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

15 / 57

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

38 / 57

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