Claudio ; Morana

Fabio Bagliano

Business Cycle Comovement in the G-7: Common Shocks or Common Transmission Mechanisms?

Keywords: business cycle comovement, factor vector autoregressive model, transmission mechanisms business cycle comovement, factor vector autoregressive model, transmission mechanisms. JEL classi…cation: C32, E32

What are the sources of macroeconomic comovement among G-7 countries? Two main candidate explanations may be singled out: common shocks and common transmission mechanisms. In the paper it is shown that they are complementary, rather than alternative, explanations. By means of a large-scale factor vector autoregressive (FVAR) model, allowing for full economic and statistical identi…cation of all global and idiosyncratic shocks, it is found that both common disturbances and common transmission mechanisms of global and country-speci…c shocks account for business cycle comovement in the G-7 countries. Moreover, spillover e¤ects of foreign idiosyncratic disturbances seem to be a less important factor than the common transmission of global or domestic shocks in the determination of international macroeconomic comovements.

Introduction

What are the sources of macroeconomic comovement among countries? Two main candidate explanations may be singled out: common shocks and common transmission mechanisms. Yet, rather than being alternative explanations, they may be held as complementary. In fact, while a common shock is necessary in order to contemporaneously destabilize both the domestic and foreign economies, the propagation of the shock may lead to common macroeconomic ‡uctuations only if similar transmission mechanisms are at work. Several papers have recently dealt with the above issue, mainly focusing on the role of global shocks in a¤ecting the synchronization and volatility of output ‡uctuations for G-7 countries. Three key results can be pointed out.

First, the degree of synchronization of cyclical ‡uctuations for the G-7 economies has changed over time. For instance, Kose, Otrok and Whiteman (2005) have found that business cycle synchronization has increased in the "globalization" period (1986)(1987)(1988)(1989)(1990)(1991)(1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001) relative to the "Bretton Woods" period (1960)(1961)(1962)(1963)(1964)(1965)(1966)(1967)(1968)(1969)(1970)(1971)(1972), but has decreased with respect to the "common shocks" years (1973)(1974)(1975)(1976)(1977)(1978)(1979)(1980)(1981)(1982)(1983)(1984)(1985). 1 Several explanations, also related to the so called "great moderation" 2 can be suggested for the above …ndings, such as a decrease in the prominence of common shocks, structural change in the composition of output, as well as better macroeconomic policies. In this respect, since a key role for US macroeconomic shocks in the determination of global shocks can be expected, the moderation in output ‡uctuations in the US might have spilled over to the other G-7 countries. Changes in the transmission mechanism, as well as in domestic shocks, should however not be excluded. For instance, in the light of the prolonged Japanese stagnation of the 1990s, and therefore of the more idiosyncratic behavior shown by this latter country relative to the other G-7 economies, the moderation in Japan's output ‡uctuations is likely to be related more to domestic economic developments rather than to the size of global shocks or to US spillovers. Interestingly, changes in business cycle synchronization have also a¤ected the G-7 members di¤erently, leading to increased economic coordination within fairly homogeneous groups, such as the English speaking countries and the euro-zone countries, and to a reduction in the coordination between the two groups. Second, the importance of global shocks relative to domestic disturbances has increased over time at all forecasting horizons. In fact, while in the 1960s and 1970s the own shocks were the dominant factors for output ‡uctuations in the short term and global shocks were the main source of output variability in the medium to long term, in the 1980s and 1990s, apart from Japan, ‡uctuations were determined by the global shocks at all the forecasting horizons [START_REF] Kose | Understanding the evolution of world business cycles[END_REF]. Moreover, also the nature of the global shocks has changed over time. In fact, while for the 1960s and 1970s the global shocks could be related to US monetary policy, the oil price and the price of industrial materials (Stock and Watson, 2003), in more recent periods the global shocks could be linked to productivity changes and monetary policy disturbances [START_REF] Kose | Understanding the evolution of world business cycles[END_REF]. Similarly, [START_REF] Bagliano | International macroeconomic dynamics: A factor vector autoregressive approach[END_REF] found a key role for global demand and productivity shocks since the 1980s for the G-7 countries, while global stock market and oil price shocks have been less important to explain macroeconomic ‡uctuations. Evidence of a similar transmission mechanism of global shocks for the G-7 countries, particularly for the US, the UK, Canada and the euro area, is also found by [START_REF] Bagliano | International macroeconomic dynamics: A factor vector autoregressive approach[END_REF] and [START_REF] Canova | On the sources of business cycles in the G-7[END_REF], while the more idiosyncratic behavior found for Japan is fully coherent with the structural change associated with the long stagnation su¤ered from this latter country over the 1990s.

Finally, common economic ‡uctuations may also be related to the spillover of domestic shocks among G-7 countries. Stock and Watson (2003) documented a small but not negligible contribution of domestic shocks to other countries' economic ‡uctuations, particularly at long forecasting horizons. Interestingly, a leading role for US domestic shocks in a¤ecting other economies, with the US leading the beginning and end of recessions among the G-7 and other industrialized countries, particularly in the 1970s and 1990s has also been pointed out [START_REF] Chauvet | International business cycles G-7 and OECD economies[END_REF]. Moreover, Pesaran, Schuermann and Weiner (2004) and Dees, di Mauro, [START_REF] Dees | Exploring the international linkages of the euro area: a global VAR analysis[END_REF] found that a negative US stock market shock leads to a contraction in all foreign stock markets, followed also by a slowdown in real activity in all countries. On the other hand, a positive US short (long) term rate shock leads to a permanent of geographical clusters, pointing to two groups of countries, namely the US, the UK, Canada, and France, Italy, Germany, respectively. Moreover, Stock and Watson (2005b) point to the existence of a common euro zone factor for the 1984-2003 period. Also, [START_REF] Bagliano | International macroeconomic dynamics: A factor vector autoregressive approach[END_REF] have found that regional similarities seem to characterize more the real side of the economy than the nominal side. Finally, interesting regional similarities have been pointed out by [START_REF] Andreano | Further evidence on business cycle asymmetries in G7 countries[END_REF] concerning asymmetries in business cycle ‡uctuations and by [START_REF] Furceri | Business-cycle synchronization in the EMU[END_REF] concerning comovements within the euro-zone.. increase in the US short (long) term rate, but only to a temporary increase in the short (long) term rate for the euro area.

In the light of the available evidence, therefore, while the interactions related to global shocks have been studied in depth for the G-7 economies, a thorough assessment of the role of domestic shocks and economic spillovers in explaining common economic ‡uctuations is still lacking. In fact, while there is a large number of studies devoted to the analysis of the e¤ects of domestic shocks, carried out by means of single-country small scale macroeconometric models, few attempts have been made so far to set the analysis in the framework of a multi-country, large-scale model. This latter framework is likely to lead to a more accurate description of the economic interactions within and across countries, since the estimation of domestic shocks is carried out conditionally onto the identi…cation and estimation of common global shocks. Moreover, the multi-country framework allows for a more accurate analysis of spillover e¤ects than two-country macroeconometric models.

