Looking at Future

8/8/2019 Looking at Future

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A Markov-switching model of ination: looking at the future during 25

Anlisis Econmico

Nm.59,vo.XXVSeundocutrmestrede2010

(Recibido:agosto/09aprobado:marzo/010)

Abstract

In this paper, we analyze the dynamic of ination in Venezuela, during the last eighteen years,throuhMrkov-swtchnestmtonofNewKeynesnPhpscurve.EstmtonscrredoutusntheEMorthm.Themodesestmtesdstnushbetweennormorbckwrdooknremendrtonexpecttonremeconsstentwthepsodesofhhuncertntyrerdntheperformnceoftheeconomy.Thschrcterztonofre-gimes is based on two elements: the description of the process of formation of inationaryexpecttonsndthemneconomceventsoccurreddurnechreme.

Keywords: regime swiching, Phillips curve, inationary expectations.

JEL Classication: C29, E31, D84.

A Markov-switching model of

inflation: looking at the future during

uncertain times

*SenorResercherttheBncoCentrdeVenezue([email protected]).**SenorResercherttheBncoCentrdeVenezuendProfessorttheUnversddCentrdeVenezue

([email protected]).OpnonsonthspperrefuresponsbtyoftheuthorsnddonotcompromsethoseoftheBncoCentrdeVenezue.WerertefuforthereserchssstnceofJesonPrez,ndcommentsofHrodZvrcendlenFernndez.aerrorsndomssonsreourown.

Carolina Pagliacci*

Daniel Barrez**


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26 Pagliacci, Barrez

Introduction

SncethesemnworkofHmton(1989)mnyreserchershvedevotedtostudy-

ntheeconomcrowthfromtheperspectveofremechnes,dentfyntwophsesntheeconomccyce:expnsonsndcontrctons.Throuhtme,Mrkov-swtchnmodes(msm) have experienced renements in the applied econometrictechnques,buttherestmtonhsmostykepttheornsprtofHmtonswork:dstnushnbetweenremesofrecessonsndexpnsons.Fornstnce,pperssuchsKmndMurry(2002)ndKhnndRch(2007)hvencorportedtheoccurrenceofremeswtchnnthenon-observbecomponentsofrowth(snstte-spcemodes).DebodndRudebush(1996)studythebusnesscycessumnthtthetrnstonmtrxthtovernstheprocessofswtchnsvrbe

nstedofbenconstnt.aesspopur,butreymportntuseofthemsmhsbeenthestudy

of non-linearities in ination. In an early work, Evans and Wachtel (1993) focus onanalyzing the sources of uncertainty that affect the dynamics of ination and agentsinationary expectations collected in surveys. Assuming that ination can eitherfoowrndomwkprocessornutoreressveprocess,theseuthorsestbshedthttheswtchbetweenthesetworemesexpnsthepresenceofdscretejumpsin the USA ination during the postwar period. Also, the uncertainty attached to thechanges of regimes is identied as the source of the recurrent differences betweenthe forecasts of ination collected in surveys and the actual rates of ination. Otherppers,keSmon(1996)ndBx(1999),emphszetheuseof msmtoexpnvisible changes in the ination dynamics and to improve ination forecasts. Simon(1996) models ination in Australia incorporating information of the output gap.More recently, Demers (2003) describes the non-linearities in Canadian inationthrouhtheestmtonofMrkov-swtchnbckwrdooknPhpscurve.

In Venezuela, ination dynamics has also been subject to importantchanges probably due to the continuous modications impinged to the exchange rateremettmesofexterncrss.Thesechnes,orpresumbystructurbreksin the ination dynamics, make linear models inappropriate tools for analyzingination through time. In order to fully capture these non-linearities, the objectiveof this paper is to model Venezuelan ination through the estimation of a Markov-swtchnNewKeynesnPhpscurve.Thedvnteofthstypeofnon-nermodessthttheyowcombnntheexstenceofdfferentstochstcprocessesfor ination without imposing too many restrictions to the data generating process.Ontheotherhnd,theestmtonofNewKeynesnPhpscurve,nsmrfashion as in Demers (2003), provides a basic understanding of the behavior of


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ination from an economic point, using a theoretical structure that admits incor-porating variables that traditionally have had a predominant gure in explainingination in Venezuela, such as the output gap. In fact, several works in Venezuela,

such as Dorta, lvarez and Bello (2002), Arreaza, Blanco and Dorta (2003) andDorta (2006), estimated the impact of the output gap on ination for different timeperiods, but using exclusively linear models. In our specication, we additionallyallow the process of money creation by the public sector to inuence the behavior ofination. We also incorporate the rate of growth of the nominal exchange rate as anexplanatory variable, to capture possible changes in its pass-through on ination.1

