## _wp1433: Appendix A — Simulation Under Imperfect Credibility

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---

### I. Scope and main analytical insight
- Focus: role of fiscal and monetary policy credibility and transparency in transmitting commodity price fluctuations in small open economies.
- Modeling approach: sticky-price small open economy DSGE model with heterogeneous households and a commodity sector; monetary and fiscal policies follow systematic rules but may be perceived as non-credible by private agents with Bayesian learning.
- Core analytical result:
  - When private agents believe policies may deviate from stated rules, the effects of a positive commodity price shock are magnified: output and consumption expand considerably, inflation rises, monetary policy must tighten strongly, and investment can be negatively affected in some cases.
- Empirical complement: cross-country regressions relate output volatility to export-price (commodity-price) volatility interacted with measures of credibility and transparency; preliminary results indicate monetary policy transparency and fiscal credibility reduce the incidence of export price volatility on output volatility, and that having an explicit fiscal rule and an inflation-targeting regime contribute to isolating the economy from terms-of-trade fluctuations.

### II. Model structure — agents, production, assets, and shocks
- Agents and preferences:
  - Two household types: Ricardian and non-Ricardian; non-Ricardian share λ in [0,1].
  - Consumption aggregator: CES between domestic and imported goods with elasticity Cη.
  - Ricardian consumption exhibits external habit formation; Ricardian households hold money (M), foreign bonds (B*), and domestic contingent bonds (qd).
- Assets and frictions:
  - Domestic households pay a premium Θ when borrowing abroad depending on net foreign asset position.
  - Investment subject to adjustment cost S(.); capital accumulation with depreciation δ.
- Production:
  - Two domestic sectors: differentiated goods (domestic consumption and exports) and a commodity sector (completely exported, requires no input).
  - Firms face Calvo-style nominal rigidities; independent Calvo probabilities for domestic and export prices.
  - Importers face price stickiness (incomplete pass-through).
- Commodity and foreign sectors:
  - Commodity endowment Co tY is exogenous and entirely exported; a share χ of commodity revenues accrues to the government.
  - Law of one price for the commodity: PtCo = St PCo,*.
  - Relative commodity price (log deviations) follows AR(1) with persistence parameter PCoρ.

### III. Monetary and fiscal rules — specification under perfect credibility
- Monetary policy (perfect-credibility rule):
  - Interest-rate rule responds smoothly to deviations of inflation expectation from target π with interest-rate smoothing parameter iφ and inflation feedback πφ.
  - Monetary policy shock tMP,ε is i.i.d. with mean 0 and standard deviation 2 MP σ ; 2 MP σ measures degree of commitment / credibility of the monetary authority.
- Fiscal policy (Structural Balance Fiscal Rule variant):
  - Government sets public expenditure consistent with a structural-balance target (assumed zero share of GDP), accounting for potential GDP, commodity-price-related revenues (share χ), and debt-service terms.
  - Public expenditure deviates by an i.i.d. shock tG,ε with mean zero and variance 2 G σ ; 2 G σ measures fiscal authority commitment / credibility.

### IV. Imperfect credibility and lack of transparency — beliefs and learning
- Private-sector perceptions under imperfect credibility:
  - Agents believe authorities may follow alternative perceived rules that react to commodity prices:
    - Perceived monetary rule includes commodity-price feedback parameter πν; simulation value used: πν = 0.005.
    - Perceived fiscal rule includes commodity-price feedback parameter Gν; simulation value used: Gν = 0.5.
  - Agents consider four possible policy cases (both credible; fiscal credible only; monetary credible only; neither credible) and assign probabilities pr i,t to each case. Prior probabilities at t=0 for cases i = 2,3,4 are ,0|0 i pr = 0.25.
- Transparency as measurement noise:
  - Observed deviations of policy instruments include measurement errors e1,t (monetary) and e2,t (fiscal) with zero mean and standard deviations 2 1 σ and 2 2 σ respectively; 2 1 σ and 2 2 σ define monetary and fiscal transparency.
- Learning implementation:
  - Private agents update beliefs and inferred discretionary components using a Kalman-filter/Bayesian learning algorithm based on observed noisy signals (tMP dev, tG dev) to obtain pr i,t|t and inferred policy shocks.

