## _wp0917 - Results from a VAR for the Euro Area 1991Q1 to 2007Q1, Conditional on the US

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### Introduction and research question
- Context: surge in global liquidity up to August 2007 driven by low interest rates in the U.S., the euro area, and Japan, financial globalization, and financial innovation.
- Research focus: whether global excess liquidity (proxied by U.S. and Japanese excess liquidity) affects euro area (EA) inflation and whether global liquidity regimes change the effectiveness of euro area monetary policy.

### Measurement and methodology
- Excess liquidity definition:
  - Levels of M2 in excess of money demand implied by longer-run interest rates and output developments (P* or real monetary gap approach).
  - Excess liquidity in logs: m~t ≡ (mt - pt) - (m*t - p*t) with p* = y* + v*.
  - Equilibrium velocity modeled as v* = c + β i*.
  - Final working formula (in text notation): real excess liquidity ~ function of real money, potential output, equilibrium interest rate, constant c, and β.
- Data and computation choices:
  - Monetary aggregate: M2- for the US, M2 for the euro area, and M2+CDs for Japan.
  - Potential output and equilibrium interest rates: HP-trends of actual real GDP and 3-month treasury interest rates in percent; HP filter weighting factor set to 1,600; HP applied after AR-extension to reduce endpoint bias.
  - Estimated semi-elasticities (β) from OLS money demand regressions over 1970Q1 to 2007Q1: about 0.02 for the US and the euro area, and about 0.06 for Japan.
  - Stationarity: JP and US excess liquidity stationary at least at the 10 percent level over 1970Q1 to 2007Q1; EA shows signs of non-stationarity driven by recent observations (stationarity not rejected at 10 percent for samples ending in 2005Q4).
- VAR frameworks used:
  - Simple bivariate autoregressive forecasting model for inflation (equation (5)), lag length m set to 4.
  - Unconditional and regime-conditional EA VAR (5 variables: real GDP, CPI, M2, 3-month interest rate, real effective exchange rate), lag length set to 4, Cholesky identification with ordering Yt = (y, p, m, i, s)′.
  - VAR sample for regime/impact analysis: 1991Q1 to 2007Q1 (62 quarterly observations after data restrictions).

### Stylized facts on excess liquidity comovement
- Sample windows:
  - Long-run measures computed over 1970Q1 to 2007Q1 (Figure 1 covers 1970Q1–2008Q2 in text discussion).
  - Dynamic correlation analysis reported for 1971Q1–2007Q1 and 1991Q1–2007Q1.
- Empirical patterns:
  - 1970s–1980s: little comovement across US, JP, and EA excess liquidity.
  - Since early 1990s: marked increase in comovement; dynamic correlation coefficients for any regional pair easily exceed 0.8 in 1991Q1–2007Q1.
  - Lead-lag patterns:
    - US and JP excess liquidity tend to lead EA excess liquidity.
    - Highest correlation when US leads EA by about 2 years.
    - JP leads EA by about three to six quarters.
  - VAR impulse responses: EA excess liquidity reacts consistently and significantly positive to US excess liquidity shocks (smaller reaction to JP shocks).

### Impact of global excess liquidity on euro area inflation — within sample
- Bivariate autoregressive results (Table 1):
  - US excess liquidity: consistently positive and often statistically significant determinant of future EA inflation at horizons up to 12 quarters, especially at horizons ≥4 quarters.
  - JP excess liquidity: positive but less pronounced role; marginally significant across horizons in the post-1990 period.
  - EA excess liquidity: limited within-sample explanatory power over full 1971Q2–2007Q1 sample; in the 1991Q1–2007Q1 sample EA liquidity significantly related to inflation at horizons of 6 quarters and higher.
- Quantitative magnitudes:
  - A ten percent increase in excess liquidity leads to an increase in future inflation of between 0.3 and 1 percentage point depending on horizon (short-run effects reported; long-run coefficients tend to be higher).
  - Example long-run statement: long-run impact of a one-time increase of 10 percent in US excess liquidity is about 3.0 percentage points.

