## wp1789 — Appendix A–B summary

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---

### Model structure and key features
- Panel dynamic stochastic general equilibrium (DSGE) model of the world economy disaggregated into forty national economies.
- Core structural elements:
  - Short run nominal price and wage rigidities via monopolistic competition, staggered reoptimization, and partial indexation.
  - Habit persistence in consumption, adjustment costs in residential and business investment, variable capital utilization, and involuntary unemployment.
  - Households differentiated into three types: bank intermediated, capital market intermediated, and credit constrained.
  - Banks perform global financial intermediation subject to financial frictions and regulatory constraints; issue risky mortgage and corporate loans at infrequently adjusted predetermined rates.
  - Financial accelerator mechanisms linked to collateralized borrowing by developers and firms.
  - Short run incomplete exchange rate pass through with import price rigidities.
- Solution and estimation:
  - Approximate linear state space representation estimated by Bayesian maximum likelihood conditional on priors common across economies.
  - Theoretical steady state assumes zero inflation, productivity and labor force growth, and public and national financial wealth except where specified.

### Agents and sectors (concise)
- Households:
  - Three types: bank intermediated (measure Bϕ with 01Bϕ), capital market intermediated (measure Aϕ with 01Aϕ), credit constrained (measure Cϕ with 01Cϕ and Bϕ+Aϕ+Cϕ=1).
  - Preferences include consumption, housing services, labor supply, real property balances, and portfolio balances with external habit formation and CES sub-utilities.
  - Bank-intermediated households hold deposits and domestic real estate; capital-market intermediated households hold internationally diversified bonds and equities.
- Developers and housing:
  - Housing produced by monopolistically competitive developers; developers maintain debt equal to a fraction of housing value given mortgage loan to value ratio limit Dϕ.
  - Residential investment features convex adjustment costs; housing stock evolves with depreciation Hδ where 01Hδ.
- Firms and production:
  - Multi-industry production with energy (k=1) and nonenergy commodity (k=2) industries producing internationally homogeneous goods; other industries produce heterogeneous goods.
  - Firms maintain corporate debt equal to a fraction of physical capital value given corporate loan to value limit Fϕ.
  - Business investment with convex adjustment costs; capital utilization costs increasing in utilization.
- Banking:
  - Intermediate banks issue differentiated mortgage and corporate loans, obtain deposits and money market funding, accumulate bank capital from retained earnings, and satisfy regulatory capital requirement Rκ.
  - Loan rate stickiness: intermediary banks adjust gross loan rates infrequently (Calvo-style) with fraction Cω of non-adjusting banks.
  - Regulation cost decreases in capital-to-assets ratio; bank capital evolves with destruction and retained earnings adjustment costs.

### International trade, prices, and financial markets
- Exchange rates and terms of trade:
  - Nominal effective exchange rate Eit, real effective exchange rate Θit, internal and external terms of trade definitions; endogenous terms of trade shifter υT ensures multilateral trade consistency.
  - Commodity prices (energy and nonenergy) modeled with Phillips-curve–type dynamics and depend on world variables.
- Portfolio and asset pricing:
  - Portfolio returns and prices incorporate international diversification and risk premia (duration, equity, housing risk premia).
  - Long term bonds modeled as perpetual bonds with coupon decay at rate Bω.
- Market clearing and external accounts:
  - Final goods, import, export, and bank loan markets clear. Current account equals national saving less investment; multilateral consistency imposes world-weighted balances sum to zero.

### Policy frameworks embedded
- Monetary policy:
  - Nominal policy interest rate follows a partial-adjustment rule (equation (109)/(151)) accommodating flexible inflation targeting (j=0), managed exchange rate (j=1), and fixed exchange rate regimes (j=2); for fixed regimes rule can track anchor economy yields with parameter values such as iξ=1.
  - Monetary policy shocks Pν are mean zero and serially uncorrelated.
- Fiscal policy:
  - Public consumption follows a countercyclical expenditure rule with partial adjustment (equation (110)); tax rates on corporate earnings and labor income follow acyclical revenue rules with partial adjustment (equation (111)); real lump-sum transfers to credit constrained households follow rule (112).
  - Money market relationship links gross short-term bond yield to nominal policy rate with credit risk premium Sυ (equation (113)).
  - Government dynamic budget constraint aggregates public financial wealth holdings and flows (equation (114)).
- Macroprudential policy:
  - Regulatory capital requirement follows a countercyclical capital buffer rule with partial adjustment (equation (115)).
  - Loan-to-value ratio limits for mortgages and corporate loans follow partial-adjustment rules (equation (116)).
  - Loan default rates follow partial-adjustment attractor relationships (equation (117)).
  - Macroprudential shocks νκ, νϕ and default shocks enter as stochastic drivers.

### Empirical framework, data and estimation
- Linearization and estimation:
  - Equilibrium conditions linearized around deterministic steady state; response coefficients depend on structural parameters, some restricted to coincide across economies.
  - Estimation by Bayesian maximum likelihood with multivariate normal priors; inference based on asymptotic normal approximation around posterior mode (differential evolution algorithm for optimization).
- Data and sample:
  - Estimation uses cyclical components of 659 endogenous variables for forty economies over 1999Q1 through 2016Q1.
  - Economies: Argentina, Australia, Austria, Belgium, Brazil, Canada, Chile, China, Colombia, the Czech Republic, Denmark, Finland, France, Germany, Greece, India, Indonesia, Ireland, Israel, Italy, Japan, Korea, Malaysia, Mexico, the Netherlands, New Zealand, Norway, the Philippines, Poland, Portugal, Russia, Saudi Arabia, South Africa, Spain, Sweden, Switzerland, Thailand, Turkey, the United Kingdom, and the United States.
  - Observed variables include: output and consumption prices, quantities (output, private consumption, exports, imports), nominal policy, money market and long-term rates, housing and equity prices, bilateral exchange rates, wages, unemployment, employment, public domestic demand, fiscal balance ratio, commodity prices.
- Data preprocessing:
  - Cyclical components estimated via Hodrick-Prescott–type filter generalized by Vitek (2014).
  - For variables with long run growth: difference order = 2 and smoothing parameter = 16,000.
  - For non-growing variables: difference order = 1 and smoothing parameter = 400.
- Prior calibration and regime classification:
  - Monetary regimes assigned consistent with IMF (2015); flexible inflation targeting in Australia, Canada, Chile, the Euro Area, Japan, Mexico, Norway, Poland, Sweden, the United Kingdom and the United States; managed exchange rate in Argentina, Brazil, China, Colombia, the Czech Republic, India, Indonesia, Israel, Korea, Malaysia, New Zealand, the Philippines, Russia, South Africa, Switzerland, Thailand and Turkey; fixed exchange rate in Denmark and Saudi Arabia.
  - Contagion classifications: listed high and low debt and equity contagion economies.
  - Quotation currency: United States.
- Estimation results:
  - Parameter posterior means reported in Appendix B (Table 1 and Table 2); most posterior means close to priors due to tight priors, but several parameters updated substantially by data.
  - Estimation period effectively 1999Q3 through 2016Q1 for parameter results.

### Inference: impulse response and historical decomposition findings
- Shock categories analyzed: domestic and foreign productivity, labor supply, consumption, residential and business investment demand shocks; credit, duration, housing and equity risk premia; mortgage and corporate loan rate markups and defaults; monetary, government expenditure, tax rates, capital requirement and loan-to-value limit shocks; currency risk premium and commodity price markup shocks.
- Representative dynamic effects (median responses, cross-economy patterns):
  - Aggregate supply shocks:
    - Output rises less than potential → output gap falls; unemployment rises; lower price and wage inflation.
    - Monetary authority cuts nominal policy rate; capital-market and bank lending rates decline; currency depreciates; terms of trade worsen; money and bank credit rise.
    - Productivity shock: employment falls; labor supply shock: employment rises.
    - Fiscal balance ratio falls despite higher tax revenues (higher public domestic demand); net government debt ratio falls due to higher potential output.
    - Current account balance ratio falls; net foreign asset ratio falls; rest-of-world exports and output increase.
  - Aggregate demand shocks:
    - Output rises more than potential → output gap rises; unemployment falls; higher price and wage inflation.
    - Monetary authority raises nominal policy rate; capital-market and bank lending rates increase; currency appreciates; terms of trade improve.
    - Money and bank credit rise; employment rises.
    - Fiscal balance ratio improves → net government debt ratio falls.
    - Current account balance ratio falls → net foreign asset ratio falls; rest-of-world exports and output increase.
  - Credit/duration risk premium shocks:
    - Tightening reduces private domestic demand—particularly residential and business investment.
    - Output falls more than potential → output gap falls; unemployment rises; lower price and wage inflation.
    - Quantitative examples:
      - A one percentage point credit risk premium induced nominal money market interest rate increase → 0.5 percent median peak output loss.
      - A one percentage point nominal long term bond yield increase via duration risk premium → 0.4 percent median peak output loss.
    - Monetary authority cuts nominal policy rate but money stock and bank credit fall; employment falls; fiscal balance ratio deteriorates; net government debt ratio rises; current account balance ratio improves; net foreign asset ratio rises; rest-of-world exports and output fall.
    - International contagion transmits higher money market rates or long-term yields to recipient economies.
  - Housing and equity risk premium shocks:
    - Housing risk premium (price of housing +10 percent) raises consumption and residential investment; equity risk premium (price of equity +10 percent) raises all private demand components.
    - Output rises more than potential → output gap rises; unemployment falls; higher price and wage inflation.
    - Quantitative magnitudes:
      - A ten percent housing price increase via housing risk premium → 0.7 percent median peak output gain.
      - A ten percent equity price increase via equity risk premium → 0.2 percent median peak output gain.
    - Monetary authority raises the policy rate; currency appreciates; bank capital ratio rises; employment rises; fiscal balance improves; current account weakens; rest-of-world exports and output increase.
  - Mortgage and corporate loan rate markups and default shocks:
    - Increases in loan rates or defaults tighten financial conditions, lowering private demand and output more than potential → output gap falls; unemployment rises; lower inflation and wages.
    - Monetary authority cuts policy rate; currency depreciates; money stock and bank credit fall (for rate markups) or bank capital ratio falls (for defaults); employment falls; fiscal balance deteriorates; net government debt rises; current account improves; rest-of-world exports and output fall.
    - Corporate loan shocks propagate internationally via nonfinancial corporate borrowing weights.

