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The exchange rate and the monetary transmission mechanism in Germany
F. Smets and R. Wouters
This paper was presented at the conference on General Equilibrium and
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November 1998. The other papers presented at this conference are also
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The exchange rate and the monetary transmission mechanism in Germany
Frank Smets and Raf Wouters
THE EXCHANGE RATE AND THE MONETARY TRANSMISSION MECHANISM IN
GERMANY∗
Frank Smets and Raf Wouters
ABSTRACT
For the conduct of monetary policy under floating exchange rates it is important to understand
the role of the exchange rate in the monetary transmission mechanism (MTM). The timing and the
magnitude of the effects of a change in the exchange rate on output and inflation may be quite
different from traditional interest rate channels, thereby affecting optimal policy. In this paper we
examine the exchange rate channel in the MTM in Germany by estimating an identified VAR
model. Two features of the results are highlighted. The effect of a policy shock on the exchange
rate accelerates the pass-through of policy into prices and leads to a different response of the
various components of GDP. We then show that these qualitative effects can be duplicated in a
general equilibrium model for a semi-small open economy with sticky prices and wages that is
calibrated to capture the main features of the German economy.
∗
This paper was written while the first author was at the BIS. The views espressed are solely our own, and not
necessarily those of the BIS, the ECB or the National Bank of Belgium.
Correspondence: Frank Smets, European Central Bank, Kaiserstrasse 29, D-60311 Frankfurt am Main, tel: 49-69-1344
6550, fax: 49-69-1344 6000, e-mail: [email protected]; Raf Wouters, National Bank of Belgium, tel: 32-2-221 2803,
fax: 32-2-221 3162.
-1-
INTRODUCTION
Recently an increasing number of papers have analysed the implications of the openness of an
economy for the conduct of monetary policy under floating exchange rates and explicit inflation
targeting more specifically 1. This is of considerable interest as most of the inflation targeting
regimes have been established in small open economies 2. One implication of openness is that the
conventional interest rate channels in the monetary transmission mechanism (MTM) are
supplemented by significant exchange rate channels. Understanding the role of the exchange rate
in the MTM is important because the timing and the magnitude of the effects of a change in the
exchange rate on output and inflation may be quite different, thereby affecting optimal policy.
The important role of the exchange rate in the practical conduct of policy in open economies is
also reflected in the use by a number of central banks of a so-called monetary conditions index
(MCI) – a weighted average of a short-term interest rate and an exchange rate – to assess the
stance of monetary policy. In such MCIs the relative weight on the exchange rate depends on its
relative importance in affecting aggregate demand 3.
Identified Vector Autoregressions (VARs) are a useful tool to empirically examine the MTM
because they allow to separate the endogenous reaction of the monetary authorities to
developments in the economy from exogenous monetary impulses. The estimated effects of such
policy shocks can then be used to assess the validity of calibrated dynamic general equilibrium
(CDGE) models by comparing them with the theoretical impulse response functions of those
models. In contrast to VAR-models, such structural models can be used to do policy analysis 4.
Because of its focus on the United States, both the VAR and CDGE literatures have often ignored
the open-economy aspects of the monetary transmission mechanism. For example, in the recent
extensive survey of the VAR literature on the effects of monetary policy by Christiano et al
(1998) only two pages are devoted to the open economy. More recently, an increasing number of
studies have looked at other countries than the United States and have been confronted with the
crucial role of the exchange rate in both the identification of the policy shocks and in the
transmission mechanism 5. Similarly, the question of monetary policy in an open economy has
received little attention in the CGE literature. Various authors have examined whether and how
1 See, for example, Svensson (1998), Conway et al (1998), Bharucha and Kent (1998), Ball (1998).
2 See Svensson (1998) for references to the large literature on inflation targeting.
3 MCIs therefore ignore other exchange rate channels such as the direct price effect. For a discussion of the usefulness
of MCIs see Gerlach and Smets (1998) and Eika et al (1997).
4 See Christiano et al (1998) for a lucid explanation of this research strategy in the context of monetary policy.
5 See, for example, Clarida and Gertler (1997), Bernanke and Mihov (1997), Cushman and Zha (1997), Smets (1997),
Kim and Roubini (1995) and Barran et al (1997).
-2-
two-country general equilibrium models can explain international comovements of output,
exchange rates and asset returns 6. Only a few, however, have explicitly analysed the various
exchange rate channels in a small open-economy model 7.
In this paper we attempt to fill this gap. First, we provide evidence on the role of the exchange
rate in the MTM in a relatively open economy by estimating an identified VAR model using
quarterly data series for Germany over the post Bretton Woods period. In contrast to other VAR
studies that have analysed the German economy, we focus in particular on the open-economy
aspects both by emphasising the role of the exchange rate in the identification of the monetary
policy shocks and by examining how the policy transmission through the exchange rate may alter
the effects of policy on output and prices. To do so, we analyse the effects of a policy tightening
on the different components of GDP including exports and imports and various price indices such
as the GDP deflator and export and import prices.
In the second part of the paper, we then show that the estimated qualitative effects of a policy
shock can be duplicated in a general equilibrium model for a semi-small open economy that is
calibrated to capture the main features of the German economy. Following Kollman (1997) and
Svensson (1998), the model features an open economy with two varieties of goods, domestically
produced and import goods, and with sticky prices and wages.
Several characteristics of the monetary transmission mechanism in an open economy are common
to the empirical and theoretical impulse response functions. With sticky prices, a monetary policy
tightening results in a substantial real appreciation of the exchange rate. Moreover, in the presence
of a risk premium the exchange rate may continue to appreciate before falling back to its long-run
equilibrium. This real appreciation has two clearly discernible effects. First, its immediate impact
is to lower the prices of imported goods. This accelerates the impact of a policy tightening on
consumer prices in two ways. It reduces the prices of imported consumer goods. It also reduces
the price of imported intermediate goods thereby reducing the marginal cost of firms. Second, the
loss of competitiveness following the real appreciation has substitution effects as both domestic
and foreign demand will shift towards goods produced abroad. This leads to a fall in net exports
and a fall in output putting further pressure on domestic prices.
6 See, for example, Chari, Kehoe and McGratten (1996), Backus, Kehoe and Kydland (1995), Kollman (1998).
7 Two exceptions are Kollman (1997) and Svensson (1998).
-3-
1
THE MONETARY TRANSMISSION MECHANISM IN GERMANY
In this section we describe the VAR model we use to analyse the effects of a monetary policy
shock on the German economy. We, first, describe the estimated VAR and some of the
diagnostics. Then, we discuss our strategy to identify monetary policy shocks. The basic results
are discussed in the third subsection. Finally, the fourth and fifth subsections contain some
extensions and a short evaluation of the results.
1.1
The VAR-model
The variables included in each of the estimated VAR-models can be partitioned into four groups.
The first group consists of US real GDP, y tf , and the US federal funds rate, stf . These variables
are included to capture world economic and financial conditions which are bound to have
significant effects on an open economy such as the German one 8. In all of the results reported
below we assume that both of these foreign variables are exogenous to the German block of the
VAR-model. In other words, while US output and interest rates influence the German variables,
there is no feedback from the German to the US variables (Cushman and Zha, 1997).
The second group of variables consists of the two goal variables of the central bank: German real
GDP, y t , and the German consumer price index, cpt . The third group includes the two financial
variables which capture the stance of monetary policy in an open economy: the German day-today rate, st , and the real trade-weighted DM exchange rate, xt . Finally, the last group consists of
other variables that are included in the VAR to analyse their response to a policy shock. In the
benchmark model this group includes German real net exports, nxt , German import prices, mpt ,
and German export prices, xpt 9. In the extended VARs discussed below additional variables are
included in this fourth group.
8 Initially we also included a world commodity price index. However, as removing this variable did not appear to
affect the estimated impulse responses, we excluded it from the VAR to increase the degrees of freedom.
9 To overcome the problem of the break in the statistical series due to reunification in 1991, the West-German and allGerman series on GDP, net exports and prices were spliced in the first quarter of 1991. Net exports refers to the log
difference between exports and imports of goods and services in the national accounts. The terms of trade is the
corresponding log difference between the export and import deflator. The trade-weighted DM exchange rate is
calculated by the BIS. With the exception of the interest rates, all variables are measured in percentage logs.
-4-
Using standard notation, the vector of endogenous variables in the benchmark model can thus be
[
written as: x’’t = y tf
st f
yt
cpt
st
xt
nxt
mpt
]
xpt . The benchmark VAR-
model is then given by:
xt = A( L) xt −1 + u t ,
(1)
where ut is the vector of reduced-form residuals.
Equation (1) is estimated using quarterly data over the post-Bretton Woods period 1974:1-1997:4.
In contrast to many other VAR studies on the monetary transmission mechanism, we use quarterly
data in order to be able to analyse the effects of a policy shock on the various components of GDP
which are only available on a quarterly basis. The post-Bretton Woods sample was chosen
because it captures a reasonably stable policy regime in which the Bundesbank pursued monetary
policy under floating exchange rates using money aggregates as intermediate targets. We can not
reject stability over this sample using a series of tests suggested by Bernanke and Mihov (1998).
Finally, following Sims (1980) a sequence of likelihood ratio tests was used to determine the lag
length of 3 quarters.
1.2
The identification of monetary policy shocks
In order to identify the monetary policy shocks from the reduced-form residuals in equation (1),
we use a block-recursive short-run identification scheme as in Sims (1980), Christiano et al.
(1998) and Bernanke and Mihov (1998). In this scheme the US variables are assumed to
contemporaneously cause the German variables. Similarly, German output and inflation are
