecastsisalsorejected.
Theremainderofthepaperisorganizedasfollows.Section
2 describes the data andpresents some descriptive statistics.
Section3outlinestheempiricalmethodologyanddiscussesour
main findings. The lastsection concludes andincludes some
policyconsiderations.
2. Dataissuesanddescriptivestatistics
Since the early1990s decade there has been a significant
growthinpublishedeconomicanalysisstemmingfrombanks,
corporationsandindependentconsultantsaroundtheworld,and
a parallel growth in “consensus forecasting” services which
bringtogetherinformationfromthesedifferentprivatesources.
Since1989ConsensusEconomicshaspublishedmonthly
fore-castsformainmacroeconomicvariablespreparedbypanelsof
private sector forecasters. In additionto individual forecasts,
the service publishes thearithmetic averageof each variable,
theso-called“consensusforecast”forthatvariable.Thisseems
a promisingalternative toofficial forecasts for mostusers of
economicforecastsinsteadofsomenaivemodel.9
Thispaperusesthemeanoftheprivateanalysts’monthly
con-sensusforecastsoftheinflationrateforthecurrentandnextyear
fortheperiodfromOctober1989toSeptember2014.Our
sam-pleiscomprisedof14LatinAmericancountries.10The“event”
beingforecastedisannualaverageinflationrate.Everymonth
anewforecastismadeof theevent.Hence,foreachyear,the
sequenceofforecastsisthe24forecastsmadebetweenJanuary
ofthepreviousyearandDecemberoftheyearinquestion.Our
9ThisisacknowledgedbyArtis(1996),whomakesavisualcomparisonof IMFandConsensusEconomicsforecastsforrealGDPandinflation,and con-cludesthatthereis“littledifferencebetweenWEOandConsensuserrors”.Ina similarvein,Loungani(2001)plotsIMFandConsensusEconomicsrealGDP forecastsandnotesthat“theevidencepointstonear-perfectcollinearitybetween privateandofficial(multilateral)forecasts...”
10Countrylistincludes:Argentina,Brazil,Bolivia,Chile,Colombia,Costa Rica,DominicanRepublic,Ecuador,Mexico,Panama,Paraguay,Peru,Uruguay, andVenezuela.
0 10 0 20 0 30 0 1990 1995 2000 2005 2010 2015 year meangr mediangr pctile_75gr pctile_25gr
Fig.1.Interquartilerangeofinflationrate,1989–2014.
Note:Brazilisexcludedfromthesample.Inadditiontothemeaninflation(blue), themedian(red)andtopandbottomquartilesaredisplayed(yellowandgreen, respectively).
Source:IMFIFSandauthors’calculations.
datasetalsoincludesactualdataontheactualinflationratefrom
theInternationalMonetaryFund’sInternationalFinancial
Statis-tics(IMF’sIFS).11 Finally, usingquarterly GDPseries(from
IMF’sIFS),recessionepisodesareidentifiedbasedonthe
clas-sicaldefinitionof abusinesscycleusing quarterlychangesin
the level of real GDP (Burnsand Mitchell, 1946).Countries
areclassifiedasbeinginarecessioninagivensurveymonth
ifthe respectiveforecasted yearfallsinthe recessionyearas
definedfollowingNBER’sapproachfor datingturning points
inthebusinesscycle.Informationondifferentfinancialcrises
comesfromLaevenandValencia’s(2012)database.
Webeginbyplottingtheinterquartilerangeoftheactual
infla-tionrateinoursampleofLatinAmericancountries(excluding
Brazilthatwitnessedseveralhyperinflationepisodesduringthe
1990s).AsshowninFig.1,themeaninflationfortheregionhas
slowlycomedownstartingintheearly1990stostabilizearound
muchlowervalues(historicallyspeaking)sincethe2000s.
Fig.2,plotsthedistributionofinflationforecastsatselected
horizons(h=21,15,9,3)withthedistributionofactual
infla-tionrate.Bothdataandforecastsarepooledacrossthedifferent
countriescomposingourregionalLatinAmericansample.The
keypurposeistoshowthattheforecastsdisplaythereasonable
propertythattheystarttomirrorthedataastheforecasthorizon
drawstoaclose.Asthevalueofh(theforecasthorizon)gets
smaller,thedistributionoftheforecastsstartstomovecloserto
thedistributionofthedata.
11 At this point a caveat should be made. Data revisions have worried economistsformanyyearsnow(seeCroushore,2011forarecentsurvey)and policy-makershavetobasetheirdecisionsonpreliminaryandpartiallyrevised data,sincethemostrecentdataareusuallytheleastreliableasitsimply trans-latesanoisyindicatorforfinalvalues(Koenigetal.,2003).Weareawarethat datarevisionsposechallengestoforecastersandthatforecastingstudiesshould reflectthetrueforecastingperformancebyusingreal-timedatainsteadoffinal data(StarkandCroushore,2002).However,inthepresentcaseitisdifficultto findreliable,consistentandcomparablereal-timevintagesforinflationrates.
