Monetary Policy and Exchange Rate
Interactions in an Open Economy
Hilde C. Bjørnland*
University of Oslo and Norges Bank
May 3, 2005
[PRELIMINARY AND INCOMPLETE]
COMMENTS ARE WELCOME
Abstract
This paper analyses the effects of monetary policy in an open economy through
structural VARs, paying particular attention to a possible interdependence between
the monetary policy stance and exchange rate movements. Previous studies of the
effects of monetary policy in open economies have typically found only small (and
even puzzling) effects on the exchange rate. However, many of these studies have
disregarded a possible interaction between monetary policy and exchange rate
movements by placing zero restriction on their contemporaneous correlation. By
instead imposing a long-run restriction on the real exchange, thereby allowing the
interest rate and the exchange rate to react simultaneously to any news, we find the
interdependence to increase considerably. In particular, a monetary policy shock now
implies a strong and immediate appreciation of the exchange rate. However, the
qualitative properties of a monetary policy shock found in the established literature
are still preserved. In particular, a monetary policy shock that increases the interest
rate temporarily lowers output and has a sluggish but negative effect on consumer
price inflation.
Keywords: VAR, monetary policy, exchange rate interactions, identification.
JEL-codes: E61, E52, E43.
* Valuable comments and suggestions from Leif Brubakk, Sharon McCaw and Kjetil Olsen
are gratefully acknowledged. The views expressed are those of the author and should not be
interpreted as reflecting those of Norges Bank.
1
1 Introduction
Recently, there has been a great deal of interest in quantifying the effects of monetary policy
on a set of macroeconomic aggregates. These empirical studies have been particularly
successful in extracting information useful to evaluate the fit of the newly developed dynamic
stochastic general equilibrium (DSGE) models like those of Christiano et al. (2005) and Altig
et al. (2003) for the closed economy and Adolfson et al. (2005) for the open economy. In
particular, the authors estimate the parameters of the DSGE model by matching conditional
dynamics in response to certain structural shocks. For instance, the impulse response to a
monetary policy shock is specified and taken as given; the DSGE parameterization is
thereafter chosen to give the same answer. According to Faust (2005), “Clarifying the
identification in this way could make more productive the efforts to constructively critique the
models by both central bank staff and outside observers.”
The quantitative effects of monetary policy shocks have to a large extent been
addressed in terms of vector autoregressive (VAR) models, initiated by Sims (1980). Through
the recent applications of Leeper et al. (1996) and Christiano et al. (1999, 2005), one has
reached a consensus on how monetary policy affects the closed economy (like the U.S.). In
particular, a contractionary monetary policy shock that increases the interest rate, gradually
lowers output and has a sluggish but eventually negative effect on inflation (that peaks after
1-2 years). These results have been found using VARs that are identified with some sort of
recursive identification strategy between the macroeconomic environment and monetary
policy. However, studies identifying monetary policy without this restriction, have also found
similar results, see for example Faust et al. (2004) and the references therein1.
VAR studies of the open economy have on the other hand provided less of a
consensus with regard to the effects of monetary policy, and have along certain dimensions
even provided some puzzling results. The exchange rate, in particular, has been a troublesome
issue. According to Dornbusch’s (1976) well known exchange rate hypothesis, a
contractionary monetary policy shock (that increases the domestic interest rates relative to
foreign interest rates) will lead to an impact appreciation followed by a persistent depreciation
of the domestic currency. This view underlies most models for policy analysis, as emphasised
by Walsh (2003).2
However, when confronted with data for the open economy, very few VAR studies
have found support for Dornbusch overshooting. Instead they have found that following a
contractionary monetary policy, the real exchange rate either actually depreciates, or, if it
appreciates, it does so for a prolonged period of up to three years, thereby giving a humpshaped response that violates the uncovered interest parity (UIP) condition. In the literature,
the first phenomenon has been termed the exchange rate puzzle, whereas the second has been
1
An exception is Uhlig (2005), who using sign restrictions finds monetary policy to have no clear
effect on GDP, although prices move gradually as expected.
2
Walsh (2003, pp. 513-514) argues that "The real exchange rate does not overshoot; it falls below the
baseline and then returns smoothly to its initial level. This behaviour is consistent with the empirical
evidence of Eichenbaum and Evans (1995)". However, as we will see below, this result is actually not
at all consistent with Eichenbaum and Evans (1995), who finds a persistent overshooting of up to three
years.
2
referred to as delayed overshooting or forward discount puzzle, see Cushman and Zha (1997).
Most of the recent VAR studies of the open economy, including Eichenbaum and Evans
(1995), Kim and Roubini (2000) and Kim (2000) for the G7 countries, Peersman and Smets
(2002) and Smets and Wouters (2002) for the aggregate Euro area, Mojon and Peersman
(2003) for individual Euro area countries and Lindé (2003) for Sweden, have found evidence
of at least one these puzzles, which is in sharp conflict to conventional wisdom. On the other
hand, evidence of these puzzles has been so persuasive that the puzzles themselves are now
considered consensus, as is evident from the following quote in Adolfson et al. (2005, p. 37):
“Still, we find the empirical relevance of the nominal and real frictions to be such
that the impulse response functions to a policy shock are very similar to the ones generated in
identified VARs…There is, however, one exception and that is the real exchange rate.
Although the nominal frictions in the model provides some persistence in the real exchange
rate following a policy shock, it is evident that the model does not provide us with a humpshaped response of the real exchange rate which is a persuasive feature of estimated VARs.”
