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