Table1
Stylizedfactsoninflationforecastingperformance.
Horizon Pooled Currentyear Yearahead
Sample Allsample,N=14
ME 16.38 11.21 21.55
MAE 22.00 18.18 25.81
RMSE 24201.37 18779.75 29622.99
Sample Allsample,excludingBrazil,N=13
ME 0.396 −0.18 0.97
MAE 3.15 2.30 4.01
RMSE 45.34 28.36 62.33
Notes:Thistablepresentssomedescriptivestatisticsfortheentiresample,as wellasforthesampleexcludingtheoutlierBrazil.ME,MAEandRMSEstand forthemeanforecasterror,theabsoluteforecasterrorandthemeansquare forecasterror,respectively.
Now,forecastingaccuracyshouldcontaintwoaspectsofthe
forecastascomparedtotheactualoutcome(MussoandPhillips,
2002).Thefirstoneishowclosebothareinquantitativeterms
bymeansofanumberof“standardmeasures”,whilethesecond
onereferstothecapacityof theforecast topredictthe
direc-tionofchangeinthefinaloutcome.Define,foreachcountryi
duringyeart,eit=Ait−Fit,whereerepresentsforecasterror,
Fdenotestheforecast,andAdenotesitsrespectiverealization
(inourcaseitcorrespondstothemoving averageof monthly
reported inflationrates). In terms of “standardmeasures” we
usethreeconventionalerrormeasurestoassessrelative
perfor-mance:theaverageforecastbias(ME),12themeanabsoluteerror
(MAE)andtherootmeansquarederror(RMSE).Whilethese
measureshaveanumberoflimitations,theRMSEhasinvariably
beenusedasstandardforjudgingthequalityofpredictions.13
TheME,MAEandRMSEstatisticsarereportedinTable1.14
Themean errorispositiveandmuchlargerthanonepoint
whenwepoolallcountriestogether,includingBrazil.However,
this masks very different country experiences and excluding
Brazilgivesaconsiderablybetterpicture fortheperformance
ofinflationforecasts.Focusingonthebottompanel,themean
errorremainspositive(meaningthatinflationisunder-predicted)
butsmallerthanonepoint(withtheabsoluteerroronlyslightly
larger). Splitting the sample between current and year-ahead
forecastsalsouncoversinterestingfindings.Incurrentyear
fore-casts,thereisinfact overpredictionof inflation(asshownby
thecoefficientof−0.18).Notsurprisingly,absoluteerrors
(irre-spectivelyofthesampleunderscrutiny)arealwayssmallerfor
currentyearthanforyearaheadforecasts(inlinewithevidence
presentedinFig.1aboutforecastsconvergingtoactualsasthe
12Definedastheaveragedifferencebetweentheactualvalueanditsforecasted value.Forexample,apositivevalueforbiasindicatesthatonaverageoverthe wholerunofforecastsfortheinflationrate,theactualvaluewasunder-estimated, sothattheforecastsweretoolow.
13TheRMSEmaybethemostpopularmeasureamongstatisticianspartially becauseofitsmathematicaltractability.Morerecently,researchersseemto pre-fertheso-calledPercentBetter,theMeanAbsolutePercentageErrorandthe RelativeAbsoluteError.ForareviewseeArmstrongandCollopy(1992).
14Thesametablewasalsodonesplittingthesampleintwotimeperiods,from 1989until2002andfrom2003until2014.Forreasonsofeconomyofspace, resultsareavailableuponrequest.
Fig.2. Distributionofactualandforecastedinflationrate,1989–2014. Source:Consensus,IMFIFSandauthors’calculations.
horizondrawstoaclose).Thisseems,onaverage,arelatively
goodperformanceforinflationforecastsintheregionasresults
provideevidenceofhardlyenormouserrorstraditionally.Infact,
therelationshipbetweeninflationandtheaccuracyofinflation
predictions inhigh-inflation countries,such as thoseinLatin
America,tendstobenegative(seeMaskusandPourgerami,1990
andreferencestherein).Thereasonforthepotentiallynegative
effectofinflationoninflationuncertainty(whereuncertaintyis
equated withlackof predictability) isthat inahigh-inflation
environmenteconomicagentsinvestmoreresourcesin
gener-atingaccurateinflationforecastsandindevelopinginstruments
capableofreducingtheuncertaintycostsofhighinflation.
AsEdwards(1993)putsit,“contrarilytopopularmythology,
notallcountriesinLatinAmericahavehadlonginflationary
his-tories”.Moreover,asIMF(2016a)pointsout,the“regionalmix”
intermsofeconomicoutlooksisimpressive.Thesetwogiveus
sufficientreasonstoinspect inflationforecastingperformance
country-by-country.Fig.3showsthecountry-by-countrymean
errorforbothcurrentandyear-aheadforecasts.Someinteresting
differencescanbehighlighted.First,ParaguayandArgentinaare
examplesofcountriesforwhichforecastsarelargerthan
real-izedinflation,thatis,forecastersoverpredictinflation.Onthe
contrary,forMexico,Ecuador,DominicanRepublicandCosta
Rica theoppositeapplies.Countriesforwhichthemeanerror
isrelativelysmallerorclosetozeroisUruguay,Colombiaand
Chile(forbothforecasthorizons).