Oneofthechenesthtrseswthntheevutonofmsmwthexo-enousexpntoryvrbessthtthechrcterztonofremescnnotbedoneprortoestmtonnymore.itsnoonercerthttheremescpturedbythstype of models (even in a two-regime setting) refer to high and low ination regimes,noousystsdonentheterturewhenconsderncontrctonsndexpn-sonsoftheeconomy.Onthecontrry,fterseectnthepproprtenumberofremes,weneedtomkeuseoftheestmtonresutsndthentureofthereton-ship established between ination and its explanatory variables, to understand andchrcterzethetypesofremesfound.Tocompetethecteorztonofremes,we also observe the classication of periods provided by the probabilistic estimatesofthemostkeyremeprevntechpontnhstoryonwthnformtonboutthemneconomchstorcevents.Thstsk,thouhmorecompcted,reveals a richer approach to understanding the dynamic of ination.

anothermportntfeturethtcomeswththeestmtonofNewKeynesian curve Phillips with inationary inertia is that endows the model with asufciently rich dynamical structure that can be employed to describe the processof formation of inationary expectations. In the spirit of Sargent (1987), and dif-ferently than the approach of Evans and Wachtel (1993), in this paper, inationaryexpecttonsressumedtobe thesoutonof thedynmcmodeestmtedneach regime. This interpretation of how inationary expectations are formed allows

linking the behavior of expected ination to the time trajectory of the explanatoryvrbes,ndoffersnddtonntutonofwhtfctorsmydrvethechnesin the ination dynamics.

inordertoestmtethetypeofmsmwereproposn,weneedtodpttheEMorthmexpnednHmton(1990),whchsmnyppedtou-toreressveprocesseswthconstntmenperreme.WechoseusntheEM

1Mendoz (2006) studes excusvey the phenomenon of the pss-throuh of the nomn exchne rte nMendoz(2006)studesexcusveythephenomenonofthepss-throuhofthenomnexchnertenVenezuenthecontextofnon-nervarestmtedwthsmoothtrnstontechnques.


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zt=1xkvectorthtcontnstheexpntoryvrbes(coudncudeedvuesofy);

bsi=kx1 vector of coefcients associated to regime si,whchby

denition is unobservable; and esi,t~N(0,s2)ssossoctedwthremesi.

ThetotnumberofpossberemesorhddensttessvenbyN,ndthe realizations of particular states are governed by the following rst-order MarkovprocessQt,suchtht:

Pr qt = sj| qt1= si( ) =pij

Pr q1 = si( ) = i

pij = 1

j=1

N

, i =1i=1

N

1 si,sj N

(2)

Thesepijscnbeorderednsocedtrnstonprobbtymtrx P,whetheuncondtonprobbtesofhddensttes(pi)rerepresentedwthcoumnvectorPofntprobbtes,sfoows:

P =

p11

p12

M

p1N

p21

p22

M

p2N

K

L

K

L

pN1

pN2

M

pNN

, =

1

2

M

N

(3)

Thebovedescrptonmpestht,oncereztonofremeoccurstvenpontntme,theobservbevrbeytexhbtscondtonmenequ

toztbsi.Then,thereztonofthenexthddensttesrndomdrwovernedbythe transition probabilities dened in P.Thecompetemodecnbechrcterzedbythesetofprmeters={P,P,B},whereB={bs1,bs2,,bsN,s12,s22,sN2}depctstheretonshpbetweentheendoenousndtheexpntoryvrbesofthemodeforNdfferentremes.

Theestmtonofthebovemodesperformedthouhthempementtonof the EM algorithm, which nds the set of parameters that maximizes the likeli-hoodfunctonof theobserveddtthrouhntertveexpecttonprocess.WechoseusntheEMorthm,stsdonenmostofthenon-economcterture,


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becuse()thsorthmsquterobustwthrespecttopooryseectedstrtnvuesndquckymovestoresonbereonofthekehoodsurfce(Hm-ton,1990).Thsmpesthtfordfferentstrtnvues,theorthmconveres

tothesmesoutonwthretveyfewtertonsndmnmzestheprobemofevutnhundredsofntvues.

gventhestructureofthemode,thetheoretckehoodfunctonforsequenceofobserveddtYT={y1,y2,,yT}hstoconsderthepossbesequenceofhddensttesthtcoudhveoccurred,nmet ST={q1,q2,,qT}.Thssthecsebecusehddensttescondtontheprobbtydstrbutonsoftheendoenousvrbe,ndctnthtjontprobbtyofhddensttesndobservtonsmustexst.Therefore,knowntheprmetersofthemodendprtcursequenceST, this joint probability can be dened as:

Pr YT,S

T)= Pr q1( ) Pr qt qt1( )

t= 2

T

Pr y t qt,z t( )t=1

T

)

(4)

andthetheoretckehoodfunctonfortheentresmpeL(Y/)cnbesmpywrttens:

L Y( )= Pr YT, ST ( )S

= Pr q1( ) Pr qt qt1( )t= 2

T

Pr yt qt,z t( )t=1

T

S

(5)

Where,fornstnce:

g S( )S

=qT= s1

SN

q T1= s1

SN

g q1,q2,K ,qT( )q1= s1

SN

.

