The Search and matching Model

Transcription

1 The Search and matching Model THE GREAT RECESSION AND OTHER BUSINESS CYCLES April 2018

2 The DMP search and matching model An equilibrium model of unemployment Firms and workers have to spend time and resources before a match is formed. (A model of frictional unemployment) A match involves rents and a positive surplus Search externalities Based on Diamond (1982), Mortensen (1982), Pissarides (1985). The model we ll use is closer to Pissarides (1985). (Also in Pissarides (2000), and LS ch )

3 Assumptions Risk neutral firms and workers Discrete time; future values discounted by a factor β = 1 1+r No labor force participation decision. All unemployed workers search for jobs Firms decision is how many vacancies to maintain Unemployed workers and open vacancies meet according to a matching technology Timing: match at t; begin production at t + 1 Surplus is divided according to bargaining; bargaining occurs every period A constant exogenous separation rate λ

4 Firms Produce a final homogeneous good CRS production technology - produce p units with one unit of labor (all workers are identical and equally productive) Maintain v open vacancies at a cost c per vacancy, per period Free entry - many potential firms/vacancies willing to enter if there are positive profits

5 Matching Technology M(v, u) = Av α u 1 α M = number of new hires v = number of open vacancies u = number of unemployed/searchers

6 Firms and workers take these probabilities parametrically. This is a source for search externality. Matching Technology Constant returns to scale Properties Constant elasticities M v v M = αavα 1 u 1 α v M = u 1 α αavα M = α Define the tightness ratio θ v u ; with CRS: Job filling prob: q(θ) = M v = Avα u 1 α v = A ( ) v α 1 u = Aθ α 1 Job finding prob: µ(θ) = M u = Avα u 1 α u = A ( v u) α = Aθ α = θq(θ)

7 Bellman Values The rest of the model can be described with a set of 4 Bellman equations: V = the value of an unfilled vacancy J = the value of a filled/active job to the firm U = the value of an unemployed worker W = the value of an employed worker We use to denote next period s variables

8 The Value of an Open Vacancy V = max{0, c + βe [ q(θ)j + (1 q(θ))v ] } Can choose note to open a vacancy - value is zero If a vacancy is open : Pay a flow cost c With prob q the job is filled; prob (1 q) the job is not filled Because of timing assumption, discount by a factor β. Can think about J V as a capital gain ; this is the surplus the firm derives from a match

9 Value of a Filled Job J = p ω + βe [ λv + (1 λ)j ] The value of an active job to the employer consists of productivity p the wage that is paid to the worker ω Continuation With prob λ the match is separated and the firm receives a value V With prob (1 λ) the match continues and the firm receives a value J next period

10 The Zero Profit Condition The central condition of the model...with free entry and exit Assume V > 0 for the given costs and probabilities, more vacancies created θ increases job filling probability q(θ) = Aθ α 1 declines V declines Assume V < 0 for the given costs and probabilities, some existing vacancies close (generate zero value) θ decreases job filling probability q(θ) = Aθ α 1 invreases V increases V=0 in equilibrium V = 0 c = βq(θ)e [J ] J = p ω + βe [λv + (1 λ)j ] = p ω + β(1 λ)e [J ]

11 Workers U = z + βe [ µ(θ)w + (1 µ(θ))u ] W = ω + βe [ λu + (1 λ)w ] All workers are either working or searching All workers are equally productive An employed worker receives a wage ω; unemployed workers receive constant unemployment benefits z per period An unemployed worker finds a job with prob µ(θ); An employed worker separates from job with prob λ

12 Wage Bargaining Once there is a match, there exists a (total) surplus W U + J V = W U + J This surplus needs to be divided between the worker and the employer Both the worker and the employer have outside options in the event of disagreement. (Worker can get the value U; Firm receives the value V = 0). This implies that reservation wages exist, and the actual wage is between them Bargain every period (the outside options may change as shocks hit the economy)

13 Nash Bargaining With Nash bargaining: Denote by τ the worker s share of the match surplus The wage level is maximizing the Nash product ω = argmax (W U) τ (J V ) 1 τ = argmax (W U) τ J 1 τ

