## Quarterly Projection Model for the Bank of Ghana — Working Paper No. WP/2024/237 (excerpt)

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### FPAS development and role
- The Bank of Ghana (BOG) established the Forecasting and Policy Analysis System (FPAS) as critical analytical infrastructure for forward-looking policy.
- FPAS development:
  - technical assistance from the IMF, including collaboration between the co-authors of this paper.
  - practical elements: establishing a modeling team; approving a well-structured internal forecast calendar; developing a range of analytical tools integrated in the policy process.
- References in the text for further FPAS element summaries: Bank of Ghana (2022) and IMF (2024).

### Monetary policy framework and operational setup
- Institutional and policy objectives:
  - BOG granted operational independence to pursue price stability.
  - Price stability defined as medium-term headline inflation target of 8±2 percent.
  - BOG also promotes economic growth and ensures financial stability while operating independently of instructions from the Government or other authorities.
- Operational instrument and exchange rate regime:
  - interest rate-based framework with the short-term Monetary Policy Rate (MPR) as the main instrument.
  - de jure flexible exchange rate regime with occasional targeted FX operations to avoid excessive volatility and disorderly market conditions.
  - policy does not resist gradual nominal depreciation of the cedi in line with macroeconomic fundamentals.

### QPM at the heart of FPAS
- The semi-structural Quarterly Projections Model (QPM) is central to BOG’s FPAS and underpins regular Monetary Policy Committee (MPC) cycles.
- Model outputs appear in MPC Press Releases and Monetary Policy Reports.
- The QPM follows the canonical framework introduced in Berg et al. (2006a, 2006b) with country-specific extensions and documents crucial extensions vis‑à‑vis earlier versions in Bank of Ghana (2022) and Abradu‑Otoo et al. (2022).

### Key QPM extensions and model structure
- Sectoral GDP decomposition:
  - GDP decomposed into agriculture, oil, and non‑agriculture non‑oil (NANO) sectors.
  - Rationale:
    - agriculture: volatility driven by climatic conditions,
    - oil: driven by external crude oil price developments and important for FX inflows,
    - NANO: services and manufacturing reflect domestic business cycle and demand-side inflationary pressures.
  - Decomposition permits matching pandemic impacts: oil and agriculture output gaps largely neutral while NANO output gap was profoundly negative.
- CPI decomposition and supply-side channels:
  - CPI broken into food and non-food indices.
  - Food inflation Phillips curve expanded by an additional term to capture price pressures from agri‑food production (propagation of climate shocks).
  - Sector-specific inflation expectations consider headline CPI and include cross-sector shock terms to capture tight comovement and spillovers between food and non-food prices.
- Additional model elements:
  - New Keynesian rigidities allowing short-term nominal interest rate changes to have real effects in the near- to medium-run.
  - Small open economy features: impact of foreign variables and exchange rate dynamics.
  - Extensions capture fiscal policy effects and limited monetary policy credibility tied to historical deviations of inflation from target.

### Stylized facts and macroeconomic context motivating QPM design
- Average real GDP growth, 2014–2023:
  - overall: 4.2 percent,
  - services: 4.7 percent,
  - industrial sector: 3.5 percent (oil production growing by 6.9 percent),
  - agriculture: 4.6 percent.
- Growth outturns:
  - 2020: 0.5 percent,
  - 2021: 5.1 percent,
  - 2023: 2.9 percent.
- Policy response and program:
  - Government initiated Post COVID-19 Program for Economic Growth (PC-PEG) in 2023.
  - program supported by a 3-year IMF Extended Credit Facility (ECF) arrangement.
- Trade and external sector (2014–2023 averages as share of nominal GDP):
  - total exports averaged 24.2 percent,
  - total imports averaged 23.8 percent.
- Core export commodities:
  - cocoa, gold, and oil collectively accounted for over 80 percent of export proceeds from 2014 to 2023.
- Current account and reserves:
  - 2023: positive current account balance attributed to increased oil production and higher gold exports plus lower external debt servicing following debt restructuring negotiations.
  - From 2014 to 2023, median annual depreciation rate against the USD was 11.3 percent.
  - Gross reserves averaged approximately 3.7 months of import cover over the period.
- Inflation history by regime:
  - IT regime (2007-2023): 14.8 percent,
  - direct control (1972–1991): 48.8 percent,
  - monetary targeting (1992–2001): 28.4 percent,
  - preparatory stage of IT (2002-2006): 20.2 percent.
- Contribution to headline inflation:
  - Between 2014 and 2016, non-food inflation explains, on average, about 79.8 percent of headline inflation dynamics (non-food consumption basket share was 56.88 percent).
  - The contribution of non-food inflation to headline inflation has been on a downward trajectory subsequently.

