## Box 1. The Canonical QPM

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---

### Overview and purpose
- Introduces a QPM-based conceptual framework to analyze weather-related shocks (e.g., floods, droughts) and their implications for monetary policy in developing economies.
- Framework objective: provide a macroeconomically consistent narrative behind forecasts involving weather-related shocks, while maintaining the parsimonious structure of QPMs used by central banks (CBs).
- Focus: temporary shocks and policy-relevant, business-cycle horizon effects; excludes long-term climate change effects and large natural disasters.
- Monetary policy remit in the analysis: interest rate dynamics and nominal exchange rate when relevant; excludes fiscal measures, energy transition policies, and non-interest CB tools.

### Core modeling feature
- Central nexus: agriculture production ↔ food prices, captured in reduced-form within the QPM in line with practice at the Bank of Ghana and National Bank of Rwanda.
- Key structural decompositions introduced in the QPM:
  - Aggregate demand split into agriculture and non-agriculture sectors.
  - Headline CPI disaggregated into food and non-food (core) prices.
  - External balance considerations to capture import substitution when domestic agriculture output is impaired.
- Rationale: food products are subsistence goods with low price elasticity, requiring minimum supply from domestic and/or imported sources.

### Three analytical dimensions (conceptual framework)
- (I) Economic characteristics and frictions
  - Sectoral decomposition of GDP and CPI (agriculture vs non-agriculture; food vs non-food).
  - Food share in CPI and agriculture share in GDP.
  - Imports substituting for domestic agricultural goods.
  - Central bank (CB) credibility and anchoring of inflation expectations.
- (II) Properties of the shocks
  - Shock types: food inflation Phillips curve shocks and agricultural production shocks—both are supply-side in nature.
  - Shock duration: transitory vs permanent; increased volatility and higher frequency of shocks.
- (III) Monetary policy and exchange rate framework
  - Exchange rate flexibility (fixed vs managed vs flexible).
  - Price stability objective: targeting CPI versus targeting core inflation.
  - Degree of central bank credibility and inflation-expectations anchoring.

### Model structure and core equations (canonical QPM configuration)
- Four key blocks: Aggregate demand; Aggregate supply (Phillips curve); Uncovered interest rate parity (UIP); Monetary policy reaction function.
- Representative equations (as presented in source):
  - Aggregate demand / open-economy IS curve:
    - 푦̂t = 푎1 푦̂t−1 + 푎2 Et 푦̂t+1 − 푎3 rmcit + 푎4 푦̂t* + 휀t y,  (B1)
    - rmcit = 푎5 r̂t + (1−푎5)(−ẑt).
  - Aggregate supply / Phillips curve:
    - 휋t = 푏1 휋t−1 + (1−푏1) Et 휋t+1 + 푏2 rmc t + 휀t π,  (B2)
    - rmc t = 푏3 푦̂t + (1−푏3) ẑt.
  - UIP for nominal exchange rate:
    - st = Et st+1 + it* − it + premt4 + 휀t s.  (B3)
    - Change in real exchange rate: Δz t = Δs t + πt* − πt.
  - Monetary policy rule (forward-looking):
    - it = g1 it−1 + (1−g1)[it n + + g2(Et πt+3 yoy − π̅) + g3 푦̂t] + 휀t i.  (B4)

### Demand- and supply-side decompositions
- Total output gap:
  - 푦̂t = ωa 푦̂ta + (1−ωa) 푦̂tna.  (1)
  - Agriculture gap: 푦̂ta = 푎6 푦̂t−1 a + 휀t y a.  (4)
  - Non-agriculture gap: 푦̂tna = 푎1 푦̂t−1 na + 푎2 Et 푦̂t+1 na − 푎3 rmcit + 푎4 푦̂t* + 휀t y na.  (2)
  - Real monetary conditions index: rmcit = 푎5 r̂t + (1−푎5)(−ẑt).  (3)
- Headline CPI decomposition:
  - pt = ωf pt f + (1−ωf) pt nf.  (5)
  - Non-food inflation: πt nf = b1 nf πt−1 nf + (1−b1 nf) πt e,nf + b2 nf rmc t nf + 휀t π nf.  (6)
  - Food inflation (includes agriculture gap channel):
    - πt f = b1 f πt−1 f + (1−b1 f) πt e,f + b2 f rmc t f − ba 푦̂ta + 휀t π f.  (7)

### Expectations, credibility, and exchange rate regime
- Inflation expectations with credibility channel:
  - πt e,j = Et πt+1 j + b5 j incred t,  (9) for j ∈ {nf, f}.
  - Credibility stock: incred t = β1 incred t−1 + (1−β1) β2 (πt−1 yoy − π̅) + 휀t incred.  (10)
- Modified UIP and hybrid exchange rate expectations:
  - st = st e + it* − it + premt4 + 휀t s.  (11)
  - st e = c1 Et st+1 + (1−c1)(st−1 + 24 Δs̅t).  (12)
  - Benchmark: de jure floating with some rigidity (captures occasional targeted FX operations).

