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Foreign Entanglements: Estimating the Source and Size of Spillovers Across Industrial Countries

Author(s):
International Monetary Fund. Research Dept.
Published Date:
June 2009
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The extent of spillovers across industrial regions remains an area of considerable interest and uncertainty. The importance of common or global factors in national output fluctuations is widely recognized, given the long history of substantial international business cycle fluctuations (see Bordo and Helbling, 2004). Consequently, a large body of literature has sought to measure the contribution of common factors to national business cycle fluctuations. In recent studies, dynamic factor models have been the main preferred approach because these models reduce common variations across individual countries to a small number of significant but unrelated factors (Gerlach, 1988;Gregory, Head, and Raynauld, 1997; Kose, Otrok, and Whiteman, 2003; and Stock and Watson, 2005).

The common factors in such studies, however, are typically difficult to interpret, because basic factor model decompositions are atheoretical and lack a structural identification scheme. The common factor could reflect global shocks, spillovers from one country to others, or idiosyncratic shocks that happen to be correlated across countries.1 So far, plausible schemes to distinguish between common shocks and spillovers have not been developed, so questions such as whether or not U.S. shocks account for a significant share of common output fluctuations remain unanswered.2 A related literature uses generalized vector autoregressions (VARs) to model links across large numbers of countries, but again common shocks and spillovers remain essentially undifferentiated (Pesaran, Schuermann, and Weiner, 2004; and Dees and others, 2007).

This paper uses a new approach for solving this identification issue. We construct an aggregate of smaller countries as a proxy for global shocks. This aggregate includes Australia, Canada, Denmark, Korea, Mexico, Norway, New Zealand, South Africa, Sweden, Switzerland, Taiwan, and the United Kingdom. For convenience, we will henceforth call this group the rest of the world. The rest of the world contains a set of countries that is diverse in terms of both geography and industrial structure. Given the wide differences of the constituent countries, any shock to this aggregate is a strong candidate for a global disturbance. Because the individual economies involved are both varied and small relative to the United States, the euro area, and Japan, they are unlikely to have significant direct effects on them. Spillovers from the rest of the world to these major regions can thus be regarded as a reasonable measure of the impact of global shocks.

We also introduce a procedure to calculate uncertainty across VAR identification schemes, which allows us to examine the robustness of our results to differing assumptions about the direction of causation between contemporaneous shocks. We find that, with the important exception of the global disturbance, specification uncertainty rarely influences the statistical significance of the results.

Using VARs of growth across the four regions, we can therefore differentiate between the effects of global, U.S., euro area, and Japanese shocks. U.S. shocks generate significant spillovers to other regions of one-quarter to one-half the size of the U.S. shock after two years, but those from the euro area and Japan are smaller and insignificant in almost all cases. Spillovers from the rest of the world, on the other hand, are sensitive to the identification of the correlated component of shocks across regions as either emanating from the United States or representing a global shock; correlations with euro area and Japanese shocks matter less. In our baseline specification, the response of the euro area and Japan is two-thirds the size of the shock to the rest of the world and the impact on the United States is one-third the size of the shock.

Having estimated overall spillovers across countries, we go on to quantify the contributions to spillovers of each of the major channels through which shocks are propagated—trade, commodity prices, and financial markets. By contrast, the international business cycle literature has focused on the factors associated with higher correlations across countries more than on quantifying the contribution of each of these factors to spillovers (Kose, Prasad, and Terrones, 2004; Baxter and Kouparitsas, 2005; Kose, Otrok, and Whiteman, 2005; and Imbs, 2006). Meanwhile, large-scale models that capture trade linkages more completely than financial ones have difficulty in explaining the degree of co-movement across countries present in the data (Kose and Yi, 2006).

Spillovers from trade, commodity prices, and financial markets are identified by extending the VAR to include the contribution of real exports to growth, the change in real commodity prices, the levels of short-term interest rates and bond yields, and the change in real equity prices for the regions under analysis. This method can be used as a cross-check on the plausibility of the main results. Encouragingly, the aggregate impact of these separate channels corresponds reasonably closely to the direct estimation of impulses. We find that financial variables play the largest role in the transmission of global and U.S. shocks, and, consistent with other literature on the dominance of U.S. markets in generating financial spillovers, there is little feedback from other regions to the United States.

