Production Synergies, Technology Adoption, Unemployment, and Wages

Production Synergies, Technology Adoption, Unemployment, and Wages ∗ Gwen Eudey Miguel Molico Board of Governors University of Western Ontario Washington, DC 20551 London, Ontario, Canada N6A5C2 gwen.eudey@frb.gov mmolico@julian.uwo.ca April 2001 Abstract Recentempiricalworkrevealsconsiderableheterogeneityintheuseof technologieswithinindustries,suggestingtechnologyadoptiondependson factorsotherthanindustrytype. Wepresentamodelinwhichthefactors thatleadtoheterogenoustechnologyadoptionplayakeyeconomicrolein explaining otheraspects oftheU.S.economythat havebeen the focus of recent theoretical work, including wage and technology dispersion within and between skill groups and the U-shaped pattern of measured productivity that many other researchers have attributed to learning economies orto production externalities. The views expressed here are those of the authors and do not necessarily reflect those ∗ of the Federal Reserve Boardor the Federal Reserve System. Wethankparticipantsat the Essex Search Conference and the meetings of the Society of Economic Dynamics for their comments. 1

1 Introduction Recent empirical work with firm-level data reveals considerable heterogeneity in the use of technologies within industries. This evidence suggests that there may be no single best capital vintage for any firm, but rather that the optimal technologydecisionmaydependonfactorsotherthanindustrytype. Wepresent amodelinwhichthefactorsthatleadtoheterogeneoustechnologyadoptionplay a key economic role in explaining other aspects of the U.S. economy that have been the focus of recent theoretical work, including wage dispersion within and between skill groups and the U-shaped pattern of measured productivity that many other researchers have attributed to learning economies or to production externalities.1 There are three key assumptions in the model: (1) Production depends on the synergy between the characteristics of the firm, the technology, and the worker; (2) Labor market frictions affect the expected return from search, and thereforethemakeupofacceptablematches; and(3)Workersareheterogenous. Technology adoption is endogenous on the production synergies of potential matches, the expected return from search of any potential match, and the cost of switching technologies. Technology adoption immediately affects current production, and there is a one-time immediate fixed cost to switching technologies; this cost is shared by the worker and firm in the division of the joint surplus. The timing is as follows. Firms, holding a technology type, randomly meetworkersonthelabormarket. Thepairjointlydeterminewhattechnology adoption decision, including the possibility of maintaining the current holding, wouldmaximizetheirjointsurplusintheeventofamatch. Ifthejointsurplus would be positive, the match is formed. The model has no analytical solution. We numerically solve the model under alternative specifications for the cost of capital, skill-composition of the workforce,andthenumberofavailabletechnologies. Theseexercisesaremeant to demonstrate the plausible effect of the significant drop in the cost of hightech capital, the increase in college education, and the technological revolution of the 1970s-1990s might have effected technology adoption, wage dispersion, unemployment, and productivity in both the intermediate and long-run. In summary, we find that because technology adoption depends on the cost and availability of complementary inputs, any change in fundamentals can affect the matching decision by firms and workers. Any disruption to the matching decision will, in turn, lead to a fall in productivity until the economy returns to a balance in which the number of match breaks equals the number formed. Importantly, we find the U-shaped pattern of productivity can be the result of any economic shock that affects the allocation of workers across firms: a Ushaped pattern of productivity may not be the result of “creative destruction” norofanytechnologicalinnovation. Moreoveractual creativedestructioninour model—atemporaryfallinproductivityastheeconomyrespondstoaproductiv- 1See Greenwood and Jovanovic (1998) for an application of the learning model to the IT revolution; see Aghion and Howitt (1994) for a model in which creative destruction is generatedbyanegativeproductionexternalityfollowingtechnologyadoption. 2

ityshock—isnot theresultoflearningeconomiesnorofany(explicit)production externalities, but rather purely the consequence of labor market frictions. The introduction continues with a review of the empirical evidence and related litereature. The model is presented in Section 2. In Section 3 we define an equilibrium and discuss its computation. Numerical solutions are discussed in Section 4, followed by a discussion of dynamicsbetween equilibria in Section 5. Section6discussestherelevanceofthemodeltostudyofU.S.dataoverthe transition to what has been dubbed the “new economy.” 1.1 Worker and firm heterogeneity 1.1.1 Heterogenous production practices within industries The term “production practice” refers to technologies which affect the productivity of the worker-firm match, but which are not inherent to (nonseparable from) either. It is clear that the usefulness of technologies varies across industries. Empirical work which focuses on technology adoption tries to control for industry effects, with focus on other influences on the technology adoption decision—includingcost,marketnicheofthefirm,andworkforcecharacteristics. Doms,Dunne,andTroske(1997),inastudywhichlinkstheSurveyofManufacturing Technology to the Worker-Establishment Characteristic Database, find a correlation between the level of technology use and worker skill within industries; moreover, by looking at changes in technology adoption and in the skill level of the firm’s workforce, they find that it is firms that have already employed skilled workers that buy high-tech capital, and not the other way around. In other words, the technology adoption decision depends on the current worker-firm match.2 Other surveys which document heterogeneity in technology adoption within manufacturing industries include Siegel (1999) and Hwang and Weil (1999). Ourinterestinheterogenousproductionpracticessuggestsadeparturefrom the “vintage capital” framework in which there is a single best technology for any type of firm. Acemoglu and Shimer (1999) present a model of wage and technology dispersion in which, under the assumption that workers heterogenously engage in search intensity, firms will heterogenously engage in capital development in order to attract (heterogenously) informed workers. Acemoglu (1998) and Kiley (1999) both have interesting search models in which technology adoption is endogenous on the relative supply of skilled workers. In both modelsthereturntodeveloping capitalgoodsthatarecomplementarytoskilled labor riseswithanincreasein therelativesupply of educatedworkers. InAcemoglu’s model there are two final goods, each type produced in only one way withonetypeofworker;asinAghionandHowitt(1994),theabilityofthefirm 2Notably,however,thereisoneexceptiontothisgeneralresult: purchaseofcomputertechnologiesleadstoskill-upgrading(throughretrainingorotherwise—theirdatadonotindicate) of the workforce. Siegel (1999) also finds that adoption of “linked advanced manufacturingtechnologies”(largelydatabasemanagementsystems)leadstrainingofexistingpersonell. One logical extension of our model would be to incorporate learning effects or to otherwise endogenizeworkerskills. 3

