Job Uncertainty and Deep Recessions

We study a heterogeneous agents model which combines matching frictions in the labor market with incomplete asset markets and nominal rigidities. Workers can experience job terminations that send them into short term unemployment or more serious job terminations that require a more di¢ cult search process, a state we call for mis-match. We show an increase in job uncertainty decreases aggregate demand which lowers hiring and therefore produces even more job uncertainty and potentially a deep recession. The ampli(cid:133)cation mechanism is small when asset markets are complete, prices are (cid:135)exible or unemployment is predominantly short term. Quantitatively, with a moderate and em-pirically plausible amount of mis-match, the model can account for the amplitude of the increase in unemployment during the Great Recession, for the increase in unemployment duration, and for much of the shift and movement along the Beveridge curve.


Introduction
The Great Recession and its aftermath have witnessed unprecedented increases in the level and the duration of unemployment in the United States. The unemployment rate in September 2012 remains above 8 percent having surpassed 10 percent in late 2009 and the number of unemployed workers who have been out of work for 6 months or more now accounts for more than 40 percent of total unemployment, see Figure 1. 1 Much attention has already been devoted to examining these developments, 2 but relatively little work has explored the idea that the labor market crisis itself may have been an important source of the recession. In this paper we show that shocks that impact on future job prospects can be ampli…ed signi…cantly when a vicious circle of feedback arises between the labor market to the goods market. We demonstrate that such an ampli…cation mechanism can arise when unemployment risk has a large impact on household savings, when aggregate demand has a strong impact on …rms' hiring decisions, and when at least some fraction of the unemployed face signi…cantly depressed labor market outcomes. We argue that all of these circumstances are relevant for the Great Recession and thus that the labor market ampli…cation mechanism is key for understanding the depth of the Great Recession. We examine a model where a menu of frictions interact. First, households face idiosyncratic unemployment risk and asset markets are incomplete. Speci…cally, we assume that households have access only to a nominal state-non-contingent bond and must observe a borrowing limit.
Actual asset markets may be more sophisticated than this but the key assumption is that households cannot fully insure against idiosyncratic risks originating in the labor market. Mar-1 Elsby, Hobijn andŞahin (2010) provide a very insightful discussion of the labor market developments during the Great Recession. time, mis-match curbs the incentive of …rms to exploit the labor market conditions to post more vacancies. Fewer vacancies, in turn, increase the expected income loss associated with unemployment because the job …nding rate declines. Therefore, a vicious circle may appear in which deteriorating job prospects may trigger lower demand which worsens the labor market outlook even further. Under these circumstances, job uncertainty can trigger a deep recession.
We carefully calibrate parameters pertaining to preferences and technology including the extent of nominal rigidities. We calibrate the shock to the aggregate job separation rate by matching the experience of the U.S. economy during the early parts of the Great Recession.
In particular, we feed into the model processes for job separations and for the share of job separations that send workers to the mis-match state which match the US time series for permanent layo¤s and the share of unemployed workers who have been out of work for 6 months or more. The resulting calibration of the size of the mis-match shock is consistent with the estimates of Garlevy (2011) andŞahin et al (2012) regarding the importance of mis-match unemployment during the Great Recession. 6 The model is shown to produce a large recession in response to these shocks and we …nd an increase in the unemployment rate and a decrease in vacancies that closely resemble their empirical counterparts. This also means that the model produces the movement along and shift in the Beveridge curve observed in the US during the Great Recession.
