## MONETARY POLICY ANALYSIS WITH A QUARTERLY PROJECTION MODEL

## Source details

**Canonical URL:** [MONETARY POLICY ANALYSIS WITH A QUARTERLY PROJECTION MODEL](https://www.imf.org/-/media/files/publications/selected-issues-papers/2024/english/sipea2024036.pdf)

## Other formats

- [Markdown version](/-/media/files/publications/selected-issues-papers/2024/english/sipea2024036.pdf.md)
- [Structured JSON version](/-/media/files/publications/selected-issues-papers/2024/english/sipea2024036.pdf.json)

---

### Introduction
- Context and challenge:
  - Interest rates in Hungary rose sharply in response to inflation above 25 percent y/y in 2023-Q1 and large depreciation in the forint.
  - As inflationary pressures have eased and the exchange rate has stabilized, the base rate has been reduced to 7.0 percent in June 2024 but remains restrictive.
  - Reuters survey median expectation: policy rate is expected to fall to around 6¼ percent by the end of 2024.
- Key trade-off:
  - Balancing risks of loosening too quickly (inflation takes longer to return to target) versus loosening too slowly (larger costs to output) requires careful calibration.
- Approach:
  - The paper uses the IMF’s Quarterly Projection Model (QPM) to provide a quantitative guide to the calibration of monetary policy in Hungary.

### Overview of the Quarterly Projection Model (QPM)
- Model characterization:
  - Semi-structural new-Keynesian model with nominal rigidities and rational expectations; forward-looking and endogenous interest rates.
  - Filters macro variables into trends and gaps; requires judgement to identify trends.
- Core equations (standard QPM):
  - IS curve: aggregate demand responds to real interest rates, credit conditions, and the exchange rate.
  - Phillips curve: inflation depends on output gap, exchange rate and relative prices.
  - Policy (Taylor) rule: interest rates respond to deviations in expected inflation from target and the output gap.
  - Uncovered interest parity (UIP): exchange rate relates to expected interest rate differentials and a risk premium.
- Hungary-specific adaptations:
  - Greater sectoral detail for inflation (core goods and services separated).
  - Exchange rate risk premium explicitly included in the policy rule.
  - Inclusion of changes in credit spreads and effects of widespread interest rate caps since 2022 that hinder transmission.

### The QPM and Monetary Policy in the Baseline
- Baseline versus unconstrained policy rule projections:
  - Baseline is conditioned on a market path for interest rates consistent with median Reuters poll (first year).
    - Implied average quarterly interest rates: fall to 6¼ percent in 2024-Q4 and 5¾ percent by 2025-Q2.
  - Unconstrained policy rule allows rates to respond endogenously via the model’s Taylor rule.
- Inflation and drivers under baseline:
  - Model projects inflation picks up from 3.7 percent y/y in 2024 Q1 to 4.2 percent by end-2024, above tolerance band of target.
  - Drivers:
    - Indirect tax increases on fuel.
    - Pickup in core inflationary pressures.
    - Fading external disinflationary impulses (falling commodity prices and forint appreciation).
    - Elevated services inflation due to second-round effects and low relative services prices.
- Policy stance and neutral rate:
  - Beyond 2025-Q2, policy switches to model’s rule; policy is somewhat restrictive through 2025 but significantly less so than in previous year.
  - By 2026, ex-ante real policy rate settles at neutral level of around 2 percent.
- Policy recommendation from QPM:
  - Further cuts in interest rates should proceed cautiously and gradually.
  - The model’s policy rule implies slightly more restrictive policy than the baseline to bring down inflation more quickly, improving welfare even with a slightly more gradual recovery.

