Macroeconomics of the Labor Market

Macroeconomics of
the Labor Market
By Christian Merkl
CES-Lecture 2:
The Search and Matching Model
and the Business Cycle
Munich, August 2013
Labor Market Flows
The Simplest Model
Exogenous job destruction
Employed
Unemployed
Matching function
For matches: bargaining
Vacancy posting
Firms
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Strengths of Search
and Matching
• Elegance
• Efficiency (under certain conditions)  twin
brother of RBC
• Consistent dynamic framework
• Model of labor market flows
• Weaknesses?  More on this issue later
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The Matching Function
• Assume the following matching function, which
is increasing in both arguments, concave and
homogenous of degree 1
• Typically the matching function is specified as a
Cobb-Douglas function (everything will be
written in discrete time)
• Microfoundations?
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Labor Market Tightness
•
denotes the labor market tightness
• By using the homogeneity of the function, we
can rewrite the rate at which vacant jobs
become filled as
• Trading externalities!
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Employment Dynamics
• Let’s assume that there is a constant and exogenous job
separation rate .
• Workers’ job finding rate:
• In equilibrium the number of workers who become
unemployed must be equal to the number of workers
who find a new job.
• Employment to unemployment flows:
• Unemployment to employment flows:
• Employment dynamics equation:
• Steady state employment:
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Sequence of Decisions
1. The firm has to post a vacancy.
2. The unemployed worker has to search.
3. The two parties have to meet and to make a
match.
4. Since the search process was expensive, a job
match yields a rent which is shared according
to a bargaining rule.
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Job Creation 1:
Present Value of a Vacant Firm
• Present value of a vacant firm:
• Present discounted value: minus vacancy
posting costs plus future expected present
value.
• Free entry condition: Firms will post vacancies
until the value of V is driven to 0.
• Thus:
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Job Creation 2:
Present Value of a Matched Firm
• Present value of a matched firm J:
• The return for the firm is equal to the goods price
minus the wage plus the future value of the
match.
• Job creation condition:
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Workers’ Present Value
• Present value of an unemployed worker:
• Present value of an employed worker:
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Wage Determination
• Nash bargaining solution:
• Thus:
• In terms of the wage:
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Equilibrium
• Three steady steate equations (in continuous
time, see Pissarides) and the corresponding
dynamic equations in discrete time:
Beveridge curve
Job creation curve
Wage curve
• Thus, the typical demand and supply diagram is
replaced.
Note that Pissarides (2000) uses different letters (c are vacancy posting costs, beta is the bargaining power, p is the
productivity, r is the discount factor).
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Graphical Illustration 1:
Wages and Market Tightness
Wage Curve
Job Creation
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Graphical Illustration 2:
Vacancies and Unemployment
v
Job Creation (JC)
Beveridge Curve (BC)
u
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Model Parametrization
•
•
•
•
•
•
•
Separation rate (s): 0.1 (exogenous)
Discount rate (r): 0.012
Value of leisure (b): 0.4
Matching function ( ): 1.355*theta^-0.72
Bargaining power (beta): 0.72 ( Hosios rule)
Cost of posting a vacancy (c): 0.213
The market tightness is normalized to 1
See Shimer (2005, p.38)
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Remember the Basic
Model Structure
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Business Cycle Facts
and the Model
Taken from Shimer (2005, pp. 28 & 39).
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Some Analytics:
Flexible Wage Case
• The flexible wage case
w  A
• We can rewrite the job-finding rate as
  1   A 

jfr  
  1  1     
1

• After some algebra, it can be shown that the
elasticity of the job finding rate with respect to a is
 ln jfr 1  

 ln A

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Some Analytics:
Wage Rigidity Case
• Assume that the wage is a constant:
wc
• We can rewrite the job-finding rate as
  A  c 

jfr  
  1  1     
1

• After some algebra, it can be shown that the
elasticity of the job finding rate with respect to a is
 ln jfr 1   A

