Sectoral Shocks, Reallocation, and Labor Market Policies

Board of Governors of the Federal Reserve System International Finance Discussion Papers ISSN 1073-2500 (Print) ISSN 2767-4509 (Online) Number 1361 December 2022 Sectoral Shocks, Reallocation, and Labor Market Policies Joaquin Garcia-Cabo, Anna Lipinska, Gaston Navarro Please cite this paper as: Garcia-Cabo, Joaquin, Anna Lipinska, and Gaston Navarro (2022). “Sectoral Shocks, Reallocation, and Labor Market Policies,” International Finance Discussion Papers 1361. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/IFDP.2022.1361. NOTE: International Finance Discussion Papers (IFDPs) 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 International Finance Discussion Papers Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers. Recent IFDPs are available on the Web at www.federalreserve.gov/pubs/ifdp/. This paper can be downloaded without charge from the Social Science Research Network electronic library at www.ssrn.com.

Sectoral Shocks, Reallocation, and Labor Market Policies Joaqu´ın Garc´ıa-Cabo∗ Anna Lipin´ska† Gasto´n Navarro‡§ December 9, 2022 Abstract Unemployment insurance and wage subsidies are key tools to support labor markets in recessions. Wedevelopamulti-sectorsearchandmatchingmodelwithon-the-jobhumancapital accumulation to study labor market policy responses to sector-specific shocks. Our calibration accountsforstructuraldifferencesinlabormarketsbetweentheUnitedStatesandtheeuroarea, including a lower job-finding rate in the latter. We use the model to evaluate unemployment insurance and wage subsidy policies in recessions of different duration. We find that, after a temporary sector-specific shock, unemployment insurance improves both productivity and reallocation toward productive sectors at the cost of initially higher unemployment and, thus, human capital destruction. In the United States, unemployment insurance is preferred to wage subsidies when it does not distort job creation for too long. By contrast, wage subsidies reduce unemployment and preserve human capital, at the cost of limiting reallocation. In the euro area, where the job-finding rate is lower, subsidies are preferred. Keywords: Labor Market Policies, Search and Matching Frictions, Reallocation. JEL Classification: E24, J64, J68. ∗Federal Reserve Board: joaquin.garcia-caboherrero@frb.gov. †Federal Reserve Board: anna.lipinska@frb.gov ‡Federal Reserve Board: gaston.m.navarro@frb.gov §We would like to thank Dario Caldara, Almut Balleer, and Andrea Raffo for their insightful comments, as well as seminar participants at the Bank of Italy, Bank of England, the Federal Reserve Board International Finance Workshop, and the EU Commission Brussels 2022 Conference. We are grateful to Amanda Wilcox and Carolyn Davin for outstanding research assistance. The views expressed in this paper do not necessarily reflect the views of the US Federal Reserve System. 1

1 Introduction Recent recessions—including the 2009 Global Financial Crisis (GFC) and the more recent COVID- 19 pandemic—had heterogeneous effects across sectors. Interestingly, policy responses to these recessions varied across countries. While the United States largely supported unemployed workers by extending unemployment insurance (UI), several European countries expanded short-time work subsidies(WS)topreventrapidjobdestructioninaffectedsectors(Giupponi,LandaisandLapeyre, 2021). These different approaches to fight recessions raise natural questions: Which labor market policy, UI or WS, is preferable during recessions, and why did different countries opt for different policies? While both policies provide support to workers during recessions, they also have costs. On the one hand, generous unemployment benefits can deter employment, thus generating human capital losses from permanent separations—which are estimated to be large and persistent, especially during recessions (Davis and von Watcher, 2011). On the other hand, subsidizing declining sectors might prevent an efficient sectoral reallocation of workers, thus weighing on aggregate productivity (Restuccia and Rogerson, 2008). Intuitively, the tradeoff of these costs crucially depends on how quickly workers can reallocate across sectors and how persistent the recession is expected to be. In this paper, we develop a multi-sector search and matching model to study labor market policy responses to sector-specific shocks. We focus on UI and WS policies, the two labor market policies most commonly used in recent years. The model incorporates key features to address the policytradeoffs just discussed. Weargue that labor market flexibility, as measured by labor market flows, is key to determine which policy is preferred. Our model extends an off-the-shelf search and matching model in a few dimensions. We assume that workers accumulate job-specific human capital when employed, which is lost upon permanent separation. Firms and workers can endogenously decide to terminate a match, and thus a match duration responds to UI and WS policies. Similarly, workers can only sluggishly reallocate across sectors, making the persistence of the recession key for reallocation gains. Additionally, we assume wage rigidity, which yields inefficient separations and thus possible welfare gains from labor market 2

policies. Finally,weaddtemporarylay-offsandrecall,aubiquitousfeatureintheU.S.labormarket (Fujita and Moscarini, 2017). We use key labor market statistics to calibrate two versions of the model: one matched to the U.S. economy and a second one matched to the euro-area economy. We label the U.S. calibration as a flexible economy, as it features high job-finding rates, and the euro-area calibration as a rigid economy, as job-finding rates are lower. We show that both calibrations deliver a good fit for each respective economy and that they are consistent with the key empirical evidence we present in this paper. In particular, we document that sectoral reallocation, measured following the index proposed by Chodorow-Reich and Wieland (2020), is higher in the United States during recessions compared to the euro area. We use the model to evaluate UI and WS policies in a short-lived recession induced by a sectorspecific shock. In particular, we aim to recreate the initial shock to the services sector during the first half of 2020, when public health restrictions led to a rapid closure of high-contact services. Our main finding is that, in response to a short-lived sectoral shock, UI policy is preferable in the flexible economy, while WS are preferable in the rigid economy. In the flexible economy, UI policiesgeneratealargerinitialeconomiccontractionbutalsoafasterrecovery. Thatis,withhigher job-finding rates, UI policies promote necessary reallocation to unaffected sectors, thus achieving a faster recovery. In contrast, with lower job-finding rates in the rigid economy, UI policies do not generate such a fast recovery, making WS more appealing. We compute the welfare gains of each policy, measured as the present discount value of workers’ consumption and firms’ profits, net of the policy cost. Our welfare analysis shows that UI benefits consumers at the expense of firms, while WS improves welfare of firms, and to some extent, that of consumers. In the United States, UI is preferable as consumer gains more than offset firms’ losses. In the euro area, firms losses from UI make this policy welfare deteriorating, making WS preferred. Thus, our results rationalize the difference in policies usually implemented in the United States versus the euro area. Finally, we show that, while some UI policies may boost reallocation, they may also have the oppositeeffectiftheUIincreaseistoogenerous. Generousbenefitsleadtolargerwagesandthusto lower profits for firms, which may reduce vacancy postings and job creation. This distortion effect 3

of UI is amplified in the presence of wage rigidity and is particularly strong in persistent recessions, as firms are less willing to pay higher wages for an extended period. We argue that front-loading UI extensions may ameliorate this distortion. Related Literature Our analysis is related to several strands of the literature that study the macroeconomic effects of labor market policies. In terms of modeling strategy, we follow standard search and matching models of the labor market in the spirit of Shimer (2005). In addition, we introduce recall and temporary layoffs as in Fujita and Moscarini (2017), allowing firms the option to recall furloughed workers. We depart from these models by introducing an important inefficiency in terms of wage rigidities, in line with evidence from Gertler, Huckfeldt and Trigari (2020). Finally, we introduce different economic sectors that lead to labor market segmentation. This assumption results in different sectoral jobfinding rates that depend on sector-specific productivity and will prove to be key in understanding theeffectoflabormarketpoliciesonlaborreallocationinresponsetosectoralshocks. Whileseveral papers in the literature have used multi-sector search models (see, for instance, Chodorow-Reich and Wieland (2020) and Visschers and Carrillo-Tudela (2021)) to study the role of sectoral shocks in driving aggregate fluctuations, the aim of this paper is to study the effectiveness of labor market policies in the presence of sectoral shocks. Ourpaperdirectlyspeakstotheliteraturethatstudiestheroleoflabormarketpoliciesoverthe businesscycle(see,forexample,Gnocchi,LagerborgandPappa(2015)andMitmanandRabinovich (2015)). For instance, Cacciatore and Fiori (2016) and Cacciatore, Duval, Fiori and Ghironi (2016) study the role of labor market regulations in the short run, such as a reduction in firing costs and unemployment benefits. Our analysis provides a framework to study a variety of policies not only at the aggregate level, but also by sector and to study short- versus long-run effects of these interventions. It is important to mention two recent papers that study the role of market policies, with an application to the recent COVID-19 recession. Gertler, Huckfeldt and Trigari (2021) study the effect of the Paycheck Protection Program in the U.S. labor market during the COVID-19 recession and find that this program facilitated hiring and worker recall. Birinci, Karahan, Mercan and See (2021) study the optimal labor market policy mix in response to the COVID-19 shock, and 4

