## _wp11108

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---

### Model purpose, structure, and scope
- Incorporates a small open economy model for Egypt into the IMF’s Global Projection Model (GPM), creating the extended model called GPM+.
- GPM encompasses 6 main blocks: United States, Euro Area, Japan, Emerging Asia, Latin America and other countries.
- GPM+ is a canonical small open economy satellite linked to GPM; it takes developments in GPM regions as given and does not feed back into GPM.
- GPM+ features five reduced-form behavioral equations for: the output gap, unemployment, inflation, nominal interest rate, and the exchange rate, plus identities for equilibrium interest rate, output and unemployment.
- GPM+ links to the rest of the world via three exogenous variables: foreign output gap, real world interest rate, and real world equilibrium interest rate (weighted averages across six GPM blocks using Egypt’s trade shares).
- Trade-share weights used in construction of the real effective exchange rate gap:
  - United States (0.14), EU (0.33), Japan (0.05), Emerging Asia (0.13), LA (0.02), others (0.33).

### Data, sample, estimation method, and priors
- Benchmark sample period: 2005: Q3 through 2010: Q2 (reflecting CBE adoption of the interest rate corridor in June 2005 and move toward inflation targeting).
- Data sources and availability (selected):
  - Real GDP (LGDP): Central Bank of Egypt — 2005Q3-2010Q2
  - CPI (LCPI): Central Bank of Egypt — 2005Q3-2010Q3
  - Unemployment Rate (UNR): CAPMAS, Egypt — 2005Q3-2010Q4
  - Nominal Interest Rate (RS): Overnight Interbank Rate — 2005Q3-2010Q5
  - Real Effective Exchange Rate (LZ): INS Database, IMF — 2005Q3-2010Q6
  - Foreign variables: GPM Historical Estimate (September 17, 2010) — 2005Q3-2010Q8–Q10 (depending on series)
- Estimation approach: regularized maximum likelihood (a penalized likelihood approach).
  - Regularization parameter used in reported results: ݌ = 0.01 (where ݌ = 0 corresponds to the maximum likelihood estimation).
- Priors guided by previous GPM applications and Egypt-specific calibrations; some parameters (steady-state inflation target, steady-state real interest rates) calibrated using sample averages.
- Structural shocks assumed independent, normally distributed, and uncorrelated over time; small and tight priors used for standard deviations of shocks to potential output.

### Core model equations and transmission channels
- Output gap (IS curve): depends on forward and backward looking elements, lagged short-term interest rate gap, real effective exchange rate gap, and foreign output gap.
- Real effective exchange rate determined via a real interest parity condition with a risk premium; real equilibrium exchange rate follows a stochastic law of motion.
- Inflation dynamics: hybrid New Keynesian Phillips curve linking current inflation to future expected inflation, lagged inflation, lagged output gap, and change in the real effective exchange rate (pass-through).
- Monetary policy: Taylor-type rule with interest rate smoothing, responding to the output gap and deviation of expected inflation from its target; model-consistent expected inflation (4π) derived from the Kalman filter and policy rate used is the CBE’s deposit rate.
- Two monetary transmission channels:
  - Interest rate channel (coefficient of real interest rate gap in IS curve).
  - Exchange rate channel (direct effect on output gap and pass-through in Phillips curve).

### Main empirical findings and model performance
- Output gap and growth:
  - Positive output gap widened since 2005, driven by undervalued exchange rate and favorable external environment, then declined sharply since the global crisis; gap has been somewhat negative since the middle of 2009 though not statistically different from zero.
  - Growth declined after the Lehman shock to below 5 percent (year-over-year) from an average 7 percent prior to the crisis.
- Inflation and expectations:
  - Inflation (12-month) since 2007 shows a gradual increasing trend with several double digit episodes (spikes in 2004, 2006–07, 2008).
  - CBE launched its core inflation index in October 2009 and communicates a comfort zone for inflation covering the 6–8 percent range.
- Monetary policy framework and behavior:
  - Since 2003 devaluation, exchange rate stable; operational move away from excess reserves targeting toward open market operations after June 2005 with an interest rate corridor and central bank notes.
  - Overnight interbank rate moved more smoothly since 2005; three month T-bill rates have tracked overnight rate but tended to decline relative to it during strong capital inflows.
- Transmission and coefficients (selected estimated results):
  - Relative size of backward-looking to forward-looking component in output gap evolution: about 3.
  - Output gap coefficients: beta1 (lag of output gap) ModeDispersion 0.453 0.057; beta2 (lead of output gap) ModeDispersion 0.164 0.033; beta3 (real interest rate gap lagged) ModeDispersion 0.079 0.041; beta4 (real exchange rate gap lagged) ModeDispersion 0.047 0.006; beta5 (real foreign output gap lagged) ModeDispersion 0.093 0.012.
  - Phillips curve: forward-looking weight about two-third for Egypt (versus median about 0.55 for other emerging markets); lambda1 (expected inflation) ModeDispersion 0.647 0.071; lambda2 (lag of output gap) ModeDispersion 0.479 0.078; lambda3 (real exchange rate depreciation) ModeDispersion 0.091 0.037.
  - Nominal interest rate rule: gamma1 (lag of nominal interest rate) ModeDispersion 0.865 0.058; gamma2 (deviation of inflation from target) ModeDispersion 1.273 0.117; gamma3 (output gap) ModeDispersion 0.31 0.108.
  - Estimated coefficient for the real interest rate gap in Egypt is “less than one half on average” of comparable coefficients in other countries, implying a weaker interest rate transmission channel.
  - Nominal interest rate inertia in Egypt is higher than in other countries, making real interest rates pro-cyclical and magnifying economic fluctuations.
- Forecast performance (one-year-ahead root mean squared forecast errors):
  - Annual growth: slightly higher than one percent.
  - Annual inflation: slightly higher than 5.5 percent.
  - Table 3a RMSEs for Egypt (selected): Real GDP Growth (y-o-y): 1Q Ahead 0.77, 4Q Ahead 1.23, 8Q Ahead 1.00; Nominal Interest Rate: 1Q Ahead 0.62, 4Q Ahead 1.09, 8Q Ahead 1.45; Inflation (y-o-y): 1Q Ahead 1.73, 4Q Ahead 5.59, 8Q Ahead 5.70.

