## Appendix I. Out-of-sample forecast performance (RMSEs)

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---

### I. Introduction and purpose
- The IMF’s Global Projection Model (GPM) is a general equilibrium model incorporating country or regional reduced-form macro model blocks interconnected through economic and financial linkages.
- This paper extends the six-region GPM framework (GPM6) by introducing additional blocks for four large euro area (EA) economies: Germany, France, Italy, and Spain.
- The existing EA block (15.1 percent of world GDP) is decomposed into five blocks: Germany (GR), France (FR), Italy (IT), Spain (SP), and the rest of EA (EX), introducing a bottom-up component to complement the top-down forecast for the euro area.

### II. Model design and structure (EA4 GPM vs GPM6)
- Core modeling approach:
  - Inherits GPM6 core macro structure: New-Keynesian Phillips Curve, IS Curve, and monetary policy reaction function.
  - Combines structural DSGE elements with multivariate time-series estimates for trade and financial linkages to improve empirical fit.
- Major modeling changes for EA4 GPM:
  - EA block broken into five country/region blocks to allow country-specific shocks to generate spillovers and feedbacks within the euro area.
  - Monetary policy is modeled at the EA level (currency union) while allowing heterogeneous country-level credit conditions.
  - Introduces nonlinearities: the zero lower bound (ZLB) on nominal interest rates and a convex/flattening Phillips Curve.
- Aggregate demand, inflation, and exchange rate treatment:
  - Aggregate demand: New Keynesian IS where the output gap is affected by the real interest rate gap, real effective exchange rate gap, foreign demand, financial conditions (bank lending tightening, BLT), commodity prices, disturbances, and leads/lags.
  - Core inflation: New Keynesian Phillips Curve with lagged output gap, real effective exchange rate gap, backward- and forward-looking inflation terms.
  - Real exchange rate: linked to real interest rate differentials through a real uncovered interest parity condition blended with model-consistent expectations and lags.

### III. Country-level features and spillovers
- Country blocks and heterogeneity:
  - Germany, France, Italy, and Spain share similar structural form with country-specific parameters and country-level BLT measures (an increase of the index means tightening).
  - Rest of EA (EX) modeled as a residual, with dynamics derived after solving the EA block and the four large economies.
- Spillovers:
  - Short-term effects of shocks to output, real effective exchange rates, and commodity prices are country-specific with spillovers across EA members.
  - Monetary policy reacts to EA-level inflation and output gap but heterogeneous credit conditions affect EA inflation and expectations.
  - Spillover coefficients linking EA economies to the rest of EA and the world are calculated from elasticities in GPM6.
  - For a given shock, the biggest spillover to Germany comes from the rest of the world (RC6, including UK and China) besides the rest of EA, while France, Italy, and Spain are more exposed to intra-EA shocks.

### IV. Nonlinearities and modeling options
- Zero lower bound (ZLB) on nominal interest rates explicitly modeled.
- Phillips Curve nonlinear specification:
  - Convex shape: steep when output gap is largely positive; flattens under significant slack.
  - Functional form similar to Laxton et al (1995), Debelle et al (1997), and Laxton et al (1999).
  - Option to non-linearize λ1 and λ3 to enhance price flexibility or real exchange rate convergence within the union.

### V. Parameterization, estimation, and model fit
- Calibration and estimation approach:
  - Calibration/Bayesian estimation strategy balancing theoretical priors and empirical data; many parameters calibrated to account for country-level heterogeneity.
  - Quarterly Bank Lending Survey data begin in 2003, limiting degrees of freedom.
- Estimated parameters:
  - Six parameters per large EA country estimated (24 in total); parameters for the rest of world taken from GPM6.
  - The six estimated parameters per country include elasticities with respect to real interest rates and real exchange rates in aggregate demand (ρ and η), coefficients on the output gap and real exchange rate in the Phillips curve (λ coefficients), and short-term adjustment terms in gas and food price equations.
  - Priors chosen as corresponding EA parameters in GPM6.
- Estimation findings:
  - Parameters generally not significantly different from priors; data not highly informative.
  - Country differences:
    - Germany’s and France’s output estimated most sensitive to real interest rate movements; Italy and Spain the least sensitive (ρ parameters).
    - Phillips curves for core inflation in all countries but France estimated steeper (λ) than in the eurozone as a whole.
  - Short sample precluded testing for structural breaks around the global financial crisis.

