aggregate demand, idle time, and unemploymentsaez/galleons-nber-july2014.pdfaggregate demand + + + +...
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Aggregate Demand, Idle Time,
and Unemployment
Pascal Michaillat (LSE) & Emmanuel Saez (Berkeley)
July 2014
1 / 46
Motivation
1974 1984 1994 2004 2014 3%
5%
7%
9%
11%
Unem
plo
ym
ent ra
te
2 / 46
Motivation
1974 1984 1994 2004 2014 3%
5%
7%
9%
11%
Unem
plo
ym
ent ra
te
Technology?
Aggregate demand?
2 / 46
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 / 46
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 / 46
The available models
1. matching model of the labor market
I realistic mechanism + tractable
I but no aggregate demand
2. ?
3. New Keynesian DSGE model
I many shocks + quantitatively realistic
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
but difficult to analyze
4 / 46
This model
equilibrium version of the Barro-Grossman model, with
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
5 / 46
Basic model (no labor market)
6 / 46
Setup
static model
measure 1 of identical households
production takes place within households
households cannot consume own production
households trade production on frictional market
7 / 46
Matching function and tightness
v visits
k units of produced good
8 / 46
Matching function and tightness
visits v
capacity k
sales
purchases
CRS matching function h(k,v)
8 / 46
Matching function and tightness
sales = =
purchases = =
output: y = h(k,v)
capacity k tightness: x = v / k
visits v 8 / 46
Low product market tightness
9 / 46
High product market tightness
10 / 46
Matching cost: ρ goods per visit
output =
[1+ τ(x
+)
]· consumption
proof:
y︸︷︷︸output
= c︸︷︷︸consumption
+ ρ · v︸︷︷︸trading
= c+ρ · yq(x)
⇒ y ·[
1− ρ
q(x)
]= c
⇒ y =
1+ρ
q(x−)−ρ
· c≡ [1+ τ(x+)
]· c
11 / 46
Tightness and aggregate supplypr
oduc
t pric
e
product market tightness: x
quantity of produced good12 / 46
Tightness and aggregate supply
capacity: k
prod
uct m
arke
t tig
htne
ss x
quantity of produced good12 / 46
Tightness and aggregate supply
output: y = f(x) k
capacity k
quantity of produced good
prod
uct m
arke
t tig
htne
ss x
12 / 46
Tightness and aggregate supply
output y
consumption:
capacity k
quantity of produced good
prod
uct m
arke
t tig
htne
ss x
12 / 46
Tightness and aggregate supply
idle timetrading cost
capacity koutput y
consumption
aggregate supply c
quantity of produced good
prod
uct m
arke
t tig
htne
ss x
12 / 46
Nonproduced good
valued by consumers
in fixed supply
traded on a perfectly competitive market
examples: real money, land, gold, fixed capital
as in Barro & Grossman [1971], Hart [1982], and
Blanchard & Kiyotaki [1987]
13 / 46
Households
take price p and tightness x as given
choose c, m to maximize utility χ
1+χ· c ε−1
ε︸ ︷︷ ︸produced good
+1
1+χ·m ε−1
ε︸ ︷︷ ︸nonproduced good
ε
ε−1
subject to budget constraint
m︸︷︷︸numeraire
+p · (1+ τ(x)) · c︸ ︷︷ ︸produced good
= µ︸︷︷︸endowment
+ f (x) ·p · k︸ ︷︷ ︸labor income
14 / 46
Optimal consumption decision
first-order condition
(1+ τ(x)) ·p︸ ︷︷ ︸product price
· 11+χ
·m− 1ε︸ ︷︷ ︸
MU of nonproduced good
=χ
1+χ· c− 1
ε︸ ︷︷ ︸MU of produced good
aggregate demand (as m = µ):
cd(x,p) =χε ·µ
(1+ τ(x))ε ·pε
15 / 46
Tightness and aggregate demandpr
oduc
t mar
ket t
ight
ness
x
consumption c
cd(x, p) =�✏ · µ
(1 + ⌧(x))✏ · p✏
16 / 46
Definition of 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 efficient price
17 / 46
Comparative statics
with fixed price and efficient price
18 / 46
Increase in AD with fixed price
AS
AD
capacity koutput y
equilibrium
prod
uct m
arke
t tig
htne
ss x
quantity19 / 46
Increase in AD with fixed price
AS
AD
quantity
capacity koutput ypr
oduc
t mar
ket t
ight
ness
x
19 / 46
Increase in AS with fixed price
AD
AScapacity koutput y
prod
uct m
arke
t tig
htne
ss x
quantity20 / 46
Comparative statics with fixed price
effect on:
output tightness idle time
