Description
Questionnaire surveys made at currency markets around the world reveal that currency
trade to a large extent not only is determined by an economy’s performance or expected performance.
Indeed, a fraction is guided by technical trading, which means that past exchange rates are assumed to
provide information about future exchange rate movements. The purpose of this paper is to ask how a
successful monetary policy should be designed when technical trading in the form of trend following is
used in currency trading.
Journal of Financial Economic Policy
Optimal monetary policy under heterogeneity in currency trade
Mikael Bask
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To cite this document:
Mikael Bask, (2009),"Optimal monetary policy under heterogeneity in currency trade", J ournal of Financial
Economic Policy, Vol. 1 Iss 4 pp. 338 - 354
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Optimal monetary policy under
heterogeneity in currency trade
Mikael Bask
School of Business and Economics, A
?
bo Akademi University,
Turku, Finland
Abstract
Purpose – Questionnaire surveys made at currency markets around the world reveal that currency
trade to a large extent not only is determined by an economy’s performance or expected performance.
Indeed, a fraction is guided by technical trading, which means that past exchange rates are assumed to
provide information about future exchange rate movements. The purpose of this paper is to ask how a
successful monetary policy should be designed when technical trading in the form of trend following is
used in currency trading.
Design/methodology/approach – The paper embeds an optimal policy rule into Gal? ´ and
Monacelli’s dynamic stochastic general equilibrium (DSGE) model for a small open economy, which is
augmented with trend following in currency trading, to examine the prerequisites for a successful
monetary policy. Speci?cally, the conditions for a determinate rational expectations equilibrium (REE)
that also is stable under least squares learning are in focus. The paper also computes impulse-response
functions for key variables to study how the economy returns to steady state after being hit by a shock.
Findings – The paper ?nds that a determinate REE that also is stable under least squares learning
often is the outcome when there is a limited amount of trend following in currency trading, but that a
more ?exible in?ation rate targeting in monetary policy sometimes cause an indeterminate REE in the
economy. Thus, strict, or almost strict, in?ation rate targeting in monetary policy is recommended also
when there is technical trading in currency trading and not only when all currency trading is guided by
fundamental analysis (in the form of rational expectations). This result is a new result in the literature.
Originality/value – There are already models in the literature on monetary policy design that
incorporate technical trading in currency trading into an otherwise standard DSGE model. There is
also a huge amount of DSGE models in the literature in which monetary policy is optimal. However,
the model in this paper is the ?rst model, to the best of the author’s knowledge, where technical trading
in currency trading and optimal monetary policy are combined in the same DSGE model.
Keywords Determinacy, DSGE model, Least squares learning, Targeting rule, Technical trading
Paper type Research paper
1. Introduction
Interest rate rule
Taylor (1993) has demonstrated that Federal Reserve’s policy, during late 1980s and
early 1990s, could be described by an interest rate rule on the following form:
r
t
¼ 0:04 þ 1:5ðp
t
20:02Þ þ 0:5ð y
t
2 yÞ; ð1Þ
The current issue and full text archive of this journal is available at
www.emeraldinsight.com/1757-6385.htm
JEL classi?cation – E52, F31, F41
This paper has bene?tted from presentations at various conferences and seminars as well as
from comments and suggestions by two anonymous referees. The usual disclaimer applies.
The MATLAB routines that have been used in the preparation of this paper are available on
request from the author. When impulse-response functions were computed, MATLAB routines
developed by Michael Woodford were utilized that are available at: www.columbia.edu/,mw2230/
Tools/
JFEP
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Journal of Financial Economic Policy
Vol. 1 No. 4, 2009
pp. 338-354
qEmerald Group Publishing Limited
1757-6385
DOI 10.1108/17576380911050061
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where r
t
is Federal Reserve’s operating target for the funds rate, p
t
is the in?ation rate
according to the gross domestic product (GDP) de?ator, y
t
is the logarithm of real GDP,
and y is the logarithm of potential real GDP. In particular, the rule in equation (1)
prescribes setting the funds rate in response to the in?ation rate and the output gap,
where the latter variable is the difference between the two measures of GDP.
Instrument or targeting rule?
Svensson(2002, 2003) argues that aninstrument rule, suchas the Taylor rule inequation(1),
is inferior to a targeting rule in monetary policy since the instrument rule is not consistent
with optimizing behavior on the part of the central bank. Speci?cally, the targeting rule is
derived from the optimization of an objective function (or the minimization of a
loss-function). For this reason, when embedding an interest rate rule into a dynamic
stochastic general equilibrium (DSGE) model, Svensson (2002, 2003) argues that all agents
in the model should behave optimally; households should maximize utility, ?rms should
maximize pro?t, and the central bank should maximize welfare[1].
Let us use Svensson’s (2003, p. 429) own words to make the point clear:
Monetary policy by the world’s more advanced central banks these days is at least as
optimizing and forward-looking as the behavior of the most rational private agents. I ?nd it
strange that a large part of the literature on monetary policy still prefers to represent central
bank behavior with the help of mechanical instrument rules.
Hence, we focus on targeting rules or optimal policy rules in this paper.
A determinate and learnable rational expectations equilibrium?
Typically, in the literature, conditions for determinacy of the rational expectations
equilibrium (REE) are examined since the central bank would like to avoid coordination
problems in the economy. For instance, without imposing additional restrictions into a
rational expectations model, it may not be known in advance which REEthat agents will
coordinate on, if there will be any coordination at all. To give an example, the effects of
monetary policy may not be known beforehand: is it the case that agents will coordinate
on a REEthat has undesirable properties, like a high-in?ation rate, or on a REEin which
the price level is stable?
Another problemis the computation of time-paths of economic variables whenagents
are assumed to have rational expectations since it is not self-evident that they have
perfect knowledge of the economy’s law of motion. For example, it is a well-known fact
that the transmission mechanism for monetary policy has a complicated structure and
this also means that there are disagreements about the exact nature of the mechanism.
We therefore ask the following question in this paper: can agents eventually learn the
REE, if they can make use of data generated by the economy itself to improve their
knowledge of its law of motion? The concept of learning that we make use of is least
squares learning[2].
Heterogeneity in currency trade
Questionnaire surveys made at currency markets around the world reveal that
currency trade to a large extent not only is determined by an economy’s performance or
expected performance. Indeed, a fraction is guided by technical trading, which means
that past exchange rates are assumed to provide information about future exchange
Optimal
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rate movements. A simple example of technical trading that we make use of in this
paper is trend following.
See Oberlechner (2004) for an in-depth discussion of two large questionnaire
surveys conducted at the European and the North American markets, Gehrig and
Menkhoff (2006) for a survey on trading behavior that includes references to several
other surveys made at currency markets (Cheung and Chinn, 2001; Lui and Mole, 1998;
Menkhoff, 1997; Oberlechner, 2001; Taylor and Allen, 1992) and Neely (1997) for a
layman’s guide on technical trading. Other terms for technical trading are chartism and
technical analysis[3].
Aim of the paper
We embed an optimal policy rule into Gal? ´ and Monacelli’s (2005) DSGE model for a
small open economy, which is augmented with trend following in currency trading, to
examine the prerequisites for a successful monetary policy. Speci?cally, the conditions
for a determinate REE that also is stable under least squares learning are in focus. We
also compute impulse-response functions for key variables to study how the economy
returns to steady state after being hit by a shock. The reason why an otherwise
standard DSGE model is used in the analysis is to facilitate for the reader in what way
the inclusion of trend following in currency trading may change the ?ndings compared
with those in a standard DSGE model.
Relation to the literature
Since anoptimal policyrule inthe formof anexpectations-basedrule is derivedherein, this
paper relates to Evans and Honkapohja (2003a, b, c, 2006) who examine the desirability of
an expectations-based rule in a DSGE model for a closed economy from a learning
perspective. Two other papers that alsofocus onthe learnabilityof a determinate REE, but
for an open economy, are Bullard and Schaling (2009) and Llosa and Tuesta (2008). The
former paper examines optimal policy in a two-country model, whereas the latter paper
examines instrument rules in the same DSGE model as in this paper. However, none of
these papers incorporate technical trading in currency trading into the model.
Papers that incorporate technical trading in currency trading into a DSGE model
include Bask (2007b, 2009b) and Bask and Selander (2009). However, the interest rate
rule is not an optimal policy rule in these papers. Instead, an instrument rule is used by
the central bank. Thus, the originality in the present paper is, to the best of our
knowledge, that monetary policy is optimal in a DSGE model that has been augmented
with technical trading in currency trading. Be aware that the fractions of fundamental
and technical analyses in currency trading are exogenous in this paper as also is the case
in Bask (2009b) and Bask and Selander (2009). Thus, making the fractions endogenous
as in Bask (2007b), but assuming that monetary policy is optimal, is saved for future
research.
Outline of the paper
The DSGE model we examine is outlined in Section 2. Thereafter, in Section 3, we
derive the optimal policy rule for the central bank, whereas the conditions for a
determinate REE that also is stable under least squares learning are in focus in Section
4. Impulse-response functions for key variables are computed in Section 5 and the
paper is concluded in Section 6 with a discussion.
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2. DSGE model
A DSGE model with imperfect competition and nominal rigidities is presented in
Gal? ´ and Monacelli (2005) for a small open economy. Speci?cally, their model consists
of an IS curve[4]:
x
t
¼ x
e
tþ1
2a r
t
2
1
1 2d
· p
e
tþ1
2d De
e;m
tþ1
þp
e;
*
tþ1
_ _ _ _
2rr
t
_ _
; ð2Þ
an AS curve:
p
t
¼ bp
e
tþ1
þgð1 2dÞx
t
þd De
t
2bDe
e;m
tþ1
þp
*
t
2bp
e;
*
tþ1
_ _
; ð3Þ
and a condition for uncovered interest rate parity:
r
t
2r
*
t
¼ De
e;m
tþ1
; ð4Þ
where x
t
is the output gap, r
t
is the nominal interest rate, p
t
is the consumer price index
(CPI) in?ation rate, e
t
is the nominal exchange rate, and rr
t
is the natural rate of
interest. The superscripts “e” and “e,m” denote expectations and market expectations
in currency trade, respectively, and an asterisk in the superscript denotes a foreign
quantity.
b [ [0,1] is the discount factor that is used when the representative household in the
home country maximizes a discounted sum of instantaneous utilities derived from
consumption and leisure. d [ [0,1] is the share of consumption in the home country
allocated to imported goods, which means that d is an index of openness of the
economy. Finally, a and g are functions of parameters in the Gal? ´ and Monacelli (2005)
model[5].