14 Deriving the Wage Function (1) Take the first order condition of the Nash product (and set equal to zero) Note that (W U) ω = 1 and J ω = 1 τ (W U) τ 1 (W U) J 1 τ + (W U) τ τ J (1 τ)j ω ω = 0 τ (W U) τ 1 J 1 τ (W U) τ (1 τ)j τ = 0 τ (W U) τ 1 J 1 τ = (W U) τ (1 τ)j τ τj = (1 τ) (W U) Surpluses are proportional; Bilateral efficiency: when the firm s surplus is positive, so is the worker s surplus

15 Deriving the Wage Function (2) Rearrange the last equation τj = (1 τ)(w U) = (W U) τ(w U) W U = τ(j + W U) = τ Total Surplus J = T S (W U) = T S τt S = (1 τ)t S The Nash rule implies that total surplus is divided according to the bargaining weights. The bargaining weights reflect the worker/firm share of the surplus

16 Deriving the Wage Function (3) To actually derive the wage function, let s substitute the values U, W, J into the first order condition τj = (1 τ)(w U) τ [ p ω + (1 λ)βe [ J ]] = (1 τ){ω + βe [ (1 λ)w + λu ] z βe [ µ(θ)w + (1 µ(θ))u ] } = (1 τ){ω z + βe{w [1 λ µ(θ)] U [1 µ(θ) λ]}} = (1 τ){ω z + (1 λ µ(θ))βe [ W U ] }

17 τ [p ω] + τ(1 λ)βe [ J ] = (1 τ)(ω z) (1 τ)µ(θ)βe [ W U ] +(1 τ)(1 λ)βe [ W U ] With the assumptions on bargaining, we know that τj = (1 τ)(w U) every period. Therefore the last term on the LHS and the last term on the RHS cancel, and we have τ(p ω) = ω z τω + τz (1 τ)µ(θ)βe [ W U ] ω = τp + (1 τ)z + (1 τ)µ(θ)βe [ W U ]

18 The Wage Equation interpretation ω = τp + (1 τ)z + (1 τ)µ(θ)βe [ W U ] The wage is a function of productivity the value of leisure (unemployment benefits) an opportunity cost when the worker takes a job, he forgoes the opportunity to find a different job (with probability µ)

19 The Wage Equation as a function of current period variables In most cases we want to express the wage as a function of current period variables. This usually involve expressing ω as a function of θ (the tightness ratio). This, in turn, reduces the solution of equilibrium to one equation with one unknown θ. Use three assumptions/results: First, note that τj = (1 τ)(w U). Therefore we can write the last equation as ω = τp + (1 τ)z + τµ(θ)βe [ J ] Second, recall that µ(θ) = θq(θ) (using the prob defined by the matching technology) ω = τp + (1 τ)z + τθq(θ)βe [ J ]

20 The Wage Equation as a function of current period variables Finally, note that in any equilibrium the zero profit condition c = βq(θ)e [J ] must hold: ω = τp + (1 τ)z + τθc The interpretation is the same as before. The first two terms depend on productivity and flow value of leisure. The last term still reflects to the opportunity cost: When θ is higher, the job finding rate µ(θ) is higher easier to find a job the outside option of remaining unemployed is better, and therefore the wage must be higher. Alternative interpretation cost saving

21 Unemployment This is the final piece needed before defining the steady state of the model. Based on transitions each period: a fraction λ of employed workers transition for emp to unemp a fraction µ(θ) of unemployed transition from unemp to emp recall that we assume that everyone is in the labor force n + u = 1 u = (1 µ(θ))u + λ(1 u)

22 Steady State Equilibrium A steady state equilibrium is a triple (u, θ, ω) that satisfies the zero profit condition (job creation condition): c = βq(θ ss )J ss the wage equation: ω ss = τp + (1 τ)z + τθ ss c the unemployment equation u ss = (1 µ(θ ss ))u ss + λ(1 u ss ) λ = u ss (λ + µ(θ ss )) u ss = λ λ + µ(θ ss )

23 Steady State Equilibrium Use the definition of the value J in steady state: J ss = p ω ss + β(1 λ)j ss J ss = p ωss 1 β(1 λ) Substitute back in the job creation condition c = βq(θ ss )J ss = βq(θ ss p ω ss ) 1 β(1 λ) or c βq(θ ss ) = p ωss 1 β(1 λ) The job creation equation and the wage equation: two equations with two unknowns θ ss, ω ss can solve for θ ss, ω ss. Once we have a solution for θ we can solve for µ, and solve for u ss.