### Monetary policy transmission, interest rates, and credibility
- Monetary Policy Rate (MPR) steers inflation to the medium-term target and anchors short-term market rates; interbank rate has broadly moved in lockstep with the policy rate.
- Historical real policy rate:
  - From 2014 to 2021 real policy rate averaged 7.15 percent.
  - Real interest rate turned negative starting early-2022.
  - Real interest rate turned back positive in late-2023, attributed to IMF-supported reforms, tight monetary policy stance, relatively stable exchange rate, and effective liquidity sterilization.
- Monetary policy rule (Taylor-type, equation (21)):
  - it = γ1 it−1 + (1 − γ1)[Et πt+1 + r̅t + γ2(Et4πt+3 − π̅t) + γ3 ŷt] + ε_t_i
  - interbank rate: ib_t = i_t + sp_t (equation (22))
  - spread dynamics: sp_t = κ1 sp_t−1 + ε_t_sp (equation (23))

### Core model equations and key calibrated parameters
- Aggregate output gap composition:
  - ŷ_t = ω1 ŷ_t^agr + ω2 ŷ_t^oil + (1 − ω1 − ω2) ŷ_t^nano (equation (1))
  - Output shares: ω1 = 0.2; ω2 = 0.07; NANO sector accounts for 73 percent of total GDP (empirical finding).
- Real monetary conditions index:
  - rmci_t = η1 r̂_t + (1 − η1)(− ẑ_t) (equation (3))
- Phillips curves and expectations (selected equations):
  - Non-food Phillips curve (equation (11)) and food Phillips curve (equation (16)) include forward- and backward-looking expectations, real marginal costs, imported inflation proxy m_t, and cross-sector spillovers β4_nf and β4_f.
  - Food Phillips curve includes − β5_f ŷ_t^agr (equation (16)) with β5_f capturing elasticity of food inflation to agriculture output gap.
- Exchange rate dynamics (modified UIP, equation (18)):
  - s_t = s_t+1^e + i_t^* − i_b_t + prem_t^4 − c1 ŷ_t^oil + ε_t_s
  - s_t+1^e = c2 Et s_t+1 + (1 − c2)(s_t−1 + 2/4 Δs̅_t) (equation (19))
  - prem_t = b1 prem_t−1 + (1 − b1) prem_ss + ε_t_prem (equation (20))
- Selected calibrated parameter values:
  - Non-Food Inflation: β1_nf = 0.7; β2_nf = 0.4; β3_nf = 0.1; β4_nf = 0.2
  - Food Inflation: β1_f = 0.5; β2_f = 0.2; β3_f = 0.1; β4_f = 0.2; β5_f = 1
  - Credibility: τ1_nf = 0.5
  - Food CPI weight: ψ = 0.4312
  - Real marginal cost shares: φ_nf = 0.7; φ_f = 0.6
  - NANO output gap: α1 = 0.4; α2 = 0.3; α3 = (not fully listed in excerpt)
  - Agriculture gap AR(1): σ1 = 0.5
  - Oil gap AR(1): σ2 = 0.5

### Impulse Response Functions (IRFs) and shock propagation
- IRF setup:
  - model economy assumed initially in equilibrium; one-time single shocks applied; magnitudes are deviations from steady state (annual headline inflation steady state equals the 8 percent inflation target).
- Adverse non-food supply shock:
  - immediate rise in overall inflation driven by non-food prices; food prices quasi-stable on impact.
  - central bank raises nominal interest rates; real interest rate gap becomes contractionary starting three quarters after the shock.
  - real exchange rate appreciates, tightening real monetary conditions; aggregate demand declines and output gap turns negative.
  - non-food and headline inflation return to target within about eight quarters.
  - compared with previous model, headline inflation increases relatively more in the current extended model and nominal interest rate response is slightly larger; negative output gap is slightly milder because interest rates affect only the NANO sector directly.
- Adverse food supply shock:
  - mirrors non-food shock logic: immediate cross-sector spillovers, larger headline inflation in current model, stronger nominal interest rate response, tighter real monetary conditions; pass-through to aggregate output is lower because nominal rates primarily affect NANO.
- Exchange rate depreciation shock:
  - immediate nominal and real depreciation improves competitiveness and stimulates aggregate demand → positive output gap.
  - higher real marginal costs raise food and non-food prices; monetary authority raises nominal interest rates to restore equilibrium.
  - current model shows lower short- to medium-run positive output gap and slightly higher headline inflation than previous model.
- Monetary policy shock (unexpected increase in policy rate):
  - tightens real interest rate gap, causes nominal appreciation, tightens real monetary conditions, dampens aggregate demand producing a negative output gap and headline inflation below target; monetary authority then eases.
  - negative output gap is lower in current model due to GDP disaggregation.

### Interaction between food prices and agriculture output — agriculture shock experiment
- Agriculture sector explicitly linked to food CPI subcomponent via the food Phillips curve (equation (16)).
- Calibration note: food inflation is more volatile and less persistent relative to non-food prices; agriculture supply shocks implicitly capture climate events.
- Agriculture shock experiment:
  - current model: a shock that reduces agricultural output by 5 percent (simulated as a 5 percent drop in εt yagr) with persistency σ1 = 0.5.
  - counterfactual one-sector model: a 1 percent drop in the aggregate demand equation (equivalent interpretation using 20 percent share of agriculture).
- Comparative findings:
  - multi-sector model: reduced agriculture production → lower total output and higher food and headline inflation; central bank tightens interest rates, producing nominal exchange rate appreciation and slightly lower non-food inflation.
  - one-sector model: lower total output resembles an adverse demand shock and is marginally deflationary; implies a slightly accommodative interest rate stance unless an explicit Phillips curve shock is added.
- Implication: sectoral disaggregation produces materially different monetary policy trade-offs when agriculture shocks occur.

