Learning on the Job and the Cost of Business Cycles

econstor A Service of zbw Make Your Publications Visible. Leibniz-Informationszentrum Wirtschaft Leibniz Information Centre for Economics Walentin, Karl; Westermark, Andreas Working Paper Learning on the job and the cost of business cycles Sveriges Riksbank Working Paper Series, No. 353 Provided in Cooperation with: Central Bank of Sweden, Stockholm Suggested Citation: Walentin, Karl; Westermark, Andreas (2018) : Learning on the job and the cost of business cycles, Sveriges Riksbank Working Paper Series, No. 353, Sveriges Riksbank, Stockholm This Version is available at: http://hdl.handle.net/10419/189953 Standard-Nutzungsbedingungen: Terms of use: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Documents in EconStor may be saved and copied for your personal and scholarly purposes. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. www.econstor.eu If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. SVERIGES RIKSBANK WORKING PAPER SERIES 353 Learning on the Job and the Cost of Business Cycles Karl Walentin and Andreas Westermark March 2018 (Revised June 2018) WORKING PAPERS ARE OBTAINABLE FROM www.riksbank.se/en/research Sveriges Riksbank • SE-103 37 Stockholm Fax international: +46 8 21 05 31 Telephone international: +46 8 787 00 00 The Working Paper series presents reports on matters in the sphere of activities of the Riksbank that are considered to be of interest to a wider public. The papers are to be regarded as reports on ongoing studies and the authors will be pleased to receive comments. The opinions expressed in this article are the sole responsibility of the author(s) and should not be interpreted as reflecting the views of Sveriges Riksbank. Learning on the Job and the Cost of Business Cycles Karl Walentinyand Andreas Westermarkz Sveriges Rikbank Working Paper Series No. 353 June 2018 Abstract We show that business cycles reduce welfare through a decrease in the average level of employment in a labor market search model with learning on-the-job and skill loss during unemployment. A negative correlation between unemployment and vacancies implies, via the concavity of the matching function, that business cycles reduce the average number of new jobs and employment. Learning on-the-job implies that the decrease in employment reduces aggregate human capital. This, in turn, reduces the incentives to post vacancies, further decreasing employment and human capital. We quantify this mechanism and …nd large output and welfare costs of business cycles. Keywords: Search and matching, labor market, human capital, stabilization policy, skill loss. JEL classi…cation: E32, J64. We are deeply indebted to Axel Gottfries and Espen Moen as well as our discussants Marek Ignaszak, Tom Krebs and Oskari Vähämaa for detailed feedback on this paper. We are also grateful to Olivier Blanchard, Tobias Broer, Carlos Carillo-Tudela, Melvyn Coles, Shigeru Fujita, Jordi Galí, Christopher Huckfeldt, Gregor Jarosch, Philip Jung, Per Krusell, Lien Laureys, Jeremy Lise, Kurt Mitman, Fabien Postel-Vinay, Morten Ravn, Jean-Marc Robin, Richard Rogerson, Larry Summers, and conference and seminar participants at Bank of England, Barcelona GSE Summer Forum (SaM), Board of Governors, CEF (Bordeaux), Conference on Markets with Search Frictions, EEA (Lisbon), Essex Search and Matching Workshop, Georgetown University, Greater Stockholm Macro Group, Labor Markets and Macroeconomics Workshop in Nuremberg, National Bank of Poland, Nordic Data Meetings, Normac, NYU Alumni Conference, Royal Economic Society Annual Meeting (Bristol), Sciences Po, 22nd T2M conference, UCLS (advisory board meeting), Uppsala University and University of Cambridge for useful comments. We thank SNIC, the National Supercomputer Centre at Linköping University and the High Performance Computing Center North for computational resources. The opinions expressed in this article are the sole responsibility of the authors and should not be interpreted as re‡ecting the views of Sveriges Riksbank. y Research Division, Sveriges Riksbank, SE-103 37, Stockholm, Sweden. e-mail: karl.walentin@riksbank.se. z Research Division, Sveriges Riksbank, SE-103 37, Stockholm, Sweden. e-mail: andreas.westermark@riksbank.se. 1 1 Introduction A major question in macroeconomics is how large the welfare costs of business cycles are. Since Lucas (1987), it has been well established that the cost of aggregate consumption ‡uctuations is negligible. Business cycles can induce welfare costs in other ways though, e.g., through their e¤ect on the crosssectional distribution of consumption (Imrohoro¼ glu, 1989, and many others). Furthermore, business cycles may a¤ect welfare negatively by reducing the average level of output, a view that has been argued by DeLong and Summers (1989), Hassan and Mertens (2017) and Summers (2015). Another strand of the literature highlights the e¤ect of human capital dynamics on macroeconomic ‡uctuations, see e.g., Kehoe, Midrigan and Pastorino (2015) and Krebs and Sche¤el (2017). Our paper adds to this literature by presenting a new mechanism for how business cycles reduce the level of output. We show that business cycles substantially reduce the level of employment, output and welfare in a labor market search model with human capital dynamics. The key mechanism of the paper is as follows: It is well established that the Beveridge correlation is negative, i.e. that vacancies and unemployment are negatively correlated in the data (see e.g., Fujita and Ramey, 2012). Via the matching function, this implies that business cycles tend to reduce the average number of new jobs and hence employment. At an intuitive level, this happens because vacancies and therefore job …nding rates in general are high when unemployment is low, thereby yielding fewer new jobs than in the absence of business cycles.1;2 Then, since learning on-the-job and skill loss during unemployment implies that average human capital is increasing in employment, it follows that aggregate volatility reduces human capital. This, in turn, reduces the incentives to post vacancies, further reducing employment and so on in a vicious circle. This ampli…cation mechanism for how aggregate volatility 1 In a simple search and matching model with a standard Cobb-Douglas matching function, the number of new jobs is given by 1 ! vt ut : mt = ft ut = ut where f denotes the job …nding rate and ! 2 (0; 1) is the matching function elasticity with respect to unemployment. Clearly, the number of new jobs is a nonlinear and concave function of vacancies (v) and unemployment (u), indicating that volatility matters for the average number of new jobs. Let bars denote variables in absence of aggregate volatility and “E” denote the unconditional expectation in an economy with aggregate volatility. Using the employment ‡ow equation 1 ut = (1 ) (1 ut 1 ) + mt and letting denote the exogenous separation rate, we can derive an expression for the change in the number of new jobs induced by aggregate volatility: Em m +f (1 !) f cov (v; u) v f var (u) + Ef u f Eu where we have used the …rst-order approximation of cov (f; u) = (1 !) f =v cov (v; u) f =u var (u) . As can be seen from the expression above, the number of new jobs and hence employment is lower under aggregate volatility if the Beveridge correlation is negative (i.e. cov (v; u) < 0) and Ef f 0. This result is related to Jung and Kuester (2011) that states conditions on cov (f; u) and Ef f for when aggregate volatility implies a reduction of employment. 2 More generally, any convex cost (or concave bene…t or production function) in any cyclical variable tends to induce a negative relationship between aggregate volatility and average consumption or employment. Prominent examples are convex capital adjustment costs and convex vacancy posting costs, both of which are commonly assumed in the business cycle literature. 2 Figure 1: Illustration of main mechanism - how aggregate volatility reduces employment, human capital and thereby output. reduces employment, human capital and thereby output is illustrated graphically in Figure 1. The size of the cost of business cycles generated by this mechanism is accordingly largely determined by how sensitive the human capital distribution is to changes in employment and how sensitive job creation is to changes in the human capital distribution. Since our mechanism works through the average level of consumption, it is fundamentally di¤erent from most of the cost of business cycles literature, which analyses the e¤ects of business cycles on welfare through (aggregate or idiosyncratic) consumption volatility. Our ampli…cation mechanism also extends beyond the cost of business cycles. For example, the e¤ect of a change in taxation or unemployment bene…ts that a¤ects average employment will be ampli…ed by the human capital mechanism that we have outlined. We use a search and matching framework with general human capital dynamics (learning on-thejob and skill loss during unemployment) to model the relationship between business cycles and the average level of output. As argued above, an important determinant of the size of the cost of business cycles is how sensitive job creation is to changes in the human capital distribution of both unemployed and employed workers. Thus, we allow for on-the-job search to capture the e¤ect of employed workers’ human capital on job creation. In addition, to allow for a ‡exible bargaining framework in a context with on-the-job search, we use the bargaining protocol from Cahuc, Postel-Vinay and Robin (2006), henceforth CPVR. This framework implies that workers get the value of their outside option plus a 3 share of the value of the match above the outside option. We allow for positive bargaining power of workers since bargaining power tend to be important for welfare in search and matching models. We are not aware of any previous model that uses the bargaining framework of CPVR in a setting with aggregate uncertainty using global solution methods. In this paper, we propose and implement an algorithm for solving models where workers with positive bargaining power that can search onthe-job meet …rms with di¤erent levels of productivity. Thus, the paper also makes a methodological contribution. In our mind, our solution algorithm is useful for future research where heterogeneity in the labor market interacts with the business cycle. The main purpose of our exercise is to provide a credible quanti…cation of the cost of business cycles through the mechanism we have sketched above. One key determinant of this cost is the speed of human capital accumulation when employed relative to the loss during unemployment. We estimate the human capital gains when employed by matching the empirical “return to experience” (wage pro…le of employed workers) reported by Buchinsky et al. (2010). The model is calibrated by matching the return to experience and other relevant moments, including volatility of GDP and unemployment, standard worker ‡ow moments and the degree of wage dispersion. We then compute the cost of business cycles by comparing the equilibrium for our full model to the equilibrium from the same model, but without aggregate volatility. We …nd that business cycles reduce steady state employment, GDP and welfare by substantial amounts. In particular, eliminating aggregate volatility increases welfare (GDP) by 0:52-1:49 percent (1:45 percent), depending on the interpretation of the ‡ow value of unemployment. These are fairly large e¤ects. Accounting for the transition dynamics, the welfare gains