Sand in the Wheels of the Labor Market: The Effect of Firing Costs on Employment

Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 796 April 2004 Sand in the Wheels of the Labor Market: The Effect of Firing Costs on Employment Andrea De Michelis NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References in publications to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors. Recent IFDPs are available on the Web at www.federalreserve.gov/pubs/ifdp/.

Sand in the Wheels of the Labor Market: The Effect of Firing Costs on Employment Andrea De Michelis* Abstract: This paper examines the effects of firing costs in a dynamic general equilibrium model where firms face stochastic demand. It derives analytically two simple closed-form equations, one for the supply of labor, the other for its demand. These equations determine the comparative static effects of changes in firing costs on the labor market. When negative shocks are more likely to occur than positive shocks, and when the frequency of these shocks is high, firing costs have a substantial negative impact on aggregate employment. In addition, product market integration, as it has occurred in the formation of the European Union, induces firms to be more wary of future possible downturns and therefore intensifies the negative consequences of firing costs. Keywords: employment protection legislation, European labor markets. JEL Classifications: E24, L16, J50. * Staff economist of the Division of International Finance of the Federal Reserve Board. E-mail: Andrea.DeMichelis@frb.gov. This paper is an updated version of chapter 1 of my dissertation. I am extremely grateful to George Akerlof and Chad Jones for guidance, encouragement and patience. I received useful comments and suggestions from seminar participants at UC Berkeley, the ECB, Tilburg University, IIES (Stockholm), Warwick Univerisity, the Federal Reserve Board, Baruch College, Southern Methodist University and Florida International University. Special thanks to Andrew Figura, Johnathan Leonard and David Romer. The views in this paper are solely the responsibility of the authors and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or of any other person associated with the Federal Reserve System.

1 Introduction Employment in Europe has been stagnant for the last thirty years; unemployment has risen and participationinthe workforcehas fallen. Thesedramatic events have occurred against a backdrop oflegislativeeffortstomakeitmoredifficultforEuropeanfirmstolayoffworkers. Thesehighand rising firing costs are among the leading suspects as the reason for the poor performance of labor marketsinseveral Europeancountries.1 There exists a large literature that analyzes the effects of job security regulations on the functioning of the labor market. Most available evidence indicates that firing costs have a negative impact on employment (Heckman and Pages, 2000). Yet, no consensus has emerged from the theoretical side of the debate. This disagreement is not surprising since the effect of firing costs on employment are deeply ambiguous. The first impact of job security provisions is to increase employment by discouraging layoffs when firms are hit by negative shocks. Conversely, the fear of high firing costs in the event of a future downturn acts as a hiring cost, effectively reducing the creation of new jobs when firms are hit by positive shocks. Which of the two channels dominates dependsonthespecificationofthemodeland,inparticular,onthenatureofuncertainty. Thispaperwilldevelopatractablegeneralequilibriummodelthatdeliversaclearandintuitive understanding of how the labor market is affected by job security regulations. Specifically, we will spell out precise conditions under which firing costs reduce aggregate employment and will illustratetheseresultswithsimplecomparativestatics. We make three main assumptions. The first is that of monopolistic competition in the product market, which determines the size of the rent. The second is to represent uncertainty by letting demand for each product increase or decrease, according to a simple Markov process, in steps. Thethirdisthatoflinear layoffcosts,whichyieldspartialbutinstantaneousadjustment. Thisapproachallowsustoderiveanalyticallysimpleexpressionsthatcharacterizefirms’hiring and firing policies. At each level of demand, there is an upper threshold of employment above which firms are firing workers; and a lower threshold, below which firms are hiring workers. We 1Much of the current job security regulations were introduced between the 1950s and the 1970s. The recession followingthe 1973 oil shock gavean additional impetus to goverments to adopt various protective measures. Since then,thebroadevolutionhasbeentowardsderegulation,butatanextremlyslowpace(OECD,1999). 1

canthensolvefor thesteady-stateprobabilityof employmentat all levels,andaggregatetoderive an expression for the expected value of total labor demand. Finally, since demand for the firms’ productsdependupontheprices,wecomputetheoptimalpricesthatthefirmswillchargefortheir goods,aswellastheequilibriumwageratethatequatesthesupplyoflabortothedemandforlabor. The model derives explicit expressions for the supply of and the demand for labor, and thus sheds light on the ambiguity of the effects of firing costs on aggregate employment. It shows that whentheeconomyis“depressed,”theseeffectswillbenegative. Ournotionofdepressedeconomy referstoasituationinwhichtheMarkovprocessissuchthattheprobabilitytomovedownwardis greater than the probability to move upward, so firms are more likely to think that they will have to be firing workers than hiring them in the near future. On the other hand, firing costs will have a positive effect on employment when the economy is doing well, and firms are more likely to be hiring workers than firing them. Thus, the model yields the theory underlying the view that the poor performance of Europe’s labor markets is the result of the interaction between “bad” labor marketinstitutionsandadverseshocks(BlanchardandWolfers,2000). In addition, comparative static exercises indicate that these negative effects become stronger when the economy is more “turbulent”. Our notion of turbulence pertains to the frequency of the demandshocks. Thus,themodelalsoprovidesrigorousfoundationforthelong-standingargument that when demand is stable and growing, the hiring policy of firms is not affected by job security provisions; while, when demand turns flat and volatile, severance payments and rules become importantobstaclestoemploymentcreation(Blanchardetal.,1986,LjungqvistandSargent,2002). The model provides the answer to another important question. Besides the increase in firing costs, another major change has been the creation of the European Union. This historical event, together with globalizationand privatization of public companies, ischanging theeconomic landscape from a collection of small national protected markets to a single large competitive market. Weattributetothisongoingprocessageneralfallinthemarketpowerofexistingfirms. Themodel allows an assessment of how high firing costs interact with deregulation in the product market to determineaggregateemployment. The last part of the paper is devoted to the simulation of the model using plausible parameter values. As the aim of the paper is to explain the poor performance of Europe’s labor market, we 2

1.15 1.10 USA 1.05 1.00 UK ITA 0.95 GER 0.90 FRA 0.85 1973 1978 1983 1988 1993 1998 Figure1: Employment-populationratio(baseyear1973) needtocheckhowwellthemodelcanreproducetheexperienceofmostEuropeancountries. Here, weneedtokeepinmindthatemploymentandunemploymentarenotmirrorimagesofeachother. If workers’ participation decisions are influenced by job protection policies (as shown by Lazear, 1990),areductioninemploymentwillbeassociatedwithadeclineinparticipationrates. Thus,the unemploymentrateisnotthebestindicationofhowinstitutionaldifferencesaffectthefunctioning of the labor market. Figure 1 shows, instead, the ratio between employment and working age population for selected Europeancountries and the US since 1973.2 One fact strongly comes out: asignificantdownwardtrendinmostEuropeancountries,whichisevenmorestrikingifcompared withtheexperiencefortheUS. 2AllemploymentfiguresinthepaperarebasedonBLSdatawhichputforeigncountriesonasimilarbasisasthe US.SeeCapdeviellleandSherwood(2002)foradetailedpresentationoftheBLSinternationaldata. In Figure 1, we normalized the employment-population ratios across country using 1973 as a base year. This is becausesocialnormshaveasubstantialimpactonlaborpartecipation, especiallyforwomenandyoungindividuals. By indexing our data with a base year, we want to direct the reader’s attention to the change in the employmentpopulationratiothatoccuredovertime. 3

Ourmodelwilldeliverthisdownwardtrend. Highlayoffcostshaveasizeablenegativeimpact onemploymentwhentheeconomyisdepressedandturbulent. Inaddition,wewillshowthatafall in the market power of firms, while it stimulatesproduction and employment, also causes firms to bemorefearfulofpossiblefuturedownturnsandthereforeincreasestheprospectivecostsofhiring workers. In other words, product market deregulations generate better results for employment whenassociatedwithlowlayoff costs. The remainder of this paper is organized as follows. Section 2 discusses the related literature. Section 3 sets up a simple model of an economy with both product and labor market regulations. Section4solvesforthesteady-stategeneralequilibrium,inwhichbothemploymentandthewage are endogenously determined. Section 5 presents numerical simulations to examine how the variousdimensionsofregulationaffectthefunctioningofthelabormarket.Finally,section6discusses possibleextensionsofthebasicmodelandsummarizestheconclusions. 2 Literature Review The goal of this section is to motivate our contribution by discussing the existing literature on employment protection regulations. Both theoretical and applied work have been carried out on thistopic. On the theoretical side, we can identify at least three different approaches to the question of whether layoff costs have a significant impact on employment. Bentolila and Bertola (1989) analyzethecaseofafirmthatfacesuncertaintyinthereturnstolaborinadynamicpartialequilibrium model. Assuming linear and asymmetric adjustment costs, they show that dismissal costs have a negligible effect on hiring decisions and, surprisingly, slightly increase average employment. These results are quite sensitive to different assumptions about the persistence of the shocks, the magnitude of the discount rate, and the cyclicality of voluntary quits. Thus, less persistent shocks andlowerdiscountratescauselayoffcoststohavelargernegativeeffectsonemployment,because both factors reduce hiring relative to firing (Bentolila and Saint-Paul, 1994). In addition, allowing for a procyclical - rather than constant - quit rate increases the fear of dismissal costs as fewer workersleavetheirjobsvoluntarilyduringdownturns. InDeMichelis(2003),weshowthatlayoff 4

