## 1.     Priors

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---

### I. INTRODUCTION
- South Africa brought inflation under control following a sharp depreciation at the end of 2001; inflation peaked at 11.3 percent in October 2002.
- Subsequent appreciation of the rand and monetary tightening led to a steady decline of inflation; inflation remained within the official target range of 3 to 6 percent for several years.
- Improvements in the South African Reserve Bank’s (SARB) inflation targeting framework strengthened credibility and anchored inflation expectations.
- More recently, energy and food price shocks, together with a thriving economy, have contributed to higher inflation.
- Inflation targeting is associated with: lower inflation in the long run; smaller inflation response to oil-price and exchange-rate shocks; strengthened monetary policy independence; improved monetary policy efficiency; and inflation outcomes closer to desired levels.
- Challenges for emerging market economies in conducting inflation targeting:
  - Credibility issues that weaken optimal macroeconomic policy design and reduce effectiveness of monetary policy.
  - Weak institutions leading to currency substitution or liability dollarization, or fiscal dominance.
  - Large exchange rate and other external shocks that introduce substantial volatility.
- South Africa is not particularly affected by currency substitution or liability dollarization; macroeconomic policies have been impressive and the sharp depreciation in 2001-02 indicates no “fear of floating” (though the exogeneity of that depreciation is unclear).
- In small open, globally integrated economies, a coherent forward-looking framework is essential to assess effects of external and domestic shocks on inflation and gauge policy response.
- The paper estimates, with Bayesian methods, a small dynamic macroeconomic model for South Africa that:
  - Assesses impact on inflation dynamics of exchange rates, domestic prices, domestic and external demand.
  - Displays empirical features of the monetary transmission mechanism in South Africa.
  - Evaluates policy responses to shocks affecting inflation.
  - Incorporates forward-looking behavior of private agents and the monetary authority; embodies the role of monetary policy as an anchor for inflation and expectations; supports central inflation forecast within inflation targeting.

### II. A SMALL OPEN ECONOMY MODEL
- Model features:
  - Small open economy with forward-looking aggregate supply and demand and stylized lags in the monetary transmission channel.
  - Includes internal shocks and external shocks from the rest of the world (represented by the U.S., kept exogenous).
  - Quarterly frequency; main equations: aggregate supply (New Keynesian Phillips curve), aggregate demand, uncovered interest parity (real), and monetary reaction function.
- Aggregate supply (augmented New Keynesian Phillips curve):
  - Equation includes expected inflation four quarters ahead (π4 t+4), past inflation (π4 t−4), output gap (ygap t), and rate of real exchange rate depreciation (zt); a residual captures other temporary exogenous effects (e.g., supply or oil shocks).
  - Notation preserved: π4 t is annual inflation rate; πt is annualized quarterly inflation rate; ygap t is output gap; zt is log of real exchange rate (increase = real depreciation); cpi t and s t definitions provided in text.
  - Backward-looking component rationales: indexation schemes or presence of irrational price setters; leads to substantial inertia in inflation.
- Aggregate demand:
  - Domestic output gap (ygap t) depends on expected and past domestic output gap, lagged gap between real interest rates (RR t) and equilibrium real interest rate (RR equi), lagged gap (zgap t) between real exchange rate and equilibrium, and foreign output gap (ygap* t); residual captures other temporary exogenous effects (e.g., fiscal policy).
  - Only deviations from long-run equilibrium matter.
  - Past demand effects: habit persistence in consumption or adjustment costs of investment; future demand effects: intertemporal smoothing or forward-looking investment choices.
- Uncovered interest parity (real terms):
  - Determines real exchange rate with parameter δ and residual for exogenous exchange rate shocks.
  - Model displays Dornbusch-style overshooting with δ = 1, but δ commonly set less than one to avoid excessive predicted volatility.
- Monetary policy reaction function:
  - Short-term nominal interest rate (RS t) set according to rule involving inflation target 4 quarters ahead (arg4 4 Tet t π+), expected inflation deviations, output gap, lagged policy rate (interest rate smoothing), and residual capturing policy mistakes.
  - Taylor Principle: coefficient on expected inflation deviations (γπ) must be larger than one to ensure stability (holds strictly without interest rate smoothing).
  - High interest rate smoothing (high Lag R γ) commonly found empirically.

