## Appendix A. Description of the Multivariate Panel Data Set ## Source details **Canonical URL:** [Appendix A. Description of the Multivariate Panel Data Set](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2013/_wp13253.pdf) ## Other formats - [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2013/_wp13253.pdf.md) - [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2013/_wp13253.pdf.json) --- ### Model framework and purpose - Structural macroeconometric panel unobserved components model of the world economy disaggregated into thirty five national economies. - Embeds an approximate linear panel dynamic stochastic general equilibrium (DSGE) model at cyclical frequencies and flexible random-walk trend components to preserve robustness to intermittent structural breaks. - Incorporates nominal and real rigidities, macrofinancial linkages, and international trade, financial and commodity price linkages as conduits for spillover transmission. - Uses functional form restrictions on selected aggregators and parameter restrictions on selected equilibrium conditions to circumvent tracking bilateral trade and financial flows. - Estimation and forecasting proceed in a Bayesian framework that conditions on judgment in estimation and forecasting. ### Data, sample, and observed variables - Sample period: 1999Q1 through 2012Q4 (estimation results reported for 1999Q3 through 2012Q4). - Number of economies modeled: thirty five (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). - Number of observed endogenous variables: four hundred one. - Observed macroeconomic and financial market variables include: the price of output, the price of consumption, the quantity of output, the quantity of domestic demand, the nominal policy interest rate, the short term nominal market interest rate, the long term nominal market interest rate, the price of equity, the nominal bilateral exchange rate, the quantity of public domestic demand, the ratio of the fiscal balance to nominal output, the ratio of the trade balance to nominal output, and the prices of energy and nonenergy commodities. - Data sources: where available, GDS and WEO databases; otherwise IFS. Calibration uses WEO, WDI, EWN, BIS, IFS, DOTS, CPIS. ### Household, production, trade, and policy structure (model ingredients) - Heterogeneous households: continuum indexed by [0,1] differentiated by credit constrained vs. unconstrained types with measures Uϕ and Cϕ, Uϕ + Cϕ = 1. - Financial assets: internationally traded and local currency short term bonds (discount), long term bonds (perpetual), and stocks; CES intratemporal subutilities and multiple nested CES aggregators for asset vintages, economies, industries, and firms. - Preferences: include external habit formation and precautionary savings; parameters and shocks explicitly defined using notation ν, ψ, μ, ϕ, θ, etc. - Production: industries k = 1,...,M including energy (k = 1) and nonenergy commodity (k = 2); decreasing returns to scale for exports, constant returns to scale for domestically consumed differentiated goods; final output is a Leontief aggregator; intermediate firms monopolistically competitive with Calvo-type price stickiness. - Import/export sectors: Leontief aggregators for final imports/exports; CES import composition; Monacelli-style nominal import price rigidity with partial indexation and time-varying probability of optimal price adjustment. - Monetary policy: nominal policy interest rate follows a partial-adjustment rule with regime-specific target variables (flexible inflation targeting, managed exchange rate, fixed exchange rate). Monetary policy shocks are mean zero and serially uncorrelated (P_it^ν). - Fiscal policy: fiscal authority controls public consumption and the labor/earnings tax rate via partial adjustment fiscal expenditure and revenue rules; fiscal shocks G_it^ν and T_it^ν are mean zero and serially uncorrelated. Government budget constraint and asset holdings across domestic short and long term bonds explicitly specified. - Asset market relationships: money market links short-term yield to policy rate plus internationally and serially correlated credit risk premium shock S_it^υ; bond and stock relationships include duration and equity risk premium shocks with international contagion specifications. ### Approximate linear panel unobserved components representation - Cyclical components (denoted x̂_it) obtained by linearizing equilibrium conditions around a stationary deterministic steady state (abstracting from long-run balanced growth and featuring zero inflation and net financial asset holdings unless stated). - Trend components follow independent random walks; cyclical and trend components are additively separable: x_it = x̂_it + x_it (trend). - Innovations assumed independent and multivariate normal. - Bilateral and world weights: exports Z = X, imports Z = M, average Z = T; portfolio weights based on debt Z = B and equity Z = S; world weights based on output ZY = Y, money market cap ZM = M, bond market cap ZB = B, stock market cap ZS = S. - Key cyclical relationships preserved in original notation: output price Phillips curve (equation 64), consumption price Phillips curve (65), output demand (66), domestic demand (67), nominal ex ante portfolio return (68), monetary policy rule in cyclical form (69), money market (70), bond market (71), stock market (72), profits (73), foreign exchange (74), internal terms of trade (75), external terms of trade and import price Phillips curve (76), commodity price Phillips curve (85), fiscal and national accounting cyclical relationships (77–84). ### Trend component specification - Trend components (prices, quantities, interest rates, equity price, bilateral exchange rates, fiscal and trade balances) follow random walks with independent innovations (equations 86–98; interest rate trends 92–94; equity and bilateral FX 95–96; fiscal/trade balance trends 97–98). - Real rates and real bilateral exchange rates satisfy Fisher-like relationships in both cyclical and trend components. - Treatment of structural breaks: extends Hodrick-Prescott filter to allow time-varying smoothing parameter; allows at most one structural break per observed variable; smoothing parameter may switch from 6400 to 1600 for one period if the normalized objective does not exceed that for U.S. output. - Prior trend estimates and mean squared error matrices impose stochastic restrictions; proportionality factor for trend judgment set to 10^8 to minimize its influence while ensuring stationarity of cyclical estimates. ### Estimation approach and computational details - Estimation: Bayesian procedure conditioning on common structural parameter priors and judgment on trend paths; inference based on asymptotic normal approximation around posterior mode. - State space: cyclical second-order linear rational expectations system solved using Klein (2000); Kalman filter and de Jong (1989) smoother for state estimation and smoothing. - Signal equation extension: includes time-deterministic coefficient matrix for alternative estimates/forecasts as stochastic restrictions (equation 106). - Posterior mode obtained by maximizing log posterior kernel with modified steepest ascent; starting values via differential evolution algorithm (Storn and Price (1997)). - Posterior identification checks: Klein (2000) sufficient condition satisfied near posterior mode; Hessian estimator not nearly singular at posterior mode indicating local identification. - Priors: structural parameters centered within empirical literature ranges; monetary regimes specified by country; capital controls in China, India, Saudi Arabia; quotation currency U.S. dollar; great ratios and bilateral weights calibrated to 2010 observed values. - Joint estimation uses levels of four hundred one variables for thirty five economies; posterior mode computed for sample 1999Q3–2012Q4. ### Estimation results (high-level and selected parameter posteriors) - Posterior modes of most structural parameters are close to prior means due to tight priors, but data are informative for several parameters producing substantial updates. - Selected global priors and selected posteriors (preserve numeric precision): - α: Prior 0.9000 0.0900; Posterior Mode 0.9056 - β: Prior 0.9756 0.0000 - χ (B): Prior 0.5000 0.0500; Posterior Mode 0.5365 - χ (S): Prior 0.5000 0.0500; Posterior Mode 0.5058 - η: Prior 4.5000 0.4500; Posterior Mode 4.6184 - μ: Prior 0.2500 0.0250; Posterior Mode 0.2496 - ω (Y): Prior 0.9167 0.0917; Posterior Mode 0.8815 - ω (M): Prior 0.8333 0.0833; Posterior Mode 0.8849 - ω (1Y): Prior 0.3333 0.0333; Posterior Mode 0.3326 - ω (2Y): Prior 0.3333 0.0333; Posterior Mode 0.3432 - φ (C): Prior 0.5000 0.0500; Posterior Mode 0.4987 - φ (1L): Prior 0.1000 0.0100; Posterior Mode 0.1081 - φ (2L): Prior 0.2000 0.0200; Posterior Mode 0.2094 - ψ (M): Prior 1.5000 0.1500; Posterior Mode 1.5499 - ρ (i): Prior 0.8500 0.0850; Posterior Mode 0.8053 - ρ (G): Prior 0.8500 0.0850; Posterior Mode 0.8207 - ρ (τ): Prior 0.8500 0.0850; Posterior Mode 0.8448 - σ: Prior 3.5000 0.3500; Posterior Mode 3.6285 - ρ (aggregate): Prior 0.7500 0.0750; Posterior Mode 0.8470 - νρ (C): Prior 0.7500 0.0750; Posterior Mode 0.7323 - νρ (X): Prior 0.7500 0.0750; Posterior Mode 0.7224 - νρ (M): Prior 0.7500 0.0750; Posterior Mode 0.7734 - νρ (iS): Prior 0.7500 0.0750; Posterior Mode 0.7358 - νρ (B): Prior 0.7500 0.0750; Posterior Mode 0.7745 - νρ (S): Prior 0.7500 0.0750; Posterior Mode 0.7376 - νρ (general): Prior 0.7500 0.0750; Posterior Mode 0.7921 - Innovation variances driving cyclical components are within literature ranges after rescaling; variances for trend innovations vary considerably across economies and variables. - Unobserved components: intermittent structural breaks prevalent; time-varying smoothing/trend estimator and prior uncertainty used to control for these; initial conditions for some state variables treated as parameters and calibrated to match initial realizations or prior trend estimates. ### Key substantive findings and policy-relevant analysis - Output gap and global dynamics: - Smoothed model-consistent output gap estimates indicate the synchronized buildup in excess demand prior to the global financial crisis was primarily driven by excessive expansion of