## _wp07182 - Decomposition of Responses to Rest of World GDP Shocks

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---

### I. Introduction and identification strategy
- Purpose:
  - Quantify spillovers across four regions—United States (US), euro area (EA), Japan (JP), and an aggregate of small industrial countries (rest of the world, ROW: Australia, Canada, Denmark, Norway, New Zealand, Sweden, Switzerland)—and distinguish global shocks from regional shocks.
- Key identifying assumption:
  - Shocks to the ROW aggregate are a strong candidate for global disturbances because constituent countries are diverse and individually small.
- Empirical tool:
  - Vector autoregressions (VARs) of quarterly growth (difference in logarithm of real GDP) across the four regions.
- Central empirical innovations:
  - Average impulse responses across a range of “plausible” Cholesky orderings rather than a single ordering.
  - Procedure to calculate uncertainty across VAR identification schemes (specification uncertainty) and combine it with parameter uncertainty.
- High-level preview of findings:
  - U.S. and global shocks generate significant spillovers to other regions of about ⅓ to ½ the size of the initial shock after two years.
  - Spillovers from the euro area and Japan are smaller and insignificant in most cases.
  - Financial variables play the largest role in transmitting global and U.S. shocks.

### II. New approach to identifying VARs (ordering averaging and uncertainty)
- Problem:
  - Cholesky decomposition requires an ordering; ordering is ambiguous for cross-country growth VARs.
- Method:
  - Compute orthogonalizing matrix A as a weighted combination of Cholesky decompositions; weight α defines prior on contemporaneous spillover direction.
  - Two-variable example: A = α·(Cholesky 1) + (1−α)·(Cholesky 2), with α interpreted as prior on relative importance of one direction of contemporaneous causation.
  - The prior is updated by the estimated variance-covariance matrix of residuals (entries σij).
- Uncertainty decomposition:
  - Total variance of impulse responses approximated by (i) average variance due to parameter uncertainty across orderings plus (ii) variance of responses across orderings (specification uncertainty).
  - Assumes correlation of parameter-uncertainty errors across orderings is unity (upper limit approximation).
- Practical implementation:
  - Averages across eight Cholesky orderings (symmetric between US and ROW; EA and JP orderings interchangeable) represent even priors on many directions of causation.
  - Two “extreme” orderings examined: ROW, US, EA, JP (ROW first) and US, EA, JP, ROW (US first).

### III. Data, VAR specification, and sample splits
- Data:
  - Quarterly growth series (difference in logarithm of real GDP) for US, EA, JP, ROW from 1970 to 2006.
  - Euro area official data extend back to 1991 and were spliced back to 1970 using Fagan, Henry, and Mestre (2005) estimates.
  - ROW constructed with equal weights across listed small industrial countries.
- VAR specification:
  - Growth in levels (first differences of log GDP); four lags used in VAR.
  - Sample split at Q1 1988 to form subperiods 1970–1987 and 1988–2006.
- Residual properties (full sample):
  - Two large residual correlations of order 0.4 to 0.5: between US and ROW, and between EA and ROW.
  - Equation variances decline in the second period: US variance declines by a factor of five; Japan variance falls by around one-quarter.

### IV. How large are spillovers? — full-sample and ordering sensitivity
- Aggregate/average results (average across eight orderings):
  - Typical U.S. shock:
    - Initial US GDP shock: ¾ percent initially; rises to around 1¼ percent after 2 years.
    - Spillovers: gradually rise to about ½ percent in EA, JP, and ROW real GDP after two years — "somewhere around 40 percent of any U.S. shock spills over to the other regions" after two years.
    - Statistical significance: all these responses are significant except that of Japan (high volatility/noise in JP growth).
  - Euro area shocks:
    - Domestic shocks ~½ percent of GDP.
    - Negligible impact on other regions; small positive short-run effects significant only for ROW; negligible and insignificant after two years.
  - Japan shocks:
    - Spillovers generally small; only significant to EA in some specifications with magnitude similar to US spillovers to EA (not robust across subsamples).
  - ROW shocks:
    - Average shock to ROW ~½ percent of real GDP.
    - Average spillovers to other regions statistically insignificant.
    - Ordering sensitivity: if ROW is placed first (interpreting ROW shocks as global), estimated spillovers approximately double and become statistically significant for EA and for the first few quarters for US. If ROW is last, spillovers are negligible.
- Ordering-driven uncertainty:
  - Main specification uncertainty centers on spillovers from ROW to other regions; spillovers from US to others are robust across orderings.
  - Placing ROW first reduces contemporaneous spillovers assigned to US; placing ROW last implies ROW reflects negligible contemporaneous influence on major regions.
  - Prior weight on direction of causation between US and ROW is even (four orderings with US before ROW, four with ROW before US).