costscandepresslabordemandwhenquitsareprocyclical. Hopenhayn and Rogerson (1993) develop a general equilibrium model that incorporates the structure presented by Bertola and Bentolila. Calibrating the stochastic process driving labor productivity to match US evidence on job creation and destruction, they find that layoff costs reduce the turnover rate and the overall efficiency of the economy, and have a sizable negative impact on aggregate employment. These results (however) depend greatly on the assumption of decreasing returns to scal: higher firing costs increase firms’ size, and thus result into lower productivity, lower demandandloweremployment. The search and matching framework by Mortensen and Pissarides has been adapted to study how job protection provisions affect the functioning of the labor market. Blanchard (2000) and various coauthors show that costly layoffs reduce workers’ flows to and from employment. This causeslongerunemploymentspells,whiletheimpactonunemploymentisambiguous. Ljungqvist and Sargent (2002), on the other hand, calibrate a search model to show that the combination of highseverancepaymentswithincreasingeconomicturbulencecangenerateasignificantfallinthe rateofemployment. On the empirical side, most available evidence shows a consistent, although not always statistically significant, negative impact of job security provisions on employment. This is true not onlyintheWesternworld(Lazear,1990,AddisonandGrosso,1996)butinLatinAmericaaswell (Heckman and Pages, 2000). In contrast, the evidence regarding the impact on unemployment is ambiguous,butwesuspectthatthereareconceptualreasonsforsuchfindings. Specifically,Bertola (1990), Blanchard (2000), and Nickell (1997) find no effect of job security regulations on unemployment, while Lazear (1990) and Scarpetta (1996) find positive effects. Yet, it should not be a surprise that a negative impact on employment is not always mirrored in a positive effect on unemployment. Lazear(1990)showsthatjobsecuritypoliciesaffectworkers’participationdecision: thus,areductioninemploymentwillcauseadeclineinparticipationrates. One point on which the literature has converged is the formalization of the adjustment cost function. A series of studies indicate that convexity à la Tobin’s q is not the best way to proceed (Hamermesh 1993, 1995, and Hamermesh and Pfann, 1996). The last study, for example, concludes: “Adjustment costs are definitely not uniformly symmetric and convex.” (p. 1281) Thus, 5

we make the choice to follow the new standard assumption (since Nickell, 1986) of asymmetric linear adjustment costs. In particular, we formalize employment protection as a state-mandated cost that a firm has to pay if it wants to lay off an employee. We think of it as a cost to the firmworker pair, rather thanatransfer fromthefirmto theworker: the conventional wisdomisthat, in most European countries, the legal and administrative costs associated with dismissals exceed the monetaryvalueof severancepayments(Blanchard,2000). Summarizing, the assertion that job security does not have a negative impact on employment is based on indirect evidence concerning unemployment, not employment. However, this finding is not supported by a rigorous theoretical argument. The ambition of this paper is to fill this gap. We will show that high layoff costs significantly reduce employment when the economy is in a phase of depression and high volatility, but not when it is booming and uncertainty is small. This result offers an explanation for why, in the early1970s, European labor markets began to perform poorly. In addition, we will also explain how the interaction of layoff costs and the degree of competitionamongfirmsisimportanttoassesstheimpactofjobsecurityregulationsonaggregate employment. It has been argued that product market constraints might significantly contribute to the poor performance of European labor markets. A recent and small literature attempts to formalize this ideainsimplemodels3. Inparticular,BlanchardandGiavazzi(2001)developageneralequilibrium model to analyze how the interaction of product and labor market deregulations can give rise, in the short run, to lower real wages and higher unemployment and, in the long run, to a recovery of thelabor shareandadecreaseofequilibriumunemployment. We follow Blanchard and Giavazzi in modeling product market regulations as determining the degree of market power of firms. But, while they identify labor market regulations with the bargainingpower of workers, wefocus our attention ontheimpact of employment protectionregulations. As high firing costs are likely to strengthen the hands of workers in bargaining, leading to higher wages, one might be tempted to argue that our paper has nothing new to add. However, costlylayoffsalsoaffectlaborflows–layoffsdirectly,hiringsindirectly–andnotonlythebargaining strength of workers. Thus, our contribution to this literature is to explain how the interaction 3Tothebestofourknowledge,LeonardandVanAudenrode(1993)werethefirsttoarguethisconjecture. 6

of product market regulations and firing restrictions affect aggregate employment in a stochastic environment. Unfortunately, there is little direct evidence on the size and importance of product market constraints. A rare exception is a paper by Goldberg and Verboven (2001) in which the authors examine the European car market from 1980 to 1993: while they document a significant price dispersion across country, their findings also suggest that price discrimination plays a minor and diminishing role. Since labor demand is derived from the behavior of firms, it seems reasonable that regulations in the product market might inhibit the redeployment of workers and hence affect firms’hiringandfiringpolicies. Before we start spelling out the details of the model, we want to clarify what we mean by the termfiring,incasethereaderstillhadsomedoubt. Inthispaper,afiredworkerisalaidoffworker, not a worker fired with cause. This distinction is important because job security provisions can affect labor markets through two different channels. First, such regulations raise the costs that firms must bear in order to adjust their stock of employees. And this is what this paper is about. However, they also change the relation between employer and employee as it becomes harder to firethoseworkerswhoarenotsufficientlyproductive. Onthisissue,see,amongothers,Kuglerand Saint-Paul (2000). Anyway, for the remainder of the paper, we will use the terms “fire,” “layoff” and“dismiss”interchangeablytoindicateadecreaseintheemploymentlevelofagivenfirm. 3 The Model 3.1 Setup Demand side. This is a discrete-time model with infinite horizon. At time 0, the representative agent’spreferencearegivenby: 1 t M 1 γ α ∞ γ t − β U 0 E0 C t N t , (1) = 1 δ P − β (cid:5) t (cid:6) t 0 (cid:116) + (cid:117) (cid:116) (cid:117) (cid:59)= whereδistherateoftimepreference,t denotestime,andE0 istheexpectationoperatorconditional on information available in period 0. The first term inside the square brackets gives the effect on 7

utilityofaconsumptionindexoverdifferentiatedgood x . (SeebelowforimportantdetailsonC.) i The second term gives the effect of real money balances. Nominal money balances, M, are deflated by the nominal price index, P, associated with the composite good C. The parameter γ denotes the importance of C relative to M/P in utility; γ [0, 1]. The reason why we include ∈ money in the utility function is to avoid Say’s law. It is a well-known fact in economic theory that thesupplyofproductsbythemonopolisticallycompetitivefirms–aswechoosetomodel the supply side in this model – automatically generates its own demand unless agents have the choice between these goods and something else (Hart, 1982). If there were only this type of good, the equilibrium in the labor market would be always indeterminate. Here, we follow Blanchard and Kiyotaki (1987), and assume that the choice is between buying goods and holding money. This is mostsimplyandcrudelyachievedbyhavingrealmoneybalancesintheutilityfunction. The third termgives the disutility fromwork; N is the amount of work supplied by the household. Theparameterα measurestheimportanceofleisureinutility. Thetermβ 1istheelasticity − of marginal disutility of labor. We assume α > 0 and β > 1. Since leisure enters utility as an additivelyseparableterm,weruleoutanyincomeeffectsonthesupplyoflabor. Thebudgetconstraintis: n p xDdi M V w N M (1 r )V G , (2) i,t i,t t t 1 t t t 1 t t t 0 + + + = + − + + + (cid:61) where p and xD denotethepriceandthedemandforgoodx inperiodt, V denotesnetassets i,t i,t i t 1 + (besides money) at the end of period t, w denotes the wage rate in period t, G denotes lump t t transfers in period t (see below for details). We assume that V and M are both positive and 0 0 exogenouslydetermined. All of the above is quite standard. Now, we introduce our first new idea. We assume that there is a measure n of differentiated goods and demand varies across goods, that is consumers like different products differently. Specifically, we divide the x ’s goods into m taste groups and i m assumesymmetricdemandwithineachgroup. Thetasteparameterτ takesvalueintheset θ , j j 1 = θ j 1, and θ j is increasing in j: thus, products located in higher taste groups (i.e. highe(cid:106)r j)(cid:107)will ≥ be in higher demand. We use τ to denote the taste for good i. We can therefore define a “tastei 8

adjusted”compositegood: n σ σ 1 σ 1 C n 1/σ τ x σ− di − , σ > 1, t − i,t i,t ≡ 0 (cid:124) (cid:61) (cid:125) (cid:98) (cid:99) anda“taste-adjusted”priceindex(seeappendixA.1fordetails): 1 n 1 σ P n 1 τσ 1p1 σdi − . (3) t ≡ − i,t− i,−t 0 (cid:124) (cid:61) (cid:125) Thus, the composite good C is the usual index à la Dixit and Stiglitz except for the presence of the taste parameter, τ. The interpretation is straightforward: goods in higher demand, i.e. with higher τ, provide more consumption-utility. The term n 1/σ is added to neutralize the variety − effect,thusanincreaseinthenumber ofproductsdoesnot increaseutilitydirectly. Theparameter σ denotes the elasticity of substitution across all products. We make the usual assumption that σ > 1toguaranteetheexistenceofanequilibrium. The price index is also standard but for τ. Again, the intuition is very simple. Recall that the price index measures the least expenditure that buys one unit of the composite good. Thus, equation (3) says that the prices of goods in higher demand must be discounted more as they providemoreconsumption-utility. Uncertainty. Demand for each good x is uncertain. Specifically, we assume that the taste i parameterτ isstochasticandfollowsanm-stepMarkovprocesswheretheupwardtransitionprobabilityiss andthe downward transition probabilityisq. Notethat s andq donot sumto1 so that there is a nonzero probability that demand remains constant. If the demand shifter hits one of the extreme states θ or θ , it stays there until demand reverts towards the center. Thus, for example, 1 m Pr τ θ τ θ 1 s. i,t 1 i,t 1 1 = − = = − (cid:106)In section(cid:110)4.2, we will(cid:107)show that this specification with taste shocks is perfectly equivalent to (cid:110) thestandardassumptionofproductivityshocks. Thus,whileourmodelattributesalluncertaintyto shocksonthedemandside,thereisanalternativeinterpretationofthesamestructureinwhichthe disturbances reflect supply shocks. Of course, the truth lies in the middle and both types of shock areimportant. 9