### Selected calibration values (as printed in source)
- Non-agriculture gap parameters:
  - 푎1: 0.4
  - 푎2: 0.3
  - 푎3: 0.2
  - 푎4: 0.1
  - 푎5: 0.5
- Agriculture gap:
  - 푎6: 0.35
- Output shares:
  - ωa: 0.2
- Non-food inflation:
  - b1 nf: 0.5
  - b2 nf: 0.4
  - b3 nf: 0.4
- Food inflation:
  - b1 f: 0.3
  - b2 f: 0.2
  - b3 f: (value not printed in provided excerpt)
- CPI weights:
  - ωf: 0.4

### Key model-based findings
- Both food price shocks and agriculture output shocks are supply-side in nature and can raise headline inflation while reducing aggregate output.
- Higher food expenditure shares imply higher vulnerabilities to weather-related shocks.
- Substituting damaged domestic agricultural output with imports:
  - Puts additional pressures on the exchange rate and on inflation.
- Central bank credibility and well-anchored inflation expectations:
  - Make economies more resilient to weather-related shocks.
  - Minimize second-round effects and can allow CBs to “look through” weather-related supply shocks.
  - Alleviate trade-offs implied by more volatile food prices.
- Exchange rate flexibility:
  - Can support stabilization of the economy after weather-related shocks.
- Targeting core inflation (rather than headline CPI):
  - Can allow a CB to “look through” initial food price spikes if the CB is credible.
  - Can be costly over the medium run if the CB is not credible.
- Increased volatility or permanently more volatile food price shocks:
  - Complicate CB trade-offs and make policy choices more acute.

### Simulation design and notable numeric scenarios
- Two shock types simulated:
  - Food price shock (ε_t^π_f) calibrated so annual food inflation rises by 1 percentage point above equilibrium in the first quarter.
  - Agricultural production (harvest) shock (ε_t^y_a).
- Food CPI weight sensitivity (calibration comparison):
  - ω_f =0.25 (blue solid lines) versus ω_f =0.5 (red dotted lines).
  - For same initial increase in food inflation from an agriculture production shock:
    - During the first year and peaking in the fourth quarter, annual headline inflation is "about one-third higher" for ω_f =0.5 relative to ω_f =0.25.
    - Interest rate response is 10 basis points higher under ω_f =0.5 calibration.
  - Baseline ωf calibration: ωf: 0.4 (noted as representative for Sub-Saharan Africa).
- Import-substitution extension: simulation of a 10 percent agriculture production shock:
  - ε_t^y_a = −10 (scenario).
  - Extended-model parametrization used:
    - d_1 =0.5, d_2 =1, d_3 =0.4, d_4 =1 in (15)
    - d_5 =1 in (16)
    - f_1 =0.5 and f_2 =4 in (17)
    - The foreign output gap in equation (2) is turned off by setting a_4 =0
    - A current account gap term is added in equation (2) with an elasticity of 0.25
  - Comparative outcome:
    - Import substitution weakens current account and official reserves, raises sovereign risk perceptions, exerts depreciation pressures; nominal exchange rate can depreciate immediately despite tighter interest rate trajectory, increasing imported inflationary pressures and requiring even tighter interest rates.
- Policy frontier exercise:
  - Baseline shock calibration: SDs of all shocks set to zero except shocks in Phillips curves for non-food and food CPI components (휀푡휋푛푓 and 휀푡휋푓), which have unit SDs.
  - Policy parameter varied: g2 between 0.5 and 5 in steps of 0.1; g1 and g3 kept at baseline.
  - Increased shock volatility scenario: food price shock SD increased by 50 percent.
    - Result: maintaining stable headline inflation under 50 percent more volatile food price shocks requires tighter interest rate reaction, increasing output and exchange rate volatility by a factor of approximately two.
  - Credibility improvement scenario: setting 훽2 = 0.25 (instead of baseline 훽2 = 0.5) can restore much of the initial trade-off geometry.

### Policy implications and operational insights
- Monetary policy trade-offs:
  - Supply shocks to food raise headline inflation and lower output, creating a trade-off for inflation-targeting central banks, particularly in LIDCs and EMs with high food CPI weights and weaker credibility.
- Role of credibility:
  - Strengthening central bank credibility limits second-round effects, reduces the required tightening cycle, and mitigates the inflation-output trade-off.
  - Full credibility calibration example: set b5nf = b5f = 0 produces milder tightening and less adverse output impact relative to imperfect credibility.
- Exchange rate framework:
  - Exchange rate flexibility (benchmark 휔s = 0) provides shock absorption; managed/quasi-fixed regimes (e.g., 휔s = 0.5) can yield more volatile and pronounced macro responses and require larger initial interest rate increases.
- Price index for policy:
  - Core-based (non-food) targeting can reduce interest rate tightening and inter-sector spillovers if the CB is credible; non-credible core targeting can worsen inflation and output outcomes through credibility loss.
- Complementary tools:
  - IMF’s Integrated Policy Framework (IPF) highlights potential use of foreign exchange interventions, macroprudential measures, and capital flow measures in specific cases to mitigate trade-offs.

