## 1. QPM Projections Under the Baseline Monetary Policy Path and an Unconstrained

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---

### A. Introduction
- Interest rates in Hungary rose sharply in response to inflation above 25 percent y/y in 2023-Q1 and large depreciation in the forint.
- The base rate was reduced to 7.0 percent in June 2024 but remains restrictive.
- Reuters survey median expects the policy rate to fall to around 6¼ percent by the end of 2024.
- Policy trade-off: loosening too quickly (inflation re-accelerates) vs loosening too slowly (larger output costs) — careful calibration required.

### B. Overview of the Quarterly Projection Model (QPM)
- Model type and key features:
  - Semi-structural new-Keynesian model with nominal rigidities and rational expectations.
  - Filters variables into trends and gaps; identifying trends requires judgement.
- Four core equations/mechanisms:
  - IS curve: aggregate demand ↔ real interest rates, credit conditions, exchange rate.
  - Phillips curve: inflation ↔ output gap, exchange rate, relative prices.
  - Policy (Taylor) rule: interest rates respond to expected inflation deviations and output gap.
  - Uncovered interest parity (UIP): exchange rate ↔ expected interest rate differentials and a risk premium.
- Hungary-specific adaptations:
  - Greater sectoral detail for inflation: disaggregation into core goods and services (and other sectors).
  - Exchange rate risk premium explicitly included in the policy rule.
  - Model includes changes in credit spreads and risk-free rates; accounts for interest rate caps affecting transmission.

### C. The QPM and Monetary Policy in the Baseline
- Projection assumptions:
  - Baseline: conditioned on market participants’ expectations (median Reuters poll).
    - Implies average quarterly interest rates fall to 6¼ percent in 2024-Q4 and 5¾ percent by 2025-Q2.
  - Unconstrained policy rule: interest rates respond endogenously via the model’s Taylor rule.
- Baseline projection outcomes:
  - Inflation picks up from 3.7 percent y/y in 2024 Q1 to 4.2 percent by end-2024, above the tolerance band of the target.
  - Drivers of the pickup:
    - Increases in indirect taxes on fuel.
    - Pickup in core inflationary pressures and persistent elevated services inflation.
    - Fading disinflationary impulses (falling commodity prices, forint appreciation) reveal elevated services inflation.
- Mechanisms for services inflation persistence:
  - Past increases in goods and commodities prices feed through as intermediate inputs.
  - Delayed nominal wage response to higher past inflation.
  - Low relative services prices imply services inflation must remain elevated to restore relative prices.
- Policy-rule implications:
  - Beyond 2025-Q2 the model’s policy rule applies; by 2026 ex-ante real policy rate settles at neutral level of around 2 percent.
  - Model suggests more cautious and somewhat more gradual easing than market path because inflation remains somewhat elevated after external disinflation fades.
  - Welfare comparison: under an unconstrained policy rule (equal weights on inflation and output gap), welfare is improved relative to the baseline market-rate path, despite a slightly more gradual recovery.

### D. Alternative Scenarios and Sensitivities
- Exchange rate risk premium shock:
  - If risk premium rises temporarily by 2½pp (weakening the currency), interest rates should stay elevated longer to partially mitigate inflation from depreciation; growth is weaker as a cost.
  - If risk premium normalizes faster, interest rates can fall toward neutral more quickly.
- Parameter sensitivity scenarios (summary of four illustrated scenarios):
  - Scenario 1: Services inflation persistence increased by 50 percent (strong second-round effects via wage growth/price indexation).
    - Result: higher inflation forecast; interest rates remain tighter through 2024-25; neutral level not reached until 2026.
  - Scenario 2: Policymaker places higher weight on output in policy rule (equal to inflation) with little interest rate smoothing.
    - Result: interest rates fall faster in 2024, closing output gap slightly faster but causing higher inflation; expectations lead to more restrictive rates later; welfare lower despite stronger growth.
  - Scenario 3: Longer lags of monetary policy transmission to output (weaker housing-channel transmission).
    - Result: output recovers more slowly; little change in policy rate path due to low Phillips curve slope; inflation projection little changed.
  - Scenario 4: Trend real rate (r*) is 1 percent lower than estimated.
    - Result: lower path for interest rates over projection; little change to output gap or inflation paths.