increase in: y x 1− f (x)
aggregate demand + + −aggregate supply + − +
21 / 46
Definition of efficient price
c*
x*
slack equilibrium
AS
AD
prod
uct m
arke
t tig
htne
ss x
consumption c
price is too high
22 / 46
Definition of efficient price
c*
x*
AS
tight equilibrium
AD
prod
uct m
arke
t tig
htne
ss x
consumption c
price is too low
22 / 46
Definition of efficient price
c*
x*
AS
efficient equilibrium
AD
prod
uct m
arke
t tig
htne
ss x
consumption c
price is efficient
22 / 46
Comparative statics with efficient price
effect on:
output tightness idle time
increase in: y x 1− f (x)
aggregate demand 0 0 0
aggregate supply + 0 0
23 / 46
Complete model
24 / 46
Labor market and unemployment
recruiters
labor force hemployment llabor supply n
number of workers
labo
r mar
ket t
ight
ness
θ
producers unemployment
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)︸︷︷︸selling probability
· a ·nα︸ ︷︷ ︸production
− [1+ τ̂(θ)] ·w ·n︸ ︷︷ ︸wage of producers + recruiters
26 / 46
Optimal employment decision
first-order condition:
f (x)︸︷︷︸selling probability
·α ·a ·nα−1︸ ︷︷ ︸MPL
= [1+ τ̂(θ)]︸ ︷︷ ︸matching wedge
· w︸︷︷︸real wage
labor demand: demand for producers
nd(θ ,x,w) =[
f (x) ·a ·α(1+ τ̂(θ)) ·w
] 11−α
27 / 46
Partial equilibrium on labor market
labor force hemployment l
number of workers
labo
r mar
ket t
ight
ness
θ
labor demand
labor supply
partial equilibrium
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 ·αw
) 11−α
·(
11+ τ̂(θ)
) α
1−α
frictional unemployment from τ̂(θ)> 0
classical unemployment from w > a ·α
Keynesian unemployment from f (x)< 1
30 / 46
Comparative statics with fixed prices
effect on:
product labor
output tightness tightness employment
increase in: y x θ l
aggregate demand + + + +technology + − + +labor supply + − − +mismatch − + + −
31 / 46
Comparative statics with efficient prices
effect on:
product labor
output tightness tightness employment
increase in: y x θ l
aggregate demand 0 0 0 0
technology + 0 0 0
labor supply + 0 0 +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:
1974 1979 1984 1989 1994 1999 2004 2009 201355%
60%
65%
70%
75%
80%
85%
34 / 46
Fluctuations in product market tightness: rigid price
1974 1979 1984 1989 1994 1999 2004 2009 2013−0.16
−0.12
−0.08
−0.04
0
0.04
0.08
Lo
g−
de
via
tio
n f
rom
HP
tre
nd
35 / 46
Fluctuations in labor market tightness: rigid real wage
1974 1979 1984 1989 1994 1999 2004 2009 2013−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6L
og
−d
evia
tio
n f
rom
HP
tre
nd
36 / 46
Labor demand
or labor supply shocks?
37 / 46
Source of labor supply and demand shocks
labor demand: AD, technology
labor supply: mismatch, job search, participation
38 / 46
Effect of labor supply and demand shocks
labor supply 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
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1974 1979 1984 1989 1994 1999 2004 2009 2013−0.04
−0.03
−0.02
−0.01
0
0.01
0.02
0.03
0.04Labor market tightness (left scale)
Employment (right scale)
40 / 46
Cross-correlogram: labor market tightness and employment
−4 −3 −2 −1 0 1 2 3 4−0.2
0
0.2
0.4
0.6
0.8
1
Lags (quarters)41 / 46
Labor demand shocks:
AD or technology shocks?
42 / 46
Effect of AD and technology 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
−0.15
−0.12
−0.09
−0.06
−0.03
0
0.03
0.06
0.09
1974 1979 1984 1989 1994 1999 2004 2009 2013−0.1
−0.08
−0.06
−0.04
−0.02
0
0.02
0.04
0.06
Product market tightness (left scale)
Output (right scale)
44 / 46
Cross-correlogram: 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)45 / 46
Conclusion
tractable model of unemployment fluctuations
empirical series to measure tightness
I product market tightness
I labor market tightness
origins of unemployment fluctuations
1. importance of price and wage rigidity (not flexibility)
2. importance of labor demand shocks (not labor supply)
3. importance of AD shocks (not technology)
46 / 46