### V. Subsample results (1970–1987 versus 1988–2006)
- Principal themes across subsamples:
  - Relative decline in average size and variability of US shocks at home and associated spillovers (the great moderation).
    - All IRFs from US shocks approximately halve between the first and second samples.
  - Decline in importance of spillovers from Japan to other regions.
  - Larger role played by spillovers from ROW in the later period.
- Interpretation:
  - Great moderation in US macroeconomic volatility is the primary driver behind moderated global output volatility (since domestic shocks in EA, JP, ROW remain similar).
  - Rising importance of ROW spillovers and falling Japanese spillovers consistent with financial markets being the main conduit: Japan’s financial links were limited during its banking problems; increasing financial globalization amplified ROW/global financial shocks.
- Variance decomposition (share explained after eight quarters; qualitative summary):
  - US shocks fall in relative importance in variance decompositions across regions in second sample.
  - EA shocks increase in relative importance.
  - JP shocks generally decline in importance.
  - ROW shocks become more important.

### VI. Identification of transmission channels: trade, commodity prices, financial conditions
- Augmented VAR approach to isolate channels:
  - Trade channel:
    - Add contribution of net exports to growth for US, EA, JP as first variables in VAR (ROW excluded from trade equations).
    - In this augmented VAR, spillovers associated with net trade should be identified with shocks to net trade rather than GDP.
  - Commodity prices:
    - Change in real oil and nonoil commodity prices (calculated using US GDP deflator) included as exogenous variables (current value + four lags).
  - Financial variables:
    - Change in real equity prices (real equity = nominal series divided by region’s GDP deflator): included as contemporaneous value + first lag as exogenous.
    - Nominal government bond yields and nominal short-term interest rates: contemporaneous value + first lag as exogenous.
  - Main implementation:
    - Add each variable separately to the basic GDP VAR to keep systems small; also report results from a VAR including all variables jointly.
- Quantification approach:
  - Spillover from a given channel = GDP response in baseline VAR − GDP response in augmented VAR that includes the channel variable.
  - Independent-channel approach treats channels separately; sum of channel-specific spillovers is not constrained to equal aggregate spillover (serves as cross-check).
- Key channel findings:
  - Financial variables play the largest role in the transmission of global and U.S. shocks.
  - Little feedback from other regions to the United States, consistent with U.S. market dominance in generating financial spillovers.
  - Aggregate impact of individual channels corresponds reasonably closely to direct estimation of impulses; cross-check supports plausibility of main results.

### VII. Key quantitative highlights and robustness
- Sample and specification:
  - Quarterly data, 1970–2006; split at first quarter of 1988 for subperiod analysis.
  - Four lags in VAR.
- Representative magnitudes:
  - Typical US GDP shock: ¾ percent initially; ~1¼ percent after 2 years.
  - Spillovers from a US shock to other regions: about ½ percent after two years (≈40 percent of initial US shock).
  - Average ROW shock: ~½ percent of real GDP.
  - Residual correlations of order 0.4 to 0.5 between US–ROW and EA–ROW for full sample.
- Robustness methods:
  - Averaging across eight orderings used to reduce sensitivity to Cholesky ordering.
  - Specification uncertainty explicitly computed and added to parameter uncertainty; main effect of specification uncertainty is on ROW-origin spillovers.
  - Two extreme orderings (ROW-first and US-first) documented to illustrate bounds of estimated spillovers.
- Temporal changes (numerical):
  - US variance declines by a factor of five between subsamples.
  - JP variance falls by around one-quarter.
  - IRFs to US shocks approximately halve in magnitude in 1988–2006 relative to 1970–1987.
- Residual correlation and variance-covariance exact entries (selected key values as reported):
  - Full sample correlation matrix (United States / Euro area / Japan / Rest of world):
    - United States 1.000 0.22 0.17 0.42
    - Euro area 0.22 1.000 0.16 0.48
    - Japan 0.17 0.16 1.000 0.04
    - Rest of world 0.42 0.48 0.04 1.00
  - Full sample variance-covariance matrix (United States / Euro area / Japan / Rest of world):
    - United States 0.60 0.09 0.12 0.16
    - Euro area 0.09 0.24 0.07 0.12
    - Japan 0.12 0.07 0.84 0.02
    - Rest of world 0.16 0.12 0.02 0.24
  - Variance decompositions (share explained after eight quarters; Full sample / 1970–1987 / 1988–2006):
    - Forecast variable: United States — United States 83.3 75.1 71.9; Euro area 5.4 6.7 8.0; Japan 3.5 8.7 6.8; Rest of world 7.7 9.5 13.4
    - Forecast variable: Euro area — United States 13.8 14.1 6.8; Euro area 60.7 49.8 66.4; Japan 15.2 27.6 6.8; Rest of world 10.3 8.6 20.0
    - Forecast variable: Japan — United States 2.9 10.8 9.1; Euro area 1.7 2.7 6.9; Japan 94.5 83.7 78.0; Rest of world 0.8 2.7 5.9
    - Forecast variable: Rest of world — United States 17.6 19.8 8.3; Euro area 12.4 11.2 24.1; Japan 1.7 4.6 9.4; Rest of world 68.2 64.4 58.1

### VIII. Appendix methodological notes and fit
- VAR specifications include 4 lags in main reported results; extending to 8 lags does not materially change the small impact of trade links.
- The trade VAR uses up "over one-third of the degrees of freedom in the subsamples."
- Adding all three financial variables into the VAR simultaneously produces results similar to including them separately, suggesting relative orthogonality of these financial channels.
- Specification fits spillovers across regions better than it identifies sources of fluctuations within each region; fit is especially better where the response itself is statistically significant.