There are two types of behavior in currency trading:
(1) trend following; and
(2) trading that is based on fundamental analysis.
When trend following is used, it is believed that the exchange rate will increase
(decrease) between time periods t and t þ 1, if it increased (decreased) between time
periods t 2 1 and t[6], [7]. When fundamental analysis is used, agents have rational
expectations regarding the next time period’s exchange rate change (if they have been
able to learn the economy’s law of motion), which means that market expectations can
be summarized as follows:
De
e;m
tþ1
¼ vDe
e;c
tþ1
þ ð1 2vÞDe
e;f
tþ1
¼ vDe
t
þ ð1 2vÞDe
e
tþ1
; ð5Þ
where v [ [0,1] is the degree of trend following in currency trading. “e,c” and “e,f”
denote expectations according to chartism and fundamental analysis, respectively.
Since the behavior of currency traders is central in the model, a few words should be
mentioned regarding the existence of a direct exchange rate channel in the AS curve in
equation (3). Speci?cally, the size of the channel is d(1 2 bv), which means that the
channel increases in size with the openness of the economy and decreases in size with
the discount factor as well as the degree of trend following in currency trading[8].
Moreover, when chartism is used more extensively in currency trade, the current
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exchange rate change not only has a smaller effect on the in?ation rate (i.e. the
exchange rate channel has a smaller size), but also the expected exchange rate change
has a larger effect on the same variable[9].
3. Optimal monetary policy
The model is closed by deriving an interest rate rule for the central bank that
minimizes the following objective function:
L
t
¼ zx
2
t
þp
2
t
; ð6Þ
given the economy’s law of motion in equations (2)-(5). Thus, we assume that there is no
commitment mechanism available for the central bank, which means that the optimal
policy rule is derived under discretion in monetary policy. Then, the optimization
problem for the central bank is:
min
x
t
;p
t
L
t
¼ min
x
t
;p
t
zx
2
t
þp
2
t
; ð7Þ
subject to[10]:
p
t
¼ 2
ð1 2bvÞd
av
2g
_ _
ð1 2dÞx
t
; ð8Þ
which has the ?rst-order condition:
x
t
¼
ð1 2bvÞd
av
2g
_ _
·
1 2d
z
· p
t
¼ Ap
t
: ð9Þ
Be aware that the central bank controls the exchange rate change when optimizing
the objective function in equation (6), even though this variable does not appear
explicitly in the optimization problem in equations (7) and (8). The objective function
in equation (6) is often referred to as ?exible in?ation rate targeting, where z ¼ 0 is
strict targeting, and the condition in equation (9) is often referred to as a speci?c
targeting rule.
After combining the economy’s law of motion in equations (2)-(4) with the speci?c
targeting rule in equation (9), but without imposing the condition that agents have
rational expectations, we have the following optimal policy rule[11]:
r
t
¼ const: þk
x
x
e
tþ1
þk
p
p
e
tþ1
þk
De
De
t
; ð10Þ
where[12]:
k
x
¼
Agð1 2dÞ
2
21 þd
Að1 2dÞðag þbdÞ 2a
k
p
¼
Að1 2dÞðag þbÞ 2a
Að1 2dÞðag þbdÞ 2a
k
De
¼
Að1 2dÞd
Að1 2dÞðag þbdÞ 2a
_
¸
¸
¸
¸
¸
¸
¸
¸
¸
_
¸
¸
¸
¸
¸
¸
¸
¸
¸
_
ð11Þ
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This rule is an expectations-based rule since agents do not have rational expectations
in the derivation of it (Evans and Honkapohja, 2003b). Note that the interest rate set by
the central bank depends on the current exchange rate change and not the expected
exchange rate change. This result follows from substituting the ?rst-order condition
for optimal policy in equation (9) into the economy’s law of motion in equations (2)-(4).
4. A determinate REE that is stable under least squares learning
Let us examine under what conditions our economy is characterized by a determinate
REE that also is stable under least squares learning. Recall that if there is a
determinate REE in the economy, we also know that it is E-stable since the dating of
expectations is time-t (McCallum, 2007). Hence, since an E-stable REE is a necessary
and a suf?cient condition for a least squares learnable REE, all determinacy regions in
parameter space that are found below are also regions for a determinate REE that is
stable under least squares learning (Marcet and Sargent, 1989).
The complete model, or economy, in matrix form is[13]:
G· y
t
¼ Q· y
e
tþ1
þLþJ· rr
t
; ð12Þ
where:
G ¼
1 0
adv
12d
a
2gð1 2dÞ 1 2dð1 2bvÞ 0
0 0 2v 1
0 0 2k
De
1
_
¸
¸
¸
¸
¸
_
_
¸
¸
¸
¸
¸
_
; ð13Þ
Q ¼
1
a
12d
2
adð12vÞ
12d
0
0 b 2bdð1 2vÞ 0
0 0 1 2v 0
k
x
k
p
0 0
_
¸
¸
¸
¸
¸
_
_
¸
¸
¸
¸
¸
_
; ð14Þ
and:
y
t
¼ ½x
t
; p
t
; De
t
; r
t
?
0
: ð15Þ
The exact form of the matrices L and J does not matter when examining whether the
economy has a determinate REE. Then, since there is one variable that is predetermined,
r
t
, exactly one eigenvalue of the matrix G
21
· Qmust be outside the unit circle to have a
determinate REE[14]. However, if more than one eigenvalue are outside the unit circle,
we have an indeterminate REE, and if all eigenvalues are inside the unit circle, there is no
stable REE in the economy (Blanchard and Kahn, 1980).
Deriving analytical conditions for determinacy is not meaningful since these
expressions would be too large and cumbersome to interpret. Consequently, we adopt
the same strategy as in other papers within this area of research and illustrate our
?ndings for determinacy using calibrated values of the structural parameters.
Speci?cally, we use two sets of parameter calibrations in the numerical analysis, where
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the ?rst calibration (often used in the literature) comes from Woodford (1999) and is
based on US data:
a ¼
1
0:157
; b ¼ 0:99; g ¼ 0:024:
_
ð16Þ
The second calibration comes from Clarida et al. (2000) and is also based on US data[15]:
{a ¼ 1; b ¼ 0:99; g ¼ 0:3: ð17Þ
Clearly, even though the time periods in Clarida et al. (2000) and Woodford (1999)
calibrations are somewhat different, there are still large differences in the magnitudes of
the parameters aand g. We will not discuss possible reasons for these differences herein.
We will instead utilize the fact that the parameter calibrations are very different to check
the robustness of our ?ndings[16]. Finally, the degree of openness of the economy is
d ¼ 0.4, which is the same value as in Gal? ´ and Monacelli (2005).
See Figure 1 for regions in the (v,z)-space that are associated with a determinate REE,
an indeterminate REE and no stable REE when the Woodford (1999) calibration is used.
Not surprisingly, when the degree of trend following in currency trading is large,
there is no stable REE in the economy and this is because there is no mechanism in
technical trading that forces the economy to equilibrium. Moreover, when the amount
Figure 1.
Regions in parameter
space that are associated
with a determinate REE,
an indeterminate REE and
no stable REE
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Degree of trend following in currency trade
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i
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a
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a
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t
a
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g
e
t
i
n
g
Region for a determinate REE that is stable under learning (see light area) and
regions for an indeterminate REE (see dark area) and no stable REE (see white area)
Source: The Woodford (1999) calibration is used
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of trend following in currency trading is more limited, there is either a determinate
REE or an indeterminate REE in the economy. However, when in?ation rate targeting
is strict, or almost strict, there is a determinate REE in the economy. This is an
interesting result since almost strict in?ation rate targeting most likely is optimal in
monetary policy[17].
Finally, when there is no trend following in currency trading, there is a determinate
REE in the economy that also is stable under least squares learning. This result is not
either surprising since Evans and Honkapohja (2003b) show that a DSGE model for a
closed economy has this property when the central bank is using an expectations-based
rule in its policy[18]. The same result also holds when the Clarida et al. (2000) calibration
is used in the numerical analysis.
In Figure 2, we show the same regions in the (v,z)-space as in Figure 1, but the
Clarida et al. (2000) calibration is now used.
As before, when the degree of trend following in currency trading is large, there
is no stable REE in the economy, but the difference is now that this region in
the (v,z)-space is somewhat smaller. Moreover, a qualitative difference between
Figures 1 and 2 is that there is always a determinate REE when the economy is stable
and when the Clarida et al. (2000) calibration is used. This means that monetary policy
is never associated with the indeterminacy problem in this case.
Figure 2.
Regions in parameter
space that are associated
with a determinate REE,
an indeterminate REE and
no stable REE
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Degree of trend following in currency trade
F
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Region for a determinate REE that is stable under learning (see light area) and
region when there is no stable REE (see white area)
Source: The Clarida et al. (2000) calibration is used
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5. Impulse-response functions
Having established under what conditions the economy is characterized by a determinate
REE, we shift focus to the computation of impulse-response functions for key variables.
For this sake, we assume that the shock (impulse) is channeled through the natural rate of
interest. Speci?cally, in time period t ¼ 1, a shock is hitting the economy such that
Drr
1
¼ 1[19]. Thereafter, if there is a determinate REE in the economy (as is the case
throughout this section), it will return to steady state and depending on the parameter
setting, the convergence is fast or slow as well as oscillating or non-oscillating.
In Figures 3-5, impulse-response functions for the output gap, the CPI in?ation rate,
the nominal exchange rate change and the nominal interest rate are shown, where the
Woodford (1999) calibration is used.
In Figure 3, there is a small amount of trend following in currency trading (v ¼ 0.1)
and in?ation rate targeting is almost strict (z ¼ 0.05) with the effect that the economy’s
adjustment path to steady state is fast and non-oscillating. In Figure 4, when a larger
amount of trend following is used in currency trading (v ¼ 0.35; z ¼ 0.05), the
adjustment path is still non-oscillating, but the return of the economy to steady state is
very slow. In Figure 5, when in?ation rate targeting is more ?exible (z ¼ 0.5; v ¼ 0.35),
the economy’s adjustment path to steady state is again faster but now oscillating.
That the return of the economy to steady state is very slow in Figure 4 is because
the mechanism that forces the economy to equilibrium has been weakened by trend
following, or trend extrapolation, in currency trading[20]. Further on, the shock’s effect
Figure 3.