The justification for these idiosyncratic demand/productivity shocks is a series of studies by Leonard (1987) and Davis and Haltiwanger (1992). These authors provide evidence that gross rates of job creation and destruction are remarkably large. For the US manufacturing sector, they amount to roughly 10% in a typical year. In this paper, we suggest that idiosyncratic shocks of significantsizearethesourceforthisobservedheterogeneityofemploymentchangesacrossfirms. While these shocks occur at a micro-level, this setup provides a simple framework to analyze the effects of macro shocks as well. If s q, firms are uniformly distributed over the line of = measure n: thereis thesame number offirms ineachtaste group. Firmsfacean idiosyncraticrisk but aggregate demand is stable. Furthermore, the closer to 1 is the sum of s and q, the higher is the uncertainty that firms must face. If s q, the distribution of firms is no longer uniform. In (cid:47)= particular,wecanmodela“depressed”economysettingq > s. Asnegativeshocksaremorelikely tooccurthanpositiveshocks,theeconomyconvergestoasteady-statewherethemajorityoffirms are in states of low demand. Thus, we can formalize a recession - a macro shock - by raising q relativetos. Regulations. As we discussed in the introduction, we (partially) follow Blanchard and Giavazzi(2001)intheirmodelingproductmarketregulationandassumethatgovernmentscanaffect theelasticityofsubstitution. Specifically,weassumethatthegovernmentsetsσ. We make the choice to identify labor market regulations with employment protection institutions which we formalize as state-mandated costs that a firm has to pay when it lays off an employee. We think of it as a cost to the firm-worker pair, rather than a transfer from the firm to theworker. Thiscapturesthefactthat,inmostEuropeancountries,firmsconsiderlegalandadministrativecostsassociatedwithlayoffs-duetonoticeperiods,plantclosinglegislation,bureaucratic procedures-tovastlyexceedthemonetaryvalueof theseverancepayments.4 In particular, we follow the recent literature and specify asymmetric linear adjustment costs. The firm bears a layoff cost, f, per dismissed worker while, for simplicity, we set hiring costs to 4Furthermore, the potential impact of severance payments could be undone by designing a wage contract that cancels out the effect of a transfer from firms to laid off workers. For example, as in the efficiency wage model of ShapiroandStiglitz(1984),wecouldhaveworkerspostabondofthevalueofthetransferwhichtheywouldforfeit in case they aredismissed. Alternatively and more realistically, think of an employment packagewhich pays rising wagesovertime. Thisisinfactequivalenttoaconstantwage,exceptthatthefirmkeepspartoftheearlypaymentsas abondandreturnsittotheworkerlaterifsheisstillemployed. 10

zero: f Z ,if Z > 0 i,t i,t F(Z ) (4) i,t =  0,otherwise,  where Z L L , thus Z > 0 represents the number of layoffs in firm i.5 Note that i,t i,t 1 i,t t ≡ − − this implies that there are no voluntary quits. Recall the discussion of the literature in section 2 abouthowthepresenceofquitsaffectslabordemandinthisclassofmodels. Iftheturnoverrateis constant, there are fewer workers to lay off when firms are hit by a negative shock. Hence, labor demandislessnegativelyaffectedbydismissalcosts(BertolaandBentolila,1989). However,this argument fails to realize that quits are procyclical (Akerlof et al., 1988, and Burda and Wyplosz, 1988). Inthiscase,fewerworkerswillleavetheirjobsvoluntarilyduringdownturns,increasingthe fearofhighlayoffcostsandsoinducingfirmstobemorereluctanttohire. InDeMichelis(2003), we show that firing costs can depress labor demand when quits are procyclical. Summarizing, we feel confident that allowing for voluntary labor turnover would not weaken the argument against employment protection laws. At the same time, algebra is much easier and we are able to derive closedformsolutions. While job security regulations impose a cost to the worker-firm pair, we assume that they are not a deadweight loss to the economy as a whole. We think that the related legal fees and administrative duties are eventually spent to purchase goods x ’s. Thus, for simplicity, we assume i that they are rebated to the representative agent as a lump sum transfer; the expression for G in t thebudgetconstraint(2)isgivenby: n G F(Z )di. t i,t = 0 (cid:61) This is a technical assumption to simplify algebra. Since total adjustment costs also enter the budget constraint through the expression for assets (the agent owns the firms), these two terms cancel each other out. Nonetheless, note that this simplification goes against the argument that costly layoffs negatively affect aggregate employment since we are ruling out any direct effect of 5The assumption of zero hiring cost does not affect the qualitative conclusions of the paper. It could be easily relaxedatthecostoflongerandmorecumbersomenotation. Furthermore,notethataslaborishomogenoeus,netandgrosslaborflowscoincide. 11

firingcostsontotalincome.6 Firms and technology. There is a continuum of firms of measure n producing differentiated goodsusinghomogeneouslabor, L. Eachproduct, x ,isproducedbyasinglefirmbutallfirmsuse i thesamelineartechnology: x AL , i [0,n]. (5) i,t i,t = ∈ Thus,laborproductivityisalways A. Ofcourse,laborissuppliedbytherepresentativeagent. Firms are placed in a monopolistically competitive market. We make the standard assumption that firmstakethebehaviorofotherexistingfirmsasgiven. The firm chooses an employment and firing policy each period to maximize the present discountedvalueofexpectednetrevenuesovertheinfinitefuture: t 1 ∞ v i,1 max E0 p i,t x i,t w t L i,t F(Z i,t ) (6) = 1 r − − { xi,t,Li,t,Zi,t } ∞t = 0 (cid:11) (cid:59) t = 0 (cid:116) + t (cid:117) (cid:100) (cid:101) (cid:12) subject to(1),(2),(4),(5), and L is given. Note that the information set in period t includes information on the value of τ . 0 t Finally,weassumethat all firmsareownedbytherepresentativeagents. 4 Solution of the Model Definitionofequilibrium. Acompetitiveequilibriumforthiseconomyisacollectionofquantities xD, V , M , N , x , Z ,L , v andprices w ,r , p suchthat: i,t t + 1 t t i,t i,t i,t i,t + 1 t N,i 0,n t t i,t t ∈ N,i ∈{ 0,n } (cid:81) (cid:82) ∈ ∈{ } (cid:106) (cid:107) taking w ,r , p asgiven,therepresentativeagentchooses xD, N , V and M tomax- • t t i,t i,t t t + 1 t imize((cid:106)1)subjectto(cid:107)thebudgetconstraint (2)and M 0 > 0and V 0 given; taking w ,r , p and L asgiven,eachfirmi chooses x , L and Z tosolve(6); t t i,t 0 i,t i,t i,t • (cid:106) (cid:107) w ,r , p aresuchthatallmarketsclear: t t i,t • (cid:106) (cid:107) 6In fact, this is the argument exploited by Hopenhayn and Rogerson (1993): firing costs are equivalent to a less productive technology, and so reduce employment and welfare. Here, we want to show that firing costs can have a negativeeffectonemploymentthroughadifferentchannel. 12

xD x (marketforgoodi) i,t = i,t M M (moneymarket) t 0 = n L Z di N (labor market) 0 i,t − 1 + i,t = t (cid:53)n(cid:98) (cid:99) v di V (assetmarket). 0 i,t + 1 = t + 1 (cid:53) We solve only for the steady-state equilibrium in which all prices and quantities are time invariant. Thus, in order to simplify notation, we choose, whenever possible, to omit the time index fortheremainderofthepaper. Weproceedby solvingfirst for thepartial equilibrium, inwhichpricesareexogenous. Specifically, in section 4.1, we characterize the behavior of the representative agent, in section 4.2 the behavior of firms, and in sections 4.3 and 4.5, we aggregate the individual behavior in the steadystate. Finally, in section 4.5, we solve for the steady-state general equilibrium in which prices are endogenousandmarketsclear. 4.1 The representative agent’s problem Astheeconomyisinastationarystate,thevalueofaggregateassetsforthewholeeconomyisnot timedependent: V V , t 0 = for all t. Furthermore, for the same reason, consumption is stationary as well. Thus, the Euler condition implies that the interest rate is equal to the rate of time preference: r r δ. Hence, t = = theagent choosesnottosaveandeachperiod,spendsallof hercapitalincome. Since there are no intertemporal links, we can characterize the behavior of the representative agent with a relation between real money balances and aggregate demand, a demand function for n each product and a labor supply equation (see appendix A.1 for details). Let X p x di /P ≡ 0 i i be an index for real aggregate consumption expenditures, which we call “aggrega(cid:98)te(cid:53)demand”(cid:99) for short. Then,inequilibrium,wefindthat: γ M X . (7) = 1 γ P − 13

Inequilibrium,desiredrealmoneybalancesareproportionaltoconsumptionexpenditures. Demandforgoodi sgivenby: X p σ xD i − τσ 1 . (8) i = n P i − (cid:114) (cid:115) Asinastandardmonopolisticallycompetitivemodel,thedemandforeachtypeofgoodrelative to aggregate demand is a function of the ratio of its price to the price index, with elasticity σ. − Furthermore,ahigherdemandshifter,τ ,causesdemandtobehigher. i Finally,aggregatelabor supplyisgivenby: χ w 1 β 1 N − , (9) = α P (cid:114) (cid:115) whereχ γγ(1 γ)1 γ. Thus,labor supplyisincreasingintherealwage. − ≡ − 4.2 The firm’s problem We characterize the behavior of firms using dynamic programming. All firms solve the same problem,thus,tosimplifynotation,weomit thegoods’index,i. Let the state variable be L and the control variable L, where L and L areyesterday’s and 1 1 − − today’s levels of employment, respectively. Combine equations (5) and (8) to substitute for p and x intothefirm’sobjectivefunction. Itisconvenienttosolvethefirm’smaximizationproblemusing dynamic programming. Let v(L τ ,τ) be the value function where L is the state variable, 1 1 1 − ; − − τ andτ thevaluesofthedemandshifteroneperiodbackandinthecurrentperiod,respectively7. 1 − 1 σ 1 v(L 1 τ 1 ,τ) max (cid:80)(τL) σ− wL F(Z) Ev(L τ,τ 1 ) , (10) − ; − = L − − + 1 r ; (cid:124) + (cid:125) 1 σ 1 where Z L 1 L. Note that (cid:80) P(X/n)σ A σ− is constant with respect to the choice = − − ≡ variable, L. Furthermore, as A and τ have the same exponent, the above expression makes clear 7Thevaluefunctiondependsonthelaggedvalueofthedemandshifterbecausetoday’sadjustmentcostsdepend onhowafirmgottothecurrentstate,byfiringorhiringworkers. 14

