A Model of Aggregate Demand,

Idleness, and Unemployment

Pascal Michaillat (LSE) & Emmanuel Saez (Berkeley)

June 2014

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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

5 / 25

Overview of the model

6 / 25

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

7 / 25

Formalization of matching process

v  visits  

k  slots  available  

8 / 25

Formalization of matching process

visits  v    

capacity  k    

           sales  

         purchases  

CRS  matching  func8on  h(k,v)

8 / 25

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�)

8 / 25

Formalization of matching process

selling  probability  f(x)    

buying  probability  q(x)    

output  y

capacity  k    

visits  v    

8ghtness  x    

8 / 25

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

9 / 25

Supply side on product marketpr

ice

quantity of produced goods

product market tightness: x

10 / 25

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

10 / 25

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

12 / 25

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