### V. Calibration and simulation design — key parameter values and shock
- Key calibrations:
  - Ratio of total exports to GDP: 33 percent.
  - Commodity production: 10 percent of GDP.
  - Fiscal commodity revenues: 4 percent of GDP.
  - Government spending: 12 percent of GDP; biased toward domestically produced goods.
  - Intertemporal elasticity of substitution: 1.0.
  - Labor supply elasticity: unitary.
  - Elasticity of substitution between domestic and imported goods: 1.0.
  - Shares of domestic goods: consumption 65 percent; investment 50 percent.
  - Monetary policy smoothing coefficient: 0.75.
  - Monetary policy inflation feedback coefficient: 1.5.
- Shock and expectations:
  - Simulated commodity price shock: positive 25% on impact.
  - Commodity price persistence: PCoρ = 95.0.
  - Private sector prior probabilities: pr i,0 = 0.25 for i = 2,3,4.
  - Perceived policy-feedback parameters under imperfect credibility: πν = 0.005; Gν = 0.5.

### VI. Simulation scenarios and principal quantitative outcomes
- Baseline (both rules credible and transparent):
  - Small expansion in output; almost no change in inflation.
  - Moderate real exchange-rate appreciation.
  - Public expenditure slightly responds per the fiscal rule; public saving rises.
  - Aggregate consumption barely moves on impact; investment increases; current account improves.
  - Interpretation: countercyclical/a-cyclical, transparent, credible policies isolate the economy from commodity shocks.
- Imperfect credibility + lack of transparency (agents assign 25% prior that authorities deviate; learning is slow):
  - Assumed parameterization reported: 0.05% MP σ =, 0.10% G σ =, 1 2%σ = and 2 2%σ =.
  - Much larger increases in output and demand relative to full credibility; inflation rises substantially.
  - Households expand consumption persistently; perceived loose monetary stance and persistent fiscal expansion reinforce demand.
  - Investment increases initially; labor demand and marginal costs rise => substantive inflation increase.
  - Monetary authority (actually following its rule) tightens aggressively and persistently to bring inflation back to target; real exchange rate initially depreciates (due to a fall in real interest rate from expected inflation), then appreciates after monetary tightening.
  - Current account increase is smaller than under full credibility due to larger investment and smaller private savings.
- Monetary-policy transparent but lacking credibility:
  - Monetary measurement error standard deviation set to 1 0%σ = (monetary transparency improvement).
  - Faster learning that monetary policy is not deviating => probabilities on cases with non-credible monetary policy converge quickly toward zero.
  - Output and inflation still rise more than under full credibility but less than the non-transparent case; responses are more muted and less persistent.
  - Interest-rate response is smaller and less persistent than in the non-transparent case; monetary policy is more effective.
- Credible and transparent monetary policy (monetary σ set effectively to zero in simulations):
  - Private agents learn immediately that monetary policy follows its rule.
  - Inflation remains virtually stable after the shock due to anchored expectations.
  - Output and employment expand strongly because of fiscal non-credibility, but converge quickly toward the perfect-credibility path.
  - Consumption increases less than in the non-credible monetary case; investment rises less or can be lower than under perfect credibility because monetary policy shifts composition of demand (more consumption, less investment).
  - Monetary tightening to counter perceived fiscal expansion leads to larger real exchange-rate appreciation than in the perfect-credibility both-policies case.
- Monetary credible and transparent + fiscal transparent but lacking credibility:
  - If both monetary and fiscal transparency measures are small (text example sets 0 21 σσσ MP .), private agents learn rapidly that neither policy deviates.
  - Macro responses are virtually the same as under perfect credibility; only short-run differences on impact due to prior beliefs.
  - Monetary policy stabilizes inflation with small currency appreciation; output and aggregate demand responses are muted and near perfect-credibility paths, preserving investment.