### Policy transmission and macroprudential roles
- Monetary transmission:
  - Raising nominal policy rate increases capital market and bank lending rates, tightens financial conditions, reduces private demand, appreciates currency, improves terms of trade, reduces exports via expenditure switching, and lowers output relative to potential; output gap falls and unemployment rises.
  - Example magnitudes consistent with other numerical examples (e.g., one percentage point nominal policy rate increase generates substantial median peak output losses).
- Fiscal transmission:
  - Countercyclical public consumption and tax rules stabilize public and national financial wealth; transfers to credit constrained households redistribute wealth and equalize steady-state consumption across households.
  - Government budget dynamics explicitly tracked; fiscal rules respond to public and national asset ratios.
- Macroprudential transmission:
  - Countercyclical capital buffer and loan-to-value limit rules adjust regulatory requirements in response to credit growth and asset price changes.
  - Macroprudential instruments influence bank lending rates, credit growth, and asset prices via regulatory constraints and loan-to-value limits, interacting with monetary and fiscal policy to affect output and financial stability.

### Empirical results: business cycle, output gap, and historical decompositions
- Output gap estimation:
  - Output gap is model-defined; smoothed full-sample estimates and decompositions into capital vs. labor utilization contributions reported (Figure 1).
  - Historical patterns:
    - Gradual global expansion up to the Global Financial Crisis (GFC), synchronized across advanced and emerging economies.
    - Abrupt synchronized contraction during the GFC, concentrated in advanced economies.
    - Protracted contractions in the Euro Area periphery during the Euro Area Sovereign Debt Crisis.
    - Post-crisis divergence: advanced economies experienced sluggish expansions, emerging economies experienced contractions.
  - Attribution:
    - Advanced-economy cycle dynamics primarily driven by labor utilization fluctuations.
    - Emerging-economy cycle dynamics primarily driven by capital utilization fluctuations.
- Historical decompositions:
  - Deviations of consumption price inflation from trend primarily attributed to economy-specific combinations of domestic and foreign macroeconomic and financial shocks, and world terms of trade shocks.
  - Contribution of domestic vs foreign shocks generally decreases with trade openness and increases with monetary policy autonomy.
  - Output growth deviations primarily attributed to economy-specific domestic and foreign macroeconomic and financial shocks; financial shocks generally amplified business cycle fluctuations, policy shocks generally mitigated them.
  - Global patterns summarized for pre-GFC, GFC, and post-crisis periods.

### Forecasting and predictive performance
- Sequential unconditional forecasts of inflation and output growth:
  - Holdout sample: 2005Q2 through 2016Q1, horizons one through eight quarters.
  - Benchmark: driftless random walk; performance measured by logarithm of the U statistic.
  - Results:
    - Inflation: root mean squared prediction error reductions 27 percent lower (on average across economies and horizons) relative to random walk.
    - Output growth: root mean squared prediction error reductions 34 percent lower (on average across economies and horizons) relative to random walk.
  - Sequential unconditional forecasts capable of predicting business cycle turning points and fairly accurately predicted the severity of the synchronized global contraction at the GFC for most economies.

### Estimation practice, simplifications, and identification
- Restricted approximation for estimation:
  - Estimation generally uses a restricted approximate linear rational expectations representation consolidating or eliminating weakly identified exogenous variables (e.g., residential and business investment demand consolidated; corporate and labor tax shocks consolidated).
  - Impulse response analysis uses the unrestricted representation.
- Identification and normalization:
  - Bilateral and world weights calibrated using 2014 observed values normalized to sum to one.
  - Macroeconomic and financial great ratios calibrated to match observed or averaged values in 2014.
  - All innovations assumed independent and multivariate normal for identification.

### Data and calibration (key points)
- Sample period for estimation: 1999Q1 through 2016Q1.
- Number of economies: forty (listed above).
- Data sources: GDS, WEO, Bloomberg, Bank for International Settlements, IFS, WDI, DOTS, CPIS (where available).
- Key variable measurements:
  - Price of output: seasonally adjusted GDP price deflator.
  - Price of consumption: seasonally adjusted consumer price index.
  - Quantity of output: seasonally adjusted real GDP.
  - Quantity of private consumption: seasonally adjusted real private consumption expenditures.
  - Exports/imports: seasonally adjusted real export revenues/import expenditures.
  - Price of housing: broad residential property price index.
  - Nominal wage: derived from quadratically interpolated annual labor income share.
  - Unemployment rate: seasonally adjusted share of total unemployment in total labor force.
  - Employment: seasonally adjusted total employment.
  - Public domestic demand: sum of quadratically interpolated annual real consumption and investment expenditures of general government.
  - Fiscal balance: quadratically interpolated annual overall fiscal balance of general government.
  - Energy and nonenergy commodity prices: broad commodity price indexes in United States dollars.
  - Financial market variables: central bank policy rate, three month Treasury bill yield, ten year government bond yield, broad stock price index in domestic currency, domestic currency price of one United States dollar. All financial variables expressed as period average values.
- Calibration: based on annual data from IMF, BIS, and World Bank Group databases; macroeconomic and financial great ratios from WEO, WDI, BIS, and IFS; bilateral trade and financial weights from DOTS, BIS, CPIS, and WDI.

### Appendix B highlights — parameters, figures, and experiments
- Parameter estimation — endogenous variables (Table 1):
  - Selected posterior means (examples preserve numeric precision):
    - C α: Post. Mean 0.9040
    - L α: Post. Mean 0.6999
    - G ρ: Post. Mean 0.8037
    - H χ: Post. Mean 2.1093
    - K χ: Post. Mean 1.2974
    - B χ: Post. Mean 1.4882
    - C χ: Post. Mean 10.0127
    - σ: Post. Mean 2.7111
    - V: Post. Mean 0.0999
    - η: Post. Mean 0.0100
    - K η: Post. Mean 0.4978
    - π ξ0: Post. Mean 1.7586
    - ... (Table 1 contains many additional parameter priors and posteriors reported with exact numeric precision).
- Parameter estimation — exogenous variables (Table 2):
  - Selected posterior means and variance entries (scientific notation preserved where used):
    - ρA: Post. Mean 0.7883
    - ρN: Post. Mean 0.7990
    - C νρ: Post. Mean 0.3749
    - I νρ: Post. Mean 0.6189
    - X νρ: Post. Mean 0.7976
    - 2 M νσ: Post. Mean 8.86×10+0
    - 2 Y θσ: Post. Mean 2.34×10+6
    - 2 L θσ: Post. Mean 1.97×10+7
    - 2 M θσ: Post. Mean 9.72×10+3
    - 2 H νσ: Post. Mean 1.51×10+0
    - 2 B νσ: Post. Mean 6.67×10−1
    - 2 S νσ: Post. Mean 1.32×10+1
    - 2 σA: Post. Mean 6.08×10−2
    - 2 σN: Post. Mean 1.16×10+0
    - 2 I νσ: Post. Mean 3.06×10+0
    - 2 X νσ: Post. Mean 6.02×10+0
    - ... (Table 2 contains many additional variance and scale parameters reported with exact numeric precision).
- Figure set and impulse response experiments:
  - Figure 1: Output Gap Estimates decomposed into capital and labor utilization contributions for all forty economies (years 2000–2016).
  - Figures 2–44: Impulse responses to a comprehensive set of normalized shocks (examples preserve normalization exactly):
    - Productivity shocks (one percent increase in potential output)
    - Consumption shocks (consumption +1 percent)
    - Residential investment shocks (residential investment +1 percent)
    - Business investment shocks (business investment +1 percent)
    - Credit risk premium shocks (nominal money market interest rate +1 percentage point)
    - Duration risk premium shocks (nominal long term bond yield +1 percentage point)
    - Housing risk premium shocks (price of housing +10 percent)
    - Equity risk premium shocks (price of equity +10 percent)
    - Mortgage and corporate loan rate markup shocks (nominal mortgage/corporate loan rate +1 percentage point)
    - Default shocks (mortgage/corporate loan default rate +1 percentage point)
    - Monetary policy shocks (nominal policy interest rate +1 percentage point)
    - Government expenditure and tax shocks (primary fiscal balance ratio +1 percentage point)
    - Capital requirement shocks (bank capital ratio requirement +1 percentage point)
    - Loan-to-value limit shocks (mortgage/corporate LTV limit −1 percentage point)
    - Currency risk premium shocks (currency depreciates by ten percent in nominal effective terms)
    - Energy and nonenergy commodity price markup shocks (price +10 percent)
  - Impulse response panels report a wide set of variables with units preserved exactly (e.g., Consumption Price Inflation (Percentage Points), Output (Percent), Nominal Policy Interest Rate (Percentage Points), Money Stock (Percent), Bank Credit (Percent), Unemployment Rate (Percentage Points), Net Government Debt Ratio (Percentage Points), Net Foreign Asset Ratio (Percentage Points), Price of Energy Commodities (Percent), etc.).
- Figures 45–46: Historical decompositions of consumption price inflation and output growth into trend and shock-group contributions (domestic/foreign macroeconomic, domestic/foreign financial, domestic/foreign policy, world terms of trade) for 2005–2016.
- Figures 47–49: Forecast performance statistics and sequential unconditional forecasts of consumption price inflation and output growth (holdout sample performance horizons 1–8 quarters; panels through 2018 for sequential forecasts).