to update to the best capital vintage arrives idiosyncratically, so that heterogeneous production practices are the result of an exogenous timing constraint, rather than by choice. In the Kiley model there is one final good that can be produced in two ways—using skilled or unskilled workers with complementary capital inputs. Specialization in the pairing of skilled and unskilled workers withonlyonetypeoftechnologymakesitsothatneithertheAcemoglunorthe Kiley model offers a unified explanation of wage dispersion within skill groups as well within firm type. 1.1.2 Wage dispersion across and between worker types Chinhui,Murphy,andPierce(1993)documentthatreturnstoeducation(dispersionbetweenworkertypes)fellinthe1970sandthenroseinthe1980s,whereas wage dispersion within education classes rose over both samples. Although the authors find that most of the wage distribution is explained by education, there are essentially two theories which describe wage dispersion within educationclasses: thefirstisthatthereareunobservableskillsthatarenotrelatedto education,thesecondisthatlabormarketfrictionsallowworkerswithidentical characteristics to nonetheless earn different returns to their labor input. In our framework workers can be divided into groups with different skills; these skills might include attributes which are unobservable to the econometrician in the applied labor research, but all skills are assumed to observable to firmsinourmodeleconomy. Relativedemandfor,andproductivityof,workers with different skills can lead to wage dispersion between skill groups. Search frictions in the labor market can lead to wage dispersion within skill groups. This aspect of the model is also found in Albrecht and Vroman (1999). 2 The Model 2.1 The Environment Time is discrete. The economy is populated by a continuem of infinitely lived workerswithmassnormalizedtounity. WorkersareofLdistincttypes,indexed l = 1,...,L. Let γ denote the fraction of workers of type l. At any point in l time,workerscaneitherbeemployedorunemployed. Whileunemployed,agents enjoy flow utility b p(t) > 0 where p(t) grows at constant rate g, the rate of · technologicalprogress. Whileemployed,agentsgetpaidwages. Similarly,there is a continuum of firms with mass F. Firms are of I distinct types, indexed i = 1,...,I. All firms produce an identical good (utility). Neither workers or firms can change their type3. Agents are impatient and discount the future at discount factor 0<β <1. To produce output a firm must be matched with a worker and use some technology. There is a menu of available technologies, indexed z = 1,...,Z. 3Forthesakeofsimplicity,thetypeofanagentisviewedhereasanintrinsicandunchangeable characteristic. Allowing agents to choose or change their type, say through training, wouldbeaninterestingextension. 4

Technologyvintageisdenotedbyasubscript;anewvintagearriveseachperiod and offers an increase in any match synergy at rate g. The quantity of output whichcanbeproducedinanygivenmatchdependsonthecharacteristicsofthe firm, the worker, and the technology adopted. Potential output is given by a matrix of production synergies, y (i,z ,l) where T t. t T ≤ The synergy model is designed toreflect the fact that firms may have many alternative production methods at their disposal, and that the optimal production method will depend on the availability of complementary labor inputs (distribution of unemployed workers across type). We assume that technologies are rankable for all firm and worker pairs.4,5 Furthermore, technologies are costly. Holding a technology while matched involves a per period operating cost of hc p(t)>0. In addition, there is a fixed · cost to adopting (switching to) a new technology.6 Let sc(z ,z) p(t) denote 0 · the cost of switchingfrom technology z to z , regardless of the vintageof either 0 technology. We assume that sc(z ,z ) > 0, sc(z ,z ) > 0, and sc(z ,z ) > 0 t T t0 T t0 t for z = z, t = T.7 Also, let sc(z, ) p(t) > 0 denote the cost of adopting 0 6 6 ∅ · technologyz (ofanyvintage)whenthefirmisnotholdinganytechnology(new entrant).8 Technologies become available for production as soon as they are acquired. We assume a search friction in the labor market. Workers and firms meet randomly. Thearrivalofasuitable matchdependsontherateatwhichworkers and firms meet as well as the probability that the potential match is desirable. The probability that an worker (firm) meets a firm (worker) of a certain type is equal to the probability that it meets someone times the probability that that vacant firm (unemployed worker) is of that particular type. Following Mortensen and Pissarides (1998) we characterize the arrival of meetings as a matching function v v a m =Fα , u u ³ ´ ³ ´ 4In principle, in case of indifference between technologies, one could assume the use of a randomization mechanism (lottery) to solve the technology adoption decision problem, but thereislittleinsightgainedfromtheaddedcomplication. 5The production matrix could be defined to reflect the notion that there is a single best technology which would, all other things being equal, maximize output for all worker-firm pairs (a vintage capital representation), or that there is a different best technology for each firm type, regardless of the worker with which the firm type is paired (vintage capital by industryorotherfirmcharacteristic). Definingtheproductionmatrixineitherofthoseways eliminatesthetechnologyadoptiondecisionproblemfortheworker-firmpair;forthisreason theframeworkneststhosemodelsinwhichtechnologyisanimbeddedfirmcharacteristic. 6Thespecificationisquitegeneral-thecostofswitchingfromatobmaydifferfromthat ofswitchingfrombtoa,andmaydifferfromthecostofpurchasinganentrytechnology. 7Amodelinwhichfirmscostlessllyswitchtoahigh-productivitytechnologyuponmeeting askilledworkerispresentedinShi(1998). 8We assume that new firms can enter the labor market by purchasing some technology. Unrestrictedentryimplies,thatinequilibrium,thevalueofavacancyisdrivendowntothe costofpurchasingthattechnology. Thisinturnimpliesthatnovacantfirmhasanincentive toswitchtechnologies. 5