### Impact of global excess liquidity on euro area inflation — out-of-sample (Granger-causality via forecasting)
- Forecasting exercise design:
  - Rolling pseudo out-of-sample forecasts for k = 1,...,12 quarter horizons with baseline training period 1971Q2 to 1990Q4 and forecasting period 1991Q1 to 2007Q1 (yielding between 54 and 64 forecasts depending on horizon).
  - Benchmark model: AR(4) using four lagged quarter-on-quarter inflation rates.
  - Competing models: AR(4) augmented with EA, US, or JP excess liquidity.
- RMSE and forecasting gains (Figure 3 / Appendix Figure A1):
  - Model including US excess liquidity produces RMSEs lower than benchmark at all horizons; particularly notable gains at horizons of one year or longer.
  - Average gains in forecasting inflation over the AR(4) model increase from about 0.2 percentage points one quarter ahead to about 0.7 and 1 percentage point six and twelve quarters ahead, respectively.
  - Adding JP excess liquidity yields smaller gains; adding EA excess liquidity does not improve forecasting accuracy at any horizon in the baseline exercise.
- Interpretation:
  - US excess liquidity appears Granger-causal for EA inflation in the sense of improving out-of-sample forecasting accuracy.
  - Possible reasons: US measure proxies global liquidity which moves less idiosyncratically; direct channels via global asset and commodity prices; indirect channels via EA liquidity reaction; or reduced domestic monetary policy effectiveness under global liquidity regimes.

### VAR evidence on monetary policy effectiveness under excess liquidity regimes
- Regime definition and sample facts:
  - An excess liquidity regime is defined as periods where the respective excess liquidity measure is positive.
  - In 1991Q1–2007Q1 sample, US excess liquidity regime present for the eight quarters between 2003Q2 and 2005Q1.
  - EA or JP register excess liquidity in 38 quarters in this sample.
  - Global excess liquidity regime (both US and JP positive) coincides with the US excess regime in the sample.
- Conditional VAR specification:
  - Substitute it in Yt with Dtit and (1-Dt)it to let interest-rate related components vary by regime; include Dt and d(Dt) as exogenous variables.
- Key impulse response findings (Figures 4 and 5):
  - Unconditional VAR (1991Q1–2007Q1): standard negative output response to interest rate shock, maximum impact around 4 quarters; price level response negative direction but not significantly negative.
  - Conditional on US (global) excess liquidity regime:
    - No excess liquidity regime: interest rate shock yields significant negative responses in real GDP and in prices.
    - Excess liquidity regime: reaction of real GDP to interest rate shock minimal and not different from zero; price level hardly moves after interest rate shock.
  - For EA- and JP-based regimes no consistent evidence that they impede the interest rate channel in the same way as US/global regimes.
- Robustness and caveats:
  - Results robust to estimation in first or annual differences and to slightly different definitions of the US excess regime (e.g., lower c in equation (4) to extend regime).
  - Caution: the US excess liquidity regime covers a relatively short time span and coincides with periods of little ECB policy rate movement and structural events (euro changeover). Data limitations noted.

### Conclusions and policy implications
- Comovement and leadership:
  - Excess liquidity in EA shows considerable comovement with US and JP; US excess liquidity often leads EA developments, especially post-1990.
- Inflation link:
  - U.S. excess liquidity consistently has positive impact on future EA inflation up to 12 quarters ahead and improves out-of-sample forecasting accuracy.
  - JP and EA excess liquidity have smaller or limited marginal contributions.
- Mechanisms and interpretations:
  - Global liquidity (proxied by US) matters more for EA inflation than domestic liquidity; possible channels include:
    - Indirect effects via EA liquidity responding to global developments (quantity-theoretic channel).
    - Direct effects via international asset and commodity prices.
    - Reduced monetary policy effectiveness under global excess liquidity (credit channel attenuation).
- Policy-relevant takeaways:
  - Correcting for long-run output and interest rate effects is essential when measuring excess liquidity for inflation analysis.
  - Monitoring global liquidity conditions—especially U.S. excess liquidity—helps interpret regional liquidity signals and the inflation outlook.
  - There is suggestive evidence that global excess liquidity regimes can weaken the domestic interest-rate transmission mechanism, implying central banks may face reduced scope to influence domestic financing conditions during global liquidity surges.
- Recent context note:
  - Since the onset of the financial turmoil in August 2007, the measure of U.S. excess liquidity remained subdued despite policy rate cuts and liquidity actions; this would suggest contained inflationary pressures in the euro area from global liquidity developments, although the global crisis may constrain central bank policy room for maneuver beyond liquidity stocks and flows.