that,whilewemodeluncertaintycomingfromtasteshocks,thesamestructurewouldariseiffirmlevelsupplyshockswerethesourceofrisk. Inotherwords,ifτ denotedidiosyncraticproductivity shocksandconsumershadsymmetricdemandsacrossallgoods,firmswouldsolvethesamemaximizationproblemasinequation(10). Theoptimizationproblemdefinedin(10)isnon-standardbecausethederivativeoftheobjective functionchangeswiththesignof Z. Thefirstorderconditionwithrespectto L infactyields: ∂v(L 1 τ 1 ,τ) σ 1 σ 1 1 1 ∂Ev(L τ,τ 1 ) − ; − − (cid:80)τ σ− L −σ w ; ∂L = σ − + 1 r ∂L = + f,if Z > 0 ∂F(Z) −  f, 0 ,if Z 0 (11) = ∂L =   ∈ − =   0,(cid:100)Z < 0.(cid:101)     The above system is analogous to the deterministic expressions derived by Nickell (1986). The difference between σ σ− 1(cid:80)τ σ σ− 1 L −σ 1 and w gives the net (of the wage) product the marginal workerwhileEv (cid:41) (L τ,τ 1 )/(1 r)denotestheexpectedpresentdiscountedvalueofthemarginal ; + worker in the next period. Thus, the left hand side of the above equation can be interpreted as the net shadow value of the current marginal worker. If Z > 0, some workers are being laid off and equation (11) states that, at the optimum, the firm equates the expected discounted value of the future savings due to dismissing the marginal employee to the layoff cost today. Inaction, i.e. Z 0, is optimal when the net expected cost of themarginal worker is smaller than the dismissal = cost and greater than the zero cost of hiring. If Z < 0, the firm is hiring and equation (11) states that,attheoptimum,thefirmsetstozerothenetshadowvalueof themarginalworker. m Recall that τ takes value in the set θ . Thus, the first order condition in (11) implicitly j j 1 = defines the hiring and firing policy for (cid:106)each(cid:107)firm in state j. When a firm moves from a higher to a lower state, it will lay off some workers but it will set employment above the optimally desired level,atwhichthemarginalproductoflaborisequaltothewage. Theintuitionbehindthisresultis straightforward: asthefirmfacesadjustmentcosts,theadjustmentwillbepartial. Furthermore,the linearspecificationoftheadjustmentcostimpliesthatalltheadjustmentoccursimmediately: there is no advantage to smooth layoffs over time. This result is in sharp contrast with the implication 15

of convex adjustment costs à la Tobin’s q. Thus, equation (11) identifies a firing threshold, LF, j at which employment will be set when a firm falls from state j 1 to state j. Similarly, when a + firmmovesfromahighertoalowerstate,itwillhireadditionalworkersbutitwillsetemployment level below the optimally desired level. The firm takes into account that some workers may have to be fired in the future if demand turns down, and this is costly. This prospective cost acts as a hiring cost, deterring thecreation of newjobsingood states. Again, thelinear specification of the adjustmentcostimpliesthatalltheadjustmentoccursimmediately. Thus,foreach j,equation(11) identifies a hiring threshold, LH, at which employment will be set when a firm jumps from state j j 1tostate j. − We set the values of structural parameters and exogenous variables to ensure that LF < j 1 − LH < LF < LH for all j’s so that when a firm is hit by a negative shock it will lay off some j j j 1 + workersandwhenitishitbyapositiveshockitwillhiresomeworkers. Inotherwords,weassume that the demand shocks, i.e. the difference between θ and θ , are large enough to induce the j j 1 − firmtochangeitsemploymentleveleachtimeitishit byashock.8 In appendix B, we report the details of the derivation of the hiring and firing thresholds in the steady-state equilibrium, when the probability mass over the employment is not time dependent. Here,wejust presentanddiscusstheresults. Thefiringthresholdinstate j isequalto: σ 1 σ σ 1 (cid:80)θ σ− LF − j , (12) j =  σ w r s f  − 1+r +   for j 1,...,m 1. As is intuitive9, LF varies positively with the demand shifter, θ , labor = − j j productivity, A, the dismissal cost, f, and the probability of a positive shock, s; negatively with the wage, w. Setting f 0 in equation (12), we find the employment level at which the marginal = productoflaborisequaltothewage, L .10 Itisstraightforwardtocheckthat LF > L . Inwords, ∗j j ∗j when a firm shifts from a higher to a lower state, the presence of dismissal costs deters firing and 8Alternatively,wecouldthinkthatittakestwoormoreconsecutivepositive(ornegative)shockstomakethefirm want to hire (layoff). However, this alternative assumption would just complicate notation without adding any new insight. 9Recallthatwehavedefined(cid:80) P X 1 µ µ A1 1 µ andµ 1 . = n + + = σ 1 10SeetheAppendixDforacompleteanalysisofthebenchmark−caseofzerolayoffcosts. (cid:98) (cid:99) 16

thus increases labor demand. However, until a positive shock occurs in the future, these extra workerskeeponbeingexcessive. Thehiringthresholdinstate j isequalto: σ 1 σ σ 1 (cid:80)θ σ− LH − j , (13) j q =  σ w f  + 1 r +   for j 2,...,m. As it is intuitive, LH varies positively with the demand shifter, θ , and labor = j j productivity, A;negativelywiththewage,w,thedismissalcost, f,andtheprobabilityofanegative shock,q. Itisstraightforwardtocheckthat LH < L . Inwords,whenafirmshiftsfromalowerto j ∗j ahigherstate,thepresenceof dismissalcostsdetershiringandthusdecreaseslabordemand. This fear of hiring, however, has a negligible impact unless the likelihood of a future negative shock is highenough. Note that we have not discussed how LF and LH vary with σ. This is because (cid:80) depends on j j P and both vary with σ. Thus, we postpone this discussion for when we find an expression for P inequilibrium. 4.3 The steady-state distribution of firms Inordertoderiveaggregatelabordemand,wehavefirsttodeterminethedistributionoffirmsover the employment line; that is, for example, how many firms are employing LF workers. In the i1 steady-state equilibrium, there is uncertainty at the firm-level but the aggregate economy is in a stationary state, for any given pair s and q.11 A basic feature is that the number of new hires will beequaltothenumberoflayoffs. Recall that we set the values of structural parameters and exogenous variables to ensure that LF < LH < LF < LH for all j’s. Thus, even if a firm initially employs more than LF, over j 1 j j j 1 m − + 11Irrespectiveoftheinitialconditions,thestochasticprocessconvergestowardsasteady-statewheretheprobability massatanylevelofemploymentisnottimedependen. Formally,thisresultcomesfromtheassumptionthatweare consideringadiscretetimefinite-stateMarkovchainwhichisergodic,i.e. irreduciblewithaperiodic,recurrentstates. An ergodicMarkov chain converges toa distribution wheretheprobabilityof being in state j is independent of the initial state. For a proof of this result and a thorough analysis of the stationarity, the limit theorem and the ergodic theoremforMarkovchains,seeGrimmettandStirzaker(1995),section6.4,pp.207-218,andsection9.5,pp.367-380. 17

time, it will fall over time at or below LH . Similarly, in steady-state, no firm will have LH i,m 1 1 − workers. Inotherwords, LH and LF arethetwoextremesofthedistribution. 1 m We are now ready to derive the probability distribution of firms along the employment line. Let λ indicate the percentage of firms that employ LH workers, and ω indicate the percentage j j j of firms that employ LF. Thus, for example, the probability that a firm is at LH is equal to the j j probabilitythatafirmwasinthesamestateintheprecedingperiodanddidnotmove,(1 s q)λ , j − − plustheprobabilitythatthefirmwasinstate j 1andmoveduptostate j,s ω λ . Note j 1 j 1 − − + − that if a firmwas in state j 1 and moved down, then it would set employm(cid:98)ent to LF not(cid:99)to LH: + j j λ doesnotdependdirectlyonthepercentageoffirmsinstate j 1. Insteadystate,theseweights j + aretimeinvariantandsumuptoone,sothatweneedtosolvethefollowingsystem: λ (1 s q)λ s ω λ j j j 1 j 1 = − − + − + −  ω j (1 s q)ω j q(cid:98) λ j 1 ω j 1(cid:99)   = − − + + + +     ω 1 (1 s)ω 1 q(λ 2 (cid:98) ω 2 ) (cid:99)   = − + +    λ (1 q)λ s(ω λ )  m m m 1 m 1  = − + − + − m (ω λ ) 1    j = 1 j + j =      (cid:51)ω m = λ 1 = 0.      The first two equations form a system of two second order linear difference equations in λ j and ω . The other four equations give the boundary conditions. The solution of the above system j yields: j 1 λ (cid:27) s − for j 2,3,..., m 1, j = q = − (cid:114) (cid:115)j ω (cid:27) s for j 2,3,...,m 1, j = q = − ω (cid:27) (cid:114)s(cid:115) 1 , 1 = q + (cid:114) (cid:115) m 1 λ (cid:27) s 1 s − , m = q + q (cid:114) (cid:115)(cid:114) (cid:115) m 1 1 m s − 1 − where(cid:27) s 2s q − 1 . Notethat (cid:27) isdecreasingin s. ≡ (cid:11) q + q(cid:114) (cid:115) q s − 1 + (cid:12) q (cid:114) (cid:115) 18

