Download Fiscal Spillovers and Monetary Policy Transmission in the Euro Area

Fiscal Spillovers and Monetary Policy Transmission
in the Euro Area
Josef Hollmayr∗
15.04.2011
PRELIMINARY VERSION
Abstract
In this paper I set up a basic open New-Keynesian model with government spending
shocks for each of the eleven original member countries of the Euro area that are tied
together with the GVAR methodology of trade weights between the countries. Fiscal
spillovers are positive if small countries increase their government spending and negative
in the case of bigger countries as the increase in the common interest rate is overcompensating the positive effect. Because of bayesian estimation of the single countries with
lots of time series spillovers are mostly significant, unlike in most of the other GVAR
studies. Through a shock to the common Taylor rule monetary transmission with respect
to output and inflation can be analyzed. The effect is qualitatively the same but differs
in terms of magnitude depending on the countries, especially for inflation. Finally I show
that it makes a difference if euro area aggregates are targeted by monetary policy or the
single countries’ response added up with interlinkages taken care of.
JEL codes: E52, E58, E62, F41, F42, C11, C22
Keywords: DSGE, Global Vector Error Correction Model, Fiscal Policy,
Monetary Policy Transmission, Spillovers
∗
Department of Money and Macroeconomics, Goethe University Frankfurt am Main (email:[email protected]). I thank various colleagues in my department for continuous and
helpful comments and advice, especially Jorgo Georgiadis, Björn Kraaz, Björn Hilberg, Cristian Badarinza,
Emil Margaritov and also Stephane Des at the ECB. Furthermore I thank participants in the Money and
Macro Brown Bag seminar at Goethe University. All remaining errors are mine.
2
1
Introduction
In this paper I put the Euro area and all its member countries centerstage and analyze the
combination of their different fiscal policies and the one monetary policy. Especially the
monetary transmission in the single member countries and the fiscal spillovers between those
countries are examined. Furthermore I capture the interdependency between the two and
present it first in a stylized two country simulation exercise and later in a fully blown up
model. Major results are that monetary transmission differs across countries quantitatively
but not qualitatively. Fiscal spillovers matter and are sizeable for some big countries. Moreover monetary policy conduct on the aggregate euro area level yields different outcomes than
on the aggregated country level.
In the past many different strings have evolved in the literature concerning these policies.
Fiscal analysis has until recently very often been empirical and dealt with the multiplier
determination in a closed economy, starting with Blanchard, Perotti (2002). Work on fiscal spillover analysis in open economies has equally been unstructured most of the time
(Beetsma, Klassen, Cimadomo (2007)). Only recently have fiscal topics found entrance in
structural models, eg. DSGE models. (Cwik and Wieland (2009), Corsetti et al. (2009)).
In another branch the monetary transmission of ECB policy on the member countries has
been heatedly discussed at the very beginning of the establishment of the Eurozone with
data on the pre-monetary union situation (for example in Ehrmann (2000) and McAdam and
Morgan (2001)). Those studies were mostly empirical and neglected a fiscal side that could
interfere with monetary transmission at least theoretically. But it seems that research action
in this field has heavily cooled down since then with the exception of Weber et al. (2008).
Then there is a different branch of literature that looks at both policies at the same time.
One important started with Leeper (1991) who has looked at so called active and passive
policies of both authorities and identified areas of (in-)determinacy. This field of the fiscal
theory of the price level has become a very debated one with Chung et al. (2007) and Buiter
(2002) as active discussants. With respect to monetary and fiscal policy in a monetary union
in the beginning of the creation of the Euro Area many papers have been written on fiscal
policies of certain countries free riding at the disadvantage of others and how one common
monetary policy could react to this (an example hereof would be Gali and Perotti (2003))
None of these different strings has so far to my knowledge been considered together. So analysis in a large macroeconomic and macroeconometric framework is to my knowledge extremely
rare so far with the important exception of Gali and Monacelli (2008). In the present study
I perform a model basedempirical analysis on these two policies jointly where fiscal spillovers
and monetary policy transmission in the member countries of the euro area are analyzed. The
open New Keynesian model that is set up for each of the eleven original member countries
consists of households, firms, a retailer and a fiscal authority. Monetary policy is determined
at the union wide level.
3
Given the model I start with a simple two country simulation example in order to build up
intuition and see how fiscal and monetary policy interact with each other. Given that both
countries are identical monetary transmission differs depending on how big the government
sector is in both economies and how large automatic stabilizers are, i.e. the response of government expenditure on output in the fiscal rule. By the same token do fiscal spillovers both
to output and inflation vary depending on the reaction of the union wide monetary policy on
output and inflation.
The data for the estimation part are given by the key macroeconomic variables output, inflation, government expenditure and the common euro area short term interest rate going back
to the beginning of the single monetary policy in 1999Q1 and lasting until 2009Q4. The first
step of the estimation methodology consists of deriving the steady states for the model to be
estimated. This is done by the means of a Global Vector Error Correction Model (GVECM)
where the three endogenous variables are output, inflation and government expenditure and
the common factor is the short term interest rate. After getting the global solution I take
infinite forecasts and define this as the steady state. The deviations of steady state are then
obtained simply by the subtraction of those from the actual data observations each country
(DPSS, 2010).
Subsequently I estimate the model with Bayesian methods where the priors are of course
the same for each country. The aggregate euro area economy is estimated beforehand so
that the parameters for the Taylor rule can be incorporated as calibrated ones for the countrybycountry estimation. After the estimation of the parameters the equations are written
in system based form and tied together with the GVAR methodology, developed by Pesaran
et al. (2004), based on the trade weights between the countries. The global, recursive solution
is finally obtained by solving the rational expectations model with the algorithm by Binder
and Pesaran (1995).
The results of the dynamic analysis, exclusively built on generalized impulse responses show
that the sign of fiscal spillovers depend heavily on two competing channels: the interest rate
channel and the trade channel. On the one hand for spillovers from big countries the interest
rate channel dominates which leads to negative spillovers. On the other hand, little countries’
government expenditure does not raise the common interest rate by much so the interest rate
channel is not operative and is overcompensated by the trade channel. Through a shock to
the common Taylor rule monetary transmission with respect to output and inflation can be
analyzed. The effect is qualitatively the same but differs in terms of magnitude depending
on the countries with Finland for example displaying the smallest negative inflation response
to a monetary tightening. Due to the estimation strategy the spillovers are unlike most of
the other GVAR studies highly significant. Confidence bands are calculated by drawing from
the parameter distributions of the Bayesian estimation. Finally I show that it makes a difference if euro area aggregates are targeted by monetary policy or the single countries’ response
added up. The responses are amplified and more persistent if the GVAR approach is used
4
as opposed to an aggregate Euro area estimation. As a result it is at least advisable for the
European Central Bank to think about whether the aggregation as in the New Area Wide
Model makes sense to infer optimal policy or invest more research into different monetary
transmission across countries to come up with a country by country decision and aggregate
up afterwards. The paper is organized like this: in section 2 I will present the model set up
I will use later in the estimation section. The gist of the New-Keynesian model will also be
used in section 3 where I try to build intuition and simulate a two-country example. Section
4 is about the estimation step of the euro area countries, before I show how the solution will
look like in section 5. The results of the dynamic analysis are discussed in section 6. Section
7 finally concludes.
2
Model
The model I set up follows the one of Gali and Monacelli (2008). As their model puts
an economy centerstage that is part of a monetary union I use many of their assumptions
and structural equations. The model is structured in discrete time and features an infinite
horizon. The agents in the open economy are households and entrepreneurs that are infinitely
lived and retailers that contribute the nominal friction to the model. Finally there is a fiscal
authority that is country specific and a monetary authority that is supranational. That is
the interest rate rt is not countryspecific which is also indicated by the missing subscript i
that denotes country i with i = 1 : 11.
2.1
Households
Most of the household’s equations and definitions are standard in the open economy literature.
Households in country i maximize their expected lifetime utility which consists of consumption
and labor and is given by
E0
X
βit U Cti , Lit .
(1)
The parameter βi denotes as usual the degree of impatience. The period utility of households
in country i looks like the following
U (C, L) ≡
(Cti )(1−σi ) (Lit )(1−φi )
−
1 − σi
1 − φi
(2)
with σi being the parameter for intertemporal elasticity of substitution and φi as the parameter governing the disutility of labor. The lifetime utility function is maximized under the
5
series of budget constraints which are given by
Z1
0
1
i
Pti (j)Ci,t
(j)dj
+
11 Z
X
i
Ptf (j)cif,t (j)dj + Pi,t Ci,t + Rt Dti ≤ Dt−1
+ Wti Lit − Tti
k=1 0
where Di,t is a one-period deposit1 , Wi,t is the wage and Ti,t denotes lump-sum taxes and
summing up over all remaining countries k (k 6= i). Aggregate consumption in the economy
i is given by the composite consumption index.
Cti
≡
i )(1−α) (C i )α
(Ci,t
F,t
(1 − α)(1−α) αα
(3)
i and abroad C i (in the whole union)
Both consumption of goods j produced at home Ci,t
f,t
are given by the CES functions