### Alternative Scenarios and Sensitivities
- Exchange rate risk premium shocks:
  - If risk premium rises temporarily by 2½pp (weakening the currency), interest rates should stay elevated longer—mitigating inflation rise but weakening growth.
  - If risk premium normalizes faster, rates can fall toward neutral more quickly.
- Alternative model calibrations (Figure 3 scenarios):
  - Scenario 1: Services inflation persistence increased by 50 percent → higher inflation forecast; interest rates remain tighter through 2024-25 and do not reach neutral until 2026.
  - Scenario 2: Policymaker places higher weight on growth (equal to inflation) and little interest rate smoothing → interest rates initially fall faster in 2024, closing output gap quicker but producing higher inflation; expectations lead to more restrictive rates later and lower welfare despite stronger growth.
  - Scenario 3: Longer lags of monetary policy to activity → output recovers more slowly; little change to policy rate path because Phillips curve slope is low; inflation projection little changed.
  - Scenario 4: Trend real rate (r*) 1 percent lower than estimated → lower path for interest rates with little change to output gap or inflation paths.
- Uncertainty assessment:
  - Fan charts (bootstrap of residuals) are wide, indicating high uncertainty around projections.
  - Fan chart for inflation is asymmetric with mean above baseline, reflecting past large supply shocks; risks to baseline inflation may be skewed to the upside.
  - Communication of likely future interest rate path should convey uncertainty; policy ought to loosen cautiously given chance of persistent/reoccurring shocks.

### Impulse Response Functions and Sectoral Spillovers
- Monetary policy shock (Figure 5) findings:
  - A 1pp temporary but persistent increase in the policy rate reduces output by around 0.15 percent and reduces inflation by a peak of 0.4pp.
  - Peak inflation impact occurs within under a year—implying a low sacrifice ratio.
  - Strong exchange rate channel: 74 percent of the CPI basket is goods compared to 55 percent in the euro area.
- Core goods inflation shock and spillovers (Figure 6):
  - A cost-push shock in core goods temporarily increases core goods inflation and, via higher aggregate prices and nominal wages, raises services marginal costs and services inflation.
  - Temporary goods shock induces a smaller but persistent increase in services inflation, delaying return to target.
  - With monetary policy response, CPI inflation returns to target in two years; if policy response is delayed by a year, inflation takes an additional year to return to target.

### Conclusion
- Main takeaway:
  - After large interest rate reductions, QPM projections suggest the next phase of monetary policy normalization should proceed cautiously and more gradually.
  - Rationale: pace of disinflation expected to slow as external disinflation fades and second-round effects push up services inflation.
  - A more gradual reduction than market expectations would produce a slightly smaller inflation pickup end-2024 and inflation closer to target in 2025.
- Caveats:
  - Model may misidentify sizes of key gaps (output or real rate gaps) and may not capture all features of the post-Covid inflation surge due to reduced-form nature.
  - Results should be used alongside other analysis and expert judgement; data should be monitored closely to assess realism of projections.

### Calibration and estimation approach
- Calibration objective:
  - The model is calibrated to produce plausible impulse responses that also correspond with those from the literature, including Szilágyi et al (2013) and Békési et al (2016).
- Use of parameters:
  - The main parameters are summarized in Table 1. The baseline projections use the calibrated model.
- Bayesian cross-check:
  - As a cross-check, select important parameters are estimated over 2006-2024 Q1 using Bayesian techniques, using the calibrated values as priors.
  - Estimated values are reported alongside the calibrated values and are in most cases close to the calibrated values.