### III. BAYESIAN ESTIMATION OF THE MODEL
- Rationale for Bayesian methods:
  - Work well in short samples; particularly suitable for South Africa given structural breaks around early 1990s.
- Data and sample:
  - Main estimation sample: 1994-2005; robustness checks for 2000-2005 showed similar results.
  - Nine series used: CPIX inflation (πt) from SARB; from IFS dataset: short-term nominal interest rate (RS t, three-month government bonds), bilateral real exchange rate versus the U.S. (z t), U.S. short-term real interest rate (RR t* = nominal three-month U.S. treasury bills minus one-year inflation rate); Appendix describes derivation of remaining five series: domestic output gap (ygap t), U.S. output gap (ygap* t), real exchange rate gap (zgap t), equilibrium domestic real interest rate (RR .Equi t), and inflation target (arg4 4 Tet t π+).
- Estimation setup:
  - θ is vector of eighteen parameters (twelve structural model parameters plus steady state real interest rate and autoregressive terms for five observable variables exogenous to theoretical model).
  - Priors summarized in Table 1 (distribution types chosen based on admissible ranges).
- Numerical implementation:
  - Posterior modes found using Sims’ algorithm; local optimum checked.
  - Metropolis-Hastings algorithm with 500,000 replications used to draw from posterior density.
  - Acceptance rate around 30 percent; convergence achieved based on Brooks and Gelman (1998) criterion.
- Estimation highlights:
  - Posterior mean and 90 percent confidence intervals reported.
  - Notable characteristics:
    - Inflation is reasonably forward looking: 0.44 is the coefficient of lead inflation.
    - Interest rates are highly sluggish: 0.75 is the coefficient of lagged interest rate in the monetary reaction function.
  - Data are informative about most parameters, except parameters reflecting inflation and output weights in the monetary reaction function.

### IV. SHOCK SCENARIOS
- A. Monetary transmission mechanism (model response to a 100 basis point monetary policy shock):
  - Lowers domestic demand.
  - Appreciates the exchange rate.
  - Prices fall.
  - Central bank lowers interest rates which fall below control about a year after the shock.
  - Effects on inflation and output peak several quarters after the initial monetary contraction.
  - Exchange rate: immediate nominal appreciation of less than one percent; nominal appreciation peaks at about 1.5 percent two quarters later.
- B. Exchange rate, price, and demand shocks:
  - Exchange rate shock:
    - An unanticipated immediate appreciation of ten percent lowers inflation by about 0.6 percentage points one year later.
    - Monetary policy reacts immediately by lowering interest rates by about 30 basis points; cumulative response amounts to 100 basis points after one year.
    - Output falls by about 0.6 percentage points below potential, with about a one-year lag, and then recovers.
  - Price shock (e.g., international oil or food price shock):
    - A price shock that initially raises the annualized quarterly inflation rate by one percentage point requires an increase in the nominal interest rate of about 140 basis points above the baseline after three quarters.
    - This increases the real interest rate by about one percentage points for several quarters.
    - Associated output cost: output gap peaks at about a negative 1 percentage point of GDP after two years and remains negative for about five years—mainly due to inflation inertia in the model.
- Additional note:
  - Estimated monetary transmission lags are consistent with Smal and de Jager (2001), who find a transmission lag of about 6-8 quarters in South Africa.

### MAIN CONCLUSIONS AND KEY FINDINGS
- The paper employs Bayesian methods to estimate a dynamic small open economy model tailored to the South African economy under an inflation targeting regime.
- The model emphasizes the role of monetary policy as an anchor for inflation and inflation expectations and can be used to integrate short-term inflation outlook into a consistent medium-term forward-looking framework.
- Although model and estimation uncertainties are acknowledged as large, the estimated model reproduces key empirical features of the monetary transmission mechanism and helps assess dynamic responses of macro variables to shocks.
- Selected scenario magnitudes and dynamics:
  - Exchange rate shocks: Dornbusch-style overshooting (1=δ) would make effects on inflation and output even less persistent.
  - Exogenous demand shock of one percent of GDP raises the output gap; inflation increases by 0.2 percent after about 1 year; policy rate rises by almost half of a percent; nominal and real exchange rate appreciate by about 2 percent in two years.
  - Interest rate shocks: short-term and real interest rate responses deviate up to about 1.2 percentage points; output gap deviations roughly -0.30 to 0.15 percentage points; year-on-year CPIX inflation deviations roughly -0.20 to 0.05 percentage points.
  - Price (supply) shocks: inflation responses up to about 1.2 percentage points (year-on-year CPIX inflation deviations) with associated exchange rate and output gap dynamics.