*Source: IMF working paper section "5. Results from a VAR for the Euro Area 1991Q1 to 2007Q1, Conditional on the US" (content unit provided).*

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

### _wp0917 - References

### Table
- Table 1. The Impact of EA, US, and JP Excess Liquidity on Future Inflation................................................................11

### Figures
- 1.         Excess         Liquidity,         1970Q1–2008Q2...............................................................................9
- 2. Dynamic Correlation Coefficients of Excess Liquidity.................................................9
- 3. RMSEs for Alternative Models of Euro Area Inflation for the Forecasting Period 1991Q1 to 2007 Q1......................................................................................................13
- 4. Results from an Uncionditioanl VAR for th Euro Area 1991Q1 to 2007Q1...............16

*Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp0917.pdf*

### 5. Results from a VAR for the Euro Area 1991Q1 to 2007Q1, Conditional on the US

### 5. Results from a VAR for the Euro Area 1991Q1 to 2007Q1, Conditional on the US

### Introduction and research question
- Context: surge in global liquidity up to August 2007 driven by low interest rates in the U.S., the euro area, and Japan, financial globalization, and financial innovation.
- Research focus: whether global excess liquidity (proxied by U.S. and Japanese excess liquidity) affects euro area (EA) inflation and whether global liquidity regimes change the effectiveness of euro area monetary policy.

### Measurement and methodology
- Excess liquidity definition: levels of M2 in excess of money demand implied by longer-run interest rates and output developments (P* or real monetary gap approach).
- Key equations and assumptions:
  - Excess liquidity in logs: m~t ≡ (mt - pt) - (m*t - p*t) with p* = y* + v*.
  - Equilibrium velocity modeled as v* = c + β i*.
  - Final working formula (in text notation): real excess liquidity ~ function of real money, potential output, equilibrium interest rate, constant c, and β.
- Data and computation choices:
  - Monetary aggregate: M2- for the US, M2 for the euro area, and M2+CDs for Japan.
  - Potential output and equilibrium interest rates: HP-trends of actual real GDP and 3-month treasury interest rates in percent; HP filter weighting factor set to 1,600; HP applied after AR-extension to reduce endpoint bias.
  - Estimated semi-elasticities (β) from OLS money demand regressions over 1970Q1 to 2007Q1: about 0.02 for the US and the euro area, and about 0.06 for Japan.
  - Stationarity: JP and US excess liquidity stationary at least at the 10 percent level over 1970Q1 to 2007Q1; EA shows signs of non-stationarity driven by recent observations (stationarity not rejected at 10 percent for samples ending in 2005Q4).
- VAR frameworks used:
  - Simple bivariate autoregressive forecasting model for inflation (equation (5)), lag length m set to 4.
  - Unconditional and regime-conditional EA VAR (5 variables: real GDP, CPI, M2, 3-month interest rate, real effective exchange rate), lag length set to 4, Cholesky identification with ordering Yt = (y, p, m, i, s)′.
  - VAR sample for regime/impact analysis: 1991Q1 to 2007Q1 (62 quarterly observations after data restrictions).

### Stylized facts on excess liquidity comovement
- Sample windows:
  - Long-run measures computed over 1970Q1 to 2007Q1 (Figure 1 covers 1970Q1–2008Q2 in text discussion).
  - Dynamic correlation analysis reported for 1971Q1–2007Q1 and 1991Q1–2007Q1.
- Empirical patterns:
  - 1970s–1980s: little comovement across US, JP, and EA excess liquidity.
  - Since early 1990s: marked increase in comovement; dynamic correlation coefficients for any regional pair easily exceed 0.8 in 1991Q1–2007Q1.
  - US and JP excess liquidity tend to lead EA excess liquidity: highest correlation when US leads EA by about 2 years; JP leads EA by about three to six quarters.
  - VAR impulse responses indicate EA excess liquidity reacts consistently and significantly positive to US excess liquidity shocks (smaller reaction to JP shocks).

### Impact of global excess liquidity on euro area inflation — within sample
- Bivariate autoregressive results (Table 1):
  - US excess liquidity: consistently positive and often statistically significant determinant of future EA inflation at horizons up to 12 quarters, especially at horizons ≥4 quarters.
  - JP excess liquidity: positive but less pronounced role; marginally significant across horizons in the post-1990 period.
  - EA excess liquidity: limited within-sample explanatory power over full 1971Q2–2007Q1 sample; in the 1991Q1–2007Q1 sample EA liquidity significantly related to inflation at horizons of 6 quarters and higher.
- Quantitative magnitudes:
  - A ten percent increase in excess liquidity leads to an increase in future inflation of between 0.3 and 1 percentage point depending on horizon (short-run effects reported; long-run coefficients tend to be higher).
  - Example long-run statement: long-run impact of a one-time increase of 10 percent in US excess liquidity is about 3.0 percentage points (reported in text as an example of larger long-run impact relative to short-run).

