AN AGGREGATE MODEL FOR THE EUROPEAN UNION
Alberto BAGNAI
Francesco CARLUCCI
University of Rome I, Department of Public Economics
9, Via del Castro Laurenziano, 00161 Rome, Italy
tel. +39-6-49766354
fax +39-6-4462040
e-mail [email protected]
An aggregate model for the EU
Abstract - We present the structure and properties of an aggregate model for the
European Union considered as a whole. Such a model can be complementary to those
consisting of an aggregation of national sub-models, and is probably superior to them in
several economic policy analyses. The equations have been estimated by a two-stage
procedure that takes into account the possible presence of structural breaks in the longrun parameters. The estimation of the error correction models allows for the nonlinearity
and simultaneity of the dynamic system. The estimation results have led to equations
endowed with high fitting power, supporting the hypothesis that behavioural equations
for the EU can be defined at a supranational level in a meaningful way. The validity of
this aggregate approach is confirmed by several simulation experiments.
Article title abbreviation: A model for the EU
Acknowledgements: We thank for their helpful comments an anonymous referee and the
participants at the workshop on ‘Economic Modelling for Forecasting and Impact
Analysis’, Joanneum Research Institute, Vienna, May 2001. A grant from MURST
(60% Ateneo funds) for the quantitative data processing is also gratefully
acknowledged.
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An aggregate model for the EU
INTRODUCTION
The growing integration, both real and financial, of the Member States of the
European Union (EU) makes it useful to treat the European economic system as a single
entity, using variables that are directly related to the European market rather than to the
individual domestic markets. It is therefore appropriate to build an analytical model for
the European economy considered as a single entity, rather than by linking several
national models, each constituted by country-specific functions of consumption,
investment, money demand, and so on. Indeed, while the aggregation of various national
models makes it possible to study problems that are still quite interesting within the
European economy (for instance, the convergence of inflation and monetary dynamics)
the construction of a single model for the entire EU economy using aggregate European
data can be justified on the grounds of at least three arguments:
i) in the eyes of economists, political decision makers, and the public at large, the
European economy is viewed more and more frequently as a whole, with reference to a
European rate of inflation, unemployment, and so on, in addition to the individual
French, German, Italian etc. rates;
ii) analyses of interactions between the three poles of the world economy, the USA,
Japan, and Europe, are more convincing and probably more accurate, if the economy of
Europe, like that of the US, is treated unitarily;
iii) the effects of the enlargement of the EU cannot be easily identified and examined
within the individual Member States; its economic consequences can be determined in a
more careful and reliable way for the European system as a whole.
We therefore present an aggregate econometric model for the EU, composed of 34
equations, of which 20 are stochastic and 14 are identities and definitory equations; the
exogenous variables are 14. The model is estimated on yearly data from 1960 through
1997 and takes three sectors into consideration: the private sector, government (which
aggregates the Public Administration and the Central Bank), and the rest of the world1.
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An aggregate model for the EU
Its theoretical structure is based on the open economy portfolio and macroeconomic
equilibrium scheme, with a certain relaxation of some extreme assumptions about the
regime of exchange rates, the formation of expectations and the management of
monetary policy.
The data result from the aggregation of time series for the twelve countries
constituting the EU in 1995.2 The model should thus be considered as virtual, since the
number of countries constituting the European Community changed during the sample
period. This “virtuality” of the model is required in order to construct a sufficiently long
statistical sample and to analyse an economic system close to that of the current
European Union. On the other hand, the “virtuality” may determine problems of nonhomogeneity of the sample data, both because the interdependence between the twelve
countries considered has grown over time, and because by extending our sample back
we necessarily include in it some major exogenous shocks (such as the oil-price shocks
of the 1970s). However, since European economic integration is an ongoing process,
beginning with the European treaties of the 1950s and proceeding since then at different
rates in different economic sectors, it is impossible to identify a single date (or even a
number of dates) to be taken as a watershed between an “old” and a “new” European
economy. We have therefore chosen to adopt an economic specification that is general
enough both to provide a valid approximation of the underlying economic structure over
the whole sample, and to enable us to detect and represent the relevant structural
changes in the different economic sectors.
It should be stressed that despite these difficulties the literature already presents
several studies that analyse the EU economy at an aggregate level, referring in
particular to its degree of monetary integration (see Den Butter and Van Dijken [5],
Spencer [34], Kremers and Lane [22]). These studies broadly agree that aggregate
EU-wide money demand functions outperform the disaggregated national functions in
explaining European money demand, thus satisfying Grunfeld and Griliches’ [13]
prediction criterion for aggregation. Moreover, aggregate sub-models for some sets of
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An aggregate model for the EU
European or non-US OECD countries already feature in several multi-country
macroeconometric models (see Sims [32], Haas and Masson [14]). A more organic
analysis is carried out by Dramais [8], who proposes an aggregate econometric model,
composed of 54 equations, for the ten-country European Community, and illustrates
its properties by means of several economic policy simulations. Dramais’ research
program, like that followed in the present work, contrasts with the customary practice
of modelling the EU economy by linking national models, as is the case in the Eurolink,
COMET and QUEST models.
In constructing the model we had to cope with a number of problems deriving from
the aggregation of data, the non-stationarity of variables, the simultaneity of equations,
and the nonlinearity of the relationships. European aggregate time series were found to
have stochastic trends, so that standard estimation techniques produce spurious
relations, and partial adjustment schemes, widely adopted in previous European models,
lead to biased dynamic properties (Hendry et al. [19]). Non-stationarity was dealt with
by using Engle and Granger's [10] two-stage estimator: in the first stage, static equations
representing long-run relationships were estimated, verifying the cointegration hypothesis
of variables in each equation; in the second stage, Error Correction Models (ECMs)
representing the short-run dynamic adjustments that develop around long-run equilibria
were constructed. As for aggregation, recent studies (e.g. Lewbel [23]) prove that
under cointegration the aggregation bias vanishes asymptotically: therefore, aggregation
does not prevent us from obtaining consistent estimates of the long-run parameters. As
stated before, because of the growing interdependence of the countries considered, the
equations of the model are likely to display structural changes. We therefore extended
our modelling approach in order to take into account the presence of structural shifts in
the long-run parameters, as well as the simultaneity and nonlinearity of the adjustment
equation.
The estimated covariance matrices of residuals and parameters were then used to
perform several stochastic simulation experiments aimed at evaluating the impact of a
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An aggregate model for the EU
number of exogenous variables on the European macroeconomic framework. In
particular, we simulated the impact of a decrease in public consumption of the same size
experienced by the European economy at the beginning of the 1990s, a terms of trade
deterioration, and an exchange rate devaluation, and compared the simulation results
both with previous studies and with current European economic perspectives.
The paper falls in five Sections. Section 1 contains the structure and properties of the
theoretical model. Section 2 describes the estimation methods applied in this work
pointing out their advantages. Section 3 reports some comments on the estimation
results, while Section 4 describes some dynamic multipliers and Section 5 synthesises
the conclusions. A series of Appendices and Tables report the empirical results of the
estimation and simulation.
1. THE THEORETICAL REFERENCE MODEL
In designing the structure of the underlying theoretical model we started from the
open economy portfolio and macroeconomic equilibrium scheme consisting of three
sectors (the private sector, government, the rest of the world) and four markets (output,
domestic money, foreign money, bonds). Wealth evolves following the public budget
and balance of payments stock/flow identities, and is allocated among several financial
instruments in function of their relative yields, with a feedback on consumption and
money demand functions. The properties of this model have been studied by Branson
and Buiter [4] and O’Connel [25] among others, who show that in the long run both
fiscal and monetary policies are efficient: an increase in public expenditure determines an
increase in output and an appreciation of the exchange rate, while an expansionary
monetary policy produces an increase in output and an exchange rate devaluation.
These effects do not depend on the expectations regime, since they hold under the polar
hypotheses of static expectations and perfect foresight.3 Our reference model extends
this base scheme in several respects.
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An aggregate model for the EU
In the income-expenditure block, the division of absorption between consumption
and investment is represented, and exports are not exogenous.
In the supply side, long-run labour demand derives from cost minimization under
unrestricted Cobb-Douglas technology with labour augmenting technological progress,4
and wage determination is based on Desai’s [6] analysis of the Phillips curve, where the
equilibrium growth of real wages is related to productivity growth and the rate of
unemployment;5 the costs of labour and imported inputs in turn determine the prices of
the demand components.
The assumption of a balanced public budget is relaxed, and the yield of foreign assets
owned by government is considered as exogenous. In the financial sector the
hypotheses of perfect capital mobility and perfect substitutability between domestic and
foreign bonds are abandoned. Therefore, domestic interest rates are no longer
exogenously determined, and portfolio choices are made taking also the foreign rate into
account.6 Furthermore, the foreign net assets of residents are not explicitly represented
by means of a demand function. Therefore, wealth is defined as the sum of domestic
money, foreign money and domestic public debt securities owned by residents. Capital
movements are endogenised directly in function of the interest rate differential between
Europe and the USA. This extended theoretical scheme is represented in Table 1; the
meaning of variables can be found in Appendix B.
[Table 1 about here]
It is worth comparing this structure with that of our closest antecedent, COMPACT
(Dramais [8]). Both models consist of about the same number of equations7 and adopt a
similar framework. In both, the choice was made not to derive the long-run factor
demands consistently from a joint optimisation process. In particular, while the long-run
labour demand functions derive in both models from static cost minimization, the longrun investment functions differ significantly: fixed capital formation is represented in our
model by an accelerator equation augmented with the cost of capital, and in
COMPACT by an adjustment equation à la Knight and Wymer [21],8 where investment
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An aggregate model for the EU
depends on the ratio of expected output to the capital stock. A further difference
concerns the short-run labour demand, which in our model follows naturally from error
correction around the neoclassical static demand function, while in COMPACT it is
determined by a rationing mechanism whose inputs are the neoclassical labour demand,
“keynesian” labour demand, and labour supply.