### VII. Empirical evidence — cross-country regressions and findings
- Econometric specification:
  - Regressions: ΔσYi = α0 + α1 ΔσPx i + α2 (ΔσPx i × qi) + εi, where ΔσYi is GDP-growth volatility for country i, ΔσPx i is exported-commodity-price volatility, and qi measures credibility/transparency.
- Measures used:
  - Commodity-price volatility proxies:
    - Standard deviation of export deflator growth.
    - CV index: commodity price index constructed by Céspedes and Velasco (weights of two main commodity exports); sample reduced when used.
    - Export-deflator volatility interacted with share of commodity goods in total exports (robustness).
  - Monetary-transparency index: EG-DE index (Eijffinger and Geraats (2006), extended by Dincer and Eichengreen).
  - Fiscal-transparency index: Open Budget Index (OBI) by the International Budget Partnership (surveys since 2006).
  - Monetary credibility proxy: standard deviation of residuals from country-level time-series regressions modeling the systematic behavior of the monetary authority (larger residual standard deviation = less credible).
  - Fiscal credibility proxy: standard deviation of structural balance (computed using 1985-2000 data for credibility measures).
- Sample periods:
  - GDP-growth volatility: generally measured 1995-2010; alternate estimations 1998-2008 when using CV index.
  - Credibility measures computed using 1985-2000.
- Main econometric findings:
  - Export-price volatility generally increases GDP-growth volatility (statistically significant when using export deflator; not always significant with CV index).
  - Interaction results:
    - Monetary transparency significantly reduces the impact of export-price volatility on output volatility (specification example: coefficient -4.12e-05* X Mon. Transp., SE (2.16e-05)).
    - Lower fiscal credibility amplifies the effect of export-price volatility on output (example: 8.4e-05* X Fiscal Cred., SE (3.22e-05)).
    - SD Exports Defl. X Fiscal Rule: -0.00105*** (SE (0.000232)).
    - SD Exports Defl. X Inf. Target: -0.000932*** (SE (0.000322)).
  - Robustness with primary-export shares (Table 3):
    - SD Exports Defl. X % Prim. Exports/GDP: coefficients include 8.49e-06** (SE (3.85e-06)) and 1.07e-05*** (SE (3.24e-06)).
    - SD Exports Defl. X % Prim. Exports/GDP X Mon. Transp.: -1.88e-06* (SE (1.08e-06)).
    - SD Exports Defl. X % Prim. Exports/GDP X Inf. Target: -2.07e-05*** (SE (6.29e-06)).
  - Statistical details (selected examples):
    - SD Exports Defl. coefficient examples: 0.000846* (SE (0.000352)); 0.00113*** (SE (0.000265)); 0.000790** (SE (0.000365)).
    - Observations across columns range: 7 to 139; R-squared examples: 0.080, 0.194, 0.219, 0.137, 0.234.
    - Table 3 observations: 29 to 130; R-squared examples: 0.042, 0.138, 0.184.
  - Some sample-sensitive and counterintuitive results when using CV index; interpretation affected by sample size and data limitations.

### VIII. Policy implications and concluding points
- Institutional arrangements that enhance transparency (clear communication of objectives, instruments, decisions; disclosure of procedures and forecasts) strengthen the ability of policymakers to anchor expectations and make macro rules effective against commodity-price shocks.
- Reputation and commitment to systematic rules increase policy effectiveness; both transparency and reputation improve credibility of countercyclical/a-cyclical macro policies and mitigate the macroeconomic effects of external shocks.
- Practical policy takeaway:
  - Implement monetary regimes that enhance exchange-rate flexibility and transparent communications (inflation reports, procedural openness).
  - Adopt credible fiscal rules (or mechanisms like stabilization funds/structural balance rules).
  - Combined monetary and fiscal transparency and credibility help isolate commodity-rich economies from terms-of-trade volatility.

*Source: appendix A: Simulation Under Imperfect Credibility (extracted content from _wp1433 PDF chapter).*

### References ................................................................................................26

### _wp1433 - References ................................................................................................26

### Tables
- Table  1. Baseline Parameterization ..................................................................29
- Table  2.  Relationship between GDP growth Volatility and Terms of trade Volatility (I)....42
- Table  3.  Relationship between GDP growth Volatility and Terms of trade Volatility (II)....43

### Figures
- Figure 1. Market beliefs to a commodity price shock under perfect and imperfect credibility...33
- Figure 2. Impulse-response to a commodity price shock under perfect and imperfect credibility
...................................................................................................................................................... 34
- Figure 3. Market beliefs to a commodity price shock under perfect and imperfect credibility.The 
role of monetary policy transparency ................................................................
.......................... 35
- Figure 4. Impulse-response to a commodity price shock under perfect and imperfect credibility. 
The role of monetary policy transparency. .................................................................................. 36
- Figure 5. Market beliefs to a commodity price shock under perfect and imperfect credibility. 
The role of monetary policy transparency and reputation ................................
........................... 37
- Figure 6. Impulse-response to a commodity price shock under perfect and imperfect credibility. 
The role of monetary policy transparency and reputation ........................................................... 38
- Figure 7. Market beliefs to a commodity price shock under perfect and imperfect credibility. 
The role of monetary and fiscal policy transparency and monetary policy reputation ................ 39
- Figure 8. Impulse-response to a commodity price shock under perfect and imperfect credibility. 
The role of monetary and fiscal policy transparency and monetary policy 
reputation.....................................................................................................40
- Figure 9. Volatility, Transparency and Credibility.......................................................41