I. A New Approach to Identifying VARs

In order to identify independent impulse response functions (IRFs) from a VAR, procedures generally transform the errors across the individual regressions so that they are orthogonal (an exception, called generalized impulse responses, is discussed further below). Traditionally, this is done using a Cholesky decomposition, which assumes that all of the correlations between errors are assigned to the equation that is earliest in the ordering. For example, in a three-variable VAR, all of the correlation between the errors in the first equation and the second and third ones is assigned to the first, but any remaining correlation between the errors in the second and third equations is assigned to the second.

Such an approach works well if there is a relatively clear ordering for the Cholesky decomposition. For example, in small monetary VARs containing inflation, output, and interest rates, it appears intuitive to assume that easily adjustable interest rates respond to shocks in more slow-moving inflation and output, and not the other way around. However, it is much less clear that such a stark assumption about causation is appropriate in a VAR containing growth across countries. Accordingly, although results for some individual Cholesky orderings are reported, the empirical results below focus on an average of impulse responses across a range of “plausible” Cholesky orderings.

This procedure has a strong Bayesian flavor. The weights assigned to the various orderings can be seen as placing priors on the relative importance of spillovers going from variable A to B as opposed to those from B to A. These priors are then updated using the estimated variance-covariance matrix of equation errors. Note, however, that this updating depends only on the parameters of the variance-covariance matrix, not on the full probability distribution, which is used in traditional Bayesian methods.3

The underlying approach is easily illustrated using a two-variable VAR. Consider the matrix A that transforms the estimated errors e from such a VAR into orthogonalized errors ɛ. Mathematically, ɛ = Ae. For the two possible Cholesky decompositions, the matrix A is

where σij is the relevant entry in the estimated variance-covariance matrix of the equation errors (for example, σ11 is the variance of the error on the first variable in the first equation). The zeros in the lower left cell of the first matrix and the upper right cell of the second indicate that in each of these decompositions, contemporaneous feedback between the two variables flows in only one direction.

By putting weight on both decompositions, however, our procedure allows such feedback to go in both directions. More specifically, the procedure assigns a (user-defined) weight of α to the first Cholesky decomposition and (1—α) to the second. The matrix that decomposes the equation errors into their orthogonalized versions is now:

One way of interpreting the weight α is that it defines the prior probability on the source of contemporaneous correlation between the two error terms. Note, however, that this prior is modified by the estimated parameters of the variance-covariance matrix of errors (σ11, σ12, and σ22). Mathematically,

where aij is the relevant entry of the matrix A. The relative importance assigned to each possible direction of causation depends on both the prior (α) and on the ratio of the variance of the errors in the first equation (σ11) and the second one (σ22). Therefore, the estimated magnitude of spillovers depends on both the prior and on the estimated variances and covariances of the errors in the VAR (which are not affected by the ordering of the variables). This updating of the priors by the distribution of the error terms turns out to be important in interpreting the results, as discussed further below.

The intuition of this example can be generalized to the n-variable case, with the complication that adding variables to the VAR makes it more difficult to define the errors in each equation (the e’s), as account has to be taken of correlations with errors from a greater number of equations. But, once this has been done, the rest of the logic of this two-variable case holds.

In addition, it is possible to calculate how uncertainty over the correct Cholesky ordering adds to the variance around the IRFs, over and above the usual variance associated with uncertainty about the underlying parameters of the VAR. Sticking with the two-variable example, let xt¯ represent the average impulse response for period t across the two decompositions (so that xt¯=αx¯1t+(1-α)x¯2t). The variance of the IRF can be written as

where subscript i on the left-hand side indicates the different orderings (1 and 2). Variation across orderings produces the fourth and fifth terms in Equation (4), which we call specification uncertainty. Subscript j indexes the individual observations represented in the sample from which the standard errors are calculated. This generates the first three terms in Equation (4), reflecting the familiar uncertainty associated with each individual identification scheme, coming from the imprecision with which the coefficients of the VAR are estimated (recall that the coefficient estimates are independent of the choice of ordering).

Given that the individual identification schemes differ only in their assumptions about the ordering of the variables, the errors across individual orderings are likely to be highly correlated. Accordingly, we assume that the correlation across different orderings is unity. Given this assumption, the first three terms of Equation (4) can be approximated by taking the weighted average of the variances of each of the decompositions. The final line of Equation (4) reflects the uncertainty due to variation in the response across orderings and is simply the variance of the response across these decompositions.

Hence, the uncertainty associated with identification can be approximated by simply adding the average variance of the impulse responses across identification schemes to the variance associated with parameter uncertainty. Given our assumption of a perfect correlation of errors associated with parameter uncertainty across orderings, this is an upper limit for the true value of this variance. This procedure can again be generalized to the n-variable case.

