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\title{On the European Monetary System: \\
the Spillover Effects of German Shocks and Disinflation}
\author{by\\Julius Horvath$^\&$\\\\Magda Kandil$^{\&\&}$\\and\\
Subhash C. Sharma$^{\&}$\\\\$^\&$ Department of Economics\\
Southern Illinois University\\
Carbondale, IL 62901\\\\
$^{\&\&}$ Department of Economics\\
University of Wisconsin-Milwaukee\\
Milwaukee, WI 53201}
\begin{document}
\maketitle
\newpage
\begin{abstract}

We analyze the disinflationary experience between 1979-1993 for two
traditionally inflationary
countries of the European Monetary System: France and Italy.  For
each country, a
vector autoregressive model is estimated.  Shocks in the
model combine domestic and foreign sources.  The latter capture the
world oil price shocks as well as nominal and real shocks originating in
Germany.
Under investigation is the hypothesis that shocks originating in Germany
have a spillover disinflationary effect in France and Italy.  The empirical
evidence provides support to the validity of this hypothesis.
Furthermore, German shocks account
for an important share of the total price variance in France and Italy.
These results indicate that the
interaction between countries of the European Monetary System has
contributed to the success of the disinflationary experiences of the
eighties.  The evidence sheds, therefore, some light on potential
benefits that may be further realized as countries of the European Monetary
System move towards their objective of achieving a single currency under
a unified monetary system.
\end{abstract}
\newpage
\baselineskip=22pt
\section{Introduction}
The monetary system of the western European countries can be broadly
characterized as a system of two exchange rate regimes: the managed
float relative to the U.S. dollar and the fixed, but adjustable, peg
in the European Monetary System (EMS).  Most of the Western European
countries opted for a fixed, but adjustable, exchange rate regimes in
the late 1970s.  This system was motivated by the desire of these
countries to guarantee the stability of the intra European trade.
Subsequently, the EMS has evolved in 1979 as a set of arrangements that
include the exchange rate mechanism.
According to this arrangement, currencies of member countries
could not fluctuate
around fixed parities by more than \underline{+} 2.25\%.\footnote{For
some currencies this band was wider
with a maximum of \underline{+} 6 percent.
If the bilateral rates diverge from the agreed parity, both central
banks
would begin
symmetric compulsory intervention with the aim to bring
the exchange rate close to its fixed parity.  In July 1993,
these bands were
widened to \underline{+}
15 percent.  Our sample period does not
capture the span after the summer of 1993.}
Adjustments of these pegged rates were possible with the mutual agreement
of all countries involved.\footnote{From its beginning there were around
a dozen of major alignments, most of them at the beginning of the functioning
of the EMS.}
Given this arrangement, there are two
interesting aspects that pertain to
the functioning of the EMS: policy
coordination among the EMS member countries and its impact on the evolution
of inflation in some member countries.
\par Inflation rates of some member countries of the European Monetary
System (EMS) declined from peaks well above 10\% in the early 1980s to
2-3\% in the 1990s.  This decline has occurred when inflation rates all
over the developed world have decreased.  Nonetheless, since low inflation
rates have occurred within the EMS, it has led to opinions that there are
features in the EMS arrangements that have facilitated, or at least
contributed to the success of the disinflation process.
\par
The European
Monetary System consists of eight countries:
Belgium, Denmark, France, Germany, Ireland, Italy, Luxemborg, and the
Netherlands.
This set of countries contains some traditionally inflationary
countries, as Italy, France, and Ireland,
countries with distinguished anti-inflationary bias, as Germany, and
countries in between as the four countries of the core.  When the EMS was
founded in March 1979, there was a wide range of inflation rates among the
members.  Germany was at the low end, with an average inflation rate of
4 percent,
while France and Italy were at the other
extreme, with an average inflation rate of 13 percent for Italy and
slightly under 10 percent for France.  The rates for other members, such as
Belgium, Denmark, and the Netherlands were between 6.5 percent and 8.9
percent; Collins (1990).  In this paper, we concentrate on the relationship
between the low inflation country, Germany, and the inflation-prone
countries, France and Italy.\footnote{Despite Ireland's
historical inflationary experience, Ireland is not connected to Germany
as France and Italy, which are geographically much closer.  In addition,
France, Germany and Italy are the cornerstone of the European integration.
They have been members of the European Community since 1956.  In contrast,
Ireland joined the European Community much later (in the 1970s).}
\par
Traditionally, when there was a possibility of realignments, or under
flexible exchange rate regimes, countries like France and Italy, had relatively
high inflation,
despite the efforts of their governments to decrease the inflationary
trend.\footnote{Among the incentives for the
government to inflate
are usually domestic political distortions, strong trade
unions, and expansionary government policies.
``This happens because the public understands
such incentives, anticipates the actions of monetary authorities and
effectively neutralizes them, with the result that higher inflation is
generated....."(Giovannini, 1992, p. 803). } Thus, it could be argued that
relatively high inflation in France
and Italy before the 1980s resulted from credibility problems.  In other
words, both governments lacked strong commitment to monetary discipline.
Indeed, Fischer (1987) described the European Monetary System as ``an
arrangement for France and Italy to purchase a commitment to low inflation
by accepting German monetary policy."\footnote{The quotation is based
on Giavazzi and Giovannini (1989, p. 85).}
\par How does the working of the European Monetary System provide
commitment for disinflation?
Two explanations are commonly offered in the literature with respect to this
question.  Frattiani and von Hagen (1992) summarize them into cooperative
and disciplinary interpretations of the EMS.  The cooperative interpretation
assumes that monetary policies were formed as a joint effort of member
governments, while
the disciplinary interpretation stresses the ``spillover
effect" stemming from the presence of the Bundesbank in the system.