### Decomposition of food inflation Phillips curve and historical mapping
- Subsample analyzed: 2008Q1-2022Q1.
- Food price dynamics driven primarily by inflation expectations:
  - backward-looking expectations: moderate persistence and inertia.
  - forward-looking expectations: reflect aggregate price prospects across sectors and intersectoral spillovers.
- Contribution of agriculture GDP links food inflation dynamics to domestic agri-food supply; model can map historical narratives (examples cited for 2014 and 2016 in BOG reports).

### Sectoral business cycle dynamics and empirical findings
- Rationale: decomposing GDP into agriculture, oil, and NANO captures sectoral drivers of the business cycle and inflation; agriculture and oil driven by idiosyncratic/international events and do not necessarily follow domestic cycle or monetary stance.
- Empirical findings:
  - NANO sector accounts for 73 percent of total GDP and is the primary determinant of the aggregate business cycle.
  - COVID-19 assessment (2020-21): lockdowns were strictly imposed for most NANO activities while agriculture and oil faced less severe restrictions; NANO recorded large negative output gap while oil and agriculture were close to neutral.

### Counterfactual scenarios and policy trade-offs (2022Q1–2023Q4)
- Methodology: forecasts conditioned on ex‑post full sample estimated structural shocks and/or setting interest rate trajectories.
- Counterfactual 1: Interest rate strictly follows QPM Taylor‑type reaction function
  - assumption: no monetary discretion.
  - results:
    - counterfactual policy path peaks at a quarterly average of 34 percent in 2023Q1.
    - actual gradual policy adjustments peaked at an average of 30 percent in 2023Q4.
    - Taylor‑rule path would have produced lower nominal depreciation and inflation (annual price dynamics over 2023 about 5 percentage points lower than realized).
    - trade-off: substantially steeper negative output gap bottoming out at about −4 percent in mid-2023, implying weaker real sector activity and higher job losses.
- Counterfactual 2: Constant interest rate at pre‑crisis level (extreme scenario)
  - assumption: MPR kept at pre‑crisis level of 14.2 percent (average over 2021Q4); monetary policy shocks unanticipated initially (2022Q1-Q3) and anticipated thereafter (2022Q4-2023Q4) to reflect credibility dynamics.
  - results:
    - overly‑stimulatory conditions would lead to unanchored expectations and an overheated economy.
    - massive exchange rate depreciation reaching 40 GHS/USD by 2023Q1.
    - spiraling inflation above 150 percent by end-2023.
- Policy insight: BOG’s cautious, gradual rate increases during 2022-23 supported the real sector by minimizing output and job losses while allowing somewhat higher inflation relative to a stricter rule‑following path.

### Model applications, strengths, limitations, and planned extensions
- Applications:
  - IRFs illustrate propagation of fundamental shocks and monetary responses needed to stabilize the economy.
  - QPM assesses interaction between food and non-food prices and central bank credibility mechanisms for policy responses.
  - Practical tool for real-time policy analysis and forecasting, refined from Abradu‑Otoo et al. (2022).
- Limitations:
  - model is linear and displays limitations during severe shock events (e.g., COVID-19, recent debt sustainability crisis); BOG staff introduce expert judgements in practice to address such episodes.
  - model parsimoniously considers only the interest rate instrument and price stability objective, with a simplified fiscal block; in practice, BOG also focuses on financial stability and the government uses a large number of fiscal instruments.
- Planned extensions:
  - several ongoing extensions aim to directly address limitations (IMF (2024) referenced).
  - a satellite extension incorporating a detailed fiscal block differentiating foreign and domestic (currency) debt is being documented for a forthcoming working paper.

### Key quantitative facts and calibrated values (selected)
- Price stability target: 8±2 percent.
- Average real GDP growth, 2014–2023: 4.2 percent.
- Sector growth (2014–2023 averages): services 4.7 percent; industrial 3.5 percent; agriculture 4.6 percent; oil production growth 6.9 percent.
- Growth outturns: 2020 = 0.5 percent; 2021 = 5.1 percent; 2023 = 2.9 percent.
- Exports/imports (2014–2023 averages): exports 24.2 percent of GDP; imports 23.8 percent of GDP.
- Median annual depreciation (2014–2023): 11.3 percent vs USD.
- Gross reserves: approximately 3.7 months of import cover (2014–2023 average).
- Inflation by regime: IT (2007-2023) 14.8 percent; direct control (1972–1991) 48.8 percent; monetary targeting (1992–2001) 28.4 percent; preparatory IT (2002-2006) 20.2 percent.
- Non-food contribution to headline inflation (2014–2016): 79.8 percent (non-food consumption basket share 56.88 percent).
- Selected calibrated parameters: ψ = 0.4312; β1_nf = 0.7; β2_nf = 0.4; β3_nf = 0.1; β4_nf = 0.2; β1_f = 0.5; β2_f = 0.2; β3_f = 0.1; β4_f = 0.2; β5_f = 1; τ1_nf = 0.5; φ_nf = 0.7; φ_f = 0.6; α1 = 0.4; α2 = 0.3; σ1 = 0.5; σ2 = 0.5; ω1 = 0.2; ω2 = 0.07.