### Hungary: QPM Parameters (selected entries)
- IS curve / Policy rule
  - Persistence 푏ଵ௔: Value 0.5; Estimated 0.43
  - Expected output 푏ଵ௕: Value 0.05; Estimated 0.05
  - Interest rate channel 푏ଶ: Value 0.1; Estimated 0.10
  - External demand 푏ଷ: Value 0.3; Estimated 0.40
  - Weight on real rate gap in monetary conditions index 푏ସ: Value 0.8
- Policy rule (continued)
  - Interest rate smoothing 푔ଵ: Value 0.7; Estimated 0.73
  - Weight on inflation deviation 푔ଶ: Value 1.2; Estimated 1.06
  - Weight on output gap 푔ଷ: Value 0.25; Estimated 0.31
  - Weight on exchange rate premium ℎଵ: Value 0.2
- Core services Phillips curve
  - Persistence 훼ଵଵ: Value 0.4; Estimated 0.37
  - Real marginal costs 훼ଵଶ: Value 0.1; Estimated 0.07
  - Loading on output gap in real marginal costs 훼ଵଷ: Value 0.75
  - Loading on non-core costs 훼ଶସ: Value 0.75; Estimated 0.83
- Core goods Phillips curve
  - Persistence 훼ଶଵ: Value 0.4; Estimated 0.52
  - Real marginal costs 훼ଶଶ: Value 0.1; Estimated 0.09
  - Loading on output gap in real marginal costs 훼ଶଷ: Value 0.2
- Unprocessed food Phillips curve
  - Persistence 훼సଵ: Value 0.5; Estimated 0.27
  - Real marginal costs 훼సశ: Value 0.1; Estimated 0.15
  - Weight on output gap in real marginal costs 훼సଷ: Value 0.3
- Fuel Phillips curve
  - Persistence 훼సଵ: Value 0.3; Estimated 0.29
  - Real marginal costs 훼సశ: Value 0.4; Estimated 0.13
  - Loading on output gap in real marginal costs 훼సଷ: Value 0.0
- Regulated prices Phillips curve
  - Persistence 훼ଵహ: Value 0.1
  - Real marginal costs 훼శహ: Value 0.2
  - Loading on output gap in real marginal costs 훼ଷహ: Value 0.9
- Exchange rate
  - Exchange rate persistence 푒ଵ: Value 0.3

### Key methodological note
- The calibrated parameter set is the basis for baseline projections; Bayesian estimation over 2006-2024 Q1 serves as a robustness check, with most estimated values close to the calibrated priors.

*Chris Jackson. 2024. “Monetary Policy Analysis with a Quarterly Projection Model, Hungary” IMF Selected Issues Paper (SIP/2024/036).*

### 2022. As inflationary pressures have eased, the base rate has been reduced but remains restrictive.

### MONETARY POLICY ANALYSIS WITH A QUARTERLY PROJECTION MODEL

### Introduction
- Context and challenge:
  - Interest rates in Hungary rose sharply in response to inflation above 25 percent y/y in 2023-Q1 and large depreciation in the forint.
  - As inflationary pressures have eased and the exchange rate has stabilized, the base rate has been reduced to 7.0 percent in June 2024 but remains restrictive.
  - Reuters survey median expectation: policy rate is expected to fall to around 6¼ percent by the end of 2024.
- Key trade-off:
  - Balancing risks of loosening too quickly (inflation takes longer to return to target) versus loosening too slowly (larger costs to output) requires careful calibration.
- Approach:
  - The paper uses the IMF’s Quarterly Projection Model (QPM) to provide a quantitative guide to the calibration of monetary policy in Hungary.

### Overview of the Quarterly Projection Model (QPM)
- Model characterization:
  - Semi-structural new-Keynesian model with nominal rigidities and rational expectations; forward-looking and endogenous interest rates.
  - Filters macro variables into trends and gaps; requires judgement to identify trends.
- Core equations (standard QPM):
  1. IS curve: aggregate demand responds to real interest rates, credit conditions, and the exchange rate.
  2. Phillips curve: inflation depends on output gap, exchange rate and relative prices.
  3. Policy (Taylor) rule: interest rates respond to deviations in expected inflation from target and the output gap.
  4. Uncovered interest parity (UIP): exchange rate relates to expected interest rate differentials and a risk premium.
- Hungary-specific adaptations:
  - Greater sectoral detail for inflation (core goods and services separated).
  - Exchange rate risk premium explicitly included in the policy rule.
  - Inclusion of changes in credit spreads and effects of widespread interest rate caps since 2022 that hinder transmission.