The first approach is expected to maximize the role of domestic policies and,
subsequently, domestic shocks in determining the success of the domestic
disinflation policy in the high inflation countries of the EMS.  In contrast,
the second approach is expected to maximize the role of the German monetary
policy, and subsequently German monetary shocks in determining the success
of the domestic disinflation policy in the high inflation countries of the
EMS.
\par There are strong points that argue for the validity of both approaches.
The establishment of the EMS was the result of efforts of a number of
countries that aimed at establishing joint monetary policy as the outcome
of a cooperative decision-making process of all member countries.  Indeed,
some authors (see, e.g., Melitz (1988) and Fratianni and von Hagen (1992))
are of the opinion that the EMS was characterized by cooperation in terms
of monetary policies.
However,
advocates
of the disciplinary view recall that
previous fixed exchange rate arrangements
were characterized by
a hegemonic solution in which one country, usually the largest one,
independently determined monetary policy for the system as a whole.
Similar to the position of the Great
Britain in the classical gold-standard period, or the United States in the
Bretton Woods period, Germany
in the European Monetary System
is seen as the hegemonic country, the inflationary
anchor of the system.  In words of Giavazzi and Giovannini (1989) ``Germany
is the center country and runs monetary policy for the whole system."
\par From a practical standpoint,
it is possible for the German dominance
to arise within the European Monetary System.  If there is a fixed exchange
rate arrangement among n countries, there are only n-1 exchange rates
to be fixed.  Thus, assuming that n-1 countries exhibit monetary policy
aimed at maintaining the pegged exchange rate, then the nth country
could pursue an independent monetary policy.  Why Germany is the proper
candidate to play hegemonic role in the formulation of European monetary
policies?  Among the arguments for German dominance, usually the size of
the German economy and the high credibility of the Bundesbank are mentioned.
The credibility argument rests usually on Barro and Gordon (1983) who
showed that the credibility of the monetary authority is crucial in determining
the inflationary trend in a country.
It is, therefore, plausible to perceive a scenario in which countries with
traditionally higher inflation, by joining the EMS, actually delegated part
of their monetary autonomy to the Bundesbank and achieved lower inflation
in return.  As suggested by Thygesen (1988, p. 5-6): ``By pegging to the
less inflationary currencies over long intervals, with the prospect that they
cannot fully devalue in accordance with their excess inflation on the
infrequent occasions of a realignment, the authorities of the weaker
currencies gain credibility for their disinflationary stance."
\par Giavazzi and Giovannini (1989) argue that Germany was the only member
country in the EMS whose domestic monetary conditions were relatively
unanffected by the events originating from other member countries.  They
showed that the difference between onshore and offshore Deutschemark interest
rates were considerably less affected in times of realignments than the
French or the Italian interest rates.
They concluded that German monetary policy was more independent of international
conditions than was the French or the Italian policy.  Cohen and
Wyplosz (1989) use a vector autoregressive model of interest rates and
monetary base to test the German dominance hypothesis.  Their conclusion
was that German monetary variables affect nominal variables in the other
EMS countries.  Fratianni and von Hagen (1992) use a vector autoregressive
model to estimate cross-country monetary base growth rates.  They refuted
the hypothesis of German dominance, ``these results do not imply dominance
by the DM area, but they tell us that there is indeed a large degree of
conformity of EMS policies with regard to outsiders."
\par As to the success of the disinflation policy within countries of the
EMS, Collins (1988) agreed that there is no overwhelming evidence that the
EMS members performed substantially better than non-EMS members in decreasing
inflation rates in the period under consideration.  Frankel and Phillips
(1991)
did not find support for the idea that imported credibility has helped
to decrease inflation rates in France and Italy.  They emphasized the change
in domestic government policies with respect to their support of the EMS
as the factor behind disinflation.  This argument rests on the fact that the
EMS was initially quite soft as a disinflationary mechanism.  Major
alignments occurred between 1979 and 1983.  During that time, the French
and Italian governments did not keep the nominal exchange rates pegged for
too long as they were prepared for adjustments if the pressure on the
exchange rates was considered excessive.  In March 1983, the French
government decided to hold firmly on the pegged rates.  The Italian
government decided in a similar spirit somewhat earlier.
 \par In an effort to reconcile the previous differences,
 the present investigation
 will aim at developing direct evidence on
the
effect of German monetary dominance in determining disinflation in other
EMS member countries.
Specifically, we focus on the relative importance of domestic cooperative
policies versus German spillover policies in determining
disinflation in the two traditionally inflationary countries of the
EMS: France and Italy.  Towards this objective, we devise a model that
includes five shocks:\footnote{
Traditionally, models of exchange rates, as for example, Fleming and
Mundel model, would suggest that the importance of foreign shocks on the
inflation rate depends on the exchange rate regime.  Fixed exchange rate
regimes, as in
the EMS, are supposed to lead to the transmission of inflation
from one country to another, while flexible exchange rates would insulate the
economy from the outside disturbances.  The theoretical work of Turnovsky
(1981) and Marston (1985) in the traditional Mundell-Fleming setting with
rational expectations, and of Stockman and Svensson (1987) and Svensson and
van Wijinbergen (1989) in intertemporal optimization setting showed that
insulation of the home economy from foreign disturbances, even under
flexible exchange rates, applies only for some special cases.  For a more
elaborate discussion of this topic, see, for example, Genberg, Salemi and
 Swoboda
(1987).  The views also widely differ in assessing the role of the
exchange rate regime in a disinflation process.}
shocks originating from the world oil market, real
and monetary shocks originating from Germany, and real and nominal shocks
originating from the home country.  The investigation will then focus on
analyzing the effects of these shocks on price inflation in France and Italy.
\section{Empirical Framework}
The disciplinary interpretation of the EMS stresses that the decreased
inflation rate in France and Italy hinges on the effects of the shocks
originating in Germany.