*Source: wpiea2024237-print-pdf (excerpt).*

### 2007. Recognizing the intricate nature of monetary policy transmission, which involves multiple

### 2007. Recognizing the intricate nature of monetary policy transmission, which involves multiple

### FPAS development and role
- The Bank of Ghana (BOG) established the Forecasting and Policy Analysis System (FPAS) as a critical analytical infrastructure to guide forward-looking policy decisions.
- FPAS was developed with technical assistance from the IMF, including collaboration between the co-authors of this paper.
- FPAS practical elements include:
  - establishing a modeling team,
  - approving a well-structured internal forecast calendar,
  - developing a range of analytical tools integrated in the policy process.
- For further details, the text refers to Bank of Ghana (2022) and IMF (2024) for summaries of FPAS elements developed during the IMF technical assistance project.

### Monetary policy framework and operational setup
- Within the inflation-targeting (IT) framework, the BOG is granted operational independence to pursue its primary objective of price stability.
- Price stability is currently defined as medium-term headline inflation target of 8±2 percent.
- The Bank also promotes economic growth and ensures financial stability while operating independently of any instructions from the Government or other authorities.
- Operational instrument:
  - interest rate-based framework with the main instrument being the short-term Monetary Policy Rate (MPR).
- Exchange rate regime:
  - de jure flexible exchange rate regime,
  - occasional targeted FX operations to avoid excessive volatility and disorderly market conditions,
  - policy does not resist gradual nominal depreciation of the cedi in line with macroeconomic fundamentals.

### QPM at the heart of FPAS
- Macroeconomic forecasting is integral to the Bank’s monetary policy formulation since adoption of the IT framework.
- The semi-structural Quarterly Projections Model (QPM) is central to BOG’s FPAS.
- Model-based results underpin regular Monetary Policy Committee (MPC) cycles; QPM-based forecasts appear in MPC Press Releases and Monetary Policy Reports.
- The paper documents the latest version of BOG’s QPM, including crucial extensions vis-à-vis earlier versions in Bank of Ghana (2022) and Abradu-Otoo et al. (2022).
- The QPM follows the canonical framework introduced in Berg et al. (2006a, 2006b) while incorporating country-specific extensions.

### Key QPM extensions and model structure
- Sectoral GDP decomposition:
  - GDP is modeled by decomposing aggregate demand into separate equations for agriculture, oil, and non-agriculture non-oil (NANO) sectors.
  - Rationale:
    - agriculture: volatility driven by climatic conditions,
    - oil: driven by external crude oil price developments and important for FX inflows,
    - NANO: services and manufacturing reflect domestic business cycle and demand-side inflationary pressures.
  - Decomposition allows matching pandemic-related lockdown impacts: oil and agriculture output gaps largely neutral, NANO output gap profoundly negative.
- CPI decomposition and supply-side channels:
  - CPI broken into food and non-food indices; food inflation Phillips curve expanded by an additional term to capture price pressures from agri-food production.
  - This additional term approximates propagation of climate shocks (e.g., unfavorable weather → lower agricultural production → higher food prices) in a reduced-form, model-consistent way.
  - Sector-specific inflation expectations consider headline CPI and include cross-sector shock terms to capture tight comovement and spillovers between food and non-food prices.
- Additional model elements:
  - incorporates New Keynesian rigidities allowing short-term nominal interest rate changes to have real effects in the near- to medium-run.
  - accounts for Ghana’s small open economy dimension, including impact of foreign variables and exchange rate dynamics.
  - extensions capture fiscal policy effects and limited monetary policy credibility tied to historical deviations of inflation from target.

### Model applications, simulations, and trade-offs
- The paper:
  - documents how shock propagation differs from Abradu-Otoo et al. (2022),
  - analyzes transmission and policy implications of shocks directly affecting agriculture output (e.g., climate phenomena).
- Counterfactual simulation example:
  - A counterfactual interest rate trajectory following the Taylor-type reaction function during 2022-23 suggests a tighter policy stance which would:
    - lower inflation rate by about 5 percentage points compared to actual outcomes,
    - at the cost of 1-1.5 percent lower output.