Hence, the key advantage of the approach proposed in this paper is in the accurate estimation of domestic shocks, which is carried out conditionally on a large information sets composed of nominal and real variables for …ve regions: the US, Japan, the Euro-12 area, the UK and Canada. In this multi-country, large scale macroeconometric model the role of common transmission mechanisms and international spillovers of domestic shocks has been further assessed by means of a new econometric approach, based on the Stock and Watson (2005a) Factor Vector Autoregressive Approach (F-VAR). The proposed approach modi…es the Stock-Watson F-VAR model in order to allow for a more straightforward interpretation of the global shocks and for the full economic and statistical identi…cation of all idiosyncratic (region-speci…c) disturbances.

The key …ndings of the paper are as follows. First, we …nd that both common shocks and common transmission mechanisms explain business cycle comovements for the G-7 countries. Second, not only global shocks, but also idiosyncratic domestic shocks, matter. Yet, common shocks are only a necessary but not su¢ cient condition for generating comovements, since without a common transmission mechanism the initial impulse provided by the shock would not be similarly transmitted across countries over time. In this respect, some stylized facts can be noted. For instance, responses of the short and long-term interest rates consistent with a "Taylor-rule"monetary policy and with the expectation theory of the term structure of interest rates …nd empirical support for the G-7 economies. Moreover, evidence of signi…cant wealth/Tobin's "q"e¤ects can be found, as well as of stag ‡ationary e¤ects of oil price shocks and the e¤ectiveness of the external demand channel in boosting output in the short term. Third, the spillover e¤ects of idiosyncratic shocks, though not negligible, seem to be a less important factor than the common transmission of own domestic or global shocks in the determination of macroeconomic comovements among the G-7 countries.

After this introduction, the paper is organized as follows. In section two the econometric methodology is introduced, while in section three the data and the empirical results are presented and discussed; section four summarizes our main conclusions.

Econometric methodology

Following Stock and Watson (2005a), consider the factor model

X t = F t + D(L)X t 1 + v t (1) F t = (L)F t 1 + t ; (2)
where X t is a n-variate vector of variables of interest, F t is a r-variate vector of unobserved common factors, with n r factor loadings matrix , v t is a n-variate vector of idiosyncratic i.i.d. shocks, t is a r-variate vector of global i.i.d. shocks driving the common factors, with E jt v is = 0 for all i; j; t; s, and D(L); (L) are matrices of polynomials in the lag operator of order p with all the roots outside the unit circle, i.e. By substituting (2) into (1), the vector autoregressive form (F-VAR) of the factor model can be written as

D(L) =

F t X t = (L) 0 (L) D(L) F t 1 X t 1 + " Ft " Xt ; (3)
where

" Ft " Xt = I t + 0 v t ;
with variance covariance matrix

E" t " 0 t = " = 0 0 0 0 0 0 + v ;
where

E t 0 t = and Ev t v 0 t = v :
The inversion of the F-VAR form yields the vector moving average form (VMA) for the X t process

T 1 T X t=1 [(I D(L)L) X t F t ] 0 [(I D(L)L) X t F t ] ;
where T is the sample size, and solved following an iterative procedure, avoiding convergence problems associated with, for instance, one-step Kalman …lter based estimation. Given a preliminary estimate of D(L), the common factors can be estimated as the principal components of the …ltered variables (I D(L)L) X t . Then, conditional on the estimated factors, an estimate of and an updated estimate of D(L) can be obtained by OLS from (1). This procedure is then iterated until convergence. Once the …nal estimate of fF t g is available, the (L) matrix is obtained by applying OLS to [START_REF] Bai | Estimating cross-section common stochastic trends in nonstationary panel data[END_REF]. Finally, by also employing the …nal estimates of and D(L), the restricted VAR coe¢ cients in (3) can be obtained. To obtain estimates of the common factors, Stock and Watson (2005a) apply the principal components analysis directly to the whole set of variables in X t . This method exploits all available information in the observed series, but can make the economic interpretation of the factors extremely di¢ cult. Therefore, to avoid this shortcoming, a di¤erent strategy is employed: the data set is divided into categories of variables and an estimate the factors is obtained as the …rst principal component for each sub-set (category) of series. For example, a "global output growth factor" is estimated as the …rst principal component from the set of the GDP growth rates of the countries under study; a "global stock price factor" is obtained in the same way from the set of the rates of change in real stock prices, and so on. Therefore, the r static factors in F t are separately estimated as the …rst principal components from the relevant sub-sets of variables. This estimation procedure can make it easier to give an economic content to the factors and is applied in each step of the iteration process described above. Moreover, separate estimation also avoids contamination from series potentially unrelated to the phenomenon of interest, which could undermine the asymptotic theory justifying the use of principal components analysis. In fact, the latter assumes that the variability of the common component is not too small and that the cross-correlation in the idiosyncratic errors is not too large. If noise is added to the information set it can be expected that, as more variables are included, the average size of the common factors will decrease, while the correlation across idiosyncratic components will increase. Hence, beyond a certain threshold, increasing the cross-sectional dimension of the information set is not desirable, and could also negatively a¤ect the explanatory power of the model (see [START_REF] Boivin | Are more data always better for factor analysis?[END_REF]. Finally, Monte Carlo results reported in [START_REF] Morana | Multivariate modelling of long memory processes with common components[END_REF] suggest that, despite the asymptotic results, in practice principal components analysis is a very e¤ective tools (in terms of root mean square error) to extract common factors from a set of dependent variables also when the cross sectional dimension is as low as two units.

Identi…cation of structural shocks

Since the shocks to the common factors in f t g have the nature of reducedform innovations, being linear combinations of underlying structural global disturbances, an identi…cation scheme must be used in order to extract the structural shocks driving factor dynamics and to proceed to their economic interpretation. The identi…cation of the structural shocks in the F-VAR model above can be carried out as follows. By denoting as t the r structural global shocks, the relation between reduced form and structural form disturbances can be written as t = H t ; where H is square and invertible. The identi…cation of the structural shocks amounts to the identi…cation of the elements of the H matrix. It is assumed that E [ t 0 t ] = I r , and hence H H 0 = I r : The vector moving average (VMA) representation of the dynamic factor model in structural form can then be written as

X t = B (L) t + C(L)v t ; (4)
where B (L) = B(L)H 1 : With r factors, r(r 1)=2 restrictions need to be imposed in order to exactly identify the structural shocks. Given the interpretation of the factor shocks in the present framework, the structuralization of the disturbances in f t g is achieved by assuming a lower triangular structure for the H matrix, with the ordering based on plausible assumptions of the relative speed of adjustment to shocks. In particular, we order …rst the factors related to slow-moving variables (output growth, in ‡ation), followed by the factors extracted from intermediate (interest rates, money growth) and relatively fast-moving variables (stock prices, exchange rates, oil price). The H matrix is then written as Finally, a similar procedure can be used to obtain structural disturbances from the vector of idiosyncratic shocks fv t g. By denoting as t the n-variate vector of the idiosyncratic structural shocks, the VMA representation of the dynamic factor model in (4) can be written as

H = 2
X t = B (L) t + C (L) t ; (5)
where C (L) = C(L) 1 ; and t = v t ; with an n n invertible matrix; moreover, E [ t 0 t ] = I and E i;t 0 j;t = 0 for any i; j: We achieve the iden-ti…cation of the structural idiosyncratic shocks in t by imposing exclusion restrictions on their contemporaneous impact on the variables in X t : this requires the identi…cation of the elements of the n n matrix C 0 = 1 . To this aim, we …rst exploit the distinction between slow, intermediate, and fast-moving variables introduced above and order the elements of X t and t into r stacked sub-vectors, with the slow-moving variables (and the corresponding disturbances) in the upper position followed by the intermediate and fast-moving variables. Each sub-vector has m elements, containing the same variable for the m countries (or regions) under study. Within each subvector, the countries are ordered in terms of GDP size, placing the relatively large region …rst (the US, Japan, and the Euro-12 area), followed by the smaller countries (the UK and Canada).