However, one major obstacle when taking the closed economy VAR to the open
economy, is how to properly address a possible simultaneity problem between monetary
policy and the exchange rate. In particular, almost all of the studies of open economies like
those referred to above deals with a possible simultaneity problem by either (i) restricting the
exchange rate from reacting contemporaneously to a monetary policy shock or (ii) placing
zero contemporaneous restrictions on the response of the systematic interest rate setting to an
exchange rate shock.3
The first assumption is equivalent to assuming that the exchange rate must have been
fixed for the whole period under investigation; e.g. Mojon and Peersman (2003). This
assumption is the most implausible and least used, in particular in the post Bretton Woods era
where most exchange rates have been floating. However, even in periods where the exchange
rate has been partly fixed (managed float), it is reasonable to expect a contemporaneous effect
of monetary policy actions on the exchange rate. Very few (industrialised) countries have
managed to maintain a fixed exchange rate for a prolonged period, and even less so for the set
of diverse countries analysed in Mojon and Peersman (2003) where the exchange rate puzzle
is particularly pronounced.4
The second set of restrictions implies a reversing of the contemporaneous feedback,
which is equivalent to assuming that the monetary authority ignores any surprise movement in
exchange rates that have occurred during the time in which decisions on the policy variables
are made. As will be discussed in more detail below, to assume that the policymakers do not
pay attention to surprise movements in the exchange rate when setting policy is highly
unlikely. Or, to cite Faust and Rogers (2003, p. 1406), “If literally true, this would be quite
3
Kim and Roubini (2000) provide evidence of delayed overshooting in only some individual countries
(e.g. Canada and France). However, compared to most other studies, they allow for a simultaneous
response between the interest rate and the exchange rate, and estimate instead an explicit reaction
function of the monetary authorities. However, the domestic interest rate is restricted from reacting
contemporaneously to a foreign interest rate shock, which is at odds with evidence from financial
markets data..
4
The restriction is placed on a set of diverse countries such as Finland, France, Greece, Ireland, Italy
and Spain.
3
disappointing to those of us who inform the Federal Reserve Board on a real-time intraday
basis regarding surprising movements in financial markets.”5 Empirical studies that assume
that the monetary policymaker can react to all shocks within a period except those to the
exchange rate, therefore seems implausible.
However, it is one thing to assume that the policymakers are informed on a daily
basis of surprise movements in the exchange rate. It is quite another to assume that the
policymakers will act accordingly to the news. This discussion involves two distinct and
separate issues. First, there is the issue of whether the central bank should actually target the
exchange rate above what is implied by the inflation target. From a theoretical point of view,
in the presence of complete exchange rate flexibility, the closed and the open economy
version of optimal monetary policy model can be considered isomorphic to one another.
Hence, the best outcome is found when policymakers are inward looking, solely focusing on
domestic targets (i.e. Rogoff, 2000; Clardia, Gali and Gertler, 2001).
However, empirical evidence indicates that the exchange rate is not fully flexible, and
that there are substantial deviations from the law of one price for traded goods prices (Rogoff,
1996). Under the circumstances of incomplete pass-through, the analysis of monetary policy
in an open economy will be substantial different from the one of a closed economy. In
particular, strict adherence to inward-looking policy objectives such as stabilisation of
domestic output and inflation can not be optimal when firms’ markups are exposed to
exchange rate fluctuations. Hence, the monetary authorities may attempt to affect the
expected future path of the real exchange rate (see for example Corsetti and Pesenti, 2001;
Monacelli, 2003).
Secondly, even if the exchange rate is not among the target variables, the central bank
may still pay attention to where the exchange rate is heading. The fact that the exchange rate
is determined in a forward-looking manner that reflects the expected future return on the
asset, may by itself provide important information about the expected development of the
determinants of the targeting variables.”
Thus, if the exchange rate is likely (even just in some periods) to respond
immediately to a monetary policy shock, and monetary policy may respond quickly (at least
within the month or quarter which is the usual sampling frequency in these studies), to an
exchange rate shock, the structural shocks cannot be recovered using either of the recursive
short-run restrictions on the parameters, a common practice in the VAR literature on open
economies.
This point has been forcefully made in Faust and Rogers (2003), who by relaxing
what they call dubious restrictions and imposing at most rather mild sign restrictions (or shape
restrictions) are able to test the implications of the contemporaneous restrictions most
commonly used in the VAR literature. By doing so, they find that the delayed overshooting
result is sensitive to dubious assumptions. By eliminating this assumption, their results allow
5
The view that monetary authorities pay attention to financial markets is also supported by Bjørnland
and Leitemo (2004), who show that once one allow the central bank to react immediately to news in the
financial market (and stock market in particular), the interaction between monetary policy and stock
market developments increase significantly.
4
for an early peak in the exchange rate, which might give a role for the conventional
overshooting model. On the other hand, the authors find that very little of the exchange rate
variation is due to these monetary policy shocks and that the bulk of the exchange rate
variation after a policy shock is due to large variation form UIP. Hence, the overshooting can
not be driven by the Dornbusch's mechanism.
On the other hand, using the same kind of procedure as Faust and Rogers (2003), but
imposing restrictions on the impulses responses for several periods, rather than on the impact
effect only (as is what Faust and Rogers do), Scholl and Uhlig (2005) find more evidence of
both the exchange rate puzzle as well as the delayed overshooting puzzle. However, the peak
appreciation happens somewhat faster than the three year horizon found in Eichenbaum and
Evans (1995).
There are at least two problems related to this alternative identification strategy. First,
by dropping implausible assumptions, the authors may no longer be able to identify the items
of interest. In particular, the monetary policy shock that is identified and well interpreted in
the closed economy VAR applications, may no longer be the same shocks that are studied
using this alternative restriction.
Second, in event analysis where actual monetary policy actions that are perceived as a
surprise on the market are collected and analysed, authors such as Zettelmeyer (2004) among
others finds that a surprise monetary policy shock that increases the interest rate has a
substantial appreciating effect on the exchange rate in a small open economy. This link
between surprise monetary policy actions and initial exchange rate responses could therefore
be a feature that the identified VAR models at least on impact should be able to replicate.