### Stylized facts and macroeconomic context motivating QPM design
- Average real GDP growth, 2014–2023:
  - overall: 4.2 percent,
  - services: 4.7 percent,
  - industrial sector: 3.5 percent (oil production growing by 6.9 percent),
  - agriculture: 4.6 percent.
- Growth outturns:
  - 2020: 0.5 percent (lowest, due to COVID-19 lockdowns),
  - 2021: 5.1 percent (rebound),
  - 2023: 2.9 percent (slowed due to acute economic crisis with constrained domestic financing and loss of access to international capital markets).
- Policy response:
  - Government initiated Post COVID-19 Program for Economic Growth (PC-PEG) in 2023,
  - program supported by a 3-year IMF Extended Credit Facility (ECF) arrangement.
- Trade and external sector (2014–2023 averages as share of nominal GDP):
  - total exports averaged 24.2 percent,
  - total imports averaged 23.8 percent.
- Core export commodities:
  - cocoa, gold, and oil collectively accounted for over 80 percent of export proceeds from 2014 to 2023.
- Current account:
  - persistent deficits historically, but improved post-2016.
  - 2023: positive current account balance attributed to increased oil production and higher gold exports plus lower external debt servicing following debt restructuring negotiations.
- Exchange rate and reserves:
  - From 2014 to 2023, median annual depreciation rate against the USD was 11.3 percent.
  - Gross reserves averaged approximately 3.7 months of import cover over the period (noting significantly lower levels during the recent crisis and rebound in 2023 under the 3-year IMF ECF arrangement).
- Inflation history and targeting:
  - BOG defines price stability as medium-term headline inflation of 8 percent ±2 percentage points.
  - Since formal adoption of IT in 2007, there has been a reduction in volatility and level of headline inflation.
  - Average headline inflation by regime:
    - IT regime (2007-2023): 14.8 percent,
    - direct control (1972–1991): 48.8 percent,
    - monetary targeting (1992–2001): 28.4 percent,
    - preparatory stage of IT (2002-2006): 20.2 percent.
- Contribution to headline inflation:
  - Between 2014 and 2016, non-food inflation explains, on average, about 79.8 percent of headline inflation dynamics (compared with a share of non-food consumption basket of 56.88 percent). The contribution of non-food inflation to headline inflation has been on a downward trajectory subsequently.

### Model limitations and planned extensions
- Important shortcomings of the BOG QPM:
  - model is linear and displays limitations during severe shock events (e.g., COVID-19 pandemic, recent debt sustainability crisis).
  - BOG staff introduce specific expert judgements in practice to address such episodes.
  - model parsimoniously considers only the interest rate instrument and price stability objective, with a simplified fiscal policy block.
  - in practice, BOG also focuses on financial stability and the government uses a large number of fiscal instruments.
- Future extensions:
  - several ongoing extensions aim to directly address limitations (IMF (2024) referenced for additional discussions).
  - a satellite extension incorporating a detailed fiscal block differentiating foreign and domestic (currency) debt is being documented for a forthcoming working paper.

*Source: wpiea2024237-print-pdf (excerpt).*

### 62.4  percent  between  2017  and  2020,  and  further  down  to  51.4  percent  between  2021  to 2023

### wpiea2024237-print-pdf - 62.4 percent between 2017 and 2020, and further down to 51.4 percent between 2021 to 2023

### Inflation dynamics and sectoral interactions
- "62.4 percent between 2017 and 2020, and further down to 51.4 percent between 2021 to 2023 (Figure 5)."
- Sector-specific price dynamics:
  - Prior to the pandemic, an upward trend in non-food prices relative to food prices.
  - Reversal of that trend in recent years.
  - Important inter-sectoral linkages generate spillovers in price formation; these are incorporated in the model via:
    - specific adjustment in the inflation expectations’ formation process, and
    - introduction of additional sectoral shock feedback mechanisms.
- Headline CPI definition:
  - pt = ψ p_tf + (1 − ψ) p_tnf + ε_t_p (equation (10))
  - ψ is the weight of food items in the CPI basket; approximation errors captured by ε_t_p.

### Monetary policy transmission and interest rates
- The central bank relies on the Monetary Policy Rate to steer inflation to the medium-term target and anchor short-term market interest rates.
- Interbank rate has broadly moved in lockstep with the policy rate (Figure 6), indicating a working interest rate pass-through mechanism that influences financing costs across the yield curve and retail loan and deposit rates.
- Historical real policy rate and developments:
  - From 2014 to 2021 real policy rate averaged 7.15 percent.
  - Real interest rate turned negative starting early-2022 (after COVID-19 and Russia–Ukraine-related shocks and loss of access to international capital markets).
  - Real interest rate turned back positive in late-2023, attributed to IMF-supported reforms, tight monetary policy stance, relatively stable exchange rate, and effective liquidity sterilization.
- Monetary policy rule (Taylor-type):
  - it = γ1 it−1 + (1 − γ1)[Et πt+1 + r̅t + γ2(Et4πt+3 − π̅t) + γ3 ŷt] + ε_t_i (equation (21))
  - Interbank rate: ib_t = i_t + sp_t (equation (22))
  - Time-varying spread dynamics: sp_t = κ1 sp_t−1 + ε_t_sp (equation (23))