The decision to neglect the interrelations between factor demands depends mainly on
the lack of reliable figures for the stock of European physical capital. In COMPACT
this variable is reconstructed using a “permanent inventory” relation starting from a
judgmental initial value. The introduction of a proxy for the capital stock is appealing
from a theoretical point of view; however, the resulting investment function, together
with the rationing mechanism in the labour demand, is charged by Dramais himself with
the “pessimistic” behaviour of his model, whose response to real (e.g. fiscal) shocks
appears to be too low, both in itself and in comparison with previous European models.
Other minor differences between the two models regard production and inflation
expectations, which are represented in COMPACT through extrapolative schemes, and
also the formation process of revenues and the structure of public accounts, which in
COMPACT are described in greater detail. As for the expected variables, we decided
not to consider them because we have serious doubts about their effectiveness within
annual models. In fact, setting aside any consideration about the empirical relevance of
expectations defined over an annual time span, as well as of extrapolative schemes,
Hendry and Neale [18] show that in estimating long-run relationships by cointegration
the bias derived from ignoring the difference between actual and expected values will in
any event vanish asymptotically. Indeed, while it is generally true that in this case the
short-run dynamics will still be affected by a specification error bias, it can be argued
that when using annual data the extent of this short-run bias will be negligible for
forecasting and policy analysis purposes.
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An aggregate model for the EU
2. ESTIMATION
As previously pointed out, the Dickey-Fuller [7] unit root test shows that the
European aggregate time series possess stochastic trends: in particular, real variables
appear to be I(1), while prices and nominal variables are mostly I(2), as implied by
Desai’s [6] model. Moreover, most endogenous variables enter the model both in
logarithms (in the behavioural equations) and in natural units (in identities), and some
explanatory variables are constructed as ratios or products of endogenous variables.
Therefore, the system of equations is nonlinear in variables, and the variables are, in
turn, non-stationary.9
In the absence of estimators that take into joint consideration the simultaneity and
nonlinearity of the equations as well as the non-stationarity of the variables, we have
utilised an estimation procedure that deals with these characteristics in two successive
steps: in the first, the non-stationarity of the variables is dealt with by using cointegration
analysis; in the second we allow for simultaneity and nonlinearity in the variables of the
system by using an appropriate estimator for the short-run dynamic equations. The
cointegration was tested by using Engle and Granger’s [10] cointegrating regression
ADF (CRADF) test, based on the OLS estimation of the static long-run relationships;
the simultaneous nonlinear estimation of the ECM was then performed using the Internal
Instrumental Variables (IIV) estimator (Bowden and Turkington [2]).
Some comments about this procedure are in order.
First, the aggregation of data coming from different economic systems could be
questioned as giving rise to unreliable results because of the aggregation bias. However,
several economic and statistical arguments suggest that in our case this problem might
not be as serious as it appears to be at first. In particular, as far as money demand is
concerned, several studies point out that because of the high degree of currency
substitution and portfolio diversification within European countries, the use of aggregate
data, while probably producing some aggregation bias, is at the same time likely to
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An aggregate model for the EU
reduce the specification bias determined at the single-country level by the omission of
significant foreign or aggregate variables.10 From a statistical point of view, on the other
hand, recent developments in the theory of cointegration provide comforting results by
demonstrating that cointegration can eliminate aggregation bias in much the same way
that it eliminates simultaneity or error in variables bias. Sufficient conditions for the
aggregation bias to vanish asymptotically are provided by Ghose [11] in the linear
aggregation case and by Lewbel [23] in the log-linear aggregation case. In the latter
case, which is more suited to our needs, it is shown that OLS estimates of long-run
aggregate elasticities are consistent even in the presence of a small-sample aggregation
bias, provided that the joint distribution of the disaggregated regressors meets some
relatively loose conditions;11 some preliminary empirical investigations show that these
conditions appear to be met by most of the time series considered in the present model.
Second, since the powers of integration and cointegration tests depend on the time
span (the number of years) of the sample and not on the number of observations (Shiller
and Perron [31]), the size of our sample, consisting of 38 annual observations from
1960 to 1997, is not so small as it might seem. However, as the usual critical values
refer to samples composed of several dozens of observations, we utilised instead the
small sample critical values of Blangiewicz and Charemza [1].
Third, the long data samples required by cointegration analysis lead to problems of
non-homogeneity of the data. These problems were to be expected in our case, both
because our aggregate data reflected a growing degree of interdependence between the
underlying national economies, and because these economies as a whole were affected
by a number of exogenous shocks in the reference period.12 Structural shifts in the longrun parameters determine a loss of power in the cointegration tests, leading the
researcher to accept the null of no cointegration too often. To overcome this difficulty,
when the customary cointegration test failed to reject the null we adopted the procedure
of Gregory and Hansen [12], which tests the null of no cointegration against the
alternative of cointegration in the presence of structural breaks. The breaks are
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An aggregate model for the EU
modelled using the dummy variable ϕτt = I( t>[Tτ] ), where I is the indicator function, T
is the sample size, τ the relative timing of the change point, and [.] the integer part
function. Three kinds of break are considered:
Model C - level shift:
yt = µ1 + µ2ϕτt + α ’xt + zt
Model C/T - level shift with trend:
yt = µ1 + µ2ϕτt + βt + α ’xt + zt
Model C/S - regime shift:
yt = µ1 + µ2ϕτt + α 1’xt + α 2’xtϕτt + zt
where yt is the dependent variable, xt a vector of k explanatory variables, α , β and the
µj are parameters, ϕτt is the shift dummy variable and zt is the cointegrating residual.
Models C and C/T allow the equilibrium relation to shift, while model C/S allows it to
rotate as well.
The test statistic is evaluated as ADF i* = inf ADF i (τ) , where ADF i(τ) is the
τ
cointegrating ADF statistic calculated using the OLS residuals in model i (i = C, C/T,
C/S). In other words, ADF i* is the smallest among the ADF statistics that can be
evaluated in model i across all possible dates of structural break. As we generally had
no a priori information on the shape of the relevant alternative, we calculated the ADF i*
statistics for each of the three models C, C/T and C/S. Where the null of no
cointegration was rejected in favour of more than one alternative, we chose either the
model corresponding to the more significant statistic, or that with the more meaningful
parameters from the point of view of economic theory. The lagged OLS residuals from
this model were included as an error correction term in the short-run adjustment
equation.
Fourth, OLS estimates of long-run static equations with cointegrated variables are
consistent even in the presence of simultaneity (Park and Phillips [26]). Vice versa, OLS
estimates of adjustment equations, used in the construction of most European models,
are affected by simultaneity bias, which is aggravated by the nonlinearity in variables of
the equations. To cope with this, we used the Internal Instrumental Variables (IIV)
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An aggregate model for the EU
(Bowden and Turkington [2]). In order to define this estimator we write the ECM
equations system using Hatanaka’s [16] notation:
Gi
∑β
Ki
ij
f j(yt, xt) +
j =1
∑γ
h =1
ih
x th = uit
t = 1,...,T ; i = 1,..., G
where yt is the vector of all G endogenous variables in t; xt is the vector of all K
exogenous variables; f j(yt,xt) are the nonlinear functions (linearly independent and not
depending on unknown parameters) representing the nonlinearity of the system; β ij and
γih are parameters; Gi≤G is the number of endogenous variables in the i-th equation; Ki
≤K is the number of exogenous variables in the i-th equation; uit is the structural residual
of the i-th equation in t. The f j(.)’s are the endogenous functions and the model is
assumed to contain n>G such functions; the Ki exogenous variables are assumed to
include the error term estimated in the first stage by the OLS estimator and lagged by
one period.
Following Hatanaka [16, note 6], we substituted G from the n endogenous functions
by introducing auxiliary variables zjt= f j(yt,xt) that enter the model linearly; the equations
can thus be normalised so that the endogenous functions appear only in the right-hand
member:
(1)
yi = Yig β i + Xiγ i + ui = Hiδ i + ui
where yi is the vector of T observations related to the i-th endogenous variable; Yig is
the T×(Gi-1) matrix of observations related to the Gi-1 endogenous functions not
removed from the i-th equation; Xi is the T×Ki matrix of predetermined variables; ui is
the T×1 vector of structural disturbances in the i-th equation; Hi = [Yig M Xi] and δ i = [
β i', γ i']' is the vector of Gi + Ki - 1 structural parameters in the i-th equation.
Using this notation, the IIV estimator is defined as:
δ$ i = ( Z'Hi)-1Z'yi
i = 1,..., G
where Z is the T×(Gi+Ki-1) matrix of internal instruments, of which the t-th row is:
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An aggregate model for the EU
[f 1 ( y$ t, xt), ..., f G1 −1 ( y$ t, xt), x 1,t,..., x Ki ,t ]
$ =X(X'X)-1X'Y; X is the T×K matrix of all
where y$ t is the t-th row of the T×G matrix Y
predetermined variables; and Y is the T×G matrix of all endogenous variables. Bowden
and Turkington [2, 3] show that this estimator is superior to the NL2SLS especially in
the estimation of macroeconomic models of medium-large size characterised by
logarithmic nonlinearities, such as ours.
3. THE EMPIRICAL MODEL
According to the unit-root tests (not reported) all variables utilised in the stochastic
equations turned out to be integrated of order greater than zero; in particular, real
variables are I(1) and prices and nominal variables are I(2).