### IX. Findings by type of variable (summary)
- Trade:
  - Impact of direct trade links is small even with 4 lags included.
  - Small impact plausibly reflects that international trade accounts for only a fraction of activity among main economic regions.
  - Caveat: result would not necessarily hold for immediate neighbors (example: U.S. trade likely matters for Canada).
- Commodity prices:
  - Impact on real GDP generally limited.
  - Direction depends on trade structure:
    - ROW: activity rise tends to raise global commodity prices and has a positive impact on ROW real GDP (ROW has sizable commodity exports).
    - Japan: higher global commodity prices are negative for Japanese activity (Japan is a significant commodity importer).
    - US and EA: responses mixed; responses to the global shock are always negative (global commodity price shocks likely dominated by oil prices).
- Financial variables:
  - Largest estimated contributions to spillovers almost universally come from financial variables.
  - Effects largest and generally positive for U.S. spillovers and for ROW.
  - Impact on EA and JP spillovers less consistent and often negative.
  - Short-term interest rates tend to be the most important single financial factor; bond yields and equity prices also matter.
  - Monetary policy and broader financial conditions both drive spillovers.
  - The three financial channels (short-term interest rates, bond yields, equity prices) appear relatively independent and distinct.

### X. Aggregate patterns, conclusions, and policy implications
- Aggregate spillover patterns:
  - Summing individual-source impacts provides only a limited explanation for domestic shocks; for spillovers the correspondence between summed individual sources and the average specification is generally close.
  - Main exceptions: response of EA real GDP to JP shocks is not robust; response of US output to EA shocks (sum of components implies an implausibly large negative effect).
  - A VAR including all channels simultaneously appears less capable of mimicking the initial IRFs, particularly regarding U.S. spillovers—supporting view that channels operate relatively independently.
- Main conclusions:
  - United States creates the largest spillovers to other regions: regardless of identifying assumptions, the United States generates statistically significant spillovers to the euro area and the rest of the world; the effect on foreign output is about ⅓ to ½ the size of the shock to U.S. GDP.
  - Significant spillovers from global shocks (proxied by aggregate of seven smaller industrial countries) exist, but their size is uncertain and depends on priors about simultaneity with U.S. shocks.
  - Euro area and Japan generally have limited effects on other parts of the world.
  - Smaller U.S. domestic shocks appear central to the global moderation in output fluctuations between the 1970s/1980s and the 1990s/2000s: U.S. domestic shocks fell notably; domestic shocks elsewhere remained stable.
  - Main source of spillovers is global financial conditions (short-term interest rates, bond yields, equity prices); trade and commodity prices are less potent.
  - Reduction in global financial volatility from a more stable U.S. environment was crucial for lower global output volatility; more stable U.S. monetary policy helped stabilize real and financial uncertainty at the center of the system.
  - Large macroeconomic models that capture trade linkages better than financial ones have consistently failed to find large spillovers across major global regions; this paper suggests financial linkages are the crucial omitted channel.
- Policy and research implications:
  - Analysis of global spillovers should focus more on financial linkages and the macroeconomic consequences of financial conditions.
  - Documenting the macroeconomic effects of financial market linkages is an important future task.
  - Suggested extension: examine spillovers from major industrial countries or regions onto other economies by adding growth of another region last in the VAR (left for future work).

*Source: _wp07182 - 7. Decomposition of Responses to Rest of World GDP Shocks (IMF working paper content provided).*

### References..............................................................................................................

### _wp07182 - References....................................................................................................................................17

### Tables
- 1.  Correlations of VAR Residuals ..............................................................................................19
- 2.  Variance-Covariance of VAR Residuals ................................................................................20
- 3.  Variance Decompositions of Real GDP .................................................................................21

### Figures
- 1.  Responses to Shocks to GDP Across Eight VARs .................................................................22
- 2.  Responses Across Specifications ............................................................................................24
- 3.  Responses to Shocks to GDP with Euro Area First................................................................26
- 4.  Responses to Shocks to GDP Across Eight VARs by Subsample .........................................28
- 5.  Decomposition of Responses to GDP Shocks ........................................................................30
- 6.  Responses by Identification Method.......................................................................................32

*Source PDF filename: _wp07182 - References..............................................................................................................*