### VI. Calibrated and estimated parameters; spillover coefficients (selected values)
- Appendix IV describes calculation of the spillover coefficients.
- Selected estimated/calibrated parameter values reported exactly as in the source:
  - Distrmeansecalibrated: beta3gamma 0.10 0.20 0.13 0.10 0.07 0.06 0.10
  - beta4gamma 0.07 0.20 0.08 0.11 0.05 0.09 0.07
  - lambda2xgamma 0.24 0.20 0.35 0.23 0.40 0.38 0.24
  - lambda3xgamma 0.15 0.20 0.12 0.12 0.13 0.10 0.15
  - iota_gas1beta 0.14 0.10 0.27 0.17 0.32 0.24 0.14
  - iota_cfood1beta 0.31 1.00 0.23 0.38 0.49 0.28 0.31
- Selected calibrated parameters (exactly as listed):
  - alpha1.........0.72 0.72 0.72 0.72 0.72
  - alpha2.........0.10 0.10 0.10 0.10 0.10
  - alpha3*.........0.10 0.10 0.10 0.10 0.10
  - alpha4*.........0.20 0.20 0.20 0.20 0.20
  - beta1.........0.76 0.76 0.76 0.76 0.76
  - beta2.........0.04 0.04 0.04 0.04 0.04
  - beta5.........-0.01 -0.01 -0.01 -0.01 -0.01
  - beta6.........0.00 0.00 0.00 0.00 0.00
  - beta_fact.........0.55 0.55 0.55 0.55 0.55
  - beta_fact_res.........2.00 2.00 2.00 2.00 2.00
  - chi.....................1.00
  - delta.....................0.10
  - dot_lz_bar_ss_EU.....................0.00
  - gamma1.....................0.69
  - gamma2.....................1.31
  - gamma4.....................0.20
  - iota_cfood2.........0.03 0.03 0.03 0.03 0.03
  - iota_food3.....................0.10
  - iota_gas2.........0.34 0.34 0.34 0.34 0.34
  - iota_oil3.....................0.10
  - kappa1*.........20.08 20.08 20.08 20.08 20.08
  - kappa2*.........0.00 0.00 0.00 0.00 0.00
  - lambda1x.........0.70 0.70 0.70 0.70 0.70
  - lambda4x.........0.05 0.05 0.05 0.05 0.05
  - phi.....................0.83
  - tau.........0.20 0.20 0.20 0.20 0.20
  - theta.........0.30 0.30 0.30 0.30 0.30
- Table 2: Spillover coefficients across countries and regions. Note: “The direct impacts of foreign demand shocks are the spillover coefficients multiplied by (calibrated at 2).”

### VII. Simulation results — shocks and mechanisms
- Shock categories analyzed:
  - (1) Negative demand shocks from one (or all) major EA country, or from outside the EA.
  - (2) Shocks deviating the interest rate from the monetary reaction function.
  - (3) Financial (BLT) shocks.
- Country-specific negative demand shock in Germany (key dynamics):
  - A negative one percentage point country specific demand shock emanating from Germany lowers demand in other economies immediately.
  - Core inflation drops and the ECB lowers interest rates; euro gradually depreciates.
  - Depreciation mutes headline inflation response; headline inflation declines more quickly due to decline of oil price in the first few quarters.
  - In a currency union bilateral nominal exchange rates cannot adjust; relative price adjustment occurs through inflation and real unit labor cost.
  - German inflation needs to fall faster than in other countries; ECB area-wide reaction leads to German real interest rates increasing more than in other countries.
  - As the shock fades, German real interest rates converge back faster than in other countries, temporarily boosting German economy and causing headline and core inflation in Germany to overshoot steady state before converging.
  - Conclusion: country-specific demand shocks amplify price volatility and cyclicality in the source country due to absence of exchange rate channel.
- Common euro-area negative demand shock:
  - All countries affected equally; no significant bilateral real exchange rate adjustment required.
  - Cyclicality in prices disappears; monetary authority decreases area-wide nominal interest rates; real interest rates drop in all countries.
  - Initial drop in inflation gradually fades across countries; cross-country differences smaller than with country-specific shocks.
- EA-wide interest rate shock:
  - A transitory drop in EA interest rate raises the output gap in all countries.
  - Country-level differences: boost to output most significant for Germany, somewhat lower in Italy and Spain.
    - Reasons: (1) Germany and France have largest estimated sensitivity of output to real interest rate changes; (2) Germany’s response amplified by spill-back from rest of world.
  - Core inflation response similar; Germany’s inflation most responsive.
- Bank Lending Tightening (BLT) shocks:
  - Country-specific (German) BLT increase: long-lasting and slowly evolving effect on output and prices; drop in output and lower inflation; monetary reaction is gradual decrease in interest rates.
  - Magnitude of impact on output in EA countries outside Germany not very significant and not very different.
  - Country-specific shocks generate cyclicality because bilateral real exchange rate adjustments occur via prices.
  - Common bank lending tightening: impacts on output far larger, more synchronized across countries, and cyclicality less prominent.
  - Appendix II: When monetary policy is at the zero lower bound, negative output effects are larger than when simulations start at the non-stochastic steady state.
- Counterfactual exercises on BLT:
  - Counterfactual: If BLT levels had stayed constant at pre-Great Financial Crisis level after 2007Q4, around 2 percent of the euro area’s output drop during the first wave of the Financial Crisis (2008-2009) can be attributed to tightening in credit conditions.
    - This negative “financial” shock was more or less evenly distributed across countries except Spain, which suffered disproportionately.
    - Inflation would have been higher for a prolonged period of about four years.
  - Counterfactual for late 2011/early 2012: If BLT remained flat after 2011Q3, the second financial shock would have had a more diverse and muted impact.
    - German and Spanish output were hardly affected; France and Italy would have reacted more strongly.
    - Inflation would have been significantly higher (by about 0.5 percent) for two to three years after the shock.
    - Spain’s muted response in the second shock arises from a much larger loss in output during the first shock.

