INTERNATIONAL RESEARCH
WO R K I N G PA P E R S E R I E S
FORUM ON MONETARY POLICY
N O 6 1 1 / A P R I L 2 0 0 6
MONETARY POLICY,
DETERMINACY,
AND LEARNABILITY
IN THE OPEN ECONOMY
ISSN 1561081-0

by James Bullard

9 7 7 1 5 6 1 0 8 1 0 0 5
and Eric Schaling

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W O R K I N G PA P E R S E R I E S
N O 6 1 1 / A P R I L 2 0 0 6
INTERNATIONAL RESEARCH
FORUM ON MONETARY POLICY
MONETARY POLICY,
DETERMINACY,
AND LEARNABILITY
IN THE OPEN ECONOMY 1
by James Bullard 2
and Eric Schaling 3
In 2006 all ECB
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1 This paper was written while Eric Schaling was a visiting scholar at the Research Department of the Federal Reserve Bank of
St. Louis. The authors thank Ed Nelson for helpful discussions concerning open economy New Keynesian models. Any views expressed
are those of the authors and do not necessarily reflect the views of the Federal Reserve Bank of St. Louis, the Federal Reserve System,
or the European Central Bank.
2 Research Division, Federal Reserve Bank of St. Louis, P.O. Box 442, St. Louis, MO 63166-0442, United States;
e-mail: bullard@stls.frb.org
3 Department of Economics University of Johannesburg, and CentER for Economic Research, Tilburg University. Address: P.O. Box 524,
2006, Auckland Park, Johannesburg, Republic of South Africa ; Telephone: + 27 (11) 489-2927 ; e-mail: esc@eb.rau.ac.za

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International Research Forum on Monetary Policy:
Third Conference

This paper was presented at the third conference of the International Research Forum on
Monetary Policy which took place on May 20-21, 2005 at the ECB. The Forum is sponsored
by the European Central Bank, the Board of Governors of the Federal Reserve System, the
Center for German and European Studies at Georgetown University and the Center for
Financial Studies at Goethe University. Its purpose is to encourage research on monetary
policy issues that are relevant from a global perspective. It regularly organises conferences
held alternately in the Euro Area and the United States. The conference organisers were
Ignazio Angeloni, Matt Canzoneri, Dale Henderson, and Volker Wieland. The conference
programme, including papers and discussions, can be found on the ECB’s web site
(http://www.ecb.int/events/conferences/html/intforum3.en.html)
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ISSN 1561-0810 (print)
ISSN 1725-2806 (online)