This explanation implies a large weight of German disturbances in explaining
domestic prices in France and Italy.  In contrast, the cooperative
interpretation of the EMS suggests that the decreased inflation rate in
the 1980s is primarily attributable to the change in domestic economic
policies.  That is, German disturbances
are likely to have a low weight in explaining domestic prices in France and
Italy.
\par To shed some light on these alternative hypotheses, we examine
a multivariate system that includes the real world oil price (WOP), the real
gross domestic product in 1990 constant prices of Germany (GRGDP),
seasonally adjusted narrow money of Germany (GNM), real gross domestic
products in 1990 constant prices
for France (FRGDP) or Italy (IRGDP),
and the consumer price index for France (FCPI) or Italy (ICPI).
Our objective is to examine the sources of disturbances that affected
the inflation rate in Italy and France.
The data are quarterly from 1979.I to 1993.II.  All data are taken from
{\em International Financial Statistics} available from the International
Monetary Fund.
\par The world real oil price represents changes in prices of basic
commodities which could have an impact on the domestic price level
as supply components or through their impact on
the prices of domestic substitutes.
The EMS began to function at the beginning of 1979 during the second
world oil
price shock.  However, during
most of the 1980s, the real oil price was
more or less stable and somewhat declining in real terms.  Real GDP in
Germany approximates real
(supply-side) shocks.  Real output growth keeps prices from rising in
Germany which is likely to have a spillover disinflationary effect on
prices in other member countries of the EMS according to the disciplinary
explanation of disinflation.  Shocks to the narrow money of Germany are
included to test for the spillover disinflationary effect of German
monetary policy.  In addition to foreign shocks, inflation is likely to
vary in response to real and nominal domestic shocks.  Shocks to real
GDP approximate real domestic supply shocks.  Output expansion is likely
to moderate domestic price inflation.  In addition shocks to the consumer
price index approximate domestic nominal shocks.  These shocks capture
the effects of
domestic spending as well as
demand-side policies that aim at controlling price inflation.
\par In order to
approximate relations among
domestic and foreign shocks in the model,
we rely on recently developed
techniques for imposing long-run constraints.  First,
we estimate
a vector autoregressive model and impose the constraints implied by
structural relations among the model's variables.
Secondly,
we estimate a
vector autoregressive model and impose the constraints implied by the
long-run cointegration results
among the model's variables.
Having imposed the relevant constraints, we approximate the effects of the
model's shocks on price inflation using the impulse response function.
In addition, we rely on the variance decomposition results to measure
the share of the model's shocks to total price variability.
\section{Methodology and Empirical Results}
The variables of interest are
denoted in the empirical model as follows:
the world real oil price $(O^f)$,
real output in Germany $(Y^f$), the money supply in Germany $(M^f)$,
domestic real output in Italy or France $(Y^d)$, and the domestic price
level in Italy or France $(P^d)$ where the superscript $f$ denotes
foreign
variables
and the superscript $d$ denotes domestic
variables.
Let $X=(O^f,Y^f,M^f,Y^d,P^d)'$ and $u=(u^{Of},u^{Yf},u^{Mf},u^{Yd},u^{Pd})'$
is the vector of five disturbances.  We assume that these five disturbances
are uncorrelated and, therefore, their covariance matrix is diagonal, i.e.,
$E(u_tu'_t)=\Sigma,$ which is assumed to be diagnonal and $Eu_tu'_s=0$
for $s\neq t$.  Alternatively, shocks are normalized such that $E(u_tu'_t)=I$.
\par The variables in $X$ contain unit roots.  However, $\Delta X_t$
is stationary
(see Table 1 for details)
and we assume that it follows a stationary process of the form:
\begin{equation}\Delta X_t=A(L)u_t=\sum_{j=0}^\infty
A_ju_{t-j},\end{equation}
where $A_{j}$ are matrices in the lag operator $L$.  In detail, (1) is
written as:
\begin{eqnarray}\Delta O^f_t&=&a_{11}(L)u^{Of}_t+a_{12}(L)u^{Yf}_t+
a_{13}(L)u^{Mf}_t+a_{14}(L)u^{Yd}_t+a_{15}(L)u^{Pd}_t\\
\Delta Y^f_t&=&a_{21}(L)u^{Of}_t+a_{22}(L)u^{Yf}_t+
a_{23}(L)u^{Mf}_t+a_{24}(L)u^{Yd}_t+a_{25}(L)u^{Pd}_t\\
\Delta M^f_t&=&a_{31}(L)u^{Of}_t+a_{32}(L)u^{Yf}_t+
a_{33}(L)u^{Mf}_t+a_{34}(L)u^{Yd}_t+a_{35}(L)u^{Pd}_t\\
\Delta Y^d_t&=&a_{41}(L)u^{Of}_t+a_{42}(L)u^{Yf}_t+
a_{43}(L)u^{Mf}_t+a_{44}(L)u^{Yd}_t+a_{45}(L)u^{Pd}_t\\
\Delta P^d_t&=&a_{51}(L)u^{Of}_t+a_{52}(L)u^{Yf}_t+
a_{53}(L)u^{Mf}_t+a_{54}(L)u^{Yd}_t+a_{55}(L)u^{Pd}_t\end{eqnarray}
where $a_{ij}(L)=\sum_{k=0}^\infty a_{ij,k}L^k$.
Furthermore, we also adopt the notation that $a_{ij}(1)$ is the sum of all
coefficients and gives the effect of $u_{jt}$ on variable $i$ over time.
\par
In order to decompose disturbances in the variables into the five sources
specified in the model, restrictions on the multivariate dynamic system in
(1) are necessary.
To assure the exogeneity of the shocks in the VAR model,
the relationship between variables
will be analyzed under two sets of constraints:
(i) theoretical constraints, as implied by the
assumptions of structural relationships
among the model's variables,
and (ii) atheoretical
constraints,
as implied by the results of cointegration tests
among the model's variables.