### Impulse responses, pass-through, and variance decomposition
- Impulse responses (selected):
  - Foreign output gap shock:
    - Increased external demand widens Egypt’s output gap.
    - Current and expected exchange rate appreciation can make inflation negative in initial periods via pass-through.
    - Nominal interest rate peaks about 7 periods after the shock; inertia makes the real interest rate negative in the short run (periods 2 to 5) and positive in the medium term.
  - Foreign real interest rate shock:
    - Positive foreign real interest rate shock leads to depreciation of the Egyptian pound, increasing output gap and inflation via pass-through; nominal interest rate inertia makes the real interest rate negative in the first couple of periods.
  - Monetary policy shock:
    - One standard deviation increase in nominal interest rate (about one percent) would appreciate the exchange rate by 2–3 percentage points and create a negative output gap of about 0.4 percentage points in the short run; negative inflation lasts nearly 10 periods.
- Pass-through:
  - Estimated pass-through of the exchange rate to inflation in Egypt is relatively low compared to other emerging market economies; pass-through rate reached 0.23 at its peak within one year.
- Variance decomposition (selected shares of variation in output growth):
  - demand shocks: 26 percent
  - monetary policy shocks: 27 percent
  - shocks to the equilibrium real interest rate: 28 percent
  - external shocks (foreign real interest rates and foreign demand shocks) explain only 3–4 percent of the variation in output growth or the output gap, but contribute more to real exchange rate movements.
  - Table 3b entries (example): Growth (y-o-y) — Output Gap Shock 26; Philips Curve Shock 7; Nom. Int. Rate Shock 27; Equilib. Real Int. Rate Shock 28; Equilib. Real Exchange Rate Shock 24; Foreign Real Interest Rate Shock 34; Foreign Output Gap Shock 33; Others 44 (values correspond to the source matrix layout).

### Policy experiments, optimal policy, and scenario simulations
- Definitions of optimal policy:
  - Ramsey optimal policy (social planner’s solution).
  - Optimal policy rule (minimizes the weighted average of the variance of inflation and the output gap, given estimated parameters other than the Taylor rule coefficients).
- Ramsey optimal policy example parameters and implications:
  - discount factor: 0.98 (8 percent of the annual discount rate)
  - weight of the output gap in objective function: 6
  - model-consistent variance of inflation is nine times as large as that of the output gap.
  - Implications: central bank should take quick and front-loaded responses to shocks; Ramsey policy raises interest rates quickly and significantly immediately after shocks, producing an exchange rate appreciation (negative sign indicates appreciation in GPM+), contrasting with the estimated Taylor rule.
- Optimal monetary policy rule findings:
  - Optimal rule requires much larger responses of nominal interest rate to inflation and the output gap than the estimated Taylor rule.
  - Stronger interest rate transmission implies the central bank should emphasize the interest rate channel and accept more interest rate volatility relative to exchange rate volatility.
  - Relative standard deviation of the real interest rate to the real exchange rate increases with stronger interest rate transmission; relative volatility under optimal policies is substantially larger than under the estimated Taylor rule across ranges of the real interest rate coefficient.
- Scenario simulations (shocks and key outcomes):
  - Capital inflows shock (temporary):
    - With the estimated Taylor rule, increased capital inflows result in real appreciation; policies resisting nominal appreciation to preserve competitiveness lead to higher inflation due to weak interest-rate transmission.
    - Monetary policy responses that resist appreciation send contradictory signals to the private sector.
  - Adopting credible inflation targeting (assumed credible announcement in period 1):
    - With credible inflation targeting, inflation declines to the target prior to changes in the target level, indicating well-anchored inflation expectations in a forward-looking framework.
    - Real interest rate is negative during the first couple of periods to create exchange rate appreciation expectation; real exchange rate depreciates first before it appreciates.
    - Dynamics reflect active use of the exchange rate channel due to weak interest rate transmission.
  - Supply shocks to the Phillips curve:
    - Under the estimated Taylor rule, central bank relies on the exchange rate channel (initial depreciation).
    - Under the optimal policy rule with inflation targeting, real exchange rate does not depreciate first; real interest rate turns positive after period two, responding to increased inflation and reducing need to use the exchange rate channel.
  - Delaying monetary policy tightening to capital inflows and supply shocks:
    - Delaying tightening leads to higher costs: more required appreciation expectation later, larger initial exchange rate depreciation, and higher inflation via pass-through, price effect of foreign demand, and negative real interest rate.
    - The inflation spike under the optimal policy rule is smaller than under the estimated Taylor rule, reflecting less required appreciation to contain inflation due to more active interest-rate responses.
- Shock specifications used in simulations (selected):
  - Capital inflows:
    - (i) final demand increase by 0.5 percentage points (equivalent to 2 percentage points annually) as a share of GDP from period 1 to 12 and gradual decline thereafter (AR(1) coefficient 0.9);
    - (ii) temporary decline in sovereign spreads by 100 bp from period 1 to 12 and gradual decline thereafter (same AR(1)).
  - Adopting inflation targeting:
    - Initial inflation before announcement set at 5 percent; central bank keeps inflation target at 5 percent until 12th period (3 years), reduces to 3 percent until period 32, and after period 33 reduces target by 0.5 percentage points every two years.
  - Supply shocks in Phillips curve:
    - Given 5 percent initial inflation, a half percentage point shock to inflation from period one to four and gradual decline thereafter (AR(1) coefficient 0.3).
  - Delaying tightening:
    - Characterized by half of the increase in the nominal interest rate in periods one to four compared to the tightening implied by capital inflows and supply shock scenarios.
- Figures and simulation outputs preserved in the source (Figures 10–19) show impulse responses and simulated scenarios for variables Y (output gap), PIE (inflation), RS (nominal interest rate), RR (real interest rate), LZ (real effective exchange rate), LS (nominal effective exchange rate), among others.

### Policy implications, recommendations, and limitations
- Policy implications and recommended directions:
  - Strengthen monetary policy responsiveness: increase sensitivity of the nominal interest rate rule to inflation and to the output gap to reduce volatility in inflation and the output gap.
  - Recognize limited external spillovers via foreign output: weak transmission from foreign output suggests domestic stabilizers and export composition matter for crisis resilience.
  - Address weak interest-rate transmission: weak interest rate channel and high policy-rate inertia imply alternative tools or structural reforms may be needed to improve monetary transmission effectiveness.
  - Greater use of the interest rate channel (larger responses to inflation and output gap) would reduce reliance on the exchange rate channel and lower the costs of anchoring expectations.
- Limitations and avenues for future work:
  - Paper focuses on Q3 2005 to Q2 2010, after implementation of a new monetary policy framework; estimates may be distorted by the global financial crisis and policy responses.
  - GPM+ does not include fiscal and financial sectors; analysis based on a more detailed model and additional sample period after Q2 2010 is promising for future study.

*Source: _wp11108 (IMF Working Paper content unit).*

### 1.   Priors and Estimates for Key Variables ............................................................................