3. Methodologyandresults
3.1. Anassessmentofthequalityofinflationforecasts 3.1.1. Rationalityofinflationforecasts
Thekeyforanassessmenton“rationality”or“unbiasedness”
lies, firstly,in the available informationat the timethe
fore-castwaselaborated(data,policymeasures),andsecondlyinthe
Argenna Bolivia Chile Colombia Costa Rica Dominican Republic Ecuador Mexico Panama Paraguay Peru Uruguay Venezuela
Fig.3.Meanforecasterrorbyhorizon. Source:Consensus,IMFIFSandauthors’calculations.
benchmarkstandards,aswedidintheprevioussection,
deter-mineswhichonehassmallererrors;itdoesnotindicatehowto
improveupontheobservedrecord.Rationalitytestsdetermine
whetherornotthepredictionsareoptimalwithregardstoa
par-ticularinformationset(Wallis,1989).Aforecastisunbiasedif
itsaveragedeviationfromtheoutcomeiszero.15Wetestforthe
presenceofbiasininflationforecasterrorsbyadoptinga
statis-ticalapproachandconsideringsymmetriclossfunctionsonthe
partoftheagenciesgeneratingtheforecasts.Weuse:
At+h−Ft+h=α+εt+h (1)
wheretheforecasthorizonh=1,...,24.At+histheactualvalue
of variablex int+h, and Ft+h isthe forecast for t+h made
att. Ft+h is unbiased if we cannot reject the null hypothesis
thatα=0(HoldenandPeel,1990).Iftheestimatedcoefficient
is significantly larger or smaller than zero, the forecasts are
biased towardoptimism or pessimism,respectively. This last
pointiscloselyrelatedtoabehavioraleconomicsconcept:the
anchoringheuristic (Tversky andKahneman, 1974) whichis
increasinglyconsideredwhenexplainingbiasedforecasts.The
underlyingmechanismistypicallydescribedasinHarvey(2007)
whostates that forecasterstendto“usethe lastdatapoint in
theseries asamentalanchorandthenadjustaway fromthat
anchor totake account of the major feature(s) of the series.
However,asadjustmentistypicallyinsufficient,theirforecasts
arebiased”.16Anotherprominentexplanationofsystematically
biasedforecastspointstoreputational concernsof forecasters
tryingtostrategically concealtheir inabilityto predict future
values.Thisresults instrong incentives for herdingbehavior
15 Asarule,ifforecastsareinlinewiththeRationalExpectationsHypothesis (REH)formulatedbyMuth(1961),theyshouldbeunbiased.TheREHstates thatmarketparticipantsuseallcost-efficientknowledgetoforecast.
16 Therearemanytimeseriesforecastingexperimentsinvestigatingindividual predictionbehavior(e.g.ReimersandHarvey,2011).
Table2 Rationalitytest.
Horizon Pooled Currentyear Yearahead
Sample Allsample,excludingBrazil
α 0.396*** −0.180 0.972*** (0.111) (0.124) (0.182) Country Argentina α −2.672*** −3.733*** −1.61** (0.644) (1.035) (0.761) Country Bolivia α −0.023 −0.287* 0.241 (0.168) (0.151) (0.299) Country Chile α 0.178* 0.168* 0.189 (0.095) (0.099) (0.163) Country Colombia α 0.173** 0.167** 0.178 (0.086) (0.078) (0.155)
Country CostaRica
α 1.558*** 0.884*** 2.232***
(0.167) (0.178) (0.272)
Country DominicanRepublic
α 2.726*** 1.435*** 4.016*** (0.640) (0.545) (1.150) Country Ecuador α 3.621*** 2.205*** 5.036*** (0.714) (0.663) (1.256) Country Mexico α 1.335*** 0.675*** 1.996*** (0.248) (0.246) (0.425) Country Panama α 0.073 −0.123 0.270 (0.107) (0.102) (0.187) Country Paraguay α −1.911*** −2.092*** −1.730*** (0.269) (0.336) (0.421) Country Peru α −0.499*** −0.062 −0.937*** (0.145) (0.149) (0.245) Country Uruguay α −0.006 −0.140 0.128 (0.249) (0.284) (0.411) Country Venezuela α 0.346 −1.668*** 2.360** (0.611) (0.558) (1.061)
Note:ThedependentvariableisConsensusforecasterror.Eachcellreports theresultsofaregressionofforecasterrorsonaconstantforthepoolofall countriesinoursample(thatexcludesBrazil)and eachindividualcountry. Heteroskedastic-consistentrobuststandarderrorsarereportedinparenthesis.