Studies like Scholl and Uhlig (2005) who finds that the exchange rate initially depreciates
after the contractionary monetary policy shock, is therefore highly implausible
This paper analyses the effects of monetary policy in an open economy through
structural VARs, paying particular attention to a possible interdependence between the
monetary policy stance and exchange rate movements. In particular, we impose a combination
of short-run and long-run restriction on the parameters of the VAR model, so that without
deviating too much from the existing literature, we can identify monetary policy shocks
without having to restrict the contemporaneous simultaneity between interest rate and
exchange rate movements.
The analysis is applied to Norway. To our knowledge, there have been no similar
studies of monetary policy in Norway before. On the other hand, it is only recently that
Norway abandoned a regime of targeting exchange rates, and can now be appropriately
described as following some kind of Taylor rule for monetary policy. This paper therefore
contributes to the literature on how monetary policy can be identified and analysed in a small
open economy, as well as establishing some stylized facts on the effects of monetary policy in
Norway.
We find that a contractionary monetary policy shock has the usual effects identified
in other international studies: temporarily increasing the interest rate, lowering output and a
sluggish but negative effect on consumer price inflation (and real wages). On the other hand,
5
contrary to most of the international studies, we find a substantial effect on the exchange rate
which appreciates immediately.
In section 2 we discuss the VAR methodology used to identify monetary policy
shocks and section 3 discusses the empirical results. Section 4 provides robustness checks and
Section 5 concludes.
2 The identified VAR model
In this study we explicitly account for the interdependence between monetary policy and
exchange rates within a VAR model by imposing a combination of short-run and long-run
restrictions. In particular, we build on the traditional VAR literature in that we identify
recursively a standard structure between macroeconomic variables and monetary policy, so
that monetary policy can react to all shocks, but the macroeconomic variables react with a lag
to the monetary policy shocks. However, our approach differs from the traditional method in
that we also allow monetary policy to respond to the contemporaneous exchange rate, which
itself is allowed to react simultaneously to all shocks. We must have an alternative restriction
in order to identify and orthogonalise all shocks. We therefore assume instead that monetary
policy shocks can have no long-run effects on real exchange rates. By using only one long-run
restriction, we address the simultaneity problem without deviating extensively from the
established literature (i.e., Christiano et al., 1999 for closed economies and Lindé (2003) open
economies) of identifying a monetary policy shock as an exogenous shock to an interest rate
reaction function (the systematic part of monetary policy). Once allowing for full simultaneity
between monetary policy and the exchange rate, the VAR approach is likely to give very
useful information about the simultaneous interaction between monetary policy and exchange
rates in open economies. However, given that we essentially replace one (short run)
restriction on the contemporaneous interaction between interest rates and exchange rates, with
another (long-run) restriction, the plausibility of this restriction has to be tested, through a
series of robustness tests.
The choice of variables in the VAR model are chosen to reflect the theoretical set up
of a New-Keynesian small open economy model, such as that described in Clarida, Galí and
Gertler (1999) and Svensson (2000). In particular, the VAR model comprises the log of the
annual changes in the domestic consumer price index6 (CPI) (πt) – referred to hereafter as
inflation, log of real GDP (yt), the three month (NIBOR) interest rate (it), the log of the
foreign interest rate (it*) and the log of the real exchange rate against a basket of trading
partners (et) (for details, see appendix A).7
Below we will show that a combination of short-run and long-run restrictions on the
estimated VAR model will be sufficient to allow monetary policy stance and exchange rates
to react simultaneously to the identified shocks.
6
7
Adjusted for energy price changes and taxes (CPI-ATE).
However, as is demonstrated below, other variables were also tried out.
6
2.1 Identification
Throughout this paper, we follow what has now become standard practice in VAR analysis
(see for example Christiano et al. 1999) and identify monetary policy shocks with the shock in
an equation of the form
it = f (...)t + σε tMP ,
(1)
where it is the instrument used by the monetary authority (usually the interest rate) and f is a
linear function that relates the instrument to the information set (feedback rule). The monetary
policy shock ε tMP is normalised to have unit variance, and σ is the standard deviation of the
monetary policy shock. We assume that ε tMP is orthogonal to the elements in the information
set (…). Having identified the feedback rule (from the variables that are in the information
set) the VAR approach concentrates on deviations from this rule. Hence, such deviations
provide researchers with an opportunity to detect the responses of macroeconomic variables
to monetary policy shocks that are not expected by the market. Obviously, we then assume
that the market also knows the rule.
Below we first set out to follow standard practice in many recent VAR applications,
namely to identify the different structural shocks through a series of contemporaneous
restrictions on the effects of the shocks onto the variables. In particular, it is commonly
assumed that macroeconomic variables such as output and prices do not react
contemporaneously to monetary shocks, whereas there might be a simultaneous feedback
from the macro environment to monetary variables, see for example Sims (1980, 1992), and
Christiano et al. (1999) among many others. Bagliano and Favero (1998) show that when
monetary policy shocks are identified in this recursive way on a single monetary policy
regime, these shocks suggest a pattern for the monetary transmission mechanism that is
consistent with the impulse responses of monetary policy shocks identified instead using
financial market information from outside the VAR, such as in Rudebusch (1998). This would
also limit the practical importance of the Lucas critique, since a stable regime does not require
any re-parameterization.
However, as discussed above, a more profound problem with this recursive
identification is that once one include high frequency data such as the exchange rate into the
VAR, it becomes difficult to assume an exclusion restriction between the simultaneous
response in the interest rate and the exchange rate to any kind of news.
To be able to solve this simultaneity problem, we therefore use instead a long-run
restriction that does not limit the contemporaneous response of the variables. This restriction
identifies monetary policy shocks as those shocks that have no long-run effect on the level of
the real exchange rate. This is a standard neutrality assumption in the monetary policy
literature, used among other in Clarida and Gali (1994) in a different application. It implies
that PPP will hold in the long-run, at least with respect to the monetary policy shock, which is
perfectly consistent with the Dornbusch's hypothesis discussed above.