### 1.   Priors and Estimates for Key Variables

### Model purpose and structure
- The paper incorporates a small open economy model for Egypt into the IMF’s Global Projection Model (GPM), creating the extended model called GPM+.
- GPM is the main quarterly projection model used in the IMF Research Department and encompasses 6 main blocks: United States, Euro Area, Japan, Emerging Asia, Latin America and other countries.
- GPM+ is a canonical small open economy satellite linked to the broader GPM; it takes developments in GPM regions as given and does not feed back into GPM.
- GPM+ features five reduced-form behavioral equations describing movements in: the output gap, unemployment, inflation, nominal interest rate, and the exchange rate, plus identities for equilibrium interest rate, output and unemployment.
- Equations are comparable to reduced-form DSGE models (e.g., Gali and Monacelli (2005)) but include lagged effects (especially in the Phillips Curve) to capture inflation indexation and backward-looking expectations.
- GPM+ is intended for understanding past developments, assessing external shocks, and performing policy simulations, not for studying structural changes.

### Context and motivation
- Since mid 2005 Egypt experienced significant economic reform, increasing real and financial linkages with the rest of the world, and a transition towards inflation targeting in monetary policy.
- Studying transmission of shocks from main trading partners’ economic activity and global interest rates to Egypt is important for policy analysis and for making consistent inflation forecasts and policy simulations.

### Main empirical findings (as reported)
- The output gap in Egypt increased during 2005–2008, reflecting a depreciated exchange rate and positive external demand. The output gap shrank sharply in 2009 as external demand declined during the global financial crisis and monetary policy remained tight.
- The estimated output gap has been somewhat negative but not statistically significant since the middle of 2009.
- Response of the Egyptian output gap to the foreign output gap is relatively small; this is consistent with Egypt’s relatively strong growth performance during the recent global crisis and may reflect export structure/composition and weak financial linkages with advanced countries.
- The estimated Phillips Curve indicates that supply shocks and expected inflation (including inflation inertia) components are the main determinants of inflation.
- Increased foreign real interest rate has a positive effect on the output gap in Egypt, mainly through real depreciation.
- The interest rate channel of monetary policy transmission appears weak for Egypt, consistent with Mashat and Billmeier (2007).
- Egypt’s nominal interest (policy) rate exhibits high inertia, which causes real interest rates to be pro-cyclical and magnifies economic fluctuations.
- Increasing the response of the nominal interest rate to inflation and to the output gap would be desirable for the Central Bank of Egypt (CBE) to reduce fluctuations in inflation and the output gap.
- After a large devaluation in 2003, the CBE anchored inflation expectations until the end of 2007 mainly through the exchange rate channel.

### Empirical approach and estimation
- The extension to GPM+ for Egypt uses data, an estimation strategy, and parameter estimates described in later sections (data sources in Appendix II; estimation method in Appendix III).
- Estimation uses a Bayesian-like method called regularized maximum likelihood.
- The paper presents estimated main variables: the output gap, the Phillips Curve, and the nominal interest rate rule (Taylor rule), together with estimated impulse responses.
- Impulse responses emphasize: response to external demand shocks (to study spillovers) and response to domestic interest rate shocks (to study monetary transmission).

### Policy implications and recommended directions
- Strengthen monetary policy responsiveness: Increasing the sensitivity of the nominal interest rate rule to inflation and to the output gap can reduce volatility in inflation and the output gap.
- Recognize limited external spillovers via foreign output: Egypt’s weak transmission from foreign output suggests domestic stabilizers and export composition matter for crisis resilience.
- Address weak interest-rate transmission: The weak interest rate channel and high policy-rate inertia imply alternative tools or structural reforms may be needed to improve monetary transmission effectiveness.

*Source: _wp11108 - 1.   Priors and Estimates for Key Variables (IMF Working Paper excerpt).*

### conclusions for the conduct of monetary policy going forward. Conclusion will be briefly

### _wp11108 - conclusions for the conduct of monetary policy going forward. Conclusion will be briefly

### Macroeconomic developments and monetary policy in Egypt
- Growth and reforms
  - Egypt’s long-run growth performance during 1980–2000 was strong compared to the average of emerging market economies, though well below high-growth emerging market economies in Asia.
  - Growth accelerated with reforms since 2004 (tariff reduction, tax administration and public expenditure management, exchange rate unification, business environment improvements).
  - Main drivers of strong growth during FY2004/05–07/08:
    - Strong external demand prior to the global financial crisis;
    - Improved competitiveness supported by productivity gains and an undervalued exchange rate after the significant devaluation of the Egyptian pound in 2003;
    - Strong capital (FDI) inflows.
  - Growth declined after the Lehman shock to below 5 percent (year-over-year) from an average 7 percent prior to the crisis.

- Inflation and expectations
  - Inflation (12-month) since 2007 shows a gradual increasing trend with several double digit episodes: spike in 2004 (pass-through from 2003 devaluation); spike in 2006–07 (avian flu and world commodity price increases); spike in 2008 (world commodity price increases).
  - Expected inflation (Consensus Forecast) after 2007 has been substantially higher than before 2007, implying recent spikes fed into higher expected inflation due partly to rigidities and distortions in price and wage settings.
  - The CBE launched its core inflation index in October 2009.
  - The CBE communicates a comfort zone for inflation covering the 6–8 percent range.

- Exchange rate and interest rate framework
  - Since the large devaluation in early 2003, Egypt’s exchange rate (both effective term and vis-à-vis the U.S. dollar) has been stable.
  - The CBE operationally moved away from excess reserves targeting toward open market operations after June 2005, introducing an interest rate corridor, central bank notes, and developing inflation forecasting models.
  - Overnight interbank rate has moved more smoothly since 2005; three month T-bill rates have generally tracked the overnight interbank rate but have tended to decline relative to it during periods of strong capital inflows (e.g., 2007–early 2008, and after July 2010), implying capital inflows partly went into short-term fixed income securities.

### Description of the GPM+ model and key mechanisms
- Model scope
  - GPM+ is a small open economy model linked to the rest of the world via three exogenous variables: foreign output gap, real world interest rate, and real world equilibrium interest rate (weighted averages across six main GPM blocks using Egypt’s trade shares).
  - The model includes stochastic laws of motion for equilibrium output, unemployment, real interest rate, real exchange rate, and inflation (or inflation target).