Impulse-response
functions when a smaller
amount of trend following
is used in currency trading
and in?ation rate
targeting is almost strict
0 10 20 30 40 50 0 10 20 30 40 50
0 10 20 30 40 50 0 10 20 30 40 50
–1.5
–1
–0.5
0
0.5
1
1.5
2
2.5
3
3.5
Output gap
–0.2
–0.1
0
0.1
0.2
0.3
0.4
0.5
CPI inflation rate
–0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Nominal exchange rate change
–0.16
–0.14
–0.12
–0.1
–0.08
–0.06
–0.04
–0.02
0
Nominal interest rate
Source: The Woodford (1999) calibration is used
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on the in?ation rate is, of course, larger when in?ation rate targeting is more ?exible as
in Figure 5. At the same time, this also means that the shock’s effect on the output gap
is smaller since relatively more weight is placed by monetary policy on the output
gap’s deviation from its target, which is no output gap.
The parameterizations of the interest rate rule are not very different in the three
cases: r
t
¼ const: þ0:129x
e
tþ1
þ0:452p
e
tþ1
20:369De
t
, r
t
¼ const: þ0:098x
e
tþ1
þ0:934
p
e
tþ1
20:045 De
t
, and r
t
¼ const: þ0:095x
e
tþ1
þ0:994p
e
tþ1
20:004De
t
, respectively[21].
Note that the Taylor principle is not satis?ed in any of the rules (i.e. k
p
ò 1). Still, the
economy returns to steady state in each case after being hit a shock.
Impulse-response functions for the output gap, the CPI in?ation rate, the nominal
exchange rate change and the nominal interest rate are shown in Figures 6-8, where the
Clarida et al. (2000) calibration is used.
Roughly speaking, the assumptions behind Figures 3 and 6, Figures 4 and 7, and
Figures 5 and 8 are the same, even though a somewhat larger amount of trend
following in currency trading is allowed for in Figures 7 and 8 (v ¼ 0.5). As before, the
return of the economy to steady state is very slow in one case (Figure 8), even though it
does not correspond to the case when the Woodford (1999) calibration was used
(Figure 4), but it is never oscillating in the cases examined. Also, the shock’s effect on
the output gap is smaller and its effect on the in?ation rate is somewhat larger when
in?ation rate targeting is more ?exible (Figure 8).
Figure 4.
Impulse-response
functions when a larger
amount of trend following
is used in currency trading
and in?ation rate
targeting is almost strict
0 100 200 300 400 500
–0.7
–0.6
–0.5
–0.4
–0.3
–0.2
–0.1
0
0 100 200 300 400 500
0 100 200 300 400 500 0 100 200 300 400 500
–0.7
–0.6
–0.5
–0.4
–0.3
–0.2
–0.1
0
Output gap CPI inflation rate
–0.6
–0.4
–0.2
0
0.2
0.4
0.6
0.8
1
1.2
Nominal exchange rate change
–0.7
–0.6
–0.5
–0.4
–0.3
–0.2
–0.1
0
Nominal interest rate
Source: The Woodford (1999) calibration is used
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The parameterizations of the interest rate rule are now r
t
¼ const: þ0:237x
e
tþ1
þ1:908p
e
tþ1
20:612De
t
, r
t
¼ const: þ0:972x
e
tþ1
þ1:071p
e
tþ1
20:626De
t
, and r
t
¼ const:
þ0:619x
e
tþ1
þ0:953p
e
tþ1
20:032De
t
, respectively. Note that the Taylor principle is
satis?ed in the ?rst rule (i.e. k
p
. 1), which corresponds to the case in which the
economy’s adjustment path to steady state is the fastest of the six cases examined.
6. Discussion
We have embedded an expectations-based optimal policy rule into Gal? ´ and Monacelli’s
(2005) DSGE model for a small open economy, which has been augmented with trend
following in currency trading, to examine the prerequisites for a successful monetary
policy.
We found that a determinate REE that also is stable under least squares learning
often is the outcome when there is a limited amount of trend following in currency
trading, but that a more ?exible in?ation rate targeting in monetary policy sometimes
cause an indeterminate REEinthe economy. Thus, whenin?ation rate targeting is strict,
or almost strict, there is a determinate REEin the economy that also is stable under least
squares learning. This means that the effects of monetary policy are predictable, which
is not the case when the economy suffers from the indeterminacy problem.
Thus, strict, or almost strict, in?ation rate targeting in monetary policy is
recommended also when there is technical trading in currency trading and not only
Figure 5.
Impulse-response
functions when a larger
amount of trend following
is used in currency trading
and in?ation rate
targeting is more ?exible
0 20 40 60 80 100 0 20 40 60 80 100
0 20 40 60 80 100 0 20 40 60 80 100
–0.1
–0.05
0
0.05
0.1
0.15
Output gap
–0.6
–0.4
–0.2
0
0.2
0.4
0.6
0.8
1
1.2
CPI inflation rate
–3
–2
–1
0
1
2
3
4
5
Nominal exchange rate change
–0.8
–0.6
–0.4
–0.2
0
0.2
0.4
0.6
Nominal interest rate
Source: The Woodford (1999) calibration is used
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when all currency trading is guided by fundamental analysis (in the form of rational
expectations). In other words, strict, or almost strict, in?ation rate targeting in
monetary policy is a robust policy against technical trading in currency trading and
this result is a new result in the literature on monetary policy design.
We also computed impulse-response functions for key variables to study how the
economy returns to steady state after being hit by a shock. One ?nding that stands out
is that the shock’s effect on the output gap is smaller and its effect on the in?ation rate
is larger when in?ation rate targeting is more ?exible. Moreover, depending on the
parameter setting used in the numerical analysis, the convergence to steady state is
fast or slow as well as oscillating or non-oscillating.
Making the fractions of the two types of behavior in currency trading endogenous
would, of course, be an interesting complement to this paper. A setup similar to the one
in Brock and Hommes (1997) could be used for this aim:
.
fundamental analysis in currency trading is costly to use; and
.
most traders use the trading strategy that has been more successful in the past to
predict exchange rate movements.
In Bask (2007b), this setup is used in a DSGE model in which the central bank is using
an instrument rule in its policy with the result that chaotic dynamics and long swings
may be present in the exchange rate.
Figure 6.
Impulse-response
functions when a smaller
amount of trend following
is used in currency trading
and in?ation rate
targeting is almost strict
0 5 10 15 20 25
0 5 10 15 20 25
–0.2
0
0.2
0.4
0.6
0.8
1
1.2
Output gap
0 5 10 15 20 25
–0.005
0
0.005
0.01
0.015
0.02
0.025
CPI inflation rate
–0.4
–0.35
–0.3
–0.25
–0.2
–0.15
–0.1
–0.05
0
0.05
Nominal exchange rate change
0 5 10 15 20 25
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0.02
Nominal interest rate
Source: The Clarida et al. (2000) calibration is used
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Impulse-response
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amount of trend following
is used in currency trading
and in?ation rate
targeting is almost strict
0 5 10 15 20 25
0 5 10 15 20 25
0 5 10 15 20 25
0 5 10 15 20 25
–0.8
–0.7
–0.6
–0.5
–0.4
–0.3
–0.2
–0.1
0
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–0.7
–0.6
–0.5
–0.4
–0.3
–0.2
–0.1
0
CPI inflation rate
–0.4
–0.3
–0.2
–0.1
0
0.1
0.2
0.3
0.4
Nominal exchange rate change
–0.35
–0.3
–0.25
–0.2
–0.15
–0.1
–0.05
0
Nominal interest rate
Source: The Clarida et al. (2000) calibration is used
Figure 8.
Impulse-response
functions when a larger
amount of trend following
is used in currency trading
and in?ation rate
targeting is more ?exible
0 50 100 150 200 250
0 50 100 150 200 250
0 50 100 150 200 250
0 50 100 150 200 250
–0.08
–0.07
–0.06
–0.05
–0.04
–0.03
–0.02
–0.01
0
Output gap
–0.7
–0.6
–0.5
–0.4
–0.3
–0.2
–0.1
0
CPI inflation rate
–0.8
–0.6
–0.4
–0.2
0
0.2
0.4
0.6
Nominal exchange rate change
–0.7
–0.6
–0.5
–0.4
–0.3
–0.2
–0.1
0
Nominal interest rate
Source: The Clarida et al. (2000) calibration is used
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Notes
1. See Clarida et al. (1999) for an early review of interest rate rules in DSGE models. Woodford’s
(2003) seminal work on rules in monetary policy should also be part of the reading list.
2. See Evans and Honkapohja (2001, 2009) for an introduction to this literature and Bullard
(2006) for a review of interest rate rules in DSGE models from a learning perspective.
3. See Hommes (2006) for a survey of the literature on heterogeneous agent models in
economics and ?nance, and De Grauwe and Grimaldi (2006) for an introduction to exchange
rate determination in a behavioral ?nance framework.
4. See Bask and Selander (2009) for the derivation of equations (2) and (3) using equations in
Gal? ´ and Monacelli (2005).
5. a depends on the openness index, d, the intertemporal elasticity of substitution in
consumption, the elasticity of substitution between domestic and foreign goods in
consumption, and the elasticity of substitution between foreign goods in consumption.
g depends on a, the discount factor, b, the intertemporal elasticity of substitution in labor
supply and the share of ?rms that set new prices in each time period (Calvo, 1983). See Bask
(2009b) for the exact relationships.
6. To minimize the number of structural parameters in the model, the two consecutive
increases (decreases) in the exchange rate are of the same size.
7. A more sophisticated technical trading rule, like the moving averages (MA) technique, would
also be desirable to examine in the Gal? ´ and Monacelli (2005) model. However, this would
complicate the analysis of the resulting DSGE model considerably and it is not even certain
that the dynamics is affected that much compared to when simple trend following is used in
currency trading. This conclusion comes from the asset pricing model in Bask (2009a), where
it was found that the exchange rate in time periods t 2 t
0
, t
0
$ 2, had a second-order effect
on the current exchange rate, whereas the exchange rate in the previous time period had a
?rst-order effect. See also Bask (2007a) for the MA technique in a Dornbusch-style model.
8. Substitute equation (5) into equation (3), which gives p
t
¼ · · · þdð1 2bvÞDe
t
2dbð1 2vÞ
De
e
tþ1
· · ·.
9. By substituting the parameter values used in the numerical analysis below (Section 4), we
can conclude that the size of the exchange rate channel varies between 0.004 (when there is
no fundamental analysis in currency trade) and 0.4 (when there is only fundamental analysis
in currency trade).
10. First, replace De
e;m
tþ1
in equations (2)-(4) with the expression in equation (5). Second, neglect
from constants and variables dated at time t þ 1 in the equations. Third, replace r
t
in
equation (2) with the expression in equation (4). Finally, solve equation (2) for De
t
, substitute
the expression into equation (3) and the constraint in equation (8) is derived.