Our approach has some similarities, but also important differences, from generalized IRFs (Pesaran and Shin, 1998). First, although our procedure puts explicit weights on various Cholesky orderings, generalized response functions implicitly put an equal weight on all possible orderings. In our context, this implies assuming that shocks coming from the euro area, Japan, and the United States are equally likely to create spillovers to the other regions, whereas the approach adopted in this paper puts a stronger prior on U.S. shocks being the source of such spillovers. Second, although our responses are to shocks that have been orthogonalized and hence can be used to decompose the impact of each shock on the system, the generalized responses involve underlying shocks that are correlated and hence “overfit” the system. Finally, our distinction between parameter and ordering uncertainty has not been applied to generalized responses, although it appears it could be.

II. How Large Are Spillovers?

Data on quarterly growth (measured as the difference in the logarithm of real GDP) for the four regions were collected from 1970 through the fourth quarter of 2007. The official euro area data extend back to 1991, and earlier data were spliced back to 1970 using the estimates in Fagan, Henry, and Mestre (2005). For the rest-of-world aggregate, each country’s growth rate is weighted by the size of its GDP in purchasing-power-parity (PPP) terms. The weighted-average growth rate is then used to construct an index of real GDP, which implies approximately equal effects from North America, Europe, and Asia (at least toward the end of the sample).4

Regressions were run on the full sample and its first and second halves, with the split between the two subsamples being set at the first quarter of 1988. This break was chosen to differentiate the relatively turbulent 1970s and 1980s, with large oil shocks and rampant inflation, from the period after inflation had been controlled, which also includes the great moderation in real output variability that became apparent in the late 1990s. The basic VARs contain GDP growth for each of the four regions. Four lags were used in the VAR, following Perez, Osborn, and Artis (2006) and Stock and Watson (2005).5

A major focus of the empirical analysis is examining the robustness of the results to alternative orderings of the contemporaneous correlations across shocks in the VAR. Table 1 reports the correlation of these shocks for the full sample period and the two subperiods (in the bottom left triangle of each block). For the full sample, there are two correlations of 0.4 or more in the VAR residuals—those between shocks to growth in the United States and the rest of the world, and between the euro area and the rest of the world. Hence, using the rest of the world as a proxy for global shocks has reduced, but not eliminated, the correlation of these shocks with those from the United States and euro area.

Table 1.Correlations, Variances, and Covariances of VAR Residuals
Covariance
United StatesEuro areaJapanRest of worldVariance of

Domestic Shocks
Full Sample: 1970:Q1 to 2007:Q4
Correlation
United States0.080.110.150.58
Euro area0.230.070.090.23
Japan0.170.170.110.82
Rest of world0.410.380.250.25
First Half of Sample: 1970:Q1 to 1987:Q4
Correlation
United States0.160.350.361.14
Euro area0.260.080.130.34
Japan0.350.150.130.88
Rest of world0.540.370.220.39
Second Half of Sample: 1988:Q1 to 2007:Q4
Correlation
United States0.02–0.060.030.21
Euro area0.160.060.040.12
Japan–0.170.210.040.59
Rest of world0.210.350.170.11
Source: Authors’ calculations.
Source: Authors’ calculations.

Table 1 also reports the variances and covariances of shocks over the three samples, to give a sense of the relative size of disturbances across regions. Shocks to the United States and Japan are significantly larger than those to the euro area and the rest of the world. As a result, the covariance between shocks to growth in the United States and the rest of the world is significantly larger than that between the euro area and the rest of the world, even though the correlations between the VAR residuals are similar. This means that, when the prior weights are updated with the United States-rest of the world covariance, the U.S. weight will be reduced and that on the rest of the world will be increased. In addition, consistent with the onset of the great moderation, the variance of all of the shocks declines in the second period. The moderation has been largest in the United States (whose variance is lower by a factor of five) and smallest in Japan (whose variance falls by only one-third).6

This paper does not take a strong view on the appropriate ordering in the VAR. Rather, results are averaged across several plausible orderings, in order to allow for the possibility of spillovers in either direction between countries.7 This allows for two-way causation between the United States and the other two major industrial regions. Using U.S., EA, JP, and ROW to represent the United States, euro area, Japan, and the rest of the world, respectively, the simple average across the following eight Cholesky decompositions is reported (in order of independence from other regions):

  • U.S., EA, JP, ROW;

  • U.S., JP, EA, ROW;

  • U.S., EA, ROW, JP;

  • U.S., JP, ROW, EA;

  • ROW, U.S., EA, JP;

  • ROW, U.S., JP, EA;

  • EA, ROW, JP, U.S.;

  • JP, ROW, EA, U.S.