- Core equations and channels
  - Output gap (IS curve) depends on forward and backward looking elements, lagged short-term interest rate gap, real effective exchange rate gap, and foreign output gap.
  - Real effective exchange rate is endogenously determined via a real interest parity condition with a risk premium.
  - Inflation dynamics follow a hybrid New Keynesian Phillips curve linking current inflation to future expected inflation, lagged inflation, lagged output gap, and change in the real effective exchange rate (pass-through).
  - Monetary policy follows a Taylor-type rule with interest rate smoothing, responding to the output gap and deviation of expected inflation from its target; the model-consistent expected inflation (4π) is derived from the Kalman filter and the policy rate used is the CBE’s deposit rate.
  - Two channels for monetary transmission: interest rate channel (coefficient of real interest rate gap in IS curve) and exchange rate channel (direct effect on output gap and pass-through in Phillips curve).

- Trade-share weights used in construction of the real effective exchange rate gap
  - United States (0.14), EU (0.33), Japan (0.05), Emerging Asia (0.13), LA (0.02), others (0.33).

### Data, priors, estimation method, and identification
- Data and sample
  - Data include unemployment, seasonally adjusted real GDP, overnight interbank rate, nominal and real effective exchange rates, and CPI.
  - Benchmark sample period: 2005: Q3 through 2010: Q2 (reflecting CBE adoption of the interest rate corridor in June 2005 and move toward inflation targeting).

- Estimation method and priors
  - GPM+ estimated using regularized maximum likelihood (a Bayesian-like technique combining priors and data likelihood).
  - Priors guided by previous GPM applications, Moursi and Mossallamy (2009), Kriljenko et al. (2009), and calibration exercises for Egypt.
  - Some parameters (steady-state inflation target, steady-state real interest rates) calibrated using sample averages.
  - Structural shocks are assumed independent, normally distributed, and uncorrelated over time; small and tight priors used for standard deviations of shocks to potential output to reflect relatively smooth potential output.

- Identification issues
  - Identification is challenging because many equations are based on gaps; tight priors or direct calibration are necessary for parameters that cannot be identified without pinned-down equilibrium values (e.g., effect of exchange rate gap on output gap).

### Estimated parameters, model performance, and interpretation
- IS curve and transmission
  - Relative size of backward-looking to forward-looking component in the output gap evolution is about 3, implying significant habit formation in expenditure.
  - Coefficients for real exchange rate and foreign output gap are similar to other countries.
  - Estimated coefficient for the real interest rate gap in Egypt is significantly smaller—“less than one half on average”—than in other countries, implying a weaker interest rate transmission channel; the central bank needs to move policy rates more actively to affect output gap and inflation.

- Phillips curve
  - Forward-looking component is slightly more dominant in Egypt: the weight of the forward-looking component is about two-third for Egypt (versus a median of about 0.55 for other emerging markets).
  - A large coefficient for the output gap in the Phillips curve for Egypt relative to other countries reflects larger volatility of inflation in Egypt.
  - High persistence (lagged inflation coefficient) increases the cost of disinflation (larger sacrifice ratio).

- Interest rate rule and policy inertia
  - Coefficient on the lag of the nominal interest rate in Egypt is higher than in other countries, implying stronger inertia.
  - Nominal interest rate in Egypt has responded less to inflation than in other countries in the short run, making the real interest rate pro-cyclical and limiting the stabilizing role of interest rate policy; non-interest rate channels have been mainly used to mitigate inflationary pressures and anchor expectations.

- Forecast performance
  - One-year-ahead root mean squared forecast errors:
    - Annual growth: slightly higher than one percent.
    - Annual inflation: slightly higher than 5.5 percent.
  - Model forecast errors for growth and interest rates are comparable to previous GPM applications; inflation forecast error is significantly higher, suggesting room to improve inflation dynamics modeling (e.g., incorporating administered prices and commodity prices).

### Output gap, inflation, interest rate dynamics, impulse responses, variance decomposition
- Estimated historical dynamics
  - Estimated output gap has been somewhat negative since the middle of 2009, though not statistically different from zero.
  - Positive output gap widened since 2005, driven by undervalued exchange rate and favorable external environment, then declined sharply since the global crisis due to weak external demand and increased real interest rates.
  - Recent sharp real appreciation began to negatively affect the output gap since the beginning of 2009.
  - Supply shocks and inflation inertia have been main determinants of inflation dynamics; large supply shocks were significant in the 2008–2009 surge.
  - Exchange rate appreciation has helped mitigate inflationary pressures via pass-through.

- Drivers of nominal interest rate
  - Inertia is the main determinant of the nominal interest rate; output gap and deviation from inflation target have played a relatively limited role.
  - Inertia prevented timely monetary policy responses to spikes (e.g., commodity prices in early 2008 and the global financial crisis).

- Impulse responses (selected)
  - Foreign output gap shock:
    - Increased external demand widens Egypt’s output gap.
    - Current and expected exchange rate appreciation can make inflation negative in initial periods via pass-through.
    - Nominal interest rate peaks about 7 periods after the shock; inertia makes the real interest rate negative in the short run (periods 2 to 5) and positive in the medium term.
  - Foreign real interest rate shock:
    - A positive foreign real interest rate shock leads to depreciation of the Egyptian pound, increasing output gap and inflation via pass-through.
    - Nominal interest rate inertia makes the real interest rate negative in the first couple of periods, making monetary policy pro-cyclical and further increasing output gap and inflation.
  - Monetary policy shock:
    - One standard deviation increase in nominal interest rate (about one percent) would appreciate the exchange rate of the Egyptian pound by 2–3 percentage points and create a negative output gap of about 0.4 percentage points in the short run.
    - Exchange rate appreciation and negative output gap cause negative inflation that lasts nearly 10 periods; negative inflation raises real interest rate, causing further appreciation and output gap decline.

- Pass-through
  - Estimated pass-through of the exchange rate to inflation in Egypt is relatively low compared to estimates for other emerging market economies.

*Source: _wp11108 - conclusions for the conduct of monetary policy going forward. Conclusion will be briefly (PDF chapter/section).*

### 0.23 at its peak within one year

### 0.23 at its peak within one year

### Pass-through to inflation
- Pass-through rate of the exchange rate to inflation reached 0.23 at its peak within one year (Figure 8).
- Rabanal (2005), following McCarthy (1999), found pass-through somewhere between 6–27 percent depending on model specification.
- Rabanal (2005) suggests the low pass-through could be due to the high share of administered prices in Egypt’s CPI index.

### Variance decomposition (key real variables)
- Variation in output growth in Egypt is driven mainly by:
  - demand shocks: 26 percent
  - monetary policy shocks: 27 percent
  - shocks to the equilibrium real interest rate: 28 percent
- External shocks (foreign real interest rates and foreign demand shocks) explain only 3–4 percent of the variation in output growth or the output gap, but make a more significant contribution to real exchange rate movements.
- Large allocations to nominal interest rate (surprise policy) shocks and equilibrium real interest rate reflect differences between the model-implied interest rate path (based on the estimated Taylor rule) and the actual policy rate path, notably during 2008–2009.

