mortensen, pissarides - job creation and job destruction in the theory of unemployment

7/27/2019 Mortensen, Pissarides - Job Creation and Job Destruction in the Theory of Unemployment

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The Review of Economic Studies Ltd.

Job Creation and Job Destruction in the Theory of UnemploymentAuthor(s): Dale T. Mortensen and Christopher A. PissaridesSource: The Review of Economic Studies, Vol. 61, No. 3 (Jul., 1994), pp. 397-415Published by: Oxford University Press

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Reviewof EconomicStudies 1994) 61, 397-415 0034-6527/94/00200397$02.00?31994The Reviewof EconomicStudiesLimited

J o b Creation a n d J o bDestruction i n t h e Theory o f

UnemploymentDALE T. MORTENSENNorthwestern University

andCHRISTOPHERA. PISSARIDESLondon School of Economics

First version received December 1991;final versionaccepted December 1993 (Eds.)In thispaperwe modelajob-specifichockprocessn thematchingmodelof unemploymentwith non-cooperativewagebehaviour.We obtainendogenous ob creationandjob destructionprocesses nd study heirproperties.We show that an aggregate hock nducesnegative orrelationbetween ob creationandjob destructionwhereasa dispersionhockinducespositivecorrelation.The ob destruction rocesss shown o havemorevolatiledynamics han the ob creationprocess.

In simulationswe show that an aggregate hock process proxies reasonablywell the cyclicalbehaviour f job creationandjob destructionn the UnitedStates.

1. INTRODUCTIONRecentmicroeconomicvidence romtheU.S. andothercountrieshas shownthat argejobcreationandjob destruction lows co-existat all phasesof the businesscycle.'Individualestablishments ave diverseemployment xperiencesven withinnarrowlydefinedsectorsand regardless f the state of aggregateconditions.In this paperwe developa model ofendogenous ob creationand ob destruction ndincorporatet intothematching pproachto equilibrium nemploymentndwagedetermination.n ourmodel,establishments avediverse xperiences ecauseof persistent diosyncratichocks.We examine heimplicationsof the modelfor the processesof job creationandjob destructionand for the aggregatebehaviourof unemployment ndjob vacancies.The economy we examinehas a continuumof jobs that differwithrespect o valuesof labourproduct.Eachjob is designedto producea singleunit of a variation on acommonproduct.Each variation s uniqueto thejob and commandsa relativepricethatis subject o idiosyncratic isk,due to either asteorproductivity hocks.A key assumptionis that investment s irreversible,o an existingjob cannot switch the variation of itsproductonce the job has been created. But before creation,technology s fully flexibleand the firmcan choose the variationof its product.We model the idiosyncratic isk forexisting obsas ajumpprocesscharacterized ya Poisson arrival requency nd a drawing

1. For the U.S. see Leonard 1987), Davis and Haltiwanger1991) and Blanchard nd Diamond 1990),for GermanyBoeriandCramer 1991) and for Italy Continiand Revelli(1988).397


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398 REVIEW OF ECONOMIC STUDIESfrom a commondistribution f relativeprices.Largenegativeshocksinduce ob destruc-tion but the choice of when to destroythe job is the firm's.Jobcreationdependson theinformation vailable opotentialemployers. nempiricalwork two sources of newjobs are usuallygiven, existing firmsand new entrants.Mostnew job creationover the cycle is by existingfirms;in Davis and Haltiwanger's1990,1991)study of U.S. manufacturingstablishments,irms hreeyearsor underaccountforonly about 18%of total job creation.Existing firmshave good informationabout theprofitabilityof new differentiated roductswithintheirsectors, so a naturalassumptionto make is thatnew jobs aremoreproductive hanexistingones. We take thisassumptionto its extremeand assumethat newly-createdobs are the most profitablen the market.An assumptionof thiskindis lesseasily ustifiedfjob creation s by newentrants,a routethat we do not pursuehere.2Followingon from our assumptionthat idiosyncraticrisk is job-specific,we alsomodelthe matchingprocessas takingplace between ndividualob vacanciesand unem-ployedworkers,rather hanbetweenmultiple-jobirmsand workers.Consequently,withtheproductivity f newjobs at the uppersupportof the distributionanda largenumberof potential obs, there s a zero-profit onditionfor a newjob vacancythat canproducethe most highlyvaluedproduct n themarket.Given our assumptionof constantreturnsin the matchingtechnology,zero expectedprofit on a new vacancy is equivalentto amarginalproductivity onditionforany job -thatproduces he most highlypricedproductvariation.3Wagesare the outcomeof a bilateralbargain hat takesplacewhenunmatched obsand workersmeet and is revisedcontinuously n the face of productivityshocks. Anequilibriums a timepathforthe numberofjob/workermatches andhenceemployment)impliedby thematching awandrationalnon-cooperative ehaviourbyindividualworkersandemployers.We study both the aggregate teadystate of theequilibrium eterministicprocessand the dynamicadjustmentsn response o persistentaggregate hocks.In the next section,variousconceptsand notation are defined.Followingthat, inSection 3, the implicationsof micro and macro parameters or job creation and jobdestruction nd for steady-state acancyandunemploymentevelsarederived.The effectsof persistent"cyclical" hanges n the common macroand microparameters re studiedin Section 4. Section5 simulatesan exampleof the model and shows that our modelsolutionsproxyreasonablywelltheobservedbehaviour fjobcreationand ob destructionfoundin the U.S. data.

2. CONCEPTSAND NOTATIONEach firmhas one job that can be in one of two states,filledand producingor vacantandsearching. obs thatare not activelyproducingor searching redestroyed.Followingthe empirical iterature,we say thatjob creationtakesplace when a firmwith a vacantjob and a workermeet andstartproducing; peninga newjob vacancy s notjob creation,

2. Newentrants ave onaverage horter ivesthanexisting irms,whichwouldcontradict urassumptions.In a recentpaperrelated o ours,Caballeroand Hammour 1991)study thecyclicalbehaviour f job creationand job destructionn a vintagemodelof embodied echnical hangeby assuming hat newentrantsadoptthemostadvanced echnology.Anotherrecentpaper hat addresses hequestionof cyclical hanges njob creationand ob destructions by BertolaandCaballero1991),whereexisting irmsmoveprobabilisticallyetween wostates,good andbad,andjobs formaftera matchingprocess.3. For morediscussionof theunemploymentmodelsee the book by Pissarides1990)and thestochasticgeneralization ndcalibration y Mortensen1990).


