## Appendix IV: Actual and One-Step Ahead Forecasts

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---

### I. Introduction — motivation and objectives
- Problem: Use of monetary policy for macroeconomic stabilization in low-income countries, particularly Sub-Saharan Africa (SSA), poses challenges distinct from industrial countries.
- Key contextual features emphasized:
  - Need to coordinate monetary and exchange rate policy with fiscal policy to manage large volatile aid inflows and/or government revenues from natural resource exploitation.
  - Potential adverse effects on tradable sector (“Dutch disease”).
  - Monetary policy in SSA often focuses on the supply of and demand for the monetary base; interest rates are reliable instruments only where inter-bank money markets and secondary government debt markets are well developed.
  - Dominance of commercial banks and information asymmetries imply a prominent credit channel in transmission (Bernanke and Gertler 1995).
- Research objective:
  - Evaluate monetary policy tradeoffs in low-income countries using a DSGE model estimated on Mozambique data.
  - Compare three central bank instrument deployment rules: exchange rate stabilization; CPI inflation stabilization; nontradable inflation stabilization.
  - Incorporate foreign exchange sales and open market operations in monetary policy analysis (as in Adam and O’Connell 2005, Buffie et al. 2004).
- High-level result preview:
  - Both nontradable and CPI inflation targeting perform better than an exchange rate peg, consistent with NOEM model findings.

### II. DSGE model — structure and key mechanisms
- Model class and rationale:
  - Open-economy DSGE based on Kollmann (2002) and Saxegaard (2006a), augmented for SSA features: monetary authority affects money supply via foreign exchange sales and bond transactions; credit frictions; learning by doing.
  - Microfoundations: optimizing households and firms; forward-looking agents; structural interpretation of equations.
- Four sources of inefficiency included to justify stabilization policy:
  - Monopolistically competitive product markets.
  - Sluggish price adjustment using Rotemberg (1982) specification.
  - Capital and investment adjustment costs using Christiano et al. (2005).
  - Adjustment costs in commercial bank reserves and an interest rate spread depending on firms’ net worth.
- Financial and monetary mechanics:
  - Financial intermediary converts deposits into loans and reserves; lending rate is a markup over deposit rate, with markup g(.) a function of firms’ beginning-of-period net worth.
  - Central bank balance sheet: M + ΔRe + ΔZ = ΔB1 + Δ... (see equation (0.29)).
  - Fiscal agent controls government spending, taxation, net domestic borrowing; monetary authority controls international reserves.
- Policy rule parametrizations:
  - Fiscal rule form includes parameters ω and ι determining fraction of aid used to reduce taxes vs increase expenditure and allocation between private and public sector (equation (0.33)). Assumption: fiscal regime unchanged and foreign aid is fully spent unless otherwise stated.
  - Foreign exchange intervention rule (equation (0.34)) with parameters 1z, 2z, 3z, 4z governing commitment to reserves level, “absorb as you spend,” crawling peg (crawl from π − π*), and use of reserves to target inflation respectively.
  - Open-market/bond operations rule (equation (0.35)) with parameters 1b, 2b, 3b, 4b governing sterilization, inflation targeting commitment, output gap considerations, and phasing-out of bond operations.
- Stochastic environment:
  - Model includes 14 structural shocks:
    - Two preference shocks to marginal utility of consumption and labor (u_C,t, u_L,t).
    - A shock to technology (u_Y,t).
    - A shock to investment (u_I,t).
    - A shock to the markup (u_ν,t) — assumed white noise.
    - Four external shocks: aid (u_A,t), world inflation (π* shock), world interest rates (u_i*,t), terms of trade (u_tot,t).
    - Shock to share of capital expenditure in government expenditure (u_μ,t).
    - Shock to learning by doing (u_γ,t).
    - Shock to lending rates and commercial bank reserves (u_i,t).
    - Shock to government bonds and foreign currency reserves (u_BZ,t).
  - Except the markup shock, all shocks follow a first-order autoregressive process.

### III. Estimation and empirical findings
- Data and sample:
  - Quarterly Mozambican data covering 1996Q1 to 2005Q4 on 18 macro variables: GDP, consumption, exports, imports, real exchange rate, inflation, export price inflation, import price inflation, M2, currency in circulation, deposit rates, lending rates, foreign currency reserves, government bonds, commercial bank reserves, aid, government spending, and lending to the private sector.
- Pre-estimation transformations:
  - Variables transformed to real per capita measures.
  - Time trend removed using Hodrick-Prescott filter.
  - Seasonal effects removed using X12arima where evident; variables demeaned.
- Estimation approach:
  - Fix parameters determining steady-state (guided by Tarp et al. (2002) and calibration summarized in Appendix 1).
  - Estimate dynamic parameters via Bayesian methods using priors informed by theory and empirical evidence; diffuse priors where guidance is weak.
  - Implementation using DYNARE and Metropolis-Hastings with two separate chains of 100000 draws each.
- Estimation performance and diagnostics:
  - Bayesian estimation yields plausible parameter estimates broadly in line with prior studies.
  - Prior and posterior distributions (Appendices 2 and 3) used to assess informativeness of data vs prior.
  - One-step ahead forecasts compare reasonably well with actual data (series and comparisons displayed in Appendix IV).

