Animal Spirits, Persistent
Unemployment and the Belief
Function
Duke University, February 2011
Roger E A Farmer
Department of Economics UCLA
1
Main Question
Is the economy self-correcting?
Yes
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Classical economics
New-Keynesian economics
No
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2
Keynes of the General Theory
Old-Keynesian economics
The Goals of This Research
Replace New-Keynesian Economics
Why?
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Degree of price stickiness is inconsistent with micro evidence
Cannot explain inflation persistence
There is no unemployment in the canonical model
Welfare costs of business cycles are trivial
Cannot explain asset price bubbles
Alternative: Old Keynesian economics
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3
Main Idea
Put in a search model of the labor market
Drop the Nash bargain
Replace the Nash bargain with demand determination of
output through self-fulfilling expectations
Costly Search and Recruiting
Externality supports different allocations as equilibria
Animal spirits select an equilibrium
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4
Connection with New-Keynesian Theory
New Keynesian economics assumes sticky prices.
Deviations from the natural rate of unemployment are
temporary.
Old Keynesian economics assumes flexible prices. There is
a continuum of steady state unemployment rates indexed
by beliefs.
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5
Connection with Search Theory
Two kinds of multiplicity in search models
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Finite multiplicities: Diamond 1982,1984
Steady state Continuum: Howitt and McAfee 1987
Continuum follows from bilateral monopoly
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6
A Model
One Lucas tree – non reproducible
One good produced by labor and capital
No disutility of work – everyone wants a job
Everyone fired and rehired every period
No uncertainty
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The Labor Market
Finding a job uses resources
Two technologies
Production technology
Matching technology
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8
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Terminology
9
K
Number of trees (Normalized to 1)
H
Time endowment of household
(Normalized to 1)
c
Consumption in units of commodities
y
Output in units of commodities
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Terminology
10
w
r
Money wage
pk
Relative price of a tree
p
Money price of a commodity
Money rental rate
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Terminology
L
Employment
X
Production workers
V Recruiters
L  X V
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Technologies

Production
technology
LH V
Match
technology
yK
1
X
1/ 2
H 1
12
1/ 2
K 1
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Planning Problem
c   L 1  L  

y
L*
X*
13
U*
V*
L*
1
L
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Decentralizing
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Need headhunting firms
Pay unemployed workers
Pay corporate recruiters
Sell matches
We don’t see these markets
14
More Terminology
q
Probability of a worker being
hired
q
One recruiter hires this many
workers
L  qH
L  qV
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Decentralization
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Agents take wages and prices as given
Households take hiring probability as given
Firms take hiring effectiveness as given
All markets clear
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Firm’s Problem
max pt yt  wt Lt  rt Kt
Lt  qtVt
Lt  X t  Vt

yt  K t X t
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1
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Firm’s Problem
 
1
max pt Kt  Lt 1 
  qt

 pt yt  rt Kt



 wt Lt  rt Kt
Firm acts like a firm in an auction
market but takes q as given
1    pt yt  wt Lt
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1
q is an externality that represents
market tightness.
For any given q there is a zero
profit equilibrium
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Market Tightness
 
1
yt  Kt  Lt 1 
  qt
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1


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q is an indicator of market tightness
For every value of q there is a different zero profit
equilibrium
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Comparison with the Classical Model
Classical
1    py  wL
1    py  wL
L 1
w 1
1    py

w
L  1    py
L
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Old Keynesian
Commodities c
Dollars (wage units) C
The Production Function,
Aggregate Supply and Demand
Labor
Production Function
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Labor
Aggregate Supply
Data Used in This Study
20
I use the output gap
instead of
unemployment for
more direct
comparison with
new-Keynesian
literature
15
10
5
0
-5
-10
55
60
65
70
75
80
85
90
95
00
Deviations of Real GDP from Trend
CPI Inflation
Treasury Bill Rate
22
05
Augmented Dickey-Fuller Tests for a Unit
Root in Individual Series
P-value of a unit
root
T-Bill Rate
CPI Inflation
GDP (deviation
from trend)
Full sample
0.24
0.36
0.12
1952.1 – 1979.4
0.92
0.99
0.41
1983.1 – 2007.4
0.41
0.01
0.12
Even after taking out a linear trend -- gdp is still extremely
persistent. We cannot reject the hypothesis of a unit root in
deviations of gdp from trend.
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The New-Keynesian Model
ayt  aEt  yt 1   it  Et  t 1     zd t
it   t   y t  b
 t   Et  t 1     y t  z s t 
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The Old-Keynesian Model
ayt  aEt  yt 1   it  Et  t 1     zd t
it   t   y t  b
Et  xt 1   xt  zs t
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xt  y t  pt
Steady States of the Two Models
 b
 
, i   , y  0
 1
i   ,
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i  b     y
Estimation
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I estimated both models with MCMC in Dynare
For each model I ran 150,000 replications
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Comparison of the Two Models
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Sample 1952.1:2007.4
Log Data Density
New-Keynesian Model
2324.10
Old-Keynesian Model
2329.25
Posterior odds ratio of
new versus old Keynesian
model
0.0058
Why?
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In the data GDP, the interest rate and inflation are well
described by a cointegrated VAR
NK and OK -- fit is close BUT NK must assume NR is a
random walk
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Conclusion
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In the old-Keynesian model the economy drifts like a boat
on the ocean
An interest rate policy rule, like the Taylor rule, pushes
the boat in one direction or another.
Open question
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Is it better to target the level of the pricing kernel rather than
its rate of change?