Then, the elements of C 0 are identi…ed by imposing a lower triangular structure of the form:

C 0 = 0 B @ C 0 11 0 . . . . . . . . . C 0 r1 C 0rr 1 C A
where each block C 0 ij has dimension m m. This structure implies that structural idiosyncratic shocks to relatively "faster" variables (in any country) have no contemporaneous impact on "slower"variables (in any country). Moreover, we impose a lower triangular structure also on each block on the main diagonal of C 0 , i.e. (for j = 1; :::r) which implies that structural idiosyncratic disturbances to relatively "smaller" regions do not have impact e¤ects on "larger"economies. Hence, for instance, the block C 0 11 contains the impact responses of the GDP growth rates for the various regions (in the order: US, Japan, the Euro area, the UK and Canada) to region-speci…c structural shocks to GDP growth. Operationally, the estimation of the matrix is then carried out as follows: 1) regress "X;t on ^ t by OLS and obtain vt as residuals;

C 0 jj = 0 B @ c 0 jj;11 0 . . . . . . . . .
2) from t = 1 v t we have E [ t 0 t ] = 1 v ( 1 ) 0 = I: Hence, ^ 1 = chol( ^ v ).
The identi…cation scheme performed allows for exact identi…cation of the n structural idiosyncratic shocks, imposing n(n 1)=2 zero restrictions on the contemporaneous impact matrix.

By following a thick modelling estimation approach (Granger and Jeon, 2004) and computing generalized impulse response functions [START_REF] Pesaran | Generalised impulse response analysis in linear multivariate models[END_REF] as well, the problem of sensitivity of the results to the ordering of the variables chosen for the identi…cation of both the factor and idiosyncratic innovations can be accounted for.

The proposed methodology can be considered as a special case of the F-VAR approach of Stock and Watson (2005a), holding when the number of static and dynamic factors is equal. Di¤erently from Stock and Watson, the global factors are estimated using the relevant sub-sets of variables, rather than the entire data set; this approach has the advantage of allowing for a more clear-cut interpretation of the global shocks. Moreover, the issue of the identi…cation of all the idiosyncratic shocks is explicitly addressed.

Concerning the proposed estimation procedure, the use of the principal components estimator for the estimation of persistent processes has been justi…ed by recent theoretical developments of [START_REF] Bai | Inferential theory for factor models of large dimensions[END_REF][START_REF] Bai | Estimating cross-section common stochastic trends in nonstationary panel data[END_REF]) and [START_REF] Bai | A panick attack on unit roots and cointegration[END_REF], allowing for an accurate estimation of the factors in the current framework. 5 Moreover, di¤erently from the F-VAR approach of Favero, Marcellino and Neglia (2005) and Bernanke, Boivin and Eliasz (2005), the 5 In particular, [START_REF] Bai | Inferential theory for factor models of large dimensions[END_REF] considers the generalization of the principal components analysis to the case in which the series are weakly dependent processes, establishing consistency and asymptotic normality when both the unobserved factors and the idiosyncratic components show limited serial correlation, and the latter also display heteroschedasticity in both their time-series and cross-sectional dimensions. In Bai (2002) consistency and asymptotic normality is derived in the case of I(1) unobserved factors and I(0) idiosyncratic components, also allowing for heteroschedasticity in both the time-series and cross-sectional dimensions of the latter component. Moreover, [START_REF] Bai | A panick attack on unit roots and cointegration[END_REF] have established consistency also for the case of I(1) idiosyncratic components. As pointed out by [START_REF] Bai | A panick attack on unit roots and cointegration[END_REF], consistent estimation should also be achieved by principal components techniques in the intermediate case of long-memory processes, and Monte Carlo results reported in [START_REF] Morana | Multivariate modelling of long memory processes with common components[END_REF] support this conclusion. proposed method has the advantage of using an iterated procedure in estimation, recovering, asymptotically, full e¢ ciency, and also allowing the imposition of appropriate restrictions concerning the lack of Granger causality of the variable versus the factors, as in Stock and Watson (2005a).

In addition, relatively to the approach employed by Pesaran, Schuermann and Weiner (2004) and Dees, di Mauro, [START_REF] Dees | Exploring the international linkages of the euro area: a global VAR analysis[END_REF] to study the international transmission of shocks, we model all variables as endogenous from the outset, instead of modelling each country separately, with foreign variables treated as weakly exogenous. Moreover, in our framework the unobservable factors can be interpreted as global factors, while in Pesaran, Schuermann and Weiner (2004) the interpretation is less straightforward. 6 Finally, while in our approach the weighting in the construction of the common factors is chosen optimally (by using principal components analysis), in Pesaran, Schuermann and Weiner (2004) the weighting is somewhat arbitrary, albeit based on sound economic justi…cations.

3 Empirical results

Data

Quarterly data for …ve countries or regions (the US, Japan, the Euro-12 Area, the UK, and Canada), have been employed over the period 1980:1-2005:2. Eight variables for each country have been considered: real GDP, the real oil price, the real stock market price index, the real e¤ective exchange rate, the CPI price index, nominal money balances 7 and the nominal short and long term interest rates (on three-month government bills and ten-year government bonds, respectively). 8 The persistence properties of the data have been assessed by means of unit roots tests. In addition to the standard ADF [START_REF] Said | Testing for unit roots in autoregressive moving average model of unknown order[END_REF] and KPSS (Kwiatkowski, Phillips, Schmidt and Shin, 1992) tests, also the Enders and Lee (2005) ADF test 6 In fact, what is denoted as global factor in Pesaran, Schuermann and Weiner ( 2004) is just a summary feature for all the variables which may have an impact on a given country, but for parsimony reasons are not modelled in detail. This is because when the unobserved component is estimated, the own country variables are neglected. However, it is hard, for instance, to justify the exclusion of US data when the global factors for the US are computed. 7 Nominal money balances are given by M2 for the US, M2+CD for Japan, M3 for the euro area and Canada, and M4 for the UK. The aggregates employed are the one usually employed to measure broad money in each of the countries investigated. 8 The source of the euro-area aggregate data is the European Central Bank. All other data are taken from Datastream. and a modi…ed version of the KPSS test have been employed in order to account for structural change. In those tests the deterministic component t is modelled by means of the [START_REF] Gallant | The Fourier ‡exible form[END_REF] ‡exible functional form, whereby t = 0 + 1 t + 2 sin(2 t=T ) + 3 cos(2 t=T ), capturing not only a deterministic process of gradual change in a time-varying intercept, but also the presence of sharp breaks and of various forms of non linear trends (Enders and Lee 2005). In the case of the KPSS test with the adaptive trend, critical values have been obtained by means of Monte Carlo simulation with 10,000 replications.