We conduct an extensive robustness analysis of our results using a simpli…ed model in which we impose a no-borrowing constraint on the households. Although this model features no wealth inequality in equilibrium, we …nd that it produces results that are quite similar to the benchmark model. Using this model, we demonstrate that the ampli…cation mechanism is 6 Barlevy (2011) estimates the extent mis-match from the shift in the Beveridge curve post-August 2008. Daly et al (2012) instead use the instability of the Beveridge curve during the Great Recession to derive an estimate of the change in the natural rate of unemployment.Şahin et al (2012) posit a model composed of many distinct labor markets and use this to measure mis-match unemployment. In an application to US data, they use dispersion in unemployment across industries, occupations, education and geography to estimate the extent of mis-match. neutralized when either prices are ‡exible or asset markets are complete. In the latter case, an increase in job separations have limited impact on aggregate demand which reduces the adverse impact of the worsening labor market conditions. When prices are ‡exible, …rms have a strong incentive to cut prices when aggregate demand declines which moderates very signi…cantly the recessionary impact of the increase in job separations. We …nd that the model produces very similar results for the unemployment dynamics when either prices are ‡exible or asset markets are incomplete. In both cases, the model fails to reproduce the changes observed in unemployment and in vacancies observed during the Great Recession. In other words, it is the interaction between precautionary savings motives and nominal rigidities that produces the ampli…cation mechanism. We also …nd that mis-match is crucial. When unemployment duration is short, an increase in job separations has limited impact on aggregate demand because there is little incentive on the part of employed workers to engage in precautionary savings against unemployment that have the mean duration observed in post-WWII U.S. data. Moreover, in such a labor market …rms have a strong incentive to post vacancies when unemployment rises which reduces the adverse impact of an adverse shock to job separations.
We also examine the robustness of the results to key assumptions made in our analysis. First, we investigate the importance of wage setting. The benchmark model assumes that the real wage is …xed, an assumption that is not obviously contradicted by the data in the last recession at least, see also Shimer (2012). We replace this assumption with a Nash bargaining model and …nd that the results are sensitive to the assumptions made regarding workers'outside option should the partners disagree during the bargaining process. If a failed bargaining processes may send workers into mis-match unemployment, nominal wages may fall su¢ ciently that the ampli…cation mechanism does not arise. Assuming alternatively that a failed bargaining process sends workers into the high search e¢ ciency state only, the results under Nash bargaining are extremely similar to the benchmark model that assumes constant real wages. Another assumption in the benchmark model is that …rms are owned by risk neutral entrepreneurs.
These entrepreneurs thus pick up any impact that comes through changes in …rms'pro…ts. We report results for an alternative economy in which …rms are owned by households and …nd these to be practically identical to the benchmark model.
The paper is closely related to the seminar contribution of Den Haan, Ramey and Watson (2000). In their analysis, matches are endogenously terminated and they examine how productivity shocks are propagated due to matching frictions and household savings decisions. Our analysis is also related to a number of other recent papers that have examined aggregate ‡uctuations in incomplete markets settings. Gomes, Greenwood and Rebelo (2002) and Krusell et al (2009) both study models that introduce frictional labor markets in a general equilibrium incomplete markets model with idiosyncratic risk. The former authors compute the welfare costs of business cycles while the latter authors examine how labor market uncertainty in ‡uences inequality and how imperfect insurance a¤ects unemployment and other labor market outcomes. Krusell, Mukoyama andŞahin (2011) and Challe and Ragot (2012) instead investigate the role of precautionary savings for aggregate ‡uctuations in an incomplete markets setting with unemployment risk. 7 The latter of these authors show that precautionary savings may be Also related to our analysis is a stream of recent papers that examine the impact of uncertainty shocks. In our model, asset market incompleteness implies that shocks to job termination 7 The latter of these papers do not explicitly model labor market matching. rates produce idiosyncratic uncertainty and we …nd that this is important for understanding the impact of labor market shocks on aggregate demand. Baker, Bloom and Davis (2012) suggest that policy uncertainty may have contributed signi…cantly to the Great Recession. Closer to our analysis, Schalle (2012) investigates the impact of idiosyncratic productivity volatility shocks on unemployment in a directed search model with heterogeneous …rms. He …nds that the uncertainty e¤ects induced by the volatility shocks can explain some of the rise in unemployment but not its persistence. Basu and Bundick (2012) analyze the e¤ects of aggregate uncertainty shocks dynamic stochastic general equilibrium model with a representative consumer. Consistently with our analysis of the impact of idiosyncratic uncertainty, they …nd that nominal rigidities amplify the impact of uncertainty shocks. Basu and Bundick (2012) also demonstrate that a zero lower bound on the nominal interest rate may further amplify the impact of uncertainty shocks. Related to this, Rendahl (2012) shows how news shocks can generate severe recessions in a zero lower bound environment in a model with frictional labor markets. We will abstract from issues related to a lower bound on the nominal interest rate.