### MODEL ESTIMATION: PRIORS (SELECTED) AND POSTERIOR ESTIMATES (SELECTED)
- Priors (selected):
  - απ mean 0.250, beta, standard deviation 0.10
  - αy mean 0.300, gamma, standard deviation 0.10
  - αz mean 0.150, beta, standard deviation 0.05
  - βyld mean 0.050, beta, standard deviation 0.02
  - βylg mean 0.700, beta, standard deviation 0.05
  - βrr mean 0.120, gamma, standard deviation 0.03
  - βz mean 0.050, gamma, standard deviation 0.01
  - βf mean 0.200, gamma, standard deviation 0.05
  - γlg mean 0.500, beta, standard deviation 0.10
  - γπ mean 2.000, gamma, standard deviation 0.30
  - γy mean 0.300, beta, standard deviation 0.05
  - δ mean 0.500, beta, standard deviation 0.10
  - λ1 mean 0.800, beta, standard deviation 0.05
  - λ2 mean 0.800, beta, standard deviation 0.05
  - λ3 mean 0.800, beta, standard deviation 0.05
  - λ4 mean 0.500, beta, standard deviation 0.25
  - λ5 mean 0.700, beta, standard deviation 0.10
  - RR steady state mean 3.500, gamma, standard deviation 1.00
  - sd of supply shock 2.000, inv. gamma ∞
  - sd of interest shock 2.000, inv. gamma ∞
  - sd of demand shock 1.000, inv. gamma ∞
  - sd of exchange rate shock 3.000, inv. gamma ∞
  - sd of ygap* 0.500, inv. gamma ∞
  - sd of RR* 1.000, inv. gamma ∞
  - sd of zgap 5.000, inv. gamma ∞
  - sd of RR equi 0.300, inv. gamma ∞
  - sd of π4 target 0.500, inv. gamma ∞
- Posterior estimates (selected means and 90% confidence intervals):
  - απ mean 0.434, 90% CI 0.233 to 0.631
  - αy mean 0.228, 90% CI 0.105 to 0.339
  - αz mean 0.146, 90% CI 0.076 to 0.208
  - βyld mean 0.043, 90% CI 0.016 to 0.068
  - βylg mean 0.746, 90% CI 0.682 to 0.809
  - βrr mean 0.086, 90% CI 0.055 to 0.117
  - βz mean 0.027, 90% CI 0.019 to 0.035
  - βf mean 0.143, 90% CI 0.091 to 0.194
  - γlg mean 0.700, 90% CI 0.607 to 0.793
  - γπ mean 1.932, 90% CI 1.433 to 2.401
  - γy mean 0.283, 90% CI 0.207 to 0.360
  - Δ (delta) mean 0.434, 90% CI 0.372 to 0.498
  - λ1 mean 0.877, 90% CI 0.830 to 0.922
  - λ2 mean 0.879, 90% CI 0.838 to 0.921
  - λ3 mean 0.804, 90% CI 0.739 to 0.872
  - λ4 mean 0.982, 90% CI 0.967 to 0.998
  - λ5 mean 0.991, 90% CI 0.986 to 0.996
  - RR steady state mean 3.422, 90% CI 2.263 to 4.540
  - sd of supply shock mean 2.657, 90% CI 2.172 to 3.104
  - sd of interest shock mean 1.286, 90% CI 1.058 to 1.513
  - sd of demand shock mean 0.579, 90% CI 0.471 to 0.687
  - sd of exchange rate shock mean 6.291, 90% CI 5.157 to 7.346
  - sd of ygap* mean 0.482, 90% CI 0.401 to 0.559
  - sd of RR* mean 0.541, 90% CI 0.451 to 0.628
  - sd of zgap mean 5.557, 90% CI 4.651 to 6.414
  - sd of RR equi mean 0.212, 90% CI 0.176 to 0.246
  - sd of π4 target mean 0.205, 90% CI 0.169 to 0.241