The tests have been carried out directly on the series used in the empirical analysis, i.e. the growth rate of real GDP (denoted by g), the rate of in ‡ation ( ), the levels of the long-term and short-term nominal interest rates (l and s, respectively), the nominal money growth rate (m), and the rates of change of the real e¤ective exchange rate (e), the real stock price (f ), and the real price of oil (o). The unit root tests reported show slightly di¤erent results for real and nominal variables. While the …ndings are clear-cut for all the real variables, apart from real output growth for Japan, pointing to I(0) stationarity, for the nominal variables, as well as for real output growth for Japan, stationarity can be found only for the series in deviation from a non linear deterministic component. As far as the nominal variables are concerned, the latter, as argued in [START_REF] Bierens | Non parametric nonlinear cotrending analysis, with an application to interest and in ‡ation in the United States[END_REF] and [START_REF] Morana | A small scale macroeconometric model for the euro-12 area[END_REF], can be associated with successful long-run monetary policy management. In fact, the outcome of monetary policy decisions should shape the trend behavior of the nominal variables, and the latter should be better understood in terms of a deterministic rather than a stochastic process. 9 Di¤erently, for real output growth for Japan the nonlinear component accounts for the slowdown in economic growth due to the stagnation of the 1990s.

On the basis of the above results, the stationary representation of the F-VAR model has been augmented by including the adaptive speci…cation for the deterministic component suggested by Enders and Lee (2005). 10 9 For instance, the setting of the policy interest rate by the central bank renders the latter a step-wise deterministic process, inducing a non-linear deterministic trend both in short and long term interest rates series. 10 Hence, the deterministic component included in the ith equation of ( 1) is speci…ed as

i;t = i;0 + i;1 t + i;2 sin(2 t=T ) + i;3 cos(2 t=T ).
Detailed results are not reported for reasons of space, but are available upon request from the authors. See also [START_REF] Bagliano | International macroeconomic dynamics: A factor vector autoregressive approach[END_REF].

The F-VAR model

The econometric analysis has been implemented in two steps. In the …rst step global macroeconomic dynamics have been investigated in order to specify the F-VAR model. Then, in the second step, the F-VAR model has been estimated and impulse response analysis and forecast error variance decomposition carried out.

Common macroeconomic factors

As pointed out in the theoretical section, principal components analysis has been carried out on each sub-set of variables, and the common factor, within each sub-set, has been estimated by the …rst principal component. In fact, for all the sub sets of series of interest, only the latter can be interpreted in terms of global factor, a¤ecting all the variables belonging to each subgroup, and explaining a sizable proportion of their variability.

As far as the output series (g) are concerned, the global factor (…rst principal component) explains about 40% of total variance, also accounting for 66% of US output variance and 56% of output variance for Canada, while …gures for the UK and the euro area are somewhat lower (43% and 32%, respectively), and only 4% for Japan. On the other hand, all the remaining factors are idiosyncratic. On the basis of the large proportion of variance of the US series explained by the factor it is possible to associate the global output factor to business cycle developments in the US. A similar …nding holds for the real stock return series (f ) as well. In fact, also in this latter case a single global factor explains a large proportion (about 60%) of total variance and the bulk of the variance for US stock returns (80%). The corresponding …gures for the other regions are also high: 70% for Canada and the UK, and 55% for the euro area. Again, the global factor does not capture ‡uctuations of the Japanese stock returns (4%). 11 A single factor can also be detected for the oil price (o) series, explaining over 90% of total variance, as well as the variance of each single oil price series. This latter …nding is expected, since heterogeneity among the oil price series is only due to the exchange rate component. 12 the common global factor explains about 95% and 88% of total variance for the long-term (l) and short-term (s) nominal interest rates, respectively, and about 70% and 49% of total variance for in ‡ation ( ) and nominal money growth (m), respectively. Hence, only for nominal money growth there is evidence of non-negligible idiosyncratic factors. Moreover, apart from the nominal interest rate series, for which the proportion of variance explained by the …rst principal component ranges between 82% and 97% for all individual series, the proportion of in ‡ation variance explained by the …rst principal component is equal to 56% for Japan and 74% on average for the other four countries, while for nominal money growth the …gure for Japan (70%) is greater than the average …gure for the other four countries (43%). 13 To explore in more depth the comovements in the nominal variables, principal components analysis has been carried out on the whole set of series. According to the results, there is clear evidence of a global factor driving all nominal variables, since the …rst principal components explains about 65% of total variance, and, on average, 57% of total in ‡ation variance, 84% of total nominal short-term rates variance, 92% of total nominal long-term rates variance, and 35% of total nominal money growth variance.

Hence, in the light of the above …ndings, four global factors have been retained for the F-VAR analysis, namely an "output growth factor", a "stock returns factor", a real "oil price factor", and an "in ‡ation factor", the latter capturing the common driving force of the whole set of nominal variables. The estimated factors have then been included in the F-VAR model as starting estimates of the elements of vector F t , in the …rst step of the iterative procedure described in section 2. 14

Policy analysis

On the basis of misspeci…cation tests, the lag length of the F-VAR is set equal to one. 15 Overall, the econometric model is composed of 39 equations. The …rst 35 equations refer to the endogenous variables (real output growth, in ‡ation, the nominal short-term interest rate, the nominal long-term rate, nominal money growth, real exchange rate returns, and real stock returns) rates. 13 The more idiosyncratic behavior of the Japanese economy over the time span investigated is consistent with the very di¤erent macroeconomic conditions (economic stagnation) which have characterized this country, relative to the other economies, over the 1990s. 14 More detailed results of the …rst step of the analysis are reported in [START_REF] Bagliano | International macroeconomic dynamics: A factor vector autoregressive approach[END_REF]. 15 Evidence of serial correlation at the 1% level is detected only for the UK and US output growth rates equations. Signi…cant ARCH e¤ects are found for the UK output growth and short-term rate equations and for the euro-area long-term rate equation. for the …ve regions in the system; each equation contains 43 parameters (35 on lagged endogenous variables, 4 on lagged endogenous factors, i.e. the oil price factor, the output growth factor, the stock returns factor, and the in ‡ation factor, and 4 on the deterministic trend components). The remaining 4 equations refer to the global factors and contain 8 parameters each (4 on lagged endogenous factors, and 4 on the deterministic trend components). The estimation period is 1980:1-2005:2. The F-VAR model has been estimated following the iterative procedure described in the methodological section.

Forecast error variance decomposition Since, on the basis of previous evidence in the literature [START_REF] Bierens | Non parametric nonlinear cotrending analysis, with an application to interest and in ‡ation in the United States[END_REF][START_REF] Morana | A small scale macroeconometric model for the euro-12 area[END_REF], the non-linear deterministic component in the in ‡ation factor (capturing a gradual downward trend in the level of in ‡ation rates, interest rates, and monetary growth) is likely to re ‡ect the true common nominal component related to e¤ective long-term monetary policy management, the structural disturbance to the in ‡ation factor may re ‡ect other macroeconomic forces. In particular, in the light of recent results by [START_REF] Gordon | What caused the decline in U.S. business cycle volatility?[END_REF], pointing to an important contribution provided by productivity growth in determining US in ‡ation dynamics, this latter shock may be related to the supply-side of the economy (i.e. a common productivity disturbance). Consistently with the results of the impulse response analysis, the disturbance to the output growth factor may capture global demand-side shocks, and the remaining factor disturbances capture innovations to the common factors driving real stock returns and real oil price changes. As shown in [START_REF] Bagliano | International macroeconomic dynamics: A factor vector autoregressive approach[END_REF], the proposed interpretations for the global shocks are fully consistent with the results of the impulse response analysis.