The four orderings on the left place U.S. shocks ahead of those of other countries, implying that the U.S. economy is the most important driver of global fluctuations. In two decompositions, the rest of the world is ordered first as it is assumed to be a proxy for global shocks, but the euro area and Japan are each placed first in one ordering.

As discussed above, the choice of orderings can be seen as defining “priors” on the relative importance of contemporaneous spillovers from one area to another. The above orderings give, for example, a 50 percent probability that the correlation between U.S. and rest-of-world shocks is driven by the United States, and another 50 percent probability that it is driven by the rest of the world. The other probabilities are 75:25 United States-euro area and United States-Japan, and 50:50 euro area-Japan, rest of world-euro area, and rest of the world-Japan.

The average results are augmented by presenting three “extreme” orderings that illustrate the range of potential outcomes—namely orderings one, five, and seven. The first assumes that the contemporaneous correlation between U.S. shocks and those of other regions is driven by the United States, in effect saying that the rest of the world represents small countries that create no contemporaneous spillovers to other regions. The second assumes that all contemporaneous correlation between shocks to the rest of the world and those of other regions are global shocks that spill over onto the main industrial regions (as discussed above, the prior in our averaging procedure puts an even chance on these two interpretations). Finally, we also examine ordering seven to show the sensitivity of the results to the assumption that correlation among global shocks is driven by the euro area.

Full Sample Results

Figure 1 contains IRFs showing the impact on the level of real GDP over eight quarters averaged across eight Cholesky decompositions. The first column reports the impact of a shock to U.S. real GDP first on itself, then on the euro area, on Japan, and, finally, on the rest of the world. The second, third, and fourth columns report IRFs for shocks to the euro area, Japan, and rest of the world in the same order. Each graph reports the response ± two standard error bands that only account for coefficient uncertainty, and an additional set of bands incorporating the specification uncertainty discussed above.

Figure 1.Responses to Shocks to GDP Across Eight VARs

(In percent)
(In percent)

Source: Authors’ calculations.

Spillovers from the United States to other regions are of economic and statistical significance. A typical shock to the level of U.S. GDP is ¾ percent initially and rises to over 1 percent after two years. The initial impact elsewhere is small, but gradually builds to ½ percent or more in the euro area and rest of the world, and slightly over ¼ percent in Japan.8 Hence, after two years, the spillover of U.S. shocks to other regions is somewhere between one-quarter and one-half the size of the initial shock. These responses are significant except that of Japan.

By contrast, a shock to euro area real GDP has a negligible impact on other regions. Domestic shocks of the order of ½ percent of GDP have insignificant positive effects on the other regions in the short run that die out over two years. Spillovers from Japan are only significant to the euro area, where their size is similar to those from the United States. However, as discussed below, this result is not robust across subperiods.

Spillovers from the rest of the world are the most sensitive to the Cholesky ordering. The last column of Figure 1 shows that the average shock to the rest of the world is some ½ percent of real GDP, with spillovers to other regions statistically insignificant in all cases. However, it is the sizable uncertainty engendered by differences across specifications that keeps the rest of world from having a significant impact on euro area, and, in the early quarters, the United States. This uncertainty is mainly reflected in spillovers from the rest of the world, rather than vice versa, because of the larger variance of U.S. shocks compared with shocks to the rest of the world, as discussed in the theory section above.

Sensitivity to Cholesky Ordering

The average results across eight orderings allow the magnitude of spillovers to be calculated given prior convictions on the source of contemporaneous correlation between shocks, but analysis of the individual orderings illustrates the range of possible estimates. As can be seen in Figure 2, the main uncertainty across specifications is in the estimated spillovers from the rest of the world. If the rest of the world is placed first—and hence the correlation between its shock and fluctuations in other regions reflects global disturbances—the estimated spillovers approximately double, and are statistically significant for all regions.9 By contrast, when the rest of the world is last in the VAR all spillovers are negligible. This is consistent with the interpretation of the shock implicit in each ordering—when it is a global shock, it matters for other regions, but it is unimportant when interpreted as an impulse emanating from small countries.

Figure 2.Sensitivity to Cholesky Ordering

(In percent)
(In percent)

Source: Authors’ calculations.

Spillovers from the rest of the world thus depend crucially on whether their output fluctuations can be assumed to accurately reflect global shocks. When the rest of the world is placed first in the ordering, and hence all disturbances to this aggregate are assumed to be global shocks, they average about 0.6 percent of GDP. The impact on the euro area and Japan rises to a similar value after two years, but the U.S. response remains relatively constant at about two-thirds of the global shock. This suggests that global disturbances have a significant impact on other regions, with the estimated size depending crucially on the chosen prior—particularly as regards the direction of causation between shocks to the United States and the rest of the world.

