Demand-driven Job Separation: Reconciling Search Models with the Ins and Outs of Unemployment

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Demand-driven Job Separation: Reconciling Search Models with the Ins and Outs of Unemployment Regis Barnichon 2009-24 NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

Demand-driven Job Separation Reconciling Search Models with the Ins and Outs of Unemployment (cid:3) RØgis Barnichon Federal Reserve Board 05 May 2009 Abstract This paper presents a search model of unemployment with a new mechanism of job separation based on (cid:133)rms(cid:146)demand constraints. The model is consistent with the cyclical behavior of labor market variables and can account for three stylized facts about unemploymentthattheMortensen-Pissarides(1994)modelhasdi¢ cultiesexplainingjointly: (i) the unemployment-vacancy correlation is negative, (ii) the contribution of the job separation rate to unemployment (cid:135)uctuations is small but non-trivial, (iii) movements in the job separation rate are sharp and short-lived while movements in the job (cid:133)nding rate are persistent. In addition, the model can rationalize two hitherto unexplained (cid:133)ndings: why unemploymentin(cid:135)owswerelessimportantinthelasttwodecades,andwhytheasymmetric behavior of unemployment weakened after 1985. JEL classi(cid:133)cations: J63, J64, E24, E32 Keywords: Search and Matching Model, Gross Worker Flows, Job Finding Rate, Job Separation Rate (cid:3)I would like to thank Mike Elsby, Bruce Fallick, Nobu Kiyotaki, Chris Pissarides, John M. Roberts, Dan Sichel, Jae W. Sim and Carlos Thomas for helpful suggestions and discussions. The views expressed here do not necessarily re(cid:135)ect those of the Federal Reserve Board or of the Federal Reserve System. Any errors are my own. E-mail: regis.barnichon@frb.gov 1

1 Introduction The Mortensen-Pissarides (1994, henceforth MP) search and matching model has emerged as a powerful tool to study unemployment and the labor market, and an extensive literature has introduced equilibrium unemployment into general equilibrium models through a search framework.1 In parallel to these theoretical developments, many studies have documented the empirical properties of job and worker (cid:135)ows over the business cycle.2 In particular, Shimer (2007) focuses on individual workers(cid:146)transition rates and (cid:133)nds that the contribution of the job separation rate (JS) to unemployment(cid:146)s variance is small over the post-war period and even smaller since the mid-80s. Movements in the job (cid:133)nding rate (JF), on the other hand, account for three-quarters of unemployment(cid:146)s variance over the post-war period.3 However,theMPmodelhasdi¢ cultiesexplainingthelowcontributionofthejobseparation rateaswellasotherstylizedfactsaboutunemploymentanditstransitionprobabilities. Instead, I present a search and matching model with a new mechanism of job separation based on (cid:133)rms(cid:146)demand constraints that is remarkably successful at matching the data. Despite a small number of parameters, the model is consistent with the behavior of labor market variables, can rationalize a low, yet non-trivial, contribution of the job separation rate and can explain the declining contribution of JS since 1985. Shimer(cid:146)s (2007) evidence on the low contribution of the job separation rate led to a recent modeling trend that treats the job separation rate as acyclical.4 However, such a conclusion may be too hasty. First, while the jury is still out on the precise contribution of JS to unem- 1See, for example, Merz (1995), Andolfatto (1996), den Haan, Ramey and Watson (2000), Walsh (2004), Blanchard and Gali (2008), Gertler and Trigari (2009), Trigari (2009) among many others. 2For work on gross worker (cid:135)ows and gross job (cid:135)ows, see, among others, Darby, Plant and Haltiwanger (1986), Blanchard and Diamond (1989, 1990), Davis and Haltiwanger (1992), Bleakley et al (1999), Fallick and Fleischman (2004), Fujita and Ramey (2006) and Fujita (2009). Shimer (2007), Elsby, Michaels and Solon (2008),Elsby,Hobijn,andSahin(2008)andFujitaandRamey(2008)focusinsteadontransitionratesbetween employment, unemployment and out of labor force. 3In this paper, as in much of the literature on unemployment (cid:135)uctuations, I omit (cid:135)uctuations in inactivityunemployment (cid:135)ows, and focus only on employment-unemployment (cid:135)ows. See Shimer (2007) for evidence supporting this assumption. Furthermore, I will interchangeably use job separation probability or employment exit probability when referring to the probability that an employed worker becomes unemployed. 4See e.g. Hall (2005), Blanchard and Gali (2008), and Gertler and Trigari (2009). 2

ployment (cid:135)uctuations, Shimer(cid:146)s (2007) estimate amounts to a non-trivial 25 percent over the post-war period.5 The contribution of JS indeed drops to only 5 percent over 1985-2007, but it is important to understand the reasons behind this decline. In addition, as Blanchard and Diamond (1990) (cid:133)rst showed, the number of hires tends to increase in recessions while the job (cid:133)nding rate decreases. This happens because the pool of unemployed increases proportionally more than unemployment out(cid:135)ows and suggests that unemployment in(cid:135)ows play an important role in recessions. Finally, an important characteristic of unemployment is its asymmetric behavior, the fact that increases in the unemployment rate are steeper than decreases, and I (cid:133)nd that this asymmetry disappears after 1985. Again, this suggests that an asymmetric mechanism such as job separation is driving the response of unemployment to shocks, but that this mechanism is weaker since the mid-80s. A natural candidate to account for both unemployment out(cid:135)ows and in(cid:135)ows is the MP model with endogenous separation, but the model has di¢ culties generating three stylized facts about cyclical unemployment and its transition probabilities: (i) the unemploymentvacancy correlation is negative, (ii) JS is half as volatile as JF but is three times more volatile thandetrendedrealGDPand(iii)movementsinJSaresharpandshort-livedwhilemovements in JF are persistent and mirror the behavior of unemployment. Indeed, Ramey (2008) and Elsby and Michaels (2008) show that for plausible parameter values, the MP model generates an upward-sloping Beveridge curve as well as too much volatility in JS relative to JF.6 Moreover, I simulate a MP model with AR(1) productivity shocks and (cid:133)nd that it generates counterfactually similar dynamic properties for the job (cid:133)nding rate and the job separation rate. These empirical issues arise because in a MP model calibrated with plausible idiosyncratic productivity shocks, job destruction is the main margin of adjustment in employment and (cid:147)drives(cid:148)the job creation margin; a burst of layo⁄s generates higher unemployment, makes workers easier to (cid:133)nd and stimulates the posting of vacancies. This mechanism explains why 5See Elsby, Michaels and Solon (2008) and Fujita and Ramey (2007). 6See also Costain and Reiter (2005) and Krause and Lubik (2007) for similar claims but with a search and matching framework that is slightly di⁄erent than Mortensen and Pissarides (1994). See Section 6 for a review of the literature. 3

the MP model can generate a counterfactually positive unemployment-vacancycorrelation and counterfactually similar impulse responses for -JF and JS. Themaincontributionofthispaperistopresentanewmodelofendogenousseparationthat is consistent with the three stylized facts about unemployment and its transition probabilities. Inasearchandmatchingmodelofthelabormarket, demand-constrained(cid:133)rmshavethechoice between two labor inputs; an extensive margin (number of workers) subject to hiring frictions and a (cid:135)exible but more expensive intensive margin (hours per worker). Moreover, while hiring is costly and time consuming, (cid:133)ring is costless and instantaneous. The model is closest to Krause and Lubik(cid:146)s (2007) New-Keynesian search model with endogenous job destruction (cid:224) la Mortensen-Pissarides (1994), but with one important di⁄erence: there are no match-speci(cid:133)c productivity shocks and job separation does not depend on the productivity of each match.7 Instead, whenfacedwithlowerthanexpecteddemand, (cid:133)rmscanchoosetolayo⁄extraworkers to save on labor costs. With demand-driven job separation, I show that endogenous job separation is zero in steady-state, so that (cid:133)rms cannot reduce (cid:133)ring but must post vacancies to increase employment. Because of hiring frictions, (cid:133)rms hoard labor and only use the job separation margin for large negative shocks. Consistent with fact (ii), JS is less volatile than JF, and the contribution of JS to unemployment (cid:135)uctuations is not necessarily large. In fact, the model can closely match an empirical contribution of JS of 25 percent over the post-war period. Further, contrary to a standard MP model, vacancy posting is the main variable of adjustment of employment, and job separation is only used in exceptional circumstances. As a result, and consistent with fact (iii), adjustments in JS are sharp and short-lived while JF inherits the persistence of aggregate demand shocks. As in the MP model, a burst of layo⁄s increases unemployment and decreases the expected cost of (cid:133)lling a vacancy, so that (cid:133)rms want to pro(cid:133)t from exceptionally low labor market tightness to increase their number of new hires. However, because of demand constraints, the incentive is much weaker than in the MP 7Trigari(2009) and Walsh (2005) are two other important examples of New-Keynesian models with endogenous job destruction. Unlike Krause and Lubik (2007), they introduce a separation between (cid:133)rms facing price stickiness(theretailsector)and(cid:133)rmsevolvinginasearchlabormarketwithoutnominalrigidities(thewholesale sector). 4

model; gross hires may go up in recessions, in line with Blanchard and Diamond (1990), but consistent with fact (i), (cid:133)rms post fewer vacancies, and the unemployment-vacancy correlation is negative. Another contribution of the paper is to provide an explanation for the decline in the contribution of JS and the weaker asymmetry in unemployment since 1985. The model implies that these two (cid:133)ndings are by-products of the Great Moderation.8 Because of hiring frictions, (cid:133)rms hoard labor and do not lay-o⁄workers in small recessions, preferring to reduce hours per worker. Sincethelasttworecessions(1991and2001)wererelativelymild, (cid:133)rmsmadelittleuse of the job separation margin, and the contribution of JS, as well as the asymmetric behavior of unemployment, declined.9 Interestingly, the current recession that started in December 2007 is a lot more pronounced and is witnessing a large increase in the job separation rate (see Barnichon, 2009), consistent with the model(cid:146)s prediction. Therefore, treating JS as acyclical may be especially inappropriate in times of higher macroeconomic volatility. The remainder of the paper is organized as follows: Section 2 discusses the importance of understanding (cid:135)uctuations in the job separation rate; Section 3 documents three stylized facts about unemployment and its (cid:135)ows that the MP model has di¢ culties explaining; Section 4 presents a search model with demand-driven job separation and Section 5 confronts it with the data; Section 6 reviews the literature on the empirical performance of MP models with endogenous job destruction, and Section 7 o⁄ers some concluding remarks. 2 The importance of understanding unemployment in(cid:135)ows In this section, I highlight a number of empirical points that suggest that layo⁄s play an important role in unemployment (cid:135)uctuations and that assuming a constant job separation rate can lead to misinformed conclusions about the behavior of unemployment. 8Theso-called"GreatModeration"referstothedramaticdeclineinmacroeconomicvolatilityenjoyedbythe US economy since the mid 80s. (see, for example, McConnell and Perez-Quiros, 2000) 9Interestingly, Petrongolo and Pissarides (2008) show that the UK also experienced a remarkable decline in thecontributionsofJS,butonlyafter1993. ThisisconsistentwiththepredictionsofthemodelastheUKhad its last large recession (excluding the current one) during the 1992-1993 EMS crisis. 5