### IV. Monetary policy rules in a shock-prone economy — experiments and results
- Simulation design:
  - Analyze response to:
    - Persistent technology shock (autocorrelation coefficient 0.8).
    - Persistent aid shock that raises aid by 2 percent of steady-state GDP.
  - Policy rules evaluated: CPI inflation targeting (b2 = 10? — text: "CPI inflation ( 24 10bz== )"), nontradable inflation targeting (same but with nontradable inflation), and nominal exchange rate depreciation targeting (3z = 10, crawl equal to long-run inflation differential).
  - Parameterization mostly set to estimated values; all aid is spent by government in these experiments.
- Impulse response highlights — unanticipated technology shock:
  - Output rises under all policy rules.
  - Labor falls due to sticky prices and productivity increase (declining marginal costs and incomplete price adjustment).
  - Monetary responses differ:
    - Under nontradable inflation targeting (PID), government increases base money; interest rates fall.
    - CPI inflation targeting: less base money expansion due to imported inflation effects.
    - Exchange rate targeting: interest rate falls only via nominal rigidities; monetary policy does not offset falling marginal costs.
  - Inflation dynamics:
    - Inflation increases under PID due to expansionary monetary policy.
    - Inflation falls under exchange rate targeting as monetary policy does not offset lower marginal costs.
  - Competitiveness adjustment:
    - Under exchange rate targeting, competitiveness improves via price declines.
    - Under PID and CPI targeting, competitiveness improves via nominal exchange rate depreciation.
- Impulse response highlights — unanticipated aid shock:
  - Aid shock (fully spent) increases demand for nontradables and imports → GDP and labor increase; trade balance deteriorates.
  - Monetary responses:
    - Under CPI and nontradable inflation targeting, authorities contract base money → interest rates rise sharply.
    - Under exchange rate targeting, base money contracted only to offset exchange rate pressure from trade balance deterioration → smaller interest rate rise.
  - Volatility outcomes:
    - Inflation volatility is higher under exchange rate targeting than under inflation targeting.
    - Real exchange rate volatility is higher when monetary authorities stabilize the nominal exchange rate.
  - Sterilization effect:
    - Under inflation targeting where part of base money increase is sterilized, interest rates remain high due to persistent increase in government bonds.
    - Persistent inflation under inflation targeting reflects higher marginal costs from higher interest rates associated with sterilization.

### V. Quantitative evaluation (Table 1: Standard Deviations of Macroeconomic Variables and Welfare)
- CPI Inflation Targeting:
  - GDP: 0.4822
  - Consumption: 0.3023
  - Net Exports: 0.0438
  - CPI Infl.: 0.0049
  - Nom. Ex. Rate: 0.0424
  - Real Ex. Rate: 0.0518
  - Interest Rate: 0.0369
  - Welfare: -7.2561
- NTP Inflation Targeting:
  - GDP: 0.4842
  - Consumption: 0.3025
  - Net Exports: 0.0425
  - CPI Infl.: 0.0103
  - Nom. Ex. Rate: 0.0382
  - Real Ex. Rate: 0.0510
  - Interest Rate: 0.0355
  - Welfare: -7.2578
- Crawling Ex. Rate Peg:
  - GDP: 0.4892
  - Consumption: 0.3033
  - Net Exports: 0.0541
  - CPI Infl.: 0.0391
  - Nom. Ex. Rate: 0.0072
  - Real Ex. Rate: 0.0521
  - Interest Rate: 0.0410
  - Welfare: -7.2861
- Key quantitative conclusions:
  - Exchange rate peg is significantly less successful than inflation targeting at stabilizing the real economy due to higher interest rate volatility (though differences are relatively small).
  - Exchange rate peg implies significantly higher CPI inflation volatility which, despite lower nominal exchange rate volatility, leads to higher real exchange rate volatility.
  - CPI and nontradable inflation targeting perform relatively similarly in macroeconomic volatility terms; CPI targeting shows slightly better overall welfare but differences are small compared to differences between inflation targeting and exchange rate peg.

### VI. Policy implications and conclusions
- Main policy-relevant findings:
  - In a shock-prone SSA environment with large and volatile aid inflows, an exchange rate peg generally performs worse than inflation-targeting variants in terms of macroeconomic volatility and welfare.
  - Exchange rate targeting produces higher CPI inflation volatility and higher real exchange rate volatility, undermining tradable sector performance.
  - “Lite” inflation targeting regimes that combine foreign exchange interventions and open market operations may be more suitable for SSA countries during a gradual transition to fully-fledged inflation targeting, given shallow financial markets and the need for a nominal anchor.
- Contribution:
  - Provides a benchmark estimated DSGE model for an SSA country (Mozambique) — the first such estimation for SSA excluding South Africa — incorporating SSA characteristics (aid shocks, closed capital account assumed, credit frictions, learning by doing) for monetary policy analysis.