### Real economy and fiscal interactions
- Aggregate output gap composition:
  - ŷ_t = ω1 ŷ_t^agr + ω2 ŷ_t^oil + (1 − ω1 − ω2) ŷ_t^nano (equation (1))
  - ω1 and ω2 are sector-specific weights for agriculture and oil.
- NANO output gap (investment-savings framework) depends on:
  - lag ŷ_t−1^nano, one-quarter-ahead expectations Et ŷ_t+1^nano, real monetary conditions index rmci_t, fiscal impulse (fimp_t) averaged over last four quarters, foreign output gap ŷ_t^*, and a demand shock ε_t_y_nano (equation (2)).
- Real monetary conditions index:
  - rmci_t = η1 r̂_t + (1 − η1)(− ẑ_t) (equation (3))
  - r̂_t is the RIR gap (deviation of real interest rate from neutral), ẑ_t is the RER gap.
- Fiscal block and fiscal impulse:
  - Primary deficit decomposition: def_t = def_cyc,t + def_str,t (equation (4))
  - Cyclical deficit: def_cyc,t = − f1 ŷ_t (equation (5))
  - Structural deficit AR(1): def_str,t = f2 def_str,t−1 + (1 − f2) def_str,ss + ε_t_str_def (equation (6))
  - Fiscal impulse: fimp_t = ε_t_str_def (equation (7))
  - f2 captures persistence; f1 represents counter-cyclicality of fiscal policy.

### Aggregate supply, Phillips curves, and expectations
- Non-food Phillips curve (quarter-on-quarter annualized non-food inflation π_t^nf):
  - π_t^nf = β1_nf π_t−1^nf + (1 − β1_nf − β3_nf) π_t+1^e,nf + β2_nf rmc_t^nf + β3_nf m_t + β4_nf ε_t_πf + ε_t_πnf (equation (11))
  - π_t+1^e,nf = Et π_t+1 + τ1_nf incred_t (equation (12))
  - incred_t = β1 incred_t−1 + (1 − β1) β2 (π_t−1_yoy − π̅_t) + ε_t_incred (equation (13))
  - rmc_t^nf = φ_nf ŷ_t^nano + (1 − φ_nf) ẑ_t (equation (14))
  - m_t = Δs_t + π_t^* − Δz̅_t (imported inflation proxy) (equation (15))
  - β4_nf captures food price shock spillover into non-food.
- Food Phillips curve:
  - π_t^f = β1_f π_t−1^f + (1 − β1_f − β3_f) π_t+1^e,f + β2_f rmc_t^f + β3_f m_t + β4_f ε_t_πnf − β5_f ŷ_t^agr + ε_t_πf (equation (16))
  - rmc_t^f = φ_f ŷ_t^nano + (1 − φ_f) ẑ_t (equation (17))
  - β5_f captures elasticity of food inflation with respect to agriculture output gap (captures climate-related supply effects).

### Exchange rate (UIP) and external sector
- Nominal exchange rate modified UIP:
  - s_t = s_t+1^e + i_t^* − i_b_t + prem_t^4 − c1 ŷ_t^oil + ε_t_s (equation (18))
  - s_t+1^e is hybrid expectation: s_t+1^e = c2 Et s_t+1 + (1 − c2)(s_t−1 + 2/4 Δs̅_t) (equation (19))
  - Sovereign risk premium prem_t modeled as AR(1): prem_t = b1 prem_t−1 + (1 − b1) prem_ss + ε_t_prem (equation (20))
- Oil output gap included to capture FX inflows and exchange rate appreciation pressures.
- External variables (US economy proxies) treated as exogenous and modeled as univariate AR-type processes x_t = k_x x_t−1 + (1 − k_x) x_ss + ε_t_x (equation (24)).

### Model structure, calibration, and parameters
- QPM core blocks: aggregate demand, Phillips curves, UIP, monetary policy reaction function.
- Variables (except interest rates and fiscal balance) expressed in logarithms or gaps (denoted with “hats”); time subscripts index quarters.
- Calibration rationale: small samples, structural breaks, simultaneity, unobserved components, and rational expectations limit full estimation; calibration used drawing on data properties, monetary framework features, and expert judgement.
- Selected calibrated parameter values (as presented):
  - Non-Food Inflation: β1_nf = 0.7; β2_nf = 0.4; β3_nf = 0.1; β4_nf = 0.2
  - Food Inflation: β1_f = 0.5; β2_f = 0.2; β3_f = 0.1; β4_f = 0.2; β5_f = 1
  - Credibility: τ1_nf = 0.5
  - Food CPI weight: ψ = 0.4312
  - Real marginal cost shares: φ_nf = 0.7; φ_f = 0.6
  - NANO output gap: α1 = 0.4; α2 = 0.3; α3 = (not fully listed in excerpt)
  - Agriculture gap AR(1): σ1 = 0.5
  - Oil gap AR(1): σ2 = 0.5
  - Output shares: ω1 = 0.2; ω2 = 0.07

### Model results and applications
- The chapter introduces impulse response functions (IRFs) to illustrate propagation mechanisms of fundamental shocks and the monetary policy responses needed to stabilize the economy.
- The QPM incorporates interaction between food and non-food prices and central bank credibility mechanisms to assess inflation dynamics and required policy responses.
- The model is described as a practical tool for real-time policy analysis and forecasting, refined from Abradu-Otoo et al. (2022) and consistent with QPM traditions (Berg et al. (2006a, 2006b)).