### Appendix
- Appendix

*Source: _wp1433 - References ................................................................................................26*

### appendix A: Simulation Under Imperfect Credibility..................................................31

### appendix A: Simulation Under Imperfect Credibility

### I. Introduction — scope and main analytical insight
- Focus: role of fiscal and monetary policy credibility and transparency in transmitting commodity price fluctuations in small open economies.
- Modeling approach: sticky-price small open economy DSGE model with heterogeneous households and a commodity sector; monetary and fiscal policies follow systematic rules but may be perceived as non-credible by private agents with Bayesian learning.
- Core analytical result: when private agents believe policies may deviate from stated rules, the effects of a positive commodity price shock on macro variables are magnified — output and consumption expand considerably, inflation rises, monetary policy must tighten strongly, and investment can be negatively affected in some cases.
- Empirical complement: cross-country regressions relate output volatility to export-price (commodity-price) volatility interacted with measures of credibility and transparency; preliminary results indicate monetary policy transparency and fiscal credibility reduce the incidence of export price volatility on output volatility, and that having an explicit fiscal rule and an inflation-targeting regime contribute to isolating the economy from terms-of-trade fluctuations.

### II. Model structure — agents, production, assets, and shocks
- Agents and preferences:
  - Two types of households: Ricardian and non-Ricardian (non-Ricardian share indexed by λ in [0,1]).
  - Consumption aggregator is CES between domestic and imported goods with elasticity Cη.
  - Ricardian consumption exhibits external habit formation; Ricardian households hold money (M), foreign bonds (B*), and domestic contingent bonds (qd).
- Assets and frictions:
  - Domestic households pay a premium Θ when borrowing abroad depending on net foreign asset position.
  - Investment subject to adjustment cost S(.); capital accumulation with depreciation δ.
- Production:
  - Two domestic sectors: differentiated goods (domestic consumption and exports) and a commodity sector (completely exported, requires no input).
  - Firms face Calvo-style nominal rigidities in price setting (domestic and export prices have independent Calvo probabilities).
  - Importers also face price stickiness (import pass-through incomplete).
- Commodity and foreign sectors:
  - Commodity endowment Co tY is exogenous and entirely exported; a share χ of commodity revenues accrues to the government.
  - Law of one price for the commodity: PtCo = St PCo,* (equation (10)).
  - Relative commodity price (log deviations) follows AR(1) (equation (11)) with persistence parameter PCoρ.

### III. Monetary and fiscal rules — specification under perfect credibility
- Monetary policy (perfect-credibility rule):
  - Interest-rate rule responds smoothly to deviations of inflation expectation from target π with interest-rate smoothing parameter iφ and inflation feedback πφ (equation (14)).
  - Monetary policy shock tMP,ε is i.i.d. with mean 0 and standard deviation 2 MP σ ; 2 MP σ measures degree of commitment / credibility of the monetary authority.
- Fiscal policy (Structural Balance Fiscal Rule variant):
  - Government sets public expenditure consistent with a structural-balance target (assumed zero share of GDP), accounting for potential GDP, commodity-price-related revenues (share χ), and debt-service terms (equations around (15)).
  - Public expenditure deviates by an i.i.d. shock tG,ε with mean zero and variance 2 G σ ; 2 G σ measures fiscal authority commitment / credibility.