### Limitations noted for future research
- Not modeling non-linearities (e.g., asymmetric effects, tipping points).
- Excludes fiscal policy responses.
- Does not model direct links between weather variables and economic data.
- Lacks granular sectoral or geographic heterogeneity.
- Limited financial-sector modeling and macro-financial linkages.

*Source: Box 1. The Canonical QPM, IMF Working Paper excerpt (wpiea2025095-print-pdf).*

### Box 1. The Canonical QPM ...............................................................................................

### Box 1. The Canonical QPM

### Overview and purpose
- Introduces a QPM-based conceptual framework to analyze weather-related shocks (e.g., floods, droughts) and their implications for monetary policy in developing economies.
- Framework objective: provide a macroeconomically consistent narrative behind forecasts involving weather-related shocks, while maintaining the parsimonious structure of QPMs used by central banks (CBs).
- Focus: temporary shocks and policy-relevant, business-cycle horizon effects; excludes long-term climate change effects and large natural disasters.
- Monetary policy remit in the analysis: interest rate dynamics and nominal exchange rate when relevant; excludes fiscal measures, energy transition policies, and non-interest CB tools.

### Core modeling feature
- Central nexus: agriculture production ↔ food prices, captured in reduced-form within the QPM in line with practice at the Bank of Ghana and National Bank of Rwanda.
- Key structural decompositions introduced in the QPM:
  - Aggregate demand split into agriculture and non-agriculture sectors.
  - Headline CPI disaggregated into food and non-food (core) prices.
  - External balance considerations to capture import substitution when domestic agriculture output is impaired.
- Rationale: food products are subsistence goods with low price elasticity, requiring minimum supply from domestic and/or imported sources.

### Three analytical dimensions (conceptual framework)
- (I) Economic characteristics and frictions
  - Sectoral decomposition of GDP and CPI (agriculture vs non-agriculture; food vs non-food).
  - Food share in CPI and agriculture share in GDP.
  - Imports substituting for domestic agricultural goods.
  - Central bank (CB) credibility and anchoring of inflation expectations.
- (II) Properties of the shocks
  - Shock types: food inflation Phillips curve shocks and agricultural production shocks—both are supply-side in nature.
  - Shock duration: transitory vs permanent; increased volatility and higher frequency of shocks.
- (III) Monetary policy and exchange rate framework
  - Exchange rate flexibility (fixed vs managed vs flexible).
  - Price stability objective: targeting CPI versus targeting core inflation.
  - Degree of central bank credibility and inflation-expectations anchoring.

### Key model-based findings (as summarized in Table 1 and text)
- Both food price shocks and agriculture output shocks are of supply-side nature.
- Both types of shocks imply monetary policy trade-offs and can raise headline inflation while reducing aggregate output (Figure references in source).
- Higher food expenditure shares (food share in CPI) imply higher vulnerabilities to weather-related shocks.
- Substituting damaged domestic agricultural output with imports:
  - Puts additional pressures on the exchange rate and on inflation.
- Central bank credibility and well-anchored inflation expectations:
  - Make economies more resilient to weather-related shocks.
  - Minimize second-round effects and can allow CBs to “look through” weather-related supply shocks.
  - Alleviate trade-offs implied by more volatile food prices.
- Exchange rate flexibility:
  - Can support stabilization of the economy after weather-related shocks.
- Targeting core inflation (rather than headline CPI):
  - Can allow a CB to “look through” initial food price spikes if the CB is credible.
  - Can be costly over the medium run if the CB is not credible.
- Increased volatility or permanently more volatile food price shocks:
  - Complicate CB trade-offs and make policy choices more acute.

### Modeling and policy implications
- QPM extensions enable identification of supply- and demand-side transmission channels, and assessment of variables’ responses within a general equilibrium system.
- Important model calibrations and country characteristics to consider when applying the canonical QPM to a specific economy:
  - Food weight in the consumption basket.
  - Agricultural value added and employment shares.
  - Degree of exchange rate flexibility and external vulnerabilities.
  - Degree of inflation expectations anchoring and CB credibility.
  - Definition of the price index relevant for the price stability objective (headline CPI vs core inflation).
- Policy interpretation:
  - In advanced economies (AEs) with well-anchored expectations and high CB credibility, supply shocks from weather may often be “looked through.”
  - In low-income developing countries (LIDCs) and emerging markets (EMs) with higher food expenditure shares and weaker credibility, avoiding second-round effects may require tighter monetary policy, making the monetary policy trade-off more stringent.

*Source: Box 1. The Canonical QPM, IMF Working Paper excerpt.*

### 3. Model Structure

### 3. Model Structure

### Overview
- The core of the benchmark model structure follows to some extent the Bank of Ghana QPM, as described in detail in Abradu-Otoo et al. (2022) and Abradu-Otoo et al. (2024).
- Certain Ghana-specific elements and parameter values are adjusted to render the model more generally applicable to LIDCs and/or EMs with an inflation targeting regime and floating exchange rate.
- Additional simulations explore the implications of other monetary policy frameworks.

