## _wp12149

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---

### Introduction and purpose
- Develops a structural macroeconometric model of the world economy disaggregated into thirty five national economies to incorporate monetary and fiscal transmission mechanisms and extensive macrofinancial linkages, both within and across economies.
- Motivated by the global financial crisis and by gaps identified in the literature, including Dées, Pesaran, Smith and Smith (2010) and Pesaran, Schuermann and Weiner (2004).
- Demonstrates monetary policy analysis, fiscal policy analysis, spillover analysis, and forecasting within a Bayesian framework that conditions on judgment in estimation and forecasting.

### Model scope, data, and calibration
- Model disaggregation: thirty five economies — Argentina, Australia, Austria, Belgium, Brazil, Canada, China, the Czech Republic, Denmark, Finland, France, Germany, Greece, India, Indonesia, Ireland, Italy, Japan, Korea, Mexico, the Netherlands, New Zealand, Norway, Poland, Portugal, Russia, Saudi Arabia, South Africa, Spain, Sweden, Switzerland, Thailand, Turkey, the United Kingdom, and the United States.
- Observed endogenous variables: a total of four hundred one endogenous variables across the thirty five economies.
- Sample period for joint estimation: 1999Q1 through 2011Q3; parameter estimation results reported for sample period 1999Q3 through 2011Q3.
- Primary data sources: GDS and WEO databases compiled by the International Monetary Fund; supplemental sources: IFS, CEIC, EMED where IMF data unavailable.
- Calibration and weights:
  - Great ratios from WEO and WDI.
  - Bilateral trade weights from DOTS.
  - Portfolio weights from CPIS, BIS, and WDI.
- Quotation currency for FX transactions: United States.
- Monetary policy treated as flexible inflation targeting in all economies except Argentina, China, the Czech Republic, Denmark, India, Indonesia, Russia, Saudi Arabia and Thailand (managed exchange rate regimes).
- Capital controls apply in China, India, and Saudi Arabia.

### Model structure and shocks
- Unobserved components representation: each observed variable decomposed into cyclical component (ˆxit) and trend component (xit) with additive separability xit = ˆxit + xit.
- Cross-economy equality restrictions on structural parameters; responses vary with structural characteristics (export openness Xi/Yi, import openness Mi/Di, commodity intensities zCOMi Xi/Xi or zCOMi Mi/Mi).
- Linkages included:
  - Trade linkages via trade-weighted averages (Zitx) with bilateral weights wZij for ZX, ZM, and ZT.
  - Portfolio linkages via portfolio-weighted averages (ZB, ZS).
  - World aggregates via money market capitalization (ZM), bond market capitalization (ZB), stock market capitalization (ZS), and output (ZY) weights wi.
  - Commodity price linkages with separate treatment of energy (j = 1) and nonenergy (j = 0) commodities.
- Major cyclical relationships and shocks (selected):
  - Domestic supply shock νˆY,P,it with ˆεY,P,it ~ iid (0,ˆσ2Y,P).
  - Import supply shock νˆM,P,it with ˆεM,P,it ~ iid (0,ˆσ2M,P).
  - Domestic private demand shock νˆC,it with ˆεC,it ~ iid (0,ˆσ2C,it).
  - Export demand shock νˆX,it with ˆεX,it ~ iid (0,ˆσ2X,it).
  - Monetary policy shock ˆεP,it ~ iid (0,ˆσ2P,i).
  - Credit risk premium shock νˆS,it with ˆεS,it ~ iid (0,ˆσ2S,it).
  - Duration risk premium shock νˆL,it with ˆεL,it ~ iid (0,ˆσ2L,it).
  - Equity risk premium shock νˆSTK,it with ˆεSTK,it ~ iid (0,ˆσ2STK,it).
  - World commodity price shocks (energy and nonenergy) with ˆεz,COM,t ~ iid (0,ˆσ2z,COM,t).
- Trend components largely follow random walks with innovations distributed ~ iid as specified in equations (20)–(32); all innovations assumed independent (identifying restriction).

### Estimation procedure and priors
- Bayesian estimation in state-space form: Kalman filter and smoother used for unobserved component estimation (de Jong (1989)); Klein (2000) procedure ensures unique stationary solution for cyclical dynamics.
- Parameters θ estimated via posterior mode maximization of posterior kernel; asymptotic normal approximation to posterior around mode used for inference.
- Prior setup:
  - Informative independent priors for conditional mean parameters centered within literature ranges.
  - Diffuse priors for variance-only parameters.
  - Judgmental trend paths derived from Hodrick and Prescott (1997) preliminary filter; stochastic restrictions rescaled by factor 2^2.
  - Numerical maximization: modified steepest ascent starting from differential evolution algorithm.

### Estimation results — highlights and selected parameter values
- Posterior mode obtained; Klein (2000) sufficient condition for unique stationary rational expectations equilibrium satisfied in a neighborhood around posterior mode.
- Hessian estimator not nearly singular at posterior mode → local identification.
- Posterior modes of most structural parameters close to prior means; some substantial updates where data are informative.
- Estimated variances of innovations driving cyclical components are within literature ranges (after rescaling); trend innovation variances vary considerably across economies and variables.
- Selected parameter posterior modes and SEs (from Table 1):
  - 1,1 φ: Prior 0.4900; Posterior SE 4.9e–3; Posterior mode 0.4897
  - 1,2 φ: Prior 0.4900; Posterior SE 4.9e–3; Posterior mode 0.4859
  - 1,1 θ: Prior 0.0075; Posterior SE 7.5e–4; Posterior mode 0.0077
  - 1,2 θ: Prior 0.3500; Posterior SE 3.5e–2; Posterior mode 0.3580
  - 3,1 φ: Prior 0.8500; Posterior SE 8.5e–3; Posterior mode 0.8467
  - 3,1 θ: Prior -0.7500; Posterior SE 7.5e–2; Posterior mode -0.7528
  - 3,3 θ: Prior 0.5000; Posterior SE 5.0e–2; Posterior mode 0.5233
  - 4,1 θ: Prior 1.0000; Posterior SE 1.0e–1; Posterior mode 1.0463
  - 5,1,0 θ: Prior 1.2500; Posterior SE 1.3e–1; Posterior mode 1.2902 (reported for multiple countries)
  - 5,1,1 θ: Prior 1.5000; Posterior SE 1.5e–1; Posterior mode 1.5194 (reported for multiple countries)
  - 6,0 λ: Prior 1.0000; Posterior SE 1.0e–1; Posterior mode 0.9699 (reported for multiple countries)
  - 7,1 φ: Prior 0.2400; Posterior SE 2.4e–3; Posterior mode 0.2415
  - 8,1 θ: Prior 1.0000; Posterior SE 1.0e–1; Posterior mode 1.0336
  - 9,1,0 θ: Prior -1.0000; Posterior SE 1.0e–1; Posterior mode -0.9609 (reported for multiple countries)
  - 13,1,1 θ: Prior 1.5000; Posterior SE 1.5e–1; Posterior mode 1.5123
- Selected posterior standard deviations (country cross-section examples):
  - 2ˆ,YPi σ: Argentina 1.6e–1; Australia 1.4e–1; Switzerland 2.1e–1; Russia 1.9e–1; Portugal 1.8e–1; Saudi Arabia 1.8e–1
  - 2ˆ,MPi σ: Argentina 7.5e+0; Australia 6.7e+0; United States 9.7e+0; Japan 7.6e+0; Russia 7.6e+0; Turkey 7.6e+0

### Impulse responses — structural shock mappings and quantified effects
- Shocks and calibration in figures:
  - Domestic supply shock: raises consumption price inflation by one percentage point.
  - Domestic private demand shock: raises domestic demand by one percent.
  - Domestic monetary policy shock: raises nominal policy interest rate by one percentage point.
  - Domestic credit risk premium shock: raises short-term nominal market interest rate by one percentage point.
  - Domestic duration risk premium shock: raises long-term nominal market interest rate by one percentage point.
  - Domestic equity risk premium shock: raises price of equity by ten percent.
  - Domestic fiscal expenditure shock: reduces fiscal balance to nominal output by one percentage point.
  - Domestic fiscal revenue shock: raises fiscal balance to nominal output by one percentage point.
  - World energy commodity price shock: raises price of energy commodities by ten percent.
  - World nonenergy commodity price shock: raises price of nonenergy commodities by ten percent.
- Typical generalized response patterns (selected quantified results):
  - Domestic monetary policy shock (one percentage point increase in nominal policy interest rate):
    - Peak contraction of output averages 0.5 percent across economies within a range of 0.2 to 0.7 percent.
    - Peak decrease in inflation averages 0.3 percentage points within a range of 0.1 to 0.4 percentage points.
  - Domestic fiscal expenditure shock (one percentage point decrease in fiscal balance to nominal output):
    - Peak expansion of output averages 1.0 percent within a range of 0.2 to 1.7 percent; peak expansion tends to decrease with trade openness.
  - Domestic fiscal revenue shock (one percentage point increase in fiscal balance to nominal output):
    - Peak contraction of output averages 0.6 percent within a range of 0.1 to 1.0 percent; peak contraction tends to decrease with trade openness.
- Common qualitative dynamics across shocks:
  - Supply shocks: persistent hump-shaped contraction of output, central bank raises nominal policy interest rate, currency generally appreciates in real effective terms, fiscal balance tends to deteriorate, current account generally improves.
  - Private demand shocks: persistent hump-shaped expansion of output and inflation, central bank raises nominal policy interest rate, currency appreciates, fiscal balance improves, current account deteriorates.
  - Credit/duration risk premium shocks: persistent contractions of output and inflation, central bank tends to cut nominal policy interest rate for stabilization; currency responses differ (credit shock → currency appreciates; duration shock → currency depreciates).
  - Equity risk premium shocks: persistent expansion of output and inflation, central bank tends to raise nominal policy interest rate, currency appreciates, fiscal balance improves.