assumed to be contemporaneously predetermined with respect to the two financial variables, the
German interest rate and exchange rate. In other words, the current day-to-day rate and the
exchange rate may respond to current output and inflation shocks, but not vice versa, i.e. policy or
exchange rate shocks have only lagged effects on output and inflation. Finally, in order not to
restrict the effects of a policy shock on the other variables, these are ordered last.
Within each of the blocks a recursive identification scheme which corresponds to the ordering of
the variables in equation (1) is implemented. The only exception is the identification within the
policy block, where a recursive identification structure is inappropriate. To see this, consider the
following short-run reduced-form model:
-5-
uts = α1ε tp + α 2ε tx ,
utx = β1ε tp + β 2ε tx
(2)
(3)
where the left-hand variables are the interest rate and exchange rate residuals after the effects of
the other shocks have been removed and ε tp and ε tx denote a policy shock and an exchange rate
shock respectively.
A recursive identification scheme would imply that either α 2 or β1 is equal to zero. Consider
first equation (3). Obviously, with free international capital mobility innovations in the policy rate
will have an immediate impact on the exchange rate ( β1 > 0 ) through the interest rate parity
condition. A causal ordering whereby the exchange rate innovations come before the interest rate
innovations is thus inappropriate. Alternatively, one could restrict α 2 in equation (2) to be equal
to zero, effectively assuming that the central bank does not contemporaneously respond to
exchange rate shocks. While such an assumption may be appropriate for a large, relatively closed,
economy such as the United States (Eichenbaum and Evans, 1995), it is not convincing for open
economies, in particular with quarterly data. Grilli and Roubini (1995) have shown that in open
economies this assumption can lead to an exchange rate puzzle, i.e. a tightening of the policy
instrument leads to a depreciation of the exchange rate. As discussed below this is also the case in
our data set.
Various alternative strategies have been followed in the literature to solve the identification
problem in equations (2) and (3). One commonly applied strategy is to use instrumental variables
to estimate the effect of an exchange rate shock on the interest rate ( α 2 ). Under the assumption
that the monetary authority does not directly respond to the foreign interest rate, one possible
instrument is the foreign interest rate innovation (Bernanke and Mihov (1997), Kim and Roubini
(1995) and Clarida and Gertler (1997)). The latter three studies include a bilateral dollar-DM
exchange rate in the VAR and use the US interest rate as the instrument. Because we use a tradeweighted exchange rate in our VAR, this assumption is less attractive in this paper 10.
10 When we apply this identification strategy to our data set, we find that α 2 is implausibly large, but very imprecisely
estimated. The implicit short-run weight on the exchange rate is about 0.5.
-6-
Cushman and Zha (1997) apply the Sims and Zha (1998) identification scheme to an open
economy VAR for Canada. They assume that the central bank only responds to current financial
variables (such as the exchange rate) which are contemporaneously observed. In contrast, the
central bank does not react to current output and prices which are only observed with a lag.
However, the exchange rate is affected by all variables in the VAR including current output and
prices. Under these assumptions, current output and price innovations can be used as instruments
to estimate the policy reaction to the exchange rate. Because our model is estimated on quarterly
data, the assumption that the central bank has no information about current output and prices is
inappropriate, making this identification scheme less appealing for our purposes.
Finally, a number of authors have used foreign exchange rates to identify exchange rate shocks.
Smets (1997) for France and Italy and Shioji (1998) for Spain use the bilateral dollar-DM
exchange rate as an instrument to estimate the response of policy to exchange rate shocks. For
European countries other than Germany this works nicely because of the well-known stylised fact
that changes in the bilateral dollar-DM rate often lead to pressures on their bilateral exchange rate
with the DM.
A somewhat different identification strategy is to use institutional knowledge of the central bank’s
operating procedures to distinguish policy from exchange rate shocks. Mojon (1998) uses the
spread between the day-to day rate and the tender rate to identify exchange rate shocks in France
since 1987. This procedure is attractive because a description of French operating procedures
reveals that the central bank often allowed exchange market pressures to show up in this spread.
Smets (1996) suggests that rather than estimating the response of the policy rate to exchange rate
pressures one could use the weight ( ω ) used by central banks in monetary conditions indices
(MCIs) to solve the identification problem. In this case the policy shock can be defined as:
ε tp = (1 − ω )u ts + ω u tx
(4)
Comparing equations (2) and (3) with (4), the relative weight of the exchange rate in the MCI is
given by ω = −α 2 /( β 2 − α 2 ) . Since one would expect α 2 , which captures the effect of
exchange rate shocks on the domestic interest rate, to be non-positive (an appreciation of the
exchange rate leads to a fall in policy rates) and β 2 to be positive, this weight should lie between
zero and one in a successful identification scheme.
-7-
Graph 1 Estimates of the weight on the exchange rate (ω) in Germany
(Estimation period: 1975:1-97:4)
10-year moving window estimates
2.0
1.5
1.5
1.0
1.0
Omega
Omega
Recursive estimates
2.0
0.5
0.5
0.0
0.0
-0.5
-0.5
-1.0
-1.0
1985
1987
1989
1991
1993
1995
1997
1985
1987
1989
1991
1993
1995
1997
If the value of ω were known as in Canada and New Zealand where the central banks use an MCI
as operating target variable, then the identification problem is potentially solved as one can define
the policy shock according to (4). However, the Bundesbank has never used an MCI in
conducting monetary policy. We therefore follow Smets (1997) and empirically estimate the
weight over the sample period by running the following regression using innovations in the
bilateral yen-dollar rate as an instrument:
uts = −ω /(1 − ω )utx
(5)
Over the whole sample the point estimate of ω is 0.26 with a t-statistic of 2.16. Graph 1 which
gives the recursive estimates of ω , shows that there is no evidence of instability over the sample
period. The right-hand panel which plots 10-year moving window estimates shows that the weight
was very imprecisely estimated during the 1970s, but is since then quite precisely estimated at
around 0.20. The point estimate of ω comes surprisingly close to the MCI weight that
international organisations have used to measure the policy stance in Germany 11. In what follows
we will identify a policy shock by imposing a weight of 0.25 in equation (4) 12.
11 For example, see IMF (1996, p.16) and OECD (1996, p.31)
12 The two-step procedure proposed in Smets (1997) has the advantage that in estimating the weight one can use
information that is not included in the VAR-model. In this paper we verified that including the yen-dollar rate in the
VAR-model does not materially affect the reported results.
-8-
1.3
The effects of a monetary policy shock on the German economy
Graph 2 shows the effects of a policy shock on real GDP, the CPI index, the day-to-day interest
rate, the real effective exchange rate (in the left-hand panel) and real net exports, the terms of
trade, import prices and the nominal trade balance (in the right-hand panel). First consider the
left-hand panel of Graph 2. A monetary policy tightening is characterised by a significant increase
in the day-to-day rate and a sharp real appreciation of the exchange rate. Consumer prices fall
relatively quickly and after some pause continue to fall after two years. Real GDP falls
significantly after two quarters and then returns to baseline.
Several features of these impulse response patterns are worth noting. First, the interest rate
tightening is relatively modest compared to a typical tightening in closed economy VAR-models
for the US economy (For example, Christiano et al (1998)). The policy rate increases by only 15
basis points on impact and returns to zero after three quarters. This finding is quite common in the
literature on open-economy VARs. One example is Cushman and Zha (1997), who find that a
monetary policy tightening leads to an immediate rise in the 3-month Treasury bill rate of less
than five basis points. Similarly, using a different identification scheme Kim and Roubini (1995)
estimate typical interest rate tightenings of less than 20 basis points for the G7 countries excluding
the United States. These findings are in contrast with VAR-models that treat these countries as
closed economies and do not include the foreign interest rate. For example, Gerlach and Smets
(1995) estimate three-variable identified VARs for the G7 countries and find that over the period
1979-1993 a typical policy shock consists of an interest rate tightening of more than 40 basis
points 13.
Second, while the interest rate tightening is relatively small, the effect on the exchange rate is
very strong. This is somewhat of a puzzle as the exchange rate response is much larger than one
would expect on the basis of the uncovered interest rate parity theory. In addition, the exchange
rate continues to appreciate for two quarters, which is in contrast with the overshooting
hypothesis. The hump-shaped exchange rate response to a monetary policy shock was also noted
by Eichenbaum and Evans (1995) for the United States. One possible explanation is that our
identification procedure puts too much weight on the exchange rate innovations in the
measurement of the monetary policy shock. Graph 3 plots the estimated impulse responses for
13 A likely explanation is that in this case both domestic and foreign policy shocks are included.
-9-
Graph 2 The effects of a monetary policy shock in Germany
(Estimation period: 75:1-97:4)
0.16
0.16
0.00
0.08
-0.16
Real trade balan
Real GDP
0.00
-0.08
-0.16
-0.32
-0.48
-0.64
-0.80
-0.24
-0.96
-0.32
-1.12
0
5
10
15
20
-0.00
0
5
10
15
20
0
5
10
15
20
0
5
10
15
20
0
5
10
15
20
0.75
-0.05
Terms of trade
Consumer prices
0.50
-0.10
-0.15
-0.20
0.25
0.00
-0.25
-0.30
-0.25
0
5
10
15
20
0.25
0.32
0.20
0.16
0.00
Import prices
Day-to-day rate
0.15
0.10
0.05
0.00
-0.16
-0.32
-0.48
-0.64
-0.05
-0.80
-0.10
-0.96
0
5
10
15
20
1.50
0.25
1.25
0.00
Nom. trade balan
Real exchange ra
1.00
0.75
0.50
0.25
-0.25
-0.50
0.00
-0.25
-0.75
0
5
10
15
20
different assumed weights on the exchange rate. From the second column it is clear that halving
the weight on the exchange rate, increases the size of the typical interest rate tightening, while it
lowers the effect on the exchange rate making the overall picture more consistent with interest
rate parity.
Third, in closed economy VAR-models the typical output and inflation response is that output
falls quite rapidly, while prices respond with a considerable lag and often not very significantly
(Christiano et al (1998)). In contrast, in our open economy VAR, the direct price effect of an
exchange rate appreciation on import prices is quite strong, leading to a much more rapid and
significant negative response of consumer prices. In the next subsection we analyse this direct
price channel by comparing the effects on various price indices. The crucial role of the direct
- 10 -
Graph 3 Sensitivity to different exchange rate weights
Real GDP
Omega=0.00
Omega=0.125
0.2
0.2
0.1
0.1
0.1
-0.0
-0.0
-0.0