### E. Fan Charts and Uncertainty
- Fan chart construction:
  - Bands produced using bootstrap: residuals sampled randomly with replacement and used to shock the model quarter-by-quarter.
  - Observations during 2020-21 are excluded from sampling.
  - Fan chart for interest rates assumes no shocks to future policy rate; monetary policy reacts endogenously to drawn shocks each period.
- Key observations:
  - Fan charts are wide → high uncertainty around projections.
  - Inflation fan chart is asymmetric: mean projection lies above the baseline.
    - Reason: incidence of large supply shocks increasing inflation in recent data.
    - Implication: risks to baseline inflation may be skewed to the upside.
  - Communication of future policy path should convey substantial uncertainty.
  - Policy implication: monetary policy should loosen but cautiously given the chance of persistent or recurrent supply shocks.

### F. Impulse Response Functions
- Monetary policy shock (summary of Figure 5 results):
  - A 1pp temporary but persistent increase in the policy rate:
    - Reduces level of output by around 0.15 percent.
    - Reduces inflation by a peak of 0.4pp.
    - Peak inflation impact occurs under a year → low sacrifice ratio.
  - Exchange rate channel importance:
    - Large share of tradables in CPI: 74 percent goods vs 55 percent in the euro area.
- Core goods inflation shock and sectoral spillovers (summary of Figure 6 results):
  - A cost-push shock in core goods temporarily increases core goods inflation.
  - Through higher overall price level and subsequent nominal wage adjustment, services marginal costs rise, increasing services prices.
  - Result: a temporary goods-sector shock induces a smaller but persistent increase in services inflation, delaying return to target.
  - With a monetary policy response, CPI inflation returns to target in two years.
  - If policy response is delayed by one year, inflation takes an additional year to return to target.

### G. Conclusions and Policy Messages (Monetary Policy)
- QPM provides a quantitative guide for calibrating monetary policy amid large shocks; interest rates are endogenous and projections are forward-looking and internally consistent.
- Baseline (market path) implies gradual easing: rates to 6¼ percent in 2024-Q4 and 5¾ percent by 2025-Q2, but inflation may remain above target (4.2 percent by end-2024).
- The model’s unconstrained policy rule advocates slightly tighter policy than the market path to bring inflation closer to target on average in 2024-25, improving welfare despite slower recovery.
- Key risks and operational recommendations:
  - Exchange rate behavior is a binding constraint; temporary rises in exchange rate risk premium (e.g., +2½pp) justify keeping rates elevated longer.
  - Given wide and asymmetric uncertainty (fan charts), policymakers should communicate uncertainty and proceed cautiously when loosening policy.
  - Timely monetary policy response to sectoral cost-push shocks materially shortens the time for inflation to return to target.

### Model structure and calibration (selected technical points)
- Behavioral equations cover aggregate demand and supply, sectoral Phillips curves (five sectors: core services, core goods, unprocessed food, fuel, regulated prices), the Taylor-type policy rule, and UIP with an exchange rate premium.
- Policy rule incorporates interest rate smoothing, a trend real rate pinned to the 10-year BUBOR interest swaps rate, and an inflation measure that strips out indirect taxes (휋휋_CPI_adj).
- Key calibrated/estimated parameters (selected entries preserved verbatim as presented):
  - IS curve: Persistence b1a : 0.5 0.43; Expected output b1b : 0.05 0.05; Interest rate channel b2 : 0.1 0.10; External demand b3 : 0.3 0.40; Weight on real rate gap in MCI b4 : 0.8.
  - Policy rule: Interest rate smoothing g1 : 0.7 0.73; Weight on inflation deviation g2 : 1.2 1.06; Weight on output gap g3 : 0.25 0.31; Weight on exchange rate premium h1 : 0.2.
  - Core services Phillips curve: Persistence α11 : 0.4 0.37; Real marginal costs α12 : 0.1 0.07; Loading on output gap α13 : 0.75.
  - Core goods Phillips curve: Persistence α21 : 0.4 0.52; Real marginal costs α22 : 0.1 0.09; Loading on non-core costs α24 : 0.75 0.83.
  - Exchange rate persistence c1 : 0.3.
- Calibration and estimation:
  - Model calibrated for plausible impulse responses consistent with the literature.
  - Selected parameters estimated over 2006-2024 Q1 using Bayesian techniques with calibrated priors; estimated values generally close to calibrated values.

