Adaptive Learning and Monetary Policy in an Open Economy: Lessons from Japan

Adaptive Learning and Monetary Policy in an Open Economy:
Lessons from Japan *

Yu-chin Chen a and Pisut Kulthanavit b

First Draft: June 2006; June 2008





Abstract

Motivated by Japan's economic experiences and policy debates over the past two
decades, this paper uses an open economy dynamic stochastic general equilibrium model
to examine the volatility and welfare impact of alternative monetary policies. To capture
the dynamic effects of likely structural breaks in the Japanese economy, we model
agents’ expectation formation process with an adaptive learning framework, and compare
four Taylor-styled policy rules that reflect concerns commonly raised in Japan's actual
monetary policy debate. We first show that imperfect knowledge and the associated
learning process induce higher volatility in the economy, while retaining some of the
policy conclusions from rational-expectations setups. In particular, explicit exchange rate
stabilization is unwarranted, and under volatile foreign disturbances, policymakers should
consider targeting domestic price inflation rather than consumer price inflation.
However, contrary to results based on rational expectations, we show that even though
highly inflation-sensitive rules do raise output volatility, they may nevertheless improve
overall welfare in an adaptive learning setting by smoothing inflation fluctuations. Our
findings suggest that previous policy conclusions that are based on partial equilibrium
analyses, or that ignore likely deviations from rational expectations, may not be robust.

JEL classification: D84; E52; F41
Keywords: Adaptive learning; Monetary policy rules; Open economy

____________________________
* We thank, without implicating, Drew Creal, George Evans, Seppo Honkapohja, Ben McCallum,
Athanasios Orphanides, Richard Startz, George Waters, John Williams, Noah Williams, Wei-Choun Yu,
and seminar participants at the Federal Reserve Bank of San Francisco and University of Washington for
useful comments and suggestions. We also thank Arita Thatte for research assistance. Any remaining
errors are our own.
a Department of Economics, 206 Condon Hall, Box 353330, University of Washington, Seattle, WA
98195, U.S.A.; Tel: 1-206-543-6197; Fax: 1-206- 685-7477; E-mail: yuchin@u.washington.edu
b Department of Economics, Condon Hall, Box 353330, University of Washington, Seattle, WA
98195, U.S.A.; E-mail: pisutk@u.washington.edu

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1. Introduction

The Japanese economy and its dramatic turns during the last two decades have generated
fervent research interests, ranging from the liquidity traps, to the appropriate monetary
and fiscal responses, to the structural dynamics of the underlying economy.1 On the
empirical front, several papers point out that contrary to the experiences of other major
OECD economies since the 1980s, Japan did not undergo a “great moderation” in the
cyclical volatility of its economic activity; rather, it may have switched from a moderate
growth-low volatility regime to a low growth-high volatility regime.2 What can account
for these empirical patterns? Some researchers attribute the volatility to policy mistakes,
arguing in particular that more desirable economic performance could have been
achieved had the Bank of Japan (BOJ) adopted a looser inflation policy stance. Concerns
have also been raised as to whether it was prudent for the BOJ to engage in exchange rate
stabilization rather than focusing solely on output and inflation targeting.
Motivated by these discussions, this paper aims to conduct a systematic evaluation of
the volatility and welfare consequences of alternative monetary policy choices, using a
dynamic stochastic general equilibrium (DSGE) model with explicit micro-foundations
and welfare measures. While our goal is not to explicitly model the Japanese economy
and all of its intricacies, we introduce an additional element – adaptive learning – into our
standard open economy model. We argue that the stock market and real estate bubbles,
along with their subsequent bursts, represent important structural shifts in the Japanese
economy over this period, and under these unusual circumstances, the public’s
expectations of how the economy would evolve may not converge immediately to the
rational expectation outcome, as standard models assume.3 The expectation-formation
process may further interact with monetary policy actions to influence macroeconomic
dynamics, even alter the desirability of various policy options.4 In other words, standard

1 See, for example, Krugman et al. (1998), Kuttner and Posen (2001), McCallum (2003), and Svensson
(2003a).
2 Over the past two decades, Japan’s real GDP growth rates and its GDP per-capita growth both exhibit
higher volatility than is observed in other industrialized countries, as shown in Table 1.1, and for example,
Bernanke (2004), Stock and Watson (2005), Summers (2005), and Yu (2005).
3 For example, Orphanides and Williams (2007 a,b) discuss how a constant gain learning framework can
reflect public agents’ concern over potential structural shifts in the economy.
4 Here we are not referring to the excess volatility associated with the indeterminacy of equilibria as
discussed in Bernanke and Woodford (1997), Bullard and Mitra (2002), and others. We consider only