*Source: wp1789 (paper content provided in source PDF).*

### Appendix A. Data Description ...........................................................................................

### Appendix A. Data Description

### Location
- Page: 67

### Appendix B. Tables and Figures

### Location
- Page: 69

### Tables
- Table 1. Parameter Estimation Results, Endogenous Variables
- Table 2. Parameter Estimation Results, Exogenous Variables

### Figures
- Figure 1. Output Gap Estimates
- Figure 2. Impulse Responses to a Domestic Productivity Shock
- Figure 3. Impulse Responses to a Foreign Productivity Shock
- Figure 4. Impulse Responses to a Domestic Labor Supply Shock
- Figure 5. Impulse Responses to a Foreign Labor Supply Shock
- Figure 6. Impulse Responses to a Domestic Consumption Demand Shock
- Figure 7. Impulse Responses to a Foreign Consumption Demand Shock
- Figure 8. Impulse Responses to a Domestic Residential Investment Demand Shock
- Figure 9. Impulse Responses to a Foreign Residential Investment Demand Shock
- Figure 10. Impulse Responses to a Domestic Business Investment Demand Shock
- Figure 11. Impulse Responses to a Foreign Business Investment Demand Shock
- Figure 12. Impulse Responses to a Domestic Credit Risk Premium Shock
- Figure 13. Impulse Responses to a Foreign Credit Risk Premium Shock
- Figure 14. Impulse Responses to a Domestic Duration Risk Premium Shock
- Figure 15. Impulse Responses to a Foreign Duration Risk Premium Shock
- Figure 16. Impulse Responses to a Domestic Housing Risk Premium Shock
- Figure 17. Impulse Responses to a Foreign Housing Risk Premium Shock
- Figure 18. Impulse Responses to a Domestic Equity Risk Premium Shock
- Figure 19. Impulse Responses to a Foreign Equity Risk Premium Shock
- Figure 20. Impulse Responses to a Domestic Mortgage Loan Rate Markup Shock
- Figure 21. Impulse Responses to a Foreign Mortgage Loan Rate Markup Shock
- Figure 22. Impulse Responses to a Domestic Corporate Loan Rate Markup Shock
- Figure 23. Impulse Responses to a Foreign Corporate Loan Rate Markup Shock
- Figure 24. Impulse Responses to a Domestic Mortgage Loan Default Shock
- Figure 25. Impulse Responses to a Foreign Mortgage Loan Default Shock
- Figure 26. Impulse Responses to a Domestic Corporate Loan Default Shock
- Figure 27. Impulse Responses to a Foreign Corporate Loan Default Shock
- Figure 28. Impulse Responses to a Domestic Monetary Policy Shock
- Figure 29. Impulse Responses to a Foreign Monetary Policy Shock
- Figure 30. Impulse Responses to a Domestic Government Expenditure Shock
- Figure 31. Impulse Responses to a Foreign Government Expenditure Shock
- Figure 32. Impulse Responses to a Domestic Corporate Tax Rate Shock
- Figure 33. Impulse Responses to a Foreign Corporate Tax Rate Shock
- Figure 34. Impulse Responses to a Domestic Labor Income Tax Rate Shock
- Figure 35. Impulse Responses to a Foreign Labor Income Tax Rate Shock
- Figure 36. Impulse Responses to a Domestic Capital Requirement Shock
- Figure 37. Impulse Responses to a Foreign Capital Requirement Shock
- Figure 38. Impulse Responses to a Domestic Mortgage Loan to Value Limit Shock
- Figure 39. Impulse Responses to a Foreign Mortgage Loan to Value Limit Shock
- Figure 40. Impulse Responses to a Domestic Corporate Loan to Value Limit Shock
- Figure 41. Impulse Responses to a Foreign Corporate Loan to Value Limit Shock
- Figure 42. Impulse Responses to a Currency Risk Premium Shock
- Figure 43. Impulse Responses to an Energy Commodity Price Markup Shock
- Figure 44. Impulse Responses to a Nonenergy Commodity Price Markup Shock
- Figure 45. Historical Decompositions of Consumption Price Inflation
- Figure 46. Historical Decompositions of Output Growth
- Figure 47. Forecast Performance Evaluation Statistics
- Figure 48. Sequential Unconditional Forecasts of Consumption Price Inflation
- Figure 49. Sequential Unconditional Forecasts of Output Growth

*wp1789 - Appendix A. Data Description (pdf)*

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

### wp1789 - References

### H3 Model structure and key features
- Panel dynamic stochastic general equilibrium (DSGE) model of the world economy disaggregated into forty national economies.
- Core structural elements:
  - Short run nominal price and wage rigidities via monopolistic competition, staggered reoptimization, and partial indexation (following Smets and Wouters (2003) and Christiano, Eichenbaum and Evans (2005)).
  - Habit persistence in consumption, adjustment costs in residential and business investment, variable capital utilization, and involuntary unemployment (Galí (2011)).
  - Households differentiated into three types: bank intermediated, capital market intermediated, and credit constrained.
  - Banks perform global financial intermediation subject to financial frictions and regulatory constraints; issue risky mortgage and corporate loans at infrequently adjusted predetermined rates (building on Hülsewig, Mayer and Wollmershäuser (2009) and Gerali, Neri, Sessa and Signoretti (2010)).
  - Financial accelerator mechanisms linked to collateralized borrowing by developers and firms (Kiyotaki and Moore (1997)).
  - Short run incomplete exchange rate pass through with import price rigidities (Monacelli (2005)).
- Solution and estimation:
  - Approximate linear state space representation estimated by Bayesian maximum likelihood, conditional on prior information concerning generally common structural parameters across economies.
  - Theoretical steady state assumes zero inflation, productivity and labor force growth, and public and national financial wealth, except where otherwise specified.

### H3 Agents and sectors (concise)
- Households:
  - Three types: bank intermediated (measure Bϕ with 01Bϕ), capital market intermediated (measure Aϕ with 01Aϕ), credit constrained (measure Cϕ with 01Cϕ and Bϕ+Aϕ+Cϕ=1).
  - Preferences include consumption, housing services, labor supply, real property balances, and portfolio balances with external habit formation and CES sub-utilities.
  - Bank-intermediated households hold deposits and domestic real estate; capital-market intermediated households hold internationally diversified bonds and equities.
- Developers and housing:
  - Housing produced via monopolistically competitive developers; developers maintain debt equal to a fraction of housing value given mortgage loan to value ratio limit Dϕ (financial accelerator).
  - Residential investment features convex adjustment costs; housing stock evolution with depreciation Hδ where 01Hδ.
- Firms and production:
  - Multi-industry production with energy (k=1) and nonenergy commodity (k=2) industries producing internationally homogeneous goods; other industries produce heterogeneous goods.
  - Firms maintain corporate debt equal to a fraction of physical capital value given corporate loan to value limit Fϕ (financial accelerator).
  - Business investment with convex adjustment costs; capital utilization costs increasing in utilization.
- Banking:
  - Intermediate banks issue differentiated mortgage and corporate loans, obtain deposits and money market funding, accumulate bank capital from retained earnings, and satisfy a regulatory capital requirement Rκ.
  - Loan rate stickiness: intermediary banks adjust gross loan rates infrequently (Calvo-style) with fraction Cω of non-adjusting banks.
  - Regulation cost decreases in capital-to-assets ratio; bank capital evolves with destruction and retained earnings adjustment costs.