private domestic demand in most economies. - Excessive expansion of net exports was a major contributor in major surplus economies (e.g., China and Germany). - The global financial crisis triggered a rapid synchronized unwinding of excess demand, producing substantial excess supply pressure in many economies. Collapses in private domestic demand in major deficit economies (e.g., United Kingdom and United States) coincided with collapses in net exports in major surplus economies. - Transmission channels emphasized: interest rate channel, exchange rate channel, macrofinancial amplification through duration, credit and equity risk premia, and international trade and commodity price spillovers. ### Shock-specific impulse response highlights (selected quantitative summaries preserved) - Domestic productivity shock: - Persistent hump-shaped increase in inflation and persistent hump-shaped contraction of output; central bank typically raises nominal policy interest rate; real effective exchange rate appreciates; fiscal balance deteriorates; current account balance generally improves via terms-of-trade improvement. - Domestic intertemporal substitution shock: - Persistent hump-shaped expansion of output and persistent hump-shaped increase in inflation; central bank raises nominal policy interest rate; real effective exchange rate appreciates; fiscal balance improves; current account balance deteriorates. - Domestic monetary policy shock: - Persistent increase in the nominal policy interest rate (except under fixed exchange rate regimes) leads to real effective appreciation and persistent hump-shaped contraction of output accompanied by persistent decrease in inflation. - Quantified response: in response to a one percentage point increase in the nominal policy interest rate, the median peak contraction of output is 0.3 percent across economies within a range of 0.1 to 0.4 percent. - Domestic credit risk premium shock (short-term nominal market interest rate): - Persistent increase in the short term nominal market interest rate: currency appreciates in real effective terms except under a currency union; persistent hump-shaped contraction of output and persistent decrease in inflation. - Quantified response: in response to a one percentage point increase in the short term nominal market interest rate, the median peak contraction of output is 0.2 percent across economies, within a range of 0.0 to 0.3 percent. - Central bank generally cuts the nominal policy interest rate to stabilize inflation and output; fiscal balance deteriorates; current account improves. - Domestic duration risk premium shock (long-term nominal market interest rate): - Persistent increase in the long term nominal market interest rate: persistent hump-shaped contraction of output and persistent hump-shaped decrease in inflation. - Quantified response: in response to a one percentage point increase in the long term nominal market interest rate, the median peak contraction of output is 0.4 percent across economies, within a range of 0.1 to 0.8 percent. - Central bank tends to cut the nominal policy interest rate; currency depreciates in real effective terms; fiscal balance deteriorates; current account improves. - Domestic equity risk premium shock (price of equity): - Persistent increase in the price of equity: persistent hump-shaped expansion of output and persistent hump-shaped increase in inflation. - Quantified response: in response to a ten percent increase in the price of equity, the median peak expansion of output is 0.2 percent across economies, within a range of 0.0 to 0.5 percent. - Central bank usually raises the nominal policy interest rate; currency appreciates; fiscal balance improves; current account deteriorates. - Domestic fiscal expenditure shock (improvement in fiscal balance): - Persistent improvement in fiscal balance driven by fiscal expenditure: persistent contraction of output and generally decrease in inflation. - Quantified response: in response to a one percentage point increase in the ratio of the primary fiscal balance to nominal output, the median peak expansion of output is 1.1 percent within a range of 0.2 to 1.8 percent; response tends to decrease across economies with their trade openness. - Central bank usually cuts the nominal policy interest rate; currency depreciates; current account improves. - Domestic fiscal revenue shock (improvement in fiscal balance): - Persistent improvement in fiscal balance driven by fiscal revenue: persistent contraction of output and generally decrease in inflation. - Quantified response: in response to a one percentage point increase in the ratio of the primary fiscal balance to nominal output, the median peak contraction of output is 0.5 percent within a range of 0.1 to 0.7 percent, and tends to decrease across economies with their trade openness. The central bank... ### Shock responses under specific regimes and commodities - Domestic monetary policy shock (fixed exchange rate regime): - Transient increase in the nominal policy interest rate induces only a transient appreciation in real effective terms; fiscal balance deteriorates due to fall in output; current account improves commensurate with larger fall in domestic demand. - Shock responses: energy and nonenergy commodity price markup shocks: - World energy or nonenergy commodity price markup shock raises inflation and central bank raises nominal policy interest rate. - For net exporters: currency appreciates in real effective terms; terms-of-trade driven expansion of domestic demand occurs; output expands; fiscal and current account balances tend to improve. - For net importers: currency depreciates; terms-of-trade driven contraction of domestic demand occurs; output contracts; fiscal and current account balances tend to deteriorate. ### Forecast error variance decompositions — methodology and key findings - Methodology: decompositions measure contributions of mutually exclusive sets of structural shocks to unpredictable variation in endogenous variables at different horizons, averaged over the business cycle. - Endogenous variables analyzed: consumption price inflation, output, domestic demand, nominal policy interest rate, real effective exchange rate, ratio of the fiscal balance to nominal output, ratio of the current account balance to nominal output. - Structural shock sets: domestic supply, foreign supply, domestic demand, foreign demand, world monetary policy, world fiscal policy, world risk premium, world terms of trade shocks. - Key findings: - Inflation: primarily driven by supply shocks, and to a lesser extent demand and monetary policy shocks, at all horizons. Contributions of domestic vs. foreign supply and demand shocks generally decrease across economies with their trade openness and increase with their monetary policy autonomy. - Output: primarily attributable to demand shocks, together with monetary policy shocks, at high frequencies. Supply shocks are major contributors at low frequencies. - Domestic demand: domestic demand shocks are large contributors at all frequencies; fiscal policy shocks significant at high frequencies. - Nominal policy interest rate: primarily driven by monetary policy shocks at all horizons; supply shocks major at long horizons. - Real effective exchange rate: most unpredictable variation attributed to risk premium shocks, and to a lesser extent monetary policy shocks, at all frequencies. - Fiscal balance: primarily driven by fiscal policy shocks at short horizons; monetary policy contributions increase with net government debt positions; supply shocks major at long horizons. - Current account: most unpredictable variation attributed to demand and risk premium shocks at all horizons. ### Historical decompositions — inflation and output growth - Inflation deviations from implicit targets: primarily attributed to economy-specific combinations of domestic and foreign supply and demand shocks, together with world risk premium and terms of trade shocks. - Output growth and business cycle dynamics: - Primarily attributed to economy-specific combinations of domestic and foreign demand shocks, together with world fiscal policy and risk premium shocks. - Major deficit economies (United Kingdom, United States): business cycles primarily driven by domestic demand shocks. - Major surplus economies (China, Germany): business cycles primarily driven by foreign demand shocks. - Business cycle fluctuations typically 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. - Global financial crisis dynamics: - Build up: positive domestic and foreign demand shocks contributed to accumulation of excess demand globally, amplified by world risk premium shocks; synchronized rise in inflation. - During crisis: negative domestic and foreign demand shocks, amplified by world risk premium shocks, rapidly eliminated excess demand producing excess supply pressure; synchronized global recession mitigated by unsystematic monetary and fiscal interventions and reflected in synchronized fall in inflation. - Post-crisis recovery: positive domestic and foreign demand shocks, generally amplified by world risk premium shocks, gradually reduced excess supply pressure; synchronized recovery decelerated by world fiscal policy shocks, particularly in the Euro Area periphery. ### Spillover analysis — framework, shocks, and main findings - Framework: estimated panel unobserved components model with trade, financial and commodity price linkages; macroeconomic shocks transmitted via direct financial linkages; financial shocks also transmitted via indirect contagion effects. - Systemic economies considered: China, the Euro Area, Japan, the United Kingdom and the United States. - Macroeconomic shocks considered: productivity, intertemporal substitution, monetary policy, fiscal expenditure, fiscal revenue shocks. - Financial shocks considered: credit risk premium, duration risk premium, equity risk premium shocks. - Simulated conditional betas (output comovement): - 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. - Implies weak international business cycle comovement beyond close trading partners, except during episodes of financial stress when financial shocks amplify contagion effects. - Macroeconomic shock spillovers: generally small but