4.4 The partial equilibrium As the measure of firmis n, there are nλ firms employing LH workers and nω firms employing j j j LF workers. Thus, we can easily compute the steady-state aggregate labor demand as a weighted j sumof LH and LF: j j m L nλ LH nω LF PE j j j j = + j 1 (cid:59)= (cid:114) (cid:115) σ 1 σ m q σ r s σ n − (cid:80) w f − λ θσ 1 w + f − ω θσ 1 , (14) = σ + 1 r j j− + − 1 r j j− (cid:130) (cid:4) (cid:116) (cid:117) j 1 (cid:116) + (cid:117) (cid:116) + (cid:117) (cid:59)= where L denotesaggregatelabordemandinPartial Equilibrium. PE Unfortunately,theexpressionin(14)isnotconvenienttoillustratethequalitativeeffectsofthe key parameters, f and σ, on labor demand. The following approximation is extremely useful to understand the economic intuition behind the analytical result. As m increases, the total number ofemployeesoffirmsintheextremestates1andm becomesverysmallsince LF and LH become 1 m a small fraction of the total. Thus, for m large enough, we can ignore the impact of these two extremesontheaggregatelabordemand. Thismethodologygreatlysimplifiesalgebraandnotation and we can focus on where the driving forces are at work.12 Since ω sλ for j 2, 3, ..., j = q j = m 1,onecanshowthat L is(approximately) proportionalto: PE − q σ s r s σ − − L (cid:21) w f w + f , (15) PE ≈ + 1 r + q − 1 r (cid:5) (cid:6) (cid:116) + (cid:117) (cid:116) + (cid:117) where(cid:21) n σ 1(cid:80) σ m 1 λ θσ 1 . Theaboveexpressionrevealsthesourceoftheambigu- ≡ σ− j −2 j j− = ity about how(cid:98)job sec(cid:99)ur(cid:51)ity prov(cid:114)isions af(cid:115)fect the labor market. On one hand, firing costs increase employment by discouraging layoffs when firms are hit by a negative shock: this is captured by the second term inside the square brackets of equation (15). On the other hand, the fear of firing costs in the event of a future downturn acts as hiring costs, effectively reducing the creation of newjobswhenfirmsarehitbyapositiveshock: thisiscapturedbythefirstterminsidethesquare 12We check the accuracy of these approximation by carrying out simulations for both the exact case and for the approximatecase. 19

brackets of equation (15). The latter channel dominates when the probability of a negative shock is greater than the probability of a positive shock, so firms are more likely to think that they will have to be laying off workers rather than hiring them. In such a case, the marginal hired worker willbecomeexcessiverelativelysoon. Thus,wefindthatlayoffcostsreducelabordemandwhenq isgreater thans,andthiseffect becomesstronger when, foragivenq/s,q getslargerelativetor. Welabelsuchaneconomy“depressed”and“turbulent”. Bycontrast,ifwelettheMarkovprocess be symmetric, i.e. q s, labor demand is slightly increasing in f – the main result of Bertola = and Bentolila (1990). Summarizing, the interaction between institutions and the macroeconomic environmentiscrucialtounderstandtheimpactoffiringcostsonthelabormarket. Finally,notethat L doesnot dependonthemeasureof firms,n. Thiscanbeeasilychecked PE 1 σ 1 substituting P(X/n)σ A σ− for (cid:80) in equation (14). This result comes from the specification of theutilityfunctionsinceaggregatedemandturnsouttobeindependentof n. 4.5 The general equilibrium In partial equilibrium, eachfirmsets its price, p , freelyaccordingtothe first order condition(11) i and takes aggregate demand, X, as given. In general equilibrium, instead, prices and aggregate demandareendogenouslydetermined. InappendixC,weshowthat all firmsatanyfiringthresholdschargethesameprice, pF: w r s f pF σ − 1+ + r (16) = σ 1(cid:114) A (cid:115) − Since w r s f is the cost of the marginal worker in a firing threshold and A denotes labor − 1+r + productivity, w r s f /A represents the cost of the marginal unit of output. Thus, equation − 1+r + (16)saysthat(cid:114)equilibrium(cid:115)priceisasimplemarkupovermarginalcost.13 Similarly,allfirmsatany hiringthresholdschargethesameprice, pH: q w f pH σ + 1 + r (17) = σ 1(cid:114) A (cid:115) − 13Asusual,themarkuprate,µ,isgivendemand’selastictyaccordingto: µ 1/(σ 1). ≡ − 20

q Since w f is the cost of the marginal worker in a hiring threshold, we find once again + 1 r + thestandardconditionthatequilibriumpriceisamarkupovermarginalcost. Substituting(16)and (17)for pF and pH intoequation(3),wefindanexpressionforthepriceindexasafunctionofthe structuralparametersofthemodel: 1 σ/(σ 1) m q 1 σ r s 1 σ 1 σ P − θσ 1 λ w f − ω w + f − − . (18) GE = A j− j + 1 r + j − 1 r (cid:11) (cid:130) (cid:4)(cid:12) j 1 (cid:116) + (cid:117) (cid:116) + (cid:117) (cid:59)= Secondly, in general equilibrium, aggregate demand, X, is endogenously determined: in par- 1 σ 1 ticular, it isproportional to real money balances. Hence, weneedtoexpress(cid:80) P(X/n)σ A σ− = as a function of M and the structural parameters of the model, and then substitute this expression for (cid:80) into equation (14). Simple algebra (again see appendix C for details) yields the following equationforaggregatelabordemandinGeneral Equilibrium: σ σ m θσ 1 λ w q f − ω w r s f − γ σ 1 j 1 j− j + 1 r + j − 1+r L GE M − = (cid:116) (cid:114) + (cid:115) (cid:114) + (cid:115) (cid:117) . (19) = 1 γ σ (cid:51) 1 σ 1 σ − m j 1 θσ j− 1 λ j w + 1 q r f − + ω j w − r 1+r s f − = + + (cid:116) (cid:117) (cid:114) (cid:115) (cid:114) (cid:115) (cid:51) In order to compare partial and general equilibrium, it is again convenient to carry the same approximationasinsection4.5whichyield: σ σ w q f − s w r s f − γ σ 1 + 1 r + q − 1+r L M − + + , (20) GE ≈ 1 γ σ (cid:114) (cid:115)1 σ (cid:114) (cid:115)1 σ − w + 1 q r f − + q s w − 1 r +r s f − + + (cid:114) (cid:115) (cid:114) (cid:115) and then put side by side expressions (15) and (20). If the economy is depressed and turbulent, that is if q is large relative to s andr, we still find that layoff costs have a negative effect on labor 1 σ demand.14 However,thiseffectisnowweakerbecauseofthepresenceoftheterm w q f − + 1 r + (cid:114) (cid:115) σ σ 1 14Notethat w q f > w q f − asσ > 1andthatwestillhave w q f > s w r s f . + 1 r + 1 r + 1 r q − 1+r Thus,thedomi (cid:114) natingt + erm (cid:115) is w (cid:114) q f + − σ(cid:115) whichisdecreasingin f. (cid:114) + (cid:115) (cid:114) + (cid:115) + 1 r + (cid:114) (cid:115) 21

in the denominator of the above expression. Intuitively, the presence of layoff raises the marginal cost of production, and thus the price, for all firms at any hiring threshold. Since these types of firmsaredominatinginadepressedandturbulenteconomy,thepriceindex P riseswith f. Ceteris paribus, a higher price level causes higher production and so higher employment. But, things are notequal,aswelearneddiscussing L ,ifq islargerelativetos andr,thepresenceoflayoffcosts PE detershiringmorethanfiring. Itturnsoutthatthissecondeffectdominates: L isdecreasingin f GE evenifnotasmuchas L . Summarizing,layoffcostsinduceeachfirmatanyhiringthresholdsto PE reduceemployment but theresultingfall inproductionraisesthegeneral level ofprices,lessening theincentivetoemployfewerworkers. Finally, equilibrium aggregate employment is given by the intersection of equation (19) with the labor supply schedule. Using the expression (18) to substitute in for P equation (9), it is straightforwardtoshowthataggregatelaborsupplyingeneralequilibriumisgivenby: 1 N (σ − 1) Aχw β − 1 1 m θσ 1 λ w q f 1 − σ ω w r + s f 1 − σ (β − 1)(σ − 1) , GE = σα j− j + 1 r + j − 1 r (cid:5) (cid:130) (cid:4)(cid:6) (cid:116) (cid:117) j 1 (cid:116) + (cid:117) (cid:116) + (cid:117) (cid:59)= (21) and,withtheusualapproximation,wefind: 1 (σ 1) Aχw β 1 1 q 1 − σ s r s 1 − σ (β − 1)(σ − 1) N − − (cid:21) w f w + f . GE ≈ σα + 1 r + q − 1 r (cid:11) (cid:5) (cid:6)(cid:12) (cid:116) (cid:117) (cid:116) + (cid:117) (cid:116) + (cid:117) (22) Theaboveexpressionmakesclearthat,foradepressedandturbulenteconomy,aggregatelabor supply is decreasing in f. Intuitively, this happens because the fall in production causes a rise in the price index, and thus a fall in the real wage. Note how this price effect counterbalances the priceeffectoflabordemand,thereforeintensifyingthenegativeimpactoffiringcostsonaggregate employment. The intersection of equations (19) and (21) gives the equilibrium wage, w , and the equilib- EQ rium level of employment, L . As for a depressed and turbulent economy, firing costs shift to EQ theleftbothlabordemandandlabor supplyschedules,we findthatfiringcostshurtemployment. 22

5 Numerical Simulations In this section, we examine the effects of product and market regulations on the functioning of the labor market. We run numerical simulations using the exact expressions for labor demand and supply, equations (19) and (21), and plausible parameter values. The goal is to assess the quantitative effects of firing costs and the markup rate, and to see if we can replicate, at least partially,thedownwardtrendintheemployment-populationratiodepictedinFigure1. First, we present and discuss the several assumptions we need to make about the parameter values. The first two concern the size and the probability of shocks. The problem is that there are no estimates of q, s, and the θ ’s: we can only try to infer their sizes from firms’ reaction to shocks. j DavisandHaltiwanger(1992) measureestablishmentlevel employmentchangesintheUSmanufacturing sector. Three of the main findings of the paper are that: (i) “most of annual job creation and destruction reflects persistent establishment-level employment changes,” (ii) “job destruction ishighlyconcentrated,”and(iii)the“rateofjobreallocationisofimpressivemagnitude”(p. 821). Therefore, we suppose that firms are hit by large and infrequent shocks. In other words, the transition probabilities, q and s, seem to be small, but when these shocks occur the taste/productivity parameter,θ ,seemstovaryconsiderably. j Furthermore, most European countries experienced substantially higher productivity growth and substantially lower probability of negative demand shocks in the 1950s and 1960s than subsequently. In other words, the slowdown in the rate of productivity growth, the increase in real oil prices, and the increase in real interest rates and the fiscal cuts associated with the launch of theEuroprofoundlyalteredthemacroeconomicenvironmentwherefirmsoperate. Forthisreason, we think we characterize as “depressed” most of the European economies in the last thirty years. In other words, we will simulate an economy where firms are hit more often by negative than by positiveshocks,i.e. q < s. Another important assumption must be made about the elasticity of labor supply with respect to the real wage. Equation (9) yields an elasticity equal to α/χ(β 1). Using γ 2/3 which − = yieldsχ 0.5,sowecaninferα/(β 1)fromestimatesoftheelasticityofthelaborsupplywith ≈ − respect to the real wage. Here, we set a value for the elasticity of 0.5, bigger than conventional 23

microestimatesbutsmallerthanthoseoftenassumedinaggregatemodels. Summarizing,weneed α/(β 1) 2,whichisconsistent withα 2andβ 2. − = = = Finally, our last key assumption pertains to the degree of competition among firms. The literature indicates that the markup rate varies considerably across industries (Roger, 1995). Unfortunately, our model does not allow for firm’s heterogeneity besides the level of demand. Thus, with thiscaveat inmind,wesetthemarkuprateµ 1 30%(oralternativelyσ 13/3 4). We ≡ σ 1 = = ≈ − thinkthiscorrespondstoaplausiblesituationwherefirmshavesignificant marketpower. Thevalueoftheotherparametersare: A 1, M 10,n 10,m 10,δ r 4%. = = = = = = Thebenchmarkcase(q .08,s .06,µ 30%) • = = = 1 0.98 o ati 0.96 R n o ati ul 0.94 p o P n -t e m 0.92 y o pl m E 0.9 0.88 0.86 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Firing cost (as a fraction of the yearly wage) Figure2: Thebenchmarkcase: adepressedandturbulenteconomy For a given set of parameters, we first compute the employment and the wage when firing costs are zero. Then, we use this employment level as a measure of the population for our simulatedeconomy,andthiswagerateasareferencefor thesizeofthefiringcost. 24

