Aggregate Demand, Idle Time,
and Unemployment
Pascal Michaillat (LSE) & Emmanuel Saez (Berkeley)
November 2014
1 / 46
Motivation
Unemployment rate
11%
9%
7%
5%
3%
1974
1984
1994
2004
2014
2 / 46
Motivation
11%
Unemployment rate
Technology?
9% Aggregate demand?
7%
5%
3%
1974
1984
1994
2004
2014
2 / 46
Motivation
11%
Unemployment rate
Technology?
Mismatch?
9% Aggregate demand?
Low job search?
Low participation?
7%
5%
3%
1974
1984
1994
2004
2014
2 / 46
Motivation
11%
Unemployment rate
Technology?
Mismatch?
9% Aggregate demand?
Low job search?
Low participation?
7%
5%
Transfers?
Monetary policy?
Unemployment insurance?
Payroll tax?
Nothing?
3%
1974
1984
1994
2004
2014
2 / 46
The available models
1. matching model of the labor market
I
tractable
I
but no aggregate demand
2. ?
3. New Keynesian DSGE model with matching
frictions on the labor market
I
many shocks, including aggregate demand shocks
I
but greater complexity
3 / 46
The general disequilibrium model?
vast literature after Barro & Grossman [1971]
recent revival after Great Recession
I
Mankiw & Weinzierl [2011]
I
Caballero & Farhi [2014]
captures important intuitions, especially effect of
aggregate demand on unemployment
but difficult to analyze
4 / 46
This model
architecture of the Barro-Grossman model with
matching frictions on product + labor markets:
simple general equilibrium model
with aggregate demand and unemployment
comparative statics: aggregate demand, technology,
mismatch, labor supply
graphical representation of GE and welfare
5 / 46
Basic model (no labor market)
6 / 46
Setup
static model
measure 1 of identical households
production of services takes place within households
households cannot consume own services
households trade services on frictional market
7 / 46
Matching function and tightness
k units of services
v visits
8 / 46
Matching function and tightness
capacity k sales
CRS matching function h(k,v)
purchases
visits v 8 / 46
Matching function and tightness
tightness: x = v / k capacity k sales = =
output: y = h(k,v)
purchases = =
visits v 8 / 46
Low product market tightness
9 / 46
High product market tightness
10 / 46
Matching cost: ρ ∈ (0, 1) service per visit
output = 1 + τ(x ) · consumption
+
proof:
y
y = |{z}
c
+ ρ ·v = c+ρ ·
|{z}
|{z}
q(x)
consumption matching
output
ρ
⇒ y· 1−
=c
q(x)
ρ
· c ≡ 1 + τ(x ) · c
⇒ y = 1 +
+
q(x ) − ρ
−
11 / 46
product market tightness x
Tightness and aggregate supply
capacity: k
quantity of services
12 / 46
Tightness and aggregate supply
product market tightness x
capacity k
output: y = f(x) k
quantity of services
12 / 46
Tightness and aggregate supply
product market tightness x
output y
capacity k
consumption:
quantity of services
12 / 46
Tightness and aggregate supply
product market tightness x
aggregate supply c
consumption
output y
capacity k
matching
idle time
cost
quantity of services
12 / 46
Money
money in fixed supply µ
real money balances in households’ utility function
as in Barro & Grossman [1971]
and as in Blanchard & Kiyotaki [1987]
13 / 46
Households
take price p and tightness x as given
choose c, m to maximize utility
ε−1
ε−1
χ
m ε
1
ε
·c +
·
1+χ
1+χ
p
| {z } |
{z
}
produced good
real money balances
subject to budget constraint
m +p · (1 + τ(x)) · c =
|{z}
|
{z
}
numeraire
services
µ
|{z}
endowment
+ f (x) · p · k
| {z }
labor income
14 / 46
Optimal consumption decision
first-order condition
− 1
1
m ε
1
χ
·
· c− ε
(1 + τ(x)) ·
=
| {z } 1 + χ
p
1+χ
{z
} | {z }
relative price |
MU of real money
MU of services
aggregate demand (as m = µ):
ε
χ
µ
d
c (x, p) =
·
1 + τ(x)
p
15 / 46
Tightness and aggregate demand
product market tightness x
cd (x, p) =
✓
1 + ⌧ (x)
◆✏
·
µ
p
consumption c
16 / 46
Equilibrium
equilibrium is (x, p) such that supply = demand:
cs (x) = cd (x, p)
1 equation, 2 variables: indeterminacy
need a price mechanism to select equilibrium
I
fixed price
I
competitive price in the sense of Moen [1997]
I
also in the paper: Nash bargaining & partially rigid price
17 / 46
Comparative statics
with fixed price
and competitive price
18 / 46
Increase in AD with fixed price
output y
capacity k
product market tightness x
AS
equilibrium
AD
quantity
19 / 46
Increase in AD with fixed price
output y
capacity k
product market tightness x
AS
AD
quantity
19 / 46
Increase in AS with fixed price
output y
product market tightness x
AS
capacity k
AD
quantity
20 / 46
Comparative statics with fixed price
effect on:
output
tightness
increase in:
y
x
aggregate demand
+
+
+
−
aggregate supply
21 / 46
Definition of competitive price
product market tightness x
AS
price is too high
x*
slack equilibrium
AD
c*
consumption c
22 / 46