concentrated and gravity-like. - Financial shock spillovers: generally large and diffuse; transmitted via international comovement in financial asset prices and require strong international comovement in risk premia; contagion strongest from the United States, strong to emerging economies with open capital accounts, moderate to advanced economies, weak to emerging economies with closed capital accounts. - Spillover impulse response patterns (summary): - Productivity shock in a systemic economy: recipient currencies generally depreciate; recipient terms-of-trade driven inflation increases and output expands; fiscal and current account balances usually improve. - Intertemporal substitution shock in a systemic economy: recipient economies experience inflation increases and output expansions, amplified by currency depreciations; fiscal and current account balances tend to improve. - Monetary policy shock in a systemic economy: recipient currencies generally depreciate; foreign demand driven decreases in inflation and contractions of output occur; fiscal and current account balances usually deteriorate. - Credit/duration risk premium shocks in a systemic economy: recipient short- and long-term nominal market interest rates increase (international money and bond market contagion); decreases in inflation and contractions of output in recipient economies occur, with deteriorations of fiscal and current account balances. - Equity risk premium shock in a systemic economy: recipient equity prices generally increase; increases in inflation and expansions of output in recipient economies occur, with improvements in fiscal and current account balances. - Fiscal expenditure/revenue shocks improving fiscal balance in a systemic economy: foreign demand driven decreases in inflation and contractions of output in recipient economies arise, amplified by appreciations of their currencies; recipient fiscal and current account balances tend to deteriorate. ### Forecasting — methodology, results, and diagnostics - Bayesian forecasting procedure combines restricted forecasts from the panel unobserved components model with judgment. - State space formulation: signal equations (104) and (106), state equation (105); prediction, Bayesian updating, and smoothing equations (128)–(143), (134)–(137), (138)–(143). - Combined forecasts are recursive weighted averages of restricted model forecasts and IMF judgmental forecasts: - Restricted forecasts generated subject to constant real effective exchange rates and common assumptions for energy and nonenergy commodity prices. - Weight on restricted forecasts decreases with objective uncertainty and increases with subjective uncertainty of judgmental forecasts. - Forecast results and diagnostics: - Sequential unconditional forecasts: model capable of predicting business cycle turning points; suggested a synchronized global moderation was overdue prior to the global financial crisis; underpredicted severity of synchronized global recession and overpredicted its disinflationary impact; forecasted synchronized global recovery but systematically underpredicted its weakness in most advanced economies. - Conditional forecasts: combined forecasts of inflation and output growth generally lie between restricted forecasts and judgmental forecasts; restricted forecasts tend to lie near unrestricted forecasts; forecasts point to gradual cyclical expansion in most advanced economies and subdued output growth in many emerging economies. - Conditional forecast decompositions: effects on unrestricted forecasts from conditioning on constant real effective exchange rates and paths for commodity prices primarily measured by contributions from world risk premium and terms of trade shocks; effects on restricted forecasts from judgment primarily measured by domestic supply and demand shocks. Domestic supply shocks of variable sign account for most persistent discrepancies between restricted and judgmental forecasts; negative domestic demand shocks account for patterns in economies undergoing balance sheet deleveraging with spillovers to close trading partners. ### Figures and tables (contents summary) - Table 1: Parameter Estimation Results — global priors and selected posteriors (rescaled observed endogenous variables by factor of 100). - Figures include: Output Gap Estimates; Impulse Responses to domestic and world shocks (productivity, intertemporal substitution, monetary policy, credit/duration/equity risk premia, fiscal expenditure/revenue, world energy and nonenergy commodity price markup shocks); Forecast Error Variance Decompositions (consumption price inflation, output, domestic demand, nominal policy interest rate, real effective exchange rate, fiscal balance ratio, current account ratio); Historical Decompositions (consumption price inflation, output growth); Simulated Conditional Betas of the Output Gap; Peak Impulse Responses to foreign/systemic shocks; Sequential Unconditional and Conditional Forecasts and their Decompositions. - Figure notes preserve response horizons and units (e.g., consumption price inflation and nominal policy interest rate expressed as annual percentage rates; response horizons 0–48–121–1620; conditional forecasts include symmetric 90 percent confidence intervals). ### Policy implications and recommendations (model applications) - Monetary policy tradeoffs: productivity shocks that raise inflation while contracting output pose tradeoffs—central banks typically raise policy rates to stabilize inflation, producing output contractions and exchange rate appreciation; policymakers should weigh inflation stabilization costs against output losses. - Macroprudential importance: macrofinancial linkages—credit, duration and equity risk premia—amplify shocks and transmit spillovers; monitoring and macroprudential policies may help limit amplification. - Fiscal policy design: model quantifies effects of fiscal shocks on output, balances and net foreign asset positions, informing design of countercyclical automatic stabilizers and fiscal sustainability assessments. - Trend specification: robust trend specification (random-walk trends with allowance for structural breaks) is crucial for policy analysis and forecasting in presence of intermittent structural breaks; policymakers should treat trend-based judgment and structural break detection as integral to policy formulation. ### Conclusion — scope, contributions, and limitations - Model develops a structural macroeconometric panel unobserved components representation of thirty five economies, encompassing a panel DSGE approximation with monetary and fiscal transmission and extensive macrofinancial linkages. - Demonstrated applications: accounting for business cycle fluctuations, quantifying monetary and fiscal transmission mechanisms, generating conditional forecasts of inflation and output growth. - Uses a Bayesian approach for conditioning on judgment in estimation and forecasting. - Consolidates theoretical and empirical knowledge about world business cycle dynamics and highlights model deficiencies—many trace to specifications of capital and labor input markets in the underlying panel DSGE model; extending these specifications is an objective for future research. *Source: _wp13253 - Appendix A. Description of the Multivariate Panel Data Set (extracted content from the supplied PDF).* ### Appendix A. Description of the Multivariate Panel Data Set ..................................................48 ### Appendix A. Description of the Multivariate Panel Data Set ### Appendices - Appendix A. Description of the Multivariate Panel Data Set ..................................................48 - Appendix B. Tables and Figures ..............................................................................................50 ### Tables - 1. Parameter Estimation Results ..............................................................................................50 ### Figures - 1. Output Gap Estimates ..........................................................................................................52 - 2. Impulse Responses to a Domestic Productivity Shock ........................................................53 - 3. Impulse Responses to a Domestic Intertemporal Substitution Shock .................................54 - 4. Impulse Responses to a Domestic Monetary Policy Shock .................................................55 - 5. Impulse Responses to a Domestic Credit Risk Premium Shock..........................................56 - 6. Impulse Responses to a Domestic Duration Risk Premium Shock .....................................57 - 7. Impulse Responses to a Domestic Equity Risk Premium Shock .........................................58 - 8. Impulse Responses to a Domestic Fiscal Expenditure Shock .............................................59 - 9. Impulse Responses to a Domestic Fiscal Revenue Shock ...................................................60 - 10. Impulse Responses to a World Energy Commodity Price Markup Shock ........................61 - 11. Impulse Responses to a World Nonenergy Commodity Price Markup Shock ..................62 - 12. Forecast Error Variance Decompositions of Consumption Price Inflation .......................63 - 13. Forecast Error Variance Decompositions of Output ..........................................................64 - 14. Forecast Error Variance Decompositions of Domestic Demand .......................................65 - 15. Forecast Error Variance Decompositions of the Nominal Policy Interest Rate ................66 - 16. Forecast Error Variance Decompositions of the Real Effective Exchange Rate ...............67 - 17. Forecast Error Variance Decompositions of the Fiscal Balance Ratio ..............................68 - 18. Forecast Error Variance Decompositions of the Current Account Balance Ratio .............69 - 19. Historical Decompositions of Consumption Price Inflation ..............................................70 - 20. Historical Decompositions of Output Growth ...................................................................71 - 21. Simulated Conditional Betas of the Output Gap................................................................72 - 22. Peak Impulse Responses to Foreign Productivity Shocks .................................................73 - 23. Peak Impulse Responses to Foreign Intertemporal Substitution Shocks ...........................74 - 24. Peak Impulse Responses to Foreign Monetary Policy Shocks ..........................................75 - 25. Peak Impulse Responses to Foreign Credit Risk Premium Shocks ...................................76 - 26. Peak Impulse Responses to Foreign Duration Risk Premium Shocks ...............................77 - 27. Peak Impulse Responses to Foreign Equity Risk Premium Shocks ..................................78 - 28. Peak Impulse Responses to Foreign Fiscal Expenditure Shocks .......................................79 - 29. Peak Impulse Responses to Foreign Fiscal Revenue Shocks ............................................80 - 30. Sequential Unconditional Forecasts of Consumption Price Inflation ................................81 - 31. Sequential Unconditional Forecasts of Output Growth .....................................................82 - 32. Conditional Forecasts of Consumption Price Inflation ......................................................83 - 33. Conditional Forecasts of Output Growth ...........................................................................84 - 34. Conditional Forecast Decompositions for Consumption Price Inflation ...........................85 - 35. Conditional Forecast Decompositions for Output Growth ................................................86 *Source: _wp13253 - Appendix A. Description of the Multivariate Panel Data Set* ### References ............................................................................................................. ### _wp13253 - References ### Model framework and purpose - Develops a structural macroeconometric panel unobserved components model of the world economy disaggregated into thirty five national economies. - Embeds an approximate linear panel dynamic stochastic general equilibrium (DSGE) model at cyclical frequencies and flexible random-walk trend components to preserve robustness to intermittent structural breaks. - Incorporates nominal and real rigidities, macrofinancial linkages, and international trade, financial and commodity price linkages to serve as conduits for spillover transmission. - Derivation imposes functional form restrictions on selected aggregators and parameter restrictions on selected equilibrium conditions to circumvent tracking bilateral trade and financial flows. - Estimation and forecasting proceed in a Bayesian framework that conditions on judgment in estimation and forecasting. ### Data, estimation sample, and observed variables - Sample period: 1999Q1 through 2012Q4 (estimation results reported for 1999Q3 through 2012Q4). - Number of economies modeled: thirty five (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). - Number of observed endogenous variables: four hundred one. - Observed macroeconomic and financial market variables include: the price of output, the price of consumption, the quantity of output, the quantity of domestic demand, the nominal policy interest rate, the short term nominal market interest rate, the long term nominal market interest rate, the price of equity, the nominal bilateral exchange rate, the quantity of public domestic demand, the ratio of the fiscal balance to nominal output, the ratio of the trade balance to nominal output, and the prices of energy and nonenergy commodities. ### Household, production, trade, and policy structure (model ingredients) - Heterogeneous households: continuum indexed by [0,1] differentiated by credit constrained vs. unconstrained types with measures Uϕ and Cϕ, Uϕ + Cϕ = 1. - Financial assets: internationally traded and local currency short term bonds (discount), long term bonds (perpetual), and stocks, with CES intratemporal subutilities and multiple nested CES aggregators for asset vintages, economies, industries, and firms. - Preferences: include external habit formation in consumption and precautionary savings motive; parameters and shocks explicitly defined (e.g., ν, ψ, μ, ϕ, θ, etc.) with the same notation as the source. - Production: industries k = 1,...,M including energy (k = 1) and nonenergy commodity (k = 2) produced under decreasing returns to scale for exports; other industries produce differentiated goods under constant returns to scale. Final output: Leontief aggregator over industries; industry final output: CES over intermediate goods; intermediate firms are monopolistically competitive and may be price stickly per Calvo-type mechanisms. - Import and export sectors: Leontief aggregators for final imports/exports; CES production/functions for import composition; Monacelli-style nominal import price rigidity with partial indexation and time-varying probability of optimal price adjustment. - Monetary policy: nominal policy interest rate follows a partial-adjustment monetary policy rule with regime-specific target variables (flexible inflation targeting, managed exchange rate, fixed exchange rate). Monetary policy shocks are mean zero and serially uncorrelated (P_it^ν). - Fiscal policy: fiscal authority controls public consumption and the labor/earnings tax rate via partial adjustment fiscal expenditure and revenue rules; fiscal shocks G_it^ν and T_it^ν are mean zero and serially uncorrelated. Government budget constraint and asset holdings across domestic short and long term bonds are explicitly specified. - Asset market relationships: money market linking short-term yield to policy rate plus internationally and serially correlated credit risk premium shock S_it^υ; bond and stock relationships involve duration and equity risk premium shocks with international contagion specifications. ### Approximate linear panel unobserved components representation - Cyclical components (denoted with a hat, e.g., x̂_it) are obtained by linearizing equilibrium conditions around a stationary deterministic steady state (abstracting from long-run balanced growth and featuring zero inflation and net financial asset holdings unless stated). - Trend components follow independent random walks; cyclical and trend components are additively separable: x_it = x̂_it + x_it (trend). - Innovations are assumed independent and multivariate normal as an identifying restriction. - Bilateral and world weights: exports for Z = X, imports for Z = M, average for Z = T; portfolio weights based on debt (Z = B) and equity (Z = S); world weights based on output (ZY = Y), money market capitalization (ZM = M), bond market cap (ZB = B), stock market cap (ZS = S). - Key cyclical relationships (preserved notation and form): output price Phillips curve (equation 64), consumption price Phillips curve (65), output demand (66), domestic demand (67), nominal ex ante portfolio return (68), monetary policy rule in cyclical form (69), money market (70), bond market (71), stock market (72), profits (73), foreign exchange relationship (74), internal terms of trade (75), external terms of trade dynamics and import price Phillips curve (76), commodity price Phillips curve (85), fiscal and national accounting cyclical relationships (77–84). ### Trend component specification - Trend components of prices, quantities, interest rates, equity price, bilateral exchange rates, fiscal and trade balances follow random walks with independent innovations; precise equations are provided for each (e.g., equations 86–98; interest rate trends 92–94; equity and bilateral FX 95–96; fiscal/trade balance trends 97–98). - Real rates and real bilateral exchange rates satisfy the usual Fisher-like relationships in both cyclical and trend components. ### Estimation approach and computational details - Estimation: Bayesian procedure conditioning on common structural parameter priors and judgment on trend paths; inference based on asymptotic normal approximation around posterior mode. - State space representation: cyclical second-order linear rational expectations system solved using Klein (2000) procedure; Kalman filter and de Jong (1989) smoother used for state estimation and smoothing. - Signal equation extension: includes time-deterministic coefficient matrix for alternative estimates/forecasts as stochastic restrictions (equation 106). - Posterior mode obtained by maximizing log posterior kernel with modified steepest ascent; starting values via differential evolution algorithm (Storn and Price (1997)). - Posterior identification checks: Klein (2000) sufficient condition satisfied in neighborhood of posterior mode; Hessian estimator not nearly singular at posterior mode indicating local identification. - Priors: structural parameters centered within empirical literature ranges; monetary regimes specified by country; capital controls in China, India, Saudi Arabia; quotation currency is U.S. dollar; great ratios and bilateral weights calibrated to 2010 observed values. - Treatment of structural breaks in trends: extends Hodrick-Prescott filter to allow time-varying smoothing parameter, allowing at most one structural break per observed variable; smoothing parameter may switch from 6400 to 1600 for one period if the normalized objective does not exceed that for U.S. output. Prior trend estimates and their mean squared error matrices are used to impose stochastic restrictions; proportionality factor for trend judgment set to 10^8 to minimize its influence on posterior trend estimates while ensuring stationarity of cyclical estimates. ### Estimation results (high-level) - Parameters: posterior modes of most structural parameters are close to prior means due to tight priors, but data are informative for several parameters producing substantial updates and revised impulse responses. - Innovation variances: estimated variances driving cyclical components are within ranges reported in the literature after data rescaling; variances for trend component innovations vary considerably across economies and variables. - Unobserved components: intermittent structural breaks are prevalent; the time-varying smoothing/trend estimator and prior uncertainty used to control for these; initial conditions for some state variables are treated as parameters and calibrated to match initial realizations or prior trend estimates. - Posterior mode computed for sample 1999Q3–2012Q4; joint estimation