find that a joint intervention of UI and payroll subsidies is optimal. Yet, neither of these papers takes into account the tradeoff generated by these policies in facilitating labor reallocation across industriesatthecostofdestroyingmatch-specificproductivity, whichwemodelexplicitlyandshow its importance in the aftermath of a sectoral shock. Empirically, there have been a number of studies that separately analyzed WS and UI policies. Studies on WS predominantly use European data during the 2009 financial crisis. Using Italian data, Giupponi and Landais (2018) find that when the shock is persistent adverse selection of low productivity firms prevents reallocation. In a related manner, using French data Cahuc, Kramarz andNevoux(2018)showthatWSprogramsweresuccessfulatsupportingemploymentinfirmsthat faced strong but temporary negative revenue shocks. Cooper, Meyer and Schott (2017) also find positiveeffectsinsupportingemployment,butatthecostofallocativeefficiencyusingGermandata. Finally, Balleer, Gehrke, Lechthaler and Merkl (2016) argue that WS programs are successful in supporting employment provided they are part of the automatic stabilizer toolkit. A more recent paper by Gehrke and Hochmuth (2021) studies the non-linear effects of WS over the business cycle, finding that these policies are not as effective outside of recessions. With regard to UI, a large literature has tried to quantify the effects of UI extensions on unemployment and workers’ incentives to take jobs, finding in many case that extending UI can lead to longer unemployment episodes (see for instance Nakajima (2012) and Pei and Xie (2021)). Relative to UI design, Mitman and Rabinovich (2015) study the optimal level and duration of UI during recession of different persistence. In a COVID-19 application, Mitman and Rabinovich (2021) assess the U.S. policy, finding that a large, transitory, and front-loaded policy, similar to the one implemented in early 2020, is optimal. Finally, Ganong, Greig, Liebeskind, Noel, Sullivan and Vavra (2021) study the 2020 expansion of UI, finding that larger benefits did not lead to a strong decrease in employment. In this paper, we take stock of both the empirical and theoretical literature to provide a structural analysis of labor market policies focusing on the selection and reallocation effects and also importance of the persistence of recessions in evaluating the policy response. Section 2 documents empirical evidence on sectoral reallocation across countries, section 3 presents the structural model, and section 4 provides the calibration for the flexible and rigid 5

economies. Section 5 describes the simulation of a short-lived recession for the flexible and rigid economies, as well as the model predictions on reallocation and welfare under WS and UI for these economies. Section 6 discusses the role of recession persistence and policy design in our findings. Section 7 concludes. 2 Sectoral Reallocation: Cross-Country Evidence In this section, we document empirically how labor reallocation behaves over the business cycle and how it relates to unemployment and productivity changes. We present our results for both the euro area and the United States. We analyze labor reallocation, relying on the reallocation index proposed by Chodorow-Reich and Wieland (2020) (hereafter, CRW index) based on employment growth dispersion across industries. In particular, reallocation across a number I of industries between t and t+j is given by I (cid:12) (cid:12) 1 (cid:88) (cid:12)1+g i,t,t+j (cid:12) R t,t+j = s i,t(cid:12) −1(cid:12). (1) 2 (cid:12) 1+g (cid:12) t,t+j i In equation (1), g and g represent the aggregate and sectoral growth rates of employment e i and e , respectively, and s = ei is the share of employment in sector i relative to the aggregate.1 i i e The index can take values between 0 and 1. R = 0 implies that the employment growth rate t,t+j in every industry between t and t+j is identical. The index takes the value R = 1 when all t,t+j employment inexistingindustriesattdisappearsbyt+j andnewindustries withzeroemployment at t account for all the employment in t+j. We compute the index using aggregate data from 10 industries, following theStandard Industrial Classification (SIC) and homogenizing across the United States and the euro area. Data from the United States come from the Bureau of Labor Statistics and for the euro area from Eurostat. We compute year-over-year employment growth rates.2 1AsarguedinVisschersandCarrillo-Tudela(2021),thepre-multiplicationoftheindexby0.5aimstoavoiddouble counting from net inflows into some industries that are net outflows from other industries. 2We exclude employment in agriculture for these calculations. We have performed robustness in calculating this index. In particular, we have used NAICS industry classifications leading to a total of 19 industries, instead of 10. The reallocation index implied by a higher disaggregation is slightly larger, as expected, but comes at the cost of a shorter time span. We have also calculated the index with quarterly growth rates instead of year, leading to very 6

Figure 1: Reallocation Index: Euro Area and United States Figure 1 presents the comparison between reallocation indexes in the United States and the euro area. While both economies present low industry reallocation during expansions, reallocation increases during a recession. The reallocation increase is larger in the United States, relative to the euro area, and particularly sharp in the COVID-19 recession, when unemployment reached historically high peaks in the United States. Thus, the reallocation data suggest that the U.S labor market appears to be more dynamic than its euro-area counterpart. We confirm these findings when estimating a structural vector autoregression (SVAR) model, which provides a more systematic analysis of the relation between reallocation, productivity, and unemployment.3 In particular, we use these three variables in the SVAR, which we estimate separately for the United States and the euro area. We identify shocks following a Cholesky decomposition, with variables ordered as productivity, unemployment, and reallocation. The data similar, although slightly noisier results. These findings can be found in the appendix. 3We also computed the cyclical correlations between unemployment and reallocation for both economies, using a Hodrick-Prescott filter with smoothing parameter 1600. Unemployment and reallocation are highly correlated contemporaneously in the United States (0.79). In the euro area, the correlation is also positive, but weaker (0.40). Wealsoinspectedthecorrelationbetweencyclicalproductivityandreallocation,findingthatitiscontemporaneously weakly positive in the United States (0.12) and negative in the euro area (-0.60). Finally, increases in reallocation today are positively correlated with future productivity in both economies. 7

are quarterly and are between 1990:Q3 and 2022:Q2 for the United States, and between 1995:Q3 and 2022:Q2 for the euro area.4 We are interested in the average behavior of the reallocation, productivity, and unemployment variables during recessions. As such, we analyze an exogenous 1 percentage point increase in unemployment, which we refer to as an “unemployment shock.”5 The results are presented in figure 2. In the United States, the unemployment shock leads to a Figure 2: Impulse Responses to 1 pp Unemployment Shock in the Euro Area and the United States contemporaneous sharp increase in U.S. unemployment, which quickly reverts back to zero. At the same time, U.S. productivity and reallocation increase after the unemployment shock. In the euro area, interestingly, the unemployment shocks lead to a more persistent increase in unemployment. Productivity does not strongly react—the 90 percent confidence interval around the impulse response of productivity always contains zero—while reallocation mildly decreases for a couple of periods. UI policies typically implemented in the U.S. tend to boost unemployment and reallocation more than the WS policies typically implemented in the euro area. In order to understand the exact role of both institutions and policies we develop a structural model in the next section. Our goal is to assess the effectiveness of the WS and UI policies in response to sector-specific shocks, and quantify the winners and losers from the two policy choices in labor markets with different 4See the appendix for more details on data sources and computations. 5This unemployment shock may represent any combination of shocks that increase unemployment while not affecting productivity contemporaneously. 8

institutions. 3 Model In this section, we present a multi-sector search and matching model of the labor market. We assumeworkersaccumulatejob-specifichumancapitalwhileemployed,andtheycandecidewhether to leave or stay with the match at any time. Firms can also decide whether to temporarily or permanently separate from workers. Job-specific human capital is preserved when firms recall workersontemporarylayoffbutislostwhentheseparationispermanent. Workerscanmoveacross sectors, but reallocation is sluggish due to matching frictions and because searching in a different sector only occurs with a certain probability. Finally, matches are subject to wage rigidity, and thus productivity changes do not immediately pass through to wages. We provide a more detailed description in the next subsection. 3.1 Environment Time is discrete, infinite, and indexed by t = 1,2,.... The economy is populated by a continuum of workers and firms. Firms post vacancies in order to find workers. The cost of a vacancy is κ and the probability of contacting a worker is q . Firms belong to a sector indexed by s, and we assume t there are two sectors in the economy: s = 1,2. Upon forming a match, the firm and the worker draw a match-specific productivity z distributed according to G(z ). We consider deterministic 0 0 transition dynamics where agents have perfect foresight, and we use time t to denote the aggregate state of the economy. A match can be either active or idle. We refer to a worker in an idle match as in temporary unemployment or furlough. The match-specific productivity evolves stochastically following a Markov chain: z(cid:48) ∼ Pa(z(cid:48)|z) for active matches and z(cid:48) ∼ Pi(z(cid:48)|z) for idle matches. Under both processesPa(z(cid:48)|z)andPi(z(cid:48)|z), aproductivityofz = 0isanabsorbingstate—akintoanexogenous separation. When the match dissolves permanently, either exogenously or endogenously, z is lost. The output of an active firm produces an match at is given as: y (s,z) = x (s)z, where x (s) is the t t t sector-specific productivity. 9