Figure 2 shows the result of the simulation exercise. On the horizontal axes, we report the firing cost as a fraction of the reference wage level. On the vertical axis, we report the ratio between equilibrium employment and the measure for population. The message is clear: high layoff costs reduce employment. Even the magnitude of this change is consistent with Europe’s experience in the past thirty years: an increase in the layoff costs from one to two times the reference annual wage causes a fall in the employment-population ratio of about 5%. Wealsoneedtocomment ontheconvexshapeofthelinedepictedinFigure2. Specifically, employment becomes slightly increasing when firing costs are extremely high. Not surprisingly, if job security provisions are very strict, firms stop firing workers: in our model, LF j moves very close to LH . The other side of the coin is that adjustment costs paid by firms j 1 + become very high, causing a sharp fall in profits. It seems reasonable that when profits are too low, some firms will leave the market, causing a fall in employment. Thus, future work shouldextendthemodelbyallowingfirmstoexit(andenter)themarketinordertoaccount fortheimpactoffiringcostsontheextensivemargin. Higherfrequency(q .12,s .09,µ 30%) • = = = Ljungqvist and Sargent (2002) show how an increase in economic turbulence – which they measure as workers’ income variability – in conjunction with high unemployment benefits andlayoffcostscancontributetopersistentlyhighunemployment. Inthispaper,bycontrast, we focus on the effect of job security provisions on the labor demand side. Still, we reach a similar conclusion. An increase in economic turbulence – here defined as the frequency of shocks to products’ demand – is associated with a more negative impact of firing costs on employment. For example, in Figure 3, we raise the transition probabilities (while keeping theirratioconstant),andwefindthatanincreaseinthelayoffcostsfromonetotwotimesthe reference annual wage now causes a fall in the employment-population ratio of about 7%. Thecomparisonwiththebenchmarkcase(thedottedline)makesevidentthat,inadepressed economy, an increase in the frequency of shocks intensifies the negative consequences of firingcostsonemployment. 25

1 0.98 0.96 o i at R n 0.94 o ati lu o p 0.92 P n -t e m y 0.9 o pl m E 0.88 0.86 0.84 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Firing cost (as a fraction of the yearly wage) Figure3: Higherfrequencyofshocks: amoreturbulent economy Lower marketpower (s .06,q .08,µ 15%) • = = = Martins et al. (1996) provide estimates of the markup rate over the period 1970-92, for 36 manufacturing industries in 14 OECD countries. Interestingly for us, they document a downward trend in all European countries they examine. Their results confirm the common belief that the ongoing product market deregulation – associated with the process of Europeanintegration–isreducingthemarketpower offirms. InFigure4,wereducethemarkupratefrom30%to15%,andthesimulationexerciseshows that lowering the market power intensifies the negative consequences of layoff costs. For example, an increase in the layoff costs from one to two times the reference annual wage causes a fall in the employment-population ratio of about 8%. Intuitively, the decrease in rents induces firms to be more worried about future possible adverse shocks when they are hiringnewworkers. Thecomparisonwiththebenchmarkcase(thedottedline)clearlyshows that, in a depressed economy, a fall in the markup rate increases the negative consequences 26

1 0.98 0.96 0.94 o ati R n 0.92 o ati ul o p 0.9 P n -t e m y0.88 o pl m E 0.86 0.84 0.82 0.8 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Firing cost (as a fraction of the yearly wage) Figure4: Theeffectsof firingcostswithlowmarkuprate of firingcosts. 6 Conclusions While most empirical evidence links high firing costs to low levels of employment, no agreement has yet emerged about the proper way to model this effect. We have argued that a suitable model must solve five problems simultaneously. The first of these is that the modeling of firing costs involvesestablishing,fordifferentfirms,anupperthresholdofemployment. Abovethisthreshold, firms fire workers. Second, such a model must establish a lower threshold of employment. Below this threshold, firms hire workers. Third, because the effects of firing costs involves the hires and fires that are made, demand must be represented as subject to shocks; otherwise there will be neither hires nor fires. Fourth, it is necessary to solve for the steady-state probabilities of employment at all levels, and aggregate to compute total steady-state employment. Finally, since aggregate demand depends upon the prices that firms will charge for their goods, it is necessary 27

to solve for the optimal prices, as it is also necessary to compute the wage rate that will clear the labormarket. We were able to accomplish all five of these steps using standard modeling techniques. We assumed that uncertainty is governed by a simple m-state Markov chain, which enabled us to derive analytical solutions for labor supply and labor demand. In contrast, a standard assumption in the previous relatedliterature was to characterizeuncertainty witha continuous-timestochastic process. This choice required that the models had to be solved numerically, so that the forces drivingtheresultswerehiddenbeneaththesurface. Our analytic solutions, instead, clearly show when firing costs have positive or negative effect on employment. The reasons for such effects are also clear. Job security legislation reduces aggregate employment when (i) negative shocks are more likely to occur than positive shocks, and when (ii) the frequency of shocks is high. In addition, we find that product market deregulation, with an associated fall in market power, induces firms to be more concerned about future possible downturns,intensifyingthenegativeconsequencesoffiringcosts. 28

References Addison,J.andGrosso,J.(1996),“JobSecurityProvisionsandEmployment: RevisedEstimates,” IndustrialRelations,Vol.35,N.4. Akerlof, G., Rose, A. and Yellen, J. (1988), “Job Switching and Job Satisfaction in the US Labor Market,”BrookingPaperofEconomicActivity,Vol.2,pp.495-582. Bentolila S. and Bertola, G. (1989), “Firing Costs and Labour Demand: How Bad is Eurosclerosis?,”ReviewofEconomicStudies,Vol.57,pp.381-402. Bentolila S. and Saint-Paul, G. (1994), “A Model of Labour Demand with Linear Adjustment Costs,”LabourEconomics,Vol.1,pp.303-326. Bertola,G.(1990),“JobSecurity,EmploymentandWages,”EuropeanEconomicReview,Vol.34, pp.851-886. Blanchard,O.(1997),“TheMediumRun,”mimeo,MIT. Blanchard,O.(2000),“EmploymentProtection,Sclerosis,andtheEffectofShocksonUnemployment,”Lecture3,LionelRobbinsLectures,LondonSchoolofEconomics. Blanchard, O., Dornbusch, R., Drèze, J., Giersch, H., Layard, R. and Monti, M. (1986), “Employment and Growth in Europe: A Two Handed Approach,” in Blanchard, O., Dornbusch, R. and Layard, R. (eds.), Restoring Europe’s Prosperity; Macroeconomic Papers fromthe Centrefor EuropeanPolicyStudies,MITPress,pp.95-124. Blanchard, O. and Giavazzi, F. (2001), “Macroeconomic Effects of Regulation and Deregulation inGoodsandLaborMarkets,”NBERWorkingPaper,N.8120. Blanchard, O. and Kiyotaki, N. (1987), “Monopolist Competition and the Effects of Aggregate Demand,”AmericanEconomicReview,Vol.77,N.4,pp.647-666. Blanchard,O.andWolfers,J.(2000),“ShocksandInstitutionsintheRiseofEuropeanUnemployment.TheAggregateEvidence,”EconomicJournal,Vol.110,N.1,pp.1-33. 29

Burda, M.andWyplosz, C.(1988), “GrossLabor Market Flowsin Europe: SomeStylizedFacts,” CEPRDiscussionPaper,N.439. Capdeviellle, P.and Sherwood,K. (2002), “ProvidingComparable International Labor Statistics,” MonthlyLaborReview,Vol.6,pp.3-14. Davis,S.andHaltiwanger,J.(1992),“GrossJobCreation,GrossJobDestruction,andEmployment Reallocation,”QuarterlyJournalof Economics,Vol.107,N.3,pp.819-863. DeMichelis,A.(2003),“CostlyLayoffswithProcyclicalQuits,”inEssaysontheMacroeconomic EffectsofLaborMarket Rigidities,Chapter2,Ph.D.Thesis,U.C.Berkeley,pp.40-61. Goldberg, P. and Verboven, F. (2001), “The Evolution of Price Dispersion in the European Car Market,”Reviewof EconomicStudies,Vol.68,pp.811-848. Grimmett,G.andStirzaker,D.(1995),ProbabilityandRandomProcesses,2ndedition,Clarendon Press,Oxford. Kugler, A,andSaint-Paul, G. (2000),“HiringandFiringCosts,AdverseSelectionandLong-term Unemployment,”mimeo,UniversitatPompeuFabra. Hart,O.(1982),“AModelofImperfectCompetitionwithKeynesianFeatures,”QuarterlyJournal ofEconomics,Vol.97,pp.109-138. Hamermesh,D.(1993),LaborDemand,PrincetonUniversityPress. Hamermesh, D. (1995), “Labour Demand and the Source of Adjustment Costs,” The Economic Journal,Vol.105,pp.620-634. Hamermesh,D.andPfann,G.(1996),“AdjustmentCostsinFactorDemand,”JournalofEconomic Literature,Vol.34,pp.1264-1292. Heckman, J. and Pages, C. (2000) “The Cost of Job Security Regulation: Evidence from Latin AmericanLaborMarkets,”NBERWorkingPaper,N.7773. Hopenhayn, H. and Rogerson, R. (1993), “Job Turnover and Policy Evaluations: a General EquilibriumAnalysis,”Journalof PoliticalEconomy,Vol.101,pp.915-938. 30