of eliminating business cycles are smaller, 0:20-1:09 percent. Human capital dynamics are pivotal for the results - if we disable them in our model, the implied employment, GDP and welfare losses from business cycles are negligible. Note that, since we assume risk neutral agents and hence abstract from, e.g., the direct welfare costs of consumption volatility, we do not capture the full welfare cost of business cycles and our results can accordingly be interpreted as a lower bound for these costs. There is indicative empirical support for the relationship between aggregate volatility, unemployment and output implied by our model. Hairault et al. (2010) uses data for 20 OECD countries for the period 1982-2003 and …nds signi…cant positive e¤ects of TFP volatility on average unemployment. There is also ample evidence of a signi…cant negative relationship between volatility of output and the average growth rate of output, see e.g., Ramey and Ramey (1995) and Luo et al. (2016). Direct evidence of human capital dynamics, in the form of e¤ects on measurable skills, is documented by Edin and Gustavsson (2008). They …nd sizeable skill loss e¤ects of unemployment. Additional indirect evidence is provided by Schmieder, von Wachter and Bender (2016). They estimate a substantial 4 casual e¤ect on the re-employment wage of an additional month of unemployment, also indicating considerable loss of human capital. There is also evidence that local labor market conditions a¤ect future “employability”of workers. Yagan (2017) establishes a strong link between local shocks to employment growth during the Great Recession, 2007-2009, and the 2015 employment rates of workers exposed to these shocks and argues that this link is due to depreciation of general human capital during non-employment spells. There are a number of papers analyzing related issues in a search and matching labor-market setting. Dupraz, Nakamura and Steinsson (2017) use a model with downward nominal wage rigidities to analyze the e¤ects of varying the in‡ation target on unemployment, output and welfare in a business cycle setting. The e¤ects of business cycles on average unemployment and output can be large if the in‡ation target is low, due to the inability of real wages to fall and thereby clear the market in response to contractionary shocks. Den Haan and Sedlacek (2014) quantify the cost of business cycles in a setting where an agency problem generates ine¢ cient job separations in downturns, thereby reducing average employment and GDP. Our framework does not include any such agency problem and is bilaterally e¢ cient. Jung and Kuester (2011) quantify the e¤ects on employment and welfare of the negative correlation between the job …nding rate and the unemployment rate. They do so in a simpler setting than ours, using a solution method of local second-order approximations, with wages assumed to be independent of labor market tightness.3 This issue is also studied by Hairault et al. (2010). Both Jung and Kuester (2011) and Hairault et al. (2010) …nd substantially smaller e¤ects on GDP and welfare of business cycles than our results indicate. Furthermore, our model also shares mechanisms with a number of papers that analyze earnings losses from job displacement (Burdett, Carrillo-Tudela and Coles, 2015, Huckfeldt, 2016, Jarosch, 2015, Jung and Kuhn, 2018, and Krolikowski, 2017). Finally, Laureys (2014) analyzes the e¤ects of skill loss in a business cycle setting. The paper is outlined as follows. Section 2 presents the model, Section 3 documents the calibration and Section 4 provides the quantitative results. Finally, Section 5 concludes. 2 Model We set up a business cycle model with a search and matching labor market and human capital dynamics. We allow for on-the-job search to capture the direct e¤ect of employed workers’ human capital on vacancy postings. The basic building blocks of our model are similar to Lise and Robin 3 In an extension they allow for learning on-the-job, but assume a weaker dependence of human capital on employment than we do. Furthermore, Jung and Kuester do not describe our main mechanism, the vicious circle laid out in Figure 1. 5 (2017), henceforth LR, except for the wage bargaining where we follow CPVR.4 This wage setting framework implies that workers get the value of their outside option plus a share , re‡ecting their bargaining strength, of the value of the match above the outside option. When a worker is hired out of unemployment the outside option is the value of unemployment. If instead an employed worker receives a poaching o¤er from another …rm, the outside option is the value of the second-best match. In terms of human capital dynamics, the model is in the tradition of Pissarides (1992) and Ljungqvist and Sargent (1998). As in these papers, we model general human capital as stemming from learning on-the-job and skill loss during unemployment. Worker human capital, denoted by x, follows a stochastic process and 0 xe (x; x ) ( 0 xu (x; x )) denote the Markov transition probability for the worker’s human capital level while employed (unemployed).5 Firm match-speci…c productivity is denoted by y. To summarize the above aspects of our model, in any time period there is heterogeneity across employed workers in terms of human capital x; match-speci…c productivity y and wage w. Unemployed workers only di¤er in terms of their human capital. Utility is linear in consumption and there is no physical capital. Each …rm employs (at most) one worker, and output from a match is p (x; y; z) = xyz where z is an aggregate TFP shock with Markov transition probability (z; z 0 ). Note that the assumption of risk neutral agents implies that we abstract from, e.g., the direct welfare costs of consumption volatility. Thus, we do not capture the full welfare cost of business cycles and our results only re‡ect one of several factors a¤ecting these costs. 2.1 Timing Let us start the detailed model description by providing an overview of the timing protocol. The sequence of events within a period are as follows. First, the aggregate productivity shock z and the idiosyncratic human capital shocks x are realized. Second, a fraction of workers die and are replaced by newborn unemployed workers with human capital at the lowest possible level, x. Third, 4 Compared to LR, the features we add are i) positive bargaining power of workers, and ii) learning on the job as well as skill loss during unemployment. A simpli…cation compared to LR is that in our model the match-speci…c productivity y of a match is not known when a vacancy is posted. 5 Our human capital dynamics di¤er slightly from Ljungqvist and Sargent (1998, 2008) and Jung and Kuester’s (2011) extension with human capital in that we do not assume a sudden loss of general human capital when a worker separates from a job. These papers abstract from heterogeneity in match-speci…c productivity and presumably therefore assume, as a short-cut, that part of the human capital loss occurs when a worker is separated from a job. This reduces the dependence of the human capital distribution on employment (or any endogenous variable in the model), especially if one only allows for exogenous separations. 6 separations into unemployment occur. Then, …rms post vacancies and workers search for jobs. Finally, new matches are formed, wages are set and production takes place. 2.2 Separations The ability of recently separated workers to search for jobs within the period, makes it convenient to de…ne match values and match surplus both before and after the search phase has occurred, i.e., at the separation stage and the matching stage. The surplus of a match at the separation stage is S s (x; y; z; ) where denotes the endogenous aggregate state. Matches with S s (x; y; z; ) < 0 are endogenously dissolved. In addition, a fraction of matches are exogenously destroyed every period. The stock of unemployed workers after separations when the aggregate productivity evolves from z to z is: 1 2 )4 us (x; z) = 1 fx = xg + (1 + X X y2Y x 1 2X x X u (x 1; z 1) xu (x 1 ; x) (1) 1 2X (1 fS s (x; y; z; ) < 0g + 1 fS s (x; y; z; ) 0g) h (x 1 ; y; z 1 ) 3 xe (x 1 ; x)5 where 1 fg is the indicator function, u (h) is the distribution of unemployed (employed) workers at the end of a period, X is the set of human capital states and Y is the set of match-speci…c productivities. Here, the …rst term is the newborn workers and the remaining terms captures the evolution of the surviving workers. The stock of matches of type (x; y) at this point is: hs (x; y; z) = (1 ) (1 ) x 2.3 X 1 2X 1 fS s (x; y; z; ) 0g h (x 1 ; y; z 1 ) xe (x 1 ; x) : (2) Search and matching An employed worker exerts search e¤ort s1 . The search e¤ort of unemployed workers is normalized to unity. Accordingly, the aggregate amount of search e¤ort is: L X us (x; z) + s1 x2X XX hs (x; y; z) : (3) x2X y2Y Vacancy posting costs are linear and each vacancy posted incurs a cost of c0 . The free entry condition for vacancy creation therefore implies: c0 = qJ (z; ) : 7 (4) where q is the probability of a …rm meeting a worker and J is the expected value of a new match for a …rm, as de…ned below. We assume the following Cobb-Douglas meeting function: M L! V 1 min ! ; L; V (5) where V is the number of vacancies posted. The probability of a …rm meeting a worker (assuming an interior solution) is: q= V L where M = V ! ; is labor market tightness. Together with the matching function (5), this implies that equilibrium vacancy postings are determined by: J (z; ) c0 V =L 1 ! : (6) We can then write labor market tightness as a function of z and : J (z; ) c0 (z; ) = 1 ! : (7) Finally, the probability that an unemployed worker meets a …rm (the job meeting rate) is, assuming an interior solution: f (z; ) = 2.4 M = L (z; )1 ! : (8) Values A worker who is unemployed during the production phase receives a ‡ow payo¤ of b (x; z) representing unemployment insurance, utility of leisure and value of home production.6 The value of unemployment at the matching stage is: B (x; z; ) = b (x; z) X X X 1 + [ f z0; 1+r 0 0 0 + 1 x 2X z 2Z y 2Y 0 0 0 f z; B x ; z0; (9) 0 0 B x0 ; z 0 ; ] xu 0 + x; x0 max P x0 ; y 0 ; z 0 ; 0 B x0 ; z 0 ; 0 ;0 g y0 z; z 0 ; where r is the discount rate, Z is the set of aggregate productivity states, P the value of a match and g (y) is the probability density function (pdf) of the productivity of newly created matches. Thus, B 6 Unemployment insurance is …nanced by lump-sum taxation on all workers. 