i
Ci,t
≡
Z1
()
 −1
i
Ci,t
(j)
(−1)
dj 
(4)
0
and for the imported goods
i
CF,t
≡
11 Z
X
cif,t
(5)
k=1
respectively. Here cif,t is written as the log of consumption of the imported goods bundle of a
special country (k 6= i). Symmetrically it must also hold for every other country in the union

i
≡
Cf,t
Z1
()
 −1
i
(j)
Cf,t
(−1)
dj 
(6)
0
The second function denotes the imported goods of country i from the rest of the union. αi
is a parameter that is bounded between 0 and 1 and is commonly referred to as the openness
parameter. More precisely it is the weight that is attached to consumption of domestically
produced and foreign produced goods respectively. Of course this parameter, as any other
parameter, is different for every country i in the monetary union. The consumer price index
in country i is then given as
i
Pc,t
≡ (Pti )(1−α) (Pt∗ )α
(7)
The usual demand functions depend on the price of the good j with respect to the aggregate
price in the economy. The exponent − makes the demand function downward sloping.
1
Deposits are internationally tradable, see explanation later in this section
6
Therefore consumption demand for good j in country i is written like this:
i
Ci,t
(j)
=
Pti (j)
Pti
−
i
Ci,t
(8)
Git
(9)
Government demand for good j takes the same form:
Git (j)
=
Pti (j)
Pti
−
Finally the demand for goods j produced abroad (imported goods) in country i is given by
i (j)
the demand of consumption of foreign goods Cf,t
i
Cf,t
(j)
=
Ptf (j)
Ptf
!−
i
Cf,t
.
(10)
Note that government expenditure is only directed to internally produced goods. There is no
demand schedule of government that hinges on imported goods. This is an assumption that
facilitates aggregation later on. Furthermore for the spillover analysis this clear cut assumption is useful as a government expenditure shock only stimulates the domestic economy and
only through this can it spillover to the foreign economies. If I loosened up this assumption
the economies would be even more heavily intertwined and results would be not as precise
to analyze. The price level indices are assumed to follow the well-known rule. Pti is the price
level index of domestically produced goods,i.e. the domestic price index.

Pti ≡ 
Z1
1
 (1−)
Pti (j)(1−) dj 
(11)
0
Due to the fact that the law of one price is assumed to hold I can write the foreign produced
goods’ price level index in