### Hungary's corporate sector risk: machine learning approach — objectives and findings
- Objectives:
  - i) Explore determinants of firms’ PDs over two decades using firm-specific and macro factors.
  - ii) Examine influence of these determinants on firms’ PDs during and after the pandemic.
- Data and sample:
  - PD estimates from Credit Research Initiative, National University of Singapore (NUS-CRI) with PDs transformed via a logistic (logit) function.
  - Firms’ financial ratios from Orbis; macro variables (GDP growth, 10-year government bond yields, CDS spreads, EUR/HUF) from Haver.
  - Sample period: 2000-2022.
  - Matched sample: 527 firm-year observations, 55 unique firms, average 24 firms per year.
  - Robustness exercise expands sample to listed firms in Bulgaria, Croatia, Czech Republic, Poland, Romania, Slovakia, Slovenia — bringing firms and firm-year observations to 1,182 and 10,086 respectively.
- Methodology and model selection:
  - Candidate ML models: elastic net, decision tree, K-nearest neighbors, random forest.
  - Model selection based on out-of-sample predictive performance via cross-validation (folds by random allocation, firm size, and time).
  - Random forest had the best predictive performance (highest average coefficient of determination across cross-validation schemes).
- Determinants and interpretability (Shapley-value-based):
  - Top contributors to PD predictions (ranked by average absolute contribution):
    - Return on assets (ROA) — firm profitability.
    - Firm size.
    - Cash equivalents to current liabilities (CE/CL) — liquidity buffers.
    - Sovereign risk premia (CDS) — fourth most important factor.
  - Directional and nonlinear effects:
    - High PD risks associated with low ROA, small firm size, low CE/CL.
    - High CDS associated with high PD risks.
    - Long-term interest rates and currency value play a relatively minor role but explain some PD variation.
    - GDP growth has very limited role in predicting corporate risk, possibly due to correlation with firm profitability ratios included in model.
  - Non-linearity and interaction highlights:
    - Contributions to predicted PDs from ROA and firm size fall sharply when returns become positive or firms are sufficiently large.
    - Contributions from sovereign risk premia and long-term interest rates increase substantially when CDS spreads rise above around 170 and when bond yields are higher than 7 percent.
    - Interaction effects: liquidity buffers (higher CE/CL) amplify the risk-reducing effects of profitability and size; larger firms benefit more from declines in long-term interest rates than smaller firms.

### Pandemic-era changes in predicted PDs and main contributors
- Method: Shapley values averaged across firms by year; differences across years capture contributions to changes in predicted PDs.
- At the onset of the pandemic in 2020:
  - Deteriorating profitability contributed the most to the observed rise in Hungarian corporate sector risk in 2020.
  - Other contributors included firms’ liquidity buffers and size, GDP growth, and sovereign risk premia, though to a limited extent.
- In 2021:
  - Reversals in contributions of risk factors occurred.
  - Improvement in firms’ profitability played the most significant role in reducing corporate sector risk, followed by a decline in CDS spreads and improvements in revenue growth and GDP growth.
- 2021–2022 developments:
  - Firm-specific risk factors continued to improve in 2022, but their beneficial effects were more than offset by higher interest rates and rising sovereign risk premia.
  - Monetary tightening in 2022 increased corporate sector risk, notably because many corporate loans are set to mature within the next few years and could be repriced at higher interest rates.
- Robustness:
  - Expanded country-sample checks (regional listed firms) confirm baseline results on determinants and evolution of corporate sector risk.