Active matches re-set wages subject to a Calvo-style friction. New matches have flexible wages given initial productivity z and sectoral productivity x(s). After observing the realized match and 0 sectoral productivity, z and x, a match re-sets wages with probability λ. After the wage-setting stage, the worker decides whether to stay in the match or quit. If the worker decides to stay, the firm has the next move and has three options: to remain active, to remain idle, or to terminate the match. If the match remains active, output is produced, the worker gets wage w, and the operating cost c must be paid. If the match is idle, the worker goes into temporary unemployment, no wages o are paid, and the firm faces a cost c of keeping the idle match. At any point, a furloughed worker i can be either recalled or terminated at no cost to the firm. If the match is terminated, the firm ceases to exist. Unemployedworkerscanbeeitherinfurloughorunmatched. Theyareattachedtothelastsectorwheretheyworked,s,andsearchforajobinsectors˜withprobabilityπ (s,s˜) ≤ π (s,s)—which u u may differ across furloughed and unmatched workers, u = U,F. The probability that a worker contactsafirmissector-specificandgivenbyf (s). Thereisnocostofsearchingwhileunemployed, t and job offers can be rejected. Unemployed workers receive benefits b that do not expire. t The timing of events is as follows: (1) productivity shocks are realized, (2) unemployed and furloughed workers search for jobs and matching occurs, (3) wage renegotiation occurs with probability λ, (4) employed and furloughed workers decide whether to stay in the match or quit, (5) remaining matches decide whether to be active, idle, or exit, and (6) production and consumption takes place. All of the following value functions below are written at point (6). 3.2 Search and Matching Technologies Firms direct vacancies toward each sector s—that is, markets are segmented. Let be v number of vacancies posted in sector s, and n the number of workers searching for a job in that sector— including unmatched and furloughed workers. The total number of matches is then given by the constant-return-to-scale matching function with matching efficiency φ (as in den Haan, Ramey and 10

Watson (2000)): φnv m = . (2) 1 [nη +vη]η The worker’s job-contact probability f and the firm’s worker-contact rate q are given by m m f(s) = q(s) = . (3) n v Market tightness θ(s) is defined as the ratio of vacancies to searchers: θ(s) = v/n. 3.3 Firms Let J (z,w,s) be the maximal attainable value for a firm in an active match with productivity z, t wages w, and sector s, at time t. Analogously define V (z,w,s) as the value for a firm in an idle t match. The value for an active firm is J (z,w,s) = Π+βE (cid:2)(cid:0) 1−ηa (z(cid:48),w(cid:48),s) (cid:1) max (cid:8) J (z(cid:48),w(cid:48),s),V (z(cid:48),w(cid:48),s),0 (cid:9) |z (cid:3) (4) t t t+1 t+1 t+1 Π = y (z,s)−(1−σ )w−c t t o    w w.p. λ w(cid:48) = (5)   w∗ (z(cid:48),s) w.p. 1−λ t+1 where ηa(·) is the quitting decision of a worker in an active match. The firm’s profits, Π, are t given by output net of wages and operating costs, including the subsidy to the wage bill σ . The t continuation value in (4) shows an active firm’s three options each period: continue the match, set the match to be idle, or terminate the match. The next-period wage w(cid:48) adjusts with probability 1−λ, in which case it is set with a rule w∗(·), which we discuss in more detail later. t The value for firm in an idle match is V (z,w,s) = −c +βE (cid:2)(cid:0) 1−fi (z(cid:48),w,s) (cid:1)(cid:0) 1−ηi (z(cid:48),w(cid:48),s) (cid:1) max (cid:8) J (z(cid:48),w(cid:48),s),V (z(cid:48),w(cid:48),s),0 (cid:9) |z (cid:3) t i t t+1 t+1 t+1 t+1 (6) 11

where ηi(·) is the quitting decision of a worker in an idle match, and fi(·) is the probability that an t t idle/furloughed worker will find and accept another job—we will return to this topic later. Note thatthecontinuationvalueforanidlefirminequation(6)isthesameasforanactivefirm,although the stochastic process for z may be different. Let ea(z,w,s) be the decision of a firm to exit an active match, and d (z,w,s) the decision to t t set a match to be idle. Similarly, let ei(z,w,s) be the decision to exit an idle match and r (z,w,s) t t the decision to recall an idle worker. These decisions are given as    0 if max{J t (z,w,s),V t (z,w,s)} ≥ 0 ea(z,w,s) = (7) t   1 otherwise    0 if J t (z,w,s) ≥ V t (z,w,s) d (z,w,s) = (8) t   1 otherwise ei(z,w,s) = ea(z,w,s) (9) t t r (z,w,s) = 1−d (z,w,s). (10) t t That is, a firm terminates the match if the values of being active or idle are both below zero, and the firm make a match idle when the value is larger that being active. 3.4 Workers Let W (z,w,s) be the maximal attainable value for a worker in an active match with productivity t z, wage w, and sector s, at time t. Analogously define F (z,w,s) as the value of a worker in an t idle match. Let U (s) be the value of being unemployed when attached to sector s. The value of t being in an active match is given as (cid:104) (cid:110) (cid:111) (cid:105) W (z,w,s) = w+βE max Wˆ (z(cid:48),w(cid:48),s),U (s) |z (11) t t t+1 t+1 where next-period wages, w(cid:48), are given as in equation (5). The continuation value in equation (11) is the maximum between quitting (being unemployed) or staying in the match. The value of 12

staying in the match, Wˆ (z,w,s), is given as t Wˆ (z,w,s) = (1−ea(z,w,s)){(1−d (z,w,s))W (z,w,s)+d (z,w,s)F (z,w,s)} (12) t t t t t t +ea(z,w,s)U (z,w,s). t t Thus, the value of staying in a match accounts for the exit and idle decisions, ea(·) and d (·), which t t the firm will make later in the period. While idle, a furloughed worker receives unemployment benefit b and searches for jobs at intensity ζ < 1. The probability of finding a job in sector s˜ is the compound of the job-finding probability f (s˜) times the probability of switching sectors π (s,s˜). Upon receiving and accepting t F an offer, the worker starts with initial productivity z and wages w . When recalled, the worker 0 0 returns to the same wage w they had before. Thus, the value F (z,w,s) of being in an idle match t is given as (cid:34) (cid:32) (cid:88) (cid:110) (cid:111) F (z,w,s) = b +βE π (s,s˜) (1−ζf (s˜))max U (s),Fˆ (z(cid:48),w,s) (13) t t t F t+1 t+1 t+1 s˜ (cid:33) (cid:35) (cid:90) (cid:110) (cid:111) +ζf (s˜) max W (z ,w∗ ,s˜),max{Fˆ (z(cid:48),w,s),U (s)} dG(z ,s) |z t+1 t+1 0 0t t+1 t+1 0 where w∗ = w∗(z ,s) is the initial wage of a newly formed match, and Fˆ(z,w,s) is the value of 0t t 0 t staying in the idle match as Fˆ(z,w,s) = (1−ei(z,w,s))[r (z,w,s)W (z,w,s)+(1−r (z,w,s))F (z,w,s)] (14) t t t t t t +ei(z,w,s)U (s) t t which incorporates the exit and recall decisions, ei(·) and r (·), which the firm will make later in t t the period. We can now compute fi(·), the probability that a furloughed worker will find and accept a job t offer, which we use in equation (6) to define the value of a firm in an idle match. In particular, the 13