where v and u are the vacancy and unemployment rates, respectively.9 For simplicity define θ v, a measure of market tightness. As θ rises, workers are ≡ u morelikelytomeetwithfirms,andm(θ)isthefunctionthatcharacterizesthat arrival rate. For firms, the arrival rate of unemployed workers is equal to m(θ); θ the arrival rate falls with a rise in θ. Let f denote the fraction of vacant firms that are of type (i,z ) at the izT,t T beginingofperiodt. Similarly,letf denotethefractionofunemployedworkers l,t thatareoftypelatthebeginingofperiodt. Attimet,aworkerfacesanarrival rateof vacant firmsoftype (i,z ) givenbym(θ ) f . Similarly afirm faces T t · izT,t an arrival rate of unemployed workers of type l equal to m(θt) f . θt · l,t At the beginning of each period existing matches are exogenously randomly terminated with probability δ. 2.2 Matching, technology adoption and surplus sharing We define the net surplus of a match to be the gain of forming the match over and above the expected value of continued search. Let L (i,z ,l) denote the t T expected discounted lifetime utility of a worker of type l that enters period t employed by a firm of type i holding technology z , and U (l) denote the T t expected lifetime utilityof an unemployedworker of typel at theend of period t. Similarly,letO (i,z ,l)denotethevalueofafirmoftypeithatentersperiod t T tmatchedwithaworkeroftypelandholdingtechnologyz,andV (i,z )denote t T the value of a vacant firm of type (i,z ) at the begining of period t. The net T surplus of a match, at time t, between a worker of type l and a firm of type i currently holding technology z , conditional on switching to technology z is T τ0 defined to be: S i,zT,lz y (i,z ,l) hc p(t) sc(z ,z ) p(t)+βL (i,z ,l) U (l) t | τ0 ≡ t τ0 − · − τ0 T · t+1 τ0 − t +βO (i,z ,l) βV (i,z ). ¡ ¢ t+1 τ0 − t+1 s00 wherez isthetechnologythatthefirmwillcontinuetosearchwithshouldthe s00 match not be formed. When an unemployed worker and a vacant firm meet they must decide whether or not to match conditional on their optimal technology adoption decision. Agents must first determine which technology would maximize the net surplus of the match. Let ζ (i,z ,l) denote such technology, i.e., t T ζ (i,z ,l) argmaxS (i,z ,lz ). (1) t T ≡ z t T | τ0 τ0 9Alternatively, the matching function can be expressed in terms of vacancy and unemployementlevels. M(VC,UN)=VCαUNα. 6