11. First, replace De
e;m
tþ1
in equations (2) and (3) with the expression in equation (4). Second,
replace x
t
in equations (2) and (3) with the expression in equation (9). Third, solve equation (3)
for p
t
and substitute the expression into equation (2). Finally, solve equation (2) for r
t
and the
rule in equations (10) and (11) is derived.
12. const: ¼ k
De
p
*
t
2dk
p
p
e;
*
tþ1
þdk
p
r
*
t
þak
x
rr
t
:
13. The ?rst row in equations (12)-(15) is equation (5) substituted into equation (2), the second
row is equation (5) substituted into equation (3), the third row is equation (5) substituted into
equation (4), and the fourth row is equation (10).
14. It is not always self-evident which variables in a model that are predetermined. However, by
looking at the entries in the relevant matrix:
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21
· Q ¼
2 2 2 0
2 2 2 0
2 2 2 0
2 2 2 0
_
¸
¸
¸
¸
¸
_
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¸
¸
¸
¸
¸
_
;
we conclude that r
t
is predetermined and this is because there are predetermined
relationships between current and expected values of x
t
, p
t
and De
t
(see the ?rst three rows in
the matrix), and that r
t
only depends on the expected values of the same variables and not
the expected value of itself (see the fourth row in the matrix).
15. Clarida et al. (2000) estimate different interest rate rules to evaluate Federal Reserve’s policy
during 1960-1996 using a standard DSGE model. They found that the policy during the
Volcker-Greenspan period was more successful to stabilize the economy than the policy
during the pre-Volcker period. Even though their evaluation of Federal Reserve’s policy is
somewhat simplistic, it is very intriguing.
16. At a ?rst sight, it may look as a shortcoming that we illustrate the properties of our economy
using parameter calibrations based on US data, even though our economy is not a small
economy. However, it is not a shortcoming for two reasons. First, our economy is not an
approximation of reality, but a caricature of it (Gibbard and Varian, 1978). This means that
we are only able to make qualitative and not quantitative conclusions about reality in the
numerical analysis. Second, the fact that the Clarida et al. (2000) and the Woodford (1999)
calibrations are very different means that we should not take the magnitudes of the point
estimates of a and g too gravely.
17. Woodford (2003) has looked into this matter in a standard DSGE model and ?nd that almost
strict in?ation rate targeting is optimal in monetary policy (z ¼ 0.048). We do not derive the
optimal degree of targeting herein since we have not established an exact relationship
between the representative household’s utility function and the objective function that the
central bank is optimizing.
18. Recall that the optimal policy problem in a small open economy is isomorphic to the optimal
policy problem in a closed economy (Clarida et al., 2001).
19. We have set p
*
t
¼ p
e;
*
tþ1
¼ r
*
t
¼ 0 in all computations in this section. Also, rr
0
¼ 0.
20. We also observe that the very slow return of the economy to steady state is even slower
when the amount of trend following in currency trading approaches the limit to have a
determinate REE in the economy. This result is not shown in a ?gure.
21. That the economy oscillates back to steady state in Figure 5 is due to the fact that there are
imaginary roots to the characteristic equation that describes the economy’s law of motion.
Thus, it is not possible to conclude that the economy must be oscillating just by looking at
the parameterization of the interest rate rule.
References
Bask, M. (2007a), “Chartism and exchange rate volatility”, International Journal of Finance and
Economics, Vol. 12, pp. 301-16.
Bask, M. (2007b), Long Swings and Chaos in the Exchange Rate in a DSGE Model with a Taylor
Rule, Bank of Finland Research Discussion Paper 19/2007.
Bask, M. (2009a), “Announcement effects on exchange rates”, International Journal of Finance
and Economics, Vol. 14, pp. 64-84.
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U
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S
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T
Y
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2
1
:
3
7
2
4
J
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n
u
a
r
y
2
0
1
6
(
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T
)
Bask, M. (2009b), “Instrument rules in monetary policy under heterogeneity in currency trade”,
Journal of Economics and Business, Vol. 61, pp. 97-111.
Bask, M. and Selander, C. (2009), “Robust Taylor rules under heterogeneity in currency trade”,
International Economics and Economic Policy, Vol. 6, pp. 283-313.
Blanchard, O.J. and Kahn, C.M. (1980), “The solution of linear difference models under rational
expectations”, Econometrica, Vol. 48, pp. 1305-11.
Brock, W.A. and Hommes, C.H. (1997), “A rational route to randomness”, Econometrica, Vol. 65,
pp. 1059-95.
Bullard, J.B. (2006), “The learnability criterion and monetary policy”, Federal Reserve Bank of
St Louis Review, Vol. 88 No. 3, pp. 203-17.
Bullard, J.B. and Schaling, E. (2009), “Monetary policy, determinacy, and learnability in a
two-block world economy”, Journal of Money, Credit and Banking, Vol. 41, pp. 1585-612.
Calvo, G.A. (1983), “Staggered prices in a utility-maximizing framework”, Journal of Monetary
Economics, Vol. 12, pp. 383-98.
Cheung, Y.-W. and Chinn, M.D. (2001), “Currency traders and exchange rate dynamics: a survey
of the US market”, Journal of International Money and Finance, Vol. 20, pp. 439-71.
Clarida, R., Gal? ´, J. and Gertler, M. (1999), “The science of monetary policy: a new Keynesian
perspective”, Journal of Economic Literature, Vol. 37, pp. 1661-707.
Clarida, R., Gal? ´, J. and Gertler, M. (2000), “Monetary policy rules and macroeconomic stability:
evidence and some theory”, Quarterly Journal of Economics, Vol. 115, pp. 147-80.
Clarida, R., Gal? ´, J. and Gertler, M. (2001), “Optimal monetary policy in open versus closed
economies: an integrated approach”, American Economic Review (AEA Papers and
Proceedings), Vol. 91, pp. 248-52.
De Grauwe, P. and Grimaldi, M. (2006), The Exchange Rate in a Behavioral Finance Framework,
Princeton University Press, Princeton, NJ.
Evans, G.W. and Honkapohja, S. (2001), Learning and Expectations in Macroeconomics,
Princeton University Press, Princeton, NJ.
Evans, G.W. and Honkapohja, S. (2003a), “Adaptive learning and monetary policy design”,
Journal of Money, Credit and Banking, Vol. 35, pp. 1045-72.
Evans, G.W. and Honkapohja, S. (2003b), “Expectations and the stability problem for optimal
monetary policies”, Review of Economic Studies, Vol. 70, pp. 807-24.
Evans, G.W. and Honkapohja, S. (2003c), “Friedman’s money supply rule vs optimal interest rate
policy”, Scottish Journal of Political Economy, Vol. 50, pp. 550-66.
Evans, G.W. and Honkapohja, S. (2006), “Monetary policy, expectations and commitment”,
Scandinavian Journal of Economics, Vol. 108, pp. 15-38.
Evans, G.W. and Honkapohja, S. (2009), “Learning and macroeconomics”, Annual Review of
Economics, Vol. 1, pp. 421-49.
Gal? ´, J. and Monacelli, T. (2005), “Monetary policy and exchange rate volatility in a small open
economy”, Review of Economic Studies, Vol. 72, pp. 707-34.
Gehrig, T. and Menkhoff, L. (2006), “Extended evidence on the use of technical analysis in foreign
exchange”, International Journal of Finance and Economics, Vol. 11, pp. 327-38.
Gibbard, A. and Varian, H.R. (1978), “Economic models”, Journal of Philosophy, Vol. 75, pp. 664-77.
Hommes, C.H. (2006), “Heterogeneous agent models in economics and ?nance”, in Tesfatsion, L.
and Judd, K.L. (Eds), Handbook of Computational Economics, Volume 2: Agent-Based
Computational Economics, Elsevier/North-Holland, Amsterdam.
Optimal
monetary
policy
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Llosa, L.-G. and Tuesta, V. (2008), “Determinacy and learnability of monetary policy rules in
small open economies”, Journal of Money, Credit and Banking, Vol. 40, pp. 1033-63.
Lui, Y.-H. and Mole, D. (1998), “The use of fundamental and technical analyses by foreign
exchange dealers: Hong Kong evidence”, Journal of International Money and Finance,
Vol. 17, pp. 535-45.
McCallum, B.T. (2007), “E-stability vis-a-vis determinacy results for a broad class of linear rational
expectations models”, Journal of Economic Dynamics and Control, Vol. 31, pp. 1376-91.
Marcet, A. and Sargent, T.J. (1989), “Convergence of least squares learning mechanisms in
self-referential linear stochastic models”, Journal of Economic Theory, Vol. 48, pp. 337-68.
Menkhoff, L. (1997), “Examining the use of technical currency analysis”, International Journal of
Finance and Economics, Vol. 2, pp. 307-18.
Neely, C.J. (1997), “Technical analysis in the foreign exchange market: a layman’s guide”, Federal
Reserve Bank of St Louis Review, Vol. 79 No. 5, pp. 23-38.
Oberlechner, T. (2001), “Importance of technical and fundamental analysis in the European
foreign exchange market”, International Journal of Finance and Economics, Vol. 6,
pp. 81-93.
Oberlechner, T. (2004), The Psychology of the Foreign Exchange Market, Wiley, Chichester.
Svensson, L.E.O. (2002), “In?ation targeting: should it be modeled as an instrument rule or a
targeting rule?”, European Economic Review, Vol. 46, pp. 771-80.
Svensson, L.E.O. (2003), “What is wrong with Taylor rules? Using judgment in monetary policy
through targeting rules”, Journal of Economic Literature, Vol. 41, pp. 426-77.
Taylor, J.B. (1993), “Discretion versus policy rules in practice”, Carnegie-Rochester Conference
Series on Public Policy, Vol. 39, pp. 195-214.
Taylor, M.P. and Allen, H. (1992), “The use of technical analysis in the foreign exchange market”,
Journal of International Money and Finance, Vol. 11, pp. 304-14.
Woodford, M. (1999), Optimal Monetary Policy Inertia, NBER Working Paper No. 7261.
Woodford, M. (2003), Interest and Prices: Foundations of a Theory of Monetary Policy, Princeton
University Press, Princeton, NJ.
Corresponding author
Mikael Bask can be contacted at: [email protected]
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This article has been cited by:
1. Mikael Bask. 2014. A CASE FOR INTEREST RATE INERTIA IN MONETARY POLICY.
International Journal of Finance & Economics 19, 140-159. [CrossRef]
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doc_854267581.pdf
Questionnaire surveys made at currency markets around the world reveal that currency
trade to a large extent not only is determined by an economy’s performance or expected performance.