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policy conclusions from rational expectation models may not always be appropriate when
agents’ expectations are knocked out of equilibrium by exogenous events such as
structural breaks. To model such dynamics and study its implications, we assume
exogenous small deviations from rational expectations and employ the adaptive learning
framework developed by Evans and Honkapohja (hereafter EH, 2001).5 In this setup,
private agents are bounded rational and have only partial information: they know the
functional form but not the associated parameter values for the equations that govern the
dynamics of the economy. As such, they rely on past data and a recursive learning
algorithm – least squares or constant gain learning – to form their forecasts and make
consumption and production decisions.6 They update their beliefs regarding the unknown
parameters over time as new data become available.
Introducing explicit welfare evaluations and adaptive learning, this paper examines
the volatility and welfare impact of alternative monetary policy rules. Our aim is to see
whether the public's expectation-formation process, interacting with monetary policy
choices, can induce excess volatility in the benchmark economy and/or alter the preferred
policy action.7 To allow for explicit welfare calculations, we adopt a standard micro-
founded New Keynesian open economy model, as in Gali and Monacelli (hereafter GM,
2005), and study the dynamics of the economy under both rational expectations and
adaptive learning.8 To close the model, we envision the monetary authority to follow
variants of the “operational” Taylor interest rate rule (McCallum and Nelson 1999, 2004),
and adjust the short-term nominal interest rate linearly in response to deviations of the
observed data from their target levels.9 We consider four monetary policy rules that

learnable or expectationally stable equilibria in this paper, which means that economic agents can
coordinate to reach them.
5 We choose the adaptive learning setup for its relative ease of implementation as well as certain technical
advantages over alternative methods. For a detailed discussion, we refer interested readers to EH (2001).
6 Specifically, agents estimate the parameters in the reduced-form equilibrium laws of motions for the
economy. See Section 4 for more details.
7 We emphasize that deviations from rational expectation and the learning behavior are especially well-
justified when the economy is experiencing parameter instabilities or has undergone structural shifts.
8 We follow the previous literature, e.g., McCallum (2003) and McCallum and Nelson (2000), in applying a
small open economy model to analyze the Japanese monetary policy. In addition, we note that the goal of
this paper is not to provide a realistic model for the Japanese economy specifically; rather, our research
questions are motivated by the Japanese experience.
9 We assume the monetary authority can commit to a simple operational rule, and abstract away from
discretionary optimal monetary policy considerations. In addition, since the monetary rule is based on
observable data, our model does not assume any information asymmetry between the public and the central

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encapsulate the major points raised in the discussions concerning Japan's recent monetary
policy actions. The first rule, which we treat as a benchmark, is a Taylor rule with the
standard weights of 1.5 and 0.5 on lagged inflation and output gap deviations
respectively. The second policy rule, capturing “the tighter rule” commonly discussed, is
more aggressive on inflation control. The third rule captures exchange rate stabilization
motives and targets the terms of trade in addition. Lastly, motivated by parallel
discussions in the rational expectations-based monetary policy literature, we consider a
rule that targets domestic producer price (DPP) inflation instead of CPI inflation.10 For
each of these rules, we examine how the volatilities of output and inflation differ, and
then use a second-order approximation of the representative consumer’s utility function
to compute the welfare losses under rational expectations, least squares learning, and
constant gain learning.11
Our simulation results show that first of all, the learning process introduces excess
volatility in the economy, leading to significant increases in the variances of both output
and inflation from the rational expectation results. This finding suggests that the
volatility impact of structural shifts in an economy may be amplified by the uncertainty
and learning dynamics they generate, as agents can only revise expectation errors over
time. This offers another potential explanation for the aforementioned empirical patterns
observed in Japan. Second, even though tighter inflation control can lead to excess
output volatility as a trade-off, in a learning environment, it may dampen inflation
volatility significantly, thus improve overall welfare. This finding shows that it may not
be prudent to judge policy rules against the same optimal benchmark when agents’
expectations may be deviating from the rational expectations equilibrium, such as right
after major structural shifts. Lastly, we show that rules that depend on the terms of trade,
either explicitly or through a CPI target, generate substantially higher welfare loss than
rules that focus on DPP inflation. Especially when an economy is subject to persistent

bank. Note also that under operational rules, the central bank does not need to engage in any learning
behavior.
10 See Aoki (2001) and Woodford (2003), among others.
11 The expected welfare loss of a policy rule that deviates from the optimal first-best policy can be
approximated by a weighted sum of the variances of domestic producer price inflation and the domestic
output gap. See Woodford (2003), GM (2005), and Section 3.2 for further discussions.