7
Assume that Zt is the (5x1) vector of the macroeconomic variables discussed above,
which can be ordered as follows: Zt = (∆it*, ∆yt, πt, ∆it, ∆et)’, where we for now assume that
all variables but inflation are first differenced to obtain stationarity.8 The reduced form VAR
can be written in matrix form as
A(L)Zt =v t ,
∞
where A(L)=
(2)
∑A L
j
j
is the matrix lag operator, A0=I and vt is a vector of reduced form
j=0
residuals with covariance matrix Ω. Assuming A(L) to be invertible, (2) can be written in
terms of its moving average
Z t =B(L)v t ,
(3)
where B(L)=A(L)-1. The identification of the relevant structural parameters, given the
estimation of the reduced form, is a traditional problem in econometrics. A structural model is
obtained by assuming orthogonality of the structural shocks and imposing some plausible
restrictions on the elements in B(L). Following the literature, we assume that the underlying
orthogonal structural disturbances (εt) can be written as linear combinations of the
innovations (vt), i.e.,
v t =Sε t .
(4)
The VAR can then be written in terms of the structural shocks as
Z t =C(L)ε t ,
(5)
B(L)S=C(L) .
(6)
where
Clearly, if S is identified, we can derive the MA representation in (5) since B(L) can be
calculated from the reduced form estimation of (2) . Hence, to go from the reduced form VAR
to the structural interpretation, one needs to apply restrictions on the S matrix. Only then can
one recover the relevant structural parameters from the covariance matrix of the reduced form
residuals.
To identify S, we first assume that the εt‘s are normalised so they all have unit
variance. The normalisation of cov(εt) implies that SS’ = Ω. With a five variable system, this
8
This assumption is further discussed and relaxed in the empirical analysis below.
8
imposes 15 restrictions on the elements in S. However, as the S matrix contains 25 elements,
to orthogonalise the different innovations, ten more restrictions are needed. Of these, there
will be nine contemporaneous restrictions directly on the S matrix. These are consistent with a
Cholesky decomposition used on the part of the S matrix that ignores the open economy
variables, and as discussed above, are standard in the VAR literature on monetary policy
shocks. In addition we impose one commonly accepted neutrality restriction on the long-run
multipliers of the C(L) matrix, namely that a monetary policy shock can have no long-run
effects on the real exchange rate.
With a five variables VAR, we are able to identify five structural shocks; The first
two are of primary interest and can be interpreted as monetary policy shocks (εtMP) and real
exchange rate shocks (εtER). We follow standard practice in the VAR literature and only
loosely identify the last three shocks as inflation shocks (interpreted as cost push shocks)
(εtCP), output shocks (εtY) and foreign interest rate shocks (εti*). Ordering the vector of
uncorrelated structural shocks as εt = (εti*, εtY, εtCP, εtMP, εtER)’ and following the standard
literature in identifying monetary policy shocks, the recursive order between monetary policy
shocks and the macroeconomic variables implies the following restriction on the S matrix
⎡S11
⎡ ∆i *⎤
⎢
⎢ ∆y ⎥
⎢S21
⎢
⎥
⎢π ⎥ = B( L) ⎢S31
⎢
⎢
⎥
∆
i
⎢S41
⎢
⎥
⎢S
⎢⎣ ∆e ⎥⎦
⎣ 51
t
0
0
0
S22 0
0
S32 S33 0
S42 S43 S44
S52 S53 S54
0 ⎤ ⎡ε
⎥⎢ Y
0 ⎥ ⎢ε
0 ⎥ ⎢ε CP
⎥⎢
S45 ⎥ ⎢ε MP
⎢
S55 ⎥⎦ ⎢ε ER
⎣
i*
⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥⎦ t
(7)
The standard Cholesky restriction, namely to assume that macroeconomic variables do not
simultaneously react to the policy variables, while the simultaneous reaction from the
macroeconomic environment to policy variables is allowed for, is taken care of by placing the
macroeconomic variables above the interest rate in the ordering, and assuming zero
restrictions on the relevant coefficients in the S matrix as described in (7). Foreign interest
rates are placed first in the ordering, reflecting small country assumptions.
However, we are still one restriction short of identification. The standard practice in
the VAR literature, namely to place the exchange rate last in the ordering and assuming S45 =
0, (so that neither macroeconomic nor monetary variables can react simultaneously to the
exchange rate shock, while the exchange rate is allowed to react simultaneously to all other
variables), would have provided enough restriction to identify the system, thereby allowing
for the use of the standard Cholesky recursive decomposition (e.g. Lindé 2003).
However, if that restriction is not valid but is nonetheless imposed, the estimated
responses to the structural shocks will be severely biased. The standard test in the literature,
namely to include one variable above the other and then rearrange the order to test if that
makes a difference, will not produce the correct impulse responses if there is a genuine
simultaneous relationship between the two variables. Most likely it will lead to the effects of
9
the shocks being underestimated, as a recursive ordering will always either a) disregard the
simultaneous reaction of the monetary policy stance to the exchange rate shocks, or b)
exclude the simultaneous reaction of the exchange rate to the monetary policy shocks. This
will effectively be demonstrated in the next section.
Instead, we impose the restriction that a monetary policy shock can have no long-run
effects on the real exchange rate, which as discussed above, is a plausible neutrality
assumption securing PPP with respect to the monetary policy shock. This can be found simply
by setting the values of the infinite number of relevant lag coefficients in (5),
∑
∞
j =0
C54, j ,
equal to zero. By using this long-run restriction rather than a contemporaneous restriction
between asset prices and monetary policy shocks, S45 may be different from zero. However,
by using the long-run restriction, we have enough restriction to identify and orthogonalise all
shocks. Writing the long-run expression of (6) as
B(1)S=C(1) ,
(8)
where B(1)= ∑ j=0 B j and C(1)= ∑ C j indicate the (5x5) long-run matrix of B(L) and C(L)
j=0
∞
∞
respectively, the long-run restriction that C54(1) = 0 implies
B41 (1)S14 +B42 (1)S24 +B43 (1)S34 +B44 (1)S44 +B45 (1)S54 =0 .