The remainder of the paper is organized as follows. Section 2 sets of the model economy. In Section 3 we study a version of the model in which there is no wealth inequality in equilibrium.
Section 4 presents the results from the main model. Section 5 concludes and summarizes.

The Model Economy
The economy is inhabited by households, …rms which are owned by entrepreneurs, and by a government which is in charge of monetary and …scal policy. We introduce a number of frictions in goods, asset and labor market by combining three workhorse models in macroeconomics.
First, the labor market is characterized by Diamond-Mortensen-Pissarides matching frictions which we extend by introducing di¤erential matching prospects across unemployed workers.
Secondly, as in Bewley (1977) and Aiyagari (1994), asset markets are incomplete. Speci…cally, following Krusell and Smith (1997), the model features idiosyncratic and aggregate risk in an incomplete markets set-up. Third, we assume that …rms are monopolistically competitive and set prices in an environment with nominal rigidities in price setting. We adopt the set-up of Rotemberg (1982) where …rms face quadratic costs of adjusting nominal prices. We examine the response of the economy to stochastic job separation shocks and shocks that a¤ect the amount of labor market mis-match.
Households. There is a continuum of mass 1 of in…nitely lived households indexed by i 2 (0; 1).
Households have rational expectations and maximize the expected present value of their utility stream. A household is either working (matched with a …rm) or unemployed and looking for a job. Unemployed workers di¤er in the e¢ ciency of the matching technology that they face.
This feature produces heterogeneity across unemployed workers in the expected duration of unemployment spells. Asset markets are assumed to be incomplete which produces an incentive for precautionary savings to insure against unemployment and other shocks. Di¤erences in labor market histories and asset market incompleteness in combination produce wealth inequality across households.
Households consume a basket of consumption goods varieties: where c j i;t denotes household i's consumption of goods of variety j and > 1 is the elasticity of substitution between consumption goods. Variety j is purchased at the nominal price P j;t .
It follows that household i's demand for variety j is given as: where P t is the price index associated with the consumption basket de…ned in (1): A household that is employed in period t works full-time hours (normalized to one unit), receives a real wage w t , pays a lump-sum social security tax T h t , and experiences a job termination with probability x;t 1. A fraction r;t of the workers that experience a job termination make a transition to unemployment state r, r = s; l, s;t + l;t = 1.
An unemployed household in state r receives (gross of taxes) unemployment bene…ts r 0 and …nds a new job with probability r;t . We assume that l;t < s;t and will therefore, slightly imprecisely, refer to the two groups of unemployed workers as short-and long-term unemployed. 8 We will assume that s l so that the risk of a longer unemployment spell is not o¤set by higher bene…ts. An appealing interpretation of the two types of unemployed workers is that type l unemployed workers are mis-matched and face a more demanding job search process.
We have in mind that mis-matched workers may need to move across professions, sectors or geographical areas to …nd a new job after a job termination.
Job terminations occur at the end of the period while new job matches are formed at the beginning of the period. Households are informed about the job loss probabilities at the beginning of the period and therefore have within-period perfect foresight about the share of currently employed workers who will lose their jobs and about the share of these that become short-and long-term unemployed. However, households face idiosyncratic uncertainty about both the identity of the workers who lose their jobs, about the unemployment state should they lose their job, and about future job separation rates.
Households have access to a state non-contingent bond which carries a (gross) nominal interest rate of R t . We impose a borrowing constraint by assuming that there is a utility cost of holding debt. 9 Let b h i;t denote household i's holding of bonds at the end of period t. We assume that there is a utility cost function, ', and a debt limit b 0 so that This implies that no household chooses b h i;t < b.
