EUROPEAN
CENTRAL
BANK
WO R K I N G PA P E R S E R I E S
WORKING PAPER NO. 120
LEARNING STABILITY IN
ECONOMICS WITH
HETEROGENEOUS AGENTS
BY SEPPO HONKAPOHJA
AND KAUSHIK MITRA
January 2002
EUROPEAN
CENTRAL
BANK
WO R K I N G PA P E R S E R I E S
WORKING PAPER NO. 120
LEARNING STABILITY IN
ECONOMICS WITH
HETEROGENEOUS AGENTS*
BY SEPPO HONKAPOHJA
AND KAUSHIK MITRA
January 2002
The views expressed in this paper are those of the authors and do not necessarily reflect those of the European Central Bank.
* This work was in part carried out when the first author visited the European Central Banks Directorate General Research
as part of their Research Visitor Programme and the second author the Research Department of the Bank of Finland.
Financial support from Academy of Finland, Yrjö Jahnsson Foundation and Nokia Group is also gratefully acknowledged.
© European Central Bank, 2001
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All rights reserved.
Reproduction for educational and non-commercial purposes is permitted provided that the source is acknowledged.
The views expressed in this paper are those of the authors and do not necessarily reflect those of the European Central Bank.
ISSN 1561-0810
Contents
Abstract
4
Non-technical summary
5
1
Introduction
7
2
The framework
2.1 Economic applications
9
10
3
Heterogenous forecasts and expectational stability
12
4
RLS learning with different initial beliefs
16
5
RLS learning with different gain sequences
18
6
RLS learning and SG learning
20
7
Application to market model
7.1 E-stability of the REE
7.2 Heterogenous learning in the market model
24
25
25
8
Case with rational and learning agents
8.1 Application to monetary policy
8.1.1 Central bank has RE while private sector is learning
8.1.2 Central bank is learning while private sector has RE
27
29
29
30
9
Lagged endogenous variables
9.1 General analysis
9.2 Application to Cagan model
9.2.1 RLS and SG learning in Cagan model
31
31
33
35
10
Concluding remarks
36
References
36
A
40
40
42
Appendix
A.1 Convergence of the learning algorithms
A.2 Proof of proposition 14
European Central Bank Working Paper Series
ECB Working Paper No 120 January 2002
45
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