Ptf ≡ 
Z1
1
 (1−)
Ptf (j)(1−) dj 
(12)
0
After using the definitions above and combining them in the familiar way the budget constraint can then finally be written in the aggregate form.
i
i
Pc,t
Cti + Rt Dti ≤ Dt−1
+ Wti Lit − Tti
As all countries i are members of one currency union, there are no exchange rates to
consider. Terms of trade, however, exist and are defined in the following way. The bilateral
7
terms of trade between the home country i and any foreign country k (k 6= i) are given by
i
Sf,t
≡
Ptk
Pti
i.e. the price level of goods produced in country k expressed in country i’s price level. The
effective terms of trade for country i are then obtained by aggregating over the ten other
countries:
Sti =
11
11
k=1
k=1
X f
X
Pt∗
= exp
(pt − pit ) = exp
sif,t
i
Pt
i ).
where small letters denote as before the log of the respective variable. (here: sif,t ≡ logSf,t
By the same token also the CPI price index (inflation) and domestic price index (inflation)
are related in the following way:
i
Pc,t
= Pti (Sti )α
This equation can be expressed in logs like this:
i
= πti + α∆sit )
pic,t = pit + αsit (πc,t
Under the assumption of perfectly tradable securities over all countries, i.e a complete
market across the whole monetary union the Euler equation for households is the same in all
countries k (k ∈ 1 : 11, k 6= i)
β
Ctk
k
Ct+1
!−σ
k
Pc,t
k
Pc,t+1
!
= Qt,t+1
(13)
Given the Euler equation for the home country i and the foreign country k we can combine
both equations over the same return and obtain
i (1−α)
Cti = υi Ctk (Sk,t
)
(14)
where i and k denote two countries out of the eleven member countries. According to Gali and
Monacelli (2008) υi denotes a constant that summarizes the initial conditions and is assumed
to be the same for all countries. More precisely I set it to one for all countries without loss
of generality. After log-linearizing and summing up over the ten other foreign countries one
arrives at
c̃it = c̃∗t + (1 − α)s̃it
(15)
8
2.2
Firms
Firms operate in this model with a fixed technology which is set to 1 and labor. There is no
capital involved in this economy. The production of firm j using labor that is provided by
households is equal to:
Yi,t (j) = ALi,t (j)
with A being time invariant technology, Yi,t (j) the production of firm j and Li,t (j) labor input
to produce good j. The real marginal costs are then simply given by the real wage
M Ci,t =
Wi,t
.
Pi,t
In terms of price setting I assume that retailers set their prices according to the Calvo (1983)
mechanism, i.e. each period (1 − θ) of all firms are able to reset their prices optimally.
Deviating slightly from Gali and Monacelli (2008) I allow that firms that cannot reoptimize
their prices in period t index their prices to the lagged inflation rate. This is congruent with
e.g. Smets and Wouters (2003) and Christiano et al. (2005). Those firms that are not able
to reoptimize their prices in period t set them according to the following rule:
Pit = π̃t Pu,t−1
(16)
with π̃t given by the following formulation:
$
π̃t = πt−1
πt1−$ 2
(17)
The effect later in the log-linearized Phillips curve will be that inflation is not only depending
on its lead but also on its lag besides the marginal cost term. Profits of firm j (in nominal
terms) are then given by
Πi,t (j) = (Pi,t (j) − M Ci,t )
Pi,t (j)
Pi,t
Yi,t (j)
(18)
The first order conditions are standard and can be found in the appendix.
2.3
Monetary and fiscal rules
The government is divided up into a monetary authority and a fiscal authority. Both institutions follow a policy rule whereas the monetary policy is not determined within the country
but at the monetary union level. The union wide central bank sets the common interest rate
2
Christiano et al. (2007) use a similar formulation where contemporaneous inflation is substituted by an
inflation target
9
according to the widely used Taylor rule ?. Here the monetary response is not delivered with
respect to a certain country specific output gap and inflation gap i.e. the deviation from its
steady state or target but the GDP weighted aggregate deviations of all member countries’
output and inflation gap3 . In addition to that the interest rate depends also on its lagged
value. In total the interest rate rule looks like this:
¯t + γ3 ỹ¯t + t,T R
r̃t = γ1 r̃t−1 + γ2 π̃
(19)
The policy rule of the fiscal side determines the government expenditure for each country. It
would be worthwile to compare results both of the spillover scenario and also with respect
to monetary transmission if there was a union wide fiscal rule, too. This, however, is beyond
the scope of this paper. The policy rule incorporates also lagged government expenditure
and reacts contemporaneously and negatively to deviations of the output gap. This can be
thought of as an automatic stabilizer framework, as government expenditure increases to
boost economic output if GDP is below its steady state. This fiscal rule is ad hoc and far
from being an optimal rule as one that was derived in Schmitt-Grohe and Uribe (2007). It
finally takes the form
g̃i,t = δ1 g̃i,t−1 − δ2 ỹi,t + t,F R
2.4
(20)
Market clearing
The following condition secures that the market for good j in country i clears if good j is
consumed in the home country (regardless if it produced at home or abroad) or by the local
government:
Yti (j)
Z
i
Ci,t
(j) + Git (j)
!
!
#
i − "
Z
f
i
P
Pc,t
Pt (j)
c,t
=
(1 − α)
Cti + α
Ctf df + Git
Pti
Pti
Pti
i − Z
Pt (j)
i α i
i α
i 1−α f
i
=
(1 − α)(St ) Ct + α(St )
(St )
Ct df + Gt
Pti
i Pt (j)
=
[Cti (Sti )α + Git ].
Pti
=
i
Ci,t
(j)
+
By the fact that the aggregate output (determined by all goods j) is given by Yti ≡
R
(21)
(22)
(23)
(24)
Yti (j)
−1
dj
it is possible to write the market clearing condition like this:
Yti = Cti (Sti )α + Git
3
(25)
The GDP weights used are taken from the year 2008, averaging over the whole sample size would not
¯t and output ỹ¯t are written as averages of deviations
make a sizeable difference; note that inflation π̃
−1
10
The set of the linearized equations (and major steps of deriving them) are given in appendix
8.1.
3
3.1
Simulation
Set-Up
To provide an intuition of how the fiscal and the monetary side in a monetary union interact,
I provide a simple two country simulation example. For this exercise the equations of the
model section are used with a plausible(?) calibration (see appendix B). The only difference
to the original equations is that both the IS-curve of the home country and of the foreign
country are not forward looking as otherwise the Blanchard-Kahn conditions would not be
fulfilled and the system is indeterminate. In order to satisfy these conditions also the reaction
of output to the real interest rate has to be very low. Therefore two parameters are chosen
to be much larger than usual. The habit parameter h is set to 0.9 and the CES-utility
parameter to over 10. In this set-up these restrictions are tolerable as we are not interested
in the actual size of the impulse response functions but in the difference if parameters and
therefore monetary and fiscal policy change. During the whole simulation exercise I look at
two exactly equal countries both in terms of structure as well as in terms of parametrization.
3.2
Shock to the Government Expenditure Rule
When a government expenditure shock in country i hits the economy output in this country
rises which entails the union wide interest rate to also increase. The effect on the other
country is twofold. First due to fiscal spillovers output in country j should also rise. Foreign
output and government expenditure both enter the IS-curve. On the other hand a rise in
the common interest rate leads to a drop in output. It depends on the the parameters
chosen which effect prevails. Furthermore not only parameters of the interest rate rule also of
the government expenditure rule and the steady state ratio of government expenditure over
output determine the size of the spillovers and the interest rate. As can be seen in figure
1 after a shock to government expenditure in the home country the interest rate responds
differently depending on the parameters chosen in the monetary policy rule. The interest
rate is highest if a high value is attached to inflation and a low value to output. As a result
inflation in the foreign country decreases the most whereas the drop in output is also the
largest. The same holds true if a very low value is attached to the deviation of inflation.
Then both foreign GDP’s and inflation’s deviation of their steady state is much smaller.
11
3.3
Shock to the Taylor Rule
If the union wide interest rate is shocked both economies react exactly symmetrically as both
are set up in this way. However, one can see differences of how output and inflation and also
government expenditure react to this shock depending on which parameters are set (Figure
2). The smallest response in both output and inflation is generated by a high government
to output ratio and a high coefficient in the government expenditure rule. If the government
interferes actively in the economy and large automatic stabilizers are at work the recession
is lower and the recovery faster than in any other case. If the coefficient of the government
expenditure rule is large government expenditure is higher and therefore boosting output.
This is also the case if the government to output ratio is small but the effect on output is
of course smaller. The most amplified response is seen if the government to output ratio is
low and the coefficient of the government expenditure rule on output is also low. Both the
automatic stabilizer and also the part of the government are much smaller and therefore the
responses of GDP and inflation not as well dampened as before. The effects on inflation are
following the same pattern.
3.4
Connection between Both Policies
As this is a general equilibrium model interest rates react to government expenditure and
vice versa even with the correlation between the monetary policy shock and the government
expenditure shock being set to zero. As seen above if government expenditure is shocked
the spillovers are not exclusively but also to a certain degree influenced by the monetary
policy set up, i.e. how strongly does the monetary authority respond to output and inflation.
After a shock to the interest rate, however, the set up of the government plays a big role.
Thus, the monetary transmission depends heavily on how big the government to output ratio
is and how large automatic stabilizers are. In reality the connection between both policies
is certainly more elaborate and the response to each other’s behavior is also not certainly
contemporaneously. But this example serves as a starting step for the blown-up and total
global model with all the eleven member countries of the euro area and answers the question