### VII. Appendices and supporting material (selected numerical content)
- Appendix 1: CALIBRATION (selected entries)
  - θ: 1.5 — Home elasticity of substitution
  - η: 3.5 — Foreign elasticity of substitution
  - ψ−1: 1.5 — Inverse of Frisch elasticity
  - ε: 2 — Inverse of elasticity of money supply
  - α(d): 0.731 — Share of nontradables in CPI
  - ν/(ν−1)(): 1.09 — Markup factor for intermediary goods.
  - ς: 0.15 — Cost share of borrowing
  - α: 0.41 — Cost share of capital
  - δ: 0.025 — Quarterly depreciation rate of capital
  - β: (1.093/1.123)^(1/4) — Quarterly subjective discount rate
  - γu: 0.5 — Steady-state learning by doing
  - μu: 0.3 — Steady-state share of government investment
  - π*: (1.093)^(1/4) — Steady-state CPI inflation
  - π: (1.059)^(1/4) — Steady-state foreign inflation
  - 1+i: (1.123)^(1/4) — Steady-state domestic interest rate
  - 1+i*: (1.117)^(1/4) — Steady-state foreign interest rate
  - (0/C) MMD+: 0.22 — Currency to M2 Ratio
  - (0/MD) Y+: 0.7 — M2 to GDP Ratio
  - TY: 0.15 — Steady-state tax to GDP ratio
  - AY: 0.15 — Steady-state aid to GDP ratio
  - Z: 4.6 months of imports — Steady-state level of foreign currency reserves
- Appendix I: Parameter Estimates and Priors (selected entries)
  - Cost of Non-tradable Goods Price Adjustment: Density normal, S.D. 100.000, Mean 86.8394, Posterior 101.4355, 117.1080
  - Habit Persistence: Density beta, S.D. 0.4000, Mean 0.2534, Posterior 0.3833, 0.5036
  - Capital Stock Adjustment Costs: Density normal, S.D. 1.0000, Mean 0.9078, Posterior 1.0412, 1.1971
  - Investment Level Adjustment Costs: Density normal, S.D. 80.000, Mean 0.623276, Posterior 76.56489, 0.0185
  - Share of Aid Spent: Density normal, S.D. 1.0000, Mean 0.9647, Posterior 1.1450, 1.3188
  - Share of Aid Spent by Public Sector: Density normal, S.D. 1.0000, Mean 1.0438, Posterior 1.1920, 1.2892
  - Commercial Bank Reserve Smoothing (Bonds): Density gamma, S.D. 0.2000, Mean 0.0797, Posterior 0.1440, 0.2190
  - Commercial Bank Reserve Smoothing (Lending): Density gamma, S.D. 0.2000, Mean 0.1036, Posterior 0.1592, 0.2119
  - Commercial Bank Reserve Smoothing (Deposits): Density gamma, S.D. 0.2000, Mean 0.0424, Posterior 0.1012, 0.1510
  - Interest Rate Spread Markup Factor: Density normal, S.D. 10.000, Mean 8.18819, Posterior 19.7740, 11.5823
  - International Reserves Stabilization: Density normal, S.D. 0.0010, Mean -0.0121, Posterior 0.7730, 0.1737
  - Exchange Rate Stabilization: Density normal, S.D. 0.5000, Mean 0.1816, Posterior 0.3193, 0.4713
  - Absorption: Density normal, S.D. 0.5000, Mean 0.6741, Posterior 0.7971, 0.9065
  - International Reserves Sterilization: Density normal, S.D. 0.5000, Mean 0.2949, Posterior 0.4751, 0.6245
  - Inflation Stabilization: Density normal, S.D. 0.5000, Mean 0.3079, Posterior 0.4630, 0.6291
  - Output Stabilization: Density normal, S.D. 0.5000, Mean 0.0570, Posterior 0.1634, 0.2490
  - Bond Stabilization: Density normal, S.D. 0.0010, Mean 0.0950, Posterior 0.1991, 0.2953
  - Technology Shock Persistence: Density beta, S.D. 0.8000, Mean 0.5890, Posterior 0.7430, 0.9471
  - Aid Shock Persistence: Density beta, S.D. 0.8000, Mean 0.6551, Posterior 0.7735, 0.9077
  - International Reserves Shock Persistence: Density beta, S.D. 0.8000, Mean 0.7996, Posterior 0.8725, 0.9606
  - Size of Technology Shock: Density invgamma, S.D. 0.002, Mean 0.0048, Posterior 0.0048, 0.0248
  - Size of Aid Shock: Density invgamma, S.D. 0.100, Mean 0.0196, Posterior 0.0122, 0.0329
  - Size of Investment Shock: Density invgamma, S.D. 5.000, Mean 0.0136, Posterior 1.3207, 0.0248
  - Size of Interest Rate Spread Shock: Density invgamma, S.D. 10.000, Mean 15.65742, Posterior 2.479324, 24.7542

*Source: Appendix IV of _wp07282 (Mozambique DSGE model estimation and monetary policy experiments).*

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

### _wp07282 - References..............................................................................................................

### References
- References................................................................................................................................21

### Appendix I: Calibration
- Appendix I: Calibration ...........................................................................................................25

### Appendix II: Estimation Results
- Appendix II: Estimation Results ..............................................................................................26

### Appendix III: Prior and Posterior Distributions
- Appendix III: Prior and Posterior Distributions.......................................................................27

*Source: _wp07282 - References..............................................................................................................*

### Appendix IV: Actual and One-Step Ahead Forecasts .............................................................31

### Appendix IV: Actual and One-Step Ahead Forecasts

### I. Introduction — motivation and objectives
- Problem: Use of monetary policy for macroeconomic stabilization in low-income countries, particularly Sub-Saharan Africa (SSA), poses challenges distinct from industrial countries.
- Key contextual features emphasized:
  - Need to coordinate monetary and exchange rate policy with fiscal policy to manage large volatile aid inflows and/or government revenues from natural resource exploitation.
  - Potential adverse effects on tradable sector (“Dutch disease”).
  - Monetary policy in SSA often focuses on the supply of and demand for the monetary base; interest rates are reliable instruments only where inter-bank money markets and secondary government debt markets are well developed.
  - Dominance of commercial banks and information asymmetries imply a prominent credit channel in transmission (Bernanke and Gertler 1995).
- Research objective:
  - Evaluate monetary policy tradeoffs in low-income countries using a DSGE model estimated on Mozambique data.
  - Compare three central bank instrument deployment rules: exchange rate stabilization; CPI inflation stabilization; nontradable inflation stabilization.
  - Incorporate foreign exchange sales and open market operations in monetary policy analysis (as in Adam and O’Connell 2005, Buffie et al. 2004).
- High-level result preview:
  - Both nontradable and CPI inflation targeting perform better than an exchange rate peg, consistent with NOEM model findings.