8 is the ‡ow payo¤ b plus the job meeting rate f (z 0 ; plus (1 f (z 0 ; 0 )) 0) times the discounted value of a job tomorrow times the discounted value of being unemployed tomorrow. The max operator ensures that only matches with positive surplus are formed. Note that while a worker is unemployed his human capital (weakly) decreases from x to x0 with probability 0 xu (x; x ). The match value at the matching stage, using that the job meeting rate for employed workers is s1 f (z 0 ; 0 ), can be written as follows: P (x; y; z; ) = p (x; y; z) + f X y~0 2Y + 1 s1 f z 0 ; s1 f z 0 ; 0 0 X X 1 [ 1 1+r 0 0 x 2X z 2Z P x0 ; y; z 0 ; P x0 ; y; z 0 ; ) poP (1 0 0 max P x0 ; y~0 ; z 0 ; + g] xe x; x0 B B s x0 ; z 0 ; 0 P x0 ; y; z 0 ; 0 ) poP + (1 0 ;0 g y~0 B (10) z; z 0 where y~0 denotes the match quality of the poaching …rm and where the indicator for non-separation is: poP B = 1 P s x0 ; y; z 0 ; 0 B s x0 ; z 0 ; 0 : Here, B s is the value when unemployed and P s is the value of the match at the separation stage as de…ned below. The …rst term in (10) is the ‡ow output, the second term the value when the match separates tomorrow, the third term the value when receiving a poaching o¤er tomorrow and the last term the value when not receiving a poaching o¤er tomorrow. Also note that, regardless of what happens tomorrow, human capital while employed today increases from x to x0 with probability 0 xe (x; x ). Since we allow for a positive bargaining power of workers, the values at the separation stage di¤er from the values at the matching stage. In particular, at the separation stage, the value of search includes the share of the surplus received when hired at the matching stage. Accordingly, the value for an unemployed worker at the separation stage is: B s (x; z; ) = (1 f (z; )) B (x; z; ) X + f (z; ) [B (x; z; ) + y~2Y (11) max fP (x; y~; z; ) B (x; z; ) ; 0g] g (~ y) : Analogously, the corresponding match value at the separation stage is: P s (x; y; z; ) = (1 s1 f (z; )) P (x; y; z; ) X + s1 f (z; ) [P (x; y; z; ) + max fP (x; y~; z; ) y~2Y 9 (12) P (x; y; z; ) ; 0g] g (~ y) : Then, we can simply de…ne the surplus of a match at the matching stage as: S (x; y; z; ) = P (x; y; z; ) B (x; z; ) (13) B s (x; z; ) : (14) and the surplus of a match at the separation stage as: S s (x; y; z; ) = P s (x; y; z; ) Recalling that workers receive a value corresponding to their outside option plus a share of the surplus of the match, the expected value of a new match for a …rm is: J (z; ) = 1 XX s u (x; z) max f(1 L ) S (x; y; z; ) ; 0g g (y) (15) x2X y2Y + 1 XXX s1 hs (x; y~; z) max f(1 L ) (S (x; y; z; ) S (x; y~; z; )) ; 0g g (y) : x2X y2Y y~2Y Note that the match-speci…c productivity, y, is observed when the …rm meets a worker after the vacancy has been posted.7 The …rst term in (15) refers to expected surplus from recruiting out of the pool of unemployed (us ), and the second term refers to expected surplus from recruiting from employed workers (hs ). In the classical search and matching model, an increase in (steady state) employment decreases the vacancy …lling rate through the matching function and hence reduces vacancy posting. The same applies here; see (4). In our model, as can be seen from (15), there are two additional channels a¤ecting job creation. First, an increase in employment leads to a larger fraction of new hires coming from other …rms. For at given level of worker human capital, the surplus to the …rm of poaching workers from other …rms is lower than from hiring unemployed workers, and hence this mechanism also reduces the incentives to post vacancies. Second, and counteracting the …rst two e¤ects, a higher employment level increases average human capital among both pools of workers the …rms hires from, which leads to stronger incentives for vacancy posting. This last e¤ect is the ampli…cation mechanism sketched in Figure 1. Let us here mention a computational aspect of the model. Solving the model is non-trivial because current values (9) and (10) depend on the probability of receiving a job o¤er the next period. This, in turn, depends on the next period’s labor market tightness. Next period’s tightness is fully determined by the expected value of a new match to a …rm in the next period, i.e. J (z 0 ; 7 This assumption substantially simpli…es the computation of the equilibrium. 10 0 ). As can be seen from (15), this depends on the distribution of unemployed workers across human capital and the distribution of matches over human capital and match-speci…c productivity. Hence, the endogenous aggregate state can be written as a function of L and the two terms within the summations in (15). Thus, three moments fully capture the implications of this large-dimensional object. We then use a Krusell and Smith (1998)-like algorithm to let these three moments summarize and predict the labor market tightness, thereby enabling us to solve the model. For details on the solution algorithm, see Appendix A.2. 2.5 Distributional dynamics For a new match to be formed, two conditions are required: the two parties must meet according to the meeting function (5) and the match must be an improvement over the status quo (the current match or unemployment). The unemployment distribution after matching accordingly is: 0 u (x; z) = us (x; z) @1 M X 1 fS (x; y; z; ) L y2Y 1 0g g (y)A : (16) The corresponding expression for the distribution of matches is: M h (x; y; z) = hs (x; y; z) + us (x; z) 1 fS (x; y; z; ) L | {z 0g g (y) } mass hired from unemployment M X 1 fS (x; y~; z; ) > S (x; y; z; )g g (~ y) hs (x; y; z) s1 L y~2Y | {z } mass lost to more productive matches M X s +s1 h (x; y~; z) 1 fS (x; y; z; ) > S (x; y~; z; )g g (y) : L y~2Y | {z } (17) mass poached from less productive matches 2.6 Wage determination and worker values Let W (w; x; y; z; ) denote the present value to a worker with human capital x in a match with productivity y, wage w and aggregate productivity z. These worker values are determined according to the bargaining protocol in CPVR and are detailed as follows. Denote the renegotiated wage by w0 . Workers hired out of unemployment receive the wage w0 such that their value is equal to the value of unemployment plus a share of the match surplus: W w0 ; x; y; z; = B (x; z; ) + S (x; y; z; ) : (18) For employed workers who have received a poaching o¤er, the bargaining protocol implies that 11 these workers receive a present value W (w0 ; x; y; z; ) equal to the value of the second-best match that they have encountered during a spell of continuous employment plus a share of the di¤erence in surplus between the best and second-best match. Formally, if a worker of type x employed at a …rm of type y meets a …rm of type y~ then, if S (x; y; z; ) < S (x; y~; z; ), the worker switches to the new …rm and gets the wage w0 satisfying W w0 ; x; y~; z; If, instead, S (x; y; z; ) = P (x; y; z; ) + [S (x; y~; z; ) S (x; y; z; )] : (19) S (x; y~; z; ), the worker remains in his current match and gets a wage w0 that satis…es: W w0 ; x; y; z; = max fP (x; y~; z; ) + [S (x; y; z; ) S (x; y~; z; )] ; W (w; x; y; z; )g : (20) Note that, in case the value at the current wage is higher than the one implied by the outside option, the wage is unchanged. Wages for workers who do not receive poaching o¤ers can also be rebargained, as aggregate or idiosyncratic shocks might a¤ect the various values. First, if the wage is such that it implies a worker value that is larger than the match value, then the match would break down unless there is renegotiation. Hence, the wage is then set so that W (w0 ; x; y; z; ) = P (x; y; z; ). Second, if the wage is such that the worker value is lower than B (x; z; ) + S (x; y; z; ), the worker can ask for a renegotiation with unemployment as the outside option. Hence, the wage is then set so that W (w0 ; x; y; z; ) = B (x; z; ) + S (x; y; z; ). Finally, the current wage w is unchanged when the value W is in the bargaining set: B (x; z; ) + S (x; y; z; ) 6 W (w; x; y; z; ) 6 P (x; y; z; ) : (21) To solve for wages, we compute the value for a worker earning w today, given that future values are (partially) determined by (18)-(21). An employed worker earning the wage w in the current period faces four possibilities in the next period: i) staying employed and not meeting any new …rm, ii) staying employed and receiving a successful poaching o¤er and switching jobs, iii) staying employed and receiving an unsuccessful poaching o¤er (and staying in the old job) and iv) separating. Note that, if the worker becomes separated in the next period he still has a chance to …nd a new job within the period. Imposing an interior solution for M , M = L! V 1 ! and using the de…nition of q, the probability of meeting a new …rm for an employed worker is s1 f (z 0 ; 12 0 ). Then, given the wage, w, the worker value (at the matching stage) is: W (w; x; y; z; ) = w + +s1 f z 0 ; 0 0 X X 1 [ 1 1+r 0 0 s0 f 1 x 2X z 2Z X 0 poy~>y Wp;~ y >y + 1 0 poy~>y Wp;~ y s1 f z 0 ; +s0 @B x0 ; z 0 ; 0 + f z0; 0 S x0 ; y 0 ; z 0 ; 0 y 0 2Y 0 Wnp (22) g (~ y )g y y~2Y X 0 1 g y0 A ] xe x; x0 z; z 0 ; where s0 = 1 S x0 ; y; z 0 < 0 + 1 S x0 ; y; z 0 ; 0 Wnp = min P x0 ; y; z 0 ; 0 poy~>y = 1 S x0 ; y~; z 0 ; > S x0 ; y; z 0 ; 0 S x0 ; y~; z 0 ; 0 0 0 0 Wp;~ y >y = P x ; y; z ; 0 Wp;~ y y 0 0 + = max P x0 ; y~; z 0 ; 0 ; max W w; x0 ; y; z 0 ; 0 + S x0 ; y; z 0 ; 0 0 ; B x0 ; z 0 ; S x0 ; y; z 0 ; 0 0 + S x0 ; y; z 0 ; 0 ; W w; x0 ; y; z 0 ; 0 0 S x0 ; y~; z 0 ; 0 ; 0 the value when not receiving a poaching o¤er, po where s0 denotes separations, Wnp y~>y a successful 0 0 poaching o¤er, Wp;~ y >y the value of a successful poaching o¤er and Wp;~ y y the value of an unsuccessful poaching o¤er. 2.7 Wage distribution When determining the wage distribution, it follows from the description of the wage setting above that the current wage of the worker is a state variable. The distribution of matches over w, x and y after separations is: hs;w (w; x; y; z) = (1 ) (1 ) x X 1 2X 1 fS s (x; y; z; ) 0g hw (w; x 1 ; y; z 1 ) xe (x 1 ; x) : (23) Analogously to (17) in section 2.5, we de…ne hw (w; x; y; z), i.e., the distribution after matching and wage rebargaining; see Appendix A.1. 3 3.1 Calibration Distributions and shock processes The log of the exogenous part of TFP, z; follows an AR(1) process approximated by a Markov chain. The log of match productivity, g (y), is normally distributed and its mean value is normalized to 13 0.5. The number of gridpoints for x, y and z are 10, 8 and 5, respectively.8 The wage grid contains 15 points and is chosen separately for each parameter vector so as to only cover the relevant wage interval.9 In constructing the grid for human capital, x, we, as e.g., Jarosch (2015), follow Ljungqvist and Sargent (1998, 2008) in using an equal-spaced grid and in setting the ratio between the maximum and minimum value of x to 2. The structure of the transition matrices 0 xe (x; x ) and 0 xu (x; x ) for human capital also closely follows Ljungqvist and Sargent. Abstracting from the bounds, the probability of an employed worker to increase his human capital by one gridpoint is xup and the probability for an unemployed worker to decrease his human capital by one gridpoint is xdn . With the reciprocal probabilities, the human capital of a worker is unchanged. Note that there is very little direct evidence on the shape of human capital dynamics. However, Edin and Gustavsson (2008) …nd that skill loss appears to be linear in time out-of-work, in line with the assumption above. 3.2 Calibration approach The frequency of the model is monthly. We calibrate the model based on U.S. data. Parameters whose values are well established in the literature or can be set based on model-independent empirical evidence are set outside the model. Table 1 documents these parameter values and their sources. ! c0 r Table 1: Parameters set outside the model Explanation Value Source Matching function elasticity 0:5 Pissarides (2009) Exogenous match separation rate 0:030 Fujita-Ramey (2009) Vacancy posting cost 0:06375 Fujita-Ramey (2012) Retirement rate 1=(40 12) 40-year work-life TFP shock persistence 0:960 Hagedorn-Manovskii 1=12 Interest rate 1:05 1 Annual r of 5% The meeting function elasticity, !, is set in line with the convention in the literature. The exogenous match separation rate, , is set equal to the mean E2U transition rate reported by Fujita and Ramey (2009), adjusted for workers …nding a new job the same month as they lost the old job.10 This adjustment implies that the separation rate exceeds the E2U rate by a factor of 1/(1-job …nding rate). By using Fujita and Ramey’s number for E2U transitions, which is 0.020, we control for the fact that empirically, but not in our model, workers ‡ow in and out of the labor force. We set the vacancy posting cost c0 along the lines for Fujita and Ramey (2012) who refer to evidence that vacancy costs 8 For z, we use Tauchen and Hussey’s (1991) discretization of AR(1) processes with optimal weights from Flodén (2008). This algorithm has been shown by Flodén (2008) to also be accurate for processes with high persistence. 