24 Graphical Representation I Similar to the usual labor demand and labor supply curves we can look at the job creation condition and the wage equations graphically. The price is still the real wage ω. The quantity is the tightness ratio θ. The wage equation implies that when θ increases, ω should increase an upward sloping curve (acts like a supply curve) Looking at the job creation condition: when θ increases, q(θ) decreases, and so the left hand side of the equation increases. For the equation to hold, the wage should adjust so that the RHS increased as well. It is clear that the wage should decrease. This establishes an inverse relation between θ and ω a downward sloping curve (acts like a demand curve)

25 !! Graphical Representation I!!!! "#$%!%&'#()*+!,*-!./%#()*+!0,12!!!

26 Graphical Representation II Alternatively, we can describe the steady state equilibrium on the v, u space. First, substitute the wage equation into the job creation condition. This results in one equation with one unknown θ. The solution itself is independent of u. Therefore, when a solution exists, we can describe the relation between u and v as a linear line with a slope θ. (Recall that θ v u.) We can also use the steady state unemployment equation u = λ λ+µ to plot the Beveridge Curve: a negative relation between unemployment and vacnacnies.

27 !! Graphical Representation II!!!! "#$!%&'()*#+!,"-.! /'0'&*12'!-3&0'!!!

28 Comparing steady states To develop some intuition, let s look at a few simple examples. Higher unemployment benefits z: ω = τp + (1 τ)z + τθc clearly the wage curve should shift up A new equilibrium with a lower θ and a higher wage. The lower θ implies a flatter JC line in the (v, u) space moving down along the Beveridge curve to an equilibrium with higher u and lower v. Makes sense... higher unemployment benefits imply that the outside option for the worker is better, increasing the worker s reservation wage and the equilibrium wage. This implies that matches are less profitable to firms, leading to creation of fewer vacancies. What does this model miss? insurance aspects of unemployment benefits.

29 Higher separation rate λ Comparing steady states c βq(θ ss ) = The JC condition: p ωss 1 β(1 λ) λ does not enter the wage equation directly, so no shift of the wage curve A higher λ reduces the value of the RHS of the JC equation Since the RHS, the LHS should as well q(θ), and θ for any level of wages The JC curve shifts down. New steady state at lower θ and a lower ω Moving down along the Beveridge Curve

30 Comparing steady state Higher labor productivity p A direct effect on wages through the wage equation. Wage curve shifts up. A direct effect on job creation: p RHS LHS q(θ) θ JC curve shifts up; wage curve shifts up; Based on the diagram alone, ambiguous prediction with respect to θ, and the wage increases If we use the JC equation, and substituting for the wage: c βq(θ ss ) = (p z)(1 τ) τθss c 1 β(1 λ) we can see that as long as τ < 1, the effect on θ will be positive. Higher θ implies a move up along the Beveridge curve to a new steady state with higher v and lower u

31 Business Cycles Application The examples can be interpreted as the long run response to permanent shocks. In business cycles analysis, we are often interested in the short and medium run responses to transitory (yet persistent) shocks. For that, we have to look at the dynamic problem, rather than focusing on steady state. In many cases the starting point is calibrating the model and calculating a non-stochastic steady state. Then the model is hit by stochastic shocks, and we use that to evaluate the response of the model variables to the shocks. Popular way to evaluate a model: second moment statistics