Given the assumption that technologies arerankable for allfirm andworker pair, ζ is a singleton. If, conditional on the optimal technology adoption decision, the net surplus of the match is nonnegative, S [i,z ,lζ (i,z ,l)] 0, t T | t T ≥ then the match is formed and the optimal technology, ζ (i,z ,l), is adopted. t T Production occurs immediately using the optimal technology and the surplus is shared between the worker and the firm according to Nash bargaining. The Nashassumptionisconvenientbecauseifthematchisacceptablefor oneparty, it is acceptable to both, and it reduces bilateral bargaining to a rule. Let SW [i,z ,lζ(i,z ,l)] denote the net surplus of a worker of type l from an act T T | ceptablematchwithafirmoftypeicurrentlyholdingtechnologyz conditional T onadoptingtheoptimaltechnology,andπdenotetheworker’sshareofthetotal net surplus. Then, SW [i,z ,lζ (i,z ,l)] π S [i,z ,lζ (i,z ,l)] t T | t T ≡ · t T | t T = w [i,z ,lζ (i,z ,l)]+βL [i,ζ (i,z ,l),l] U (l), t T | t T t+1 t T − t where w denotes the current period wage. Simple algebra yields, w [i,z ,lζ (i,z ,l)] = π y[i,ζ (i,z ,l),l] hc p(t) (2) t T | t T ·{ t T − · sc[ζ (i,z ,l),z ] p(t) − t T T · +βO [i,ζ (i,z ,l),l] βV (i,z ) t+1 t T − t+1 s00 (1 π) βL [i,ζ (i,z ,l),l] U (l) . − − ·{ t+1 t T − t } Note that, because there is technological progess as well as a fixed cost of changingtechnologies,therewillbeanoptimalrateatwhichthefirmandworker jointly determine to upgrade, or switch, to the latest vintage. The lower the switching cost, the faster the rate of technology adoption. The faster the rate of technological progress, the greater the depreciation in the value of a match withanoldtechnology(astheworker’sthreatpointrises);asinMortensenand Pissarides (1998b), the relationship between the upgrade (in their terminology, the implementation cost) and the increase in the unemployment benefit, will determinetheeffectofanincreaseintherateofexogenoustechnologicalprogress on joint match surplus. 2.3 Value Functions 2.3.1 Value of Employment Aworker whobecomesorthat remainsunemployedthisperiodearnsanunemployment benefit, b p(t), at the end of the period and will search for employ- · ment next period. The expected return from search next period depends on the thickness of the market, the distribution of vacancies across firm type, and the expected return from running into each type of firm. In equilibrium, the expected probability that an unemployed worker meets a vacant firm of type (i,z ) in period t+1 must be equal to the frequency of that type of meetings. T Thus in equilibrium, surpressing vintage subscripts, 7

I Z U (l) = b+β m(θ ) f (3) t t+1 iz,t+1 · · i=1z=1 XX max [w i,z,lζ (i,z,l) +βL i,ζ (i,z,l),l ,U (l) { t+1 | t+1 t+2 t+1 t+1 } +β[1 m(θ )]U (l). − £t+1 t+1 ¤ £ ¤ An unemployed worker will meet no one on the labor market with probability [1 m(θ )],inwhichcasetheworkercontinuestobeunemployedandsearches t+1 − the following period. A worker meeting noone is no better or worse off than a worker that has rejected a match. 2.3.2 Continuation value of employment Those workers for whom matches have been terminated exogenously become unemployed. Workers in surviving matches have the choice of continuing the match or immediately receiving utility from unemployment. Suppressing vintage subscripts, L (i,z,l)=δU (l)+(1 δ)max w (i,z,lz)+βL (i,z,l),U (l) (4) t t t t+1 t − { | } Note that, given we have assumed that the list of technologies is fixed; although the technology type won’t change, the vintage will be upgraded over time. 2.3.3 Value of a vacancy Unlike unemployed workers, there is no benefit accrued to the vacant firm. Moreover, vacant firms pay a utility-denominated vacancy (or search) cost vc · p(t)eachperiod.Thesearchcostispaidwhetherornotthefirmmeetsaworker intheperiod. Conditionalonmeeting, amatchisformedifthejoint surplusis greaterthanorequaltozero. Incasethefirmdoesnotmeetaworkeritremains vacant. Once again, in equilibrium, the probability that a firm meets a worker of a certain type must be equal to the frequency of that meeting. Vacant firms may choose to upgrade or change their technology type to improve the return from searching. where we will assume throughout what follows that sc(z ,z )=sc(z ,z )= sc(z ,z ) t τ t0 τ − τ t 8

The return from searching is equal to L m(θ ) V (i,z ) = max vc p(t)+ t f t T l,t {− · θ · t l=1 X max y[i,ζ (i,z ,l),l] w [i,z ,lζ(i,z ,l)] { t T − t T | T sc[ζ(i,z ,l),z ] p(t) hc p(t) (5) T T − · − · +βO [i,ζ (i,z ,l),l],βV (i,z ) t+1 t T t+1 s00 } m(θ ) +β 1 t V (i,z ),0 . − θ t+1 s00 } t ∙ ¸ 2.3.4 Continuation value of an operating firm As long as the menu of technologies is fixed, the continuing operating firm will never change technologies or break the match unless the match is terminated exogenously; thematchpair willupgradethecurrenttechnologyattheoptimal rate,dependingontherelationbetweeng andsc(z ,z ). Thosefirmsforwhich t T matches have been terminated exogenously become vacant and either enter the labor market the following period after making their technology adoption decisionor theyexit. Firmsinsurvivingmatcheshavethechoiceofcontinuingthe match, searching the next period with the firm’s optimal search technology, or exiting. Note that the firm only pays the operating cost hc p(t) if the match · is maintained. Suppressing the vintage subscripts, O (i,z ,l) = δβ[V (i,z ) sc(z ,z ) p(t)] (6) t τ t+1 s00 − s00 τ · +(1 δ) max y(i,ζ (i,z ,l),l) w (i,z ,lζ (i,z ,l)) − · { t τ − t τ | t τ sc[ζ (i,z ,l),z ] p(t) hc p(t) − t τ τ · − · +βO (i,ζ (i,z ,l),l),βV (i,z ) sc(z ,z ) p(t) . t+1 t τ t+1 s00 − s00 τ · } 3 Equilibrium Thefirmentryconditionandthesteady-statederivationofthevaluefunctions, together with the flow equations into and out of unemployment, determine the long-run equilibrium of the system. 3.1 Firm entry To close the model we assume that a new firm may enter the labor market (searchforaworker)onlyafter ithaspurchasedatechnology. Becausethecost of entry increases at rate g (as do all costs in the model) regardless of which vintageispurchased,newentrantswillalwayssearchwiththelatesttechnology. The equilibrium value of a new entrant, V (i,z ), is equal to the cost of entry: t t V (i,z )=sc(z,0) p(t) (7) t t · 9