### 7.  Decomposition of Responses to Rest of World GDP Shocks ................................................34

### 7.  Decomposition of Responses to Rest of World GDP Shocks

### I. Introduction and identification strategy
- Purpose: quantify spillovers across four regions—United States (US), euro area (EA), Japan (JP), and an aggregate of small industrial countries (rest of the world, ROW: Australia, Canada, Denmark, Norway, New Zealand, Sweden, Switzerland)—and distinguish global shocks from regional shocks.
- Key identifying assumption: shocks to the ROW aggregate are a strong candidate for global disturbances because constituent countries are diverse and individually small.
- Main empirical tool: vector autoregressions (VARs) of quarterly growth (difference in logarithm of real GDP) across the four regions.
- Central empirical innovations:
  - Average impulse responses across a range of “plausible” Cholesky orderings rather than a single ordering.
  - Procedure to calculate uncertainty across VAR identification schemes (specification uncertainty) and combine it with parameter uncertainty.
- Main high-level empirical findings preview:
  - U.S. and global shocks generate significant spillovers to other regions of about ⅓ to ½ the size of the initial shock after two years.
  - Spillovers from the euro area and Japan are smaller and insignificant in most cases.
  - Financial variables play the largest role in transmitting global and U.S. shocks.

### II. New approach to identifying VARs (ordering averaging and uncertainty)
- Problem: Cholesky decomposition requires an ordering; ordering is ambiguous for cross-country growth VARs.
- Method:
  - Compute orthogonalizing matrix A as a weighted combination of Cholesky decompositions; weight α defines prior on contemporaneous spillover direction.
  - For two-variable example, A = α·(Cholesky 1) + (1−α)·(Cholesky 2), with α interpreted as prior on relative importance of one direction of contemporaneous causation.
  - The prior is updated by the estimated variance-covariance matrix of residuals (entries σij).
  - Uncertainty decomposition: total variance of impulse responses approximated by (i) average variance due to parameter uncertainty across orderings plus (ii) variance of responses across orderings (specification uncertainty). Assumes correlation of parameter-uncertainty errors across orderings is unity (upper limit approximation).
- Practical implementation:
  - Use averages across eight Cholesky orderings (specified in the source in symmetric fashion between US and ROW, and interchangeable EA and JP orderings) to represent even priors on directions of causation in many links.
  - Examine two “extreme” orderings in detail: ROW, US, EA, JP (ROW first) and US, EA, JP, ROW (US first).

### III. Data, VAR specification, and sample splits
- Data:
  - Quarterly growth series (difference in logarithm of real GDP) for US, EA, JP, ROW from 1970 to 2006.
  - Euro area official data extend back to 1991 and were spliced back to 1970 using Fagan, Henry, and Mestre (2005) estimates.
  - ROW constructed with equal weights across listed small industrial countries.
- VAR specification:
  - Growth in levels (first differences of log GDP); four lags used in VAR.
  - Sample split at Q1 1988 to form subperiods 1970–1987 and 1988–2006.
- Residual properties:
  - For full sample, two large residual correlations of order 0.4 to 0.5: between US and ROW, and between EA and ROW.
  - Equation variances decline in the second period, largest fall in US (variance declines by a factor of five) and smallest in Japan (variance falls by around one-quarter).

### IV. How large are spillovers? — full-sample and ordering sensitivity
- Aggregate/average results (average across eight orderings):
  - Typical U.S. shock:
    - Initial US GDP shock: ¾ percent initially; rises to around 1¼ percent after 2 years.
    - Spillovers: gradually rise to about ½ percent in EA, JP, and ROW real GDP after two years — "somewhere around 40 percent of any U.S. shock spills over to the other regions" after two years.
    - Statistical significance: all these responses are significant except that of Japan (high volatility/noise in JP growth).
  - Euro area shocks:
    - Domestic shocks ~½ percent of GDP.
    - Negligible impact on other regions; small positive short-run effects significant only for ROW; negligible and insignificant after two years.
  - Japan shocks:
    - Spillovers generally small; only significant to EA in some specifications with magnitude similar to US spillovers to EA (not robust across subsamples).
  - ROW shocks:
    - Average shock to ROW ~½ percent of real GDP.
    - Average spillovers to other regions statistically insignificant.
    - Ordering sensitivity: if ROW is placed first (interpreting ROW shocks as global), estimated spillovers approximately double and become statistically significant for EA and for the first few quarters for US. If ROW is last, spillovers are negligible.
- Ordering-driven uncertainty:
  - Main specification uncertainty centers on spillovers from ROW to other regions; spillovers from US to others are robust across orderings.
  - Placing ROW first reduces contemporaneous spillovers assigned to US; placing ROW last implies ROW reflects negligible contemporaneous influence on major regions.
  - The prior weight on the direction of causation between US and ROW is even (four orderings with US before ROW, four with ROW before US).

### V. Subsample results (1970–1987 versus 1988–2006)
- Three principal themes across subsamples:
  - Relative decline in average size and variability of US shocks at home and associated spillovers (the great moderation).
    - All IRFs from US shocks approximately halve between the first and second samples.
  - Decline in importance of spillovers from Japan to other regions.
  - Larger role played by spillovers from ROW in the later period.
- Interpretation:
  - Great moderation in US macroeconomic volatility is the primary driver behind moderated global output volatility (since domestic shocks in EA, JP, ROW remain similar).
  - Rising importance of ROW spillovers and falling Japanese spillovers consistent with financial markets being the main conduit: Japan’s financial links were limited during its banking problems; increasing financial globalization amplified ROW/global financial shocks.
- Variance decomposition summary (after 8 quarters; qualitative reporting):
  - US shocks fall in relative importance in variance decompositions across regions in second sample.
  - EA shocks increase in relative importance.
  - JP shocks generally decline in importance.
  - ROW shocks become more important.