\subsection{Imposing Structural Constraints}
In model (1), we assume
the following constraints:
\begin{itemize}\item $u_t^{Of}$ is exogenous to the remaining four variables
in a sense that in the long-run the remaining four macro variables have no
impact on the world real oil price.  This assumption yields four restrictions.
\item Real output and the monetary aggregate in Germany (the hypothesized
more dominant country in the EMS) are not affected in the long-run by
movements of variables from less dominant countries.  These assumptions
yield four restrictions.
\item The aggregate supply curve is vertical in the long-run for Germany.
This implies that in the long-run, the effect of monetary shocks on real
output vanishes.  This assumption yields one restriction.
\item The aggregate supply curve is vertical in the long-run for the home
country.  This implies that in the long-run, the effect of domestic nominal
shocks on real output vanishes.  This assumption yields one restriction.
\end{itemize}
\par In
order to identify the model, we can estimate a finite order VAR, i.e.,:
\begin{equation}\Delta X_t=\sum_{i=1}^nB_i\Delta X_{t-i}+e_{t}
\end{equation}
\par
The estimation of the VAR model in (7) requires, however,
that we determine the
appropriate lag length of the variables in the model
where the maximum lag length $n$ is chosen such that the residuals $e_t$
are white noise.
We use the likelihood
ratio test, as outlined in Hamilton (1994), p. 296-8.\footnote{In this
test, we use a modification of the likelihood ratio test to take into account
the small sample bias, as suggested by Sims (1980, p. 17).}
Table 2 presents the results of the likelihood
ratio tests for lag determination.
The null hypothesis that a set of variables is generated from a VAR system
with $n$ lags is tested against the alternative specification of $n_1$
lags where $n<n_1$.
Based on the Chi-square significance level, there is a clear support for
the null hypothesis of four lags for France.  For Italy, the evidence
appears less conclusive.  The probability of accepting the null hypothesis
of four lags is the largest.  Nonetheless, the difference in probability
of accepting the null hypothesis of four lags is not largely pronounced
compared to the probability of accepting the null hypothesis of two lags.
We determined the optimal lag length to be four lags, however.
Choosing a lag span shorter than one year would probably not provide for
significant dynamics of the system and more lags will take away too many
degrees of freedom.\footnote{We do not allow for different lag length
since it is common to use the same lag lengths for all equations in order
to preserve the symmetry of the system.
For previous applications
of this approach, see, .e.g., Bayoumi and Eichengreen (1992) and
Blanchard and Quah (1989).}
Since the
elements of $\Delta X_t$ are stationary, the system in (7) can be inverted
to obtain an infinite order MA representation, i.e.,:
\begin{equation}\Delta X_t=e_t+C_1e_{t-1}+C_2e_{t-2}+....\end{equation}
Comparing (1) and (8), we observe that $u$, the vector of original
(structural) disturbances and $e$, the vector of innovations are
related, i.e.,:
\begin{equation}e_t=A_0u_t,\end{equation}
and $A_j=C_jA_0$ for all $j$.  Thus, knowing $A_0$, we can recover $u$ from
$e$, and also obtain $A_j$ from $C_j$.  Furthermore, from (9) we also note
that:
\begin{equation}E(e_te_t')=\Omega=A_0E(u_tu_t')A'_0=A_0A_0'\end{equation}
Since $\Omega$ is a symmetric matrix with known elements, it imposes 15
restrictions on the matrix of contemporaneous effects, $A_0$, which has
25 elements.  Additional ten restrictions are needed to identify $A_0$, so
that the orthogonal shocks $u_{it}$ can be recoverd using equation (9).
The traditional method is to pick $A_0$ as the Choleski factorization of
$\Omega$ which has been criticized on the grounds that it imposes an
arbitrary structure on the orthogonal $u_{it}$ sequences.  Blanchard and
Quah (1989) propose an interesting way of circumventing the problem of
arbitrary identification.  This can be seen from the relationship between
the matrices of long-term effects.
If we evaluate the polynomials embedded in equations (1) and (8) at
$L=1$, and note the relationship that $A_1=C_1A_0$, where $C_1$
contains known elements.  Once $A_0$
is identified, one can recover the orthogonal shocks using equation (9).
In order to identify the shocks, we impose the following ten restrictions
on the long-run matrix $A(1)$, which were discussed earlier.
Note that these restrictions transform $A(L)$ at $L=1$ into:
\begin{equation}
\left[
\begin{array}{c c c c c }
a_{11}(1)&0&0&0&0\\
a_{21}(1)&a_{22}(1)&0&0&0\\
a_{31}(1)&a_{32}(1)&a_{33}(1)&0&0\\
a_{41}(1)&a_{42}(1)&a_{43}(1)&a_{44}(1)&0\\
a_{51}(1)&a_{52}(1)&a_{53}(1)&a_{54}(1)&a_{55}(1)\\
\end{array}\right]\end{equation}
Furthermore, the above restrictions on the long-run sum of impulse responses
imply nothing about the effect of shocks on prices.  Instead, the model
allows the estimation of the weight of domestic and foreign factors in
determining inflation
in France and Italy.
\par Once the VAR is estimated and the reduced-form shocks are obtained,
we proceed with the second step,
we
recover
the structural shocks.
This identification procedure guarantees that
the shocks are not correlated among each other by imposing structural
 constraints
on the long-run relation between the reduced-form shocks.
Figures 1 and 2 give
the impulse response functions of price inflation in Italy and France to
innovations in all five variables.
The impulse response functions appear similar for all five variables in both
countries.
Two shocks are driving
the domestic price level upward: domestic nominal shocks and real
world oil
price shocks.