### Applications of GPM+: Monetary policy implications

#### A. Optimal monetary policy
- Two definitions of optimal policy (minimizing the present value of weighted quadratic inflation and output gap subject to the estimated model):
  - Ramsey optimal policy (social planner’s solution).
  - Optimal policy rule (minimizes the weighted average of the variance of inflation and the output gap, given all estimated parameters other than the Taylor rule coefficients).
- Ramsey optimal policy (example parameters):
  - discount factor: 0.98 (8 percent of the annual discount rate)
  - weight of the output gap in objective function: 6
  - model-consistent variance of inflation is nine times as large as that of the output gap.
- Implications of Ramsey optimal policy:
  - central bank should take quick and front-loaded responses to shocks.
  - Ramsey policy raises interest rates quickly and significantly immediately after shocks to fully remove inflationary demand pressures, producing an exchange rate appreciation (negative sign indicates appreciation in the GPM+), contrasting with responses under the estimated Taylor rule.
- Optimal monetary policy rule findings:
  - optimal rule requires much larger responses of nominal interest rate to inflation and the output gap than the estimated Taylor rule (Table 5).
  - If interest rate increases reduce inflation more via output-gap channel than via exchange-rate pass-through, the central bank should emphasize the interest rate channel—implying more interest rate volatility relative to exchange rate volatility.
- Figure 9 (summary interpretation):
  - The relative standard deviation of the real interest rate to the real exchange rate increases with stronger interest rate transmission (proxied by a larger coefficient on real interest rate in the IS curve).
  - For all ranges of the coefficient for real interest rate, relative volatility under optimal policies is substantially larger than under the estimated Taylor rule, suggesting the CBE has used the exchange rate channel more actively than the interest rate channel and that there is scope to increase use of the interest rate channel.

#### B. Policy scenario simulations
- Simulations compare the estimated Taylor rule and the optimal interest rate rule (with coefficient 6 for the volatility of the output gap), with all variables as deviations from steady state. Shocks summarized in Appendix IV.
- Capital inflows shock (temporary), proxied by a positive demand shock and a decline in the risk premium in the real interest rate parity:
  - With the estimated Taylor rule, increased capital inflows result in real appreciation.
  - Policies resisting nominal appreciation to preserve competitiveness lead to higher inflation due to weak interest-rate transmission; central bank reliance on the exchange rate channel to contain inflationary pressure is reinforced.
  - Monetary policy responses that resist appreciation send contradictory signals to the private sector.
- Adopting inflation targeting framework (credible announcement in period 1; assumed credible commitment):
  - With credible inflation targeting, inflation declines to the target prior to changes in the target level, indicating well-anchored inflation expectations in a forward-looking framework.
  - Real interest rate is negative during the first couple of periods to create exchange rate appreciation expectation; real exchange rate depreciates first before it appreciates. Similar dynamics occur prior to reductions in the target (period 25–30).
  - These dynamics are consistent with active use of the exchange rate channel reflecting weak interest rate transmission.
- Supply shocks to the Phillips curve:
  - Under the estimated Taylor rule with shocks, the central bank relies on the exchange rate channel (initial depreciation).
  - Under the optimal policy rule with inflation targeting, real exchange rate does not depreciate first; the real interest rate turns positive after period two, responding to increased inflation, reducing the need to use the exchange rate channel.
  - Increased response of interest rate to inflation and output gap (more countercyclical monetary policy) reduces reliance on the exchange rate channel to anchor expectations.
- Delay in tightening monetary policy to capital inflows and supply shocks:
  - Delaying tightening leads to higher costs: more required appreciation expectation later, larger initial exchange rate depreciation, and higher inflation via pass-through, price effect of foreign demand, and negative real interest rate.
  - The inflation spike under the optimal policy rule is smaller than under the estimated Taylor rule, reflecting less required appreciation to contain inflation due to more active interest-rate responses.

### Conclusions and policy implications
- Summary of analytical focus:
  - Applied GPM+ to estimate output gap, decomposition of the Phillips curve and nominal interest rate, and responses to external and policy shocks.
  - Simulated economy’s response under different policy frameworks, including inflation targeting.
- Main findings:
  - After a positive output gap during 2005–08 (reflecting a depreciated exchange rate and positive external demand), the gap shrank sharply in 2009 with the global financial crisis. The estimated gap has been somewhat negative but not statistically significant since the middle of 2009.
  - The estimated Phillips curve indicates that supply shocks and expected inflation (including inflation inertia) are the main determinants of inflation.
  - Increased foreign real interest rate has a positive effect on the output gap in Egypt, mainly through real depreciation.
  - Interest rate channel of monetary policy transmission appears weak.
  - Egypt has high inertia in its nominal interest (policy) rate which causes real interest rates to be pro-cyclical, magnifying economic fluctuations.
  - Increasing the response of nominal interest rate to inflation and the output gap is desirable for the CBE to reduce fluctuations in inflation and the output gap.
- Limitations and avenues for future work:
  - Paper focuses on Q3 2005 to Q2 2010, after implementation of a new monetary policy framework; estimates may be distorted by the global financial crisis and policy responses.
  - GPM+ does not include fiscal and financial sectors; analysis based on a more detailed model and additional sample period after Q2 2010 is promising for future study.