### IV. Imperfect credibility and lack of transparency — beliefs and learning
- Private-sector perceptions:
  - Under imperfect credibility, private agents believe monetary and/or fiscal authorities may follow alternative perceived rules that react to commodity prices:
    - Perceived monetary rule includes commodity-price feedback parameter πν (equation (16)); simulation value used: 0.005 (πν = 0.005).
    - Perceived fiscal rule includes commodity-price feedback parameter Gν (equation (17)); simulation value used: 0.5 (Gν = 0.5).
  - Agents consider four possible policy cases (both credible; fiscal credible only; monetary credible only; neither credible) and assign probabilities pr i,t to each case. Prior probabilities at t=0 for cases i = 2,3,4 are ,0|0 i pr = 0.25.
- Transparency as measurement noise:
  - Observed deviations of policy instruments include measurement errors e1,t (monetary) and e2,t (fiscal) with zero mean and standard deviations 2 1 σ and 2 2 σ respectively (equations (18) and (19)); 2 1 σ and 2 2 σ define monetary and fiscal transparency.
- Learning implementation:
  - Private agents update beliefs and inferred discretionary components using a Kalman-filter/Bayesian learning algorithm based on observed noisy signals (tMP dev, tG dev) to obtain pr i,t|t and inferred policy shocks.

### V. Calibration and simulation design — key parameter values and shock
- Key calibrations (as summarized in the text):
  - Ratio of total exports to GDP: 33 percent.
  - Commodity production: 10 percent of GDP.
  - Fiscal commodity revenues: 4 percent of GDP.
  - Government spending: 12 percent of GDP; biased toward domestically produced goods.
  - Intertemporal elasticity of substitution: 1.0.
  - Labor supply elasticity: unitary.
  - Elasticity of substitution between domestic and imported goods: 1.0.
  - Shares of domestic goods: consumption 65 percent; investment 50 percent.
  - Monetary policy smoothing coefficient: 0.75.
  - Monetary policy inflation feedback coefficient: 1.5.
- Shock and expectations:
  - Simulated commodity price shock: positive 25% on impact.
  - Commodity price persistence: PCoρ = 95.0.
  - Private sector prior probabilities: pr i,0 = 0.25 for i = 2,3,4.
  - Perceived policy-feedback parameters under imperfect credibility: πν = 0.005; Gν = 0.5.

### VI. Simulation scenarios and principal quantitative outcomes
- Baseline (both rules credible and transparent):
  - Small expansion in output; almost no change in inflation.
  - Moderate real exchange-rate appreciation.
  - Public expenditure slightly responds per the fiscal rule; public saving rises.
  - Aggregate consumption barely moves on impact; investment increases; current account improves.
  - Interpretation: countercyclical/a-cyclical, transparent, credible policies isolate the economy from commodity shocks.
- Imperfect credibility + lack of transparency (agents assign 25% prior that authorities deviate; learning is slow):
  - Assumed for this scenario (as reported): 0.05% MP σ =, 0.10% G σ =, 1 2%σ = and 2 2%σ =.
  - Much larger increases in output and demand relative to full credibility; inflation rises substantially.
  - Households expand consumption persistently; perceived loose monetary stance and persistent fiscal expansion reinforce demand.
  - Investment increases initially; labor demand and marginal costs rise => substantive inflation increase.
  - Monetary authority (actually following its rule) tightens aggressively and persistently to bring inflation back to target; real exchange rate initially depreciates (due to a fall in real interest rate from expected inflation), then appreciates after monetary tightening.
  - Current account increase is smaller than under full credibility due to larger investment and smaller private savings.
- Monetary-policy transparent but lacking credibility:
  - Monetary measurement error standard deviation set to 1 0%σ = (text states "1 0%σ ="; presented as monetary transparency improvement).
  - Faster learning that monetary policy is not deviating => probabilities on cases with non-credible monetary policy converge quickly toward zero.
  - Output and inflation still rise more than under full credibility but less than the non-transparent case; responses are more muted and less persistent.
  - Interest-rate response is smaller and less persistent than in the non-transparent case; monetary policy is more effective.
- Credible and transparent monetary policy (monetary σ set effectively to zero in simulations):
  - Private agents learn immediately that monetary policy follows its rule.
  - Inflation remains virtually stable after the shock due to anchored expectations.
  - Output and employment expand strongly because of fiscal non-credibility, but converge quickly toward the perfect-credibility path.
  - Consumption increases less than in the non-credible monetary case; investment rises less or can be lower than under perfect credibility because monetary policy shifts composition of demand (more consumption, less investment).
  - Monetary tightening to counter perceived fiscal expansion leads to larger real exchange-rate appreciation than in the perfect-credibility both-policies case.
- Monetary credible and transparent + fiscal transparent but lacking credibility:
  - If both monetary and fiscal transparency measures are small (text example sets 0 21 σσσ MP . in words: monetary credible and transparent and fiscal transparent but lacking credibility), private agents learn rapidly that neither policy deviates.
  - Macro responses are virtually the same as under perfect credibility; only short-run differences on impact due to prior beliefs.
  - Monetary policy stabilizes inflation with small currency appreciation; output and aggregate demand responses are muted and near perfect-credibility paths, preserving investment.

