Curva de Phillips y Tasa Natural de Desempleo

7/27/2019 Curva de Phillips y Tasa Natural de Desempleo

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The Phillips Curve and the Natural Rate of InflationAuthor(s): David G. HulaSource: Policy Sciences, Vol. 24, No. 4 (Nov., 1991), pp. 357-366Published by: SpringerStable URL: http://www.jstor.org/stable/4532234 .

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358withrespectto the unemployment ate is less than one for Canada,Italy, heUnitedKingdom,andWestGermany.Hsing'sresults mplya relatively steep'Phillipscurvefor the U.S.- a result nconsistentwithdownwardnflexibilityof nominalwagesandtargetpricingpractices.Accurate statisticalestimation of the Phillipscurverequiresthat supply-side shocks be includedas explanatoryvariables,measured n as preciseafashionas possible.Some empiricalstudies of the Phillipscurve are ratherlacking n this respect.Hsing's1989 studymakes a commendableattempt ocapturethe effects of supply-sideshocksby using a binaryvariablewith avalue equalto one during periodswhen supply-sideshockswere especiallypronounced.Perhapsa still betterapproach s to includeexplanatoryvari-ables whichpreciselymeasurethe values of the most importantsupply-sideshocks for eachyearof the sampleperiod.Empirical nvestigation onductedin this studyuses thisapproach o obtain a new estimateof thePhillipscurvefor the U.S.economy.As previouslymentioned,cost-plustargetpricingpracticesanddownwardwagerigidityresulting romimperfectcompetition n both outputand inputmarketsshould resultin a relatively lat Phillipscurve.Under whatcircum-stanceswill the Phillipscurvetend to be 'flat' n a perfectlycompetitiveecon-omy?Thisstudyalsodevelopsa theoreticalmodelof thePhillipscurveat theindustryevel of aggregationo answer hisquestionand to provideadditionalinsights ntothenatureof theinflation-unemploymentelationship.

II. Derivationandanalysisof the shortrunPhillipscurveThe short runPhillipscurvefor an entireeconomy maybe thoughtof as aweightedaverageaggregateof all the short runPhillipscurvesapplicabletoparticularndustrieswithinthe economy.Industry-specifichortrunPhillipscurvesmaybe aggregatedn this fashion becauselaborimmobilitiesusuallyprevent workers who become unemployedin one industryfrom quicklyobtainingemploymentin anotherindustry;re-trainingof workers is bothcostly and time-consuming,and many laid-off workers are reluctant o re-train because they believe their lay-offsare only temporary.The short runinflation-unemploymentrade-offfundamentally ccurs at the industry evelof aggregation.The short run industryPhillipscurvedepictingthe relationshipbetweenthe growthrate of industry output price and the unemploymentrate forindustryworkers s obtainedby holdingshort runcost andsupplyconditionsconstant,and increasing ndustrydemandfrom a given initialposition bysuccessivelygreater ncrements,with the initialpositionof demandbeingthesame before each demand shift. Each demandincrease' will result n a par-ticularprice rise and a particular orrespondingnflationrate,with the un-employmentrateassociatedwitheachinflationratebeingdictatedby the out-



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359put levelthat resultsafterthe demandshift occurs.Supposeanindustry acesa lineardemand unction

Pd= a- a2Qd + Y,wherePd is demandprice,Qd is industryquantitydemanded,a1 and a2 arepositiveconstants,andy is the exogenousdemandshockwhichgenerates hePhillipscurverelationship,whichmaybe due to expansionarymonetaryorfiscalpoliciesor anyother factor.Theindustry'supply unction2sPs = P3 + P4Q,

where Ps is supply price, Qs is industry quantity supplied, and ,33and 14 arepositiveconstants. ndustry quilibriums achievedwhen

Pd- Psor

a1 - a2Qd + Y = p03+ 34QsIn equilibrium, Qd = Qs = Qe, where Qe is industry equilibrium quantity,so

al -a2Qe + Y = 3 + P4Qeand

Qe Cal+ y - P334 + a2

The change n industryequilibrium utputresultingroma one unitchange ny isgivenbydQe 1dy 34+ a2