uses levels of four hundred one variables for thirty five economies. ### Key substantive findings and policy-relevant analysis - Output gap and global dynamics: - Smoothed model-consistent output gap estimates (conditional on structural parameter priors and trend judgments) indicate that the synchronized buildup in excess demand prior to the global financial crisis was primarily driven by excessive expansion of private domestic demand in most economies. - Excessive expansion of net exports was also a major contributor in major surplus economies (e.g., China and Germany). - The global financial crisis triggered a rapid synchronized unwinding of excess demand, producing substantial excess supply pressure in many economies. Collapses in private domestic demand in major deficit economies (e.g., United Kingdom and United States) coincided with collapses in net exports in major surplus economies. - Impulse response insights (selected): - Domestic productivity shock: persistent hump-shaped increase in inflation and persistent hump-shaped contraction of output; central bank typically raises nominal policy interest rate to control inflation; real effective exchange rate appreciates; fiscal balance deteriorates due to fall in output; current account balance generally improves via terms-of-trade improvement. - Domestic intertemporal substitution shock: persistent hump-shaped expansion of output and persistent hump-shaped increase in inflation; central bank raises nominal policy interest rate to stabilize; real effective exchange rate appreciates; fiscal balance improves; current account balance deteriorates due to larger rise in domestic demand. - Domestic monetary policy shock: a persistent increase in the nominal policy interest rate (except under fixed exchange rate regimes) leads to real effective appreciation and a persistent hump-shaped contraction of output accompanied by a persistent decrease in inflation. - Quantified response: in response to a one percentage point increase in the nominal policy interest rate, the median peak contraction of output is 0.3 percent across economies within a range of 0.1 to 0.4 percent. - Transmission channels emphasized: interest rate channel, exchange rate channel, macrofinancial amplification through duration, credit and equity risk premia, and international trade and commodity price spillovers. ### Policy implications and recommendations (implicit in model applications) - Monetary policy faces tradeoffs when productivity shocks raise inflation while contracting output; central banks typically raise policy rates to stabilize inflation, producing output contractions and exchange rate appreciation—policymakers should weigh inflation stabilization costs against output losses in such episodes. - The model highlights the importance of macrofinancial linkages—credit, duration and equity risk premia—in amplifying shocks and transmitting spillovers; monitoring and macroprudential policies may help limit amplification. - Fiscal policy responses are characterized via expenditure and revenue rules with partial adjustment; the model quantifies effects of fiscal shocks on output, balances and net foreign asset positions, informing design of countercyclical automatic stabilizers and fiscal sustainability assessments. - Robust trend specification (random-walk trends with allowance for structural breaks) is crucial for policy analysis and forecasting in presence of intermittent structural breaks; policymakers should treat trend-based judgment and structural break detection as integral to policy formulation. *Italic: Source — _wp13253 - References (extracted content from the supplied PDF)._ ### 0.2 percentage points within a range of 0.2 to 0.3 percentage points. The fiscal balance ### _wp13253 - 0.2 percentage points within a range of 0.2 to 0.3 percentage points. The fiscal balance ### Domestic monetary policy shock (fixed exchange rate regime) - A transient increase in the nominal policy interest rate: - Induces only a transient appreciation of the currency in real effective terms. - The fiscal balance deteriorates due to the fall in output. - The current account balance improves commensurate with the larger fall in domestic demand. ### Domestic credit risk premium shock (short-term nominal market interest rate) - A persistent increase in the short term nominal market interest rate: - The currency appreciates in real effective terms except under a currency union. - There arises a persistent hump shaped contraction of output, accompanied by a persistent decrease in inflation. - In response to a one percentage point increase in the short term nominal market interest rate: - The median peak contraction of output is 0.2 percent across economies, within a range of 0.0 to 0.3 percent. - The central bank generally cuts the nominal policy interest rate to stabilize inflation and output. - The fiscal balance deteriorates due to the fall in output. - The current account balance improves reflecting the larger fall in domestic demand. ### Domestic duration risk premium shock (long-term nominal market interest rate) - A persistent increase in the long term nominal market interest rate: - There arises a persistent hump shaped contraction of output, accompanied by a persistent hump shaped decrease in inflation. - In response to a one percentage point increase in the long term nominal market interest rate: - The median peak contraction of output is 0.4 percent across economies, within a range of 0.1 to 0.8 percent. - The central bank tends to cut the nominal policy interest rate to stabilize inflation and output. - The currency depreciates in real effective terms. - The fiscal balance deteriorates due to the fall in output. - The current account balance improves commensurate with the larger fall in domestic demand. ### Domestic equity risk premium shock (price of equity) - A persistent increase in the price of equity: - There arises a persistent hump shaped expansion of output, accompanied by a persistent hump shaped increase in inflation. - In response to a ten percent increase in the price of equity: - The median peak expansion of output is 0.2 percent across economies, within a range of 0.0 to 0.5 percent. - The central bank usually raises the nominal policy interest rate to stabilize inflation and output. - The currency appreciates in real effective terms. - The fiscal balance improves due to the rise in output. - The current account balance deteriorates reflecting the larger rise in domestic demand. ### Domestic fiscal expenditure shock (improvement in fiscal balance) - A persistent improvement in the fiscal balance driven by fiscal expenditure: - There arises a persistent contraction of output, generally accompanied by a decrease in inflation. - In response to a one percentage point increase in the ratio of the primary fiscal balance to nominal output: - The median peak expansion of output is 1.1 percent within a range of 0.2 to 1.8 percent. - The response tends to decrease across economies with their trade openness. - The central bank usually cuts the nominal policy interest rate to stabilize inflation and output. - The currency depreciates in real effective terms. - The current account balance improves, reflecting the larger fall in domestic demand than in output. ### Domestic fiscal revenue shock (improvement in fiscal balance) - A persistent improvement in the fiscal balance driven by fiscal revenue: - There arises a persistent contraction of output, generally accompanied by a decrease in inflation. - In response to a one percentage point increase in the ratio of the primary fiscal balance to nominal output: - The median peak contraction of output is 0.5 percent within a range of 0.1 to *Source: _wp13253 - 0.2 percentage points within a range of 0.2 to 0.3 percentage points. The fiscal balance* ### 0.7 percent, and tends to decrease across economies with their trade openness. The central bank ### _wp13253 - 0.7 percent, and tends to decrease across economies with their trade openness. The central bank ### Shock responses: energy and nonenergy commodity price markup shocks - In response to a world energy or nonenergy commodity price markup shock (increase in the price of energy or nonenergy commodities): - Inflation increases and the central bank raises the nominal policy interest rate. - For net exporters of energy or nonenergy commodities: - The currency generally appreciates in real effective terms. - Terms of trade driven expansion of domestic demand occurs, mitigated by monetary policy tightening. - Output expands in spite of terms of trade driven expenditure switching. - The fiscal and current account balances tend to improve. - For net importers of energy or nonenergy commodities: - The currency generally depreciates in real effective terms. - Terms of trade driven contraction of domestic demand occurs, amplified by monetary policy tightening. - Output contracts in spite of terms of trade driven expenditure switching. - The fiscal and current account balances tend to deteriorate. ### Forecast error variance decompositions — methodology and shock set - Forecast error variance decompositions measure contributions of mutually exclusive sets of structural shocks to unpredictable variation in endogenous variables at different horizons, averaged over the business cycle. - Endogenous variables analyzed: consumption price inflation, output, domestic demand, nominal policy interest rate, real effective exchange rate, ratio of the fiscal balance to nominal output, ratio of the current account balance to nominal output. - Structural shock sets under consideration: domestic supply shocks, foreign supply shocks, domestic demand shocks, foreign demand shocks, world monetary policy shocks, world fiscal policy shocks, world risk premium shocks, world terms of trade shocks. ### Forecast error variance decompositions — key findings - Inflation: - Primarily driven by supply shocks, and to a lesser extent demand and monetary policy shocks, at all horizons. - Contributions of domestic supply and demand shocks relative to foreign supply and demand shocks generally decrease across economies with their trade openness and increase with their monetary policy autonomy. - Output: - Primarily attributable to demand shocks, together with