*Source: _wp11108 - 0.23 at its peak within one year*

### REFERENCES

### _wp11108 - REFERENCES

### References cited
- Al-Mashat, Rania and Andreas Billmeier (2007): “Monetary Transmission Mechanism in Egypt,” IMF Working Paper 07/285.
- Andrle. Michal, Charles Freedman, Roverto Garcia-Saltos, Danny Hermawan, Douglas Laxton and Haris Munandar (2009): “Adding Indonesia to the Global Projection Model,” IMF Working Paper 09/253.
- Canales-Kriljenko, J., C. Freedman, R. Garcia-Saltos, M. Johnson, and D. Laxton (2009): “Adding Latin America to the Global Projection Model,” IMF Working Paper 09/85.
- Carabenciov, I., I. Ermolaev, C. Freedman, M. Juillard, O. Kamenik, D. Korshunov and D. Laxton (2008a): “A Small Quarterly Projection Model of the U.S. Economy,” IMF Working Paper No. 08/278.
- Carabenciov, I., I. Ermolaev, C. Freedman, M. Juillard, O. Kamenik, D. Korshunov, D. Laxton, and J. Laxton (2008b): “A Small Quarterly Multi-Country Projection Model,” IMF Working Paper No. 08/279.
- Carabenciov, I., I. Ermolaev, C. Freedman, M. Juillard, O. Kamenik, D. Korshunov, D. Laxton, and J. Laxton (2008c): “A Small Quarterly Multi-Country Projection Model with Financial-Real Linkages and Oil Prices,” IMF Working Paper No. 08/280.
- Collins, S. and B. Bosworth (1996): “Economic Growth in East Asia: Accumulation versus Assimilation,” Brookings Papers on Economic Activity 2: 135–203.
- Enders, Klaus-Stefan (2007): “Egypt—Searching for Binding Constraints on Growth,” IMF Working Paper No. 07/57.
- Gali, Jordi (2008): Monetary Policy, Inflation, and the Business Cycle, Princeton University Press, Princeton, New Jersey.
- Gali, Jordi and Tommaso Monacelli (2005): “Monetary Policy and Exchange Rate Volatility in a Small Open Economy,” Review of Economic Studies, 72, 707–734.
- International Monetary Fund (2007): Arab Republic of Egypt, 2007 Article IV Consultation Staff Report, Washington, D.C.
- International Monetary Fund (2010): Arab Republic of Egypt, 2010 Article IV Consultation Staff Report, Washington, D.C.
- International Monetary Fund (2011, forthcoming): Arab Republic of Egypt, 2011 Article IV Consultation Staff Report, Washington, D.C.
- McCarthy, J., (1999): “Pass-Through of Exchange Rate and Import Prices to Domestic Inflation in Some Industrialized Economies,” BIS Working Paper No. 79.
- Moursi, Tarek Abdelfattah and Mai El Mossallamy (2009): “Monetary Policy Analysis with New Keynesian Models for Egypt,” Mimeograph, IDSC.
- Rabanal, Pau (2005): “Exchange Rate Pass-Through,” Chapter I in Selected Issues for Egypt, IMF Country Report 05/179.

### Key parameter priors and posterior estimates (selected entries from Table 1)
- alpha1 Unemployment gap: lag of unemployment gap — Mode 0.8 Dispersion 0.1 ModeDispersion 0.774 0.103
- alpha2 Unemployment gap: output gap — Mode 0.3 Dispersion 0.03 ModeDispersion 0.296 0.033
- beta1 Output gap: lag of output gap — Mode 0.5 Dispersion 0.05 ModeDispersion 0.453 0.057
- beta2 Output gap: lead of output gap — Mode 0.2 Dispersion 0.03 ModeDispersion 0.164 0.033
- beta3 Output gap: real interest rate gap lagged — Mode 0.2 Dispersion 0.03 ModeDispersion 0.079 0.041
- beta4 Output gap: real exchange rate gap lagged — Mode 0.05 Dispersion 0.005 ModeDispersion 0.047 0.006
- beta5 Output gap: real foreign output gap lagged — Mode 0.1 Dispersion 0.01 ModeDispersion 0.093 0.012
- gamma1 Nominal Interest Rate: lag of nominal interest rate — Mode 0.7 Dispersion 0.1 ModeDispersion 0.865 0.058
- gamma2 Nominal Interest Rate: deviation of inflation from target — Mode 1.3 Dispersion 0.1 ModeDispersion 1.273 0.117
- gamma3 Nominal Interest Rate: output gap — Mode 0.3 Dispersion 0.1 ModeDispersion 0.31 0.108
- lambda1 Inflation: expected inflation — Mode 0.5 Dispersion 0.1 ModeDispersion 0.647 0.071
- lambda2 Inflation: lag of output gap — Mode 0.5 Dispersion 0.1 ModeDispersion 0.479 0.078
- lambda3 Inflation: real exchange rate depreciation — Mode 0.15 Dispersion 0.05 ModeDispersion 0.091 0.037
- phi Expected real exchange rate: weight of forward looking component — Mode 0.5 Dispersion 0.1 ModeDispersion 0.596 0.056
- rho Equilibrium Real Interest Rate: steady state real interest rate — Mode 0.1 Dispersion 0.01 ModeDispersion 0.104 0.013
- tau Growth Rate of Equilibrium Output: steady state growth rate — Mode 0.5 Dispersion 0.1 ModeDispersion 0.501 0.109
- betaf Foreign output gap: lag of foreign output gap — Mode 0.8 Dispersion 0.1 ModeDispersion 0.855 0.077
- rhobarf Real equilibrium interest rate (foreign): steady state real interest rate — Mode 0.5 Dispersion 0.1 ModeDispersion 0.098 0.064
- rhof Real interest rate (foreign): steady state real interest rate — Mode 0.5 Dispersion 0.1 ModeDispersion 0.177 0.142
- pief_ss Steady state foreign inflation (level) — Mode 20.1 Dispersion 2.0 ModeDispersion 25 0.137
- rhopief Foreign Inflation: steady state foreign inflation — Mode 0.5 Dispersion 0.1 ModeDispersion 0.423 0.07
- growth_ss Steady state growth rate of potential output — Mode 50.5 Dispersion 5.9 ModeDispersion 26 0.326

### Standard deviations of shocks (selected entries from Table 1)
- std_RES_LGDP_BAR Level shock to potential output — 0.05 0.02 0.092 0.024
- std_RES_Y Shock to output gap — 0.5 0.1 0.478 0.081
- std_RES_G Growth shock to potential output — 0.05 0.02 0.097 0.023
- std_RES_UNR_GAP Shock to unemployment gap — 0.5 0.2 0.287 0.084
- std_RES_UNR_BAR Shock to equilibrium level of unemployment — 0.5 0.1 0.557 0.08
- std_RES_PIE Shock to inflation — 10.2 3.13 5 0.15
- std_RES_RR_BAR Shock to real equilibirum interest rate — 10.1 1.768 0.104
- std_RES_RS Shock to nominal interest rate — 10.2 0.99 0.155
- std_RES_PIETAR Shock to inflation target — 0.5 0.2 0.325 0.082
- std_RES_RR_DIFF Shock to uncovered interest parity (risk premium shock) — 10.2 1.861 0.208
- std_RES_LZ_BAR Shock to equilibirum level of real exchange rate — 10.2 2.629 0.13
- std_RES_YF Shock to foregin output gap — 10.2 0.987 0.096
- std_RES_RRF_BAR Shock to foreign equilibrium real interest rate — 0.5 0.2 0.154 0.019
- std_RES_RRF Shock to foreign real interest rate — 0.25 0.2 0.52 0.06
- std_RES_PIESTR Shock to foreign inflation rate — 0.5 0.2 1.413 0.096

### Calibrated parameters (Table 2)
- alpha3 Persistence in the growth rate of equilibrium unemployment — 0.5
- rr_bar_ss Steady-state value of equilibrium real interest rate — 3
- rrf_bar_ss Steady-state value of equilibrium real interest rate (foreign) — 2
- std_RES_UNR_G Standard deviation of shocks to the growth rate of equilibrium unemployment — 0.04