Thts,theke-hoodfunctonmustconsderpossbesequencesofhddensttes,ndnotonyprtcursequence.

However,theexpressonstompementtheEMorthmredervednotbydrectymxmznthekehoodfunctonn(5),butbymxmznnterntveexpressonQ((l),(l-1))thtmkesexpctthefctthtmxmztonschevedtertveybyconsderndverseprmetervuesforthemode.Theproof of this equivalence can be read either in Hamilton (1990) or Welch (2003).Theprtcurformforthsterntveexpressonsvenby:

Q

l( ),

l1( )( ) = ln Pr YT, ST l( )( )S

Pr YT, ST l1( )( )

(6)


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Theargumentsof(6)denotetheexistenceofasequenceparameters{(1),

(2),,(l)}thatareusedinthedifferentiterationsofthemaximizationprocess.Thisfunction,accordingtoHamilton(1990),canbeinterpretedastheexpected

log-likelihood(forallsequencesofhiddenstates)oftheobservablevariablepa-

rameterizedby(l),wheretheweightsoftheexpectationoperatoraregivenbythe

jointprobabilityofdataandhiddenstatesparameterizedby(l-1).

Therefore, the application of the EM algorithm entails nding a sequence

ofestimatedparameters (1),

(2 ),,

( l){ }suchthatL((l)) L((l-1))isalwayssatised for any lthiterationofthealgorithm.Therecursiveapplicationofthisprocedure

leads eventually to nd a xed point where(l)=(l-1)issatisfactorilyapproximated,

and(l)=argmaxL(),thatis,(l)isthemaximumlikelihoodestimator.IntheEMalgorithm,theanalyticalfunctionalformsfortheparameter

estimates are obtained by solving the rst order conditions that maximize expression

(6)respectto(l).AmongtheseFOCs,Hamilton(1990)showsthattheestimation

of the regression parameters in (1) satises:

lnPr YT, S

T

l( )( )

l( )

( l)S

Pr YT, ST l1( )( )= 0

(7)

Sincethesequencesofhiddenstatesarenotdirectlyobservedbythe

econometrician,thentheyareinferredfromthesequenceofrealizationsoftheob-

servedvariableYT,whichentailstore-writingPr(YT,ST/(l-1))=Pr(ST,YT/(l-1))Pr(YT/(l-1)).Afterseveralalgebraicmanipulations,andachangeofrepresenta-tionofthesequencesofhiddenstates,Hamilton(1990)showsthatthemaximum

likelihoodestimatorB(l) must satisfy:

t=1

T

ln f y t qt = si, z t,

( l)( )

(l)

( l)

Pr qt= si YT, Z

T,

( l1)( )qt= s1

SN

=0

(8)

Where:

f(yt/qt=si,zt,B)=densityfunctionofytconditionalontheparameters

oftheregressionmodel,ontheassumedhiddenstateqt,andonztwhich

isarowvectorofdimensionkcontaininginformationonthelaggeden-

dogenousvariableandontheexogenousvariablesofthemodel(xt),such

thatzt={yt-1,yt-2,yt-p,x1t,x2t,,x(k-p)t}andpisthenumberoflagsfortheendogenousvariable.


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Ontheotherhnd,Pr(qt = si/YT,ZT,((l-1))stheprobbtythtthehddensttesihsoccurredttme t,condtonontheentredtsmpe:YT={y1,y2,,yT}ndZT={z1,z2,,zT},evutedntheprmeterestmtesfromtheprecednterton.inourmode,sredystted,wessumethtthecondtonsuchtht

f y t qt= si, z t,( ) =1

2 si2exp

y t z tsi( )2

2 si2

The specic form of the EM algorithm used in the estimation process ispresentednappendxa.atheeconometrcprormmnscrredoutnguss.

2. A Phillips curve estimation with Markov-switching

In this section, ination is analyzed through the estimation of a two-regime NewKeynesian Phillips curve. We model ination strictly as a function of lagged ination,indicating that only inationary inertia (and not inationary expectations) determinesthe level of the structural or underlying ination. Statistically, this simplifying as-sumptonwowfttnthemodewthnthecssofmodespresentedn(1),ndwsoenbeshowntheenthofthempctofshockshttntheeconomyin each regime. Theoretically, the existence of inationary inertia is related to the

existence of a staggered price setting, which means that, if rms change pricestdfferenttmes,djustmentofthereteprceevetoshockstkesoner,evenwhenndvduschneprcesfrequenty(B,MnkwndRomer,1988).This is equivalent to stating that during periods of high inationary (or price level)nert,shockshvererndonerstneffects.Furthermore,nncreseninationary inertia would imply a higher dispersion in the timing of price adjust-ments by individual rms, or equivalently, a larger coordination failure betweenrms in acknowledging the occurrence of aggregate demand shocks.