### II. DSGE model — structure and key mechanisms
- Model class and rationale:
  - Open-economy DSGE based on Kollmann (2002) and Saxegaard (2006a), augmented for SSA features: monetary authority affects money supply via foreign exchange sales and bond transactions; credit frictions; learning by doing.
  - Microfoundations: optimizing households and firms; forward-looking agents; structural interpretation of equations.
- Four sources of inefficiency included to justify stabilization policy:
  - Monopolistically competitive product markets.
  - Sluggish price adjustment using Rotemberg (1982) specification.
  - Capital and investment adjustment costs using Christiano et al. (2005).
  - Adjustment costs in commercial bank reserves and an interest rate spread depending on firms’ net worth.
- Financial and monetary mechanics:
  - Financial intermediary converts deposits into loans and reserves; lending rate is a markup over deposit rate, with markup g(.) a function of firms’ beginning-of-period net worth.
  - Central bank balance sheet: M + ΔRe + ΔZ = ΔB1 + Δ... (see equation (0.29)).
  - Fiscal agent controls government spending, taxation, net domestic borrowing; monetary authority controls international reserves.
- Policy rule parametrizations:
  - Fiscal rule form includes parameters ω and ι determining fraction of aid used to reduce taxes vs increase expenditure and allocation between private and public sector (equation (0.33)). Assumption: fiscal regime unchanged and foreign aid is fully spent unless otherwise stated.
  - Foreign exchange intervention rule (equation (0.34)) with parameters 1z, 2z, 3z, 4z governing commitment to reserves level, “absorb as you spend,” crawling peg (crawl from π − π*), and use of reserves to target inflation respectively.
  - Open-market/bond operations rule (equation (0.35)) with parameters 1b, 2b, 3b, 4b governing sterilization, inflation targeting commitment, output gap considerations, and phasing-out of bond operations.
- Stochastic environment:
  - Model includes 14 structural shocks:
    - Two preference shocks to marginal utility of consumption and labor (u_C,t, u_L,t).
    - A shock to technology (u_Y,t).
    - A shock to investment (u_I,t).
    - A shock to the markup (u_ν,t) — assumed white noise.
    - Four external shocks: aid (u_A,t), world inflation (π* shock), world interest rates (u_i*,t), terms of trade (u_tot,t).
    - Shock to share of capital expenditure in government expenditure (u_μ,t).
    - Shock to learning by doing (u_γ,t).
    - Shock to lending rates and commercial bank reserves (u_i,t).
    - Shock to government bonds and foreign currency reserves (u_BZ,t).
  - Except the markup shock, all shocks follow a first-order autoregressive process.

### III. Estimation and empirical findings
- Data and sample:
  - Quarterly Mozambican data covering 1996Q1 to 2005Q4 on 18 macro variables: GDP, consumption, exports, imports, real exchange rate, inflation, export price inflation, import price inflation, M2, currency in circulation, deposit rates, lending rates, foreign currency reserves, government bonds, commercial bank reserves, aid, government spending, and lending to the private sector.
- Pre-estimation transformations:
  - Variables transformed to real per capita measures.
  - Time trend removed using Hodrick-Prescott filter.
  - Seasonal effects removed using X12arima where evident; variables demeaned.
- Estimation approach:
  - Fix parameters determining steady-state (guided by Tarp et al. (2002) and calibration summarized in Appendix 1).
  - Estimate dynamic parameters via Bayesian methods using priors informed by theory and empirical evidence; diffuse priors where guidance is weak.
  - Implementation using DYNARE and Metropolis-Hastings with two separate chains of 100000 draws each.
- Estimation performance and diagnostics:
  - Bayesian estimation yields plausible parameter estimates broadly in line with prior studies.
  - Prior and posterior distributions (Appendices 2 and 3) used to assess informativeness of data vs prior.
  - One-step ahead forecasts compare reasonably well with actual data (referenced in Appendix 4).

