The unemployment volatility puzzle SH November 2011

Transcription

1 The unemployment volatility puzzle SH November 2011 Mortensen & Pissarides search and matching model standard theory of equilibrium unemployment o (other theory: Layard Nickell Jackman wage & price curves) Combined with RBC- models to derive model of business fluctuations with labour market fluctuations Shimer AER 2005: model cannot explain the cyclical behaviour of two of its central variables: unemployment and vacancies Compares predictions of standard search model with empirical data for the U.S. Look at two shocks: changes in labour productivity and in separation rate of employed worker 1

2 Effects in search models: Higher labour productivity: more profitable to open vacancies, and unemployment falls workers threat points increase, and wages rise mitigates increase in profitability of opening vacancies overall, little impact on vacancies and unemployment Sharp contrast to evidence: large fluctuations in vacancies and unemployment, with small changes in wages Higher separation rate: leads to higher unemployment, but does not affect relative value of unemployment and vacancies leads to counterfactually positive correlation between unemployment and vacancies 2

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4 Mortensen-Pissarides search model Model in continuous time All jobs and workers are homogeneous Employers may post vacancy, paying a flow cost c Unemployed workers receive utility z (unemployment benefits) Stochastic matching of workers and firms: matching function m(u,v), u is unemployment rate, v is vacancy rate θ=v/u is labour market tightness o Vacancy finds worker at rate q(θ), q (θ) < 0 o Job finding rate f(θ), where f(θ)= θq(θ) and f (θ) > 0 Output = p when a match occurs Exogenous separation rate s 4

5 Value of job J = discounted future profit stream (r is interest rate) Discrete time (= profit this period+value next period) Can be re-arranged to Asset equation rj = p w sj => Job creation condition: V is value of vacancy rv = -c + q(θ)(j-v) ( = flow value + expected change in asset value) V = 0 (free entry of vacancies push the value down to zero) => = expected cost of finding a worker => 5

6 Asset value unemployed worker U Asset value employed worker W ru = z + f(θ)(w-u) rw = w s(w-u) The wage is set by bargaining, giving the worker a share β of the total surplus from the match W U = β( J + W V U) Can show (Pissarides, 2009, p 1346), that this gives w = ru + β(p ru) or Wage equation: w = (1-β)z + β(p + cθ) Wage is increasing in benefits z, productivity p and tightness θ 6

7 Wage w Wage curve Job creation Tightness θ 7

8 Wage w Wage curve Job creation Tightness θ Increased productivity leads to shift in both curves 8 Wage increase dampens the rise in tightness

9 Empirical evidence: large fluctuations in v/u ratio 9

10 Model: Small fluctuation in v/u ratio 10

11 Possible resolutions: Shimer (AER, 2005), Hall (AER, 2005): Wage rigidity o Empirical evidence suggest that wages are rigid o Rigid wages for existing workers is consistent with efficiency, as long as separations are efficient (i.e. wages change if necessary to avoid separation) Hagedorn & Manovski(2008): Small gain of being employed (z close to p) o Implies that small productivity changes leads to large changes in the profitability of a job => large change in vacancies o But implausible and inconsistent with evidence (makes unemployment volatility very sensitive to value of z) 11

12 Pissarides, Econometrica: Is wage stickiness the answer? Argues that Vacancies depend on the wage for new matches Empirical evidence shows that wages are more flexible for new matches Wage rigidity is not the reason for unemployment volatility Suggest different explanation the existence of fixed costs to vacancy creation If vacancy costs rise less than in proportion to the duration of vacancies, the firm s incentive to post vacancies remain high in a boom, leading to more volatility in vacancies and unemployment 12

13 Distinguishing between new and continuing jobs: 13

14 Nash bargaining for new jobs gives a job creation condition that is identical to the one in the canonical model: If the economy shifts between to states i and j: 14

15 Empirical evidence: Should not look at times series evidence of aggregate wages, because it includes continuing wages is affected by composition bias (low productive workers more likely to lose their jobs in a downturn, dampening the fall in aggregate wages) Panel data studies show that wages of new hires are procyclical 15

16 Fixed costs of hiring H 16

17 Makes the v-u ratio much more sensitive to changes in productivity, consistent with empirical evidence 17