### Impact of global excess liquidity on euro area inflation — out-of-sample (Granger-causality via forecasting)
- Forecasting exercise:
  - Rolling pseudo out-of-sample forecasts for k = 1,...,12 quarter horizons with baseline training period 1971Q2 to 1990Q4 and forecasting period 1991Q1 to 2007Q1 (yielding between 54 and 64 forecasts depending on horizon).
  - Benchmark model: AR(4) using four lagged quarter-on-quarter inflation rates.
  - Competing models: AR(4) augmented with EA, US, or JP excess liquidity.
- RMSE and forecasting gains (Figure 3):
  - Model including US excess liquidity produces RMSEs lower than benchmark at all horizons; particularly notable gains at horizons of one year or longer.
  - Average gains in forecasting inflation over the AR(4) model increase from about 0.2 percentage points one quarter ahead to about 0.7 and 1 percentage point six and twelve quarters ahead, respectively.
  - Adding JP excess liquidity yields smaller gains; adding EA excess liquidity does not improve forecasting accuracy at any horizon in the baseline exercise.
- Interpretation:
  - US excess liquidity appears Granger-causal for EA inflation in the sense of improving out-of-sample forecasting accuracy.
  - Possible reasons: US measure proxies global liquidity which moves less idiosyncratically; direct channels via global asset and commodity prices; indirect channels via EA liquidity reaction; or reduced domestic monetary policy effectiveness under global liquidity regimes.

### VAR evidence on monetary policy effectiveness under excess liquidity regimes
- Regime definition and sample facts:
  - An excess liquidity regime is defined as periods where the respective excess liquidity measure is positive.
  - In 1991Q1–2007Q1 sample, US excess liquidity regime present for the eight quarters between 2003Q2 and 2005Q1.
  - EA or JP register excess liquidity in 38 quarters in this sample.
  - Global excess liquidity regime (both US and JP positive) coincides with the US excess regime in the sample.
- Conditional VAR specification:
  - Substitute it in Yt with Dtit and (1-Dt)it to let interest-rate related components vary by regime; include Dt and d(Dt) as exogenous variables.
- Key impulse response findings (Figures 4 and 5):
  - Unconditional VAR (1991Q1–2007Q1): standard negative output response to interest rate shock, maximum impact around 4 quarters; price level response negative direction but not significantly negative.
  - Conditional on US (global) excess liquidity regime:
    - No excess liquidity regime: interest rate shock yields significant negative responses in real GDP and in prices.
    - Excess liquidity regime: reaction of real GDP to interest rate shock minimal and not different from zero; price level hardly moves after interest rate shock.
  - For EA- and JP-based regimes no consistent evidence that they impede the interest rate channel in the same way as US/global regimes.
- Robustness and caveats:
  - Results robust to estimation in first or annual differences and to slightly different definitions of the US excess regime (e.g., lower c in equation (4) to extend regime).
  - Caution: the US excess liquidity regime covers a relatively short time span and coincides with periods of little ECB policy rate movement and structural events (euro changeover). Data limitations noted.

### Conclusions and policy implications
- Comovement and leadership:
  - Excess liquidity in EA shows considerable comovement with US and JP; US excess liquidity often leads EA developments, especially post-1990.
- Inflation link:
  - U.S. excess liquidity consistently has positive impact on future EA inflation up to 12 quarters ahead and improves out-of-sample forecasting accuracy.
  - JP and EA excess liquidity have smaller or limited marginal contributions.
- Mechanisms and interpretations:
  - Global liquidity (proxied by US) matters more for EA inflation than domestic liquidity; possible channels include:
    - Indirect effects via EA liquidity responding to global developments (quantity-theoretic channel).
    - Direct effects via international asset and commodity prices.
    - Reduced monetary policy effectiveness under global excess liquidity (credit channel attenuation).
- Policy-relevant takeaways:
  - Correcting for long-run output and interest rate effects is essential when measuring excess liquidity for inflation analysis.
  - Monitoring global liquidity conditions—especially U.S. excess liquidity—helps interpret regional liquidity signals and the inflation outlook.
  - There is suggestive evidence that global excess liquidity regimes can weaken the domestic interest-rate transmission mechanism, implying central banks may face reduced scope to influence domestic financing conditions during global liquidity surges.
- Recent context note:
  - Since the onset of the financial turmoil in August 2007, the measure of U.S. excess liquidity remained subdued despite policy rate cuts and liquidity actions; this would suggest contained inflationary pressures in the euro area from global liquidity developments, although the global crisis may constrain central bank policy room for maneuver beyond liquidity stocks and flows.