### VI. Identification of transmission channels: trade, commodity prices, financial conditions
- Augmented VAR approach to isolate channels:
  - Trade channel: add contribution of net exports to growth for US, EA, JP as first variables in VAR (ROW excluded from trade equations).
    - In this augmented VAR, spillovers associated with net trade should be identified with shocks to net trade rather than GDP.
  - Commodity prices: change in real oil and nonoil commodity prices (calculated using US GDP deflator) included as exogenous variables (current value + four lags).
  - Financial variables:
    - Change in real equity prices (real equity = nominal series divided by region’s GDP deflator): included as contemporaneous value + first lag as exogenous.
    - Nominal government bond yields and nominal short-term interest rates: contemporaneous value + first lag as exogenous.
  - Main implementation: add each variable separately to the basic GDP VAR to keep systems small; also report results from a VAR including all variables jointly.
- Quantification approach:
  - The spillover from a given channel equals the difference between the GDP response in the baseline VAR and the GDP response in the augmented VAR that includes the channel variable.
  - This independent-channel approach treats channels separately; the sum of channel-specific spillovers is not constrained to equal the aggregate spillover from the base VAR (provides cross-check).
- Key channel finding (summary statement from source):
  - Financial variables play the largest role in the transmission of global and U.S. shocks.
  - Consistent with literature on dominance of U.S. markets in generating financial spillovers, there is little feedback from other regions to the United States.
  - Aggregate impact of individual channels corresponds reasonably closely to direct estimation of impulses (cross-check supports plausibility of main results).

### VII. Key quantitative highlights and robustness
- Sample and specification:
  - Quarterly data, 1970–2006; split at first quarter of 1988 for subperiod analysis.
  - Four lags in VAR.
- Representative magnitudes:
  - Typical US GDP shock: ¾ percent initially; ~1¼ percent after 2 years.
  - Spillovers from a US shock to other regions: about ½ percent after two years (≈40 percent of initial US shock).
  - Average ROW shock: ~½ percent of real GDP.
  - Residual correlations of order 0.4 to 0.5 between US–ROW and EA–ROW for full sample.
- Robustness:
  - Averaging across eight orderings used to reduce sensitivity to Cholesky ordering.
  - Specification uncertainty explicitly computed and added to parameter uncertainty; main effect of specification uncertainty is on ROW-origin spillovers.
  - Two extreme orderings (ROW-first and US-first) documented to illustrate bounds of estimated spillovers.
- Temporal changes:
  - US variance declines by a factor of five between subsamples; JP variance falls by around one-quarter.
  - IRFs to US shocks approximately halve in magnitude in 1988–2006 relative to 1970–1987.

*Source: _wp07182 - 7.  Decomposition of Responses to Rest of World GDP Shocks (IMF working paper content provided).*

### Appendix Figures A5 and A6, while results for the average procedure over the two

### _wp07182 - Appendix Figures A5 and A6, while results for the average procedure over the two

### Key methodological notes and fit
- VAR specifications include 4 lags in the main reported results; extending VAR lags to 8 does not materially change the small impact of trade links.
- The trade VAR uses up "over one-third of the degrees of freedom in the subsamples."
- Adding all three financial variables into the VAR simultaneously produces results similar to including them separately, suggesting relative orthogonality of these financial channels.
- The specification fits spillovers across regions better than it identifies sources of fluctuations within each region; fit is especially better where the response itself is statistically significant.

### Findings by type of variable
- Trade
  - The impact of direct trade links is small even with 4 lags included in the specification.
  - The small impact plausibly reflects that international trade accounts for only a fraction of activity among the main economic regions in the world.
  - Caveat: this result would not necessarily hold for immediate neighbors (example given: U.S. trade likely matters for Canada).
- Commodity prices
  - The impact of commodity prices on real GDP is generally limited.
  - Direction of effect depends on the trade structure of the region:
    - Rest of the world: a rise in activity tends to raise global commodity prices and has a positive impact on real GDP (rest of the world has sizable commodity exports).
    - Japan: as a significant commodity importer, higher global commodity prices are negative for Japanese economic activity.
    - United States and euro area: responses are mixed, but responses to the global shock are always negative (global commodity price shocks likely dominated by oil prices).
- Financial variables
  - The largest estimated contributions to spillovers almost universally come from financial variables.
  - Effects are largest and generally positive for U.S. spillovers and for the rest of the world.
  - Impact of financial market shocks on euro area and Japanese spillovers is less consistent and often negative.
  - Short-term interest rates tend to be the most important single financial factor; bond yields and equity prices also matter.
  - Monetary policy and broader financial conditions both drive spillovers.
  - The three financial channels (short-term interest rates, bond yields, equity prices) appear relatively independent and distinct in transmitting shocks.