### VII. Empirical evidence — cross-country regressions and findings
- Econometric specification:
  - Regressions of the form: ΔσYi = α0 + α1 ΔσPx i + α2 (ΔσPx i × qi) + εi (equation (20)), where ΔσYi is GDP-growth volatility for country i, ΔσPx i is exported-commodity-price volatility, and qi measures credibility/transparency.
- Measures used:
  - Commodity-price volatility proxies:
    - Standard deviation of export deflator growth.
    - CV index: commodity price index constructed by Cespedes and Velasco (weights of two main commodity exports); sample reduced when used.
    - Export-deflator volatility interacted with share of commodity goods in total exports (robustness).
  - Monetary-transparency index: EG-DE index (Eijffinger and Geraats (2006), extended by Dincer and Eichengreen).
  - Fiscal-transparency index: Open Budget Index (OBI) by the International Budget Partnership (surveys since 2006).
  - Monetary credibility proxy: standard deviation of residuals from country-level time-series regressions modeling the systematic behavior of the monetary authority (larger residual standard deviation = less credible).
  - Fiscal credibility proxy: standard deviation of structural balance (computed using 1985-2000 data for credibility measures).
- Sample periods:
  - GDP-growth volatility: generally measured 1995-2010 (specifications (1)—(6)); alternate estimations 1998-2008 when using CV index (specifications (7)—(11)).
  - Credibility measures computed using 1985-2000 (to focus on credibility prior to the volatility window).
- Main empirical findings:
  - Export-price volatility generally increases GDP-growth volatility (statistically significant when using export deflator; not always significant with CV index).
  - Interaction results:
    - Monetary transparency significantly reduces the impact of export-price volatility on output volatility (specification (1)).
    - Lower fiscal credibility amplifies the effect of export-price volatility on output (specification (4)).
    - Inflation-targeting regimes and explicit fiscal-rule dummies reduce the impact of export-price and commodity-price volatility on output volatility (specifications (5), (6), and (11)).
  - Robustness: interacting export-deflator volatility with share of primary exports yields similar results — monetary transparency, fiscal credibility, and IT regimes reduce the impact of export-price volatility on output.
  - Some counterintuitive or sample-sensitive results: in some specifications using the CV index, less monetary credibility appears to dampen the impact (specification (8)), but sample size and data limitations affect statistical significance and interpretation.

### VIII. Policy implications and concluding points
- Institutional arrangements that enhance transparency (clear communication of objectives, instruments, decisions; disclosure of procedures and forecasts) strengthen the ability of policymakers to anchor expectations and make macro rules effective against commodity-price shocks.
- Reputation and commitment to systematic rules increase policy effectiveness; both transparency and reputation improve credibility of countercyclical/a-cyclical macro policies and mitigate the macroeconomic effects of external shocks.
- Practical policy takeaway: implementing monetary regimes that enhance exchange-rate flexibility, credible fiscal rules (or mechanisms like stabilization funds/structural balance rules), and transparent communications (inflation reports, procedural openness, fiscal disclosure) collectively help isolate commodity-rich economies from terms-of-trade volatility.

*Source: appendix A: Simulation Under Imperfect Credibility (extracted content from the supplied IMF PDF chapter).*

### REFERENCES

### _wp1433 - REFERENCES

### Key literature cited
- Extensive citations on monetary policy credibility, transparency, inflation targeting, fiscal rules, and commodity price effects, including works by Altig et al. (2011); Aizenman, Hutchison, and Noy (2011); Bornhorst et al. (2011); Barro and Gordon (1983); Blanchard and Galí (2009); Blanchard and Riggi (2013); Calvo (1983); Calvo and Reinhart (2002); Cecchetti and Krause (2002); Céspedes and Velasco (2011); Demertzis and Hughes Hallett (2007); Dincer and Eichengreen (2007, 2009); Geraats (2006); Eijffinger and Geraats (2006); Erceg et al. (2000, 2003); Galí et al. (2007); Gürkaynak et al. (2007); Hameed (2005); Kumar et al. (2009); Kydland and Prescott (1977); Levin et al. (2004); Mankiw, Reis, and Wolfers (2004); Marcel et al. (2001); Medina and Soto (2007); Schmitt-Grohé and Uribe (2003).