To assess the relative contribution of global and idiosyncratic disturbances to macroeconomic ‡uctuations in each region, Table 1 reports, for each endogenous variable, the median forecast error variance decomposition at the one-quarter and …ve-year horizons, obtained from the structural VMA representation of the four-factor F-VAR model in [START_REF] Bagliano | International macroeconomic dynamics: A factor vector autoregressive approach[END_REF]. 16 Some commonalities are found among the regions under study. In particular, two key results can be noted.

First, nominal variables (in ‡ation, interest rates, and money growth) seem to be driven by global dynamics. In fact, in all regions global disturbances explain the bulk of their variability at all forecasting horizons (92%-100% at the …ve-year horizon and 86%-99% at the one-quarter horizon, with the exception of the euro-area money growth (55%) and in ‡ation (15%) …gures). Di¤erently, for the real variables more mixed results are found. In fact, while for real output growth the global shocks tend to dominate at the …ve-year horizon (50%-89%), apart from the UK (39%), in the very short term the idiosyncratic disturbances slightly dominate in the US, the UK and Canada (50%-72%), but not in the euro area (34%) and in Japan (5%). In the case of real stock returns, the global shocks dominate at all forecasting horizons in the US, in the euro area and in the UK (53%-87%), but not in Canada and Japan (23%-36%). Finally, the bulk of variability of the real exchange rate changes is explained by the idiosyncratic shocks in all regions at all forecasting horizons (79%-100%), with the only exception of the euro area in the very short term (42%). Hence, di¤erently from the nominal side, idiosyncratic shocks do seem to play a signi…cant role in explaining real-side macroeconomic variability.

Second, when the speci…c source of shocks (global and idiosyncratic) is investigated, further di¤erences between the nominal and real variables can be noted. In fact, while the global supply-side (in ‡ation) disturbance explains the bulk of variability of the nominal variables at all horizons (53%-99%), apart from the euro-area in ‡ation in the very short term (11%), for the real output series both the global supply and demand (output) shocks are important determinants, exercising similar e¤ects, at all horizons, for the US and Canada (24%-25% and 16%-34%, respectively). Di¤erently, for the euro area, Japan, and the UK the supply-side shock has a dominant role (19%-80%). Moreover, except for Canada, the supply disturbance also dominates the ‡uctuations in real stock returns (19%-70%). On the other hand, the output idiosyncratic shock (i.e. the region-speci…c disturbance to the output growth series) seems to matter most for output ‡uctuations, explaining almost all the residual variability in all regions, particularly at the very short term horizon, while in the longer term other idiosyncratic shocks matter as well. The latter …ndings are interesting, possibly pointing to a di¤erent role of demand/…scal policy in the various countries. While productivity dynamics tend to be global a¤ecting both real and nominal variables, more heterogeneity can be found for demand policies, which seems to be carried out more e¤ectively in the US, given the medium term impact which can be detected for this latter country only.

Moreover, also for the real exchange rate series idiosyncratic shocks do matter, albeit the importance of the non-own idiosyncratic disturbances (i.e. region-speci…c shocks to variables other than the exchange rate) is more noticeable, pointing to stronger spillover e¤ects than for the other real variables. Finally, the oil price and global stock market shocks play only a minor role in explaining macroeconomic ‡uctuations at all forecasting horizons.

Overall, our …ndings are broadly consistent with previous evidence for the G-7 countries. In particular, the important role of global shocks in explaining output ‡uctuations since the 1980s pointed out by Stock and Watson (2005b) is further quali…ed, since our analysis allows to disentangle the contribution of global supply and demand shocks, and to account for the contribution of idiosyncratic shocks. Moreover, the evidence that output ‡uctuations are determined by a small number of global shocks is consistent with the …ndings of Kose, Otrok and Whiteman (2003), although, di¤erently from previous results in the literature (Canova and de Nicolò, 2003), a dominant role of demand over supply shocks is not found. And, again di¤erently from Canova and de Nicolò (2003), our …ndings suggest that the synchronization of the G-7 business cycle may depend also on common sources of shocks, rather than only on similarities in the transmission mechanism. Indeed, as shown by the results of the impulse response analysis in [START_REF] Bagliano | International macroeconomic dynamics: A factor vector autoregressive approach[END_REF] summarized below, a similar transmission mechanism for the global shocks holds for the G-7 countries. Finally, as in Stock and Watson (2005b), we …nd a negligible role for global oil price shocks (and global stock market disturbances) in shaping common international macroeconomic dynamics.

Impulse response functions

The analysis of the impulse response functions allows to assess di¤erences and commonalities across regions in the transmission mechanisms of various disturbances. As far as the global shocks are concerned, we brie ‡y summarize the main …ndings, given that the focus of the study is on the transmission of idiosyncratic shocks. Firstly, there is evidence of a similar transmission mechanism of global disturbances for the regions under study, particularly for the US, the UK, Canada and the euro area, while the more idiosyncratic behavior of Japan can be explained by this country's much di¤erent macroeconomic framework, especially in the 1990s. More speci…cally, a positive global demand shock has a positive and permanent impact on both output and prices in all regions, leading to a temporary increase in short-term and long-term interest rates (a response consistent with a "Taylor-rule" monetary policy reaction and with the expectations theory of the term structure), and in real stock prices. A negative global supply (productivity) disturbance has negative impact on output and a positive impact on prices, also leading to a temporary increase in interest rates, with signi…cantly negative e¤ects on real stock prices in the US and the UK. In addition, a positive oil price shock, leading to a contraction in real output and in real stock prices and to an increase in prices, is partially accommodated by the monetary authorities since nominal money balances tend to increase, while the temporary reaction of interest rates is weak. Finally, some evidence of a signi…cant "wealth"or Tobin's "q"e¤ects is found, with a positive global stock market shock leading to a permanent increase in real stock prices, real output, the price level, and nominal money balances. 17 The e¤ects of idiosyncratic domestic shocks The results of the impulse response analysis of the region-speci…c disturbances are shown in Table 2, Panels A and B. 18 In the …rst panel, the signs of the average e¤ects of each shock over three horizons, i.e. within quarter (very short term), beyond one quarter and within three years (short term) and beyond three years (medium to long term), are reported: a positive signi…cant e¤ect is denoted by "+", a negative signi…cant e¤ect is denoted by "-", and a null or not signi…cant e¤ect is denoted by "0". 19 To give a broad picture of the impulse response results, panel B of Table 3 reports the number of regions (from 0 to 5) showing a negative, zero and positive response of each variable (in columns) to the domestic idiosyncratic shocks (in rows) for three forecasting horizons, i.e. within quarter (very short term, vs), beyond one quarter and within three years (short term, s), and beyond three years (medium to long term, ml).

Several …ndings can be noted. First, a positive idiosyncratic output shock, which has a permanent and signi…cant impact on real output, determines on impact a signi…cant decline in the price level in Japan, the UK, and Canada. In the medium to long term the price level decline is signi…cant only in the euro area, whereas no signi…cant response is detected in the US at any horizon. This pattern is broadly consistent with the interpretation of the idiosyncratic output shock as a domestic productivity disturbance. Moreover, the lack of signi…cance for the US provides further support to the interpretation of global output shocks in terms of US shocks. Short term interest rates show a signi…cant decrease on impact in three regions (the euro area, the UK and Canada), pointing to monetary policy accommodation, whereas in the US no signi…cant reaction of the short rate is, consistently, again detected. On the other hand, no interesting consequences can be detected for the other variables.