### Model Components (canonical QPM configuration)
- The model consists of four key equations or blocks, in line with the canonical QPM specification introduced in Berg et al. (2006):
  - Aggregate demand
  - Aggregate supply (or Phillips curve)
  - Uncovered interest rate parity (UIP)
  - Monetary policy reaction function
- This canonical configuration is adjusted and extended to better reflect the key mechanisms and channels for the propagation of weather-related shocks.

### Adjustments and Extensions for Weather-Related Shocks
- The canonical QPM configuration is adjusted and extended to better reflect the key mechanisms and channels for the propagation of weather-related shocks.
- Adjustments include Ghana-specific elements and parameter values modified to be applicable to LIDCs and/or EMs with an inflation targeting regime and floating exchange rate.
- Additional simulations are used to explore implications under other monetary policy frameworks.

### Notation and Conventions
- Variables are expressed in logarithms or gaps (denoted with “hats”).
- Time subscripts represent quarters.

*Source: wpiea2025095-print-pdf — 3. Model Structure*

### Box 1. The Canonical QPM

### Box 1. The Canonical QPM

### Model overview
- The canonical QPM is a New-Keynesian model with sticky nominal prices, demand-determined output, and non-neutral monetary policy.
- Key features emphasized for weather-shock analysis:
  - Decomposition of output into agriculture and non-agriculture sectors.
  - Decomposition of headline inflation into food and non-food (core) components.
  - Monetary policy reacts to headline CPI and the total output gap under an inflation-targeting framework with a floating exchange rate (allowing some rigidity).
  - Formation of inflation expectations includes a monetary policy credibility channel to capture second-round effects and weaker anchoring in LIDCs and EMs.

### Core equations and mechanisms
- Aggregate demand / open-economy IS curve for the output gap (푦̂t):
  - 푦̂t = 푎1 푦̂t−1 + 푎2 Et 푦̂t+1 − 푎3 rmcit + 푎4 푦̂t* + 휀t y,  (B1)
  - rmcit = 푎5 r̂t + (1−푎5)(−ẑt).
  - Relates the output gap to its lag, expected lead, real monetary conditions index (rmci), foreign output gap (푦̂t*), and aggregate demand shocks (휀t y).

- Aggregate supply / forward-looking Phillips curve for inflation (휋t):
  - 휋t = 푏1 휋t−1 + (1−푏1) Et 휋t+1 + 푏2 rmc t + 휀t π,  (B2)
  - rmc t = 푏3 푦̂t + (1−푏3) ẑt.
  - Relates inflation to lag, expected lead, real marginal costs (rmc), and cost-push shocks (휀t π).

- Uncovered interest parity (UIP) for nominal exchange rate (st):
  - st = Et st+1 + it* − it + premt4 + 휀t s.  (B3)
  - Change in real exchange rate: Δz t = Δs t + πt* − πt.

- Monetary policy rule (forward-looking reaction function for policy rate it):
  - it = g1 it−1 + (1−g1)[it n + + g2(Et πt+3 yoy − π̅) + g3 푦̂t] + 휀t i.  (B4)
  - Policy rate depends on lagged rate, neutral nominal rate (it n), expected three-quarter-ahead annual inflation deviation (Et πt+3 yoy − π̅), total output gap, and monetary policy shocks (휀t i).

### Demand-side structure and agriculture channel
- Total output gap composition:
  - 푦̂t = ωa 푦̂ta + (1−ωa) 푦̂tna,  (1)
  - ωa is the share of agriculture value added in GDP (assumed constant).
  - Agriculture gap follows an exogenous autoregressive process:
    - 푦̂ta = 푎6 푦̂t−1 a + 휀t y a.  (4)
  - Non-agriculture gap follows an IS-type equation:
    - 푦̂tna = 푎1 푦̂t−1 na + 푎2 Et 푦̂t+1 na − 푎3 rmcit + 푎4 푦̂t* + 휀t y na.  (2)
  - Real monetary conditions index (rmci):
    - rmcit = 푎5 r̂t + (1−푎5)(−ẑt).  (3)
  - Interpretation: Agriculture is volatile and driven by weather shocks; rmci captures combined real interest rate gap (r̂t) and real exchange rate gap (ẑt) effects.

### Supply-side structure and inflation decomposition
- Headline CPI decomposition:
  - pt = ωf pt f + (1−ωf) pt nf.  (5)
  - ωf is the food expenditure weight in the consumption basket.

- Non-food (core) inflation (quarter-on-quarter annualized):
  - πt nf = b1 nf πt−1 nf + (1−b1 nf) πt e,nf + b2 nf rmc t nf + 휀t π nf.  (6)

- Food inflation (adds agriculture gap channel):
  - πt f = b1 f πt−1 f + (1−b1 f) πt e,f + b2 f rmc t f − ba 푦̂ta + 휀t π f.  (7)
  - The −ba 푦̂ta term links agricultural output shortfalls to upward food-price pressure; ba measures strength of that channel.

