A Model of Aggregate Demand, Idleness, and Unemployment Pascal Michaillat (LSE) & Emmanuel Saez (Berkeley) June 2014 1 / 25
A Model of Aggregate Demand,
Idleness, and Unemployment
Pascal Michaillat (LSE) & Emmanuel Saez (Berkeley)
June 2014
1 / 25
Motivation
1974 1984 1994 2004 2014 3%
5%
7%
9%
11%
Unem
plo
ym
ent ra
te
2 / 25
Motivation
1974 1984 1994 2004 2014 3%
5%
7%
9%
11%
Unem
plo
ym
ent ra
te
Technology?
Aggregate demand?
2 / 25
Motivation
1974 1984 1994 2004 2014 3%
5%
7%
9%
11%
Unem
plo
ym
ent ra
te
Technology?
Aggregate demand?
Mismatch?
Low job search?
Low participation?
2 / 25
Motivation
1974 1984 1994 2004 2014 3%
5%
7%
9%
11%
Unem
plo
ym
ent ra
te
Technology?
Aggregate demand?
Mismatch?
Low job search?
Low participation?
Monetary policy?
Unemployment insurance? Payroll tax? Nothing?
Transfers?
2 / 25
The available models
1. matching model of the labor market
I tractable + microfounded + comparative statics
I but no product market + no aggregate demand
2. ?
3. New Keynesian DSGE model
I product market + many shocks + realistic quantitatively
I but greater complexity + reliance on simulations
3 / 25
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
but difficult to manage rationing, to analyze, and to
map with data
4 / 25
This model
equilibrium version of the Barro-Grossman model, built
on matching frictions on product + labor markets:
graphical representation of GE and welfare
frictional + classical + Keynesian unemployment
broad range of comparative statics
empirical measures of slack
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Overview of the model
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A static model with 3 goods
nonproduced good (“gold”): fixed supply, valued
by workers, traded on competitive market
produced good (“services”): produced by firms,
valued by workers, traded on frictional market
labor: fixed supply, hired by firms, traded on
frictional market
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Formalization of matching process
v visits
k slots available
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Formalization of matching process
visits v
capacity k
sales
purchases
CRS matching func8on h(k,v)
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Formalization of matching process
sales = =
purchases = =
output: y = h(k,v)
visits v
capacity k
k · h (1, x)
v · h
✓1
x, 1
◆
8ghtness: x = v / k
k · f(x+)
v · q(x�)
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Formalization of matching process
selling probability f(x)
buying probability q(x)
output y
capacity k
visits v
8ghtness x
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Formalization of matching process
8 / 25
Formalization of matching process
selling probability f(x)
buying probability q(x)
output y
capacity k
8ghtness x
visits v
8 / 25
Formalization of matching process
8 / 25
Formalization of matching cost
matching cost = ρ services per visit
output dissipated by visits = c · τ(x+)
proof: y︸︷︷︸output
= c︸︷︷︸consumption
+ ρ · v︸︷︷︸visits
= c+ρ · yq(x)
⇒ y ·[
1− ρ
q(x)
]= c
⇒ y =
1+
ρ
q(x−)−ρ
· c≡
[1+ τ(x
+)
]· c
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Supply side on product marketpr
ice
quantity of produced goods
product market tightness: x
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Supply side on product market
capacity: k
quantity of produced goods
prod
uct m
arke
t tig
htne
ss x
10 / 25
Supply side on product market
output: y = f(x) k
capacity k
quantity of produced goods
prod
uct m
arke
t tig
htne
ss x
10 / 25
Supply side on product market
output y
consumption:
capacity k
quantity of produced goods
prod
uct m
arke
t tig
htne
ss x
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Supply side on product market
idle laborvisits
capacity koutput y
consumption
quantity of produced goods
prod
uct m
arke
t tig
htne
ss x
aggregate supply c
10 / 25
Supply side on labor market
recruiters
labor force h employment l labor supply n
number of workers
labo
r mar
ket t
ight
ness
θ
producers unemployment
11 / 25
Partial equilibrium on product market
aggregate demandaggregate
supply
capacityoutput
quantity of produced goods
prod
uct m
arke
t tig
htne
ss x
partial equilibrium
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Partial equilibrium on labor market
0 0
labor force employment
labor supply
partial equilibrium
labor demand
labo
r mar
ket t
ight
ness
θ
number of workers 13 / 25
Keynesian, classical, and frictional unemployment
unemployment determined by three sources:
recruiting costs (frictional)
real wage (classical)
probability to sell production (Keynesian)
14 / 25
General equilibrium
4 variables:
I product market tightness + price
I labor market tightness + wage
2 equations:
I aggregate demand = aggregate supply
I labor demand = labor supply
2 equations but 4 variables: indeterminacy
need price-setting and wage-setting mechanism
15 / 25
Welfare
price too high
quantity
slack market demand
supplytig
htne
ssnumber of trades
16 / 25
Welfare
price too low
quantity
demand
supplytig
htne
ssnumber of trades
tight market
16 / 25
Welfare
efficient market
demand
efficient price (Hosios)
quantity
tight
ness
supply number of trades
16 / 25
Overview of the empirical analysis
17 / 25
Capacity utilization in Survey of Plant Capacity
1974 1979 1984 1989 1994 1999 2004 2009
60%
65%
70%
75%
80%
18 / 25
Log product market tightness
1974 1979 1984 1989 1994 1999 2004 2009
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
19 / 25
Evidence of price rigidity
1974 1979 1984 1989 1994 1999 2004 2009
−0.6
−0.4
−0.2
0
0.2
Log−
devi
atio
n fro
m H
P tre
nd
stand. dev. = 14%
20 / 25
Evidence of wage rigidity
1974 1979 1984 1989 1994 1999 2004 2009−0.6
−0.4
−0.2
0
0.2
0.4
Log−
devi
atio
n fro
m H
P tre
nd
stand. dev. = 25%
21 / 25
Positive AD shock with rigid price
aggregate supply capacityoutput
equilibrium
aggregate demand
prod
uct m
arke
t tig
htne
ss
quantity of produced goods22 / 25
Positive AD shock with rigid pricepr
oduc
t mar
ket t
ight
ness
aggregate demand
aggregate supply capacityoutput
quantity of produced goods22 / 25
Positive AS shock with rigid price
aggregate demand
aggregate supply capacityoutputpr
oduc
t mar
ket t
ight
ness
quantity of produced goods23 / 25
Evidence of AD shocks
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6Log−deviation from HP−trend
Pro
duct m
ark
et tightn
ess
1974 1979 1984 1989 1994 1999 2004 2009−0.08
−0.06
−0.04
−0.02
0
0.02
0.04
0.06
Outp
ut
24 / 25
Product market tightness and output
−4 −3 −2 −1 0 1 2 3 4−0.2
−0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
Lags (quarters)
Sample crosscorrelation
25 / 25