Second, a positive shock to (i.e. an appreciation of) the real exchange rate 17 See [START_REF] Bagliano | International macroeconomic dynamics: A factor vector autoregressive approach[END_REF] for additional details. 18 For reasons of space, plots are not reported. They are however available upon request from the authors. 19 Standard errors have been computed by simulation. The statistical signi…cance has been evaluated at the 5% level. has a permanently negative e¤ect on real output in the euro area, Japan and an only temporary e¤ect in the same direction in Canada, while the e¤ect is permanently positive for the US and not signi…cant for the UK. This latter …nding shows that a decrease in competitiveness is going to a¤ect negatively the countries that are more sensitive to international trade conditions (euro area, Japan), possibly through a weakening of the external demand channel. In fact, the medium to long run impact on the price level is negative for Japan, the euro area, and Canada. An opposite reaction can be found for the US economy, where the appreciation of the exchange rate increases both output and (in the short term) the price level. Moreover, with few exceptions, nominal interest rates tend to be una¤ected, while the reaction of stock prices and nominal balances is mixed.

Third, a temporary increase in the short term rate leads to a similar temporary increase in the long term interest rate in all regions, consistently with standard interpretations of the transmission of shocks along the term structure based on the expectation theory. Consistent with standard economic assumptions, the restrictive monetary policy also exercises a negative impact on output (signi…cant for the euro area, the UK, and Canada only) and stock prices (apart from the UK), leading to a real appreciation of the exchange rate in all regions. Finally, the impact of the shock on the price level and on nominal money balances is less clear-cut, with some evidence of price and liquidity puzzles. 20 Similar e¤ects concerning the impact on the exchange rate and stock prices can be found for the long term rate shock, while the impact on the other variables is less clear-cut.

Fourth, a positive shock to real stock prices has a (signi…cant) positive impact on real output only for the US (in the short run), Canada, and the euro area, pointing to signi…cant wealth e¤ects. Finally, while results for the price level and money balances are mixed, an appreciation of the real exchange rate is found for the US, the euro area and the UK, possibly re ‡ecting second-round e¤ects related to capital in ‡ows.

Finally, concerning the impact of idiosyncratic in ‡ation and money balance shocks, interesting similarities can be found across the G-7 countries, with the in ‡ation shock yielding a positive and permanent impact on the price level in all regions and a signi…cant expansion in real output only in the US, the euro area and the UK, while the money balance shock leads to non signi…cant e¤ects on real stock prices in all regions (apart from the F o r P e e r R e v i e w euro area). Moreover, while for the euro area and the UK an increase in the price level and in the short and long term interest rates, and a decline in real output can be found, for Japan and the US no signi…cant impacts are found. Di¤erently, for more mixed results can be found for Canada.

Therefore, from the above speci…c …ndings and the overall picture reported in Panel B of Table 3, some broad conclusions on the existence of commonalities in the transmission mechanism of domestic shocks can be drawn. First, the output shock, which can be interpreted in terms of a domestic productivity shock in the light of the (short term) negative correlation with the price level, triggers a broadly similar monetary policy reaction in the short term in several countries, with the short term rate showing some accommodation, and the long term rate and the stock market mostly una¤ected. Also the real exchange rate tends to depreciate. Second, an "exchange rate channel" seems to be e¤ective to stimulate the domestic economy through an external demand e¤ect, as a real depreciation tends to have a positive short-term impact on output, prices and the stock market, with interest rates mostly una¤ected. The output e¤ect seems to be stronger for the regions for which international trade is more important, such as the euro area and Japan. Third, evidence of a transmission mechanism for interest rate shocks, working through the term structure of interest rates (in a manner broadly consistent with the expectation theory), is found in all regions in the short term. Moreover, a short term rate increase in general leads to a contraction in the output level, while the exchange rate tends to appreciate over the short and the medium to long-term horizons, and the stock market falls, particularly in the very short term.

The impulse responses to other idiosyncratic disturbances yield more mixed results, with clear-cut evidence available only for some of the variables under study. Yet, although di¤erences in the transmission mechanism of domestic shocks can then be observed across regions, the latter mostly concern the nominal shocks, which, according to the forecast error variance decomposition results, only explain a small proportion of the overall macroeconomic variability. 21 21 The robustness analysis, carried our by comparing the orthogonal impulse responses with the generalized impulse responses [START_REF] Pesaran | Generalised impulse response analysis in linear multivariate models[END_REF], in general supports the above …ndings, particularly for the real output shock and the real e¤ective exchange rate shock. In fact, the comparison allows to strengthen the interpretation of the former shock in terms of a productivity disturbance, since a negative correlation between real output and prices is found in all regions, apart from the euro area. Moreover, the negative correlation between the exchange rate and output developments is also a robust …nding, as well as the transmission of interest rate shocks along the term structure and the e¤ects of short-term rate shocks on real output (with the only exception of the UK). Detailed results are available upon request from the authors. The e¤ects of idiosyncratic foreign shocks Table 3 shows, for each region, the e¤ects of idiosyncratic foreign shocks on the domestic endogenous variables over the three forecasting horizons used above (i.e. within the quarter -very short term-, beyond one quarter and within three years -short term-, and beyond three years -medium to long term-). 22 Panel A reports the proportion of negative (and statistically signi…cant at the 5% level), zero and positive (and statistically signi…cant) responses of each variable (in columns) in each region (in rows), to (positive) idiosyncratic orthogonal disturbances to all foreign variables, for a total of 28 impulse responses for each cell. The last three columns of the panel ("T OT ") report the same proportions referred to the responses of all variables in each region to all foreign shocks (for a total of 196 impulse responses). To summarize information for the whole of the regions considered, Panel B displays the proportion of negative (and signi…cant), zero and positive (and signi…cant) responses of each variable (in columns) in all …ve regions to all foreign idiosyncratic orthogonal (positive) shocks to the variables in rows (for a total of 20 impulse responses for each cell), over the same three forecasting horizons.

A general impression about the overall importance of spillovers of foreign disturbances on the domestic economies can be gathered by looking at the last three columns of Panel A of the table: at the medium to long run horizon, the response of domestic variables to foreign shocks of all sources is (statistically) zero in about 70% of the cases for the US and the UK, whereas for Japan and the euro area the fraction is about 60%; Canada displays the stronger long run reaction, with only about 50% of zero responses. Yet, it is di¢ cult to determine clear-cut patters of response of domestic variables to foreign shocks, since in general the fractions of positive and negative reactions to foreign shocks are similar. However, it is possible to note that, in general, for all the regions, apart from Canada, the variable showing the strongest reactivity to foreign shocks is the real exchange rate. In ‡ation and the money supply also show a strong reactivity to foreign shocks in all countries, with the exception of the US. In this latter country, as in the UK, real output shows a fairly high proportion of signi…cant responses. While the stock market is the variable which shows the strongest reactivity for Canada, for all other regions it does not appear to be strongly a¤ected by foreign shocks. Finally, in all regions domestic interest rates do not show any signi…cant reaction in the long run to any foreign disturbance; moreover, especially in the US, the UK and Canada, the short term rate (…rmly controlled by the monetary policymaker) does not react even over the one quarter-three year horizon. 22 For reasons of space plots are not reported. They are however available upon request from the authors. 3. First, a positive foreign output shock is more likely to a¤ect positively domestic output (50% of the times in the short and medium to long term horizons) than leaving it una¤ected or negatively a¤ected. As shown by the reaction of the nominal interest rates and money balances, the foreign output shock is in general accommodated over the intermediate horizon, with nominal interest rates being more likely to decrease or remain unchanged, and the money supply to increase or remain unchanged. Finally, the evidence points to a likely transitory appreciation of the real exchange rate, while the domestic stock market is largely una¤ected by the shock.