how both are important for each other and should be analyzed at the same time. This is
especially the case because all countries are displayed with the same structure used in this
set-up (with forward looking IS-curves).
12
4
Estimation
4.1
Data
Altogether I use five variables in the GVAR. All of them have a quarterly frequency and start
at the beginning of the introduction of the Euro, at the first quarter of 1999. The sample
ranges until the fourth quarter of 2009 which yields 44 time observations. I am aware that the
sample length is not very big and shortcomings in the results may also be attributed to the
lack of data observations. The reason why I do not want to go further back is because I want
to concentrate only on the Euro zone and its common monetary policy which exists only since
then 4 . The cross section encompasses the eleven original members of the Euro area5 . Three
of the five variables are country specific and two are common to all countries. The common
variables are the short term interest rate and the oil price. The short term interest rate
is taken from the Area Wide Model (AWM) database of the ECB. The oil price, originally
expressed in dollars is divided by the bilateral exchange rate to the Euro and stems from
the same source 6 . The other three variables are real GDP, inflation, and real government
expenditure. All of them are taken from the OECD quarterly database. Inflation is calculated
as growth rates from country specific CPI indices. Real GDP is derived by taking nominal
GDP, that is seasonally adjusted, for every country and dividing it by the CPI index of the
respective country. Government expenditure is derived in the same way. For this series the
seasonal adjustment is performed by EViews with the X12 program and the additive option.
As is common in GVAR studies I take the logs of all variables (instead of inflation the log of
the price index) and perform a unit root test for all variables that I use in this estimation.
As expected and usual for example in Pesaran et al. (2004) the log of the price level is I(2)
in most of the countries. Therefore the first difference of this series is taken what is also in
line with the variable in the DSGE model. All other variables remain in logs and are not
differenced. In order to obtain the trade weights that are used to link the countries with each
other I take the trading data (imports and exports) of Eurostat of all countries with respect
to each other and divide the trade amount of country i with respect to country j by the full
trade amount of country i. The trade matrix that is finally used is displayed in appendix
section 8.4.
4
As a robustness check I also redo the whole estimation with data going back to 1971Q1. The difference
in the results is only minor.
5
These are: Austria, Belgium, Germany, Finland, France, Ireland, Italy, Luxembourg, Netherlands, Portugal and Spain
6
The oil price is added as further common factor as this is the case in most of the GVAR studies so far.
Confer for example Pesaran et al. (2004) and Dees et al. (2009). Furthermore also in structural open economy
models the oil price is considered as major input factor and modeled explicitly, see de Walque et al. (2005)
13
4.2
Deviations from Steady State
There are different methods of obtaining the deviations of steady states in a multi dimensional time series. As Dees et al. (2010) show there are three predominant ones. Either one
assumes (or actually proves) that the time series are not integrated and in this case also not
cointegrated both within and between countries, then one can regress each time series on an
intercept term and a trend and the corresponding residuals are the deviations for every time
t.
The next possibility is to use the Hodrick-Prescott filter for each of the time series. If dealing
with quarterly data as in the present context a smoothing parameter (λ) of 1600 is chosen as
is common in the literature. Dees et al. (2010) perform their calculation of the deviation from
steady states with this device and actually show that for the forward looking components
in the New Keynesian model the estimated parameters using the Hodrick-Prescott filtered
deviations are understated compared to the last and most appropriate alternative: the Global
Vector Error Correction Model (GVECM)7 .
Using this method the cointegration relations both within and between the countries are
accounted for properly. Furthermore it can be shown that this method is equivalent to a
multivariate Beveridge-Nelson Decomposition (see also Garrat et al. (2006) and Arino and
Newbold (1998)). In this set up with eleven countries I find that there are altogether 12
cointegration relations and as this fact needs to be taken into account appropriately I opt for
the GVECM approach to derive the deviations from steady state. The two first alternatives
would not take into account that some of those variables have common european trends. In
order to do so I perform a GVECM (explained in detail below in the appendix section 8.5)
with the three endogenous variables (GDP, government expenditure and inflation) and the
two weakly exogenous variables (the short term interest rate and the oil price). Given the
global solution I finally calculate the infinite horizon forecasts. These values are taken as my
steady state values and deducted from the actual observations. Let the actual observations
of the eleven countries be given by xt = (x01,t , x02,t , ..., x011,t ), then the deviations of the steady
states are calculated as follows:
x̃t = xt − xPt
(26)
The permanent component xPt is further decomposed into a deterministic and a stochastic
component:xPt = xPd,t + xPs,t where the deterministic component is given by xPd,t = µ + gt,
an intercept term and the trend. The stochastic component xPs,t is then defined as the longhorizon forecast (without the permanent-deterministic component):
xPs,t = lim Et (xt+h − xPd,t+h ) = lim Et [xt+h − µ − g(t + h)]
h→∞
7
h→∞
For a general critique of the Hodrick-Prescott Filter when using non-stationary series refer to ?
(27)
14
For a detailed explanation confer to the paper by Dees et al. (2010). As a robustness analysis I
also performed the estimation with the deviations from steady state obtained by the HodrickPrescott Filter. In this set-up, results will be presented in a later version of this paper.
4.3
Bayesian Estimation of Each Country
With the obtained deviations from the steady states and the completed linearized model
(see appendix section 8.2), the next step is the estimation. Also in terms of estimations
there are several possibilities at hand. Dees et al. (2010) opted for the instrumental variables
approach where each equation in every country is estimated separately. The Taylor rule and
the exchange rate equation were estimated by OLS whereas the Phillips-curve and the IScurve due to the terms containing expectations were estimated with instrumental variables.
In both cases the instrumental variables of both inflation and GDP were their lagged terms.
In this approach, however, one loses the interactions within the system that a DSGE-model
represents. Another approach, estimating each country as a system is the Maximum likelihood
estimation. This method, however, requires good knowledge of the parameter values and the
concept is situated near to actual calibration. Two more possibilities are GMM estimation and
Bayesian estimation. Both are also system based but according to An and Schorfheide (2006)
the GMM estimation is based on equilibrium relationships whereas Bayesian estimation fits
the solved DSGE-model to a vector of aggregated time series and is therefore superior. Once
the Bayesian estimation is chosen there are different options, too. If I estimate country
by country the Taylor Principle
8
is certainly not satisfied, as this would imply a value of
bigger than 15 or even 20. Secondly, another possibility would be to estimate all countries
at once. This would imply, however, that I would have to renounce on all foreign variables
as observables because the foreign variables are a linear combination of the endogenous ones
and therefore the rank condition of the data matrix cannot be verified. Lastly I retreat to
the option to estimate the Euro area economy beforehand to estimate the coefficients in the
Taylor rule. These I include then as calibrated parameters (along with the parameters of
the IS and the PC curve) when I estimated each country separately with the overall euro
area-wide IS and PC curve being present. The parameters that are estimated are the ones of
the IS curve, the PC curve and the government expenditure rule of the respective country.
The estimation itself is carried out in the way An and Schorfheide (2006) propose in their
work. With respect to priors of the deep parameters (habit, openness etc.) I rely heavily
on previous studies of estimated DSGE-models and take of course the same for each of the
countries. Along with Smets and Wouters (2007) I take the prior for habit of consumption
to be 0.7 and the utility function parameters of labor to be 2. The same holds true for the
8
the response of the interest rate on inflation in any country being bigger than one in the Euro area wide
Taylor rule
15
nominal rigidity with θ and $ being chosen to be 0.75. The other utility function prior on
consumption is set to be 3 according to Lubik and Schorfheide (2005). The openness prior
α is set to 0.2. The government share of output γ is according to many studies around 30%
and its prior is set to 0.35 in this study. Although this parameter can be calibrated exactly
as it denotes the steady state ratio I opt for letting it estimate it because the number of
parameters compared to the number of time series used is quite low anyways and the fit will
be very good. Lastly there is the fiscal rule where the autoregressive parameter’s prior shape
is the uniform distribution. The prior for the coefficient on output is chosen to be 0.3. This
is line with the studies of Leeper (1991),Schmitt-Grohe and Uribe (2007), etc. For the overall
Euro area estimation beforehand the Euro area-wide parameters are chosen in exactly the
same way. The priors for the Taylor rule are also chosen to be uniformly distributed for the
autoregressive parameter and the responses to inflation deviations and output deviations 1.5
and 0.5 respectively, the values that Taylor (1993) found in his seminal work. In the end I
obtain the estimated values of the deep parameters which are (together with the priors, and
the prior shape) shown in table 1 in appendix section 3.
5
Solution
5.1
Stacking according to GVAR Methodology
After having estimated the parameters one can bring the model in the following form:
Ai,0 xi,t = Ai,1 xi,t−1 + Ai,2 Et (xi,t+1 ) + Ai,3 x∗i,t + Ai,4 x∗i,t−1 + Ai,5 Et x∗i,t+1 + i,t
where the matrices are given
by:

1
 δ

Ai,0 =  2,i
−β3,i
−γ3

−α2,i
 0

Ai,3 = 
 0
0
−α1,i
0
1
0
β4,i
1
0
−γ2

α3,i
0 

 Ai,4 =
0 
0

α4,i
α12,i
 0
0 


 Ai,1 = 
 0
0 
1

α6,i

 0

 0
0

−α7,i
0 


0 
0
−α5,i
δ1,i
0
0
0

α10,i

 0
Ai,5 = 
 0
0
0
0
β2,i
0


0
α8,i
 0
0


 Ai,2 = 
 0
0
γ1
0

−α9,i
0
0
0
α12,i
0
β1,i
0

0
0


0
0
−α11,i

0



0
0
Then as before in the deviations from steady state case we use the same method and stack the
country matrices once again one below the other: Therefore we construct new trade weighting
matrices for all countries Wi,new . The difference to the one before was that in the derivation
of the deviations from steady state x∗i,t comprised all three foreign variables whereas in the
DSGE model there is no foreign inflation incorporated, so the last line of each Wi drops out.
0
0
As before the matrix zi,t = (xit , x∗it )0 is defined and every country can be expressed in the
following way:
Ai,z0 zi,t = Ai,z1 zi,t−1 + Ai,z2 Et (zi,t+1 ) + i,t
16
with Ai,z0 = (Ai,0 , −Ai,3 ) , Ai,z1 = (Ai,1 , Ai,4 ) and Ai,z2 = (Ai2 , Ai5 ) By the well known
transformation of before zi,t = Wi,new xt we can actually stack the 11 countries below each
other and get the global solution:
A0 xt = A1 xt−1 + A2 Et (xt+1 ) + t