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C O N T E N T S
Abstract
4
Non-technical summary
5
1. Introduction
7
1.1 Overview
7
1.2 Main findings
8
1.3 Recent related literature
9
1.4 Organization
11
2. A two-country New Keynesian model
12
2.1 Overview
12
2.2 Environment
12
3. Instrument rules
15
3.1 Simple Taylor-type rules
15
3.2 Instrument rules with international
variables
23
3.3 Two PPP instrument rules
32
4. Targeting rules
35
4.1 Overview
35
4.2 Non-cooperative discretionary policy
35
4.3 Cooperative discretionary policy
42
5. Asymmetry in monetary policy
46
5.1 An exchange rate peg
46
6. Conclusion
50
References
51
European Central Bank Working Paper Series
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Abstract
We study how determinacy and learnability of global rational ex-
pectations equilibrium may be affected by monetary policy in a sim-
ple, two country, New Keynesian framework. The two blocks may be
viewed as the U.S. and Europe, or as regions within the euro zone. We
seek to understand how monetary policy choices may interact across
borders to help or hinder the creation of a unique rational expecta-
tions equilibrium worldwide which can be learned by market partic-
ipants. We study cases in which optimal policies are being pursued
country by country as well as some forms of cooperation. We find
that open economy considerations may alter conditions for determi-
nacy and learnability relative to closed economy analyses, and that
new concerns can arise in the analysis of classic topics such as the de-
sirability of exchange rate targeting and monetary policy cooperation.
Keywords: Indeterminacy, monetary policy rules, new open economy
macroeconomics, international policy coordination. JEL codes: E520,
F330.
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Non-technical summary
In the workhorse New Keynesian macroeconomic model, whether the
rational expectations equilibrium is unique or not may be significantly in-
fluenced by monetary policy choices. Policymakers that implement policy
which conforms to the Taylor principle–that is, policy reacts sufficiently
aggressively to both inflation and real developments in the economy–can
often ensure that the rational expectations equilibrium is unique. Policy-
makers that fail to adhere to this principle by being too passive can cause
the same economy to possess a continuum of equilibria. All of these equilibria
are equally consistent with rational expectations, but generally have higher
variance, possibly much higher variance, than the unique equilibrium asso-
ciated with the more aggressive policy. The high variance equilibria come
from volatile, but still rational, expectations, and are to be avoided both
according to the model and according to practical ideas about policymaking.
The general conclusion for the closed economy has been that monetary pol-
icy should be appropriately aggressive in reacting to economic developments
in order to keep expectations well-anchored, thus avoiding the unpleasant
volatile equilibria that could otherwise exist.
How might this policy recommendation be affected when one turns to the
open economy environment? Our primary concern in this paper is to provide
an analysis of this question.
Extensions of the New Keynesian macroeconomic model to the open econ-
omy have recently been developed. We adopt one of these, a simple frame-
work for a two-country world due to Clarida, Gali, and Gertler (2002). This
framework allows comparison to the more common single country and small
open economy analyses as special cases. The model has a natural separation
between countries: Roughly, after making certain adjustments to parame-
ters accounting for the degree of openness of each economy, this version of
the open economy New Keynesian macroeconomic model is qualitatively the
same as the standard closed economy model. We exploit this feature exten-
sively in this paper. We show that the nature of monetary policy in each
country can lead to more or less international feedback, and complicate or
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simplify the conditions under which monetary policy affects the uniqueness
and learnability of rational expectations equilibrium.
We consider both instrument rules and targeting rules. The instrument
rules we study are Taylor-type policy rules in which the monetary authority
reacts to deviations of inflation from target and deviations of output from
potential, and possibly to other, international variables, when setting their
nominal interest rate target. Instrument rules have no claim to optimality,
but are thought to be a type of robust policy that would work reasonably well
even if the large degree of model uncertainty is taken into account. Targeting
rules represent optimal policy given an objective assigned to the central bank,
and so are finely calibrated to the details of the particular model under study.
Targeting rules give a better idea of the nature of optimal policy in the model
at hand, but may not describe actual policy or perform well should the model
environment change.
We are able to show how the conditions for uniqueness of rational ex-
pectations equilibrium, and the learnability of that equilibrium, depend on
the nature of monetary policy in each country. One interesting aspect of
this analysis is that in a multiple country world, the uniqueness of worldwide
rational expectations equilibrium naturally depends jointly on the policies
adopted by the major players in the world economy. It may be possible
that one player is following a passive policy which, if followed by all coun-
tries worldwide, would lead to scope for endogenous volatility worldwide.
However, there may be ways in which a second policymaker can mitigate
the threat multiple equilibria posed by the first policymaker. This logic sug-
gests a novel sense in which international policy coordination may be critical:
only through coordination can the uniqueness of worldwide equilibrium be
assured.
We conclude that considerations about the uniqueness and learnability of
worldwide equilibrium can alter the evaluation of monetary policy options in
an international context.
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1
Introduction
1.1
Overview
New Keynesian macroeconomic models have become a workhorse for studying
a variety of monetary policy issues in closed economy environments. An
important component of this effort has been the development of the idea that
equilibrium determinacy and learnability may be significantly influenced by
monetary policy choices.1 Recently, simple extensions of the New Keynesian
model to open economy environments have been developed. Our primary
concern in this paper is to provide an analysis of the extent to which the
findings concerning determinacy and learnability for the closed economy New
Keynesian framework may be altered when open economy considerations are
brought to bear. Our learnability criterion is that of Evans and Honkapohja
(2001).
Our approach to this question is to adopt a simple framework for a two-
country world due to Clarida, Gali, and Gertler (2002). This framework
provides one straightforward extension of the New Keynesian model to two
countries and allows comparison to the more common single country and
small open economy analyses as special cases. The model has a natural
separation between countries that Clarida, Gali, and Gertler (2002) discuss
in some detail. Roughly, after making certain adjustments to parameters
accounting for the degree of openness of each economy, this version of the
open economy New Keynesian model is qualitatively the same as the stan-
dard, Clarida, Gali, and Gertler (1999)-style closed economy New Keynesian
model. We exploit this feature extensively in this paper. We show that the
nature of monetary policy in each country can lead to more or less interna-
tional feedback, and complicate or simplify the conditions for determinacy
and learnability of worldwide equilibrium.
1 See, for instance, Woodford (2003), Bullard and Mitra (2002), Evans and Honkapohja
(2003a,b), and Preston (2003).
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1.2
Main findings
We are able to make some progress analytically in showing how determinacy
and learnability conditions depend on the nature of monetary policy in each
country, the conditions under which one policymaker can or cannot mitigate
the threats of indeterminacy and expectational instability posed by another
country, and the degree to which international policy coordination may fail or
succeed in delivering determinacy and learnability of worldwide equilibrium.
The main findings are as follows. Instrument rules which are focussed on
domestic inflation and domestic output gaps lead to world determinacy and
learnability conditions which must be met in each economy independently of
whether they are met in the partner economy. Policymakers in even a large
economy cannot take actions which will mitigate the threats of indeterminacy
and expectational instability stemming from poor policy choices made by the
partner.
For targeting rules, this result has a natural counterpart when policymak-
ers in each country pursue non-cooperative optimal policy under discretion.
The choice of how to implement the optimality condition stemming from
the minimization problem faced by the monetary authorities can easily be
made inappropriately, leading to indeterminacy and expectational instability.
But the objectives of the two monetary authorities in this case involve only
domestic variables and so under the most natural implementation strategies
determinacy and learnability will again hinge on certain conditions being met
in each economy independently of the conditions for the partner economy.
On the other hand, instrument rules which include responses to inter-
national economic conditions induce international feedback between the two
economies even when there would otherwise be no such feedback. Policy
choices in each economy will then influence all aspects of the conditions for
determinacy and learnability of worldwide equilibrium. The separability of
conditions between countries breaks down. Policymakers in a large country
would then have some potential to render worldwide equilibrium determinate
and learnable even if not all players worldwide are pursuing policies which
meet minimal conditions for determinacy and learnability when viewed in
isolation.
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This second result again has a natural counterpart in the case of targeting
rules, in the situation where the two countries agree to try to pursue the
gains from cooperation which may exist in the model. In this case, the joint
objective of the policymakers will involve weighted averages of inflation and
output gaps in the two economies. Implementation strategy will again be an
issue. Determinacy and learnability conditions will hinge on the nature of
the joint policy of the two central banks, and one policy authority may be
able to choose policy to deliver worldwide determinacy and learnability even
if the partner authority adopts a policy which would be inconsistent with
those objectives viewed in isolation.
We conclude that determinacy and learnability considerations can alter
the evaluation of monetary policy options in an international context.
1.3
Recent related literature
The seminal work on the New Keynesian framework and the role of mone-
tary policy is Woodford (2003). We have chosen to follow the extension to a
two-country environment proposed by Clarida, Gali, and Gertler (2002). We
stress that alternative extensions may produce substantively different find-
ings concerning determinacy and learnability than the ones we report here,
and for this reason we think it would be interesting to carry out the analysis
below in other environments. Still, we think that Clarida, Gali, and Gertler
(2002) provides a natural starting point.
Batini, Levine, and Pearlman (2004) study indeterminacy in a two-country
New Keynesian model. Their focus is on the relationship between many-
period forward-looking inflation forecast rules and indeterminacy conditions.
We do not consider rules in this class in this paper. When forward-looking
rules are considered here, they arise from the implementation of certain opti-
mality considerations and do not involve forecasts more than one period into
the future.
De Fiore and Liu (forthcoming) study indeterminacy in a small open
New Keynesian economy. Their model is somewhat different from the one
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Document Outline