-0.1
-0.1
-0.1
-0.2
-0.2
-0.2
-0.3
-0.3
0
5
10
15
CPI
Interest rate
5
10
15
20
0.10
0
0.05
0.05
0.05
-0.00
-0.00
-0.05
-0.05
-0.05
-0.10
-0.10
-0.10
-0.15
-0.15
-0.15
-0.20
-0.20
-0.20
-0.25
-0.25
-0.30
-0.30
5
10
15
20
10
15
20
0.36
0.30
0.30
0.30
0.24
0.24
0.24
0.18
0.18
0.18
0.12
0.12
0.12
0.06
0.06
0.00
0.00
-0.06
-0.06
-0.12
10
15
20
5
10
15
20
1.50
1.50
1.25
1.25
1.25
1.00
1.00
1.00
0.75
0.75
0.75
0.50
0.50
0.50
0.25
0.25
0.25
0.00
0.00
0.00
-0.25
-0.25
-0.25
-0.50
-0.50
-0.50
0
5
10
15
20
0
5
10
15
20
0.25
0.00
0.00
0.00
-0.25
-0.25
-0.50
-0.50
-0.50
-0.75
-0.75
-0.75
-1.00
-1.00
5
10
15
20
5
10
15
20
0.8
0.8
0.6
0.6
0.6
0.4
0.4
0.4
0.2
0.2
0.2
0.0
0.0
0.0
-0.2
-0.2
-0.2
-0.4
0
5
10
15
20
15
20
0
5
10
15
20
0
5
10
15
20
0
5
10
15
20
10
15
20
-1.25
0
0.8
-0.4
10
-1.00
-1.25
0
5
0.25
-0.25
-1.25
0
-0.12
0
1.50
0.25
20
0.06
0.00
-0.06
5
15
-0.30
5
0.36
0
10
-0.25
0
0.36
-0.12
5
0.10
-0.00
0
Exchange rate
-0.4
0
20
0.10
Trade balance
-0.3
-0.4
-0.4
Terms of trade
Omega=0.25
0.2
-0.4
0
5
10
15
20
0
5
exchange rate channel in explaining these results can also be seen from comparing the estimated
impulse responses with those obtained from assuming a zero weight on the exchange rate
innovation in the measured monetary policy shock (the left-hand column of Graph 3). Without a
positive exchange rate response prices fall much less significantly. Also note that, as in Grilli and
Roubini (1995), this identification scheme leads to an exchange rate puzzle.
The right-hand panel of Graph 2 shows the effects of the policy tightening on the real and nominal
trade balance and the terms of trade. As import prices respond much stronger to the exchange rate
appreciation than export prices, the terms of trade improves significantly. This relative price effect
leads to an improvement in the nominal trade balance. However, the real appreciation of the
exchange rate also has a strong and significant negative impact on real net exports. Overall, this
quantity effect dominates the valuation effect, so that the nominal trade balance deteriorates on
- 11 -
Graph 4 The ordering of the trade balance and the J-curve effect
Real trade balance
Base case
Reverse ordering
0.16
0.16
0.00
0.00
-0.16
-0.16
-0.32
-0.32
-0.48
-0.48
-0.64
-0.64
-0.80
-0.80
-0.96
-0.96
-1.12
-1.12
Terms of trade
0
5
10
15
1.0
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0
0.0
-0.2
-0.2
0
Import prices
1
2
3
4
5
6
7
8
9
10 11
12 13
14
15
16
17
18 19
20
-0.4
-0.4
5
10
15
0
20
0.50
0.50
0.25
0.25
0.00
0.00
-0.25
-0.25
-0.50
-0.50
-0.75
-0.75
5
10
15
20
-1.00
-1.00
-1.25
-1.25
0
Nom. trade balance
0
20
5
10
15
20
0.50
0.50
0.25
0.25
0.00
0.00
-0.25
-0.25
-0.50
-0.50
0
5
10
15
20
0
5
10
15
20
-0.75
-0.75
0
5
10
15
20
impact. Thus, in contrast to Cushman and Zha (1997) for Canada we do not find evidence of a Jcurve effect for Germany. Of course, this finding depends in part on the ordering of variables in
the VAR. If we assume that monetary policy has no immediate impact on net export volumes,
then one can get a J-curve effect as shown in Graph 4.
1.4
Extensions
In this section we analyse the effects of the policy shock on alternative price indices and the
components of GDP by including these as a tenth variable in the estimated VAR system. The lefthand panel of Graph 5 summarises the effects on various price indices. The strongest effect of the
monetary policy tightening is on the prices of tradable goods. Import prices fall on impact by
about 30 basis points and continue to fall afterwards to a maximum of 64 basis points below
- 12 -
-0.00
0.16
-0.05
0.08
-0.10
Real GDP
Consumer prices
Graph 5 Extended VAR results: effects of a policy shock
-0.15
-0.20
-0.25
-0.32
5
10
15
20
0
0.10
-0.0
0.05
-0.2
-0.05
-0.10
-0.15
10
15
20
-0.6
-0.8
-1.0
-1.2
-0.20
-1.4
-0.25
-1.6
0
5
10
15
20
0
0.32
0.32
0.16
0.16
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
0.00
0.00
-0.16
-0.16
Imports
Import prices
5
-0.4
-0.00
Exports
Export prices
0
-0.32
-0.48
-0.64
-0.32
-0.48
-0.64
-0.80
-0.80
-0.96
-0.96
-1.12
0
5
10
15
20
0
1.5
0.12
1.0
Domestic demand
0.18
0.06
GDP deflator
-0.16
-0.24
-0.30
0.00
-0.06
-0.12
-0.18
-0.24
-0.30
5
10
15
20
0.5
0.0
-0.5
-1.0
-1.5
-2.0
0
5
10
15
20
0
0.4
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
0.08
Output per man-hour
0.3
0.2
0.1
Earnings
0.00
-0.08
-0.0
-0.1
-0.2
-0.3
-0.4
-0.5
0.00
-0.08
-0.16
-0.24
-0.32
-0.40
-0.48
-0.56
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
0
5
10
15
20
baseline. Export prices also fall significantly but only after three quarters and by a maximum of
only 15 basis points. As noted before, the net impact is a significant improvement of the terms of
trade. As the consumer price index contains a significant share of imported goods, it also falls
significantly by 10 to 15 basis points in the first three quarters. Domestic prices on the other hand
do not fall on impact. In fact both the GDP deflator and nominal earnings rise in the first two
quarters after the monetary policy tightening, before falling significantly following the creation of
a negative output gap.
The right-hand panel of Graph 5 gives the effects of a policy tightening on various components of
real GDP. Due to the strong real appreciation of the DM, exports fall significantly following the
- 13 -
policy tightening. In contrast, imports only start falling when output falls after about two quarters.
As a result, the real trade balance deteriorates very significantly putting a drag on output demand.
The effect on domestic demand mirrors the development in domestic prices. Domestic demand
actually rises following the tightening, before falling significantly below baseline after about a
year. This increase in demand is visible in both consumption and investment. One potential
explanation is that the strong terms-of-trade improvement has a temporary positive effect on both
profits and wages boosting consumption and investment. Another possible explanation is that the
real appreciation creates positive wealth effects as Germany was a net foreign creditor over the
sample period. A third possible explanation is a misspecification of the policy shocks. If exchange
rate shocks also capture expected positive demand shocks, then our identification procedure may
result in a temporary rise in demand following a policy tightening.
Finally, the lower right-hand graph shows that following a policy tightening productivity falls
significantly in line with the fall in output. This suggests that there is significant labour hoarding
in response to a fall in aggregate demand.
1.5
Summary of the empirical results
Before continuing with the second part of the paper in which we discuss a DGE model for a semismall open economy such as Germany, it is useful to review the main results of the empirical
analysis that we want the CGE model to reproduce. First, the interest rate and the exchange rate
channel have different effects on the various components of GDP. While a rise in interest rates
mainly affects the interest-rate-sensitive components of domestic demand, the associated
appreciation of the exchange rate has its most important effect on net exports through relative
price effects. As a result the interest rate channel leads to an improvement of the trade balance,
while the exchange rate channel leads to a deterioration in the trade balance. Second, the
exchange rate has important direct effects on the prices of tradable goods, in particular import
prices, making the pass-through of policy to prices much more direct than in closed-economy
models.
- 14 -
2
THE MTM IN A DGE MODEL OF A SEMI-SMALL OPEN ECONOMY
2.1 A DGE model for a semi-small open economy
In this section a small general equilibrium model for an open economy with nominal rigidities is
presented. The model is a version of the one considered in Kollman (1997 and 1998) and features
monopolistic competition in both goods and labour markets. The economy produces a good that is
an imperfect substitute for a foreign imported good. The economy also imports a third good,
’energy’, that is used in fixed proportions in the production process. Nominal prices and wages are
sticky and determined through overlapping price and wage contracts à la Calvo (1983). Money is
introduced through the money-in-the-utility-function approach.
Using this model, we discuss the different channels of the monetary transmission mechanism in
an open economy. As in a closed-economy model, the real interest rate affects the intertemporal
decisions of households and firms. In addition, the associated change in the exchange rate affects
the price level directly through the import price of final goods and indirectly through the cost of
imported energy. Finally, the exchange rate also affects output and aggregate demand through
relative price and wealth effects.
In order to allow for a direct comparison of the theoretical results with the empirical VAR results,
monetary policy shocks enter the model directly through an interest rate reaction function, instead
of through the money supply equation. As the model does include a well-defined money-demand
equation, money becomes endogenous. In the impulse response functions of Graph 6 and 7 we
plot the money stock that is consistent with this reaction function 14.
Except in the market of exportable goods in which the economy faces a downward sloping
demand curve, the economy considered in this model is assumed to be small. As a result, the
world variables, and in particular the world interest rate, are considered to be exogenous. With
infinite-lived agents and standard utility functions this creates the well-known problem of
explosive solution paths for net foreign assets whenever shocks drive the domestic interest rate
away from the foreign interest rate. One commonly used solution is to assume finite-lived agents
as in Blanchard (1985). In this paper, we take a somewhat different approach by introducing net
14 Traditionally, monetary general equilibrium models of this kind have had difficulties producing a strong liquidity
effect. In our model, we get a strong liquidity effect by assuming a small consumption elasticity of money demand. In
addition, because of sticky prices, the expected inflation effect is also limited.
- 15 -
foreign assets in the utility function. This gives rise to a well-defined demand for net foreign
assets and introduces a risk-premium in the uncovered interest rate parity condition.
In what follows we present a sketch of the main building blocks of the open-economy model. A
full description can be found in Wouters (1998). Wouters (1998) also presents the response of the
economy to alternative shocks such as a productivity shock, a money demand shock, a foreign
demand shock, a public expenditures shock and an energy and foreign price shock. In addition, he
performs stochastic simulations in the face of productivity and money shocks to examine whether
the model can generate statistics that are close to the historical statistics for Germany.
2.1.1 Technologies and firms
The country produces a single final good and a continuum of intermediate goods indexed by j
where j is distributed on the unit interval ( j ∈ [0,1]). The final good sector is perfectly
competitive and uses as inputs domestic and imported intermediate goods. The final good is used
for consumption by the representative household and the government and for investment by the
firms that rent out capital. There is monopolistic competition in the markets for intermediate
goods: each intermediate good is produced by a single firm.
Final good sector
The final good is produced using domestic and imported intermediate goods in the following CES
technology:
[(
Yt = y tH
)
1 /(1+γ )
( )
+ y tF
]
1 /(1+γ ) (1+γ )
(6)
where γ is a parameter and ytH and y tF are indices of domestic and imported intermediate
goods. ytH can be written as:
y
H
t
1
=  ∫ y tH, j
0
( )
1 /(1+υ )