9 The coarseness of the wage grid is less restrictive than it seems, as we map each “o¤-the-grid” wage to the two nearest grid points using the inverse of the distance to the grid point as weight. Furthermore, the wage grid has no impact on the allocations in the model. 10 This calibration approach for assumes that the average endogenous separation rate in our model is negligible. We con…rm this ex post - it is merely 0.0034 at the monthly frequency, i.e. 10% of the total separation rate. 14 are 6.7 hours per week posted. We set the retirement (or death) rate to match an average work-life of 40 years, as e.g. Huckfeldt (2016). To compute the persistence of the AR process for TFP, we follow along the lines of Hagedorn and Manovskii (2008). Speci…cally, we simulate a monthly Markov chain to match a quarterly autocorrelation of (HP-…ltered) log labor productivity of 0:765. Finally, we set r to yield an annualized interest rate of 5% as in LR. Parameter s1 xup b0 y 100 z Table 2: Parameters obtained by Explanation Matching function productivity Relative search intensity of employed Human capital gain, probability Unemployment payo¤ Bargaining strength of workers Match-speci…c productivity dispersion TFP shock std.dev. moment-matching Value Main identifying moment 0.686 U2E transition rate, mean 0.426 J2J transition rate, mean 0.0427 Return to experience 0.374 Unemployment, std.dev. 0.848 Wage elasticity wrt prod. 0.259 Wage disp: Mean-min ratio 0.698 GDP, std.dev. The remaining parameters of our model are calibrated jointly to match key moments. For simplicity, and in line with most of the literature, ‡ow payo¤ from unemployment is b (x; z) = b0 , i.e. invariant of aggregate productivity and human capital. Table 2 documents the 7 calibrated parameters and the 7 moments matched, including the main identifying moment for each parameter. We minimize the squared percentage deviation between model and data moments. Let us now motivate the choice of moments. Note …rst, that since we are interested in the cost of business cycles from a mechanism driven by unemployment volatility, it is important to match GDP and unemployment volatility. Turning to identi…cation, the model parameters are jointly estimated, but some moments are more informative about certain parameters. The mean transition rate from unemployment to employment is informative about the matching function productivity : The job-to-job transition rate is informative about the relative search intensity of employed workers s1 . Return to experience, measured as the average percentage wage increase while employed, is informative about on-the-job accumulation of human capital, xup .11 Unemployment volatility is informative about the unemployment payo¤ parameter, b0 . As pointed out by Hagedorn and Manovskii (2008), wage elasticity with respect to labor productivity is informative regarding worker bargaining strength, : Wage dispersion 11 As in Jarosch (2015), we impose a relationship between xup and xdn such that the number of increases in human capital roughly equals the number of decreases to minimize bunching at end-points of the human capital grid X. In particular, letting utot denote the (implicitly, through the mean values of E2U and U2E) targeted value of unemployment, we impose (1 ) xup 1 utot x = (1 ) xdn utot x + (x x) where x is the distance between two gridpoints and x represents average human capital for dying workers. For computational reasons, we set x to the midpoint of the grid. Furthermore x is the lower bound of the grid, representing the human capital of newly born workers. This implies x] 1 utot xdn = xup 1 (1 [x . There will still be some upward drift, and thereby upper end-point bunching, in utot ) x utot the human capital distribution if an above-proportional fraction of the unemployed are at the lower bound of the human capital grid, unless this is o¤set by the analogous force of above-proportional fraction of employed workers at the upper bound. 15 is informative about the dispersion of match-speci…c productivity, y. Finally, the volatility of GDP and unemployment are both informative about the standard deviation of the aggregate productivity process. Table 3: Data moments and matched model moments Moment Data source Target value (data) Model value U2E transition rate, mean Fujita-Ramey (2009) 0.340 0.357 J2J transition rate, mean Moscarini-Thompson 0.0320 0.0290 Unemployment, std.dev. BLS 1980-2010 0.107 0.0973 GDP, std.dev. BEA 1980-2010 0.0136 0.0136 Wage disp: Mean-min ratio Hornstein et al. 1.50 1.70 Wage elasticity wrt productivity Hagedorn-Manovskii 0.449 0.445 Return to experience Buchinsky et al. 0.0548 0.0518 Notes: U2E and J2J transition rates are at a monthly frequency. Unemployment is a quarterly mean of a monthly series. This variable, as well as GDP, labor productivity and aggregate wages (at the quarterly frequency), have been logged and HP-…ltered with = 1; 600, both in the data and the model. Let us comment on the more unusual data used. The relevant measure of wage dispersion for our model is “residual” wage dispersion, i.e. controlling for heterogeneity not present in the model, such as education, sex, race etc. We take the mean-min ratio (capturing the minimum by the 10th wage percentile) from Hornstein, Krusell and Violante (2007) as our measure of wage dispersion. We use their preferred measure of 1.50, which is an average of their ratios from census, OES and PSID data. Similarly to Kehoe et al. (2015) we use estimates from Buchinsky et al. (2010) to obtain the “return to experience”. Speci…cally, from Buchinsky’s estimated coe¢ cients we obtain the marginal return to experience of a worker in his third year of employment. We then match that to the wage increase of workers in the model who works for three years for the same employer. We can thereby keep the match-speci…c productivity …xed and obtain a clean measure of the e¤ect of human capital on wages. We believe that their estimate of return to experience captures general human capital and not …rm-speci…c human capital since Buchinsky et al. (2010) control for …rm-speci…c seniority. 4 Results 4.1 Targeted moments and the parameter estimates The moment-matching exercise can be evaluated by comparing the last two columns in Table 3. The model is able to …t most of these moments well, with less than 10 percent deviation for all but one moment, wage dispersion. It might appear surprising that we need to calibrate the volatility of (the exogenous part of) TFP, 16 but this is necessary since the model has internal ampli…cation and propagation of the exogenous TFP shocks, as the distribution of human capital of workers, the productivity of matches and sorting between workers and jobs varies over the cycle. All of this implies that measured TFP in our model is a combination of exogenous TFP and endogenous propagation.12 The above moment-matching exercise determines the 7 parameters in Table 2. The value for s1 in Table 2 indicates that employed workers meet prospective employers slightly below half as often as unemployed workers. We follow LR and report the replacement ratio for unemployed workers as a fraction of the output of the best possible match. The value of b0 implies that this ratio is 0:600, averaged over the human capital values. We …nd that worker bargaining strength is fairly high, 0:848. Given their centrality for our mechanism, we report and comment in more detail on our estimates of the parameters determining the human capital dynamics. The estimated Markov transition probability (xup = 0:0427) imply that the expected monthly human capital increase for an employed worker is 0:207 percent, while the expected decrease when unemployed is 1:41 percent (for xdn = 0:557).13 We know of only one direct measure in the literature of general human capital loss while nonemployed: Edin and Gustavsson (2008). They use a Swedish panel of individual level data that includes test results on labor market-relevant general skills and information about employment status between test dates. First, they …nd that time-out-of-work (compared to employment) implies skill loss, signi…cant at the 1% level. Second, this skill loss appears to be linear in time out-of-work. Third, the speed of skill loss is substantial; being out-of-work for a year implies losing skills equivalent to 0.7 years of schooling. The human capital dynamics can be compared to estimates in models broadly similar to ours.14 Huckfeldt (2016) reports a 0:330 percent expected monthly human capital increase for workers in skillintensive jobs (0:220 percent in skill-neutral jobs). For unemployed workers Huckfeldt obtains a gradual 12 One could potentially also calibrate the persistence of exogenous TFP jointly with the 7 parameters in Table 2 to match e.g., the persistence of GDP. However, to reduce computational complexity we calibrate this parameter as outlined above. Moreover, the persistence of GDP turns out to be fairly well matched in our calibration; it is 0.801 in the model compared to 0.867 in the data. 13 This value takes into account the distribution of employed and unemployed workers across the human capital grid, including the e¤ects of the bounds of the human capital grid. 14 First, there is an older empirical literature that attributes all wage loss when re-employed after an unemployment spell to human capital loss and furthermore assumes that the wage equals marginal product of labor. This is not consistent with our model so we can not use that literature for calibration or straight comparison. Second, some papers look at the e¤ect on wages of an additional month of unemployment. The estimates in Neal (1995) imply that an additional month of unemployment reduces the re-employment wage by 1:5%, which, under the assumption that the wage equals marginal product of labor, is very much in line with the results here. Recent results by Schmieder et al. (2016) shows that re-employment wages decrease by 0:8% per (additional) month unemployed. This is somewhat lower than our result, but reasonably well in line if we think that there is some surplus sharing so that wages decrease less than human capital for an additional month of unemployment. 17 human capital decrease of 1:13 percent per month.15 Jarosch (2015) reports only the monthly human capital Markov transitions probabilities: 0:0141 for employed and 0:131 for unemployed. In Jarosch (2015), for an employed worker with the mid-point of human capital, this implies an expected increase of 0:134 percent, and for the unemployed worker with the mid-point of human capital, it implies a 1:25 percent decrease. To sum up this comparison to the literature, our human capital accumulation for employed workers is in between the estimates of Huckfeldt (2016) and Jarosch (2015), while for unemployed workers our value is about as large as their estimates. 