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MORTENSEN& PISSARIDES JOB CREATIONAND DESTRUCTION 399thoughwe mightrefer to it as creatinga job vacancy.Job destruction akesplacewhena filled ob separatesand leavesthe market.Similarly,workerscanbeeitherunemployed ndsearching r employedandproduc-ing. We do not considersearchon thejob to avoidcomplicatinghe model,thoughourassumptionson technologyand wages implythat thereare incentives o search on thejob, unless the cost of on-the-jobsearch s too high.4Wagesarechosen so as to shareatall times the surplusfrom a job match in fixedproportions.The worker'sshare is fl.5Consequently,moreproductiveobs offerhigherwagesandsince ob vacanciesarecharac-terizedby the best technology n the market,newjobs offerthe highestwage.Eachjob is characterized y a fixedirreversibleechnologyandproducesa unit of adifferentiated roduct whose priceis p + uc. This pricecan be referred o as eithertheproductivityof the job or simplyas its price.p and a are common to all jobs whereas?isjob specific. is an aggregate omponentof productivity hat does not affectthedisper-sion of prices.Theparameter reflectsdispersion, nincreasen a representing symmet-ricmeanpreservingpread nthejob-specific hockdistribution requivalently nincreasein price variance.Theprocessthatchanges heidiosyncraticomponentof price s PoissonwitharrivalrateA.Whenthere is change,the newvalue of ? is a drawing romthe fixeddistributionF(x), which has finite upper supportcu and no mass points. Withoutfurther oss ofgenerality,F(x) can be endowed with zero mean and a unit varianceso that a is thestandarddeviationof thejob-specific omponentau.6Modellingthe arrivalprocessas Poissonimpliespersistence n job-specificshocks,butconditionalon change, hefirm's nitialconditionsdo not affect ts nextprice.Exogen-ous eventsthataffect hepersistence rdistribution f idiosyncratichocks(microshocks)shift A and a respectively.Events that affect the productivityof all jobs by the sameamountandin thesamedirection macroshocks) arereflectedn changes n the commonpricecomponentp.Firmscreate obs thathavevalueof productequalto theuppersupportof thepricedistribution,p + asu. Once a job is created,however,the firm has no choice over itsproductivity.Thus, ob productivity s a stochasticprocesswithinitialcondition heuppersupportof the distributionand terminalstate the reservationproductivityhat leads tojob destruction.Both ob creationand ob destruction recostless,so we caneitherassumethat the firmcan choose its technologyafter it is matchedto a workeror before it ismatched,withidenticalresults. n thelattercase,when a vacancy s hitby an idiosyncraticshock it exits and re-enters t thebest technology,so all activevacanciescanproduce heproductvariation hatcommandspricep + Eu.Filled obs, however,do not alwaysexitwhenthey arehit by shocks,becausethereis a cost of recruiting,modelledas a per-unitcost of maintaining vacancy,c. Existing illed obs aredestroyedonlyif theidiosyncraticcomponentof theirproductivity alls belowsome criticalnumberEd < u. Therefore, herate at whichexisting obs aredestroyed s AF(Ed).The rate at whichvacantjobs and unemployedworkersmeet is determinedby thehomogeneous-of-degree-one atching unctionm(v,u), wherev and u representhenum-ber of vacanciesand unemployedworkersrespectively,normalizedby the fixed labour4. On-the-job earch ntroducesnew resultsby drawing he distinctionbetweenworkerflows andjobflows.Herethetwoflowsareidentical.Theresults hat wehighlightn thispaperarenotaffectedby theabsenceof on-the-job earch.SeeMortensen1993).5. For motivationanddiscussionof thiswagerule,which s the one most frequently sed in the searchliterature,eeDiamond(1982),Mortensen1982)andPissarides1990).6. Note, except orthe lack of masspointsand a finiteupper upport estriction,hereare no othershaperequirements.


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400 REVIEW OF ECONOMIC STUDIESforcesize.Since vacanciesofferthehighestwageno job seeker urnsdown a vacancy,sothe transition rate for vacancies is q= m(v, u)/v = m(1,u/v), with q'(v/u) < 0 and elasticitystrictlybetween-1 and 0. The rate at which seekersmeetvacancies s vq/u=m(v/u, 1).Job creation is defined by the number of matches, m(v, u) = vq(v/u).

The unknownsof the model are the numberof job vacanciesv and unemploymentu, whichdetermine, hrough he matching echnology, ob creation,andthe criticalvaluefor the idiosyncratic omponentof productivity, d, that induces ob destruction.

3. STEADY STATESTheassumptions hatvacancies ost c perunit timeandthatjobs are createdat theupperend of thepricedistributionmply

rV= -c + q(vlu) [A6u) -VI, (1where Vand J(e) are respectivelyhe asset values of a vacancyand of a filledjob withidiosyncraticomponentE. Jobcreationuntil the exhaustionof all rentsimplies

rV=0. (2)Inorder o determine heproductivity-contingentage,w(?), we denotetheworker'sasset value from a match with idiosyncratic omponent? by W(E)and his asset value

fromunemployment y U. Totalmatchsurplus sS(e) = J(A) + W(E)- U. (3)

The wageis set to split the surplus n fixedproportionsat all times, soW(C)-U= ,BS(E), (4)

wherefi is a constantbetween0 and 1.Since irmshavetheoptionofclosing obsat nocost,a filled obcontinuesnoperationfor as long as its valueis abovezero. Hence,filled obs aredestroyedwhena productivityshockx arrives hatmakesJ(x) = (1 - P)S(x) negative.Foranyrealization , J(E) solves,

rJ(E)=p+uc-w(e)+2A(1-f,) Jr{maxS(x),0]-S(e)}dF(x). (5)Similarly, he value of thejob to the workersolves,

rW(c)=w(e)+2A3 {max[S(x), 0]-S(e)}dF(x). (6)Finally,thepresentvalue of incomeof an unemployedworker s definedby

rwU= b+vqlu)r [(ou)n-oU)], (7)where b is thfeexogenous value of leisure or unemployment income.