dj 

1+υ
(7)
where υ is a parameter, and y tH, j denotes the quantity of domestic intermediate good of type j
that is used in final goods production, at date t.
- 16 -
The cost minimisation conditions in the final goods sector can be written as:
y Hj ,t
 p Hj ,t
= H
p
 t
ytH
 pH 
=  t 
 Pt 




−
−
1+υ
υ
y tH and
(8)
1+γ
γ
Yt
(9)
where p Hj ,t is the price of the home intermediate good j , ptH is the price of the domestically
produced composite intermediate good and Pt is the price of the final good. Perfect competition
in the final goods market implies that the latter two can be written as:
1
−1 / υ
p =  ∫ (ptH, j ) dj 
0

−υ
H
t
[(
Pt = ptH
)
−1 / γ
(10)
( )
+ ptF
]
−1 / γ −γ
(11)
Intermediate goods producers
Each intermediate good j is produced by a firm j using the following technology:
y j ,t ≤ (1 + ie ) AK αj ,t H 1j−,tα ,
(12)
where y j ,t (1 + ie ) is the firm’s value-added, A is a productivity parameter, K j ,t is the physical
capital stock and H j ,t is an index of different types of labor used by the firm. This index is given
by:
H j ,t
 1 1+1φ 
=  ∫ h j ,τ ,t dτ 
 0

1+φ
,
(13)
where φ is a parameter and h j ,τ ,t is the quantity of type τ labor used by firm j at time t. Energy
is used in a fixed proportion, ie , of value-added.
- 17 -
Cost minimisation implies:
h j ,τ ,t
w
=  τ ,t
 Wt
Wt H j ,t
Rt K j ,t
=



− (1+φ ) / φ
H j ,t and
1−α
α
(14)
(15)
where Rt is the rental rate of capital, wτ ,t is the wage rate for type τ labor and Wt is an
aggregate wage index, given by:
1

−1 / φ
Wt =  ∫ (wτ ,t ) dτ 
0

−φ
(16)
Equation (15) implies that the capital-labour ratio will be identical across intermediate goods
producers and equal to the aggregate capital-labour ratio.
As the production function exhibits constants returns to scale, the firm’s average and marginal
cost are equal and given by:
MC t = AC t =
Rt
i
Wt
i
+ s t p te e =
+ s t pte e
K
H
1 + ie (1 + ie ) Ft
1 + ie
(1 + ie ) Ft
i
1
= Wt1−α Rtα (α −α (1 − α ) −(1−α ) ) + s t p te e
A
1 + ie
(17)
where Ft K and Ft H are respectively the marginal value-added of capital and labour, st is the
nominal exchange rate and pte is the foreign-currency price of energy. This implies that also the
marginal cost is independent of the intermediate good produced.
Total demand for firm j ’s good equals the sum of domestic and foreign demand:
y j ,t = y Hj ,t + x Hj ,t ,
(18)
where export demand for good j is in turn given by:
x Hj ,t
 p Hj ,t
= H
p
 t




−
1+υ
υ
xtH ,
(19)
- 18 -
and xtH is aggregate world demand for the country’s exports.
Using equations (8), (18) and (19), nominal profits of firm j are then given by:
π j ,t = ( p Hj ,t
 p Hj ,t
− MC t ) H
p
 t




−
1+υ
υ
(y
H
t
+ xtH
)
(20)
Each firm j has market power in the market for its own good and maximises expected profits
using a discount rate ( βρ t ) which is consistent with the pricing kernel for nominal returns used
by the country’s shareholders-households: ρ t + k
Vt C+ k 1
= C
, where Vt C is the marginal utility of
Vt Pt + k
consumption at time t (see section 2.1.2).
The model of price determination, inspired by Calvo (1983), assumes that firms are not allowed to
change their prices unless they receive a random 'price-change signal'. The probability that a
given price can be changed in any particular period is constant ( 1 − ς ) and determines the
fraction of all prices that are changed in each period. A producer who is 'allowed' to set a new
price at time t will maximise the following intertemporal profit function:
∞
∑ς
k =0
k
β k Et ρ t + k π t + k
(21)
Profit maximisation implies the following mark-up equation:
∞
∑β ς
i
p
H
j ,t
= (1 + υ )
i =0
i
∞
∑β ς
i
i =0
1+υ
υ
( )
E t ρ t +i p
i
H
t +i
y t +i MCt +i
1+υ
υ
( )
Et ρ t +i ptH+i
(22)
yt +i
Equation (22) shows that the price set by firm j , at time t, is a function of expected future
marginal costs. The price will be a mark-up over these weighted marginal costs. If prices are
perfectly flexible ( ς = 0 ), the mark-up will be constant and equal to 1 + υ . With sticky prices the
mark-up becomes variable over time when the economy is hit by exogenous shocks. A positive
demand shock lowers the mark-up and stimulates employment, investment and real output.
Through this last channel the model obtains a Keynesian character.
- 19 -
The definition of the price index in equation (10) implies that its law of motion is given by:
(p )
H −1 / υ
t
( )
= ς ptH−1
−1 / υ
( )
+ (1 − ς ) p Hj ,t
−1 / υ
(23)
Finally, using equations (8), (12), (15), (18) and (19) the aggregate demand for capital is given by:
 αWt
yt