- Real marginal costs for sector j ∈ {nf, f}:
  - rmc t j = b3 j 푦̂t na + (1−b3 j − b4 j) ẑt + b4 j r̂p t.  (8)
  - r̂p t is the relative prices gap (food relative to non-food); coefficients allow different sensitivity to domestic vs imported price pressures and intersectoral spillovers.

### Expectations formation and central bank credibility
- Inflation expectations include a credibility channel:
  - πt e,j = Et πt+1 j + b5 j incred t,  (9) for j ∈ {nf, f}.
- Credibility stock (incred t) evolves as:
  - incred t = β1 incred t−1 + (1−β1) β2 (πt−1 yoy − π̅) + 휀t incred.  (10)
  - β1 measures persistence of (in)credibility; β2 reflects impact of latest inflation deviation; 휀t incred is a shock.
- Implication: If b5 j > 0, weaker credibility leads expectations to depend on the credibility stock, producing more persistent/un-anchored expectations and stronger second-round effects—relevant for LIDCs and EMs.

### Exchange rate expectations and regime
- Modified UIP and hybrid expectation formation:
  - st = st e + it* − it + premt4 + 휀t s.  (11)
  - Exchange rate expectations hybrid rule:
    - st e = c1 Et st+1 + (1−c1)(st−1 + 24 Δs̅t).  (12)
  - c1 governs degree of forward-looking versus backward-looking exchange rate expectations; Δs̅t is trend-consistent exchange rate change (trend RER depreciation plus inflation-target differential).
- Benchmark assumes de jure floating regime with some rigidity to capture occasional targeted central bank FX operations.

### Monetary policy operationalization
- Taylor-type reaction function (benchmark variant):
  - it = g1 it−1 + (1−g1)[Et πt+1 + r̅t + g2(Et πt+3 yoy − π̅) + g3 푦̂t] + 휀t i.  (13)
  - g1 controls interest rate smoothing; r̅t is the real neutral rate; Et πt+3 yoy − π̅ is three-quarter ahead expected annual inflation deviation; 휀t i is monetary policy shock.
- Price stability objective defined in terms of headline CPI; output objective uses total output gap.

### Calibration (selected parameter values)
- Non-agriculture gap
  - 푎1: 0.4
  - 푎2: 0.3
  - 푎3: 0.2
  - 푎4: 0.1
  - 푎5: 0.5
- Agriculture gap
  - 푎6: 0.35
- Output shares
  - ωa: 0.2
- Non-food inflation
  - b1 nf: 0.5
  - b2 nf: 0.4
  - b3 nf: 0.4
- Food inflation
  - b1 f: 0.3
  - b2 f: 0.2
  - b3 f: (value not printed in provided excerpt)
- CPI weights
  - ωf: 0.4

### Analytical and policy implications highlighted
- Weather-related shocks primarily affect agriculture output (modeled via 휀t y a), transmitting into food inflation through the agriculture gap (−ba 푦̂ta).
- Real monetary conditions mainly affect non-agricultural activity; hence monetary policy has stronger demand-side effects on non-agriculture.
- Weaker central bank credibility (captured by incred t and b5 j > 0) amplifies second-round effects: supply-driven food price shocks can become more persistent in headline inflation through expectation channels, constraining the central bank’s ability to "look through" transitory shocks.
- Exchange rate dynamics (hybrid expectations, c1) and sovereign risk premium (premt4) are important for imported-price pressures and real monetary conditions.
- Calibration is based on the Bank of Ghana QPM parameterization with adjustments for a generic EMDE; calibration is preferred due to data limitations and to align with semi-structural central bank modeling practice.

*Source: Box 1. The Canonical QPM, from the supplied IMF Working Paper content.*

### 0.3 Credibility

### 0.3 Credibility

### 4. Model Results — overview
- The QPM-based exercises simulate weather-related disturbances via two shocks:
  - a food price shock (ε_t^π_f in equation (7)) calibrated so annual food inflation rises by 1 percentage point above equilibrium in the first quarter.
  - an agricultural production (harvest) shock (ε_t^y_a in equation (4)).
- Responses are expressed as percentage deviations from steady states; horizons shown in figures are quarterly with the shock occurring in the first quarter.
- Source note: "Based on iterative analysis and partly on Abradu-Otoo et al. (2024)." Figures described are authors’ simulations.

### 4.1 Weather shocks are inherently supply-side — key findings
- Both food price shocks and agriculture output shocks are supply-side in nature but differ quantitatively:
  - Food price shock:
    - Passes through to core inflation via intersectoral spillovers and relative price effects.
    - Temporarily raises inflation expectations above the target (credibility channel exacerbates this—see subsection 4.4).
    - Requires monetary policy tightening (higher interest rates).
    - Real exchange rate (RER) appreciates due to nominal appreciation (higher domestic interest rates) and a positive inflation differential.
    - Tighter monetary conditions (overvalued exchange rate and higher interest rates) constrain aggregate demand, producing a negative non-agriculture output gap and helping return inflation to target.
  - Agriculture (harvest) shock:
    - More persistent and larger overall effects for the same initial increase in food inflation.
    - Directly reduces agriculture value added (significant on impact) with moderate recovery due to transitory nature.
    - Total output declines more because agriculture output is directly affected; non-agriculture output contraction arises from required tighter monetary policy.
    - Accelerated inflation dynamics require a relatively higher interest rate, accentuating the inflation-output trade-off.
- Policy implication:
  - In LIDCs and EMs with limited price-stability histories and weak central bank credibility, monetary policy may need to prioritize price stability and address supply-side shocks even at the cost of output losses.