In addition, output growth is disinflationary in both countries, as evident
by the negative response of price to the shocks to the growth of domestic
real output.
More importantly, the results using structural VAR provide
support to the spillover disinflationary effect of German shocks.
The response of price inflation to monetary and real
shocks originating from Germany is negative
in France and Italy.
That is, output growth in Germany is an important factor in controlling
price inflation that has a strong spillover effect on disinflation in
France and Italy.  In addition, the design of monetary policy in Germany
that aims at controlling price inflation has had a strong spillover effect
on disinflation in France and Italy.
\par In the next step, we calculate the percentage of the expected
n-period ahead squared forecast error (variance decomposition) of price
in Italy and France, as produced by the innovation in the structural
model of (9).
The results are represented in Table 3.
The weights of real and nominal shocks
originating from Germany account
for a large share of price
variability.  Specifically, the proportion of price variance in France
associated with German shocks ranged from 62.78 percent after two quarters
to 67.99 percent after 24 quarters.  In Italy, the proportion of price
variance associated with German shocks ranged from 28.53 percent after
two quarters to 41.72 percent after 24 quarters.  In addition, real oil price
shocks are an important determinant of price variability which is
particularly evident for Italy.  The share of world real oil price of
price variability ranges from 10.56 percent after two quarters to 6.01
percent after 24 quarters in France.  In contrast, this share ranges from
26.44 percent after two quarters in Italy to 25.15 percent after 24
quarters in Italy.  The proportion of price
variance in France associated with domestic real and nominal shocks
ranges from 26.65 percent after two quarters to 26.00 percent after 24
quarters.  In Italy, the proportion of price variance associated with
domestic real and nominal shocks ranges from 45.02 percent after two
quarters to 33.13 percent after 24 quarters.
\par Overall, the evidence
imposing structural constraints provides strong support to the
disinflationary share of German shocks in determining price variability
in France and Italy.  Specifically, imposing structural constraints
isolates exogenous shocks originating in
Germany, which appear important in explaining a large share
of price variability in France and Italy over time.
In addition, the structural constraints account for the dependency of
domestic shocks on German shocks in the long-run.  By accounting for
this dependency, the exogenous component of domestic shocks appears less
important in explaining price variability in France and Italy over time.
\par In summary, the impulse response functions
from the structural VAR model indicate that
innovations from domestic nominal variables and from world
real oil price exhibit an upward effect on price inflation in France and
Italy.  In contrast,
the effect of
nominal and real shocks originating from Germany is
negative on price
inflation in France and Italy.
In addition, the results of variance decomposition indicate
that the exogenous
shocks originating from Germany, not only drive the price level
downward, but also explain quite a large part of the total variation of
price.
\subsection{Imposing Cointegration Constraints}
\par Since variables in log levels are non-stationary, we need to consider
the long-run constraint implied by cointegration, i.e., whether the
nonstationarity in level is due to a smaller number of common stochastic
trends.
\par The test for cointegration follows the suggestions of Johansen (1988).
Consider the unrestricted VAR from equation (7):
$$X_t=\sum_{i=1}^nB_iX_{t-i}+e_t$$
This model can be represented in the form:
\begin{equation}\Delta X_t=\sum_{i=1}^{n-1}\Pi_i\Delta X_{t-i}+
\Pi X_{t-n}+e_t
\end{equation}
where
\begin{eqnarray}\Pi_i&=&-I+B_1+....+B_i,\nonumber\\
&=&-(I-B_1....-B_i),\nonumber\end{eqnarray}
where ($I$ is a unit matrix) and $n$= maximum lag length.  The rank of
matrix $\Pi$ can at most be five, the number of variables in the $X_t$
vector.  If the rank of matrix $\Pi=5,$ the vector X is integrated of
order zero, i.e., stationary.  If the rank of matrix $\Pi<5$, the rank
determines the number of cointegrating vectors in the VAR model explaining
$X_t$.  Hence, in our VAR model explaining five variables, there are
at most four cointegrating vectors.
\par Table 5 presents the likelihood ratio results for the null hypothesis
that the number of cointegrating vectors=0,1,2,3,4.
The cointegration analysis reported in Table 4
shows that the joint process of five variables in both models is
cointegrated at the five percent level of significance.  These results
indicate
that this five variable system can be characterized by a lesser
number of common stochastic trends which drive the system.\footnote{All
pairwise combinations of real world oil price with the rest of the variables,
as well as all pairwise combinations of the narrow money of Germany with the
rest of the variables are not cointegrated at the five percent significance
level.  Thus, the cointegrating relationship rests on the strength of
the relationship of real output of Germany with real output of France and
Italy.  Evidently, a common component of the long-run movement of real
output is due to technological shocks which spread across borders.}
For the model of France, we detected two cointegrating vectors.  For the model
of Italy, we detected three cointegrating vectors.
Accordingly,
the residuals from the cointegrating regressions with the dependent
and all independent variables expressed in levels are included in the
estimation of the VAR system in (12).  This vector error correction model
imposes the constraint implied by the cointegration relationship among the
variables in the system.
Thus, we rely
on the restricted vector
autoregressive system with the appropriate number of error correction terms.
\par Having estimated the vector autoregression model,
we then focus on the effects of
innovations in the system, as represented by the impulse-response function
and the variance decomposition.
Figures 3 and 4 report the response of price
to one standard deviation innovation in all five variables
of the vector autoregressive model for Italy and
France.\footnote{The order of variables is WOP, GRGDP,
GNM, FRGDP, FCPI
in the model for France and WOP, GRGDP, GNM, IRGDP, ICPI in the model
for Italy.}  The impulse response functions show that price inflation, in
France and Italy, accelerates in response to a rise in the world real oil
price.  In addition, nominal domestic shocks have long-lasting effects on
price inflation in both countries.  The inflationary effect of
the domestic nominal shocks appears larger, however, than that of the real
world oil price shocks in France.