### VIII. Forecast performance (RMSEs) and illustrative forecasts
- Root Mean Squared Errors (Table A1) — Real GDP growth (q/q saar) RMSE by horizon:
  - EA (GPM6): 1Q ahead 2.8, 2Q ahead 2.7, 8Q ahead 2.9
  - EA (EA4 GPM): 1Q ahead 2.8, 2Q ahead 2.7, 8Q ahead 2.7
  - Germany: 1Q ahead 3.6, 2Q ahead 3.5, 8Q ahead 3.7
  - France: 1Q ahead 3.0, 2Q ahead 2.7, 8Q ahead 2.2
  - Italy: 1Q ahead 3.9, 2Q ahead 3.5, 8Q ahead 3.1
  - Spain: 1Q ahead 4.7, 2Q ahead 3.6, 8Q ahead 2.7
- Headline inflation (q/q saar) RMSE by horizon:
  - EA (GPM6): 1Q ahead 1.3, 2Q ahead 1.1, 8Q ahead 1.2
  - EA (EA4 GPM): 1Q ahead 1.7, 2Q ahead 1.6, 8Q ahead 1.4
  - Germany: 1Q ahead 1.4, 2Q ahead 1.4, 8Q ahead 1.5
  - France: 1Q ahead 1.7, 2Q ahead 1.7, 8Q ahead 1.5
  - Italy: 1Q ahead 2.0, 2Q ahead 2.1, 8Q ahead 2.0
  - Spain: 1Q ahead 2.3, 2Q ahead 2.8, 8Q ahead 3.1
- Summary of forecast performance:
  - Forecast performance for real GDP growth at EA level close to GPM6, with marginal improvement over longer horizon.
  - Country-level: more challenging to forecast Spain and Italy’s growth in the short run; performance improves at longer horizons.
  - Inflation: EA4 GPM underperforms GPM6 in the short run; difference diminishes over time.
  - Overall: disaggregated model does not have worse longer-term forecast performance than aggregated model at eurozone level while enabling country-level forecasts.
- Illustrative forecasting exercise (EA4 GPM June 2014 vs WEO April 2014) — selected forecasts (period averages and specific vintages preserved exactly):
  - Table 3A. Selected Euro Area Countries: Growth Forecasts, 2014-16 (WEO April 2014 / EA4 GPM June 2014) (2014 / 2015)
    - Germany 1.7 1.6 2.1 1.8
    - France 1.0 1.5 0.7 1.3
    - Italy 0.6 1.1 0.2 1.3
    - Spain 0.9 1.0 1.0 1.2
    - Euro Area 1.2 1.5 1.0 1.6
  - Table 3B. Selected Euro Area Countries: Inflation (Headline), 2014-16 (Percent, period average, yoy) (2014 / 2015)
    - Germany 1.4 1.4 1.2 1.4
    - France 1.0 1.2 1.0 1.1
    - Italy 0.7 1.0 0.6 0.9
    - Spain 0.3 0.8 0.2 0.7
    - Euro Area 0.9 1.2 0.6 1.1
  - EA4 GPM June 2014 forecast summary relative to WEO April 2014:
    - 2014 growth revised down in France (from 1.0 to 0.7 percent) and Italy (from 0.6 to 0.2 percent); offset by higher growth in Germany and Spain.
    - Euro area projected to grow at 1.0 percent in 2014, slightly below April 2014 WEO forecast of 1.2 percent.
    - Inflation expected to edge down to 0.6 percent in 2014 (compared to 0.9 percent in April 2014 WEO), before a modest pickup in the following year.
- Forecasting practice used:
  - Global conditions imported from GPM6 and treated as exogenous.
  - “Nowcasting” methods leveraged high frequency indicators (country-level industrial production and PMIs).
  - ECB policy action assumed: a policy rate cut of 10 to 15 basis points expected in early June.
  - Fiscal stance of four large EA economies and EA overall assumed broadly unchanged from previous forecasting round.