The extreme ordering with the rest of the world first also results in about a 25 percent reduction in the size of contemporaneous spillovers from the United States to other regions, relative to the average. However, U.S. spillovers to the euro area and rest of world remain statistically significant in both of the extreme orderings where those regions are placed first. When the euro area is placed first, its shocks impact growth in the United States and the rest of the world, but the effects still die out after a year, but the estimated responses to Japanese shocks show almost no variation across these orderings.

Results by Subsample

The results from estimating the baseline “average” VAR over the periods 1970-87 and 1988-2007 are reported in Figure 3.10 In addition, the dotted line shows the responses from a VAR using the coefficients for 1988-2007 but the distribution and magnitude of shocks from 1970 to 1987.11 This allows us to attribute variation in spillovers over time into portions that are related to the changing nature of business cycle comovement across regions (the gap between the dashed and dotted lines) and those that merely reflect differences in the size of shocks (the gap between the dotted and solid line). Three shifts over time are apparent—namely, the relative decline in the average size (and hence variability) of U.S. shocks at home and associated spillovers, the fall in the importance of spillovers from Japan to other regions, and the larger role played by spillovers from the rest of the world.

Figure 3.Responses to Shocks to GDP Across Eight VARs by Subsample

(In percent)
(In percent)

Source: Authors’ calculations.

Focusing initially on results for the United States, the first column of Figure 3 shows that all of the responses to U.S. shocks decrease significantly between the first and second samples. However, for the euro area and the rest of the world, most of the decline is due to the reduction in shocks emanating from the United States. As shown by the close correspondence between the dotted and dashed lines, there is little difference in the transmission of U.S. shocks to other regions when the magnitude of shocks is held constant. The “great moderation” in U.S. macroeconomic volatility cuts U.S. spillovers to other regions by a half, but the response of the other economies to a U.S. shock of a given size has remained relatively constant, consistent with the findings of Stock and Watson (2005) and Perez, Osborn, and Artis (2006).

In the other three regions, by contrast, changes in cross-country linkages have contributed more to differences in spillovers over time, but there is less evidence of moderation in domestic shocks. The responses to euro area shocks show the least variation, with the Japanese cycle becoming slightly more sensitive to them.12 The decline in spillovers from Japan has been driven entirely by a change in the comovement of other countries’ business cycles—consistent with the observation that the intense economic difficulties experienced by Japan after the bursting of the real estate bubble in the late 1980s had relatively limited impact elsewhere. Similarly, spillovers from the rest of the world to the euro area and Japan have risen, despite a slight fall in the initial magnitude of the typical shock, as the propagation of these shocks has become much more powerful. This is consistent with the view that rising globalization has made the world more sensitive to global events, although this pattern is not seen in the U.S. response to global shocks.

The main implication of these results is that the great moderation in U.S. output volatility is an important factor behind the decline in fluctuations elsewhere. As domestic shocks in the other three regions have not varied as much over time, and tighter linkages with the rest of the world have offset Japan’s loss of influence, it follows that lower global volatility is related to the increased stability of U.S. activity and corresponding reduction in spillovers to the rest of the world.13Table 2 presents variance decompositions, which relate the share of variability in each region’s output accounted for by fluctuations in the other regions, and shows that U.S. shocks fall in relative importance in all cases. Meanwhile, Japanese shocks have declined in importance and fluctuations in the rest of the world and euro area explain an increasing share of the cyclical movements of other regions.

Table 2.Variance Decompositions of Real GDP(In percent)
Share Explained After Eight Quarters
Forecast VariableShare Explained byFull sample1970–871988–2007
United StatesUnited States83.173.877.7
Euro area5.45.25.8
Japan3.08.27.2
Rest of world8.512.99.3
Euro areaUnited States12.613.17.5
Euro area63.252.367.4
Japan13.926.34.3
Rest of world10.48.220.9
JapanUnited States2.311.110.1
Euro area1.94.15.1
Japan92.679.069.4
Rest of world3.25.915.4
Rest of worldUnited States22.326.09.5
Euro area8.16.314.1
Japan4.310.84.7
Rest of world65.256.971.7
Source: Authors’ calculations.
Source: Authors’ calculations.