32 Unemployment 11 Unemployment Year

33 Unemployment - trend and deviations 2.5 Trend Year 0.3 Deviaions Year

34 Unemployment and vacancies 0.3 Deviaions 0.2 unemployment vacancies Year

35 Shimer s puzzle Can the model explain business cycles (v, u, θ)? The exercise goes as follows: Shocks to: Given shocks to the model and parameters... What s the volatility of u and v in the model? How does this volatility compares with the data? labor productivity (BLS) Separations (CPS, time aggregation) Value of leisure = 0.4 Matches elasticity = 0.72 Bargaining power = Matches elasticity (Hosios)

36 Shimer s puzzle Results Quarterly Summary Statistics from U.S. Data, 1951:1 to 2003:4 u v v/u p Std Dev Quarterly Autocorrelation Correlation u Correlation v Correlation v u Correlation p

37 Shimer s puzzle Results Quarterly Summary Statistics from Model Simulations u v v/u p Std Dev Quarterly Autocorrelation Correlation u Correlation v Correlation v u Correlation p

38 Unemployment and productivitiy 0.3 Deviaions unemployment Productivity Year

39 Mechanisms If productivity falls or separations increase then: Value of a filled job goes down BUT! Vacancies go down Wage goes down Unemployment goes up These feedback effects increase vacancies back

40 What if productivity was very volatile? 0.6 Deviaions 0.4 unemployment 20*Productivity Year

41 Three types of solutions Robert Hall (2005) - Fine tune the model Hall, R.E., Employment Fluctuations with Equilibrium Wage Stickiness. American Economic Review 95, Marcus Hagedorn and Iourii Manoskii (2008) - Change the calibration Hagedorn, M., Manovskii, I., The Cyclical Behavior of Equilibrium Unemployment and Vacancies Revisited. American Economic Review 98(4), Zvi Eckstein, et al (2015) - Change the shock Eckstein, Z., et al., Financial Risk and Unemployment. Unpublished.

42 Three types of solutions Hall (2005) Introduces Sticky wages Strenghtens shock b/c firms need to pay the previous wage Hagedorn and Manovskii (2008) change the calibration as follows: a very high leisure value (0.955) a low bargaining power for workers (0.05) Wages do not change very much (i.e., sticky) Eckstein, et al (2015) use different shocks: Interest rate: cost of capital and cost of vacancy fluctuate Financial spread: implies a high probability of default and separation Model s volatility of both v and u is same magnitude of data

43 Eckstein-et al Results Quarterly Summary Statistics from the Calibrated Model u v v/u r Std Dev Quarterly Autocorrelation Correlation with u Correlation with v Correlation with θ Correlation r

44 Unemployment and interest rate 0.4 Deviaions 0.3 unemployment interest rate Year

45 Financial Risk and Unemployment Zvi Eckstein, Ofer Setty, David Weiss Tel Aviv U. and IDC, Tel Aviv U., Tel Aviv U. February /37

46 Introduction Volatility in unemployment u, vacancies v, tightness θ = v u Firms experience a large volatility in financial risk: Interest rate fluctuations (BAA) Spread ( default) fluctuations (BAA-Treasury) Relationship? 2/37

47 q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q Unemployment, Interest rate and Spread Recessions Unemployment rate Figure: US time-series data /37

48 q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q Unemployment, Interest rate and Spread Recessions Unemployment rate Credit spread Figure: US time-series data /37

49 q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q Unemployment, Interest rate and Spread Recessions Unemployment rate Credit spread BAA interest rate Figure: US time-series data Spread & interest rate Granger cause u with lag 2. 5/37

50 Research question & Methodology How does financial risk (interest rate and credit spread) affect unemployment, vacancies, and market tightness? What are the mechanisms? What is the quantitative power? 6/37

51 Research question & Methodology How does financial risk (interest rate and credit spread) affect unemployment, vacancies, and market tightness? What are the mechanisms? What is the quantitative power? Methodology: Use a search-and-matching (DMP) model with capital Exogenous financial intermediary cost and default shocks together determine interest rate and default Outline mechanisms for how shocks affect Calibrate Model to US economy (w/o targeting volatility) Ask how much volatility is generated 6/37