### SECOND-MOMENT COMPARISON (1994-2005 SAMPLE VERSUS MODEL)
- π4t: Data 1.8, Model 2.5
- RS t: Data 3.2, Model 3.4
- Ygap t: Data 0.9, Model 1.3
- zt - z-1: Data 6.5, Model 6.4

### POLICY IMPLICATIONS AND INTERPRETATION
- Monetary policy:
  - γπ captures monetary authorities' aggressiveness; a higher γπ implies a larger interest rate response to a given inflationary shock and tends to frontload output costs.
  - LagRγ measures aversion to changing interest rates; a higher coefficient implies slower monetary reaction.
  - Given real-time uncertainty about the output gap, the coefficient on the output gap (YGAPγ) is advised to be rather small.
- Exchange rate expectations and pass-through:
  - δ (0<δ<1) determines degree to which exchange rate expectations are forward looking; δ close to 1 implies forward-looking expectations and Dornbusch-style overshooting.
  - αz relates to the weight of imported goods in the CPI basket and the pass-through of foreign-currency prices onto domestic-currency prices of imports.
- Aggregate demand and transmission:
  - Output gap inertia captured by Lag ygap β tends to be substantial; RRgap β measures interest rate effects and larger values imply more effective monetary policy.
  - Effects of exchange rates (Zgap β) and foreign output (*ygap β) are larger in more open economies.
  - Significant lags in monetary transmission imply the sum of RRgap β and Zgap β should be relatively small compared to Lag ygap β.

### STEADY STATE AND ESTIMATION ASSUMPTIONS (SELECTED NUMERIC ASSUMPTIONS)
- arg4Tet t π = 4.5 percent.
- *tRR = 2.25 percent.
- .EquitRiskP = 1.25 percent.
- In steady state these imply a real interest rate of about 3.5 percent and a nominal short-term rate of about 8 percent.
- Output HP filter smoothing parameter used: 1600.
- Potential output growth convergence assumption: long run potential output growth of 4.0 percent.
- South African equilibrium real interest rate (.EquitRR) assumed equal to 1 percent in 1994 and reaching 3.5 percent from 2007q4 onwards.
- Inflation target path (LRX filter passing through): 6 percent in 2001q1, 5.5 percent in 2003q1, 5 percent in 2004q1, 4.5 percent in 2005q1.

### MODEL EXTENSIONS AND DYNAMICS
- A richer model includes:
  - A second lag for inflation in the aggregate supply equation to capture inertia.
  - A lag of the change in the real exchange rate into the supply equation to capture pass-through.
  - A second lag of the real interest rate gap into the aggregate demand equation to better capture monetary policy transmission.

*Source: _wp0848 - 1.     Priors (IMF working paper content provided).*

### 1.     Priors ..........................................................................................................

### 1.     Priors

### I. INTRODUCTION
- South Africa brought inflation under control following a sharp depreciation at the end of 2001; inflation peaked at 11.3 percent in October 2002.
- Subsequent appreciation of the rand and monetary tightening led to a steady decline of inflation; inflation remained within the official target range of 3 to 6 percent for several years.
- Improvements in the South African Reserve Bank’s (SARB) inflation targeting framework strengthened credibility and anchored inflation expectations.
- More recently, energy and food price shocks, together with a thriving economy, have contributed to higher inflation.
- Inflation targeting is associated with: lower inflation in the long run; smaller inflation response to oil-price and exchange-rate shocks; strengthened monetary policy independence; improved monetary policy efficiency; and inflation outcomes closer to desired levels (as discussed in Roger and Stone (2005) and Mishkin and Klaus Schmidt-Hebbel (2007)).
- Challenges for emerging market economies in conducting inflation targeting (Calvo (2001), Mishkin (2004)):
  - Credibility issues that weaken optimal macroeconomic policy design and reduce effectiveness of monetary policy.
  - Weak institutions leading to currency substitution or liability dollarization, or fiscal dominance.
  - Large exchange rate and other external shocks that introduce substantial volatility.
- South Africa is not particularly affected by currency substitution or liability dollarization; macroeconomic policies have been impressive and the sharp depreciation in 2001-02 indicates no “fear of floating” (though the exogeneity of that depreciation is unclear).
- In small open, globally integrated economies, a coherent forward-looking framework is essential to assess effects of external and domestic shocks on inflation and gauge policy response.
- This paper estimates, with Bayesian methods, a small dynamic macroeconomic model for South Africa that:
  - Assesses impact on inflation dynamics of exchange rates, domestic prices, domestic and external demand.
  - Displays empirical features of the monetary transmission mechanism in South Africa.
  - Evaluates policy responses to shocks affecting inflation.
  - Incorporates forward-looking behavior of private agents and the monetary authority; embodies the role of monetary policy as an anchor for inflation and expectations; supports central inflation forecast within inflation targeting.