Drawing on these results, we estimated by OLS the long-run equations between I(1)
variables; where the variables involved were I(2), one unit root was removed by
differencing before estimating the cointegrating regression. Appendix A reports the
estimates of the long-run equations together with a cointegration test statistic. In 11 out
of 20 cases the CRADF statistic proved significant; in the remaining 9 cases we
tentatively assumed that the failure to reject the null was determined by the loss of
power induced by a structural shift in the long-run parameters, and we tested again the
null of no cointegration with Gregory and Hansen’s procedure. The tests were carried
out at the 10% level. The null of no cointegration was always rejected, with the possible
exception of equations 2 (investment), 3 (exports), 14 (interest payments on public
debt) and 17 (short-term interest rate). Even in these cases the error-correcting term in
the short-run equations proved always to be significant, which can be construed as
indirect evidence of cointegration.
The lagged OLS residuals of static equations were then considered as predetermined
variables in the IIV estimation of the ECM. The first stage of the IIV estimation was
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An aggregate model for the EU
performed by projecting the endogenous variables included among the explanatory
$ were then inserted in the
variables onto the 14 exogenous variables; the projections Y
nonlinear functions appearing in matrix Yig of equation (1), producing the internal
instrumental variables. In order to improve the efficiency of estimation, in the second
stage all the I(0) predetermined variables were inserted in the instruments matrix Z, in
addition to the internal instruments.
The IIV estimates of ECM are shown in Appendix A, with their diagnostics
described in Appendix C. The fit of the equations, measured by the generalised R 2 of
Pesaran and Smith [28], is very good,13 the parameters are highly significant, with some
minor exceptions, and the residuals pass all the simultaneous equations diagnostic tests
for autocorrelation, homoskedasticity, normality, linearity of the functional form, and
orthogonality of instruments with respect to residuals.
3.1 The real sector
In the private consumption function neither the inflation nor the wealth effect proved
statistically significant. Consumption and disposable income are not cointegrated
according to the standard CRADF test; on the contrary, Gregory and Hansen’s
procedure rejects the null of no cointegration in favour of model C/T with a regime shift
after 1972, corresponding to the first oil price shock. The equation of investment is not
completely satisfactory from a statistical point of view. Our preferred specification
relates real investment to real GDP and the long-run real interest rate. These variables
do not cointegrate, and Gregory and Hansen’s procedure did not point out any
significant structural break. However, the error-correcting residuals prove significant in
the short-run equation. The long-run elasticity of investment to output is close to one,
while the impact elasticity is very large, at 208%. The impact of interest rates on
investment is significant but not large. The long-run semielasticity of investments with
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An aggregate model for the EU
respect to real interest rates is equal to 0.012, corresponding to an average elasticity of
4.2%.
As for the trade flows, exports react to world demand (measured by imports of nonEU countries) by a long-run elasticity equal to 91%, while the long-run elasticity of
imports to the European GDP is about 172%. Gregory and Hansen’s procedure
suggests a possible structural break in exports between 1991 and 1992. In both
equations relative prices have no significant impact effect.
As stated before, the long-run labour demand was specified starting from the
conditional labour demand function under unrestricted Cobb-Douglas technology, which
can be written in log-linear form as
lnNt = k -
W
b
ln  t
a + b  PIt

1
 +
ln Y 90 t + ut
 a+b
(2)
where a and b are the elasticities of output with respect to labour and capital
respectively, and k is a constant depending on a, b and a scale factor; the variables are
defined in Appendix B. In Equation (2) the cost of capital is proxied by the deflator of
fixed capital formation PIt. Estimation by Engle and Granger’s [10] procedure gave a
CRADF of –1.35, well within the acceptance region of the null of no cointegration. We
decided therefore to re-estimate (2) by Gregory and Hansen’s [12] procedure. The null
of no cointegration was rejected in favour of the C/T model
lnNt = 10.58 + 0.04 I(t>1987) – 0.07 ln (W/PI)t + 0.15 lnY90t – 0.0008t
with R 2 = 0.93 and ADF(C/T) statistic equal to –5.60 (significant at 2.5%). The time
trend, whose inclusion was suggested by the procedure, can be construed in this context
as a proxy for Harrod-neutral technological progress. We decided therefore to include
it, giving it with the same status as the other economic variables, i.e. allowing also its
coefficient to shift. The resulting equation is reported as Equation 5 in Appendix A and
allows the intercept as well as the three coefficients of lnY90t, ln(W/PI)t and t to shift.
Interestingly enough, in this equation the structural break is located in 1982, i.e., exactly
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An aggregate model for the EU
within the period in which the European unemployment rate experienced an
unprecedented rise, going from 5.3 in 1979 to 10.6 in 1984.
Real wages rise in the long run following the growth in the average productivity of
labour; deviations from this trend are explained by unemployment, which enters the
equation with a total elasticity of about 2% at the end of the sample. The relatively low
coefficient of the error-correction term (equal to -.49) means that adjustments of real
wages to the unemployment rate are fairly slow. These results support, at the aggregate
level, conclusions similar to those reached at the level of the single OECD countries (see
Elmeskov and MacFarlan [9]), according to which the persistence of unemployment in
Europe is largely due to the slowness of adjustment processes in the labour market.
In the price equations we imposed first-degree homogeneity, which was verified
indirectly by cointegration tests on the residuals.
3.2 The public-finance and financial sector
In the public-finance block, direct taxes and social transfer payments react to
nominal GDP, while social security contributions are related to wages. As all variables
involved are I(2), in these equations the long-run equilibrium was estimated in first
differences.
The money demand equation relates real M2 to real GDP, the short-term interest
rate, and the European currency/USD exchange rate. The exchange rate enters with a
negative sign, which means that a devaluation determines a decrease in domestic money
demand.
In the representation of interest rates, the significant positive effect of the public
deficit/GDP ratio on the long-term interest rate is worth noting. The increase of one
point in this ratio determines an increase in the long-term rate equal to about 0.33
percentage points in the long run, with an impact multiplier equal to roughly 0.40
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An aggregate model for the EU
percentage points. On the contrary, the short-term rate dynamics are mainly determined
by international interest rates.
The exchange rate is explained by domestic and foreign (i.e. US) short-term interest
rate and inflation rate. Finally, capital movements are a function of the domestic and
foreign interest rates.
4. THE DYNAMIC MULTIPLIERS IN SOME SIMULATION EXPERIMENTS
The behaviour of the model was analysed through a number of experiments of expost deterministic and stochastic simulation, aimed at evaluating the model’s stochastic
properties (such as the bias of deterministic simulations and the variability of ex-post
stochastic simulations) and quantifying the intensity of its transmission mechanisms. In
this section we report some results relative to the dynamic multipliers of the model.
The multipliers were evaluated by stochastic simulation within the sample (years
1984-1993), taking both structural and parameter disturbances into account,14
according to the following three hypotheses:
a) a permanent decrease in real public consumption, G90, equal to 1% of GDP;
b) a deterioration in the international terms of trade (a 5% permanent increase in
import prices in dollars, PMD, and a 5% permanent decrease in world export prices in
dollars, PXW);
c) a devaluation of the nominal exchange rate (a 5% permanent increase in the
European currency/USD exchange rate, USD).
The dynamic multipliers and their dispersions were calculated using Hall’s [15]
method, which reduces the simulation variance by using the same pseudorandom
disturbances for both the baseline and the perturbed solution in a given replication. For
every multiplier we performed one thousand replications in antithetical pairs.
In the Tables and Figures reporting the results, the deviations of the perturbed
simulations from the controls are expressed in absolute terms for the variables measured
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An aggregate model for the EU
in percent points (such as interest rates, inflation rates, and so on) and in percent terms
for the others. Standard deviations of multipliers are reported in round brackets, while in
the Figures a pair of dotted lines shows the approximate 95% confidence intervals of the
multipliers.
4.1 Fiscal shock
The first experiment analysed a restrictive fiscal shock consisting in a permanent
decrease in real public consumption, G90, equal to 1% of real GDP. The effects on real
and financial variables are illustrated in Table 2 and Figure 1.
As shown in the previous Section, both investments and imports have large impact
elasticities with respect to GDP. However, the responses of these two variables have
opposite effects on aggregate GDP and therefore tend to cancel each other out.
Consumption, in turn, reacts more slowly to disposable income. Therefore, the impact
Keynesian multiplier is negligible and in the first year the real GDP decrease does not
differ significantly from the size of the shock.
[Table 2 and Figure 1 about here]
The fall in demand involves an increase in the unemployment rate, which at first is
quite small, though significant, at about 0.4%. This increase reflects on price dynamics,
with a significant fall in the inflation rate. The reduction in government consumption
reduces the public deficit-to-GDP ratio, though automatic stabilisers keep this decrease
at about 0.7 points. Both the public deficit and the inflation response (via the short-term
interest rate) determine a decrease in the long-run interest rate.
From the second year onwards the Keynesian multiplier develops its effects on
aggregate GDP, and the consequences of output dynamics on unemployment and
inflation become more apparent. After the fourth year the fall in real wages feeds back
on unemployment, bringing it back towards its reference path. The fall in GDP reacts
also on the fiscal sector, where the public deficit/GDP ratio comes back to its reference
18
An aggregate model for the EU
path and displays an increase starting from the sixth year after the shock (this multiplier,
however, is quite dispersed). Meanwhile, once the initial shock has been absorbed, the
GDP components and the GDP itself approach the control path.
It is of some interest to compare the response of our model with that of COMPACT
(see Table 4 in Dramais [8]).15 Since the latter considers an expansionary fiscal shock,
we performed the same simulation experiment with our model and compared the results
in Figure 2, where the solid and dotted lines represent, as before, the multipliers of our
model together with their 95% confidence intervals, while the dashed lines are the
corresponding COMPACT multipliers (not available for the inflation rate).