probability fi(·) is given as t (cid:88) (cid:90) (cid:110) (cid:111) fi(z,w,s) = π (s,s˜)ζf (s˜) I W (z ,w∗ ,s˜) > max{Fˆ(z(cid:48),w,s),U (s)} dG(z ,s) (15) t F t t 0 0t t t 0 s˜ where I{} is an indicator function. Thus, the probability fi(·) compounds the probability that a t worker searches in sector s˜and receives an offer better than staying furloughed. Finally, the value of being unemployed for a worker attached to sector s is given as (cid:32) (cid:90) (cid:88) U (s) = b +β π (s,s˜) f (s˜) max{W (z ,w∗ ,s˜),U (s)}dG(z ,s) (16) t t U t+1 t+1 0 0t t+1 0 s˜ (cid:33) +(1−f (s(cid:48)))U (s) . t+1 t+1 The quit decisions for workers in an active and idle match, ηa(·) and ηi(·), are given as t t    0 if W t (z,w,s) ≥ U t (s) ηa(z,w,s) = (17) t   1 otherwise    0 if F t (z,w,s) ≥ U t (s) ηi(z,w,s) = (18) t   1 otherwise. 3.5 Wage Setting Wages are set following a simple rule that splits the (discounted) per-period flows of profits and unemployment benefits. In particular, the re-set wage w∗(z,s) function is given as t w∗(z,s) = ωΠ¯ (z,s)+(1−ω)¯b (19) t t t where Π¯ (z,s) and ¯b are given as t t n (cid:88) Π¯ (z,s) = E [Ω (y (z ,s)−c )|z] t t t+j t+j t+j o j=0 n (cid:88) ¯b = Ω b t t+j t+j j=0 14

where weights Ω ≥ 0 ∀j and (cid:80)n Ω = 1. t+j j=0 t+j This wage rule is similar to a static Nash bargain that splits current profits, with ω akin to the worker’s bargaining power. However, because wages are re-set infrequently, the values Π¯ and ¯b t t also incorporate expected future paths for productivity and benefits. As in Cooper et al. (2017),we assume the subsidy does not enter the division of surplus between the firm and worker. However, current or expected increases in benefits do pass through to wages. OurwagespecificationisanalternativetosettingwagesviaNashbargainingoverthefirm’sand worker’s value functions. In the presence of wage rigidity, Nash bargaining over values would be computationally intensive, especially with heterogeneous productivity across workers and multiple sectors. Our simple rule is meant to ease the computational burden in an economically intuitive manner. 3.6 Free Entry Let µW(z,w,s) be the measure of workers in an active match with productivity z and wages w in t sector s at time t. Analogously define µF(z,w,s) as the measure of workers in an idle match, and t let µU(s) be the measure of unmatched workers. t Let n (s) be the number of workers searching for a job in sector s. Let MF(s) and MU(s) t t t be the number of furloughed and unmatched workers who would accept a job offer if they were to receive one. Then (cid:26) (cid:90) (cid:27) (cid:88) n (s) = π (s˜,s)µU(s˜)+π (s˜,s)ζ dµF(z,w,s˜) t U t F t s˜ (cid:88) (cid:90) (cid:16) (cid:17) MF(z ,s) = π (s˜,s)ζ I W (z ,w∗ ,s) ≥ Fˆ(z,w,s˜) dµF(z,w,s˜) t 0 F t 0 0t t t s˜ MU(z ,s) = (cid:88) π (s˜,s)I(cid:0) W (z ,w∗ ,s(cid:48)) ≥ U (s˜) (cid:1) µU(s˜) t 0 U t+1 0 0t t t s˜ where we set w∗ as a function of z . 0t 0 15

The free entry condition for job creation is given as (cid:20)(cid:90) (cid:21) κ = q (s) max{J (z ,w∗ ,s),0}p (z ,s)dG(z ,s) (20) t t 0 0t t 0 0 z0 where p (z ,s) = MF t (z0,s)+MU t (z0,s) is the probability that the worker accepts an offer. Equation t 0 nt(s) (20) equates the cost of creating a vacancy to the expected profit of finding a worker. Note that, upon the realization of the initial productivity z , the firm can decide not to create the position. 0 3.7 Equilibrium We define a recursive equilibrium in this model as (i) a set of value functions: J, V, W, F, and U; (ii) separation, idle, and recall decisions for the firm: ea, d, ei, and r; (iii) a quitting decision for the workers: ηa, and ηi; and (iv) a distribution of workers across states and sectors µW, µF, and µU such that the firm’s and worker’s decisions are optimal and the free entry condition is satisfied. 4 Quantitative Analysis: Flexible versus Rigid Labor Markets For the quantitative analysis, we extend the model from the previous section by including a set of Gumbel shocks for firm and worker decisions. These decisions resemble those in discrete choice models, and the shocks help smooth the computational burden. We describe the full model with Gumbel shocks in the appendix and proceed to the calibration next. 4.1 Calibration and Model Assessment In this section, we assess the ability of the model to replicate common labor market features and to account for structural differences in labor markets across countries. For this reason, we provide two calibrations for the economy in steady state: one that aims at replicating the U.S. (flexible) labor market’s more prominent features and a second one for the euro-area’s (rigid) labor market. Next, we describe the common parameters and the labor market specific calibration for these two economies. 16

4.1.1 Common Parameters across Labor Markets The calibration is monthly. Common parameter choices across labor markets are summarized in Table1anddescribednext. Firm’sandworkersdiscountthefutureatamonthlyrateofβ = 0.991/3, consistentwitha4percentannualinterestrate. Weassumetherearetwosectorsthataresymmetric in steady state. There exists an exogenous separation probability for active matches of 1.4 percent at a monthly frequency in each sector. Moreover, furloughed and unemployed workers continue searching in the same sector with a monthly probability of π (s,s) = 0.75 and π (s,s) = 0.50, F U respectively in line with empirical findings (see, for instance, Visschers and Carrillo-Tudela (2021), supplemental appendix B). We set furloughed workers’ search efficiency to ψ = 0.75 relative to unemployment to account for the lower effort exerted by those furloughed relative to permanently unemployed in looking for new jobs. For wages, we set n = 8 and the forward-looking weights in the wage function Ω ∀j ∈ (0,n) to be 1/9. We set the firm’s bargaining power ω = 0.55, t+j which generates an elasticity of wages relative to a change in unemployment benefit b as reported in Mitman and Rabinovich (2015). We set the matching function elasticity η to be 1.50, in line with Schaal (2017) and Blanco and Navarro (2017) We assume match productivity z follows an AR(1) process with long-run productivity z¯, persistence ρz, and variance σz, as lnz = (1−ρz)z¯+ρzlnz +σz(cid:15) . (21) t t−1 t We follow Kehoe, Midrigan and Pastorino (2019) and set z¯= 2.7, ρz = 0.995, and σz = 0.065. We discretize the process for z into a Markov process with 90 points using Tauchen’s method. We calibrate the initial productivity value z as 0.65z¯. 0 4.1.2 Calibration: Parameterizing Two Distinct Labor Markets Weturnnexttodescribingthechoiceofparametersthatwillcharacterizetwoeconomieswithlabor market structural differences: the United States (which we refer to as a flexible economy) and the euro area (rigid economy). For each economy, there are two sets of parameters, some externally 17

Table 1: Calibration: Common External Parameters Parameter Description Value β Discount factor 0.991/3 δ Monthly exogenous separation rate: Active 0.014 η Matching function elasticity 1.50 ω Firm’s bargaining power 0.55 π Rate of sectoral persistence: Furloughed 75% F π Rate of sectoral persistence: Unemployed 50% U ψ Search efficiency idle 0.75 µ¯ Long-run match productivity 2.7 ρ Persistence match productivity 0.995 z σ Std. dev match productivity 0.065 z set, shown in Table 2, and the remaining internally calibrated by solving the model to target some distinct moments of each labor market, shown in Table 5. We set five external parameters to characterize each economy: the monthly workers’ job contact rate (f) and firms’ contact rate (q) in each sector, the probability of re-bargaining wages every period (λ), and the baseline labor market policies for UI (b) and WS (σ) in steady state.6 Table 2: Calibration: External Parameters - Flexible and Rigid Economies Parameter Description Flex value Rigid value f Worker’s job contact rate 45% 20% q Firm’s contact rate 70% 50% λ Probability of wage adjustment 1/9 1/13 b Unemployment insurance 0.40 0.65 σ Wage subsidy to firms 0% 0% The seven remaining parameters are set to match eight data moments. These parameters are all jointly estimated. In particular, we estimate the monthly separation rate from furlough into unemployment, δ , as well as the Gumbel shocks received by firms when making their ac- F tive/idle/separation decisions ρ and ρ ; active and furloughed workers’ quitting decisions J,V M,0 6Giventhevaluesforf andq,weobtainavalueformatchingefficiencyψandvacancycostκineachlabormarket. We estimate ψ to be 0.92 and 0.58, and κ to be 5.31 and 4.75 in the flexible and rigid markets, respectively. 18