2.1 The small and declining contribution of unemployment in(cid:135)ows In two in(cid:135)uential papers, Shimer (2007) and Hall (2005) argue that the contribution of unemployment in(cid:135)ows to unemployment (cid:135)uctuations is much smaller than the contribution of unemploymentout(cid:135)ows, andmoredramaticallythat(cid:135)uctuationsintheemploymentexitprobability are quantitatively irrelevant in the last two decades. Indeed, Shimer (2007) shows that (cid:135)uctuations in the job separation rate accounts for 25% of the variance of the cyclical component of unemployment over 1948-2007 but for only 5% over the last 20 years.10 As a result, a large number of recent papers assume a constant separation rate when modeling search unemployment.11 However, a contribution of 25 percent is not trivial.12 Furthermore, if assuming a constant separation rate seems reasonable over the last two decades, it brushes aside the reasons behind the decline in the contribution of JS since the mid-80s. Since the assumption(cid:146)s validity depends on whether the smaller contribution of JS is a permanent or temporary phenomenon, one needs to understand the reasons behind the decline in the importance of unemployment in(cid:135)ows. 2.2 Gross hires tend to increase in recessions Analyzing gross (cid:135)ows data, Blanchard and Diamond (1990), Fujita and Ramey (2006) and Elsby, Michaels and Solon (2008) show that the number of hires tends to increase in recessions whilethejob(cid:133)ndingratedecreases. Sincethe(cid:135)owfromunemploymenttoemploymentisequal to the job (cid:133)nding probability times the number of unemployed, this implies that the pool of unemployed increases proportionately more than the (cid:135)ow. This observation is hard to recon- 10Using Shimer(cid:146)s (2007) data, Fujita and Ramey (2008) report a higher contribution for the job separation rate (15%) over 1985-2004. However, they use a parameter of 1600 for their HP (cid:133)lter while Shimer (2007) uses a parameter of 105 arguing that a lower parameter removes much of the cyclical volatility of the variable of interest. Since the precise contribution of JS is not critical for my argument, I only report Shimer(cid:146)s (2007) estimates. 11Examples include Hall (2005), Shimer (2005), Hagedorn and Manovskii (2006), Costain and Reiter (2007), Trigari (2006), Barnichon (2008), and Thomas (2008). 12Elsbyetal(2008)cautionagainstsomechangesinthecyclicalcompositionofunemploymentthatcouldbias Shimer(cid:146)s (2007) conclusions. Fujita and Ramey (2008) extend Shimer(cid:146)s analysis using an alternative dataset, gross(cid:135)owsfrom theCPSover1976-2006,andestimatethatthecontributionofthejobseparationrateiscloser to 40 percent. 6

cile with a constant job separation rate, but a burst of layo⁄s would increase unemployment independentlyofJFandcouldexplainwhyunemploymentincreasesfasterthanthejob(cid:133)nding rate in recessions. 2.3 Unemployment displays asymmetry in steepness An important characteristic of unemployment is its asymmetric behavior, and a large literature has documented a non-trivial asymmetry in steepness for the cyclical component of unemployment.13 Put di⁄erently, increases in unemployment are steeper than decreases. Table 1 presents the skewness coe¢ cients for the (cid:133)rst-di⁄erences of monthly unemployment and industrial production.14 Unemployment presents strong evidence of asymmetry in steepness but this is not the case of industrial production. This suggests that an asymmetric mechanism such as job separation is driving the response of unemployment to shocks. Further, we can see in Table 1 that the asymmetric behavior of unemployment is much weaker over 1985-2007. Again, before assuming a constant separation rate and thus no asymmetry in unemployment, it is important to understand the reasons behind this phenomenon. 3 Unemployment transition probabilities and the MP model The evidence presented in the previous section underscores the importance of understanding bothunemployment(cid:135)ows; theout(cid:135)owsaswellasthein(cid:135)ows. TheMortensen-Pissarides(1994) search and matching model with endogenous separation explicitly model both (cid:135)ows and is therefore a natural candidate to study the determinants of unemployment. In this section, I study the empirical performances of the MP model with respect to unemployment and its (cid:135)ows. 13See, among others, Neftci (1984), Delong and Summers (1984), Sichel (1993) and McKay and Reis (2008) for evidence of asymmetry at quarterly frequencies. 14Following Sichel (1993), I report Newey-West standard errors that are consistent with the presence of heteroskedasticity and serial correlation up to order 8. The results do not change when allowing for higher orders. 7

3.1 Three facts about unemployment and its transition probabilities I now highlight three stylized facts about unemployment and its transition probabilities. Table 2 summarizes the detrended US data for unemployment, vacancies, labor market tightness, job (cid:133)nding probability, job separation probability, hours per worker and real GDP over 1951- 2006.15 Fact 1: The Beveridge Curve and the correlations between JF, JS and unemployment A well documented fact about the labor market is the strong negative relationship between unemployment and vacancies, the so-called Beveridge curve. At quarterly frequencies, Table 2 shows that the correlation equals 0:90 over 1951-2006. A point that has attracted less (cid:0) attention is the fact that JF is very highly correlated with unemployment ( 0:95) but that (cid:0) this is less the case for the JS-unemployment correlation (0:61). Finally, the JF-JS correlation is negative and equals 0:48. (cid:0) Fact 2: The employment exit probability is half as volatile as the job (cid:133)nding probability and is three times more volatile than output AsShimer(2007)(cid:133)rstemphasizedandasTable2shows,theemploymentexitprobabilityis about 55% less volatile than the job (cid:133)nding probability. Moreover, JS and JF are respectively three times and six times more volatile than detrended real GDP.16 Fact 3: Movements in the job separation rate are sharp and short-lived while movements in the job (cid:133)nding rate are persistent and mirror the behavior of unemployment. Lookingattheautocorrelationcoe¢ cientsforthe(cid:135)owprobabilityseriesfromShimer(2007) over 1951-2006, Table 2 shows that the employment exit probability is much less persistent 15SeasonallyadjustedunemploymentuisconstructedbytheBLSfromtheCurrentPopulationSurvey(CPS). Theseasonallyadjustedhelp-wantedadvertisingindexvisconstructedbytheConferenceBoard. Labormarket tightness is the vacancy-unemployment ratio. JF and JS are the quarterly job (cid:133)nding probability and employment exit probability series constructed by Shimer (2007). Hours per worker h only covers 1956-2006 and is the sum of the quarterly average of weekly manufacturing overtime of production workers and the average over 1956-2006 of weekly regular manufacturing hours of production workers from the Current Employment Statistics from the BLS, and y is real GDP. All variables are reported in logs as deviations from an HP trend with smoothing parameter (cid:21)=105. 16The latter observation is similar to Shimer(cid:146)s (2005) (cid:133)nding that the job (cid:133)nding rate is roughly six times more volatile than detrended labor productivity. 8

than the job (cid:133)nding probability with respective coe¢ cients equal to 0:65 and 0:91. Fujita and Ramey (2007) document the cross-correlations of the job separation rate, the job (cid:133)nding rate, and unemployment at various leads and lags, and observe that while the job (cid:133)nding rate seems to move contemporaneously with unemployment, the job separation rate leads unemployment. This is apparent in Figure 1 which plots the cross-correlations using Shimer(cid:146)s (2007) data for the job separation probability and the job (cid:133)nding probability. In addition, while correlations with JF are spread symmetrically around zero, correlations with JS display a very strong asymmetry. The unemployment-job separation rate correlation decreases very fast at positive lags of unemployment and is virtually nil after one year. Using real GDP instead of unemployment, similar conclusions emerge. In addition, we can see that the employment exit probability leads GDP while the job separation probability lags GDP.17 Another way to assess the dynamic properties of unemployment and its transition probabilities is to consider the impulse response functions to technology shocks and monetary policy shocks in structural VARs. Following Barnichon (2008), Canova, Michelacci and Lopez-Salido (2008)andFujita(2009), Iuselong-runrestrictionsinaVARwithoutputperhour, unemployment, job(cid:133)ndingprobabilityandemploymentexitprobabilityover1951-2006asinGali(1999) to identify the impact of technology shocks, and I use a VAR with a recursive ordering with unemployment, job (cid:133)nding probability, employment exit probability and the federal funds rate over 1960-2006 to estimate the e⁄ect of monetary policy shocks.18 Figure 2 plots the impulse response functions to a positive technology shock and a monetary shock. In both cases, the employmentexitprobabilityismuchlesspersistentthanthejob(cid:133)ndingprobability. Moreover, the job (cid:133)nding probability response mirrors that of unemployment while the employment exit probability response leads the response of unemployment and reverts to its long-run value a year before the other variables. 17Similarly,administrativedataonNewClaimsfortheFederal-StateUnemploymentInsuranceProgram (see e.g. Davis, 2008) are routinely used by forecasters as a leading indicator of the business cycle. 18For the two VARs, I use the same dataset as the one reported to construct Table 2. Labor productivity x is taken from the U.S. Bureau of Labor Statistics (BLS) over 1951:Q1 to 2006:Q4 and is measured as real t average output per hour in the non-farm business sector. Following Fernald (2007), I allow for two breaks in (cid:1)ln x , 1973:Q1 and 1997:Q1, and I (cid:133)lter unemployment, JF and JS with a quadratic trend. t 9

3.2 Confronting the MP models with the Facts In this section, I examine whether the MP model can account for the stylized facts. A number of variants of the MP model have been developed since the seminal work of Mortensen and Pissarides (1994). This section focuses on the standard MP model but in Section 6, I review the di⁄erent variants and study how they fare relative to the standard MP model. Toillustratemystatements, Ilog-linearizeandsimulateacalibratedversionofaMPmodel with AR(1) productivity shocks. The model and its calibration are standard, and I leave the details for the Appendix.19 Figure 3 plots the impulse responses of labor market variables to a negative productivity shock, and Table 3 presents summary statistics for simulated data. Fact 1 and2 aredi¢ culttoreproduce, apointforcefullymadebyRamey(2008)andElsby and Michaels (2008). After calibrating the MP model with plausible idiosyncratic productivity shocksandparametervalues, theseauthors(cid:133)ndthatthemodelgeneratesapositivecorrelation between unemployment and vacancies and too much (cid:135)uctuation in JS relative to JF. Indeed, Figure 3 shows a simultaneous increase in unemployment and vacancy posting. This positive correlation emerges because a (large) burst of layo⁄s generates higher unemployment which makes workers easier to (cid:133)nd and stimulates the posting of vacancies. Table 3 con(cid:133)rms this result and shows that the unemployment-vacancy correlation is positive at 0:96. Figure 3 also shows the much stronger response of the job separation rate relative to that of the job (cid:133)nding rate, and looking at Table 3, the standard deviation of JF is only 0:013 while the standard deviation of JS is much higher at 0:096. Turning to Fact 3, MP models generate counterfactually similar dynamic properties for the job (cid:133)nding rate and the job separation rate in response to AR(1) productivity shocks. As Figure 3 shows, the response of the productivity threshold a~ below which (cid:133)rm and worker t decide to separate mirrors the response of the aggregate productivity shock A , and JS inherits t the persistence of the aggregate shock. Further, the job (cid:133)nding probability depends directly on the vacancy-unemployment ratio via the matching function. As a result, the large and 19I thank Carlos Thomas for providing his Matlab code used in Thomas (2006). 10