### H3 International trade, prices, and financial markets
- Exchange rates and terms of trade:
  - Nominal effective exchange rate Eit, real effective exchange rate Θit, internal and external terms of trade definitions; endogenous terms of trade shifter υT ensures multilateral trade consistency.
  - Commodity prices (energy and nonenergy) modeled with Phillips-curve–type dynamics and depend on world variables.
- Portfolio and asset pricing:
  - Portfolio returns and prices incorporate international diversification and risk premia (duration, equity, housing risk premia).
  - Long term bonds modeled as perpetual bonds with coupon decay at rate Bω (Woodford (2001)).
- Market clearing and external accounts:
  - Final goods, import, export, and bank loan markets clear. Current account equals national saving less investment; multilateral consistency imposes world-weighted balances sum to zero.

### H3 Policy frameworks embedded
- Monetary policy:
  - Nominal policy interest rate follows a partial-adjustment rule (equation (109)/(151)) that accommodates flexible inflation targeting (j=0), managed exchange rate (j=1), and fixed exchange rate regimes (j=2). For fixed regimes, rule can track anchor economy yields with parameter values such as iξ=1 in that case.
  - Monetary policy shocks Pν are mean zero and serially uncorrelated.
- Fiscal policy:
  - Public consumption follows a countercyclical expenditure rule with partial adjustment (equation (110)); tax rates on corporate earnings and labor income follow acyclical revenue rules with partial adjustment (equation (111)); real lump-sum transfers to credit constrained households follow rule (112).
  - Money market relationship links gross short-term bond yield to nominal policy rate with credit risk premium Sυ (equation (113)).
  - Government dynamic budget constraint aggregates public financial wealth holdings and flows (equation (114)).
- Macroprudential policy:
  - Regulatory capital requirement follows a countercyclical capital buffer rule with partial adjustment (equation (115)).
  - Loan-to-value ratio limits for mortgages and corporate loans follow partial-adjustment rules (equation (116)).
  - Loan default rates follow partial-adjustment attractor relationships (equation (117)).
  - Macroprudential shocks νκ, νϕ and default shocks enter as stochastic drivers.

### H3 Empirical framework, data and estimation
- Linearization and estimation:
  - Equilibrium conditions linearized around deterministic steady state; response coefficients depend on structural parameters, some restricted to coincide across economies.
  - Estimation by Bayesian maximum likelihood with multivariate normal priors; inference based on asymptotic normal approximation around posterior mode (differential evolution algorithm for optimization).
- Data and sample:
  - Estimation uses cyclical components of 659 endogenous variables for forty economies over 1999Q1 through 2016Q1.
  - Economies: Argentina, Australia, Austria, Belgium, Brazil, Canada, Chile, China, Colombia, the Czech Republic, Denmark, Finland, France, Germany, Greece, India, Indonesia, Ireland, Israel, Italy, Japan, Korea, Malaysia, Mexico, the Netherlands, New Zealand, Norway, the Philippines, Poland, Portugal, Russia, Saudi Arabia, South Africa, Spain, Sweden, Switzerland, Thailand, Turkey, the United Kingdom, and the United States.
  - Observed variables include: output and consumption prices, quantities (output, private consumption, exports, imports), nominal policy, money market and long-term rates, housing and equity prices, bilateral exchange rates, wages, unemployment, employment, public domestic demand, fiscal balance ratio, commodity prices.
- Data preprocessing:
  - Cyclical components estimated via Hodrick-Prescott–type filter generalized by Vitek (2014).
  - For variables with long run growth (prices, quantities, housing price, equity price, bilateral exchange rate, wage, employment, public domestic demand, commodity prices): difference order = 2 and smoothing parameter = 16,000.
  - For non-growing variables (policy rate, money market rate, long term yield, unemployment, fiscal balance ratio): difference order = 1 and smoothing parameter = 400.
- Prior calibration and regime classification:
  - Monetary regimes assigned consistent with IMF (2015): flexible inflation targeting in Australia, Canada, Chile, the Euro Area, Japan, Mexico, Norway, Poland, Sweden, the United Kingdom and the United States; managed exchange rate in Argentina, Brazil, China, Colombia, the Czech Republic, India, Indonesia, Israel, Korea, Malaysia, New Zealand, the Philippines, Russia, South Africa, Switzerland, Thailand and Turkey; fixed exchange rate in Denmark and Saudi Arabia.
  - Contagion classifications: high debt contagion economies: Argentina, Brazil, Colombia, Indonesia, Mexico, the Philippines, Poland, Russia, South Africa, Thailand and Turkey; low debt contagion: Chile, China, India, Malaysia. High equity contagion economies: Argentina, Brazil, Colombia, India, Indonesia, Mexico, the Philippines, Poland, Russia, South Africa, Thailand and Turkey; low equity contagion: Chile, China, Malaysia.
  - Quotation currency: United States.
- Estimation results:
  - Parameter posterior means reported in Appendix B (Table 1 and Table 2); most posterior means close to priors due to tight priors, but several parameters updated substantially by data.
  - Estimation period effectively 1999Q3 through 2016Q1 for parameter results.

### H3 Inference: impulse response and historical decomposition findings
- Shock categories analyzed: domestic and foreign productivity, labor supply, consumption, residential and business investment demand shocks; credit, duration, housing and equity risk premia; mortgage and corporate loan rate markups and defaults; monetary, government expenditure, tax rates, capital requirement and loan-to-value limit shocks; currency risk premium and commodity price markup shocks.
- Representative dynamic effects (median responses, cross-economy patterns):
  - Aggregate supply shocks (productivity or labor supply increase):
    - Output rises less than potential → output gap falls; unemployment rises; lower price and wage inflation.
    - Monetary authority cuts nominal policy rate; capital-market and bank lending rates decline; currency depreciates (nominal and real), worsening terms of trade; money and bank credit rise.
    - For productivity shock: employment falls (higher labor productivity). For labor supply shock: employment rises (larger labor force).
    - Fiscal balance ratio falls despite higher tax revenues (higher public domestic demand), but net government debt ratio falls due to higher potential output.
    - Current account balance ratio falls due to terms-of-trade deterioration and higher imports; net foreign asset ratio falls. Rest-of-world exports and output increase due to higher imports.
  - Aggregate demand shocks (consumption, residential, business investment increase):
    - Output rises more than potential → output gap rises; unemployment falls; higher price and wage inflation.
    - Monetary authority raises nominal policy rate; capital-market and bank lending rates increase; currency appreciates; terms of trade improve.
    - Money and bank credit rise; employment rises.
    - Fiscal balance ratio improves (higher tax revenues) → net government debt ratio falls.
    - Current account balance ratio falls (higher imports) → net foreign asset ratio falls; rest-of-world exports and output increase.
  - Credit/duration risk premium shocks (tighter financial conditions):
    - Credit risk premium shock increasing nominal money market rate or duration risk premium raising nominal long term bond yield reduces private domestic demand—particularly residential and business investment.
    - Resultant output falls more than potential → output gap falls; unemployment rises; lower price and wage inflation.
    - Example quantitative magnitudes: a one percentage point credit risk premium induced nominal money market interest rate increase → 0.5 percent median peak output loss; a one percentage point nominal long term bond yield increase via duration risk premium → 0.4 percent median peak output loss.
    - Monetary authority cuts nominal policy rate but money stock and bank credit fall; employment falls; fiscal balance ratio deteriorates; net government debt ratio rises; current account balance ratio improves (lower imports) raising net foreign asset ratio; rest-of-world exports and output fall.
    - International contagion: credit or bond market contagion transmits higher money market rates or long-term yields to recipient economies to varying degrees.
  - Housing and equity risk premium shocks (looser financial conditions):
    - Housing risk premium shock (increasing house prices) raises consumption and residential investment; equity risk premium shock (higher equity prices) raises all private demand components.
    - Output rises more than potential → output gap rises; unemployment falls; higher price and wage inflation.
    - Quantitative magnitudes: a ten percent housing price increase via housing risk premium → 0.7 percent median peak output gain; a ten percent equity price increase via equity risk premium → 0.2 percent median peak output gain.
    - Monetary authority raises the policy rate; currency appreciates; bank capital ratio rises; employment rises; fiscal balance improves; current account weakens (higher imports); rest-of-world exports and output increase. Equity shocks propagate via international stock market contagion.
  - Mortgage and corporate loan rate markups and default shocks:
    - Increases in loan rates or defaults tighten financial conditions, lowering private demand (consumption and investment), reducing output more than potential → output gap falls; unemployment rises; lower inflation and wages.
    - Monetary authority cuts policy rate to mitigate increases in lending rates; currency depreciates; money stock and bank credit fall (for rate markups) or bank capital ratio falls (for defaults); employment falls; fiscal balance deteriorates; net government debt rises; current account improves (lower imports).
    - Corporate loan shocks propagate internationally via nonfinancial corporate borrowing weights, raising effective corporate loan rates in recipient economies and reducing global demand.