ρ and ρ ; and furloughed and unemployed workers decisions to accept new jobs ρ and W,U F,U H,W0 ρ , respectively. In terms of data moments, we present the full set of moments and associated U,W0 values in Table 3 and briefly describe them next. We target the average unemployment rate for each economy (5.8 percent for the United States and 9.5 percent for the euro area) as well as the stock of workers in permanent unemployment and those in temporary layoffs.7 We also target transitions in and out of furlough, and, particularly for the United States we target the reported transitions in Gertler et al. (2021). For the last two moments we target the monthly transition rates from unemployment to employment, a standard value in the literature for the United States (Shimer (2012) and Gertler et al. (2021)), and we take the mid-range of the estimates presented by Balleer et al. (2016) and Hobijn and S¸ahin (2009) for the euro area. Finally, we target a pure recall rate from furlough of 76 percent in both economies, which is in the mid-range of the non-imputed and imputed values reported by Fujita and Moscarini (2017) for temporary layoff workers (we use recall rates excluding permanent separators, as, in our model, these workers do not have a recall option). The estimated parameters are presented in Table 5 in the appendix. 4.1.3 Model Assessment: Flexible Labor Market We next assess the predictions of the calibrated flexible labor market model in steady state. The resultsarepresentedinTable3. ThecalibratedmodelprovidesagoodfitfortheU.S.labormarket. Intermsoftargetedmoments,themodelreplicatesthetotalunemploymentrateanddecomposition betweenpermanentlyunemployedandfurloughedworkers. Wefindamonthlytransitionprobability fromfurloughtoemploymentof60.1percent, slightlyhigherthaninthedata, butwedoagoodjob in matching that, among furloughed workers returning to active employment, 78.5 percent of those transitions are driven by recalls. This result implies that, given the job-contact rate and search effectiveness, actual job-to-job transitions account for only 21.5 percent of furlough transitions to employment. We find a transition probability from unemployment to employment of 45 percent; hence, there are virtually no rejections of employment offers from unemployed workers in steady 7These moments are calculated from the Current Population Survey (CPS) averages between 1990 and 2019 for the United States and from Eurostat averages during the 1998-2019 period for the euro area, and pulled via Haver Analytics. 19

state, as all workers start with the same initial productivity z and wage w . The model also 0 0 successfully matches the data in moments that were not originally targeted. In particular, the rate of monthly total transitions in each sector from employment to unemployment is 2.3 percent, in line with Kehoe et al. (2019) using CPS data. Given our calibrated exogenous separation rate, the monthly rate for endogenous separations is 0.9 percent. We obtain a replacement rate of UI relative to newly employed workers of about 35 percent (Shimer, 2005), as is regularly assumed for the United States, and the profit share for the newly hired, w /π, accounts for about 51 percent of 0 the profit of the firm. Table 3: Model Assessment: Flexible and Rigid Economies Targeted Moments Moment Description Flex data Flex model Rigid data Rigid model U +I Total unemployment rate 5.84% 5.82% 9.52% 9.52% U Permanent unemployment rate 5.09% 5.11% 9.47% 9.48% I Temporary unemployment rate 0.75% 0.71% 0.05% 0.04% U −E Job acceptance rate 30.00% 45.00% 20.00% 20.00% F −E Furlough-to-employment rate 48.10% 60.10% 10.00% 15.13% F −U Furlough-to-unemployment rate 20.70% 22.78% 80.00% 74.70% F −F Furlough-to-furlough rate 31.20% 17.12% 10.00% 10.17% Recall Recall rate from furlough 75.70% 78.48% 75.70% 57.10% 4.1.4 Calibration: Rigid Labor Market We next describe the calibration and model assessment of a more rigid labor market in terms of policiesandemploymentprotectionrelativetotheUnitedStates. Wetargettheeuro-areaeconomy for this exercise. As in the previous economy, we have two sets of parameters: one is set externally tocommonvaluesintheliteratureanddata,andweestimatetheothersetinternallytomatchsome data moments. The five externally set parameters are displayed in the right column of Table 2. The monthly job contact rates for workers and firms are set to 20% and 50% respectively, implying longer unemployment episodes in European economies relative to the United States, and in line with empirical findings by Hobijn and S¸ahin (2009). We assume the wage duration is also longer– meaning higher rigidity–and set λ = 1/13. This assumption is in line with the evidence presented 20

by Lamo and Smets (2010), that documents an average duration of wages of 15 months. In terms of policies, UI is more generous, so we set b = 0.65, and we keep assuming that there is no subsidy in steady state. The seven remaining parameters are set to match the same data objects as in the U.S. calibration, with some of them taking different values compared to the United States. In this case, we target an average unemployment rate that matches the average euro-area unemployment rate of 9.52 percent during the 1998–2019 period, and we put virtually all the unemployed workers in permanent unemployment (9.47 percent) to match the infrequent use of temporary layoffs in the euro area, where employment protection usually requires consensus between firms and workers’ representatives for these types of separations. We target monthly transition rates from furlough to employment of 10 percent and from furlough to unemployment of 80 percent. This calibration increases employment rigidity by not allowing furloughs to be a realistic option firms can use to manage their workforce in the euro area compared to the United States. Finally, we target an unemployment-to-employment monthly flow rate of 20 percent, in the mid-range of the estimates presented by Balleer et al. (2016) and Hobijn and S¸ahin (2009), and the same recall share assumed in the U.S. exercise. The estimated parameters for the rigid calibration are presented in the last two columns of Table 5 in the appendix. 4.1.5 Model Assessment: Rigid Labor Market The model predictions for the rigid economy are presented in the last two columns of Table 3. Once again, the model does a good job of replicating the main labor market outcomes from the euro-area economy. Specifically, we match the unemployment rate very well, and there is an almost negligible fraction of workers in temporary unemployment. We also assess the performance of the model relative to non-targeted moments. The sectoral monthly separation rate is 2.1 percent, which is very similar to the U.S. estimate and in line with the findings from Hobijn and S¸ahin (2009) that most of the unemployment differences between these economies arise from differences in job-finding rates, not separation rates. It is important to highlight that the replacement rate of UI relative to newly employed workers is higher compared with the flexible economy, resulting in 21

wages representing a larger fraction of a firm’s output and reduced profit margins for firms. 5 Model Simulation: A Crisis Experiment We analyze a short-lived recession that results in an abrupt decrease in output and a rapid increase in unemployment. We aim to recreate the initial shock to the services sector—as well as the initial policy response—observed in the first half of 2020, when public health restrictions aimed at containing the spread of the COVID-19 virus led to a rapid closure of high-contact services. That is, we do not target the whole COVID-19 recession, as many other factors and subsequent closures played a role in the recovery of the economy, but just the initial sectoral shock. Thus, we assume that sectoral productivity x in only one of the sectors falls by ∆ and returns at rate ρ: x x = µ (1−∆ ), and x = (1−ρ)µ +ρx ∀t ≥ 2. The other sector remains unaffected. In 1 x x t x t−1 the flexible labor market, we set ∆ = 0.225 and ρ = 0.75, which generates a 9 percentage point x unemployment increase, as observed at the start of the COVID-19 recession in the United States. The flexible labor market calibration includes an extension of the UI policy for about four months that more than doubles the replacement rate for new workers and then returns to the standard amount. This type of UI extension is similar to the policy adopted in the United States at the start of the COVID-19 recession, and the cost of the policy amounts to 1 percent of GDP.8 In the rigid labor market, we set ∆ = 0.37 and ρ = 0.75, in order to target an unemployment increase x of about 0.9 percent. The calibration of the rigid labor market economy includes WS policy for 12 months, amounting also to a cost of 1 percent of GDP. 9 The calibration of the rigid economy aims at mimicking the dynamics of a euro-like labor market and policies adopted at the beginning 8Our calibration intends to mimic the introduction of the extension, which took place in mid-April and lasted through the end of July 2020. For that reason, we give workers only half of the more generous extension during the first month and the complete, twice-as-large replacement rate in the next three months. In the figures and the remainder of the paper, we denote this policy as UI extension, but we acknowledge that this policy is a temporary increaseinUI.Thereportedcostoftheextendedpolicy(seeGanongetal.(2021))isabout1percentofannualGDP. 9For comparability across exercises, we also use 1 percent as the relevant policy cost. Moreover, this is in line with expenditures during the first 12 months after the COVID-19 shock in countries such as Spain (see ”https://www.lamoncloa.gob.es/serviciosdeprensa/notasprensa/trabajo14/Paginas/2021/050521paroregistrado.aspx”) and Germany, as reported in ”https://www.economist.com/business/2021/06/26/germanfirms-are-conflicted-about-the-kurzarbeit-furlough-scheme”. This leads to an implied subsidy of 4 percent to the wage bill for all active firms. 22