persistent increase in job separation leads to a persistent decrease in labor market tightness, and hence to a persistent fall in JF. Thus, JF and JS display very similar impulse responses and share the same autocorrelation coe¢ cient (Table 3). However, Figure 2 shows that in the data, the job separation rate returns faster to its long run level than the job (cid:133)nding rate, and Table 2 shows that JS is a lot less persistent than JF. 4 A search and matching model with endogenous separation Inthissection,Ipresentasearchandmatchingmodelinwhichendogenousseparationisdriven by demand constraints. 4.1 The model I develop a partial equilibrium model in which (cid:133)rms are demand constrained. Since my goal is to evaluate the model along the labor market dimension, I follow a reduced-form approach that allows for more tractability and facilitates computation.20 This search model is similar to Krause and Lubik (2007) in that it assumes large demandconstrained (cid:133)rms with many workers. However, unlike Krause and Lubik (2007), there are no match-speci(cid:133)c productivity shocks, and job separation does not depend on the productivity of each match. Instead, when faced with lower than expected demand, (cid:133)rms can choose to layo⁄ extra workers to save on labor costs. Firms and the labor market Iconsideraneconomypopulatedbyacontinuumofhouseholdsofmeasureoneandacontinuum of (cid:133)rms of measure one. At each point in time, (cid:133)rm i needs to satisfy demand for its product 20Thanks to the reduced-form approach, the model has only two state variables and is easier to solve numerically. In the Appendix, I show that this partial-equilibrium model is a reduced-form version of a general equilibrium model with monopolistically competitive (cid:133)rms and nominal rigidities. 11

yd and hires N workers to produce a quantity it it ys = N h(cid:11) (1) it it it where I normalize the aggregate technology index to one, and h is the number of hours it supplied by each worker and 0 < (cid:11) 1.21 (cid:20) In a search and matching model of the labor market, workers must be hired from the unemployment pool through a costly and time-consuming job creation process. Firms post vacancies at a unitary cost c (in units of utility of consumption), and unemployed workers search for jobs. Vacancies are matched to searching workers at a rate that depends on the number of searchers on each side of the market. I assume that the matching function takes the usual Cobb-Douglas form so that the (cid:135)ow m of successful matches within period t is t given by m t = m 0 u (cid:17) t v t 1 (cid:0) (cid:17) where m 0 is a positive constant, (cid:17) (0;1), u t denotes the number of 2 1 unemployed and v = v di the total number of vacancies posted by all (cid:133)rms. Accordingly, t 0 it the probability of a vRacancy being (cid:133)lled in the next period is q((cid:18) ) m(u ;v )=v = m (cid:18) (cid:17) t t t t 0 (cid:0) (cid:17) where (cid:18) vt is the labor market tightness. Similarly, the probability for an unemployed t (cid:17) ut worker to (cid:133)nd a job is JF t = (u t ;v t )=u t = m 0 (cid:18) t 1 (cid:0) (cid:17) . Because of hiring frictions, a match formed at t will only start producing at t+1. Matches are terminated at an exogenous rate (cid:26)(cid:22) but the (cid:133)rm can also choose to destroy an additional fraction (cid:26) of its jobs, so that the job separation it rate JS = (cid:26)(cid:22)+(cid:26) . t it The timing of the model is similar to that of Krause and Lubik (2007). Denote n the (cid:0)it employment of (cid:133)rm i at the beginning of period t. Once the uncertainty is resolved, (cid:133)rms can decide whether to lay-o⁄a fraction (cid:26) of its employment n in order to begin production with it (cid:0)it n+ = (1 (cid:26) )n workersandpaythecorrespondingwagebill. Attheendoftheperiod,q((cid:18) )v it (cid:0) it (cid:0)it t it matches are created but an additional fraction (cid:26)(cid:22) of (cid:133)rm(cid:146)s beginning of period employment n (cid:0)it 21Themodeldoesnotexplicitlyconsidercapitalfortractabilityreasonsbut(1)canberationalizedbyassuming aconstantcapital-workerratio K Ni i t t andastandardCobb-Douglasproductionfunctiony it =A t (N it h it )(cid:11)K i 1 t(cid:0) (cid:11). Assuming instead decreasing returns in employment does not change the conclusions of the paper. Similarly, assuming (cid:11)=1 does not change any of the results. 12

is destroyed.22 The (cid:133)rm enters next period with n = (1 (cid:26)(cid:22) (cid:26) )n +q((cid:18) )v workers. (cid:0)it+1 (cid:0) (cid:0) it (cid:0)it t it From now on, I will only consider the beginning of period employment n = n , so that it (cid:0)it for a (cid:133)rm i posting v vacancies at date t, its the law of motion for employment is given by it n = (1 (cid:26)(cid:22) (cid:26) )n +q((cid:18) )v it+1 it it t it (cid:0) (cid:0) and its production function takes the form ys = (1 (cid:26) )n h(cid:11): it it it it (cid:0) Households I follow Merz (1995) and Andolfatto (1996) in assuming that households form an extended family that pools its income. There are 1 n unemployed workers who receive unemployment t (cid:0) bene(cid:133)ts b in units of utility of consumption, and n employed workers who receive the wage t payment w from (cid:133)rm i for providing hours h . Consequently, the value of unemployment U it it t in terms of current consumption is b U = +(cid:12)E [JF W +(1 JF )U ] t t t+1 t+1 t+1 t+1 (cid:21) (cid:0) t and the value W from employment for a worker working for (cid:133)rm i in terms of current conit sumption is (cid:21) W = w h h1+(cid:27)h +(cid:12)E [(1 JS )W +JS U ] it it (cid:0) (cid:21) (1+(cid:27) ) it t (cid:0) t+1 it+1 t+1 t+1 t h where (cid:21) and (cid:27) are positive constants and (cid:21) = 1 the marginal utility of consumption with h h t Ct " C = 1 C " (cid:0)" 1 di " (cid:0) 1 ;" > 1. t 0 it (cid:18) (cid:19) R 22Labor market tightness is given by (cid:18) t = 1 (cid:0) 0 1 R( 0 1 1 (cid:0) v (cid:26) it i d t) i n(cid:0)it di . R 13

Wage bill setting The (cid:133)rms and workers bargain individually about the real wage. To keep the model simple, I assume that the (cid:133)rm owns all the bargaining power and pays a wage equal to the worker(cid:146)s reservation wage w .23 That way, I can show:24 it fl b h1+(cid:27)h w = +(cid:21) it : (2) it h (cid:21) (cid:21) (1+(cid:27) ) t t h The (cid:133)rm(cid:146)s problem Firm i will choose a sequence of vacancies v and job separation (cid:26) to minimize its it it f g f g expected present discounted cost of satisfying demand for its product yd subject to the law it of motion for employment. Formally, the (cid:133)rm minimizes (cid:8) (cid:9) u(C ) c min E (cid:12)j 0 t+j 1 (cid:26) n w + v vit;(cid:26) it t j u 0 (C t ) (cid:20) (cid:0) it+j i;t+j i;t+j (cid:21) t+j i;t+j (cid:21) X (cid:0) (cid:1) subject to the demand constraint yd = (1 (cid:26) )n h(cid:11) it it it it (cid:0) the law of motion for employment n = (1 (cid:26)(cid:22) (cid:26) )n +q((cid:18) )v it+1 it it t it (cid:0) (cid:0) and the bargained wage b h1+(cid:27)h w = +(cid:21) it : it h (cid:21) (cid:21) (1+(cid:27) ) t t h 23Extendingthemodelbygivingsomebargainingpowertotheworkerdoesnotchangeanyoftheresults. Ifthe (cid:133)rm(cid:146)sbargainingpowerisinstead(cid:13) <1,theequilibriumwageisgivenbyw =(1 (cid:13)) (cid:21) h i 1 t +(cid:27)h(cid:0) (cid:11) + ct(cid:18) + it (cid:0) h (cid:21)t (cid:21)t t (cid:18) (cid:19) (cid:13) bt + (cid:21)h h1+(cid:27)h and the rest of the analysis goes through. (cid:21)t (cid:21)t(1+(cid:27)h) it (cid:16)24The derivation is re(cid:17)latively standard and is available upon request. 14

Closing the model The law of motion for aggregate demand is lnY = (cid:26) lnY +" y with " y N(0;(cid:27)y) t y t 1 t t (cid:0) (cid:24) and since (cid:133)rms are identical, in equilibrium, y = Y i. Averaging (cid:133)rms(cid:146)employment, total it t 8 employment evolves according to n = (1 (cid:26) (cid:26) )n +v q((cid:18) ), and the labor force being t+1 t+1 t t t (cid:0) (cid:0) normalized to one, the number of unemployed workers is u = 1 n Finally, as in Krause t t. (cid:0) and Lubik (2007), vacancy posting costs are distributed to the aggregate households so that C = Y in equilibrium. t t 4.2 Dynamics of the model I now present the (cid:133)rst-order conditions for vacancy posting and job separation and discuss somepropertiesofthemodel. Ishowthat, withaggregatedemandconstraints, endogenousjob separation is zero in steady-state, so that (cid:133)rms cannot reduce (cid:133)ring but must post vacancies to increase employment. Because hiring is costly and time consuming, a trade-o⁄ emerges between the intensive and the extensive margin. Consequently, (cid:133)rms hoard labor and only (cid:133)re workers when demand falls below a certain threshold. An increase in output volatility raises the contribution of unemployment in(cid:135)ows since (cid:133)rms are more likely to face large negative shocks and resort to the job separation margin. The vacancy posting condition The optimal vacancy posting condition takes the form c c t t+1 = E (cid:12) (1 (cid:26) )(cid:31) + (1 (cid:26)(cid:22) (cid:26) ) (3) q((cid:18) ) t t+1 (cid:0) it+1 it+1 q((cid:18) ) (cid:0) (cid:0) it+1 t t+1 (cid:20) (cid:21) 15

with (cid:31) , the shadow value of a marginal worker, given by it @n w 1 @w it it it (cid:31) = = w (h )+ h it (cid:0) @n (cid:0) it it (cid:11) it @h it it Since 1 is the expected duration of a vacancy, equation (3) has the usual interpretation: q((cid:18)t) each (cid:133)rm posts vacancies until the expected cost of hiring a worker ct equals the expected q((cid:18)t) discounted future bene(cid:133)ts (cid:31) it+j 1 j=1 from an extra worker. Because the (cid:133)rm is demand constrained, the (cid:135)ow value(cid:8)of a m(cid:9)arginal worker is not his contribution to revenue but his reduction of the (cid:133)rm(cid:146)s wage bill. The (cid:133)rst term of (cid:31) is the wage payment going to an extra it worker, while the second term represents the savings due to the decrease in hours and e⁄ort achieved with that extra worker. Indeed, looking at the wage equation (2), we can see that the (cid:133)rm can reduce hours per worker and lower the wage bill by increasing its number of workers. With (cid:31) > 0, the marginal worker reduces the cost of satisfying a given level of demand. it Similarly to Woodford(cid:146)s (2004) New-Keynesian model with endogenous capital, the marginal contribution of an additional worker is to reduce the wage bill through substitution of one input for another. Here, the intensive and the extensive margins are two di⁄erent inputs. The former is (cid:135)exible but costly, while the latter takes time and resources to adjust. The (cid:133)rm chooses the combination of labor margins that minimizes the cost of supplying the required amount of output. Using the wage equation (2), I can rewrite the marginal worker(cid:146)s value as b 1+(cid:27) h1+(cid:27)h (cid:31) = + h 1 (cid:21) it : (4) it (cid:0)(cid:21) (cid:11) (cid:0) h (cid:21) (1+(cid:27) ) t t h (cid:18) (cid:19) 1 Since h = y i d t (cid:11) and n is a state variable, the (cid:133)rm relies on the intensive margin to it (1 (cid:0) (cid:26) it )nit it (cid:16) (cid:17) satisfydemandintheshort-run,andthelevelofhoursperworkercaptures(cid:147)demandpressures(cid:148) and the (cid:133)rm(cid:146)s incentives to post vacancies. With 1+(cid:27)h > 1, the longer hours are, the larger (cid:11) is the wage bill reduction obtained with an extra worker. As hours increase because of higher demand for the (cid:133)rm(cid:146)s products, the worker(cid:146)s marginal value increases, and the (cid:133)rm posts more 16