### Forecast error variance decompositions — drivers by variable and horizon
- Shock categories considered: domestic supply, foreign supply, domestic demand, foreign demand, world monetary policy, world fiscal policy, world risk premium, world terms of trade.
- Inflation:
  - Unpredictable variation in inflation primarily driven by domestic and foreign supply shocks, and to a lesser extent world monetary policy shocks, at all horizons.
  - Contribution of domestic supply shocks relative to foreign supply shocks generally decreases with trade openness and increases with monetary policy autonomy.
- Output:
  - High frequencies: primarily attributable to domestic and foreign demand shocks, together with world risk premium shocks.
  - Low frequencies: domestic and foreign supply shocks, together with world monetary policy shocks, are major contributors.
- Domestic demand:
  - Domestic demand shocks are larger contributors at all frequencies; foreign demand shocks are smaller contributors.
  - World fiscal policy shocks significant at high frequencies.
- Nominal policy interest rate:
  - Short horizons: primarily driven by world monetary policy shocks.
  - Long horizons: domestic and foreign supply shocks become major contributors; relative domestic supply contribution decreases with trade openness and increases with monetary policy autonomy.
- Real effective exchange rate:
  - High frequency variation attributed to world monetary policy and risk premium shocks; low frequency driven by domestic and foreign supply shocks.
- Fiscal balance:
  - Short horizons: driven primarily by world monetary and fiscal policy shocks and to a lesser extent domestic and foreign demand shocks.
  - Long horizons: domestic and foreign supply shocks and demand shocks are major contributors.
- Current account balance:
  - High frequency: domestic and foreign demand shocks, together with world monetary policy shocks for economies with high net foreign asset or debt positions.
  - Low frequency: domestic and foreign supply shocks major contributors.

### Historical decompositions and episodes
- Variables decomposed: consumption price inflation, output growth, fiscal balance ratio, current account ratio (Figures 21–24).
- Business cycle and crisis episodes:
  - Build up to global financial crisis: excess demand primarily from private domestic demand expansion in many economies; net exports major contributor in surplus economies (China, Germany, Japan); amplification by world risk premium and terms of trade shocks.
  - Global financial crisis: rapid synchronized unwinding of excess demand into excess supply; negative domestic and foreign demand shocks amplified by world risk premium shocks; mitigated by unsystematic monetary and fiscal interventions with large fiscal deteriorations.
  - Post-crisis recovery: positive domestic and foreign demand shocks gradually reduced excess supply; recovery decelerated by world fiscal policy shocks which contributed to moderate to large fiscal improvements.
- Economy-specific attributions:
  - Major deficit economies (Spain, United States): business cycles primarily driven by domestic demand shocks.
  - Major surplus economies (China, Germany): business cycles primarily driven by foreign demand shocks.
  - Structural fiscal balances: generally deteriorated recently, particularly in advanced economies.
  - Potential output growth: stabilized at relatively low levels in advanced economies and at relatively high levels in emerging economies.

### Spillovers and systemic transmission
- Systemic economies analyzed: China (CHN), the Euro Area (EUR), Japan (JPN), the United Kingdom (GBR), and the United States (USA).
- Transmission channels: trade, financial, commodity price linkages; monetary and fiscal policy responses mediate spillovers.
- Shock types considered: macroeconomic (supply, private demand, monetary, fiscal expenditure, fiscal revenue) and financial (credit risk premium, duration risk premium, equity risk premium).
- Key findings on spillover patterns:
  - On average over the business cycle, macroeconomic shocks from systemic economies generate most output spillovers to the rest of the world; macro shocks contribute more to business cycle fluctuations than financial shocks.
  - During financial stress episodes (e.g., global financial crisis), financial shocks cause uniformly strong international business cycle comovement via contagion effects.
  - Macroeconomic shock spillovers: small but concentrated and gravity-like (bilateral trade and proximity); supply shocks can dilute gravity via terms of trade shifts.
  - Financial shock spillovers: large and diffuse; operate through international comovement in financial asset prices and risk premia; contagion intensity strongest from the United States.
- Model instability observations:
  - Greece and Portugal (and to a lesser degree Spain) are nearly dynamically unstable in the estimated model: selected foreign shocks (notably foreign supply shocks causing large terms of trade shifts) trigger disruptive internal adjustments to maintain external debt sustainability—reflecting currency union membership, low cyclical stabilization weights in monetary policy, low trade openness, and high net foreign debt positions.
  - Ireland and Italy are not nearly dynamically unstable, partly due to low net foreign debt positions.

### Forecasting methodology and performance
- Bayesian forecasting combines restricted forecasts from the estimated model with judgmental (subjective) forecasts:
  - Restricted forecasts subject to constraints: constant real effective exchange rates, common energy and nonenergy commodity price paths, and zero lower bound on nominal policy interest rate in the Euro Area, Japan, the United Kingdom, and the United States.
  - Weight on restricted forecasts decreases with objective uncertainty and increases with subjective uncertainty; judgmental forecast uncertainty represented by forecast error covariance matrix rescaled by factor of 2^2.
  - Computationally efficient Bayesian updating and smoothing equations provided (equations (60)–(75)).
- Performance:
  - Sequential unconditional forecasts indicated the model could predict business cycle turning points and signaled a synchronized global moderation was overdue before the global financial crisis.
  - The model underpredicted the severity of the synchronized global recession and overpredicted its disinflationary impact.
  - The model forecast a synchronized global recovery but systematically underpredicted its sluggishness in balance-sheet deleveraging economies (Spain, the United Kingdom, the United States), in part due to violation of the zero lower bound constraint on the nominal policy interest rate.
- Conditional forecast decompositions:
  - Imposing the zero lower bound is generally disinflationary and contractionary.
  - Effects of deterministic restrictions mostly measured by world risk premium, world terms of trade, and world monetary policy shocks.
  - Effects of judgmental stochastic restrictions largely measured by domestic supply and private demand shocks; negative domestic private demand shocks account for much discrepancy in deleveraging economies.

### Applications, limitations, and suggested future research
- Demonstrated applications: accounting for business cycle fluctuations; quantifying monetary and fiscal transmission mechanisms; spillover analysis; generating conditional forecasts of inflation and output growth within a unified structural Bayesian framework that conditions on judgment.
- Limitations:
  - Structural interpretations of some orthogonal shocks are ambiguous; microeconomic foundations could be strengthened.
  - A more sophisticated procedure for generating judgment about trend component paths that accounts for structural breaks associated with financial crises seems warranted.