### IV. Monetary policy rules in a shock-prone economy — experiments and results
- Simulation design:
  - Analyze response to:
    - Persistent technology shock (autocorrelation coefficient 0.8).
    - Persistent aid shock that raises aid by 2 percent of steady-state GDP.
  - Policy rules evaluated: CPI inflation targeting (b2 = 10? — text: "CPI inflation ( 24 10bz== )", nontradable inflation targeting (same but with nontradable inflation), and nominal exchange rate depreciation targeting (3z = 10, crawl equal to long-run inflation differential).
  - Parameterization mostly set to estimated values; all aid is spent by government in these experiments.
- Impulse response highlights — unanticipated technology shock:
  - Output rises under all policy rules.
  - Labor falls due to sticky prices and productivity increase (declining marginal costs and incomplete price adjustment).
  - Monetary responses differ:
    - Under nontradable inflation targeting (PID), government increases base money; interest rates fall.
    - CPI inflation targeting: less base money expansion due to imported inflation effects.
    - Exchange rate targeting: interest rate falls only via nominal rigidities; monetary policy does not offset falling marginal costs.
  - Inflation dynamics:
    - Inflation increases under PID due to expansionary monetary policy.
    - Inflation falls under exchange rate targeting as monetary policy does not offset lower marginal costs.
  - Competitiveness adjustment:
    - Under exchange rate targeting, competitiveness improves via price declines.
    - Under PID and CPI targeting, competitiveness improves via nominal exchange rate depreciation.
- Impulse response highlights — unanticipated aid shock:
  - Aid shock (fully spent) increases demand for nontradables and imports → GDP and labor increase; trade balance deteriorates.
  - Monetary responses:
    - Under CPI and nontradable inflation targeting, authorities contract base money → interest rates rise sharply.
    - Under exchange rate targeting, base money contracted only to offset exchange rate pressure from trade balance deterioration → smaller interest rate rise.
  - Volatility outcomes:
    - Inflation volatility is higher under exchange rate targeting than under inflation targeting.
    - Real exchange rate volatility is higher when monetary authorities stabilize the nominal exchange rate.
  - Sterilization effect:
    - Under inflation targeting where part of base money increase is sterilized, interest rates remain high due to persistent increase in government bonds.
    - Persistent inflation under inflation targeting reflects higher marginal costs from higher interest rates associated with sterilization.
- Overall quantitative evaluation (Table 1: standard deviations and welfare)
  - Table 1: Standard Deviations of Macroeconomic Variables (values preserved exactly)
    - CPI Inflation Targeting:
      - GDP: 0.4822
      - Consumption: 0.3023
      - Net Exports: 0.0438
      - CPI Infl.: 0.0049
      - Nom. Ex. Rate: 0.0424
      - Real Ex. Rate: 0.0518
      - Interest Rate: 0.0369
      - Welfare: -7.2561
    - NTP Inflation Targeting:
      - GDP: 0.4842
      - Consumption: 0.3025
      - Net Exports: 0.0425
      - CPI Infl.: 0.0103
      - Nom. Ex. Rate: 0.0382
      - Real Ex. Rate: 0.0510
      - Interest Rate: 0.0355
      - Welfare: -7.2578
    - Crawling Ex. Rate Peg:
      - GDP: 0.4892
      - Consumption: 0.3033
      - Net Exports: 0.0541
      - CPI Infl.: 0.0391
      - Nom. Ex. Rate: 0.0072
      - Real Ex. Rate: 0.0521
      - Interest Rate: 0.0410
      - Welfare: -7.2861
  - Key quantitative conclusions:
    - Exchange rate peg is significantly less successful than inflation targeting at stabilizing the real economy due to higher interest rate volatility (though differences are relatively small).
    - Exchange rate peg implies significantly higher CPI inflation volatility which, despite lower nominal exchange rate volatility, leads to higher real exchange rate volatility.
    - CPI and nontradable inflation targeting perform relatively similarly in macroeconomic volatility terms; CPI targeting shows slightly better overall welfare but differences are small compared to differences between inflation targeting and exchange rate peg.

### V. Policy implications and conclusions
- Main policy-relevant findings:
  - In a shock-prone SSA environment with large and volatile aid inflows, an exchange rate peg generally performs worse than inflation-targeting variants in terms of macroeconomic volatility and welfare.
  - Exchange rate targeting produces higher CPI inflation volatility and higher real exchange rate volatility, undermining tradable sector performance.
  - “Lite” inflation targeting regimes that combine foreign exchange interventions and open market operations may be more suitable for SSA countries during a gradual transition to fully-fledged inflation targeting, given shallow financial markets and the need for a nominal anchor.
- Contribution:
  - Provides a benchmark estimated DSGE model for an SSA country (Mozambique) — the first such estimation for SSA excluding South Africa — incorporating SSA characteristics (aid shocks, closed capital account assumed, credit frictions, learning by doing) for monetary policy analysis.

*Source: Appendix IV of the referenced IMF working paper (Mozambique DSGE model estimation and monetary policy experiments).*