vacancies to increase employment. Indeed, 1+(cid:27)h 1 measures the di⁄erence between the two (cid:11) (cid:0) labor inputs (the intensive and the extensive margins) in terms of the cost of providing the required amount of output. The intensive margin displays decreasing returns with (cid:11)<1 and its cost increases at the rate 1+(cid:27) so that the cost of producing a given quantity yd increases h it at the rate 1+(cid:27)h > 1. For the extensive margin, on the other hand, both output and costs (cid:11) increase linearly, so that the rate is one. The larger the di⁄erence between the two rates, the stronger is the incentive for the (cid:133)rm to avoid increases in hours per worker, and the more volatile are vacancy posting and unemployment. The job separation condition For the job separation condition, I get the (cid:133)rst-order condition @(1 (cid:26) )n w c (cid:0) it it it = n E (cid:12) (1 (cid:26) )(cid:31) + t+1 (1 (cid:26)(cid:22) (cid:26) ) @(cid:26) (cid:0) it t t+1 (cid:0) it+1 it+1 q((cid:18) ) (cid:0) (cid:0) it+1 it (cid:20) t+1 (cid:21) that I can rewrite using the vacancy posting condition (3) as c t (cid:31) = : (5) (cid:0) it q((cid:18) ) t Because hiring is costly, the (cid:133)rm hoards labor and does not lay-o⁄ workers with a small negative marginal value. It will only (cid:133)re workers when demand is so low that the marginal valueof(cid:133)ringaworker (cid:31) islargeenoughtoequalthecostofhiringaworker(orequivalently, it (cid:0) the expected bene(cid:133)t of keeping that worker). Furthermore, (5) implies that there cannot be any endogenous separation in steady state, and the (cid:133)rm must post vacancies to increase employment. In steady-state, because of a constant rate of attrition (cid:26)(cid:22), the (cid:133)rm must replenish its stock of workers by constantly posting a minimal number of vacancies. This implies that the (cid:133)rm is satisfying its vacancy posting condition and the steady-state marginal value of a worker is (cid:31) = c (1 (cid:12)(1 (cid:26)(cid:22))): Since (cid:3) (cid:12)q((cid:18)(cid:3)) (cid:0) (cid:0) (cid:31) > 0, the (cid:133)rm does not satisfy its job separation condition and (cid:26) = 0, so that JS = (cid:26)(cid:22). (cid:3) (cid:3) 17

Starting from the steady-state equilibrium, a positive shock does not lead to a burst of (cid:147)un- (cid:133)ring(cid:148)as the (cid:133)rm cannot lower (cid:26) 0 (i.e. keep workers that it would have otherwise (cid:133)red) it (cid:21) and must use the job creation margin. To visualize the mechanisms driving vacancy posting and job separation, Figure 4 plots the relationshipbetweenthemarginalvalueofaworkerandhoursperworker,aproxyfor(cid:147)demand pressure(cid:148). In steady-state, the value of a marginal worker is positive and equals the net cost of hiring. When demand goes up, hours per worker increase and with them the marginal value of a worker, leading the (cid:133)rm to post more vacancies. For small negative shocks such that ct (cid:31) 0, the (cid:133)rm hoards labor and posts fewer vacancies. For large negative shocks, (cid:0)q((cid:18)t) (cid:20) it (cid:20) however, (cid:31) ct , and the (cid:133)rm uses the job separation margin, and one can observe a it (cid:20) (cid:0)q((cid:18)t) burst of layo⁄s.25 Finally, an implication of labor hoarding is that an increase in output volatility raises the contribution of the job separation rate to unemployment (cid:135)uctuations since the (cid:133)rm is more likely to face large negative shocks and resort to the job separation margin. For the same reason, the asymmetric behavior of unemployment will be less pronounced in times of lower output volatility. 5 Confronting the model with the data In this section, I study whether a calibrated version of the model generates realistic impulse response functions, can quantitatively account for the stylized facts about unemployment and its transition probabilities, and can rationalize the small and declining contribution of unemploymentin(cid:135)ows,theincreaseingrosshiringduringrecessionsaswellastheweakerasymmetry in unemployment since 1985. 25Notethatthe(cid:133)rm(cid:146)sbehaviorisconsistentwiththeestablishmentlevelevidencefromDavis,Fabermanand Haltiwanger (2006). 18

5.1 Calibration First, I discuss the calibration of the model; and Table 4 lists the parameter values. An attractive feature of the model is its small number of (standard) parameters. Whenever possible, I use the values typically used in the literature. I assume a monthly frequency, as a monthly calibration is better able to capture the high rate of job (cid:133)nding in the US. I set the monthly discount factor (cid:12) to 0:993 and the returns to hours (cid:11) to 0:65. Turning to the labor market, I set the matching function elasticity to (cid:17) = 0:72 as in Shimer (2005). I set the exogenous component of the separation rate to 0.032, which is the average value of the 5-year rolling lower-bound of Shimer(cid:146)s (2007) employment exit probability series.26 A worker (cid:133)nds a job with probability (cid:18)q((cid:18)) = 0:3 so that equilibrium unemployment equals 10 percent.27 The scale parameterofthematchingfunctionsm ischosensuchthat,asindenHaanandKaltenbrunner 0 (2009), a (cid:133)rm (cid:133)lls a vacancy with a probability q((cid:18)) = 0:34. Shimer (2005) sets the income replacementratioto40percent,sothatwithalaborincomeshareof65percent,theunemployment bene(cid:133)ts-output ratio b = 0:28. The steady-state ratio of vacancy-posting costs to GDP is set to 1% following most of the literature.28 As in Trigari (2009) and Christo⁄el, Kuester and Linzert (2006), I choose (cid:27) = 10, i.e. an hours per worker elasticity of 0:1. Finally, I h set the standard deviation of output (cid:27)y = 0:0014 and the (cid:133)rst-order coe¢ cient (cid:26) = 0:93 in y order to match the persistence and volatility of HP-detrended real GDP, converted to monthly frequency. I numerically solve the model using policy function iterations with intergrid cubic spline interpolation on a grid with (30;30) points for (n ; y ). Employment n is discretized t t t over [0:8;1], and I follow Tauchen (1986) to construct the transition matrix for y . In the t Appendix, I describe the numerical algorithm used to solve the (cid:133)rm(cid:146)s problem 26Recall that endogenous separation cannot be negative in the model, so that the empirical counterpart of the exogenous job separation rate (cid:26)(cid:22) is the lower bound of JS. Since JS displays low-frequency movements (see e.g. Davis, 2008) that I abstract from in this paper, I estimate (cid:26)(cid:22) as the mean of the 5-year rolling lower-bound of JS. The results of the paper do not rely on this particular estimate of (cid:26)(cid:22). 27Thisvalueimpliesasteady-stateunemploymentequalto10percent,whichisreasonableif,asinMerz(1995), Andolfatto (1996), den Haan, Ramey, and Watson (2000) and others, model unemployment also includes those individuals registered as inactive that are actively searching. 28See e.g. Andolfatto (1996), Blanchard and Gali (2006) and Gertler and Trigari (2009). 19

5.2 Impulse response functions Figure 5 and 6 show the simulated impulse response functions of unemployment, hours per worker, the job (cid:133)nding rate, and the job separation rate after respectively a positive and a negative one standard-deviation aggregate demand shock. The asymmetric nature of the labor market is clearly apparent. Following a positive aggregate demand shock, unemployment declines progressively while hours per worker react on impact. After two quarters, hours per worker are back to their long-run value while unemployment starts its mean reversion. After a negative shock, however, unemployment responds on impact because of a burst of layo⁄s. Thanks to the strong response of the job separation rate, (cid:133)rms rely less on their intensive marginandmakeasmalleradjustmenttotheirnumberofpostedvacancies. Notethatvacancy posting decreases but does not drop to zero, so that the (cid:133)rms are simultaneously (cid:133)ring and posting vacancy.29 This is due to the AR(1) structure of the shocks hitting the economy. Since hiring takes one period and since shocks are mean-reverting, the (cid:133)rm anticipates the need for future higher employment and post vacancies (albeit less so than in normal times) to satisfy the expected increase in demand next period.30 Becauseitiscostlesstoadjustthenumberofworkersthroughtheseparationmargin,layo⁄s show no persistence: (cid:133)rms (cid:133)re as many workers as necessary, and endogenous job separation reverts quickly to zero. The job (cid:133)nding rate, on the other hand, is persistent and mirrors the behavior of unemployment after two quarters. Unlike a standard MP model (see Figure 3) or Krause and Lubik (2007), an increase in job separation does not lead to an increase in vacancy postings, and unemployment and vacancy 29Interestingly, this behavior is consistent with establishment level evidence as Davis, Faberman and Haltiwanger (2008) show that (cid:133)rms with decreasing levels of employment continue to display a positive amount of vacancy posting and hiring. 30I can prove this result by contradiction. If vacancy posting dropped to zero after a large adverse demand shock, labor market tightness would drop to zero, and hiring cost would be null. The (cid:133)rm would then layo⁄ enough workers to satisfy (5), i.e. (cid:31) = 0: In fact, with no hiring frictions, the (cid:133)rm has no reason to hoard t labor, the problem becomes static and the (cid:133)rm (cid:133)res as many workers as necessary to satisfy its current period optimal allocation between hours per worker and number of workers. However, with a mean-reverting shock and the additional exogenous job separation occurring between periods, the (cid:133)rm expects higher demand next period, will need more workers and therefore posts vacancies (at no cost since (cid:18) = 0). This contradicts my initial assumption, so that labor market tightness cannot be zero. 20

are negatively correlated. The intuition for these results is as follows. Looking at Figure 4, (cid:133)rms use the job separation margin when the marginal value of a worker falls below ct . (cid:0)q((cid:18)t) However,afterthisburstoflayo⁄s,themarginalvalueofaworkerliesattheboundarybetween thelaborhoardingregionandthelay-o⁄regionsince(cid:31) = ct . Thisimpliesthatifaggregate t (cid:0)q((cid:18)t) demand is persistent, the worker(cid:146)s marginal value in the next period will not be far o⁄ the labor hoarding-layo⁄threshold, and there will not be another large burst of layo⁄s. Further, since the labor hoarding-layo⁄boundary is located in a region in which (cid:133)rms lower the number of posted vacancies, the (cid:133)rm is unlikely to post more vacancies as it lays o⁄workers.31 Finally, Figure 7 shows that the model is consistent with the fact that gross hiring tends to increase during recessions as well as with Fujita(cid:146)s (2009) empirical impulse response for gross hires. A burst of layo⁄s decreases labor market tightness and lowers hiring costs as the expected cost of (cid:133)lling a vacancy declines. This leads the (cid:133)rm to pro(cid:133)t from an exceptionally low labor market tightness to increase new hires: the job (cid:133)nding rate goes down but less than unemployment, and hiring increases. An interesting implication of the model is that this phenomenon becomes stronger with the size of the shock. As Figure 7 illustrates, the larger the adverse demand shock, the more the (cid:133)rm resorts to the job separation margin, the more labor market tightness decreases and the stronger is the (cid:133)rm(cid:146)s incentive to pro(cid:133)t from lower hiring costs by increasing gross hires. 5.3 Simulation Using a calibrated version of the model, I simulate 600 months (i.e. 50 years) of data, and I repeat this exercise 500 times. I (cid:133)rst evaluate the model by considering the moments of simulateddatatotestwhetherthemodelisconsistentwiththethreefactsaboutunemployment and its transition probabilities. Then I study whether the model can account for the small and declining contribution of unemployment in(cid:135)ows, as well as the fact that unemployment displays no steepness asymmetry since 1985. 31However, this is not necessarily the case if the shock is not persistent. In that case, (cid:31) is more likely to f itg shift quickly from negative values (with (cid:133)ring) to positive values (with more vacancies). 21