III. What Are the Sources of Spillovers?

This section builds on the analysis of the geographic provenance of spillovers by estimating the linkages by which these spillovers are transmitted across borders. Three potential channels are considered—trade, commodity prices, and financial conditions. It should be recognized from the outset that this procedure is more applicable to identifying spillovers across regions than the sources of fluctuations in a domestic economy, which can be driven by additional factors such as consumer and business confidence.

The four-variable VAR in the previous section is augmented by adding each factor as an exogenous variable in a separate VAR run. This procedure amounts to assuming that each channel is independent of the others, and hence its impact can be estimated separately.14 The response of GDP to foreign activity in the augmented VAR can be thought of as the size of the spillover excluding the channel present as an exogenous variable. The individual channel’s contribution to spillovers, then, equals the difference between this response and the one from the original VAR, as in Equation (5):

where Ci,j is the contribution of channel j in period i, and ri and ri,j are the overall response and the response from the VAR with channel j included, respectively. The sum of the spillovers coming from the individual sources is not constrained to equal the overall spillover estimated in the base VAR, so it provides an alternative estimate of the size of spillovers that can be used to verify the main results. We also report results from a VAR in which all the exogenous variables are included, which indicates the extent of multicollinearity between the three channels.

Measuring the Channels

To identify trade spillovers, we use the contribution of exports to GDP growth. As imports are a function of domestic activity, contemporaneous movements in a country’s imports and its output are likely to capture domestic factors in addition to the effects of foreign activity on income. Fluctuations in exports, however, are mainly a function of foreign income and their contemporaneous correlation with domestic demand can be considered exogenous to domestic factors. If the effects of shocks to foreign growth on domestic activity are accounted for by movements in domestic exports, then there is evidence of spillovers through trade. Similarly, if a shock to a major economy’s exports affects its GDP, and in turn this feeds through into growth in another country, this is a trade spillover. The contribution for the rest-of-world aggregate is excluded, however, because these countries are proxying for global shocks, and it is not clear that global exports can be considered to be exogenous to the global economy.15 The lag structure should be short to prevent reverse causality from GDP shocks to exports in future periods from contaminating the estimates. Therefore, the contemporaneous and only one lagged value are included, given the evidence of some autocorrelation in the variable.16

Spillovers from financial channels are captured by including short-term interest rates (the yield on three-month government securities), long-term interest rates (the yield on 10-year government securities), and equity prices for the United States, euro area, and Japan.17 The interest rates are expressed in levels, as yields approximate a random walk. Equity prices were deflated by the country’s GDP deflator, then expressed in quarterly percent changes. Because of the possibility of collinearity among the three variables, they enter as a group in a single VAR rather than individually. The contemporaneous value and first lag of each variable is included, in order to allow for transmission lags. One concern is whether these variables fully capture all financial factors, such as the state of the banking system. To investigate this issue, we also added series on equity prices of the financial sector for the United States, euro area, and Japan. However, the results were similar to the baseline and are not reported for brevity (they are available from the authors on request).

The commodity prices used are the oil price and the nonenergy component of the Goldman Sachs Commodity Index, a broad measure with weights based on global production. Because both track prices in dollars, they are converted into real terms using the U.S. GDP deflator. The real prices then enter the VAR in quarterly percent changes. The contemporaneous value and four lags are used in order to allow for transmission lags.

Full Sample Results

Figure 4 presents the contributions of each of these three channels averaged over eight orderings.18 The line in each graph represents the direct estimate of the average response, as in Figure 1. Although, as expected, the specification does not do a particularly good job at identifying the sources of fluctuations within each region, the fit is better for spillovers across regions, especially in cases where the response itself is statistically significant.

Figure 4.Decomposition of Responses to GDP Shocks with Financial Variables Included Jointly

(In percent)
(In percent)

Source: Authors’ calculations.

The results for each type of variable can be summarized as follows:

  • Trade. The impact of direct trade links is generally small. Even the largest trade spillover, from the United States to the euro area, explains less than half of the transmission of U.S. shocks. Trade channels account for about 20 percent of U.S. spillovers to the rest of the world and the rest of the world’s spillovers to the euro area, and estimates for the other bilateral pairs are even smaller. The magnitudes we find here plausibly reflect the fact that international trade accounts for only a fraction of activity among the main economic regions in the world, and hence that the impact of trade shocks is inevitably relatively minor.19

  • Commodity prices. The impact of commodity prices on real GDP spillovers is also limited.20 Because the rest of the world aggregate has several sizable commodity exporters, a rise in activity elsewhere, which will tend to raise global commodity prices, has a mild positive impact on real GDP. Responses for the other three regions, which are net commodity importers, are mixed, but tend more toward the negative side in their response to the rest of the world, which may reflect the influence of global supply shocks.