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MORTENSEN& PISSARIDES JOB CREATIONAND DESTRUCTION 401Adding up the value expressions 5)-(7) and makinguse of the sharingrule (4), weget,

(r+)A)S(e) =p+ as-b+ A {max [S(x), O]dF(x)-f(vq/u)S(Eu). (8)Since S(E) is monotonicallyncreasing n e, job destruction atisfies he reservation rop-erty.There is a unique reservationproductivityEd7 that solves J(ed) = ( - P)S(Ed) = 0,such that jobs that'get a shock 6< Ed are destroyed.This conditionand the fact thatS'(e) = a/(r + A) imply,afterintegrationby parts,

rEU(r+ A)S(E)=p + ag- b + A S'(X)[I- F(X)]dx- P(vqlu)S(Eu)Ed

=p+ Ug-b+ ? f [1 -F(x)]dx-P(vq/u)S(Eu). (9)Since S(Eu)=J(A6)/(0 -f) and S(ed)=0, (1), (2) and (9) imply,

PiC v cp+CTSd=b+ a - F(X)]dx. (10)IflOu r-TA EdThis is one of the key conditionsof the model. It gives the reservationproductivityntermsof the ratio of vacanciesto unemployment nd the parameters f the model, so,with knowledgeof v/u, it can be usedto derivethejob destruction ate,AF(ed).The left-hand ide of (10) is the lowest priceacceptable o firmswitha filled ob. Thisis less thanthe opportunity ost of employmentbecauseof the existenceof a hiringcost.The opportunitycost of employmentto the workeris the value of leisure b plus theexpectedgainfromsearch,whichin equilibriums equalto the secondterm on the right-hand side of (10). The thirdtermis a measureof the extent to which the employer swillingto incuran operational oss now in anticipationof a future mprovementn thevalue of the match'sproduct,i.e., it is the option value of retainingan existingmatch.That this is positive is indicative of the existenceof "labourhoarding"at low pricerealizations.8

Holding the v/u ratio constant, it is easily establishedby differentiationhat thereservation roductivity ddecreaseswith the difference etween heaggregate roductivityparameter,p, and the value of leisure,b. It is also easily established hat becausethedecrease n gd increases heoptionvalueof ajob, theincreasenp reduces he reservationpricep + USd: the rangeof pricesobservedat highercommonpriceexpands.The termflcv/(l - f)u standsfor the expectedgainfromsearch,which,without on-the-jobsearch,has to be given upwhenthe workeracceptsajob. A higherexpectedreturnfromsearch ncreases he opportunity ost of employmentand so leads to higherEd andto morejob destruction.An increasein A increasesthe option value of a job because ob-specificproductvaluesare now lesspersistent.So, at higherA ajob experiencing bad shockis lesslikelyto be destroyed.In contrast,a higherdiscountrate, r, reduces utureprofitabilityat all7. The reservationroductivity,rprice, sobviously + a6d Werefer o ed as thereservationroductivityto avoidthe more cumbersomeeservation alueof the idiosyncraticomponentof productivity.8. It caneasilybe checked hat if c=O, J(eu) =0 from(1) and(2) and so 8d= Eu: giventheexogeneityofp, b and a, jobs areeithercreatedat theuppersupportof thepricedistribution r destroyedwithout imit.


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MORTENSEN & PISSARIDES JOB CREATION AND DESTRUCTION 403

V/U JD

JcEd

FIGURE 1The joint determination of v/u and 8d

The effect of disperion,a, is to increasev/u at given Ed and so shiftJC up. It alsoincreases d at givenv/u, so it shiftsJD to the right.The overalleffect is an increase nE.9 As withA,the diagramgivesan ambiguous ffecton v/u but it can be establishedbydifferentiationhat v/u unambiguouslyncreases n a, regardless f the relationbetweenp and b (see the Appendix).The finalequation of the modelis the steady-state onditionfor unemployment, rBeveridgecurve.The flow out of unemployment qualsthe flow into unemployment tpointson the curve. The endogenous ob separation ateis AF(ed)and thejob matchingrateper unemployedworker s m(v/u, 1), so the equationfor the Beveridge urve s

U AF(Ed) (14)AF(ed)+m(v/u, 1)

It is conventional to draw the Beveridgecurve convex to the origin in vacancy-unemployment pace, but differentiation f (14) shows that in this model there is anambiguityabout the curve'spreciseshape.On theone hand,highervacanciesmplymorejob matchings, o unemployment eeds to be lowerfor stationarymatchingrate.On theotherhand,highervacanciesalso implymorejob destruction, hroughthe effectsof v/uon Ed, so unemploymentneedsto be higherto maintainstationary ob destruction ate.Thus,whether hecurveslopesdown ornot dependson the relative trengthof each effect.In modelswithoutan endogenous ob destruction ateonly the former(matching)effectis present and in that case the homogeneityof the matchingfunctionensures that theBeveridge urve s convex to theorigin. Sinceempiricallyhatshape s moreplausible,weshall assume here that the matchingeffect on the Beveridgecurve dominates the jobdestruction ffect and the curveslopesdown. This is shown in Figure2.In orderto obtain thesteady-state quilibrium acancyandunemploymentombina-tion we draw a line throughthe origin to represent he equilibrium olution for v/u,obtained rom(10) and(13) and illustratedn Figure1.We refer o this as thejobcreation

9. The Appendix shows that the condition for a positive effect of a on Ed, when variations in v/u aretaken into account, is now weaker. A sufficient condition for such an effect, though not necessary, is that p > b.