(9)
So far, output, price and foreign interest rate shocks have been only loosely identified.
However, they can be further interpreted by examining the first three columns of S. The first
column imply that foreign interest rate are only affected by foreign monetary policy
contemporaneously, which is a plausible small country assumption. The next two columns
imply that while price shocks can affect all variables but output contemporaneously, output
shocks can affect both output and prices contemporaneously. Hence, it seems reasonable to
interpret price shocks as a cost push shock (moving prices before output), whereas output
shocks will be dominated by both demand shocks (in the short run) and supply shocks (in the
long-run).9
3 Empirical results
The model is estimated using quarterly data from 1993Q1 to 2004Q3. Using an earlier
starting period will make it hard to identify a stable monetary policy regime, as monetary
policy prior to 1993 experienced important structural changes and unusual operating
procedures. In particular, prior to 1993 Norway has been targeting the exchange rate,
implying that in some periods when there was depreciation pressure, the interest rate was
immediately increased to offset this pressure. Hence, the interest rate and the exchange rate
have been observed to move in the same direction in periods. Nevertheless, we have also
9
We have also experienced with alternating the order of the first three variables in Z, without much
effects on results.
10
experimented with an earlier starting period, 1987. With a few exceptions, this did not change
the results in any important ways (see section 4 below).
With the exception of the real exchange rate which is modelled in first differences,
the variables are modelled in levels, as is standard practice in many of the VAR models.10
However, Giordani (2004) has argued that following the theoretical model set up in Svensson
(1997) as a data generating process in monetary policy studies, rather than including output in
levels, we should either include the output gap in the VAR, or the output gap along with the
trend level of output. However, as pointed out by Lindé (2003), a practical point that Giordani
does not address is how to compute trend output (thereby also the output gap). We therefore
instead follow Lindé (2003), and include a linear trend in the VAR along with output in
levels. In that way we try to address this problem by modelling the trend implicit in the VAR.
Also, the use of a trend in the VAR serves as a good approximation for ensuring that the VAR
is invertible if the variables are non-stationary, in particular given the short span of data we
are using.
The fact that the real exchange rate is modelled in first differences implies that the
long-run restriction of monetary policy shocks on the level of the exchange rate is eventually
zero (c.f. Blanchard and Quah 1989). However, in section 4 we test the robustness of our
results to other VAR specifications, among other by investigating the time series properties
more carefully. There are no qualitative changes to the impact of the shocks.
The lag order of the VAR-model is determined using the Schwarz and Hannan-Quinn
information criteria and the F-forms of likelihood ratio tests for model reductions. A lag
reduction to two lags could be accepted at the one percent level by all tests. Using two lags in
the VAR, there is no evidence of autocorrelation, heteroscedasticity or non-normality in the
model residuals.
3.1 Event analysis
Before we start with the VAR analysis, we perform a simple event analysis similar to that of
Zettelmeyer (2004), where actual monetary policy actions that are perceived as a surprise on
the market are collected and analysed. We focus on the period since 1999, which is the time at
which Norges Bank announced (unofficially) that it was going to pursue its target of
stabilising the exchange rate by targeting a stable inflation rates vis-à-vis the trading partners.
From 2001 however, Norway formally adopted an inflation targeting framework. The
approach is described in more detail in appendix A.
We find that a surprise monetary policy shock that increases the interest rate has a
substantial appreciating effect on the exchange rate in a small open economy. In particular, a
surprise monetary policy shock in Norway that increase the interest rate by one percentage
point, implies an immediate appreciation of the exchange rate by 1-2 percentages. Hence,
10
Based the standard Augmented Dickey Fuller (ADF) unit root test, we can not reject that any of the
variables except inflation are integrated of first order. However, none of the variables are cointegrated.
The variables should therefore be represented in first differences. However, due to the low power of the
ADF tests to differentiate between a unit root and a persistent (trend-) stationary process, we can not
rule out that the variables could equally well be represented in levels, but with a trend.
11
the impact appreciation following a contractionary monetary policy is a feature that the VAR
model should be able to account for.
3.2 Cholesky decomposition
We will start by presenting exhaustive results using different Cholesky orderings and varying
the number of variables somewhat, before we discuss in detail the results using the structural
model. Since our prime interest is to understand the interactions between monetary policy and
the different macroeconomic variables in all figures we focus on illustrating the impact of the
monetary policy shock. The impact of the other shocks to the model can be obtained from the
author on request.
Figure 1 gives the impulse responses of the interest rate, exchange rate, inflation and
GDP to a monetary policy shocks (normalised so the response of the interest rate is one
percentage point the first quarter), for the basic Cholesky ordering discussed above (interest
rate ordered before the exchange rate). The upper and lower dashed lines plotted in each
graph are one-standard-error bands.11
Figure 1. Response to a monetary policy shock, using the Cholesky decomposition
a) Interest rate (percentage point)
b) Exchange rate (percentage)
1.2
1
1
0.8
0.6
0.8
0.4
0.6
0.2
0.4
0
0.2
-0.2
0
-0.4
-0.2
-0.6
-0.4
-0.8
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
1
c) GDP (percentage)
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
d) Inflation (percentage point)
0.3
0.15
0.2
0.1
0.1
0.05
0
0
-0.1
-0.05
-0.2
-0.1
-0.3
-0.15
-0.4
2
-0.2
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
The effect of the monetary policy shock increases interest rates temporarily. The exchange
rate appreciates immediately, but then depreciates back to baseline, before it appreciates and
reaches its maximum after 7 quarters. The effect thereafter dies out. Hence, there is evidence
11
They were generated from 2500 draws by Monte Carlo integrations following Sims and Zha (1999).