### Aggregate spillover patterns and comparisons
- Summing individual-source impacts provides only a limited explanation for domestic shocks; for spillovers the correspondence between summed individual sources and the average specification is generally close.
- Main exceptions:
  - Response of euro area real GDP to Japanese shocks is not robust.
  - Response of U.S. output to euro area shocks: the sum of individual components implies an implausibly large negative effect.
- A VAR including all channels simultaneously appears less capable of mimicking the initial IRFs, particularly regarding U.S. spillovers—supporting the view that channels operate relatively independently.

### Main conclusions and implications
- The United States creates the largest spillovers to other regions:
  - Regardless of identifying assumptions, the United States generates statistically significant spillovers to the euro area and the rest of the world.
  - The effect on foreign output is about ⅓ to ½ the size of the shock to U.S. GDP.
- There are significant spillovers from global shocks (proxied by an aggregate of seven smaller industrial countries), but their size is uncertain and depends on priors about simultaneity with U.S. shocks.
- The euro area and Japan generally have limited effects on other parts of the world.
- Smaller U.S. domestic shocks appear central to the global moderation in output fluctuations between the 1970s/1980s and the 1990s/2000s:
  - U.S. domestic shocks fell notably; domestic shocks elsewhere remained stable.
- The main source of spillovers is global financial conditions (short-term interest rates, bond yields, equity prices); trade and commodity prices are less potent.
- The reduction in global financial volatility from a more stable U.S. environment was crucial for lower global output volatility; more stable U.S. monetary policy helped stabilize real and financial uncertainty at the center of the system.
- Large macroeconomic models that capture trade linkages better than financial ones have consistently failed to find large spillovers across major global regions; this paper suggests financial linkages are the crucial omitted channel.

### Policy and research implications
- Analysis of global spillovers should focus more on financial linkages and the macroeconomic consequences of financial conditions.
- Documenting the macroeconomic effects of financial market linkages is an important future task.
- A suggested extension: examine spillovers from major industrial countries or regions onto other economies by adding growth of another region last in the VAR (left for future work).

*Source: _wp07182 - Appendix Figures A5 and A6, while results for the average procedure over the two*

### References

### _wp07182 - References

### Cited works
- Bayoumi, T. and A. Swiston, 2007, “The Ties that Bind: Measuring International Bond Spillovers Using Inflation-Indexed Bond Yields,” IMF Working Paper WP/07/128.
- Bordo, M, and T. Helbling, 2004, “Have National Business Cycles Become More Synchronized?” In Siebert, H. (ed.), Macroeconomic Policies in the World Economy (Berlin-Heidelberg: Springer Verlag).
- Canova, F. and H. Dellas, 1993, “Trade Interdependence and the International Business Cycle,” Journal of International Economics, Vol. 34 (February), pp. 23–47.
- Ehrmann, M., and M. Fratzscher, 2005, “Equal Size, Equal Role? Interest Rate Interdependence Between the Euro Area and the United States,” Economic Journal, Vol. 115 (October), pp. 928–48.
- Fagan, G., J. Henry, and R. Mestre, 2005, “An Area-Wide Model for the Euro Area,” Economic Modelling, Vol. 22 (January), pp. 39–59.
- Faust, J., J. Rogers, S. Wang, and J. Wright, 2007, “The High-Frequency Responses of Interest Rates to Macroeconomic Announcements,” Journal of Monetary Economics, Vol. 54 (May), pp. 1051–68.
- Gerlach, H., 1988, “World Business Cycles under Fixed and Flexible Exchange Rates,” Journal of Money, Credit, and Banking, Vol. 20 (November), pp. 621–32.
- Gregory, A., A. Head, and J. Raynauld, 1997, “Measuring World Business Cycles,” International Economic Review, Vol. 38 (August), pp. 677–701.
- International Monetary Fund, 2000, “Box 1.2. Risky Business: Output Volatility and the Perils of Forecasting in Japan,” World Economic Outlook (October), pp. 18–19.
- Juillard, M., P. Karam, D. Laxton, and P. Pesenti, 2006, “Welfare-Based Monetary Policy Rules in an Estimated DSGE Model of the U.S. Economy,” ECB Working Paper No. 613.
- Kose, M., C. Otrok, and C. Whiteman, 2003, “International Business Cycles: World, Region, and Country-Specific Factors,” American Economic Review, Vol. 93 (September), pp. 1216–39.
- Leamer, E., 1978, Specification Searches: Ad Hoc Inference with Non Experimental Data, New York: John Wiley and Sons.
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### Tables
- Table 1. Correlations of VAR Residuals
  - Second half of sample: 1988Q1 to 2006Q2
  - First half of sample: 1970Q1 to 1987Q4
  - Full sample: 1970Q1 to 2006Q2
  - Correlation matrices (as presented):
    - Full sample matrix (United States / Euro area / Japan / Rest of world):
      - United States 1.000 0.22 0.17 0.42
      - Euro area 0.22 1.000 0.16 0.48
      - Japan 0.17 0.16 1.000 0.04
      - Rest of world 0.42 0.48 0.04 1.00
    - First half of sample:
      - United States 1.000 0.27 0.36 0.43
      - Europe 0.27 1.000 0.14 0.50
      - Japan 0.36 0.14 1.000 0.20
      - Rest of world 0.43 0.50 0.20 1.00
    - Second half of sample:
      - United States 1.000 0.09 -0.13 0.32
      - Euro area 0.09 1.000 0.24 0.52
      - Japan -0.13 0.24 1.000 -0.15
      - Rest of world 0.32 0.52 -0.15 1.00
  - Source: IMF staff calculations.