### IX. Appendices (additional simulation details and calibration)
- Appendix II: Additional simulation results
  - Simulations starting at the zero lower bound of interest rates starting from 2014Q1.
  - Figures listed include country-specific one percentage point negative demand shocks for Germany, France, Italy, Spain; a one percentage point common negative demand shock in the euro area; country-specific and common BLT shocks; a one percentage point negative demand shock in the US; a 10 percent negative oil price shock.
- Appendix III: Euro area forecasts from the EA4 GPM
  - Figure A10: Euro area forecasts from the EA4 GPM (dashed line represents vintage forecast of previous WEO round in Q4 2013).
- Appendix IV: Modified Notation in Country Blocks
  - Country-specific output gap equation replaces aggregate equation and denotes spillover coefficients from country j to country i explicitly.
  - Inflation equations replaced with formulations denoting quarter-on-quarter core inflation and year-on-year core and headline inflation.
- Appendix V: Calibration of Spillover Coefficients (methodology)
  - Spillover coefficient decomposition:
    - (i) the change in output growth in country i for a given change in country i’s export growth to country j;
    - (ii) the change in country i’s export growth to country j for a given change in import demand growth by country j from country i;
    - (iii) the change in growth of imports by country j from country i for a given shock to demand growth in country j.
  - Transformations and assumptions:
    - (ii) assumed: 1 by assumption ij X M ji Δ = Δ
    - For (iii): elasticity of imports by country j in response to a given change in demand growth derived from simple VAR analysis; changes in import-demand growth assumed distributed uniformly across all trade partners.
  - For (i): impact of change in growth rate of exports from i to j on country i’s GDP growth uses a Keynesian-type multiplier and scales export change to total exports from i using historical export shares.
  - Numerical illustration note: If country i’s exports to country j increase by 10 percent, and country i’s imports to country j represent 50 percent of its total exports, then total exports have only increased by 5 percent.

### X. Conclusions and policy-relevant implications
- EA4 GPM enhances GPM6 by disaggregating the EA block into Germany, France, Italy, Spain, and Rest of EA, capturing intra-EA dynamics and spillovers with greater detail while retaining EA-wide monetary policy.
- Key mechanisms and implications:
  - In a currency union, bilateral nominal exchange rates cannot adjust; relative price adjustment occurs through inflation differentials and real unit labor cost, amplifying price cyclicality under country-specific shocks.
  - Spillovers from tight credit conditions in each EA country limited by direct trade channels and small confidence spillovers; synchronized tightening across banks can generate large, synchronized negative impacts.
  - Monetary policy uses conventional inflation-forecast-based reaction functions at EA level; non-conventional policies (e.g., targeted LTROs) can be represented as EA-wide or country-level shocks to bank lending conditions.
- Forecasting and modeling practice:
  - Inclusion of country-level information improves consistency with country forecasts and allows richer policy analysis.
  - Model performance can be improved by integrating additional information, including better use of high frequency indicators.
- Future research priorities:
  - Construct a version of EA4 GPM incorporating ongoing GPM6 research (better integration of high frequency indicators; further decomposition of Emerging Asia and RC6 blocks).
  - Enhanced representation of linkages between EA and emerging market economies to analyze interactions among these economies.

*Source: Appendix I. Out-of-sample forecast performance (RMSEs) — _wp1550 (IMF working paper content provided).*

### Appendix I. Out-of-sample forecast performance (RMSEs) ...................................................22

### Appendix I. Out-of-sample forecast performance (RMSEs)

### I. Introduction and purpose
- The IMF’s Global Projection Model (GPM) is a general equilibrium model incorporating country or regional reduced-form macro model blocks interconnected through economic and financial linkages.
- This paper extends the six-region GPM framework (GPM6) by introducing additional blocks for four large euro area (EA) economies: Germany, France, Italy, and Spain.
- The existing EA block (15.1 percent of world GDP) is decomposed into five blocks: Germany (GR), France (FR), Italy (IT), Spain (SP), and the rest of EA (EX), introducing a bottom-up component to complement the top-down forecast for the euro area.

### II. Key model design and structure (EA4 GPM vs GPM6)
- Core modeling approach:
  - Inherits GPM6 core macro structure: New-Keynesian Phillips Curve, IS Curve, and monetary policy reaction function.
  - Combines structural DSGE elements with multivariate time-series estimates for trade and financial linkages to improve empirical fit.
- Major modeling changes for EA4 GPM:
  - Breaks the EA block into five country/region blocks to allow country-specific shocks to generate spillovers and feedbacks within the euro area.
  - Monetary policy is modeled at the EA (euro area) level to reflect the currency union, while allowing heterogeneous country-level credit conditions.
  - Introduces nonlinearities: the zero lower bound (ZLB) on nominal interest rates and a convex/flattening Phillips Curve (steep when output gap is positive, flattening under significant slack).
- Aggregate demand, inflation, and exchange rate treatment:
  - Aggregate demand follows a New Keynesian IS curve where the output gap is affected by the real interest rate gap, real effective exchange rate gap, foreign demand, financial conditions (bank lending tightening, BLT), commodity prices, disturbances, and leads/lags.
  - Core inflation follows a New Keynesian Phillips Curve with lagged output gap, real effective exchange rate gap, backward- and forward-looking inflation terms encapsulating expectations formation.
  - Real exchange rate dynamics are linked to real interest rate differentials through a real uncovered interest parity condition blended with model-consistent expectations and lags.