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404 REVIEW OF ECONOMIC STUDIESv

Jobcreation

Beveridgecurveu

FIGURE 2Equilibriumacanciesandunemployment

condition. Given the reservationproductivity, quilibrium acanciesand unemploymentare givenat the intersection f thejob creationcondition and the Beveridge urve.The job creationflow is m(v, u) and the job destruction low is AF(ed)(I - u). Theanalysisthat follows derives he initialimpactof parameter hangeson each conditionalon currentunemployment, . Obviously,unemployment ventuallyadjuststo equatethetwoin steadystate.Note that an increasenjob creationrotates hejob creationconditionup in v/u spacewhile an increase njob destruction hifts the Beveridge urve out.A positive netaggregateproductivityhock, represented y eitheran increasenp ora fall in b, increasesv/u and decreasesEd, so it rotates hejob creationcondition n Figure2 up and shifts the Beveridgecurve in. In other words,job creationincreasesandjobdestructiondecreases n responseto a positivemacro shock.Eventually,unemploymentfalls but theeffect on vacancies s ambiguous.The differences etween heseimplicationsand those of thepurematchingmodelis theshift in theBeveridge urveand theresultingambiguityof the vacancyeffect.

An increase n thevarianceof the idiosyncratichock increasesbothjob creationandjob destruction. ts effects n vacancy-unemploymentpaceareto shiftthe Beveridge urveout and rotate thejob creation ine up. Equilibrium acancies ncreasebut the effectonunemployments ambiguous.In contrast, a reduction n persistence, hown by an increase n A, rotates the jobcreationconditiondown and shifts theBeveridge urveout, giventhereservation roduc-tivity.The effectonjob destructions mitigatedand can be reversedn principle, hus notshiftingthe Beveridge urve, by the reduction n the reservation roductivitynducedbyan increase n shockfrequency.Whetheror not a sign reversaloccursdependscriticallyon themagnitudeof thediscountrate, r, and on the extent of thedispersionn theshock,a, as theeffectof Aon thereservation roductivityallswitheither(thedirecteffect endsto zero as r-+0 or c -+0) by virtueof (10).4. CYCLICAL SHOCKS

In this section we extend the model to the case whereone of the aggregatevariableschangesprobabilistically.We modelin detail the casewhere he commonpricecomponent


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MORTENSEN& PISSARIDES JOB CREATIONAND DESTRUCTION 405p takes two values, a high value p* and a low value p, according o a Poissonprocesswithratep. The Poisson processcaptures he important eature hat characterizeyclicalshocks, a positiveprobability ess than one that boom or recessionwillend withina finiteperiodof time.We also discussthecyclical mplications f changes n thedisperionof thejob-specificshocks.The purposeof this analysis s to bringout the differencesbetweenthe steady-stateequilibrium tudied so far and the equilibriumobtainedwhen thereisanticipationof aggregateproductivity hange.In themodel of Section 3 the steady-state quilibriumolutionsfor Ed and v/u for agiven pricep are given by equations(10) and (13). Sincein modelling he exhaustionofrents fromnew jobs both Ed and v were treatedas forward-lookingump variables,andhistorydid not matter n eitherof theexpressionsderived or them,the solutionsfor thetwo variablesumpbetween he steady-state quilibrium air Ed and v/u on theone handand Ed*and (v/u)* on the other,as price umpsbetweenp andp*. In contrast,unemploy-ment is a sticky variable,sinceit changesaccording o the lawsgoverning he matchingtechnology.The differential quationdescribinghe evolution of unemploymentor anygiven price p is

u=(1-u)AF(ed)-um(v/u, 1). (15)The steady-stateanalysis leads us to expect that sincep*>p, E* < Ed and (v/u)*>v/u. Therefore,when price drops from p* to p, some marginal obs are immediatelydestroyedandsome vacancies losedown.In contrast,whenprice ncreases romp top*,newvacanciesareopenedup butnothinghappens o employment nimpact.Thisasymme-try will turn out to have an importantcyclical implication or the behaviourof thejob

creationandjob destruction ates.As before, obs aredestroyedwhenever heir valuefalls below zero. Equations(1)-(4) of the steady-statemodel still hold for eachp. Theexpressions or the returns rom afilled ob, employmentandunemployment, 5)-(7), need to be modified o reflect he factthat commonprice may now change.Moving directly o the valueequationfor thejob'snet surplus 8), denotingby S*(e) thesurplus rom a filled ob whencommonprice sp*,andnotingthat if S(e) -Ed,

(16)rgu(r+2A+p)S*(E)=p*+ae-b+2A S(x)dF(x)- (vq/u)*S*(eu)+pS(e) _Ed,Ed (17)

(r.+A+P)S*(E)=p + u-b+ S*(x)dF(x)1-3(vq/u)* S*(u) d> eed.(18)

Equation 16) givesthesurplus romthe ob whenprice s at thelow valuep. It is indenticalto (8), exceptthat the possibilityof the price changing ormp to p*, at rateP, adds thetermp[S*(E) - S(E)] to the net return rom thejob. Equation(17) is the price equaltothe high valuep*. When e>_ Ed, the job surviveswhen the price drops fromp* to p;therefore, he net return rom thejob when the transitions expected allsby theexpectedcapitalloss p[S*(E) - S(E)]. In (18), priceis againatp*, but now thejob's idiosyncraticcomponent s belowEd . Jobs in this situationaredestroyedwhenprice dropsfromp* to


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406 REVIEWOF ECONOMICSTUDIESp, so theexpectationof thepricechange eads to the loss of thejob's surpluswithoutanygain (for thesejobs and by the definitionof Ed, S(E) Ed * and, from (16)and (17), OS*(E)/OE= /(r+ A)for e? Ed. Hence, integrationof (18) by parts gives,

(r+ A+ p)S*(e) =p* + sE-b-,(vqlu)*S*(,U)('rEd ATo - U+ [ [I-F(x)]dx+ X [I -F(x)]dx, Ed> E d* (19)

The reservation hockin the "boom"(when pricep* >p) therefore olves,PC AurEd Au ('enp*+UaE=b+, [ -F(x)]dx - [ -F(x)]dx. (20)

1-0 u -r+A+p~~~~C * IdA comparisonof (20) withtheequivalent xpressionn the steady state, (10), showsthat, given v/u, the only change introducedby the anticipationof the price fall is areductionn the optionvalue of thejob. The anticipationof a pricedropacts to increasethe rate at whichfuturereturnsarediscounted n therangeof Ewhere hejob is destroyedin the event of a pricedrop, from the constantr to the constantr+p. Obviously,thischange does not affectany of the equilibriumpropertiesof the reservationproductivitypreviouslyderived.In "recession" he expressionsdetermining he value of a job are (16) and (17).Differentiationwithrespect o E gives,