### AI, green transition, and regional labor markets — model findings and policy propositions
- AI model and main finding:
  - A Cobb-Douglas aggregated task-based model calibrated to Hungary links AI productivity effects to the share of digitally skilled labor in each region.
  - Result: thriving regions are likely to enjoy higher productivity gains from AI, potentially widening regional income disparities.
  - Caveat: AI adoption remains low and model estimates are highly stylized; interpret with caution.
- Mitigation via digital infrastructure investment:
  - Increased investment in digital infrastructure (e.g., internet access and digitized public services) can help narrow income gaps across regions.
  - The IMF AI Preparedness Index is used as a standard indicator in the analysis.
- Green transition patterns and mechanisms:
  - Green transition may deepen disparities due to regional heterogeneity in carbon intensity and employment composition.
  - In Hungary, the green share of total employment tends to be larger in higher-income regions.
  - Greenness of labor markets is positively correlated with educational attainment.
- Policy levers to reduce green-transition disparities:
  - Targeted spending and incentives for green investments.
  - Reskilling workers (training) to reduce disparities in green employment.
  - Prioritizing and incentivizing private R&D investment.
  - Empirical evidence: regressions show training and R&D incentives reduce disparities in regional green job shares.
- Overall conclusion on transitions:
  - Twin digital and green transitions can worsen regional disparities unless policies target digital readiness, green investment, reskilling, and regional governance improvements.

### Final policy recommendations (synthesis)
- Monetary policy:
  - Proceed with gradual and cautious easing relative to market expectations given persistent services inflation and upside risks to inflation.
  - Keep rates elevated longer if exchange rate risk premium rises (e.g., temporary +2½pp) to partially offset depreciation-driven inflation.
  - Communicate uncertainty clearly using fan charts and scenario analysis.
  - Respond promptly to sectoral cost-push shocks to shorten the time for inflation to return to target.
- Corporate-sector monitoring:
  - Monitor interest rate and maturity risks closely given corporate loan maturities and potential repricing at higher rates.
  - Track sovereign risk premia (CDS) as a significant driver of corporate PDs.
  - Strengthen firms’ liquidity buffers and profitability to reduce PD vulnerabilities.
- Regional and structural policies:
  - Invest in digital infrastructure and education in lagging regions to contain AI-induced divergence.
  - Provide incentives for green private investments and green R&D; undertake reskilling programs to facilitate worker transitions.
  - Improve regional governance (anti-corruption, regulatory quality) to promote balanced and sustainable convergence.

*Prepared by Chris Jackson (RES); July 18, 2024. Source: 1hunea2024002-print-pdf.*

### 1. QPM Projections Under the Baseline Monetary Policy Path and an Unconstrained

### MONETARY POLICY ANALYSIS WITH A QUARTERLY PROJECTION MODEL

### A. Introduction
- Interest rates in Hungary rose sharply in response to inflation above 25 percent y/y in 2023-Q1 and large depreciation in the forint.
- The base rate was reduced to 7.0 percent in June 2024 but remains restrictive.
- Reuters survey median expects the policy rate to fall to around 6¼ percent by the end of 2024.
- Balancing risks: loosening too quickly (inflation re-accelerates) vs loosening too slowly (larger output costs) requires careful calibration.