*Italic: Source — wpiea2024237-print-pdf (excerpt provided).*

### 0.1 RMCI

### wpiea2024237-print-pdf - 0.1 RMCI

### Impulse Response Functions (IRFs)
- Setup and purpose
  - IRFs are generated from a QPM exercise assuming the model economy initially in equilibrium and applying a one-time single shock; magnitudes are deviations from the associated steady state (example: annual headline inflation equilibrium is given by the 8 percent inflation target, so inflation responses are presented as percentage points deviation from the target).
  - Comparison is made between the current (extended) model and the previous model documented in Abradu‑Otoo et al. (2022).
- Adverse non-food supply shock (e.g., one-off increase in energy prices)
  - In the current model:
    - Overall inflation immediately increases, driven primarily by a rise in non-food prices; food prices are quasi-stable on impact.
    - Central bank raises nominal interest rates; real interest rate gap becomes contractionary starting three quarters after the shock.
    - Real exchange rate appreciates (negative real exchange rate gap), tightening real monetary conditions.
    - Aggregate demand declines and output gap becomes negative.
    - Non-food and headline inflation return to target within about eight quarters.
  - Compared to previous model:
    - Headline inflation increases relatively more in the current extended model because forward-looking agents in both sectors incorporate spillovers and second‑round effects.
    - Previous model showed a significant decline in food inflation to the shock; the current model’s food inflation dynamics are more stable.
    - Monetary authority raises nominal interest rate by a slightly larger margin in the current model; negative output gap is slightly milder because interest rates affect only the NANO sector directly in the current model.
- Adverse food supply shock
  - Dynamics mirror the non-food shock logic: immediate price spillovers across sectors, second‑round expectation effects, higher headline inflation in current model, and stronger nominal interest rate response resulting in tighter real monetary conditions.
  - Because nominal interest rates primarily affect NANO output in the current model, pass-through to aggregate output is lower and the negative output gap is comparatively milder than in the previous model.
- Exchange rate depreciation shock
  - Price rigidities cause immediate nominal and real depreciation, improving competitiveness and stimulating aggregate demand; leads to a positive output gap.
  - Positive output gap and depreciation raise real marginal costs, increasing both food and non-food prices and hence headline inflation.
  - Monetary authority raises nominal interest rates, bringing real rates above neutral and strengthening the currency over time, steering output and inflation back to steady state.
  - Differences vs previous model:
    - Short- to medium-run positive output gap is lower in the current model due to sectoral disaggregation (agriculture and oil separated from sectors affected by exchange rate dynamics).
    - Headline inflation is slightly higher in the current model due to updated Phillips curves accounting for second‑round effects and spillovers.
    - Monetary authority hikes nominal interest rate slightly more aggressively in the current model.
- Monetary policy shock
  - An unexpected increase in the monetary policy rate tightens the real interest rate gap and causes nominal appreciation (real exchange rate overvalued), tightening real monetary conditions, dampening aggregate demand and producing a negative output gap.
  - Headline inflation declines below target (both non-food and food inflation slow); monetary authority then eases to restore equilibrium.
  - Overall transmission mechanisms are qualitatively similar across current and previous models, but:
    - The negative output gap is lower in the current model due to GDP disaggregation (nominal rates affect sectors disproportionately).
    - Food and non-food inflation responses differ slightly because inflation expectations formation now incorporates overall headline inflation and cross‑sector shocks.

### Interaction between Food Prices and Agriculture Output
- Model structure and purpose
  - Agriculture sector is separated from food CPI subcomponent and directly linked within the food inflation Phillips curve (equation (16)), enabling a reduced-form analysis of climate-related shocks without explicitly modeling climate variables.
  - Calibration: food inflation is more volatile and less persistent relative to non-food prices; food inflation is directly impacted by agriculture supply (value added) and implicitly by climate events.
- Agriculture output shock experiment
  - Current model experiment: a shock that reduces agricultural output by 5 percent (simulated as a 5 percent drop in εt yagr in equation (8)) with persistency determined by 휎1 = 0.5.
  - Counterfactual one-sector model experiment: a 1 percent drop in the aggregate demand equation (equivalent to εt ynano in (2) in a counterfactual model with no sectoral decomposition; interpretation consistent with 5 percent agricultural shock multiplied by the calibrated 20 percent share of agriculture in total GDP).
- Key comparative findings
  - Current multi‑sector model (blue lines in Figure 12):
    - Reduced agriculture production leads to a decrease in total output and a rise in food and headline inflation (i.e., agriculture shocks act as inflationary supply‑type disturbances).
    - Central bank tightens interest rate stance to limit second‑round effects, producing nominal exchange rate appreciation and slightly lower non-food inflation.
  - Simple one‑sector model (red dashed lines in Figure 12):
    - Lower total output from agriculture decline resembles an adverse demand‑type shock and is marginally deflationary, implying a slightly accommodative interest rate stance.
    - To mimic agricultural supply effects in the one‑sector model one would need to add an explicit Phillips curve shock to approximate food price increases.
- Implication
  - The extended model explicitly separates demand- and supply-side price pressures originating from agriculture and food prices, producing materially different monetary policy trade‑offs compared to a one‑sector model.