A1,zj W1

 A
 2,zj W2 
Aj = 



...
A11,zj W11

with

1,t


 2,t 
t = 

 ... 
11,t

and t as the stacked error term over all countries:
Transposing finally yields the
global solution:
xt = Axt−1 + BEt (xt+1 ) + ut
This procedure is similar to Dees et al. (2010), their study, however, features no foreign
variables that are forward looking.
5.2
Solution to Rational Expectations Model
Finally I have arrived at the multivariate form of the equation:
xt = Axt−1 + BEt (xt+1 ) + ut
with A and B being matrices of the size 44x44 (N · KxN · K). In order to obtain the global
solution and be able to perform dynamic analysis one has to get rid of the expectations term
and need to formulate the equation in the following form.
xt = Φxt−1 + ut .
There are different ways of solving a rational expectations system. For a literature review
see Binder and Pesaran (1995). In the following I will use their suggestion (Binder and
Pesaran (1995), Binder and Pesaran (1997)) of how to solve this rational expectations system.
According to this solution mechanism Φ is the solution to the quadratic matrix equation:
BΦ2 − Φ + A = 0 That quadratic matrix equation is solved by a back-substitution procedure
where an initial guess Φ0 is iterated until convergence of Φz = (Ik − BΦz−1 )−1 A is achieved.
The convergence criterion is in my example (kΦz − Φz−1 kmax ≤ 10−6 ), where z indicates the
iteration step.
17
6
Results
The results will be ordered in the following way: firstly fiscal spillovers between major European countries are displayed and explained. Then I will discuss the monetary transmission of
the European central bank with respect to countries’ output and inflation. In a third part I
compare the monetary transmission if Euroland is taken as an aggregate entity to the single
countries responses added up. Finally redoing the whole estimation I assume that also fiscal
policy is decided on a European level (not finished in this version, will be shown in a later
version of this paper). All corresponding figures are in the appendix.
6.1
Fiscal Spillovers
In order to obtain fiscal spillovers, government spending of a particular country is shocked
and the effects on inflation and output in the other countries analyzed. The overall pattern
is straightforward. Two different channels are at work: the interest rate channel and the
trade channel. If a big country increases interest rate spending it boosts its own output
and also a bit inflation. This entails monetary policy to raise the interest rate because
the central bank reacts to a GDP-weighted average of output and inflation. The increase
of the interest rate overcompensates the positive spillovers via the trade channel and turn
output in the other countries negative. Inflation spillovers are going in the same direction
but much less pronounced. The reason for this is that in the new-keynesian Phillips curve in
an open economy context output enters positively but with a coefficient of smaller than one
into current inflation. This holds particularly true in the case of Spain which is depicted in
Figure 9 and also for Germany (Figure 7). In the latter case unfortunately not all responses
are statistically significant. Here the reaction of all economies displays exactly the expected
response. For France (Figure 8) things look a bit more mixed. With respect to some countries,
such as Portugal and Italy, the interest rate channel dominates and the reaction takes the
usual form. For the other countries, however, a spillovers are positive both for output and
inflation. Here the trade channel seems to be overcompensating the impact of the interest rate
channel. The results look differently if small economies such as Portugal and Luxembourg
experience a positive shock to their government expenditure shock. Then, due to the fact
that their output rise does not account for much in the overall output that the central bank
includes in its objective function, the interest rate rise is not sufficient to lead to negative
output in the other member countries and the trade channel dominates. Although fiscal
spillovers are very small in scale they most of the time are significant at the 90% level. For
the two small countries (Luxembourg and Portugal) plotted it can be seen that the responses
of the other countries’ output is positive throughout entailing also inflation to go up. One
exception is visible in both cases: the spillover to Italy from both countries are negative also
18
here. The explanation herefore is perhaps that the coefficient of the real interest rate of
the Italian IS-curve is so big (the CES-parameter in the utility is lowest in Italy) that the
interest rate channel can dominate also in the case where a small economy raises government
spending and therefore only a tiny reaction of the common interest rate suffices to decrease
Italian output.
6.2
Monetary Policy Transmission
Whenever error bands are shown in the results, then I drew all parameter values from the
bayesian posterior distribution and redid the whole calculation for every (altogether 1000)
replication once again. So far the drawings stem from the variances
9
where the covariances
between the parameters are not regarded. This will be improved in a later version of this
paper. Due to the fact that the number of parameters is small in comparison to the number
of time series used in the estimation the error bands of every parameter are very small
and therefore also the confidence bands of the final results, although they display the 99%
significance level. If we look at Figure 3 we can observe that the Impulse Response Functions
of a monetary contraction on output are very similar across countries. The qualitative result
is the same for all countries. A contraction is followed by a negative output deviation with
the smallest responses seen in Spain with a negative value of −0.05% of output deviation and
a bigger one in all the other countries. The shock has the size of one standard deviation for
all the rest of the analysis. Regarding the case where government expenditure reacts to a
monetary policy contraction (Figure 4) the result is more mixed. As explained before in the
simple simulation example, it very much depends how big the government is in the economy
and how the automatic stabilizers look like. Other parameters play also an important role.
Therefore we do not only get quantitatively but also qualitatively different results. In general
the normal response is a positive government expenditure behavior as output is declining.
In the case of Ireland, however, the sign is reversed and public expenditure increases. This
is due to the parameters found in the estimation process with an automatic stabilizer which
is negative. In other words, government expenditure goes up if output increases. This is
the only country that displays this phenomenon, but this is only slightly significant at our
significance level. Lastly I look at the effect of an increase in the policy rate on inflation
(Figure 5). Here, as in the case with output, inflation is going down, as theory predicts (see
for example Christiano et al. (2005)). All of the responses are highly significant (again at
the 99% level). The smallest effect on inflation is seen in Finland, the other responses are
relatively similar with maximal values of −0.03% to −0.07%.
9
all of the parameters of the posterior distribution are normally distributed, regardless of how the prior
distribution is assumed to look
19
6.3
Comparison of Aggregate vs. Single Countries Added-Up
Finally the last exercise is to compare the response of output and inflation to a euro area
wide interest rate shock once in the whole euro area model and once where all countries
are estimated separately and possible spillovers are taken care of. The whole Euro Area
was estimated in the very beginning as a GDP-weighted average of output, inflation and
government expenditure deviations. Here we take the impulse responses of an interest rate
shock on output and inflation. At the same time in the subsection before we have seen the
effects of an interest rate shock on the various countries for output and inflation. These
responses are now aggregated up using again the same GDP weights of before. As seen above
