slides - aggregate demand, idle time, and...
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Aggregate Demand, Idle Time,
and Unemployment
Pascal Michaillat
Emmanuel Saez
Quarterly Journal of Economics, 2015
1 / 57
unemployment fluctuations remain
insufficiently understood
1980 1990 2000 2010 3%
5%
7%
9%
11%
Unem
plo
ym
entra
te
2 / 57
unemployment fluctuations remain
insufficiently understood
1980 1990 2000 2010 3%
5%
7%
9%
11%
Unem
plo
ym
entra
te
technology?aggregatedemand?
2 / 57
unemployment fluctuations remain
insufficiently understood
1980 1990 2000 2010 3%
5%
7%
9%
11%
Unem
plo
ym
entra
te
mismatch?jobsearch?labor-forceparticipation?
technology?aggregatedemand?
2 / 57
modern models
matching model of the labor market
• tractable
• but no aggregate demand
New Keynesian model with matching frictions on
the labor market
• many shocks, including aggregate demand
• but fairly complex
3 / 57
general-disequilibrium model
vast literature after Barro & Grossman [1971]
• revival after the Great Recession
captures effect of aggregate demand on
unemployment
but limited role of supply-side factors in
demand-determined regimes
and difficult to analyze because of multiple regimes
4 / 57
the model in this paper
Barro-Grossman architecture
but matching structure on product + labor markets
• instead of disequilibrium structure
• advantage: markets can be too slack or too
tight but remain in equilibrium
aggregate demand, technology, mismatch, and labor
supply (search / participation) affect unemployment
simple: graphical representation of equilibrium5 / 57
basic model:
only product market
6 / 57
structure
static model
measure 1 of identical households
households produce and consume services
• no firms: services produced within households
• households cannot consume their own services
services are traded on matching market
households visit other households to buy services
7 / 57
matching function and tightness
vvisits
kservices
8 / 57
matching function and tightness
v visits
sales
purchases
CRSmatchingfunctionh(k,v)
k services
8 / 57
matching function and tightness
sales= =
purchases= =
output:y = h(k,v)
k servicestightness:x = v / k
v visits8 / 57
low product market tightness
9 / 57
high product market tightness
10 / 57
evidence of unsold capacity
1990 2000 2010 0%
10%
20%
30%Idleness, non-manufacturingIdleness, manufacturingUnemployment
11 / 57
matching cost: ρ ∈ (0,1) service per visit
consumption ≡ output net of matching services
• consumption, not output, yields utility
key relationship: output = [1+ τ(x)] · consumption
matching wedge τ(x) summarizes matching costs
y︸︷︷︸output
= c︸︷︷︸consumption
+ ρ · v︸︷︷︸matching services
= c+ρ · yq(x)
⇒ y =
1+
ρ
q(x−)−ρ
· c≡
[1+ τ(x
+)
]· c
12 / 57
evidence of matching costs
1997 2002 2007 2012
Th
ou
san
ds
of
wo
rker
s
0
250
500
750
PurchasingRecruiting
workers devoted to purchasing (matching on product market)
workers devoted to recruiting (matching on the labor market)
13 / 57
consumption < output < capacity
output y < capacity k because the matching
function prevents all services from being sold
• formally: selling probability f (x)< 1
consumption c < output y because some services
are devoted to matching so cannot provide utility
• formally: matching wedge τ(x)> 0
consumption is directly relevant for welfare
14 / 57
aggregate supply
aggregate supply indicates the number of services
consumed at tightness x, given the supply of
services k and the matching process
cs(x) =f (x)
1+ τ(x)· k = [f (x)−ρ · x] · k
it is equivalent to represent aggregate supply (and
demand) in terms of output instead of consumption
but consumption representation is linked to welfare
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tightness and aggregate supply
capacity: k
prod
uctm
arkettightne
ss x
quantityofservices16 / 57
tightness and aggregate supply
output: y = f(x) . k
capacity k
quantityofservices
prod
uctm
arkettightne
ss x
idletime
16 / 57
tightness and aggregate supply
aggregatesupply:
output y capacity k
quantityofservices
prod
uctm
arkettightne
ss x matchingcost
cs(x) = [f(x) � ⇢x]k
16 / 57
tightness and aggregate supply
idletimematching
cost
capacity koutput y
consumption
aggregatesupply cs(x)