• Monetary policy, determinacy, and learnability in the open economy
• International Research Forum on Monetary Policy: Third Conference
• Contents
• Abstract
• Non-technical summary
• 1 Introduction
  • 1.1 Overview
  • 1.2 Main findings
  • 1.3 Recent related literature
  • 1.4 Organization
• 2 A two-country New Keynesian model
  • 2.1 Overview
  • 2.2 Environment
• 3 Instrument rules
  • 3.1 Simple Taylor-type rules
    • 3.1.1 The dynamic system
    • 3.1.2 Determinacy
    • 3.1.3 Learnability
    • 3.1.4 Quantitative effects
  • 3.2 Instrument rules with international variables
    • 3.2.1 Consumer versus producer price inflation
    • 3.2.2 The dynamic system
    • 3.2.3 Determinacy and learnability
  • 3.3 Two PPP instrument rules
• 4 Targetingrules
  • 4.1 Overview
  • 4.2 Non-cooperative discretionary policy
    • 4.2.1 The policy problem
    • 4.2.2 Two implementations
    • 4.2.3 Summary for discretionary non-cooperative policy
  • 4.3 Cooperative discretionary policy
    • 4.3.1 Overview
    • 4.3.2 The policy problem
    • 4.3.3 One implementation
    • 4.3.4 Summary for cooperative policy
• 5 Asymmetry in monetary policy
  • 5.1 An exchange rate peg
    • 5.1.1 Overview
    • 5.1.2 The policy problem
    • 5.1.3 The policy rule
    • 5.1.4 The dynamic system, determinacy, and learnability
• 6 Conclusion
• References
• European Central Bank Working Paper Series

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