of the COVID-19 recession.10 In both the flexible and rigid labor market, we analyze the predictions of the model under three policy alternatives: (a) our benchmark calibration with baseline UI, (b) the UI extension, and (c) WS policy only to the affected sector (sector 2) that lasts for 12 months. 5.1 Policy Alternatives in a Flexible Labor Market As can be seen in Figure 3, a negative productivity shock results in a strong contraction in output accompanied by a spike in unemployment, increasing both permanent and temporary layoffs. Importantly, the UI extension (light blue line) leads to the strongest contraction on impact but to the fastest recovery afterwards among the three policy alternatives considered. The UI extensions leads to an initial strong economic contraction because it leads to higher wages, as the top-right panel of Figure 3 shows. Higher wages increase the measure of firms who decide to separate from workers, either permanently or temporarily (furloughed). Additionally, in the presence of rigid wages, many employed workers quit to find jobs with higher wages. Quits are larger in the affected sector but also occur in the unaffected sector. The job-finding rate decreases sharply in the affected sector, reflecting its lower productivity. Interestingly, the job-finding rate also declines in the unaffected sector, though much less sharply. The reason is that, after the shock, a larger share of unemployed workers are furloughed, and they reject job offers in hopes of being recalled. TheUIextensionleadstoasmallerdeclineinthejob-findingrate. TheUIextensionfront-loads quits initially, but later decreases them below the steady state as the economy recovers. As such, firms’ expected value of a new job is higher, and thus the number of job posting is higher than in the benchmark policy. At the same time, the average match productivity increases (in line with the cleansing effect), which further helps to speed up the recovery, even as new matches are formed. A WS policy only to the affected sector11 reduces temporary layoffs and prevents permanent job destruction (upper-middle panel of Figure 3), resulting in a smaller increase in unemployment. 10In the appendix, we present an additional quantitative example of a prolonged recession with a smaller initial shock, which is more similar to the 2008–09 crisis. 11AWScost-neutralpolicycomparedtotheUIpolicyintheflexibleeconomyisgivenbya4.5percentsubsidyfor all active firms. 23

Figure 3: Flexible Economy: Policy Alternatives in the Short-Lived Recession Sector 1 refers to the unaffected sector and sector 2 the sector affected by the shock. The WS policy leads to a smaller contraction in output, but at the cost of lower labor productivity (lower-middle panel of Figure 3). As low-wage, low-productivity jobs are profitable under the subsidy, there is less of a cleansing effect associated with the recession, and both wages and match productivity fare worse than both the UI and benchmark policies. Overall, the differences between benchmarkandWSpoliciesaresmall,asinthiseconomyfirmscanalwaysrecallfurloughedworkers as the shock wanes. To sum up, the UI extension and WS policies produce a tradeoff between higher/lower unemployment and lower/higher productivity. At the same time, as we show in more detail in the following, the UI policy benefits consumers at the expense of firms, while the WS policy protects firms’ profits. 24

5.2 Policy Alternatives in a Rigid Labor Market Figure 4: Rigid Economy: Policy Alternatives in the Short-Lived Recession Sector 1 refers to the unaffected sector and sector 2 the sector affected by the shock. Figure 4 shows the rigid economy response. While the output contraction is similar to that in the flexible economy, unemployment increases less in the rigid economy but takes about the same time to return to its steady-state level. In this economy with low job-finding rates, small increases in unemployment can have persistent effects (Duval and Vogel, 2008). Recall that, in the rigid economy, unemployment is mainly composed of permanent separators, since temporary layoffs and subsequent recall are not possible. The WS policy (red line) produces a contraction in output similar to the benchmark policy but succeeds in stemming persistent increases in unemployment. Under this policy, unemployment increases for only a couple of quarters relative to steady state, but it overshoots and temporarily declines below its long-run value. The overshoot occurs because, despite the productivity shock, 25

WS policy increases firms’ profits, thus leading to more vacancy postings and higher job-finding rates. Note that in this economy, where furloughs are not available, WS alleviate firm’s wage bill while keeping workers employed and increasing firms’ flexibility. Compared to the flexible economy, the UI policy results are less attractive in the rigid economy, asitleadstoastrongeroutputcontractionbutdoesnotresultinafasterrecovery.12. Unemployment in particular takes longer to recover because of a lower job-finding rate and the absence of a recall option. As in the previous example, the unemployment–productivity tradeoff still exists under these policies. However, firms’ losses from permanent separations in the rigid economy will become larger and more persistent. For this reason, WS policy seems ex-ante a preferred option, as it protects firms’ profits, which we discuss in more detail below. 5.2.1 Labor Market Policies and the CRW Reallocation Index: Model Predictions We apply the CRW reallocation index to our model simulated data for the flexible and rigid economies. As Figure 5 shows, our crisis experiment leads to higher reallocation in both economies, consistent with our empirical findings. Moreover, the model predicts lower reallocation in the rigid economy compared with the flexible economy, also in line with the evidence presented. As discussed earlier, UI policy and WS policy have opposite effects on unemployment, with the former encouraging quits and separations and the latter preventing job destruction. Consistently, UIpolicyleadstolargerinitialreallocation,whileWSpolicydoestheopposite. Yet,thereallocation increase using UI policies would be smaller in the rigid economy than in the flexible one, showing that both policies and labor market features explain the difference in reallocation found empirically between the United States and the euro area. 5.2.2 Welfare Quantification We quantify the welfare implications of UI and WS policies. We define total welfare as a sum of the present discounted value of consumption (PDVC) for the measure of workers (employed and 12A UI cost-neutral policy compared to the WS policy in the rigid economy is given by a 21 percent increase in the replacement rate during the first month, followed by 42 percent increase in the three remaining months of UI extension. 26

Figure 5: CRW Index in the Short-Lived Recession: Model unemployed) and the present discounted value of profits (PDVP) for the measure of firms minus the discounted cost of policy (PD cost).13 We present our results for both the flexible and rigid economy in Table 4. Table 4: Welfare Comparison: Percentage Loss Relative to Steady State Benchmark UI WS A) PDVC - flexible −0.25% −0.05% −0.22% B) PDVP - flexible −0.55% −0.57% −0.40% C) PD Cost - flexible 0.05% 0.14% 0.17% Total = A+B-C −0.85% −0.77% −0.79% A) PDVC - rigid −0.13% −0.07% −0.12% B) PDVP - rigid −0.58% −0.67% −0.44% C) PD Cost - rigid 0.01% 0.14% 0.13% Total = A+B-C −0.73% −0.87% −0.69% Note: Columns may not add up due to rounding. We find that for the flexible economy, UI and WS produce similar total welfare gains relative to the benchmark policy. Yet, the decomposition of gains into consumption and firms’ profits 13Wecalculatewelfarefor120periodsfollowingtheshockoncetheeconomyhasarguablyreturnedtosteadystate. 27

differs significantly. WS improves mainly firms’ profits and to a lesser extent consumption because PDVP is minimized when jobs are protected (under WS policy) and match-specific human capital is preserved. On the contrary, UI policy improves consumption at the expense of lower profits. UI policy, by construction, insures consumption and increases wages in both sectors, thus delivering the highest consumption gains. WS policy, despite protecting jobs, maintains low-productivity matches with lower wages. Although the consumption loss relative to the benchmark policy is smaller, consumers are worse off under the WS policy than under the UI policy. Welfare tradeoffs are similar for the rigid economy, but their quantification changes. The UI policy,whileimprovingconsumerwelfare,generatesalargedeclineinfirms’PDVPsuchthatoverall welfareworsensrelativetothebenchmarkpolicy. ThelargedeclineofPDVPunderUIpolicyinthe rigid economy is due to lower job-finding rates and a higher replacement rate. In this scenario, WS policy remains the only welfare-improving policy option despite being less preferred by consumers compared to UI policy. WS prevents the persistent losses from job destruction and thus delivers the smallest total welfare loss. These welfare results seem to rationalize why the United States typically relies on UI policies, whereas the euro area relies more on WS policies. Next, we discuss how the benefits of UI policy may vary with the persistence of the recession. 6 Discussion: UI Policy Design and Persistence of Recession OurpreviousanalysisshowsthatanincreaseinUIbenefitspromotesreallocationatthestartofthe recession. Thus, a UI policy could be particularly useful in a long-lived recession, when reallocation to the unaffected sector is more desired. However, as we discussed, a UI policy affects reservation wages and firms’ profits and thus generates distortions in job creation. In this section, we discuss in more detail the effects of UI and WS by inspecting the role of shock persistence and policy design in the economy. We focus on the flexible economy, where we found UI and WS policies to be welfare improving. We feed the economy the same initial shock ∆ as before but consider different persistence levels: x ρ = [0.75,0.85,0.98]. We first analyze three different durations of the UI policy: (1) a front-loaded 28