*Source: _wp12149 (IMF working paper — Appendices A and B, main text summaries and parameter estimation results)*

### 1. Parameter Estimation Results ................................................................

### 1. Parameter Estimation Results ................................................................
..............................34

### Figures
- 1. Output Gap Estimates, Decomposition by Source of Demand ............................................36
- 2. Output Gap Estimates, Decomposition by Source of Stimulus ...........................................37
- 3. Simulated Unconditional Correlations .................................................................................38
- 4. Impulse Responses to a Domestic Supply Shock ................................................................39
- 5. Impulse Responses to a Domestic Private Demand Shock ..................................................40
- 6. Impulse Responses to a Domestic Monetary Policy Shock .................................................41
- 7. Impulse Responses to a Domestic Credit Risk Premium Shock..........................................42
- 8. Impulse Responses to a Domestic Duration Risk Premium Shock .....................................43
- 9. Impulse Responses to a Domestic Equity Risk Premium Shock .........................................44
- 10. Impulse Responses to a Domestic Fiscal Expenditure Shock ...........................................45
- 11. Impulse Responses to a Domestic Fiscal Revenue Shock .................................................46
- 12. Impulse Responses to a World Energy Commodity Price Shock ......................................47
- 13. Impulse Responses to a World Nonenergy Commodity Price Shock................................48
- 14. Forecast Error Variance Decompositions of Consumption Price Inflation .......................49
- 15. Forecast Error Variance Decompositions of Output ..........................................................50
- 16. Forecast Error Variance Decompositions of Domestic Demand .......................................51
- 17. Forecast Error Variance Decompositions of the Nominal Policy Interest Rate ................52
- 18. Forecast Error Variance Decompositions of the Real Effective Exchange Rate ...............53
- 19. Forecast Error Variance Decompositions of the Fiscal Balance .......................................54
- 20. Forecast Error Variance Decompositions of the Current Account Balance ......................55
- 21. Historical Decompositions of Consumption Price Inflation ..............................................56
- 22. Historical Decompositions of Output Growth ...................................................................57
- 23. Historical Decompositions of the Fiscal Balance ..............................................................58
- 24. Historical Decompositions of the Current Account Balance .............................................59
- 25. Simulated Conditional Betas of the Output Gap................................................................60
- 26. Peak Impulse Responses to Foreign Supply Shocks..........................................................61
- 27. Peak Impulse Responses to Foreign Private Demand Shocks ...........................................62
- 28. Peak Impulse Responses to Foreign Monetary Policy Shocks ..........................................63
- 29. Peak Impulse Responses to Foreign Credit Risk Premium Shocks ...................................64
- 30. Peak Impulse Responses to Foreign Duration Risk Premium Shocks ...............................65
- 31. Peak Impulse Responses to Foreign Equity Risk Premium Shocks ..................................66
- 32. Peak Impulse Responses to Foreign Fiscal Expenditure Shocks .......................................67
- 33. Peak Impulse Responses to Foreign Fiscal Revenue Shocks ............................................68
- 34. Sequential Unconditional Forecasts of Consumption Price Inflation ................................69
- 35. Sequential Unconditional Forecasts of Output Growth .....................................................70
- 36. Conditional Forecasts of Consumption Price Inflation ......................................................71
- 37. Conditional Forecasts of Output Growth ...........................................................................72
- 38. Conditional Forecast Decompositions for Consumption Price Inflation ...........................73
- 39. Conditional Forecast Decompositions for Output Growth ................................................74

* _wp12149 - 1. Parameter Estimation Results ................................................................*

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

### _wp12149 - References .............................................................................................................

### Introduction and purpose
- Develops a structural macroeconometric model of the world economy disaggregated into thirty five national economies to incorporate monetary and fiscal transmission mechanisms and extensive macrofinancial linkages, both within and across economies.
- Motivated by the global financial crisis and by gaps identified in the literature, including Dées, Pesaran, Smith and Smith (2010) and Pesaran, Schuermann and Weiner (2004).
- Demonstrates monetary policy analysis, fiscal policy analysis, spillover analysis, and forecasting within a Bayesian framework that conditions on judgment in estimation and forecasting.

### Model scope and data
- Model disaggregation: thirty five economies — Argentina, Australia, Austria, Belgium, Brazil, Canada, China, the Czech Republic, Denmark, Finland, France, Germany, Greece, India, Indonesia, Ireland, Italy, Japan, Korea, Mexico, the Netherlands, New Zealand, Norway, Poland, Portugal, Russia, Saudi Arabia, South Africa, Spain, Sweden, Switzerland, Thailand, Turkey, the United Kingdom, and the United States.
- Observed endogenous variables: a total of four hundred one endogenous variables across the thirty five economies.
- Sample period for data used in joint estimation: 1999Q1 through 2011Q3; parameter estimation results reported for sample period 1999Q3 through 2011Q3.
- Estimation uses judgmental conditioning on trend paths derived from Hodrick and Prescott (1997) filter preliminary estimates.

### Panel unobserved components model — structure
- Two separable components per variable: cyclical component (denoted ˆxit) and trend component (denoted xit), with additive separability xit = ˆxit + xit.
- Cross-economy equality restrictions imposed on structural parameters, with response coefficients varying across economies according to structural characteristics (e.g., export openness Xi/Yi, import openness Mi/Di, commodity intensities zCOMi Xi/Xi or zCOMi Mi/Mi).
- Linkages included:
  - Trade linkages via trade-weighted averages (Zitx) with bilateral weights wZij for exports (ZX), imports (ZM), and their average (ZT).
  - Portfolio linkages via portfolio-weighted averages with bilateral weights for debt (ZB) and equity (ZS).
  - World aggregates via world weights wi based on money market capitalization (ZM), bond market capitalization (ZB), stock market capitalization (ZS), and output (ZY).
  - Commodity price linkages with separate treatment of energy and nonenergy commodities.

### Major cyclical relationships and shocks (selected)
- Domestic supply relationship: cyclical output price inflation ˆπY,it depends on past and expected future cyclical components and contemporaneous cyclical output; driven by domestic supply shock νˆY,P,it with ˆεY,P,it ~ iid (0,ˆσ2Y,P).
- Import supply relationship: cyclical consumption price inflation ˆπC,it depends on past/expected components, contemporaneous cyclical output, terms of trade, and relative domestic currency commodity import prices; import supply shock νˆM,P,it with ˆεM,P,it ~ iid (0,ˆσ2M,P).
- Demand relationships:
  - Output cyclical component ˆlnYit follows stationary AR(1) driven by monetary conditions index (MCI) and export demand shock νˆX,it with ˆεX,it ~ iid (0,ˆσ2X,it).
  - Domestic demand ˆlnDit follows stationary AR(1) driven by financial conditions index (FCI) and private domestic demand shock νˆC,it with ˆεC,it ~ iid (0,ˆσ2C,it).
- Monetary policy rule: cyclical policy interest rate ˆPit responds to weighted average of past and desired cyclical components; monetary policy shock ˆεP,it ~ iid (0,ˆσ2P,i). Flexible inflation targeting regime (j = 1) except for specified managed regimes.
- Money, bond, and stock market relationships include spread, duration risk, and equity risk premium shocks:
  - Short-term nominal spread dynamics driven by net foreign assets to nominal output and credit risk premium shock νˆS,it with ˆεS,it ~ iid (0,ˆσ2S,it).
  - Long-term nominal market interest rate dynamics driven by short-term nominal market interest rate and duration risk premium shock νˆL,it with ˆεL,it ~ iid (0,ˆσ2L,it).
  - Equity price dynamics driven by expected output, tax revenue ratio, and short-term real market interest rate; equity risk premium shock νˆSTK,it with ˆεSTK,it ~ iid (0,ˆσ2STK,it).
- Real bilateral and effective exchange rate relationships driven by short-term output-based real interest differentials and exchange rate risk premium shocks with sensitivity depending on capital controls.
- Terms of trade dynamics ΔˆlnTit driven by deviations of import-weighted real effective exchange rate from terms of trade and a terms of trade shock with ˆεit ~ iid (0,ˆσ2it).
- Commodity market relationship: cyclical relative price of commodity ˆlnPz,COM,t driven by contemporaneous cyclical world output and world commodity price shock with ˆεz,COM,t ~ iid (0,ˆσ2z,COM,t); response coefficients vary by commodity market (energy j = 1, nonenergy j = 0).

### Trend components
- Trend changes for prices, quantities, and public demand follow random walks with innovations distributed ~ iid (0,·) as specified in equations (20)–(25), preserving the model's robustness to intermittent structural breaks.
- Trend changes for nominal policy rate, short-term and long-term nominal market rates follow random walks (equations (26)–(28)).
- Trend components of real interest rates satisfy expected-real-rate identity: Eti+1(rPZ,it) = rPZ,it + ... (as specified).
- Trend changes for equity price and nominal bilateral exchange rate follow random walks (equations (29)–(30)).
- Trend components for fiscal and external ratios (FB/PY, CA/PY, PB/PY, B/PY, TB/PY) follow specified random-walk or identity conditions (equations (31)–(32) and subsequent relations).
- Identifying restriction: all innovations are assumed independent, implying multivariate normality.