Households face a sequence of budget constraints: n i;t indicates the employment status of household i at date t while I r;t indicates the unemployment state status: Employed households solve the dynamic programming problem: subject to the budget constraint in equation (5) setting n i;t = 1. u (c i;t ) is a concave utility function. V e i (b i;t 1 ; S t ) is the value for a household that is employed at the beginning of the period given her assets, b i;t 1 , and given an aggregate state vector S t which is speci…ed is the value for an unemployed household who is faced with state r = s; l unemployment. 2 (0; 1) is the subjective discount factor, and E t is the conditional expectations operator. x;t r;t is the probability that a worker who is employed at the beginning of the period makes a transition to unemployment state r and P r=s;l x;t r;t 1 r;t+1 is the probability of not being employed at the beginning of period t + 1.
A type r unemployed worker faces the problem: subject to the budget constraint in equation (5) setting n i;t = 0 and I r;t = 1. > 0 denotes the utility of leisure enjoyed by an unemployed household (having normalized the utility of leisure of employed households to zero). As a matter of consistency, we will make the assumption that S for all b h and S so that no employed household has an incentive to voluntarily leave their current job. Under the condition that s;t+1 > l;t+1 the condition that for all b and S. 10 Entrepreneurs. Consumption goods are produced by a continuum of monopolistically competitive …rms indexed by j 2 (0; 1) which are owned by risk neutral entrepreneurs. We let < 1 denote the measure of entrepreneurs. Entrepreneurs discount utility at the rate and make decisions on the pricing of their good, on vacancy postings, and on their consumption and savings policies. In return for managing (and owning) the …rm, they are the sole claimants to its pro…ts (but will also have to stand ready to cover losses). We assume that entrepreneurs can save but face a no-borrowing constraint. This no-borrowing constraint implies that the entrepreneur …nances hiring costs through retained earnings. 11 Output is produced by according to a linear technology: where A > 0 and n j;t denotes entrepreneur j's input of labor which is purchased from the households. Firms are assumed to be su¢ ciently large (i.e. the mass of entrepreneurs is small relative to the mass of households) that there are no indivisibility problems associated with the full-time hours assumption made earlier. 10 The formulation of the unemployed workers problems in equations (7) assumes that there are no ‡ows between the two unemployment states during unemployment. However, all workers face identical job prospects upon employment. The …rst of these assumptions is easily relaxed and immaterial for the results as long as the ‡ow out of unemployment is su¢ ciently small for type l workers relative to type s workers. 11 In the equilibrium, < 1=R so entrepreneurs will be borrowing constrained.
Following Rotemberg (1982) we assume that there are nominal rigidities in the form of quadratic costs of price adjustment which, together with frictional labor markets, implies that …rms face a dynamic optimization problem. Given risk neutrality, entrepreneurs set prices to maximize the present discounted value of pro…ts: E t 1 X s=0 s P j;t+s P t+s mc j;t+s y j;t+s 2 P j;t+s P j;t+s 1 P j;t+s 1 2 y t+s ! (9) subject to: Equation (10) is the demand for goods variety j. y t , which is de…ned formally below, can be interpreted as aggregate real income. In equation (9) 0 indicates the size of costs of changing prices with = 0 corresponding to ‡exible prices. mc j;t denotes real marginal costs.
The …rst-order condition for this problem is given as: In a symmetric equilibrium, which will be the focus of our analysis, this simpli…es to: Firms hire labor in a frictional labor market. The law of motion for employment in …rm j is given as: where h j;t denotes hires made by …rm j in period t. The number of hires in turn is given as: where v j;t is the number of vacancies posted by the …rm and f;t is the job …lling probability. We assume that …rms are su¢ ciently large that f;t can be interpreted as the fraction of vacancies that lead to a match. 12 The cost of posting a vacancy is given by > 0. Therefore, real marginal costs are given as: which incorporates the fact that hiring in period t impacts on future marginal costs through future hiring cost savings.
Finally, the budget constraint of entrepreneurs can be expressed as: where b e j; 1 0 is given, d j;t denotes entrepreneur j's consumption in period t and b e j;t their bond purchases in period t. Condition (16) imposes the no-borrowing constraint on entrepreneurs. T e t are employer contributions to social security.
Labor Market. We assume that the matching technology is given as: where m t denotes the measure of matches between …rms (vacancies) and unemployed workers at date t, u r;t is the measure of type r unemployed workers at date t and v t is the measure of vacancies posted by the …rms. > 0, and 2 (0; 1) are constant parameters. The parameter q 2 (0; 1] is the probability that a type l unemployed worker is searching for a job at date t.