K t = ∫ K j ,t dj =
(1 + ie ) A  (1 − α ) Rt
0
1



1−α
 ptH 
 H 
 pt 
−
1+ν
ν
,
(24)
where ptH is determined by the following law of motion:
1+υ
H − υ
t
(p )
( )
= ς ptH−1
−
1+υ
υ
( )
+ (1 − ς ) p Hj ,t
−
1+υ
υ
(25)
Capital rental firms
Physical capital is a homogenous factor of production that is owned by firms that rent capital to
producers of intermediate goods. Capital accumulation is given by:
K t +1 +
2
ψ (K t +1 − K t )
= K t (1 − τ ) + I t ,
2
Kt
(26)
where ψ is an adjustment-cost parameter, τ is the depreciation rate and I t is gross investment.
Capital rental firms maximise the following profit function:
∞
∑β
k =0
k
Et ρ t + k ( Rt + k K t + k − Pt + k I t + k ) ,
(27)
giving rise to the following first-order condition for capital:


R 
Qt = Et  βρ t +1 p t +1  Qt +1 − τ + t +1  ,
p t +1 


(28)
where Tobin’s Q is given by:
Qt = 1 + ψ
K t +1 − K t
Kt
(29)
- 20 -
2.1.2 The household sector
There is a continuum of households indicated by index τ . Households differ in that they supply a
differentiated type of labour. So each household has a monopoly power over the supply of its
labour. Each household τ maximises a utility function that is separable in its inputs :
( )
1
Vt =
C tτ
1−σ
τ
1−σ
1  M tτ

+κ
1 − Γ  Pt



1− Γ
1  s t Ftτ

+ι
1 − µ  Pt



1− µ
− lτ ,t
(30)
Utility depends on consumption of goods, Ctτ , real cash balances, M tτ / Pt , real net foreign
assets, st Ftτ / Pt and labour supply lτ ,t . In the benchmark parameterisation the utility function is
linear in leisure. Together with the assumption of indivisible labour, this yields an infinite macroeconomic elasticity of labour supply. Households act as price-setters in the labour market.
Household τ ’s intertemporal utility function is given by:
∞
Et ∑ β jVtτ+ i ,
(31)
k =0
where β is the discount factor.
Households hold money balances M t , domestic government bonds Bt , foreign interest bearing
bonds Ft and domestic equity Vt . Bonds are one-period bonds with price bt for the domestic
bonds and f t for the foreign bonds. The budget constraint faced by the household is then given
by:
w
Bτ
Fτ
Vτ Mτ
Bτ
Fτ
Vτ
M tτ
+ bt t + st f t t + d t t = t −1 + t −1 + s t t −1 + d t t −1 + τ ,t lτ ,t − C tτ − Ttτ
Pt
Pt
Pt
Pt
Pt
Pt
Pt
Pt
Pt
(32)
Households maximise the objective function (31) subject to the intertemporal budget constraint
(32) and the demand for their labour given in equation (14). As in the goods market, we assume
that wages can only be changed after some random 'wage-change signal' is received. The
probability that a particular household can change its nominal wage in period t is constant and
equal to 1 − ξ . A household τ which receives such a signal in period t, will thus set a new
nominal wage wτ taking into account the probability that it remains unchanged in the future.
- 21 -
This maximisation yields the following first-order conditions for consumption, wealth allocation
and wage-setting, where λt is the Lagrange multiplier, it is the nominal rate of return on
domestic bonds ( 1 + it = 1 bt ) and itF is the foreign-currency rate of return on foreign bonds
( 1 + itF = 1 f t ):
c
V t = λt
(33)
 λt +1  Vt MIP λt
βE t 
=
+
pt
pt
 pt +1 
(34)
λ
 λ
βEt  t +1 (1 + it ) = t
 pt +1
 pt
(35)
 λ t +1 st +1
Vt sF P λt
F 
βE t 
(1 + it ) +
=
pt
pt
 pt +1 s t

(36)
λ d  λ
βEt  t +1 t +1  = t
 pt +1 d t  pt
(37)
∞
wτ ,t = (1 + φ )
1+φ
φ
t +i
Et ∑ β ξ W
i
i =0
∞
i
1+φ
φ
t +i
E t ∑ β i ξ iW
i =0
H t +i
VC
H t +i t +i
Pt +i
(38)
Combining equations (33) and (35) gives the usual first-order condition for consumption growth.
Equations (33), (34) and (35) together result in a money demand equation. Real money holdings
depend on consumption, with an elasticity that is possibly smaller than one, and the velocity of
money depends positively on the interest rate. Equations (35) and (36) give the uncovered interest
rate parity condition for nominal exchange rate determination augmented with a risk premium
reflecting the household’s preference for net foreign assets. Equation (37) shows that the expected
holding return on equity equals the expected one-period interest rate under certainty equivalence.
- 22 -
Note that equations (33) to (37) have been written in aggregate terms, i.e. the household’s
subscript τ has been deleted. Under the assumption that, first, markets are complete and thus
consumption growth across households is perfectly correlated and, second, each household starts
with the same initial wealth, consumption and asset allocation will be the identical across
households (Erceg, 1997).
Finally, equation (38) shows that the nominal wage at time t of a household τ that is allowed to
change its wage is set so that the present value of the marginal return to working is a mark-up
over the present value of marginal cost (the subjective cost of working)
15
. When wages are
perfectly flexible ( ξ = 0 ), the real wage will be constant mark-up over the ratio of the marginal
disutility of labour and the marginal utility of an additional unit of consumption.
Given equation (16), the law of motion of the aggregate wage index is given by:
(Wt )−1 / φ
= ξ (Wt −1 )
−1 / φ
+ (1 − ξ )(wτ ,t )
−1 / φ
(39)
2.1.3 The government sector
For completeness and to get a realistic representation of the final demand components, we also
introduce a government sector. However, by assuming that all taxes are lump-sum and that the
households have infinite horizons, the behaviour of the private sector will not be affected. The
government has to satisfy the following budget restriction:
bt Bt = Bt −1 + − ,
Gt T t
pt
pt
(40)
which states that the primary deficit, G − T , and the debt service has to be financed by the
emission of new public debt Bt at the current price bt . To rule out explosive debt dynamics, the
following endogenous tax behaviour is assumed:
B
B0 
,
Tt = g  t −
p
p
t
t


(41)
where the reaction coefficient g is greater than the real interest rate ( g > i − π ). This ensures a
15 Standard RBC models typically assume an infinite supply elasticity of labour to get realistic business cycle
properties for the behaviour of real wages and employment. An infinite supply elasticity limits the increase of marginal
costs and prices following an expansion of output in a model with sticky prices, which helps generating real persistence
of monetary shocks. The introduction of nominal wage rigidity in this model makes the simulation outcomes less
dependent on this assumption as wages and the marginal cost become less sensitive to output shocks at least over the
short term.
- 23 -
stable public debt at the long term objective B o .
2.1.4 The balance of payments and foreign demand
The accumulation of foreign assets Ft is determined by the current account relation:
s t f t Ft s t Ft −1 ptH H
ptF F
pte
=
+
xt − s t
y t − st
IEt
Pt
Pt
Pt
Pt
Pt
(42)
The net foreign asset position depends on the interest payments on existing net foreign assets and
the trade balance, which is given by the difference between the real value of exports, X tH , and
the real value of imports of final goods, Yt F , and energy inputs, IE t . Energy acts only as an input
in the production process:
IEt =
ie
yt
1 + ie
(43)
The demand for exports is a function of the terms of trade ( st ptF / ptH ) and demand in the rest of
the world ( ROWt ):
x
H
t
 pH
=  t F
 st p t
−ϑ