### 4.2 The role of the food weight in the CPI basket — key findings and numeric comparisons
- Calibration compared two food CPI weights:
  - ω_f =0.25 (blue solid lines)
  - ω_f =0.5 (red dotted lines)
- For the same initial increase in food inflation from an agriculture production shock:
  - Higher food CPI weight (ω_f =0.5) produces more pronounced effects on non-food and headline inflation.
  - During the first year and peaking in the fourth quarter, annual headline inflation is "about one-third higher" for ω_f =0.5 relative to ω_f =0.25.
  - Interest rate response is 10 basis points higher under ω_f =0.5 calibration.
  - Differential impact on output is minimal between calibrations.
- Cross-country implication:
  - Food CPI weights are highest in Sub-Saharan Africa (averaging around 40 percent, cited as baseline calibration) and lowest in AEs (below 20 percent).
  - Therefore, LIDCs and EMs are more vulnerable to weather-related shocks and face more acute trade-offs compared to AEs.
- Note: Agriculture value added share (ω_a), set to 0.2 in baseline, has similar implications as food CPI weight.

### 4.3 The role of imports in substituting domestic agricultural goods — model extension and results
- Model extension introduces BOP variables (ratios to GDP): current account, capital account, and official reserves; and replaces foreign output gap with a current account gap term.
- Current account gap equation (15) specification (verbatim):
  - 0 = ĉa_t + f̂a_t  (14)
  - ĉa_t = d_1 ĉa_{t−1} + (1−d_1)[ d_2 ŷ_t^* − d_3 ŷ_t^{na} + d_4 ẑ_t ] + ε_t^{ca}  (15)
    - where ŷ_t^* = foreign demand for domestically produced goods
    - ŷ_t^{na} = domestic demand for imports (proportional to non-agriculture GDP)
    - ẑ_t = impact of RER gap on the current account
    - ε_t^{ca} = current account shock
- Private capital flows and sovereign risk premium specifications (verbatim):
  - pft = p̄f + d_5 (prem_t − p̄rem) + ε_t^{pf}  (16)
  - prem_t = f_1 prem_{t−1} + (1−f_1)[ p̄rem − f_2 Δres_t ] + ε_t^{prem}  (17)
    - Δres_t = change in official reserves; ε_t^{prem} = risk premium shock
- Simulation scenario: a 10 percent agriculture production shock (ε_t^y_a = −10).
- Extended-model parametrization used in describing results (verbatim):
  - d_1 =0.5, d_2 =1, d_3 =0.4, d_4 =1 in (15)
  - d_5 =1 in (16)
  - f_1 =0.5 and f_2 =4 in (17)
  - The foreign output gap in equation (2) is turned off by setting a_4 =0
  - A current account gap term is added in equation (2) with an elasticity of 0.25
- Comparative results (benchmark without BOP vs extended with BOP and import substitution):
  - Both models show similar direct impacts on food inflation.
  - When domestic agricultural losses are substituted with imports:
    - Current account and official reserves weaken.
    - Sovereign risk perceptions deteriorate (via equation (17)), exerting depreciation pressures on the exchange rate.
    - Nominal exchange rate depreciates immediately despite a tighter interest rate trajectory.
    - Weaker currency increases imported inflationary pressures, requiring an even tighter interest rate stance that further dampens aggregate demand.
  - Policy implication:
    - Food import dependence raises vulnerabilities, including terms-of-trade shocks originating from global weather disruptions, which can amplify inflation and necessitate tighter monetary policy while worsening external positions.

### 4.4 The role of monetary policy credibility — mechanism and model treatment
- Second-round effects and entrenched supply shocks work through inflation expectations persistently deviating from the inflation target; these drive monetary tightening in the simulations.
- The benchmark model incorporates a monetary policy credibility channel by calibrating b_5^{nf} and b_5^{f} in equation (9) to positive values, making credibility particularly significant for non-food inflation expectations (text ends while specifying b_5^{nf}).
- Mechanism summary:
  - Positive calibration of credibility parameters increases the sensitivity of inflation expectations to observed inflation developments.
  - Weaker credibility leads to larger deviations of expectations from target, necessitating stronger interest rate responses and exacerbating the inflation-output trade-off in LIDCs and EMs.