8S(E) S*(6) a > (21)and so integrationof (16) by parts gives,

(r+A+ p)S(e)=p+uc-b+ r [1 F(x)]dx-p(vqlu)S(?u)+S*(?)- (22)From (17) and (18) it follows that for E= Ed,

S*(ed) = u( -) (23)r+ A.+ PEvaluating 22) at E= Ed and substitutingS*(ed) from (23) into it gives the expressionfor the reservationproductivityat low commonp,

P+ bd=b c v_ r -F(x)]dx , (Ed -Ed)- (24)1 -Pu rA .Ed r+;t+pIn contrast to the reservationproductivityduring boom, the probability hat pricewillincrease ncreases he option valueof the marginalob in recession.Thus, firms are lesslikelyto destroya job in recession he higherthe transitionrateto the boom.Conditions(20) and (24) show that when cyclicalshocks are anticipated, he gapbetweenthe reservationproductivityat high and low commonpriceis less than impliedby thesteady-state nalysis.Thegap growsas theprobability f changing tate(measuredby the Poissonratep) falls.Apartfrom thatchange, however, he previousanalysisstill


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MORTENSEN& PISSARIDES JOBCREATIONAND DESTRUCTION 407holds,with a higherprobability hat a given ob willbe destroyed n recession, ollowingan idiosyncratichock,than in the boom.Job creation is found by computingthe value of jobs at the uppersupportof theprice distribution.From (16) we can write

(r+2+u)S(E) = (E-Ed) +,[S*(E) -S*(Ed)] (25)and from(17),

(r+2+u)[S*(e) -S*(ed)]=uf(e ed)+uS(e). (26)Solving(25) and (26) gives,

S(E) = ( Ed) (27)

Giventhe reservationproductivity,his is the sameexpressionas the one holdingin thesteadystate, (12). Therefore,vacancycreation n recession olves an expression imilar o(13),{v c 1 + A(q) r+ (28)

Equations(17) and (18) imply that the value of jobs in theboom,when 8 > Ed, is,S* = ,yC Q)+ A - S(e). (29)

r+t+p r+t+pMakinguse of (27) andevaluatingat ? = c,,we get, for vacancycreationat highp whereS*(u) = c/(1 - P)q(v/u)*,q(v/u)* c(r+2u)/(I -fl) (30)u(eV/U-=d4)-, P(?d- ed)/(r+ + p)

Therefore, omparingwith(13), evenforgivenreservation rices ob creation n theboomis less when there is the expectationof cyclicalchange.Now a comparisionof (30) with(28) showsthat (v/u)* > v/u, i.e. that there s morejob creation n the boom than in recession.The fact that Ed>80, however, mpliesthatwhen the cyclicalshocks are anticipated i.e. whenp > 0), thejob creationrateis likelyto exhibit esscyclicalityhanwhenp = 0. Forgivenvaluesof thereservation roductivities,p > 0 leaves ob creationat lowp unaffected, s in (28), but reduces hehigher ob creationrate at high p, as in (30). Of course, p also influences he reservationproductivitiesbutan examinationof thejob creation conditionsshows that that influence s not likelytoinfluenceob creation n one statedifferentlyromjob creation n the other state.Theanticipation f cyclical hocksnarrowshegapbetween hereservation roductiv-ities at the two prices,p andp*, so job destruction luctuates ess as pricechanges han acomparisonof the two steady states would imply.But the adjustmentdynamicsof jobdestructionas pricechangesare likely to increasethe cyclicalityof thejob destructionrate, at least for a short periodafter the changein price.Considerfirstwhat happenswhen price increases romp to p*. Firmsopen up morejob vacanciesand hold on tomorejobs after unfavourableob-specificshocks. Thus the job creationrate, vq(v/u),increasesand thejob destructionrate, (1- u)AF(ed),decreases, nducinga fall in unem-ploymentthrough(15). Since neitherv/u nor cdhas dynamicsof its own at givenp, the


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408 REVIEWOF ECONOMICSTUDIESdecrease n unemploymentnducesa fall in job creation(to maintainv/u constantv hasto fall when u falls)and an increasenjob destruction,until there s convergence o a newsteady state, or until there s a new cyclicalshock.Whenpricefalls fromp* to p the dynamicsof job creationfollowa patternsimilarto that after the priceincrease: v/u)* falls once for all, job creationfalls on impactbutagain ncreases sunemployment egins o rise.The dynamicsof job destruction, owever,are different,because the rise in the reservationproductivityrom E* to Ed Jeads o animmediatedestruction f all jobs with idiosyncraticomponentsbetween he two reserva-tion productivities. ob destructionalso rises for reasons similarto the ones that led toits decreasewhen price ncreased, incewithhigherreservation roductivityirmsaremorelikely to destroy obs as they are hit by job-specific hocks.Butthe increase n job destruc-tion immediately fter the cyclicaldownturnhas no counterpartn the behaviourof thejob destructionrate when priceincreases,or in the behaviourof the job creation rate.This impartsa cyclicalasymmetryn thejob destruction ateandin the dynamicbehaviourof unemployment.The short-run yclicalityof thejob destruction ateincreases, hejobdestructionrate leads thejob creationrate as a cause of the rise in unemployment ndthe speedof changeof unemployment t the startof recession s faster than its speedofchangeat the start of the boom.At this level of generality, ur analysis s not yetin a positionto confirm he empiricalfindingson the cyclicalbehaviourof job creationand job destruction.But the resultsofthis sectionareconsistentwith some of those findings.Firstly, obcreationand ob destruc-tion move in oppositedirectionswhen the economy is hit by a cyclical shock, as in themodel of this paper.Secondly,empiricallyob creation luctuatesess than ob destruction.Ouranalysishas shown thatif wetakethesteady-state nalysisasa yardstick,he anticipa-tion of cyclicalshockscausesan asymmetrynjob creation,reducing t in the boom butnot in recession.Sincein the boom job creation s alreadyhigher, his result s consistentwiththe finding hat it does not fluctuatemuch.No sucharguments an be made forjobdestruction.Thirdly,our analysishas shownthat if we take the short-rundynamics ntoaccount,there s also an asymmetrynjob destructionwhich is consistentwith thefindingthat job destruction s more "cyclical".Job destruction ncreasesmore rapidly and bymore at the start of recession han it decreasesat the startof the boom. The latterclaimis also consistentwith observationson the behaviourof unemployment,hat entryintounemploymenteadsexit as thecause of the risein unemployment.Thesimulationof thenext section confirms hese claims.In contrast,the cyclical mplicationsof (probabilistically)nticipated hanges n thedispersionof prices,as measuredby the dispersionparametera, are not consistentwiththeempiricalindings n two out of the threepredictionsisted n theprecedingparagraph.If dispersion ollows a Poisson processwith a high value a and a low value au*, obcreationandjob destructionmovein the same directionas a fluctuates.Theanticipationof changesin cf increases ob creation when a rises, over and above its alreadyhighsteady-state alue.Butas previously, ob destruction isesmorerapidlywhen a risesthanit falls whena falls.