### Estimation procedure
- Bayesian estimation of parameters and unobserved components treating the model as the joint probability distribution of the data.
- State-space formulation: cyclical component dynamics converted to a unique stationary solution (Klein (2000) procedure) and combined with trend dynamics and signal equation for judgmental information (equations (33)–(40)).
- Kalman filter and smoother (de Jong (1989)) used for state estimation; Bayesian updating and smoothing equations provided (equations (41)–(52)).
- Parameters θ estimated via posterior mode maximization of posterior kernel (equations (53)–(59)); asymptotic normal approximation to posterior around mode used for inference.
- Prior setup:
  - Parameters associated with conditional mean: informative independent priors centered within ranges from existing literature.
  - Parameters associated exclusively with conditional variance: diffuse priors.
  - Judgmental trend paths derived from Hodrick and Prescott (1997) preliminary filter; stochastic restrictions rescaled by factor 2^2.
  - Great ratios and bilateral trade and equity weights calibrated to observed 2005 values; all world and bilateral weights normalized to sum to one.
  - Monetary policy represented as flexible inflation targeting in all economies except Argentina, China, the Czech Republic, Denmark, India, Indonesia, Russia, Saudi Arabia and Thailand (managed exchange rate regime in these exceptions).
  - Capital controls apply in China, India, and Saudi Arabia.
  - Quotation currency for FX transactions: United States.
- Numerical maximization strategy: modified steepest ascent with starting values from differential evolution algorithm (Storn and Price (1997)).

### Estimation results — highlights
- Posterior mode obtained; Klein (2000) sufficient condition for unique stationary rational expectations equilibrium satisfied in a neighborhood around posterior mode.
- Hessian estimator not nearly singular at posterior mode → local identification of linear state-space representation.
- Posterior modes of most structural parameters are close to prior means due to tight priors; however, substantial updates from prior to posterior for some parameters indicate data informativeness.
- Estimated variances of innovations driving cyclical components are within ranges reported in existing literature (after data rescaling).
- Estimated variances of innovations driving trend components vary considerably across economies and observed variables.
- Unobserved components: smoothed estimates of the output gap and monetary conditions gap produced (plotted in referenced figures).

### Applications demonstrated
- Accounting for business cycle fluctuations.
- Quantifying monetary and fiscal transmission mechanisms.
- Generating conditional forecasts of inflation and output growth.
- Monetary and fiscal policy analysis, spillover analysis, and forecasting within a unified structural Bayesian framework that conditions on judgment.

*Source: _wp12149 - References*

### Appendix B. These estimates are conditional on past, present, and future information.

### _wp12149 - Appendix B. These estimates are conditional on past, present, and future information.

### Decomposition of output gap: domestic demand vs net exports
- The gradual global synchronized accumulation of excess demand pressure during the build up to the global financial crisis was primarily driven by the excessive expansion of private domestic demand in most economies.
- During the same period of widening global current account imbalances, excessive expansion of net exports was a major contributor to excess demand pressure in major surplus economies such as China, Germany, and Japan.
- The global financial crisis triggered a rapid global synchronized unwinding of excess demand pressure, resulting in substantial excess supply pressure in many economies.
- During the crisis episode of narrowing global current account imbalances:
  - Collapses in private domestic demand in major deficit economies such as France, the United Kingdom, and the United States coincided with collapses in net exports in major surplus economies.

### Decomposition of output gap: monetary conditions vs real conditions
- The build up to the global financial crisis featured loose financial conditions in many economies, notably France, Germany, and the United States, accompanying the accumulation of excess demand pressure.
- During the global financial crisis, monetary and financial conditions abruptly tightened in these and many other economies.

### Monetary and fiscal policy analysis: framework and measures
- Analysis is conducted within an estimated panel unobserved components model, quantifying dynamic interrelationships among instrument, indicator, and target variables using:
  - Simulated unconditional correlations.
  - Estimated impulse response functions.
  - Forecast error variance decompositions.
  - Historical decompositions.

### Simulated unconditional correlations: key findings
- The output gap and the monetary conditions gap are both leading indicators of inflationary or disinflationary pressure.
- Predictability of deviations of inflation from its implicit target varies across economies and horizons:
  - Relatively unpredictable in economies with flexible inflation targeting regimes, particularly relatively small and open ones such as Australia, Canada, New Zealand, Norway, Sweden, and the United Kingdom.
  - Slightly more predictable in economies with managed exchange rate regimes, reflecting lower monetary policy autonomy.
  - Relatively predictable within the Euro Area, whose member economies lack monetary policy autonomy.
- Horizon differences:
  - The output gap is generally slightly more useful for predicting inflation at short horizons.
  - The monetary conditions gap tends to be slightly more useful at long horizons.
- Monetary conditions gap as a leading indicator of business cycle fluctuations:
  - More useful for predicting the output gap in economies with high dependence on private domestic demand.
  - Less useful for predicting the output gap in relatively open economies (high dependence on foreign demand) and economies with relatively large governments (high dependence on public domestic demand).

### Impulse response functions: structural shocks and typical dynamics
- Structural shocks considered include:
  - Domestic supply shocks.
  - Domestic private demand shocks.
  - Domestic monetary policy shocks.
  - Domestic credit risk premium shocks.
  - Domestic duration risk premium shocks.
  - Domestic equity risk premium shocks.
  - Domestic fiscal expenditure shocks.
  - Domestic fiscal revenue shocks.
  - World energy commodity price shocks.
  - World nonenergy commodity price shocks.
- Response patterns (generalized):
  - Domestic supply shock (persistent increase in inflation):
    - Persistent hump shaped contraction of output.
    - Central bank raises nominal policy interest rate.
    - Currency generally appreciates in real effective terms.
    - Fiscal balance tends to deteriorate due to the fall in output.
    - Current account balance generally improves reflecting larger fall in domestic demand.
  - Domestic private demand shock (persistent hump shaped expansion of output):
    - Persistent hump shaped increase in inflation.
    - Central bank raises nominal policy interest rate to stabilize inflation and output.
    - Currency appreciates in real effective terms.
    - Fiscal balance improves due to rise in output.
    - Current account balance deteriorates reflecting larger rise in domestic demand.
  - Domestic monetary policy shock (persistent increase in nominal policy interest rate):
    - Currency appreciates in real effective terms.
    - Persistent hump shaped contraction of output; persistent decrease in inflation.
    - Quantified response: in response to a one percentage point increase in the nominal policy interest rate:
      - The peak contraction of output averages 0.5 percent across economies within a range of 0.2 to 0.7 percent.
      - The peak decrease in inflation averages 0.3 percentage points within a range of 0.1 to 0.4 percentage points.
    - Fiscal balance deteriorates due to fall in output.
    - Current account balance generally improves reflecting larger fall in domestic demand.
  - Domestic credit risk premium shock (persistent increase in short term nominal market interest rate):
    - Currency generally appreciates in real effective terms.
    - Persistent hump shaped contraction of output; persistent decrease in inflation.
    - Central bank tends to cut nominal policy interest rate to stabilize inflation and output.
    - Fiscal balance deteriorates due to fall in output.
    - Current account balance generally improves reflecting larger fall in domestic demand.
  - Domestic duration risk premium shock (persistent increase in long term nominal market interest rate):
    - Persistent hump shaped contraction of output; generally accompanied by persistent hump shaped decrease in inflation.
    - Central bank tends to cut nominal policy interest rate.
    - Currency depreciates in real effective terms.
    - Fiscal balance deteriorates due to fall in output.
    - Current account balance improves reflecting larger fall in domestic demand.
  - Domestic equity risk premium shock (persistent increase in price of equity):
    - Persistent hump shaped expansion of output; generally accompanied by persistent hump shaped increase in inflation.
    - Central bank tends to raise nominal policy interest rate.
    - Currency appreciates in real effective terms.
    - Fiscal balance generally improves due to rise in output.
    - Current account balance deteriorates reflecting larger rise in domestic demand.
  - Domestic fiscal expenditure shock (persistent deterioration in fiscal balance):
    - Persistent expansion of output; generally accompanied by persistent hump shaped increase in inflation.
    - Quantified response: in response to a one percentage point decrease in the ratio of the fiscal balance to nominal output:
      - The peak expansion of output averages 1.0 percent within a range of 0.2 to 1.7 percent.
      - The peak expansion tends to decrease across economies with their trade openness.
    - Central bank generally raises nominal policy interest rate.
    - Currency appreciates in real effective terms.
    - Current account balance deteriorates, reflecting larger rise in domestic demand than in output.
  - Domestic fiscal revenue shock (persistent improvement in fiscal balance):
    - Persistent contraction of output; generally accompanied by persistent hump shaped decrease in inflation.
    - Quantified response: in response to a one percentage point increase in the ratio of the fiscal balance to nominal output:
      - The peak contraction of output averages 0.6 percent within a range of 0.1 to 1.0 percent.
      - The peak contraction tends to decrease across economies with their trade openness.
    - Central bank generally cuts nominal policy interest rate.
    - Currency depreciates in real effective terms.
    - Current account balance improves, reflecting larger fall in domestic demand than in output.
  - World energy or nonenergy commodity price shock (persistent increase in commodity prices):
    - Inflation generally increases; central bank tends to raise nominal policy interest rate.
    - For net exporters:
      - Currency generally appreciates in real effective terms.
      - Generally induces persistent terms of trade driven expansion of domestic demand mitigated by monetary policy tightening, eventually translating into persistent expansion of output.
      - Fiscal balance tends to improve.
      - Current account balance may improve or deteriorate.
    - For net importers:
      - Currency generally depreciates in real effective terms.
      - Generally induces persistent terms of trade driven contraction of domestic demand amplified by monetary policy tightening, translating into persistent contraction of output.
      - Fiscal balance tends to deteriorate.
      - Current account balance may deteriorate or improve.