### Forecast RMSEs (Table 3a)
- Egypt
  - Real GDP Growth (y-o-y): 1Q Ahead 0.77, 4Q Ahead 1.23, 8Q Ahead 1.00
  - Nominal Interest Rate: 1Q Ahead 0.62, 4Q Ahead 1.09, 8Q Ahead 1.45
  - Inflation (y-o-y): 1Q Ahead 1.73, 4Q Ahead 5.59, 8Q Ahead 5.70
- Indonesia
  - Real GDP Growth (y-o-y): 1Q Ahead 0.58, 4Q Ahead 1.30, 8Q Ahead 1.05
  - Nominal Interest Rate: 1Q Ahead 0.71, 4Q Ahead 2.00, 8Q Ahead 2.56
  - Inflation (y-o-y): 1Q Ahead 0.47, 4Q Ahead 1.75, 8Q Ahead 1.94
- Latin America
  - Real GDP Growth (y-o-y): 1Q Ahead 0.50, 4Q Ahead 1.42, 8Q Ahead 1.30
  - Nominal Interest Rate: 1Q Ahead 0.89, 4Q Ahead 2.58, 8Q Ahead 2.16
  - Inflation (y-o-y): 1Q Ahead 0.70, 4Q Ahead 2.41, 8Q Ahead 1.05
- Note: RMSEs for Indonesia from Andrle et. al (2009) sample period 2000Q1-2. RMSEs for Latin America from Kriljenko et. al. (2009) sample period 2004Q1.

### Variance decomposition (Table 3b, % of variation accounted by different shocks) — selected entries
- Growth (y-o-y) — Output Gap Shock 26; Philips Curve Shock 7; Nom. Int. Rate Shock 27; Equilib. Real Int. Rate Shock 28; Equilib. Real Exchange Rate Shock 24; Foreign Real Interest Rate Shock 34; Foreign Output Gap Shock 33; Others 44 (table shows multiple columns; values above correspond to the matrix layout in the source)
- Output Gap — entries by shock in table include values such as 18, 10, 13, etc., laid out in the source matrix.

### Estimated parameters of selected variables in the GPM+ for Egypt (Table 4)
- Coefficients across Output Gap Equation, Philips Curve, Nominal interest rate: values in the table include series such as 0.45, 0.164, 0.079, 0.047, 0.093, 0.647, 0.479, 0.091, 0.865, 1.273, 0.31 (Egypt row)
- Comparable rows for Indonesia, Latin America, Brazil, Chile, Columbia, Mexico, Peru with values reproduced in the source (e.g., Indonesia row begins 0.428 0.149 0.164 0.035 0.178 0.27 0.209 0.107 0.628 1.384 0.186).

### Estimated and optimal Taylor rule (Table 5)
- Table lists estimated Taylor rule and optimal response of interest rate to output gap and variance values. Selected entries:
  - Estimated Taylor rule coefficients: 1.3, 0.3, 0.00 1440.00016 (table formatting in source)
  - Other rows include sequences: 151.517.70.000880.00020; 223.211.00.000970.00012; 513.19.40.001060.00008; 1010.310.50.001110.00007; 1510.811.20.001120.00007 (values presented in the source table).

### Figures, impulse responses, and simulated scenarios (figure captions and notes preserved)
- Figure 10: Impulse Responses to Foreign Output Gap Shock. Note labels: Y (output gap), PIE (inflation), RS (nominal interest rate, policy rate), GROWTH4 (annual growth rate), PIE4 (y-o-y annual inflation rate), RR (real interest rate), LZ (real effective exchange rate), LS (nominal effective exchange rate), LSDIF (annualized nominal depreciation, positive values indicate a depreciation).
- Figure 11: Impulse Responses to Foreign Real Interest Rate. Same set of variable labels as Figure 10.
- Figure 12: Impulse Responses to Nominal Interest Rate. Same set of variable labels as Figure 10.
- Figure 13: Impulse Responses of Main Variables to Temporary Demand Shock. Panels shown for:
  - Impulse Responses of the Output Gap (Based on the Estimated GPM, 2005/06-09/10)
  - Impulse Responses of Inflation (Based on the Estimated GPM, 2005/06-09/10)
  - Impulse Responses of Nominal Interest Rate (Based on the Estimated GPM, 2005/06-09/10)
  - Impulse Responses of Real Interest Rate
  - Impulse Responses of Nominal Exchange Rate
  - Impulse Responses of Real Exchange Rate
  - Legend entries: Estimated GPM; Optimal policy rule; Optimal Ramsey policy
- Figure 14: Impulse Responses of Main Variables to Persistent (Foreign) Demand Shock. Panels for Output Gap, Inflation, Nominal Interest Rate, Real Interest Rate, Nominal Exchange Rate, Real Exchange Rate. Legend entries: Estimated GPM; Optimal policy rule; Optimal Ramsey policy. Periods quarterly, sample noted as 2005/06-09/10.
- Figure 15: Simulated Responses of Main Variables with Capital Inflows Derived from the Estimated GPM. Panels include Output Gap, Inflation, Nominal Interest Rate, Real Interest Rate, Nominal Exchange Rate, Real Exchange Rate. Legend entries: Estimated Taylor rule; No nominal exchange rate peg; Nominal exchange rate peg; (Periods, quarterly). Shocks added: Risk premium shock in the real interest rate parity; Output gap shock.
- Figure 16: Simulated Responses of Main Variables with Inflation Targeting from the Estimated GPM. Panels include Output Gap, Inflation, Nominal Interest Rate, Real Interest Rate, Nominal Exchange Rate, Real Exchange Rate. Legend entries: Estimated Taylor rule, with IT; Optimal policy rule with coeffieict for output gap 6, with IT. (Periods, quarterly).
- Figure 17: Simulated Responses of Main Variables to Supply Shocks Derived from the Estimated GPM. Panels as above with legend entries: Estimated Taylor rule with shocks; Estimated Taylor rule with shocks, adopting IT; Optimal policy rule (output gap coefficient =6) with shocks, adopting IT. (Periods, quarterly). Shock added: Supply shocks.
- Figure 18: Simulated Responses to Capital Inflows and Delaying Tightening Derived from the Estimated GPM (Part I). Panels for Output Gap, Inflation, Nominal Interest Rate, Real Interest Rate, Nominal Exchange Rate, Real Exchange Rate. Legend: Estimated Taylor rule with IT; Estimated Taylor rule with IT, delaying tightening; Estimated Taylor rule with IT, delaying tightening but increasing response to inflation twice. Shocks added: Risk premium shock in the real interest rate parity; Output gap shock.
- Figure 19: Simulated Responses to Supply Shocks and Delaying Tightening Derived from the Estimated GPM (Part II). Panels and legend similar to Figure 17/18. Shock added: Supply shocks.