[Figure 2 about here]
As stressed in Section 1, the main differences between the two models lie in the
supply side specification. However, in the medium run, employment is driven in both
models by neoclassical factor demand equations based on very similar technologies.16
Therefore, we should expect any difference in the employment multipliers to vanish
eventually. This is confirmed by our results: both models feature a zero long-run
multiplier of the unemployment rate. However, the shocks are more persistent in our
model, where it takes eight years to bring the multiplier back to zero (as compared to
five years in COMPACT). This difference is influenced ceteris paribus by the long-run
elasticity of labour demand to relative factor prices, which in COMPACT, owing to the
CES specification of potential labour demand, equals the elasticity of substitution,
estimated at 0.96, while in our model the factor prices elasticity equals 0.46. Therefore,
the response of unemployment to the increase in real wages is larger and more rapid in
COMPACT than in our model.
On the other hand, the long-run multipliers differ significantly in the fiscal sector.
While COMPACT features persistent effects of the fiscal shock on the public
deficit/GDP ratio, with an impact multiplier of 0.9 percentage points slowly decreasing
to 0.7 after five years, in our model the impact of 0.7 is nearly offset after 4 years and
rebounds to negative (though imprecisely estimated) values in the longer run. This
19
An aggregate model for the EU
difference can be traced back to the different response of GDP to real shocks in
COMPACT, where after the second year the GDP starts to decrease towards its
reference path, while in our model it takes about eight years for the GDP to come back
to the control solution. The lower response of GDP limits the operation of the automatic
stabilisers, thus determining persistent effects on the public deficit-to-GDP ratio, and
therefore on the long-term interest rates.17
It is of some interest to remark that this standard experiment provides some insight
into the European unemployment dynamics in the 1990s. The shock considered here is
of about the same size as the decrease in public consumption experienced in the
European Union in the transition from the 1980s to the 1990s. From 1987 to 1990 the
public consumption/GDP ratio fell from 21.3% to 20.3% and despite some
countercyclical swing remained consistently lower during the 1990s (with a sample
average of 20.3%, compared with 21.3% in the previous decade).18 The responses of
unemployment and inflation were very close to those implied by the model. In particular,
unemployment, which was at 8.1% in 1991, rose by 0.3 percentage points in 1993 and
then more quickly reaching a maximum of 11.1% in 1994 (i.e. four to five years after the
fiscal shock). It then took about six years to come back to the initial value, with an
estimated 8.3% in 2000.
While this analysis is obviously subject to a ceteris paribus clause, as public
consumption was certainly not the only relevant variable that underwent a shock in the
last decade, we find that there are striking similarities between the model and the actual
dynamics, in particular as far as the persistence of the shock is concerned.
4.2 Worsening of international terms of trade
Table 3 and Figure 3 report the results of a second simulation experiment, carried
out under the hypothesis of a permanent worsening of international terms of trade with a
20
An aggregate model for the EU
5% increase in import prices (in dollars) and a 5% decrease in world export prices (in
dollars).
[Table 3 and Figure 3 about here]
In the first year this worsening produces an increase in relative export prices and
relative import prices; in the meantime the increase in import prices causes an increase in
domestic prices (the inflation rate increases by 0.88% with respect to the control
solution), determining a decrease in disposable income in real terms. As a consequence,
imports, real consumption, and (with a time lag) exports diminish significantly, and the
decrease in imports is not such as to balance the decrease in other items in the national
budget, so that GDP decreases by about 0.33%.
The impact effects of this recessionary impulse on the labour market are very limited,
with a small and imprecise negative response, but from the second year onward
unemployment begins to rise and remains significantly above the control line for about
six years. The rise in unemployment dampens the effects on inflation, which comes back
to the control line after three years. The dynamics of prices and interest rates influences
the exchange rate, which devaluates in response to the consumer price inflation.
As the years pass, the inflation rate converges to its control path, while the effects on
output and the unemployment rate appear more persistent. At the end of the period,
consumption, imports and exports are lower than their control solutions, real GDP is
lower in a range of 0.11-0.79 percentage points (evaluated by the approximate 95%
confidence interval of the stochastic simulation), the interest rate and the exchange rate
do not significantly differ from the control solution, and the public deficit-to-GDP ratio
exceeds the control solution by 0.07-1.07 percentage points.
4.3 Devaluation of the exchange rate
In the last simulation experiment, set forth in Table 4 and Figure 4, we analysed the
effects of a 5% depreciation of the nominal ECU/USD exchange rate.
21
An aggregate model for the EU
[Table 4 and Figure 4 about here]
Depreciation in the exchange rate exerts its effects mainly through the price system.
In the first year the relative prices of imports increase and those of exports decrease. As
a consequence, imports decrease by 0.63% but the overall effect on GDP is negative as
the response of exports is delayed and the increase in domestic prices causes a
reduction in the purchasing power of households in real terms and therefore a reduction
in consumption, which, through the multiplier, leads to a decrease in GDP equal to
0.25% with respect to the control value. From the third year onward the recessionary
impulse is dampened by the recovery of investments, which react to the decrease in the
real interest rate. At the same time, the impulse spills over into the labour market, giving
rise to a period of stagflation, where inflation ranges from about 0.1 to 0.3 points and
unemployment from about 0.1 to 0.2 points above the control. This stagflation extends
over about four to six years (the unemployment multiplier becomes not significantly
different from zero starting from the fifth year). At the end of the period, the inflation rate
returns to the reference values, the long-term interest rate is slightly under the control
solution, GDP is decreasing and unemployment is increasing.
As far as prices are concerned, the response of our model is quite close to that of
COMPACT (see Table 8 in Dramais [8]). However, the response of real GDP is of
opposite sign in our model, mainly because the response of exports to relative prices is
lagged, and the impact response of investments is negative, as a result of the increase in
the real rate of interest.
Also in this case it is of some interest to compare the orders of magnitude of the
model responses with the current European economic trends. Since the inception of the
EMU the European currency has experienced a swift devaluation of about six times the
amount hypothesised in our experiment. Two years later European inflation is estimated
at 3%, namely about six times the response implied by our model. To the extent that this
correspondence can be construed as a validation of the model, in the absence of
positive shocks or of corrective actions one can expect in the coming years a further
22
An aggregate model for the EU
increase of unemployment in a range between 0.6 and 1.2 points, coupled with
persistent inflation, slowly recovering from 3%.
5. CONCLUSIONS
We have presented the structure and properties of an aggregate econometric model
for the EU as a whole, consisting of 34 equations, of which 20 are stochastic, based on
an open economy portfolio and macroeconomic equilibrium scheme, and estimated on
annual data aggregated over the twelve-member EU, ranging from 1960 to 1997.
As stressed in the introduction, this aggregate approach (intended here in the
meaning of supranational aggregation, i.e. aggregation of different countries) is not a
novelty and has already been pursued in the literature both at the single equation and at
the simultaneous equations level. In particular, a number of recent studies apply it to the
analysis of the European demand for money, showing that aggregate functions
outperform the disaggregated (i.e. national) ones under a number of criteria. Moreover,
aggregate sub-models related to some subset of European or OECD countries do
already feature in most multi-country models. However, these aggregate sub-models are
explicitly considered as ancillary blocks, designed for simulation purposes in order to
represent the repercussions between a national model (or a set of linked national
models) of interest on one hand, and the “rest of the world” on the other hand. Even
Dramais [8] considers his aggregate COMPACT model as a temporary experience in a
research programme envisaging another multi-country model of the European economy.
In this study we started from a different premise, namely, that the specification of an
aggregate European model provides a valuable economic research tool in itself, as it is
certainly complementary, and probably superior for several policy analyses, to the
linkage of country submodels.
On the basis of this premise we applied advanced methods of estimation and analysis
to our aggregate data set. Our research strategy takes into account the non-stationarity
23
An aggregate model for the EU
of the time series data by applying cointegration analysis, extended in order to cope with
the possible presence of structural breaks in the long-run parameters, as well as with the
nonlinearity and simultaneity of the dynamic equations system. In about half of the
stochastic equations Gregory and Hansen’s [12] procedure revealed the existence of
structural breaks in the long-run parameter. The dates of these structural breaks are
determined endogenously by the procedure and appear to be meaningful from an
economic point of view. The estimation by Internal Instrumental Variables of the ECMs
has led to equations with excellent statistical properties, thus favouring the hypothesis
that behavioural equations can be defined in a meaningful way for the European Union
as a whole. The analysis of simulation experiments related to a set of standard
hypotheses (decrease in public expenditure, terms of trade shock, and so on) confirmed
the assumption that the model constitutes an agile and effective tool for the study of the
European economy at an aggregate level. In particular, the model was shown to be an
improvement over previous aggregate explanations of the European economy in that its
dynamic multipliers provide a better account of certain recent stylised facts, such as the
unemployment and inflation behaviours in the last decade.
Our empirical research strategy has a further advantage, in that some recent studies
(see Lewbel [23]) demonstrate that cointegration can eliminate the log-linear
aggregation bias in the same way that it eliminates the simultaneity bias. Although these
results rest on asymptotic arguments, they indicate that cointegration methods present
distinct advantages in the estimation of aggregate behavioural equations.
However, we do not believe it appropriate to think of aggregation in purely statistical
terms. The progress of European economic and political integration makes it obvious to
think of Europe as a single area. Therefore, the approach adopted in this paper will
present itself eventually as a more and more natural option. Nevertheless, and despite
the encouraging statistical evidence provided here as well as in other recent studies, we
do not believe that this approach will ever replace that based on the linkage of national
models, for the same reason for which these models, in turn, do not hinder the
24
An aggregate model for the EU
development of regional models. As a matter of fact, apart from the theoretical and
statistical aspects, the aggregation level is a choice of model design, dictated by the
nature of the problems of interest. In this respect some problems offer themselves
naturally to an aggregated analysis: the prediction of “European” variables, as well as
the study of the interactions between Europe and the other poles of the world economy,
are two possible examples. On the other hand, problems where the coordination
between national (or even regional) policy makers, or the spill-over from one region or
area to another, is crucial (such as, for instance, the study of the relations between
labour mobility and unemployment, or the analysis of the convergence of national or
regional economies), require a “disaggregated” framework, i.e. the linkage of national or
regional models.