### Forecast error variance decompositions
- Forecast error variance decompositions measure contributions of mutually exclusive structural shocks to unpredictable variation in endogenous variables at different horizons, on average over the business cycle.
- Estimated decompositions are provided for:
  - Consumption price inflation.
  - Output.
  - Domestic demand.
  - The nominal policy interest rate.
  - The real effective exchange rate.
  - The ratio of the fiscal balance to nominal output.
  - The ratio of the current account balance to nominal output.

*Source: _wp12149 - Appendix B.*

### Appendix B. The sets of structural shocks under consideration are domestic supply shocks,

### _wp12149 - Appendix B. The sets of structural shocks under consideration are domestic supply shocks,

### Forecast error variance decompositions — drivers of unpredictable variation
- The sets of structural shocks under consideration are domestic supply shocks, foreign supply shocks, domestic demand shocks, foreign demand shocks, world monetary policy shocks, world fiscal policy shocks, world risk premium shocks, and world terms of trade shocks.
- Inflation:
  - Unpredictable variation in inflation is primarily driven by domestic and foreign supply shocks, and to a lesser extent world monetary policy shocks, at all horizons.
  - The contribution of domestic supply shocks relative to foreign supply shocks is generally decreasing across economies with their trade openness and increasing with their monetary policy autonomy.
- Output:
  - Unpredictable variation in output tends to be primarily attributable to domestic and foreign demand shocks, together with world risk premium shocks, at high frequencies.
  - The contribution of domestic demand shocks relative to foreign demand shocks is generally decreasing across economies with their trade openness.
  - At low frequencies, domestic and foreign supply shocks, together with world monetary policy shocks, are major contributors to unpredictable output fluctuations.
- Domestic demand:
  - Domestic demand shocks are larger contributors to unpredictable variation at all frequencies; foreign demand shocks are smaller contributors.
  - World fiscal policy shocks tend to be significant contributors to unpredictable domestic demand fluctuations at high frequencies.
- Nominal policy interest rate:
  - Unpredictable variation is primarily driven by world monetary policy shocks at short horizons.
  - At long horizons, domestic and foreign supply shocks are also major contributors; the relative contribution of domestic supply shocks is generally decreasing with trade openness and increasing with monetary policy autonomy.
- Real effective exchange rate:
  - Most unpredictable high frequency variation is attributed to world monetary policy and risk premium shocks.
  - Domestic and foreign supply shocks are major contributors at low frequencies.
- Fiscal balance:
  - Unpredictable variation in the fiscal balance is primarily driven by world monetary and fiscal policy shocks, and to a lesser extent domestic and foreign demand shocks, at short horizons.
  - At long horizons, domestic and foreign supply shocks, and to a lesser extent domestic and foreign demand shocks, are major contributors.
- Current account balance:
  - Most unpredictable high frequency variation is attributed to domestic and foreign demand shocks, together with world monetary policy shocks for economies with high net foreign asset or debt positions.
  - The contribution of domestic demand shocks relative to foreign demand shocks tends to be decreasing with trade openness.
  - Domestic and foreign supply shocks are major contributors at low frequencies.

### Historical decompositions — time-varying contributions to realizations
- Variables covered: consumption price inflation, output growth, the ratio of the fiscal balance to nominal output, and the ratio of the current account balance to nominal output (plotted in Figure 21 through Figure 24 of Appendix B).
- Inflation deviations from implicit targets:
  - Attributed primarily to economy specific combinations of domestic and foreign supply and demand shocks, together with world risk premium and terms of trade shocks.
  - Implicit inflation targets have generally stabilized at relatively low levels in advanced economies, particularly those with well established flexible inflation targeting regimes such as Australia, Canada, New Zealand, Norway, Sweden, and the United Kingdom.
- Output growth and business cycles:
  - Business cycle dynamics around relatively stable potential output growth rates are primarily due to economy specific combinations of domestic and foreign demand shocks, together with world fiscal policy and risk premium shocks.
  - Major deficit economies (Spain and the United States): business cycle fluctuations primarily driven by domestic demand shocks.
  - Major surplus economies (China and Germany): business cycle fluctuations primarily driven by foreign demand shocks.
  - In both groups, these fluctuations have usually been amplified by world risk premium shocks and mitigated by world fiscal policy shocks.
  - Potential output growth rates: generally stabilized at relatively low levels in advanced economies and at relatively high levels in emerging economies.
- Fiscal balance:
  - Fluctuations around structural balances primarily attributed to world fiscal policy shocks, together with economy specific combinations of domestic and foreign demand shocks.
  - These fluctuations have usually been amplified by world risk premium shocks, reflecting discretionary fiscal policy effects on nominal market interest rates.
  - Structural fiscal balances have generally deteriorated recently, particularly in advanced economies.
- Current account balance:
  - Fluctuations around structural balances primarily attributed to economy specific combinations of domestic and foreign demand shocks.
  - Contributions broadly balanced in major surplus and deficit economies, with notable exceptions: Spain (domestic demand shocks dominated) and China (foreign demand shocks dominated).
- Global financial cycle episodes:
  - Build up to the global financial crisis: positive domestic and foreign demand shocks contributed to excess demand, generally amplified by world risk premium shocks; synchronized global rise in inflation usually amplified by world terms of trade shocks.
  - Global financial crisis: negative domestic and foreign demand shocks, amplified and accelerated by world risk premium shocks, rapidly eliminated excess demand and often created excess supply; mitigated by unsystematic monetary and fiscal policy interventions, with fiscal interventions contributing to large deteriorations in fiscal balances; synchronized global fall in inflation usually amplified by world terms of trade shocks.
  - Post-crisis recovery: economy specific combinations of positive domestic and foreign demand shocks, generally amplified by world risk premium shocks, have gradually reduced excess supply; recovery decelerated by world fiscal policy shocks, which contributed to moderate to large improvements in fiscal balances.