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and volatile foreign shocks, stabilizing DPP inflation dominates CPI inflation targeting
under both rational expectations and adaptive learning.12
While our simple model is too stylized to capture the richness of Japan’s actual
economy, our findings, based on a structural general equilibrium model with a welfare-
theoretic loss function, support some of the views raised in the literature; namely, the
high output volatility observed may be the result of an overly restrictive monetary policy
and engagement in exchange rate stabilization. However, we note that despite raising
output volatility, tighter inflation control may nevertheless improve overall welfare when
agents have imperfect knowledge, and the optimal rule derived from rational expectation
models may no longer apply.
The rest of the paper is organized as follows. Section 2 reviews recent literature on
Japan’s monetary policy and motivates the policy rules we choose to evaluate. Section 3
presents the open economy general equilibrium model and specifies the four monetary
policy rules. Section 4 discusses the equilibrium concepts and solution methodology for
rational expectations and adaptive learning. Section 5 describes the calibration and
simulation procedures and presents our findings. Section 6 concludes.

2. Monetary Policy in Japan

The economic bubble Japan experienced in the 1980s and the economy’s ensuing
downturn have stimulated extensive research and discussions. While problems with the
banking sector, corporate structure, and excessive speculative behavior are all major
contributing factors, this paper draws specifically from two debates concerning the Bank
of Japan’s monetary policy stance during this period. The first questions whether the
BOJ should have adopted a lower interest rate, and the second asks whether exchange
rate stabilization was prudent.
A common criticism of BOJ’s policy is that it was overly restrictive, arguing that a
lower interest rate on several occasions, both pre- and post-collapse of the bubble, would

12 While previous studies based on rational expectations such as GM (2005) reach a similar conclusion
concerning domestic inflation targets, they do not consider adaptive learning interacting with policy rules
that are second best. We have already shown that policy conclusions based on rational expectations may
not always carry over to the learning framework. In fact, under learning, a domestic inflation target is not
always preferred, but depends on the relative sizes of foreign shocks versus domestic shocks (see Chen and
Kulthanavit 2008 for further details.)

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have brought about more favorable economic outcomes more quickly. This view is
commonly justified by comparing BOJ’s actual policy with some variants of the
benchmark Taylor rule that sets the interest rate response to CPI inflation gap (deviation
from its target) to be 1.5, and the response to the output gap to be 0.5, while assuming a 2
percent per annum real interest rate. Following this approach, Bernanke and Gertler
(1999), Jinushi et al. (2000), and McCallum (2000, 2003), for example, all conclude that
BOJ’s policy was too tight during some sub-periods over the 1980s-1990s.13 Figure 1
shows that compared to the operational, or lagged data-based, version of the benchmark
Taylor rule, BOJ’s actual rate was indeed high, especially between 1981 and 1989.14
During the aftermath of the bubble, many argue that the BOJ kept the interest rate
high for too long, failing to properly accommodate the structural shift. Jinushi et al.
(2000) and Ito and Mishkin (2004), for instance, argue that the BOJ should have adopted
the zero interest rate policy (ZIRP) much earlier than the official announcement in
February 1999.15 In March 2000, the BOJ temporarily abandoned the ZIRP and raised
the call rate for a year, drawing widespread criticism. Ito and Mishkin (2004), for
example, call this interest rate hike “a clear policy mistake.” Using a monetary-base rule
instead to analyze Japanese monetary policy-setting, McCallum (2003) reaches a similar
conclusion: BOJ’s policy had been too tight since the mid-1990s.16
A second debate in this literature concerns the merit of exchange rate stabilization.
Several studies point out that in practice, the BOJ often engaged in exchange rate
management, rather than focusing solely on output and inflation targeting. According to
McKinnon and Ohno (1997), for a decade since 1985, the BOJ systematically reacted to
the Yen/Dollar real exchange rate by adjusting the instrument rate to counter yen

13 We note that these papers don't always agree on the exact periods over which the policy was too tight.
Bernanke and Gertler (1999), for example, consider the policy to be too tight since 1992, but too lax over
1987-89. Generally, a tight or overly restrictive monetary policy refers to a case where the actual
instrument rate is above the target rate suggested by the benchmark Taylor rule.
14 We see that based on Japanese data, the mechanical benchmark Taylor rule may at times suggest an
interest rate below the zero lower bound. We do not address the practical and modeling difficulties
associated with hitting the zero lower bound in this paper. However, we consider alternative inflation
targets and find the qualitative conclusions to be the same.
15 Under ZIRP, the BOJ vowed to keep the call rate at zero until concern about deflation was dispelled.
16 One difficulty in using the Taylor rule to evaluate monetary policy is choosing the appropriate measure
of the output gap, which can affect the policy implications (see Ito and Mishkin 2004, Kuttner and Posen
2004). To avoid this problem, McCallum (2003) considers a monetary base rule that responds to deviations
of nominal GDP growth from its target and the average rate of base velocity growth over the past four
quarters.