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An aggregate model for the EU
4.
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An aggregate model for the EU
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Hendry, D F and Neale, A J ‘Interpreting long-run equilibrium solutions in
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Hendry, D F, Pagan, A R and Richard, J D ‘Dynamic specification’, in Griliches,
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An aggregate model for the EU
20.
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Knight M D and Wymer C ‘A macroeconomic model of the United Kingdom’
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Kremers, J J M and Lane, T D ‘Economic and monetary integration and the
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Lewbel, A ‘Aggregation with log-linear models’ Review of Economic Studies,
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McCarthy, M D ‘Some notes on the generation of pseudo-structural errors for
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Park, J Y and Phillips, P C B ‘Statistical inference in regressions with integrated
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Spencer, P ‘Monetary integration and currency substitution in the EMS: The case
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29
An aggregate model for the EU
APPENDIX A: EQUATIONS
We report here the estimated equations of the model together with their diagnostics,
whose meanings are summarised in Appendix C.
1. Private consumption
Long-run equation
lnC90t = 0.34 + 0.02ϕt + 0.002 t + 0.89 ln(YD/PC)t + z$ 1,t
sample: 60-97
ϕ1,t = I(t>1972) ;
ADF(C/T) = -4.98* [-4.99]
Short-run equation
(1 – 0.19L) ∆ln C90t =
(2.5)
sample: 62-97
0.003
(1.7)
+ 0.70∆ln (YD/PC)t
(8.2)
- 0.55 z$ 1,t-1
(3.8)
2
GR = 0.60
LMI = 0.09; LMF = 0.59; LMN = 0.88; LMO = 0.35; LMA = 0.24
2. Gross fixed capital formation
Long-run equation
lnINPR90t = -0.70 + 0.92 lnY90t - 0.012 (RL-100×∆lnPY)t + z$ 2,t
sample: 61-97
CRADF(0) = -2.2 [-3.2]
Short-run equation
(1 -0.22L) ∆ln INPR90t =
(3.2)
-0.06 + 2.08 ∆ln Y90t
(7.1) (13.6)
-0.22 z$ 2,t-1
(2.6)
+0.001 t
(4.5)
sample: 63-97
-0.004∆(RL-100×∆lnPY)t
(0.8)
2
GR = 0.71
LMI = 0.59; LMF = 0.42; LMN = 0.70; LMO = 0.06; LMA = 0.36
3. Exports of goods and services
Long-run equation
lnX90t = 0.73 – 0.21ϕ3,t + 0.91 ln M 90W t - 0.12 ln(PX/ PX W ×USD)t + z$ 3,t
sample: 60-97
ϕ3,t = I(t>1991) ;
ADF(C) = -4.58 [-4.92]
Short-run equation
30
An aggregate model for the EU
∆ln X90t = 0.04 + 0.52∆ln M 90W
(3.6) (5.0)
t-
0.001t- 0.34 z$ 3,t-1
(2.7) (3.2)
2
sample: 62-97
GR = 0.52
LMI = 0.09; LMF = 0.26; LMN = 0.59; LMO = 0.28; LMA = 0.44
4. Imports of goods and services
Long-run equation
lnM90t = -7.49 + 1.72 lnY90t - 0.21 ln(PM/PY)t + z$ 4,t
CRADF(0) = -3.1* [-3.2]
sample: 60-97
Short-run equation
∆ln M90t =
-0.04
(3.2)
sample: 62-97
+ 2.54∆ln Y90t
(10.3)
+ 0.001 t
(2.7)
-0.27 z$ 4,t-1
(2.0)
2
GR = 0.77
LMI = 0.29; LMF = 0.44; LMN = 0.92; LMO = .85; LMA = 0.25
5. Total employment
Long-run equation
lnNt = 8.98 – 5.87ϕ5,t + (0.34+0.76ϕ5,t) lnY90t – (0.26-0.20ϕ5,t) ln(W/PI)t +
- (0.0007+0.019ϕ5,t) t + z$ 5,t
sample: 60-97
ϕ5,t = I(t>1982) ;
ADF(C/S) = -5.25 [-5.75]
Short-run equation
(1- 0.88L) ∆ln Nt = -0.002 +
(5.6)
(0.8)
sample: 62-97
0.64 ∆ln Y90t - 0.54 ∆ln(W/PI)t
(4.1)
(3.2)
2
GR = 0.66
LMI = 0.92; LMF = 0.45; LMN = 0.19; LMO = .89; LMA = 0.06
6. Gross wages
Long-run equation
∆ln(W/PC)t - ∆ln(Y90/N)t = 0.02 – 0.002 U + z$ 6,t
sample: 61-97
CRADF(0) = -3.5** [-2.7]
31
-0.67 z$ 5,t-1
(3.0)
An aggregate model for the EU
Short-run equation
∆2ln Wt =
0.002 + 0.87 ∆2lnPCt
+ 0.63 ∆2ln(Y90/N)t
- 0.01 ∆Ut -0.49 z$ 6,t1
(1.3)
(3.4)
(3.5)
(3.7)
(4.3)
+ 0.03 D70t
(2.7)
sample: 63-97
2
GR = 0.36
LMI = 0.66; LMF = 0.35; LMN = 0.51; LMO = 0.56; LMA = 0.00
7. Deflator of private consumption
Long-run equation
∆lnPCt = 0.0008 + 0.86 ∆lnWt + 0.14 ∆lnPMt - ∆ln(Y90/N)t + z$ 7,t
sample: 61-97
CRADF(0) = -3.7** [-3.2]
Short-run equation
∆2ln PCt = 0.001 + 0.73∆2ln Wt
(1.2)
(3.6)
sample: 62-97
+ 0.08∆2ln PMt -0.52 z$ 7,t-1
(2.8)
(4.1)
2
GR = 0.64
LMI = 0.90; LMF = 0.80; LMN = 0.77; LMO = 0.22; LMA = 0.83
8. Deflator of gross fixed capital formation
Long-run equation
∆lnPIt = -0.02 + 0.80 ∆lnWt + 0.20 ∆lnPMt + z$ 8,t
sample: 61-97
CRADF(0) = -3.2** [-3.2]
Short-run equation
∆2ln PIt = 0.0002 + 0.70 ∆2lnWt + 0.10∆2lnPMt -0.63 z$ 8,t-1
(0.1)
(2.5)
(3.6)
(4.7)
sample: 63-97
2
GR = 0.33
LMI = 0.25; LMF = 0.65; LMN = 0.49; LMO = 0.42; LMA = 0.10
9. Deflator of exports of goods and services
Long-run equation
∆lnPXt = 0.002 + 0.38 ∆lnWt + 0.62 ∆lnPMt + z$ 9,t
sample: 60-97
CRADF(2) = -3.7** [-3.2]
32
-0.04 D76t
(3.2)
An aggregate model for the EU
Short-run equation
∆2ln PXt =
-0.00 + 0.04 ∆2lnWt
(0.0) (0.2)
+ 0.58∆2lnPMt
(44.3)
- 0.32 z$ 9,t-1
(2.9)
2
sample: 63-97
GR = 0.96
LMI = 0.60; LMF = 0.71; LMN = 0.55] LMO =.18; LMA = 0.85
10. Deflator of public consumption
Long-run equation
∆lnPGt = 0.56 ∆lnPCt + 0.44 ∆lnWt + z$ 10,t
CRADF(0) = -4.7** [-3.2]
sample: 61-97
Short-run equation
∆2ln PGt = -0.0005 + 1.16 ∆2lnPCt - 1.09 z$ 10,t-1
(0.4)
(7.5)
(8.2)
2
sample: 63-97
GR = 0.43
LMI = 0.98; LMF = 0.47; LMN = 0.47; LMO = 0.03; LMA = 0.21
11. Direct taxes
Long-run equation
∆lnDTt = -0.01 + 1.38 ∆lnYt + z$ 11,t
CRADF(0) = -6.5** [-2.7]
sample: 61-97
Short-run equation
∆2lnDTt =
-0.00 + 1.76 ∆2lnYt
(0.2) (4.6)
sample: 63-97
-1.06 z$ 11,t-1
(6.1)
2
GR = 0.63
LMI = 0.07; LMF = 0.93; LMN = 0.74; LMO = 0.39; LMA = 0.89
12. Social security contributions
Long-run equation
∆lnSCt = 0.02 + 0.92 ∆lnWt + z$ 12,t
sample: 61-97
CRADF(0) = -4.3** [-2.7]
33
An aggregate model for the EU
Short-run equation
∆2lnSCt =
-0.66 z$ 12,t- + 0.06 D73t
-0.00
-0.05 D92t
1
(0.8)
sample: 63-97
(4.5)
(3.1)
(2.8)
2
GR = 0.50
LMI = 0.64; LMF = 0.29; LMN = 0.84; LMO = 0.46; LMA = 0.67
13. Government social transfer payments
Long-run equation
∆lnSBt = 0.01 + 1.03 ∆lnYt + z$ 13,t
sample: 61-97
CRADF(1) = -4.7** [-2.7]
Short-run equation
∆2ln SBt = -0.00 -0.80 z$ 13,t-1 - 0.11 D70t +0.10 D75t
(0.6) (7.6)
(4.6)
(4.3)
sample: 63-97
2
GR = 0.71
LMI = 0.16; LMF = 0.34; LMN = 0.41; LMO = 0.21; LMA = 0.99
14. Interest payments on public debt
Long-run equation
lnIPDt = 0.45 –1.51ϕ14,t + (0.85+0.37ϕ14,t) ln(RL×B/100)t + z$ 14,t
sample: 60-97
ϕ14,t = I(t>1978)
ADF(C/S) = -4.3 [4.95]
Short-run equation
(1-0.45L) ∆lnIPDt =
(3.6)
sample: 63-97
0.01
(1.1)
+ 0.43∆ln(RL×B/100)t
(5.0)
-0.21 z$ 14,t-1
(2.8)
2
GR = 0.88
LMI = 0.24; LMF = 0.05; LMN = 0.11; LMO = 0.62; LMA = 0.96
15. Demand for M2
Long-run equation
ln(M2/PY)t = - 9.02 + 1.48 lnY90t - 0.003 RBt - 0.08 USDt + z$ 15,t
sample: 60-97
CRADF(0) = -6.8** [-4.35]
Short-run equation
34
An aggregate model for the EU
∆ln (M2/PY)t =
sample: 62-97
0.00+ 1.29 ∆lnY90t - 0.004∆RBt - 0.08 ∆USDt - 0.86 z$ 15,t-1
(0.6) (4.6)
(1.4)
(1.8)
(4.2)
2