the responses of the single countries of both output and inflation are all qualitatively correct
but and quantitatively definitely not understating the effects. The result here in Figure
6 is that both in terms of magnitude as well as in terms of persistence both output and
inflation are responding heavier if one looks first at the single countries and then aggregate
them up with GDP weights. As a result one can claim that the New Area Wide Model
would definitely understate the responses of an interest rate shock as this approach does not
account for spillovers between the countries. For a closer look at discriminating between an
aggregated VAR and a GVAR approach see also Badarinza and Hollmayr (2011). The effect
of output is actually five times higher and a few periods more persistent. Inflation is more
than twice as high and even more persistent than in the case of output.
6.4
Estimation with a fiscal policy rule at the Euro Area level
For this section I redo the whole bayesian estimation of every country with one important
difference. Each country now has neither monetary nor fiscal policy at its disposal. Both
policies are determined at the Euro Area level. Herby the same procedure is chosen as with
the Taylor rule: in the countercyclical component output is a GDP-weighted average of all
member countries. I compare this set up to the ”usual” monetary transmission above where
each country could decide over its fiscal policy. In figure 10 one sees that now a positive shock
to the interest rate induces both greater heterogeneity in the countries’ inflation response and
in their resulting output as well. For example Ireland displays the biggest output contraction
with around 0.7% and France the least with around 0.2%. Finland and Germany are also
experiencing considerably bigger output losses than most of the other countries. The same
holds true for the persistence and the slight overshooting phase that is taking longer for those
with lower output on impact. With respect to inflation the monetary transmission is not as
heterogenous as in the output case but certainly more than in the case with country dependent
fiscal rules. Here Portugal is displaying the biggest inflation reduction (0.23%) and Finland
the lowest (0.14%) of all eleven countries countries. The reason why the heterogeneity in
20
the monetary transmission is increasing with a supranational fiscal authority is in built in
the way I model the economies. As those are general equilibrium models an interest rate
decrease (increase) is followed on every individual country level by a decrease (increase) of
the fiscal rule that runs countercyclically with respect to output. This direct nexus is gone
if one considers a Euro Area wide fiscal rule, as this is now only reacting to the aggregate
(GDP-weighted) output and the exact transmission is blurred by the coefficients of how the
aggregate government expenditure feeds back into the IS and Phillips curve to stabilize output
and inflation.
7
Conclusion
This paper adds an important insight on how to conduct monetary policy to the existing
literature. First of all it states that monetary policy should not be looked at independently
from fiscal decisions and the characteristics of the fiscal sector in a monetary union. The
importance of automatic stabilizers and the size of the government in the economy matter
for monetary transmission. This is both shown in a simulated model as well as in a set-up
with all eleven original member countries of the euro area being linked. Secondly, it makes
a sizeable difference if monetary policy looks at the aggregate level (such as the New area
wide model) to form decisions or responds to the situation at the country level and aggregate
those responses up. Here the aggregation of quite diverse countries in the Euro area is not
fully appropriate. As is shown in the result section if monetary policy reacts to the Euro area
as one aggregate country there are smaller and less long-lasting effects than in the other case
when single countries’ effects are added up with an appropriate weighting scheme. Equally
important is to note that fiscal spillovers not only matter for monetary transmission but
also vice versa. The emphasize that the central bank puts on responding to inflation or
output deviations influences fiscal spillovers, where according to the data used in this paper
the bigger countries have more influence on smaller and neighboring ones. Spillovers in this
context depend on the assumption that the countries are actually linked according to the
trade weights used in the GVAR context. Especially if there are some big and dominating
countries as is the case in the Euro area one of the conditions for the GVAR methodology
to use (trade weights going to zero) no longer holds. More work is needed in this respect to
model the interdependencies between the countries better and make the model set up richer
(for example distortionary taxation) in order to draw better informed conclusions.
21
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23
8
Appendix
8.1
First Order Conditions of the DSGE Model
To be completed!
8.2
The Linearized System
IS-equation of Country i:
∗
∗
ỹi,t = αi,1 g̃i,t − αi,2 ỹi,t
+ αi,3 g̃it
+ αi,4 ỹi,t−1 − αi,5 g̃i,t−1 −
∗
∗
∗
+ αi,6 ỹi,t−1
− αi,7 g̃i,t−1
+ αi,8 ỹi,t+1 − αi,9 g̃i,t+1 + αi,10 ỹi,t+1
−
∗
− αi,11 g̃i,t+1
− αi,12 (r̃t − π̃i,t+1 ) + i,t,IS
PC-equation of Country i:
π̃i,t = βi,1 π̃i,t+1 + βi,2 π̃i,t−1 + βi,3 ỹi,t − βi,4 g̃i,t + i,t,P C
Government Expenditure Rule:
g̃i,t = δ1 g̃i,t−1 + δ2 ỹi,t + t,T R
(28)
r̃t = γ1 r̃t−1 + γ2 π̄t + γ3 ȳt + t,T R
(29)
Taylor Rule of ECB:
where the combined parameters are related to the ”deep” parameters in the following way:
24
IS-curve:
α1 = γ
α2 =
α3 =
α4 =
α5 =
α6 =
α7 =
α8 =
α9 =
α10 =
α11 =
α12 =
α
1−α
αγ
1−α
h
1+h
hγ
1+h
hα
(1 + h)(1 − α)
hαγ
(1 + h)(1 − α)
1
1+h
γ
1+h
α
(1 + h)(1 − α)
αγ
(1 + h)(1 − α)
(1 − h)(1 − γ)
(1 + h)(1 − α)σc
PC-curve:
β1 =
β2 =
β3 =
β4 =
β
1 + β$
$
1 + β$
(1 − βθ)(1 − θ)
1
1
(
+ φ)
1 + β$
θ
1−γ
1
(1 − βθ)(1 − θ) γ
1 + β$
θ
1−γ
25
8.3
Simulation Results
Parameters Used:
Description
Degree of Openness
Impatience
Habit
SS Ratio GE/Output
Elasticity of Substitution
Indexation prices
Calvo wages
Autoregressive Component
Response to Inflation
Response to Output
Autoregressive Component
Response to Output
8.4
Parameters
α
β
h
γ
σc
$
θ
ρr
γπ
γy
ρg
δy
Values
0.2
0.99
0.9
0.25
15
0.75
0.75
0.8
2
0.5
0.8
0.5
Estimation Results
8.4.1
The Trade Matrix
Countries
AT
BE
GE
FI
FR
IR
IT
LU
NL
PO
ES
AT
BE
GE
FI
FR
IR
IT
LU
NL
PO
ES
0.0000
0.0130
0.1178
0.0336
0.0180
0.0132
0.0547
0.0153
0.0197
0.0101
0.0161
0.0343
0.0000
0.1417
0.0823
0.1735
0.2482
0.0805
0.2968
0.2296
0.0519
0.0607
0.6552
0.2979
0.0000
0.3964
0.3301
0.2620
0.3480
0.3009
0.4144
0.2083
0.2547
0.0106
0.0097
0.0223
0.0000
0.0094
0.0147
0.0140
0.0041
0.0188
0.0087
0.0100
0.0676
0.2456
0.2224
0.1133
0.0000
0.1550
0.2504
0.2014
0.1418
0.1652
0.2986
0.0064
0.0448
0.0229
0.0229
0.0199
0.0000
0.0184
0.0048
0.0216
0.0170
0.0185
0.1338
0.0748
0.1531
0.1096
0.1636
0.0930
0.0000
0.0649
0.0828
0.0780
0.1567
0.0031
0.0228
0.0110
0.0027
0.0109
0.0021
0.0054
0.0000
0.0049
0.0054
0.0034
0.0540
0.2384
0.2044
0.1657
0.1036
0.1220
0.0926
0.0667
0.0000
0.0703
0.0782
0.0051
0.0101
0.0190
0.0141
0.0222
0.0177
0.0160
0.0143
0.0132
0.0000
0.1032
0.0300
0.0429
0.0855
0.0594
0.1487
0.0720
0.1198
0.0308
0.0532
0.3852
0.0000
26
8.4.2
Bayesian Estimation Results
Description
Parameters
Prior Mean
Prior Shape
AU
BE
GE
FI
FR
IR
IT
openness
habit
government size
nominal mark-up
lagged inflation
time preference
CES utility consumption
CES utiliy labor
AR parameter fiscal rule
coefficient on Y fiscal rule
α
h
γ
θ
ϑ
β
σ
φ
δ1
δ2
0.2000
0.7000
0.3500
0.7500
0.7500
0.9750
3.0000
2.0000
0.3000
normal
normal
normal
normal
normal
normal
normal
normal
uniform
normal
0.2425
0.3566
0.4155
0.7868
0.6337
0.9769
1.1764
2.3145
0.4497
0.2155
0.2045
0.3690
0.4033
0.7160
0.8657
0.9705
0.9712
2.5008
0.5537
0.2988
0.1724
0.3616
0.4602
0.8075
0.6157
0.9822
0.9618
1.8169
0.5861
0.3037
0.2980
0.3537
0.3148
0.8988
0.2946
0.9596
1.7756
1.1418
0.2186
0.2699
0.1612
0.3695
0.3480
0.7344
0.7351
0.9841
1.2831
2.1817
0.6834
0.2404
0.1435
0.3879
0.4576
0.8147
0.7013