### The QPM and Monetary Policy in the Baseline
- Baseline versus unconstrained policy rule projections:
  - Baseline is conditioned on a market path for interest rates consistent with median Reuters poll (first year).
    - Implied average quarterly interest rates: fall to 6¼ percent in 2024-Q4 and 5¾ percent by 2025-Q2.
  - Unconstrained policy rule allows rates to respond endogenously via the model’s Taylor rule.
- Inflation and drivers under baseline:
  - Model projects inflation picks up from 3.7 percent y/y in 2024 Q1 to 4.2 percent by end-2024, above tolerance band of target.
  - Drivers: indirect tax increases on fuel, pickup in core inflationary pressures, fading external disinflationary impulses (falling commodity prices and forint appreciation), elevated services inflation due to second-round effects and low relative services prices.
- Policy stance and neutral rate:
  - Beyond 2025-Q2, policy switches to model’s rule; policy is somewhat restrictive through 2025 but significantly less so than in previous year.
  - By 2026, ex-ante real policy rate settles at neutral level of around 2 percent.
- Policy recommendation from QPM:
  - Further cuts in interest rates should proceed cautiously and gradually.
  - The model’s policy rule implies slightly more restrictive policy than the baseline to bring down inflation more quickly, improving welfare even with a slightly more gradual recovery.

### Alternative Scenarios and Sensitivities
- Exchange rate risk premium shocks:
  - If risk premium rises temporarily by 2½pp (weakening the currency), interest rates should stay elevated longer—mitigating inflation rise but weakening growth.
  - If risk premium normalizes faster, rates can fall toward neutral more quickly.
- Alternative model calibrations (Figure 3 scenarios):
  - Scenario 1: Services inflation persistence increased by 50 percent (strong second-round effects) → higher inflation forecast; interest rates remain tighter through 2024-25 and do not reach neutral until 2026.
  - Scenario 2: Policymaker places higher weight on growth (equal to inflation) and little interest rate smoothing → interest rates initially fall faster in 2024, closing output gap quicker but producing higher inflation; expectations lead to more restrictive rates later and lower welfare despite stronger growth.
  - Scenario 3: Longer lags of monetary policy to activity → output recovers more slowly; little change to policy rate path because Phillips curve slope is low; inflation projection little changed.
  - Scenario 4: Trend real rate (r*) 1 percent lower than estimated → lower path for interest rates with little change to output gap or inflation paths.
- Uncertainty assessment:
  - Fan charts (bootstrap of residuals) are wide, indicating high uncertainty around projections.
  - Fan chart for inflation is asymmetric with mean above baseline, reflecting past large supply shocks; risks to baseline inflation may be skewed to the upside.
  - Communication of likely future interest rate path should convey uncertainty; policy ought to loosen cautiously given chance of persistent/reoccurring shocks.

### Impulse Response Functions and Sectoral Spillovers
- Monetary policy shock (Figure 5):
  - A 1pp temporary but persistent increase in the policy rate reduces output by around 0.15 percent and reduces inflation by a peak of 0.4pp; peak inflation impact occurs within under a year—implying a low sacrifice ratio.
  - Strong exchange rate channel: 74 percent of the CPI basket is goods compared to 55 percent in the euro area.
- Core goods inflation shock and spillovers (Figure 6):
  - A cost-push shock in core goods temporarily increases core goods inflation and, via higher aggregate prices and nominal wages, raises services marginal costs and services inflation.
  - Temporary goods shock induces a smaller but persistent increase in services inflation, delaying return to target.
  - With monetary policy response, CPI inflation returns to target in two years; if policy response is delayed by a year, inflation takes an additional year to return to target.

### Conclusion
- Main takeaway:
  - After large interest rate reductions, QPM projections suggest the next phase of monetary policy normalization should proceed cautiously and more gradually.
  - Rationale: pace of disinflation expected to slow as external disinflation fades and second-round effects push up services inflation.
  - A more gradual reduction than market expectations would produce a slightly smaller inflation pickup end-2024 and inflation closer to target in 2025.
- Caveats:
  - Model may misidentify sizes of key gaps (output or real rate gaps) and may not capture all features of the post-Covid inflation surge due to reduced-form nature.
  - Results should be used alongside other analysis and expert judgement; data should be monitored closely to assess realism of projections.