4.2 Welfare measure As is standard in the cost of business cycle literature since Lucas (1987), we report the fraction of expected consumption agents are willing to forego to eliminate business cycles. Speci…cally to our model, the linearity of utility in consumption makes welfare calculations straightforward, since then the ‡ow of aggregate welfare is proportional to aggregate consumption. To compute market consumption, we deduct vacancy posting costs from GDP. Note that one may interpret the unemployment payo¤, b, in two ways, which has di¤erent welfare implications. In the …rst interpretation, b is home production (or equivalently, from a welfare perspective, utility of leisure) in which case the welfare relevant quantity is the sum of market consumption and the unemployment payo¤. In the second interpretation, b is a pecuniary transfer with no direct e¤ect on aggregate utility. We report results for both interpretations.16 4.3 Results for cost of business cycles Our main exercise is to compute the consequences for welfare, GDP and employment of eliminating aggregate volatility.17 As documented in Table 4, we …nd that in our model the elimination of aggregate volatility increases steady state GDP by a substantial amount, 1:45 percent.18 This also has consequences for steady state consumption and welfare, which increase by 0:52-1:49 percent depending on the interpretation of the unemployment payo¤. As we will document below, these fairly large e¤ects are due to the positive relationship between employment and human capital accumulation. Another 15 The comparison of skill losses during unemployment to Huckfeldt’s results is clouded by the fact that, in contrast to our model, he allows for both gradual and sudden loss of human capital during unemployment. Our (gradual) human capital loss estimates for unemployed workers will therefore tend to be higher than his. 16 There is also an intermediate case where b consists of both home production and transfers. The welfare gain of eliminating aggregate volatility generated by our mechanism will then fall between these two cases. 17 We do this by setting exogenous productivity z constant and equal to the average in the stochastic simulation. 18 This indicates that the Oi-Hartman-Abel e¤ect, where higher aggregate volatility increases output and employment, is relatively unimportant; see Bloom et al. (2018). Moreover, the counteracting e¤ect emphasized in Laureys (2014) working through compositional e¤ects on job creation does not seem to be important here. 18 way to describe the consequences of removing aggregate volatility is through the e¤ects on the unemployment rate which falls from 6:16 percentage points to 4:90 percentage points, corresponding to a 20 percent decrease. From an accounting perspective, the increase in GDP can be decomposed into the increase in employment and the change in the average level of human capital of employed workers19 ; E (x h ( )) = PT t 1 h (x; y; zt ) T X X X t xh (x; y; zt ) : x2X y2Y Of these two, the increase in employment accounts for the vast majority. To understand the e¤ects of human capital on employment, recall from (15) that job creation is a¤ected by the human capital of both employed and unemployed workers. In our calibration, the e¤ects through the unemployed dominates. This is partly due to that the average levels of human capital for the unemployed changes more; E (x u ( )) = PT t increases by 4:36 percent while E (x 1 u (x; zt ) T X X t xu (x; zt ) x2X h ( )) increases by 0:18 percent. In addition, job creation is much more sensitive to changes in human capital of the unemployed. Speci…cally, the elasticity of J (z; ) with respect to E (x u ( )) is 1:27 while the elasticity of J (z; ) with respect to E (x is 0:39. It may be surprising that the change in E (x h ( )) h ( )) is so moderate. However, the reason is that the composition of the employed workers is a¤ected by the elimination of business cycles. Speci…cally, in the absence of aggregate volatility, the positive e¤ect that higher employment has on human capital is counteracted by the tendency that …rms tend to hire a larger fraction of workers with low human capital. Table 4: Steady state e¤ects of eliminating business Baseline Welfare, b transfer, (GDP-vacancy cost) 1.49 Welfare, b home prod, (GDP-vacancy costs+b u) 0.52 GDP 1.45 Employment 1.34 E (x u ( )) 4.36 E (x h ( )) 0.18 19 cycles (in percent) No human capital dynamics 0.26 0.02 0.25 0.34 0 0 Although negligible for our exercise, there are other factors than human capital a¤ecting average productivity. Examples include the change in the average level of match-speci…c productivity, E (y h ( )), and the changed degree of sorting between workers and …rms (as well as the covariation between any of these objects with the cycle). 19 4.3.1 The importance of human capital dynamics Let us now quantify the importance of the change in the human capital distribution for the cost of business cycles. To do this we perform a counterfactual exercise where we keep the human capital distribution of the population (i.e. combining employed and unemployed workers) …xed when we remove the aggregate volatility, thus shutting down the last (ampli…cation) mechanism discussed in conjunction with equation (15). All other aspects of the computation is the same as in the baseline exercise.20 The last column of Table 4 con…rms the importance of learning on-the-job, as the version of our model without human capital dynamics implies that aggregate ‡uctuations have negligible e¤ects on the average level of welfare, GDP and employment. Note that the assumption of risk neutral agents implies that only changes in levels of consumption and employment matter for welfare. We thus abstract from the welfare costs of consumption volatility. Our results captures only one of several factors that account for the total cost of business cycles and can be viewed as a lower bound of this cost. 4.3.2 Accounting for the transition We now compute the welfare consequences of eliminating aggregate volatility taking the transition dynamics into account. This is unique in the macro-labor literature on the cost of business cycles; previous studies have only compared steady state quantities. As reported in Table 5, we …nd that in our model, the elimination of aggregate volatility when taking the transition into account, increases welfare by 0:20-1:09 percent depending on the interpretation of the unemployment payo¤.21 We note that the welfare gains from removing business cycles are lower when accounting for the transition than when simply comparing steady states. The gains when accounting for the transition are lower for two reasons: discounting of the increased future consumption and the extra vacancy posting costs related to the increase in employment along the transition path. Note also that the transition to the non-stochastic steady state is reasonably fast; the half-time of the transition of GDP is 4:5 years. Table 5: Welfare e¤ects of eliminating business cycles (in percent) Welfare, b transfer 1.09 Welfare, b home prod 0.20 20 We …x the human capital distribution by setting xup = xdn = = 0 and assume that it is given by the average distribution in the baseline calibration with aggregate volatility. We also keep the incentives for job creation and destruction unchanged, i.e. S and B are computed with the baseline human capital parameters. 21 We compute welfare when taking the transition into account in the following way. First, we simulate the economy with aggregate volatility for several thousand periods. We then draw 1000 starting points for the transition from this simulation and compute welfare in each of these starting points, given that productivity is constant at its mean value for all future periods. Finally, we calculate the mean across the 1000 transitions. 20 4.3.3 Robustness Two key determinants of the cost of business cycles in our model are i) how sensitive the human capital distribution is to the change in (un)employment, and ii) how sensitive job creation is to changes in the human capital distribution of both unemployed and employed workers. An important factor a¤ecting the sensitivity of the human capital distribution is the range of values that human capital can take and an important factor a¤ecting the sensitivity of job creation to human capital is the bargaining strength of workers. Thus, to judge the robustness of the results we re-calibrate it under alternative assumptions on the human capital distribution and the bargaining power and report the steady state welfare, GDP and employment cost of business cycles in Table 6. First, we document what the cost of business cycles is when allowing for a wider range of values for human capital. Recall that in our main calibration we have followed Ljungqvist and Sargent (1998, 2008) and assumed that the ratio between the highest and the lowest human capital value is 2. Huckfeldt (2016) instead …nds a ratio of 15.25. Here we illustrate the e¤ects of changing the assumption regarding the human capital range in the direction of Huckfeldt by assuming that the maximum ratio of human capital is 4. We then re-calibrate the model by matching the same moments as above in Table 3. We …nd that eliminating aggregate volatility lead to an increase of welfare and GDP of 0:94-1:94 and 1:89 percent, respectively. In other words, the cost of business cycles increase substantially. The main di¤erence compared to our baseline calibration is that GDP increases much more than employment indicating that the wider human capital range generated a larger increase in average productivity from the elimination of business cycles. The result of this exercise implies that the cost of business cycles might be substantially higher than what we obtain when using the quite conservative parametrization of the human capital range from Ljungqvist and Sargent (1998, 2008). Second, we explore the sensitivity of our results to the bargaining strength of workers. In particular, we …x the bargaining power at 0:50, as is commonly done in the literature that, di¤erently from our setup, considers Nash bargaining with unemployment as the (only) outside option of the worker. We then re-calibrate the model by matching the same moments as above in Table 3, except the elasticity of wages, that was used to identify bargaining power in the baseline calibration. We …nd that when = 0:50; the elimination of business cycles have somewhat larger e¤ects on all variables compared to our baseline calibration. 21 Table 6: Steady state e¤ects of Model version Baseline Wider human cap. range = 0:50 5 eliminating business Welfare, b transfer 1.49 1.94 1.78 cycles under alternative Welfare, b home prod 0.52 0.94 0.56 assumptions (in percent) GDP Employment 1.45 1.34 1.89 1.43 1.83 1.42 Conclusions A central question in macroeconomics is how large the welfare costs of business cycles are. We show that cyclical variation in unemployment reduces aggregate welfare in a labor market search model with general human capital dynamics since it drives down the level of employment, output and consumption. The key mechanism of the paper concerns learning on-the-job and skill loss during unemployment and is as follows. Empirically, the Beveridge correlation is negative, i.e., vacancies and unemployment are negatively correlated. This, in turn, means that business cycles tend to reduce the average number of matches and hence employment through the matching function. Then, since learning on-the-job and skill loss during unemployment implies that human capital is increasing in the employment rate, it follows that aggregate volatility reduces human capital. This, in turn, reduces incentives to post vacancies, further reducing employment. We …nd that the steady state output and welfare gains from eliminating business cycles are large - they amount to 1:45 percent and 0:52-1:49 percent, respectively. The alternative parameter assumptions explored indicate that the cost of business cycles might be higher than this. We also show that human capital dynamics is pivotal for the results - if we disable this mechanism in our model, the implied gains in employment, output and welfare from eliminating business cycles are negligible. To conclude, let us brie‡y discuss some broader implications of our results. In our model, there is only one type of aggregate shock. If we view this shock as a “catch-all” for any variation in …rm revenues including e¤ects of …scal and monetary policy, we can draw interesting policy conclusions. In particular, a policy that successfully stabilizes unemployment (or job …nding rates) raises the average level of output. For this reason, our paper rationalizes an unemployment stabilization mandate for monetary and …scal policy. In this sense we reach the same conclusion as Berger et al. (2016) and Galí (2016) but for a very di¤erent reason. Berger et al.’s argument is about unemployment stabilization reducing idiosyncratic risk related to layo¤s, while Galí’s mechanism is about hysteresis due to insideroutsider dynamics. Our mechanism is about unemployment stabilization leading to a higher average level of output, thereby more closely related to the argument by Summers (2015) that stabilization policy can have major e¤ects on average levels of output over periods of decades. 