0.9809
0.9503
2.4539
0.8662
-0.0652
0.1395
0.5336
0.3141
0.7465
0.7860
0.9502
0.7049
2.4962
0.2491
0.1506
Description
Parameters
Prior Mean
Prior Shape
LU
NL
PO
ES
Average
EURO
openness
habit
government size
nominal mark-up
lagged inflation
time preference
CES utility consumption
CES utiliy labor
AR parameter fiscal rule
coefficient on Y fiscal rule
α
h
γ
θ
ϑ
β
σ
φ
δ1
δ2
0.2000
0.7000
0.3500
0.7500
0.7500
0.9750
3.0000
2.0000
normal
normal
normal
normal
normal
normal
normal
normal
uniform
normal
0.1481
0.4324
0.4233
0.8182
0.7421
0.9593
0.8428
1.3682
0.4140
0.2660
0.2257
0.4054
0.3649
0.7587
0.7804
0.9663
1.0029
1.8503
0.8029
0.2659
0.1393
0.3774
0.2745
0.7008
0.6921
0.9800
1.6908
1.5272
0.7857
0.2626
0.2482
0.3458
0.4073
0.7157
0.9211
0.9837
2.7303
2.1207
0.5476
0.3048
0.1945
0.3903
0.3876
0.7864
0.6617
0.9721
1.1176
2.1294
0.5153
0.2020
0.7920
0.1126
0.9421
0.7944
0.9642
2.3936
1.8408
0.9510
0.0526
8.5
Figures
0.3000
27
−3
4
−5
Home GDP
x 10
2
3
Foreign GDP
x 10
0
High Pi+high Y
2
−2
Low Pi+low Y
Low Pi + high Y
1
0
0
10
20
30
40
50
−6
time
Home Inflation
−3
4
−4
High Pi + low Y
x 10
0
10
20
40
50
10
20
30
time
Foreign GE
40
50
10
20
40
50
−4
0
3
x 10
30
time
Foreign Inflation
−2
2
−4
1
0
0
10
20
30
40
50
−6
time
Home GE
0
−5
0.01
4
0.008
x 10
3
0.006
2
0.004
1
0.002
0
0
10
20
30
40
50
time
Interest Rate
0
0
30
time
0.015
0.01
0.005
0
0
10
20
30
40
50
time
Figure 1: Simulation: Shock to the GE rule
28
−3
1
−3
Home GDP
x 10
1
0
Foreign GDP
x 10
0
High Pi+high Y
−1
−1
Low Pi+low Y
−2
High Pi + low Y
−3
−4
0
10
20
30
40
−3
50
−4
time
Home Inflation
−3
5
−2
Low Pi + high Y
x 10
0
−5
−5
−10
−10
0
10
30
40
50
−15
time
Home GE
−3
4
20
x 10
3
2
2
1
1
0
10
20
30
20
40
50
10
20
30
time
Foreign GE
40
50
10
20
40
50
x 10
0
−3
4
3
0
10
−3
5
0
−15
0
40
50
time
Interest Rate
0
x 10
0
30
time
Foreign Inflation
30
time
1
0.5
0
−0.5
0
10
20
30
40
50
time
Figure 2: Simulation: Shock to the Taylor Rule
29
Austria GDP
Belgium GDP
Germany GDP
0.05
0.05
0.05
0
0
0
−0.05
−0.05
−0.05
−0.1
−0.1
−0.1
−0.15
−0.15
−0.15
−0.2
0
10
20
30
−0.2
0
time
France GDP
10
20
30
−0.2
0
time
Finland GDP
0.05
0
0.05
0.05
0
0
−0.05
−0.05
−0.1
−0.1
−0.15
−0.15
10
20
time
Ireland GDP
30
10
30
−0.05
−0.1
−0.15
0
10
20
30
−0.2
0
time
Italy GDP
10
20
30
−0.2
0.05
0.05
0.05
0
0
0
−0.05
−0.05
−0.05
−0.1
−0.1
−0.1
−0.15
−0.15
−0.15
−0.2
0
10
20
0
time
Luxembourg GDP
30
−0.2
0
time
Portugal GDP
10
20
30
time
Spain GDP
0.05
−0.2
0
20
time
Netherlands GDP
10
20
30
time
0.02
0
0
−0.02
−0.05
−0.04
−0.1
−0.15
−0.06
0
10
20
time
30
−0.08
0
10
20
30
time
Figure 3: Shock to the Interest Rate, Effect on Countries’ Output
30
Austria Gov.Exp.
Belgium Gov.Exp.
Germany Gov.Exp.
0.15
0.15
0.3
0.1
0.1
0.2
0.05
0.05
0.1
0
0
0
−0.05
0
10
20
30
−0.05
0
time
France Gov.Exp.
10
20
30
−0.1
0.15
0.3
0
0.1
0.2
−0.02
0.05
0.1
−0.04
0
0
−0.06
−0.05
0
10
20
30
−0.1
0
time
Italy Gov.Exp.
10
20
30
−0.08
0.2
0.2
0.06
0.15
0.15
0.04
0.1
0.1
0.02
0.05
0.05
0
0
0
0
10
20
30
−0.05
0
time
Portugal Gov.Exp.
0.15
0.15
0.1
0.1
0.05
0.05
0
0
10
20
time
10
20
30
time
Spain Gov.Exp.
0.2
0
0
time
Luxembourg Gov.Exp.
0.08
−0.02
0
time
Finland Gov.Exp.
30
−0.05
0
10
20
−0.05
0
10
20
time
Ireland Gov.Exp.
30
10
20
30
time
Netherlands Gov.Exp.
10
20
30
time
30
time
Figure 4: Shock to the Interest Rate, Effect on Countries’ Government Expenditure
31
Austria Inflation
Belgium Inflation
0.02
0
Germany Inflation
0.1
0.02
0.05
0
0
−0.02
−0.05
−0.04
−0.02
−0.04
−0.06
−0.08
0
10
20
30
−0.1
time
France Inflation
0.02
5
0
0
−0.02
−5
−0.04
−10
−0.06
−15
0
10
20
30
time
−3
Finland
Inflation
x 10
−0.06
0
10
20
time
Ireland Inflation
30
0.02
0
−0.02
−0.08
0
10
20
30
−20
−0.04
0
time
Italy Inflation
10
20
30
−0.06
0
time
Luxembourg Inflation
0.1
0.02
0.05
0
0
−0.02
10
20
30
time
Netherlands Inflation
0.02
0
−0.02
−0.04
−0.05
−0.1
−0.04
0
10
20
30
−0.06
−0.06
0
time
Portugal Inflation
10
20
30
time
Spain Inflation
0.02
−0.08
0
10
20
30
time
0.02
0
0
−0.02
−0.02
−0.04
−0.04
−0.06
−0.08
0
10
20
time
30
−0.06
0
10
20
30
time
Figure 5: Shock to the Interest Rate, Effect on Countries’ inflation
32
Output transmission
0.05
AU
BE
0
GE
FI
−0.05
FR
IR
−0.1
IT
LU
NL
−0.15
P
ES
−0.2
0
5
10
15
20
25
20
25
20
25
time
Inflation transmission
0.02
0
−0.02
−0.04
−0.06
−0.08
0
5
10
15
time
Gov.Exp. transmission
0.05
0.04
0.03
0.02
0.01
0
−0.01
−0.02
0
5
10
15
time
33
4
−3
x 10 Spillover to Austria
−4
5
2
0
Confidence Band Output
Confidence Band Inflation
−2
−4
2
Output
Inflation
0
10
20
30
time
−3
x 10 Spillover to Finland
Spillover to Germany
0.15
0
0.1
−5
0.05
−10
0
−15
5
0
x 10 Spillover to Belgium
0
10
20
30
time
−4
x 10 Spillover to France
−0.05
1
0
0.5
−5
0
−10
−0.5
−15
−1
0
10
20
time
−3
x 10 Spillover to Ireland
0
10
0
10
30
−2
−4
−6
1
0
10
20
30
time
−3 Spillover to Italy
x 10
−20
5
0
0
−1
−5
−2
−10
−3
−15
0
10
20
30
time
−4
Spillover
to
Luxembourg
x 10
−1.5
2
20
30
time
−3
Spillover
to Netherlands
x 10
0
−2
−4
5
0
10
20
30
time
−4
Spillover
to Portugal
x 10
−20
2
0
1
−5
0
−10
−1
−15
0
10
20
time
30
−2
−4
0
10
20
30
−6
time
−3Spillover to Spain
x 10
0
10
20
20
time
30
time
Figure 7: Spillovers from Germany
30
34
4
−4
x 10 Spillover to Austria
−4
15
15
5
Conf. Band Output
5
Conf. Band Inflation
Output
Inflation
0
10
20
30
time
−4
x 10 Spillover to Finland
0
−5
0
0
10
20
30
−5
time
Spillover to France
0.1
8
6
2
10
20
time
−4
x 10 Spillover to Ireland
0
10
0
10
30
4
2
0
0
5
0
6
0.05
4
−2
−4
x 10Spillover to Germany
10
0
8
20
10
2
−2
x 10 Spillover to Belgium
0
0
10
20
30
time
−4 Spillover to Italy
x 10
−0.05
4
0
0
10
20
30
−2
time
−4
Spillover
to
Luxembourg
x 10
5
2
20
30
time
−4
Spillover
to Netherlands
x 10
0
−5
0
−10
−15
−20
2
−5
−2
0
10
20
30
time
−4
Spillover
to Portugal
x 10
−4
4
0
10
20
30
−10
time
−3Spillover to Spain
x 10
3
0
2
−2
1
−4
−6
0
0
10
20
time
30
−1
0
10
20
20
time
30
time
Figure 8: Spillovers from France
30
35
1
−4
x 10 Spillover to Austria
−5
5
0.5
0
Conf. Band Inflation
−5
0
10
20
30
time
−4
x 10 Spillover to Finland
−10
2
0
0
−2
−2
−4
−4
−6
5
−2
Output
Inflation
0
10
20
30
time
−4 Spillover to Italy
x 10
−6
5
0
10
20
30
−4
time
−4
x 10 Spillover to France
2
0
10
20
30
−4
time
−5
Spillover
to
Luxembourg
x 10
2
0
−5
−5
−2
−10
−10
−4
5
10
20
30
time
−4
Spillover
to Portugal
x 10
−15
−5
0.04
−10
0.02
−15
0
0
10
20
time
10
20
30
−6
30
−0.02
20
time
−4
x 10 Spillover to Ireland
0
10
0
10
30
0
10
20
20
30
time
−4
Spillover
to Netherlands
x 10
20
time
0.08
0.06
−20
0
time
Spillover to Spain
0
10
−2
0
0
0
0
0
−15
−4
x 10Spillover to Germany
2
Conf. Band Output
−0.5
2
4
0
0
−1
x 10 Spillover to Belgium
30
time
Figure 9: Spillovers from Spain
30
36
5
−5
x 10 Spillover to Austria
−5
8
4
6
3
4
Conf. Band Output
2
−4
x 10Spillover to Germany
x 10 Spillover to Belgium
1
2
Conf. Band Inflation
1
0
2
0
Output
Inflation
0
10
20
30
time
−4
Spillover
to Finland
x 10
−2
15
0
10
20
30
time
−5
Spillover
to France
x 10
5
10
20
time
−4
x 10 Spillover to Ireland
0
10
0
10
30
1
5
0.5
0
0
0
1.5
10
1
0
0
10
20
30
time
−5 Spillover to Italy
x 10
−5
6
0
10
20
30
time
−5
Spillover
to
Luxembourg
x 10
20
30
time
−5
Spillover
to Netherlands
x 10
8
6
4
0
0
4
2
2
−5
−10
0
0
10
20
30
−2
time
Spillover to Portugal
0.15
3
0.1
2
0.05
1
0
0
−0.05
0
10
20
time
30
−1
0
0
10
20
30
−2
time
−3Spillover to Spain
x 10
0
10
20
20
time
30
time
Figure 10: Spillovers from Portugal
30
37
15
−6
x 10 Spillover to Austria
−5
10
5
5
Conf. Band Inflation
0
Output
Inflation
0
10
20
30
time
−5
Spillover
to Finland
x 10
−5
3
2
0.5
1
0
0
−0.5
−1
1
2
0
1
−1
0
10
20
30
time
−5 Spillover to Italy
x 10
−2
0
10
20
30
time
−5
Spillover
to France
x 10
−2
5
0
10
20
30
−10
time
Spillover to Luxembourg
0
0.01
0
−1
0
−1
−2
−0.01
−2
1
10
20
30
time
−5
Spillover
to Portugal
x 10
−0.02
3
0.5
2
0
1
−0.5
0
−1
0
10
20
time
30
−1
10
20
time
−6
x 10 Spillover to Ireland
0
10
0
10
30
−5
1
0
0
0
0.02
−3
−5
x 10Spillover to Germany
4
Conf. Band Output
0
1.5
8
6
10
−5
x 10 Spillover to Belgium
0
10
20
30
−3
20
30
time
−5
Spillover
to Netherlands
x 10
time
−5Spillover to Spain
x 10
0
10
20
20
time
30
time
Figure 11: Spillovers from Luxembourg
30
38
Output transmission
0.1
0
AU
−0.1
BE
GE
−0.2
FI
−0.3
FR
IR
−0.4
IT
LU
−0.5
NL
P
−0.6
ES
−0.7
−0.8
0
5
10
15
20
25
20
25
time
Inflation transmission
0.1
0.05
0
−0.05
−0.1
−0.15
−0.2
−0.25
0
5
10
15
time
Figure 12: Common Fiscal Rule