### III. Country-level features and spillovers
- Country blocks and heterogeneity:
  - Germany, France, Italy, and Spain each have a similar structural form but country-specific parameters and country-level BLT measures (an increase of the index means tightening).
  - The rest of EA (EX) is modeled as a residual, with dynamics derived after solving the EA block and the four large economies.
- Spillovers:
  - Short-term effects of shocks to output, real effective exchange rates, and commodity prices are country-specific with spillovers across EA members.
  - Monetary policy reacts to EA-level inflation and output gap but allows heterogeneous credit conditions to affect EA inflation and expectations.
  - Spillover coefficients linking EA economies to the rest of EA and the world are calculated from elasticities in GPM6.
  - For a given shock, the biggest spillover to Germany comes from the rest of the world (RC6, including UK and China) besides the rest of EA, while France, Italy, and Spain are more exposed to intra-EA shocks.

### IV. Nonlinearities and important modeling options
- Zero lower bound (ZLB) on nominal interest rates is explicitly modeled.
- Phillips Curve nonlinear specification:
  - Convex shape: steep or close to vertical when the output gap is largely positive; flattens when there is significant slack.
  - Functional form similar to Laxton et al (1995), Debelle et al (1997), and Laxton et al (1999).
  - Model contains an option to non-linearize λ1 and λ3 to enhance price flexibility or real exchange rate convergence within the union.

### V. Parameterization, estimation, and model fit
- Calibration and estimation approach:
  - A calibration/Bayesian estimation strategy balances theoretical priors and empirical data; many parameters are calibrated to account for country-level heterogeneity (Table 1).
  - Quarterly Bank Lending Survey data begin in 2003, limiting degrees of freedom in estimation.
- Estimated parameters:
  - Only six parameters per large EA country were estimated (24 in total; parameters for the rest of world are taken from GPM6) using Bayesian methods.
  - The six estimated parameters per country are:
    - Elasticities with respect to real interest rates and real exchange rates in the aggregate demand equation (ρ and η as specified in the model).
    - Coefficients on the output gap and on the real exchange rate in the Phillips-curve equation (λ coefficients).
    - Short-term adjustment terms in the gas and food price equations.
  - Priors were chosen as the corresponding EA parameters in GPM6.
- Estimation findings:
  - Parameters were generally not significantly different from the priors; the data were not highly informative for identifying these parameters.
  - Country differences highlighted:
    - Germany’s and France’s output were estimated to be the most sensitive to real interest rate movements, while Italy and Spain were the least sensitive (ρ parameters).
    - Phillips curves for core inflation in all countries but France are estimated to be steeper (λ) than in the eurozone as a whole, potentially reflecting greater openness of the remaining EA countries and flatter Phillips behavior.
  - The short sample size did not allow testing for structural changes in parameters around the global financial crisis.

### VI. Model applications and output summary
- The EA4 GPM permits:
  - Country-specific shock experiments (e.g., a negative demand shock in Germany) to trace intra-EA spillovers and feedbacks.
  - Counterfactual exercises involving bank lending standards and common shocks across the euro area.
  - Improved consistency of forecasts by incorporating more country-level information while retaining an EA-wide monetary policy framework.

*Source: Appendix I. Out-of-sample forecast performance (RMSEs) — _wp1550 (IMF working paper content provided).*

### Appendix IV of Carabenciov and others (2013) provides detailed description on the calculation of the

### _wp1550 - Appendix IV of Carabenciov and others (2013) provides detailed description on the calculation of the

### Calibrated and estimated parameters; spillover coefficients
- Appendix IV describes calculation of the spillover coefficients.  
- Table 1: Calibrated and estimated country-level parameters (Source: IMF staff estimations; Source: IMF staff calculations). Selected parameter values reported exactly as in the source:
  - Distrmeansecalibrated: beta3gamma 0.10 0.20 0.13 0.10 0.07 0.06 0.10
  - beta4gamma 0.07 0.20 0.08 0.11 0.05 0.09 0.07
  - lambda2xgamma 0.24 0.20 0.35 0.23 0.40 0.38 0.24
  - lambda3xgamma 0.15 0.20 0.12 0.12 0.13 0.10 0.15
  - iota_gas1beta 0.14 0.10 0.27 0.17 0.32 0.24 0.14
  - iota_cfood1beta 0.31 1.00 0.23 0.38 0.49 0.28 0.31
- Calibrated parameters (selected):
  - alpha1.........0.72 0.72 0.72 0.72 0.72
  - alpha2.........0.10 0.10 0.10 0.10 0.10
  - alpha3*.........0.10 0.10 0.10 0.10 0.10
  - alpha4*.........0.20 0.20 0.20 0.20 0.20
  - beta1.........0.76 0.76 0.76 0.76 0.76
  - beta2.........0.04 0.04 0.04 0.04 0.04
  - beta5.........-0.01 -0.01 -0.01 -0.01 -0.01
  - beta6.........0.00 0.00 0.00 0.00 0.00
  - beta_fact.........0.55 0.55 0.55 0.55 0.55
  - beta_fact_res.........2.00 2.00 2.00 2.00 2.00
  - chi.....................1.00
  - delta.....................0.10
  - dot_lz_bar_ss_EU.....................0.00
  - gamma1.....................0.69
  - gamma2.....................1.31
  - gamma4.....................0.20
  - iota_cfood2.........0.03 0.03 0.03 0.03 0.03
  - iota_food3.....................0.10
  - iota_gas2.........0.34 0.34 0.34 0.34 0.34
  - iota_oil3.....................0.10
  - kappa1*.........20.08 20.08 20.08 20.08 20.08
  - kappa2*.........0.00 0.00 0.00 0.00 0.00
  - lambda1x.........0.70 0.70 0.70 0.70 0.70
  - lambda4x.........0.05 0.05 0.05 0.05 0.05
  - phi.....................0.83
  - tau.........0.20 0.20 0.20 0.20 0.20
  - theta.........0.30 0.30 0.30 0.30 0.30
- Table 2: Spillover coefficients across countries and regions. Note: “The direct impacts of foreign demand shocks are the spillover coefficients multiplied by (calibrated at 2).” (See Appendix V for details.)