22 Berger, David, Ian Dew-Becker, Konstantin Milbradt, Lawrence Schmidt and Yuta Takahashi, 2016, “Layo¤ Risk, the Welfare Cost of Business Cycles, and Monetary Policy”, mimeo. Bloom, Nicholas, Max Floetotto, Nir Jaimovich, Itay Saporta-Eksten and Stephen. J. Terry (2018), “Really Uncertain Business Cycles”, Econometrica, Vol. 86, pp 1031-1065. Burdett, Kenneth, Carlos Carrillo-Tudela and Melvyn Coles, 2015, “The Cost of Job Loss”, mimeo. Buchinsky, Moshe, Denis Fougère, Francis Kramarz and Rusty Tchernis, 2010, “Inter…rm Mobility, Wages and the Returns to Seniority and Experience in the United States,”Review of Economic Studies, Vol. 77(3), pp 972-1001. Cahuc, Pierre, Fabian Postel-Vinay and Jean-Marc Robin, 2006, “Wage Bargaining with On-theJob Search: Theory and Evidence”, Econometrica, Vol. 74, pp 323–364. DeLong, Bradford and Lawrence Summers, 1988, “How Does Macroeconomic Policy A¤ect Output?,” Brookings Papers on Economic Activity, Vol. 19(2), pp 433–494. Den Haan, Wouter and Peter Sedlacek, 2014, “Ine¢ cient Continuation Decisions, Job Creation Costs, and the Cost of Business Cycles”, Quantitative Economics, Vol. 5(2), pp 297–349. Dupraz, Stéphane, Emi Nakamura and Jón Steinsson, 2017, “A Plucking Model of Business Cycles”, mimeo, Columbia University. Edin, Per-Anders and Magnus Gustavsson, 2008, “Time Out of Work and Skill Depreciation”, Industrial & Labor Relations Review, Vol. 61(2), article 2. Flodén, Martin, 2008, “A Note on the Accuracy of Markov-Chain Approximations to Highly Persistent AR(1)-Processes”, Economics Letters, Vol. 99, pp 516-520. Fujita, Shigeru and Garey Ramey, 2009, “The Cyclicality of Separation and Job Finding Rates,” International Economic Review, Vol. 50(2), pp 415-430. Fujita, Shigeru and Garey Ramey, 2012, “Exogenous versus Endogenous Separation”, American Economic Journal: Macroeconomics, Vol. 4(4), pp 68–93. Galí, Jordi, 2016, “Insider-Outsider Labor Markets, Hysteresis and Monetary Policy,” working paper, CREI. Hagedorn, Marcus, and Iourii Manovskii, 2008, “The Cyclical Behavior of Equilibrium Unemployment and Vacancies Revisited”, American Economic Review, Vol. 98(4), pp 1692-1706. Hairault, Jean-Olivier, Francois Langot and Sophie Osotimehin, 2010, “Matching frictions, unemployment dynamics and the cost of business cycles”, Review of Economic Dynamics, Vol. 13(4), pp 759-779 Hassan, Tarek and Thomas Mertens, 2017, “The Social Cost of Near-Rational Investment”, American Economic Review, Vol. 107(4), pp 1059–1103. Hornstein, Andreas, Per Krusell, and Giovanni Violante, 2007, “Frictional Wage Dispersion in 23 Search Models: A Quantitative Assessment.” NBER Working Paper 13674. Huckfeldt, Christopher, 2016, “Understanding the Scarring E¤ect of Recessions”, mimeo, Cornell University. Imrohoro¼ glu, Ayşe, 1989, “Cost of Business Cycles with Indivisibilities and Liquidity Constraints,” Journal of Political Economy, Vol. 97(6), pp 1364-1383. Jarosch, Gregor, 2015, “Searching for Job Security and the Consequences of Job Loss”, mimeo. Jung, Philip and Keith Kuester, 2011, “The (Un)importance of Unemployment Fluctuations for Welfare”, Journal of Economic Dynamics and Control, Vol. 35(10), pp 1744–1768. Jung, Philip and Moritz Kuhn, 2018, “Earnings Losses and Labor Mobility over the Lifecycle”, Journal of the European Economic Association, forthcoming. Kehoe, Patrick, Virgiliu Midrigan and Elena Pastorino, 2015, “Discount Rates, Learning by Doing and Employment Fluctuations”, mimeo. Krebs, Tom and Martin Sche¤el, 2017, “Labor Market Institutions and the Cost of Recessions”, IMF Working Paper 17/87. Krolikowski, Pavel, 2017, “Job Ladders and Earnings of Displaced Workers”, American Economic Journal: Macro, Vol. 9(2), pp 1–31. Krusell, Per and Anthony Smith, 1998, “Income and Wealth Heterogeneity in the Macroeconomy,” Journal of Political Economy, Vol. 106(5), pp 867-896. Laureys, Lien, 2014, “The Cost of Human Capital Depreciation during Unemployment”, Bank of England Working Paper 505. Lise, Jeremy and Jean-Marc Robin, 2017, “The Macro-dynamics of Sorting between Workers and Firms”, American Economic Review, Vol. 107(4), pp 1104–1135. Ljungqvist, Lars and Thomas Sargent, 1998, “The European Unemployment Dilemma”, Journal of Political Economy, Vol. 106(3), pp 514-550. Ljungqvist, Lars and Thomas Sargent, 2008, “Two Questions about European Unemployment”, Econometrica, Vol. 76, pp 1-29. Lucas, Robert, 1987, “Models of Business Cycles”, New York: Blackwell. Luo, Yulei, Jun Nie and Eric Young, 2016, “The Negative Growth-Volatility Relationship and the Gains from Diversi…cation”, mimeo. Moscarini, Giuseppe and Kaj Thompson, 2007, “Occupational and Job Mobility in the US”, Scandinavian Journal of Economics, Vol 109(4), pp 807–836. Neal, Derek, 1995, “Industry-Speci…c Human Capital: Evidence from Displaced Workers”, Journal of Labor Economics, Vol 13, pp 653-677. Pissarides, Christopher, 1992, “Loss of Skill During Unemployment and the Persistence of Em- 24 ployment Shocks”, Quarterly Journal of Economics, Vol. 107, pp 1371-1391. Pissarides, Christopher, 2009, “The Unemployment Volatility Puzzle: Is Wage Stickiness the Answer?”, Econometrica, Vol. 77, pp. 1339–1369. Postel-Vinay, Fabien and Jean-Marc Robin, 2002, “Equilibrium Wage Dispersion with Worker and Employer Heterogeneity”, Econometrica, Vol. 70, pp 2295–2350. Ramey, Garey and Valerie Ramey, 1995, “Cross-Country Evidence on the Link between Volatility and Growth,” American Economic Review, Vol. 85(5), pp. 1138-1151. Schmieder, Johannes, Till von Wachter and Stefan Bender, 2016, “The E¤ect of Unemployment Bene…ts and Nonemployment Durations on Wages”, American Economic Review, Vol. 106(3), pp 739–777. Summers, Lawrence, 2015, “Current Perspectives on In‡ation and Unemployment in the Euro Area and Advanced Economies”, in “In‡ation and Unemployment in Europe”, Proceedings of the ECB Forum on Central Banking, European Central Bank, Frankfurt am Main. Tauchen, George and Robert Hussey, 1991, “Quadrature-Based Methods for Obtaining Approximate Solutions to Nonlinear Asset Pricing Models”, Econometrica, Vol. 59, pp 371-396. Yagan, Danny, 2017, “Employment Hysteresis from the Great Recession”, NBER Working Paper 23844. 25 A Appendix A.1 Employment transitions When accounting for the wage distribution, the employment transition follows: hw (w ; x; y; z) = hs;w (w ; x; y; z) M X o py~>y g (~ y) L y~2Y {z } hs;w (w ; x; y; z) s1 | mass lost to more productive matches M X hs;w (w ; x; y; z) s1 1 fP (x; y~; y; z; ) > W (w ; x; y; z; )g 1 L y~2Y | {z poy~>y g (~ y) } mass lost to higher wage o¤ers from less productive matches +s1 | M X L X grid y~2Y w2W ~ hs;w (w; ~ x; y; z) 1 fw (w; ~ x; y; z; ) = w g 1 {z poy~>y g (~ y) mass gained from increased wage due to o¤ers from less productive matches X M g (y) hs (x; y~) 1 fW (w ; x; y; z; ) = P (x; y~; z; ) + L y~2Y {z | +s1 } [S (x; y; z; ) S (x; y~; z; )]g poy>~y } mass poached from less productive matches hs;w (w ; x; y; z) 1 fW (w ; x; y; z; ) 2 = BS (x; y; z; )g | {z } + X grid w2W ~ | (24) mass lost due to being outside bargaining set hs;w (w; ~ x; y; z) 1 fw (w; ~ x; y; z; ) = w g 1 fW (w; ~ x; y; z; ) 2 = BS (x; y; z; )g {z mass gained from other wages being outside bargaining set M + us (x) g (y) Sxyz 1 fW (w ; x; y; z; ) = B (x; z; ) + S (x; y; z; )g {z } |L mass hired from unemployment where W grid is the wage grid and poy~>y 1 fP (x; y~; z; ) > P (x; y; z; )g P (x; y~; y; z; ) = P (x; y~; z; ) + poy>~y [S (x; y; z; ) S (x; y~; z; )] 1 fP (x; y; z; ) > P (x; y~; z; )g BS (x; y; z; ) = [B (x; z; ) + S (x; y; z; ) ; P (x; y; z; )] Sxyz 1 fS (x; y; z; ) 26 0g } A.2 Solution algorithm A.2.1 Preliminaries As can be seen from (9) and (10), the values B and P depend on 0 through the job …nding rate, and thereby the entire expected next period distribution of matches across x and y and unemployed workers distribution over x: The challenge is to reduce the dimensionality of the distributions 0 to something manageable. The key to our algorithm is to note that all in‡uence of the endogenous distributions goes through the next period labor market tightness, 0 . In addition, according to (7) labor market tightness is only a function of J in (15). Hence, we can write as a function of the three moments that make up P P P s (15); = (m1 ; m2 ; m3 ; z). In particular, noting that x2X y2Y hs (x; y; z) = 1 x2X u (x; z) P P s s and accordingly Lt x2X u (x; z) + s1 1 x2X u (x; z) we set m1 = X us (x; z) : (25) x2X Given that Lt can be computed using m1 ; equation (15) implies that J is fully determined by the parameters , s1 , the moment m1 , and the following additional two terms: m2 = XX x2X y2Y and m3 = XXX x2X y2Y y~2Y us (x; z) max fS (x; y; z; ) ; 0g g (y) hs (x; y~; z) max fS (x; y; z; ) S (x; y~; z; ) ; 0g g (y) : (26) (27) To compute next period values of these moments we assume a linear relationship to today’s moments. Thus, we write m0m = Hm m1 ; m2 ; m3 ; z 0 : (28) Note that, similarly to LR, we can compute the evolution of the distributions us and hs and without solving for wages and worker values. However, in contrast to LR, match surpluses and the value unemployment is jointly determined with (tomorrow’s) labor market tightness. Therefore we guess functions and Hm for labor market tightness and the evolution of moments. We can then compute match values. Given the solution for match values we can compute the allocation for a sequence of aggregate productivity shocks and then update the guesses for and Hm using standard estimation methods and iterate until convergence (see Krusell and Smith (1998)). Given the above arguments it is unsurprising that the R2 of the function (m1 ; m2 ; m3 ) is approximately unity ( 0:9997). It turns out that Hm (m1 ; m2 ; m3 ; z 0 ) also has a high R2 . In the end, we can replace the distributions in 0 by (m1 ; m2 ; m3 ) so that instead of (w; x; y; z; ) the …nal state vector is (w; x; y; z; m1 ; m2 ; m3 ). 