52 Mechanisms Productivity shocks: p profits v u θ = v u 7/37

53 Mechanisms Productivity shocks: p profits v u θ = v u Interest rate rises: higher capital costs lead to a lower profits (Flow Profits) more expensive vacancies (Vacancy Cost) 7/37

54 Mechanisms Productivity shocks: p profits v u θ = v u Interest rate rises: higher capital costs lead to a lower profits (Flow Profits) more expensive vacancies (Vacancy Cost) Spread (default) rises: increase in chances of losing claim to profits (Ownership) Back to Breakdown 7/37

55 Literature DMP with productivity shocks: Puzzle: Shimer (2005) Solutions: Hall (2005), Hagedorn & Manovskii (2008)... Fundemental surplus: Ljungqvist and Sargent (2014) 8/37

56 Literature DMP with productivity shocks: Puzzle: Shimer (2005) Solutions: Hall (2005), Hagedorn & Manovskii (2008)... Fundemental surplus: Ljungqvist and Sargent (2014) DMP with financial shocks: Wasmer and Weil (2004) Petrosky-Nadeau (2014) Boeri, Garibaldi and Moen (2014) 8/37

57 Literature DMP with productivity shocks: Puzzle: Shimer (2005) Solutions: Hall (2005), Hagedorn & Manovskii (2008)... Fundemental surplus: Ljungqvist and Sargent (2014) DMP with financial shocks: Wasmer and Weil (2004) Petrosky-Nadeau (2014) Boeri, Garibaldi and Moen (2014) Financial shocks: Christiano, Eichenbaum and Trabandt (2014) Jermann and Quadrini (2012)... 8/37

58 Model Key Features Risk-neutral workers, E 0 t=0 βt i t Employed: it = w s + r f k s Unemployed: it = b + r f k s Make consumption/savings choice wrt risk free r f Banks: Competitive banks borrow from workers, lend to firms Perceive financial intermediation costs and default risk Firms: Matched: produce, pay labor & capital costs: w s, (r s + δ)k δ is the depreciation rate, r s is state dependent Unmatched: post vacancies v at a cost cs (r s ) Face state-dependent default Workers and firms match in a frictional labor market Wages - Nash Bargaining 9/37

59 Banks Banks borrow from workers at r f = 1 β β Lend to firms at rate r Default rate d (with recovery rate ζ), intermediation costs x Maximize profits given by: Free entry π b = (1 d)(1 + r x) + dζ(1 + r x) (1 + r f ) 10/37

60 Matching A C.R.S. matching function M(v, u): new matches Define market tightness as: θ = v u Job finding rate for worker: M(u,v) u = λ w (θ) Job filling rate for firm: M(u,v) v = λ f (θ) Use: M(u, v) = uv (u l +v l ) 1 l (Ramey, den Haan, and Watson) 11/37

61 Firms and Production Matched firms: output p using capital K and labor L ( Q(L, K) = min pl, K ) φ Capital per worker is k = K φp Allows constant productivity Look at business cycle frequencies Flow profits per match: π = p w s (r s + δ)k Hiring and investment 12/37

62 Separations Firms and workers face state-independent separations σ In addition firms separate at d, due to default Separation rate for firms: σs f = σ + (1 σ)d Separation rate for workers: σ w = σ 13/37

63 Value Functions - Workers Employed worker: W s = w s + r f k + β((1 σ w )E s W s + σ w E s U s ) Unemployed worker: U s = b + r f k + β(λ w (θ)e s W s + (1 λ w (θ)) E s U s ) 14/37

64 Value Functions - Firms The value of a matched firm is: (( ) ) J s = p w s (r s + δ)k + β 1 σs f E s J s + σs f E s V s Vacancy posting firm: V s = c s (r s ) + β ( ( ) ) λ f (θ)e s J s + 1 λ f (θ) E s V s, with vacancy cost: c s (r s ) = c r r s + c δ + c l 15/37

65 Wages - Nash Bargaining Wages solve: max ws (W s U s ) γ (J s V s ) 1 γ where γ is the worker s bargaining weight The solution is: W s U s = γs s ; J s = (1 γ)s s where Ss = (W s U s ) + (J s V s ) 16/37