*Source: IMF working paper section "5. Results from a VAR for the Euro Area 1991Q1 to 2007Q1, Conditional on the US" (content unit provided).*

### REFERENCES

### _wp0917 - REFERENCES

### References
- Andrés, Javier David Lopez-Salido, and Edward Nelson, 2007, “Money and the Natural Rate of Interest: Structural Estimates for the UK, the US and the Euro Area,” Research Division Federal Reserve Bank of St. Louis Working Paper Series, 2007–005A.
- Ashley, R., Clive W. J. Granger and R. Schmalensee, 1980, “Advertising and Aggregate Consumption: An Analysis of Causality,” Econometrica, Vol. 48, pp. 1149–1167.
- Assenmacher-Wesche, Katrin and Stefan Gerlach, 2007, “Understanding the Link between Money Growth and Inflation in the Euro Area,” in: David Cobham (ed.), The Travails of the Eurozone (Palgrave: Basingstoke), pp. 10–39.
- Berger, Helge and Ulrich Woitek, 2005, Does Conservatism Matter? A Time Series Approach to Central Banking, Economic Journal, Vol. 115 (July), pp. 745–766.
- Berger, Helge and Pär Österholm, 2008, “Does Money Growth Cause Inflation in the Euro Area? Evidence from Out-of-Sample Forecasts Using Bayesian VARs,” IMF Working Paper No. 08/53 (Washington: International Monetary Fund).
- Bini-Smaghi, L., 2007, Speech 11 October 2007, available online under: http://www.ecb.int/press/key/date/2007/html/index.en.html.
- D’Agostino, Antonello and Paolo Surico, 2007, “Forecasting Inflation with Global Liquidity,” Manuscript, (no month).
- Deutsche Bundesbank, 2005, “The Relationship Between Money and Prices”, Monthly Report, January, pp. 13–24.
- Ehrmann, Michael, Leonardo Gambacorta, Jorge Martínez-Pagés, Patrick Sevestre, and Andreas Worms (2003), “Financial Systems and the Role of Bank in Monetary Transmission in the Euro Area,” in: Ignazio Angeloni, Anil Kashyap, and Benoît Mojon (eds.), Monetary Transmission in the Euro Area: A Study by the Eurosystem Monetary Transmission Network, (Cambridge: Cambridge University Press) pp. 235–269.
- European Central Bank (ECB), 2008, “The External Dimension of Monetary Policy,” Monthly Bulletin, August, pp. 71-84.
- Favero, Carlo and Francesco Giavazzi, 2008, “Should the Euro Area be Run as a Closed Economy?” Amercian Economic Review: Papers and Proceedings, Vol. 98:2, pp. 138–145.
- Fischer, Björn, Michele Lenza, Huw Pill, and Lucrezia Reichlin (2008), “Money and Monetary Policy: The ECB Experience 1999–2006,” in: Andreas Beyer and Lucrezia Reichlin (eds.), The Role of Money—Money and Monetary Policy in the Twenty-First Century, Proceedings of the Forth ECB Central Banking Conference 9-10 November 2006, (Frankfurt: ECB), pp. 102–175.
- Gerlach, Stefan and Lars Svensson, 2003, “Money and Inflation in the Euro Area: A Case for Monetary Indicators?” Journal of Monetary Economics, Vol. 50(8), pp. 1649–72.
- Hallman, Jeffrey, Richard Porter, and David Small, 1991, “Is the Price Level Tied to the M2 Monetary Aggregate in the Long Run?” The American Economic Review, Vol. 81(4), pp. 841–58.
- Hofmann, Boris, 2006, “Do Monetary Indicators (Still) Predict Euro Area Inflation?” Deutsche Bundesbank Discussion Paper 18/2006.
- International Monetary Fund (IMF), 2005, Globalization and External Imbalances (Chapter III), World Economic Outlook, April, pp. 109–156.
- ———, 2007, What Is Global Liquidity (Box 1.4), World Economic Outlook, October, 34–37.