These claims can be demonstratedwith an analysissimilar to the analysisof theeffectsof cyclicalchanges n commonprice,which we sketch here.Supposeu> a* andlet p be the Poissonrate thatchangesdispersion.Commonprice s fixed atp, assumed obe at least as high as the opportupitycost of employmentb. The steady-stateanalysisimplies that thereis more job destructionand more job creation at high a, i.e. Ed ??d*and v/u>(v/u)*. Using the formerfact, we can writeexpressions imilarto (16)-(18),and so deriveexpressions imilar o (20) and (24) for the reservationproductivities.The


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MORTENSEN & PISSARIDES JOB CREATION AND DESTRUCTION 409job creation conditions then are, (28) for high a, and a conditionsimilar to (30) forlow a*.An argumentsimilar to the one used in the steady-stateanalysis(speltout in theAppendix) o demonstratehat 8(v/u)/ua>0 implies

u(Eu ?d)> (eu Ed*), (31)that is, the directeffect of dispersionon job creationdominatesthe indirecteffectthatoperatesvia the reservationproductivity.Therefore, 30) impliesthat as in the steady-stateanalysis,thereis less job creationat low or*evenif p = 0, but if p > 0, job creationat a* is lower still. Thecyclicalresponsesof job creationare enhancedwhenthedrivingforceis dispersion.In terms of the dynamics,a fall in a is followed by a loweringof the reservationproductivityand by closing down some job vacancies.This leads to a fall in both jobdestructionandjob creation,with ambiguouseffects on unemploymentrom the start.But a rise in dispersion causes an immediate rise in job destruction, as the reservationproductivitys increased,whichcauses an immediate isein unemployment.ob creationalso risesin this case and eventually hereis convergence o a new steady state, wherealthoughthereis againambiguityabout the finaldirectionof changein unemployment,it is almost certainly hecase that unemploymentalls towards ts newsteady-state alueafterits initial rise.

5. AN ILLUSTRATIVESIMULATIONAs a furthercheck on the consistencyof our main resultswith those foundin the data,we simulatehere a version of our model and comparethe resultswith existing stylizedfactsconcerning he cyclicalbehaviourof job creationand job destruction.For both theU.S. and several Europeaneconomies,these flows are relatively arge and negativelycorrelated.Furtheremore,ob destruction s morevolatile than job creation.One of themainquestions hat we askis whether hocksto commonpricep are by themselves noughto simulate the observednegativecorrelationbetween ob creationandjob destructionand the highervariance njob destruction.As a necessarypreliminary, he equilibriumonditionsand laws of motion are statedfor a generalmodel,one thatsimplyrestricts heaggregate hockto be a Markovprocess.In thiscase,anequilibrium an be characterized y two functionsof thecommoncompo-nentof pricep: thejob meetingrate per searchingworker,a(p), and thejob destructioncutoffvalueof thejob-specific omponentof price,Ed(P). Given thatS(E,p) is thesurplusvalue of a matchwithjob-specific omponentEin aggregate tatep, thejob meetingrateis definedby the freeentrycondition, .e.,

a(p)=m(-, 1) wherem(v/u, 1)(1- J)S(sup)=c (32)u v/uThecriticalvalue of thejob-specific omponentsolves

S(ed(P), P) = 0. (33)Theequilibriummatch surplus unction S(E,p) is a solution to (34)[r+X+ p]S(, p)=p+fE-b-a(p)PS(ed, p)

rgur+ S(x,p)dF(x)+p J'max{S(E,y), O}dG(y Ip) (34)Jd(P)


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410 REVIEWOF ECONOMICSTUDIESwherep is the arrivalrate for the aggregate hock processand G(y Ip) is theconditionaldistributionof the next arrivalgivenp is the currentvalue.An equilibriums a solutionfor the three functionsdefinedby (32)-(34).To describe he model'sdynamics ollowingan aggregate hock,one needsto charac-terize the process that generates the distributionof employmentover the job-specificcomponentof price. Let n,(E)represent he measureof workersemployedat jobs withjob-specific omponentequal to Eat the beginningof periodt. As all survivingoccupiedjobs flow into this set at rate AF'(E)andjobs in the set flow out at a rateequal to thearrival rate for new values of the job-specificcomponentA, providedthatjobs in thiscategoryare not destroyed, he law of motion for the distribution f employments

( 1~,I~FA. rEd(Pt) 1( [1 -A]n,() +AF j()N- n,(z)dxJ if Lu> L> Ld(P,) (35)n,?1I(L) = Ar L)[35)

0 if E< Ed(P,)where N, represents otal employmentat the beginningof period t. Note that the mostproductive jobs, those for which L = L, are excluded. The remainder N- f n(x)dx equalsthe mass of workersemployedbelow Lu after the arrival of the shock. El is the lowerbound on the idiosyncratic omponentsof productivity.Inthe empirical iterature, hejob creation destruction) lowis thesumof allpositive(negative)changes nemployment ver individual stablishmentsontained nthe industrycategoryspecified.As establishments re composedof singlejobs and jobs that arequitaredestroyed, he creation low is identical o the rateat whichvacant obs arematchedwith unemployedworkers in the model. Given that every unemployedworker finds avacancywithprobabilitya, the total creation low in periodt is