### Model Equations (key elements)
- Aggregate demand and monetary conditions index (mci) include real interest rate gap (r̂), credit risk premium (cprem) and real exchange rate gap (ẑ).
- Sectoral hybrid Phillips curves: quarterly annualized inflation in each sector j depends on past and expected inflation, real marginal costs (rmc) and cost-push shocks.
- Real marginal costs differ by sector (core services, core goods, unprocessed food, fuel, regulated prices) and include output gap, relative price gaps, and relevant commodity price gaps.
- Policy (Taylor) rule includes smoothing, responses to expected inflation deviations (striping out indirect taxes), output gap, and an exchange-rate-related term ℎ₁ Δprem to reflect central bank weight on exchange rate stabilization; trend real interest rate pinned to 10-year BUBOR swaps.
- Exchange rate determined by a UIP condition with backward-looking element and an exchange rate premium; world block uses euro area variables and April 2024 WEO projections.

*Chris Jackson. 2024. “Monetary Policy Analysis with a Quarterly Projection Model, Hungary” IMF Selected Issues Paper (SIP/2024/036). Washington, D.C.: International Monetary Fund.*

### 19.      The model is calibrated to produce plausible impulse responses that also correspond with

### sipea2024036 - 19.      The model is calibrated to produce plausible impulse responses that also correspond with

### Calibration and estimation approach
- The model is calibrated to produce plausible impulse responses that also correspond with those from the literature, including Szilágyi et al (2013) and Békési et al (2016).
- The main parameters are summarized in Table 1. The baseline projections use the calibrated model.
- As a cross-check, select important parameters are estimated over 2006-2024 Q1 using Bayesian techniques, using the calibrated values as priors. These estimated values are reported alongside the calibrated values and are in most cases close to the calibrated values.

### Hungary: QPM Parameters (selected entries from Table 1)
- IS curve / Policy rule
  - Persistence 푏ଵ௔: Value 0.5; Estimated 0.43
  - Expected output 푏ଵ௕: Value 0.05; Estimated 0.05
  - Interest rate channel 푏ଶ: Value 0.1; Estimated 0.10
  - External demand 푏ଷ: Value 0.3; Estimated 0.40
  - Weight on real rate gap in monetary conditions index 푏ସ: Value 0.8

- Policy rule (continued)
  - Interest rate smoothing 푔ଵ: Value 0.7; Estimated 0.73
  - Weight on inflation deviation 푔ଶ: Value 1.2; Estimated 1.06
  - Weight on output gap 푔ଷ: Value 0.25; Estimated 0.31
  - Weight on exchange rate premium ℎଵ: Value 0.2

- Core services Phillips curve
  - Persistence 훼ଵଵ: Value 0.4; Estimated 0.37
  - Real marginal costs 훼ଵଶ: Value 0.1; Estimated 0.07
  - Loading on output gap in real marginal costs 훼ଵଷ: Value 0.75
  - Loading on non-core costs 훼ଶସ: Value 0.75; Estimated 0.83

- Core goods Phillips curve
  - Persistence 훼ଶଵ: Value 0.4; Estimated 0.52
  - Real marginal costs 훼ଶଶ: Value 0.1; Estimated 0.09
  - Loading on output gap in real marginal costs 훼ଶଷ: Value 0.2

- Unprocessed food Phillips curve
  - Persistence 훼ସଵ: Value 0.5; Estimated 0.27
  - Real marginal costs 훼ସଶ: Value 0.1; Estimated 0.15
  - Weight on output gap in real marginal costs 훼ସଷ: Value 0.3

- Fuel Phillips curve
  - Persistence 훼ସଵ: Value 0.3; Estimated 0.29
  - Real marginal costs 훼ସଶ: Value 0.4; Estimated 0.13
  - Loading on output gap in real marginal costs 훼సଷ: Value 0.0

- Regulated prices Phillips curve
  - Persistence 훼ଵହ: Value 0.1
  - Real marginal costs 훼ଶହ: Value 0.2
  - Loading on output gap in real marginal costs 훼ଷହ: Value 0.9

- Exchange rate
  - Exchange rate persistence 푒ଵ: Value 0.3

### Key methodological note
- The calibrated parameter set is the basis for baseline projections; Bayesian estimation over 2006-2024 Q1 serves as a robustness check, with most estimated values close to the calibrated priors.

*Source: sipea2024036 - 19.      The model is calibrated to produce plausible impulse responses that also correspond with*

---


_Source: https://www.imf.org/-/media/files/publications/selected-issues-papers/2024/english/sipea2024036.pdf_