Table 5 presents the summary statistics for quarterly averages of the monthly series. A general conclusion is that given the model simplicity and its small number of parameters, the model is remarkably successful at explaining the behavior of labor market variables: the moments all have the correct sign and are close to their empirical values.32 First, the model has no problem generating Fact 1, i.e. a Beveridge curve and a negative job (cid:133)nding rate-job separation rate correlation. The model can also explain the strong unemployment-vacancies correlation ( 0:81 versus 0:90 in the data) as well as the weaker JF-JS correlation ( 0:59 (cid:0) (cid:0) (cid:0) versus 0:48 in the data). Similarly, and consistent with the data, the model generates a high (cid:0) job (cid:133)nding rate-unemployment correlation ( 0:91 versus 0:95 in the data) and a smaller job (cid:0) (cid:0) separation rate-unemployment correlation (0:47 versus 0:61 in the data). These results stem fromtheasymmetricnatureofthelabormarketandthefactthat(cid:133)rmscanadjustemployment withthejobcreationmarginatalltimesbutcanonlyusethejobseparationmarginfornegative demand shocks. For positive demand shocks, the job separation rate does not move and the correlationwithunemploymentorthejob(cid:133)ndingrateisnil. Asaresult, theJS-unemployment correlation and the JF-JS correlation are closer to a half than to one. Table 5 also shows that the model is consistent with Fact 2, as the job (cid:133)nding rate is more volatile than the job separation rate. The fact that the model has no problem matching the volatility of the job (cid:133)nding rate is a result of the demand constraints faced by (cid:133)rms. In order to satisfy an expanding demand, (cid:133)rms must increase either their extensive or their intensive margin. Since the intensive margin is relatively costly because of the high disutility cost of longer hours, most of the adjustment occurs through employment.33 Thus, the model does not su⁄er from a Shimer (2005) type puzzle as it generates enough (cid:135)uctuations in unemployment given plausible movements in output. Nonetheless, JF is slightly too volatile, a problem with 32It is important to note that I am only focusing on labor market variables. As long as aggregate demand constraintspersistlongenoughsothatmymodelisacorrectdescriptionof(cid:133)rms(cid:146)labordemandintheshort-run, I can judge of the model(cid:146)s success by considering the unconditional moments of labor market variables. 33From the log-linearized production function y^=(cid:11)h^ 1 uu^ , unemployment will be roughly 10 times more (cid:0) (cid:0)u volatilethanoutput(withanunemploymentratearound10percent)ifh^issmall. Notealsothatthismechanism is consistent with the data as the volatility in hours per worker generated by the model matches that found in the data. 22

search models of unemployment already pointed out by Fujita and Ramey (2004). This is due to the excessively rapid response of vacancies; and incorporating sunk costs for vacancy creation as in Fujita and Ramey (2004) would presumably correct this shortcoming. Finally, the job separation rate(cid:146)s volatility is close to its empirical value. Unlike standard MP models, the separation margin is only used for large negative shocks as (cid:133)rms hoard labor and only use the job separation margin for large negative shocks. Turning to Fact 3 and the dynamic properties of JF and JS, Figure 8 shows that the model is very successful at reproducing the cross-correlograms of JF, JS and unemployment. JS is notpersistentenoughasmostoftheadjustmentalongthejobseparationmargintakesplacein one period, but assuming convex costs in (cid:133)ring would probably correct this shortcoming. JF is slightly less persistent than in the data, and this is again due to excessively rapid response of vacancies. Finally, the low persistence of model JF and JS explains the low persistence of modelhoursperworkerastheintensivemarginadjuststomovementsinemploymenttoensure that the (cid:133)rm satis(cid:133)es demand at all times. Finally, in Table 6, I follow Shimer (2007), Elsby, Michaels and Solon (2008) and Fujita and Ramey (2008) and measure the contribution of JF and JS. I (cid:133)nd that the contribution of JS amounts to 22%, only slightly lower than the contribution measured by Shimer (2007). 5.4 The weaker contribution of JS since 1985 WesawinSection2thatthecontributionofJStothevarianceofunemploymentdeclinedfrom about 25 percent during the post-war period to only 5 percent over the last 20 years (Shimer, 2007). Moreover, the steepness asymmetry in unemployment disappeared after 1985. The model implies that these two (cid:133)ndings are by-products of the Great Moderation, the period of low macroeconomic volatility enjoyed by the US (and other developed countries) over 1985-2007. One insight from section 4 was that a decrease in output volatility lowers the contribution of JS and the asymmetry in unemployment as (cid:133)rms are less likely to face large negative shocks and resort to the job separation margin. Figure 6 shows this e⁄ect 23

quantitatively. As the size of the shock doubles from one half to one standard-deviation of detrended GDP, the response of JS on impact more than doubles, and unemployment shows a stronger initial response. The hours per worker response, on the other hand, does not increase with the size of the shock. To evaluate whether the decline in macroeconomic volatility can explain the weaker contribution of JS, I estimate the contribution of JS and JF on simulated data with an output volatility of (cid:27)y , consistent with the drop in volatility experienced by the US during the Great 2 Moderation. As Table 6 shows, the contribution of JS decreases to 14%, suggesting that the Great Moderation is responsible for some of the decline in the contribution of JS.34 Finally, looking at Table 6, the skewness of model unemployment also declines sharply when the volatility of output decreases, suggesting that the Great Moderation is responsible forsomeofthedeclineintheasymmetryofunemployment. Withanoutputvolatilityof(cid:27)y,the skewness of model unemployment is 0:53, close to its empirical counterpart of 0:62. But with a standard-deviation of output is (cid:27)y , model unemployment shows no evidence of asymmetry, 2 just as in the data. 6 Related literature In Section 2, I mainly focused on the canonical Mortensen-Pissarides (1994) search and matching model. However, a number of variants of the MP framework have been used to model unemployment. In this section, I review the literature on the di⁄erent variants and their empirical performances. First, while the original MP model assumes persistent idiosyncratic productivity shocks, thecomputationalcostassociatedwithkeepingtrackofthejobs(cid:146)productivitydistributionlead many researchers to assume instead i.i.d. idiosyncratic productivity shocks. Indeed, only a 34I do not claim that this is the only explanation. The increased availability of (cid:135)exible labor service such as part-timeworkandtemporaryworkortheswitchfrom manufacturingtoservicesareprobablyalsoresponsible for the decline in the contribution of the job separation rate. See, for example, Schreft, Sing and Hodgson (2005). 24

few papers solved the original MP model with endogenous separation (Mortensen-Pissarides (1994), Ramey (2008), Elsby and Michaels (2008), Pissarides (2008)), but a vast literature has solved rich general equilibrium models with search unemployment and i.i.d. idiosyncratic productivity shocks: Den Haan, Ramey and Watson (2000), Costain and Reiter (2005), Walsh (2005), Thomas (2006), Krause and Lubik (2007), Cooper, Haltiwanger and Willis (2008), Thomas and Zanetti (2008), Trigari (2009) among others. Second, variantsoftheMPmodelcanbeclassi(cid:133)edintwocategories, dependingonwhether (cid:133)rms are atomistic with only one worker or large with many workers. In their seminal paper, Mortensen and Pissarides (1994) assume the existence of a (cid:133)nite mass of workers and of an in(cid:133)nite mass of atomistic (cid:133)rms. Each non-matched (cid:133)rm can post a vacancy to form a match with one worker only. Another line of research departs from the assumption of free entry and atomistic (cid:133)rms to model instead a (cid:133)nite number of large (cid:133)rms with a continuum of jobs.35 This approach has the advantage of allowing for a more realistic representation of the (cid:133)rm as well as providing a framework to study the interaction of labor market frictions with other frictions such as nominal rigidities. While the majority of papers pursued the (cid:133)rst approach, Krause and Lubik (2007) provide a tractable example of the second approach in which the (cid:133)rms(cid:146)production function displays constant returns to employment. While aggregation is more di¢ cult with decreasing returns to employment, Elsby and Michaels (2008) present an analytically tractable model while Cooper, Haltiwanger and Willis (2008) solve and estimate a similar model with numerical methods. Krause and Lubik (2007), for MP models with large (cid:133)rms, and Costain and Reiter (2005), Thomas (2006), Ramey (2008) and Elsby and Michaels (2008), for MP models with atomistic (cid:133)rms, make the case that Fact 1 is di¢ cult to reproduce. Standard MP models are unable to replicate the Beveridge curve because a burst of layo⁄s generates higher unemployment which makes workers easier to (cid:133)nd, stimulating the posting of vacancies. Krause and Lubik (2007) show that introducing real wage rigidity allows the model to generate a Beveridge 35In this setup, entry of new (cid:133)rms is forbidden as otherwise, the model would collapse to the original MP model with atomistic (cid:133)rms and one (cid:133)rm-one worker matches. 25

curve. However, the model cannot reproduce Fact 2 as (cid:147)(cid:133)rms adjust almost exclusively via the separation rate and job creation does not play a quantitatively signi(cid:133)cant role(cid:148)(Krause and Lubik, 2007, p724). Ramey (2008) shows that a search model with on the job search can generate a Beveridge curve. However, that model cannot reproduce Fact 2 as it generates too much volatility in the job destruction rate compared to the job (cid:133)nding rate (Ramey, 2007, Figure 1). Thomas (2006) shows how (cid:133)ring costs help the MP model in generating a Beveridge curve. However, his model cannot generate Fact 3 as the impulse response of JF counterfactually mirrors that of JS. While fewer papers other than Ramey (2008) and Elsby and Michaels (2008) focused on Fact 2, Krause and Lubik (2007) show that in MP models with large (cid:133)rms, the job separation rate moves too much compared to the job (cid:133)nding rate. This is not the case in MP models with instantaneous hiring and (cid:133)ring costs (Thomas and Zanetti, 2008) and in MP models with an intensive labor margin (Trigari, 2009). However, both of these models cannot generate Fact 3: the impulse response of JF counterfactually mirrors that of JS, displays no persistence and overshoots its long-run value. Finally, a very promising line of research is the work from Cooper, Haltiwanger and Willis (2008) and Elsby and Michaels (2008). By considering large (cid:133)rms with decreasing returns to employment and idiosyncratic productivity shocks, they show that such generalized MP models can generate a Beveridge curve. Elsby and Michaels (2008) show that their model can generateelasticitiesofJSandJFwithrespecttoproductivitythatareconsistentwiththedata. However, it is di¢ cult to confront these models with the last two stylized Facts as Cooper et al (2008) do not focus on unemployment (cid:135)ows and Elsby and Michaels(cid:146)(2008) model has only two aggregate productivity states. 7 Conclusion This paper presents a search model with a demand-driven job separation mechanism that can accountforboththeout(cid:135)owsandthein(cid:135)owsofunemployment. Despitearelativelysmallnum- 26

ber of parameters, the model is successful at explaining the behavior of labor market variables and is consistent with a low, but non-trivial, contribution of JS to unemployment (cid:135)uctuations. On the other hand, the benchmark framework, the Mortensen-Pissarides search and matching model with endogenous separation, has di¢ culties explaining the low contribution of JS as well as other stylized facts. In addition, my model attributes the decrease in the contribution of JS since 1985 to the Great Moderation, the dramatic drop in macroeconomic volatility enjoyed by the US economy from the mid 80s until 2007. It also implies that the lower contribution of JS was a temporary phenomenon and that the importance of JS would increase in times of higher macroeconomic volatility such as the in current (since December 2007) recession.36 While a demand-driven job separation mechanism shows promises towards an equilibrium model of unemployment with endogenous out(cid:135)ows and in(cid:135)ows, an important extension of this model would be to incorporate idiosyncratic (productivity or demand) shocks to allow for (cid:133)rm heterogeneity. Moreover, embedding the model in a general equilibrium framework wouldallowmetostudytheimplicationsoflabormarketasymmetriesonoutputandin(cid:135)ation. Because increasing employment is more costly than lowering employment, (cid:133)rms tend to adjust pricesratherthanquantitiesafterpositivemonetaryshocksbutdotheoppositeaftermonetary contractions. Asaresult, monetarypolicywouldhaveastrongerabilitytolower, thantoraise, output. I leave these topics for future research. 36In Barnichon (2009), I provide some evidence supporting this possibility. 27