Theequilibriumvalueofavacantfirminperiodtholdinganoldervintagewillbe tieddownbythearbitrageconditionsthatthefirmwiththeoldervintagecannot gain byupgrading, nor can a firm with the latest vintagegain by downgrading, and then continuing to search. V (i,z )=sc(z, ) p(t) sc(z ,z ) p(t) (8) t t n t n t − ∅ · − − · Firms for which that equilibrium does not hold will not exist in equilibrium (f =0) becausetheywillhavegainedbyeither exitingor upgradingtothe izt n most−recent vintage. Thevalueof theupgradeorswitchingcostwilldetermine the optimal rate at which vacant firms upgrade their capital stocks. 3.2 Flows into and out of unemployment Steady-state equilibrium requires that the number of unemployed workers of each type remains constant over time. That requires that the flow out of unemployment equaltheflow in. Defining χ(i,z,l) tobe an indicator functionof whether a match is formed or not, that flow condition is satisfied by. I Z t f u m(θ) [f χ(i,z ,l)]=δ(γ f u). (9) l · · · izT · T l− l · i=1z=1T=1 XXX 3.3 Equilibrium definition and computation An equilibrium is a list of time invariant: unemployment rate, u; • market tightness, θ; • distribution of types across vacant firms, f ; • izT distribution of types across unemployed workers, f; l • matching profiles, χ (i,z ,l); • t T and value functions U (l),L (i,z ,l),V (i,z ),O (i,z ,l) t t T t T t T • { } such that equations (1)-(9) hold. In the following section we use numerical methods to characterize the equilibrium. Given parameter values we begin by guessing a matching profile χ (i,z ,l) . We then solve numerically the system of nonlinear equations { t T } (1)-(8) and verify that the conjectured matching profile is indeed an equilibrium. We repeat the procedure for all possible matching profiles to find the complete set of equilibria.10 10AcopyoftheprogramusedtogetherwiththeFortran90programmingcodeisavailable fromtheauthorsbyrequest. 10

4 Examples We present numerical solutions to a parametrization of the model that satisfies three key assumptions needed to generate heterogenous technology adoption: workers are heterogenous; production synergies depend on the firm, worker, andtechnologytype;andtherearefrictionsinthematchingprocessforworkers and firms. The parameter values are chosen to make the model as simple as possible: weassumethatthereisnogrowth(g =0),thatthereisonlyonetype of firm, two types of worker (skilled and unskilled), and that technologies are rankable by all potential worker-firm pairs. For the numerical examples that follow, we will assume the production matrix presented in Table 1.11 Table1: ProductionMatrixy(z.l) tech labor Skilled Unskilled \ High-Tech 100 0 Low-Tech 90 90 In order to demonstrate the properties of the model, we show the effect on the number and characteristicsof theequilibriaunder alternative specifications ofparametersthevalueofwhichwebelievetobecloselylinkedtotechnological progress, namely a change in the cost of switching technologies, and change in the fraction of skilled workers in the labor force, and an addition to the menu of available technologies. The remaining parameter values were set equal to: β = 0.95, δ = .05, α = 0.5, vc = hc = 5, sc(z, ) = 5 for all z, b = 1, ∅ π = 0.5; these values were chosen somewhat arbitrarily and without regard to any attempt at calibration of the model to particular employment or wage distributiondata. Inthenumericalsolutionsthatfollow,weshowonlythenontrivial equilibria in which both types of worker are employed; although other equilibria may exist we assume that in the long run workers would not choose training that would leave them unemployed with unit probability. 4.1 Example without match-determined technology adoption We set the cost of changing technology prohibitively high in order to suppress the role of endogeneous changes in the use of technologies upon meeting with a worker.12 This reduces the model to the case studied in Albrecht and Vroman (1999). Under this parameterization, the firms’ technology adoption decision is irreversible but nonetheless endogenous on the other parameter values in the 11Other parameter values were chosen fairly arbitrarily, without regard to calibrating the model tofitobservedunemploymentorvacancyrates, forexample. Ineachofthecaseswe present in the text, the remaining parameter values were set equal to: β = 0.95, δ = .05, α=0.5,vc=hc=5,sc(z, )=5forallz,b=1,π=0.5,andtheratiooffirmstothelabor ∅ forceisequalto4. 12Wesetsc(z,z)=sc(z,z)=200forthisexample. 0 0 11

