Intermediate Macroeconomics, EC2201. L3: The labour market

Transcription

1 Intermediate Macroeconomics, EC2201 L3: The labour market Anna Seim Department of Economics, Stockholm University Spring / 58

2 Contents and literature Labour market facts and developments. Labour supply and demand. Wage rigidity. The bathtub model of unemployment. Search and matching. Literature: Jones (2014), Ch. 7. Pissarides (2000), Ch. 1. Swedish Fiscal Policy Council (2011, Ch. 6; 2016, Ch. 1.3). 2 / 58

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. 3 / 58

4 Different 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. 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. 4 / 58

5 Actual unemployment = natural unemployment + cyclical unemployment. Natural unemployment = structural unemployment + frictional unemployment. 5 / 58

6 Extracted from: Jones (2014). 6 / 58

7 Extracted from: Jones (2014). 7 / 58

8 Extracted from: Jones (2014). 8 / 58

9 Extracted from: European Economic Advisory Group (EEAG) (2016), The EEAG Report on the European Economy / 58

10 The Swedish labour market, Extracted from: Swedish Fiscal Policy 2009, Report of the Swedish Fiscal Policy Council. 10 / 58

11 Extracted from: Swedish Fiscal Policy 2011, Report of the Swedish Fiscal Policy Council. 11 / 58

12 Extracted from: Swedish Fiscal Policy 2016, Report of the Swedish Fiscal Policy Council. 12 / 58

13 Extracted from: Swedish Fiscal Policy 2016, Report of the Swedish Fiscal Policy Council. 13 / 58

14 Extracted from: Swedish Fiscal Policy 2015, Report of the Swedish Fiscal Policy Council. 14 / 58

15 Extracted from: Swedish Fiscal Policy 2015, Report of the Swedish Fiscal Policy Council. 15 / 58

16 Extracted from: Swedish Fiscal Policy 2015, Report of the Swedish Fiscal Policy Council. 16 / 58

17 Extracted from: Swedish Fiscal Policy 2015, Report of the Swedish Fiscal Policy Council. 17 / 58

18 Models of the labour market 1. Models of labour supply and demand. 2. Models of labour-market flows: - The bathtub model of unemployment. - The search model by Pissarides (2000). 18 / 58

19 Models of labour supply and demand Perfectly competitive labour and goods markets: wages and prices taken as given by individual firms and workers. Labour supply: derived from workers maximising utility with respect to hours worked. Labour demand: derived from firms maximising profits with respect to employment. 19 / 58

20 Extracted from: Jones (2014). 20 / 58

21 Extracted from: Jones (2014). 21 / 58

22 The model under 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 fluctuations in employment. 22 / 58

23 Extracted from: Jones (2014). 23 / 58

24 Causes of wage rigidity Collective bargaining. Minimum-wage laws. Efficiency wages. 24 / 58

25 Alternative assumptions What happens when we relax the assumption of perfectly competitive markets? In a unionised economy, the labour supply curve is replaced by a wage-setting (WS) curve. Under monopolistic competition, the labour demand curve is replaced by a price-setting (PS) curve. 25 / 58

26 26 / 58

27 The bathtub model of unemployment Simple model of labour-market dynamics. Notation: L: the (fixed) 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-finding rate. 27 / 58

28 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) 28 / 58

29 Steady state when U t+1 = U t. 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) 29 / 58

30 Persistence and stability Equation (2) implies that unemployment evolves according to: U t+1 = sl t + (1 f s)u t. (4) The term (1 f s) captures unemployment persistence. The dynamic process (4) is stable and reaches the steady state if 0 < (1 f s) < / 58

31 Extracted from: Swedish Fiscal Policy 2011, Report of the Swedish Fiscal Policy Council. 31 / 58

32 Extracted from: Swedish Fiscal Policy 2011, Report of the Swedish Fiscal Policy Council. 32 / 58

33 A search model of the labour market Unemployed workers and firms search for each other in the labour market. The search process is costly. Workers and firms consider the implications of their actions by calculating the Present Discounted Value (PDV) associated with different states. Unemployment arises because firms are hit by exogenous shocks that trigger job separations, i.e. break up existing matches. 33 / 58

34 Notation L: the (fixed) 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 job-specific (idiosyncratic) shocks 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. 34 / 58

35 The matching function Only the ul unemployed workers search for jobs. There are vl vacancies posted by firms. Workers and jobs that are successfully matched are randomly drawn from the sets, ul and vl, respectively. Workers and firms 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 / 58