More importantly, it is interesting
to note the disinflationary effects of German shocks in France and Italy.
Shocks to real output growth in Germany decrease price inflation in
France and Italy.
That is,
output growth in Germany is an important factor in controlling
price inflation that has a strong spillover effect on disinflation in
France and Italy.
In addition, German monetary shocks have negative effects on price
inflation which appear particularly evident in France.
That is,
the design of monetary policy in Germany,
which aims at controlling price inflation, has had a strong spillover effect
on disinflation in France, and to a lesser extent in Italy.
\par We complement the observations
of the change in price inflation
with the effects of the shocks on
real output growth.
In Figures 3 and 4, we see
that real oil price shocks cause a permenant decline in real output growth.
This is consistent with the inflationary effect of oil price shocks on
price inflation in France and Italy.
The growth of output in Germany has a positive expansionary effect on
output growth in France.  This is consistent with the disinflationary
effect of real shocks in Germany on price inflation in France and Italy.
This is in contrast to the design of monetary policy in Germany which aims
at controlling the inflationary effects of the increased demand.
Consequently, monetary growth in Germany has a negative contractionary effect
on output growth in France and Italy.  Consistently,
monetary shocks in Germany have a spillover disinflationary effect
on prices, particularly in France.
Domestic shocks to output growth
have larger expansionary effect on output growth over time in Italy
compared to France.  Consistently, domestic real shocks
have disinflationary effects on price in Italy.
In contrast, nominal
domestic shocks interfere with output growth in Italy and
accelerate price inflation.  Consistently, the inflationary effect of
nominal domestic shocks appears more moderate in France
compared to Italy.
\par The results
of the forecast error variance decomposition are reported in Table 5.  The
results
shed some light on the decomposition of the variance of the domestic
price into foreign disturbances (WOP, GRGDP, GNM) as opposed to domestic
disturbances (FRGDP, FCPI) or (IRGDP, ICPI).
According to the forecast error variance decomposition,
real and nominal shocks originating from
Germany account for a large share of price variability in France and Italy.
Specifically, the proportion of price variance in France associated with
German shocks ranged from 4.13 percent after two quarters to 18.84 percent
after 24 quarters.  In Italy, the proportion of price variance associated
with German shocks ranged from 0.69 percent after two quarters to 18.45
percent after 24 quarters.
\par
Real oil price shocks and domestic price shocks appear to be important
determinants of price variability in France and Italy.  Specifically,
the proportion of price variance in France associated with domestic
real and nominal shocks
ranged from 83.46 percent after two quarters to 66.26 percent after 24
quarters.  In Italy, the proportion of price variance associated with
domestic real and nominal shocks ranged from 52.54 percent after two
quarters to 19.84 percent after 24 quarters.  In addition, real oil price
shocks explain a share of price variance that ranges from 12.42 percent
after two quarters to 14.89 percent after 24 quarters in France.  The
inflationary share of an increase in the world oil price is even more
pronounced of the price variance in Italy.  Specifically, this share
ranges from 46.78 percent after two quarters to 61.71 percent after 24
quarters.  Overall, it is interesting to observe the increased share
of foreign shocks of price variability in France and Italy over time.
That is, the spillover disinflationary
effect of German shocks appears long-lasting on price in France and Italy.
In addition, the reduction in the world oil price appears
to have long-lasting effect on disinflation
in Italy and, to a lesser extent,
France.\footnote{The results are robust with respect to a change in the
order of variables in the VAR model.  These results are available upon
request.}
\section{Conclusion}
In this paper, we use a
vector autoregressive model to evaluate
the importance of different shocks on the
inflation rate
in France and Italy between 1979 and 1993.  We classify the shocks as real
world oil price
shocks, real and monetary shocks originating from Germany, and real
and nominal domestic shocks.
We use two approaches to impose long-run constraints in order to guarantee
the exogeneity of the shocks in the model.
The first approach imposes theoretical structural constraints
that govern the long-run relations between shocks in the model.
The second approach is
atheoretical based on the results of cointegration among
the trends of the variables in the
model.
The results of both models indicate
that the effect of the shocks originating from Germany
had a decreasing impact on price inflation in France and
Italy.
In addition, the weight of
German shocks in explaining the variance of the inflation rate is large in both
countries.
This weight appears significantly larger in the structural VAR model which
isolates domestic shocks
in France and Italy from their correlation with German shocks to measure the
contribution of the exogenous component of domestic shocks to disinflation.
\par
Our results support, therefore, the view which stresses the importance of
the spillover effect from Germany in decreasing inflation in traditionally
high inflation countries of the
European Monetary System.
Nonetheless, domestic policies that
aim at expanding output growth and curbing nominal shocks are also important
components of the success of disinflation policies in France and Italy.
Coordination between policies is evident by the change in the contribution
of domestic and German shocks to price variability upon accounting for
structural correlations between the shocks in the VAR model.
The evidence, therefore, supports the spillover effects implied by the
German dominance in the European Monetary System.
Nonetheless, the
coordination of domestic policies among countries of the European Monetary
System remains necessary towards achieving a fast reduction in price
inflation.
Finally, lower world oil prices
cannot be overlooked in evaluating the success of disinflation policies
in France and Italy during the eighties and early nineties.