When q < 1, type l workers are less likely to …nd a job than type s unemployed workers and face longer expected unemployment duration. We will think of this parameter as indicating the impact of mis-match unemployment on labor market prospects.
Given the matching technology, the job …lling probability and the job …nding probabilities 12 This assumption can be relaxed which would produce ex-post heterogeneity across …rms.
are given as: where t = v t =u t denotes labor market tightness, u t is the measure of unemployed workers.
Importantly, as long as q < 1, the job …lling rate depends negatively on the share of long term unemployed because these workers match less e¢ ciently with vacancies than short term unemployed workers. 13 This externality means that it is costlier to …ll jobs in periods with high long term unemployment which makes …rm less likely to post vacancies.
The laws of motion of the stocks of employed and unemployed workers are given as: Our candidates for stochastic shocks to the economy are exogenous changes in the job separation rate, x;t , and in s;t , which determines the share of workers a¤ected job terminations that become short-term unemployed. We assume that: where x ; s 2 (0; 1) are the long-run levels of job termination and the share of short-term unemployed, respectively, while x ; s 2 ( 1; 1) denote the persistence of shocks to the job termination rate and to the share of short-term unemployed. It is assumed that " t N (0; V " ) where " t = (" x;t ; " s;t ) 0 .
We experiment with alternative assumptions regarding wage setting. All schemes that we consider are required to be consistent with a non-negative surplus of any worker-…rm matches so that none of the partners have an incentive to terminate an existing match voluntarily. In our benchmark model, we assume that real wages are constant, w t = w. 14 We examine whether the results are robust to assuming that wages are instead determined according to a Nash bargaining model. In the face of wealth heterogeneity, Nash bargaining introduces worker-speci…c wages which complicates the analysis very signi…cantly.
Government. The government is in charge of monetary and …scal policies. We assume that the government balances the budget period by period which means that: which re ‡ects the lump-sum nature of the social security taxes.
Monetary policy is speci…ed by a rule for the short-term nominal interest rate. We assume that: where R is the long-run nominal interest rate target, is the in ‡ation target, and denotes the elasticity of the nominal interest rate to deviations of in ‡ation from its target.
Equilibrium. We focus upon a recursive equilibrium in which households act competitively taking all prices for given while …rms act as monopolistic competitors setting the price of their own variety taking all other prices for given. In equilibrium, …rms are symmetric because there are no idiosyncratic productivity shocks, prices are set in a state-contingent manner, and because they assumed to be su¢ ciently large that they all hire the same number of workers. 15 We let p j;t = P j;t =P t denote the relative price of …rm j's product. Symmetry implies that this relative price equals 1 in equilibrium. 14 We have checked that the match surplus is positive for all matches in all the results that we report. 15 Firms are also assumed to be su¢ ciently big that there the full time hours assumption does not give rise to any indivisibility problems.
Households are instead heterogeneous and di¤er in their labor market status and in their wealth.
In equilibrium, aggregate savings equal zero but, since wealth matters for savings choices, the wealth distribution is an aggregate state variable which impacts both on household and on entrepreneurial choices. We let t = (b t 1 ; e t ) denote the distribution of agents over asset levels and employment states, where e it indicates the labor market status of household i (whether employed or unemployed in state r = s; l). 16 We let d t denote the associated density of the joint distribution of assets and labor market status. The relevant state vector is then de…ned as S t = t ; x;t ; s;t .
De…nition 1 A recursive monopolistic competition equilibrium is de…ned as a distribution of wealth (b; e), pricing kernels (w (S) ; (S)), decision rules c and W (b e ), and government policies (T (S) ; R (S)) such that (i) given the pricing kernel, the government policies, and the aggregate and individual states, the household decision rules solve the households problem; (ii) given the pricing kernel, government policies, and the aggregate state, the entrepreneur decision rules solve the entrepreneurs'problem and p j (b e ; S) J j=0 = 1 for all j and all (b e ; S); (iii) asset and goods market clear: (iv) the government budget constraint is satis…ed and the nominal interest is given by the policy rule in equation (24) Solution Method.