*Source: IMF Working Paper excerpt from "QPM-Based Analysis of Weather Shocks and Monetary Policy in Developing Countries" (figures and simulations described in text).*

### 0.5 and 푏

### wpiea2025095-print-pdf - 0.5 and 푏

### Monetary policy credibility and weather-related agriculture shocks
- Comparison of responses to an adverse agriculture shock between:
  - benchmark calibration featuring imperfect monetary policy credibility (blue solid lines in Figure 5), and
  - full credibility model obtained by setting 푏5푛푓 = 푏5푓 = 0 (red dotted lines in Figure 5).
- Key findings:
  - Directions and shapes of IRFs are similar across calibrations, but relative magnitudes differ, underscoring the importance of strengthening central bank credibility.
  - A more credible monetary policy framework:
    - limits second-round effects and relative price spillovers from food inflation to non-food inflation;
    - implies a milder tightening cycle (smaller interest rate response) with less adverse impact on aggregate demand;
    - partly mitigates the inflation-output trade-off posed by the shock.
  - Credibility is especially important for vulnerable economies with:
    - a higher food CPI share (see Figure 3), and/or
    - the need to substitute damaged crops with imports (see Figure 4).
- Reference to related literature and simulations: Abradu-Otoo et al. (2022) on Bank of Ghana QPM counterfactuals.

### Persistence, adaptive expectations, and modeling transitory shocks
- Backward-looking elements in behavioral equations imply persistence: e.g., the food inflation Phillips curve (7) contains the lagged term 푏1푓 휋푡−1푓 so that a one-unit period-t food price shock mechanically affects period t+1 by 푏1푓 units.
- To neutralize lagged mechanical persistence for transitory shocks, model the innovation as a moving average:
  - substitute 휀푡휋푓 in equation (7) with 휀푡휋푓 − 휌휀푡−1휋푓, where 휌 controls the extent shocks affect adaptive expectations.
- Simulation comparison (Figure 6):
  - benchmark model: 휌 = 0 (blue solid lines);
  - alternative calibration: 휌 = 0.5 (red dotted lines) representing purely transitory shocks and well-anchored expectations.
  - Result: with 휌 = 0.5 the shock has only minimal effects on key macro variables, including no central bank reaction (consistent with a “look through” approach).
- Practical application: Central Bank of Colombia uses this approach to incorporate expected El Niño/La Niña strength into inflation expectations.

### Exchange rate flexibility and the monetary policy framework
- Modified UIP condition (11’) introduces parameter 휔s to control exchange rate peg weight:
  - 푠푡 = 휔s(푠푡−1 + ∆푠̅) + (1 − 휔s)(푠푡e + 푖푡∗ − 푖푡 + prem𝑡4) + 휀푡𝑠,
  - ∆푠̅ = ∆푧̅ + 휋̅ − 휋̅∗.
- Benchmark: exchange rate flexibility ensured by setting 휔s = 0.
- Managed regime example: 휔s = 0.5 approximates a managed exchange rate (red dotted lines in Figure 7) compared to benchmark 휔s = 0 (blue solid lines).
- Findings:
  - Managed/quasi-fixed nominal exchange rate produces more volatile and pronounced fluctuations to weather shocks despite limited nominal exchange rate movement.
  - Initial policy response: interest rate needs to increase significantly due to limited expenditure switching and pass-through.
  - Over the medium run, the nominal exchange rate anchor functions like price level targeting (contrast with inflation targeting), reversing the stronger initial monetary tightening.
  - Overall, exchange rate flexibility delivers important shock-absorbing effects: smoother interest rate path and sustained return of inflation to the target.
- Calibration adjustments for managed regime:
  - limited capital controls are implicitly assumed to retain interest rate policy effectiveness;
  - increased persistence: parameters 푏1푛푓 and 푏1푓 are increased by 50 percent relative to baseline calibration to 0.75 and 0.45, respectively.

### Price index choice: headline CPI versus core (non-food) inflation targeting
- Benchmark model uses headline CPI inflation in policy reaction function (13), consistent with most inflation-targeting CB mandates.
- Alternative: use core (non-food) inflation in the reaction function to reflect underlying price pressures that central banks can influence.
- Simulation comparison (Figure 8):
  - benchmark (headline CPI target) – blue solid lines;
  - credible core-based inflation targeting – red dotted lines;
  - non-credible core targeting – green dashed lines.
- Findings:
  - Credible core-based targeting:
    - more limited inter-sectoral relative price effects;
    - significantly moderated interest rate tightening versus CPI-based targeting;
    - both non-food and headline inflation rates are lower than baseline, with roughly same output gap trajectory — indicating core targeting can alleviate trade-offs from weather shocks.
  - Non-credible core targeting (agents learn inconsistency between stated objective and operational focus):
    - initial interest rate response similar to credible case;
    - credibility damage over time leads to larger above-target inflation deviations;
    - central bank extends tightening in amplitude and duration, harming output.
- Parameterization for non-credible core targeting (formal changes):
  - 훽2 = 1 (against 0.5) to account for more rapid credibility losses;
  - 푏1푛푓 and 푏1푓 increased by 25 percent to 0.625 and 0.375, respectively;
  - 푐1 = 0.7 (against 0.6) to allow for larger exchange rate reactions.