 ROWt

(44)
2.1.5 Market equilibrium
The final goods market is in equilibrium if production equals demand by consumers, the
government and the capital accumulation firms:
Yt = C t + Gt + I t
(45)
The capital rental market is in equilibrium when the demand for capital by the intermediate goods
producers equals the supply by the capital rental firms. The labour market is in equilibrium if
firms’ demand for labour equals households’ supply.
Monetary policy is described by a simple reaction function for the interest rate with stochastic
shocks, ε tmp :
it = g (it −1 , y t y t − 4 , pt pt − 4 , ε tmp )
(46)
- 24 -
In order to maintain money market equilibrium, the money supply adjusts endogenously to meet
the money demand at those interest rates.
In the capital market, equilibrium means that the government debt is held by domestic investors at
the market interest rate it (assuming that the country is in a net foreign asset position), and that
the net foreign assets are held by investors at the going interest and exchange rates (including a
risk premium).
2.1.6 The parameterisation of the model
In the benchmark model the following values for the parameters are assumed. The share of capital
α in production is set at 0.35 and the parameter for the cost of capital adjustment is 10. In the
utility function, we set the coefficient of relative risk aversion σ equal to 2, the coefficient on
money balances, Γ , equal to 10, and the coefficient on net foreign assets, µ , equal to 100. The
choice of the coefficient of relative risk aversion and the consumption elasticity of the money
demand equation guarantees that a monetary expansion will result in a negative liquidity effect on
interest rates. The coefficient on net foreign assets is chosen so that in the benchmark case
uncovered interest rate parity almost holds.
The structure of final demand is given by the following steady-state assumptions: final import/gdp
= 0.15, energy import/gdp = 0.10, export/gdp = 0.25, consumption/gdp = 0.58, investment/gdp =
0.22, government expenditures/gdp = 0.20 and net foreign assets/gdp = 0.4. The discount factor is
set at 0.99, the rate of depreciation is 0.02 and the capital/gdp ratio is 11.0. The import and export
price elasticities are respectively set at 0.33 and 0.90. This corresponds to empirical estimates in
export and import equations for Germany as, for example, reported in Bundesbank (1998). The
long run coefficients on inflation and growth in the interest rate reaction function correspond with
those proposed by Taylor (1983). The coefficient on the lagged interest rate equals 0.85.16
In order to get a specification in which monetary expansions result in persistent effects on real
growth and inflation, we set the probability of price and wage changes equal to 0.2, which falls
within the acceptable region of empirical estimates. In this case the average duration for a fixed
price and wage contract is equal to (1-0.2)/0.2 or four quarters, which is comparable with one-
16 See Clarida et al (1997) and Peersman and Smets (1998) for estimates of the Bundesbank’s monetary policy
reaction function.
- 25 -
year Taylor-type contracts. In similar models, King and Watson (1996) use a value of 0.1,
whereas Galí and Gertler (1998) estimate a value of 0.2 in an empirical model for the US.
In general, the parameters reflect the economic structure of a large open economy such as
Germany17. The model is linearized around the steady state and solved numerically using the
Troll software.
2.2 The effects of a monetary policy tightening
2.2.1 The benchmark results
Graph 6 plots the impulse response functions to a 100 basis points shock in the interest rate.
Due to the interest rate smoothing in the central bank’s reaction function and the response to
output growth and inflation, the interest rate gradually falls back to baseline after about five
quarters. Money supply responds negatively on impact as a result of the decline in money demand
following the interest rate increase.
The exchange rate shows a strong appreciation following the restrictive monetary shock. As in
Dornbusch (1976), Chari et al. (1996) and Kollman (1997) the exchange rate overshoots its long
run equilibrium level, so that the model is potentially able to explain the high volatility of nominal
and real exchange rates. In line with the appreciation of the exchange rate, the price of imported
energy and imported final goods drops quite dramatically. As a result, the price of final
expenditures (consumer prices) falls more strongly and quicker than the price of domestically
produced goods, wages and the value added deflator. In fact, when we include backward-looking
behaviour in the price and wage equations (not reported), we can get a situation in which the
value-added deflator increases before falling in line with the other prices, which is what we found
in the VAR results for Germany as reported in Graph 5. In sum, the relative ranking of the various
price effects in the theoretical model is very similar to that in the empirical VAR results for
Germany.
Also in line with the empirical results, the terms of trade improves considerably as import prices
react much more strongly than export prices which are partially determined by slowly changing
domestic costs. This relative price effect results in an immediate and strong fall in exports, which
is consistent with the empirical findings of Section 1. Imports first decrease following the
17 Wouters (1998) compares the statistics of an extensive list of real and nominal variables generated by stochastic
simulations of the model with productivity and monetary supply shocks with the historically observed statistics of these
variables in Germany.
- 26 -
Graph 6 The MTM in a DGE-model for a semi-small open economy
Benchmark case
Interest rate
Money
Output
Exchange rate
2.5
2
1.5
1
0.5
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
-0.5
-1
-1.5
Consumer prices
Domestic-goods prices
Wages
Value-added defl.
1.0000
0.5000
0.0000
-0.5000
-1.0000
-1.5000
-2.0000
-2.5000
-3.0000
-3.5000
-4.0000
-4.5000
Consumption
Investment
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Exports
Imports
Total imports
0.5000
Import prices
0.0000
0.5000
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
0.0000
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
-0.5000
-1.0000
-0.5000
-1.0000
-1.5000
-1.5000
-2.0000
-2.5000
-2.0000
Interest rate
Inflation
Real interest rate
Expected appreciation
Net-exports
Trade balance
Terms-of-trade
2.0000
1.5
1.5000
1
1.0000
0.5
0
-0.5
0.5000
1 2
3 4
5 6
7 8
9 10 11 12 13 14 15 16 17 18 19 20
0.0000
-1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
-1.5
-0.5000
-2
-1.0000
Average mark-up
Marg. Prod. of Labour
Producer wage
Energy cost
Output
Capital
Labour
0.0000
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1.0000
-0.5000
0.8000
0.6000
-1.0000
0.4000
-1.5000
0.2000
-0.4000
21
19
17
15
13
9
7
5
11
-0.2000
3
1
0.0000
-2.0000
-2.5000
- 27 -
contraction of domestic demand, but then start increasing as the relative price effect dominates the
demand effect. The latter pattern does not correspond to the empirical impulse response of
imports shown in Graph 5. Because the empirical output effect of the monetary policy tightening
is much more persistent, the effect on imports actually never turns positive in the empirical
response functions. In both the theoretical and empirical response functions, net exports fall quite
significantly.
However, in contrast to the empirical results, the positive terms-of-trade effect dominates the
negative volume-effect in the determination of the nominal trade balance during the first four
quarters. Only after two years the nominal trade balance becomes negative. The trade balance
therefore follows a typical J-curve effect in response to a monetary policy shock. Preliminary
analysis suggests that this behaviour of the trade balance is quite robust to changes in model
assumptions and parameter values including the import and export price elasticities.
In sum, the DGE model appears to capture the open-economy aspects of the monetary
transmission mechanism in a large open economy quite well. The failure to capture the dynamics
of the transmission process of a monetary policy shock has more to do with the lags and the
persistence in the effects of a policy shock on output and inflation. As in most of the DGE
literature, the maximum effect of policy on output and inflation is contemporaneous, which is
clearly in contradiction with most of the empirical literature on the MTM (Christiano et al.
(1998)) 18. Another counterfactual result is the fact that labour employed falls immediately with
the fall in demand. Given the assumed Cobb-Douglas production function, this gives rise to an
immediate increase in labour productivity, which contradicts the fall in output per hour shown in
Graph 5.
2.2.2 Some sensitivity analysis
Graph 7 compares the effects of a policy shock in the benchmark model with those in a more
closed economy, in which the share of exports and imports in GDP is halved compared to the
benchmark case. Due to the lower import content the negative effect of a policy shock on prices is
18 Much of the current research on DGE models focuses on this issue. For example, Estrella and Fuhrer (1998) discuss
the ability of the Calvo model of price setting to match the inflation persistence in the data. Various extensions of the
basic DGE model have been proposed to increase the persistence of the output effects. For example, Jeanne (1998)
shows how the response of output to monetary shocks in a model with nominal friction in the goods market becomes
large and persistent if it is amplified by real-wage rigidity in the labour market. Fuhrer (1998) illustrate the role of habit
formation in the consumption decision to get a gradual and hump-shaped response of real variables to monetary policy
shocks. Rotemberg and Woodford (1997) assume that real decisions are made two periods in advance to get a realistic
delay in the response of the economy to monetary disturbances.
- 28 -
Graph 7 The effect of a policy shock in a more closed economy
27
25
23
21
19
17
15
13
9
11
-0.2000
7
0.0000
1
5
1.2
3
Output
1
Interest rate
-0.4000
0.8
-0.6000
0.6
-0.8000
0.4
-1.0000
27
25
23
21
19
17
15
-0.2
13
9
11
7
5
-1.4000
3
-1.2000
0
-1.6000
Exchange rate
Consumption
0.1000
2.5000
19
21
23
25
27
21
23
25
27
23
25
27
17
15
-0.2000
1.0000
-0.3000
0.5000
-0.4000
-0.5000
27
25
23
21