### II. A SMALL OPEN ECONOMY MODEL
- Model features:
  - Small open economy with forward-looking aggregate supply and demand and stylized lags in the monetary transmission channel.
  - Includes internal shocks and external shocks from the rest of the world (represented by the U.S., kept exogenous).
  - Quarterly frequency; main equations: aggregate supply (New Keynesian Phillips curve), aggregate demand, uncovered interest parity (real), and monetary reaction function. Definitions, equilibrium relations, parameter properties, values and steady-state assumptions are presented in the Appendix.
- Aggregate supply (augmented New Keynesian Phillips curve):
  - Equation includes expected inflation four quarters ahead (π4 t+4), past inflation (π4 t−4), output gap (ygap t), and rate of real exchange rate depreciation (zt); a residual captures other temporary exogenous effects (e.g., supply or oil shocks).
  - Notation preserved exactly from source: π4 t is annual inflation rate; πt is annualized quarterly inflation rate; ygap t is output gap; zt is log of real exchange rate (increase = real depreciation); cpi t and s t definitions provided in text.
  - Backward-looking component rationales: indexation schemes or presence of irrational price setters; leads to substantial inertia in inflation.
- Aggregate demand:
  - Domestic output gap (ygap t) depends on expected and past domestic output gap, lagged gap between real interest rates (RR t) and equilibrium real interest rate (RR equi), lagged gap (zgap t) between real exchange rate and equilibrium, and foreign output gap (ygap* t); residual captures other temporary exogenous effects (e.g., fiscal policy).
  - Only deviations from long-run equilibrium matter.
  - Past demand effects: habit persistence in consumption or adjustment costs of investment; future demand effects: intertemporal smoothing or forward-looking investment choices.
- Uncovered interest parity (real terms) determines real exchange rate:
  - Equation includes equilibrium real exchange rate dynamics with parameter δ and residual for exogenous exchange rate shocks.
  - Model displays Dornbusch-style overshooting with δ = 1, but δ is commonly set less than one to avoid excessive predicted volatility.
- Monetary policy reaction function:
  - Short-term nominal interest rate (RS t) set according to rule involving inflation target 4 quarters ahead (arg4 4 Tet t π+), expected inflation deviations, output gap, lagged policy rate (interest rate smoothing), and residual capturing policy mistakes.
  - Taylor Principle: coefficient on expected inflation deviations (γπ) must be larger than one to ensure stability (holds strictly without interest rate smoothing).
  - High interest rate smoothing (high Lag R γ) commonly found empirically.