Before turning to the general version of the model, we …nd it instructive to examine a special case where we impose that b = 0. The no-borrowing constraint implies that all households hold zero wealth in equilibrium so that the wealth distribution no longer is an aggregate state variable. We can therefore compute the equilibrium in a simple manner using a standard pertubation method. The relative simplicity of the numerical procedure also means that this version of the model lends itself to a rigorous robustness analysis. Although this model features no equilibrium wealth inequality, its key mechanisms are much the same as in the general version that allows for borrowing apart from the fact that there are no di¤erential impact on agents according to their wealth.

Calibration
The calibration targets and parameter values are summarized in Tables 1 and 2. One model period corresponds to a calendar month. The household utility function is assumed to be given as: ; 0 and we set = 1:5. This value is in the mid-range of empirical estimates of Attanasio and Weber (1995), Eichenbaum, Hansen, and Singleton (1988), and many others who have examined either household data or aggregate time series. determines the degree of risk aversion which matters for the household savings response to uncertainty and this is important in our model.
We assume an annual real interest rate of 3 percent and set the subjective discount factor equal to 0.99 for both households and entrepreneurs. This value is low relative to standard representative agent models but because of idiosyncratic risk and incomplete markets, agents have a strong incentive to engage in precautionary savings and a low real interest rate is required to induce zero savings in equilibrium.
We target an unemployment rate of 5 percent and a 15 percent share of long term unem-ployed (unemployed workers who have been out of work for 6 months or more) in the stationary equilibrium. These targets are close to the mean statistics for the United States in the post-1970 period. Following Rothstein (2011), we target a monthly hazard rate from unemployment to employment for a newly unemployed workers of 40 percent and a 30 percent monthly hazard rate for workers who have been unemployed for 26 weeks or more. These targets imply a steady-state job loss probability, x , of 2:95 percent per month, that s , the share of workers who experience a job loss that enter the pool of high search e¢ ciency unemployment, equals 35 percent, and that the relative search e¢ ciency of the mis-matched unemployed, q, is 50:2 percent. We assume that the matching function elasticity to unemployment is equal to 50 percent ( = 0:5), and normalize = 1. , the vacancy cost parameter, is calibrated by targeting an average hiring cost of 4:5 percent of the quarterly wage bill. Given other parameters, this implies that = 0:18.
We calibrate the bene…t levels, s and l , by targeting estimates of the consumption loss during unemployment reported by Browning and Crossley (2001). Studying Canadian data, these authors …nd that consumption drops on average 14 percent upon a permanent job loss.
They also document a lot of dispersion across workers with 25 percent su¤ering no loss while the worst hit 10 percent experience a consumption loss of 50 percent. In the the model, the borrowing limit implies that all households hold zero savings in equilibrium and therefore that consumption equals ‡ow (after tax) income. Thus, in the stationary equilibrium, 35 percent (65 percent) of the population would su¤er a consumption loss that would correspond to the di¤erence between the real wage and s ( l ). In order to moderate slightly the impact of the no-borrowing constraint, we assume that s = 0:925w and that l = 0:84w (where w is the real wage) which imply an average consumption loss upon unemployment of just below 14 percent as estimated by Browning and Crossley (2001) but has less variance across the unemployed agents.
We set the average mark-up is 20 percent which implies that , the elasticity of substitution between goods, is equal to 6. , the parameter that determines the importance of price adjustment costs, is calibrated to match price adjustment frequency of 5 months. This value is conservative but close to the value estimated by Bils and Klenow (2004). 17 This implies that = 142:86. We assume that the government's in ‡ation target = 1 so that it pursues price stability and we set = 1:5, a conventional value in the new Keynesian literature.
Finally, we estimate the parameters of the stochastic processes that determine the persistence and volatility of the job separation rate and of the share of high search e¢ ciency unemployed workers from time-series data for layo¤s and the share of workers who have been unemployed for 6 months or more. We …nd estimates of x = 0:9774 and s = 0:7926. this implies a half-life of job separation shocks of 30 months while shocks to the share of regular vs.
mis-matched unemployment die out very fast.