model; technology dispersion in this case is uninteresting since firm type is effectively, since permanently, linked to technology type. As in Albrecht and Vroman, there are multiple equilibria: a segmented equilibria in which skilled workers are picky and will only accept employment at afirm that hasthe hightech capital, and another equilbirum in which skilled workers accept employment at any firm, thus “crowding”, in Albrecht and Vroman’s terminology, the unskilled workers that can only work in the low-tech firm. There is wage disperision between skill groups in both equilibria; there is wage dispersion within the skilled-labor group in the crowding equilibrium. Ranking of the equilibria in terms of welfare is ambiguous. Productivity (outputperworker)andoutputarehigherinthesegmentedequilibrium,butso tooistheunemploymentrate. Skilledworkerwagesarehigherinthesegmented equilibrium—this is necessary in equilibrium if skilled workers are not to regret having been more picky about their matches. Unskilled workers are worse off in the segmented equilibrium because there is less entry of firms holding the low-tech capital since they will not be able to use that capital to also match with skilled workers. Segmented Equilibrium: Wage dispersion between worker types Matching profile: highly skilled workers are patient, hold out for high-tech job Firms with high-tech match with skilled workers • Firms with low-tech match with unskilled workers • u(%) F v(%) θ f f productivity output l=1 z=1 2.432 1.386 28.666 16.119 .485 .515 95.004 92.693 Wages z l Skilled Unskilled \ High-Tech 90.5 - . Low-Tech - 80.8 Crowding Equilibrium: Wage dispersion within and between worker types Matching profile: highly skilled workers impatient Firms with high-tech match with skilled workers • Firms with low-tech match with both worker types (“crowding equilib- • rium”) u(%) F v(%) θ f f productivity output l=1 z=1 1.594 1.239 20.555 15.974 .388 .372 91.865 90.401 Wages z l Skilled Unskilled \ High-Tech 89.5 - . Low-Tech 84.5 81.6 12

4.2 Example with match-determined technology adoption Sufficientlyloweringthecostoftechnologycapitaleliminates thecrowdingequilibrium in the previous example; there are three possible equilibria in this example: the segmented equilibria from before, one in which skilled workers are willingtoaccepttemporarilylowerwages(indicatedinparenthesesinthetables) in exchange for upgrading to the high-tech capital, and one in which unskilled workers are willing to accept temporarily lower wages in exchange for downgrading to the low-tech capital.13 Lowering the cost of capital raises productivity and output relative to the crowding equilibrium. Relative to the segmented equilibrium, productivity and output are higher in both equilibria in which firms endogenously tailor their technology adoption decision to the worker characteristics. In all three equilibria,workersarepairedwiththetechnologythatmaximizestheirpotential output. Loweringthecostofcapitalhasambiguouseffectsonunemployment: should the economy move to the segmented equilibrium, unemployment is either increased (relative to the crowding equilibria) or unchanged; should the economy move to either endogenous technology adoption equilibria, unemployment is reduced. The effects on wages are also ambiguous. The “endogenous technology adoption” equilibria are consistent with the findingsofDoms,Dunne,andTroske,thattechnologyadoptiondecisionsbyU.S. manufacturersvaryacrossfirmswithinthesameindustry,andthatthedecision depends on the characteristics of the workforce in place or, in our terminology, on the production synergies of the current, rather than the expected, match. Note also that there is wage dispersion within and between skill groups in both “endogenous technology adoption” equilibria that results from the cost of changing capital on joint worker-firm surplus. Also, skilled workers earn the highestwageintheequilibriuminwhichfirmsadopttechnologytomaximizethe productivityofthelow-skilledworker;thisisbecausethecostlinessofmatching with an unskilled worker lowers the firm’s threat point and therefore increases the joint surplus (and therefore wages) from skilled-worker match. Segmented Equilibrium: Firms cannot afford both to upgrade and to pay skilled-labor wages Matching profile: skilled workers do not accept sharing switching cost Firms with high-tech match with skilled workers • Firms with low-tech match with unskilled workers • u(%) F v(%) θ f f productivity output l=1 z=1 2.432 1.386 28.666 16.119 .485 .515 95.004 92.693 Wages z l Skilled Unskilled \ High-Tech 90.5 - . Low-Tech - 80.8 13Wesetsc(z,z)=sc(z,z)=90forthisexample. 0 0 13

Endogenous Technolgy Adoption Equilibrium: Change technology to maximize skilled worker output Matching profile: Skilled workers accept sharing switching cost Firms with high-tech match with skilled workers • Firms with low-tech match with skilled workers and then switch to high- • tech Firms with low-tech match with unskilled workers • u(%) F v(%) θ f f productivity output l=1 z=1 1.528 1.230 19.951 16.071 .403 .328 95.015 93.564 Wages z l Skilled Unskilled \ High-Tech 90.4 - . Low-Tech (45.4) 80.9 . Endogeous Technology Adoption Equilibrium: Change technology to maximize unskilled worker output Matching profile: high-skilled don’t accept switching cost, low-skilled do Firm with high-tech match with skilled workers • Firms with high-tech match with unskilled workers and then switch to • low-tech Firms with low-tech match with unskilled workers • u(%) F v(%) θ f f productivity output l=1 z=1 1.465 1.226 19.609 16.402 .584 .709 94.988 93.596 Wages z l Skilled Unskilled \ High-Tech 91.6 (34.8) Low-Tech - 79.8 4.3 Example with relatively more skilled workers, capital expensive We solve the model for the case in which skilled workers make up 60 percent, rather than 50 percent, of the labor force, and in which the cost of changing technologies is prohibitively high. The crowding equilibrium is eliminated, and only the segmented equilibrium remains. The increase in the relative supply of skilled workers increases entry of firms holding the high-tech capital; consequently, skilled workers hold out for a match with that type of firm. Average productivity increases relative to the earlier segmented (and therefore also the crowding) equilibrium because of the increase in mass of highly 14