  • Financial variables. The largest estimated contributions to spillovers almost universally come from financial variables.21 These effects are positive for the United States, Japan, and the rest of the world, but, perhaps somewhat surprisingly, always negative for the euro area. About half of spillovers from the United States and the rest of the world are explained by the financial channel. The United States is the least sensitive to shocks to global financial conditions. Overall, our findings imply that financial markets are the main conduit for both U.S. and global shocks but financial shocks from other regions are not as important. This is consistent with the large body of work finding that U.S. financial disturbances affect other regions with little feedback in the other direction (Ehrmann and Fratzscher, 2005; Bayoumi and Swiston, 2007; and Faust and others, 2007).

As a robustness check, Figure 5 compares the IRFs estimated for the average specification with the responses implied by summing the impact of the individual potential sources of spillovers. The results confirm that summing the individual sources of shocks provides only a partial explanation for domestic shocks. Turning to spillovers, however, the correspondence between the average IRF and the sum across channels is generally close. In addition, results are reported from a VAR where all the exogenous variables are added simultaneously. If the impact across individual spillover channels were highly correlated, this VAR would show smaller spillovers than the results from summing the three channels. The fact that there are no large divergences suggests that the various channels of spillovers can be regarded as relatively independent of each other.

Figure 5.Responses to Shocks by Identification Method

(In percent)
(In percent)

Source: Authors’ calculations.

Results by Subsample

In order to examine changes in the transmission of spillovers over time, Figures 6 and 7 present the decompositions by subsample for U.S. and rest-of-world shocks (euro area and Japanese spillovers are not reported as they are generally insignificant). For the United States, the magnitude of spillovers through all three channels declined in the second half of the sample, but the relative importance of financial linkages with the euro area and the rest of the world has increased at the expense of trade and commodity prices. For rest-of-world spillovers, financial shocks have become more important in terms of both magnitude and relative importance. They now have a stronger influence on activity in the euro area and Japan than do U.S. financial conditions. In line with previous sections, these results point to the increased stability of the U.S. economy as a major factor in the reduction in global economic volatility.

Figure 6.Decomposition of Responses to U.S. GDP Shocks by Subsample

(In percent)

Source: Authors’ calculations.

Figure 7.Decomposition of Responses to Rest of World GDP Shocks by Subsample

(In percent)

Source: Authors’ calculations.

IV. Conclusions

This paper has examined both the sources and size of spillovers across major industrial country regions. Particular attention has been given to identifying the uncertainties involved in distinguishing between spillovers emanating from the United States and from global sources, by using disturbances to an aggregate of 12 smaller countries as a proxy for global shocks.

The results suggest the following:

  • The United States creates large spillovers to other regions. Regardless of the identifying assumptions used, the United States generates statistically significant spillovers to the euro area and the rest of the world. The effect on foreign output is about one-quarter to one-half the size of the shock to U.S. GDP.

  • There also appear to be sizable spillovers from global shocks (identified as those coming from the rest-of-world aggregate). However, their magnitude and significance depend on priors, particularly on the assumed direction of causation of contemporaneous shocks between the rest of the world and the United States. Shocks to activity in the euro area and Japan generally have limited effects on other parts of the world.

  • Smaller U.S. domestic shocks appear to be central to the global moderation in output fluctuations between the 1970s/1980s and the 1990s/2000s. Although U.S. domestic shocks fell notably, the magnitude of domestic shocks elsewhere has remained stable. U.S. spillovers to other regions have fallen because of this moderation in domestic fluctuations, not because of a reduction in cross-country linkages.

  • The main source of spillovers is financial conditions. Short-term interest rates and financial conditions more generally (bond yields and equity prices) matter for transferring activity across regions, and financial linkages appear to have become more important than other channels over time. By contrast, trade and commodity prices are less potent factors in this process. These channels also seem relatively independent of each other.

Taken together, these results imply that a major factor in the reduction in output fluctuations around the world was the declining volatility of the U.S. macroeconomy and the associated stability in financial conditions. Given the importance of financial linkages, at least some of the global moderation can be attributed to steadier U.S. monetary policy. This more benign environment may well have been conducive to better domestic policies elsewhere, but the size of domestic shocks does not appear to have fallen over time in other regions to the extent that it has in the United States.

