Discussion of “Involuntary
Unemployment and the Business
Cycle”
by Lawrence J. Christiano,
Mathias Trabandt, and Karl
Walentin
Robert E. Hall
Hoover Institution and Department of Economics, Stanford
6th Banco de Portugal Monetary Conference
Lisbon
June 10 and 11, 2010
1
2
The MP paradigm
I
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Hiring and separations are flows; employment and
unemployment are state variables.
Preferences are linear, so personal wealth is not a
determinant of labor supply.
All workers hold jobs or seek work all the time;
participation is not modeled.
Job-seekers all exert the same fixed amount of effort.
Employers exert recruiting effort to the point of
eliminating any pure profit from hiring.
Workers and employers bargain over compensation with
fixed shares of the surplus around 0.5.
3
Search and matching
The job-finding rate is an increasing and concave function φ(θ)
and the vacancy-filling rate is the decreasing function φ(θ)/θ.
4
Search and matching
The job-finding rate is an increasing and concave function φ(θ)
and the vacancy-filling rate is the decreasing function φ(θ)/θ.
n=
φ(θ)
s + φ(θ)
4
Search and matching
The job-finding rate is an increasing and concave function φ(θ)
and the vacancy-filling rate is the decreasing function φ(θ)/θ.
n=
φ(θ)
s + φ(θ)
q(n) = φ(θ(n))/θ(n)
4
The employment contract
Employers pay workers wt units of output for each hour of
work in period t.
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The employment contract
Employers pay workers wt units of output for each hour of
work in period t.
Employers collect an amount yt from a new worker.
5
The employment contract
Employers pay workers wt units of output for each hour of
work in period t.
Employers collect an amount yt from a new worker.
wt is common value of marginal product of labor and marginal
value of time.
5
The employment contract
Employers pay workers wt units of output for each hour of
work in period t.
Employers collect an amount yt from a new worker.
wt is common value of marginal product of labor and marginal
value of time.
Thus the employment contract embodies efficient two-part
pricing.
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Employment function
Payoff to a vacancy:
q(nt )yt − γ
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Employment function
Payoff to a vacancy:
q(nt )yt − γ
q(n)y = γ
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Employment function
Payoff to a vacancy:
q(nt )yt − γ
q(n)y = γ
The employment rate that solves this zero-profit condition is a
function n(y), which I call the employment function.
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Employment and labor force as
percent of population
68
Participation
66
62
Unemp
ployment
Percent of pop
pulation
64
Employment
60
58
56
54
2007
2008
2009
2010
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Figure 4: Dynamic Responses of Labor Market Variables to Three Shocks
Monetary Shock
Unemployment Rate
0
Labor Force
0.1
Figure 4, neutral tech shock
0.05
−0.1
−0.2
0
0
2
4
6
8
10
12
14
0
2
4
Neutral Tech. Shock
Unemployment Rate
10
12
14
10
12
14
10
12
14
0.1
0
0.05
−0.1
0
2
4
6
8
10
12
14
Unemployment Rate
Invest. Tech. Shock
8
0.15
0.1
0
6
Labor Force
−0.05
0
2
4
6
8
Labor Force
0.15
0.1
0
0.05
−0.1
−0.2
0
0
−0.05
2
4
6
8
10
VAR 95%
12
14
VAR Mean
0
2
4
6
8
Involuntary Unemployment Model
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Relative movements of
unemployment and labor force
CTW
US data
Money
Tech
Invest
Unemployment rate, Dec 2007
Dec 2009
5.0
10.0
0
-0.09
0
-0.12
0
-0.09
Labor force Dec 2007
Dec 2009
66.0
64.6
0
0.06
0
0.09
0
0.05
d log (labor force)/d u
-0.43
-0.67
-0.75
-0.56
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Distributions of consumption
with and without perfect
unemployment insurance
Full insurance
20
18
16
14
Density
12
10
8
6
No
insurance
4
2
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Consumption while unemployed
0.8
0.9
1.0
10