27 We discretize mi on a grid. We choose fewer gridpoints for mi (2 gridpoints) than for z as mi is quantitatively less important. With the functions and Hm at hand, we solve for values B and P and then residually compute S. A.2.2 Detailed algorithm Equilibrium without aggregate volatility Obtain the equilibrium without aggregate volatility (for a …xed z = z) by the following steps: Step 1. Guess the ergodic job …nding rate f . Step 2. Use value function iteration to solve for ergodic B and P jointly. Note that the ergodic versions of B and P corresponding to expressions (9) and (10) can be written as a function of x, y, z and f only. Then compute ergodic S along the lines of (13), i.e. as P B. Step 3. Compute the ergodic distributions for u (x) and h (x; y) (see below for details). Step 4. Compute the equilibrium job …nding rate f 0 . If f 0 is close to f then we are done. Otherwise set f = df 0 + (1 d) f (where d 2 [0; 1] is a dampening parameter) and return to Step 2. To obtain the ergodic distributions for ut+1 (x) and ht+1 (x; y) simulate above until convergence in these distributions. Equilibrium with aggregate volatility Obtain the equilibrium with aggregate volatility by the following steps: Step 1. Draw a sequence fzt gt=0:::T and guess functions and Hm . Step 2. Use value function iteration to solve for B (x; z; ) in (9) and P (x; y; z; ) in (10) jointly, interpolating next period values over next period moments. Then compute S (x; y; z; ) in (13). Step 3. For each t; guess current moments (m1 ; m2 ; m3 ). i) Interpolate S on the moments. ii) Given interpolated S, we can solve for the allocation objects we are interested in: iii) Calculate ust (x) and hst (x; y) using (1) and (2) iv) Calculate Lt by aggregating over ust (x) and hst (x; y) v) Calculate Jt using (15). vi) Calculate t using (7) vii) Calculate Vt using (6) viii) Calculate ut+1 (x) and ht+1 (x; y) using (16) and employment transition (17) new new ix) Compute updated moments (mnew 1 ; m2 ; m3 ) new new x) If (mnew 1 ; m2 ; m3 ) is close to (m1 ; m2 ; m3 ) we are done. Otherwise, return to i). 28 Step 4. Update the functions 0 0 using the regressions described in A.2.1 with the time and Hm series for m1 , m2 and m3 and tightness . If 0 is we are done. Otherwise, return to Step 2 with the new guess. Given the sequence based on fzt gt=0:::T above, we use the resulting sequence of (after removing an initial burn-in period) to compute allocations and wages and then the sequence of hw t+1 to compute relevant moments of the wage distribution along the sequence where we have followed the algorithm described in section A.2.3 to compute worker values W (w; x; y; z; ) and wages w (w; x; y; z; ). A.2.3 Algorithm for determination of W and w With the functions and Hm found in section A.2.2, we solve for worker values W , noting that the state vector is (w; x; y; z; m1 ; m2 ; m3 ). The solution is obtained by value function iteration, interpolating next period values over next period moments. Once we know the worker values W we can solve for wages w residually. This amounts to rewriting equation (22) to …nd the wage that yields the right value of W for the current state vector (w; x; y; z; m1 ; m2 ; m3 ) given the expected future values for the worker. In all computations related to wages we interpolate linearly over the moments. 29 Earlier Working Papers: For a complete list of Working Papers published by Sveriges Riksbank, see www.riksbank.se Estimation of an Adaptive Stock Market Model with Heterogeneous Agents by Henrik Amilon 2005:177 Some Further Evidence on Interest-Rate Smoothing: The Role of Measurement Errors in the Output Gap by Mikael Apel and Per Jansson 2005:178 Bayesian Estimation of an Open Economy DSGE Model with Incomplete Pass-Through by Malin Adolfson, Stefan Laséen, Jesper Lindé and Mattias Villani 2005:179 Are Constant Interest Rate Forecasts Modest Interventions? Evidence from an Estimated Open Economy DSGE Model of the Euro Area by Malin Adolfson, Stefan Laséen, Jesper Lindé and Mattias Villani 2005:180 Inference in Vector Autoregressive Models with an Informative Prior on the Steady State by Mattias Villani 2005:181 Bank Mergers, Competition and Liquidity by Elena Carletti, Philipp Hartmann and Giancarlo Spagnolo 2005:182 Testing Near-Rationality using Detailed Survey Data by Michael F. Bryan and Stefan Palmqvist 2005:183 Exploring Interactions between Real Activity and the Financial Stance by Tor Jacobson, Jesper Lindé and Kasper Roszbach 2005:184 Two-Sided Network Effects, Bank Interchange Fees, and the Allocation of Fixed Costs by Mats A. Bergman 2005:185 Trade Deficits in the Baltic States: How Long Will the Party Last? by Rudolfs Bems and Kristian Jönsson 2005:186 Real Exchange Rate and Consumption Fluctuations follwing Trade Liberalization by Kristian Jönsson 2005:187 Modern Forecasting Models in Action: Improving Macroeconomic Analyses at Central Banks by Malin Adolfson, Michael K. Andersson, Jesper Lindé, Mattias Villani and Anders Vredin 2005:188 Bayesian Inference of General Linear Restrictions on the Cointegration Space by Mattias Villani 2005:189 Forecasting Performance of an Open Economy Dynamic Stochastic General Equilibrium Model by Malin Adolfson, Stefan Laséen, Jesper Lindé and Mattias Villani 2005:190 Forecast Combination and Model Averaging using Predictive Measures by Jana Eklund and Sune Karlsson 2005:191 Swedish Intervention and the Krona Float, 1993-2002 by Owen F. Humpage and Javiera Ragnartz 2006:192 A Simultaneous Model of the Swedish Krona, the US Dollar and the Euro by Hans Lindblad and Peter Sellin 2006:193 Testing Theories of Job Creation: Does Supply Create Its Own Demand? by Mikael Carlsson, Stefan Eriksson and Nils Gottfries 2006:194 Down or Out: Assessing The Welfare Costs of Household Investment Mistakes by Laurent E. Calvet, John Y. Campbell and Paolo Sodini 2006:195 Efficient Bayesian Inference for Multiple Change-Point and Mixture Innovation Models by Paolo Giordani and Robert Kohn 2006:196 Derivation and Estimation of a New Keynesian Phillips Curve in a Small Open Economy by Karolina Holmberg 2006:197 Technology Shocks and the Labour-Input Response: Evidence from Firm-Level Data by Mikael Carlsson and Jon Smedsaas 2006:198 Monetary Policy and Staggered Wage Bargaining when Prices are Sticky by Mikael Carlsson and Andreas Westermark 2006:199 The Swedish External Position and the Krona by Philip R. Lane 2006:200 Price Setting Transactions and the Role of Denominating Currency in FX Markets by Richard Friberg and Fredrik Wilander 2007:201 The geography of asset holdings: Evidence from Sweden by Nicolas Coeurdacier and Philippe Martin 2007:202 Evaluating An Estimated New Keynesian Small Open Economy Model by Malin Adolfson, Stefan Laséen, Jesper Lindé and Mattias Villani 2007:203 The Use of Cash and the Size of the Shadow Economy in Sweden by Gabriela Guibourg and Björn Segendorf 2007:204 Bank supervision Russian style: Evidence of conflicts between micro- and macro-prudential concerns by Sophie Claeys and Koen Schoors 2007:205 Optimal Monetary Policy under Downward Nominal Wage Rigidity by Mikael Carlsson and Andreas Westermark 2007:206 Financial Structure, Managerial Compensation and Monitoring by Vittoria Cerasi and Sonja Daltung 2007:207 Financial Frictions, Investment and Tobin’s q by Guido Lorenzoni and Karl Walentin 2007:208 Sticky Information vs Sticky Prices: A Horse Race in a DSGE Framework by Mathias Trabandt 2007:209 Acquisition versus greenfield: The impact of the mode of foreign bank entry on information and bank lending rates by Sophie Claeys and Christa Hainz 2007:210 Nonparametric Regression Density Estimation Using Smoothly Varying Normal Mixtures by Mattias Villani, Robert Kohn and Paolo Giordani 2007:211 The Costs of Paying – Private and Social Costs of Cash and Card by Mats Bergman, Gabriella Guibourg and Björn Segendorf 2007:212 Using a New Open Economy Macroeconomics model to make real nominal exchange rate forecasts by Peter Sellin 2007:213 Introducing Financial Frictions and Unemployment into a Small Open Economy Model by Lawrence J. Christiano, Mathias Trabandt and Karl Walentin 2007:214 Earnings Inequality and the Equity Premium by Karl Walentin 2007:215 Bayesian forecast combination for VAR models by Michael K. Andersson and Sune Karlsson 2007:216 Do Central Banks React to House Prices? by Daria Finocchiaro and Virginia Queijo von Heideken 2007:217 The Riksbank’s Forecasting Performance by Michael K. Andersson, Gustav Karlsson and Josef Svensson 2007:218 Macroeconomic Impact on Expected Default Freqency by Per Åsberg and Hovick Shahnazarian 2008:219 Monetary Policy Regimes and the Volatility of Long-Term Interest Rates by Virginia Queijo von Heideken 2008:220 Governing the Governors: A Clinical Study of Central Banks by Lars Frisell, Kasper Roszbach and Giancarlo Spagnolo 2008:221 The Monetary Policy Decision-Making Process and the Term Structure of Interest Rates by Hans Dillén 2008:222 How Important are Financial Frictions in the U S and the Euro Area by Virginia Queijo von Heideken 2008:223 Block Kalman filtering for large-scale DSGE models by Ingvar Strid and Karl Walentin 2008:224 Optimal Monetary Policy in an Operational Medium-Sized DSGE Model by Malin Adolfson, Stefan Laséen, Jesper Lindé and Lars E. O. Svensson 2008:225 Firm Default and Aggregate Fluctuations by Tor Jacobson, Rikard Kindell, Jesper Lindé and Kasper Roszbach 2008:226 Re-Evaluating Swedish Membership in EMU: Evidence from an Estimated Model by Ulf Söderström 2008:227 The Effect of Cash Flow on Investment: An Empirical Test of the Balance Sheet Channel by Ola Melander 2009:228 Expectation Driven Business Cycles with Limited Enforcement by Karl Walentin 2009:229 Effects of Organizational Change on Firm Productivity by Christina Håkanson 2009:230 Evaluating Microfoundations for Aggregate Price Rigidities: Evidence from Matched Firm-Level Data on Product Prices and Unit Labor Cost by Mikael Carlsson and Oskar Nordström Skans 2009:231 Monetary Policy Trade-Offs in an Estimated Open-Economy DSGE Model by Malin Adolfson, Stefan Laséen, Jesper Lindé and Lars E. O. Svensson 2009:232 Flexible Modeling of Conditional Distributions Using Smooth Mixtures of Asymmetric Student T Densities by Feng Li, Mattias Villani and Robert Kohn 2009:233 Forecasting Macroeconomic Time Series with Locally Adaptive Signal Extraction by Paolo Giordani and Mattias Villani 2009:234 Evaluating Monetary Policy by Lars E. O. Svensson 2009:235 Risk Premiums and Macroeconomic Dynamics in a Heterogeneous Agent Model by Ferre De Graeve, Maarten Dossche, Marina Emiris, Henri Sneessens and Raf Wouters 2010:236 Picking the Brains of MPC Members by Mikael Apel, Carl Andreas Claussen and Petra Lennartsdotter 2010:237 Involuntary Unemployment and the Business Cycle by Lawrence J. Christiano, Mathias Trabandt and Karl Walentin 2010:238 Housing collateral and the monetary transmission mechanism by Karl Walentin and Peter Sellin 2010:239 The Discursive Dilemma in Monetary Policy by Carl Andreas Claussen and Øistein Røisland 2010:240 Monetary Regime Change and Business Cycles by Vasco Cúrdia and Daria Finocchiaro 2010:241 Bayesian Inference in Structural Second-Price common Value Auctions by Bertil Wegmann and Mattias Villani 2010:242 Equilibrium asset prices and the wealth distribution with inattentive consumers by Daria Finocchiaro 2010:243 Identifying VARs through Heterogeneity: An Application to Bank Runs by Ferre De Graeve and Alexei Karas 2010:244 Modeling Conditional Densities Using Finite Smooth Mixtures by Feng Li, Mattias Villani and Robert Kohn 2010:245 The Output Gap, the Labor Wedge, and the Dynamic Behavior of Hours by Luca Sala, Ulf Söderström and Antonella Trigari 2010:246 Density-Conditional Forecasts in Dynamic Multivariate Models by Michael K. Andersson, Stefan Palmqvist and Daniel F. Waggoner 2010:247 Anticipated Alternative Policy-Rate Paths