### Simulation results — shocks and mechanisms
- Shocks analyzed grouped into three types:
  - (1) Negative demand shocks emanating from either one (or all) major EA country, or from outside the EA.
  - (2) Shocks leading to a deviation of the interest rate from the monetary reaction function.
  - (3) Financial (BLT) shocks.
- Country-specific negative demand shock in Germany (Figure 3) — key dynamics:
  - A negative one percentage point country specific demand shock emanating from Germany feeds into lower demand in other economies immediately.
  - Core inflation drops and the ECB lowers interest rates; euro gradually depreciates.
  - Depreciation mutes headline inflation response; headline inflation declines more quickly due to decline of oil price in the first few quarters.
  - In a currency union bilateral nominal exchange rates cannot adjust; relative price adjustment occurs through inflation and real unit labor cost.
  - German inflation needs to fall faster than in other countries; ECB area-wide reaction leads to German real interest rates increasing more than in other countries.
  - As the shock fades, German real interest rates converge back faster than in other countries, temporarily boosting German economy and causing headline and core inflation in Germany to overshoot steady state before converging.
  - Conclusion: country-specific demand shocks amplify price volatility and cyclicality in the source country due to absence of exchange rate channel.
- Common euro-area negative demand shock (Figure 4):
  - All countries affected equally; no significant bilateral real exchange rate adjustment required.
  - Cyclicality in prices disappears; monetary authority decreases area-wide nominal interest rates; real interest rates drop in all countries.
  - Initial drop in inflation gradually fades across countries; cross-country differences smaller than with country-specific shocks.
- EA-wide interest rate shock (Figure 5):
  - A transitory drop in EA interest rate raises the output gap in all countries, as real interest rates are temporarily reduced and the real exchange rate is temporarily more depreciated than in steady state.
  - Country-level differences: boost to output is most significant for Germany, somewhat lower in Italy and Spain.
    - Two reasons: (1) Germany and France have largest estimated sensitivity of output to real interest rate changes; (2) Germany’s output response is amplified by spill-back from rest of world given Germany’s stronger connection with non-EA economies.
  - Core inflation response follows similar pattern; Germany’s inflation most responsive to a monetary policy shock.
- Bank Lending Tightening (BLT) shocks (Figures 6 and 7):
  - Country-specific (German) BLT increase: long-lasting and slowly evolving effect on output and prices; drop in output and lower inflation; monetary reaction is gradual decrease in interest rates.
  - Magnitude of impact effect on output in EA countries outside Germany is not very significant and not very different (partly due to lack of sufficient differentiation in calibrated parameters).
  - Country-specific shocks generate cyclicality because bilateral real exchange rate adjustments occur via prices.
  - Common bank lending tightening: impacts on output are far larger, more synchronized across countries, and cyclicality is less prominent.
  - Appendix II: When monetary policy is at the zero lower bound, negative output effects are larger than when simulations start at the non-stochastic steady state.
- Counterfactual exercises on BLT (Figures 8 and 9):
  - Counterfactual: If BLT levels had stayed constant at pre-Great Financial Crisis level after 2007Q4, a significant part (around 2 percent) of the euro area’s output drop during the first wave of the Financial Crisis (2008-2009) can be attributed to tightening in credit conditions.
    - This negative “financial” shock was more or less evenly distributed across countries except Spain, which suffered disproportionately.
    - Inflation would have been higher for a prolonged period of about four years.
  - Counterfactual for late 2011/early 2012: If BLT remained flat after 2011Q3, the second financial shock would have had a more diverse and muted impact on the euro area and individual countries.
    - German and Spanish output were hardly affected by the shock; France and Italy would have reacted more strongly.
    - Inflation would have been significantly higher (by about 0.5 percent) for two to three years after the shock.
    - Note on Spain: muted response in the second shock arises from a much larger loss in output during the first shock.