- Table 2. Variance-Covariance of VAR Residuals
  - Second half of sample: 1988Q1 to 2006Q2
  - First half of sample: 1970Q1 to 1987Q4
  - Full sample: 1970Q1 to 2006Q2
  - Variance-covariance matrices (as presented):
    - Full sample matrix:
      - United States 0.60 0.09 0.12 0.16
      - Euro area 0.09 0.24 0.07 0.12
      - Japan 0.12 0.07 0.84 0.02
      - Rest of world 0.16 0.12 0.02 0.24
    - First half of sample:
      - United States 1.03 0.14 0.30 0.26
      - Europe 0.14 0.33 0.09 0.17
      - Japan 0.30 0.09 0.90 0.10
      - Rest of world 0.26 0.17 0.10 0.36
    - Second half of sample:
      - United States 0.20 0.01 -0.05 0.05
      - Euro area 0.01 0.14 0.07 0.07
      - Japan -0.05 0.07 0.71 -0.05
      - Rest of world 0.05 0.07 -0.05 0.13
  - Source: IMF staff calculations.

- Table 3. Variance Decompositions of Real GDP
  - Share explained after eight quarters
  - Full sample / 1970–1987 / 1988–2006 (values as presented):
    - Forecast variable: United States
      - United States 83.3 75.1 71.9
      - Euro area 5.4 6.7 8.0
      - Japan 3.5 8.7 6.8
      - Rest of world 7.7 9.5 13.4
    - Forecast variable: Euro area
      - United States 13.8 14.1 6.8
      - Euro area 60.7 49.8 66.4
      - Japan 15.2 27.6 6.8
      - Rest of world 10.3 8.6 20.0
    - Forecast variable: Japan
      - United States 2.9 10.8 9.1
      - Euro area 1.7 2.7 6.9
      - Japan 94.5 83.7 78.0
      - Rest of world 0.8 2.7 5.9
    - Forecast variable: Rest of world
      - United States 17.6 19.8 8.3
      - Euro area 12.4 11.2 24.1
      - Japan 1.7 4.6 9.4
      - Rest of world 68.2 64.4 58.1
  - Source: IMF staff calculations.

### Figures (responses, decompositions, and identification)
- Figure 1. Responses to Shocks to GDP Across Eight VARs
  - Source: IMF staff calculations.
  - Panel responses include: Response of U.S. GDP to U.S. GDP; Response of U.S. GDP to euro area GDP; Response of euro area GDP to euro area GDP; Response of Japan GDP to U.S. GDP; Response of rest of world GDP to U.S. GDP; Response of euro area GDP to U.S. GDP; Response of Japan GDP to euro area GDP; Response of rest of world GDP to euro area GDP.
  - Response horizons shown: 1Q 2Q 3Q 4Q 5Q 6Q 7Q 8Q.
  - Error representations: +/– 2 Standard errors parameter uncertainty only; +/– 2 Standard errors with specification uncertainty.

- Figure 1 (continued). Responses to Shocks to GDP Across Eight VARs
  - Additional panels: Response of U.S. GDP to Japan GDP; Response of U.S. GDP to rest of world GDP; Response of euro area GDP to rest of world GDP; Response of Japan GDP to Japan GDP; Response of rest of world GDP to Japan GDP; Response of euro area GDP to Japan GDP; Response of Japan GDP to rest of world GDP; Response of rest of world GDP to rest of world GDP.
  - Source: IMF staff calculations.

- Figure 2. Responses Across Specifications
  - Responses to U.S. and euro area GDP; responses categorized by Average, U.S. first, R.o.W. first.
  - Panels mirror those in Figure 1 across specification variants.
  - Source: IMF staff calculations.

- Figure 2 (continued). Responses Across Specifications
  - Responses to Japan and rest of world GDP across specification variants.
  - Source: IMF staff calculations.

- Figure 3. Response to Shocks to GDP with Euro Area First
  - VAR Ordering: Euro area, Japan, rest of world, United States
  - Panels and responses as in previous figures with +/- 2 standard errors and average response across eight VARs/United States first.
  - Source: IMF staff calculations.

- Figure 3 (continued). Response to Shocks to GDP with Euro Area First
  - Additional panels for longer-horizon responses (up to 3.0 in some panels).
  - Source: IMF staff calculations.