Results
The Impact of Shocks . Figures 2 and 3 illustrate the impact of a one standard error increase in job separations and in the share of mis-matched unemployed, respectively. We report the impact on the unemployment rate, on the share of unemployed workers who have been out of work for 6 months or more, on average unemployment duration, on the job …nding rate, on vacancies, and, …nally, on the real interest rate and the in ‡ation rate.
An increase in the job separation rate puts upward pressure on the unemployment rate. At the same time, we …nd that there is a signi…cant drop in the vacancy index which falls by 4 percent on impact and recovers only gradually over time. Thus, the increase in unemployment produced by the increase in layo¤s is propagated though fewer vacancies which together imply a signi…cant worsening of the labor market outlook and a large and very persistent decrease in the job …nding rate. An important for why the increase in job separations spill over to vacancies derive from the impact on household savings. We notice that the real interest rate drops very signi…cantly. This re ‡ects mainly that a lower real interest rate is needed to clear the asset market because households increase their precautionary savings motive in response to the bleaker jobs prospects. In conjunction this produces a large and persistent in the level and duration of unemployment. Figure 3 illustrates the impact of an (one standard deviation) increase in the share of job separations that send workers into mis-match unemployment holding constant the job separation rate. This shock has a large impact on the economy which is qualitatively similar to that of a layo¤ shock but quantitatively much larger. Mis-matched workers take on average longer to …nd a job than regular unemployed workers. This shock therefore stimulates the desire to savings which is re ‡ected in a large drop in the real interest rate. This implies that …rms face low demand for their goods and also realize that vacancies are hard to …ll because of the preponderance of low search e¢ ciency workers amongst the unemployed. Hence, vacancies fall very signi…cantly which leads to a large drop in the job …nding rate. The decrease in the job …nding rate and the lower search e¢ ciency of the stock of unemployed workers jointly imply that the unemployment rate and the average unemployment duration both increase very signi…cantly.
We …nd it useful to compare the results of the benchmark economy to two alternative economies. In the …rst alternative economy we assume that prices are ‡exible, = 0. In this economy, there is a much weaker transmission of shocks from households'demand for goods to …rms'demand for labor since …rms have a strong incentive to cut prices in response to weak goods demand. It is therefore useful to examine this alternative economy to understand how labor market frictions and idiosyncratic risk interact with goods market frictions.
In the second alternative economy we assume complete markets so that households can insure fully against idiosyncratic shocks. This is equivalent to assuming that households are organized in a single family which insures all idiosyncratic risk with the family's budget constraint being given by: where we use that intra-household insurance implies that consumption levels are equalized across households. This economy features no idiosyncratic risk and aggregate shocks in the labor market still impacts on the economy, the precautionary savings channel against idiosyncratic risk is neutralized. Figure 4 demonstrates the impact of the job separation shock in the benchmark economy and in the economies where either prices are ‡exible but asset markets are incomplete or asset markets are complete but prices are sticky. The initial increase in unemployment in the complete markets model is almost the same as in the benchmark model but falls monotonically from the second month after the increase in layo¤s and the peak increase is less than half of what is observed in the benchmark model. The reason from this is clear from the real interest rate path which shows that the demand channel is neutralized almost immediately when asset markets are incomplete. For that reason, apart from the …rst month, …rms take advantage of the ease of hiring and post more vacancies. For that reason, the job …nding rate is almost una¤ected by the increase in job terminations and the ampli…cation mechanism is almost totally neutralized.
The ‡exible price model produces very similar results to the model with complete markets with the only di¤erence being that the e¤ects are somewhat more persistent in the ‡exible price economy than in the complete markets model. The ampli…cation mechanism in the benchmark model is even stronger in response to the mis-match shock, see Figure 5. Here we …nd almost no impact on unemployment or any other variable when either prices are ‡exible or asset markets are complete.
We conclude from this that it is combination of incomplete markets and sticky prices that produce an ampli…cation mechanism in which deteriorating labor market prospects produce low demand for goods which in turn leads to weak labor demand thereby creating a vicious circle.
When asset markets are complete, there is little impact on goods demand while ‡exible prices neutralize the channel that goes from goods demand to labor demand.