- Masuch, Klaus, Huw Pill, and Caroline Willeke, 2001, “Framework and Tools of Monetary Analysis,” in: Hans-Joachim Klöckers and Caroline Willeke, Monetary Analysis: Tools and Applications, (European Central Bank: Frankfurt), pp. 117–44.
- Mishkin, Frederic, 2008, Globalization, Macroeconomic Performance, and Monetary Policy, NBER Working Paper 13948.
- Nelson, Edward, 2003, “The Future of Monetary Aggregates in Monetary Policy Analysis,” Journal of Monetary Economics, Vol. 50(5), pp. 1029–59.
- Neumann, Manfred, 1997, “Monetary Targeting in Germany,” in: Iwao Kuroda (ed.), Towards More Effective Monetary Policy, (London: Macmillan), pp. 176–210.
- Orphanides, Athanasios and Richard Porter, 2000, “P* Revisited: Money-Based Inflation Forecasts with a Changing Equilibrium Velocity,” Journal of Economics and Business, Vol. 52(1/2), pp. 87–100.
- Kashyap, Anil and Jeremy Stein, 2000, “What Do a Million Banks Have to Say About the Transmission of Monetary Policy?” American Economic Review, Vol. 90(3), pp. 407–28.
- Peersman, Gert and Frank Smets, 2001, “The Monetary Transmission Mechanism in the Euro Area: More Evidence from VAR Analysis,” ECB Working Paper, 91, December.
- Reynard, Samuel, 2007, “Maintaining Low Inflation, Money, Interest Rates, and Policy Stance,” Journal of Monetary Economics, Vol. 54(5), pp. 1441–71.
- Rüffer, Rasmus and Livio Stracca, 2006, “What is Global Excess Liquidity, And Does It Matter?” ECB Working Paper, 696.
- Saxegaard, Magnus, 2006, “Excess Liquidity and Effectiveness of Monetary Policy: Evidence from Sub-Saharan Africa,” IMF Working Paper No. 06/115 (Washington: International Monetary Fund).
- Sousa, João and Andrea Zaghini, 2004, “Monetary Policy Shocks in the Euro Area and Global Liquidity Spillovers,” ECB Working Paper, 309, February.
- Svensson, Lars, 2000, “Does the P* Model Provide Any Rationale for Monetary Targeting?” German Economic Review, Vol. 1, pp. 69–81.
- Tödter, Karl-Heinz and Hans-Eggert Reimers, 1997, “P-star as a Link Between Money and Prices in Germany,” Weltwirtschaftliches Archiv, Vol. 130, pp. 273–89.
- Von Hagen, Jürgen, 1995, “Inflation an Monetary Targeting in Germany,” in: Leonardo Leiderman and Lars Svensson (eds.), Inflation Targets, (CEPR: London), 107–21.
- Warsh, K., 2007, Speech 5 March 2007, available online under: http://www.federalreserve.gov/newsevents/speech/2007speech.htm
- Woodford, Michael, 2003, Interest and Prices: Foundations of a Theory of Monetary Policy, (Princeton University Press: Princeton).
- ———, 2007, “How Important is Money in the Conduct of Monetary Policy,” NBER Working Paper, 13325.

### Appendix: Figure A1 — RMSEs for Alternative Models of Euro Area Inflation
- Figure title: RMSEs for Alternative Models of Euro Area Inflation for the Base Period 1985Q1 to 1995Q4 and the Forecasting Period 1996Q1 to 2007Q1
- Vertical axis tick labels: 0.000, 0.002, 0.004, 0.006, 0.008, 0.010, 0.012, 0.014, 0.016, 0.018, 0.020
- Horizontal axis labels: 1 2 4 6 8 10 12 (Forecasting horizon (quarters), k=1,...12)
- Model series shown: AR(4), AR(4) + EA, AR(4) + US, AR(4) + JP
- Notes: Reported are standard Root Mean Squared Errors (RMSEs) from four forecasting models at k=1,...12 quarter horizons. A lower RMSE indicates better out-of-sample forecasting performance. See main text for details.

*Content derived from _wp0917 - REFERENCES*

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