The pressures of aggregate demand on ination are summarized by the inclusion

oftheoutputp(theiscomponent)ndvrbethtmesuresthequnttyofmoneycretedbythepubcsector(thelmcomponent)sexpntoryvrbes.Thsmoneyvrberepresentsthemnsourceofmoneysuppyntheeconomyndtstheresutofcombnnthesttemonopoyoftheoctvtywththefctthtnmportntszeofdomestic public expenditures is nanced with oil resources. Its inclusion as an additionalaggregate demand factor tries to nd out if an excess of money supply respect to the sizeof the nominal output will impinge a positive pressure on the ination rate. Ination alsodependsonthenomndeprectonofthedomestccurrency,swytocknowedethe potential impact of cost-push elements (supply shifters) on the ination dynamics.


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thtconveredtothemxmumvueoftheemprcexpectedo-kehoodfunc-tion. Initial unconditional probabilities ((0))weresetstheerodcprobbtesoftheMrkovprocess,ssuestedbyHmton(1994).

afterppyntheEMorthm,estmtonresutsresummrzednTable1. Estimated coefficients in regime 1 show that ination responds signicantlytotheexpntoryvrbesofthemodentheexpectedmntudenddrec-tion. The autoregressive component of the ination is positive and strictly less thanone, describing ination as a stationary autoregressive process. Among of aggregatedemndfctors,theoutputphstheretestexpntorypower.Thepss-throuhcoefcient indicates that a 10% depreciation of the domestic currency will cause2% of increase in the rate of ination in the rst quarter and 6.1% in a year span.Rerdnthepubcmoneysuppy,nncreseofthsvrben10pontsofthenomngdp, will boost ination in 2.8% the rst quarter and 8.5% in a year span.According to the relationship established between ination and the explanatoryvrbes,onecoudchrcterzethsremesthenormstteoftheeconomy,or at least as a regime in which ination is appropriately described by the theory.

Table 1

Two-regime coefcient estimates for the Phillips curve

Regime EstimatesParameters

1

2

R-squared

AdjustedR-squared

S.E. of regression

Sum squared resids

Source:Ownccutons.

0.0050

0.0000

0.0004

0.0311

0.0000

0.0000

0.0000

0.00000.0223

0.0012

-2.901602

45.80546

3.75882

2.200452

8.852313

-7.872397

60.438563

9.495787-2.337526

3.379271

295.1499

1987.0159

0.0000

0.5579

0.8950

0.0091

0.000368

0.000319

0.013587

0.016161

0.000523

0.000023

0.000388

0.0046720.001226

0.000106

Log likelihood

F-statistic

Prob (F-statistic)

-0.055658

0.818271

0.438148

0.279732

0.202377

-0.037591

1.191053

0.649072-0.081859

0.034802

0.4421

0.8945

0.0166

Dependent Variable: Inf

Estimation Method: EM

Sample (adjusted) : 199 0Q2 200 8Q4

Included observations: 75 after adjustmentsIterations: 70

Std. Error Prob.t-Statistc

a11a111

a22

a222

0.9913

0.9908

0.0134

0.0126


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On the contrary, at a rst glance, estimated coefcients in regime 2 seemnottoconformtotheresutsntcptedbythetheory.Themoststrknchrcter-istic of this regime is that the autoregressive coefcient of inflation 2,thouh

postve,sstrctyreterthnone.4Fromthesttstcpontofvew,thsmpesthat ination is an explosive stochastic process. In a two regimes dynamic, this doesnotseemreprobem,sncethewhoestochstcprocesscoudbeboundedbythepece-wsesttonrtyoftheseresunderreme1.indeed,thsresutscosetotheresults found in the literature in which the ination follows a random walk processin one regime, and an autoregressive process in the other (Evans and Watchel 1993;Simon 1996). Nonetheless, since the literature denes that there exists inationaryinertia when the coefcient accompanying lagged ination is positive but smallerthan one, the difcult task is to theoretically understand if, in this case, we can stillinterpret the lagged value of ination as inertia or if we need to look for an alterna-tventerprettonofthephenomenon.

Several works have analyzed ination in Venezuela, but only three ofthem have explicitly referred to the problem of inationary inertia. Dorta, uerraand Snchez (1998) in their analysis of the ination for the period 1970 to 1997,state that inationary inertia has increased since 198 mainly due to the reducedcredbtyofentsntheperformedeconomcpocy.vrez,Dortndguerr(2002), in their analysis of the period 198-2002 using a Kalman lter estimation,show that the coefcient of lagged ination has increased in a piece-wise fashion,rst during 1989-1997 and then during 1998-2002. However, this coefcient hasalways uctuated between 0.5 and 0.8, and its behavior is basically explained by theprocess of price indexation and the own volatility of ination. Additionally, uerrandPned(2004),whenstudynthempementtonofboundsystemfortheexchange rate (1997 to 2002), claim that, although the ination rate had shown adescendnpthdurnthewhoeperod,furtherdecresewsprecudedexctybecause of the existence of a greater inationary inertia. This empirical evidence,even it could related intuitively to our ndings, does not provide yet an alternative

interpretation to having an estimated coefcient on lagged ination that is greaterthnone.