Appendix: A.1 A Mortensen-Pissarides (1994) model with i.i.d. idiosyncratic productivity shocks I follow Thomas (2006), and I present an MP model with a (cid:133)nite mass of workers and an in(cid:133)nite mass of atomistic (cid:133)rms. Each non-matched (cid:133)rm can post a vacancy to form a match with one worker only. Workers are hired from the unemployment pool through a costly and time-consumingjobcreationprocess. Firmspostvacanciesataunitarycostc,andunemployed workers search for jobs. Vacancies are matched to searching workers at a rate that depends on the number of searchers on each side of the market. The matching function takes the usual Cobb-Douglas form so that the (cid:135)ow m of successful matches within period t is given by t (cid:17) 1 (cid:17) m t = m 0 u t v t(cid:0) : Accordingly, the probability of a vacancy being (cid:133)lled in the next period is q((cid:18) ) m(u ;v )=v = m (cid:18) (cid:17) where (cid:18) vt, and the probability for an unemployed worker to t (cid:17) t t t 0 (cid:0) t (cid:17) ut 1 (cid:17) (cid:133)nd a job is p((cid:18) t ) = (u t ;v t )=u t = m 0 (cid:18) t(cid:0) . In this economy, jobs are subject to idiosyncratic productivity shocks drawn from a distribution with the log-normal cdf F(a), and there exists a threshold productivity a~ such that t all jobs with productivity below it yield a negative surplus are destroyed. Therefore, total separation rate is JS = (cid:26)(cid:22)+(1 (cid:26)(cid:22))F(a~ ) with (cid:26)(cid:22) the exogenous separation rate, and the law of t t (cid:0) motion for employment is n = (1 JS )n +m(u ;v ). t t t 1 t 1 t 1 (cid:0) (cid:0) (cid:0) (cid:0) New jobs have maximum productivity aN. The value of continuing a match with idiosyncratic productivity a and aggregate productivity A is given by t t 1 J (a ) = A a w (a )+E (cid:12)(1 (cid:26)(cid:22)) J (a)dF(a): t t t t t t t t+1 (cid:0) (cid:0) Z a~t+1 The assumption of free entry and exits of (cid:133)rms ensures that the value of posting a vacancy is zero so that V = 0 = c+q((cid:18) )E (cid:12)J (aN): t t t t+1 (cid:0) 28

The value that a worker enjoys from holding a job with productivity a is given by t 1 W (a ) = w (a )+E (cid:12) (1 (cid:26)(cid:22)) J (a)dF(a)+(cid:26) U t t t t t 2 t+1 t+1 t+13 (cid:0) Z 6 a~t+1 7 4 5 and the value of being unemployed is U = b+E (cid:12) p((cid:18) )WN +(1 p((cid:18) ))U : t t t t+1 t t+1 (cid:0) (cid:2) (cid:3) In each period, (cid:133)rm and worker Nash bargain over the real wage and we have w (a ) = (cid:13)A a + t t t t c(cid:18) +(1 (cid:13))b: t (cid:0) The familiar job destruction condition is then given by J (a~ ) = 0 or t t (cid:13) 1 A a~ b c(cid:18) +E (cid:12)(1 (cid:26)) A (a a~ )dF(a) = 0 t t t t t+1 t+1 (cid:0) (cid:0) 1 (cid:13) (cid:0) (cid:0) (cid:0) Z a~t+1 and the job creation condition takes the form c = (1 (cid:13))E (cid:12) A (aN a~ ) : t t+1 t+1 q((cid:18) ) (cid:0) (cid:0) t (cid:2) (cid:3) I then solve the model by log-linearizing around the steady-state. For the calibration, I use the same parameter values as in this paper(cid:146)s model (see Table 4) whenever possible. For other parameters, I follow Thomas (2006). The aggregate productivity shock A follows an t AR(1) process such that lnA = (cid:26) lnA +" with (cid:26) = 0:95 and the standard-deviation t A t 1 t A (cid:0) (cid:27)A calibrated to match the cyclical volatility of detrended US real output. Idiosyncratic productivity lna has mean (cid:22) = 0 and standard-deviation (cid:27)a = 0:22 as in Ramey (2008) and t a Elsby and Michaels (2008). 29

A.2 A New-Keynesian search model with endogenous separation Households Iconsideraneconomypopulatedbyacontinuumofhouseholdsofmeasureoneandacontinuum of(cid:133)rmsofmeasureone. Withequilibriumunemployment,ex-antehomogenousworkersbecome heterogeneous in the absence of perfect income insurance because each individual(cid:146)s wealth di⁄ersbasedonhisemploymenthistory. Toavoiddistributionalissues,IfollowMerz(1995)and Andolfatto (1996) in assuming that households form an extended family that pools its income andchoosespercapitaconsumptionandassetsholdingtomaximizeitsexpectedlifetimeutility. There are 1 n unemployed workers who receive unemployment bene(cid:133)ts b in units of utility it (cid:0) of consumption, and n employed workers who receive the wage payment w from (cid:133)rm i for it it providing hours h . Denoting g(h ) the individual disutility from working, the representative it it family seeks to maximize E 1 (cid:12)t ln(C )+(cid:21) ln( M t ) (cid:21) h 1 n h1+(cid:27)hdi 0 t m P (cid:0) 1+(cid:27) it it t=0 (cid:20) t h Z0 (cid:21) X subject to the budget constraint 1 1 P C dj +M = n w di+(1 n )bC +(cid:5) +M jt jt t it it t t t t 1 Z0 Z0 (cid:0) (cid:0) 1 with (cid:21) , (cid:21) , (cid:27) > 0, n = n di, M nominal money holdings, (cid:5) total transfers to the m h h t 0 it t t " family and C the compositeRconsumption good index de(cid:133)ned by C = 1 C " (cid:0)" 1 di " (cid:0) 1 where t t 0 it (cid:18) (cid:19) C is the quantity of good i [0;1] consumed in period t and P is the prRice of variety i: " > 1 it it 2 is the elasticity of substitution among consumption goods. The aggregate price level is de(cid:133)ned 1 1 1 " (cid:0) as P = P1 "di . t 0 it(cid:0) 1 Z 0 @ A 30

Firms and the labor market Each di⁄erentiated good is produced by a monopolistically competitive (cid:133)rm using labor as the only input. As in the reduced-form model of the paper, at date t, each (cid:133)rm i produces a quantity ys = (1 (cid:26) )n h(cid:11): it it it it (cid:0) Beingamonopolisticproducer,the(cid:133)rmfacesadownwardslopingdemandcurveyd = (Pit) "Y it Pt (cid:0) t and chooses its price P to maximize its value function given the aggregate price level P it t and aggregate output Y . When changing their price, (cid:133)rms face quadratic adjustment costs t 2 (cid:23) Pi;t (cid:25) Y with (cid:23) a positive constant and (cid:25) the steady-state level of in(cid:135)ation.37 2 Pi;t 1 (cid:0) (cid:3) t (cid:3) (cid:0) (cid:16) (cid:17) The (cid:133)rm(cid:146)s problem Since the wage and the law of motion for employment take the same expression as in the reduced-form model, I can now state the (cid:133)rm(cid:146)s problem. Firm i will choose a sequence of price P , vacancies v and endogenous separation rate (cid:26) to maximize its value it it it f g f g f g u(C ) P c (cid:23) P 2 max E (cid:12)j 0 t+j i;t+j yd 1 (cid:26) n w v i;t+j (cid:25) Y Pit;vit;(cid:26) it t X j u 0 (C t ) " P t+j i;t+j (cid:0) (cid:0) (cid:0) it+j (cid:1) i;t+j i;t+j (cid:0) (cid:21) t+j i;t+j (cid:0) 2 (cid:18) P i;t+j (cid:0) 1 (cid:0) (cid:3) (cid:19) t+j # subject to the demand constraint P yd = (1 (cid:26) )n h(cid:11) = ( i;t ) "Y it (cid:0) it it it P (cid:0) t t the law of motion for employment n = (1 (cid:26)(cid:22) (cid:26) )n +q((cid:18) )v it+1 it it t it (cid:0) (cid:0) 37The more common assumption of Calvo-type price setting introduces ex-post heterogeneity amongst (cid:133)rms. A model with costly price adjustment avoids this complication. 31

and the bargained wage b h1+(cid:27)h w = +(cid:21) it : it h (cid:21) (cid:21) (1+(cid:27) ) t t h The central bank The money supply evolves according to M = ea:t+mt with m = (cid:26) m +"m, (cid:26) [0;1] and t t m t 1 t m (cid:0) 2 "m N(0;(cid:27)m): I interpret "m as an aggregate demand shock. t t (cid:24) Closing the model Averaging (cid:133)rms(cid:146)employment, total employment evolves according to n = (1 (cid:26)(cid:22) (cid:26) )n + t+1 t t (cid:0) (cid:0) v q((cid:18) ): The labor force being normalized to one, the number of unemployed workers is u = t t t 1 n Finally, as in Krause and Lubik (2007), vacancy posting costs are distributed to the t. (cid:0) aggregate households so that C = Y in equilibrium. t t The price setting condition The vacancy posting condition and the job separation condition are identical to the ones I report in the paper, and I do not repeat them here. For the price-setting condition, I get the standard result for models with quadratic price adjustment y y y P P it it t it it+1 (1 ") " s (cid:23) (cid:25) = E (cid:12) (cid:23)y ((cid:25) (cid:25) ) (cid:0) P (cid:0) P it (cid:0) P P (cid:0) (cid:3) t t+1 t+1 t+1 (cid:0) (cid:3) P2 t it it (cid:0) 1 (cid:18) it (cid:0) 1 (cid:19) it with the real marginal cost s given by it @(1 (cid:26) )w n s = (cid:0) it it it it @y it 1 = (cid:21) h1+(cid:27)h (cid:11)Y (cid:11) h it (cid:0) t In order to produce an extra unit of output, the (cid:133)rm needs to increase hours since employment is a state variable. As a result, the wage response to changes in hours is driving the (cid:133)rm(cid:146)s 32