### B. Overview of the Quarterly Projection Model (QPM)
- Model type and features:
  - Semi-structural new-Keynesian model with nominal rigidities and rational expectations.
  - Filters variables into trends and gaps; identifying trends requires judgement.
- Four key equations:
  - IS curve: aggregate demand ↔ real interest rates, credit conditions, exchange rate.
  - Phillips curve: inflation ↔ output gap, exchange rate, relative prices.
  - Policy (Taylor) rule: interest rates respond to expected inflation deviations and output gap.
  - Uncovered interest parity (UIP): exchange rate ↔ expected interest rate differentials and a risk premium.
- Hungary-specific adaptations:
  - Greater sectoral detail for inflation: separation of core goods and services.
  - Exchange rate risk premium explicitly included in the policy rule.
  - Model includes changes in credit spreads and risk-free rates; accounts for interest rate caps affecting transmission.

### C. The QPM and Monetary Policy in the Baseline
- Two projection assumptions:
  - Baseline: conditioned on market participants’ expectations (median Reuters poll).
    - Implies average quarterly interest rates fall to 6¼ percent in 2024-Q4 and 5¾ percent by 2025-Q2.
  - Unconstrained policy rule: interest rates respond endogenously via the model’s Taylor rule.
- Baseline projection outcomes:
  - Inflation picks up from 3.7 percent y/y in 2024 Q1 to 4.2 percent by end-2024, above the tolerance band of the target.
  - Drivers of pickup:
    - Increases in indirect taxes on fuel.
    - Pickup in core inflationary pressures and persistent elevated services inflation.
    - Fading disinflationary impulses (falling commodity prices, forint appreciation) over the forecast reveal elevated services inflation.
  - Mechanisms for services inflation persistence:
    - Past increases in goods and commodities prices feed through as intermediate inputs.
    - Delayed nominal wage response to higher past inflation.
    - Low relative services prices imply services inflation must remain elevated to restore relative prices.
- Policy rule implications:
  - Beyond 2025-Q2 the model’s policy rule applies; by 2026 ex-ante real policy rate settles at neutral level of around 2 percent.
  - Model suggests more cautious and somewhat more gradual easing than market path because inflation remains somewhat elevated after external disinflation fades.
  - Welfare comparison: under an unconstrained policy rule (equal weights on inflation and output gap), welfare is improved relative to the baseline market-rate path, despite a slightly more gradual recovery.

### D. Alternative Scenarios and Sensitivities
- Exchange rate risk premium shock:
  - If risk premium rises temporarily by 2½pp (weakening the currency), interest rates should stay elevated longer to partially mitigate inflation from depreciation; growth is weaker as a cost.
  - If risk premium normalizes faster, interest rates can fall toward neutral more quickly.
- Parameter sensitivity scenarios (illustrated in Figure 3):
  - Scenario 1: Services inflation persistence increased by 50 percent (strong second-round effects via wage growth/price indexation).
    - Results: higher inflation forecast; interest rates remain tighter through 2024-25; neutral level not reached until 2026.
  - Scenario 2: Policymaker places higher weight on output in policy rule (equal to inflation) with little interest rate smoothing.
    - Results: interest rates fall faster in 2024, closing output gap slightly faster but causing higher inflation; expectations lead to more restrictive rates later; welfare lower despite stronger growth.
  - Scenario 3: Longer lags of monetary policy transmission to output (weaker housing-channel transmission).
    - Results: output recovers more slowly; little change in policy rate path due to low Phillips curve slope; inflation projection little changed.
  - Scenario 4: Trend real rate (r*) is 1 percent lower than estimated.
    - Results: lower path for interest rates over projection; little change to output gap or inflation paths.

### E. Fan Charts and Uncertainty
- Fan chart construction:
  - Bands produced using bootstrap: residuals sampled randomly with replacement and used to shock the model quarter-by-quarter.
  - Observations during 2020-21 are excluded from sampling.
  - Fan chart for interest rates assumes no shocks to future policy rate; monetary policy reacts endogenously to drawn shocks each period.
- Key observations:
  - Fan charts are wide → high uncertainty around projections.
  - Inflation fan chart is asymmetric: mean projection lies above the baseline.
    - Reason: incidence of large supply shocks increasing inflation in recent data.
    - Implication: risks to baseline inflation may be skewed to the upside.
  - Communication of future policy path should convey substantial uncertainty.
  - Policy implication: monetary policy should loosen but cautiously given the chance of persistent or recurrent supply shocks.