3. The formation of inationary expectations

adfferentmnnertoproceedfornterpretntheestmtesobtned,prtcuryin regime 2, is to relate the magnitude of the autoregressive coefcient tothe

4a stndrd contrst of hypothess rejected the nu tht theastndrdcontrstofhypothessrejectedthenuthtthe2 1.


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inreme2,ofthereevntnformtonboutthefuturestteoftheeconomy, the most important piece to form expectations about ination is the outputp.Fornstnce,ftheeconomysexpectedtorowbovetspotenteve,then

expected ination will tend to drop below 20%, while if the economy is expectedto be in a recession, expected ination will tend to rise above 20%. Regarding theothervrbes,nexpectedncresenthequnttyofmoneywhvepostveimpact on expected ination. On the contrary, an expected increase in the exchangerate will diminish the current expected rate of ination.6 This nding, although unu-su,cnberetedtostutonsofreexchnertepprecton,wherenomndeprectonscnbepercevedsmechnsmtoreducethemss-nmentofthereal exchange rate, and therefore slow down the overall rate of ination.7

Theoretically, the fact that in regime 2 current inationary expectationsdependonentsexpecttonsonothervrbes,cnbesupportedbythepremsethtrtonentsusethereevntnformtonvbetoformtherexpect-tons,whchnthscsesthesubjectvenformtononhndboutkeyvrbessuchsrowth,exchnertendqunttyofmoney.Thswyofformnexpect-tonsowsbenthsreme2srtonexpecttonreme,sopposedtotheotherestmtedremenwhchexpecttonsreformednbckwrdooknmnner.

ifwepresumethtentsmodfytherbehvorccordntotherex-pecttons,then,usnsubjectvenformtonrerdnthefutureperformnceoftheeconomypresumbybrnsboutdjustntheprcnstrteyonoods.Rerdnthspont,wecnookforsupportnWoodford(1991)whenexpn-ntht,wthoutrequrnnyobjectvechneneconomccrcumstnces,thedereeofoptmsmofeconomcctorscnhvenmportntroenexpnnrecurrent cyclical uctuations of the business activity, and consequently ination.However,morechenntskstojustfywhytheexpectedoutputpsthevrbethtentsmostytkentoconsdertonforformntherexpect-tonsndutmteyforestbshntherprcnstrtey.Onecoudruetht,

nreme2,theexpectedoutputpbecomesthebestproxyfortheszeofthedemndthtseersofoodswoudfcenthefuture.Therefore,sdemndsexpectedtorse,revenueswbeobtnedbyncresnthemountofoodssodorproducedndprcescoudbeowedtoncreseess.atthemcroeve,snSttz(1991)ndRotemberndSoner(1991),thscoudmpythtthe

6in ths cse the nnu pss-throuh s -0.20.inthscsethennupss-throuhs-0.20.7Ths coud hppen f the reducton n ents re ncome cused by the deprecton essens more thn propor-Thscoudhppenfthereductonnentsrencomecusedbythedeprectonessensmorethnpropor-

tionally the demand in non-tradable goods, which are the main boosters of ination in situations of real exchangertepprecton.


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downwrd-soppndemndfcedbyseersndproducerswoudshftoutwrdndbecomemoreestcdurnphsesofeconomcexpnsonscompettonnthemrketsexpectedtokckn.

Empirically, the frequent occurrence of regime 2, i.e. 56% of the timesaccording to our estimations, would imply that agents expectations on ination arenverseyretedtotheexpectedeconomcrowth.infct,ooknttheposoneconomic outlook collected by the Central Bank, we veried that, on average, thereis a signicant negative correlation (-0.81) between inationary expectations andgrowth expectations. This can be veried by eyeballing igure 1.

Figure 1

Annual inationary and growth expectations

Source: Venezuelan Central Bank Surveys on Inationary and rowth Expectations.

Growth Expectations Inflationary Expectations

50

40

30

20

10

0

-10

-20

2-2000

3-2000

4-2000

1-2001

2-2001

3-2001

4-2001

1-2002

2-2002

3-2002

4-4002

1-2003

2-2003

3-2003

4-2003

2-2004

2-2004

3-2004

4-2004

1-2005

2-2005

3-2005

4-2005

1-2006

2-2006

3-2006

4-2006

1-2007

2-2007

3-2007

4-2007

1-2008

2-2008

One important result of the estimation performed is the (ltered andsmoother)probbtescomputedforechobservtonofthedependentvrbe.These probabilities reect the likelihood that each hidden state has occurred, al-owntocssfyechqurteroftheestmtonperodccordntooneoftheregimes, as shown in gure 2. Then, this classication along with the main economichstorceventsprovdesnotonofwhchcrcumstnceswerepresentdurntheoccurrenceofechreme.