Since dy = y,dQe= 14 + a2

The percentagechangein equilibrium utputfor the industryresulting romthe externaldemandshock3 sy

dQe _4 + a2 _Rq Qe a1 -133 a,-13P4 + a2

EquilibriumndustrypriceisPaa +y 3-4Pe +I X2 Ie-a,-^ ^ . +Y~~~~~_



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360Thechange nPeresultingrom a one unitexternaldemandshockis

dPe a2-1-dy 4+ a2Since dy = ,

dPey - 34+ (12So the inflation rate for the industryresultingfrom the external demandshockis

dPe YP4Pe ca,P4 + 02P3

SinceY = Rq(a, -3),

theindustrynflationrate s

Rp ( - (1)C1134 + (~2P3To obtainthe short runindustryPhillipscurve,Rq must be expressedas afunctionof the industryunemployment ate afteran externaldemand shockoccurs.Theindustry quilibrium nemploymentateUeis definedas

L- LeUe =where L is the size of the industrylabor force and Le is the equilibriumamountof labor the industryemploys.An externaldemand shockcreatesanunemployment atechangemeasuredbydU in thefollowingequation:

UA = Ue + dU,whereUA s theunemployment ate thatoccurs after he demandshock at thenew equilibrium utput,Ue is the equilibrium nemployment ate before thedemand shockoccurred,and dU is the change n the equilibrium nemploy-ment rateresultingrom the demandshift.Thelabor-output atio s denotedby 0, so that

Le = OQe,whereQeis equilibriumndustryoutputbefore the demandshift andLeis thecorrespondingamountof labor used. Parameter0 can be expected to in-creaseas outputand labor use increase,since the marginalproductof labor



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361can be expected to decrease with a fixed short run capital stock. Since 0changesasoutputand laboruse changes,

dLe = dOQe + OdQeGiventhatL-L L-Qe

L Land

dU = -1 dL = - [d0Qe+ dQe],UA maybe expressedas

L \ L /UA= LQ ,( [dOQe+OdQe]=1 L ) [Qe - dQe-OdQel\L e

=1 Q0dO Q Qe (dQe\=1- Qe- QeL L L Qe

Solving for dQe/Qe = Rq yieldsL dORq (1- UA)-1-

OQe 0SinceQ a -P

P4 + (a2theequation orRqbecomes

L(P4 + 2) dORq = (4 ) (1- UA)-- (2)

Substitution f equation 2) intoequation 1) yieldsthe equation orthe shortrun ndustryPhillipscurve,which s



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362

P (LP4)(_4 +a2) UA (LP4)(P4 + 2)p (-)(a 4 +aC23) A O(ai4+(3))

P4(al - P3) +datl4 -+a2133

Equation(3) indicates the shortrunindustryPhillipscurve is downward-slopingand linear,with its position beinginfluencednot only by the size ofthe industry abor force, the labor-outputratio,and the growthrate of thelabor-output atio asoutput ncreases,but alsobyall the model'sdemandandsupplyparameters.The slopeof theshortrun ndustryPhillipscurve s

dR = (LP4)(4 +a2)dUA (-0)(a1134 + a2p3)Theabsolutevalueof thisexpressionand thesteepnessof thePhillipscurve spositivelyaffectedby the size of the labor force and negativelyaffectedbyparameters0, a,, and ,3.The Phillipscurve s madesteeper(i.e.,the numeri-cal value of the slope is madesmaller)by increasing he values of 34and a2,since

a (dRp L(al4 + 2a2,3P4 + ac23)34 dUA (-e)(al4 +a023)2

anddRp -L4 (a1 3)P

&aa2 \ dUA I 0(uI14 + a2,3)2Underperfectlycompetitiveoutputmarketconditions, hePhillipscurvemaybe either'steep'or 'flat,'dependingupon the valuesof the variousstructuralparameters.4Growthsof productdemands over time (as measuredby in-creases n parametera for various ndustries)act to flattenthePhillipscurveovertime.

III. EmpiricalnvestigationThe functional orm chosenfor thePhillipscurveestimations asfollows:

P = ao + a (U) + a2(WG) + a3(OPG) + a4(LPG) + a5(LFG)



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363where:

P = inflationrate of outputpricesU = unemployment rateWG = wage rate growth rateOPG = oil price growth rateLPG= laborproductivity rowthrateLFG = labor force growth rate

Annual datafor the United States for the 1961-1987 period gathered romthe StatisticalAbstractf the U.S.areemployed n thisstudy.The inflationrateis measuredby the annualpercentagechangeof the ConsumerPriceIndex,thewagerate s measuredby averagehourlyearnings or allU.S.industriesncurrentdollars,oil priceis measuredby the ProducerPrice Index for refinedpetroleumproducts,andlaborproductivitys measuredby thehourlyoutputof all persons in all business.The unemploymentrate is measuredby thenumberof people unemployedas a percentof the labor forcerather hanonanhours-lostbasis.A prioritheorizingargues hat coefficientsao,a2,a3,anda5 willbe positiveand coefficientsa, and a4willbe negative.Ordinaryeastsquares yielded the following regressionresults,with t-statistics n paren-theses:

P = 0.3625 + 0.2403 (U) + 0.6335 (WG)(0.171) (1.263) (2.857)+ 0.0633 (OPG)- 0.7778 (LPG)(3.485) (-2.538)+ 0.3635 (LFG), R2 = 0.8525(0.512)

The variablesmeasuring supply-sideshocks are all statisticallysignificantwith the expected signs. Wagerategrowthand oil price growthare both sig-nificantat the one percent evel;the approximatelyqualt-statisticsor thesetwo variablesarguethat higherwage rates and higheroil prices are aboutequallystagflationaryor the U.S. economy.The estimatefor laborproduc-tivity growthis significantlynegativeat the two percentlevel, implyingthatproductivity rowthshifts the Phillipscurve inward.The insignificantly osi-tive coefficient for the unemploymentrate is not surprising,since, if thePhillipscurve is rather lat,an insignificant stimateof eithera negativeor apositive sign would be expected for the unemploymentrate variable.Theregressionresultsin generalindicate thatduringthe past threedecades thePhillipscurvefor the U.S. has been rather lat but hasalsobeenverysensitiveto supply-side hocks whichhave shiftedthePhillipscurveupwardand whichmayhaveresulted n an over-estimation f the steepnessof the Phillipscurveby researchers who ignored or inaccuratelymeasured these supply-sideinfluences.



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364IV. ThePhillipscurveas a guideto macroeconomicpolicyTheoreticalnvestigation ndempiricalestimationof thePhillipscurveassistsin the determinationof macroeconomicpolicy in at least threeways: (1) itprovidesevidenceregardingwhetherornot a Phillipscurvereallyexists; 2) itidentifies how sensitivethe Phillipscurveis to supply-sideshocks and otherfactors;and (3) it may indicate whether currentmacroeconomicpolicy isoverlyconservative r overlyexpansionary.Someanalystshavequestioned heexistenceof thePhillipscurve n lightofthe stagflationary pisodes of the 1970's. But simultaneous ncreasesin theinflationandunemployment atesdo not implya short runPhillipscurvecan-not exist;a morelikelyexplanations that the Phillipscurve has shifted out-wardduringthese stagflationarypisodes as a result of supply-sideshockssuch as higheroil prices.The empiricalresultsof this studyindicate that thepositionof the Phillipscurve is verysensitive o such shocks. The theoreticalmodel presented n thispaperdemonstrateshat the shortrunPhillipscurveexists atboththeindustryand themacroeconomyevelsof aggregation.Althoughthe existence of the Phillipscurve has been substantiated o aconsiderabledegree, the numerical value of the inflation-unemploymenttrade-off s less clear.Even if macropolicymakerspossessedthisknowledge,theywould not be able to use macropolicyto precisely peg'the inflationandunemployment ates at theiroptimal evels,which are of coursesubject o dis-pute. Unanticipatedsupply-sideshocks can occur at any time, and policy-makerscannotpredicthow muchproductdemandswillchangedue to factorsother thanchanges n macropolicyvariables.Approximateknowledgeof the numericalvalue of theinflation-unemploy-menttrade-off s nonethelessuseful to policymakerswhen the Phillipscurveis judgedto be either 'flat'or 'steep'. f the Phillipscurveis flat,then the un-employmentrate can be 'substantially'educed at the cost of increasing heinflationrateonly 'slightly.' xpansionarymacroeconomicpolicyis warrantedunder these conditions.An increase in the price of oil or other negativesupply-sideshocksmayresult n the inflationandunemployment atesbeinghigherthananticipatedafterthisactionis taken,but the effectsof the macro-economicpolicyitselfwillstillbe favorable.Conversely,f thePhillipscurve ssteep,a 'slight'reduction n the unemployment ate can only be achievedbygeneratingsubstantial'nflation.A less expansionarymacroeconomicpolicyis appropriateunder these circumstances. f the Phillipscurveis judgedtohave a 'moderate' lope, then it is not clearthatmacroeconomicpolicy,how-ever conducted,will enhance social welfare,since therewill essentiallybe a'one-for-one' rade-offof the inflationandunemploymentrates; f the infla-tion rate increasessubstantially nd the unemploymentrate decreasessub-stantially,t is not clear thatsocietywilleithergainor lose, giventhat nflationandunemploymentare both considered nherently eriousproblems.A cleargainin socialwelfareresulting rommacropolicywill onlybe possibleunderthese conditionswhen eitherthe inflation rateor the unemploymentrate is