C,= a (p,)[1 -N,]. (36)A job is destroyedfor one of two reasons. Either the aggregatestate worsensand theprevious ob-specific omponent s now below the newcutoff value or a newjob-specificcomponent alls below the existingcutoff value. Hence,

r d(Pd) Ed PdD,t= n,(x)dx +F( d(p,)) N- n(x)dx (37)

Of course,Nt+,I Nt,+ Ct,-Dt (38)

holds as an identity.For thepurposeat hand,the aggregate hock is assumed o be a three-stateMarkovchain.In the simulationreported, he process s calibrated o the quarterlydeviationsofthe log of labour productivity rom a linear trendin U.S. Manufacturing rom 1947to 1991.Giventhe standard irst-order uto-regressionmodel, the estimatedcorrelationcoefficient s 0.933 and the standarderrorof the innovation s 0.011. One can show (seeChristiano 1990) for specifics) hat the followingthree-stateMarkovchain has the same


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MORTENSEN & PISSARIDES JOB CREATION AND DESTRUCTION 411TABLE I

Parameter valuesp-b=0.075 Average net productivity r=0.01 Pure discount rateA=0.081 Job-specific shock arrival rate 1B=0.5 Worker's share of surplusa=0.0375 Job-specific shock dispersion 0=0.5 Search elasticity of matchingk=4 Matching rate scale parameter

Wold representation: states pi=p + zi, where z1= -0.053, Z2=0 and Z3=0.053, and transi-tion probabilities iry= pdG(pj Ipi) where0.933 0.067 0.000

[rij]= 0.017 0.967 0.017 (39)0.000 0.067 0.933

The distribution of the job-specific component, F, is taken to be uniform on the interval[-1, 1]. The matching function assumed is log-linear with search input elasticity equal to0, assumptions that together with equation (32) imply thejob matching rate per searchingworker is of the format(p)=k[S(c.,p)]011 -0 (40)

The remaining parameters of the model were chosen as follows. The interest rate -0.01 per quarter which reflects historical U.S. values. For lack of better information, equalbargaining power was assumed by setting /3=0.5. The elasticity of the matching functionwith respect to search input was set at 0 = 0.5 as well which is midway between the estimateobtained by Blanchard and Diamond (1989) using U.S. data and that of Pissarides (1986)from U.K. data. The scale parameter in the job matching function, k, and net averageproductivity, p - b, were set to approximate the mean, approximately 8.5%, and the vari-ability, 7%to 10%, of U.S. Manufacturing unemployment in the 1970s and 1980s. Finally,the job-specific component arrival rate, i%, nd the dispersion parameterof the job-specificcomponent, a, were set to match the average mean and standard deviation of job creationgenerated in the simulation with those reported for U.S. Manufacturing by Davis andHaltiwanger (1991). The actual values of the parameters assigned for the purpose ofsimulating the model are summarized in Table 1.The equilibrium unemployed worker meeting rates and reservation shocks for eachof the three aggregate states needed to compute the simulation are given by the follwingvectors:

0.430 0.471a 0.598 Ed= 0.241 . (42)

0.733 -0.01This solution to equation (32)-(34) for the parameter values specified in Table I wascomputed using the method developed by and reported in Mortensen (1993). The resultsof the simulation obtained using these values, the laws of motion given by equations (35)-(38), and Monte Carlo realizations of the aggregate shock generated by the chain specified


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412 REVIEW OF ECONOMIC STUDIESTABLE II

Simulation results: Means (std errors) of 100 Simulated 66 QuartersSamplesSimulation statistics Data

Mean (c) 5.23 (0.37) 5.2'Std. Dev. (c) 0.91 (0.43) 0.9'Std. Dev. (d) 1.37 (0.68) 1.6'Corr (c, d) -0.10 (0.28) -0.36'Corr (v, u) -0.26 (0.32)' U.S. Manufacturing job flow series, 1972:2-1988:4, Davis andHaltiwanger (1991).

inequation 39) are presentedn TableII. Thereported tatisticsaremeans(withstandarddeviations n parenethesis)basedon 100 simulatedsampleseach 66 quarters n length.Sample tatistics or U.S. Manufacturing ataonjobflowsfor the 66quartersrom1972:2to 1988:4 are included orcomparison. n thetable c and d represent atesof job creationand job destructiondefinedas the respectivelows normalizedby the averageof employ-ment at the beginningandend of eachperiod.Finally, u and v representunemploymentandvacancyrates respectively.The results n Table IIsuggest hecalibratedmodelcan explain he co-movement ndvariabilityoundin the Davisand Haltiwanger ata on job creationand ob destructionnU.S. Manufacturing.Specifically,or the parametervaluesthat inducea match of themodel'smean and standarddeviationof job creationwith the data, both the observedcorrelationbetweencreationand destructionand the observedstandarddeviationof jobdestructionare within one standarderror of the model's means. Although observingrealized tandarddeviationsof job creationandjob destructionof roughlyequalmagni-tude is not unlikelydue to the rather arge samplingvariation mpliedby the model,theaveragevaluesimpliedby the modelpredictthe observation hatjob destructions morevolatileoverthe available ampleof 66quarters.Finally, he modelalsoimpliesa Beveridgecurveas reflectedn the negativecorrelationbetweenunemployment nd vacancies.