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According to the classication of periods provided by the model, in manycses,thertonexpecttonremeconcdeswthepsodesofmcroeconomcinstability or with the last part of non-oating exchange rate systems that usuallyended up with speculative attacks and reforms. In fact, the rst long period of regime2 detected by the model (1991:03 to 1995:01) corresponds to a period of general(political and economic) instability coupled with a nancial crisis.8aso,sre-sponsetotherecurrentspecutvettckstothesystemofmneddevutonsapplied since 1993, at the end of this period (second quarter of 199) an exchangertecontrowsmpemented.Thesecondperodofreme2(1996:02to1996:04)correspondstotheendoftheexchnertecontrostrtedn1994ndtheben-nnofthempementtonofsystemofexchnerteboundsnJuyof1996.

Figure 2

Regime classication for ination

Source:VenezuenCentrBnksttstcsndownccutons.

0.70

0.60

0.50

0.40

0.30

0.20

0.10

1990Q2

1991Q1

1991Q4

1992Q3

1993Q2

1994Q1

1994Q4

1995Q3

1996Q2

1997Q1

1997Q4

1998Q3

1999Q2

2000Q1

2000Q4

2001Q3

2002Q2

2003Q1

2003Q4

2004Q3

2005Q2

2006Q1

2006Q4

2007Q3

2008Q2

1

2

Regine 2 Regime 1 Inflation

8 In 1992, the government in charge confronted a military cup, and during the outset of the nancial crisis inIn 1992, the government in charge confronted a military cup, and during the outset of the nancial crisis in1994,thepresdentoftheCentrBnkresnedstheresutofexstncontrdctorypocyntentonsbetweentheCentrBnkndtheExecutvePower.


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Thssystemconsstedonestbshnupperndowerboundstothetrjectoryoftheexchnerte,suchthtdevtonsoftheexchnerteoutsdetheseboundstreredddtonnterventonsoftheCentrBnknthemrket. 9Therton

expecttonsttesndetectedbythemodettheendofthesystemofbounds(2000:01 to 2001:0), just before the implementation of a oating exchange ratenMrch2002.

On the other hand, the longest episode classied by the model as belongingto the rational expectation regime (200:03 to 2008:0) does not coincide withtheoccurrenceofnyspecutvettckthtedtothebndonmentofthecurrentexchnertesystem.Moreover,nthsperodtheeconomyexhbtedhhrtesofrowthbsedonrendonncresenoprces.Nonetheess,wecoudsttethtthsrowthhsttchedhheveofuncertnty,sncethedurtonndntenstyoftheoboomcnnotbeccurteyforecstedwthnypstnform-ton.infct,mostemprcevdencesueststhtoprcescnbererdedsrndomwkprocess,ndonycnbeconsderedssttonryutoreressveprocessfnyzednveryontmespn. 10inthsneofresonn,sncetherowthoftheeconomyshhydependentonthefuturedrwofexternshocks,entsstopookntthepstnformtonofthsvrbendreverttousnthevbesubjectvenformtonontsfutureperformnce.Then,theseexpecttonsonretedemndretheonesthtchnetheformtonofexpecttonsoncur-rent ination, therefore, determine the pricing strategy of producers and sellers. Asmtteroffct,sncetheendof2006ndprtcurythestqurterof2007,theeconomcrowthhsexhbtedcertendencytosowdownwhemostndctorsof forecasted and current ination show higher levels.

Succncty,thebovenyssshowsthewytochrcterzereme2sbenconsstentwthepsodesofhhuncertntyrerdntheperformnceofthe economy, either due to propitious conditions for the collapse of non-oatingexchnertesystemsortocondtonsofhhvunerbtytoexternshocks.However,tsstqueston,whtsthesourceofthesubjectvenformtontht

repcespstnformtononvrbesndbecomesthefocpontofeconomcctorsntherbusnessdecsons?

9 In practice, this period was a type of xed exchange rate since the chosen distance between the bounds wasIn practice, this period was a type of xed exchange rate since the chosen distance between the bounds wasretveysm.

10anothersource of uncertnty n the sustnbty of suchrowth cn be ttrbuted to the mportnt nsttutonanothersourceofuncertntynthesustnbtyofsuchrowthcnbettrbutedtothemportntnsttutonchnesmpementedbytheovernmenttochevesocsteconomy,prtcurysnce2004.


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Conclusions

In this paper we have analyzed the dynamic of ination in Venezuela during the last

twentyyersthrouhMrkov-swtchnestmtonofPhpscurve.rom the point of view of ination dynamics, the model recognizes an

exposvestochstcprocessndsttonryutoreressveprocess,bothofthemwthequexpecteddurtononceoccurred.Sncetheexstenceofnexposvestochstcprocesssnoncomptbewththestndrdchrcterztonrntedtothe phenomenon of inationary inertia, we restore to interpret these results in termsof their implications for the process of formation of inationary expectations.

Fromthepontofvewoftheexpecttons,themodedstnushesbe-tweennormorbckwrdooknremendrtonexpecttonreme.