Lazear,E.(1990),“JobSecurityProvisionsandUnemployment,”QuarterlyJournalofEconomics, Vol.102,pp.699-726. Leonard,J.(1987),“IntheWrongPlaceattheWrongTime: theExtentofStructuralandFrictional Unemployment,” in Lang, K. and Leonard, J. (eds.), Unemployment and the Structure of Labor Markets,BasilBlackwell,pp.141-163. Leonard, J. and Van Audenrode, M. (1993), “Corporatism run amok: job stability and industrial policy in Belgium and the United States,” in Lang, K. and Leonard, S. (eds.), Unemployment and theStructureofLaborMarkets,BasilBlackwell,pp.141-163. Ljungqvist,L.andSargent,T.(2002),“TheEuropeanEmploymentExperience,”mimeo,Stanford University. Martins, J., Scarpetta, S. and Pilat, D. (1996), “Markup Ratios in Manufacturing Industries. Estimatesfrom14OECDCountries,”OECDWorkingPaper,N.162. Nickell,S.J.(1986),“DynamicModelofLabourDemand,”inAshenfelter,O.andR.Layard(eds.), HandbookofLaborEconomics,Vol.1,ElsevierSciencePublishers,pp.473-522. Nickell, S. J. (1997), “Unemployment and Labor Market Rigidities: Europe versus North America,”JournalofEconomicPerspectives,Vol.1,N.3,pp.55-74. OECD (1999), “Employment Protection and Labour Market Performance,” in Employment Outlook,Chapter2,pp.48-132. Roeger, W. (1995), “Can Imperfect Competition Explain the Difference between Primal and Dual ProductivityMeasures? EstimatesforUSmanufacturing,”JournalofPoliticalEconomy,Vol.103, N.2,pp.316-330. Scarpetta, S. (1996), “Assessing the Role of Labour Market Policies and Institutional Settings on Unemployment: ACrossCountryStudy,”OECDEconomicStudies,N.26,pp.43-98. Shapiro,C.andStiglitz,J.E.(1984),“EquilibriumUnemploymentasaWorkerDisciplineDevice,” AmericanEconomicReview,Vol.74,N.3.,pp.433-444. 31

A Appendix A.1 Thederivationofeachindividualdemandfunctionsandeachindividual labor supply Letusbeginwiththedefinitionofthepriceindex, P. Formally, P isgivenby: n P min p x di (23) i i = xi 0 (cid:61) σ subjecttoC ≡ n − 1/σ 0 n (τ i x i ) σ σ− 1 di σ − 1 = 1. SetuptheLagrangian: (cid:81) (cid:82) (cid:53) n n σ L p i x i di λ P 1 n − 1/σ (τ i x i ) σ σ− 1 di σ − 1 . = + − 0 (cid:11) 0 (cid:12) (cid:61) (cid:118) (cid:61) (cid:119) Thus,thefirstorderconditionwithrespectto x yields: i x λσCn 1τσ 1p σ, (24) i = P − i − i− where λ is the Lagrangian multiplier. Combining terms in the above expression, and integrating P overi gives: 1 n 1 σ λ n 1 p1 στσ 1di − . (25) ⇒ P = − i− i − 0 (cid:116) (cid:61) (cid:117) Plugging(24)and(25) into(23),weget: n n σ 1 min p x di p1 σλσCn 1τ σ− τσ 1di xi 0 i i = 0 i− P − i i − = (cid:61) (cid:61) 1 n 1 σ ... n 1 p1 στσ 1di − P, = = − i− i − = 0 (cid:116) (cid:61) (cid:117) whichisequation(3). Recall that we solve the model for the stationary equilibrium. Thus, consumption, money holding and labor supply is constant over time. The Euler condition then yields thatr δ, and so − no savings: V V . This implies that the representative agent consumes the annuity value of its t 0 = 32

n n wealth,whichisequaltototalfirms’profits: rV p x di wL F(Z )di. = 0 i i − − 0 i Wearenowreadytosolvetherepresentativeage(cid:53)nt’sutilitymaximiz(cid:53)ationproblemwithineach period. Wedothisintosteps. First,eachworkerchoosestheoptimal compositionofconsumption andmoneyholdingfor agivenlevel ofincome. SetuptheLagrangian: M 1 γ n L Cγ − λ I M p xDdi M , = P + + 0 − i i − 0 (cid:116) (cid:117) (cid:124) (cid:61) (cid:125) where I wN rV G istotalperiod’sincome. Thus,thefirstorderconditionswithrespectto ≡ + + M and xD are,respectively: i M γ 1 (1 γ)Cγ − λ (26) − P P = (cid:116) (cid:117) γC l γ − 1 M P 1 − γ Cσ 1 n −σ 1 τ i σ σ− 1 x i D −σ 1 = λp i 1 − σ, (27) (cid:116) (cid:117) (cid:98) (cid:99) Since(27)holdsforallgoodsi: xD p σ τ σ 1 i v i − , xD = p τ v (cid:116) i (cid:117) (cid:116) v (cid:117) wherev isadummyindexforthegoods. Integratingoverv andusingthedefinitionof P,weget: σ (I M M)/P p1 σ − xD + 0 − i− τσ 1 . (28) i = n P i − (cid:130) (cid:4) Let X n p xDdi /P be“aggregatedemand,”sotakingtheratioof(27)over(26)yields: ≡ 0 i i (cid:98)(cid:53) (cid:99) M 1 γ − X, P = γ whichisthesameasequation(7). Notethatwehaveusedthefactthat,inequilibrium,allmarkets must clear: xD x , M M , and L N; and that all adjustment costs are rebated to the agent i = i = 0 = n aslump-sumtransfers: G F(Z )di. = 0 i (cid:53) 33

Pluggingtheaboveexpressioninto(28)givesthedemandfunctionforgoodi,equation(8): X p σ xD i − τσ 1 . i = n P i − (cid:114) (cid:115) Hence,demandof thecompositegoodforagivenlevelofincomeis: C γ (I M )/P. (29) 0 = + The second and final step is to determine labor supply, given the demand functions for money andthecompositegood: M 1 γ α N argmaxU Cγ − Nβ = N = P − β (cid:116) (cid:117) wN rV G M α γγ(1 γ)1 γ + + + 0 N β . = − − P − β l Thefirstorderconditionwithrespectto N gives: l γγ(1 γ)1 − γ w 1/(β − 1) N − , = α P (cid:116) (cid:117) which is equation (9). As the utility function is additively separable in consumption and real balances, on the one hand, and leisure, on the other, there are no income effects on the labor supply. B The derivation of the hiring and the firing thresholds We set the values of structural parameters and exogenous variables to ensure that LF < LH < j 1 j − LF < LH for all j’s so that when a firm is hit by a negative shock it will lay off some workers j j 1 + andwhenit ishitbyapositiveshockitwillhiresomeworkers. Recall the Bellman equation (10) and the first order condition (11). The main issue is to compute ∂Ev(L τ,τ 1 )/∂L inside the first order condition. The key to the solution of this problem is ; to understand that since future employment decisions will be taken optimally, the envelope theo- 34

remensuresusthattheycanbetakenasgiven(inprobabilitydistribution)whensettingthecurrent policy. In other words, the marginal worker at period t is perceived as marginal for the infinite future. LetL betheoptimalvalueoftheemploymentlevelinthecurrentperiodasdefinedbyequation τ (11)andτ isnextperiod’svalueofthedemandshifter. Takingthederivativeofnextperiodvalue 1 functionwithrespecttotoday’scontrol variableyields: ∂V(L τ ; τ,τ 1 ) σ − 1 (cid:80)τ σ σ− 1 L−σ 1 w ∂F(Z 1 ) ∂L = σ 1 1 − − ∂L τ 1 (cid:124) 1 E1 ∂V(L 1 τ 1 ,τ 2 ) ∂F(Z 1 ) ; (30) +1 r ∂L − ∂L 1 τ + (cid:125) where Z L L . Note that τ denotes the value of the demand shifter two period ahead 1 τ 1 2 = − and E1 the expectation operator conditional to the information available in the next period. Since thefunction F(Z)isnotcontinuouslydifferentiableatzero,wehavetobecarefulwhenweexpand the expression in (30). Let consider first the case when the firm will lay off some workers in the nextperiod,i.e. Z > 0. Then,next period’sadjustment costsareequalto: 1 F(Z ) f Z . 1 1 = Usingthisresultinequation(30),wefindthattheoneperiodaheadshadowvalueofthecurrent marginal employeeisequalto: ∂V(L τ ; τ,τ 1 ) σ − 1 (cid:80)τ σ σ− 1 L−σ 1 w f 1 E1 ∂V(L 1 ; τ 1 ,τ 2 ) f f. (31) ∂L = σ 1 1 − + + 1 r ∂L − = − τ 1 + σ 1 1 We used equation (11) to substitute in 0 for σ σ− 1(cid:80)τ 1 σ− L− 1 σ − w + f + 1 1 r E1∂V( ∂ L L 1 1 ; τ1,τ2). + Intuitively, if the firmwill belaying off workersinperiod t 1, theshadowvalueof themarginal + employee in period t will be equal to the dismissal cost, f. Let now consider the case when the firmwillnotlayoffanyworkerinthenextperiod, Z 0. Then: 1 ≤ F(Z ) 0. 1 = 35