monetary policy shocks, at high frequencies. - Contribution of domestic demand shocks relative to foreign demand shocks generally decreases across economies with their trade openness. - Supply shocks are major contributors to unpredictable output fluctuations at low frequencies. - Domestic demand: - Domestic demand shocks are larger contributors to unpredictable variation at all frequencies; foreign demand shocks are smaller contributors. - Fiscal policy shocks tend to be significant contributors to unpredictable domestic demand fluctuations at high frequencies. - Nominal policy interest rate: - Primarily driven by monetary policy shocks at all horizons. - Supply shocks are also major contributors at long horizons; the relative contribution of domestic vs. foreign supply shocks generally increases across economies with their monetary policy autonomy. - Real effective exchange rate: - Most unpredictable variation attributed to risk premium shocks, and to a lesser extent monetary policy shocks, at all frequencies. - Supply and demand shocks are also major contributors at low frequencies. - Fiscal balance (ratio to nominal output): - Primarily driven by fiscal policy shocks, and to a lesser extent demand and monetary policy shocks, at short horizons. - Contribution of monetary policy shocks generally increases across economies with their net government debt positions. - Supply shocks are major contributors at long horizons. - Current account balance (ratio to nominal output): - Most unpredictable variation attributed to demand and risk premium shocks at all horizons. - Monetary policy shocks matter for economies with high net foreign asset or debt positions. - Contribution of domestic demand shocks relative to foreign demand shocks tends to decrease across economies with their trade openness. ### Historical decompositions — inflation and output growth - Historical decompositions measure time-varying contributions of the same structural shock sets to realizations of endogenous variables. - Inflation deviations from implicit targets: - Primarily attributed 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 with well established flexible inflation targeting regimes such as Australia, Canada, New Zealand, Norway, Sweden and the United Kingdom. - Output growth and business cycle dynamics: - Primarily attributed to economy specific combinations of domestic and foreign demand shocks, together with world fiscal policy and risk premium shocks. - Business cycle fluctuations in major deficit economies such as the United Kingdom and the United States have been primarily driven by domestic demand shocks. - Business cycle fluctuations in major surplus economies such as China and Germany have been primarily driven by foreign demand shocks. - In both groups, business cycle fluctuations have usually been amplified by world risk premium shocks and mitigated by world fiscal policy shocks. - Potential output growth rates have generally stabilized at relatively low levels in advanced economies, and at relatively high levels in emerging economies. - Global financial crisis dynamics: - Build up to the crisis: positive domestic and foreign demand shocks contributed to gradual accumulation of excess demand globally, amplified by world risk premium shocks; synchronized global rise in inflation, usually amplified by world terms of trade shocks. - During the crisis: negative domestic and foreign demand shocks, amplified and accelerated by world risk premium shocks, rapidly eliminated excess demand pressure, often creating excess supply pressure; synchronized global recession mitigated by unsystematic monetary and fiscal policy interventions and reflected in a synchronized global fall in inflation, usually amplified by world terms of trade shocks. - Post-crisis recovery: positive domestic and foreign demand shocks, generally amplified by world risk premium shocks, gradually reduced excess supply pressure; synchronized global recovery decelerated by world fiscal policy shocks, particularly in the Euro Area periphery. ### Spillover analysis — framework and shocks considered - Framework: estimated panel unobserved components model with trade, financial and commodity price linkages; macroeconomic shocks transmitted via direct financial linkages; financial shocks additionally transmitted via indirect financial linkages representing contagion effects. - Systemic economies considered: China, the Euro Area, Japan, the United Kingdom and the United States. - Macroeconomic shocks considered: productivity shocks, intertemporal substitution shocks, monetary policy shocks, fiscal expenditure shocks, fiscal revenue shocks. - Financial shocks considered: credit risk premium shocks, duration risk premium shocks, equity risk premium shocks. ### Spillover analysis — simulated conditional betas (output comovement) - Simulated conditional betas measure contemporaneous comovement driven by selected structural shocks, averaged over the business cycle. - 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. - Implies weak international business cycle comovement beyond close trading partners. - During episodes of financial stress in systemic economies (e.g., global financial crisis), international business cycle comovement is more uniformly strong due to prevalence of financial shocks propagating via elevated contagion effects. - Macroeconomic shock spillovers: - Generally small but concentrated; reflect bilateral trade relationships and exhibit gravity (concentrated among geographically close trading partners). - Pattern diluted by supply shocks, which are transmitted primarily via terms of trade shifts. - Financial shock spillovers: - Generally large and diffuse; transcend bilateral portfolio investment relationships (home bias). - Transmitted primarily via international comovement in financial asset prices and require strong international comovement in risk premia. - Intensity of contagion effects varies: - Uniquely strong from the United States (depth of money, bond and stock markets). - Strong to emerging economies with open capital accounts. - Moderate to advanced economies. - Weak to emerging economies with closed capital accounts. ### Spillover analysis — impulse response function findings - Productivity shock in a systemic economy (increase in inflation and contraction of output): - Recipient economies' currencies generally depreciate in real effective terms. - Terms of trade driven increases in inflation and expansions of output in recipient economies occur despite lower foreign demand. - Fiscal and current account balances usually improve in recipient economies. - Intertemporal substitution shock in a systemic economy (increase in inflation and expansion of output): - Recipient economies experience foreign demand driven increases in inflation and expansions of output, amplified by depreciations of their currencies in real effective terms. - Fiscal and current account balances tend to improve. - Monetary policy shock in a systemic economy (increase in nominal policy interest rate): - Recipient economies' currencies generally depreciate in real effective terms. - Foreign demand driven decreases in inflation and contractions of output occur in recipient economies, mitigated by terms of trade deteriorations. - Fiscal and current account balances usually deteriorate. - Credit risk premium shock in a systemic economy (increase in short term nominal market interest rate): - Short term nominal market interest rates of recipient economies generally increase (international money market contagion). - Decreases in inflation and contractions of output in recipient economies occur, with deteriorations of fiscal and current account balances. - Duration risk premium shock in a systemic economy (increase in long term nominal market interest rate): - Long term nominal market interest rates of recipient economies usually increase (international bond market contagion). - Decreases in inflation and contractions of output in recipient economies occur, with deteriorations of fiscal and current account balances. - Equity risk premium shock in a systemic economy (increase in price of equity): - Prices of equity in recipient economies generally increase (international stock market contagion). - Increases in inflation and expansions of output in recipient economies occur, accompanied by improvements in fiscal and current account balances. - Fiscal expenditure shock improving fiscal balance in a systemic economy: - Foreign demand driven decreases in inflation and contractions of output in recipient economies arise, amplified by appreciations of their currencies in real effective terms. - Recipient economies’ fiscal and current account balances tend to deteriorate. - Fiscal revenue shock improving fiscal balance in a systemic economy: - Similar effects as fiscal expenditure shock: foreign demand driven decreases in inflation and contractions of output in recipient economies, amplified by appreciations of their currencies in real effective terms, with deteriorations in fiscal and current account balances. ### Forecasting — methodology - World complexity and model misspecification motivate a Bayesian forecasting procedure combining restricted forecasts from the panel unobserved components model with judgment. - Linear state space formulation with signal equations (104) and (106), and state equation (105); prediction, Bayesian updating, and computationally efficient Bayesian smoothing equations presented (equations (128)–(143), (134)–(137), (138)–(143)). - Under multivariate normality assumptions, recursive forward evaluation of equations (128)–(137) followed by recursive backward evaluation of equations (138)–(143) yields mean squared error optimal conditional forecasts. - Combined forecasts are recursive weighted averages of restricted model forecasts and IMF judgmental forecasts: - Restricted forecasts generated subject to constant real effective exchange rates, and common assumptions for energy and nonenergy commodity prices. - Weight on restricted forecasts decreases with objective uncertainty (time varying forecast error covariance matrix) and increases with subjective uncertainty of judgmental forecasts (represented by same covariance matrix). ### Forecasting — results and diagnostic