Definition of competitive price
product market tightness x
AS
price is too low
AD
x*
tight equilibrium
c*
consumption c
22 / 46
Definition of competitive price
product market tightness x
AS
price is competitive
competitive equilibrium
x*
AD
c*
consumption c
22 / 46
Comparative statics with competitive price
effect on:
output
tightness
increase in:
y
x
aggregate demand
0
0
aggregate supply
+
0
23 / 46
Complete model
24 / 46
Labor market and unemployment
labor market tightness θ
labor supply n
producers
employment l
recruiters
labor force h
unemployment
number of workers
25 / 46
Firms
employ producers and recruiters and sell production
take real wage w and tightnesses x and θ as given
choose number of producers n to maximize profits
f (x)
|{z}
· a
· nα} −
| {z
selling probability production
ˆ )] · w · n
[1 + τ(θ
|
{z
}
wage of producers + recruiters
26 / 46
Optimal employment decision
first-order condition:
f (x)
|{z}
selling probability
ˆ )] · |{z}
·α
· nα−1} = [1 + τ(θ
w
| · a{z
| {z }
MPL
matching wedge real wage
labor demand: demand for producers
f (x) · a · α
nd (θ , x, w) =
ˆ )) · w
(1 + τ(θ
1
1−α
27 / 46
Partial equilibrium on labor market
labor market tightness θ
labor supply
employment l
labor force h
partial equilibrium
labor
demand
number of workers
28 / 46
General equilibrium (x, θ , p, w)
supply = demand on product and labor markets
cs (x, θ ) = cd (x, p)
ns (θ ) = nd (θ , x, w)
2 equations, 4 variables: indeterminacy
need price and wage mechanisms
29 / 46
Keynesian, classical, and frictional unemployment
equilibrium employment:
l=
f (x) · a · α
w
1
1−α
1
·
ˆ )
1 + τ(θ
α
1−α
ˆ )>0
frictional unemployment from τ(θ
classical unemployment from w > a · α
Keynesian unemployment from f (x) < 1
30 / 46
Comparative statics, fixed prices
effect on:
product
increase in:
aggregate demand
technology
labor supply
mismatch
labor
output
tightness
employment
tightness
y
x
l
θ
+
+
+
−
+
−
−
+
+
+
+
−
+
+
−
+
31 / 46
Comparative statics, fixed prices
effect on:
product
increase in:
aggregate demand
technology
labor supply
mismatch
labor
output
tightness
employment
tightness
y
x
l
θ
+
+
+
−
+
−
−
+
+
+
+
−
+
+
−
+
31 / 46
Comparative statics, competitive prices
effect on:
product
labor
output
tightness
employment
tightness
increase in:
y
x
l
θ
aggregate demand
0
0
0
0
+
+
−
0
0
0
0
+
−
0
technology
labor supply
mismatch
0
0
32 / 46
Rigid or flexible prices?
33 / 46
Construct proxy for product market tightness from
capacity utilization measure in Survey of Plant Capacity:
85%
80%
75%
70%
65%
60%
55%
1974 1979 1984 1989 1994 1999 2004 2009 2013
34 / 46
Fluctuations in product market tightness: rigid price
Log−deviation from HP trend
0.08
0.04
0
−0.04
−0.08
−0.12
−0.16
1974 1979 1984 1989 1994 1999 2004 2009 2013
35 / 46
Fluctuations in labor market tightness: rigid real wage
0.6
Log−deviation from HP trend
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
1974 1979 1984 1989 1994 1999 2004 2009 2013
36 / 46
Labor demand, labor supply,
or mismatch shocks?
37 / 46
Source of labor demand and supply shocks
labor demand: AD, technology
labor supply: job search, labor-force participation
38 / 46
Predicted effect of shocks
labor supply and mismatch shocks: negative
correlation between employment and labor market
tightness
labor demand shocks: positive correlation
between employment and labor market tightness
39 / 46
Evidence of labor demand shocks
0.8
Labor market tightness (left scale)
0.04
0.6
0.03
0.4
0.02
0.2
0.01
0
0
−0.2
−0.01
−0.4
−0.02
−0.6
Employment (right scale)
−0.03
−0.8
−0.04
1974 1979 1984 1989 1994 1999 2004 2009 2013
40 / 46
Cross-correlogram: labor market tightness and employment
1
0.8
0.6
0.4
0.2
0
−0.2
−4
−3
−2
−1
0
1
Lags (quarters)
2
3
4
41 / 46
Labor demand shocks:
AD or technology shocks?
42 / 46
Predicted effect of shocks
AD shocks: positive correlation between output
and product market tightness
technology shocks: negative correlation between
output and product market tightness
43 / 46
Evidence of AD shocks
0.09
0.06
0.06
Output (right scale)
0.03
0
0.04
0.02
0
−0.03
−0.02
−0.06
−0.04
−0.09
−0.06
−0.12 Product market tightness (left scale)
−0.08
−0.15
−0.1
1974 1979 1984 1989 1994 1999 2004 2009 2013
44 / 46
Cross-correlogram: product market tightness and output
0.6
0.5
0.4
0.3
0.2
0.1
0
−0.1
−0.2
−4
−3
−2
−1
0
1
Lags (quarters)
2
3
4
45 / 46
Conclusion
tractable model of unemployment fluctuations
empirical series to measure tightness
I
product market tightness
I
labor market tightness
source of unemployment fluctuations
I
importance of price and wage rigidity
I
importance of AD shocks
46 / 46
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