5. CONCLUSIONSThe model outlinedin this paper is characterized y potentially arge amountsof jobcreationandjob destruction,due to idiosyncratichocks that takeplaceindependentlyftheprocesses hatchangeaggregate onditions.Changesn aggregate onditions,however,do affectthe cutoffs that inducefirmsto open newjobs or close existingones. So, if weinterpretdifferentphasesof the cycleas equilibrium t different evels of the parameters(in our formulation,of differentvaluestakenby the commoncomponentof price,p, andthe varianceof the idiosyncratichock, ao), ob reallocation anvaryoverthecycle,evenif the processes hat causeit do not.Wehave shownthat at highercommoncomponentsof labourproductivity alterna-tivelywhen the aggregatepricedistributionranslates o the right), the probability hatan unemployedworker inds a job is higherand theprobabilityhata job is destroyed slowerwithin given finite engthsof time.An examinationof the dynamicsof job creationand job destructionwhen it is known that labourproductivitychangesrandomlyhasrevealed hat the anticipationof cyclicalchangereducesthe cyclicalityof job creation,and the short-runresponseof job destruction o shocks increases he cyclicalityof jobdestruction.Althoughempirical videnceon thecyclical ssue is inconclusive,hese results


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MORTENSEN & PISSARIDES JOB CREATION AND DESTRUCTION 413are consistent with Davis and Haltiwanger's (1990, 1991) findings. Both results can bemade stronger if aggregate events also change the degree of dispersion present inidiosyncratic shocks, provided the dispersion of productivities is lower at higher commoncomponent of labour productivity. At lower dispersion there is lessjob destruction, reinfor-cing the fall in job destruction due to higher common productivity, and less job creation,partially offsetting the higher job creation due to higher productivity. Our simulations,however, have shown that even holding dispersion constant, random changes in commonprice can proxy reasonable well the cyclical changes found in the U.S. data. In contrast,changes in the dispersion of productivities with constant aggregate productivity do notseem consistent with the finding that job creation and job destruction move in oppositedirections during the cycle, so they are unlikely to be the domininant driving force of theunemployment cycle.The aggregate unemployment model with endogenous job destruction behaves simi-larly to the standard model with exogeneous job exit, except that now shocks to theaggregate component of the value of product shift the Beveridgecurve. Thus, if there aresimultaneous aggregate and reallocation shocks, the Beveridge diagram ceases to be asuseful a tool of analysis, because the two equilibrium curves in vacancy/unemploymentspace depend on a similar set of parameters. In these circumstances, the relation betweenjob matchings on the one hand and job vacancies and unemployment on the other mightshed more light on the source of shocks than might the relation between the stock ofunemployment and the stock of vacancies. The information contained in vacancy/unem-ployment flow data is potentially more useful in distinguishing between different kinds ofshocks than the information contained in the stocks.'0

APPENDIXSteady-state Ed and v/u: dependenceon some parametersThe equilibrium conditions of interest are (10) and (13), drawn in Figure 1. In this Appendix we derive someof the results discussed in the text. For notational convenience let, in this Appendix, 0 stand for the ratio v/uand -l for the elasticity of q(v/u). By the homogeneity of the matching function, 0 < q < 1, though l is notgenerally a constant.

Dependence on ADifferentiation of (10) with respect to A gives,

r+)LF(Sd) aSd P3C 0 ac9r+)u a [1-l F(x)Jdx. (Al)Differentiation also of (13) with respect to A gives,

q 90) 0= c __ r___ A)___ Ed__A.2A 0fl )CF(9u-+d) (-MC)(Eu-+d)2 DA2

Since q'(0)


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414 REVIEW OF ECONOMIC STUDIESThe term in the square brackets of the left-hand side is negative and the term in the square brackets of the right-hand side is positive by virtue of the fact that

vEu[1F(x)Jdx < Eu-? d, (A4)so 00/OA


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MORTENSEN & PISSARIDES JOB CREATION AND DESTRUCTION 415comments of Guiseppe Bertola, Hugo Hopenhayn, Richard Rogerson, Gerard van der Berg, John Shea andthree anonymous referees.REFERENCESBERTOLA, G. and CABALLERO, R. J. (1991), "Efficiency and the Natural Rate of Unemployment: LaborHoarding in Matching Models" (Unpublished, read at the NBER conference on Unemployment and WageDetermination).BLANCHARD, 0. J. and DIAMOND, P. A. (1989), "The Beveridge Curve", Brookings Papers on EconomicActivity, 1, 1-76.BLANCHARD, 0. J. and DIAMOND, P. A. (1990), "The Cyclical Behavior of Gross Flows of Workers inthe U.S.", Brookings Papers on Economic Activity, 2, 85-143.BOERI, T. and CRAMER, U. (1991), "Why Are Establishments So Heterogeneous? An Analysis of Gross JobReallocation in Germany" (Unpublished).CABALLERO, R. J. and HAMMOUR, M. L. (1991), "The Cleaning Effect of Recessions" (mimeo).CONTINI, B. and REVELLI, R. (1988), "Job Creation and Labour Mobility: The Vacancy Chain Model andSome Empirical Findings" (R & P Working Paper No. 8/RP, Torino).CHRISTIANO, L. J. (1990), "Solving the Stochastic Growth Model by Linear-Quadratic Approximation and

by Value Function Iteration", Journal of Business and Economic Statistics, 8, 23-26.DAVIS, S. J. and HALTIWANGER, J. (1991), "Gross Job Creation, Gross Job Destruction and EmploymentReallocation" (Unpublished).DAVIS, S. J. and HALTIWANGER, J. (1990), "Gross Job Creation and Destruction: Microeconomic Evidenceand Macroeconomic Implications" (Bureau of Census, CES Paper 90-10).DIAMOND, P. A. (1982), "Wage Determination and Efficiency in Search Equilibrium", Review of EconomicStudies, 49, 217-27.JACKMAN, R. A., LAYARD, R. and PISSARIDES, C. A. (1989), "On Vacancies", O.xfordBulletin of Econom-ics and Statistics, 51, 377-394.LEONARD, J. (1987), "In the Wrong Place at the Wrong Time: The Extent of Frictional and StructuralUnemployment," in Kevin Lang and Jonathan Leonard (eds.) Unemploymentand the Structure of LaborMarkets (New York: Blackwell).MORTENSEN, D. T. (1982), "The Matching Process as a Non-cooperative/Bargaining Game", in J. J. McCall(ed.), The Economics of Information and Uncertainty(Chicago: University of Chicago Press).MORTENSEN, D. (1990), "Search Equilibrium and Real Business Cycles" (Unpublished, presented at theWorld Congress of the Econometric Society, Barcelona, August 1990).MORTENSEN, D. (1993), "The Cyclical Behaviour of Job and Worker Flows" (mimeo).PISSARIDES, C. A. (1986), "Unemployment and Vacancies in Britain", Economic Policy, 3, 499-559.PISSARIDES, C. A. (1990), Equilibrium UnemploymentTheory (Oxford: Blackwell).

mortensen, pissarides - job creation and job destruction in the theory of unemployment

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