one-month UI policy such that b = 3.75×b, (2) a four-month policy such that b = 1.9×b, new new and (3) an eight-month policy such that b = 1.4 × b. The three policy durations generate a new similar fiscal cost. We compare these policies with a twelve-month WS under the three levels of persistence. Figure 6 shows the welfare values of each UI and the WS policy for a different recession persistence ρ. We present the three welfare measures discussed before: consumers (PDVC), firms (PDVP), and total welfare by netting out the policy cost (PDVC+PDVP-Cost). The welfare values are presented relative to the benchmark so that a positive number means it is preferred to benchmark. Figure 6: Welfare Differences between UI and Benchmark Policy Total Welfare Discounted Value of Profits (PDVP) Discounted Value of Consumption (PDVC) Percentage point deviation from SS Percentage point deviation from SS Percentage point deviation from SS 0.14 0.12 0.24 0.06 0.18 0.07 0.00 0.12 −0.06 0.00 UI−1 month UI−4 months −0.12 0.06 UI−8 months WS−12 months r=0.75 r=0.85 r=0.98 −0.07 r=0.75 r=0.85 r=0.98 −0.18 r=0.75 r=0.85 r=0.98 0.00 Note: All values are expressed as percentage point difference in welfare under the UI policy relative to the benchmark policy. Welfare under each policy is calculated as percent deviations from steady state. Front-loading UI extensions (one-month UI policy; red line, left panel) is the safest option: It helps consumers while not depressing firms’ profits, regardless of the recession persistence. At the same time, such a policy does not produce significant welfare gains relative to the benchmark policy, as consumers’ gains are almost offset by the cost of the policy (not shown). Increasing UI duration can improve total welfare when the recession persistence is shorter, although the higher consumer welfare gains are offset by larger losses for firms. Yet, in very persistent recessions, frontloading becomes the best option, as a larger UI duration hurts firms’ profits and diminishes gains for workers. This finding is in line with Mitman and Rabinovich (2015), who study the optimal UI policy design and find it is optimal to front-load UI extensions in long-lived recession in order to minimize job creation distortions. 29

Contrary to UI, we find that welfare gains under WS do not change much with the persistence of the recession (dashed-line) and with the design of the policy (figures available upon request). WS preserve firms’ profits relative to the benchmark policy and do not change the outside option of workers, thus leading to fewer distortions in vacancy posting irrespective the length of the recession.14 TherelationbetweenUIdurationandreallocationisalsonotstraightforward. WhileWSalways reduce reallocation relative to the benchmark scenario, a larger UI duration does not necessarily lead to more reallocation, as Figure 7 shows. The one-month UI duration actually leads to higher reallocation for most recession persistence levels, except for the very persistent one. That is, the distortion effect of a more generous UI policy could lead to lower reallocation. Moreover, higher reallocation does not necessarily mean higher welfare: Higher reallocation occurs with longer UI duration in a very persistent recession, while welfare is larger under the one-month UI duration. Figure 7: Excess Reallocation under UI Relative to Benchmark Policy 7 Conclusions and Agenda In this paper, we developed a multi-sector search and matching model of the labor market subject to sector-specific shocks and wage rigidity. We calibrated the model to match key labor market 14Consistently, front-loading WS does not necessarily improve welfare under more persistent recessions, as withdrawingfirmsupportearlyontherecessioncanleadtojobdestructionwhensectorproductivityremainslow. While we have not analyzed subsidies of a duration longer than a year, prolonged subsidizing of industries could lead to labor misallocation, especially when the decline in productivity is persistent or even permanent. 30

features of the United States (flexible economy), and the euro area (rigid economy). We used the model to evaluate UI and WS policies, the two labor market policies most commonly used in recent years. We focused on sector-specific shocks to account broadly for the nature of recent recessions, such as the COVID-19 recession. We showed that, in such recessions, UI policies are preferred in a flexible economy, whereas WS policies are preferred in a rigid economy. Thus, our results rationalize the difference in policies usually implemented in the United States versus the euro area. We argued that UI extension can lead to higher sectoral reallocation, which may be desirable in the presence of sector-specific shocks. However, a UI extension can also distort job creation, as the larger benefits increase wages and thus decrease firms’ profits. Moreover, we argued that higher reallocation does not necessarily imply higher welfare, as high reallocation may occur because of a sector’s job-finding rate being particularly low. Overall, UI extension trades welfare gains for workers with profit losses for firms. We found that front-loading UI extensions may help make this trade-off more favorable when designing policies. We focused on simple labor market policies that resemble those implemented by several countries. Going forward, we think there are several paths in which our analysis could be enriched. First, one could extend the model to include: within-sector firm-heterogeneity, worker-specific human capital, and sector-specific business cycle shocks. Second, one could compute the optimal mix of UI and WS policies in this extended sector model. Third, one could derive what optimal reallocation should be in the presence of sector-specific shocks. We think of the optimal design of labor market policies in such a rich model as a top priority for future research. References Balleer, A., Gehrke, B., Lechthaler, W. and Merkl, C. (2016). Does short-time work save jobs? a business cycle analysis. European Economic Review, 84, 99–122. Birinci, S., Karahan, F., Mercan, Y. and See, K. (2021). Labor market policies during an epidemic. Journal of Public Economics, 194. Blanco, A. and Navarro, G. (2017). The unemployment accelerator. mimeo. 31

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A Data Description and Evidence on Reallocation Our main data sources are pulled from Haver Analytics and described next. For the United States, we use the Bureau of Labor Statistics for aggregate and industry employment and the Current Population Survey (CPS) for the unemployment rate. We construct productivity as output per employee using real GDP from the National Accounts. Then we index this series such that 2019:Q4 = 100. The time span for these variables is 1990:Q3–2022:Q2. For the euro area, the main data source is Eurostat, as they aggregate national country data for employment, unemployment, and national accounts. Eurostat provides a measure of real output per employee, indexed such that 2015 = 100, that we use in the empirical section. The time span covered is 1995:Q3–2022:Q2. For estimating the SVAR, productivity enters the system in log-differences, unemployment rate in differences, and the CRW reallocation index in levels. Figure 8: Reallocation Index: Euro Area and United States (NAICS Industry Classification) 35

Figure9: ReallocationIndex: EuroAreaandUnitedStates(SICIndustryClassification, quarterly) B Model: Quantitative Extension Let J (z,w,s) be the maximal attainable value for an active firm in a match with productivity z, t wages w, and sector s at time t. Analogously define V (z,w,s) as the value of an idle match. We t assume a Gumbel shock for each value, respectively denoted (cid:15)J and (cid:15)V. Let M (z,w,s) be the t expected value over the maximum of J (z,w,s) and V (z,w,s) integrated over the Gumbel shocks: t t M (z,w,s) = E(cid:2) max (cid:8) J (z,w,s)+(cid:15)J,V (z,w,s)+(cid:15)V(cid:9)(cid:3) . (22) t t t The value for an active firm is J (z,w,s) = Π+βE (cid:2)(cid:0) 1−ηa (z(cid:48),w(cid:48),s) (cid:1) max (cid:8) M (z(cid:48),w(cid:48),s)+(cid:15)M,0+(cid:15)0(cid:9) |z (cid:3) (23) t t t+1 t+1 Π = y (z,s)−(1−σ )w−c t t o    w w.p. λ w(cid:48) =   w∗ (z(cid:48),s) w.p. 1−λ t+1 where ηa(·) is the probability that a worker in an active match will quit. t 36