\newpage
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\newpage
\baselineskip=7pt
\begin{table}[t]
\caption{Unit Root Test Results for First-Differences}
\begin{center} 
\begin{tabular}{l| c| c c| c c}\hline
\multicolumn{1}{c}{Variable}&
\multicolumn{1}{c}{$\tau(.)$ }&\multicolumn{1}{c}{$\Phi_3$}&
\multicolumn{1}{c}{$Z(\Phi_3)$}&\multicolumn{1}{c}{$Z(t\alpha^\sim)$}&
\multicolumn{1}{c}{$Z(\alpha^\sim)$}\\
\hline
\\
WOP&-$4.8660^*$&$25.6756^*$&$27.4537^*$&-$7.3788^*$&-$40.8456^*$\\\\
GRGDP&-$5.2103^*$&$33.0988^*$&$32.8402^*$&-$8.0951^*$&-$63.4733^*$\\\\
GNM&-$4.0629^*$&$23.1935^*$&$22.7404^*$&-$6.7431^*$&-$47.0488^*$\\\\
FRGDP&-$4.5313^*$&$17.9067^*$&$19.1016^*$&-$6.1810^*$&-$52.2344^*$\\\\
FCPI&-$5.4380^*$&$5.3367^a$&4.9292&-$3.1348^a$&-$17.5578^*$\\\\
IRGDP&-$5.4107^*$&$18.4182^*$&$13.0693^*$&-$5.3061^*$&-$36.2141^*$\\\\
ICPI&-$3.8993^*$&$7.9683^*$&$7.9310^*$&-$3.9826^*$&-$25.9711^*$\\\\
\hline\\
\end{tabular} \end{center} \end{table} 
Notes:
\begin{itemize}
\item
$\tau(.)$ is the t-value according to the Augmented Dickey-Fuller Test for
the null hypothesis of nonstationarity.  The model specification for the
test employs a constant, a time trend variable, and four lags of the
dependent variable.
\item
We also use the Perron, and Phillips Perron tests.  For
these tests, we use a model with a constant and a time trend, i.e.,
$$X_t=\mu^\sim+\beta^\sim (t-{n/2})+\alpha^\sim X_{t-1}+\epsilon_t,\;\;\;\;
t=1,2,...,n.$$
$n$ is the number of observations.
In this model, the null hypothesis, $H_0:\beta^\sim=0,\alpha^\sim=1$ is
tested by using $\Phi_3$ and $Z(\Phi_3)$, and $H_0:\alpha^\sim=1$ is tested
by using the test statistic $Z(t\alpha^\sim)$ and
$Z(\alpha^\sim)$.
The critical values for $\Phi_3$ and $Z(\Phi_3)$ are given in
Dickey and Fuller (1981, p. 1063) and the critical values for
$Z(t\alpha^\sim)$ and $Z(\alpha^\sim)$ are given in Fuller (1976, p. 37
and 373).
\item $^*$ indicates that the null hypothesis of non-stationarity is
rejected at the ten percent level.
\item $^a$ denotes statistical significance at approximately 12\%.
\item WOP is the real world oil price; GRGDP is the real gross domestic
product in 1990 constant prices of Germany;
GNM is the seasonally adjusted narrow money of Germany; FRGDP and IGRDP
are real gross domestic products in 1990 constant prices for France
and Italy; and FCPI and ICPI are the consumer price index for France and
Italy.
\end{itemize}
\newpage
\baselineskip=7pt
\begin{table}[t]
\caption{Test Results for the Determination of the Lag Length in the
VAR Model}
\begin{center}
\begin{tabular}{l c c c}\hline
\multicolumn{1}{c}{Null}&
\multicolumn{1}{c}{Alternative}&\multicolumn{1}{c}{Acceptance}
&\multicolumn{1}{c}{Probability}\\
\multicolumn{1}{c}{Hypothesis}&\multicolumn{1}{c}{Hypothesis}&
\multicolumn{1}{c}{France}&\multicolumn{1}{c}{Italy}\\
\hline
\\
4 lags &8 lags&0.999&0.999\\\\
4 lags&6 lags&0.658&0.860\\\\
2 lags&4 lags&0.003&0.699\\\\
3 lags&4 lags&0.007&0.334\\\\
\hline\\
\end{tabular} \end{center} \end{table} 
Notes:
\begin{itemize}
\item Acceptance probability is based on the Chi-square distribution
for the likelihood ratio test.
\item Following the suggestions of Sims (1980, p. 17), we take into
account small sample bias by correcting the likelihood ratio statistic by the
number of parameters estimated per equation.  Thus, the likelihood ratio
test=$T-C\{log]\Sigma_0]-log]\Sigma_1]\}$, where $\Sigma_0$ and $\Sigma_1$
are the variance covariance matrices of the residuals estimated from a
VAR model with a constant and the number of lags under the null and
alternative hypotheses, respectively.  $T$ is the number of used observations
and $C$ is the number of variables in the unrestricted equations.
\item The degree of freedom for the Chi-square test equal the number of
restrictions implied by variation in the lag length.
\end{itemize}
\newpage
\baselineskip=7pt
\begin{table}[t]
\caption{Test Results for the Number of Cointegrating Vectors in
the VAR Model}
\begin{center}
\begin{tabular}{l c c c}\hline
\multicolumn{1}{c}{Null Hypothesis}&
\multicolumn{1}{c}{Likelihood}&\multicolumn{1}{c}{Ratio}
&\multicolumn{1}{c}{5\% Critical}\\
\multicolumn{1}{c}{$\#$ of Cointegrating}&\multicolumn{1}{c}{France}&
\multicolumn{1}{c}{Italy}&\multicolumn{1}{c}{Value}\\
\multicolumn{1}{c}{Vectors}\\
\hline
\\
none&$87.3387^*$&$104.1572^*$&68.52\\\\
at most 1&$50.6362^*$&$57.2226^*$&47.21\\\\
at most 2&24.2709&$30.3616^*$&29.68\\\\
at most 3&6.8793&10.5783&15.41\\\\
at most 4&0.7599&1.7744&3.76\\\\
\hline\\
\end{tabular} \end{center} \end{table} 
Notes:
\begin{itemize}
\item $^*$ denotes significance at the five percent level.