productive workers. The share of skilled workers in the unemployment distribution falls even though their number increases in the population; this is becauseofthestrongentryoffirmsholdingthehigh-techcapitalrelativetothe previous segmented equilibrium. Segmented Equilibrium: High probability of matching with a skilled worker Matching profile: highly-skilled workers are impatient Firms with high-tech match with skilled workers • Firms with low-tech match with unskilled workers • u(%) F v(%) θ f f productivity output l=1 z=1 2.402 1.365 28.516 16.213 .534 .568 96.016 93.710 Wages z l Skilled Unskilled \ High-Tech 90.9 - . Low-Tech - 80.3 4.4 Example with relatively more skilled workers, capital inexpensive We solve for the case in which the cost of changing technology is sufficiently cheaptoallowforendogenoustechnologyadoptionandinwhichskilledworkers make up 60 percent, rather than half, of the labor force. There is no crowding equilibriumbecausethe netgain of endogenouslychangingtechnologiesis positive. Inthiscasethereisalsonosegmentedequilibriumbecauseskilledworkers, inrelativelylargesupply,nolongerhavethebargainingpowertorefusetoshare the technology switching cost. Productivityandoutputincreaserelativetothecasewithfewerskilledworkerssinceallmatchesmaximizepotentialoutputaswellasbecausetherearemore skilled-labor matches. EndogenousTechnologyAdoptionEquilibrium: change technology to maximize skilled worker output Matching profile: skilled workers accept sharing switching cost Firms with high-tech match with skilled workers • Firms with low-tech match with skilled workers and switch to high-tech • Firms with low-tech match with unskilled workers • u(%) F v(%) θ f f productivity output l=1 z=1 1.638 1.247 21.115 16.082 .451 .457 96.025 94.453 Wages z l Skilled Unskilled \ High-Tech 90.2 - . Low-Tech (45.2) 81.2 . 15

EndogenousTechnologyAdoptionEquilibrium: change technology to maximize unskilled worker output Matching profile: low-skilled workers accept sharing switching cost Firms with high-tech match with skilled workers • Firmswithhigh-techmatchwithunskilledworkersandswitchtolow-tech • Firms with low-tech match with unskilled workers • . u(%) F v(%) θ f f productivity output l=1 z=1 1.317 1.205 18.119 16.577 .632 .873 95.996 94.731 Wages z l Skilled Unskilled \ High-Tech 92.2 (34.1) . Low-Tech - 79.1 4.5 Example with technological innovation Technological innovation, as distinct from technological progress (g >0), adds to the list of available technologies. The purpose of this exercise is to demonstratehowtechnologicalinnovationsmaynotonlycreatenewequilibriabutalso destroyoldones. Itisthatdestructionofoldmatchesthatwillleadtocreative destruction between equilibria; the innovation (new high-tech) in Table 2 will nothoweverleadtoadecreaseinlongrun aggregateproductivityalthoughsuch an innovation could occur. Table2: ProductionMatrixy(z.l) tech labor Skilled Unskilled \ High-Tech 100 0 Low-Tech 90 90 New High-Tech 105 85 4.5.1 three technologies, changing technologies expensive Thehigh-productivitysegmentedequilibriumiseliminatedfromthesetofequilibria that were possible before the introduction of the new high-tech capital. Only one matching profile satisfies equilibrium after the technological innovation—oneinwhichskilledworkersarepatientandproduceonlywithfirms thathavethenewhigh-techcapital,butunskilledworkersareimpatientandacceptemploymentwithfirmsholdingeither thelow-techor therelativelyunproductive new high-tech capital good. There is wage dispersion among unskilled workers. Thenewequilibrium(shownbelow)resultsinlowerwagesforunskilledworkersthanineitheroftheequilibriawhentheproductionmatrixwasasinTable1 sinceunskilledworkersmatchedwiththenewhigh-techcapitalproducelessthan 16

with the low-tech capital, reducing unskilled worker threat point and therefore reducing the unskilled worker’s wage in either match. Total output is higher aftertheintroductionofthenewhigh-techcapitalbecausetheincreasedoutput generated by skilled workers dominates the loss from unskilled workers. The welfare effect of the technologial innovation is ambiguous given the increased wage disperision between skill groups. Note too that nearly all firms carry the new technology, whereas holdings of the high-tech and low-tech capital had been much more balanced in the previous set of equilibria. Crowding Equilibrium: wage dispersion between and within worker types Matching profile: unskilled workers impatient Firms with low-tech match with unskilled workers • Firms with new high-tech match with skilled and with unskilled workers • u(%) F v(%) θ f f f productivity output l=1 z=1 z=2 1.218 1.948 17.326 16.984 .508 .000 .033 95.080 93.921 Wages z l Skilled Unskilled \ High-Tech - - . Low-Tech - 80.5 New High-Tech 97.3 78.0 4.5.2 three technologies, capital inexpensive Relative to the “cheap capital” (sc(z ,z) = 90) case before the innovation of 0 the third technology, all of the equilibria are destroyed; the only equlibrium is identical to the crowding equilibrium shown above; this is not an endogenous technology adoption equilibrium because the gain from changing from the new high-tech tothe low-tech capital upon meeting an unskilled worker is toosmall relative to the cost. The only equilibrium in this case is identical to that in which capital was expensive. Unskilled workers as a group are worse off after the innovation because most of them are employed at firms holding the new high-tech, which offers a lower return than if they were producing the the lowtech capital, as they were (at least in the second period) before the innovation. Welfare effects of the technological innovation are ambiguous. 4.6 Summary The model solutions generally contain multiple equilibria. The question of how an economic shock might affect the economy depends closely on expectations, which may determine both the starting and ending points. For example, if skilled workers did not believe that there was a good chance of meeting a firm holdingthehigh-techcapitalgood(inthetwo-technologyexample),thenapolicythatloweredthecostofcapital(capitalgainstaxreduction)orincreasedthe 17