The value for an idle match is V (z,w,s) = −c +βE (cid:2)(cid:0) 1−fi (z(cid:48),w,s) (cid:1)(cid:0) 1−ηi (z(cid:48),w(cid:48),s) (cid:1) max (cid:8) M (z(cid:48),w(cid:48),s)+(cid:15)M,0+(cid:15)0(cid:9) |z (cid:3) t i t t+1 t+1 t+1 (24) where fi(·) is the probability that an idle/furloughed worker will find and accept another job offer t (more on this later). Note that the continuation value for an idle firm in equation (24) is the same as for an active firm, although the stochastic process for z may be different. fi(z,w,s) = (cid:88) π (s,s(cid:48))ζf (s(cid:48))E(cid:2)I(cid:8) Hi(z,w,s)+(cid:15)H < W (z ,w ,s(cid:48))+(cid:15)W(cid:9)(cid:3) (25) t F t t t 0 0 s(cid:48) where π (s,s(cid:48)) is the probability that an idle worker in sector s is able to search for a job in sector F s(cid:48), and ζ represents the search intensity relative to an unemployed worker. ζ = 1 if the worker searches with the same intensity as an unemployed worker; otherwise, ζ < 1, and it is bounded below by 0. Let W (z,w,s) be the maximal attainable value for an active worker in a match with t productivity z, wages w, and sector s at time t. Analogously define F (z,w,s) as the value of a t worker in an idle match. We assume a Gumbel shock for each value, respectively denoted (cid:15)W and (cid:15)F. Let U (s) be the value of being unemployed in sector s at time t. We also add a preference t shock (cid:15)U to unemployment. Let Ha(z,w,s) be the expected value to a worker of being active at the beginning of the period. t 37

Similarly define Hi(z,w,s) as the expected value of an idle worker. Then, t (cid:104) (cid:110) (cid:111)(cid:105) Ha(z,w,s) = E max Wˆ (z,w,s)+(cid:15)Wˆ ,U (s)+(cid:15)U (26) t t t Wˆ (z,w,s) = (1−ea(z,w,s))[(1−d (z,w,s))W (z,w,s)+d (z,w,s)F (z,w,s)] t t t t t t +ea(z,w,s)U (s) t t (cid:104) (cid:110) (cid:111)(cid:105) Hi(z,w,s) = E max Fˆ(z,w,s)+(cid:15)Fˆ ,U (s)+(cid:15)U (27) t t t Fˆ(z,w,s) = (cid:0) 1−ei(z,w,s) (cid:1) [r (z,w,s)W (z,w,s)+(1−r (z,w,s))F (z,w,s)] t t t t t t +ei(z,w,s)U (s) t t where Wˆ (z,w,s) and Fˆ(z,w,s) are the values of respectively active and furloughed workers after t t quit decisions have occurred and before the firm’s decisions have taken place. We define the value of working, being furloughed and being unemployed from the production and consumption stage using the following formulas. First, a worker with an active job receives wage w and the expected discounted value Ha(z,w,s) from starting next period attached to the t firm: W (z,w,s) = w+βE (cid:2) Ha (z(cid:48),w(cid:48),s)|z (cid:3) . (28) t t t+1 A furloughed worker receives unemployment benefit b and has an expected discounted value of continuation that depends on sectoral job-contact probability f (s) and sectoral switching probat bility π (s,s(cid:48)). If the furloughed worker does not find a firm, they start next period attached to F the firm as a furloughed worker Hi(z,w,s). If the worker contacts a firm, then they can decide t whether to remain attached to the current employer or accept the new offer and start next period attached to a new firm with productivity z and wage w : 0 0 (cid:34) (cid:40) (cid:88) F (z,w,s) = b+βE π (s,s(cid:48)) (1−ζf (s(cid:48)))Hi (z(cid:48),w,s) (29) t F t+1 t+1 s(cid:48) (cid:35) +ζf (s(cid:48))max (cid:8) Hi (z(cid:48),w,s)+(cid:15)H,W (z ,w ,s(cid:48))+(cid:15)W(cid:9) |z . t+1 t+1 t+1 0 0 38

Finally, anunemployedworkerreceivesunemploymentbenefitbandhasanexpecteddiscounted value of continuation that depends on sectoral job-contact probability f (s) and sectoral switching t probability π (s,s(cid:48)). If the unemployed worker finds a job, they can decide whether to accept it U or to reject it and continue being unemployed for an additional period. If they do not find a job, they remain unemployed and attached to their last sector of employment s. (cid:88) U (s) = b +β π (s,s(cid:48))× (30) t t U s(cid:48) × (cid:8) f (s(cid:48))E(cid:2) max (cid:8) W (z ,w ,s(cid:48))+(cid:15)W,U (s)+(cid:15)U(cid:9)(cid:3) + (cid:0) 1−f (s(cid:48)) (cid:1) U (s) (cid:9) t+1 t+1 0 0 t+1 t+1 t+1 C Model Simulation: Additional Results Table 5: Calibration: Internal Parameters Parameter Description Flex value Rigid value δ Monthly exogenous separation rate: furlough 0.061 0.987 F ρ Gumble shock firm: active/inactive 0.075 0.020 J,V ρ Gumble shock firm: remain open/close 0.066 0.071 M,0 ρ Gumble shock worker: remain employed/quit 0.078 0.017 W,U ρ Gumble shock worker: remain furloughed/quit 0.120 0.044 F,U ρ Gumble shock worker: remain employed/accept new job 0.073 0.027 H,W0 ρ Gumble shock worker: remain unemployed/accept new job 0.113 0.027 U,W0 C.1 Experiment 2: Long-Lived Recession C.1.1 Long-Lived Recession: UI Extension in a Flexible Labor Market Oursecondexperimentexploreshowthepersistenceoftheshockinteractswiththepolicies. Weset ∆ = 0.10 and ρ = 0.983 so the drop is much smaller but with a sluggish recovery. We compare the x response of the economy under a smaller increase in the replacement rate compared to the shortlivedrecessionbutforequalexpenditures(asitnowlastsfor12months)andabenchmarkeconomy with no additional policies. The cost of the policy still accounts for around 1 percent of annual GDP. We present the results in Figure 10. As in the short-lived recession, the UI policy continues 39

to increase unemployment and leads to a larger contraction in output, though it does not produce a faster recovery. Reallocation is rapid and persistent. A WS policy (shown in Figure 11) would continue to limit the increase in unemployment but limit reallocation when an industry experiences a long-lasting shock. The welfare analysis, presented in Table 6, confirms our analysis in section 6 that the UI extension generates significant profit losses that result in welfare loss compared with the benchmark policy. Figure 10: Benchmark and UI Policy Response in a Flexible Economy (Long-Lived recession) Note: Sector 1 refers to the unaffected sector, and sector 2 the sector affected by the shock. SS is steady state. C.1.2 Long-Lived Recession: WS in a Rigid Labor Market We now analyze the differences for a similar recession in a rigid labor market. We set ∆ = 0.125 x and ρ = 0.983, and in this case we compare the response of the economy under a 12-month WS policyintheaffectedsectorandthebenchmarkeconomywithnoadditionalpolicies. Thecostofthe 40

Figure 11: Flexible Economy: Counterfactual Policies in the Long-Lived Recession Note: Sector 1 refers to the unaffected sector, and sector 2 the sector affected by the shock. SS is steady state. policyaccountsstillforaroundof1percentofannualGDP.Figuresfortheseresultsarepresentedin Figure 12 and Figure 13. As in the short recession, the WS policy limits job destruction, leading to asmallercontractioninoutputandacontainedunemploymentrate. However,thelowerjob-finding ratemakestherecessionevenmorepersistentdespitethesmallerincreaseinunemploymentrelative to the flexible economy. Reallocation toward the unaffected sector is more sluggish relative to the benchmark policy. A counterfactual UI policy produces higher unemployment at the beginning but induces a faster recovery relative to benchmark. Overall, firms’ losses under the UI policy are higher, making the WS policy a preferred option. 41

Figure 12: Benchmark and WS Response in a Rigid Economy (Long-Lived Recession) Note: Sector 1 refers to the unaffected sector, and sector 2 the sector affected by the shock. SS is steady state. Table 6: Welfare Comparison: Percentage Loss Relative to Steady State Benchmark UI WS A) PDVC - flexible −0.91% −0.56% −0.89% B) PDVP - flexible −1.20% −1.48% −1.06% C) PD Cost - flexible 0.03% 0.15% 0.15% Total = A+B-C −2.14% −2.19% −2.10% A) PDVC - rigid −1.00% −0.81% −0.96% B) PDVP - rigid −1.30% −1.38% −1.14% C) PD Cost - rigid 0.14% 0.18% 0.24% Total = A+B-C −2.43% −2.37% −2.34% Note: Columns may not add up due to rounding. 42

Figure 13: Rigid economy: Counterfactual Policies in the Long-Lived Recession Note: Sector 1 refers to the unaffected sector, and sector 2 the sector affected by the shock. SS is steady state. Figure 14: CRW Index in the Long-Lived Recession: Model Predictions 43