* Indicatessignificanceat10%level. **Indicatessignificanceat5%level. ***Indicatessignificanceat1%level.
amongforecasters(OttavianiandSørensen,2006;Ackertetal.,
2008).
Table2reports,forcurrentandyear-ahead,andforthepooled
sampleandeachcountryindividually,thet-testsforα=0.For
forecastsonlyinyear-aheadforecastsbutnotfor current-year
ones(theseseemunbiased).Asbefore,giventheregionalmix,
countryresultshideagreatdealofheterogeneity.More
specif-ically,inthecasesofPanamaandUruguay,inflationforecasts
seemunbiasedirrespectivelyoftheforecasthorizonconsidered.
Fortheremainderofthecountries,thenullhypothesisofrational
forecastscanberejectedineitheroneorbothhorizons.17
3.1.2. EfficiencyofInflationforecasts
AccordingtoNordhaus(1987)asequenceofefficient
fore-castsofthesameeventmustfollowamartingale.AsinGentry
(1989),we regressactualobservations onaconstantplusthe forecast:
At+h=α+βFt+h+εt+h (2)
wheretheforecasthorizonh=1,...,24.At+histheactualvalue
ofvariablexint+h,andFt+histheforecastfort+hmadeatt.
Ft+hisefficientifwecannotrejectthenullhypothesisthatα=0
andβ=1individuallyandjointly.
AsTable3shows,inallforecasthorizons,thejoint
hypothe-sisofazeroconstantandaslopecoefficientofunityisrejected,
asindicatedbytheF-statisticsandassociatedp-values.18 This
pointstoinefficiencyofinflationforecasts.Sincethedataare
pooledacrosscountriesandovertime, thereisreasonto
sus-pect that the disturbance term, εt+h,in Eq. (2) would not be
random.Weattemptedtocontrolforsomeofthepossible
cor-relations by augmentingthe regression to include year fixed
effects.Theideaisthat someyearsmaybehardertoforecast
thanothers.Ourresults (notshown)still suggestinefficiency.
Asbefore,thepooledresultshideheterogeneityandinBolivia,
Chile,Colombia,DominicanRepublic,MexicoandVenezuela,
thejointhypothesisisnotrejected.Thissuggeststhat,forthis
groupofcountries,inflationforecastsmayhavebeenefficient
overtheperiodunderscrutiny.
3.1.3. From“forecast(in-)efficiency”to“informational rigidity”
Adifferentapproachtotackleforecastefficiency was
sug-gestedbyNordhaus(1987)whodefinedanotionofefficiency
or“informationrigidity”basedonforecastrevisions.Nordhaus
(1987) and Nordhaus and Durlauf (1984) studied “forecast
smoothing”, i.e., a tendency for a revision in one direction
to be followedby further revisions inthe same direction, in
fixed-eventforecasts.Thisisanimplicationoffull-informational
17Itisworthpointingtothepossibilitythatmanyoftherejectionsofforecast optimalitymaysimplybedrivenbytheassumptionofMSElossratherthanthe absenceofforecastrationalityperse.Elliotetal.(2005)statethatMSEloss, despiteagenerallyusedassumption,isoftenhardtojustifyoneconomicgrounds andissubjecttodebateandcriticism.Infact,asymmetriclosscapturestheidea thatthecostofover-andunderpredictingagivenvariablemaybeverydifferent.
PattonandTimmermann(2007)proposeatransformationoftheforecasterror thatpossessesthesamesetofrationalitypropertiesunderasymmetriclossand nonlineardatageneratingprocesses.
18WepickOctoberandAprilofthecurrentyearandyear-aheadasexamples ofthefirstandsecondhalfofagivenforecastyear.Arbitraryselectionof dif-ferentadjacentmonths(recallthatwehaveacontinuoussequenceof24months forecast)doesnotqualitativelyalterourresults.
rationalexpectations(FIRE):successiveforecastsofthesame
event shouldbeuncorrelated.19 Recent papers addressingthe
issueofinformationrigidityonmacroforecastsincludeIsiklar
etal.(2006),Lounganietal.(2013),CoibionandGorodnichenko (2015)andJallesetal.(2015).