### H3 Policy transmission and macroprudential roles
- Monetary transmission:
  - Monetary policy shocks (raising nominal policy rate) increase capital market and bank lending rates, tighten financial conditions, reduce private demand (investment and consumption), appreciate currency, improve terms of trade, reduce exports via expenditure switching, and lower output relative to potential; output gap falls and unemployment rises.
  - Example: a one percentage point increase in nominal policy rate induced by a monetary shock generates substantial median peak output losses (consistent with other numerical examples above).
- Fiscal transmission:
  - Countercyclical public consumption and tax rules stabilize public and national financial wealth; transfers to credit constrained households redistribute wealth and equalize steady-state consumption across households.
  - Government budget dynamics explicitly tracked; fiscal rules respond to public and national asset ratios.
- Macroprudential transmission:
  - Countercyclical capital buffer and loan-to-value limit rules adjust regulatory requirements in response to credit growth and asset price changes; rules have partial adjustment dynamics and shocks.
  - Macroprudential instruments influence bank lending rates, credit growth, and asset prices via regulatory constraints and loan-to-value limits, interacting with monetary and fiscal policy to affect output and financial stability.

### H3 Empirical results: business cycle and output gap
- Output gap estimation:
  - Output gap is model-defined business cycle indicator; smoothed full-sample estimates and decompositions into capital vs. labor utilization contributions reported (Figure 1, Appendix B).
  - Historical patterns:
    - Gradual global expansion up to the Global Financial Crisis (GFC), synchronized across advanced and emerging economies.
    - Abrupt synchronized contraction during the GFC, concentrated in advanced economies at epicenter.
    - Further protracted contractions in the Euro Area periphery during the Euro Area Sovereign Debt Crisis.
    - Post-crisis divergence: advanced economies experienced sluggish expansions, emerging economies experienced contractions.
  - Attribution:
    - Advanced-economy cycle dynamics primarily driven by labor utilization fluctuations (higher labor income shares and more variable unemployment).
    - Emerging-economy cycle dynamics primarily driven by capital utilization fluctuations.

### H3 Forecasting and predictive performance
- Sequential unconditional forecasts of inflation and output growth produced by the estimated model:
  - On average across economies and horizons, these forecasts dominate a random walk by wide margins (model-based forecasting performance superior to random walk benchmark).

### H3 Estimation practice and simplifications
- Restricted approximation for estimation:
  - Estimation generally uses a restricted approximate linear rational expectations representation consolidating or eliminating weakly identified exogenous variables (residential and business investment demand consolidated into single investment demand shock; corporate and labor tax shocks consolidated into single tax rate shock; several loan-related and regulatory shocks eliminated).
  - Impulse response analysis uses the unrestricted representation because it does not depend on the innovation covariance matrix.
- Identification and normalization details:
  - Bilateral and world weights calibrated using 2014 observed values normalized to sum to one.
  - Macroeconomic and financial great ratios calibrated to match observed or averaged values in 2014.
  - All innovations assumed independent for identification; innovations distributed multivariate normal.

*Italic: Source — wp1789 (paper content provided in source PDF).*

### 0.5 percent median peak output loss. The money stock and bank credit fall, as does employment.

### wp1789 - 0.5 percent median peak output loss. The money stock and bank credit fall, as does employment.

### Summary of baseline shock effects
- Median peak output loss following baseline adverse shock: 0.5 percent.
- Money stock and bank credit: fall.
- Employment: falls.
- Fiscal balance ratio: falls (reflecting lower tax revenues and higher debt service costs), raising the net government debt ratio.
- Current account balance ratio: increases (improvement in the terms of trade and lower imports), raising the net foreign asset ratio.
- Rest of world: lower imports from the affected economy are reflected in lower exports and output abroad.

### Fiscal policy shocks (one percentage point increase in the primary fiscal balance ratio)
- General dynamics:
  - Output falls more than potential → output gap falls → unemployment rises.
  - Price and wage inflation: lower.
  - Monetary authority response: cuts the nominal policy interest rate to stimulate aggregate demand and inflation; reduction transmitted via lower capital market and bank lending interest rates to varying degrees.
  - Exchange rate: nominal and real effective depreciation → deterioration in the terms of trade.
  - Current account balance ratio: increases (lower imports) → net foreign asset ratio rises.
  - Employment: falls (in all cases).
- Specific shock magnitudes (median peak output loss from a one percentage point increase in the primary fiscal balance ratio):
  - Government expenditure shock: 1.0 percent.
  - Corporate tax rate shock: 0.4 percent.
  - Labor income tax rate shock: 0.4 percent.
- In the case of a government expenditure shock:
  - Money stock and bank credit: rise (investment is crowded in).
  - Net government debt ratio: reduced (increase in the fiscal balance ratio).

### Macroprudential and financial regulation shocks
- Types considered:
  - Capital requirement shock: increases bank capital ratio requirement.
  - Mortgage loan to value limit shock: reduces mortgage loan to value ratio limit.
  - Corporate loan to value limit shock: reduces corporate loan to value ratio limit.
- Effects:
  - Private domestic demand: declines due to tighter effective financial conditions.
    - Capital requirement shock: all components of private domestic demand decline.
    - Mortgage LTV limit shock: consumption and residential investment fall.
    - Corporate LTV limit shock: consumption and business investment fall.
  - Aggregate demand contraction → output falls more than potential → output gap falls → unemployment rises.
  - Price and wage inflation: lower.
  - Monetary authority response: cuts nominal policy interest rate to mitigate higher bank lending rates and reduce capital market rates to varying degrees.
  - Exchange rate: depreciates in nominal and real effective terms → terms of trade deteriorate.
  - Money stock and bank credit: fall.
  - Employment: falls.
  - Fiscal balance ratio: falls (lower tax revenues) → net government debt ratio rises.
  - Current account balance ratio: increases (lower imports) → net foreign asset ratio rises.
  - Rest of world: lower imports from the affected economy → lower exports and output.
  - In recipient economies under a capital requirement shock: nominal effective corporate loan rate rises to varying degrees given international nonfinancial corporate borrowing, further reducing private domestic demand and output.

### Terms of trade shocks
- Currency risk premium shock:
  - Effect: depreciates currency in nominal and real effective terms → deteriorates terms of trade.
  - Trade effects: increases exports and reduces imports via expenditure switching.
  - International borrowing channel: depreciation raises the nominal effective corporate loan rate (given international nonfinancial corporate borrowing) → reduces private domestic demand and mitigates aggregate demand expansion.
  - Aggregate outcome: output rises more than potential → output gap rises → unemployment falls.
  - Inflation: higher price and wage inflation, amplified and accelerated by exchange rate pass through.
  - Quantified example: a ten percent depreciation of the currency in nominal effective terms induced by a currency risk premium shock generates a 0.4 percent median peak output gain.
  - Monetary authority response: raises nominal policy interest rate; transmitted via increases in capital market and bank lending interest rates to varying degrees.
  - Money stock and bank credit: rise.
  - Employment: rises.
  - Fiscal balance ratio: increases (higher tax revenues) → net government debt ratio reduced.
  - Current account balance ratio: increases (higher exports and lower imports) → net foreign asset ratio rises.
- Energy and nonenergy commodity price markup shocks:
  - Directional effects depend on net commodity exporter vs net commodity importer status and commodity type.
  - Net commodity exporters:
    - Terms of trade: improvement.
    - Consumption price inflation: increases (external terms of trade).
    - Output price inflation: increases by more (internal terms of trade).
    - Private domestic demand: increases (consumption and residential investment rise).
    - Aggregate outcome: output rises more than potential → output gap rises → unemployment falls.
    - Monetary authority: raises nominal policy interest rate by more to control inflation and aggregate demand.
    - Currency: appreciates in nominal and real effective terms.
    - Money stock and bank credit: increase.
    - Employment: rises.
    - Fiscal balance ratio: increases (higher tax revenues) → net government debt ratio reduced.
    - Current account balance ratio: increases → net foreign asset ratio rises.
  - Net commodity importers: inverse effects (terms of trade deterioration, lower private demand, lower output, currency depreciation, falls in money stock, bank credit, employment, fiscal and current account ratios).

### Historical decompositions and forecasting performance
- Historical decompositions:
  - Deviations of consumption price inflation from trend primarily attributed to economy-specific combinations of domestic and foreign macroeconomic and financial shocks, and world terms of trade shocks.
  - Contribution of domestic vs foreign shocks: generally decreases with trade openness and increases with monetary policy autonomy.
  - Output growth deviations (business cycle dynamics) are primarily attributed to economy-specific domestic and foreign macroeconomic and financial shocks; financial shocks generally amplified business cycle fluctuations, policy shocks generally mitigated them.
  - Global patterns:
    - Pre-Global Financial Crisis: macroeconomic and financial shocks caused a gradual synchronized global business cycle expansion, with a synchronized global rise in inflation generally amplified by world terms of trade shocks.
    - Global Financial Crisis: adverse macroeconomic and financial shocks caused an abrupt synchronized global contraction and fall in inflation, generally amplified by world terms of trade shocks, mitigated by countercyclical unsystematic policy interventions.
    - Post-crisis: macroeconomic and financial shocks contributed to a synchronized global recovery; in the Euro Area periphery recovery was derailed by adverse financial shocks. More recently, shocks contributed to sluggish expansions in many advanced economies and contractions in many emerging economies.
- Forecasting evaluation:
  - Holdout sample: 2005Q2 through 2016Q1, horizons one through eight quarters.
  - Benchmark: driftless random walk; performance measured by logarithm of the U statistic (ratio of root mean squared prediction errors).
  - Results: model generally dominates a random walk for inflation and output growth.
    - Root mean squared prediction error reductions over the holdout sample:
      - Inflation: 27 percent lower (on average across economies and horizons).
      - Output growth: 34 percent lower (on average across economies and horizons).
  - Sequential unconditional forecasts are capable of predicting business cycle turning points and fairly accurately predicted the severity of the synchronized global contraction at the Global Financial Crisis for most economies.