quantityofservices
prod
uctm
arkettightne
ss x
16 / 57
money
money is in fixed supply µ
households hold m units of money
the price of services in terms of money is p
real money balances enter the utility function
• Barro & Grossman [1971]
• Blanchard & Kiyotaki [1987]
17 / 57
households
take price p and tightness x as given
choose c, m to maximize utility
χ
1+χ· c ε−1
ε
︸ ︷︷ ︸services
+1
1+χ·(
mp
) ε−1ε
︸ ︷︷ ︸real money balances
subject to budget constraint
m︸︷︷︸money
+ p · (1+ τ(x)) · c︸ ︷︷ ︸expenditure on services
= µ︸︷︷︸endowment
+ f (x) ·p · k︸ ︷︷ ︸labor income
18 / 57
aggregate demand
optimal consumption decision:
(1+ τ(x))︸ ︷︷ ︸relative price
· 11+χ
·(
mp
)− 1ε
︸ ︷︷ ︸MU of real money
=χ
1+χ· c− 1
ε
︸ ︷︷ ︸MU of services
money market clears: m = µ
aggregate demand gives desired consumption of
services given price p and tightness x:
cd(x,p) =(
χ
1+ τ(x)
)ε
· µp
19 / 57
linking aggregate demand and visits
there is a direct link between consumption of
services, purchase of services, and visits
if the desired consumption is cd(x,p)
the desired number of purchases is
(1+ τ(x)) · cd(x,p)
and the required number of visits is
(1+ τ(x)) · cd(x,p)q(x)
20 / 57
tightness and aggregate demand
consumption c
cd(x, p) =
✓�
1 + ⌧(x)
◆✏
· µ
p
prod
uctm
arkettightne
ss x
21 / 57
equilibrium
price p + tightness x equilibrate supply and
demand: cs(x) = cd(x,p)
the matching equilibrium is much richer than the
Walrasian equilibrium—where only the price
equilibrates supply and demand
• can describe “Walrasian situations” where price
responds to shocks and tightness is constant
• but can also describe “Keynesian situations”
where price is constant and tightness (slack)
responds to shocks 22 / 57
price mechanism
1 condition but 2 variables (x, p): we need a price
mechanism to completely describe the equilibrium
here we consider two polar cases:
• fixed price [Barro & Grossman 1971]
• competitive price [Moen 1997]
in the paper we also consider:
• bargaining (typical in the literature)
• partially rigid price23 / 57
comparative statics
24 / 57
increase in AD with fixed price (χ ↑)
AS
AD
capacityoutput
equilibrium
prod
uctm
arkettightne
ss
quantity
x
c y k25 / 57
increase in AD with fixed price (χ ↑)
AS
AD
capacityoutputprod
uctm
arkettightne
ss
quantity25 / 57
increase in AS with fixed price (k ↑)
AD
AScapacityoutput
prod
uctm
arkettightne
ss
quantity26 / 57
comparative statics with fixed price
effect on:
output tightness
increase in: y x
aggregate demand χ + +aggregate supply k + −
27 / 57
efficient equilibrium: consumption is maximum
c*
x*
AS
AD
consumption
efficientequilibrium:priceiscompetitive
prod
uctm
arkettightne
ss
28 / 57
slack equilibrium: consumption is too low
c*
x*
AS
AD
slackequilibrium:priceistoohigh
prod
uctm
arkettightne
ss
consumption29 / 57
tight equilibrium: consumption is too low
AS
AD
tightequilibrium:priceistoolow
prod
uctm
arkettightne
ss
consumptionc*
x*
30 / 57
comparative statics with competitive price: price
absorbs all shocks so tightness is constant
effect on:
output tightness
increase in: y x
aggregate demand χ 0 0
aggregate supply k + 0
31 / 57
complete model:
product + labor markets
32 / 57
labor market and unemployment
recruiters
laborforcehemployment llaborsupply ns(θ)
workers
labo
rmarkettightne
ssθ
producers unemployment
33 / 57
firms
workers are hired on matching labor market
production is sold on matching product market
firms employ producers and recruiters
• number of recruiters = τ̂(θ)×producers
• number of employees = [1+ τ̂(θ)]×producers
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
34 / 57
labor demand
optimal employment decision:
f (x)︸︷︷︸selling probability
·α ·a ·nα−1︸ ︷︷ ︸MPL
=(1+ τ̂(θ)︸︷︷︸matching wedge
)· w︸︷︷︸real wage
same as Walrasian first-order condition, except for
selling probability < 1 and matching wedge > 0
labor demand gives the desired number of producers:
nd(θ ,x,w) =[
f (x) ·a ·α(1+ τ̂(θ)) ·w
] 11−α
35 / 57
partial equilibrium on labor market
laborforceemployment
workers
labo
rmarkettightne
ss
labordemand
laborsupply
partialequilibrium
θ
n l h36 / 57
general equilibrium
prices (p,w) and tightnesses (x,θ) equilibrate supply
and demand on product + labor markets:{