in Policy Simulations by Stefan Laséen and Lars E. O. Svensson 2010:248 MOSES: Model of Swedish Economic Studies by Gunnar Bårdsen, Ard den Reijer, Patrik Jonasson and Ragnar Nymoen 2011:249 The Effects of Endogenuos Firm Exit on Business Cycle Dynamics and Optimal Fiscal Policy by Lauri Vilmi 2011:250 Parameter Identification in a Estimated New Keynesian Open Economy Model by Malin Adolfson and Jesper Lindé 2011:251 Up for count? Central bank words and financial stress by Marianna Blix Grimaldi 2011:252 Wage Adjustment and Productivity Shocks by Mikael Carlsson, Julián Messina and Oskar Nordström Skans 2011:253 Stylized (Arte) Facts on Sectoral Inflation by Ferre De Graeve and Karl Walentin 2011:254 Hedging Labor Income Risk by Sebastien Betermier, Thomas Jansson, Christine A. Parlour and Johan Walden 2011:255 Taking the Twists into Account: Predicting Firm Bankruptcy Risk with Splines of Financial Ratios by Paolo Giordani, Tor Jacobson, Erik von Schedvin and Mattias Villani 2011:256 Collateralization, Bank Loan Rates and Monitoring: Evidence from a Natural Experiment by Geraldo Cerqueiro, Steven Ongena and Kasper Roszbach 2012:257 On the Non-Exclusivity of Loan Contracts: An Empirical Investigation by Hans Degryse, Vasso Ioannidou and Erik von Schedvin 2012:258 Labor-Market Frictions and Optimal Inflation by Mikael Carlsson and Andreas Westermark 2012:259 Output Gaps and Robust Monetary Policy Rules by Roberto M. Billi 2012:260 The Information Content of Central Bank Minutes by Mikael Apel and Marianna Blix Grimaldi 2012:261 The Cost of Consumer Payments in Sweden by Björn Segendorf and Thomas Jansson 2012:262 Trade Credit and the Propagation of Corporate Failure: An Empirical Analysis by Tor Jacobson and Erik von Schedvin 2012:263 Structural and Cyclical Forces in the Labor Market During the Great Recession: Cross-Country Evidence by Luca Sala, Ulf Söderström and AntonellaTrigari 2012:264 Pension Wealth and Household Savings in Europe: Evidence from SHARELIFE by Rob Alessie, Viola Angelini and Peter van Santen 2013:265 Long-Term Relationship Bargaining by Andreas Westermark 2013:266 Using Financial Markets To Estimate the Macro Effects of Monetary Policy: An Impact-Identified FAVAR* by Stefan Pitschner 2013:267 DYNAMIC MIXTURE-OF-EXPERTS MODELS FOR LONGITUDINAL AND DISCRETE-TIME SURVIVAL DATA by Matias Quiroz and Mattias Villani 2013:268 Conditional euro area sovereign default risk by André Lucas, Bernd Schwaab and Xin Zhang 2013:269 Nominal GDP Targeting and the Zero Lower Bound: Should We Abandon Inflation Targeting?* by Roberto M. Billi 2013:270 Un-truncating VARs* by Ferre De Graeve and Andreas Westermark 2013:271 Housing Choices and Labor Income Risk by Thomas Jansson 2013:272 Identifying Fiscal Inflation* by Ferre De Graeve and Virginia Queijo von Heideken 2013:273 On the Redistributive Effects of Inflation: an International Perspective* by Paola Boel 2013:274 Business Cycle Implications of Mortgage Spreads* by Karl Walentin 2013:275 Approximate dynamic programming with post-decision states as a solution method for dynamic economic models by Isaiah Hull 2013:276 A detrimental feedback loop: deleveraging and adverse selection by Christoph Bertsch 2013:277 Distortionary Fiscal Policy and Monetary Policy Goals by Klaus Adam and Roberto M. Billi 2013:278 Predicting the Spread of Financial Innovations: An Epidemiological Approach by Isaiah Hull 2013:279 Firm-Level Evidence of Shifts in the Supply of Credit by Karolina Holmberg 2013:280 Lines of Credit and Investment: Firm-Level Evidence of Real Effects of the Financial Crisis by Karolina Holmberg 2013:281 A wake-up call: information contagion and strategic uncertainty by Toni Ahnert and Christoph Bertsch 2013:282 Debt Dynamics and Monetary Policy: A Note by Stefan Laséen and Ingvar Strid 2013:283 Optimal taxation with home production by Conny Olovsson 2014:284 Incompatible European Partners? Cultural Predispositions and Household Financial Behavior by Michael Haliassos, Thomas Jansson and Yigitcan Karabulut 2014:285 How Subprime Borrowers and Mortgage Brokers Shared the Piecial Behavior by Antje Berndt, Burton Hollifield and Patrik Sandås 2014:286 The Macro-Financial Implications of House Price-Indexed Mortgage Contracts by Isaiah Hull 2014:287 Does Trading Anonymously Enhance Liquidity? by Patrick J. Dennis and Patrik Sandås 2014:288 Systematic bailout guarantees and tacit coordination by Christoph Bertsch, Claudio Calcagno and Mark Le Quement 2014:289 Selection Effects in Producer-Price Setting by Mikael Carlsson 2014:290 Dynamic Demand Adjustment and Exchange Rate Volatility by Vesna Corbo 2014:291 Forward Guidance and Long Term Interest Rates: Inspecting the Mechanism by Ferre De Graeve, Pelin Ilbas & Raf Wouters 2014:292 Firm-Level Shocks and Labor Adjustments by Mikael Carlsson, Julián Messina and Oskar Nordström Skans 2014:293 A wake-up call theory of contagion by Toni Ahnert and Christoph Bertsch 2015:294 Risks in macroeconomic fundamentals and excess bond returns predictability by Rafael B. De Rezende 2015:295 The Importance of Reallocation for Productivity Growth: Evidence from European and US Banking by Jaap W.B. Bos and Peter C. van Santen 2015:296 SPEEDING UP MCMC BY EFFICIENT DATA SUBSAMPLING by Matias Quiroz, Mattias Villani and Robert Kohn 2015:297 Amortization Requirements and Household Indebtedness: An Application to Swedish-Style Mortgages by Isaiah Hull 2015:298 Fuel for Economic Growth? by Johan Gars and Conny Olovsson 2015:299 Searching for Information by Jungsuk Han and Francesco Sangiorgi 2015:300 What Broke First? Characterizing Sources of Structural Change Prior to the Great Recession by Isaiah Hull 2015:301 Price Level Targeting and Risk Management by Roberto Billi 2015:302 Central bank policy paths and market forward rates: A simple model by Ferre De Graeve and Jens Iversen 2015:303 Jump-Starting the Euro Area Recovery: Would a Rise in Core Fiscal Spending Help the Periphery? by Olivier Blanchard, Christopher J. Erceg and Jesper Lindé 2015:304 Bringing Financial Stability into Monetary Policy* by Eric M. Leeper and James M. Nason 2015:305 SCALABLE MCMC FOR LARGE DATA PROBLEMS USING DATA SUBSAMPLING AND THE DIFFERENCE ESTIMATOR by MATIAS QUIROZ, MATTIAS VILLANI AND ROBERT KOHN 2015:306 SPEEDING UP MCMC BY DELAYED ACCEPTANCE AND DATA SUBSAMPLING by MATIAS QUIROZ 2015:307 Modeling financial sector joint tail risk in the euro area by André Lucas, Bernd Schwaab and Xin Zhang 2015:308 Score Driven Exponentially Weighted Moving Averages and Value-at-Risk Forecasting by André Lucas and Xin Zhang 2015:309 On the Theoretical Efficacy of Quantitative Easing at the Zero Lower Bound by Paola Boel and Christopher J. Waller 2015:310 Optimal Inflation with Corporate Taxation and Financial Constraints by Daria Finocchiaro, Giovanni Lombardo, Caterina Mendicino and Philippe Weil 2015:311 Fire Sale Bank Recapitalizations by Christoph Bertsch and Mike Mariathasan 2015:312 Since you’re so rich, you must be really smart: Talent and the Finance Wage Premium by Michael Böhm, Daniel Metzger and Per Strömberg 2015:313 Debt, equity and the equity price puzzle by Daria Finocchiaro and Caterina Mendicino 2015:314 Trade Credit: Contract-Level Evidence Contradicts Current Theories by Tore Ellingsen, Tor Jacobson and Erik von Schedvin 2016:315 Double Liability in a Branch Banking System: Historical Evidence from Canada by Anna Grodecka and Antonis Kotidis 2016:316 Subprime Borrowers, Securitization and the Transmission of Business Cycles by Anna Grodecka 2016:317 Real-Time Forecasting for Monetary Policy Analysis: The Case of Sveriges Riksbank by Jens Iversen, Stefan Laséen, Henrik Lundvall and Ulf Söderström 2016:318 Fed Liftoff and Subprime Loan Interest Rates: Evidence from the Peer-to-Peer Lending by Christoph Bertsch, Isaiah Hull and Xin Zhang 2016:319 Curbing Shocks to Corporate Liquidity: The Role of Trade Credit by Niklas Amberg, Tor Jacobson, Erik von Schedvin and Robert Townsend 2016:320 Firms’ Strategic Choice of Loan Delinquencies by Paola Morales-Acevedo 2016:321 Fiscal Consolidation Under Imperfect Credibility by Matthieu Lemoine and Jesper Lindé 2016:322 Challenges for Central Banks’ Macro Models by Jesper Lindé, Frank Smets and Rafael Wouters 2016:323 The interest rate effects of government bond purchases away from the lower bound by Rafael B. De Rezende 2016:324 COVENANT-LIGHT CONTRACTS AND CREDITOR COORDINATION by Bo Becker and Victoria Ivashina 2016:325 Endogenous Separations, Wage Rigidities and Employment Volatility by Mikael Carlsson and Andreas Westermark 2016:326 Renovatio Monetae: Gesell Taxes in Practice by Roger Svensson and Andreas Westermark 2016:327 Adjusting for Information Content when Comparing Forecast Performance by Michael K. Andersson, Ted Aranki and André Reslow 2016:328 Economic Scarcity and Consumers’ Credit Choice by Marieke Bos, Chloé Le Coq and Peter van Santen 2016:329 Uncertain pension income and household saving by Peter van Santen 2016:330 Money, Credit and Banking and the Cost of Financial Activity by Paola Boel and Gabriele Camera 2016:331 Oil prices in a real-business-cycle model with precautionary demand for oil by Conny Olovsson 2016:332 Financial Literacy Externalities by Michael Haliasso, Thomas Jansson and Yigitcan Karabulut 2016:333 The timing of uncertainty shocks in a small open economy by Hanna Armelius, Isaiah Hull and Hanna Stenbacka Köhler 2016:334 Quantitative easing and the price-liquidity trade-off by Marien Ferdinandusse, Maximilian Freier and Annukka Ristiniemi 2017:335 What Broker Charges Reveal about Mortgage Credit Risk by Antje Berndt, Burton Hollifield and Patrik Sandåsi 2017:336 Asymmetric Macro-Financial Spillovers by Kristina Bluwstein 2017:337 Latency Arbitrage When Markets Become Faster by Burton Hollifield, Patrik Sandås and Andrew Todd 2017:338 How big is the toolbox of a central banker? Managing expectations with policy-rate forecasts: Evidence from Sweden by Magnus Åhl 2017:339 International business cycles: quantifying the effects of a world market for oil by Johan Gars and Conny Olovsson l 2017:340 Systemic Risk: A New Trade-Off for Monetary Policy? by Stefan Laséen, Andrea Pescatori and Jarkko Turunen 2017:341 Household Debt and Monetary Policy: Revealing the Cash-Flow Channel by Martin Flodén, Matilda Kilström, Jósef Sigurdsson and Roine Vestman 2017:342 House Prices, Home Equity, and Personal Debt Composition by Jieying Li and Xin Zhang 2017:343 Identification and Estimation issues in Exponential Smooth Transition Autoregressive Models by Daniel Buncic 2017:344 Domestic and External Sovereign Debt by Paola Di Casola and Spyridon Sichlimiris 2017:345 The Role of Trust in Online Lending by Christoph Bertsch, Isaiah Hull, Yingjie Qi and Xin Zhang 2017:346 On the effectiveness of loan-to-value regulation in a multiconstraint framework by Anna Grodecka 2017:347 Shock Propagation and Banking Structure by Mariassunta Giannetti and Farzad Saidi 2017:348 The Granular Origins of House Price Volatility by Isaiah Hull, Conny Olovsson, Karl Walentin and Andreas Westermark 2017:349 Should We Use Linearized Models To Calculate Fiscal Multipliers? by Jesper Lindé and Mathias Trabandt 2017:350 The impact of monetary policy on household borrowing – a high-frequency IV identification by Maria Sandström Conditional exchange rate pass-through: evidence from Sweden by Vesna Corbo and Paola Di Casola 2018:351 2018:352 Sveriges Riksbank Visiting address: Brunkebergs torg 11 Mail address: se-103 37 Stockholm Website: www.riksbank.se Telephone: +46 8 787 00 00, Fax: +46 8 21 05 31 E-mail: registratorn@riksbank.se