Lecture 3: Employment and Unemployment

Transcription

1 Lecture 3: Employment and Unemployment Anna Seim (with Paul Klein), Stockholm University September 26, 2016

2 Contents Dierent kinds of unemployment. Labour market facts and developments. Models of wage rigidity. The bathtub model of unemployment. Search and matching. Literature: Jones (2014), Chapter 7; Pissarides (2000); EEAG (2016).

3 Employment and Unemployment Employment: a state in which an individual has a paid job or is self-employed (operating a business). Unemployment: a state in which someone who would like to work is actively searching for a job but is not employed. Labour force: the sum of the employed and the unemployed. Employment rate: the number of people who are employed as a share of the working-age population (typically individuals aged 15-64). Unemployment rate: the number of people who are unemployed as a share of the labour force.

4 Dierent Kinds of Unemployment The natural rate of unemployment: the (hypothetical) unemployment rate that prevails if the economy is neither in a boom nor in a recession. [But see Rogerson: Theory Ahead of Language, /pk] Frictional unemployment: unemployment due to workers transitioning between jobs. Structural unemployment: unemployment due to (geographical-, skill-) mis-match and labour market institutions. Cyclical unemployment: unemployment due to the business cycle.

5 Dierent Kinds of Unemployment cont'd. Actual unemployment = natural unemployment + cyclical unemployment. Natural unemployment = structural unemployment + frictional unemployment.

6 Extracted from: Jones (2014).

7 Extracted from: Jones (2014).

8 Extracted from: EEAG (2016).

9 Long term unemployment (> 6 months)

10 Long term unemployment (> 6 months)

11 Long term unemployment (> 6 months)

12 The Swedish Labour Market, Extracted from: Swedish Fiscal Policy 2009, Report of the Swedish Fiscal Policy Council.

13 Extracted from: Swedish Fiscal Policy 2015, Report of the Swedish Fiscal Policy Council.

14 Extracted from: Swedish Fiscal Policy 2015, Report of the Swedish Fiscal Policy Council.

15 Extracted from: Swedish Fiscal Policy 2015, Report of the Swedish Fiscal Policy Council.

16 Extracted from: Swedish Fiscal Policy 2015, Report of the Swedish Fiscal Policy Council.

17 Models of the Labour Market 1. Models of wage rigidity. 2. Models of labour-market ows: - The bathtub model of unemployment. - The search model by Pissarides (2000).

18 Models of Wage Rigidity When wages are rigid, they fail to adjust in response to changes in labour supply and demand. The (New) Keynesian view: wage rigidity may cause large uctuations in employment. Wage rigidity may refer to insucient exibility, but also to the wage being determined by factors other than supply and demand.

19 Extracted from: Jones (2014).

20 Causes of Wage Rigidity Collective bargaining It takes time to renegotiate. The union may exercise monopoly power and restrict supply to maximize total wage bill. Minimum-wage laws It takes time to legislate in response to shocks. May fail to equate supply with demand in any case. But may oset monopsony power and increase employment. [pk] Empirical evidence is mixed. See the work of David Card. [pk] Eciency wages Wages may need to be kept high to incentivize eort and honesty.

21 The Bathtub Model of Unemployment Simple model of labour-market dynamics. Notation: L: the (xed) labour force. E t : the number of people employed at time t. U t : the number of people unemployed at time t. s: the separation rate. f : the job-nding rate.

22 The Bathtub Model of Unemployment Model consists of two equations. Workers in the labour force either employed or unemployed: L = E t + U t. (1) The change in unemployment is given by: U t+1 U t+1 U t = se t fu t. (2)

23 The Bathtub Model of Unemployment cont'd. Steady state when U t+1 = U t or U t = 0. Setting U t+1 = 0 in (2) and using (1) implies s(l U t ) = fu t. Divide by L to obtain s(1 u t ) = fu t, where u t = U t /L is the unemployment rate. Solving for u, we obtain: u = s s + f. (3)

24 Persistence and Stability Equation (2) implies that unemployment evolves according to: U t+1 = sl + (1 f s)u t. (4) The term (1 f s) captures unemployment persistence. The dynamic process (4) is stable and tends to return to the steady state if 0 < (1 f s) < 1.