### Model scope, conclusions, and future extensions
- Model developed: structural panel dynamic stochastic general equilibrium model of the world economy disaggregated into forty national economies.
- Key features:
  - Range of nominal and real rigidities.
  - Extensive macrofinancial linkages and diverse spillover transmission channels.
  - Financial intermediation via bank and capital market channels; financial accelerator mechanisms linked to housing and physical capital stock values.
- Demonstrated applications: monetary policy analysis, fiscal policy analysis, macroprudential policy analysis, spillover analysis, forecasting; impulse responses, historical decompositions, sequential unconditional forecasts.
- Conclusions:
  - The model consolidates existing theoretical and empirical knowledge on global business cycle dynamics and suggests explanations for its deficiencies.
  - Proposed future extensions: disaggregate bond market into sovereign versus corporate submarkets; refine international trade, financial and commodity price linkages.

### Data and calibration (key points)
- Sample period for estimation: 1999Q1 through 2016Q1.
- Number of economies: forty.
- Economies included: Argentina, Australia, Austria, Belgium, Brazil, Canada, Chile, China, Colombia, the Czech Republic, Denmark, Finland, France, Germany, Greece, India, Indonesia, Ireland, Israel, Italy, Japan, Korea, Malaysia, Mexico, the Netherlands, New Zealand, Norway, the Philippines, Poland, Portugal, Russia, Saudi Arabia, South Africa, Spain, Sweden, Switzerland, Thailand, Turkey, the United Kingdom, and the United States.
- Data sources: GDS, WEO, Bloomberg, Bank for International Settlements, IFS, WDI, DOTS, CPIS (where available).
- Key variable measurements:
  - Price of output: seasonally adjusted GDP price deflator.
  - Price of consumption: seasonally adjusted consumer price index.
  - Quantity of output: seasonally adjusted real GDP.
  - Quantity of private consumption: seasonally adjusted real private consumption expenditures.
  - Exports/imports: seasonally adjusted real export revenues/import expenditures.
  - Price of housing: broad residential property price index.
  - Nominal wage: derived from quadratically interpolated annual labor income share.
  - Unemployment rate: seasonally adjusted share of total unemployment in total labor force.
  - Employment: seasonally adjusted total employment.
  - Public domestic demand: sum of quadratically interpolated annual real consumption and investment expenditures of general government.
  - Fiscal balance: quadratically interpolated annual overall fiscal balance of general government.
  - Energy and nonenergy commodity prices: broad commodity price indexes in United States dollars.
  - Financial market variables: central bank policy rate (nominal policy interest rate), three month Treasury bill yield (nominal money market interest rate), ten year government bond yield (nominal long term bond yield), broad stock price index in domestic currency (price of equity), domestic currency price of one United States dollar (nominal bilateral exchange rate). All financial variables expressed as period average values.
- Calibration: based on annual data from IMF, BIS, and World Bank Group databases; macroeconomic and financial great ratios derived from WEO, WDI, BIS, and IFS; bilateral trade and financial weights from DOTS, BIS, CPIS, and WDI.

*Source: wp1789 - 0.5 percent median peak output loss. The money stock and bank credit fall, as does employment.*

### Appendix B. Tables and Figures

### wp1789 - Appendix B. Tables and Figures

### Parameter estimation — endogenous variables (Table 1)
- Note: All priors are normally distributed, while all posteriors are asymptotically normally distributed.
- Selected parameter priors and posteriors (as reported):
  - C α: Prior Mean 0.9000; Prior S.D. 0.0090; Post. Mean 0.9040
  - L α: Prior Mean 0.7000; Prior S.D. 0.0070; Post. Mean 0.6999
  - G ρ: Prior Mean 0.8000; Prior S.D. 0.0080; Post. Mean 0.8037
  - H χ: Prior Mean 2.1000; Prior S.D. 0.0210; Post. Mean 2.1093
  - K χ: Prior Mean 1.3000; Prior S.D. 0.0130; Post. Mean 1.2974
  - B χ: Prior Mean 1.5000; Prior S.D. 0.0150; Post. Mean 1.4882
  - C χ: Prior Mean 10.0000; Prior S.D. 0.1000; Post. Mean 10.0127
  - σ: Prior Mean 2.7000; Prior S.D. 0.0270; Post. Mean 2.7111
  - V: Prior Mean 0.1000; Prior S.D. 0.0010; Post. Mean 0.0999
  - η: Prior Mean 0.0100; Prior S.D. 0.0001; Post. Mean 0.0100
  - K η: Prior Mean 0.5000; Prior S.D. 0.0050; Post. Mean 0.4978
  - π ξ0: Prior Mean 1.7500; Prior S.D. 0.0175; Post. Mean 1.7586
  - C η: Prior Mean 1.2500; Prior S.D. 0.0125; Post. Mean 1.2471
  - Y γ: Prior Mean 0.8000; Prior S.D. 0.0080; Post. Mean 0.7973
  - L γ: Prior Mean 0.8000; Prior S.D. 0.0080; Post. Mean 0.8016
  - M γ: Prior Mean 0.8000; Prior S.D. 0.0080; Post. Mean 0.8020
  - ι: Prior Mean 1.2500; Prior S.D. 0.0125; Post. Mean 1.2456
  - 1 λT: Prior Mean 0.5000; Prior S.D. 0.0050; Post. Mean 0.4985
  - 2 λT: Prior Mean 0.0500; Prior S.D. 0.0005; Post. Mean 0.0500
  - 3 λT: Prior Mean 0.1000; Prior S.D. 0.0010; Post. Mean 0.1008
  - M μ: Prior Mean 0.2500; Prior S.D. 0.0025; Post. Mean 0.2523
  - Y ω: Prior Mean 0.9375; Prior S.D. 0.0094; Post. Mean 0.9396
  - B ω: Prior Mean 0.9500; Prior S.D. 0.0095; Post. Mean 0.9520
  - C ω: Prior Mean 0.5000; Prior S.D. 0.0050; Post. Mean 0.5001
  - L ω: Prior Mean 0.9375; Prior S.D. 0.0094; Post. Mean 0.9401
  - M ω: Prior Mean 0.7500; Prior S.D. 0.0075; Post. Mean 0.7489
  - 1 Y ω: Prior Mean 0.4286; Prior S.D. 0.0043; Post. Mean 0.4274
  - 2 Y ω: Prior Mean 0.6000; Prior S.D. 0.0060; Post. Mean 0.6009
  - B φ: Prior Mean 0.3500; Prior S.D. 0.0035; Post. Mean 0.3503
  - C φ: Prior Mean 0.5000; Prior S.D. 0.0050; Post. Mean 0.4986
  - D φ: Prior Mean 0.9000; Prior S.D. 0.0090; Post. Mean 0.9023
  - 0 M λ: Prior Mean 0.5101; Prior S.D. 0.0510; Post. Mean 0.4975
  - 1 M λ: Prior Mean 1.0203; Prior S.D. 0.1020; Post. Mean 1.0556
  - 2 M λ: Prior Mean 1.5304; Prior S.D. 0.1530; Post. Mean 1.5063
  - AB φ: Prior Mean 0.9000; Prior S.D. 0.0090; Post. Mean 0.8955
  - 0 B λ: Prior Mean 0.5101; Prior S.D. 0.0510; Post. Mean 0.4995
  - AS φ: Prior Mean 0.1000; Prior S.D. 0.0010; Post. Mean 0.1002
  - 1 B λ: Prior Mean 1.0203; Prior S.D. 0.1020; Post. Mean 1.0191
  - M ψ: Prior Mean 1.5000; Prior S.D. 0.0150; Post. Mean 1.5025
  - 2 B λ: Prior Mean 1.5304; Prior S.D. 0.1530; Post. Mean 1.5673
  - i ρ: Prior Mean 0.8000; Prior S.D. 0.0080; Post. Mean 0.7985
  - 0 S λ: Prior Mean 0.5743; Prior S.D. 0.0574; Post. Mean 0.5764
  - 1 S λ: Prior Mean 1.1486; Prior S.D. 0.1149; Post. Mean 1.1804
  - 2 S λ: Prior Mean 1.7229; Prior S.D. 0.1723; Post. Mean 1.7061