 ln A
 Ac
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Lack of Volatility:
Intuition 1
• After a productivity shock, the present value of a
job (J) and the present value of a vacancy (V)
increases.
• The zero profit condition ensures that more
vacancies are posted (as more firms enter the
market).
• However, the sensitivity of vacancies appears to
be much too small.
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Lack of Volatility:
Intuition 2
• Shimer (2005) has calibrated the bargaining power of
households to 0.72.
• This ensures Hosios’ (1990) rule ( efficiency).
• Therefore, a big part of productivity increases is
absorbed by households (wages).
• This reduces the incentive for vacancy creation.
• Thus, Shimer (2005) identifies the bargaining process as
the core of the problem.
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Solution 1: Wage Rigidity
• Hall (2005) proposes a sticky wage model as solution.
• Intuition: When wages are sticky, households wages
increase only incrementally or not at all after a
productivity shock.
• Therefore, productivity shocks affect firms’ profits by
more than before.
• More vacancies are posted and the labor market
tightness is more sensitive than under Shimer’s
calibration.
• Innovation: The model does not interfere with the
efficient formation of job matches (despite the wage
rigidity).
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Problems with
Hall’s Solution
1. The volatility of wages is zero
2. The correlation between the labor share and
labor productivity is -1.
See Hornstein et al. (2005, p. 44).
3. There is empirical evidence that wages for new
hires are not rigid (Haefke et al, 2008).
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Solution 2: The Value
of Leisure
• Hagedorn and Manovskii (2008) set the value of leisure
(b) to 0.955.
• Thus, the difference between the present value of
market activity and non-market activity is very small.
• Workers’ bargaining power can be set to 0.052.
• This leads to a very high wage share and a very low
profit share.
• Firms (relative) profits change a lot when productivity
changes.
• Therefore, the model economy’s volatilities increase.
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Problems with Hagedorn
and Manovskii’s Solution
• Hornstein et al. (2005) show that the sensitivity
of the unemployment rate to unemployment
benefit changes is much too big.
• This elasticity is about 20 times larger than in
Shimer’s (2005) calibration.
• A 15 percent increase of unemployment benefits
would double the unemployment rate.
• This is very much at odds with microeconometric
studies.
• In addition: welfare issue!
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Conclusion
• The search and matching model has difficulties
replicating the amplification effects.
• The Shimer puzzle can be fixed. However, this
implies unrealistic other negative side effects.
• Outlook: endogenous separations
• Outlook: how flexible/rigid are wages for
entrants?
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References
• Hagedorn, Marcus, and Manovskii, Iourii (2008): “The Cyclical Behavior
of Equilibrium Unemployment and Vacancies Revisited.” American
Economic Review, Vol. 98, No. 4, pp. 1692-1706 .
• Hall, Robert (2005): “Employment Fluctuations with Equilibrium Wage
Stickiness.” American Economic Review, Vol. 95, No. 1, pp. 50–65.
• Hornstein, Andreas, Krusell, Per, and Violante, Giovanni (2005):
“Unemployment and Vacancy Fluctuations in the Matching Model:
Inspecting the Mechanism.” Federal Reserve of Richmond Economic
Quarterly, Vol. 91, No. 3, pp. 19-51.
• Haefke, Christian, Sonntag, Markus, van Rens, Thijs (2008): “Wage
Rigidity and Job Creation.” IZA Discussion Papers 3714
• Hosios, Arthur (1990). “On the Efficiency of Matching and Related
Models of Search and Unemployment.” Review of Economic Studies,
Vol. 57, No. 2, pp. 279–298.
• Pissarides, Christopher (2000): “Equilibrium Unemployment.” MIT
Press, Cambridge.
• Shimer, Robert (2005): “The Cyclical Behavior of Equilibrium
Unemployment and Vacancies.” American Economic Review, Vol. 95,
No. 1, pp. 25-49.
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