We defineinitial revisionof the forecast as the change in
the forecast betweenOctober andAprilof the previousyear,
themiddlerevisionasthechangebetweenAprilofthecurrent
yearandOctoberofthepreviousyear,andthefinalrevisionas
the change betweenOctoberof the current yearandAprilof
thecurrentyear.Resultsfromregressionsoflaterrevisionson
earlierones areshowninTable4.Inall,butone,regressions,
thereisevidenceofastrongpositivecorrelationamongforecast
revisions(atthe1%significancelevel).Overall,thereisaclear
tendencyfor“forecastsmoothing”,i.e.,theestimatedcoefficient
onthelaggedrevisionpointstothepresenceof informational
rigidities.Infact,lookingatthespecificationwithbothmiddle
andinitialrevisionsincludedtogether,it takesbetween1and
1.2 months for the information to be fully incorporated into
forecasts.20
Alternatively, following Coibion and Gorodnichenko’s
(2015) approachweregress theforecast erroronthe forecast
revisionusingourfinal,middleorinitialrevisions.Theauthors
showthatthecoefficientontheforecastrevisioniszerounderthe
nulloffullinformationalrationalexpectations,whereasa
posi-tivevalueindicatesinformationrigidities.21Table5presentsthe
resultsofthistestandweobservethatthecoefficientestimates
areallpositiveandstatisticallydifferentfromzero.Thenullcan
be rejectedandthisfact goesinthe directionconsistentwith
modelswithinformationrigidity.Inthiscase,ittakesbetween
1.2and1.6monthsforinformationtobefullyincorporated.22
Overall,wecanconcludethatinflationrateforecastsare
ineffi-cient.
3.2. Inflationforecasts,recessionsandturningpoints
The recentGlobalFinancialCrisishas revivedtheinterest
not onlyin predicting recessions but also on the forecasting
performanceandaccuracyofmanymacroaggregatesthatcould
helpdeterminingupwardanddownwardmovementsinthe
busi-nesscycle(anditscorrespondingturningpoints).Wenowturn
to the examination of the inflation rate forecast performance
19Theliteraturehasidentifiedthreemainpotentialexplanationsfor“forecast smoothing”or“informationrigidity”(fordeparturefromFIRE):(i)behavioral explanations(Nordhaus,1987);(ii)sticky-information(MankiwandReis,2002) and(iii)imperfectinformation(Woodford,2002).
20MankiwandReis(2002)proposeamodelofinattentiveagentswhoupdate theirinformationsetseachperiodwithprobability(1−λ),butacquirenonew informationwithprobabilityλ,sothatλcanbeinterpretedasthedegreeof informationrigidityand1/(1−λ)istheaveragedurationbetweeninformation updates.Inthecontextofstickyinformationmodels,λ=β/(1+β),withβbeing theestimatedrigiditycoefficient.
21Onefeatureofthistestisthatitrequirestheuseoftheactualrealizations andhencerequiresaviewonwhethertousethelatestdataoranearliervintage. Ourtestsusethelatestdata.
22CoibionandGorodnichenko(2012)reportforinflationsimilarspeedforthe updatingofforecasts(1.5–2months).
Table3
Gentry’s(1989)Testofforecastefficiency.
Sample/country Independentvariables Dependentvariable:“actual”inflationrate
Apr.(t−1) Oct.(t−1) Apr.(t) Oct.(t)
All Constant −2.242 −0.470 5.615 2.034 (9.902) (5.137) (6.976) (6.481) Forecast 2.095*** 1.571*** 1.088*** 1.111*** (0.114) (0.038) (0.027) (0.026) F-statistic 47.85 114.70 6.18 9.38 p-Value 0.00 0.00 0.00 0.00
Argentina F-statistic(p-value) 0.12 0.01 0.00 0.00
Bolivia F-statistic(p-value) 0.46 0.69 0.61 0.21
Chile F-statistic(p-value) 0.35 0.91 0.59 0.36
Colombia F-statistic(p-value) 0.79 0.91 0.99 0.77
CostaRica F-statistic(p-value) 0.01 0.09 0.12 0.68
DominicanRepublic F-statistic(p-value) 0.25 0.59 0.33 0.04
Ecuador F-statistic(p-value) 0.02 0.03 0.00 0.09
Mexico F-statistic(p-value) 0.29 0.19 0.12 0.17
Panama F-statistic(p-value) 0.89 0.59 0.01 0.22
Paraguay F-statistic(p-value) 0.00 0.00 0.00 0.00
Peru F-statistic(p-value) 0.00 0.00 0.06 0.00
Uruguay F-statistic(p-value) 0.18 0.34 0.52 0.83
Venezuela F-statistic(p-value) 0.25 0.27 0.62 0.70
Notes:Theregressionisexpressedas,whereAistheactualrealizationandFistheforecast.TheF-statisticandassociatedp-valueareforthetestofthenullhypothesis thatβ0=0andβ1=1.Forcountry-levelresultsfullsetofcoefficientsandrespectivestatisticsareavailableuponrequest;theywereomittedforreasonsofparsimony. Heteroskedastic-consistentrobuststandarderrorsarereportedinparenthesis.
*Indicatessignificanceat10%level. **Indicatessignificanceat5%level. ***Indicatessignificanceat1%level.
Table4
Nordhaus’(1987)Testofforecastefficiency.