- Figure 4. Responses to Shocks to GDP Across Eight VARs by Subsample
  - Panels compare 1970–1987 and 1988–2006 subsamples for each response.
  - Source: IMF staff calculations.

- Figure 4 (continued). Responses to Shocks to GDP Across Eight VARs by Subsample
  - Continued panels for full set of bilateral responses across subsamples.
  - Source: IMF staff calculations.

- Figure 5. Decomposition of Responses to GDP Shocks
  - Responses to U.S. and euro area GDP decomposed into channels: Net exports, Commodity prices, Equity prices, Long-term interest rates, Short-term interest rates.
  - Source: IMF staff calculations.

- Figure 5 (continued). Decomposition of Responses to GDP Shocks
  - Responses to Japan and rest of world GDP decomposed into same channels.
  - Source: IMF staff calculations.

- Figure 6. Responses by Identification Method
  - Panels compare Average across eight VARs, Sum of individual spillover channels, +/– 2 Standard errors across eight VARs, Response from comprehensive VAR; with specification uncertainty noted.
  - Source: IMF staff calculations.

- Figure 6 (continued). Responses by Identification Method
  - Continued panels for remaining bilateral responses.
  - Source: IMF staff calculations.

- Figure 7. Decomposition of Responses to Rest of World GDP Shocks
  - Comparison: Rest of World First in VAR versus Rest of World Last in VAR.
  - Decomposition channels: Net exports, Commodity prices, Equity prices, Long-term interest rates, Short-term interest rates.
  - Source: IMF staff calculations.

- Figure A1. Response to Shocks to GDP
  - VAR Ordering: Rest of world, United States, euro area, Japan.
  - Panels for bilateral responses with +/- 2 standard errors.
  - Source: IMF staff calculations.

- Figure A1 (continued). Response to Shocks to GDP
  - Continued panels for full set of responses.
  - Source: IMF staff calculations.

- Figure A2. Response to Shocks to GDP
  - VAR Ordering: United States, euro area, Japan, rest of world.
  - Panels with +/- 2 standard errors.
  - Source: IMF staff calculations.

- Figure A2 (continued). Response to Shocks to GDP
  - Continued panels for full set of responses.
  - Source: IMF staff calculations.

- Figure A3. Responses to Shocks to GDP Across Eight VARs, 1970–1987
  - Panels and error representations as in Figure 1, for the 1970–1987 subsample.
  - Source: IMF staff calculations.

- Figure A3 (continued). Responses to Shocks to GDP Across Eight VARs, 1970–1987
  - Continued panels for remaining responses.
  - Source: IMF staff calculations.

- Figure A4. Responses to Shocks to GDP Across Eight VARs, 1988–2006
  - Panels and error representations as in Figure 1, for the 1988–2006 subsample.
  - Source: IMF staff calculations.

- Figure A4 (continued). Responses to Shocks to GDP Across Eight VARs, 1988–2006
  - Continued panels for remaining responses.
  - Source: IMF staff calculations.

- Figure A5. Decomposition of Responses to GDP Shocks
  - VAR Ordering: Rest of World, United States, euro area, Japan.
  - Decomposition channels: Net exports, Commodity prices, Equity prices, Long-term interest rates, Short-term interest rates.
  - Source: IMF staff calculations.

- Figure A5 (continued). Decomposition of Responses to GDP Shocks
  - Continued panels for remaining decompositions.
  - Source: IMF staff calculations.

- Figure A6. Decomposition of Responses to GDP Shocks
  - VAR Ordering: United States, euro area, Japan, rest of World.
  - Decomposition channels as above.
  - Source: IMF staff calculations.

- Figure A6 (continued). Decomposition of Responses to GDP Shocks
  - Continued panels for remaining decompositions.
  - Source: IMF staff calculations.

- Figure A7. Decomposition of Responses to GDP Shocks, 1970–1987
  - Responses to U.S. and euro area GDP; responses to Japan and rest of world GDP; decomposed into the standard channels.
  - Source: IMF staff calculations.

- Figure A7 (continued). Decomposition of Responses to GDP Shocks, 1970–1987
  - Continued panels for remaining decompositions.
  - Source: IMF staff calculations.

- Figure A8. Decomposition of Responses to GDP Shocks, 1988–2006
  - Responses to U.S. and euro area GDP; responses to Japan and rest of world GDP; decomposed into the standard channels.
  - Source: IMF staff calculations.

- Figure A8 (continued). Decomposition of Responses to GDP Shocks, 1988–2006
  - Continued panels for remaining decompositions.
  - Source: IMF staff calculations.

- Figure A9. Decomposition with Financial Variables Included Jointly
  - Responses to U.S. and euro area GDP; and Responses to Japan and rest of world GDP.
  - Decomposition channels: Net exports, Commodity prices, All financial variables (when included jointly).
  - Source: IMF staff calculations.

- Figure A9 (continued). Decomposition with Financial Variables Included Jointly
  - Continued panels for remaining decompositions with All financial variables.
  - Source: IMF staff calculations.

*Source: _wp07182 - References (PDF).*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2007/_wp07182.pdf_