In the rst regime, agents form their expectations looking at the past values of thevariables that typically determine ination: output gap, money creation and currencydeprecton.inthesecondone,entsmodetherexpecttonsmnybsedonthesubjectvenformtonvbeonthefuturerowthoftheeconomy,supportntheemprcyobservednotontht,nVenezue,stutonsofeconomccontrctonare, on average, associated with episodes of higher ination.

gventhessumptonsthtbudupmsm,tscerthtthstypeofmodescnonyoffersttstcnterprettonofwhtdrvesswtchnbetweenremes.However, in this paper the characterization of inationary expectations along withthemneconomceventsoccurreddurnechremehsprovdeduswthneconomic interpretation of which factors govern the inationary dynamics. In par-ticular, we nd that the rational expectation regime is consistent with episodesofhhuncertntyrerdntheperformnceoftheeconomyndthsuncertntyseemstohvetwodfferentsources:thecondtonsthtntcptethecopseofnon-oating exchange rate systems, and the conditions that signal vulnerability oftheeconomytoextern(o)shocks.

Thsresut,extrpoted tomoreenercontext,mycontrbute tobudconnectonbetweenmodesofcrsesdrvenbyfundments(thosenwhchsignicant economic variables are explained by the evolution of other relevant vari-bes,cedfundments)ndmodesnwhchoutcomesseemtobedrvenetherby self-fullling expectations or any other focal point of pertinent information. Thisconnectonwhtseemstoponttsthtbothtypesofmodesmhtbereevnttoexpnnthebehvorofeconomcents.athouh,whtessentytrersa modication in such behavior is some form of materialization of the uncertaintyboutfuturetmes,whchutmteychnesthenformtonsetusedbyentsto


18/22


formtherexpecttons.However,whtthspprochcnnotnswerswherethenformtonusednthesecrtcstutonscomesfrom.

Bibliographic references

lvarez ., M. Dorta y J. uerra (2002). Persistencia Inacionaria en Venezuela:evoucn,cussempccones,Estudios sobre la infacin en Venezuela,Crcs,Venezue:DeprtmentodePubcconesdebcv.

Arreaza A., Blanco E. y Dorta M. (2003). A Small Macroeconomic Scale ModelforVenezue,SeriedeDocumentosdeTrabajodelbcv, 3.

Bl.,g.MnkwndD.(1988).TheNewKeynesnEconomcsndtheOutput-Ination Tradeoff,BrookingsPapersonEconomicActivity,num.1,pp.1-82.

Blix, M. (1999). orecasting Swedish Ination with a Markov Switching var,WorkingPaperSeriesoftheSverigesRiksbank(CentralBankofSweden) ,num.76.

Dorta, M. (2006). La uncin de Produccin, el Producto Potencial y la InacinenVenezue1950-2005,SeriedeDocumentosdeTrabajodelbcv,nm.87.

Dorta M., lvarez . y Bello O. (2002) Determinantes de la Inacin en Venezuela:unnssmcroeconmcopreperodo1986-2002,Revistadelbcv,xvi,nm. 2, pp. 93-130.

Dorta M., J. uerra y . Snchez (1998). Credibilidad y Persistencia de la Inacin

enVenezue,Revistadelbcv,xii, nm. 2, pp. 135-156.Evans, M. and P. Wachtel (1993). Ination Regimes and the Sources of Uncer-

tnty,Money,CreditandBanking,25, 3, pp. 75-511.guerr,J.ndJ.Pned(2004).TryectordePotcCmbrenVenezue,

Temas de Poltica Cambiaria en Venezuela, Crcs,Venezue:DeprtmentodePubcconesdebcv.

Hmton,J.(1994).TimeSeriesAnalysis,Prnceton,NewJersey,USa:PrncetonUnverstyPress.

__________(1990).anyssofTmeSeressubjecttoChnesnReme,JournalofEconometrics, num. 5, pp. 39-70.

Khn,J.ndR.Rch(2007).TrckntheNewEconomy:usngrowthTheorytoDetectChnesnTrendProductvty,JournalofMonetaryEconomics,num.54,pp.1670-1701.

Km,C.ndC.Murry(2002).PermnentndTrnstoryComponentsofReces-sons,EmpiricalEconomics, num. 27, pp. 163-183.

Mendoz,O.(2006).lssmetrsdepss-throuhenVenezue,Monetaria,xxix, nm. 2, pp. 151-183.


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RotembersJ.ndg.Sonerg.(1991).aSuperme-TheorofprceWrsdurnBooms,NewKeynesianEconomics ,voume2,CoordinationFailuresandRealRigidities,Cmbrde,Msschusetts:mit Press, pp. 387-15.

Srent,T.(1987).MacroeconomicTheory,SnDeo,Cforn,USa:acdemcPress,inc.

Simon, J. (1996). A Markov-Switching Model of Ination in Australia, ResearchDscussonPper9611,ReserveBnkofaustr.

Sttz,J.(1991).PrceRdtesndMrketStructure,NewKeynesianEco-nomics,Voume2,CoordinationFailuresandRealRigidities ,Cmbrde,Ms-schusetts:mit Press, pp. 377-386.

Welch, L. (2003). Hidden Markov Models and the Baum-Welch Algorithm, ieeeInformationTheorySocietyNewsletter, 53, 1, pp. 10-13.