19
17
-0.6000
17
11
9
7
5
3
0.0000
-0.1000
1
27
25
23
21
19
17
15
13
11
9
7
5
3
1
0.0000
15
Net exports
Prices
13
15
13
11
9
7
5
3
1
0.0000
-0.2000
-0.3000
-0.4000
-0.2000
-0.3000
-0.4000
-0.7000
-0.5000
-0.6000
-0.7000
-0.8000
-0.8000
-0.9000
-0.5000
-0.6000
Terms-of-trade
Exports
Imports
0.5000
2.00000
1.00000
-1.0000
0.50000
-1.5000
27
25
23
21
19
17
15
13
11
9
7
5
3
1
0.00000
-2.0000
21
19
17
15
11
9
5
1
-0.5000
3
0.0000
1.50000
7
-0.1000
19
1.5000
13
-0.1000
11
9
7
5
1
3
0.0000
2.0000
13
1
0.2
- 29 -
reduced. Also the effect on net exports is less in absolute value. This is, however, mostly due to
the less pronounced effect on imports. Exports themselves are hardly affected.
Graph 8 shows the effect of introducing a more significant risk premium by lowering the
coefficient, µ , on net foreign assets in the utility function from 100 to 2. In the latter case, the
impulse response functions reveal a significant violation of the uncovered interest rate parity
condition. Consistent with the empirical findings discussed above, the initial exchange rate
appreciation is followed by a further appreciation before the exchange rate falls back to its longrun equilibrium. This result is due to the presence of a risk premium in the interest rate parity
condition which is a function of the net foreign asset position (expressed in domestic currency).
An appreciation of the domestic currency reduces the ratio of foreign assets to total wealth,
thereby reducing the risk premium. As a result, investors accept a lower expected return on
foreign assets. Equilibrium is achieved by a further appreciation of the domestic currency which
allows for a relative rise in domestic interest rates.
The persistent effect on the exchange rate gives rise to a much more persistent negative effect on
net exports. However, this does not translate into a more persistent effect on output. As show in
Graph 8, the effect on net exports is compensated by a less persistent effect on consumption.
Finally, Graphs 9 and 10 compare the benchmark simulation with two alternative degrees of wage
and price rigidity. In Graph 9 the alternative model is one in which prices are much more flexible
( ς = 0.8 ). In Graph 10 the alternative model is one in which wages are much more flexible
( ξ = 0.8 ). Graph 9 shows that higher price flexibility considerably reduces the output effects.
Prices adjust quite rapidly to their new long-run level and the terms of trade is much less affected.
As a result net exports fall much less.
As shown in Graph 10, higher wage flexibility has qualitatively very similar effects. As in Erceg
(1997), the main effect of wage rigidity is to make the output effects of a monetary policy
tightening much more persistent.
- 30 -
Graph 8 The exchange rate channel and the risk premium
27
25
23
21
19
17
15
13
9
11
7
5
3
1
27
25
23
21
-1.2000
-0.2
19
-1.0000
0
17
-0.8000
0.2
15
-0.6000
0.4
13
-0.4000
0.6
9
0.8
11
-0.2000
7
0.0000
1
1
1.2
5
Output
3
Interest rate
-1.4000
Exchange rate
Consumption
0.2000
2.5000
0.1000
2.0000
21
23
25
27
23
25
27
23
25
27
17
15
21
-0.3000
19
-0.2000
0.5000
19
1.0000
13
-0.1000
11
9
7
5
1
3
0.0000
1.5000
-0.4000
27
25
23
21
19
17
15
13
11
9
7
5
3
1
0.0000
-0.5000
Net exports
Prices
0.0000
17
15
13
11
9
7
5
3
-0.2000
1
27
25
23
21
19
17
15
13
11
9
7
5
3
1
0.0000
-0.2000
-0.4000
-0.6000
-0.4000
-0.8000
-0.6000
-1.0000
-0.8000
-1.2000
-1.4000
-1.0000
-1.6000
Exports
Terms-of-trade
Imports
1.0000
2.00000
0.5000
1.50000
-1.5000
27
25
23
21
19
17
15
13
11
9
7
5
3
1
0.00000
-2.0000
21
19
17
9
7
5
15
-1.0000
13
0.50000
11
-0.5000
3
1
0.0000
1.00000
- 31 -
Graph 9 The MTM with higher price flexibility
27
25
23
21
19
27
25
23
21
-1.4000
Exchange rate
19
21
23
25
27
19
21
23
25
27
23
25
27
17
15
11
9
-0.1000
1.0000
7
0.0000
1.5000
5
0.1000
2.0000
1
2.5000
3
Consumption
13
17
15
13
9
11
7
5
3
1
19
-1.2000
-0.2
17
-1.0000
0
15
-0.8000
0.2
9
-0.6000
0.4
11
-0.4000
0.6
7
0.8
5
-0.2000
3
0.0000
1
1
1.2
13
Output
Interest rate
-0.2000
0.5000
-0.3000
27
25
23
21
19
17
-0.4000
-0.3000
-0.4000
-0.5000
-0.6000
-0.7000
-0.8000
-0.9000
17
11
9
7
5
3
0.0000
-0.1000
-0.2000
-0.3000
1
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-0.4000
-0.5000
-0.6000
-0.7000
-0.8000
-0.9000
Terms-of-trade
Exports
Imports
0.5000
2.00000
1.00000
-1.0000
0.50000
-1.5000
27
25
23
21
19
17
15
13
11
9
7
5
3
1
0.00000
-2.0000
21
19
17
15
13
11
9
5
1
-0.5000
3
0.0000
1.50000
7
0.0000
-0.1000
-0.2000
15
Net exports
Prices
13
15
13
11
9
7
5
3
1
0.0000
- 32 -
Graph 10 The MTM with higher wage flexibility
23
25
27
25
27
25
27
25
27
21
23
23
23
19
21
21
27
25
23
21
19
17
15
13
9
11
7
5
3
-1.4000
Consumption
Exchange rate
1.0000
17
15
13
9
7
-0.1000
5
0.0000
1.5000
1
2.0000
3
0.1000
2.5000
11
1
17
-1.2000
-0.2
19
-1.0000
0
19
-0.8000
0.2
15
-0.6000
0.4
13
-0.4000
0.6
9
0.8
11
-0.2000
7
0.0000
1
1
1.2
5
Output
3
Interest rate
-0.2000
0.5000
-0.3000
27
25
23
21
19
17
-0.4000
17
11
9
7
5
3
0.0000
-0.1000
1
27
25
23
21
19
17
15
13
11
9
7
5
3
1
0.0000
-0.2000
-0.3000
-0.4000
-0.5000
-0.6000
-0.7000
-0.8000
-0.7000
-0.8000
-0.9000
-0.9000
Terms-of-trade
Exports
Imports
0.5000
2.00000
1.00000
-1.0000
0.50000
-1.5000
27
25
23
21
19
17
15
13
11
9
7
5
3
1
0.00000
-2.0000
21
19
17
15
13
11
9
5
1
-0.5000
3
0.0000
1.50000
7
-0.1000
-0.2000
-0.3000
-0.4000
-0.5000
-0.6000
15
Net exports
Prices
13
15
13
11
9
7
5
3
1
0.0000
- 33 -
CONCLUSIONS
In this paper we focused on the effects of a monetary policy shock in a large open economy like
Germany and the role of the exchange rate channel in the MTM in particular. Using an identified
VAR-model we show that a monetary tightening leads to a strong and prolonged real appreciation
of the DM exchange rate. This appreciation strengthens the effects of policy on prices through its
direct impact on imported goods prices. It also has a strong and significant effect on net exports
through the relative price effect. We then show that the estimated qualitative effects of a monetary
policy tightening in Germany can be duplicated in a general equilibrium model for a semi-small
open economy with sticky prices and wages that is calibrated to capture the main features of the
German economy.
- 34 -
- 35 -
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- 39 -
COMMENTS ON ‘THE EXCHANGE RATE AND THE MONETARY TRANSMISSION
MECHANISM IN GERMANY’ BY FRANK SMETS AND RAF WOUTERS
Antti Ripatti
In their paper “The exchange rate and the monetary transmission mechanism in Germany” Frank
Smets and Raf Wouters (hereafter SW) discuss an important aspect of the monetary transmission
mechanism in an open economy. By representing a set of stylized facts using VAR and drawing
on the German data and by deriving a corresponding dynamic stochastic general equilibrium
(DGE) model, they make a significant contribution to better understanding the functioning of
monetary policy in an open economy framework. The subject is a very challenging one since open
economy issues add to the complexity of the identification of the empirical model and the general
equilibrium framework. The work is pioneering in many respects: there are not many examples of
measuring monetary policy shocks where the central bank has to take the exchange rate channel
into account. The complexity of the DGE modelling easily explodes as the number of sectors in
the economy increases. Despite of the notable progress made by SW, there is still room for some,
hopefully, minor criticism.
1 The VAR, ‘monetary policy shock’ and the (near) unit roots
The study has two parts. The first part contains the impulse responses to ‘monetary policy shocks’
from the VAR with German variables. The second part contains the impulse responses to
‘monetary policy shocks’ from a DGE model. Since the methodology of the study is to compare
the impulse responses generated by two dissimilar models, I think it would be useful to try to
clarify what is meant by the ‘monetary policy shock’ in each model. The study follows Smets
(1997) in identifying the ‘monetary policy shock’ in the VAR; it is a weighted average of the
reduced form interest rate and exchange rate innovations. The chosen weight corresponds to
monetary conditions index (MCI) with a weight of four. This means that a one percentage point
unanticipated change in the day-to-day interest rate corresponds to a four per cent unanticipated
- 40 -
change in the trade weighted-exchange rate index 1. According to the identification scheme, when
generating a surprise the Deutsche Bundesbank is greatly influenced by unforeseen changes in the
exchange rates. This contradicts the rhetoric of the Bundesbank, which does not rely on the
exchange rate target but on monetary targeting. I believe there is room for more discussion of the
motivation for the applied identification scheme.
According to graph 3, the impulse responses are sensitive to the choice of MCI weight ω. All the
important responses (real GDP, CPI, trade balance, terms-of-trade) are influenced by the choice of
weight. Particularly the persistency of the responses is enhanced by the exchange rate channel.
The impulse responses differ somewhat from those of Grilli and Roubini (1996). However, one
should bear in mind that the studies have a different data set and a different identification scheme.
The differences are most striking in the impulse response of the USD/DEM exchange rate to the
monetary policy shock. SW report a significant appreciation whereas the exchange rates response
in Grilli and Roubini’s study does not differ significantly from zero. Grilli and Roubini’s impulse
responses (table 3, 1996) are closer to SW’s alternative where ω = 0 , i.e. the case where
monetary policy is not influenced by exchange rates.
The impulse responses of some variables decay slowly (unfortunately the time span of the figures
covers only five years). This suggests that the system might contain permanent shocks, which is
an indication of the nonstationarities in the data set at hand. It is quite likely that – within the class
of linear models - the data can be characterized as integrated processes.
It is also very likely that there is cointegration among the chosen variables. According to the
Granger representation theorem, the estimated VAR can be inverted and impulse responses
computed. The study would benefit from consideration of nonstationarity and cointegration.
Abadir et al (1998) shows that the unit root might cause a substantial bias in the VAR parameter