### F. Impulse Response Functions
- Monetary policy shock (Figure 5):
  - A 1pp temporary but persistent increase in the policy rate:
    - Reduces level of output by around 0.15 percent.
    - Reduces inflation by a peak of 0.4pp.
    - Peak inflation impact occurs under a year → low sacrifice ratio.
  - Exchange rate channel importance:
    - Large share of tradables in CPI: 74 percent goods vs 55 percent in the euro area.
- Core goods inflation shock and sectoral spillovers (Figure 6):
  - A cost-push shock in core goods temporarily increases core goods inflation.
  - Through higher overall price level and subsequent nominal wage adjustment, services marginal costs rise, increasing services prices.
  - Result: a temporary goods-sector shock induces a smaller but persistent increase in services inflation, delaying return to target.
  - With a monetary policy response, CPI inflation returns to target in two years.
  - If policy response is delayed by one year, inflation takes an additional year to return to target.

### G. Conclusions and Policy Messages
- QPM provides a quantitative guide for calibrating monetary policy amid large shocks; interest rates are endogenous and projections are forward-looking and internally consistent.
- Baseline (market path) implies gradual easing: rates to 6¼ percent in 2024-Q4 and 5¾ percent by 2025-Q2, but inflation may remain above target (4.2 percent by end-2024).
- The model’s unconstrained policy rule advocates slightly tighter policy than the market path to bring inflation closer to target on average in 2024-25, improving welfare despite slower recovery.
- Key risks and recommendations:
  - Exchange rate behavior is a binding constraint; temporary rises in exchange rate risk premium (e.g., +2½pp) justify keeping rates elevated longer.
  - Given wide and asymmetric uncertainty (fan charts), policymakers should communicate uncertainty and proceed cautiously when loosening policy.
  - Timely monetary policy response to sectoral cost-push shocks materially shortens the time for inflation to return to target.

*Prepared by Chris Jackson (RES); July 18, 2024.*

### 17.      Following a period of large interest rate reductions, the projections from the QPM

### 17.      Following a period of large interest rate reductions, the projections from the QPM

### Projections and monetary policy implications
- The QPM suggests the next phase of monetary policy normalization should proceed cautiously and more gradually.
- Rationale:
  - The model expects the pace of disinflation to slow as external disinflation forces fade and second-round effects continue to push up services inflation.
  - A more gradual reduction in interest rates than embedded in recent market expectations would deliver a slightly smaller pick-up in inflation at the end of 2024 and inflation closer to target in 2025.
- Caveats and operational guidance:
  - The model may misidentify the size of key “gaps” such as the output or real rate gaps.
  - The model has been adapted to capture some distinct features of the post-Covid inflation surge but is unlikely to capture all due to its reduced form.
  - Results from the model should be used alongside other forms of analysis and expert judgement in determining the optimal path of monetary policy.
  - Data should be watched keenly to assess the realism of the model’s projections.