66 Equilibrium Given free entry for banks: r = f(x, d r f, ζ) Solve for S s, θ s using: Free entry condition (V = 0): Evolution of surplus: S s = p b (r s +δ)k+β c s λ f (θ) = β(1 γ)e ss s (= βe s J s ) { ( ) 1 σs f (θq(θ) (1 σ)d) γ E s S s (1 γ) q(θ) } c s β 17/37

67 Abstracting from Default Default is a shock to ownership (continuation value) How big is it? Separation rate is on average 2% a month (Shimer, 2005) Default rate is on average 1% a year (Elton, 2001) Formalize that this is small using Ljungqvist and Sargent (2014) Fundamental Surplus approach 18/37

68 Calibration strategy Normalize p ( r + δ)k = 1 Flow surplus is 1 b rk, where r is deviation from mean compared with p b in the productivity shocks literature Some parameters set a priori Exogenous shocks to x (r) Set some parameters to match data moments 19/37

69 A-Priori Parameter Values Symbol Meaning Value Identification σ Job separation Literature β Discount rate Literature c Vacancy Costs Hagedorn & Manovskii (2008) γ Worker Bargaining Weight 0.50 Literature δ Depreciation Rate Annual rate of 6% 20/37

70 Calibration -Matching Moments Parameter values and identification: Parameter Meaning Value Jointly Identified b Flow utility when u 0.60 Job finding rate l Matching elasticity 0.41 Market Tightness Model fit: Moment Data Model Job Finding Rate Market Tightness /37

71 Interest Rate shocks Without default the free entry condition for banks becomes: r s = r f + x s The estimated process is given by r = ρ r r 1 + ɛ r ɛ r N(0, σ r ) Estimating the process and converting to weekly frequency: Moment Data Model Parameter Frequency Quarterly Quartelyr Weekly ρ r σ r /37

72 Results - Data versus Model u v θ r St Dev Data Model Pers Data Model Corr U Data Model Corr V Data Model Corr θ Data Model Table: Quarterly moments: data: versus Model In (var, r) correlations, var is 2 quarters lagged 23/37

73 Results - Data versus Model u v θ r St Dev Data Model Pers Data Model Corr U Data Model Corr V Data Model Corr θ Data Model Table: Quarterly moments: data: versus Model In (var, r) correlations, var is 2 quarters lagged 24/37

74 Break Down of Mechanisms Mechanisms u v θ Data Both mechanisms Profit Vacancy cost Table: Breakdown- Just Standard Deviation Reminder of mechanisms 25/37

75 Robustness Robustness u v v/u r Data Benchmark b= γ= γ= δ= /37

76 Elasticity of tightness w.r.t. the shock Example: profits channel A continuous time model w/ only profits mechanism (r s k) logθ log p = p Υ p b }{{} fundamental surplus productivity shocks 27/37

77 Elasticity of tightness w.r.t. the shock Example: profits channel A continuous time model w/ only profits mechanism (r s k) logθ log p logθ log rk = = p Υ p b }{{} fundamental surplus rk Υ p rk δk b }{{} fundamental surplus productivity shocks interest rate shocks 27/37

78 Elasticity of tightness w.r.t. the shock Example: profits channel A continuous time model w/ only profits mechanism (r s k) logθ log p logθ log rk = = p Υ p b }{{} fundamental surplus rk Υ p rk δk b }{{} fundamental surplus productivity shocks interest rate shocks Υ = (r+σ)+γθq(θ) α(r+σ)+γθq(θ) where α is the elasticity of matching w.r.t. u 27/37

79 Elasticity of tightness w.r.t. the shock Example: profits channel A continuous time model w/ only profits mechanism (r s k) logθ log p logθ log rk = = Υ = (r+σ)+γθq(θ) α(r+σ)+γθq(θ) p Υ p b }{{} fundamental surplus rk Υ p rk δk b }{{} fundamental surplus productivity shocks interest rate shocks where α is the elasticity of matching w.r.t. u p In Shimer-based calibration: p z = 1.67, rk p rk δk z = 0.83 Conclusion: elasticity is about 2 times smaller in our model, But: (r,spread) are 14 times more volatile than labor productivity 27/37