Sample Dependentvariable Independentvariables R-squared
Middlerevision Initialrevision Constant
All Finalrevision 0.239*** 0.083 0.03
(0.018) (0.063) Finalrevision 0.029*** −0.007 0.04 (0.008) (0.057) Finalrevision 0.240*** 0.013* −0.026 0.04 (0.018) (0.007) (0.058) Middlerevision 0.029 0.02 (0.039)
Note:Thedependentvariableisidentifiedincolumn2aseitherFinalRevisionorMiddleRevision.Asfortheindependentvariablesincludedineachregression, theseareidentifiedincolumns3and4togetherwithaconstantterm(column5).Heteroskedastic-consistentrobuststandarderrorsarereportedinparenthesis. **Indicatessignificanceat5%level.
* Indicatessignificanceat10%level. ***Indicatessignificanceat1%level.
duringrecessionepisodes,usingdescriptivestatisticalanalysis
andsimpleregressions.Itisimportanttolookatthebehavior
ofinflationforecasts indifferent phasesof thebusiness cycle
duetoseveralreasons:(1) thisiswhengeneralinterest(from
practitionersandpolicymakers) inpredictingthisvariableis
highest;(2)differentcentralbanksinLatinAmericamayhave
differentiatedobjectives(somemaybeconcerned solelywith
inflationwhileothersarewiderandincludeoutput,stabilityand
employmentconsiderations)whichtiefuturepolicyactionsto
alternative levels ofinflationrate23;(3) inflationexpectations
candramaticallychange around turningpoints.24 Somebasic
propertiesoftheinflationrateforecastsduringrecessionyears
aresummarizedinTable6.
Asshowninthefirstrow,asofApriloftheyearpreceding
the recession,theconsensusinflationforecastsweretoo
opti-23SeeCecchettiandEhrmann(2002)foranexaminationofthecentralbank objectivefunctionsinalargenumberofadvancedandemergingeconomies.
24SeeJalilandRua(2015)forevidence,usingnarrativerecords,onhowthe GreatDepressionintheUSin1933hasshiftedinflationexpectations.
Table5
CoibionandGorodnichenko’s(2015)Testofforecastefficiency.
Sample Independentvariables R-squared
Finalrevision Middlerevision Initialrevision Constant
All 0.514*** 0.382*** 0.09 (0.026) (0.111) 0.291*** 0.082 0.07 (0.014) (0.112) 0.201*** 0.402*** 0.23 (0.041) (0.114) 0.624*** 0.285*** 0.411*** 0.037 0.22 (0.027) (0.013) (0.038) (0.106)
Notes:Thedependentvariableistheinflationforecasterror.Asfortheindependentvariablesincludedineachregression,theseareidentifiedincolumns2–4together withaconstantterm(column5).Heteroskedastic-consistentrobuststandarderrorsarereportedinparenthesis.
*Indicatessignificanceat10%level. **Indicatessignificanceat5%level. ***Indicatessignificanceat1%level.
Table6
Forecastperformanceofconsensusinflationrateduringrecessionepisodes.
Allcountries Apr.(t−1) Oct.(t−1) Apr.(t) Oct.(t)
Numberofepisodeswhereforecast wastoooptimistic(forecast<actual) (shareintotal,inpercentage)
10(45) 12(46) 9(35) 4(18)
Averageforecasterror(allrecession episodes)
6.19 4.36 −2.68 −3.44
Note:Refertothemaintextfordetails.
Table7
DescriptiveStatisticsofConsensusInflationForecastsduringRecessionsandRecoveries.
Forecasterrors Absoluteforecasterrors Forecasterrors Absoluteforecasterrors Forecasterrors Absoluteforecasterrors
Spec. (1) (2) (3) (4) (5) (6)
Allcountries Unconditional Recessions Recoveries
Mean 0.39 3.15 1.18 8.42 0.47 6.62
Standarddeviation 6.72 5.94 14.14 11.41 10.79 8.76
Minimum -65.66 0.00 -65.66 0.02 -34.08 0.02
Maximum 69.85 69.85 46.02 65.66 46.02 46.02
mistic(definedasforecastsmallerthanactualrealization)in10
episodes corresponding to45% of the totalnumberof
reces-sionepisodes.By Apriloftheyearof therecession, inflation
forecastsweretoooptimisticinonly35% ofthetotalnumber
ofepisodes.Whileforecastersdorecognizeaslowdowninthe
inflationrateduringrecessionsintheyearinwhichtheyoccur,
resultsseemtosuggestthattheycannotanticipatesuch
down-wardrevisionintheyearprecedingtherecession.Moreover,as
showninthefinalrow,thereisasignificantupwardbiasinthe
year-aheadAprilforecaststhatonlyslowlydissipatesovertime;
wegofromameanerrorabove6pointsinApriloftheyear
pre-cedingtherecession,toameanerrorof−3pointsintheyearof
therecession.
Fig.4 presentsagraphicalsummaryof theME,MAEand
RMSEdescriptivestatistics byforecasthorizon. Aswe move
fromyear-aheadtowardscurrent-year,weseeasteadilydecline
inboththeMAEandMSE(unconditionalline).Moreover,we
havepositivevaluesforthemeanforecasterrorsformostofthe
24-monthforecasthorizonmeaningthatforecasters
underesti-matetheinflationrate.Lookingattherecession(blue)line,we
observethatittakessometimeforforecasterstorecognizethat
theeconomyishittingarecession.