### REFERENCES

### _wp07282 - REFERENCES

### References
- Adam, C., O’Connell, S. (2005), “Monetary Policy in Sub-Saharan Africa”, Unpublished Manuscript. African Department (Washington: International Monetary Fund).
- Adam, C., O’Connell, S., Buffie, E. and Pattillo, C. (2006), “Monetary Policy Responses to Aid Surges in Africa”, Unpublished Manuscript.
- Adolfson, M., Laséen, S., Lindé, J. and Villani, M. (2004), “Derivation and Estimation of a DSGE Open Economy Model with Incomplete Pass-through”, Unpublished Manuscript, Swedish Central Bank.
- Agénor, Pierre-Richard and Montiel, Peter J. 2007, “Credit Market Imperfections and the Monetary Transmission Mechanism” Unpublished Manuscript.
- Ambler, S. and Paquet, A. (1994), ”Stochastic Depreciation and the Business Cycle”, International Economic Review, 44, 101-116.
- Atta-Mensah, J. and Dib, A. (2003), “Bank Lending, Credit Shocks, and the Transmission Mechanism of Canadian Monetary Policy”, Bank of Canada Working Paper 2003-9.
- Barnichon, R. and Peiris, S.J., “Sources of Inflation in Sub-Saharan Africa” IMF Working Paper 07/32 (Washington: International Monetary Fund).
- Batini, Nicoletta, and Anthony Yates, 2003, “Hybrid Inflation and Price-Level Targeting,” Journal of Money, Credit and Banking, Vol. 35 (June), pp. 283–300.
- Bernanke, B. and Gertler, M. (1995), “Inside the Black Box: The Credit Channel of Monetary Policy Transmission,” Journal of Economic Perspectives, Vol. 9.
- Bernanke, B., M. Gertler, and S. Gilchrist. 1999. “The Financial Accelerator in a Quantitative Business Cycle Framework," Handbook of Macroeconomics, Amsterdam: North Holland.
- Bernanke, Ben S, and others, 1999, Inflation Targeting: Lessons From the International Experience (Princeton, New Jersey: Princeton University Press).
- Buffie, Edward, Christopher Adam, Stephen O’Connell, and Catherine Pattillo (2004), “Exchange Rate Policy and the Management of Official and Private Capital Flows in Africa,” IMF Staff Papers 51 (Special Issue): 126-160.
- Chistiano, L, Eichenbaum, M. and Evans, C. 2005, “Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy” Journal of Political Economy, 113.
- Clarida, R, Gali, J, and Gertler, M, (1999), “The Science of Monetary Policy: A New Keynesian Perspective” Journal of Economic Literature Vol. XXXVII.
- Clarida, R, Gali, J, and Gertler, M, (2000), “Monetary Policy Rules and Macroeconomic Stability: Theory and Evidence”, Quarterly Journal of Economics, 115.
- Clément, Jean A.P., and Shanaka J. Peiris (eds.), forthcoming, Post-Stabilization Economics in Sub-Saharan Africa: Lessons from Mozambique (Washington: International Monetary Fund).
- Devereux, M.B., Lane, P.R. and Xu, J. (2004), “Exchange Rates and Monetary Policy in Emerging Market Economies”, Institute for International Integration Studies Discussion Paper 36, Trinity College Dublin.
- Fernández-Villaverde, J. and Rubio-Ramírez, J.F. (2004), “Comparing Dynamic Equilibrium Models to Data: A Bayesian Approach, Journal of Econometrics, 123, 153-187.
- Fischer, Stanley, 1993. "The role of macroeconomic factors in growth," Journal of Monetary Economics, Elsevier, vol. 32(3), pages 485-512, December.
- Galí J., 1999. “Technology, Employment, and the Business cycle: Do Technology Shocks Explain Aggregate Fluctuations.” American Economic Review 89(1), 249.-271.
- Ghosh, A., and Stephen Phillips, 1998, “Warning: Inflation May Be Harmful to Your Growth,” IMF Staff Papers, Vol. 45, No. 4, pp. 672–710.
- Geweke J., (1998). “Using Simulation Methods for Bayesian Econometric Models: Inference, Development and Communication” Staff Report 249, Federal Reserve Bank of Minneapolis.
- International Monetary Fund (2005a), “The Macroeconomics of Managing Increased Aid Inflows: Experiences of Low-Income Countries and Policy Implications,” (Policy Development and Review Department).
- International Monetary Fund, 2005b, World Economic Outlook (Washington, September).
- International Monetary Fund, 2006, “Designing Monetary and Fiscal Policy in Low-Income Countries” IMF Occasional Paper 250.
- Juillard M., Karam P., Laxton D., Pesenti P., 2004. Welfare-based monetary policy rules in an estimated DSGE model of the US economy. mimeo, Federal Reserve Bank of New York.
- Kollman, R. (2002), “Monetary Policy Rules in the Open Economy: Effects on Welfare and Business Cycles”, Journal of Monetary Economics, 49, 989-1015.
- Loungani, P. and Swagel, P., 2001, “Sources of Inflation in Developing Countries,” IMF Working Paper 01/198 (Washington: International Monetary Fund).
- Lubik T., Schorfheide F., 2005. “A Bayesian Look at New Open Economy Macroeconomics.” mimeo.
- Pallage, S. and Robe, M. "On the Welfare Cost of Business Cycles in Developing Countries", International Economic Review, 44(2), 677-698, 2003.
- Prati, A. and Tressel, T. (2006), “Aid Volatility and Dutch Disease: Is there a Role for Macroeconomic Policies?” Unpublished Manuscript.
- Rajan, R. and Subramanian, A. (2005), “What Undermines Aid’s Impact on Growth?” IMF Working Paper 05/127.
- Rotemberg J.J., 1982. “Sticky prices in the United States.” Journal of Political Economy 90, 1187-1211.
- Sachs, J. and Warner, A. (1995), “Natural Resource Abundance and Economic Growth”, NBER Working Paper no. 5398.
- Saxegaard, M. (2006a), “Monetary Policy Rules in a Small Open Economy with External Liabilities”, Unpublished Manuscript.
- Saxegaard, M. (2006b), “Fiscal and Monetary Policy in an Estimated Model of the Philippine Economy”, Unpublished Manuscript.
- Schmitt-Grohé S., Uribe M., (2004). “Solving Dynamic General Equilibrium Models using a Second-order Approximation to the Policy Function” Journal of Economic Dynamics and Control 28, 755-775.
- Schorfheide F., 2000. “Loss Function-Based Evaluation of DSGE Models” Journal of Applied Econometrics 15, 645-670.
- Smets F., Wouters R., 2003. “An Estimated Dynamic Stochastic General Equilibrium Model of the Euro Area.” Journal of European Economic Association 1, 1123-1175.
- Smets F., Wouters R., 2005. “Comparing Shocks and Frictions in US and Euro Area Business Cycles: A Bayesian DSGE Approach.” Journal of Applied Econometrics 20(2), 161-183.
- Stone, Mark, 2003, “Inflation Targeting Lite,” IMF Working Paper 03/12.
- Tarp, Finn & Jensen, Henning Tarp & Arndt, Channing & Robinson, Sherman & Heltberg, Rasmus, 2002. "Facing the development challenge in Mozambique," Research reports 126, International Food Policy Research Institute (IFPRI).
- Taylor, J.B. (Ed.) (1998), “Monetary Policy Rules”, University of Chicago Press, Chicago.