*Source: _wp11108 - REFERENCES (IMF PDF content unit).*

### APPENDIX I. COMPLETE MODEL EQUATIONS FOR GPM+

### APPENDIX I. COMPLETE MODEL EQUATIONS FOR GPM+

### Model conventions and variables
- All variables in capital letters refer to levels of the variables (usually expressed in natural logarithm and in the case of unemployment and interest rates in terms of percentage points).
- Small letters refer to the gap of the variable from its equilibrium level measured in percentage points.
- Output level: )ln(*100 tt GDPLGDP
- Output gap: ttt LGDPLGDPy

### Output block (IS curve)
- Output gap equation (depends on own lead and lag, real interest rate gap, real effective exchange rate gap and foreign output gap):
  - y ttfttttt yzryyy 1,514131211
- Additional definitions:
  - LGDP tt tt GLGDPLGDP  4 1,
  - G ttsst GgG 1 )1(,
  - ttt ZZz

### Unemployment block (Okun’s law dynamics)
- Unemployment level: ttt UUu
- Dynamic Okun’s law:
  - u tttt yuu 211
- Additional unemployment equation components:
  - 1 UU tt   tt UU  G  
  - 31 (1) U UUG ttt GG      .

### Phillips curve
- Phillips curve specification (as presented):
  - 111   1   21   3 (1) tttt    ttt yZ         

### Real exchange rate block
- Real equilibrium exchange rate dynamics (as presented):
  - e ZZ ttfttftt e t RRRRZZ   )()()(*4 ,,1
- Auxiliary definition:
  - 111 )1(   tt e t ZZZ

### Nominal exchange rate
- Nominal exchange rate relation:
  - * tttt SZ

### Policy rule (monetary policy)
- Policy rule (nominal interest rate specification):
  - I tt Tar tttttt yRII  ])4(4)[1( 33323111
- Inflation target dynamics:
  - Tar t Tar t Tar t   1

### Real interest rate and equilibrium interest rate
- Real interest rate:
  - 1  tttt EIR
- Real interest rate gap:
  - ttt RRr
- Real equilibrium interest rate:
  - R ttt RRR 1 )1(

### Real equilibrium exchange rate
- Real equilibrium exchange rate:
  - Z ttt ZZ 1

### Foreign demand
- Foreign demand specification:
  - f y ttf ftf yy 1,,

### Data sources (variables and availability)
- Real GDP (LGDP): Quarterly average, seasonally adjusted and in logs — Central Bank of Egypt — 2005Q3-2010Q2
- CPI (LCPI): Quarterly average, seasonally adjusted and in logs — Central Bank of Egypt — 2005Q3-2010Q3
- Unemployment Rate (UNR): CAPMAS, Egypt — 2005Q3-2010Q4
- Nominal Interest Rate (RS): Overnight Interbank Rate, quarterly average — Central Bank of Egypt — 2005Q3-2010Q5
- Real Effective Exchange Rate (LZ): Based on INS trade weights — INS Database, IMF — 2005Q3-2010Q6
- Nominal Effective Exchange Rate (LS): Based on INS trade weights — INS Database, IMF — 2005Q3-2010Q7
- Real Foreign Interest Rate (RRF): Based on GPM estimates for the 6 main blocks and Egypt's trade shares — GPM Historical Estimate (September 17, 2010) — 2005Q3-2010Q8
- Real Foreign Equilibirum Interest Rate (RRF_BAR): Based on GPM estimates for the 6 main blocks and Egypt's trade shares — GPM Historical Estimate (September 17, 2010) — 2005Q3-2010Q9
- Foreign Output Gap (YF): Based on GPM estimates for the 6 main blocks and Egypt's trade shares — GPM Historical Estimate (September 17, 2010) — 2005Q3-2010Q10

### Estimation method
- Estimation approach: regularized maximum likelihood (a penalized likelihood approach).
- Objective maximized (notation as in source):
  - max ఏ logܮ (ܻ,ߠ) ߬෍݌െ  ௜ ௜ (ߠ ௜ ߠെҧ ௜ ) ଶ
- Priors interpretation:
  - Priors assumed normal with mean ߠҧ ௜ and variance  ଵ ௣ఛ ೔ .
  - Estimates truncated above and below as necessary to impose parameter space restrictions specified by ߠሾ ௜ ௅ ߠ, ௜ உ ሿ.
- Regularization parameter used in reported results:
  - ݌ = 0.01 (where ݌ = 0 corresponds to the maximum likelihood estimation).

### Shocks added to the estimated GPM+ in the simulations (scenario descriptions)
- Capital inflows:
  - (i) a final demand increase by 0.5 percentage points (equivalent to 2 percentage points annually) as a share of GDP from period 1 to 12 and a gradual decline to zero after that (following AR(1) with coefficient 0.9), and
  - (ii) a temporary decline in the sovereign spreads by 100 bp from period 1 to 12 and a gradual decline to zero after that following the same autoregressive process as the output gap shock.
- Adopting inflation targeting:
  - Initial inflation (from the steady state) before the announcement is set at 5 percent.
  - Rationale: (i) cross country studies on inflation suggests that long-run target of inflation for Egypt should be somewhere between 2 and 5 percent and (ii) current inflation is about 10 percent.
  - Policy path after announcement:
    - Central bank commits to keep its inflation target at 5 percent until 12th period (3 years).
    - After that, it reduces the target to 3 percent until period 32.
    - After period 33, the central bank reduces its target by 0.5 percentage points every two years.
  - Note: choice of the initial inflation does not matter as long as it is positive; the path incorporates a gradual decline in the target as observed in countries adopting inflation targeting.
- Supply shocks in the Phillips curve:
  - Given 5 percent initial inflation, a half percentage point shock to inflation from period one to four and a gradual decline after that, following AR(1) with coefficient 0.3.
  - This is consistent with the estimated residuals in the Phillips curve in the GPM+.
- Delaying monetary policy tightening:
  - Characterized by a half of the increase in the nominal interest rate in periods one to four compared to that implied by the scenarios of capital inflows and supply shocks.
- Baseline assumptions for simulations:
  - Variables are assumed to be in the steady state before period one, unless specially mentioned.
  - Estimated output gap is close to zero (at least not significantly different from zero).
  - Changing the initial real exchange rate level does not affect the main conclusions presented.

*Source: APPENDIX I. COMPLETE MODEL EQUATIONS FOR GPM+ (from the supplied content).*

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