real marginal cost. To get some intuition, I consider very small perturbations around the zeroin(cid:135)ation steady-state. For very small shocks, (cid:26) = 0, so that after log-linearizing the priceit setting condition and imposing symmetry in equilibrium , the average (cid:133)rm(cid:146)s real marginal cost s^ is given by t 1+(cid:27) 1+(cid:27) h h s^ = y^ 1 n^ t t t (cid:11) (cid:0) (cid:11) (cid:0) (cid:18) (cid:19) where n^ = ln nt and y^ = ln Yt . t n t y (cid:3) (cid:3) With 1+(cid:27)h(cid:0) >(cid:1)1, the real m (cid:16) arg (cid:17) inal cost increases with demand but decreases with the (cid:11) employment level. As a result, (cid:133)rms can lower the impact of shocks on their real marginal cost and optimal price by adjusting their extensive margin. In(cid:135)ation will be less responsive to shocks than in a standard New-Keynesian model without unemployment but will display more persistence. Following an increase in demand, the value of a marginal worker goes up and leads the (cid:133)rm to increase its level of employment. But this decreases future real marginal cost and leads the (cid:133)rm to post lower prices, which itself increases demand and output next period. This in turn leads to a future rise in employment, and, as the process goes on, the response to a demand shock will die out more slowly than in the standard New-Keynesian case. The possibility to lay-o⁄ workers creates an asymmetry in the behavior of employment that generates asymmetry in real marginal cost and in in(cid:135)ation. Because it is easier to (cid:133)re than hire workers, (cid:133)rms can more easily smooth (cid:135)uctuations in their real marginal cost after negative shocks than after positive shocks. As a result, a monetary policy shock has a di⁄erent impact depending on its sign. Following a negative monetary policy shock, (cid:133)rms can more easilyadjustquantitiesthanprices,butafteranegativeshock,theoppositehappensbecauseof hiringfrictions. In(cid:135)ationwillbehaveasymmetrically;displayinglargeandshortlivedresponses following positive nominal shocks but displaying small and more persistent responses following positive shocks. 33

A.3 Computation I solve the model with policy function iteration by simultaneously solving the two (cid:133)rst-order conditions for vacancy posting and job destruction: c c t t+1 = E (cid:12) (1 (cid:26) )(cid:31) + (1 (cid:26)(cid:22) (cid:26) ) (6) q((cid:18) ) t t+1 (cid:0) t+1 t+1 q((cid:18) ) (cid:0) (cid:0) t+1 t t+1 (cid:20) (cid:21) c t (cid:31) = if (cid:31) < 0 (7) (cid:0) t q((cid:18) ) t t with (cid:31) = b + 1+(cid:27)h 1 (cid:21) h 1 t +(cid:27)h the value of a marginal worker. t (cid:0)(cid:21)t (cid:11) (cid:0) h(cid:21)t(1+(cid:27)h) I use policy f(cid:0)unction it(cid:1)erations with intergrid cubic spline interpolation on a grid with (30;30) points for the two state variables n and y . Employment n is discretized over [0:8;1], t t t and I follow Tauchen(cid:146)s method (1986) to represent the AR(1) process y as a Markov chain. t Since employment will only rarely take extreme values, I allow for a higher grid density for employment around its steady-state value. The general algorithm is as follows: 1. Guess policy functions for (cid:18) (n ;y ) and (cid:26) (n ;y ) and interpolate their values with 0 i j 0 i j intergrid cubic spline interpolation for points not on the grid 2. For all n and y : i j a. If (cid:31)((cid:18) (n ;y );(cid:26) (n ;y )) > ct (cid:0) 0 i j 0 i j q((cid:18)0(ni;yj)) (cid:26) (n ;y ) = 0and(cid:133)nd(cid:18) (n ;y )tosatisfy(6)usinginterpolated(cid:18) and(cid:26) tocompute 1 i j 1 i j 0 0 the right-hand side of (6). b. Otherwise, solve jointly (6) and (7) for (cid:18) (n ;y ) and (cid:26) (n ;y ): 1 i j 1 i j 3. Repeat 2. until (cid:18) (cid:18) < " and (cid:26) (cid:26) < " : 1 0 (cid:18) 1 0 (cid:26) k (cid:0) k k (cid:0) k Since it is computationally demanding to jointly solve for (cid:18) and (cid:26), I restrict this joint calculation to the (cid:133)rst and latter steps of the computation loop. More precisely, I start with a loose value for " so that once I obtain a decent approximation for (cid:26), I only iterate on (cid:18) taking (cid:26) the policy rule (cid:26) as given. When (cid:18) converges to a good approximation, I resume solving for 34

both (cid:18) and (cid:26) simultaneously. 35

References [1] Andolfatto, D. (cid:147)Business Cycles and Labor-Market Search,(cid:148)American Economic Review, 86(1), 1996. [2] Barnichon, R. (cid:147)Productivity, Aggregate Demand and Unemployment Fluctuations,(cid:148)FinanceandEconomicsDiscussionSeries2008-47, BoardofGovernoroftheFederalReserve System, 2008. [3] Barnichon, R. (cid:147)Vacancy Posting, Job Separation, and Unemployment Fluctuations,(cid:148) Mimeo, 2009. [4] Blanchard, O.and P.Diamond, (cid:147)The cyclicalbehaviorof thegross (cid:135)ows of U.S.workers,(cid:148) Brookings Papers on Economic Activity, 2, pp. 85(cid:150)155, 1990. [5] Canova, F., C. Michelacci and D. L(cid:243)pez-Salido, (cid:147)Schumpeterian Technology Shocks,(cid:148) mimeo CEMFI, 2007. [6] Christo⁄el, K., K. Kuester and T. Linzert, (cid:147)Identifying the Role of Labor Markets for Monetary Policy in an Estimated DSGE Model,(cid:148)ECB Working Paper No 635, 2006. [7] Cooper, R., J. Haltiwanger and J. Willis, (cid:147)Search frictions: Matching aggregate and establishment observations,(cid:148)Journal of Monetary Economics, 54 pp. 56-78, 2008. [8] Costain, J. S. and M. Reiter (cid:147)Business cycles, unemployment insurance, and the calibration of matching models,(cid:148)Journal of Economic Dynamics and Control, 32(4), pp 1120-1155, 2007. [9] Davis, S. (cid:147)The Decline of Job Loss and Why It Matters,(cid:148)American Economic Review P&P, 98(2), pp. 263-267, 2008. [10] Davis, S. and J. Haltiwanger. (cid:147)The Flow Approach to Labor Markets: New Data Sources and Micro-Macro Links,(cid:148)Journal of Economic Literature, 20(3), pp. 3-26, 2006. 36

[11] Davis, S., J. Faberman, J. Haltiwanger, R. Jarmin and J. Miranda. (cid:147)Business Volatility, Job Destruction and Unemployment,(cid:148)NBER Working Paper No. 14300, 2008. [12] den Haan, W. and G. Kaltenbrunner (cid:147)Anticipated Growth and Business Cycles in Matching Models,(cid:148)Journal of Monetary Economics, Forthcoming, 2009. [13] den Haan, W., G. Ramey and J. Watson. (cid:147)Job Destruction and Propagation of Shocks,(cid:148) American Economic Review, 90 (3), pp. 482(cid:150)498., 2000. [14] DeLong, B. and L. Summers. (cid:147)Are Business Cycles Asymmetrical?,(cid:148)American Business Cycle: Continuity and Change, edited by R. Gordon. Chicago: University of Chicago Press, pp 166-79, 1986. [15] Elsby, M. and R. Michaels (cid:147)Marginal Jobs, Heterogeneous Firms and Unemployment Flows,(cid:148)NBER Working Paper No. 13777, 2008. [16] Elsby, M. R. Michaels and G. Solon. (cid:147)The Ins and Outs of Cyclical Unemployment,(cid:148) American Economic Journal: Macroeconomics, 2009. [17] Fujita, S. (cid:147)Dynamics of Worker Flows and Vacancies: Evidence from the Sign Restriction Approach,(cid:148)Journal of Applied Econometrics, Forthcoming, 2009. [18] Fujita, S. and G. Ramey. (cid:147)The Cyclicality of Job Loss and Hiring,(cid:148)Federal Reserve Bank of Philadelphia, 2006. [19] Fujita, S. and G. Ramey. (cid:147)Job Matching and Propagation,(cid:148)Journal of Economic Dynamics and Control, pp. 3671-3698, 2007. [20] Fujita, S.andG.Ramey.(cid:147)TheCyclicalityofSeparationandJobFindingRates,(cid:148)Working Paper, 2007 [21] Fernald, J. (cid:147)Trend Breaks, long run Restrictions, and the Contractionary E⁄ects of Technology Shocks,(cid:148)Working Paper, 2005. 37

[22] Gal(cid:237), J. (cid:147)Technology, Employment and The Business Cycle: Do Technology Shocks Explain Aggregate Fluctuations?,(cid:148)American Economic Review, 89(1), 1999. [23] Gertler, M. and A. Trigari (cid:147)Unemployment Fluctuations with Staggered Nash Wage Bargaining,(cid:148)Journal of Political Economy, 117(1), 2009. [24] Hall, R. (cid:147)Employment E¢ ciency and Sticky Wages: Evidence from Flows in the Labor Market,(cid:148)The Review of Economics and Statistics, 87(3), pp. 397-407, 2005. [25] Hall, R. (cid:147)Employment Fluctuations with Equilibrium Wage Stickiness,(cid:148)American Economic Review, 95(1), pp. 50-65, 2005. [26] Hall, R. (cid:147)Job Loss, Job Finding, and Unemployment in the U.S. Economy over the Past Fifty Years,(cid:148)NBER Macroeconomics Annual, pp. 101-137, 2005. [27] Krause, M and T. Lubik. (cid:147)The (Ir)relevance of Real Wage Rigidity in the New Keynesian Model with Search Frictions(cid:148), Journal of Monetary Economics, 54 pp. 706-727, 2007. [28] Mc Kay, A. and R. Reis. (cid:147)The Brevity and Violence of Contractions and Expansions,(cid:148) Journal of Monetary Economics, 55, pp. 738-751, 2008. [29] Mertz,M.(cid:147)SearchintheLaborMarketandtheRealBusinessCycle,(cid:148)JournalofMonetary Economics, 49, 1995. [30] Michelacci, C. and D. L(cid:243)pez-Salido. (cid:147)Technology Shocks and Job Flows,(cid:148)Review of Economic Studies, 74, 2007. [31] Mortensen, D. and E. Nagypal. (cid:147)More on Unemployment and Vacancy Fluctuations,(cid:148) Review of Economic Dynamics, 10, pp. 327-347, 2007. [32] Mortensen, D. and C. Pissarides. (cid:147)Job Creation and Job Destruction in the Theory of Unemployment,(cid:148)Review of Economic Studies, 61, pp. 397-415, 1994. 38