fraction of skilled workers (education subsidy) would move the economy from a low-productivitycrowdingequilibriumtoahigher-productivitysegmentedequilibrium. Consequently, the model issuggestive of achannel throughwhich differences in economic policies might plausibly explain international differences inmeasuredproductivity,unemployment,andwagedispersionamongcountries with equal access to technological innovation and identical unemployment benefit programs. Indeed, the multiple equilibria generated in many specifications ofthemodelsuggestthatsignificantdifferencesinproductivity,unemployment, and wage dispersion might result even if all fundamentals are identical. The examplesinthissectionsuggestthatcapitaltax/subsidyandeducationpolicies can work to eliminate certain equilibria, should a policymaker wish to move the economy away from a particular steady-state (given some weighting in the state utility function). The next section discusses model dynamics between steady-states. 5 Dynamics Ingeneral,onlyequations(1)-(8)needholdbetweenlong-runequilibria. Along the transition path, flows intoand out of unemployment will not be in balance, nor,byimplication,willthefractionofoperatingfirmsofeachtypebeunchanging. From the previous section, we know that a change in fundamentals may have no affect on the equilibrium at all, in which case there are no model dynamics. Alternatively, a change in fundamentals or in expectations can cause the economy to move from one equilibrium to another. Because there is only one equilibrium per matching profile, χ(i,z,l) , we can characterize the shift { } in the long-run equilibria as the dynamic response of a change in the matching profile (matches that firmsand workersare willingto accept that also supports an equilibrium). Denoting the initial and final equilibria by A and B, respectively, we solve for the transition path by the following interative process: Acceptablematcheschangefromtheset χ (i,z,l) totheset χ (i,z,l) • { A } { B } Startingfromtheoldunemploymentdistribution f ,weknowthenum- • { l }A ber of employed workers in matches for which χ (i,z,l)=χ (i,z,l) and B 6 A therefore we know f and total unemployment. { l }1 Remaining unknowns: f , θ=>i z unknowns iz • { } ∗ Equilibrium conditions: V(i,z)=nc p(t)=>i z equations • · ∗ Wealsoknowthattheflowintoemploymentforworkersthathavejustleft • matches will be greater than the flow in because the number of operating firms using the new technology is less than in the steady state (in fact, it starts at zero). 18

Update f and f as we iterate. • { l }1,...T { iz } Iteration complete (equilibrium) when equation (9) is satisfied. • TherewillbeaU-shapedpatterntoproductivityinanysituationinwhichthere is a significantly large reallocation of workers and firms across matches. Thus the U-shaped pattern of productivity in the 1970s-1990s may have had nothing todo with technological innovation at all, but rather may have purely been the result of a series of shocks to the labor market, expectations, or capital costs. This result is a significant departure from other creative destruction models, which in general rely on learning economies or production externalities to get production first to fall and then to rise following a shock. 6 Discussion: the “new economy” Recent theoretical work which has sought explanations for what appear to be at least two paradoxical developments in the U.S. economy over the past 20 or 30 years. First, significant technological innovations in high-tech (computer, communications equipment, and semiconductor) industries in the early 70s did not immediately lead to measured productivity gains. On the contrary, measured productivity growth followed a much more U-shaped pattern, falling off inthe70s and then acceleratinginthe1990s after aperiodof moderategrowth in the 1980s. Secondly, the notable rise in wage skill premium appears to have followed, rather than driven, the increase in the skill composition of the U.S. workforce, an increase which many date back to the incentives for young men to remain in school during the period of U.S. involvement in the Vietnam War. Analyses of thesequestionsisfurther complicated bythe rather different empirical properties of productivity and wage dispersion in other industrialized economies, which have had similar increases in skill composition and in access to high-tech innovations and yet not had the same U-shaped pattern to productivity nor the increase in wage dispersion observed in the U.S. data. Wefindthatamodelwhichfocuseson theimportanceofcomplementarities betweenthetechnologycharacteristicsandworkerskills,ormorespecificallyon the production synergies between the worker, firm, and technology characteristics, and in which there are frictions in the matching of those three inputs, can giveusdeeperinsightsintotheempiricalobservationsoutlinedaboveandwhich many have come to associate with the “new economy.” There are three key assumptions in the model: (1) The technology adoption decision is endogenous ontheavailabilityofcomplementaryinputsbecausethereismorethanoneway toproduceanygood;(2)labormarketfrictionsaffectproductivityand,thereby, also affect wages and wage dispersion; and (3) workers are heterogenous. 19

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