### Forecast performance (Section IV)
- Out-of-sample forecast performance measured by Root Mean Squared Errors (RMSE).
  - Comparison: RMSE of EA4 GPM with GPM6 on the EA block — model fit is similar.
  - EA4 GPM: no benchmark RMSE for the four EA countries in GPM6; RMSE presented over in-sample forecast horizons (one, four, and eight quarters) for real GDP growth and inflation in Appendix Table A1.
  - Findings:
    - Forecast performance for real GDP growth at EA level is close to GPM6, with some marginal improvement over longer horizon.
    - At country level, the model finds it more challenging to forecast Spain and Italy’s growth in the short run; performance improves markedly at longer horizons.
    - On inflation, EA4 GPM underperforms GPM6 in the short run; difference diminishes over time.
    - Overall: the more disaggregated model does not have worse longer-term forecast performance than the more aggregated model at the eurozone level, while enabling country-level forecasts.
- Illustrative forecasting exercise based on EA4 GPM carried out in 2014 Q2 (used as one input in July 2012 WEO projection):
  - Global conditions imported from GPM6 and treated as exogenous.
  - “Nowcasting” methods used, leveraging high frequency indicators (country-level industrial production and PMIs) to improve forecast quality and consistency with country-level developments.
  - Developments in EA up to 2014 Q1:
    - Q1 growth: Germany and Spain overshot April 2014 WEO forecast; France, Italy and several other EA economies underperformed.
    - Inflation dipped to new lows well below expectations.
    - Bank lending and credit growth in EA remained weak due to continued deleveraging pressures and fragmentation.
  - Forecast assumptions:
    - ECB policy action assumed: a policy rate cut of 10 to 15 basis points expected in early June.
    - Fiscal stance of four large EA economies and EA overall assumed broadly unchanged from previous forecasting round.
  - Tables 3A and 3B — selected forecasts (WEO April 2014 vs EA4 GPM June 2014):
    - Table 3A. Selected Euro Area Countries: Growth Forecasts, 2014-16
      - WEO April 2014 / EA4 GPM June 2014 (2014 / 2015)
      - Germany 1.7 1.6 2.1 1.8
      - France 1.0 1.5 0.7 1.3
      - Italy 0.6 1.1 0.2 1.3
      - Spain 0.9 1.0 1.0 1.2
      - Euro Area 1.2 1.5 1.0 1.6
    - Table 3B. Selected Euro Area Countries: Inflation (Headline), 2014-16 (Percent, period average, yoy)
      - 2014 / 2015
      - Germany 1.4 1.4 1.2 1.4
      - France 1.0 1.2 1.0 1.1
      - Italy 0.7 1.0 0.6 0.9
      - Spain 0.3 0.8 0.2 0.7
      - Euro Area 0.9 1.2 0.6 1.1
  - EA4 GPM June 2014 forecast summary relative to WEO April 2014:
    - 2014 growth revised down in France (from 1.0 to 0.7 percent) and Italy (from 0.6 to 0.2 percent); offset by higher growth in Germany and Spain.
    - Euro area projected to grow at 1.0 percent in 2014, slightly below April 2014 WEO forecast of 1.2 percent.
    - Inflation expected to edge down further to 0.6 percent in 2014 (compared to 0.9 percent in April 2014 WEO), before modest pickup in following year.

### Conclusions and policy-relevant implications (Section V)
- EA4 GPM enhances GPM6 by disaggregating the EA block into Germany, France, Italy, Spain, and Rest of EA, capturing intra-EA dynamics and spillovers with greater detail and accounting for single currency and common monetary policy.
- Key mechanisms and implications:
  - In a currency union, bilateral nominal exchange rates cannot adjust; relative price adjustment occurs through inflation differentials and real unit labor cost adjustments, amplifying price cyclicality under country-specific shocks.
  - Spillovers from tight credit conditions in each EA country are limited by direct trade channels and small confidence spillovers, but synchronized tightening across banks can generate large, synchronized negative impacts.
  - Monetary policy uses conventional inflation-forecast-based reaction functions at EA level; non-conventional policies (e.g., targeted LTROs) can be represented as EA-wide or country-level shocks to bank lending conditions.
- Forecasting and modeling practice:
  - Inclusion of country-level information improves consistency with country forecasts and allows richer policy analysis.
  - Model performance can be improved by integrating additional information, including better use of high frequency indicators.
- Future research priorities:
  - Construct a version of EA4 GPM incorporating ongoing GPM6 research (better integration of high frequency indicators; further decomposition of Emerging Asia and RC6 blocks by splitting out China and other large G20 economies).
  - Enhanced representation of linkages between EA and emerging market economies to analyze interactions among these economies.