This is a Bayesian method based on the natural conjugate prior.
12
of delayed overshooting and if we consider the initial response as small and insignificant, also
of an exchange rate puzzle.
Despite the puzzle in the exchange rate, and consistent with other studies of small
open economies, output falls gradually and reaches its minimum after a year. The effect
thereafter quickly dies out. Inflation falls by little initially, but then reaches a minimum after
approximately two years. Interestingly, there is no evidence of any price puzzle (where prices
actually increase initially) which is commonly found in the literature. The small and sluggish
effect of the monetary policy shock on inflation has also been found in other studies of open
economies such as Lindé (2003) for Sweden, but also in traditional VARs for the US
economy such as Christiano et al. (1999) and recently Faust et al. (2004), who identify
monetary policy shocks based on high-frequency futures data.
Figure 2. Response to a monetary policy shock, using two different Cholesky orderings1
a) Interest rate
b) Exchange rate
1.2
0.25
Interest rate Ii-exc)
Interest rate (exc-i)
1
Exchange rate (i-exc)
Exchange rate (exc-i)
0.2
0.15
0.8
0.1
0.6
0.05
0.4
0
0.2
-0.05
0
-0.1
-0.2
-0.15
-0.4
-0.2
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
1)
The solid line corresponds to the Cholesky decomposition where the interest rate is ordered before the exchange
rate in the VAR. In the alternative ordering (exc-i), the interest rate and the exchange rate swap places.
If there is strong simultaneity between shocks to monetary policy and exchange rate,
we would not expect that a Cholesky decomposition of the effects on shocks would pick up
this simultaneity, since one of the shocks is assumed to have no immediate effect on one of
the variables. This is investigated in Figure 2, which shows the impulse responses for the
interest rate and the exchange rate from a monetary policy shock, using two different
Cholesky decompositions. The solid line correspond to the assumption that an exchange rate
shock has no immediate effect on the interest rate (the same assumption underlying Figure 1
and used among others in Christiano and Eichenbaum, 1995, and Lindé, 2003), whereas the
dotted line corresponds to an ordering where the interest rate and the exchange rate swap
places as the ultimate and penultimate variables, so that a monetary policy shock has no
immediate effect on the real exchange rate (as was assumed in Mojon and Peersman, 2003).
Hence, whereas in the first ordering the interest rate reacts to an exchange rate shock
with a lag (one quarter), in the second ordering the interest rate can respond immediately to an
exchange rate disturbance, but at the cost of letting the exchange rate react only with a lag to
monetary policy shocks.
Figure 2 illustrates that under the restriction that either the monetary policy shock has
no immediate effect of exchange rates or the exchange rate shock has no immediate effect on
interest rates, dose not imply a lot of difference, as the exchange rate does not appear to be
13
very responsive to monetary policy shocks. On the other hand, assuming that both the
exchange rate and monetary policy react importantly to shocks in the other sector, and
interaction is important, the restriction imposed by either Cholesky ordering will distort the
estimates of the two shocks in such a way that the degree of interaction will seem
unimportant. Hence, Figure 2 may not provide us with the true responses.
Figure 3. Response to a monetary policy shock, 8-VAR; Cholesky decomposition
a) Interest rate
b) Exchange rate
1.2
1
Exchange rate (5 VAR)
Exchange rate (8 VAR)
0.8
1
Interest rate (5 VAR)
Interest rate (8 VAR)
0.8
0.6
0.4
0.6
0.2
0.4
0
0.2
-0.2
0
-0.4
-0.2
-0.6
-0.4
-0.8
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
1
2
c) GDP, consumption and investment
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
d) Inflation and nominal wage
0.5
0.05
0
0
-0.05
-0.5
-0.1
-1
-0.15
GDP (8-VAR)
Consumption (8-VAR)
Investment (8 VAR)
-1.5
Inflation (5 VAR)
Inflation (8 VAR)
Nominal wage (8 VAR)
-0.2
-2
-0.25
-2.5
-0.3
-0.35
-3
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Leeper et al. (1996) and Faust (1998) have criticised the VAR approach for lack of robustness
when additional variables are added to the model. Before we proceed using the structural
model, we therefore investigate to what extent adding important variables will change the
overall conclusions, in particular with respect to the exchange rate. We expand the model to
an eight variables VAR (8-VAR), where we now also include consumption, investment and
the nominal wage into the model. The model resembles that of Christiano et al. (2005) for the
closed economy, (although we of course still include the open economy variables; the real
exchange rate and the foreign interest rate), and the variables are ordered equivalently in the
Cholesky decomposition.12 Figure 3 gives the responses in the different variables to a
monetary policy shock. Where relevant, we compare the impulses with the same impulses
from the 5-VAR. In Frame A we plot the response in the interest rate, whereas in frame B we
graph the response in the real exchange rate (with the original standard error bands). Frame C
12
The model is not identical to that of Christiano et al (2005), as we use nominal instead of real wage
in the VAR. However, we are in particular interested in the nominal wage, as it is identified by the
central bank in Norway as an important indicator for future inflation pressure.
14
graphs the response in GDP, consumption and investment, whereas in frame D we plot the
response in inflation and nominal wage.
Following a similar contractionary monetary policy shock as in the baseline scenario,
we find that the nominal wage respond three times more than inflation, which implies a more
persistent response in the real wage than in inflation (which is confirmed if the real wage is
included in the VAR instead of the nominal wage). Consumption falls by less than output
whereas investment falls by 3-5 times more. As before, the peak response in the real variables
is found after a year, whereas inflation (and wages) peaks after two years.
Compared to the baseline five variables VAR, we see that the responses remain as in
the baseline VAR, although the maximum impact is slightly magnified. The real exchange
rate is no exception, although it now initially depreciates, before it follows the same pattern as
previously (inside the standard error bands). Hence, adding additional variables did not solve
the exchange rate puzzle.