### Appendix 1: CALIBRATION
- θ: 1.5 — Home elasticity of substitution
- η: 3.5 — Foreign elasticity of substitution
- ψ−1: 1.5 — Inverse of Frisch elasticity
- ε: 2 — Inverse of elasticity of money supply
- α(d): 0.731 — Share of nontradables in CPI
- ν/(ν−1)(): 1.09 — Markup factor for intermediary goods.
- ς: 0.15 — Cost share of borrowing
- α: 0.41 — Cost share of capital
- δ: 0.025 — Quarterly depreciation rate of capital
- β: (1.093/1.123)^(1/4) — Quarterly subjective discount rate
- γu: 0.5 — Steady-state learning by doing
- μu: 0.3 — Steady-state share of government investment
- π*: (1.093)^(1/4) — Steady-state CPI inflation
- π: (1.059)^(1/4) — Steady-state foreign inflation
- 1+i: (1.123)^(1/4) — Steady-state domestic interest rate
- 1+i*: (1.117)^(1/4) — Steady-state foreign interest rate
- (0/C) MMD+: 0.22 — Currency to M2 Ratio
- (0/MD) Y+: 0.7 — M2 to GDP Ratio
- TY: 0.15 — Steady-state tax to GDP ratio
- AY: 0.15 — Steady-state aid to GDP ratio
- Z: 4.6 months of imports — Steady-state level of foreign currency reserves