cs(x,θ) = cd(x,p)ns(θ) = nd(θ ,x,w)
2 equations, 4 variables: need price + wage
mechanisms
• fixed price and fixed wage
• competitive price and competitive wage37 / 57
effect of AD on unemployment with fixed prices
AS
ADprod
uctm
arkettightne
ss x
ADincreasessox increases:itiseasierforfirmstosell
quantity
capacityoutput
38 / 57
effect of AD on unemployment with fixed prices
laborforceemployment
workers
labo
rmarkettightne
ss θ
LD
LS
x increasessoLDandθ increase:unemploymentfalls
unemployment
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effect of AD on unemployment with fixed prices
ASpossiblefeedback:asemploymentchanges,capacityandthusxmayadjust,dampeningor
amplifyingtheinitialchangeinx
AD
quantity
capacityoutput
prod
uctm
arkettightne
ss x
38 / 57
Keynesian, classical, and frictional unemployment
equilibrium unemployment rate:
u = 1− 1h·(
f (x) ·a ·αw
) 11−α
·(
11+ τ̂(θ)
) α
1−α
if f (x) = 1, w = aαhα−1, and τ̂(θ) = 0, then u = 0
the factors of unemployment therefore are
• Keynesian factor: f (x)< 1
• classical factor: w > a ·α ·hα−1
• frictional factor: τ̂(θ)> 039 / 57
comparative statics with fixed prices
effect on:
product labor
output tightness employment tightness
increase in: y x l θ
aggregate demand χ + + + +technology a + − + +labor supply h + − + −
40 / 57
comparative statics with fixed prices
effect on:
product labor
output tightness employment tightness
increase in: y x l θ
aggregate demand χ + + + +technology a + − + +labor supply k + − + −
40 / 57
comparative statics with competitive prices: prices
absorb all shocks so tightnesses are constant
effect on:
product labor
output tightness employment tightness
increase in: y x l θ
aggregate demand χ 0 0 0 0
technology a + 0 0 0
labor supply k + 0 + 0
41 / 57
rigid or flexible prices?
42 / 57
we construct x from capacity utilization in SPC
1980 1990 2000 201055%
60%
65%
70%
75%
80%
85%Cap
acity
utiliza
tion
when utilization is low, it is hard to sell production, which indicates that
product market tightness x is low
43 / 57
fluctuations in x =⇒ rigid price
1980 1990 2000 2010−0.16
−0.12
−0.08
−0.04
0
0.04
0.08
proxy for cyclical component of x
44 / 57
fluctuations in θ =⇒ rigid real wage
1980 1990 2000 2010−0.75
−0.5
−0.25
0
0.25
0.5
cyclical component of θ
45 / 57
labor demand or
labor supply shocks?
46 / 57
labor demand and labor supply shocks
source of labor demand shocks:
• aggregate demand χ
• technology a
source of labor supply shocks:
• labor-force participation h
• h can also be interpreted as job-search effort
47 / 57
predicted effects of shocks
labor supply shocks:
• negative correlation between employment (l)
and labor market tightness (θ )
labor demand shocks:
• positive correlation between employment (l)
and labor market tightness (θ )
48 / 57
positive correlation between l and θ =⇒ labor demand
−0.8
−0.4
0
0.4
0.8
1980 1990 2000 2010 −0.04
−0.02
0
0.02
0.04cyclical component of θ
cyclical component of l
49 / 57
cross-correlogram: θ (leading) and l
−4 −3 −2 −1 0 1 2 3 4−0.2
0
0.2
0.4
0.6
0.8
1
Lags (quarters)50 / 57
aggregate demand or
technology shocks?
51 / 57
predicted effects of shocks
aggregate demand shocks:
• positive correlation between output (y) and
product market tightness (x)
technology shocks:
• negative correlation between output (y) and
product market tightness (x)
52 / 57
positive correlation between y and x =⇒ AD
−0.16
−0.08
0
0.08
1980 1990 2000 2010 −0.1
−0.05
0
0.05
cyclical component of x
cyclical component of y
53 / 57
cross-correlogram: x (leading) and y
−4 −3 −2 −1 0 1 2 3 4−0.2
0
0.2
0.4
0.6
0.8
1
Lags (quarters)54 / 57
conclusion
55 / 57
summary
we develop a tractable, general-equilibrium model of
unemployment fluctuations
we construct empirical series for
• product market tightness
• labor market tightness
we find that unemployment fluctuations stem from
• price rigidity and real-wage rigidity
• aggregate demand shocks56 / 57
applications of the model
monetary business-cycle model, with liquidity trap
• Michaillat & Saez [2014]
optimal unemployment insurance
• Landais, Michaillat, & Saez [2010]
optimal public expenditure
• Michaillat & Saez [2015]
optimal monetary policy
• Michaillat & Saez [2016]57 / 57