estimates even in moderate sample sizes 2. They also show that those transformations, which
1
The idea of using the MCI as a reference for monetary policy stance builds on the open economy IS-AS analysis
where both the short-term interest rate and the exchange rate influence inflation and output. It has been argued that there
is no change in monetary policy, if there is no change in the MCI, i.e. changes in exchange rates can be ‘sterilized’ by
the changes in the short-term interest rate. The size of such a change is given by the MCI weight. Consequently, the
pure monetary policy shock is the one that influences the level of MCI – not interest rates alone.
2
The bias is an increasing function of the VAR dimensions and a nonmonotonic function of the sample size. The bias
problem remains even in the near unit root cases (see Abadir and Hadri, 1998).
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move data significantly away from the unit roots (or near unit roots), e.g. the determination of the
cointegrating rank may reduce the bias and the potential for nonmonotonicities. In the present
study, the bias-problem is exacerbated by the fact that the dimension of the system is large. The
benefits of taking the (near) unit root issue seriously are also emphasized by Phillips (1998). He
notes (on page 45) that ‘Our asymptotic analysis shows that in nonstationary VAR models with
some roots at or near unity the estimated impulse response matrices are inconsistent at long
horizons and tend to random matrices rather than the true impulse responses.’
These empirical issues cast some doubts on the estimated impulse responses. Based on the present
study we do not know if the inconsistencies between the theoretical and the empirical models are
due to the specification of the theoretical model or the econometric problems of the empirical
model. That is, we do not know whether our measurement or the theoretical benchmark is wrong.
2 DGE model
The dynamic stochastic general equilibrium (DGE) model presented by SW is very rich. The
economy has three types of firms: final good producers who sell on the domestic market only but
who face foreign competition; intermediate good producers who may export as well; and a capital
renting firm. The economy is a semi-small open economy, where the semi stands for the fact that
the exporting firms face a downward-sloping demand curve. In other respects, it is like a small
open economy. The utility of the households contains consumption, leisure time, real money
balances and real foreign assets. The model also contains rigidities in price formation, wage
formation and in adjusting capital stock. Monetary policy follows a Taylor rule type of behaviour.
I would like to touch on these last two properties of the model. The issues of the presence of
foreign assets in the utility function and the monetary policy rule are discussed in more detail
below.
The inclusion of foreign assets in the utility function is motivated by the forward premium puzzle
3
. The foreign assets in the utility function create intrinsic demand for these assets and, hence,
3
Grilli and Roubini (1996) summarize the puzzle as follows: “If uncovered interest parity holds, a positive innovation
in domestic interest rates relative to foreign ones should be associated with a persistent depreciation of the domestic
currency after the impact appreciation, as the positive interest rate differential leads to an expected depreciation of the
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introduce a risk premium into the uncovered interest rate parity (UIP) relationship. One of the
main advantages of DGE models is that they can be used for performing welfare analysis. By
including additional factors in the utility function, this novel feature of DGE models is damaged.
Obstfeld and Rogoff (1998) offer another – more elegant and preferable – choice for generating
forward risk premia. They simply use the second order Taylor approximation of the first order
condition of their open economy DGE model, which – as in SW – contains imperfect competition
and price friction.
Another issue, related to the comparison of impulse responses, is the modelling of monetary
policy. SW assume that the Bundesbank follows a Taylor-rule type of monetary policy but with
additive uncertainty. They assume quite strong interest rate smoothing 4 behaviour; otherwise the
weights on inflation and GDP growth are as proposed by Taylor. There is, however, no guarantee
that the specified monetary policy rule determines price level. Given the fairly short impulse
responses this feature cannot be inferred from the graphs. In addition, it is somewhat odd that the
MCI approach that is used in the empirical section is not used in the theoretical section.
3 Comparison of the empirical and the theoretical model
The paper could be improved significantly with respect to the examination of the fit of the
theoretical model. It would be of value to the reader if at least some of the key impulse responses
in the empirical and theoretical models were plotted in the same graph. Now only laborious shape
comparison is possible. This informal, subjective comparison lacks statistical foundation. There is
room for statistical inference here. There are examples and methods of performing such inference
(see, e.g., by Watson 1993, Diebold et al 1998 and Ortega 1998 and the references therein).
currency. However, the data show that a positive interest differential is associated with a persistent appreciation of the
domestic currency for periods up to two years after the initial monetary policy shock.”
4
The strong interest rate smoothing might arise from the fact that the policy rate (i.e. repo rate in Germany) is kept fixed
in the period between interest rate changes (although in Germany the variable rate repo is occasionally applied).
Nevertheless, the policy rate (or shock to the policy rate) should be modelled rather as a jump process than a linear
autoregressive process.
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Graphing the impulse responses of the empirical and theoretical models in the same figure
5
reveals some inconsistencies. First, the theoretical model has some difficulties in replicating the
persistency of responses in the empirical model. As discussed by the authors, an obvious example
is GDP. Whereas in the empirical model it is almost constant during the first two quarters after the
monetary policy shock, in the theoretical model it declines instantly. This might be due to the fact
that in the theoretical model there is a strong and immediate decline in consumption and
investment (and in exports), and hence in domestic demand. In the empirical model, domestic
demand increases in the first two periods. Moreover, the output effect of the monetary policy
shock is fairly persistent in the empirical model but not in the theoretical model. The observed
delayed output effect might have something to do with the pricing-to-market behaviour in exports,
adjustment costs in investment (not only in capital stock) and/or the liquidity constraint on
consumers, whose intertemporal consumption path is not directly influenced by the interest rate
shocks. However, when included in the DGE model, any of these features would further
complicate such a model.
As reported by the authors, the response of imports is another problematic feature in the
theoretical model. Given the structure of the theoretical model the source of the problem might lie
either in the relative prices of imports, in the elasticity of substitution between imported and
domestic products or in aggregate demand. The lagged response of imports in the empirical model
(imports do not respond within the first two quarters) possibly has the same roots as in the output
case. This is because the theoretical model succeeds in replicating the impulse response pattern of
the terms of trade (i.e. the relative price) well but not the output response.
I may summarize my discussion as follows: the study has the very ambitious task of measuring
the monetary policy shock in a semi-small open economy and building a DGE model to study the
empirical facts analytically. The study succeeds in augmenting our knowledge in that field.
However, I have doubts about the econometric methods applied in estimating the impulse
responses since the empirical model does not take into account the very important – cointegration
– feature of the data. This is surprising since there is now wide knowledge of the (near) unit roots
and cointegration. It seems, without any reference to any metric, that the theoretical model
succeeds in predicting many measured empirical regularities. I still have some difficulties in
5
Because of the different definition of shocks (and difficulties in interpreting their magnitudes) this may not be a
straightforward task.
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understanding the motivation of the identification of the monetary policy shock in both models. I
consider that these issues need more clarification since the goal of the paper is to study the
monetary policy transmission mechanism.
- 45 -
References
Abadir, K. M., K. Hadri, and E. Tzavalis (1999): ‘The influence of VAR dimensions on
estimator biases’, forthcoming in Econometrica.
Abadir, K. M. and K. Hadri (1998): Is more information a good thing? Bias nonmonotonicity in
stochastic difference equations, mimeo, University of York.
Bundesbank (1995): Demand for money and currency substitution in Europe. Monthly Report,
the Deutsche Bundesbank, 33-49.
Diebold, F. X., L. E. Ohanian, and J. Berkowitz (1998): ‘Dynamic Equilibrium Economies: A
Framework for Comparing Models and Data’, Review of Economic Studies, 65, 433-452.
Grilli, V. and N. Roubini (1996): ‘Liquidity models in open economies: Theory and empirical
evidence’, European Economic Review, 40, 847-859.
Obstfeld, M. and K. Rogoff (1998): Risk and exchange rates, NBER Working Paper 6694.
Ortega, E. (1998): Assessing the fit of simulated multivariate dynamic models, Documento de
Trabajo 9821, Banco de España.
Phillips, P.C.B: (1998): ‘Impulse responses and forecast error variance asymptotics in
nonstationary VARs’, Journal of Econometrics, 83, 21-56.
Smets, F. (1997): ‘Measuring monetary policy shocks in France, Germany and Italy: the role of
exchange rate’, Swiss Journal of Economics and Statistics, 133, 597-616.
Watson, M. (1993): ‘Measures of fit for calibrated models’, Journal of Political Economy, 101,
1011-1041.