\end{itemize}
\newpage
\baselineskip=7pt
\begin{table}[t]
\caption{Variance Decomposition of Price Based on VAR Estimation with
Cointegration Constraints}
\begin{center} 
\begin{tabular}{l c c c c c}\hline
\multicolumn{1}{c}{}&
\multicolumn{1}{c}{The}&\multicolumn{1}{c}{VAR}
&\multicolumn{1}{c}{Model}&\multicolumn{1}{c}{for}&
\multicolumn{1}{c}{France}\\
\multicolumn{1}{c}{Period Ahead}&\multicolumn{1}{c}{WOP}&
\multicolumn{1}{c}{GRGDP}&\multicolumn{1}{c}{GNM}&\multicolumn{1}{c}
{FRGDP}&\multicolumn{1}{c}{FCPI}\\
\hline
\\
1&9.643&0.572&1.034&6.134&82.613\\\\
2&12.416&2.138&1.990&8.305&75.154\\\\
5&20.209&9.252&4.589&9.847&56.101\\\\
10&22.884&13.824&4.415&15.870&43.004\\\\
24&14.894&13.077&5.762&28.378&37.886\\\\
\hline
\end{tabular} \end{center} \end{table} 
\baselineskip=7pt
\begin{table}[t]
\caption{Variance Decomposition of Price Based on VAR Estimation with
Cointegration Constraints}
\begin{center} 
\begin{tabular}{l c c c c c}\hline
\multicolumn{1}{c}{}&
\multicolumn{1}{c}{The}&\multicolumn{1}{c}{VAR}
&\multicolumn{1}{c}{Model}&\multicolumn{1}{c}{for}&
\multicolumn{1}{c}{Italy}\\
\multicolumn{1}{c}{Period Ahead}&\multicolumn{1}{c}{WOP}&
\multicolumn{1}{c}{GRGDP}&\multicolumn{1}{c}{GNM}&\multicolumn{1}{c}
{IRGDP}&\multicolumn{1}{c}{ICPI}\\
\hline
\\
1&16.7643&2.8713&1.2690&0.0628&79.0325\\\\
2&34.3782&2.2957&1.2477&2.9172&59.1610\\\\
5&41.3261&4.6314&0.2598&7.9962&44.0891\\\\
10&35.1188&6.4542&0.2555&9.7694&48.4018\\\\
24&23.9132&12.9750&0.2739&10.0350&52.8026\\\\
\hline \end{tabular} \end{center} \end{table} 
Notes:
\begin{itemize}
\item
Numbers represent the percentage of the variance of the nth-period
ahead forecast error for price inflation in France and Italy that is
explained by the variables in the VAR model.
\item WOP is the real world oil price; GRGDP is the real gross domestic
product in 1990 constant prices of Germany.  GNM is the seasonally adjusted
narrow money of Germany; FRGDP and IRGDP are real gross domestic products
in 1990 constant prices for France and Italy; and FCPI and ICPI are the
consumer price index for France and Italy.
\end{itemize}
\newpage
\baselineskip=7pt
\begin{table}[t]
\caption{Variance Decomposition of Price Based on VAR Estimation with
Structural Constraints}
\begin{center}
\begin{tabular}{l c c c c c}\hline
\multicolumn{1}{c}{}&
\multicolumn{1}{c}{The}&\multicolumn{1}{c}{VAR}
&\multicolumn{1}{c}{Model}&\multicolumn{1}{c}{for}&
\multicolumn{1}{c}{France}\\
\multicolumn{1}{c}{Period Ahead}&\multicolumn{1}{c}{WOP}&
\multicolumn{1}{c}{GRGDP}&\multicolumn{1}{c}{GNM}&\multicolumn{1}{c}
{FRGDP}&\multicolumn{1}{c}{FCPI}\\
\hline
\\
1&12.184&8.119&55.946&2.029&21.720\\\\
2&10.561&9.759&53.022&2.252&24.403\\\\
5&8.128&19.943&42.707&3.894&25.326\\\\
10&7.016&26.712&38.611&4.037&23.620\\\\
24&6.009&33.868&34.119&4.780&21.222\\\\
\hline
\end{tabular} \end{center} \end{table} 
\baselineskip=7pt
\begin{table}[t]
\caption{Variance Decomposition of Price Based on VAR Estimation with
Structural Constraints}
\begin{center} 
\begin{tabular}{l c c c c c}\hline
\multicolumn{1}{c}{}&
\multicolumn{1}{c}{The}&\multicolumn{1}{c}{VAR}
&\multicolumn{1}{c}{Model}&\multicolumn{1}{c}{for}&
\multicolumn{1}{c}{Italy}\\
\multicolumn{1}{c}{Period Ahead}&\multicolumn{1}{c}{WOP}&
\multicolumn{1}{c}{GRGDP}&\multicolumn{1}{c}{GNM}&\multicolumn{1}{c}
{IRGDP}&\multicolumn{1}{c}{ICPI}\\
\hline
\\
1&9.695&14.652&11.271&10.961&53.419\\\\
2&26.443&22.734&5.797&21.535&23.488\\\\
5&28.135&32.455&1.847&12.640&24.921\\\\
10&28.462&32.281&2.441&10.036&26.778\\\\
24&25.152&38.740&2.977&5.928&27.199\\\\
\hline \end{tabular} \end{center} \end{table}
Notes:
\begin{itemize}
\item
Numbers represent the percentage of the variance of the nth-period
ahead forecast error for price inflation in France and Italy that is
explained by the variables in the VAR model.
\item WOP is the real world oil price; GRGDP is th real gross domestic
product in 1990 constant prices of Germany.  GNM is the seasonally adjusted
narrow money of Germany; FRGDP and IRGDP are real gross domestic products
in 1990 constant prices for France and Italy; and FCPI and ICPI are the
consumer price index for France and Italy.
\end{itemize}