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. 2 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. 3 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 4 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 5 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. 6 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 7 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. 8 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 9 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 10 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) 11 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: 12 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 13 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 14 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 15 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 16 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 17 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. REFERENCES 1. Blangiewicz, M and Charemza, W W ‘Cointegration in small samples: empirical percentiles, drifting moments and customized testing’ Oxford Bulletin of Economics and Statistics 1990 52(3) 303-315. 2. Bowden, R and Turkington, D ‘A comparative study of instrumental variable estimators for nonlinear simultaneous models’ Journal of American Statistical Society, 1981 76 985-996. 3. Bowden, R and Turkington, D Instrumental Variables Cambridge University Press, Cambridge (1984). 25 An aggregate model for the EU 4. 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Hendry, D F ‘Monte Carlo experimentation in econometrics’, in Griliches, Z and Intriligator, M D (eds), Handbook of Econometrics North-Holland, Amsterdam (1984). 18. Hendry, D F and Neale, A J ‘Interpreting long-run equilibrium solutions in conventional macro models: a comment’ The Economic Journal 1988 98(September) 808-817. 19. Hendry, D F, Pagan, A R and Richard, J D ‘Dynamic specification’, in Griliches, Z and Intriligator, M D (eds), Handbook of Econometrics, Elsevier, Amsterdam (1984). 27 An aggregate model for the EU 20. Johansen, S ‘Statistical analysis of cointegration vectors’ Journal of Economic Dynamics and Control 1988 12 231-254. 21. Knight M D and Wymer C ‘A macroeconomic model of the United Kingdom’ IMF Staff Papers 1978 15(4). 22. Kremers, J J M and Lane, T D ‘Economic and monetary integration and the aggregate demand for money in the EMS’ IMF Staff Papers 1990 37(4) 777805. 23. Lewbel, A ‘Aggregation with log-linear models’ Review of Economic Studies, 1992 59 635-642. 24. McCarthy, M D ‘Some notes on the generation of pseudo-structural errors for use in stochastic simulation studies’ Hickman, B G (ed) Econometric Models of Cyclical Behavior Columbia University Press, New York (1972). 25. O’Connel, J ‘Stock adjustment and the balance of payments’ Economic Notes 1984 (1) 136-144. 26. Park, J Y and Phillips, P C B ‘Statistical inference in regressions with integrated processes: part 1’ Econometric Theory 1988 4 468-497. 27. Perron, P ‘The great crash, the oil price shock, and the unit root hypothesis’ Econometrica 1989 57 1361-1401. 28 An aggregate model for the EU 28. Pesaran, M H and Smith, R J ‘A generalized R 2 criterion for regression models estimated by the instrumental variables method’ Econometrica 1994 62 705710. 29. Phillips, P C B and Hansen, B E ‘Statistical inference in instrumental variables regression with I(1) processes’ Review of Economic Studies 1990 57 99-125. 30. Roeger, W and in’t Veld, J ‘QUEST II – A Multi-Country Business Cycle and Growth Model’, Economic Papers 1997 (123) 1-50. 31. Shiller, R J and Perron, P ‘Testing the random walk hypothesis: power versus frequency of observation’ Economics Letters 1985 18 381-386. 32. Sims, C ‘Identifying policy effects’, in Bryant, R C, Henderson, D W, Holtham, G, Hooper, P and Symansky, S A (eds), Empirical Macroeconomics for Interdependent Economies, The Brookings Institution, Washington (1988). 33. Spanos, A Statistical Foundations of Econometric Modelling Cambridge University Press, Cambridge (1986). 34. Spencer, P ‘Monetary integration and currency substitution in the EMS: The case for a European monetary aggregate’ European Economic Review 1997 41 1403-1419. 35. White, H ‘A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity’ Econometrica 1980 48 817-38. 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

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# AN AGGREGATE MODEL FOR THE EUROPEAN UNION Alberto