Indeed, a fraction is guided by technical trading, which means that past exchange rates are assumed to
provide information about future exchange rate movements. The purpose of this paper is to ask how a
successful monetary policy should be designed when technical trading in the form of trend following is
used in currency trading.
Journal of Financial Economic Policy
Optimal monetary policy under heterogeneity in currency trade
Mikael Bask
Article information:
To cite this document:
Mikael Bask, (2009),"Optimal monetary policy under heterogeneity in currency trade", J ournal of Financial
Economic Policy, Vol. 1 Iss 4 pp. 338 - 354
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Optimal monetary policy under
heterogeneity in currency trade
Mikael Bask
School of Business and Economics, A
?
bo Akademi University,
Turku, Finland
Abstract
Purpose – Questionnaire surveys made at currency markets around the world reveal that currency
trade to a large extent not only is determined by an economy’s performance or expected performance.
Indeed, a fraction is guided by technical trading, which means that past exchange rates are assumed to
provide information about future exchange rate movements. The purpose of this paper is to ask how a
successful monetary policy should be designed when technical trading in the form of trend following is
used in currency trading.
Design/methodology/approach – The paper embeds an optimal policy rule into Gal? ´ and
Monacelli’s dynamic stochastic general equilibrium (DSGE) model for a small open economy, which is
augmented with trend following in currency trading, to examine the prerequisites for a successful
monetary policy. Speci?cally, the conditions for a determinate rational expectations equilibrium (REE)
that also is stable under least squares learning are in focus. The paper also computes impulse-response
functions for key variables to study how the economy returns to steady state after being hit by a shock.
Findings – The paper ?nds that a determinate REE that also is stable under least squares learning
often is the outcome when there is a limited amount of trend following in currency trading, but that a
more ?exible in?ation rate targeting in monetary policy sometimes cause an indeterminate REE in the
economy. Thus, strict, or almost strict, in?ation rate targeting in monetary policy is recommended also
when there is technical trading in currency trading and not only when all currency trading is guided by
fundamental analysis (in the form of rational expectations). This result is a new result in the literature.
Originality/value – There are already models in the literature on monetary policy design that
incorporate technical trading in currency trading into an otherwise standard DSGE model. There is
also a huge amount of DSGE models in the literature in which monetary policy is optimal. However,
the model in this paper is the ?rst model, to the best of the author’s knowledge, where technical trading
in currency trading and optimal monetary policy are combined in the same DSGE model.
Keywords Determinacy, DSGE model, Least squares learning, Targeting rule, Technical trading
Paper type Research paper
1. Introduction
Interest rate rule
Taylor (1993) has demonstrated that Federal Reserve’s policy, during late 1980s and
early 1990s, could be described by an interest rate rule on the following form:
r
t
¼ 0:04 þ 1:5ðp
t
20:02Þ þ 0:5ð y
t
2 yÞ; ð1Þ
The current issue and full text archive of this journal is available at
www.emeraldinsight.com/1757-6385.htm
JEL classi?cation – E52, F31, F41
This paper has bene?tted from presentations at various conferences and seminars as well as
from comments and suggestions by two anonymous referees. The usual disclaimer applies.
The MATLAB routines that have been used in the preparation of this paper are available on
request from the author. When impulse-response functions were computed, MATLAB routines
developed by Michael Woodford were utilized that are available at: www.columbia.edu/,mw2230/
Tools/
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Journal of Financial Economic Policy
Vol. 1 No. 4, 2009
pp. 338-354
qEmerald Group Publishing Limited
1757-6385
DOI 10.1108/17576380911050061
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where r
t
is Federal Reserve’s operating target for the funds rate, p
t
is the in?ation rate
according to the gross domestic product (GDP) de?ator, y
t
is the logarithm of real GDP,
and y is the logarithm of potential real GDP. In particular, the rule in equation (1)
prescribes setting the funds rate in response to the in?ation rate and the output gap,
where the latter variable is the difference between the two measures of GDP.
Instrument or targeting rule?
Svensson(2002, 2003) argues that aninstrument rule, suchas the Taylor rule inequation(1),
is inferior to a targeting rule in monetary policy since the instrument rule is not consistent
with optimizing behavior on the part of the central bank. Speci?cally, the targeting rule is
derived from the optimization of an objective function (or the minimization of a
loss-function). For this reason, when embedding an interest rate rule into a dynamic
stochastic general equilibrium (DSGE) model, Svensson (2002, 2003) argues that all agents
in the model should behave optimally; households should maximize utility, ?rms should
maximize pro?t, and the central bank should maximize welfare[1].
Let us use Svensson’s (2003, p. 429) own words to make the point clear:
Monetary policy by the world’s more advanced central banks these days is at least as
optimizing and forward-looking as the behavior of the most rational private agents. I ?nd it
strange that a large part of the literature on monetary policy still prefers to represent central
bank behavior with the help of mechanical instrument rules.
Hence, we focus on targeting rules or optimal policy rules in this paper.
A determinate and learnable rational expectations equilibrium?
Typically, in the literature, conditions for determinacy of the rational expectations
equilibrium (REE) are examined since the central bank would like to avoid coordination
problems in the economy. For instance, without imposing additional restrictions into a
rational expectations model, it may not be known in advance which REEthat agents will
coordinate on, if there will be any coordination at all. To give an example, the effects of
monetary policy may not be known beforehand: is it the case that agents will coordinate
on a REEthat has undesirable properties, like a high-in?ation rate, or on a REEin which
the price level is stable?
Another problemis the computation of time-paths of economic variables whenagents
are assumed to have rational expectations since it is not self-evident that they have
perfect knowledge of the economy’s law of motion. For example, it is a well-known fact
that the transmission mechanism for monetary policy has a complicated structure and
this also means that there are disagreements about the exact nature of the mechanism.
We therefore ask the following question in this paper: can agents eventually learn the
REE, if they can make use of data generated by the economy itself to improve their
knowledge of its law of motion? The concept of learning that we make use of is least
squares learning[2].
Heterogeneity in currency trade
Questionnaire surveys made at currency markets around the world reveal that
currency trade to a large extent not only is determined by an economy’s performance or
expected performance. Indeed, a fraction is guided by technical trading, which means
that past exchange rates are assumed to provide information about future exchange
Optimal
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rate movements. A simple example of technical trading that we make use of in this
paper is trend following.
See Oberlechner (2004) for an in-depth discussion of two large questionnaire
surveys conducted at the European and the North American markets, Gehrig and
Menkhoff (2006) for a survey on trading behavior that includes references to several
other surveys made at currency markets (Cheung and Chinn, 2001; Lui and Mole, 1998;
Menkhoff, 1997; Oberlechner, 2001; Taylor and Allen, 1992) and Neely (1997) for a
layman’s guide on technical trading. Other terms for technical trading are chartism and
technical analysis[3].
Aim of the paper
We embed an optimal policy rule into Gal? ´ and Monacelli’s (2005) DSGE model for a
small open economy, which is augmented with trend following in currency trading, to
examine the prerequisites for a successful monetary policy. Speci?cally, the conditions
for a determinate REE that also is stable under least squares learning are in focus. We
also compute impulse-response functions for key variables to study how the economy
returns to steady state after being hit by a shock. The reason why an otherwise
standard DSGE model is used in the analysis is to facilitate for the reader in what way
the inclusion of trend following in currency trading may change the ?ndings compared
with those in a standard DSGE model.
Relation to the literature
Since anoptimal policyrule inthe formof anexpectations-basedrule is derivedherein, this
paper relates to Evans and Honkapohja (2003a, b, c, 2006) who examine the desirability of
an expectations-based rule in a DSGE model for a closed economy from a learning
perspective. Two other papers that alsofocus onthe learnabilityof a determinate REE, but
for an open economy, are Bullard and Schaling (2009) and Llosa and Tuesta (2008). The
former paper examines optimal policy in a two-country model, whereas the latter paper
examines instrument rules in the same DSGE model as in this paper. However, none of
these papers incorporate technical trading in currency trading into the model.
Papers that incorporate technical trading in currency trading into a DSGE model
include Bask (2007b, 2009b) and Bask and Selander (2009). However, the interest rate
rule is not an optimal policy rule in these papers. Instead, an instrument rule is used by
the central bank. Thus, the originality in the present paper is, to the best of our
knowledge, that monetary policy is optimal in a DSGE model that has been augmented
with technical trading in currency trading. Be aware that the fractions of fundamental
and technical analyses in currency trading are exogenous in this paper as also is the case
in Bask (2009b) and Bask and Selander (2009). Thus, making the fractions endogenous
as in Bask (2007b), but assuming that monetary policy is optimal, is saved for future
research.
Outline of the paper
The DSGE model we examine is outlined in Section 2. Thereafter, in Section 3, we
derive the optimal policy rule for the central bank, whereas the conditions for a
determinate REE that also is stable under least squares learning are in focus in Section
4. Impulse-response functions for key variables are computed in Section 5 and the
paper is concluded in Section 6 with a discussion.
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2. DSGE model
A DSGE model with imperfect competition and nominal rigidities is presented in
Gal? ´ and Monacelli (2005) for a small open economy. Speci?cally, their model consists
of an IS curve[4]:
x
t
¼ x
e
tþ1
2a r
t
2
1
1 2d
· p
e
tþ1
2d De
e;m
tþ1
þp
e;
*
tþ1
_ _ _ _
2rr
t
_ _
; ð2Þ
an AS curve:
p
t
¼ bp
e
tþ1
þgð1 2dÞx
t
þd De
t
2bDe
e;m
tþ1
þp
*
t
2bp
e;
*
tþ1
_ _
; ð3Þ
and a condition for uncovered interest rate parity:
r
t
2r
*
t
¼ De
e;m
tþ1
; ð4Þ
where x
t
is the output gap, r
t
is the nominal interest rate, p
t
is the consumer price index
(CPI) in?ation rate, e
t
is the nominal exchange rate, and rr
t
is the natural rate of
interest. The superscripts “e” and “e,m” denote expectations and market expectations
in currency trade, respectively, and an asterisk in the superscript denotes a foreign
quantity.
b [ [0,1] is the discount factor that is used when the representative household in the
home country maximizes a discounted sum of instantaneous utilities derived from
consumption and leisure. d [ [0,1] is the share of consumption in the home country
allocated to imported goods, which means that d is an index of openness of the
economy. Finally, a and g are functions of parameters in the Gal? ´ and Monacelli (2005)
model[5].