### Appendix I: Parameter Estimates and Priors (selected entries)
- Cost of Non-tradable Goods Price Adjustment: Density normal, S.D. 100.000, Mean 86.8394, Posterior 101.4355, 117.1080
- Habit Persistence: Density beta, S.D. 0.4000, Mean 0.2534, Posterior 0.3833, 0.5036
- Capital Stock Adjustment Costs: Density normal, S.D. 1.0000, Mean 0.9078, Posterior 1.0412, 1.1971
- Investment Level Adjustment Costs: Density normal, S.D. 80.000, Mean 0.623276, Posterior 76.56489, 0.0185
- Share of Aid Spent: Density normal, S.D. 1.0000, Mean 0.9647, Posterior 1.1450, 1.3188
- Share of Aid Spent by Public Sector: Density normal, S.D. 1.0000, Mean 1.0438, Posterior 1.1920, 1.2892
- Commercial Bank Reserve Smoothing (Bonds): Density gamma, S.D. 0.2000, Mean 0.0797, Posterior 0.1440, 0.2190
- Commercial Bank Reserve Smoothing (Lending): Density gamma, S.D. 0.2000, Mean 0.1036, Posterior 0.1592, 0.2119
- Commercial Bank Reserve Smoothing (Deposits): Density gamma, S.D. 0.2000, Mean 0.0424, Posterior 0.1012, 0.1510
- Interest Rate Spread Markup Factor: Density normal, S.D. 10.000, Mean 8.18819, Posterior 19.7740, 11.5823
- International Reserves Stabilization: Density normal, S.D. 0.0010, Mean -0.0121, Posterior 0.7730, 0.1737
- Exchange Rate Stabilization: Density normal, S.D. 0.5000, Mean 0.1816, Posterior 0.3193, 0.4713
- Absorption: Density normal, S.D. 0.5000, Mean 0.6741, Posterior 0.7971, 0.9065
- International Reserves Sterilization: Density normal, S.D. 0.5000, Mean 0.2949, Posterior 0.4751, 0.6245
- Inflation Stabilization: Density normal, S.D. 0.5000, Mean 0.3079, Posterior 0.4630, 0.6291
- Output Stabilization: Density normal, S.D. 0.5000, Mean 0.0570, Posterior 0.1634, 0.2490
- Bond Stabilization: Density normal, S.D. 0.0010, Mean 0.0950, Posterior 0.1991, 0.2953
- Technology Shock Persistence: Density beta, S.D. 0.8000, Mean 0.5890, Posterior 0.7430, 0.9471
- Foreign Inflation Shock Persistence: Density beta, S.D. 0.8000, Mean 0.5928, Posterior 0.6951, 0.7942
- Labor Supply Shock Persistence: Density beta, S.D. 0.8000, Mean 0.6305, Posterior 0.7691, 0.9216
- Consumption Shock Persistence: Density beta, S.D. 0.8000, Mean 0.5092, Posterior 0.6596, 0.8185
- Aid Shock Persistence: Density beta, S.D. 0.8000, Mean 0.6551, Posterior 0.7735, 0.9077
- Foreign Interest Rate Shock Persistence: Density beta, S.D. 0.8000, Mean 0.6581, Posterior 0.8025, 0.9579
- Government Investment Shock Persistence: Density beta, S.D. 0.8000, Mean 0.4929, Posterior 0.5852, 0.6816
- Learning by Doing Shock Persistence: Density beta, S.D. 0.8000, Mean 0.6418, Posterior 0.7723, 0.9313
- Investment Shock Persistence: Density beta, S.D. 0.8000, Mean 0.6375, Posterior 0.7671, 0.9349
- Interest Rate Spread Shock Persistence: Density beta, S.D. 0.8000, Mean 0.2398, Posterior 0.3930, 0.5251
- Bond Shock Persistence: Density beta, S.D. 0.8000, Mean 0.6558, Posterior 0.7740, 0.9040
- Terms of Trade Shock Persistence: Density beta, S.D. 0.8000, Mean 0.4902, Posterior 0.6486, 0.7749
- International Reserves Shock Persistence: Density beta, S.D. 0.8000, Mean 0.7996, Posterior 0.8725, 0.9606
- Size of Technology Shock: Density invgamma, S.D. 0.002, Mean 0.0048, Posterior 0.0048, 0.0248
- Size of Foreign Inflation Shock: Density invgamma, S.D. 0.002, Mean 0.0166, Posterior 0.0084, 0.0281
- Size of Labor Supply Shock: Density invgamma, S.D. 0.100, Mean 0.0273, Posterior 0.0209, 0.0746
- Size of Consumption Shock: Density invgamma, S.D. 0.200, Mean 0.0611, Posterior 0.0529, 0.1012
- Size of Aid Shock: Density invgamma, S.D. 0.100, Mean 0.0196, Posterior 0.0122, 0.0329
- Size of Government Investment Shock: Density invgamma, S.D. 0.050, Mean 0.0016, Posterior 0.0118, 0.0023
- Size of Learning by Doing Shock: Density invgamma, S.D. 0.100, Mean 0.0132, Posterior 0.0257, 0.0431
- Size of Bond Shock: Density invgamma, S.D. 0.050, Mean 0.0241, Posterior 0.0102, 0.0873
- Size of Investment Shock: Density invgamma, S.D. 5.000, Mean 0.0136, Posterior 1.3207, 0.0248
- Size of Interest Rate Spread Shock: Density invgamma, S.D. 10.000, Mean 15.65742, Posterior 2.479324, 24.7542
- Size of Terms of Trade Shock: Density invgamma, S.D. 0.050, Mean 2.8191, Posterior 0.01304, 4.9487
- Size of International Reserves Shock: Density invgamma, S.D. 0.050, Mean 0.0145, Posterior 0.0062, 0.0268
- Size of Foreign Interest Rate Shock: Density invgamma, S.D. 0.050, Mean 0.0065, Posterior 0.0164, 0.0105
- Size of Price Markup Shock: Density invgamma, S.D. 10.000, Mean 0.0121, Posterior 1.6522, 0.049

### APPENDIX II: ESTIMATION RESULTS
- The appendix lists prior and posterior entries and a 90% interval for a wide set of parameters (φb1, φ2, φω, ι1, π2, π3, πη1, z2, z3, z1, b2, b3, b4, bY, ρ*π, ρL, ρC, ρA, ρ*i, ρμ, ργ, ρI, ρi, ρB, ρtot, ρZ, ρY, u*, uπL, uC, uA, uμ, uγ, BuI, ui, utot, uZ, u*i, uv, uu).
- Specific numeric posterior values are not printed in this listing but parameter labels and ordering are preserved.

### APPENDIX III: PRIOR AND POSTERIOR DISTRIBUTIONS (variables and series shown)
- SE_epstheta
- SE_epspistar
- SE_epsls
- SE_epscs
- SE_epsaid
- SE_epskappa
- SE_epsgovk
- SE_epslbd
- SE_epsbp
- SE_epsinv
- SE_epselas
- SE_epstot
- SE_epszshock
- SE_epsistar
- SE_epsupsilon
- SE_EOBS_dqx
- SE_EOBS_dqm
- SE_EOBS_dy
- SE_EOBS_dc
- SE_EOBS_dpi
- SE_EOBS_drer
- SE_EOBS_dm
- SE_EOBS_dmcir
- SE_EOBS_di
- SE_EOBS_dilend
- SE_EOBS_dbp
- SE_EOBS_dz
- SE_EOBS_daid
- SE_EOBS_dres
- SE_EOBS_dpim
- SE_EOBS_dpix
- d, h, phi1, phi2, iota, omega, rfin, rfin1, rfin2, efi, z1, z2, z3, b1, b2, b3, b4, rhotheta, rhopistar, rhols, rhocs, rhoaid, rhoistar, rhokappa, rhogovk, rholbd, rhoinv, rhoelas, rhobp, rhotot, rhozshock.

### APPENDIX IV: ACTUAL AND ONE-STEP AHEAD FORECASTS (series displayed)
- dpi
- dpim
- dpix
- dq
- dqm
- dqx
- drer
- dres
- dy
- daid
- dbor
- dbp
- dc
- dgov
- di
- dilend
- dm
- dmcir

*Source: _wp07282 - REFERENCES (PDF)._

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2007/_wp07282.pdf_