A Great Recession Experiment. We now turn to a Great Recession experiment. We derive estimates of the sequences of innovations to job termination and to the fraction of workers that ‡ow into high search e¢ ciency unemployment, (" x;t ; " s;t ) 2012:1 t=2007:1 , by matching the observed US time-series on layo¤s and the number of unemployed workers who have been out of work for 6 months or more (relative to the labor force). We back out these shocks for the sample period from January 2007 until January 2012. In order to avoid having too erratic shocks, we smooth both data series with a 4 months moving average …lter. We then feed the resulting shock processes into the model economy and simulate the economy in response to this particular sequence of shocks.
The …rst two panels of Figure 6 show the path of layo¤s and the fraction of long term unemployed that we target. The other two panels illustrate the time-series of unemployment and vacancies observed in US data together with the corresponding time-series implied by the benchmark model. We also show the corresponding time-series generated by the model when assuming either that there is no mis-match state, prices are ‡exible, or asset markets are complete. We initialize the unemployment rate at the steady-state and we report vacancies in terms of percentage deviations from steady-state.
The benchmark model reproduces almost exactly the observed unemployment rate. As in the actual data, unemployment starts increasing fast from early 2008 and peaks around 10 percent in late 2009 -early 2010. The model implies a slightly lower unemployment rate in the post-2011 sample than the actual value observed in the US but the di¤erence is not large.
One might think that this success in accounting for the increase in unemployment during the Great Recession derives from the fact that we are feeding the observed layo¤s into the model but this intuition is not correct. In fact, when we assume either ‡exible prices or complete markets, we can account for a maximum 1.5 percentage point increase in unemployment, less than one third of the increase implied by the benchmark model. The complete markets model, in particular, fails miserably which indicates that precautionary savings play an important role for accounting for the benchmark model's ability to produce a deep recession in response to the labor market shocks. However, although the ‡exible prices cum incomplete markets model implies a larger increase in unemployment that the sticky prices cum complete markets, it still produces very little action in unemployment.
The key reason for these di¤erences derive from how the shocks impact on vacancies. In prices or complete markets. This re ‡ects the fact that the increase in unemployment makes it attractive for …rms to hire workers because of the ease of transforming vacancies into hires. This is also the case in the benchmark model but here low demand for goods hold back …rms'hiring e¤orts. Said otherwise, while the benchmark model features a strong feedback from households to …rms which is re ‡ected in low labor demand, there is little such feedback when either prices are ‡exible or asset markets are complete.
In order to evaluate the importance of the mis-match unemployment state we also report the outcome for unemployment and vacancies when we set (" s;t ) 2012:1 t=2007:1 = 0 so that the economy is hit by job separation shocks only. In this case, we …nd a moderate increase in unemployment and a path of vacancies that are very similar to what the outcome under ‡exible prices. Thus, the increased risk for a low income state with long duration that is key for generating the ampli…cation mechanism.
Much discussion surrounding the Great Recession as focused on the relationship between unemployment and vacancies and the outward shift in the Beveridge curve that seems to have occurred since 2007. We illustrate this in Figure 7. During the early parts of the recession, there was a marked decline in both vacancies and in the unemployment rate but later on the crisis, the recovery in vacancies has been associated with only a minor decline in unemployment consistent with the view that the Beveridge curve has shifted out. In Figure 7 we also report the joint trends in unemployment and vacancies implied by our model by combining the last two panels of Figure 6. The versions of the model that assume either ‡exible prices, complete markets, or changes only in job separation rates fail to reproduce the joint decrease in unemployment and vacancies during the early parts of the recession and the implied relationship between unemployment and vacancies bear little resemblance if any to its empirical counterpart. The benchmark model instead performs extremely well at least until the later part of the recession where there is a more signi…cant rise in vacancies and drop in unemployment in the US data than predicted by the model. Nonetheless, the model is remarkably successful in accounting for the Beveridge curve.
One important lesson from this is that the success of the model in accounting for the rise in the level and unemployment during the Great Recession does not hinge on an unrealistic increase in mis-match unemployment. Instead, the key is the strong ampli…cation mechanism embedded in the model.