### Baseline parameterization (Table 1) — household, production, policy, and sectoral parameters
- Household preferences
  - β = 0.9975 (Subjective discount factor)
  - μ = 0.2 (Money demand elasticity to (1+i)/i?)
  - Cσ = 1.0 (Elasticity of intertemporal substitution in consumption)
  - Lσ = 1.0 (Inverse of the labor supply elasticity)
  - h = 0.75 (Habit formation coefficient)
  - λ = 0.7 (Fraction of Non-Ricardian Households)
- Consumption, government expenditure and investment baskets
  - Cγ = 0.65 (Share of domestic goods in consumption)
  - Cη = 1.0 (Elasticity of substitution in consumption between domestic and imported goods)
  - Iγ = 0.5 (Share of domestic goods in investment)
  - Iη = 0.5 (Elasticity of substitution in investment between domestic and imported goods)
  - Gγ = 1.0 (Share of domestic goods in gov't expenditure)
- Capital accumulation
  - Sμ = 2.0 (Investment adjustment cost coefficient)
  - δ = 6% (Depreciation rate (annual))
- Nominal rigidities
  - Lϕ = 0.75 (Prob adjusting wages)
  - Lξ = 0.5 (Wage indexation)
  - DHϕ = 0.75 (Prob adjusting DHP)
  - DHξ = 0.5 (Domestic goods indexation (home))
  - FHϕ = 0.75 (Prob adjusting FHP)
  - FHξ = 0.5 (Domestic goods indexation (abroad))
  - Fϕ = 0.75 (Prob adjusting FP)
  - Fξ = 0.5 (Imported goods indexation)
- Domestic production technology
  - Hη = 0.66 (Labor share in domestic production)
  - Hθ = 1.0 (Elasticity of substitution between labor and capital)
- Foreign sector
  - YNX/ = 1% (Net exports to GDP ratio)
  - η* = 1.0 (Price elasticity of foreign demand for domestically produced goods)
  - ρ = 0.001 (Elasticity of the external supply of debt)
  - YYCo/ = 10% (Commodity exported share in total GDP)
- Monetary policy
  - iφ = 0.75 (Interest rate smoothing)
  - πφ = 1.5 (Reaction to inflation)
- Fiscal sector
  - YG/ = 12% (Government expenditure to GDP ratio)
  - χ = 40% (Share of commodity exports sector holds for the government)
  - τ = 7.5% (Average net tax rate)

### Appendix A: Simulation under imperfect credibility — model structure and inference
- Model responses to shocks (notation preserved)
  - Monetary policy and fiscal policy shocks:
    - (A.1) ),0(~, ˆˆ 2 ,,1MPtMPtMPMPtt NQXPXσϵϵ+ = −
    - (A.2) ),0(~, ˆˆ 2 ,,1GtGtGGtt NQXPXσϵϵ+ = −
    - tXˆ is vector of endogenous variables (log deviations); tMP,ϵ and tG,ϵ are monetary and fiscal shocks; P, QMP and QG are functions of structural parameters.
  - Commodity price shock conditional responses:
    - (A.3) ***2 1,,,, 1,, ˆˆ ˆ ˆˆ ,,~(0,) ttCo iCo tCo tPCoCo tPCo tPCo tPCo XPXQpppNρϵ ε σ − − = + = + 
    - ,Co iQ corresponds to responses under case i; perfect credibility corresponds to case i = 1.
- Under imperfect credibility:
  - Private sector forms Bayesian inferences pr i,t|t (i=1,2,3,4) and uses inferred sizes of monetary and fiscal shocks ttMP|,ϵ and ttG|,ϵ to form responses; inference is updated with the Kalman Filter.
  - The private sector does not immediately infer that devMP,t = devG,t = 0 for all t even when policies follow rules (14) and (15); learning is slow.
- Kalman filter setup and computation of Kalman gain K
  - Prior probabilities ,0|0i pr enter initial matrices.
  - Iterative process to obtain K:
    1. Solve Ω from ξF Ω = Ω ξF' + ξQ (matrix equation as stated).
    2. Compute iteration using R, H, F, Q, K, and Ω with the provided matrix expressions until convergence.
    3. Iterate step 2 until difference between Ωt and Ωt−1 is small.
  - Definitions of ξF, ξQ, ξH, eR provided in the appendix with the exact block-matrix structures and parameter-dependent entries (including π, φ, ϑ, χ, σ terms as shown).