In Table7,we see that forecasters tendto slightly
under-predict the inflation rate on average, and the extent of
underpredictionseemstoincreaseduringrecessions.The
regres-sionanalysisconfirmsthatastheforecasthorizonincreasesso
dotheabsoluteforecasterrors(Table8).Moreover,the
reces-sions’dummyisstatisticallydifferentfromzeroandpositively
correlatedwithabsoluteforecasterrors.
3.2.1. Ontheefficiencypropertiesofinflationforecasts duringrecessions
Wenowexamineforecastefficiencybyconductingtwotypes
of tests. The first is due to Nordhaus (1987) who defined a
notion of “information rigidity” based on forecast revisions
inlinewiththefullinformationrationalexpectations’ (FIRE)
premise thatsuccessive revisionsshouldbeuncorrelated. The
Recessions Recoveries Unconditional
Mean Errors
0 20 40 60 80 1 3 6 9 12 15 18 21 24
Mean Absolute Errors
0 50 10 0 1 3 6 9 12 15 18 21 24
Root Mean Squared Errors
0 10 0 20 0 30 0 40 0 1 3 6 9 12 15 18 21 24 g g p g Forecast Horizon
Fig.4.Descriptivestatisticsinflationrateforecasterrors:consensus1989–2014. Source:Consensus,IMFIFSandauthors’calculations.
Table8
RegressionofInflationRateForecastErrorsonDifferentStatesoftheEconomy.
Sample Allsample
Horizon Pooled Currentyear Yearahead
Recessions 5.708*** 5.212*** 6.235*** (0.344) (0.397) (0.574) Recoveries 3.325*** 1.874*** 4.936*** (0.312) (0.362) (0.518) Horizon 0.155*** 0.135*** 0.107* (0.016) (0.039) (0.056) Constant 0.305 0.671** 0.902 (0.243) (0.291) (1.049) Obs. 2878 1511 1367 R-squared 0.165 0.144 0.159
Notes:Thedependentvariable isabsolute forecasterrors. Heteroskedastic-consistentrobuststandarderrorsarereportedinparenthesis.
* Indicatessignificanceat10%level. ** Indicatessignificanceat5%level. ***Indicatessignificanceat1%level.
observationson aconstantplus the forecast errorandjointly
testsefficiency by imposing azero intercept andunity slope
coefficient.
WefirstrunNordhaus’(1987)regressionswiththeinclusion
ofdummiesforbankingcrisisandforrecessionandrecoveries
episodestoascertaindifferencesininflationforecasts’efficiency
duringtheseeventscomparedtoaverages.Theresultssuggest
that onaverageforecastsare inefficient(Table9).Lookingat
specification3,duringrecessions,onecanseethatmiddleand
initialrevisionsinonedirectiongenerallyarefollowedbyfinal
revisionsinthesamedirection(thecoefficientsonmiddleand
initialrevisionsafterrecessionsarestatisticallysignificant).
Finally,followingGentry’s (1989)approachdefined above
wedisplaytheresultsforthejointhypothesistestingfortheslope
andinterceptcoefficientsusingtheWaldtestsinTable10.The
hypothesis of forecast efficiency is overwhelmingly rejected,
includingforrecessionepisodes.
3.2.2. Ontheefficiencypropertiesofinflationforecasts duringrecoveries
Theaboveanalysisdocumentedfailuresinforecasting
infla-tionduringrecessions.Naturallyaquestionarisesaboutinflation
forecastperformanceduringrecoveries,anotherturningpointof
thebusinesscycle.Weexplorethisquestionbriefly.InFig.4,
lookingattherecoveries’line,weobservethat,meanerrorsof
Table9
Nordhaus’(1987)Testofefficiencybasedoninflationforecastrevisionsandaccountingforrecessionandrecoveryepisodes.
Dependentvariable Finalrevisions
Sample Allsample
Spec. (1) (2) (3)
Constant −0.373 −0.938*** −0.168
(0.814) (0.331) (0.288)
Dummyforrecession 1.294 4.595*** −1.250*
(1.979) (0.722) (0.682)
Dummyforrecovery −11.094*** 1.561** −0.939*
(1.658) (0.652) (0.582)
Dummyforbankingcrisis 5.156* 3.613*** 3.106***
(2.725) (1.252) (1.152)
Middlerevision 0.496*** −0.564***
(0.099) (0.035)
Middlerevisionafterrecessions −0.611*** 0.682***
(0.056) (0.023)
Middlerevisionrecoveries 2.186*** 0.564***
(0.099) (0.035)
Middlerevisionafterbankingcrisis 0.652*** 3.732***
(0.104) (0.589)
Initialrevision −0.081*** −0.017**
(0.009) (0.008)
Initialrevisionafterrecessions 0.419*** 0.188***
(0.015) (0.015)
Initialrevisionrecoveries 2.083*** 2.007***
(0.010) (0.013)
Initialrevisionafterbankingcrisis −0.574*** 1.179***
(0.010) (0.338)
Obs. 4435 4089 4089
R-squared 0.87 0.98 0.98
Notes:Thedependentvariableistheinflationratefinalrevisions.Regressionsincludedummyvariablesforrecessionandrecoveryepisodes.Heteroskedastic-consistent robuststandarderrorsarereportedinparenthesis.