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appreciation and promote yen depreciation. Similarly, Andrade and Divino (2005) and
Jinushi et al. (2000) maintain that the BOJ was implicitly targeting exchange rate
stability. Yu (2005) further attributes the high output volatility observed in Japan during
the period 1993-2001 to an interest rate policy aimed at stabilizing the yen/dollar real
exchange rate. On the other hand, advocates in favor of exchange rate management point
out that under zero nominal interest rate, the short-term nominal rate and monetary base
are ineffective as policy instruments. As such, purchasing unconventional assets such as
long-term government bonds, foreign currencies, or even real estate may represent the
only viable alternative.17 In particular, purchasing foreign exchange may help depreciate
the yen and stimulate aggregate demand via boosting net export. While this is surely a
“beggar-thy-neighbor” policy, McCallum (2003) counters that depreciating the yen
would eventually raise Japanese income and lead to higher net imports. McCallum thus
proposes an exchange-rate targeting rule that depreciates the yen/dollar real exchange
rate when either inflation or output falls below their target values.
Much of the above debate is either conceptual in nature or relies mainly on partial
equilibrium analyses in a rational expectation framework. Our paper aims to examine
these policy choices more systematically in a general equilibrium optimization
framework that allows for explicit quantifications of welfare as well as learning behavior.

3. The Open Economy Model and Monetary Policy Rules

We take as our baseline the open economy rational expectations model from GM (2005),
and discuss in Section 5 its calibration to the Japanese economy. The model is a small
open economy version of the Calvo (1983) sticky price model commonly used for closed
economy monetary policy analyses, where the equilibrium dynamics are described by a
new Keynesian Phillips curve and a forward-looking IS equation (see Clarida et al. 1999,
for example.) International asset markets are assumed to be complete, and purchasing
power parity holds. We close the dynamic system with alternative monetary policies, all
expressed as lagged data-based Taylor rules. As the focus of this paper is to study the
dynamics of this model in a learning framework, below we present a brief sketch of the

17 The BOJ followed this strategy and raised its monthly purchase of long-term bonds from 400 billion yen
to 1.2 trillion yen in several steps between August 2001 and October 2002.

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basic model setup and the associated reduced-form dynamic equilibrium equations. We
refer interested readers to GM (2005) for more detailed derivations and discussions.

3.1 The New Keynesian Open Economy Model

Following GM (2005), our world consists of a continuum of identical small open
economies uniformly distributed on the unit interval. As preferences, production
technology, and market structures are symmetric, below we present the optimization
problems facing the representative household and firm from the perspective of one of
these economies, indexed by H (Home). We treat the rest of the world as a foreign block,
with corresponding variables denoted by a subscript F.18

The Representative Household

The home economy is inhabited by a representative household which at time 0,
maximizes the following expected lifetime utility:
1 σ
−
1
∞
⎡ C
N ϕ
+ ⎤



t
t
t
E ∑ β
−

0
t=0
⎢1
⎣ σ 1 ϕ ⎥
−
+ ⎦
where Ct and Nt are overall consumption and labor supplied. β is the household’s
discount factor, σ is the coefficient of relative risk aversion, and ϕ is the inverse of labor
supply elasticity. Consumption index Ct is a CES composite of domestic and foreign
goods (imports), defined by:
η η−



C
⎡(1
η C
η− η
η
α
α
C
η− η ⎤
≡
−
+

t
)1 ( H t )
1
,
( F,t )
(
1)
(
1)
(
1)
⎣
⎦
where η > 0 measures the elasticity of substitution between domestic and foreign
consumption baskets CH,t and CF,t. Each of these baskets is in turn a CES aggregate of a
continuum of differentiated goods, with elasticities of substitution between varieties
given by ε > 1 and γ > 1 for the home and foreign indices respectively.19 α œ [0, 1] is

18 See GM (2005) for a more detailed discussion of this world setup and the exact modeling of the foreign
block.
19 To be more precise, γ is the substitutability between good baskets produced in different foreign countries.
Each of these baskets, identical to the Home setup, is a CES aggregate of a variety of differentiated goods
with an elasticity of substitution equal to ε. See GM (2005).