### Figures: qualitative implications shown in impulse responses and beliefs (Figures 1–9)
- Figures 1–8 present:
  - Market beliefs to a commodity price shock under perfect and imperfect credibility, and the roles of:
    - Monetary policy transparency (MP Transp)
    - Monetary policy reputation (Reput)
    - Fiscal policy transparency (FP Transp)
    - Combined transparency and reputation scenarios
  - Impulse-responses to a commodity price shock under the same scenarios for variables including:
    - Inflation (y-o-y), MP Rate, GDP, RER, Real wages, Employment, Consumption, Investment, Primary surplus (% GDP), Current Account (% GDP)
  - Time axes labeled in Quarters (0–20) with deviations from steady state (%) shown in the plots.
- Figure 9 panels A–C relate:
  - A. GDP growth and export price volatility
  - B. Growth volatility and Policy Transparency
  - C. Growth volatility and Policy Credibility

### Empirical results — relationship between GDP growth volatility and terms-of-trade volatility (Tables 2 and 3)
- Table 2: Dependent variable = Standard deviation GDP growth. Selected reported coefficients and statistics (preserving formatting):
  - SD Exports Defl. coefficient examples:
    - 0.000846* (SE (0.000352))
    - 0.00113*** (SE (0.000265))
    - 0.000790** (SE (0.000365))
    - -0.000899 (SE (0.000881))
    - 0.00160*** (SE (0.000306))
    - 0.000596** (SE (0.000254))
  - SD. Comm. price interactions and coefficients include:
    - -4.12e-05* X Mon. Transp. (SE (2.16e-05))
    - -3.6e-07*** X Mon. Cred. (SE (1.2e-07))
    - 8.4e-05* X Fiscal Cred. (SE (3.22e-05))
  - Interaction examples:
    - SD Exports Defl. X Fiscal Rule: -0.00105*** (SE (0.000232))
    - SD Exports Defl. X Inf. Target: -0.000932*** (SE (0.000322))
  - Constant terms vary across specifications; example: 0.0301*** (SE (0.00502)).
  - Observations across columns range: 7 to 139; R-squared examples: 0.080, 0.194, 0.219, 0.080, 0.137, 0.234. Robust standard errors in parentheses; significance: *** p<0.01, ** p<0.05, * p<0.1.
  - Note definitions: SD Exports Defl. = Standard Deviation of Deflator of Exports Growth; SD Comm. Price = Standard Deviation of Commodity Price Growth.
- Table 3: Dependent variable = Standard deviation GDP growth — interactions with percent primary exports/GDP
  - SD Exports Defl. X % Prim. Exports/GDP reported coefficients:
    - 8.49e-06** (SE (3.85e-06))
    - 1.07e-05*** (SE (3.24e-06))
    - 5.24e-06 (SE (4.47e-06))
    - -5.51e-06 (SE (1.57e-05))
    - 5.02e-06 (SE (3.25e-06))
    - 4.07e-06 (SE (5.93e-06))
  - Interaction examples:
    - SD Exports Defl. X % Prim. Exports/GDP X Mon. Transp.: -1.88e-06* (SE (1.08e-06))
    - SD Exports Defl. X % Prim. Exports/GDP X Fiscal Cred.: 4.14e-06** (SE (1.86e-06))
    - SD Exports Defl. X % Prim. Exports/GDP X Inf. Target: -2.07e-05*** (SE (6.29e-06))
  - Constants: examples include 0.0334*** (SE (0.00320)), 0.0264*** (SE (0.00229)).
  - Observations across columns: 29 to 130; R-squared examples: 0.042, 0.138, 0.184. Robust standard errors in parentheses; significance: *** p<0.01, ** p<0.05, * p<0.1.

*Source: _wp1433 - REFERENCES (appendix material and cited references).*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2014/_wp1433.pdf_