80 Elasticity of tightness w.r.t. the shock Example: profits channel A continuous time model w/ only profits mechanism (r s k) logθ log p logθ log rk = = Υ = (r+σ)+γθq(θ) α(r+σ)+γθq(θ) p Υ p b }{{} fundamental surplus rk Υ p rk δk b }{{} fundamental surplus productivity shocks interest rate shocks where α is the elasticity of matching w.r.t. u p In Shimer-based calibration: p z = 1.67, rk p rk δk z = 0.83 Conclusion: elasticity is about 2 times smaller in our model, But: (r,spread) are 14 times more volatile than labor productivity logθ log rk σ r = /37

81 Interest Rate vs. Productivity Shocks Comparison by looking at only data: u v θ r p St Dev Pers Corr U Corr V Corr θ Table: Quarterly moments: data: In (var, r) correlations, var is 2 quarters lagged Note: exact value for σ P is Go to comparison without lag 28/37

82 Interest Rate vs. Productivity Shocks Comparison by looking at only data: u v θ r p St Dev Pers Corr U Corr V Corr θ Table: Quarterly moments: data: In (var, r) correlations, var is 2 quarters lagged Note: exact value for σ P is Go to comparison without lag 29/37

83 What About the Great Recession? Simulate the model for 2008Q2-2012Q4 30/37

84 What About the Great Recession? Simulate the model for 2008Q2-2012Q4 Simulate if the Fed had not intervened: r c = r t + (f 2008Q2 f t ) 30/37

85 What About the Great Recession? Simulate the model for 2008Q2-2012Q4 Simulate if the Fed had not intervened: r c = r t + (f 2008Q2 f t ) Data Benchmark Model Counter Factual Model Percentage points Year 30/37

86 Conclusion We studied: Mechanisms for financial risk affecting unemployment The quantitative effect of those shocks using DMP literature 31/37

87 Conclusion We studied: Mechanisms for financial risk affecting unemployment The quantitative effect of those shocks using DMP literature We found: Financial conditions matter a lot The main driving force is the interest rate 31/37

88 Calibration of vacancy cost Vacancy cost is c s (r s ) = c r r s + c δ + c l Capital component: c r r s + c δ Assume capital required one period in advance Capital share = 1 3 Labor productivity is 1 capital cost 0.5 Correct for capital in vacancies: cr r s + c δ = Labor component: c l 11% of average labor productivity based on micro evidence Total vacancy cost = = Back to Calibration 32/37

89 Hires and Investment Hires from JOLTS, Inv. is real gross private domestic Correlation = 0.73 St dev of log is 0.11 for investment, 0.10 for hires Back to Capital 33/37

90 Unemployment, Productivity, Spread unemployment spread productivity Figure: US time-series data Back Year 34/37

91 1 Unemployment, Productivity and Interest Rate unemployment interest rate productivity Figure: US time-series data Back Year 35/37

92 Compare to productivity? Standard Dev of U: 0.11 V: 0.12 Tightness ( v u ): /37

93 Compare to productivity? Standard Dev of U: 0.11 V: 0.12 Tightness ( v u ): 0.22 Productivity: 0.01 (Shimer Puzzle) 36/37

94 Compare to productivity? Standard Dev of U: 0.11 V: 0.12 Tightness ( v u ): 0.22 Productivity: 0.01 (Shimer Puzzle) Interest rate: 0.17 Spread: /37

95 Compare to productivity? Standard Dev of U: 0.11 V: 0.12 Tightness ( v u ): 0.22 Productivity: 0.01 (Shimer Puzzle) Interest rate: 0.17 Spread: 0.35 Correlation with u? P: R: 0.53 Spread: 0.71 HP Filtered time series 36/37

96 Interest Rate vs. Productivity Shocks Comparison by looking at only data: u v θ r p St Dev Pers Corr U Corr V Corr θ Table: Quarterly moments: data: (var, r) correlations are contemporaneous Note: exact value for σ P is Go back to comparison with lag 37/37