### III. BAYESIAN ESTIMATION OF THE MODEL
- Rationale for Bayesian methods:
  - Work well in short samples; particularly suitable for South Africa given structural breaks around early 1990s.
- Data and sample:
  - Main estimation sample: 1994-2005 (post-apartheid period); robustness checks for 2000-2005 (post-announcement of inflation targeting) showed similar results.
  - Nine series used: CPIX inflation (πt) from SARB; from IFS dataset: short-term nominal interest rate (RS t, three-month government bonds), bilateral real exchange rate versus the U.S. (z t), U.S. short-term real interest rate (RR t* = nominal three-month U.S. treasury bills minus one-year inflation rate); Appendix describes derivation of remaining five series: domestic output gap (ygap t), U.S. output gap (ygap* t), real exchange rate gap (zgap t), equilibrium domestic real interest rate (RR .Equi t), and inflation target (arg4 4 Tet t π+).
- Estimation setup:
  - Observables: TY over sample T; priors p(θ); posterior density p(θ|TY) as given by Bayes’ rule (formula reproduced in source).
  - θ is vector of eighteen parameters (twelve structural model parameters plus steady state real interest rate and autoregressive terms for five observable variables exogenous to theoretical model).
  - Priors summarized in Table 1 (distribution types chosen based on admissible ranges: beta between 0 and 1; gamma and inverted gamma positive). Prior means and standard deviations guided by: country-specific knowledge; stylized facts of monetary transmission; parameters from similar models (notably Berg, Karam, and Laxton (2006a, 2006b) for Canada); intuition about economic effects (Appendix discussion).
- Numerical implementation:
  - Posterior modes found using Sims’ algorithm; local optimum checked.
  - Metropolis-Hastings algorithm with 500,000 replications used to draw from posterior density.
  - Acceptance rate around 30 percent; convergence achieved based on Brooks and Gelman (1998) criterion.
- Estimation results (high-level summary; refer to Table 2 and Figure 1 in source for full details):
  - Posterior mean and 90 percent confidence intervals reported in Table 2.
  - Notable characteristics:
    - Inflation is reasonably forward looking: 0.44 is the coefficient of lead inflation.
    - Interest rates are highly sluggish: 0.75 is the coefficient of lagged interest rate in the monetary reaction function.
  - Data are informative about most parameters, except parameters reflecting inflation and output weights in the monetary reaction function (monetary reaction function mainly calibrated via priors given recent adoption of inflation targeting).
- Moments comparison:
  - Table 3 compares standard deviations of four main variables in 1994-2005 sample with those implicit in estimated model.
  - Moments are remarkably similar for nominal interest rate and change in real exchange rate; somewhat lower in the data than in the model for inflation and output gap.
- Robustness checks:
  - Re-estimation for 2000-2005: most parameters similar; main difference is less forward-looking component of inflation in 2000-2005 sample.
  - Estimation of a model with richer lag structure: parameters generally similar; richer model has lower marginal data density, suggesting the more parsimonious model is preferred.
  - Different priors tried: final results generally similar.

### IV. SHOCK SCENARIOS
- A. The Monetary Transmission Mechanism
  - Model response to a 100 basis point monetary policy shock (deviation from equilibrium solution):
    - Lowers domestic demand.
    - Appreciates the exchange rate.
    - Prices fall.
    - To counter falling prices and slowdown in output, central bank lowers interest rates which fall below control about a year after the shock.
    - Effects on inflation and output peak several quarters after the initial monetary contraction.
    - Effect on exchange rate: immediate nominal appreciation of less than one percent; nominal appreciation peaks at about 1.5 percent two quarters later.
  - These responses are consistent with other empirical studies of the monetary transmission mechanism and broadly consistent with the SARB (2007) core forecasting model (18 structural equations).
- B. Exchange Rate, Price, and Demand Shocks
  - Exchange rate shock:
    - An unanticipated immediate appreciation of ten percent lowers inflation by about 0.6 percentage points one year later.
    - Monetary policy reacts immediately by lowering interest rates by about 30 basis points; cumulative response amounts to 100 basis points after one year.
    - Output falls by about 0.6 percentage points below potential, with about a one-year lag, and then recovers.
  - Price shock (e.g., international oil or food price shock):
    - A price shock that initially raises the annualized quarterly inflation rate by one percentage point requires an increase in the nominal interest rate of about 140 basis points above the baseline after three quarters.
    - This increases the real interest rate by about one percentage points for several quarters.
    - Associated output cost: output gap peaks at about a negative 1 percentage point of GDP after two years and remains negative for about five years—mainly due to inflation inertia in the model.
- Additional notes:
  - The model’s estimated monetary transmission lags are consistent with Smal and de Jager (2001), who find a transmission lag of about 6-8 quarters in South Africa.