Our methodology allows us to identify global shocks and to estimate spillovers from contemporaneous shocks across countries. Previous work has concluded that global economic fluctuations reflect, to a large extent, common shocks rather than spillovers between countries, but this paper casts considerable doubt on that explanation. Even if there are large global shocks (an issue that remains uncertain), there are also significant spillovers from U.S. shocks.

These are transmitted through financial markets, suggesting that documenting the macroeconomic effects of these linkages is necessary in order to successfully explain spillovers across major regions. Consistent with our results, models that capture trade linkages better than financial ones have failed to find large spillovers across major global regions. Finally, a possible extension of the approach in this paper is to examine spillovers from the major industrial countries or regions onto other economies. This can be done by adding growth of other regions last in the VAR, as in Perez, Osborn, and Artis (2006) and Swiston and Bayoumi (2008).

References

Tamim Bayoumi is an assistant director with the IMF’s Western Hemisphere Department, and Andrew Swiston is a research assistant with that department. The authors gratefully acknowledge invaluable contributions from Sam Ouliaris and Thomas Helbling. Useful comments were also received from Petya Brooks, Trish Pollard, Nathan Sheets, Jeromin Zettelmeyer, participants in a seminar with U.S. government officials, participants in a Western Hemisphere Department seminar, and participants in an IMF seminar on the Macroeconomic and International Implications of Financial Market Innovation.

See, for example, Canova and Dellas (1993). There are other problems as well. For example, if countries respond differently to some common shock, say, for example, because of differences in economic structure, the estimated common factors may or may not capture the effects of these common shocks, depending on the stringency of the restrictions on the dynamic structure of the underlying model.

Stock and Watson (2005) allow for lagged spillovers of country-specific shocks, but this still leaves contemporaneous shocks unidentified.

For approaches that use Bayesian techniques to update forecasts across models, see Sala-i-Martin, Doppelhofer, and Miller (2004) and Leamer (1978). See Wright (2003) for a discussion and application of Leamer’s Bayesian model averaging technique.

Results using alternative groups of countries and weighting schemes produced similar results. The countries included are based on availability of quarterly GDP data since 1970.

Both the final prediction error and the Schwarz information criterion suggest three lags, but the Aikaike information criterion finds one lag to be sufficient.

The disproportionate fall in U.S. volatility is robust to modest changes in the sample period, and is consistent with the results in Stock and Watson (2005) and International Monetary Fund (2007). The source of the great moderation—smaller underlying shocks or better policies—remains a subject of much debate. See Stock and Watson (2003); Juillard and others (2006); and International Monetary Fund (2007).

This is also consistent with the evidence that averaging across a range of models tends to produce better forecasts than a single model. See, for example, Stock and Watson (2004).

These magnitudes are similar to those found by Perez, Osborn, and Artis (2006).

Full results for these orderings, including standard errors, are available from the authors upon request.

Results with standard errors for each period are available from the authors upon request.

See Stock and Watson (2005) and Perez, Osborn, and Artis (2006) for other examples of this approach.

Perez, Osborn, and Artis (2006) found a similar result.

This result is robust to modest changes in the sample, although if the break point is moved after 1993—leaving only one recession in the second period which is probably inadequate for accurately identifying spillovers—there is a stronger role played by moderation of shocks in other regions.

This also keeps the VARs smaller, which conserves degrees of freedom.

Results including the export contribution for the rest-of-world aggregate are similar to those reported here and are available upon request.

Estimation using zero lags showed only minor differences, while trade spillovers were smaller, on average, with four lags. Results for both specifications are available upon request.

Rest-of-world financial conditions are not included. Given that the data already include the largest financial markets and those in other major economies are highly correlated with the regions included here, the rest-of-world financial conditions variable would be unlikely to add a significant amount of information. One indication of the success of this method is that we find sizable financial spillovers from rest-of-world growth shocks even in the absence of a specific measure of the region’s financial conditions.

Decompositions based on the individual orderings discussed in the previous section are available from the authors upon request.

Experimentation with other methods of quantifying the trade channel, including making trade an endogenous variable in the VAR, or using net exports’ contribution to growth, yielded similar results. A related paper (Swiston and Bayoumi, 2008) examines spillovers to Canada and Mexico and finds that trade spillovers are stronger where there is a large amount of bilateral trade—in that case, from the United States.

Dees and others (2007) come to the same conclusion using a different methodology.

In estimates including each variable separately, they all make sizable contributions to spillovers. Therefore, while monetary policy is an important driver of spillovers, so are financial conditions more generally. Furthermore, the estimate of their joint impact is not much smaller than the sum of their individual contributions, suggesting that the effects of the three financial variables are relatively orthogonal to each other.

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