### Parameter estimation — exogenous variables (Table 2)
- Note: All priors are normally distributed, while all posteriors are asymptotically normally distributed.
- Selected entries (as reported; many variance terms reported in scientific notation):
  - ρA: Prior Mean 0.8000; Prior S.D. 0.0800; Post. Mean 0.7883
  - ρN: Prior Mean 0.8000; Prior S.D. 0.0800; Post. Mean 0.7990
  - C νρ: Prior Mean 0.4000; Prior S.D. 0.0400; Post. Mean 0.3749
  - I νρ: Prior Mean 0.6000; Prior S.D. 0.0600; Post. Mean 0.6189
  - X νρ: Prior Mean 0.8000; Prior S.D. 0.0800; Post. Mean 0.7976
  - M νρ: Prior Mean 0.8000; Prior S.D. 0.0800; Post. Mean 0.7970
  - H νρ: Prior Mean 0.6000; Prior S.D. 0.0600; Post. Mean 0.5827
  - ,iS νρ: Prior Mean 0.8000; Prior S.D. 0.0800; Post. Mean 0.7809
  - B νρ: Prior Mean 0.8000; Prior S.D. 0.0800; Post. Mean 0.8089
  - S νρ: Prior Mean 0.4000; Prior S.D. 0.0400; Post. Mean 0.4356
  - νρE: Prior Mean 0.4000; Prior S.D. 0.0400; Post. Mean 0.4164
  - 2 M νσ: Prior Mean 8.73×10+0; Prior S.D. 8.73×10−1; Post. Mean 8.86×10+0
  - 2 Y θσ: Prior Mean 2.29×10+6; Prior S.D. 2.29×10+5; Post. Mean 2.34×10+6
  - 2 L θσ: Prior Mean 2.05×10+7; Prior S.D. 2.05×10+6; Post. Mean 1.97×10+7
  - 2 M θσ: Prior Mean 1.04×10+4; Prior S.D. 1.04×10+3; Post. Mean 9.72×10+3
  - 2 H νσ: Prior Mean 1.46×10+0; Prior S.D. 1.46×10−1; Post. Mean 1.51×10+0
  - ,2 iS νσ: Prior Mean 4.49×10−2; Prior S.D. 4.49×10−3; Post. Mean 4.47×10−2
  - 2 B νσ: Prior Mean 6.55×10−1; Prior S.D. 6.55×10−2; Post. Mean 6.67×10−1
  - 2 S νσ: Prior Mean 1.36×10+1; Prior S.D. 1.36×10+0; Post. Mean 1.32×10+1
  - 2 νσE: Prior Mean 1.91×10+0; Prior S.D. 1.91×10−1; Post. Mean 1.93×10+0
  - 2 C θσ: Prior Mean 1.00×10+0; Prior S.D. ...; Post. Mean ...
  - 2 δ νσ: Prior Mean 1.00×10+0; Prior S.D. ...; Post. Mean ...
  - 2 iP νσ: Prior Mean 4.08×10−1; Prior S.D. 4.08×10−2; Post. Mean 3.55×10−1
  - 2 G νσ: Prior Mean 1.57×10+0; Prior S.D. 1.57×10−1; Post. Mean 1.57×10+0
  - 2 σA: Prior Mean 5.58×10−2; Prior S.D. 5.58×10−3; Post. Mean 6.08×10−2
  - 2 τ νσ: Prior Mean 3.66×10−2; Prior S.D. 3.66×10−3; Post. Mean 3.75×10−2
  - 2 σN: Prior Mean 1.17×10+0; Prior S.D. 1.17×10−1; Post. Mean 1.16×10+0
  - 2 κ νσ: Prior Mean 1.00×10+0; Prior S.D. ...; Post. Mean ...
  - 2 C νσ: Prior Mean 1.04×10+2; Prior S.D. 1.04×10+1; Post. Mean 9.66×10+1
  - 2 ϕ νσ: Prior Mean 1.00×10+0; Prior S.D. ...; Post. Mean ...
  - 2 I νσ: Prior Mean 2.89×10+0; Prior S.D. 2.89×10−1; Post. Mean 3.06×10+0
  - ,2 Yk θσ: Prior Mean 2.46×10+4; Prior S.D. 2.46×10+3; Post. Mean 2.46×10+4
  - 2 X νσ: Prior Mean 6.25×10+0; Prior S.D. 6.25×10−1; Post. Mean 6.02×10+0

### Output gap estimates (Figure 1)
- Note: Decomposes smoothed estimates of the output gap into contributions from capital utilization ■ and labor utilization ■.
- Country panels provided for: Argentina, Australia, Austria, Belgium, Brazil, Canada, Chile, China, Colombia, Czech Republic, Denmark, Finland, France, Germany, Greece, India, Indonesia, Ireland, Israel, Italy, Japan, Korea, Malaysia, Mexico, Netherlands, New Zealand, Norway, Philippines, Poland, Portugal, Russia, Saudi Arabia, South Africa, Spain, Sweden, Switzerland, Thailand, Turkey, United Kingdom, United States.
- Vertical axis labeled Percent with symmetric tick marks suitable to each country (examples):
  - Argentina axis range: -10.0 to 10.0 (Percent)
  - Brazil axis range: -4.0 to 4.0 (Percent)
  - Chile axis range: -5.0 to 5.0 (Percent)
  - Greece axis range: -10.0 to 10.0 (Percent)
  - South Africa axis range: -5.0 to 5.0 (Percent)
  - Spain axis range: -8.0 to 8.0 (Percent)
- Horizontal axis covers years 2000 through 2016.

### Impulse response analyses — overview of shock experiments (Figures 2–44)
- Note common methodological details repeated in figure captions:
  - Responses depict selected economies: 2.5th percentile, median, 97.5th percentile (or recipient/source economies), and the reference economy (United States).
  - Shocks are normalized (examples): productivity shocks that raise potential output by one percent; consumption shocks that raise consumption by one percent; residential investment shocks that raise residential investment by one percent; business investment shocks that raise business investment by one percent; credit risk premium shocks that raise the nominal money market interest rate by one percentage point; duration risk premium shocks that raise the nominal long term bond yield by one percentage point; housing risk premium shocks that raise the price of housing by ten percent; equity risk premium shocks that raise the price of equity by ten percent; mortgage loan rate markup shocks that raise the nominal mortgage loan rate by one percentage point; corporate loan rate markup shocks that raise the nominal corporate loan rate by one percentage point; default shocks that raise default rates by one percentage point; monetary policy shocks that raise the nominal policy interest rate by one percentage point; government expenditure shocks that raise the primary fiscal balance ratio by one percentage point; tax rate shocks that raise the primary fiscal balance ratio by one percentage point; capital requirement shocks that raise the bank capital ratio requirement by one percentage point; mortgage loan to value and corporate loan to value limit shocks that reduce the loan-to-value ratio limit by one percentage point; currency risk premium shocks that depreciate the currency by ten percent in nominal effective terms; energy and nonenergy commodity price markup shocks that raise the respective commodity price by ten percent.
  - All variables are annualized, where applicable.
  - Impulse response panels include a wide set of variables (examples of y-axis labels and units preserved exactly as in figures):
    - Consumption Price Inflation (Percentage Points)
    - Output Price Inflation (Percentage Points)
    - Output (Percent)
    - Output Gap (Percent)
    - Potential Output (Percent)
    - Consumption (Percent)
    - Residential Investment (Percent)
    - Business Investment (Percent)
    - Exports (Percent)
    - Imports (Percent)
    - Nominal Policy Interest Rate (Percentage Points)
    - Nominal Money Market Interest Rate (Percentage Points)
    - Nominal Long Term Bond Yield (Percentage Points)
    - Nominal Mortgage Loan Rate (Percentage Points)
    - Nominal Corporate Loan Rate (Percentage Points)
    - Price of Housing (Percent)
    - Price of Equity (Percent)
    - Nominal Effective Exchange Rate (Percent)
    - Real Effective Exchange Rate (Percent)
    - Terms of Trade (Percent)
    - Money Stock (Percent)
    - Bank Credit (Percent)
    - Bank Capital Ratio (Percentage Points)
    - Mortgage Loan Default Rate (Percentage Points)
    - Corporate Loan Default Rate (Percentage Points)
    - Nominal Wage (Percent)
    - Unemployment Rate (Percentage Points)
    - Employment (Percent)
    - Labor Force (Percent)
    - Capital Utilization Rate (Percent)
    - Fiscal Balance Ratio (Percentage Points)
    - Primary Fiscal Balance Ratio (Percentage Points)
    - Net Government Debt Ratio (Percentage Points)
    - Tax Revenues (Percent)
    - Public Domestic Demand (Percent)
    - Current Account Balance Ratio (Percentage Points)
    - Trade Balance Ratio (Percentage Points)
    - Net Foreign Asset Ratio (Percentage Points)
    - Price of Energy Commodities (Percent)
    - Price of Nonenergy Commodities (Percent)