decompositions - Sequential unconditional forecasts: - Model capable of predicting business cycle turning points. - Suggested a synchronized global moderation was overdue by the time of the global financial crisis. - Model underpredicted the severity of the synchronized global recession and overpredicted its disinflationary impact. - Model forecast the synchronized global recovery but systematically underpredicted its weakness in most advanced economies. - Conditional forecasts: - Combined forecasts of inflation and output growth generally lie between restricted forecasts and judgmental forecasts; restricted forecasts tend to lie near unrestricted forecasts. - Forecasts point to a gradual cyclical expansion in most advanced economies and subdued output growth in many emerging economies. - Conditional forecast decompositions: - Effects on unrestricted forecasts from conditioning on constant real effective exchange rates and given paths for energy and nonenergy commodity prices are primarily measured by contributions from world risk premium and terms of trade shocks, respectively. - Effects on restricted forecasts from conditioning on judgment concerning paths of inflation and output growth are primarily measured by contributions from domestic supply and demand shocks. - Domestic supply shocks of variable sign tend to account for most persistent discrepancies between restricted and judgmental forecasts. - Negative domestic demand shocks account for much of the patterns in economies undergoing balance sheet deleveraging, with substantial spillovers to close trading partners. ### Conclusion — model scope, contributions, and limitations - The paper develops a structural macroeconometric panel unobserved components model of the world economy disaggregated into thirty five national economies. - The model encompasses an approximate linear panel dynamic stochastic general equilibrium model featuring: - A monetary transmission mechanism. - A fiscal transmission mechanism. - Extensive macrofinancial linkages within and across economies. - Demonstrated applications: accounting for business cycle fluctuations, quantifying monetary and fiscal transmission mechanisms, generating conditional forecasts of inflation and output growth. - Framework uses a Bayesian approach for conditioning on judgment in estimation and forecasting. - The model consolidates existing theoretical and empirical knowledge about world business cycle dynamics and suggests explanations for its deficiencies. - Many deficiencies trace to specifications of capital and labor input markets in the underlying panel DSGE model; extending these specifications is an objective for future research. *Source: IMF working paper content provided in the supplied PDF excerpt.* ### Appendix A. Description of the Multivariate Panel Data Set ### Appendix A. Description of the Multivariate Panel Data Set ### Sample coverage and economies - Estimation is based on quarterly data on several macroeconomic and financial market variables observed for thirty five economies over the sample period 1999Q1 through 2012Q4. - The economies under consideration are 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. - Where available, this data was obtained from the GDS and WEO databases compiled by the International Monetary Fund. Otherwise, it was extracted from the IFS database produced by the International Monetary Fund. ### Macroeconomic variables (definitions and measurements) - Price of output - Measured by the seasonally adjusted gross domestic product price deflator. - Price of consumption - Proxied by the seasonally adjusted consumer price index. - Quantity of output - Measured by seasonally adjusted real gross domestic product. - Quantity of domestic demand - Measured by the sum of seasonally adjusted real consumption and investment expenditures. - Quantity of public domestic demand - Measured by the sum of quadratically interpolated annual real consumption and investment expenditures of the general government. - Ratio of the fiscal balance to nominal output - Fiscal balance measured by the quadratically interpolated annual overall fiscal balance of the general government. - Ratio of the trade balance to nominal output - Trade balance measured by the quadratically interpolated annual trade balance for goods and services. - Prices of energy and nonenergy commodities - Proxied by broad commodity price indexes denominated in United States dollars. ### Financial market variables (definitions and measurements) - Nominal policy interest rate - Measured by the central bank discount rate. - Short term nominal market interest rate - Measured by a three month money market rate. - Long term nominal market interest rate - Measured by the ten year government bond yield. - Price of equity - Proxied by a broad stock price index denominated in domestic currency units. - Nominal bilateral exchange rate - Measured by the domestic currency price of one United States dollar. - All financial market variables are expressed as a period average. ### Calibration and data sources - 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. - Macroeconomic great ratios are derived from the WEO and WDI databases. - Financial great ratios are derived from the EWN, BIS and IFS 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 Multivariate Panel Data Set* ### Appendix B. Tables and Figures ### _wp13253 - Appendix B. Tables and Figures ### Table 1. Parameter Estimation Results — global priors and selected posteriors - Table header: "Prior Posterior Mode Mean SE WLD ARG AUS AUT BEL BRA CAN CHN CZE DNK FIN FRA DEU GRC IND IDN IRL ITA JPN KOR MEX NLD NZL NOR POL PRT RUS SAU ZAF ESP SWE CHE THA TUR GBR USA" - Selected parameter prior and posterior entries (preserve numeric precision as in source): - α: Prior 0.9000 0.0900; Posterior Mode 0.9056 - β: Prior 0.9756 0.0000 - χ (B): Prior 0.5000 0.0500; Posterior Mode 0.5365 - χ (S): Prior 0.5000 0.0500; Posterior Mode 0.5058 - η: Prior 4.5000 0.4500; Posterior Mode 4.6184 - γ (Y): Prior 1.0000 0.0000 - γ (M): Prior 1.0000 0.0000 - μ: Prior 0.2500 0.0250; Posterior Mode 0.2496 - ω (Y): Prior 0.9167 0.0917; Posterior Mode 0.8815 - ω (M): Prior 0.8333 0.0833; Posterior Mode 0.8849 - ω (1Y): Prior 0.3333 0.0333; Posterior Mode 0.3326 - ω (2Y): Prior 0.3333 0.0333; Posterior Mode 0.3432 - φ (C): Prior 0.5000 0.0500; Posterior Mode 0.4987 - φ (1L): Prior 0.1000 0.0100; Posterior Mode 0.1081 - φ (2L): Prior 0.2000 0.0200; Posterior Mode 0.2094 - ψ (M): Prior 1.5000 0.1500; Posterior Mode 1.5499 - ρ (i): Prior 0.8500 0.0850; Posterior Mode 0.8053 - ρ (G): Prior 0.8500 0.0850; Posterior Mode 0.8207 - ρ (τ): Prior 0.8500 0.0850; Posterior Mode 0.8448 - σ: Prior 3.5000 0.3500; Posterior Mode 3.6285 - θ (Y): Prior 7.6667 0.0000 - θ (M): Prior 7.6667 0.0000 - ξ (0π): Prior 1.5000 0.1500 (posterior country entries appear in the table) - ξ (1π): Prior 1.5000 0.1500 (posterior country entries appear in the table) - ξ (0Y): Prior 0.1250 0.0125 (posterior country entries appear in the table) - ξ (1Y): Prior 0.1250 0.0125 (posterior country entries appear in the table) - ξ (1): Prior 0.0625 0.0063 (posterior country entries appear in the table) - ζ (G): Prior 2.5e–6 0.0000 - ζ (τ): Prior –2.5e–2 0.0000 - λ (0M): Prior 1.2719 0.1272 (posterior country entries appear in the table) - λ (1M): Prior 0.6359 0.0636 (posterior country entries appear in the table) - λ (2M): Prior 1.9078 0.1908 (posterior country entries appear in the table) - λ (0B): Prior 1.0801 0.1080 (posterior country entries appear in the table) - λ (1B): Prior 0.5401 0.0540 (posterior country entries appear in the table) - λ (2B): Prior 1.6202 0.1620 (posterior country entries appear in the table) - λ (0S): Prior 1.4447 0.1445 (posterior country entries appear in the table) - λ (1S): Prior 0.7223 0.0722 (posterior country entries appear in the table) - λ (2S): Prior 2.1670 0.2167 (posterior country entries appear in the table) - ρ (aggregate): Prior 0.7500 0.0750; Posterior Mode 0.8470 - νρ (C): Prior 0.7500 0.0750; Posterior Mode 0.7323 - νρ (X): Prior 0.7500 0.0750; Posterior Mode 0.7224 - νρ (M): Prior 0.7500 0.0750; Posterior Mode 0.7734 - νρ (iS): Prior 0.7500 0.0750; Posterior Mode 0.7358 - νρ (B): Prior 0.7500 0.0750; Posterior Mode 0.7745 - νρ (S): Prior 0.7500 0.0750; Posterior Mode 0.7376 - νρ (general): Prior 0.7500 0.0750; Posterior Mode 0.7921 - Selected country-level posterior scale parameters (examples from the table; full country matrices are presented in the source): - 2,iY θ σ: sample posterior entries include 4.6e+5, 3.4e+5, 3.3e+5, 4.8e+5 (country-specific) - 2,iM θ σ: sample posterior entries include 8.5e+4, 7.0e+4, 9.5e+4 (country-specific) - 2,i σ (interest rate): sample posterior entries include 1.7e+1, 1.5e+1, 2.2e+1 (country-specific) - 2,C iν σ (consumption variance): sample posterior entries include 9.5e+1, 7.7e+1, 1.1e+2 (country-specific) - 2,X iν σ (exports variance): sample posterior entries include 9.4e–1, 8.4e–1, 1.0e+0 (country-specific) - 2,M iν σ (imports variance): sample posterior entries include 3.8e+0, 3.2e+0, 3.7e+0 (country-specific) - 2,B iν σ, 2,S iν σ, and many other country-specific iν σ entries are reported in the table with scientific notation (e.g., 2.6e–2, 1.7e+0, 7.5e+0, 8.3e–2, 4.6e–1). - Priors and posteriors—notes from table: - "All priors are normally distributed, while all posteriors are asymptotically normally distributed. All observed endogenous variables are rescaled by a factor of 100." ### Figures: contents and notes (by figure title) - Figure 1. Output Gap Estimates - Note: "Decomposes smoothed estimates of the output gap ■ into contributions from domestic demand ■ and net exports ■. Smoothed estimates of the contribution from domestic demand ■ are decomposed into contributions from private domestic demand ■ and public domestic demand ■. Structural breaks are indicated by ▲." - Axis scales: examples include ranges such as -15.0 to 15.0 Percent, -30.0 to 30.0 Percent, and country time axis 2005–2012. - Figure 2. Impulse Responses to a Domestic Productivity Shock - Note: "Depicts the impulse responses of 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 ■, and the ratio of the current account balance to nominal output ■ to domestic productivity shocks which raise output price