### Decomposition of Food Inflation Phillips Curve
- Sample and drivers
  - Decomposition focuses on subsample 2008Q1-2022Q1.
  - Food price dynamics are explained primarily by inflation expectations:
    - Backward‑looking expectations indicate moderate persistence and inertia.
    - Forward‑looking expectations reflect aggregate price prospects across food and non-food sectors and intersectoral spillovers.
  - Contribution of agriculture GDP explains the linkage between food inflation dynamics and domestic supply of agri‑food goods.
- Historical narrative mapping
  - The model can map narratives from Bank of Ghana reports (examples cited for 2014 and 2016) where harvest conditions influenced observed food inflation contributions.

### Sectoral Business Cycle Dynamics
- Rationale for GDP decomposition
  - GDP is decomposed into agriculture, oil, and non‑agriculture non‑oil (NANO) sectors to better capture sectoral drivers of the business cycle and inflation.
  - Agriculture and oil are driven by idiosyncratic and international events (e.g., rainfall patterns, global geopolitical tensions) and do not necessarily follow the domestic business cycle or monetary policy stance.
  - NANO GDP better captures domestic demand‑side inflationary pressures and is more responsive to monetary policy transmission via interest rates and exchange rate.
- Empirical findings
  - NANO sector accounts for 73 percent of total GDP and is the primary determinant of the aggregate business cycle (high comovement between NANO gap and aggregate gap).
  - COVID-19 period assessment (2020-21; lockdowns in 2020Q2):
    - Pandemic-induced lockdowns were strictly imposed for most NANO activities; agriculture and oil faced less severe restrictions or exemptions.
    - Estimated output gap: large negative in NANO sector; oil and agriculture recorded higher, close‑to‑neutral output gaps.

### Counterfactual Scenarios and Policy Trade-offs
- Methodology
  - Model forecasts over 2022Q1-2023Q4 are conditioned on (i) ex‑post full sample estimated structural shocks and (ii) setting interest rate trajectories and/or interest rate shocks to specific values.
  - Approach follows comparable implementations in the literature.
- Counterfactual 1: Interest rate strictly follows QPM policy reaction function (Taylor‑type rule)
  - Assumption: no monetary policy discretion; policy rate strictly follows reaction function (equation (21)) facing the same structural shocks during 2022Q1-2023Q4.
  - Results:
    - Counterfactual policy path peaks at a quarterly average of 34 percent in 2023Q1.
    - Actual gradual policy adjustments peaked at an average of 30 percent in 2023Q4.
    - Taylor‑rule path would have produced lower nominal depreciation and inflation (annual price dynamics over 2023 about 5 percentage points lower than realized).
    - Trade-off: substantially steeper negative output gap (bottoming out at about –4 percent in mid-2023), implying weaker real sector activity and higher job losses.
- Counterfactual 2: Constant interest rate at pre‑crisis level (extreme scenario)
  - Assumption: monetary policy rate kept at pre‑crisis level of 14.2 percent (average over 2021Q4); monetary policy shocks treated as unanticipated initially (2022Q1-Q3) and anticipated thereafter (2022Q4-2023Q4) to reflect credibility dynamics.
  - Results:
    - Overly‑stimulatory conditions would lead to unanchored expectations and an overheated economy given capacity constraints.
    - Massive exchange rate depreciation reaching 40 GHS/USD by 2023Q1.
    - Spiraling inflation above 150 percent by end-2023.
- Policy insight
  - The cautious approach by BOG during 2022-23 (gradual rate increases) supported the real sector by minimizing output and job losses, while allowing somewhat higher inflation relative to a stricter rule‑following path.

### Conclusion and Policy Implications
- Model contribution and updates
  - The current QPM extends previous work by decomposing GDP into agriculture, oil, and NANO sectors and linking food and non‑food inflation expectations to headline inflation and spillovers.
  - The extended model improves assessment of business cycle position, sectoral drivers of inflation, and the monetary policy transmission mechanism.
- Monetary policy implications
  - Under certain conditions, monetary policy may need to respond more strongly to affect aggregate output because nominal interest rates have limited direct impact on agriculture and oil sectors.
  - When sector‑specific shocks spill over across sectors and forward‑looking agents internalize second‑round effects, headline inflation can rise by a larger margin, requiring a stronger policy reaction.
  - The QPM provides a practical reduced‑form framework to approximate transmission and policy implications of climate‑related shocks via agriculture supply channels without explicitly modeling climate variables.
- Operational conclusion
  - The QPM remains relevant and effective for the Bank of Ghana’s FPAS; the latest extensions enhance forecast coverage, enrich narratives, and strengthen the Bank’s forward‑looking policy framework in pursuit of its price stability objective.

*Quarterly Projection Model for the Bank of Ghana — Working Paper No. WP/2024/237*

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_Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024237-print-pdf.pdf_