There are two types of behavior in currency trading:
(1) trend following; and
(2) trading that is based on fundamental analysis.
When trend following is used, it is believed that the exchange rate will increase
(decrease) between time periods t and t þ 1, if it increased (decreased) between time
periods t 2 1 and t[6], [7]. When fundamental analysis is used, agents have rational
expectations regarding the next time period’s exchange rate change (if they have been
able to learn the economy’s law of motion), which means that market expectations can
be summarized as follows:
De
e;m
tþ1
¼ vDe
e;c
tþ1
þ ð1 2vÞDe
e;f
tþ1
¼ vDe
t
þ ð1 2vÞDe
e
tþ1
; ð5Þ
where v [ [0,1] is the degree of trend following in currency trading. “e,c” and “e,f”
denote expectations according to chartism and fundamental analysis, respectively.
Since the behavior of currency traders is central in the model, a few words should be
mentioned regarding the existence of a direct exchange rate channel in the AS curve in
equation (3). Speci?cally, the size of the channel is d(1 2 bv), which means that the
channel increases in size with the openness of the economy and decreases in size with
the discount factor as well as the degree of trend following in currency trading[8].
Moreover, when chartism is used more extensively in currency trade, the current
Optimal
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exchange rate change not only has a smaller effect on the in?ation rate (i.e. the
exchange rate channel has a smaller size), but also the expected exchange rate change
has a larger effect on the same variable[9].
3. Optimal monetary policy
The model is closed by deriving an interest rate rule for the central bank that
minimizes the following objective function:
L
t
¼ zx
2
t
þp
2
t
; ð6Þ
given the economy’s law of motion in equations (2)-(5). Thus, we assume that there is no
commitment mechanism available for the central bank, which means that the optimal
policy rule is derived under discretion in monetary policy. Then, the optimization
problem for the central bank is:
min
x
t
;p
t
L
t
¼ min
x
t
;p
t
zx
2
t
þp
2
t
; ð7Þ
subject to[10]:
p
t
¼ 2
ð1 2bvÞd
av
2g
_ _
ð1 2dÞx
t
; ð8Þ
which has the ?rst-order condition:
x
t
¼
ð1 2bvÞd
av
2g
_ _
·
1 2d
z
· p
t
¼ Ap
t
: ð9Þ
Be aware that the central bank controls the exchange rate change when optimizing
the objective function in equation (6), even though this variable does not appear
explicitly in the optimization problem in equations (7) and (8). The objective function
in equation (6) is often referred to as ?exible in?ation rate targeting, where z ¼ 0 is
strict targeting, and the condition in equation (9) is often referred to as a speci?c
targeting rule.
After combining the economy’s law of motion in equations (2)-(4) with the speci?c
targeting rule in equation (9), but without imposing the condition that agents have
rational expectations, we have the following optimal policy rule[11]:
r
t
¼ const: þk
x
x
e
tþ1
þk
p
p
e
tþ1
þk
De
De
t
; ð10Þ
where[12]:
k
x
¼
Agð1 2dÞ
2
21 þd
Að1 2dÞðag þbdÞ 2a
k
p
¼
Að1 2dÞðag þbÞ 2a
Að1 2dÞðag þbdÞ 2a
k
De
¼
Að1 2dÞd
Að1 2dÞðag þbdÞ 2a
_
¸
¸
¸
¸
¸
¸
¸
¸
¸
_
¸
¸
¸
¸
¸
¸
¸
¸
¸
_
ð11Þ
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This rule is an expectations-based rule since agents do not have rational expectations
in the derivation of it (Evans and Honkapohja, 2003b). Note that the interest rate set by
the central bank depends on the current exchange rate change and not the expected
exchange rate change. This result follows from substituting the ?rst-order condition
for optimal policy in equation (9) into the economy’s law of motion in equations (2)-(4).
4. A determinate REE that is stable under least squares learning
Let us examine under what conditions our economy is characterized by a determinate
REE that also is stable under least squares learning. Recall that if there is a
determinate REE in the economy, we also know that it is E-stable since the dating of
expectations is time-t (McCallum, 2007). Hence, since an E-stable REE is a necessary
and a suf?cient condition for a least squares learnable REE, all determinacy regions in
parameter space that are found below are also regions for a determinate REE that is
stable under least squares learning (Marcet and Sargent, 1989).
The complete model, or economy, in matrix form is[13]:
G· y
t
¼ Q· y
e
tþ1
þLþJ· rr
t
; ð12Þ
where:
G ¼
1 0
adv
12d
a
2gð1 2dÞ 1 2dð1 2bvÞ 0
0 0 2v 1
0 0 2k
De
1
_
¸
¸
¸
¸
¸
_
_
¸
¸
¸
¸
¸
_
; ð13Þ
Q ¼
1
a
12d
2
adð12vÞ
12d
0
0 b 2bdð1 2vÞ 0
0 0 1 2v 0
k
x
k
p
0 0
_
¸
¸
¸
¸
¸
_
_
¸
¸
¸
¸
¸
_
; ð14Þ
and:
y
t
¼ ½x
t
; p
t
; De
t
; r
t
?
0
: ð15Þ
The exact form of the matrices L and J does not matter when examining whether the
economy has a determinate REE. Then, since there is one variable that is predetermined,
r
t
, exactly one eigenvalue of the matrix G
21
· Qmust be outside the unit circle to have a
determinate REE[14]. However, if more than one eigenvalue are outside the unit circle,
we have an indeterminate REE, and if all eigenvalues are inside the unit circle, there is no
stable REE in the economy (Blanchard and Kahn, 1980).
Deriving analytical conditions for determinacy is not meaningful since these
expressions would be too large and cumbersome to interpret. Consequently, we adopt
the same strategy as in other papers within this area of research and illustrate our
?ndings for determinacy using calibrated values of the structural parameters.
Speci?cally, we use two sets of parameter calibrations in the numerical analysis, where
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the ?rst calibration (often used in the literature) comes from Woodford (1999) and is
based on US data:
a ¼
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; b ¼ 0:99; g ¼ 0:024:
_
ð16Þ
The second calibration comes from Clarida et al. (2000) and is also based on US data[15]:
{a ¼ 1; b ¼ 0:99; g ¼ 0:3: ð17Þ
Clearly, even though the time periods in Clarida et al. (2000) and Woodford (1999)
calibrations are somewhat different, there are still large differences in the magnitudes of
the parameters aand g. We will not discuss possible reasons for these differences herein.
We will instead utilize the fact that the parameter calibrations are very different to check
the robustness of our ?ndings[16]. Finally, the degree of openness of the economy is
d ¼ 0.4, which is the same value as in Gal? ´ and Monacelli (2005).
See Figure 1 for regions in the (v,z)-space that are associated with a determinate REE,
an indeterminate REE and no stable REE when the Woodford (1999) calibration is used.
Not surprisingly, when the degree of trend following in currency trading is large,
there is no stable REE in the economy and this is because there is no mechanism in
technical trading that forces the economy to equilibrium. Moreover, when the amount
Figure 1.
Regions in parameter
space that are associated
with a determinate REE,
an indeterminate REE and
no stable REE
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Degree of trend following in currency trade
F
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e
t
a
r
g
e
t
i
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Region for a determinate REE that is stable under learning (see light area) and
regions for an indeterminate REE (see dark area) and no stable REE (see white area)
Source: The Woodford (1999) calibration is used
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of trend following in currency trading is more limited, there is either a determinate
REE or an indeterminate REE in the economy. However, when in?ation rate targeting
is strict, or almost strict, there is a determinate REE in the economy. This is an
interesting result since almost strict in?ation rate targeting most likely is optimal in
monetary policy[17].
Finally, when there is no trend following in currency trading, there is a determinate
REE in the economy that also is stable under least squares learning. This result is not
either surprising since Evans and Honkapohja (2003b) show that a DSGE model for a
closed economy has this property when the central bank is using an expectations-based
rule in its policy[18]. The same result also holds when the Clarida et al. (2000) calibration
is used in the numerical analysis.
In Figure 2, we show the same regions in the (v,z)-space as in Figure 1, but the
Clarida et al. (2000) calibration is now used.
As before, when the degree of trend following in currency trading is large, there
is no stable REE in the economy, but the difference is now that this region in
the (v,z)-space is somewhat smaller. Moreover, a qualitative difference between
Figures 1 and 2 is that there is always a determinate REE when the economy is stable
and when the Clarida et al. (2000) calibration is used. This means that monetary policy
is never associated with the indeterminacy problem in this case.
Figure 2.
Regions in parameter
space that are associated
with a determinate REE,
an indeterminate REE and
no stable REE
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Degree of trend following in currency trade
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i
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a
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e
t
i
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g
Region for a determinate REE that is stable under learning (see light area) and
region when there is no stable REE (see white area)
Source: The Clarida et al. (2000) calibration is used
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5. Impulse-response functions
Having established under what conditions the economy is characterized by a determinate
REE, we shift focus to the computation of impulse-response functions for key variables.
For this sake, we assume that the shock (impulse) is channeled through the natural rate of
interest. Speci?cally, in time period t ¼ 1, a shock is hitting the economy such that
Drr
1
¼ 1[19]. Thereafter, if there is a determinate REE in the economy (as is the case
throughout this section), it will return to steady state and depending on the parameter
setting, the convergence is fast or slow as well as oscillating or non-oscillating.
In Figures 3-5, impulse-response functions for the output gap, the CPI in?ation rate,
the nominal exchange rate change and the nominal interest rate are shown, where the
Woodford (1999) calibration is used.
In Figure 3, there is a small amount of trend following in currency trading (v ¼ 0.1)
and in?ation rate targeting is almost strict (z ¼ 0.05) with the effect that the economy’s
adjustment path to steady state is fast and non-oscillating. In Figure 4, when a larger
amount of trend following is used in currency trading (v ¼ 0.35; z ¼ 0.05), the
adjustment path is still non-oscillating, but the return of the economy to steady state is
very slow. In Figure 5, when in?ation rate targeting is more ?exible (z ¼ 0.5; v ¼ 0.35),
the economy’s adjustment path to steady state is again faster but now oscillating.
That the return of the economy to steady state is very slow in Figure 4 is because
the mechanism that forces the economy to equilibrium has been weakened by trend
following, or trend extrapolation, in currency trading[20]. Further on, the shock’s effect
Figure 3.