inflation by one percentage point. Consumption price inflation and the nominal policy interest rate are expressed as annual percentage rates." - Response horizon shown: 0–48–121–1620 (plot ticks: 0 4 8 12 16 20) - Figure 3. Impulse Responses to a Domestic Intertemporal Substitution Shock - Note: "Depicts the impulse responses... to domestic intertemporal substitution shocks which raise domestic demand by one percent. Consumption price inflation and the nominal policy interest rate are expressed as annual percentage rates." - Response horizon shown: 0–48–121–1620 (ticks 0 4 8 12 16 20) - Figure 4. Impulse Responses to a Domestic Monetary Policy Shock - Note: "Depicts the impulse responses... to domestic monetary policy shocks which raise the nominal policy interest rate by one percentage point. Consumption price inflation and the nominal policy interest rate are expressed as annual percentage rates." - Response horizon shown: 0–48–121–1620 - Figure 5. Impulse Responses to a Domestic Credit Risk Premium Shock - Note: "Depicts the impulse responses... to domestic credit risk premium shocks which raise the short term nominal market interest rate by one percentage point. Consumption price inflation and the nominal policy interest rate are expressed as annual percentage rates." - Figure 6. Impulse Responses to a Domestic Duration Risk Premium Shock - Note: "Depicts the impulse responses... to domestic duration risk premium shocks which raise the long term nominal market interest rate by one percentage point. Consumption price inflation and the nominal policy interest rate are expressed as annual percentage rates." - Figure 7. Impulse Responses to a Domestic Equity Risk Premium Shock - Note: "Depicts the impulse responses... to domestic equity risk premium shocks which raise the price of equity by ten percent. Consumption price inflation and the nominal policy interest rate are expressed as annual percentage rates." - Figure 8. Impulse Responses to a Domestic Fiscal Expenditure Shock - Note: "Depicts the impulse responses... to domestic fiscal expenditure shocks which raise the ratio of the primary fiscal balance to nominal output by one percentage point. Consumption price inflation and the nominal policy interest rate are expressed as annual percentage rates." - Figure 9. Impulse Responses to a Domestic Fiscal Revenue Shock - Note: "Depicts the impulse responses... to domestic fiscal revenue shocks which raise the ratio of the primary fiscal balance to nominal output by one percentage point. Consumption price inflation and the nominal policy interest rate are expressed as annual percentage rates." - Figure 10. Impulse Responses to a World Energy Commodity Price Markup Shock - Note: "Depicts the impulse responses... to a world energy commodity price markup shock which raises the price of energy commodities by ten percent. Consumption price inflation and the nominal policy interest rate are expressed as annual percentage rates." - Figure 11. Impulse Responses to a World Nonenergy Commodity Price Markup Shock - Note: "Depicts the impulse responses... to a world nonenergy commodity price markup shock which raises the price of nonenergy commodities by ten percent. Consumption price inflation and the nominal policy interest rate are expressed as annual percentage rates." - Figures 12–18. Forecast Error Variance Decompositions - Figure 12: "Forecast Error Variance Decompositions of Consumption Price Inflation" — decomposes into domestic supply, foreign supply, domestic demand, foreign demand, world monetary policy, world fiscal policy, world risk premium, and world terms of trade shocks. - Figure 13: "Forecast Error Variance Decompositions of Output" - Figure 14: "Forecast Error Variance Decompositions of Domestic Demand" - Figure 15: "Forecast Error Variance Decompositions of the Nominal Policy Interest Rate" - Figure 16: "Forecast Error Variance Decompositions of the Real Effective Exchange Rate" - Figure 17: "Forecast Error Variance Decompositions of the Fiscal Balance Ratio" - Figure 18: "Forecast Error Variance Decompositions of the Current Account Balance Ratio" - All figures show horizon-dependent percent contributions with horizons 0–48–121–1620. - Figures 19–20. Historical Decompositions - Figure 19: "Historical Decompositions of Consumption Price Inflation" — decomposes observed consumption price inflation into trend plus contributions from domestic supply, foreign supply, domestic demand, foreign demand, world monetary policy, world fiscal policy, world risk premium, and world terms of trade shocks. Time axis 2005–2012; many country-specific y-axis scales (e.g., -30.0 to 40.0 Percent for some countries). - Figure 20: "Historical Decompositions of Output Growth" — similar decomposition for output growth; time axis 2005–2012; country-specific scales (examples include -50.0 to 50.0 Percent for some economies). - Figure 21. Simulated Conditional Betas of the Output Gap - Note: "Depicts the betas of the output gap with respect to the contemporaneous output gap in systemic economies conditional on all shocks ■, macroeconomic shocks ■, and financial shocks ■ in each of these systemic economies. These betas are calculated with a Monte Carlo simulation with 999 replications for 2T periods, discarding the first T simulated observations to eliminate dependence on initial conditions, where T denotes the observed sample size." - Axis range examples: -0.25 to 1.50 (per country panels CHN EUR JPN GBR USA shown along x-axis grouping). - Figures 22–29. Peak Impulse Responses to foreign/systemic shocks - Figures 22–24: Peak responses to Foreign Productivity, Intertemporal Substitution, and Monetary Policy shocks (systemic economies CHN EUR JPN GBR USA). Responses reported for consumption price inflation, output, real effective exchange rate, fiscal balance ratio, current account ratio. - Figures 25–29: Peak responses to Foreign Credit Risk Premium, Duration Risk Premium, Equity Risk Premium, Fiscal Expenditure, and Fiscal Revenue shocks. Notes emphasize that consumption price inflation and nominal policy interest rates are annual percentage rates. - Figures 30–31. Sequential Unconditional Forecasts - Figure 30: "Sequential Unconditional Forecasts of Consumption Price Inflation" — observed seasonal log differences vs sequential unrestricted forecasts; sample years plotted 2007–2014. Country-specific y-axis ranges vary widely (examples: Argentina -15.0 to 35.0 Percent; Saudi Arabia 0.0 to 70.0 Percent). - Figure 31: "Sequential Unconditional Forecasts of Output Growth" — observed seasonal log differences vs sequential unrestricted forecasts; sample years plotted 2007–2014; country-specific y-axis ranges vary (examples: Argentina -6.0 to 16.0 Percent; Saudi Arabia -50.0 to 50.0 Percent). - Figures 32–33. Conditional Forecasts (consumption inflation and output) - Figure 32: "Conditional Forecasts of Consumption Price Inflation" — observed series with unrestricted, restricted, judgmental, and combined forecasts, plus symmetric 90 percent confidence intervals (assume normally distributed innovations and known parameters). Sample years 2007–2014. Country-specific y-axis ranges vary. - Figure 33: "Conditional Forecasts of Output Growth" — analogous presentation for output growth with same forecast types and 90 percent intervals. - Figures 34–35. Conditional Forecast Decompositions - Figure 34: "Conditional Forecast Decompositions for Consumption Price Inflation" — decomposes the difference between combined forecasts and unrestricted forecasts into trend and contributions from domestic supply, foreign supply, domestic demand, foreign demand, world monetary policy, world fiscal policy, world risk premium, and world terms of trade shocks. Time axis 2007–2014. - Figure 35: "Conditional Forecast Decompositions for Output Growth" — analogous decomposition for output growth. Time axis 2007–2014. *Source: _wp13253 - Appendix B. Tables and Figures (figures and tables as presented in the supplied content).* ### References ### _wp13253 - References ### Journal articles - Calvo, G.,1983, “Staggered Prices in a Utility-maximizing Framework”, Journal of Monetary Economics, Vol. 12, pp. 383–398. - de Jong, P., 1989, “Smoothing and Interpolation with the State-space Model”, Journal of the American Statistical Association, Vol. 84, pp. 1085–88. - Engle, R., and M. Watson, 1981, “A One-factor Multivariate Time Series Model of Metropolitan Wage Rates”, Journal of the American Statistical Association, Vol. 76, pp. 774–781. - Hodrick, R., and E. Prescott, 1997, “Post-war U.S. Business Cycles: A Descriptive Empirical Investigation”, Journal of Money, Credit and Banking, Vol. 29, pp. 1–16. - Klein, P., 2000, “Using the Generalized Schur Form to Solve a Multivariate Linear Rational Expectations Model”, Journal of Economic Dynamics and Control, Vol. 24, pp. 1405–23. - Monacelli, T., 2005, “Monetary Policy in a Low Pass-through Environment”, Journal of Money, Credit and Banking, Vol. 37, pp. 1047–66. - Pesaran, H., and R. Smith, 2011, “Beyond the DSGE Straightjacket”, Manchester School, Vol. 38, pp. 5–16. - 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. 1123–75. - Storn, R., and K. Price, 1997, “Differential Evolution—A Simple and Efficient Heuristic for Global Optimization Over Continuous Spaces”, Journal of Global Optimization, Vol. 11, pp. 341–359. ### Books and monographs - Geweke, J., 2005, Contemporary Bayesian Econometrics and Statistics (Hoboken, New Jersey: John Wiley & Sons). - Kalman, R., 1960, “A New Approach to Linear Filtering and Prediction Problems”, Transactions ASME Journal of Basic Engineering, Vol. 82, pp. 35–45. ### IMF publications and working papers - International Monetary Fund, 2011, Annual Report on Exchange Arrangements and Exchange Restrictions (Washington). - _______, 2013a, Spillover Report, IMF Policy Papers (Washington). - _______, 2013b, World Economic Outlook, April 2013: Hopes, Realities, and Risks, World Economic and Financial Surveys (Washington). - Vitek, F., 2012, “Policy Analysis and Forecasting in the World Economy: A Panel Unobserved Components Approach”, IMF Working Paper 12/149 (Washington: International Monetary Fund). *Source: _wp13253 - References* --- _Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2013/_wp13253.pdf_