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

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Main Idea

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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

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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

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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

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1c L L

L

y

L* 1

L* U*

X* V*

Decentralizing

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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

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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

Firm’s Problem

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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

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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

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1 py wL

1L

1

pyw

L

1 py wL

1w

1 L py

Classical Old Keynesian

The Production Function, Aggregate Supply and Demand

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Com

modit

ies

c

Dolla

rs (

wag

e u

nit

s)

C

LaborLabor

Production Function

Aggregate Supply

Data Used in This Study

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-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

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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

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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

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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

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, , 01

bi y

,i i b y

Estimation 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

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

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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

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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?

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