*Source: _wp0848 - 1.     Priors (IMF working paper content provided).*

### 0.2 to 0.4 percent.

### _wp0848 - 0.2 to 0.4 percent.

### Main conclusions
- The paper employs Bayesian methods to estimate a dynamic small open economy model tailored to the South African economy under an inflation targeting regime.
- The model emphasizes the role of monetary policy as an anchor for inflation and inflation expectations and can be used to integrate short-term inflation outlook into a consistent medium-term forward-looking framework.
- Although model and estimation uncertainties are acknowledged as large, the estimated model reproduces key empirical features of the monetary transmission mechanism and helps assess dynamic responses of macro variables to shocks.

### Key findings on shock responses
- Exchange rate shocks:
  - With Dornbusch-style overshooting (1=δ), the effects of exchange rate shocks on inflation and output would be even less persistent.
  - Table/figure evidence shows large nominal and real exchange rate movements (e.g., nominal exchange rate deviations up to about -12 to 2 percent in Figure 3) with relatively muted inflation responses (year-on-year CPIX inflation deviations roughly -0.7 to 0.1 percentage points in Figure 3).
- Exogenous demand shocks (interpreted as fiscal-policy-type shocks not explicitly modeled):
  - A positive demand shock of one percent of GDP raises the output gap.
  - Inflation would increase only moderately: 0.2 percent after about 1 year.
  - Monetary policy tightens, bringing the policy rate up by almost half of a percent.
  - The tightening dampens demand and leads to a nominal and real exchange rate appreciation of about 2 percent in two years.
- Interest rate shocks (Figure 2):
  - Short-term and real interest rate responses show deviations up to about 1.2 percentage points.
  - Output gap and CPIX inflation responses are small in magnitude (output gap deviations roughly -0.30 to 0.15 percentage points; year-on-year CPIX inflation deviations roughly -0.20 to 0.05 percentage points).
- Price (supply) shocks (Figure 4):
  - Price shocks produce larger inflation responses (year-on-year CPIX inflation deviations up to about 1.2 percentage points) with associated exchange rate and output gap dynamics.

### Model estimation and parameter estimates
- Priors (selected):
  - απ mean 0.250, beta, standard deviation 0.10
  - αy mean 0.300, gamma, standard deviation 0.10
  - αz mean 0.150, beta, standard deviation 0.05
  - βyld mean 0.050, beta, standard deviation 0.02
  - βylg mean 0.700, beta, standard deviation 0.05
  - βrr mean 0.120, gamma, standard deviation 0.03
  - βz mean 0.050, gamma, standard deviation 0.01
  - βf mean 0.200, gamma, standard deviation 0.05
  - γlg mean 0.500, beta, standard deviation 0.10
  - γπ mean 2.000, gamma, standard deviation 0.30
  - γy mean 0.300, beta, standard deviation 0.05
  - δ mean 0.500, beta, standard deviation 0.10
  - λ1 mean 0.800, beta, standard deviation 0.05
  - λ2 mean 0.800, beta, standard deviation 0.05
  - λ3 mean 0.800, beta, standard deviation 0.05
  - λ4 mean 0.500, beta, standard deviation 0.25
  - λ5 mean 0.700, beta, standard deviation 0.10
  - RR steady state mean 3.500, gamma, standard deviation 1.00
  - sd of supply shock 2.000, inv. gamma ∞
  - sd of interest shock 2.000, inv. gamma ∞
  - sd of demand shock 1.000, inv. gamma ∞
  - sd of exchange rate shock 3.000, inv. gamma ∞
  - sd of ygap* 0.500, inv. gamma ∞
  - sd of RR* 1.000, inv. gamma ∞
  - sd of zgap 5.000, inv. gamma ∞
  - sd of RR equi 0.300, inv. gamma ∞
  - sd of π4 target 0.500, inv. gamma ∞
- Posterior estimates (selected means and 90% confidence intervals):
  - απ mean 0.434, 90% CI 0.233 to 0.631
  - αy mean 0.228, 90% CI 0.105 to 0.339
  - αz mean 0.146, 90% CI 0.076 to 0.208
  - βyld mean 0.043, 90% CI 0.016 to 0.068
  - βylg mean 0.746, 90% CI 0.682 to 0.809
  - βrr mean 0.086, 90% CI 0.055 to 0.117
  - βz mean 0.027, 90% CI 0.019 to 0.035
  - βf mean 0.143, 90% CI 0.091 to 0.194
  - γlg mean 0.700, 90% CI 0.607 to 0.793
  - γπ mean 1.932, 90% CI 1.433 to 2.401
  - γy mean 0.283, 90% CI 0.207 to 0.360
  - Δ (delta) mean 0.434, 90% CI 0.372 to 0.498
  - λ1 mean 0.877, 90% CI 0.830 to 0.922
  - λ2 mean 0.879, 90% CI 0.838 to 0.921
  - λ3 mean 0.804, 90% CI 0.739 to 0.872
  - λ4 mean 0.982, 90% CI 0.967 to 0.998
  - λ5 mean 0.991, 90% CI 0.986 to 0.996
  - RR steady state mean 3.422, 90% CI 2.263 to 4.540
  - sd of supply shock mean 2.657, 90% CI 2.172 to 3.104
  - sd of interest shock mean 1.286, 90% CI 1.058 to 1.513
  - sd of demand shock mean 0.579, 90% CI 0.471 to 0.687
  - sd of exchange rate shock mean 6.291, 90% CI 5.157 to 7.346
  - sd of ygap* mean 0.482, 90% CI 0.401 to 0.559
  - sd of RR* mean 0.541, 90% CI 0.451 to 0.628
  - sd of zgap mean 5.557, 90% CI 4.651 to 6.414
  - sd of RR equi mean 0.212, 90% CI 0.176 to 0.246
  - sd of π4 target mean 0.205, 90% CI 0.169 to 0.241