### Spillover analysis — transmission and systemic sources
- Model framework:
  - Dynamic effects of macroeconomic and financial shocks transmitted via trade, financial and commodity price linkages; monetary and fiscal policy responses are necessary to spillovers.
  - Macroeconomic shocks transmitted via direct financial linkages; financial shocks also transmitted via indirect financial linkages representing contagion effects.
- Systemic economies under consideration: China, the Euro Area, Japan, the United Kingdom, and the United States.
- Shocks considered:
  - Macroeconomic: supply shocks, private demand shocks, monetary policy shocks, fiscal expenditure shocks, fiscal revenue shocks.
  - Financial: credit risk premium shocks, duration risk premium shocks, equity risk premium shocks.
- Simulated conditional betas (output gap comovement):
  - On average over the business cycle, output spillovers from systemic economies to the rest of the world are primarily generated by macroeconomic shocks, which contribute more to business cycle fluctuations than financial shocks, implying weak international business cycle comovement beyond close trading partners.
  - During episodes of financial stress (e.g., the global financial crisis), international business cycle comovement becomes uniformly strong due to financial shocks propagating via elevated contagion effects.
  - Macroeconomic shock spillovers are generally small but concentrated and exhibit gravity (reflect bilateral trade relationships and proximity), though supply shocks dilute this pattern via terms of trade shifts.
  - Financial shock spillovers are generally large and diffuse, transcending weak bilateral portfolio investment relationships; they operate primarily through international comovement in financial asset prices and require strong international comovement in risk premia.
  - Contagion intensity varies: uniquely strong from the United States; strong to emerging economies with open capital accounts; moderate to advanced economies; weak to emerging economies with closed capital accounts.
- Impulse response functions — typical responses in recipient economies:
  - Foreign supply shock (in systemic economy): recipient currencies generally depreciate in real effective terms; effects on recipient inflation, output, fiscal and current account balances are diverse.
  - Foreign private demand shock: foreign demand driven increases in inflation and expansions of output in recipients; currencies generally depreciate in real effective terms; fiscal and current account balances tend to improve.
  - Foreign monetary policy shock (increase in nominal policy rate): recipient currencies generally depreciate in real effective terms; terms of trade driven increases in inflation and foreign demand driven contractions of output in recipients; fiscal and current account balances generally deteriorate.
  - Foreign credit risk premium shock (increase in short term nominal market interest rate): short term nominal market interest rates in recipients generally increase via international money market contagion; resulting decreases in inflation and contractions of output; fiscal and current account balances deteriorate.
  - Foreign duration risk premium shock (increase in long term nominal market interest rate): long term nominal market interest rates in recipients generally increase via international bond market contagion; resulting decreases in inflation and contractions of output; fiscal and current account balances deteriorate.
  - Foreign equity risk premium shock (increase in the price of equity): equity prices in recipients generally increase via international stock market contagion; resulting increases in inflation and expansions of output; fiscal and current account balances improve.
  - Foreign fiscal expenditure shock (deterioration in systemic fiscal balance): foreign demand driven increases in inflation and expansions of output in recipients; currencies generally depreciate in real effective terms; recipients' fiscal and current account balances tend to improve.
  - Foreign fiscal revenue shock (improvement in systemic fiscal balance): foreign demand driven decreases in inflation and contractions of output in recipients; currencies generally appreciate in real effective terms; recipients' fiscal and current account balances tend to deteriorate.
- Model instability observations:
  - Greece and Portugal, and to a lesser degree Spain, are nearly dynamically unstable in the estimated model: selected foreign shocks (notably foreign supply shocks causing large terms of trade shifts) trigger disruptive internal adjustments (large domestic demand shifts) to maintain external debt sustainability — reflecting membership of a currency union with low weights on cyclical stabilization in monetary policy, low trade openness, and high net foreign debt positions.
  - Ireland and Italy are not nearly dynamically unstable in the model, due in part to their low net foreign debt positions.

### Forecasting — methodology and results
- Bayesian forecasting procedure:
  - Combines restricted forecasts from the panel unobserved components model with judgment to respect monetary and fiscal policy relevant constraints.
  - Restricted forecasts subject to constant real effective exchange rates, common assumptions about energy and nonenergy commodity prices, and the zero lower bound constraint on the nominal policy interest rate in the Euro Area, Japan, the United Kingdom, and the United States.
  - Weight on restricted forecasts decreases with objective uncertainty (measured by time varying forecast error covariance matrix) and increases with subjective uncertainty of judgmental forecasts (represented by the same forecast error covariance matrix, rescaled by a factor of 2
2
).
  - Computationally efficient Bayesian updating and smoothing equations provided (equations (60)–(75)).
- Forecasting performance:
  - Sequential unconditional forecasts suggest the model can predict business cycle turning points and indicated a synchronized global moderation was overdue by the time of the global financial crisis.
  - The model underpredicted the severity of the synchronized global recession and overpredicted its disinflationary impact.
  - The model forecast the subsequent synchronized global recovery but systematically underpredicted its sluggishness in economies undergoing balance sheet deleveraging such as Spain, the United Kingdom and the United States, in part due to violation of the zero lower bound constraint on the nominal policy interest rate.
- Conditional forecasts and decompositions:
  - Combined forecasts (restricted + judgmental) generally lie between the restricted and judgmental forecasts; restricted forecasts tend to lie slightly below unrestricted forecasts.
  - Conditional forecast decompositions:
    - Effects on unrestricted forecasts from conditioning on constant real effective exchange rates, given commodity price paths, and the zero lower bound constraint are primarily measured by contributions from world risk premium shocks, world terms of trade shocks, and world monetary policy shocks, respectively.
    - Imposing the zero lower bound is generally disinflationary and contractionary; effects of other deterministic restrictions vary in sign.
    - Effects on restricted forecasts of imposing judgment (stochastic restrictions) are primarily measured by contributions from domestic supply shocks and domestic private demand shocks.
    - Domestic supply shocks of variable sign tend to account for most persistent discrepancies between restricted and judgmental forecasts.
    - Negative domestic private demand shocks account for much of the discrepancy in economies undergoing balance sheet deleveraging, with substantial spillovers to close trading partners.

### Conclusion — model scope, uses, and limitations
- The paper develops a structural macroeconometric panel unobserved components model disaggregated into thirty five national economies.
- Demonstrated applications: monetary policy analysis, fiscal policy analysis, spillover analysis, forecasting — including accounting for business cycle fluctuations, quantifying monetary and fiscal transmission, and generating conditional forecasts of inflation and output growth.
- Framework: Bayesian conditioning on judgment in estimation and forecasting.
- Limitations and future research directions:
  - Structural interpretations of some orthogonal shocks are ambiguous; strengthening microeconomic foundations remains an objective for future research.
  - A more sophisticated procedure for generating judgment about trend component paths that accounts for structural breaks associated with financial crises seems warranted.

*Source: Appendix B of the provided IMF working paper content unit.*

### Appendix A. Description of the Data Set

### Appendix A. Description of the Data Set

### Sample and data sources
- Estimation is based on quarterly data for thirty five economies over the sample period 1999Q1 through 2011Q3.
- Economies covered: Argentina, Australia, Austria, Belgium, Brazil, Canada, China, the Czech Republic, Denmark, Finland, France, Germany, Greece, India, Indonesia, Ireland, Italy, Japan, Korea, Mexico, the Netherlands, New Zealand, Norway, Poland, Portugal, Russia, Saudi Arabia, South Africa, Spain, Sweden, Switzerland, Thailand, Turkey, the United Kingdom, and the United States.
- Primary data sources where available:
  - GDS and WEO databases compiled by the International Monetary Fund.
- Other data sources used when IMF databases were not available:
  - IFS database compiled by the International Monetary Fund.
  - CEIC database produced by Internet Securities Incorporated.
  - EMED database produced by Emerging Markets Economic Data Limited.

### Macroeconomic variables (definitions and measurement)
- Variables included:
  - Price of output
  - Price of consumption
  - Quantity of output
  - Quantity of domestic demand
  - Quantity of public domestic demand
  - Ratio of the fiscal balance to nominal output
  - Ratio of the current account balance to nominal output
  - Prices of energy and nonenergy commodities
- Measurement definitions:
  - Price of output: seasonally adjusted gross domestic product price deflator.
  - Price of consumption: proxied by the seasonally adjusted consumer price index.
  - Quantity of output: seasonally adjusted real gross domestic product.
  - Quantity of domestic demand: sum of seasonally adjusted real consumption and investment expenditures.
  - Quantity of public domestic demand: sum of quadratically interpolated annual real consumption and investment expenditures of the general government.
  - Fiscal balance: quadratically interpolated annual overall fiscal balance of the general government, measured as the ratio of the fiscal balance to nominal output.
  - Current account balance: quadratically interpolated annual current account balance, measured as the ratio of the current account balance to nominal output.
  - Prices of energy and nonenergy commodities: proxied by broad commodity price indexes denominated in United States dollars.

### Financial market variables (definitions and measurement)
- Variables included:
  - Nominal policy interest rate
  - Short term nominal market interest rate
  - Long term nominal market interest rate
  - Price of equity
  - Nominal bilateral exchange rate
- Measurement definitions:
  - Nominal policy interest rate: central bank discount rate, expressed as a period average.
  - Short term nominal market interest rate: three month money market rate, expressed as a period average.
  - Long term nominal market interest rate: ten year government bond yield where available, and a ten year commercial bank lending rate otherwise, expressed as a period average.
  - Price of equity: proxied by a broad stock price index denominated in domestic currency units.
  - Nominal bilateral exchange rate: domestic currency price of one United States dollar expressed as a period average.

### Calibration, ratios, and weights
- Calibration is based on annual data obtained from databases compiled by the International Monetary Fund where available, and from the Bank for International Settlements or the World Bank Group otherwise.
- Great ratios are derived from the WEO and WDI databases.
- Bilateral trade weights are derived from the DOTS database.
- Portfolio weights are derived from the CPIS, BIS, and WDI databases.