GR = 0.51
LMI = 0.42; LMF = 0.85; LMN = 0.67; LMO = 0.14; LMA = 0.48
16. Demand for public debt securities
Long-run equation
lnBt = - 0.57 + 0.07 ϕ16,t + 1.00 ln(D+R) + 0.01 (RL-100×∆lnPC)t + z$ 16,t
sample: 61-97
ϕ16,t = I(t>1986)
ADF(C) = -5.3** [-4.6]
Short-run equation
∆ln Bt =
-0.002 + 1.00 ∆ln(D+R)t
(0.4)
(fixed)
-0.69 z$ 16,t-1
(5.8)
sample: 63-97
+ 0.002 ∆(RL-100×∆lnPC)t +
(0.2)
- 0.09 D75t
(3.4)
2
GR = 0.58
LMI = 0.86; LMF = 0.60; LMN = 0.59; LMO = 0.52; LMA = 0.25
17. Short-term interest rate
Long-run equation
RBt = 0.85 – 4.20 ϕ17,t + 0.17 t + 0.32 (100×∆lnPC)t + 0.40 RUS
+ z$ 17,t
t
sample: 61-97
ϕ17,t = I(t>1993)
ADF(C/T) = -4.97 [5.29]
Short-run equation
∆RBt =
0.02 + 0.46 (100×∆lnPC)t
(0.1) (1.8)
sample: 63-97
+ 0.41 ∆RUSt -0.77 z$ 17,t-1
(1.7)
(4.0)
- 2.89 D75t
(2.3)
2
GR = 0.52
LMI = 0.25; LMF = 0.24; LMN = 0.49; LMO = 0.90; LMA = 0.02
18. Long-term interest rate
Long-run equation
RLt = 3.07 – 1.03 ϕ18,t + 0.66 RBt + 0.33 (100×F/Y)t + z$ 18,t
sample: 60-97
ϕ18,t = I(t>1986)
ADF(C) = -4.87* [-4.92]
Short-run equation
∆RLt = 0.05 + 0.54 ∆RBt + 0.40 ∆(100×F/Y)t - 0.71 z$ 18,t-1 -1.26 D86t -1.50 D93t
35
+ 3.13 D92
(2.1)
An aggregate model for the EU
(0.0) (12.6)
(3.0)
(5.5)
(8.3)
(7.2)
2
sample: 62-97
GR = 0.72
LMI = 0.64; LMF = 0.26; LMN = 0.12; LMO = 0.30; LMA = 0.42
19. European currency/USD exchange rate
Long-run equation
lnUSDt = -0.20 + 2.18∆lnPCt – 5.18∆ln PCUS t- 0.008RBt + 0.04 RUS
+ z$ 19,t
t
sample: 71-97
CRADF(1) = -4.4* [-4.7]
Short-run equation
(1-0.47L) ∆ln USDt = 0.002+ 2.18 ∆2 lnPCt
(1.5)
(0.0) (2.0)
+ 0.03 ∆ RUS
t
(2.2)
-3.95∆2ln PCUS t -0.00 ∆RBt +
(3.3)
(0.2)
- 0.52 z$ 19,t-1
(3.6)
2
sample: 71-97
GR = 0.45
LMI = 0.29; LMF = 0.98; LMN = 0.48; LMO = 0.39; LMA = 0.17
20. Capital movements
Long-run equation
MK t = -13.0 – 102.3 ϕ20,t + 10.4 RLt - 12.0 RUS
+ 1.3 ∆lnUSDt + z$ 20,t
t
sample: 61-97
ϕ20,t = I(t>1991)
ADF(C) = -5.94** [-5.28]
Short-run equation
∆MK t = -3.23 -10.93 ∆RUSt + 17.13 ∆RLt + 0.90 ∆2lnUSDt
(1.2)
(1.6)
(2.7)
(2.8)
sample: 63-97
-0.84 z$ 20,t-1
(3.7)
2
GR = 0.46
LMI = 0.52; LMF = 0.92; LMN = 0.65; LMO = 0.86; LMA = 0.11
APPENDIX B: DATA DEFINITIONS, NOTATION AND SOURCES
Endogenous variables
B
Public debt securities
36
An aggregate model for the EU
C90
Private consumption (real)
D
Public debt
∆B
Variation in the stock of public debt securities
∆H
Variation in the stock of Treasury monetary base
∆R
Balance of payments (variation in reserves)
DT
Direct taxes
GB
Public deficit
GBGDP
Public deficit/GDP ratio
H
Treasury monetary base
INPR90
Private gross fixed capital formation (real)
IPD
Government interest payments
IT
Indirect taxes
M2
Money demand M2
M90
Imports of goods and services (real)
MK
Capital movements
N
Total employment
PC
Deflator: private consumption
PG
Deflator: government consumption
PI
Deflator: gross fixed capital formation
PM
Deflator: imports of goods and services
PX
Deflator: exports of good and services
PY
Deflator: GDP
R
Official reserves
RB
Short-run interest rate
RL
Long-run interest rate
SB
Social security transfers
SC
Social security contributions
U
Unemployment rate
37
An aggregate model for the EU
USD
ECU/USD nominal exchange rate
W
Nominal wages (compensation of employees)
X90
Exports of goods and services (real)
Y
GDP (nominal)
Y90
GDP (real)
YD
Disposable income
Exogenous variables
Dxx
Dummy variable equal to 1 in year 19xx, zero otherwise
FCF90
Government gross fixed capital formation (real)
G90
Government consumption (real)
ITR
Average indirect tax rate
LF
Labour force
M90 W
World (excluding EU) imports of goods and services (real)
OCE
Other current expenditures of public sector
OCR
Other current revenues of public sector
OKE
Other capital expenditures of public sector
PMD
Import prices (dollars)
PC US
US consumer price index
PX W
World (excluding EU) export prices (dollars)
R US
Interest rate on US 3-month T-Bills
VS
Change in stocks (nominal)
VS90
Change in stocks (real)
38
An aggregate model for the EU
Sources
All variables are expressed in billions of ECU, except GBGDP, RB, RL, U, ITR ,
R US , which are expressed in percentage points; PC, PC US , PG, PI, PM, PX, PY,
PMD , PX W ,
which are index numbers with basis 1990=100; USD, which is
expressed as ECU per US dollars: and N and LF , which are measured in thousands of
individuals.
National accounts data, including total employment, labour force, and compensation
of employees, are from the OECD (National accounts I). Financial and international
trade data are from the IMF (International Financial Statistics). Public sector data are
from the OECD (National Accounts II).
APPENDIX C: ESTIMATION AND HYPOTHESIS TESTS
Long-run equations and regime shifts diagnostic. CRADF(j) indicates the
cointegrating regression ADF statistic by Engle and Granger [10] evaluated including j
lags of the differenced OLS residuals in the auxiliary regression. Statistics significant at
10% (5%) are marked by one (two) asterisk(s). Near each statistic the associated 5%
critical value drawn from Table 2 of Blangiewicz and Charemza [1] is reported within
square brackets.
Where the usual cointegration test fails to reject the null, we used the GregoryHansen approach described in Section 2. The notation adopted in presenting the
estimates is slightly different from that of Section 2: ϕj,t = I( t>h ) indicates the dummy
variable that shifts in year h the parameters of the j-th long-run equation. The asymptotic
5% critical values are reported in square brackets. As before, statistics significant at
10% (5%) are marked by one (two) asterisk(s).
39
An aggregate model for the EU
Short-run equations and residuals diagnostics. The short-run equations are
estimated by IIV including as error correcting term either the usual or the “regimeshifted” cointegrating residuals. We report under the parameter estimates the
2
heteroskedasticity-consistent t statistics (White [35]). GR is the generalised R 2 of
Pesaran and Smith [28]. The equations are followed by the empirical critical values (pvalues) of some LM misspecification tests for simultaneous equations, based on the
residuals of IIV estimation (Spanos [33]), respectively for the hypothesis of no serial
correlation in the residuals (LMI), linearity of the regression function (LMF), normality
of the residuals (LMN), homoskedasticity of the residuals (LMO), and admissibility of
the instrumental variables (LMA).
40
An aggregate model for the EU
Table 1 - Relationships of the theoretical reference modela
1) C90 = f 1 [YD/PC]
.
18)
RB = f 13 [ R US , PC ]
2) INPR90 = f [Y90, R ,-100× PY ]
2
L
19)
RL = f 14 [ RB, GBGDP ]
3) X90 = f 3 [ M90 W , PX/( PX W ×USD)
20)
4) M90 = f 4 [ Y90, PM/PY ]
21)
MK = f 16 [ RL, R US ]
= C90×PC/100 + G 90 × PG / 100 + INPR90×PI/100 +
22)
& ]
DT = f 17 [ Y
+ FCF90 ×PI/100 + X90 × PX / 100 - M90 × PM / 100 + VS
23)
IT = ITR ×
.