3.3 Structural identification scheme
The alternative to the simple Cholesky decomposition was outlined in Section 2. Figure 4
shows the impulse responses of a monetary policy shock on the interest rate, exchange rate,
GDP and inflation to a monetary policy shock (normalised so the response of the interest rate
is 1 pp. the first quarter).
As for the Cholesky decomposition, the monetary policy shock increases interest rates
temporarily. There is a degree of interest-rate inertia in the model, as a monetary policy shock
is only offset by a gradual lowering of the interest rate. The nominal interest rate returns to its
steady-state value just after a year and then goes below its steady-state value. Both the
interest-rate inertia and the “reversal” of the interest rate stance are consistent with what has
become considered known to be good monetary policy conduct. As Woodford (2003a) shows,
interest-rate inertia is known to let the policymaker smooth the effects of policy over time by
affecting private sector expectations. Moreover, the reversal of the interest rate stance, though
arriving late, is consistent with the policymaker trying to offset the adverse effects of the
initial policy deviation from the systematic part of policy.
Contrary to what has been found in other open economy studies, there is no evidence
of any exchange rate puzzle as the monetary policy shock has a strong and immediate impact
on the exchange rate, which appreciates (falls) by around 0.8 percent for each 1 percentage
point increase in the interest rate. The exchange rate remains appreciated for two quarters,
before it gradually depreciates back to baseline. Hence, by allowing the interest rate and the
exchange rate to react contemporaneously to all news, the interaction increases considerable.
These results are also consistent with what we found using the event study discussed above.
Although the exchange rate remains appreciated for a few quarters, there is however,
no evidence of the u-shaped response that has been found in other studies, hence the UIP
condition does not seem to be violated. Consistent with the strong impact on the exchange
rate, both output and inflation respond by more than in the Cholesky decomposition, and the
peak respond is delayed by 1-2 quarters. Hence, GDP peaks by approximately 0.25 percent
after 5-6 quarters and inflation by 0.1 percentage points after 11 quarters.
15
Figure 4. Response to a monetary policy shock, using the structural VAR
a) Interest rate (percentage point)
b) Exchange rate (pct.)
1.2
0.6
1
0.4
0.2
0.8
0
0.6
-0.2
0.4
-0.4
0.2
-0.6
0
-0.8
-0.2
-1
-0.4
-1.2
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
1
c) GDP (percentage)
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
d) Inflation (percentage point)
0.1
0.3
0.2
0.05
0.1
0
0
-0.1
-0.05
-0.2
-0.1
-0.3
-0.15
-0.4
-0.5
-0.2
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
4 Robustness of results [To be completed]
The robustness of the results reported above deserve further discussion on at least three
issues: i) Additional variables and sample stability, ii) the time series properties of data and
implications for the specification of the VAR, iii) the importance of using some alternative,
but equally plausible identification schemes. This is examined next.
Below we compare the response in the real exchange rate using the structural VAR, but now
allowing for some additional variables into the model. Figure 5 graphs and compare the
baseline scenario with a VAR that has added the nominal wage. Clearly, the effect remains
virtually unchanged, with an initial appreciation that remains for up to three quarters before it
depreciates back to equilibrium.
16
Figure 5. Response to a monetary policy shock, using baseline structural VAR plus model
augmented with nominal wage
0.6
Baseline
Baseline + nominal wage
st+
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
-1.2
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
5. Concluding remarks
The quantitative effects of monetary policy shocks have to a large extent been addressed in
terms of vector autoregressive (VAR) models, initiated by Sims (1980). Through the
applications of Leeper et al. (1996) and Christiano et al. (1999, 2005), one has reached a
consensus on how monetary policy affects the closed economy (like the U.S.). However,
VAR studies of the open economy have provided less of a consensus with regard to the
effects of monetary policy, and have along certain dimensions even provided some puzzling
results. In particular, many VAR studies have found that following a contractionary monetary
policy, the real exchange rate either actually depreciates, or, if it appreciates, it does so for a
prolonged period of up to three years, thereby giving a hump-shaped response that violates
the uncovered interest parity condition. Similar results have been found in a series of papers
recently. The results have been so persuasive that the puzzles themselves are instead
considered consensus (or stylized facts) of which many newly developed DSGE models may
seek to replicate.
However, there is one major obstacle when taking the closed economy VAR to the
open economy. That is, how to properly address a possible simultaneity between monetary
policy and the exchange rate. In particular, most of the studies of open economies are placing
zero contemporaneous restrictions on the response of the systematic interest rate setting to an
exchange rate shock. However, recently Faust and Rogers (2003) have shown that the delayed
overshooting feature of the open economy VAR is very sensitive to this kind of restriction.
VAR models of the open economy should therefore seek to identify monetary policy without
restricting the contemporaneous response.
17
This paper therefore analyses the effects of monetary policy in an open economy
through structural VARs, paying particular attention to a possible interdependence between
the monetary policy stance and exchange rate movements. We explicitly account for the
interdependence between monetary policy and exchange rates by imposing a combination of
short-run and long-run restrictions. In particular, we build on the traditional VAR literature in
that we identify recursively a standard structure between macroeconomic variables and
monetary policy, so that monetary policy can react to all shocks, but the macroeconomic
variables react with a lag to the monetary policy shocks. However, our approach differs from
the traditional method in that we also allow monetary policy to respond to the
contemporaneous exchange rate, which itself is allowed to react simultaneously to all shocks.
We must have an alternative restriction in order to identify and orthogonalise all shocks. We
therefore assume instead that monetary policy shocks can have no long-run effects on real
exchange rates. By using only one long-run restriction, we address the simultaneity problem
without deviating extensively from the established literature of identifying a monetary policy
shock as an exogenous shock to an interest rate reaction function (the systematic part of
monetary policy).
