animal spirits, persistent unemployment and the belief function
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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
Classical economics New-Keynesian economics
No Keynes of the General Theory Old-Keynesian economics
2
The Goals of This Research Replace New-Keynesian Economics Why?
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
3
Main Idea
4
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
Connection with New-Keynesian Theory
5
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.
Connection with Search Theory
6
Two kinds of multiplicity in search models Finite multiplicities: Diamond 1982,1984 Steady state Continuum: Howitt and McAfee 1987
Continuum follows from bilateral monopoly
A Model
04/19/237
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
The Labor Market
04/19/238
Finding a job uses resources Two technologies Production technology Matching technology
Terminology
04/19/239
Number of trees (Normalized to 1)
Time endowment of household (Normalized to 1)
K
H
Consumption in units of commodities
c
y Output in units of commodities
Terminology
04/19/2310
w Money wage
kp Relative price of a tree
p Money price of a commodity
r Money rental rate
Terminology
04/19/2311
L Employment
X Production workers
V Recruiters
L X V
Technologies
04/19/2312
1 y K X
1/ 2 1/ 2L H V
Production technology
Match technology
1H 1K
Planning Problem
04/19/2313
1c L L
L
y
L* 1
L* U*
X* V*
Decentralizing
14
Need headhunting firms Pay unemployed workers Pay corporate recruiters Sell matches We don’t see these markets
More Terminology
04/19/2315
q Probability of a worker being hired
q One recruiter hires this many workers
L qV
L qH
Decentralization
04/19/2316
Agents take wages and prices as given Households take hiring probability as given Firms take hiring effectiveness as given All markets clear
Firm’s Problem
04/19/2317
max t t t t t tp y w L rK
t t tL qV
t t tL X V
1 t t ty K X
Firm’s Problem
04/19/2318
1
1max 1
t t t t t t tt
p K L w L rKq
t t t tp y r K
1 t t t tp y w L
Firm acts like a firm in an auction market but takes q as given
q is an externality that represents market tightness.For any given q there is a zero profit equilibrium
Market Tightness
19
q is an indicator of market tightness For every value of q there is a different zero
profit equilibrium
1
11
t t tt
y K Lq
Comparison with the Classical Model
20
1 py wL
1L
1
pyw
L
1 py wL
1w
1 L py
Classical Old Keynesian
The Production Function, Aggregate Supply and Demand
21
Com
modit
ies
c
Dolla
rs (
wag
e u
nit
s)
C
LaborLabor
Production Function
Aggregate Supply
Data Used in This Study
22
-10
-5
0
5
10
15
20
55 60 65 70 75 80 85 90 95 00 05
Deviations of Real GDP from TrendCPI InflationTreasury Bill Rate
I use the output gap instead of unemployment for more direct comparison with new-Keynesian literature
Augmented Dickey-Fuller Tests for a Unit Root in Individual Series
23
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.
The New-Keynesian Model
24
t t ti y b
1 1d
t t t t t t tay aE y i E z
1s
t t t t tE y z
The Old-Keynesian Model
25
t t ti y b
1 1d
t t t t t t tay aE y i E z
1s
t t t tE x x z t t tx y p
Steady States of the Two Models
26
, , 01
bi y
,i i b y
Estimation I estimated both models with MCMC in Dynare For each model I ran 150,000 replications
27
Comparison of the Two Models
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
28
Why? 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
29
Conclusion 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 Is it better to target the level of the pricing kernel
rather than its rate of change?
30
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