Confidence, Crashes and
Animal Spirits
Marseilles, March 26th 2011
Roger E A Farmer
Department of Economics UCLA
1
Unemployment and Asset
Markets during the Great
Depression
32
0
28
5
24
10
20
15
16
12
20
Black Monday
October 28th 1929
25
8
30
4
35
1928
1930
1932
1934
1936
1938
S&P 500 (Left Scale)
Unemployment Rate (Right Scale)
2
Unemployment and Asset
Markets during the Great
Recession
Lehman Brothers
Collapses
September 15th 2008
1,600
3
1,500
4
1,400
5
1,300
6
1,200
7
1,100
8
1,000
9
900
10
800
11
700
01 02
12
03
04
05
06
07
08
09
10
S&P 500 (Left Scale)
Unemployment Rate (Right Scale)
3
Main Idea





The crash caused the depression
Two Ideas in Keynes
1. Labor market is not a spot market
2. Animal Spirits
This paper builds these two ideas into
a micro-founded general equilibrium
model
4
The Market Failure




Labor market is a search market
without the Nash Bargain
Informational problem -- missing
markets
Externality supports different
allocations as equilibria
Animal spirits select an equilibrium
5
Three Models

All models are based on a Lucas tree
economy non reproducible
– Model 1 has a competitive labor market
– Model 2 has a search market closed with
the Nash Bargain
– Model 3 has a search market closed with
animal spirits
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6
In all three models





There is one unit of capital
Capital is non reproducible
There is a single produced good
Technology is Cobb-Douglas
Utility is logarithmic
7
Model 1:
1
  t 
Lt  
J  E0   log  Ct  

1    
 t 1 
At 1  pt Ct  1  it 1  At  wt Lt
Ct  St Kta Lbt , a  b  1
pk ,t K t  At
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Utility
Budget
constraint
Technology
Asset
markets
8
Model 1 solution
1.

1
 1 pt  pk ,t 1  rrt 1  

  Et 

 
Ct
pk ,t


 Ct 1 pt 1 

2.
Ct wt
b 
Lt pt
FOC for labor
3.
rrt 1
 aCt 1
pt
FOC for capital
Euler
eqn.
These equations are common to all three models
9
Model 1 solution contd.
4.
Ct   St Lt 
5.
wt
Ct Lt 
pt

b
Production
function
Labor supply
equation
These equations are different across models
10
Models 2 and 3:
 t

J  E0    log Ct 
 t 1

Ht  1
Hours
At 1  pt Ct  1  it 1  At  wt Lt
Lt  qt H t
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Utility
Budget
constraint
q tilde is taken as give by households
It is the fraction of workers who find jobs
11
Models 2 and 3: contd
St X t 

K ,V , X , L 
max
t
t
t
b
t
Lt  X t  Vt
Lt  qtVt
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wt
rrt
K t  Lt  K t
pt
pt
a
Profit
maximization
X measures production workers
V measures recruiting workers
q is taken as give by firms
It is the number of workers who can be
hired by one recruiter
12
Search Technology
Lt   Vt 
1/2
H t1/2
A social planner would
choose

L 
2
*
t

U  1 L  1
2
*
t
*
t
The socially efficient
unemployment rate
13
Planning Problem
  L 
C   SL 1   
   
C
b
The socially efficient
unemployment rate
L*
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U*
L*
1
L
14
Search Market
Equilibrium
wt
rrt
b
a
max  t St Lt  K t  Lt  K t
Kt ,Vt , X t , Lt 
pt
pt
Reduced form
profit
maximization
problem
t  1  Lt 
Aggregate
employment
15
Models 2 and 3: How are
they different?


In model 2 the wage is determined by
a Nash Bargain
In model 3 the wage is determined
competitively: the model is closed by
self-fulfilling beliefs in the asset
markets
16
Models 2 and 3:
1.

1
 1 pt  pk ,t 1  rrt 1  

  Et 

 
Ct
pk ,t


 Ct 1 pt 1 

2.
Ct wt
b 
Lt pt
FOC for labor
3.
rrt 1
 aCt 1
pt
FOC for capital
Euler
eqn.
These equations are in common with model 1
17
Closing Model 2
4.
Ct   St Lt 
b
 Lt 
1  


b
Production
function
Bargaining
weight
5.
b 1    Ct wt

 Lt  pt
Lt 1  


Bargaining
equation
18
Closing Model 2
This model implies that
Lt  
If lamda = ½ then bargaining is
socially efficient (Hosios condition)
19
Closing Model 3
4.
5.
Ct   St Lt 
b
 Lt 
1  


 pk ,t 1 
Et 
  xt
 pt 1 
b
Production
function
Self-fulfilling
beliefs in the
asset markets
20
What is x?
xt 
pk ,t
pt
exp   t 
b

xt  Et   St 1  


Stock market is a
random walk driven by
sunspots
Stock market is
efficient and driven by
fundamentals
b

xt  Et   St 1   exp  t 


Stock market is
influenced by
fundamentals but may
overreact
21
Some Implications


Confidence determines employment
through aggregate demand
In this version of the model there is
complete crowding out – government
spending will cause a fall in
consumption
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Summary




No natural rate of unemployment
Unemployment depends on animal
spirits
This version – there is complete
crowding out
Implication: control the value of the
stock market
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