25 A Search Model of the Labour Market Developed by Dale Mortensen and Chris Pissarides in the 1970s. Unemployed workers and rms search for each other in the labour market. The search process is costly. It takes time for workers and employers to nd a job Recruiting requires resources Workers and rms consider the implications of their actions by calculating the Present Discounted Value (PDV) associated with dierent states. Unemployment arises because rms are hit by exogenous shocks that trigger job separations, i.e. breakups of existing matches.

26 Notation L: the (xed) labour force. u: the unemployment rate. v: the number of vacancies as a share of the labour force. m: the matching function. θ v/u: labour-market tightness. λ: rate at which rm/worker-pair breakups occur. p: the value of output associated with one job. p c: the cost of hiring. r: the real interest rate. w: the real wage. z: the real return to unemployment. β: the relative bargaining power of workers.

27 The Matching Function Only the ul unemployed workers search for jobs. There are vl vacancies posted by rms. Workers and jobs that are successfully matched are randomly drawn from the sets, ul and vl, respectively. Workers and rms are matched according to a technology captured by the matching function: ml = m(ul,vl) (5) The function m is increasing in both arguments (ul and vl), concave, and homogenous of degree 1. (Notice that m is both a variable and a function.)

28 Job Creation and Job Destruction Incidentally: in the data, unemployment falls and rises as the job creation falls and rises, not so much as the job destruction rate falls and rises. Think of ml as a ow rate; it's a time derivative. Job creation occurs when a rm and a searching worker meet and agree to form a match at a bargained wage. A match lasts until a rm-specic, negative shock, reecting changes in technology or demand, causes job separation. The worker-rm pairs that are hit by shocks are randomly selected.

29 Matching and Labour Market Tightness Labour market tightness, θ v/u, measures the relative number of searchers in the market. The rate at which a vacant job is lled is given by q(θ) = m(ul,vl) vl ( u ) = m v,1, (6) where the last equality follows from the homogeneity of m.

30 Unemployment Dynamics Consider a small time interval, t. The mean number of workers who enter unemployment during t is λ(1 u)l t. (7) The mean number of workers who exit from unemployment during t is ml t. (8)

31 Unemployment Dynamics cont'd. It will prove useful to rewrite (8) in terms of u rather than m. Equation (6) suggests that m(u,v) = vq(θ). This implies that the outow from unemployment, (8), can be re-written as ml t = vq(θ)l t = uθq(θ)l t. (9) When t 0, the change in unemployment, du/dt, is given by the mean inow into unemployment, (7), minus the mean outow from unemployment, (9): u du dt = λ(1 u)l uθq(θ)l. (10)

32 The Beveridge Curve In the steady state u = 0, so that λ(1 u)l = uθq(θ)l. (11) Solving for u in (11), we obtain the Beveridge curve: u = λ λ + θq(θ). (12) Unemployment persists in the steady state because of the match-specic shocks causing job separations and hence a constant ow into unemployment. Notice that Equation (12) is not explicit because θ = u/v.

33 The theoretical (computed) Beveridge curve [pk] M(U,V ) = U α V 1 α α = 0.63

34 The theoretical (computed) Beveridge curve [pk] How does the curve shift if the unemployment rate is increasing or decreasing?

35 The Beveridge Curve The Beveridge curve implies that, for a given λ and θ (or, equivalently, vacancy rate v) there is a unique equilibrium unemployment rate. The parameter λ is given, but v is endogenously determined. To close the model, two more equations are needed: a job-creation condition and a wage curve. Key ideas in that context: Wage bargaining; splitting the match surplus Free entry; vacancies are posted until posting another generates zero prots

36 Digression on Hagedorn, Karahan, Manovskii & Mitman In the MP model, high unemployment benets are associated with high unemployment The reason (at least in the above version of the model) is not that it makes individual workers lazier in their search behaviour The reason is that it enhances the bargaining position of workers, leaving less surplus for the employer, reducing the number of vacancies This is a macro eectit's not about the behaviour of any individual unemployed person, it's about how many workers put upward pressure on wages and hence downward pressure on vacancies

37 Digression on Hagedorn, Karahan, Manovskii & Mitman Hagedorn, Karahan, Manovskii & Mitman (2016) establish that this macro eect exists empirically. After the recent nancial crisis in the United Sates, benet duration increase from 26 weeks to up to 99 weeks. The paper looks at bordering counties in distinct states. More generous benets in a state generates higher unemployment there via higher wages and fewer vacancies. Meanwhile, there is no evidence of the burning platform view that increased benets reduce search intensity.