*Appendix A. Description of the Data Set*

### Appendix B. Tables and Figures

### Appendix B. Tables and Figures

### Parameter estimation results (Table 1)
- Priors, posterior mean, posterior SE, and posterior mode reported for structural parameters (selected entries shown):
  - 1,1 φ: Prior 0.4900; Posterior SE 4.9e–3; Posterior mode 0.4897
  - 1,2 φ: Prior 0.4900; Posterior SE 4.9e–3; Posterior mode 0.4859
  - 1,1 θ: Prior 0.0075; Posterior SE 7.5e–4; Posterior mode 0.0077
  - 1,2 θ: Prior 0.3500; Posterior SE 3.5e–2; Posterior mode 0.3580
  - 2,1 θ: Prior 0.5000; Posterior SE 5.0e–2; Posterior mode 0.4879
  - 2,2 θ: Prior 0.3500; Posterior SE 3.5e–2; Posterior mode 0.3703
  - 3,1 φ: Prior 0.8500; Posterior SE 8.5e–3; Posterior mode 0.8467
  - 3,1 θ: Prior -0.7500; Posterior SE 7.5e–2; Posterior mode -0.7528
  - 3,2 θ: Prior -0.0150; Posterior SE 1.5e–3; Posterior mode -0.0156
  - 3,3 θ: Prior 0.5000; Posterior SE 5.0e–2; Posterior mode 0.5233
  - 3,4 θ: Prior -2.2500; Posterior SE 2.3e–2; Posterior mode -2.2445
  - 3,5 θ: Prior -1.0000; Posterior SE 1.0e–1; Posterior mode -1.0683
  - 4,1 θ: Prior 1.0000; Posterior SE 1.0e–1; Posterior mode 1.0463
  - 4,2 θ: Prior -1.2500; Posterior SE 1.3e–1; Posterior mode -1.2686
  - 5,1 φ: Prior 0.8500; Posterior SE 8.5e–3; Posterior mode 0.8498
  - 5,1,0 θ: Prior 1.2500; Posterior SE 1.3e–1; Posterior mode 1.2902 (reported for multiple countries)
  - 5,1,1 θ: Prior 1.5000; Posterior SE 1.5e–1; Posterior mode 1.5194 (reported for multiple countries)
  - 5,2,0 θ: Prior 0.1250; Posterior SE 1.3e–2; Posterior mode 0.1318 (reported for multiple countries)
  - 5,2,1 θ: Prior 0.1250; Posterior SE 1.3e–2; Posterior mode 0.1216 (reported for multiple countries)
  - 5,3,0 θ: Prior 0.0375; Posterior SE 3.8e–3; Posterior mode 0.0362 (reported for multiple countries)
  - 6,1 φ: Prior 0.2500; Posterior SE 2.5e–3; Posterior mode 0.2502
  - 6,1 θ: Prior -0.0025; Posterior SE 2.5e–4; Posterior mode -0.0025
  - 6,0 λ: Prior 1.0000; Posterior SE 1.0e–1; Posterior mode 0.9699 (reported for multiple countries)
  - 6,1 λ: Prior 0.5000; Posterior SE 5.0e–2; Posterior mode 0.4989 (reported for multiple countries)
  - 6,2 λ: Prior 1.5000; Posterior SE 1.5e–1; Posterior mode 1.5544 (reported for multiple countries)
  - 7,1 φ: Prior 0.2400; Posterior SE 2.4e–3; Posterior mode 0.2415
  - 7,2 φ: Prior 0.7400; Posterior SE 7.4e–3; Posterior mode 0.7409
  - 7,1 θ: Prior 0.1500; Posterior SE 1.5e–2; Posterior mode 0.1532
  - 7,0 λ: Prior 1.0000; Posterior SE 1.0e–1; Posterior mode 1.0372 (reported for multiple countries)
  - 7,1 λ: Prior 0.5000; Posterior SE 5.0e–2; Posterior mode 0.4895 (reported for multiple countries)
  - 7,2 λ: Prior 1.5000; Posterior SE 1.5e–1; Posterior mode 1.4786 (reported for multiple countries)
  - 8,1 φ: Prior 0.2400; Posterior SE 2.4e–3; Posterior mode 0.2398
  - 8,2 φ: Prior 0.7400; Posterior SE 7.4e–3; Posterior mode 0.7401
  - 8,1 θ: Prior 1.0000; Posterior SE 1.0e–1; Posterior mode 1.0336
  - 8,2 θ: Prior -1.0000; Posterior SE 1.0e–1; Posterior mode -0.9876
  - 8,3 θ: Prior -1.0000; Posterior SE 1.0e–1; Posterior mode -1.0017
  - 8,0 λ: Prior 1.2500; Posterior SE 1.3e–1; Posterior mode 1.2955 (reported for multiple countries)
  - 8,1 λ: Prior 0.6250; Posterior SE 6.3e–2; Posterior mode 0.6405 (reported for multiple countries)
  - 8,2 λ: Prior 1.8750; Posterior SE 1.9e–1; Posterior mode 1.9597 (reported for multiple countries)
  - 9,1 φ: Prior 0.2400; Posterior SE 2.4e–3; Posterior mode 0.2391
  - 9,2 φ: Prior 0.7400; Posterior SE 7.4e–3; Posterior mode 0.7394
  - 9,1,0 θ: Prior -1.0000; Posterior SE 1.0e–1; Posterior mode -0.9609 (reported for multiple countries)
  - 9,1,1 θ: Prior -0.2500; Posterior SE 2.5e–2; Posterior mode -0.2683 (reported for some countries)
  - 10,1 φ: Prior 0.2400; Posterior SE 2.4e–3; Posterior mode 0.2394
  - 10,2 φ: Prior 0.7400; Posterior SE 7.4e–3; Posterior mode 0.7402
  - 10,1 θ: Prior 0.0750; Posterior SE 7.5e–3; Posterior mode 0.0702
  - 10,2 θ: Prior -0.0500; Posterior SE 5.0e–3; Posterior mode -0.0488
  - 11,1 φ: Prior 0.8500; Posterior SE 8.5e–3; Posterior mode 0.8486
  - 11,1 θ: Prior 0.0100; Posterior SE 1.0e–3; Posterior mode 0.0097
  - 12,1 φ: Prior 0.8500; Posterior SE 8.5e–3; Posterior mode 0.8489
  - 12,1 θ: Prior -0.0100; Posterior SE 1.0e–3; Posterior mode -0.0103
  - 13,1 φ: Prior 0.2400; Posterior SE 2.4e–3; Posterior mode 0.2409
  - 13,2 φ: Prior 0.7400; Posterior SE 7.4e–3; Posterior mode 0.7409
  - 13,1,0 θ: Prior 0.7500; Posterior SE 7.5e–2; Posterior mode 0.7259
  - 13,1,1 θ: Prior 1.5000; Posterior SE 1.5e–1; Posterior mode 1.5123
- Prior/posterior correlations and hyperparameters (selected):
  - ˆY_P ρ: Prior 0.2500; Posterior SE 2.5e–2; Posterior mode 0.2497
  - ˆM_P ρ: Prior 0.7500; Posterior SE 7.5e–2; Posterior mode 0.7406
  - ˆC ρ: Prior 0.2500; Posterior SE 2.5e–2; Posterior mode 0.2452
  - ˆX ρ: Prior 0.7500; Posterior SE 7.5e–2; Posterior mode 0.7621
  - ˆS_i ρ: Prior 0.5000; Posterior SE 5.0e–2; Posterior mode 0.4603
  - ˆL_i ρ: Prior 0.2500; Posterior SE 2.5e–2; Posterior mode 0.2472
  - ˆSTK_P ρ: Prior 0.2500; Posterior SE 2.5e–2; Posterior mode 0.2612
  - ˆρ: Prior 0.5000; Posterior SE 5.0e–2; Posterior mode 0.5051
  - ˆρ (alternate): Prior 0.5000; Posterior SE 5.0e–2; Posterior mode 0.5165
  - ˆCOMP ρ: Prior 0.5000; Posterior SE 5.0e–2; Posterior mode 0.4917
- Selected posterior standard deviations (country cross-section; exact values reported per country):
  - 2ˆ,YPi σ: Argentina 1.6e–1; Australia 1.4e–1; Austria 1.3e–1; Belgium 1.8e–1; Brazil 1.4e–1; Canada 1.5e–1; China 1.6e–1; Czech Republic 1.5e–1; Denmark 1.4e–1; Finland 1.3e–1; France 1.4e–1; Germany 1.3e–1; Greece 1.4e–1; India 1.6e–1; Indonesia 1.6e–1; Ireland 1.4e–1; Italy 1.5e–1; Japan 1.6e–1; Korea 1.6e–1; Mexico 1.4e–1; Netherlands 1.7e–1; New Zealand 1.6e–1; Norway 1.6e–1; Poland 1.4e–1; Portugal 1.8e–1; Russia 1.9e–1; Saudi Arabia 1.8e–1; South Africa 1.4e–1; Spain 1.6e–1; Sweden 1.5e–1; Switzerland 2.1e–1
  - 2ˆ,MPi σ: Argentina 7.5e+0; Australia 6.7e+0; Austria 5.8e+0; Belgium 4.8e+0; Brazil 8.8e+0; Canada 5.7e+0; China 6.1e+0; Czech Republic 5.5e+0; Denmark 5.9e+0; Finland 5.9e+0; France 5.3e+0; Germany 5.6e+0; Greece 6.0e+0; India 6.7e+0; Indonesia 6.0e+0; Ireland 5.5e+0; Italy 6.1e+0; Japan 7.6e+0; Korea 6.4e+0; Mexico 6.8e+0; Netherlands 4.9e+0; New Zealand 6.8e+0; Norway 6.6e+0; Poland 6.2e+0; Portugal 5.7e+0; Russia 7.6e+0; Saudi Arabia 7.5e+0; South Africa 7.3e+0; Spain 5.4e+0; Sweden 5.9e+0; Switzerland 5.5e+0; Thailand 5.6e+0; Turkey 7.6e+0; United Kingdom 6.0e+0; United States 9.7e+0
  - 2ˆ,Ci σ, 2ˆ,Xi σ, 2ˆ,Pii σ, 2ˆ,Sii σ, 2ˆ,Lii σ, 2ˆ,STKPi σ, and many other country-specific posterior standard deviations are reported in the table with exact values per country (e.g., 2ˆ,Ci σ for Argentina 1.1e+0; 2ˆ,Xi σ for Argentina 1.1e+0; 2ˆ,Pii σ for Argentina 9.2e–1; etc.)
- Note: "All priors are normally distributed, while all posteriors are asymptotically normally distributed. All observed endogenous variables are rescaled by a factor of 100."