- Figures and shocks (by figure number and shock type):
  - Figure 2: Impulse Responses to a Domestic Productivity Shock (one percent increase in potential output)
  - Figure 3: Impulse Responses to a Foreign Productivity Shock (one percent increase in potential output)
  - Figure 4: Impulse Responses to a Domestic Labor Supply Shock (one percent increase in potential output)
  - Figure 5: Impulse Responses to a Foreign Labor Supply Shock (one percent increase in potential output)
  - Figure 6: Impulse Responses to a Domestic Consumption Demand Shock (consumption +1 percent)
  - Figure 7: Impulse Responses to a Foreign Consumption Demand Shock (consumption +1 percent)
  - Figure 8: Impulse Responses to a Domestic Residential Investment Demand Shock (residential investment +1 percent)
  - Figure 9: Impulse Responses to a Foreign Residential Investment Demand Shock (residential investment +1 percent)
  - Figure 10: Impulse Responses to a Domestic Business Investment Demand Shock (business investment +1 percent)
  - Figure 11: Impulse Responses to a Foreign Business Investment Demand Shock (business investment +1 percent)
  - Figure 12: Impulse Responses to a Domestic Credit Risk Premium Shock (nominal money market interest rate +1 percentage point)
  - Figure 13: Impulse Responses to a Foreign Credit Risk Premium Shock (nominal money market interest rate +1 percentage point)
  - Figure 14: Impulse Responses to a Domestic Duration Risk Premium Shock (nominal long term bond yield +1 percentage point)
  - Figure 15: Impulse Responses to a Foreign Duration Risk Premium Shock (nominal long term bond yield +1 percentage point)
  - Figure 16: Impulse Responses to a Domestic Housing Risk Premium Shock (price of housing +10 percent)
  - Figure 17: Impulse Responses to a Foreign Housing Risk Premium Shock (price of housing +10 percent)
  - Figure 18: Impulse Responses to a Domestic Equity Risk Premium Shock (price of equity +10 percent)
  - Figure 19: Impulse Responses to a Foreign Equity Risk Premium Shock (price of equity +10 percent)
  - Figure 20: Impulse Responses to a Domestic Mortgage Loan Rate Markup Shock (nominal mortgage loan rate +1 percentage point)
  - Figure 21: Impulse Responses to a Foreign Mortgage Loan Rate Markup Shock (nominal mortgage loan rate +1 percentage point)
  - Figure 22: Impulse Responses to a Domestic Corporate Loan Rate Markup Shock (nominal corporate loan rate +1 percentage point)
  - Figure 23: Impulse Responses to a Foreign Corporate Loan Rate Markup Shock (nominal corporate loan rate +1 percentage point)
  - Figure 24: Impulse Responses to a Domestic Mortgage Loan Default Shock (mortgage loan default rate +1 percentage point)
  - Figure 25: Impulse Responses to a Foreign Mortgage Loan Default Shock (mortgage loan default rate +1 percentage point)
  - Figure 26: Impulse Responses to a Domestic Corporate Loan Default Shock (corporate loan default rate +1 percentage point)
  - Figure 27: Impulse Responses to a Foreign Corporate Loan Default Shock (corporate loan default rate +1 percentage point)
  - Figure 28: Impulse Responses to a Domestic Monetary Policy Shock (nominal policy interest rate +1 percentage point)
  - Figure 29: Impulse Responses to a Foreign Monetary Policy Shock (nominal policy interest rate +1 percentage point)
  - Figure 30: Impulse Responses to a Domestic Government Expenditure Shock (primary fiscal balance ratio +1 percentage point)
  - Figure 31: Impulse Responses to a Foreign Government Expenditure Shock (primary fiscal balance ratio +1 percentage point)
  - Figure 32: Impulse Responses to a Domestic Corporate Tax Rate Shock (primary fiscal balance ratio +1 percentage point)
  - Figure 33: Impulse Responses to a Foreign Corporate Tax Rate Shock (primary fiscal balance ratio +1 percentage point)
  - Figure 34: Impulse Responses to a Domestic Labor Income Tax Rate Shock (primary fiscal balance ratio +1 percentage point)
  - Figure 35: Impulse Responses to a Foreign Labor Income Tax Rate Shock (primary fiscal balance ratio +1 percentage point)
  - Figure 36: Impulse Responses to a Domestic Capital Requirement Shock (bank capital ratio requirement +1 percentage point)
  - Figure 37: Impulse Responses to a Foreign Capital Requirement Shock (bank capital ratio requirement +1 percentage point)
  - Figure 38: Impulse Responses to a Domestic Mortgage Loan to Value Limit Shock (mortgage LTV limit −1 percentage point)
  - Figure 39: Impulse Responses to a Foreign Mortgage Loan to Value Limit Shock (mortgage LTV limit −1 percentage point)
  - Figure 40: Impulse Responses to a Domestic Corporate Loan to Value Limit Shock (corporate loan LTV limit −1 percentage point)
  - Figure 41: Impulse Responses to a Foreign Corporate Loan to Value Limit Shock (corporate loan LTV limit −1 percentage point)
  - Figure 42: Impulse Responses to a Currency Risk Premium Shock (currency depreciates by ten percent in nominal effective terms)
  - Figure 43: Impulse Responses to an Energy Commodity Price Markup Shock (price of energy commodities +10 percent)
  - Figure 44: Impulse Responses to a Nonenergy Commodity Price Markup Shock (price of nonenergy commodities +10 percent)

### Historical decompositions (Figures 45–46)
- Figure 45: Historical Decompositions of Consumption Price Inflation
  - Note: Decomposes observed consumption price inflation ■ (seasonal logarithmic difference of price of consumption) into trend component ■ and contributions from:
    - domestic macroeconomic ■
    - foreign macroeconomic ■
    - domestic financial ■
    - foreign financial ■
    - domestic policy ■
    - foreign policy ■
    - world terms of trade ■
  - Country panels for 2005–2016 with percent scales customized per country (examples preserved exactly as presented for axes).
- Figure 46: Historical Decompositions of Output Growth
  - Note: Decomposes observed output growth ■ (seasonal logarithmic difference of output) into trend component ■ and contributions from the same shock groups as Figure 45.
  - Country panels for 2005–2016 with percent scales customized per country (examples preserved exactly as presented for axes).

### Forecast evaluation and sequential unconditional forecasts (Figures 47–49)
- Figure 47: Forecast Performance Evaluation Statistics
  - Note: Depicts the horizon dependent logarithmic root mean squared prediction error ratio for consumption price inflation ■ and output growth ■ relative to a random walk, expressed in percent.
  - Horizon ticks labeled 1 through 8; panels per country with vertical axis range shown as -150 to 150 (Percent) in many panels.
- Figure 48: Sequential Unconditional Forecasts of Consumption Price Inflation
  - Note: Depicts the cyclical component of observed consumption price inflation ■ (seasonal difference of cyclical log price of consumption) versus sequential unconditional forecasts ■.
  - Panels cover 2005–2018 for each country; vertical axis ranges vary by country (examples preserved in figure panels).
- Figure 49: Sequential Unconditional Forecasts of Output Growth
  - Note: Depicts the cyclical component of observed output growth ■ (seasonal difference of cyclical log output) versus sequential unconditional forecasts ■.
  - Panels cover 2005–2018 for each country; vertical axis ranges vary by country (examples preserved in figure panels).

*Appendix B contains the tabulated parameter priors and posteriors (Tables 1–2), country-specific output gap estimates (Figure 1), an extensive set of impulse response experiments across domestic and foreign shocks (Figures 2–44), historical shock decompositions for consumption price inflation and output growth (Figures 45–46), and forecast evaluation and sequential unconditional forecast panels (Figures 47–49).*

### References

### References

### Journal articles and books
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- Christiano, L., M. Eichenbaum and C. Evans, 2005, “Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy”, Journal of Political Economy, Vol. 113, pp. 1−45.
- Erceg, C., D. Henderson and A. Levin, 2000, “Optimal Monetary Policy with Staggered Wage and Price Contracts”, Journal of Monetary Economics, Vol. 46, pp. 281−313.
- Galí, J., 2011, “The Return of the Wage Phillips Curve”, Journal of the European Economic Association, Vol. 9, pp. 436−461.
- Gerali, A., S. Neri, L. Sessa and F. Signoretti, 2010, “Credit and Banking in a DSGE Model of the Euro Area”, Journal of Money, Credit and Banking, Vol. 42, pp. 107−141.
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- Monacelli, T., 2005, “Monetary Policy in a Low Pass-Through Environment”, Journal of Money, Credit and Banking, Vol. 37, pp. 1047−1066.
- Smets, F. and R. Wouters, 2003, “An Estimated Dynamic Stochastic General Equilibrium Model of the Euro Area”, Journal of the European Economic Association, Vol. 1, pp. 1123−1175.
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- Tobin, J., 1969, “A General Equilibrium Approach to Monetary Theory”, Journal of Money, Credit and Banking, Vol. 1, pp. 15−29.
- Weber, M., 1905, The Protestant Ethic and the Spirit of Capitalism, Charles Scribner’s Sons.
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### Working papers and reports
- International Monetary Fund, 2015, Annual Report on Exchange Arrangements and Exchange Restrictions, Washington.
- Vitek, F., 2014, “Policy and Spillover Analysis in the World Economy: A Panel Dynamic Stochastic General Equilibrium Approach”, International Monetary Fund Working Paper, 200.
- Vitek, F., 2015, “Macrofinancial Analysis in the World Economy: A Panel Dynamic Stochastic General Equilibrium Approach”, International Monetary Fund Working Paper, 227.

*Source: wp1789 - References*

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_Source: https://www.imf.org/-/media/files/publications/wp/2017/wp1789.pdf_