### Second-moment comparison (sample 1994-2005 versus model)
- π4t: Data 1.8, Model 2.5
- RS t: Data 3.2, Model 3.4
- Ygap t: Data 0.9, Model 1.3
- zt - z-1: Data 6.5, Model 6.4
- These are standard deviations of 1994-2005 sample versus model-generated series.

### Policy implications and interpretation
- Monetary policy:
  - The parameter γπ captures monetary authorities' aggressiveness; a higher γπ implies a larger interest rate response to a given inflationary shock and tends to frontload output costs.
  - LagRγ measures aversion to changing interest rates; a higher coefficient implies slower monetary reaction.
  - Given real-time uncertainty about the output gap, the coefficient on the output gap (YGAPγ) is advised to be rather small.
- Exchange rate expectations and pass-through:
  - The parameter δ (0<δ<1) determines degree to which exchange rate expectations are forward looking; δ close to 1 implies forward-looking expectations and Dornbusch-style overshooting.
  - αz relates to the weight of imported goods in the CPI basket and the pass-through of foreign-currency prices onto domestic-currency prices of imports.
- Aggregate demand and transmission:
  - Output gap inertia is captured by Lag ygap β and tends to be substantial; RRgap β measures interest rate effects and larger values imply more effective monetary policy.
  - Effects of exchange rates (Zgap β) and foreign output (*ygap β) are larger in more open economies.
  - Significant lags in monetary transmission imply the sum of RRgap β and Zgap β should be relatively small compared to Lag ygap β.

### Steady state and estimation assumptions (selected numeric assumptions)
- arg4Tet t π = 4.5 percent (the mid-point of the inflation targeting range).
- *tRR = 2.25 percent (historic average for the U.S. real short-term interest rate).
- .EquitRiskP = 1.25 percent.
- In steady state these imply a real interest rate of about 3.5 percent and a nominal short-term rate of about 8 percent.
- Output HP filter smoothing parameter used: 1600.
- Potential output growth convergence assumption: long run potential output growth of 4.0 percent.
- South African equilibrium real interest rate (.EquitRR) assumed equal to 1 percent in 1994 and reaching 3.5 percent from 2007q4 onwards.
- Inflation target path (LRX filter passing through): 6 percent in 2001q1, 5.5 percent in 2003q1, 5 percent in 2004q1, 4.5 percent in 2005q1.

### Model extensions and dynamics
- A richer model includes:
  - A second lag for inflation in the aggregate supply equation to capture inertia.
  - A lag of the change in the real exchange rate into the supply equation to capture pass-through.
  - A second lag of the real interest rate gap into the aggregate demand equation to better capture monetary policy transmission.

*Source: Author’s estimate (content unit: _wp0848 - 0.2 to 0.4 percent.).*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2008/_wp0848.pdf_