Once allowing for full simultaneity between monetary policy and the exchange rate,
we find that a monetary policy shock now implies a strong and immediate appreciation of the
exchange rate. However, the qualitative properties of a monetary policy shock found in the
established literature are still preserved. In particular, a monetary policy shock that increases
the interest rate temporarily lowers output and has a sluggish but negative effect on consumer
price inflation.
References
Adolfson, M., Laséen, S., Lindé J., and M. Villani (2005), “Bayesian Estimation of an
Open Economy DSGE Model with Incomplete Pass-Through” Sveriges Riksbank Working
Paper Series No. 179.
Altig, D., Christiano, L., Eichenbaum, M. and J. Lindé (2003),“The Role of Monetary Policy
in the Propagation of Technology Shocks”, manuscript, Northwestern University.
Bagliano, Fabio C. and Carlo A. Favero (1998), “Measuring monetary policy with VAR
models: An evaluation”, European Economic Review, 42, 1069-1112.
Bjørnland, Hilde C. and Kai Leitemo (2004), “Identifying the Interdependence between US
Monetary Policy and the Stock Market”, unpublished manuscript.
Blanchard, Olivier and Danny Quah (1989), “The Dynamic Effects of Aggregate Demand and
Supply Disturbances”, American Economic Review, 79, 655-73.
18
Christiano, Laurence J., Martin Eichenbaum and Charles L. Evans (1999), “Monetary Policy
Shocks: What Have we Learned and to What End?,” in John B. Taylor and Michael
Woodford, eds., Handbook of Macroeconomics. Volume 1A. New York: Elsevier Science,
1999, pp. 65-148.
Christiano, L., Eichenbaum, M. and C.L. Evans (2005), “Nominal Rigidities and the Dynamic
Effects of a Shock to Monetary Policy”, Journal of Political Economy 113, 1-45.
Clarida, R. J. Galí and M. Gertler (1999) “The Science of Monetary Policy”, Journal of
Economic Literature, 37, pp. 1661-1707.
Clarida R. and J. Gali (1994) “Sources of real exchange rate fluctuations: how important are
nominal shocks?” Carnegie-Rochester Conference Series on Public Policy, 41, 1-56.
Clarida, R. J. Galí and M. Gertler (2001) “Optimal Monetary Policy in Open Versus Closed
Economies: An Integrated Approach”, American Economic Review Papers and Proceeding,
91, pp. 248-252.
Corsetti, G. and P. Pesenti (2001) “International dimension of monetary policy”, Mimeo
University of Rome III and Federal Reserve Bank of New York.
Dornbusch, R. (1976), “Expectations and Exchange Rate Dynamics”, Journal of Political
Economy, 84, 1161-1176.
Eichenbaum, M. and C. Evans (1995), “Some empirical evidence on the effects of shocks to
monetary policy on exchange rates”, Quarterly Journal of Economics, 110, 975-1010.
Faust, Jon (1998), “The robustness of identified VAR Conclusions About Money, CarnegieRochester Conference Series in Public Policy”, 49, 207-244.
Faust, Jon (2005), Is Applied Monetary Policy Analysis Hard? Manuscript.
Faust, Jon and Jon H. Rogers (2003), “Monetary policy's role in exchange rate behaviour”,
Journal of Monetary Economics, 50, 1403-1424.
Faust, Jon, Eric T. Swanson and Jonathan H. Wright (2004), “Identifying VARS based on
high frequency futures data”, Journal of Monetary Economics, 51, 1107-1131.
Giordani, Paolo (2004), “An alternative explanation of the price puzzle”, Journal of Monetary
Economics, 51, pp. 1271-1296.
Kim (2001) JME
19
Kim, S. and N. Roubini (2000), “Exchange rate anomalies in the industrial countries: A
solution with a structural VAR approach”, Journal of Monetary Economics, 45, 561-586.
Leeper, Eric M., Sims, Christopher A. and Tao Zha, (1996), “What does monetary policy
do?” Brookings Papers on Economic Activity, 2, 1-78.
Lindé, Jesper (2003), “Monetary Policy Shocks and Business Cycle Fluctuations in a Small
Open Economy: Sweden 1986-2002”, Sveriges Riksbank Working Paper Series No.153.
Mojon B. and G. Peersman (2003), "A VAR description of the effects of monetary policy in
the individual countries of the Euro area", In Monetary policy transmission in the Euro area, I.
Angeloni, A. Kashyap and B. Mojon (eds), Cambridge University Press, chapter 3.
Monacelli, T. (2003), “Monetary Policy in a Low Pass-Through Environment”, European
Central Bank Working Paper No. 227.
Rudebusch, Glenn D. (1998), “Do Measures of Monetary Policy in a VAR Make Sense?”,
International Economic Review, 39, pp. 907-931.
Sims, C. A. (1980), “Macroeconomics and Reality,” Econometrica, 48, pp. 1-48.
Sims, Christopher A. (1992), “Interpreting the Macroeconomic Time Series Facts: The
Effects of Monetary Policy”, European Economic Review, 36, 975-1011.
Sims, Christopher A. and T. Zha, (1999), “Error bands for impulse responses”, Econometrica,
67, 1113-1157.
Smets, Frank and Raf Wouters (2002), “Openess, imperfect exchange rate pass-through and
monetary policy”, Journal of Monetary policy, 49, pp. 947-981.
Svensson, Lars E.O. (1997), “Inflation Forecast Targeting: Implementing and Monitoring
Inflation Targets,” European Economic Review 41 (6), pp. 1111-46.
Svensson, Lars E.O. (2000), “Open-Economy Inflation Targeting,” Journal of International
Economics, 50, pp. 155-183.
Walsh, Carl, (2003), “Monetary Theory and Policy”, 2nd. ed., The MIT Press.
Zettelmeyer, Jeromin (2004), “The impact of monetary policy on the exchange rate: evidence
from three small open economies”, Journal of Monetary Economics, 51, pp. 635-652.
20