*Italic: Source: _wp1550 - Appendix IV of Carabenciov and others (2013) provides detailed description on the calculation of the — IMF staff calculations and simulations as presented in the supplied content.*

### Appendix I. Out-of-sample forecast performance (RMSEs)

### Appendix I. Out-of-sample forecast performance (RMSEs)

### Root Mean Squared Errors (Table A1)
- Real GDP growth (q/q saar) — RMSE by horizon:
  - EA (GPM6): 1Q ahead 2.8, 2Q ahead 2.7, 8Q ahead 2.9
  - EA (EA4 GPM): 1Q ahead 2.8, 2Q ahead 2.7, 8Q ahead 2.7
  - Germany: 1Q ahead 3.6, 2Q ahead 3.5, 8Q ahead 3.7
  - France: 1Q ahead 3.0, 2Q ahead 2.7, 8Q ahead 2.2
  - Italy: 1Q ahead 3.9, 2Q ahead 3.5, 8Q ahead 3.1
  - Spain: 1Q ahead 4.7, 2Q ahead 3.6, 8Q ahead 2.7
- Headline inflation (q/q saar) — RMSE by horizon:
  - EA (GPM6): 1Q ahead 1.3, 2Q ahead 1.1, 8Q ahead 1.2
  - EA (EA4 GPM): 1Q ahead 1.7, 2Q ahead 1.6, 8Q ahead 1.4
  - Germany: 1Q ahead 1.4, 2Q ahead 1.4, 8Q ahead 1.5
  - France: 1Q ahead 1.7, 2Q ahead 1.7, 8Q ahead 1.5
  - Italy: 1Q ahead 2.0, 2Q ahead 2.1, 8Q ahead 2.0
  - Spain: 1Q ahead 2.3, 2Q ahead 2.8, 8Q ahead 3.1

### Source
- Source: IMF stafff calculations.

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### Appendix II. Additional simulation results

### Simulation setup
- Simulations starting at the zero lower bound of interest rates starting from 2014Q1.

### Shocks and figures (listed in the appendix)
- Figure A1: A one percentage point negative demand shock in Germany
- Figure A2: A one percentage point negative demand shock in France
- Figure A3: A one percentage point negative demand shock in Italy
- Figure A4: A one percentage point negative demand shock in Spain
- Figure A5: A one percentage point common negative demand shock in the euro area
- Figure A6: A country-specific bank lending tightening shock in Germany
- Figure A7: A common bank lending tightening shock
- Figure A8: A one percentage point negative demand shock in the US
- Figure A9: A 10 percent negative oil price shock

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### Appendix III. Euro area forecasts from the EA4 GPM

### Forecast vintage information
- Figure A10: Euro area forecasts from the EA4 GPM
  - Note: Dashed line represents the vintage forecast of the previous WEO round in Q4 2013.
- Sources: IMF staff estimates.

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### Appendix IV. Modified Notation in Country Blocks of the EA4 GPM

### Country-specific output gap equation
- To obtain country-specific equations for output gaps, equation (1) is replaced by a country-specific formulation in which spillover coefficients appear.
- In the replacement, the spillover coefficient from country j to country i is denoted explicitly.

### Inflation equations
- Equation (2) is replaced by a formulation where:
  - denotes quarter-on-quarter core inflation,
  - and denote year-on-year core and headline inflation, respectively.

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### Appendix V. Calibration of Spillover Coefficients

### Calibration approach (following Blagrave and others (2013))
- The spillover coefficients in the EA GPM are calibrated in the following steps.
- The effect of a demand shock in country j (the shock emitter) on output in country i (the shock receiver) can be written as a function of the spillover coefficient.
- The spillover coefficient can be decomposed into three terms:
  - the change in output growth in country i for a given change in country i’s export growth to country j;
  - the change in country i’s export growth to country j for a given change in import demand growth by country j from country i;
  - the change in the growth of imports by country j from country i for a given shock to demand growth in country j.

### Transformations and assumptions
- Each of these terms can be transformed as follows:
  - (i) [first term transformed as detailed in the appendix]
  - (ii) 1 by assumption ij X M ji Δ = Δ
  - (iii) [third term transformed; involves elasticity of imports by country j in response to a given change in demand growth]
- For Eq. (iii):
  - It involves two calculations:
    - the elasticity of imports by country j in response to a given change in demand growth;
    - the relationship between the change in total import-demand growth in country j, and import-demand growth from country i.
  - Regarding the latter calculation, the appendix assumes that all changes in import-demand growth are distributed uniformly across all trade partners.
  - The elasticity of imports for a given change in demand growth are derived from the results of simple VAR analysis.

### For Eq. (i)
- Determines the impact of a change in the growth rate of country i’s exports to country j on country i’s GDP growth.
- The second element of Eq.(i) scales the size of the increase in exports from i to j to express it in terms of total exports from i, approximated using historical data on the ratio of exports from i to j as a share of total exports from i.
- The first term of Eq. (i) is described as a Keynesian-type multiplier, relating the change in the growth rate of total exports from i to the change in the growth rate of output in country i.

### Numerical illustration note
- Footnote example: If country i’s exports to country j increase by 10 percent, and country i’s imports to country j represent 50 percent of its total exports, then total exports have only increased by 5 percent.

*Source: IMF staff calculations (Appendices I–V).*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp1550.pdf_