USD = f 15 [ RB, R
US
.
.
, PC , PC US ]
5) Y90 = C90 + G 90 + INPR90 + FCF90 + X90 – M90 + VS 90
6) Y
.
×( C90×PC/100+ INPR90×PI/100+ FCF90 ×PI/100)/(1+ ITR )
7) N = f 5 [ Y90, W/PI ]
8) U = 100×( 1 - N/ LF )
9)
& - (Y90/N) = f [ U, PC ]
W
6
.
.
.
.
24)
& ]
SC = f 18 [ W
25)
IPD = f 19 [ (RL/100)×B ]
26)
& ]
SB = f 20 [ Y
27)
YD = Y + SB + IPD – DT - SC
28)
GB = G + IPD + SB + OCE - DT - IT - SC - OCR + FCF + OKE
29)
GBGDP = 100×GB/Y
.
10)
.
 PC 
& , PM ]

 = f 7[ W
 1 + ITR 
11)
& , PC ]
PG = f 8 [ W
12)
.
 PI 
& , PM ]

 = f 9[ W
 1 + ITR 
13)
& , PM ]
PX = f 10 [ W
30)
∆H = GB - ∆B
14) PM = PMD × USD
31)
∆R = X- M + MK
15) PY = 100×Y/Y90
32)
H = H-1 + ∆H
33)
R = R-1 + ∆R
34)
D = H +B
(
)
.
.
.
(
.
)
.
16) M2/PY = f 11 [ Y90, RB, USD ]
.
17) B/(D+R) = f [R , R US , PC ]
12 L
a A bar indicates an exogenous variable, a dot indicates logarithmic differences.
41
An aggregate model for the EU
Table 2 - A restrictive fiscal shock: a 1% of baseline real GDP decrease in the level of real government
consumption for the entire simulationa
Deviation from control
1 year
3 years
Real sector
Real GDP (%)
Real private consumption (%)
Gross fixed capital form. (%)
Real exports (%)
Real imports (%)
Labour market and prices
Consumer price index
- level (%)
- year to year change
GDP deflator (%)
Exports deflator (%)
Nominal wages (%)
Unemployment rate
Fiscal and monetary sector
Public deficit/GDP ratio
Short-term interest rate
Long-term interest rate
Nominal M2 (%)
Nominal USD exch. rate (%)
a
5 years
7 years
9 years
-1.03
(0.03)
-0.46
(0.06)
-2.10
(0.11)
0.00
(0.00)
-2.59
(0.08)
-1.54
(0.08)
-1.03
(0.15)
-4.21
(0.24)
-0.05
(0.02)
-3.35
(0.20)
-1.62
(0.11)
-1.08
(0.20)
-4.70
(0.35)
-0.07
(0.03)
-3.32
(0.25)
-1.34
(0.30)
-0.96
(0.65)
-3.70
(0.66)
0.10
(0.03)
-3.10
(0.63)
-0.35
(0.38 )
0.07
(0.77)
-0.28
(1.22)
0.39
(0.06)
-1.65
(0.90)
-0.85
(0.05)
-0.90
(0.05)
-0.65
(0.07)
-0.76
(0.20)
-1.75
(0.06)
0.40
(0.01)
-4.62
(0.24 )
-2.32
(0.14)
-4.70
(0.24)
-3.69
(0.50)
-7.93
(0.31)
1.72
(0.07)
-8.83
(0.42 )
-2.10
(0.20)
-9.70
(0.46)
-5.67
(0.55)
-13.48
(0.59)
1.55
(0.11)
-10.65
(0.64 )
-0.68
(0.32)
-12.53
(0.85)
-5.26
(0.86)
-14.89
(0.92)
0.58
(0.24)
-10.18
(1.03 )
0.52
(0.55)
-12.13
(1.18)
-4.26
(1.18)
-13.20
(1.60)
0.03
(0.40)
-0.73
(0.04)
-0.83
(0.05)
-0.75
(0.04)
-1.46
(0.13)
-1.19
(0.33)
-0.51
(0.07)
-0.98
(0.09)
-0.79
(0.07)
-6.17
(0.32)
-4.59
(0.77)
0.17
(0.13)
-0.33
(0.11)
-0.18
(0.09)
-11.50
(0.54)
-4.86
(0.76)
1.27
(0.39)
0.23
(0.22)
0.59
(0.25)
-14.31
(0.98)
-1.26
(1.20)
1.66
(0.68)
0.41
(0.35)
0.84
(0.42)
-12.89
(1.42)
1.66
(1.45)
Absolute or per cent (%) deviations from the control. Standard errors of the stochastic simulation in
brackets.
42
An aggregate model for the EU
Table 3 - A terms of trade shock: a 5% increase in the level of USD import prices and a 5% decrease in
the level of the USD world export prices for the entire simulationa
Deviation from control
1 year
3 years
Real sector
Real GDP (%)
Real private consumption (%)
Gross fixed capital form. (%)
Real exports (%)
Real imports (%)
Labour market and prices
Consumer price index
- level (%)
- year to year change
GDP deflator (%)
Exports deflator (%)
Nominal wages (%)
Unemployment rate
Fiscal and monetary sector
Public deficit/GDP ratio
Short-term interest rate
Long-term interest rate
Nominal M2 (%)
Nominal USD exch. rate (%)
a
5 years
7 years
9 years
-0.33
(0.03)
-0.63
(0.05)
-0.89
(0.10)
0.00
(0.00)
-0.84
(0.07)
-0.56
(0.05)
-1.14
(0.11)
-1.05
(0.16)
-0.54
(0.02)
-1.81
(0.14)
-0.52
(0.09)
-0.96
(0.14)
-1.01
(0.26)
-0.82
(0.02)
-1.74
(0.28)
-0.59
(0.11)
-1.00
(0.26)
-1.32
(0.29)
-0.97
(0.02)
-1.89
(0.22)
-0.45
(0.17)
-0.85
(0.35)
-0.82
(0.58)
-0.98
(0.03)
-1.73
(0.51)
0.84
(0.06)
0.88
(0.05)
0.15
(0.07)
3.59
(0.21)
0.58
(0.06)
-0.03
(0.01)
1.28
(0.18)
0.03
(0.09)
0.70
(0.17)
3.50
(0.38)
0.39
(0.24)
0.36
(0.05)
0.39
(0.28)
-0.56
(0.12)
-0.18
(0.33)
2.24
(0.39)
-1.34
(0.41)
0.72
(0.08)
-0.46
(0.40)
-0.35
(0.15)
-1.35
(0.50)
1.98
(0.51)
-2.45
(0.59)
0.42
(0.09)
-0.53
(0.73)
0.03
(0.29)
-1.47
(0.88)
2.47
(0.94)
-2.31
(1.17)
0.21
(0.23)
0.33
(0.04)
0.82
(0.05)
0.58
(0.04)
-0.80
(0.12)
1.19
(0.35)
0.15
(0.06)
-0.17
(0.06)
-0.05
(0.05)
-0.12
(0.22)
0.57
(0.56)
0.13
(0.08)
-0.25
(0.09)
-0.12
(0.07)
-0.79
(0.39)
-1.33
(0.54)
0.40
(0.13)
0.02
(0.09)
0.14
(0.08)
-2.15
(0.58)
-1.06
(0.56)
0.57
(0.25)
0.08
(0.14)
0.26
(0.14)
-2.18
(1.04)
0.21
(0.99)
Absolute or per cent (%) deviations from the control. Standard errors of the stochastic simulation in
brackets.
43
An aggregate model for the EU
Table 4 - Depreciation of the exchange rate: depreciation by 5% of nominal exchange rate ECU/USDa
Deviations from control
1 year
3 years
Real sector
Real GDP (%)
Real private consumption (%)
Gross fixed capital form. (%)
Real exports (%)
Real imports (%)
Labour market and prices
Consumer price index
- level (%)
- year to year change
GDP deflator (%)
Exports deflator (%)
Nominal wages (%)
Unemployment rate
Fiscal and monetary sector
Public deficit/GDP ratio
Short-term interest rate
Long-term interest rate
Nominal M2 (%)
Nominal USD exch. rate (%)
a
5 years
7 years
9 years
-0.25
(0.01)
-0.48
(0.01)
-0.66
(0.03)
0.00
(0.00)
-0.63
(0.02)
-0.20
(0.02)
-0.69
(0.04)
-0.16
(0.08)
0.14
(0.00)
-0.85
(0.06)
-0.12
(0.03)
-0.68
(0.06)
0.13
(0.11)
0.18
(0.01)
-0.80
(0.08)
-0.15
(0.05)
-0.79
(0.09)
0.10
(0.13)
0.19
(0.01)
-0.93
(0.11)
-0.24
(0.07)
-0.97
(0.13)
-0.12
(0.21)
0.18
(0.01)
-1.14
(0.16)
0.69
(0.01)
0.72
(0.01)
0.16
(0.01)
2.88
(0.00)
0.50
(0.01)
-0.03
(0.00)
1.43
(0.04)
0.32
(0.02)
1.03
(0.05)
3.16
(0.03)
1.08
(0.08)
0.11
(0.02)
1.82
(0.10)
0.17
(0.04)
1.35
(0.12)
3.37
(0.06)
1.27
(0.18)
0.20
(0.03)
2.14
(0.16)
0.16
(0.05)
1.66
(0.20)
3.51
(0.10)
1.58
(0.27)
0.08
(0.04)
2.29
(0.23)
0.03
(0.08)
1.82
(0.31)
3.62
(0.13)
1.61
(0.39)
0.16
(0.06)
0.25
(0.01)
0.67
(0.01)
0.47
(0.01)
-0.94
(0.02)
5.00
0.02
(0.02)
0.07
(0.01)
0.04
(0.02)
0.32
(0.08)
5.00
-0.06
(0.03)
0.02
(0.02)
-0.01
(0.02)
0.77
(0.16)
5.00
-0.15
(0.05)
0.04
(0.02)
-0.03
(0.02)
1.09
(0.26)
5.00
-0.25
(0.09)
-0.04
(0.04)
-0.11
(0.04)
1.10
(0.38)
5.00
Absolute or per cent (%) deviations from the control. Standard errors of the stochastic simulation in
brackets.