Pluggingtheaboveexpressionintoequation(30),wefind: ∂V(L τ ; τ,τ 1 ) σ − 1 (cid:80)τ σ σ− 1 L−σ 1 w 1 E1 ∂V(L 1 ; τ 1 ,τ 2 ) . (32) ∂L = σ 1 1 − + 1 r ∂L τ 1 + Usingequations(31)and(32)toexpandthefirstorder condition,wefind: ∂F ∂ ( L Z) = σ σ − 1 (cid:80)θ σ j σ− 1 L −σ 1 − w + 1 1 r 0 + (1 − s − q) ∂V(L ∂ ; L θ j ,θ j ) − qf , (33) + (cid:118) (cid:119) for j 2, ..., m 1. We are interested in solving for the steady-state equilibrium, when the = − probability mass at any level of employment is not time dependent. In steady-state, all firms in state j have a number of employees equal to either LH, the hiring threshold, or to LF, the firing j j threshold. Thus,usingonceagainequations(31) and(32),wefind: ∂V(L θ ,θ ) f, if L LF ; j j − = j (34) ∂L =  0, if L LH.  = j  We are now ready to find the hiring and the firing thresholds. Suppose that, in the last period, thefirmi wasinstate j 1andthisperiodisinstate j. Combingequations(33)and(34),wefind + anexpressionforthefiringthresholdinstate j: σ 1 σ 1 1 1 − (cid:80)θ σ− LF −σ w 0 (1 s q)f qf f σ j j − + 1 r − − − − = − (cid:114) (cid:115) + (cid:100) (cid:101) σ 1 σ σ 1 (cid:80)θ σ− LF − j for j 1,...,m 1, ⇒ j =  σ w r s f  = − − 1+r +   which is the same as equation (12)15. Suppose now that, in the last period, the firm i was in state j 1andthisperiodisinstate j. Combingequations(33)and(34),wefindanexpressionforthe − 15Notethatinstate1,firmswillremaininthesamestatenextperiodwithprobability(1 s) andwillmovetostate − 2withprobablitys. Thus,thefirstorderconditionis: σ 1 1 σ σ− 1(cid:80)θ 1 σ− L 1 F −σ − w + 1 1 r s0 − (1 − s)f = 0.Thisexpressionstillimpliesequation(12). + (cid:98) (cid:99) (cid:100) (cid:101) 36

hiringthresholdinstate j: σ 1 σ 1 1 1 − (cid:80)θ σ− LH −σ w 0 0 qf 0 σ j j − + 1 r + − = (cid:114) (cid:115) + (cid:100) (cid:101) σ 1 σ σ 1 (cid:80)θ σ− LH − j for j 2,...,m, ⇒ j =  σ w q f  = + 1 r +   which is the same as equation (13)16. Note that no firm is ever hiring in the lowest state, 1, or is firinginthehigheststate,m. Thus,wedonotfindexpressionsfor LH and LF. 1 m C The characterization of the general equilibrium We start by finding the equilibrium prices. Recall from the first order condition of the consumer maximizationproblem: 1 p v x i D σ τ v σ σ− 1 , (35) p = xD τ i (cid:130) v (cid:4) (cid:116) i (cid:117) wherev is(again)adummyindexforgoods. Theaboveexpressionimplies: σ σ 1 p v θ j σ − 1 θ z σ− 1. p = θ θ = i z j (cid:116) (cid:117) (cid:116) (cid:117) Thus, p pF pF. Similarly, one can check that p pH pH. Finally, equation (35) i = i = i = i = impliesthattheratiobetween pH and pF is: q w f pH + 1 r pF. + = w r s f (cid:130) − 1+r (cid:4) + Usingtheseresultsintotheexpressionforthepriceindex P,weget: 16Notethat in state m, firms will remaininthesame statenext period with probability (1 q) and will move to − statem 1withprobablityq. Thus,thefirstorderconditionis: − σ 1 1 σ σ− 1(cid:80)θ m σ− L m H −σ − w + 1 1 r q0 − (1 − q)f = 0.Thisexpressionstillimpliesequation(13). + (cid:98) (cid:99) (cid:100) (cid:101) 37

1 P =  w − p r 1 F + + r s f σ − 1 m θσ j− 1 λ j w + 1 q r f 1 − σ + ω j w − 1 r + r s f 1 − σ  −σ − 1 . (cid:130) (cid:4) (cid:130) (cid:4)  (cid:59) j = 1 (cid:116) + (cid:117) (cid:116) + (cid:117)  (36)   Using the above expression and recalling that aggregate demand is proportional to real money balances,wecanexpress(cid:80)asafunctionof pF: σ 1 X σ 1 σ 1 ApF σ− γ M (cid:41) σ 1 (cid:80) P A σ− ... = n = = w r s f 1 γ n (cid:116) (cid:117) (cid:130) − 1+r (cid:4) (cid:116) − (cid:117) + 1 m q 1 σ r s 1 σ −σ θσ 1 λ w f − ω w + f − (37) · j− j + 1 r + j − 1 r (cid:11) (cid:130) (cid:4)(cid:12) j 1 (cid:116) + (cid:117) (cid:116) + (cid:117) (cid:59)= Therefore,ingeneralequilibrium,theaggregatesupplyofgoods x ’sis: i n m σ 1 σ r s 1 p x di nA λ pHLH ω pFLF ... nApF − (cid:80) w + f − i i = j j + j j = = σ − 1 r (cid:61) 0 (cid:59) j = 1 (cid:114) (cid:115) (cid:116) (cid:117) (cid:116) + (cid:117) m w q f q 1 σ r s 1 σ · θσ j− 1 λ j w + 1 r + s z f w + 1 r f − + ω j w − 1 + r f − . j 1 (cid:130) − 1+r (cid:116) + (cid:117) (cid:116) + (cid:117) (cid:4) (cid:59)= + Usingequation(37)tosubstituteinfor(cid:80)intheaboveexpressionyields: σ n ApF γ p x di ... M. i i 0 = =  σ w r s f  1 γ (cid:61) σ 1 − 1+r − − +  (cid:114) (cid:115) n γ Recall p x di PX and X M/P,thus,theequilibriumpricechargedbyallfirmsat 0 i i = = 1 γ − anyfiringt(cid:53)hresholdisgivenby: σ ApF 1 pF σ w − 1 r + + r s f ,  σ w r s f  = ⇒ = σ 1(cid:114) A (cid:115) σ 1 − 1+r − − +  (cid:114) (cid:115) which is equation (16). Similarly, we canfindthat pH σ w q f /A, which is equation = σ 1 + 1 r − + (17). Combining the above expression with equation (36), we(cid:114)can solve (cid:115)for the price index as a 38

functionofthestructuralparametersofthemodel,equation(18): 1 σ 1 σ 1 m q 1 σ r s 1 σ −σ 1 P − A − θσ 1 λ w f − ω w + f − − , GE = σ j− j + 1 r + j − 1 r (cid:11) (cid:130) (cid:4)(cid:12) (cid:116) (cid:117) j 1 (cid:116) + (cid:117) (cid:116) + (cid:117) (cid:59)= We now have all the elements to write down an expression for aggregate labor demand in generalequilibrium, L : GE m L nλ LH nω LF ... GE j j j j ≡ + = = j 1 (cid:59)= (cid:114) (cid:115) γM σ 1 m q σ r s σ − θσ 1 λ w f − ω w + f − = 1 γ σ j− j + 1 r + j − 1 r (cid:130) (cid:4) − j 1 (cid:116) + (cid:117) (cid:116) + (cid:117) (cid:59)= 1 m q 1 σ r s 1 σ − θσ 1 λ w f − ω w + f − , · j− j + 1 r + j − 1 r (cid:11) (cid:130) (cid:4)(cid:12) j 1 (cid:116) + (cid:117) (cid:116) + (cid:117) (cid:59)= whichthesameasequation(19). Thefinalstepistosolveforlabor supplyingeneralequilibrium,equation(21): 1 χ w β 1 N − GE = α P GE (cid:116) (cid:117) 1 1 β 1 χ σ 1 m q 1 σ r s 1 σ σ 1 − Aw − θσ 1 λ w f − ω w + f − − . =  α σ j− j + 1 r + j − 1 r  (cid:5) (cid:130) (cid:4)(cid:6)  (cid:59) j = 1 (cid:116) + (cid:117) (cid:116) + (cid:117)    D The benchmark case of no adjustment costs When layoff costs are equal to zero, the firm i sets marginal the product of labor is equal to the wageinallperiods. Therefore,wehave: σ 1 σ σ 1(cid:80) ∗ θ j σ− L − . (38) ∗j =  σ w    It is easy to check that the case of zero layoff costs is yields the same steady-state distribution of firms along the employment line. Define with η the steady-state probability that a firm is in j 39

state j,thenη ω λ . Infact,itisstraightforwardtoshowthatthesolutionofη sη j j j j j 1 = + = − + (1 s q)η qη withboundaryconditionsη (1 s)η qη andη (1 q)η sη j j 1 1 1 2 m m m 1 − − + +s 1 j 1 = − + = − + − isgivenbyη q− s − for j 1,2,..., m. j = s m 1 q = q − (cid:114) (cid:115) Giventhis,iti(cid:114)sim(cid:115) mediatetofindanexpressionforequilibriumaggregateemploymentwithout layoffcosts. Letusbeginwithderivingaggregatelabordemandinpartialequilibrium, L . Recall PE thatequation(38)definestheemploymentlevel, L ,atwhichthemarginalproductoflaborisequal i∗ tothewage. Thus,wefind: (σ 1)(cid:80) σ m L n − ∗ η θσ 1 . ∗PE = σw j j− (cid:116) (cid:117) j 1 (cid:59)= Ingeneralequilibrium,weneedtoconsiderthatallfirmsset thesameprice p σ w/A ∗ = σ 1 − sothat: (cid:114) (cid:115) P σ σ − 1 w m η θσ 1 −σ − 1 1 . G∗E = (cid:114) A(cid:115) j j− (cid:130) (cid:4) j 1 (cid:59)= Similarly, we need to adjust the labor supply equation. Thus, aggregate labor demand and aggregatelabor supplywithout layoffcostsaregivenby: (σ 1)(cid:80) σ m L n − ∗ η θσ 1 ∗GE = σw j j− (cid:116) (cid:117) j 1 (cid:59)= γ (σ 1)M (cid:41) − . = 1 γ σw − Forthenumericalsimulations,itisalsouseful tocompute L ingeneralequilibrium: ∗j γ (σ 1)M L − (cid:41) θσ 1 . ∗j = 1 γ σw j− − Finally,aggregatelabor supplyingeneralequilibriumisgivenby: 1 1 β 1 σ 1χA m σ 1 − N − η θσ 1 − . G∗E =  σ α j j−  (cid:130) (cid:4) j 1 (cid:59)=   40

Summarizing,both L and N aredecreasinginµ,thusbothschedulesshiftoutfollowing ∗GE G∗E afall inµresultingintohigheremploymentandhigherwage. 41