Impulse-response
functions when a smaller
amount of trend following
is used in currency trading
and in?ation rate
targeting is almost strict
0 10 20 30 40 50 0 10 20 30 40 50
0 10 20 30 40 50 0 10 20 30 40 50
–1.5
–1
–0.5
0
0.5
1
1.5
2
2.5
3
3.5
Output gap
–0.2
–0.1
0
0.1
0.2
0.3
0.4
0.5
CPI inflation rate
–0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Nominal exchange rate change
–0.16
–0.14
–0.12
–0.1
–0.08
–0.06
–0.04
–0.02
0
Nominal interest rate
Source: The Woodford (1999) calibration is used
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on the in?ation rate is, of course, larger when in?ation rate targeting is more ?exible as
in Figure 5. At the same time, this also means that the shock’s effect on the output gap
is smaller since relatively more weight is placed by monetary policy on the output
gap’s deviation from its target, which is no output gap.
The parameterizations of the interest rate rule are not very different in the three
cases: r
t
¼ const: þ0:129x
e
tþ1
þ0:452p
e
tþ1
20:369De
t
, r
t
¼ const: þ0:098x
e
tþ1
þ0:934
p
e
tþ1
20:045 De
t
, and r
t
¼ const: þ0:095x
e
tþ1
þ0:994p
e
tþ1
20:004De
t
, respectively[21].
Note that the Taylor principle is not satis?ed in any of the rules (i.e. k
p
ò 1). Still, the
economy returns to steady state in each case after being hit a shock.
Impulse-response functions for the output gap, the CPI in?ation rate, the nominal
exchange rate change and the nominal interest rate are shown in Figures 6-8, where the
Clarida et al. (2000) calibration is used.
Roughly speaking, the assumptions behind Figures 3 and 6, Figures 4 and 7, and
Figures 5 and 8 are the same, even though a somewhat larger amount of trend
following in currency trading is allowed for in Figures 7 and 8 (v ¼ 0.5). As before, the
return of the economy to steady state is very slow in one case (Figure 8), even though it
does not correspond to the case when the Woodford (1999) calibration was used
(Figure 4), but it is never oscillating in the cases examined. Also, the shock’s effect on
the output gap is smaller and its effect on the in?ation rate is somewhat larger when
in?ation rate targeting is more ?exible (Figure 8).
Figure 4.
Impulse-response
functions when a larger
amount of trend following
is used in currency trading
and in?ation rate
targeting is almost strict
0 100 200 300 400 500
–0.7
–0.6
–0.5
–0.4
–0.3
–0.2
–0.1
0
0 100 200 300 400 500
0 100 200 300 400 500 0 100 200 300 400 500
–0.7
–0.6
–0.5
–0.4
–0.3
–0.2
–0.1
0
Output gap CPI inflation rate
–0.6
–0.4
–0.2
0
0.2
0.4
0.6
0.8
1
1.2
Nominal exchange rate change
–0.7
–0.6
–0.5
–0.4
–0.3
–0.2
–0.1
0
Nominal interest rate
Source: The Woodford (1999) calibration is used
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The parameterizations of the interest rate rule are now r
t
¼ const: þ0:237x
e
tþ1
þ1:908p
e
tþ1
20:612De
t
, r
t
¼ const: þ0:972x
e
tþ1
þ1:071p
e
tþ1
20:626De
t
, and r
t
¼ const:
þ0:619x
e
tþ1
þ0:953p
e
tþ1
20:032De
t
, respectively. Note that the Taylor principle is
satis?ed in the ?rst rule (i.e. k
p
. 1), which corresponds to the case in which the
economy’s adjustment path to steady state is the fastest of the six cases examined.
6. Discussion
We have embedded an expectations-based optimal policy rule into Gal? ´ and Monacelli’s
(2005) DSGE model for a small open economy, which has been augmented with trend
following in currency trading, to examine the prerequisites for a successful monetary
policy.
We found that a determinate REE that also is stable under least squares learning
often is the outcome when there is a limited amount of trend following in currency
trading, but that a more ?exible in?ation rate targeting in monetary policy sometimes
cause an indeterminate REEinthe economy. Thus, whenin?ation rate targeting is strict,
or almost strict, there is a determinate REEin the economy that also is stable under least
squares learning. This means that the effects of monetary policy are predictable, which
is not the case when the economy suffers from the indeterminacy problem.
Thus, strict, or almost strict, in?ation rate targeting in monetary policy is
recommended also when there is technical trading in currency trading and not only
Figure 5.
Impulse-response
functions when a larger
amount of trend following
is used in currency trading
and in?ation rate
targeting is more ?exible
0 20 40 60 80 100 0 20 40 60 80 100
0 20 40 60 80 100 0 20 40 60 80 100
–0.1
–0.05
0
0.05
0.1
0.15
Output gap
–0.6
–0.4
–0.2
0
0.2
0.4
0.6
0.8
1
1.2
CPI inflation rate
–3
–2
–1
0
1
2
3
4
5
Nominal exchange rate change
–0.8
–0.6
–0.4
–0.2
0
0.2
0.4
0.6
Nominal interest rate
Source: The Woodford (1999) calibration is used
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when all currency trading is guided by fundamental analysis (in the form of rational
expectations). In other words, strict, or almost strict, in?ation rate targeting in
monetary policy is a robust policy against technical trading in currency trading and
this result is a new result in the literature on monetary policy design.
We also computed impulse-response functions for key variables to study how the
economy returns to steady state after being hit by a shock. One ?nding that stands out
is that the shock’s effect on the output gap is smaller and its effect on the in?ation rate
is larger when in?ation rate targeting is more ?exible. Moreover, depending on the
parameter setting used in the numerical analysis, the convergence to steady state is
fast or slow as well as oscillating or non-oscillating.
Making the fractions of the two types of behavior in currency trading endogenous
would, of course, be an interesting complement to this paper. A setup similar to the one
in Brock and Hommes (1997) could be used for this aim:
.
fundamental analysis in currency trading is costly to use; and
.
most traders use the trading strategy that has been more successful in the past to
predict exchange rate movements.
In Bask (2007b), this setup is used in a DSGE model in which the central bank is using
an instrument rule in its policy with the result that chaotic dynamics and long swings
may be present in the exchange rate.
Figure 6.
Impulse-response
functions when a smaller
amount of trend following
is used in currency trading
and in?ation rate
targeting is almost strict
0 5 10 15 20 25
0 5 10 15 20 25
–0.2
0
0.2
0.4
0.6
0.8
1
1.2
Output gap
0 5 10 15 20 25
–0.005
0
0.005
0.01
0.015
0.02
0.025
CPI inflation rate
–0.4
–0.35
–0.3
–0.25
–0.2
–0.15
–0.1
–0.05
0
0.05
Nominal exchange rate change
0 5 10 15 20 25
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0.02
Nominal interest rate
Source: The Clarida et al. (2000) calibration is used
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Figure 7.
Impulse-response
functions when a larger
amount of trend following
is used in currency trading
and in?ation rate
targeting is almost strict
0 5 10 15 20 25
0 5 10 15 20 25
0 5 10 15 20 25
0 5 10 15 20 25
–0.8
–0.7
–0.6
–0.5
–0.4
–0.3
–0.2
–0.1
0
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–0.6
–0.5
–0.4
–0.3
–0.2
–0.1
0
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–0.4
–0.3
–0.2
–0.1
0
0.1
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0.3
0.4
Nominal exchange rate change
–0.35
–0.3
–0.25
–0.2
–0.15
–0.1
–0.05
0
Nominal interest rate
Source: The Clarida et al. (2000) calibration is used
Figure 8.
Impulse-response
functions when a larger
amount of trend following
is used in currency trading
and in?ation rate
targeting is more ?exible
0 50 100 150 200 250
0 50 100 150 200 250
0 50 100 150 200 250
0 50 100 150 200 250
–0.08
–0.07
–0.06
–0.05
–0.04
–0.03
–0.02
–0.01
0
Output gap
–0.7
–0.6
–0.5
–0.4
–0.3
–0.2
–0.1
0
CPI inflation rate
–0.8
–0.6
–0.4
–0.2
0
0.2
0.4
0.6
Nominal exchange rate change
–0.7
–0.6
–0.5
–0.4
–0.3
–0.2
–0.1
0
Nominal interest rate
Source: The Clarida et al. (2000) calibration is used
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Notes
1. See Clarida et al. (1999) for an early review of interest rate rules in DSGE models. Woodford’s
(2003) seminal work on rules in monetary policy should also be part of the reading list.
2. See Evans and Honkapohja (2001, 2009) for an introduction to this literature and Bullard
(2006) for a review of interest rate rules in DSGE models from a learning perspective.
3. See Hommes (2006) for a survey of the literature on heterogeneous agent models in
economics and ?nance, and De Grauwe and Grimaldi (2006) for an introduction to exchange
rate determination in a behavioral ?nance framework.
4. See Bask and Selander (2009) for the derivation of equations (2) and (3) using equations in
Gal? ´ and Monacelli (2005).
5. a depends on the openness index, d, the intertemporal elasticity of substitution in
consumption, the elasticity of substitution between domestic and foreign goods in
consumption, and the elasticity of substitution between foreign goods in consumption.
g depends on a, the discount factor, b, the intertemporal elasticity of substitution in labor
supply and the share of ?rms that set new prices in each time period (Calvo, 1983). See Bask
(2009b) for the exact relationships.
6. To minimize the number of structural parameters in the model, the two consecutive
increases (decreases) in the exchange rate are of the same size.
7. A more sophisticated technical trading rule, like the moving averages (MA) technique, would
also be desirable to examine in the Gal? ´ and Monacelli (2005) model. However, this would
complicate the analysis of the resulting DSGE model considerably and it is not even certain
that the dynamics is affected that much compared to when simple trend following is used in
currency trading. This conclusion comes from the asset pricing model in Bask (2009a), where
it was found that the exchange rate in time periods t 2 t
0
, t
0
$ 2, had a second-order effect
on the current exchange rate, whereas the exchange rate in the previous time period had a
?rst-order effect. See also Bask (2007a) for the MA technique in a Dornbusch-style model.
8. Substitute equation (5) into equation (3), which gives p
t
¼ · · · þdð1 2bvÞDe
t
2dbð1 2vÞ
De
e
tþ1
· · ·.
9. By substituting the parameter values used in the numerical analysis below (Section 4), we
can conclude that the size of the exchange rate channel varies between 0.004 (when there is
no fundamental analysis in currency trade) and 0.4 (when there is only fundamental analysis
in currency trade).