### Model equations — structure and key mechanisms
- The model consists of four main sets of behavioral equations:
  - Aggregate demand and supply
    - The output gap (푦푦�
푡푡
) is a function of its lag and its expected value, a monetary conditions index (푚푚푚푚푖푖
푡푡
), the foreign output gap (푦푦�
푡푡
∗
) and aggregate demand shocks (휖휖
푡푡
푦푦
�
).
    - Monetary conditions index composition:
      - real interest rate gap (푟푟̂
푡푡
)
      - credit risk premium (푚푚푐푐푟푟푐푐푚푚
푡푡
) — an exchange rate or country-specific risk premium and a domestic premium
      - deviations in the real exchange rate from its trend (푧푧̂
푡푡
)
    - Equations quoted:
      - 푦푦�
푡푡
=푏푏
1푎푎
푦푦�
푡푡−1
+푏푏
1푏푏
퐸퐸
푡푡
푦푦�
푡푡+1
−푏푏
2
푚푚푚푚푖푖
푡푡
+푏푏
3
푦푦�
푡푡
∗
+휖휖
푡푡
푦푦
�
      - 푚푚푚푚푖푖
푡푡
=푏푏
4
(
푟푟̂
푡푡
+푚푚푐푐푟푟푐푐푚푚
푡푡
)
+(1−푏푏
4
)(−푧푧̂
푡푡
)
  - The country risk premium explains deviations in the trend real exchange rate from relative interest rate differentials; the domestic premium reflects the difference between interbank interest rates and bank lending rates charged to the real economy.
  - Phillips curve and relative prices
    - Inflation disaggregated into five sectors: core services, core goods, unprocessed food, fuel, and regulated prices (including gas and electricity).
    - Each sector differs in price stickiness and sensitivity to output gap and external costs; sector inflation dynamics depend on aggregate output gap and relative price gap.
    - Sectoral inflation equation (quarterly annualized, sector j) — new-Keynesian hybrid Phillips curve:
      - 휋휋
푡푡
푗푗
=훼훼
푗푗1
휋휋
푡푡−1
푗푗
+(1−훼훼
푗푗1
)퐸퐸
푡푡
휋휋
푡푡+1
푗푗
+훼훼
푗푗2
푟푟푚푚 푚푚
푡푡
푗푗
+휖휖
푡푡
푗푗
    - Real marginal cost in sector j:
      - 푟푟푚푚 푚푚
푡푡
푗푗
=훼훼
푗푗3
푦푦�
푡푡
+�1−훼훼
푗푗3
�푧푧̂
푡푡
−푟푟푐푐�
푡푡
푗푗
      - Variant forms for specific j (core goods, unprocessed food, fuel, regulated prices) incorporate non-core costs, relevant real commodity price gaps, and sector-specific cost shocks (as explicitly listed in the source).
    - Aggregation of price series uses CPI weights with a persistent measurement error 휂휂
푡푡
:
      - 푐푐
푡푡
=푟푟
푆푆
푐푐
푡푡
푆푆
+푟푟
퐶퐶퐶퐶
푐푐
푡푡
퐶퐶퐶퐶
+푟푟
퐹퐹
푐푐
푡푡
퐹퐹
+푟푟
퐹퐹퐹퐹푛푛퐹퐹
푐푐
푡푡
퐹퐹퐹퐹푛푛 퐹퐹
+푟푟
푅푅푛푛 푅푅
푐푐
푡푡
푅푅푛푛 푅푅
+휂휂
푡푡
    - Relative price gaps constrained to sum to zero (as given verbatim in the source).
  - Interest rates and the policy rule
    - Monetary policy set according to a Taylor rule:
      - 푖푖
푡푡
=푔푔
1
푖푖
푡푡−1
+
(
1−푔푔
1
)(
푖푖
푡푡
푛푛
+푔푔
2
(
퐸퐸
푡푡
휋휋
푡푡+4
퐶퐶퐶퐶
−휋휋�
푡푡+4
)
+푔푔
3
푦푦�
푡푡
+ℎ
1
Δ푐푐푟푟푐푐 푚푚
푡푡
)
+휖휖
푡푡
푖푖
      - 푖푖
푡푡
푛푛
=푟푟̅
푡푡
+퐸퐸
푡푡
휋휋
푡푡+4
퐶퐶퐶퐶
      - 푟푟̅
푡푡
=휌휌
푛푛
̅
푟푟̅
푡푡−1
+
(
1−휌휌
푛푛
̅
)(
10푌푌
푡푡
퐵퐵퐵퐵퐵퐵퐵퐵 푅푅
−휋휋
푡푡
퐶퐶
)
+휖휖
푡푡
푛푛
̅
    - The Taylor rule includes term ℎ
1
Δ 푐푐푟푟푐푐 푚푚
푡푡
to reflect central bank weight on exchange rate stabilization as well as inflation and output.
    - Trend real interest rate pinned down using the 10-year BUBOR interest swaps rate.
    - Policy rule uses an inflation measure that strips out indirect taxes, 휋휋
퐶퐶퐶퐶
.
  - Uncovered interest rate parity (UIP) and the exchange rate
    - Nominal exchange rate (푠푠
푡푡
) determined by UIP with a backward-looking element:
      - 푠푠
푡푡
=
(
1−푐푐
1
)
퐸퐸
푡푡
푠푠
푡푡+1
+푐푐
1
(푠푠
푡푡−1
+
2
(
휋휋�
푡푡
−휋휋�
푡푡
∗
+푧푧̅
푡푡
)
4
+
(
푖푖
푡푡
−푖푖
푡푡
∗
+푐푐푟푟푐푐 푚푚
푡푡
)
+휖휖
푡푡
푠푠
      - Growth in trend real exchange rate (Δ푧푧̅
푡푡
) is AR(1):
        - Δ푧푧̅
푡푡
=휌휌
푧푧
Δ푧푧̅
푡푡−1
+
(
1−휌휌
푧푧
)
Δ푧푧̅
푠푠푠푠
+휖휖
푡푡
푧푧
̅
  - Exchange rate premium captures additional premium for holding the currency beyond real interest rate differential.
  - Foreign variables
    - World block: global real commodity prices – food, oil and natural gas; trends estimated with relevant gaps for domestic pressures.
    - World economy summarized by euro area variables (GDP, headline inflation, ECB’s policy rate, output gap) conditioned on April 2024 WEO projections.
    - Dynamics of world variable gaps generally modelled as AR(1).