### Policy frontiers: trade-offs between inflation, output gap, and exchange rate volatility
- QPM application: construct policy frontiers for weather-related food-price supply shocks by computing model-based unconditional standard deviations (SDs).
- Baseline shock calibration:
  - SDs of all shocks set to zero except shocks in Phillips curves for non-food and food CPI components (휀푡휋푛푓 and 휀푡휋푓), which have unit SDs.
- Policy parameter varied: coefficient on expected inflation deviation from target in interest rate rule (13), 푔2, varied between 0.5 and 5 with step 0.1; other interest-rate parameters (lag 푔1 and output gap 푔3) kept at baseline.
- Key trade-off geometry (Figure 9, blue curves = benchmark):
  - Inflation vs output gap (left panel): downward-sloping frontier — reducing output gap variability via softer inflation response (lower 푔2) increases inflation volatility; increasing 푔2 reduces inflation volatility but increases output gap volatility.
  - Inflation vs exchange rate (right panel): strong reaction to inflation ensures price stability but raises exchange rate volatility, enabling the exchange rate to act as shock absorber.
- Increased shock volatility scenario:
  - red curves: food price shock SD increased by 50 percent while non-core shock SD unchanged.
  - Effect: rightward shift of policy frontiers; maintaining stable headline inflation under 50 percent more volatile food price shocks requires tighter interest rate reaction, increasing output and exchange rate volatility by a factor of approximately two.
- Role of credibility in ameliorating trade-offs:
  - green curves: same 50 percent higher food price volatility but with improved credibility (set 훽2 = 0.25 in credibility process equation (10), instead of baseline 훽2 = 0.5).
  - Result: initial trade-off (blue curves) can be essentially restored by building central bank credibility and keeping inflation expectations aligned with target, thus minimizing second-round effects.
- Policy implications:
  - Supply-type shocks create trade-offs between inflation targeting and stabilizing the business cycle, with additional exchange rate complications for small open LIDCs/EMs.
  - IMF’s Integrated Policy Framework (IPF) discusses use of complementary tools—foreign exchange interventions, macroprudential measures, and capital flow measures—in specific cases and conditions to mitigate trade-offs.

*Source: IMF working paper — QPM-Based Analysis of Weather Shocks and Monetary Policy in Developing Countries (excerpt).*

### 5. Conclusion

### 5. Conclusion

### Overview and role of the extended QPM
- Weather-related shocks are an important source of disturbance and uncertainty, presenting significant challenges to economic policymakers, including central banks (CBs).
- The paper provides an overview of weather-relevant analytical exercises using an extended Quarterly Projection Model (QPM), whose canonical version is at the core of many Forecasting and Policy Analysis Systems (FPAS) in many CBs.
- The extended model’s simplicity, tractability, and adaptability in creating these scenarios reaffirm the QPM's role as a useful tool in supporting the monetary policy process in CBs within a continuously evolving economic landscape.

### Nexus between agricultural production and food prices
- At the core of the analytical exercises is the nexus between agricultural production and food prices, as food inflation is significantly influenced by agricultural supply, which is partly driven by unpredictable weather-related events such as rainfall patterns and droughts.
- One salient result: weather-related shocks are of a supply-side nature and present challenging trade-offs for policymakers, potentially requiring a monetary policy response if there are risks of second-round effects.

### Policy trade-offs and typical transmission
- Example transmission:
  - If agricultural production drops due to a poor harvest, it results in lower overall output and higher food and headline inflation.
  - To prevent inflation expectations from becoming unanchored and to minimize second-round effects—which is more likely in LIDCs and EMs—the central bank may initiate a tightening cycle and raise the interest rates, with further adverse impacts on aggregate demand.
- The magnitude and duration of the monetary policy response depend on key characteristics and frictions of the economy.

### Key economy characteristics and frictions affecting the response
- CPI weight of food expenditures
- GDP share of the agriculture sector
- Degree of imports substituting for damaged domestic agricultural supply
- Extent of inflation expectations’ anchoring and central bank credibility
- Specific characteristics of the monetary policy framework, including:
  - Degree of exchange rate flexibility
  - Definition of the price stability objective
- Overall implication: less-developed economies are more vulnerable and may face bigger policy challenges in responding to weather-related shocks than advanced economies.

### Limitations and directions for future research
- Important limitations of the approach presented:
  - Not explicitly considering non-linearities (e.g., asymmetric effects of shocks and “tipping points”)
  - Ignoring fiscal policy responses
  - Not modeling the direct link between weather-related variables and economic data
  - Lacking granular assessment at sectoral or geographical levels and other heterogeneities
  - Having limited modeling structure of the financial sector, which can act as a shock amplifier through macro-financial linkages
- These aspects are left for future research.

*IMF Working Paper No. WP/2024/095 — QPM-Based Analysis of Weather Shocks and Monetary Policy in Developing Countries, Section 5. Conclusion.*

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_Source: https://www.imf.org/-/media/files/publications/wp/2025/english/wpiea2025095-print-pdf.pdf_