10. First, replace De
e;m
tþ1
in equations (2)-(4) with the expression in equation (5). Second, neglect
from constants and variables dated at time t þ 1 in the equations. Third, replace r
t
in
equation (2) with the expression in equation (4). Finally, solve equation (2) for De
t
, substitute
the expression into equation (3) and the constraint in equation (8) is derived.
11. First, replace De
e;m
tþ1
in equations (2) and (3) with the expression in equation (4). Second,
replace x
t
in equations (2) and (3) with the expression in equation (9). Third, solve equation (3)
for p
t
and substitute the expression into equation (2). Finally, solve equation (2) for r
t
and the
rule in equations (10) and (11) is derived.
12. const: ¼ k
De
p
*
t
2dk
p
p
e;
*
tþ1
þdk
p
r
*
t
þak
x
rr
t
:
13. The ?rst row in equations (12)-(15) is equation (5) substituted into equation (2), the second
row is equation (5) substituted into equation (3), the third row is equation (5) substituted into
equation (4), and the fourth row is equation (10).
14. It is not always self-evident which variables in a model that are predetermined. However, by
looking at the entries in the relevant matrix:
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G
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· Q ¼
2 2 2 0
2 2 2 0
2 2 2 0
2 2 2 0
_
¸
¸
¸
¸
¸
_
_
¸
¸
¸
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¸
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;
we conclude that r
t
is predetermined and this is because there are predetermined
relationships between current and expected values of x
t
, p
t
and De
t
(see the ?rst three rows in
the matrix), and that r
t
only depends on the expected values of the same variables and not
the expected value of itself (see the fourth row in the matrix).
15. Clarida et al. (2000) estimate different interest rate rules to evaluate Federal Reserve’s policy
during 1960-1996 using a standard DSGE model. They found that the policy during the
Volcker-Greenspan period was more successful to stabilize the economy than the policy
during the pre-Volcker period. Even though their evaluation of Federal Reserve’s policy is
somewhat simplistic, it is very intriguing.
16. At a ?rst sight, it may look as a shortcoming that we illustrate the properties of our economy
using parameter calibrations based on US data, even though our economy is not a small
economy. However, it is not a shortcoming for two reasons. First, our economy is not an
approximation of reality, but a caricature of it (Gibbard and Varian, 1978). This means that
we are only able to make qualitative and not quantitative conclusions about reality in the
numerical analysis. Second, the fact that the Clarida et al. (2000) and the Woodford (1999)
calibrations are very different means that we should not take the magnitudes of the point
estimates of a and g too gravely.
17. Woodford (2003) has looked into this matter in a standard DSGE model and ?nd that almost
strict in?ation rate targeting is optimal in monetary policy (z ¼ 0.048). We do not derive the
optimal degree of targeting herein since we have not established an exact relationship
between the representative household’s utility function and the objective function that the
central bank is optimizing.
18. Recall that the optimal policy problem in a small open economy is isomorphic to the optimal
policy problem in a closed economy (Clarida et al., 2001).
19. We have set p
*
t
¼ p
e;
*
tþ1
¼ r
*
t
¼ 0 in all computations in this section. Also, rr
0
¼ 0.
20. We also observe that the very slow return of the economy to steady state is even slower
when the amount of trend following in currency trading approaches the limit to have a
determinate REE in the economy. This result is not shown in a ?gure.
21. That the economy oscillates back to steady state in Figure 5 is due to the fact that there are
imaginary roots to the characteristic equation that describes the economy’s law of motion.
Thus, it is not possible to conclude that the economy must be oscillating just by looking at
the parameterization of the interest rate rule.
References
Bask, M. (2007a), “Chartism and exchange rate volatility”, International Journal of Finance and
Economics, Vol. 12, pp. 301-16.
Bask, M. (2007b), Long Swings and Chaos in the Exchange Rate in a DSGE Model with a Taylor
Rule, Bank of Finland Research Discussion Paper 19/2007.
Bask, M. (2009a), “Announcement effects on exchange rates”, International Journal of Finance
and Economics, Vol. 14, pp. 64-84.
JFEP
1,4
352
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
3
7
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
Bask, M. (2009b), “Instrument rules in monetary policy under heterogeneity in currency trade”,
Journal of Economics and Business, Vol. 61, pp. 97-111.
Bask, M. and Selander, C. (2009), “Robust Taylor rules under heterogeneity in currency trade”,
International Economics and Economic Policy, Vol. 6, pp. 283-313.
Blanchard, O.J. and Kahn, C.M. (1980), “The solution of linear difference models under rational
expectations”, Econometrica, Vol. 48, pp. 1305-11.
Brock, W.A. and Hommes, C.H. (1997), “A rational route to randomness”, Econometrica, Vol. 65,
pp. 1059-95.
Bullard, J.B. (2006), “The learnability criterion and monetary policy”, Federal Reserve Bank of
St Louis Review, Vol. 88 No. 3, pp. 203-17.
Bullard, J.B. and Schaling, E. (2009), “Monetary policy, determinacy, and learnability in a
two-block world economy”, Journal of Money, Credit and Banking, Vol. 41, pp. 1585-612.
Calvo, G.A. (1983), “Staggered prices in a utility-maximizing framework”, Journal of Monetary
Economics, Vol. 12, pp. 383-98.
Cheung, Y.-W. and Chinn, M.D. (2001), “Currency traders and exchange rate dynamics: a survey
of the US market”, Journal of International Money and Finance, Vol. 20, pp. 439-71.
Clarida, R., Gal? ´, J. and Gertler, M. (1999), “The science of monetary policy: a new Keynesian
perspective”, Journal of Economic Literature, Vol. 37, pp. 1661-707.
Clarida, R., Gal? ´, J. and Gertler, M. (2000), “Monetary policy rules and macroeconomic stability:
evidence and some theory”, Quarterly Journal of Economics, Vol. 115, pp. 147-80.
Clarida, R., Gal? ´, J. and Gertler, M. (2001), “Optimal monetary policy in open versus closed
economies: an integrated approach”, American Economic Review (AEA Papers and
Proceedings), Vol. 91, pp. 248-52.
De Grauwe, P. and Grimaldi, M. (2006), The Exchange Rate in a Behavioral Finance Framework,
Princeton University Press, Princeton, NJ.
Evans, G.W. and Honkapohja, S. (2001), Learning and Expectations in Macroeconomics,
Princeton University Press, Princeton, NJ.
Evans, G.W. and Honkapohja, S. (2003a), “Adaptive learning and monetary policy design”,
Journal of Money, Credit and Banking, Vol. 35, pp. 1045-72.
Evans, G.W. and Honkapohja, S. (2003b), “Expectations and the stability problem for optimal
monetary policies”, Review of Economic Studies, Vol. 70, pp. 807-24.
Evans, G.W. and Honkapohja, S. (2003c), “Friedman’s money supply rule vs optimal interest rate
policy”, Scottish Journal of Political Economy, Vol. 50, pp. 550-66.
Evans, G.W. and Honkapohja, S. (2006), “Monetary policy, expectations and commitment”,
Scandinavian Journal of Economics, Vol. 108, pp. 15-38.
Evans, G.W. and Honkapohja, S. (2009), “Learning and macroeconomics”, Annual Review of
Economics, Vol. 1, pp. 421-49.
Gal? ´, J. and Monacelli, T. (2005), “Monetary policy and exchange rate volatility in a small open
economy”, Review of Economic Studies, Vol. 72, pp. 707-34.
Gehrig, T. and Menkhoff, L. (2006), “Extended evidence on the use of technical analysis in foreign
exchange”, International Journal of Finance and Economics, Vol. 11, pp. 327-38.
Gibbard, A. and Varian, H.R. (1978), “Economic models”, Journal of Philosophy, Vol. 75, pp. 664-77.
Hommes, C.H. (2006), “Heterogeneous agent models in economics and ?nance”, in Tesfatsion, L.
and Judd, K.L. (Eds), Handbook of Computational Economics, Volume 2: Agent-Based
Computational Economics, Elsevier/North-Holland, Amsterdam.
Optimal
monetary
policy
353
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
3
7
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
Llosa, L.-G. and Tuesta, V. (2008), “Determinacy and learnability of monetary policy rules in
small open economies”, Journal of Money, Credit and Banking, Vol. 40, pp. 1033-63.
Lui, Y.-H. and Mole, D. (1998), “The use of fundamental and technical analyses by foreign
exchange dealers: Hong Kong evidence”, Journal of International Money and Finance,
Vol. 17, pp. 535-45.
McCallum, B.T. (2007), “E-stability vis-a-vis determinacy results for a broad class of linear rational
expectations models”, Journal of Economic Dynamics and Control, Vol. 31, pp. 1376-91.
Marcet, A. and Sargent, T.J. (1989), “Convergence of least squares learning mechanisms in
self-referential linear stochastic models”, Journal of Economic Theory, Vol. 48, pp. 337-68.
Menkhoff, L. (1997), “Examining the use of technical currency analysis”, International Journal of
Finance and Economics, Vol. 2, pp. 307-18.
Neely, C.J. (1997), “Technical analysis in the foreign exchange market: a layman’s guide”, Federal
Reserve Bank of St Louis Review, Vol. 79 No. 5, pp. 23-38.
Oberlechner, T. (2001), “Importance of technical and fundamental analysis in the European
foreign exchange market”, International Journal of Finance and Economics, Vol. 6,
pp. 81-93.
Oberlechner, T. (2004), The Psychology of the Foreign Exchange Market, Wiley, Chichester.
Svensson, L.E.O. (2002), “In?ation targeting: should it be modeled as an instrument rule or a
targeting rule?”, European Economic Review, Vol. 46, pp. 771-80.
Svensson, L.E.O. (2003), “What is wrong with Taylor rules? Using judgment in monetary policy
through targeting rules”, Journal of Economic Literature, Vol. 41, pp. 426-77.
Taylor, J.B. (1993), “Discretion versus policy rules in practice”, Carnegie-Rochester Conference
Series on Public Policy, Vol. 39, pp. 195-214.
Taylor, M.P. and Allen, H. (1992), “The use of technical analysis in the foreign exchange market”,
Journal of International Money and Finance, Vol. 11, pp. 304-14.
Woodford, M. (1999), Optimal Monetary Policy Inertia, NBER Working Paper No. 7261.
Woodford, M. (2003), Interest and Prices: Foundations of a Theory of Monetary Policy, Princeton
University Press, Princeton, NJ.
Corresponding author
Mikael Bask can be contacted at: [email protected]
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This article has been cited by:
1. Mikael Bask. 2014. A CASE FOR INTEREST RATE INERTIA IN MONETARY POLICY.
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