[33] Neftci, S. (cid:147)Are Economic Time Series Asymmetric over the Business Cycle?,(cid:148)Journal of Political Economy, 92, pp 307-28, 1984. [34] Petrongolo, B.andC.Pissarides.(cid:147)TheInsandOutsofEuropeanUnemployment,(cid:148)American Economic Review P&P, 98(2), 256-262, 2008. [35] Pissarides, C. Equilibrium Unemployment Theory, 2nd ed, MIT Press, 2000. [36] Pissarides, C. (cid:147)The Unemployment Volatility Puzzle: Is Wage Stickiness the Answer?,(cid:148) Econometrica, Forthcoming, 2009. [37] Ramey, G. (cid:147)Exogenous vs. Endogenous Separation,(cid:148)Working Paper, 2007. [38] Schreft, S. A. Singh and A. Hodgson. (cid:147)Jobless Recoveries and the Wait-and-See Hypothesis,(cid:148)Economic Journal-Federal Reserve Bank of Kansas City, 4th Quarter, pp 81-99, 2005. [39] Shimer, R. (cid:147)The Cyclical Behavior of Equilibrium Unemployment and Vacancies,(cid:148)American Economic Review, 95(1), pp. 25-49, 2005. [40] Shimer, R. (cid:147)Reassessing the Ins and Outs of Unemployment,(cid:148)NBER Working Paper No. 13421, 2007. [41] Sichel, D. (cid:147)Business Cycle Asymmetry: a Deeper Look,(cid:148)Economic Inquiry, 31, pp. 224- 36, 1993. [42] Thomas, C. (cid:147)Firing costs, labor market search and the business cycle",(cid:148)Working Paper, 2006. [43] Thomas, C. (cid:147)Search and matching frictions and optimal monetary policy,(cid:148)Journal of Monetary Economics, 55(5), 2008. [44] Thomas, C. and F. Zanetti. (cid:147)Labor market reform and price stability: an application to the Euro Area,(cid:148)Working Paper, 2008. 39

[45] Trigari, A. (cid:147)The Role of Search Frictions and Bargaining for In(cid:135)ation Dynamics,(cid:148)IGIER Working Paper, 2006. [46] Trigari, A. (cid:147)Equilibrium Unemployment, Job Flows and In(cid:135)ation Dynamics,(cid:148)Journal of Money, Credit and Banking, 2009. [47] Walsh, C. (cid:147)Labor Market Search and Monetary Shocks,(cid:148)in Elements of Dynamic Macroeconomic Analysis, S.Altug, J.Chadha, andC.Nolan, CambridgeUniversityPress, 2004, 451-486. [48] Woodford, M. (cid:147)In(cid:135)ation and Output Dynamics with Firm-Speci(cid:133)c Investment,(cid:148)Working Paper, 2004. 40

Table1: Skewness, Monthly data du dy 0.65** 0.26 1951 2007 (0.19) (0.36) 0.09 0.17 1985 2007 (0.08) (0.12) Notes:Monthly unemployment u is constructed by the BLS from the CPS, and y isloggedreal GDP. Both series are seasonally adjustedanddetrended with an HP filter (λ=10,000).Newey Weststandard errors are reported in parentheses. ** indicates significance at the 5% level. Table 2: US Data, 1951 2006 u v (cid:181) jf js h y Standard 0.187 0.198 0.378 0.116 0.065 0.007 0.021 deviation Quarterly 0.938 0.948 0.946 0.912 0.648 0.83 0.84 autocorrelation u 1 0.90 0.97 0.95 0.61 0.50 0.69 v 1 0.98 0.92 0.55 0.63 0.78 Correlation (cid:181) 1 0.96 0.62 0.60 0.76 matrix jf 1 0.48 0.51 0.69 js 1 0.55 0.56 h 1 0.81 y 1 Notes:Seasonally adjusted unemploymentuis constructed by the BLS from the Current Population Survey (CPS). The seasonally adjusted help wanted advertising indexvis constructed by the Conference Board. Labor market tightness is the vacancy unemployment ratio.jf andjs are the quarterly job finding probability and employment exit probability series constructed by shimer (2007).Hours per workerh only covers 1956 2006 and is the sum of the quarterly average of weekly manufacturing overtime of production workers and the average over 1956 2006 of weekly regular manufacturing hours of production workers from the Current Employment Statistics from the BLS,andy isreal GDP. All variables are reported in logs as deviations from an HP trend with smoothing parameter‚=105 Table 3: Mortensen Pissarides (1994) model with productivity shocks u v (cid:181) jf js y 0.084 0.044 0.044 0.012 0.096 0.021 Standard deviation (0.01) (0.004) (0.003) (0.001) (0.009) (0.002) Quarterly 0.88 0.91 0.76 0.76 0.76 0.84 autocorrelation (0.02) (0.02) (0.04) (0.05) (0.05) (0.03) 0.96 0.96 0.97 0.97 0.99 u 1 (0.01) (0.01) (0.06) (0.06) (0.00) 0.87 0.86 0.86 0.93 v 1 (0.02) (0.03) (0.03) (0.01) 0.99 0.99 0.99 Correlation matrix (cid:181) 1 (0.00) (0.00) (0.00) 0.99 0.99 jf 1 (0.00) (0.00) 0.96 js 1 (0.00) y 1 Notes:Standard errors the standard deviation across500 model simulations over600 months are reported in parentheses. 41

Table4:Calibration, monthly frequency Discount rate β=0.991/3 Matching function elasticity σ=0.72 Shimer (2005) Bargaining weight γ=0.5 den Haan, Ramey and Probability vacancy is filled q(θ)=0.35 Watson (2000) Job finding probability θq(θ)=0.3 u=10% Exogenous separation rate r =0.0.32 Income replacement ratio b=0.28 Shimer(2005) Vacancy posting cost c=0.01 Andolfatto (1996) Returns to hours α=0.65 Disutility of hours σ=10 Trigari (Forthcoming) h AR(1) process foroutput ρ =0.93 m Standard deviation ofAD σ =0.0014 shock m Table5: MP model with demand constraints, Aggregate Demand shocks u v (cid:181) jf js h y Standard 0.174 0.470 0.623 0.173 0.061 0.007 0.020 deviation (0.021) (0.046) (0.069) (0.019) (0.006) (0.001) (0.002) Quarterly 0.86 0.65 0.75 0.75 0.15 0.14 0.84 autocorrelation (0.03) (0.06) (0.05) (0.05) (0.08) (0.08) (0.04) 0.83 0.90 0.91 0.47 0.30 0.97 u 1 (0.03) (0.02) (0.02) (0.04) (0.07) (0.01) 0.98 0.98 0.60 0.76 0.92 v 1 (0.00) (0.00) (0.03) (0.02) (0.01) 0.99 0.58 0.66 0.97 (cid:181) 1 Correlation (0.00) (0.03) (0.03) (0.01) matrix 0.59 0.65 0.97 jf 1 (0.03) (0.03) (0.01) 0.50 0.60 js 1 (0.03) (0.03) 0.48 h 1 (0.05) y 1 Notes:Standard errors the standard deviation across500 model simulations over600months are reported in parentheses. 42

Table6:Contribution of JF/JS andSkewness, model data Size of AD shocks (cid:190) ½(cid:190) 22% 13% Contribution ofJS (0.03) (0.02) 78 % 87% Contribution ofJF (0.03) (0.02) 0.53** 0.14 Skewness(dU) (0.16)) (0.17)) Notes:u andy are monthly model unemployment and output. The contributions of JF and JS are calculated using the method from Shimer (2007) and Fujita and Ramey (2007).Standard errors the standard deviation across500 model simulations over 600 months (50 years) are reported in parentheses. Figure 1: Empirical Cross-Correlograms of the Job Finding rate and the Job Separation rate with Unemployment and Output over 1951-2006. 1 1 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0 0 0.2 0.2 0.4 0.4 0.6 0.6 0.8 0.8 1 1 8 6 4 2 0 2 4 6 8 8 6 4 2 0 2 4 6 8 corr(JF,U ) corr(JS,U ) t+j t+j 1 1 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0 0 0.2 0.2 0.4 0.4 0.6 0.6 0.8 0.8 1 1 8 6 4 2 0 2 4 6 8 8 6 4 2 0 2 4 6 8 corr(JF,Y ) corr(JS,Y ) t+j t+j 43

Figure 2: Impulse response functions of Unemployment, the (minus) Job Finding probability and the Job Separation probability to monetary and technology shocks. Solid circles indicate that the response is signi(cid:133)cant at the 5% level and open circles at the 10% level. 0.06 0.04 0.02 U JF JS 0 0.02 0 2 4 6 8 10 12 14 16 18 20 Impulse Responses to a Technology shock 0.05 0 JS 0.05 U JF 0.1 0.15 0 2 4 6 8 10 12 14 16 18 20 Impulse Responses to a Monetary Policy shock Figure 3: Mortensen-Pissarides (1994) model impulse response functions to a negative one standard-deviation productivity shock. 0 0.5 1 1.5 2 0 2 4 6 8 10 12 14 16 18 20 % 15 10 5 y 0 n 5 0 2 4 6 8 10 12 14 16 18 20 % JF JS 2 1 0 1 0 2 4 6 8 10 12 14 16 18 20 % 10 A a~ 5 0 5 10 0 2 4 6 8 10 12 14 16 18 20 % u v q 44

Figure 4: Aggregate Demand and the value of a marginal worker. (cid:1)v indicates changes in posted vacancies, and (cid:26) > 0 indicates use of the job separation margin. 0.3 0.25 0.2 0.15 0.1 D v>0 0.05 0 D v<0 0.05 r >0 0.1 0.15 0.28 0.29 0.3 0.31 0.32 0.33 0.34 0.35 Hours rekroW lanigraM fo eulaV h* 45

Figure 5: Model impulse response functions to a positive one standard-deviation aggregate demand shock. 0.05 0 0.05 0.1 0.15 0.2 0 2 4 6 8 10 12 14 16 18 20 Unemployment % 0.04 0.03 0.02 0.01 0 0 2 4 6 8 10 12 14 16 18 20 Hours per Worker % 0.4 0.3 0.2 0.1 0 0 2 4 6 8 10 12 14 16 18 20 JF % 1 0.5 0 0.5 1 0 2 4 6 8 10 12 14 16 18 20 JS % Figure 6: Model impulse response functions to negative aggregate demand shocks with respective size of one and one-half standard-deviation. 0.2 0.15 0.1 0.05 0 0 2 4 6 8 Unemployment % x 10 3 2 0 2 4 6 0 2 4 6 8 Hours per Worker % 0 0.05 0.1 0.15 0.2 0 2 4 6 8 JF % 0.5 0.4 0.3 0.2 0.1 0 0 2 4 6 8 JS % 1/2s y s y 46

Figure7: Modelimpulseresponsefunctionsofgrosshirestonegativeaggregatedemandshocks of di⁄erent size. 0.035 0.5s y 0.03 1s 1.5s 0.025 0.02 0.015 0.01 0.005 0 0.005 0.01 0.015 0 2 4 6 8 10 12 14 16 18 20 Gross Hires Figure 8: Model (plain line) and empirical (dotted line) cross-correlograms of the Job Finding rate and the Job Separation rate with Unemployment and Output. 1 1 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0 0 0.2 0.2 0.4 0.4 0.6 0.6 0.8 0.8 1 1 8 6 4 2 0 2 4 6 8 8 6 4 2 0 2 4 6 8 corr(JF,U ) corr(JS,U ) t+j t+j 1 1 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0 0 0.2 0.2 0.4 0.4 0.6 0.6 0.8 0.8 1 1 8 6 4 2 0 2 4 6 8 8 6 4 2 0 2 4 6 8 corr(JF,Y ) corr(JS,Y ) t+j t+j 47