Second, a positive foreign in ‡ation shock leaves domestic output in general una¤ected in the short term; also domestic in ‡ation is in general not a¤ected within one quarter, but positively a¤ected within three years, with the e¤ect fading away at the longer horizon. In general, the monetary policy response is not accommodating, with nominal interest rates increasing on impact and the money supply contracting, albeit only transitory. Finally, the real exchange rate tends to appreciate in the short term only, while the stock market is likely to remain una¤ected over the intermediate and longer horizons.

Third, a positive foreign short term interest rate shock is likely to leave the domestic real output, the price level and the short term interest rate una¤ected at all horizons. On the other hand, the long term rate shows a temporary increase (leading to a temporary steepening of the slope of the yield curve), which disappears in the longer run. Broadly similar e¤ects are detected for the responses of domestic variables to a foreign disturbance to the long-term interest rate.

Furthermore, a positive foreign nominal money shock is likely to leave domestic output, real stock prices and the short term interest rate una¤ected at all forecasting horizons, whereas the long-term interest rate shows a temporary decrease in the short term. In the long run, domestic money supply is more likely to be una¤ected and the real exchange rate to depreciate.

A positive foreign exchange rate shock is likely to leave the domestic price level, the short and long term rates, and the money supply una¤ected at all horizons, and to cause a permanent depreciation of the domestic exchange rate, with positive e¤ects on domestic output and the stock market.

Finally, a positive foreign stock market shock is likely to leave una¤ected interest rates and money balances at all horizons, and the domestic price level in the long run, whereas the domestic stock market is as likely to show an expansion as to remain unchanged in the long term and ambiguous e¤ects are found on output and the real exchange rate. 23

Conclusions

What are the sources of macroeconomic comovement among countries? The answer provided by this paper is that both common shocks and common transmission mechanisms explain comovements of macroeconomic variables for the US, Japan, the euro area, the UK and Canada over the 1980-2005 period. These are investigated by means of a factor vector autoregressive (F-VAR) model, allowing for the identi…cation of structural global and idiosyncratic (i.e. region-speci…c) disturbances, and forecast error variance decomposition and impulse response analyses. Several results stand out.

There is clear evidence of four global factors, driving real output growth, oil price growth, real stock market returns, and the block of nominal variables (money growth, in ‡ation, and interest rates) in all regions. The forecast error variance decomposition shows that global shocks play a very important role in explaining international macroeconomic comovements, almost entirely attributable to the output growth and in ‡ation factors, broadly interpreted as re ‡ecting demand-side and supply-side forces, respectively. Yet, the existence and relevance of global shocks are only necessary but not su¢ cient conditions for generating widespread comovements, given that without a common transmission mechanism the initial impulses provided by the global shocks would not be similarly transmitted across countries over time. The impulse response analysis yields evidence of broadly similar transmission mechanisms of global disturbances, particularly in the US, the UK, Canada and the euro area, while the more idiosyncratic behavior of Japan can be attributed to this country's much di¤erent macroeconomic framework, especially in the 1990s.

Yet, global shocks and the associated transmission mechanisms may not be the only determinants of similarities of macroeconomic ‡uctuations across countries. Actually, the impulse response analysis detects various similarities across regions in the reaction to domestic shocks. For instance, a domestic productivity shock triggers a broadly similar monetary policy reaction in the 23 In general, the analysis of the generalized impulse responses support the results obtained from the orthogonalized shocks, particularly as far as the foreign output shocks (apart from the e¤ects on the exchange rate at the within quarter horizon), the foreign in ‡ation shock (except for the e¤ects on the domestic stock market in the long term), the foreign stock market shock (apart from the e¤ects on the stock market). On the other hand, less robust results are found for the nominal money balance and interest rate shocks. Finally, the …ndings are in general robust also across countries, apart from Japan, for which, when the generalized shocks are employed, no reaction to foreign shocks is found in the short term. short term in several countries. Moreover, an "exchange rate channel"seems to be e¤ective to stimulate the domestic economy through an external demand e¤ect. In addition, evidence of transmission mechanism for interest rate shocks, working through the term structure of interest rates (in a manner broadly consistent with the expectation theory), is found in all regions in the short term. Di¤erently, spillover e¤ects of foreign idiosyncratic disturbances, though not negligible, seem to be a less important factor than the common transmission of global or domestic shocks in the determination of macroeconomic comovements.

Albeit our empirical results are conditional on a speci…c identi…cation strategy, the robustness analysis, carried out by means of generalized impulse response functions, fully supports the …ndings of this paper. This table reports for each endogenous variable the median forecast error variance decomposition at the one-quarter and …ve-year horizons obtained from the structural V M A representation of the four-factor F-VAR model in [START_REF] Bagliano | International macroeconomic dynamics: A factor vector autoregressive approach[END_REF] by Monte Carlo simulation as suggested in Granger and Jean (2004). For each variable the table shows the percentage of forecast error variance attributable to each global factor shock ("output", "in ‡ation", "stock market" and "oil price") together with their sum ("All", in bold). The last two columns report for each variable the percentage of the forecast error variance attributable to the own-country idiosyncratic shock to that variable ("own") and the proportion due to all (domestic and foreign) idiosyncratic disturbances ("All", in bold). Panel A reports the proportion of negative (and statistically signi…cant at the 5% level), zero and positive (and statistically signi…cant) responses of each variable (in columns) in each region (in rows), to the idiosyncratic orthogonal disturbances to all (28) foreign variables, over three forecasting horizons, i.e. within quarter (vs), beyond one quarter and within three years (s), and beyond three years (ml). The last three columns ("T OT ") report the same proportions referred to the responses of all variables in each region to all foreign shocks (for a total of 196 impulse responses).

F

32

F

3

 3

X

  t = B(L) t + C(L)v t ; where B(L) = [I D(L)L] 1 [I (L)L] 1 and C(L) = [I D(L)L] 1 : The estimation problem may be written as follows min F 1 ;:::;F T; ;D(L); (L)

6

 6

c 0 jj;m1 c 0 jj;mm 1 C A 4

 14 See Stock and Watson (2005a) for details on alternative identi…cation strategies.

  Finally, as far as the nominal variables are concerned,

15

 15

16 Page

 16

17

 17

19

 19

20

 20

  Additional information on the spillover e¤ects of speci…c foreign disturbances are provided by Panel B of Table

21

 21

  Panel B reports the number of regions (from 0 to 5) showing a negative, zero and positive response of each variable (in columns) to each domestic idiosyncratic shocks (in rows) for three forecasting horizons, i.e. within quarter (very short term, vs), beyond one quarter and within three years (short term, s) and beyond three years (medium to long term, ml).