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365judgedto be unacceptablyhighbefore macropolicyaction is taken.In sum-mary,knowledgeof the Phillipscurve'sslope is most usefulto policymakerswhenthe inflationrate s judgedto be eitherhighlysensitiveor highly nsensi-tiveto changes n theunemployment ate.The theoreticaland empiricalevidencepresentedin this paper indicatesthat the short runPhillipscurvefor the United States is rather lat,implyingthat substantial dditionalreductionsof theU.S.unemployment ate could beachieved at a minimal nflationary ost. If this hypothesis s valid,the targetmoney supplygrowthraterangeshenceforthchosenby the FederalReservecouldandperhapsshouldbe raisedabovethosethey mightotherwisechoose.Further esearch o confirm hisrecommendations desirable.

Notes1. The analysishere will be confinedto demand ncreasesandpositive nflationrates.Demanddecreasesand deflationratescould also be generated o obtain the portionof the shortrunindustryPhillipscurve yingbelowtheunemploymentateaxis.2. In specifyingan industry upplyfunction, he industrys assumed o be purelycompetitive.Thisassumptions not crucial; heindustry upply unctioncouldalso be assumed o be theshort runmarginalcost function of a pure monopoly producerof industryoutput,and a

Phillipscurvecould then be derived orthepuremonopolist.3. Theexpression orQe substituted nto theexpression orRq does not include heexogenousdemandshocky, becausey = 0 at the initial valueof Qe. Parametery is deletedfromtheexpression orPeusedto obtain heindustrynflationratefor the same reason.4. Itis straightforwardo show that an increase n thepriceof aninputwhosemarginal roduc-tivityvaries withoutput(suchas labor)will increasethe values of both f3 and 34.An in-crease n thewageratewillshift thePhillipscurveto the right,butwillnotnecessarilymakethe Phillipscurvesteeper,since [3 and 14exertoppositeinfluenceson the Phillipscurve'sslope.

ReferencesCottrell,A. (1984). 'Keynesianism nd the Natural Rate of Unemployment:A Problem in

Pedagogy.'Journal of Post Keynesian Economics 7, 2: 263-268.Domberger, S. (1972). IndustrialStructure,Pricing, and Inflation. New York:Harper & Row.Ehrenberg, R. G. and R. S. Smith (1988). Modern Labor Economics: Theoryand Public Policy,3rd.ed.Glenview, llinois:Scott,Foresman ndCompany.Emerson,M. (1984). 'TheEuropeanStagflationDiseasein International erspective ndSomePossibleTherapy,'n M. Emerson,ed. Europe'sStagflation.Oxford:ClarendonPress, pp.

195-228.Grubb, D., R. Jackmanand R. Layard 1982). 'Causesof the CurrentStagflation,'ReviewofEconomic Studies 49, 707-730.Helliwell,J. E (1988). 'ComparativeMacroeconomicsof Stagflation,' ournalof EconomicLiterature6, 1 (March): -28.Helliwell,J.F (1986). 'Supply-SideMacroeconomics,'CanadianJournalof Economics 19, 4(November): 97-625.Hsing,Y. (1989). 'On the RelationshipBetween Inflationand Unemployment:New EvidenceFrom Six Industrialized Nations,' Journal of Post-Keynesian Economics 12, 1 (Fall):98-108.



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366Johnston,J.(1980). 'The ElusivePhillipsCurve,' ournalofMacroeconomics :265-286.Koustas,Z. (1988). 'Is There a PhillipsCurve n Canada?A RationalExpectationsApproach,'JournalofMacroeconomics 0:421-434.Lucas,R. E.,Jr. 1973). 'SomeInternational videnceon Output-Inflation radeoffs,'AmericanEconomicReview63, 4 (June): 26-334.Myatt,A. (1986). 'On the Non-Existenceof a NaturalRate of Unemploymentand KaleckianMicro Underpinnings o the Phillips Curve,'Journalof Post KeynesianEconomics 8, 3(Spring): 47-462.Perry,G. L. (1975). 'Determinants f WageInflationAround the World,'BrookingsPapersonEconomicActivity2:403-435.Phelps,E. S., et al. (1970). MicroeconomicFoundations f Employment nd InflationTheory.New York:W W.Norton,1970.Riddell, W.C. (1979). 'The EmpiricalFoundationsof the Phillips Curve: Evidence fromCanadianWageContractData,'Econometrica 7: 1-24.Sachs,J.D. (1979). 'Wages,Profits,and MacroeconomicAdjustment:A ComparativeStudy,'BrookingsPapers n EconomicActivity : 269-319.

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