### Output gap estimates and decompositions (Figures 1–2)
- Figure 1: Output Gap Estimates — decomposition by source of demand
  - Decomposes smoothed estimates of the output gap into contributions from:
    - Domestic demand ■ (further decomposed into private domestic demand ■ and public domestic demand ■)
    - Net exports ■
  - Country panels provided for Argentina, Australia, Austria, Belgium, Brazil, Canada, China, Czech Republic, Denmark, Finland, France, Germany, Greece, India, Indonesia, Ireland, Italy, Japan, Korea, Mexico, Netherlands, New Zealand, Norway, Poland, Portugal, Russia, Saudi Arabia, South Africa, Spain, Sweden, Switzerland, Thailand, Turkey, United Kingdom, United States
  - Percent scales vary by country (examples):
    - Argentina: -25.0 to 25.0 Percent
    - Australia: -5.0 to 5.0 Percent
    - Greece: -25.0 to 25.0 Percent
    - Thailand: -20.0 to 20.0 Percent
- Figure 2: Output Gap Estimates — decomposition by source of stimulus
  - Decomposes smoothed estimates of the output gap into contributions from:
    - Monetary conditions ■ (decomposed into financial conditions ■ and terms of trade ■)
    - Real conditions ■
  - Country panels and percent scales as in Figure 1, with country-specific axis ranges (examples):
    - Argentina: -40.0 to 40.0 Percent
    - Turkey: -25.0 to 25.0 Percent
    - United Kingdom: -8.0 to 8.0 Percent

### Simulated correlations and impulse responses (Figures 3–11)
- Figure 3: Simulated unconditional correlations
  - Correlations depicted:
    - Consumption price inflation with lagged output gap ■
    - Consumption price inflation with lagged monetary conditions gap ■
    - Output gap with lagged monetary conditions gap ■
  - Simulated via Monte Carlo with 999 replications for 2T periods, discarding first T observations.
- Figures 4–11: Impulse responses to domestic shocks (country panels for each shock)
  - Common set of response variables in each figure:
    - Consumption price inflation ■ (annual percentage rates)
    - Output ■
    - Domestic demand ■
    - Nominal policy interest rate ■ (annual percentage rates where applicable)
    - Real effective exchange rate ■
    - Ratio of fiscal balance to nominal output ■
    - Ratio of current account balance to nominal output ■
  - Shocks and figure mappings:
    - Figure 4: Domestic supply shock — raises consumption price inflation by one percentage point.
    - Figure 5: Domestic private demand shock — raises domestic demand by one percent.
    - Figure 6: Domestic monetary policy shock — raises nominal policy interest rate by one percentage point.
    - Figure 7: Domestic credit risk premium shock — raises short-term nominal market interest rate by one percentage point.
    - Figure 8: Domestic duration risk premium shock — raises long-term nominal market interest rate by one percentage point.
    - Figure 9: Domestic equity risk premium shock — raises price of equity by ten percent.
    - Figure 10: Domestic fiscal expenditure shock — reduces fiscal balance to nominal output by one percentage point.
    - Figure 11: Domestic fiscal revenue shock — raises fiscal balance to nominal output by one percentage point.
  - Each impulse-response figure provides country-specific dynamic responses over horizons labeled 0,4,8,12,16,20 (quarters).

### World shocks and peak responses (Figures 12–33)
- Figures 12–13: Impulse responses to world commodity price shocks
  - Figure 12: World energy commodity price shock — raises price of energy commodities by ten percent.
  - Figure 13: World nonenergy commodity price shock — raises price of nonenergy commodities by ten percent.
- Figures 26–33: Peak impulse responses to foreign (systemic economies) shocks
  - Peak responses depicted for:
    - Foreign supply shocks (Figure 26)
    - Foreign private demand shocks (Figure 27)
    - Foreign monetary policy shocks (Figure 28)
    - Foreign credit risk premium shocks (Figure 29)
    - Foreign duration risk premium shocks (Figure 30)
    - Foreign equity risk premium shocks (Figure 31)
    - Foreign fiscal expenditure shocks (Figure 32)
    - Foreign fiscal revenue shocks (Figure 33)
  - For each, peak responses shown for consumption price inflation ■, output ■, real effective exchange rate ■, fiscal balance ratio ■, current account ratio ■ to shocks in systemic economies CHN, EUR, JPN, GBR, USA.

### Forecast error variance decompositions (Figures 14–20)
- Figures decompose horizon-dependent forecast error variance into contributions from:
  - Domestic supply ■
  - Foreign supply ■
  - Domestic demand ■
  - Foreign demand ■
  - World monetary policy ■
  - World fiscal policy ■
  - World risk premium ■
  - World terms of trade ■
- Variables covered with country panels and horizons 0,4,8,12,16,20:
  - Figure 14: Consumption price inflation
  - Figure 15: Output
  - Figure 16: Domestic demand
  - Figure 17: Nominal policy interest rate
  - Figure 18: Real effective exchange rate
  - Figure 19: Fiscal balance (ratio to nominal output)
  - Figure 20: Current account balance (ratio to nominal output)

### Historical decompositions (Figures 21–24)
- Historical decompositions express observed series as sum of trend component and contributions from the same eight shock categories:
  - Figure 21: Consumption price inflation (seasonal log difference of consumption price level); panels cover 2005–2011 with country-specific percent scales.
  - Figure 22: Output growth (seasonal log difference of level of output); panels cover 2005–2011 with country-specific percent scales.
  - Figure 23: Fiscal balance (ratio to nominal output); panels cover 2005–2011 with country-specific percent scales.
  - Figure 24: Current account balance (ratio to nominal output); panels cover 2005–2011 with country-specific percent scales.

### Simulated conditional betas and forecast results (Figures 25, 34–39)
- Figure 25: Simulated conditional betas of the output gap
  - Betas of output gap with respect to contemporaneous output gap in systemic economies conditional on:
    - All shocks ■
    - Macroeconomic shocks ■
    - Financial shocks ■
  - Monte Carlo simulation with 999 replications for 2T periods; discard first T.
- Figures 34–35: Sequential unconditional forecasts
  - Figure 34: Consumption price inflation — observed versus sequential unrestricted forecasts (2007–2013 panels by country).
  - Figure 35: Output growth — observed versus sequential unrestricted forecasts (2007–2013 panels by country).
- Figures 36–37: Conditional forecasts (2007–2013)
  - Figure 36: Consumption price inflation — observed ■, unrestricted forecasts ■, restricted forecasts ■, judgmental forecasts ■, combined forecasts ■; symmetric 90 percent confidence intervals shown (dashed).
  - Figure 37: Output growth — same forecast categories and confidence intervals.
- Figures 38–39: Conditional forecast decompositions
  - Figure 38: Consumption price inflation — decomposes difference between combined forecasts and unrestricted forecasts into trend and contributions from the eight shock categories.
  - Figure 39: Output growth — analogous decomposition for output growth.

*Appendix B. Tables and Figures — extracted content as presented in the source PDF.*

### References

### _wp12149 - References

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*Content unit: _wp12149 - References*

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