Page 7 of 33 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

	Submitted Manuscript
	and estimated by the Choleski decomposition of ^ : from t = H 1 have E [ t 0 t ] = H 1 (H 1 ) 0 = I; and hence Ĥ 1 = chol( ^ ). 4	t we
	F o r
	P e
	e
	r
		R
			e
			v
			i e w
	6 4	h 11 . . .	. . .	3 7 5
		h r1	h rr
		7

Table 1

 1 Variance decomposition based on the four-factor F V AR

	o r
	P e
	e
	r
	R
	e
	v
	i e w

Table 2

 2

		Panel A: median orthogonal impulse responses to domestic shocks
			Response of domestic variables:
	Idiosyncratic shock to:	y	s	l	m	e	f
	y U S	+ + +
	U S	0 + +
	s U S	000
	l U S	00+
	m U S	000
	e U S	0 + +
	f U S	0 + 0

Table 3

 3 Panel A: E¤ects of foreign idiosyncratic orthogonal shocks

					Response of:
	Region:	y vs s ml	vs s ml	s vs s ml	l vs s ml
			:0 :29 :32	:0 :14 :18	:11 :11 :0	:11 :32 :0
	U S	0	1 :32 :25	1 :64 :57	:82 :71 1	:68 :43 1
		+	:0 :39 :43	:0 :22 :25	:07 :18 :0	:21 :25 :0
			:0 :29 :32	:07 :43 :36	:21 :46 :0	:18 :46 :0
	JA	0	1 :46 :43	:89 :32 :43	:68 :32 1	:68 :29 1
		+	:0 :25 :25	:04 :25 :21	:11 :22 :0	:14 :25 :0
			:0	:18 :14	:04 :29 :29	:11 :29 :0	:11 :32 :0
	EA	0	:92 :53 :57	:92 :32 :47	:85 :42 1	:64 :32 1
		+	:08 :29 :29	:04 :39 :24	:04 :29 :0	:25 :36 :0
			:0	:21 :21	:07 :25 :14	:18 :18 :0	:11 :14 :0
	U K	0	:93 :29 :43	:82 :36 :57	:68 :71 1	:64 :72 1
		+	:07 :50 :36	:11 :39 :29	:14 :11 :0	:25 :14 :0
			:0	:29 :32	:0	:36 :32	:11 :21 :0	:11 :29 :0
	CA	0	:89 :42 :39	:89 :36 :39	:75 :68 1	:58 :42 1
		+	:11 :29 :29	:11 :28 :29	:14 :11 :0	:31 :29 :0
					Response of:
	Region:	m vs s ml	e vs s ml	f vs s ml	T OT vs s ml
			:11 :11 :14	:36 :42 :42	:11 :18 :11	:11 :24 :12
	U S	0	:68 :50 :61	:43 :29 :29	:46 :46 :54	:73 :48 :66
		+	:21 :29 :25	:21 :29 :29	:43 :36 :36	:16 :28 :22
			:18 :21 :21	:32 :43 :43	:32 :29 :32	:18 :37 :25
	JA	0	:50 :36 :36	:29 :32 :50	:46 :50 :47	:65 :37 :57
		+	:32 :43 :43	:39 :25 :07	:22 :21 :21	:17 :26 :18
			:25 :29 :25	:29 :39 :36	:14 :11 :11	:12 :27 :20
	EA	0	:57 :39 :50	:50 :25 :28	:54 :43 :43	:72 :38 :57
		+	:18 :32 :25	:21 :36 :36	:32 :47 :47	:16 :35 :23
			:25 :25 :21	:28 :33 :25	:21 :25 :21	:16 :23 :15
	U K	0	:64 :39 :43	:36 :39 :61	:61 :46 :50	:67 :47 :65
		+	:11 :36 :36	:36 :28 :14	:18 :29 :29	:17 :30 :20
			:32 :36 :29	:36 :29 :43	:10 :21 :21	:14 :29 :22
	CA	0	:36 :43 :50	:39 :46 :29	:54 :25 :25	:63 :43 :49
		+	:32 :21 :21	:25 :25 :29	:36 :54 :54	:23 :28 :23

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

See also[START_REF] Ehrmann | Stocks, bonds, money markets and exchange rates: measuring international …nancial transmission[END_REF] and[START_REF] Hamori | The transmission mechanism of business cycles among Germany, Japan, the UK and the USA[END_REF] for additional evidence in favour of the interpretation of US macroeconomic shocks in terms of global shocks. See also[START_REF] Harvey | Evidence for common features in G7 macroeconomic time series[END_REF] for additional evidence of comovements in G-7 macroeconomic variables.

The real exchange rate changes (e) display litle evidence of comovements: the fraction of the overall variance attributable to the …rst principal component amounts to 0.37 and is widely dispersed across regions (being heavily in ‡uenced by the US series). On this basis we conclude that there is no compelling evidence of a global factor driving real exchange

The median forecast error variance decomposition, as the median impulse response functions, have been obtained using Monte Carlo simulation, as suggested in[START_REF] Granger | Thick modelling[END_REF]. For reasons of space, only the results for the within period and the …ve-year period horizons have been reported in the tables. A full set of results is available from the authors upon request.

The …nding of price and liquidity puzzles, given the large information set employed in the modelling, is quite surprising. The above puzzles are in fact usually related to misspeci…cation of the information set and, for instance, the inclusion of commodity prices tends to lessen the problem. Yet, the evidence is coherent with previous results of Dees, di Mauro,[START_REF] Dees | Exploring the international linkages of the euro area: a global VAR analysis[END_REF], where an even larger information set is used.

+ + + 000 0 0 0 + 0 0 0 0 + + 00 + + + 0 + + 0 + + 0 + + 0 0 + 0 00 +00 000 0 + 0 0 0 0 0 000 0 +00 +00 0 0 000 000 00 00 + + + + + + + + 0 + + 0 0 + 0 0 + + 0 + + + + + 0 + + + 0 +00 0 00 000 +00 + + + + + + Panel A reports the median orthogonal impulse responses of the domestic variables (indexing the columns) to idiosyncratic domestic shocks (indexing the rows) for the US, Japan, the euro area, the UK and Canada, over three forecast horizons, i.e. within quarter (impact), beyond one quarter and within three years (short term), beyond three years (medium/long term). For example, the …rst row reports the e¤ect of a disturbance to the US output on the US series. "+" denotes a positive (and signi…cant at the 5% level) e¤ect, a negative signi…cant e¤ect is denoted by " ", and a null or not signi…cant e¤ect is denoted by "0". Hence, "0 + " denotes that the shock has a zero (or not signi…cant) within quarter impact on the given variable, positive short-term e¤ects, and negative medium to long-term e¤ects. Panel B reports the proportion of negative (and statistically signi…cant at the 5% level), zero and positive (and statistically signi…cant) responses of each variable (in columns) in all …ve regions to all foreign idiosyncratic orthogonal shocks to the variables in rows (for a total of 20 impulse responses), over three forecasting horizons, i.e. within quarter (vs), beyond one quarter and within three years (s) and beyond three years (ml). Hence, entry (1,1), 0, indicates that within one quarter in no region a positive foreign output shock led to a contraction in domestic real activity. Moreover, according to entries (2,1) and (3,1), 60% of the within quarter reactions have been null, and the remaining 40% turned out positive. [START_REF] Pesaran | Generalised impulse response analysis in linear multivariate models[END_REF]