38 Firms Each rm has one vacancy that it seeks to ll by searching for workers in the market. When the vacancy is lled, the rm produces output p > 0, sold in competitive markets. When the vacancy is open, the rm faces a xed search cost p c > 0 per unit of time. The number of jobs, v is endogenous and determined by prot maximization. When each rm only has one vacancy, this corresponds to all prot opportunities from new jobs being exploited, so that V = 0.

39 Firms cont'd. Let J and V be the PDVs of expected prot from an occupied job and a vacant job, respectively. V satises the following Bellman equation: Imposing V = 0 on (13) yields: rv = pc + q(θ)(j V ). (13) J = pc q(θ). (14) Equilibrium labour market tightness ensures that the expected prot from a new job equals the expected cost of hiring a worker.

40 The Job Creation Condition To derive the job-creation condition, we need to eliminate the asset value of an occupied job, J, in (14). J satises the following equation: rj = p w λj. (15) Using (15) to eliminate J in (14), we obtain the job-creation condition: (r + λ)pc p w = 0. (16) q(θ) Equation (16) corresponds to a marginal condition for the demand for labour.

41 Workers The labour force is xed and each worker's search intensity is given. When employed, the worker earns the real wage w, determined in wage bargaining with the hiring rm. When unemployed, the worker searches for employment and enjoys the real return z, notably comprising unemployment benets. The worker's PDV of employment and unemployment play a key role in wage bargaining and are derived below.

42 Workers cont'd. Let U and W denote the PDVs of the expected income stream of an unemployed and an employed worker, respectively. U satises ru = z + θq(θ)(w U). (17) Since ru is the average expected return to human capital during the search process, it is the minimum compensation required to give up search and therefore the worker's reservation wage. W satises rw = w + λ(u W ). (18) Workers do not quit their jobs as long as W U, which holds if w z.

43 Wage Determination In equilibrium, a successful match generates economic rents that are shared in wage bargaining between the rm and worker. The bargained wage, w i, maximises the weighted product of the worker's and the rm's net return from the job match.

44 Wage Determination cont'd. Formally, the two parties face the following maximization problem: max w i (W i U) β (J i V ) (1 β), (19) where 0 β 1 is the relative bargaining power of workers and J i and W i depend on w i according to (15) and (18). Taking logs, the maximization problem, (19), may be written max w i β ln(w i U) + (1 β)(j i V ). (20)

45 Wage Determination cont'd. The rst-order condition (FOC) is: β W i + (W i U) w i (1 β) J i = 0. (21) (J i V ) w i Since (15) and (18) imply W i / w i = J i / w i, the FOC may be written W i U = β(w i + J i U V ). (22)

46 The Wage Curve To convert (22) into a wage curve, use (14), (15), (17) and (18) to get rid of the value functions. By imposing V = 0 and realising that in equilibrium all rms pay the same wage, w i = w i, the wage curve can be written w = (1 β)z + βp(1 + cθ). (23)

47 Equilibrium The steady-state equilibrium is a triple, (u,θ,w) that satises the Beveridge curve (12), the job-creation condition (16) and the wage curve (23), repeated here for convenience: u = p w λ λ + θq(θ), (r + λ)pc q(θ) = 0, w = (1 β)z + βp(1 + cθ). The unique equilibrium can be illustrated in two diagrams: one in the θ-w-plane and one in the u-v-plane.

48 Equilibrium Wages and Market Tightness

49 Equilibrium Vacancies and Unemployment

50 The Swedish Beveridge Curve Extracted from: Kocherlakota, N. (2012), "Monetary Policy Transparency: Changes and Challenges", Speech at the Data Matters Forum, Rapid City, South Dakota, May 23