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the (exogenous) share of the domestic consumption allocated to imported goods; it can be
interpreted as a measure of trade openness.
The consumer faces the following sequence of period-by-period budget constraints:
P C
P C
E Q
D
D W N
T "t
H t
H t +
F t
F t +
t ⎡
t t
t
⎤ ≤ t + t t +
,
,
,
,
, 1
⎣ +
1
+ ⎦
t
where PH,t and PF,t are the CES aggregated price indices of domestically-produced and
imported goods respectively. Q
denotes the stochastic discount factor for one-period
t,t 1
+
ahead nominal payoffs, and D is the nominal payoff in period t + 1 of the household’s
t 1
+
portfolio at the end of period t. W is the nominal wage, and T is lump-sum
t
t
transfers/taxes. We assume complete asset markets.
The consumer price index (CPI) at Home is given by:
η
−
P
(1
P
η
−
P
η
α
α
−
⎡
⎤
≡
−
+

t
)( H t )
( F t ) 1(1 )
1
1
,
,
⎣
⎦
and CPI inflation, πt, is then πt = pt – pt-1 where pt = log(Pt).


Domestic Producers

On the production side, we assume a continuum of monopolistically competing firms
each using a linear production technology which depends on the economy-wide
stochastic labor productivity At:
Yt ( j ) = At Nt ( j )
where Y ( j ) and N ( j )are the output and employment of firm j respectively.
Firms set prices in a staggered fashion à la Calvo (1983). Parameter θ denotes the
fraction of firms that faces nominal rigidity each period, so at any time t, a fraction 1 -θ
of randomly selected firms gets to set new prices optimally to maximize expected
discounted profits. A typical firm j sets its new price P in period t to maximize the
H ,t
following:
∞
E
θ Q
Y
j P
MC

t ∑
k {
⎡
( )
t t k
t k
H t −
n
⎤
, +
+
⎣
( ,
0
t+
=
k
k
) }⎦
subject to the period-by-period demand constraint:
−
⎛
ε
PH t ⎞
,
Y ( j)
C
j
C
j
t k
≤ ⎜
⎟
H t k
+
+
⎜ P
⎟ (
( )
( )
, +
F ,t+k
)
H ,
⎝
t +k ⎠

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where
n
MC is nominal marginal cost the firm faces, and C
t
H,t(j) and CF,t(j) the total
consumption of good j from home and abroad.20 As is well known in the literature, this
optimal price will involve a forward-looking term in addition to the standard
monopolistic mark-up over contemporaneous marginal cost, reflecting the firm’s concern
over the future dynamics of marginal costs up to the next price-changing opportunity.
Using lower case letters to denote the logs of the respective variables, we obtain the
following log-linear approximation for the optimal price:21
ε
p
= log(P ) = log(
) + (1− βθ ) ∞ (
∑ βθ)k E mc + p .
H ,t
H ,t
t
=
{ t+k H,
0
t
k
}
ε −1

Equilibrium

Goods-market clearing, together with log-linear approximations of the equilibrium
aggregate demand equations around the appropriate steady states, imply a forward-
looking dynamic IS equation in the domestic output gap and inflation:
1
x = E x −
r − E
−

(1).
+
π
rr
t
t t 1
( t t H,t 1+ t)
σα
The output gap variable, xt , is defined as the deviation of log domestic output from its
equilibrium level in the absence of any nominal rigidities (the flexible-price level).
Parameter sα is a function of the degree of openness and the substitutability between
domestic and foreign goods; it captures the sensitivity of home output to terms-of-trade
fluctuations.22 The home interest rate, rt, is the monetary policy instrument set by the
Central Bank. π
= p − p
is domestic producer price (DPP) inflation, with p
H ,t
H ,t
H ,t 1
−
H ,t
being the (log) domestic price index. The last term, rr , is the domestic natural interest
t
rate and one of the three stochastic driving variables in our dynamic system. It depends

20 Since all firms are symmetric, they use the same optimal price-setting rule. We can thus drop the firm-
specific index j.
21 The log-linear approximation is taken around the zero-inflation, balanced-trade steady state.
22 Expressed in terms of the structural parameters defined earlier,
σ ≡ σ /[1−α +ασγ + (1−α )(ση −
.
α
)
1 ]

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