44
An aggregate model for the EU
1
2.5
2
0.5
2
1.5
0
1.5
1
-0.5
1
0.5
-1
0.5
0
-1.5
0
-0.5
-2
-0.5
-1
-2.5
-1
-1.5
0
1
2
3
4
5
6
7
8
0
9
1
2
3
4
5
6
7
8
9
(b) Unemployment (absolute deviations)
(a) Real GDP (percent deviation)
3.5
3
2.5
2
1.5
1
0.5
0
-0.5
-1
-1.5
1
2
3
4
5
6
7
8
(d) Public deficit/GDP ratio (absolute deviations)
9
1
2
3
4
5
6
7
8
9
(c) Long term interest rate (absolute deviations)
2
1.5
1
0.5
0
-0.5
-1
-1.5
-2
-2.5
-3
0
0
6
4
2
0
-2
-4
-6
-8
0
1
2
3
4
5
6
7
(e) Inflation rate (absolute deviations)
8
9
0
1
2
3
4
5
6
7
8
9
(f) Nominal exchange rate (percent deviations)
Figure 1 Dynamic multipliers associated with a restrictive fiscal policy: permanent decrease in public consumption in real terms equal to 1% of real GDP (dotted lines
indicate the 95% confidence interval)
45
An aggregate model for the EU
2.5
0
2.5
2
-0.5
2
1.5
-1
1
-1.5
0.5
-2
0
0
-2.5
-0.5
1.5
1
0
1
2
3
4
0.5
0
5
1
2
3
4
5
0
(b) Unemployment (absolute deviations)
(a) Real GDP (percent deviation)
1
0.8
0.6
0.4
0.2
3.5
8
3
7
2.5
6
-0.6
-0.8
0.5
1
0
0
4
(d) Public deficit/GDP ratio (absolute deviations)
5
5
3
1
3
4
4
1.5
2
3
5
0
-0.2
-0.4
1
2
(c) Long term interest rate (absolute deviations)
2
0
1
2
0
1
2
3
4
(e) Inflation rate (absolute deviations)
5
0
1
2
3
4
(f) Nominal exchange rate (percent deviations)
Figure 2 A comparison with COMPACT multipliers. The solid lines are the dynamic multipliers of our model associated with an expansionary fiscal shock
(permanent increase in public consumption in real terms equal to 1% of real GDP), accompanied by their 95% confidence intervals (dotted lines); the dashed line
is the corresponding COMPACT multiplier. The inflation rate multiplier is not available for COMPACT.
46
5
An aggregate model for the EU
0
-0.2
1
0.8
0.8
0.6
0.6
-0.4
0.4
-0.6
0.2
0.4
0.2
0
0
-0.8
-1
0
1
2
3
4
5
6
7
8
-0.2
-0.2
-0.4
-0.4
9
0
(a) Real GDP (percent deviations)
1
2
3
4
5
6
7
8
9
0
(b) Unemployment (absolute deviations)
2
3
4
5
6
7
8
9
(c) Long term interest rate (absolute deviations)
1.2
1.2
3
1
0.8
2
0.4
1
0
0
-0.4
-1
0
-0.8
-2
-0.2
-1.2
-3
0.8
1
0.6
0.4
0.2
0
1
2
3
4
5
6
7
8
(d) Public deficit/GDP ratio (absolute deviations)
9
0
1
2
3
4
5
6
7
(e) Inflation rate (absolute deviations)
8
9
0
1
2
3
4
5
6
7
(f) Nominal exchange rate (percent deviations)
Figure 3 Dynamic multipliers associated with a worsening of the terms of trade: a 5% increase in import prices in dollars and a 5% decrease in world export
prices in dollars (broken lines indicate the 95% confidence interval).
47
8
9
An aggregate model for the EU
0
0.3
0.6
0.5
0.4
0.25
0.2
0.3
0.2
0.15
-0.2
0.1
0.1
0
-0.1
0.05
0
-0.05
-0.4
-0.2
-0.3
-0.1
0
1
2
3
4
5
6
7
8
9
0
(a) Real GDP (percent deviations)
1
2
3
4
5
6
7
8
9
(b) Unemployment (absolute deviations)
0.4
0.3
0.2
0.1
0
-0.1
-0.2
-0.3
-0.4
-0.5
1
2
3
4
5
6
7
8
(d) Public deficit/GDP ratio (absolute deviations)
9
1
2
3
4
5
6
7
8
9
(c) Long term interest rate (absolute deviations)
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
-0.1
-0.2
0
0
5
4,5
4
3,5
3
2,5
2
1,5
1
0,5
0
0
1
2
3
4
5
6
7
(e) Inflation rate (absolute deviations)
8
9
0
1
2
3
4
5
6
7
(f) Nominal exchange rate (percent deviations)
Figure 4 Dynamic multipliers associated with a devaluation of the exchange rate: permanent depreciation by 5% of the ECU/USD nominal exchange rate (broken
lines indicate the 95% confidence interval).
48
8
9
An aggregate model for the EU
FOOTNOTES
1
For the exact definition of the sample utilised in the estimation of each equation see App. A.
2
The current fifteen countries minus Sweden, Finland, and Austria.
3
As for the short-run properties, definite conclusions about the dynamic stability of the model are
obtained only under extreme assumptions about prices, the exchange rate, the budget deficit and the balance of
payments.
4
The Cobb-Douglas technology was chosen after some experiments with a CES technology provided
elasticities of substitution close to unity. By the way, Dramais [12] reaches very similar conclusions about
this elasticity, and even more recent multi-country models, such as Roeger and in’t Veld [30] adopt a CobbDouglas approach for modelling labour demand.
5
An important, though largely unnoticed, feature of this theoretical model is that it implies that the wage
and prices series are I(2), as generally observed in most countries.
6
The foreign interest rate, however, proved statistically insignificant in the money demand equation.
Moreover, the consumption and money demand functions do not include a wealth effect, which proved
insignificant as well.
7
About 20 of COMPACT’s 54 equations (as compared to our 34) are definitional identities. Most of
these are also present in our model but were substituted out in the formulas, thus reducing the number of
independent relationships.
8
The original formulation by Knight and Wymer [21] involves cross-equation restrictions between the
production function and the investments function, which are ignored in COMPACT.
9
Thus, simultaneous nonlinear estimation methods such as the NL2SLS, NL3SLS and NLFIML cannot be
used because of the non-stationarity of some variables; nor, on the other hand, can the FIML estimators by
Johansen [20] or the fully modified OLS estimator by Phillips and Hansen [29] be utilised because, even
allowing for the non-stationarity of variables and the simultaneity of equations, they are suited for linear
models only.
49
An aggregate model for the EU
10
Which of the two effects will prevail is, of course, an empirical question. The aggregated approach is
found to outperform the disaggregated one (based on national sub-models) under a number of empirical
criteria, among which are the dynamic properties and stability of the aggregated equation (Kremers and Lane
[22]), its predictive performance (Den Butter and Van Dijken [5]), and non-parametric tests of preference
separability (Spencer [34]). Similar arguments could probably apply to other behavioural equations, though
research in this field is still very limited.
11
More specifically, changes in the relative distribution of individuals must be independent of changes in
the mean of the distribution over time (a property known as mean scaling); a sufficient condition for mean
scaling is that the disaggregated regressors are cointegrated in levels (see Property 2 in Lewbel [23]).
12
For instance, the oil price shocks are known to have determined structural breaks in the DGP of most
economic time series (Perron [27]).
13
As the equations are estimated in first or even second differences, their measures of fit are not inflated
by the trend components of the data, as is the case e.g. in partial adjustment models. For instance, our lowest
2
2
GR (equal to 0.33 in Equation 8, specified in second differences, see Appendix A) corresponds to an R of
0.999 when the fit is measured with respect to the levels of the variables.
14
The pseudo-random disturbances of structural equations were generated through McCarthy’s [24]
method, starting from the residuals of the estimation, while the heteroskedasticity-consistent estimates (White
[35]) of the covariance matrix of IIV estimators were used to generate the pseudo-random values of
coefficients. To minimise the experimental variance, each simulation was carried out through one thousand
runs by the antithetical variables method (Hendry [17]).
15
As both models are nonlinear, the actual size of the multipliers depends on the date of the shock. In our
model this feature is accentuated by the presence of the endogenously determined structural breaks. However,
the dates of the shocks are close enough (1986 in COMPACT, 1985 in our model) to establish a reliable
comparison in this respect.
16
A linear homogenous CES with elasticity of substitution close to one in COMPACT, and (after the
regime switch) a nearly linear homogeneous Cobb-Douglas in our model.
50
An aggregate model for the EU
17
As stated before, the admittedly “pessimistic” stance of COMPACT is traced back by Dramais to two
features of his model: the rationing mechanism in the labour market, which determines a lower response of
labour demand, hence of disposable income, private consumption, and GDP, to real shocks; and the absence
of an acceleration mechanism in the investment function, which works in a similar direction.
18
These data refer to the European Union and come from the OECD Main Economic Indicators published
in the 2001/1 release of the OECD Statistical Compendium on CD-ROM.
51