36 Job creation and job destruction Job creation occurs when a firm and a searching worker meet and agree to form a match at a bargained wage. A match lasts until a firm-specific, negative shock, reflecting changes in technology or demand, causes job separation. The worker-firm pairs that are hit by shocks are randomly selected. 36 / 58

37 Matching and labour market tightness Labour market tightness, θ v/u, measures the relative number of traders in the market. The rate at which a vacant job is filled is given by q(θ) = m(ul,vl) vl = m( u,1), (6) v where the last equality follows from the homogeneity of m. 37 / 58

38 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) 38 / 58

39 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 outflow 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 inflow into unemployment, (7), minus the mean outflow from unemployment, (9): u du dt = λ(1 u)l uθq(θ)l. (10) 39 / 58

40 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 on account of the firm-specific shocks causing job separations and hence a flow into unemployment. 40 / 58

41 The Beveridge curve implies that, for a given λ and θ, there is a unique equilibrium unemployment rate. The parameter λ is given, but θ is endogenously determined. To close the model, two more equations are needed: a job-creation condition and a wage curve. 41 / 58

42 Firms Each firm has one vacancy that it seeks to fill by searching for workers in the market. When the vacancy is filled, the firm produces output p > 0, sold in competitive markets. When the vacancy is open, the firm faces a fixed search cost p c > 0 per unit of time. The number of jobs, v, is endogenous and determined by profit maximisation. When each firm only has one vacancy, this corresponds to all profit opportunities from new jobs being exploited, so that V = / 58

43 Let J and V be the PDVs of expected profit from an occupied job and a vacant job, respectively. V satisfies 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 profit from a new job equals the expected cost of hiring a worker. 43 / 58

44 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 satisfies 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. 44 / 58

45 Workers The labour force is fixed and each worker s search intensity is given. When employed, the worker earns the real wage w, determined in wage bargaining with the hiring firm. When unemployed, the worker searches for employment and enjoys the real return z, notably comprising unemployment benefits. The worker s PDV of employment and unemployment play a key role in wage bargaining and are derived below. 45 / 58

46 Let U and W denote the PDVs of the expected income stream of an unemployed and an employed worker, respectively. U satisfies 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 satisfies rw = w + λ(u W ). (18) Workers do not quit their jobs as long as W U, which holds if w z. 46 / 58

47 Wage determination In equilibrium, a successful match generates economic rents that are shared in wage bargaining between the firm and worker. The bargained wage, w i, maximises the weighted product of the worker s and the firm s net return from the job match. 47 / 58

48 Formally, the two parties face the following maximisation problem: max w i (W i U) β (J i V ) (1 β), (19) where β [0,1] 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 maximisation problem, (19), may be written max w i β ln(w i U) + (1 β)(j i V ). (20) 48 / 58

49 The first-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) 49 / 58

50 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 firms pay the same wage, w i = w i, the wage curve can be written w = (1 β)z + βp(1 + cθ). (23) 50 / 58

51 Equilibrium The steady-state equilibrium is a triple, (u,θ,w) that satisfies 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. 51 / 58

52 Equilibrium wages and market tightness 52 / 58

53 Equilibrium vacancies and unemployment 53 / 58

54 Analysis May analyse the equilibrium effects of changes in the exogenous parameters, i.e.: Labour productivity, p. The real return to unemployment, z. The relative bargaining power of workers, β. The real interest rate, r. The arrival rate of negative shocks, λ. The cost of hiring, c. The rate at which vacant jobs are filled, q. 54 / 58

55 Factors that shift the Beveridge curve to the right A higher arrival rate of negative shocks, λ. A lower rate of job matching for given levels of u and v. Corresponds to a shift in the matching function. May reflect a higher degree of mismatch in the economy. 55 / 58

56 Extracted from: Swedish Fiscal Policy 2011, Report of the Swedish Fiscal Policy Council. 56 / 58

57 Extracted from: Swedish Fiscal Policy 2011, Report of the Swedish Fiscal Policy Council. 57 / 58

58 What we did Labour market facts and developments. Labour supply and demand. Wage rigidity. The bathtub model of unemployment. Search and matching. Literature: Jones (2014), Ch. 7. Pissarides (2000), Ch. 1. Swedish Fiscal Policy Council (2011, Ch. 6; 2016, Ch. 1.3). 58 / 58