* Indicatessignificanceat10%level. **Indicatessignificanceat5%level. ***Indicatessignificanceat1%level.
variablecomparedtotheunconditionalbut,moreimportantly,
tomeanerrorsduringrecessions.Alsoittakesforecastersmuch
longerfortheconvergencewiththeunconditionallinetohappen.
Themainfindinghereisthatwhileduringrecoveries,
infla-tion is more often accurately predicted than in recessions
(Table7),regressionresultssuggestthatinflationforecastsare
equally as inefficient as those taking placeduring recessions
(Tables8and9).Moreover,duringrecoveriesmostforecasters
reviseupwardstheirinflationpredictions(Fig.5).Hence,there
is asense of “optimism”that the average economy’s growth
ispickingupwhichdriveinflationexpectationstowardshigher
levels.Allinall,ourresultssuggest“informationrigidity”in
forecastsalsoduringrecoveries.
4. Conclusion
Thispaper providesafullcharacterization ofinflationrate
forecastsusingthemeanvaluesfromConsensusEconomicsfor
a sample of 14 Latin American countriesbetween 1989 and
2014.Italsoassessestheperformanceofinflationrateforecasts
aroundbusinesscycles’turningpoints.Tothisend,wereliedon
aplethoraoftimeseriesmethodsandregressionanalyses.
0 10 0 20 0 30 0 1 3 6 9 12 15 18 21 24
1 year after recession
Fig.5.Actualandforecastedinflationrateduringrecoveries(upto1yearafter recessionended):1989–2014.
Source:Consensus,IMFIFSandauthors’calculations.
Ourresultsshowthatinflationforecastsintheregiondisplay
the standardpropertythat theystarttomirror the dataas the
fore-Table10
Gentry’s(1989)Testofforecastefficiencyunderrecessionsandrecoveries.
Sample All
Spec. (1)
Constant −0.382
(0.257)
Dummyforrecession 6.828***
(0.633)
Dummyforrecovery 0.838
(0.572)
Dummyforbankingcrisis −0.443
(0.965)
Forecast 0.994***
(0.018)
Forecastafterrecession −0.275***
(0.025)
Forecastafterrecovery −0.016
(0.027)
Forecastafterbankingcrisis 0.154***
(0.045)
Obs. 2676
R-squared 0.75
P-valuesforWaldtests
Forecastafterrecessions 0.04
Forecastafterrecession 0.00
Forecastafterrecovery 0.00
Forecastafterbankingcrisis 0.00
Notes:Thedependentvariableisactualvaluesofinflationrate.Thehypothesis fortheWaldtestisthatthevalueoftherespectivetotaleffectisnot statisti-callydifferentfromzero.Heteroskedastic-consistentrobuststandarderrorsare reportedinparenthesis.
*Indicatessignificanceat10%level. **Indicatessignificanceat5%level. ***Indicatessignificanceat1%level.
casterrorispositive,suggestingunderpredictionofinflation,but
thismasksverydifferentcountryexperiences.Infact,Paraguay
andArgentina are examples of countries for whichforecasts
arelargerthanrealizedinflation,thatis,forecastersoverpredict
inflation.Wefindevidencepointtobiasednessofinflation
fore-castsforyear-aheadforecastsbutnotforcurrentyear.Asfaras
efficiencyisconcerned,tests’resultspointtoinefficiencywhich
isalsoevidencedbyatendencytosmoothforecasts(forecast
revisionsinonedirectionarefollowingbysubsequentrevisions
inthesamedirection).Thismeansthatinformationalrigidities
arepresent,takingonaverage1.5monthsforinformationtobe
fullyincorporatedandinternalized.
Finally,focusingonbusinesscycleturningpoints,while
fore-castersdo recognize aslowdown in the inflation rate during
recessionsintheyearinwhichtheyoccur,resultsseemto
sug-gestthattheycannotanticipateadownwardrevisionininflation
forecastsintheyearprecedingtherecession. Moreover,
fore-casterstendtoslightlyunderpredicttheinflationrateonaverage,
andtheextentofunderpredictionseemstoincreaseduring
reces-sions.Thehypothesisofforecastefficiencyisoverwhelmingly
rejectedduringrecessions.Inrecoveries,thereisageneralsense
of“optimism”thattheaverageeconomy’sgrowthispickingup
whichdriveinflationexpectationstowardshigherlevels.
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