Woodford, M. (1991). Self-ullling Expectations and luctuations in AggregateDemnd,NewKeynesianEconomics ,vo.2,CoordinationFailuresandRealRigidities,Cmbrde,Msschusetts:mitPress,pp.77-110.

Appendix A

The EM algorithm

In order to estimate the model (1)-(3), the implementation of the EM algorithm innylthtertonmpesfoownthenextfoursteps.

Step 1

1.gventheestmtedprmetersntheprecednterton((t-1))ndthesequenceoftheobservbevrbeunttmet(Yt),estmtetheprobbtythtechpos-sbesttesihsoccurredttmet,computnrecursvey,fromt=1throuht=T,thefoownexpressons:

() 1 0= ( l1)

(b) t t =

t o

t t1

jN' t o t t1( )

(c) t+1 t= P

( l1)

t t

(d) f y t z t,( l1)( ) = jN' t t1 o t( )


20/22


Where: t,t/t,t+1/t,jN= column vectors of dimension N, dened as:

t=

f y t qt= s1, z t, (l1)( )

M

f y t qt= sN, z t, (l1)( )

t t=, ;

Pr qt = s1 t, ( l1)( )

M

Pr qt =sN t, ( l1)( )

, j

N=

1

M

1

f(yt/qt,zt,B(l-1))=condtondenstyforventmeperodevutednprmetersestmtesfromtheprecednterton;nd

()=neementbyeementmutpcton.Notcethtbecuseoftherecursventureoft/t,thesetofnformton

usedstYtZt,whchsoncudesthesequenceofreztonsoftheedendoenousndexoenousvrbesofthemodeunttme t(Zt).Thsmustbethecse,becusetechtmet,theorthmneedstoevutethekehoodthtprtcurhddensttehsoccurred,buttknntoconsdertonthttstrnstoncoudhvetkenpcefromnypossbesequenceoft-1hddensttes.

Step 2

Usethecompetesequenceoftheobservbevrbe(YTnstedofYt)tore-est-mtetheprobbtesthtechpossbesttesihsoccurredttmet.ThesenewprobbtesrecomputedwththeKmsorthmndrereferredbyHmton(1990,1994)ssmoothprobbtes.Thsorthmsppedrecursvey,fromt+1=Tbckwrdtot=1,ccutnthefoownexpressons:

() t+1/T=,t+1/t for t+1=T

(b) t/T=t/t{P(t+1)(t+1/Tt+1/t)}(c) i,t/T=Pr(qt=si/t,(l-1)){Pt(l-1)(t+1/Tt+1/t)}i=1,,N

Where:

()ndctesneementbyeementdvson; i,t/T=coumnvectorofdmensonN;nd Pi=estmtedithcoumnofmtrxP:


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i,t T=

Pr qt= si, qt+1= s1 T, ( l1)( )

M

Pr qt= si, qt+1=sN T, ( l1)( )

P

i

=

pi1

pi2

MpiN

,

Step 3

Re-estmtethemodeprmetersforthslthterton,bysovnthedfferentFOCsthtmxmze(6).accordntoHmton(1990,1994)thsproceduresequventtocomputn:

() Trnstonprobbtesusntheequtons:

Pi

(l)= i,t Tt=2

T

t T

t=2

T

fori=1,,N

(b) Uncondtonprobbtesofbentechsttefoown:

(l)= t Tt=1

T

T

(c) Prmetersofthereressonmoden(1),bysovntheFOCssttedn(8),suchtht:

si(l)= z ' si z( )

1

z ' si yfori=1,,N

si2=

y z si(l)( )' si y z si( l)( )jT ' si jT

fori=1,,N

Va r si( )= si2 z' siz( )

1

fori=1,,N


22/22


where:

y =

y1

y2

M

yT

z =; ; ; ; ;

z11

z12

M

z1T

z21

z22

M

z2T

K

L

K

L

zk1

zk2

M

zkT

si=

1,si

2,si

M

k,si

si=

1,si

2,si

M

T,si

jT =

1

1

M

1

si=

Pr q1= si T, ( l1)( )

0

M

0

0

Pr q2= si T, (l1)( )M

0

K

L

K

L

0

0

M

Pr qT= si T, (l1)( )

.

Step 4

Evuteftheprmeterestmteshvettnedfxedpont,thts|(l)(l-1)| 10-8.Then,verfythttheemprcexpectedo-kehoodfunctonofthedependentvrbe(forhddensttes),hssochevedmxmum.

This verication implies observing, for:

E g y (l)( )[ ] =

t=1

T

ln f y t qt= si, z t, (l)( ) Pr qt= si T, (l1)( )qt= s1

SN

thtE[g(y/(l))]E[(y/(l+1))] tolerancevalue.Themxmzton

ofthsexpectedo-kehoodfunctonshoudbeesyconfrmbesncetsby-productoftheestmtonprocess,nprtcurofthempostonoftheFOCssttedn(8).

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