### Calibration and impulse responses
- The model is calibrated to produce plausible impulse responses consistent with literature (including Szilágyi et al (2013) and Bék ési et al (2016)).
- Main parameters summarized in Table 1; baseline projections use calibrated model.
- Selected important parameters are estimated over 2006-2024 Q1 using Bayesian techniques with calibrated values as priors; estimated values are in most cases close to calibrated values.

- Table 1. Hungary: QPM Parameters (selected parameters and values as presented)
  - IS curve
    - Persistence 푏푏
1푎푎 : 0.5 0.43
    - Expected output 푏푏
1푏푏 : 0.05 0.05
    - Interest rate channel 푏푏
2 : 0.1 0.10
    - External demand 푏푏
3 : 0.3 0.40
    - Weight on real rate gap in monetary conditions index 푏푏
4 : 0.8
  - Policy rule
    - Interest rate smoothing 푔푔
1 : 0.7 0.73
    - Weight on inflation deviation 푔푔
2 : 1.2 1.06
    - Weight on output gap 푔푔
3 : 0.25 0.31
    - Weight on exchange rate premium ℎ
1 : 0.2
  - Core services Phillips curve
    - Persistence 훼훼
11 : 0.4 0.37
    - Real marginal costs 훼훼
12 : 0.1 0.07
    - Loading on output gap in real marginal costs 훼훼
13 : 0.75
  - Core goods Phillips curve
    - Persistence 훼훼
21 : 0.4 0.52
    - Real marginal costs 훼훼
22 : 0.1 0.09
    - Loading on output gap in real marginal costs 훼훼
23 : 0.2
    - Loading on non-core costs 훼훼
24 : 0.75 0.83
  - Unprocessed food Phillips curve
    - Persistence 훼훼
41 : 0.5 0.27
    - Real marginal costs 훼훼
42 : 0.1 0.15
    - Weight on output gap in real marginal costs 훼훼
43 : 0.3
  - Fuel Phillips curve
    - Persistence 훼훼
41 : 0.3 0.29
    - Real marginal costs 훼훼
42 : 0.4 0.13
    - Loading on output gap in real marginal costs 훼훼
43 : 0.0
  - Regulated prices Phillips curve
    - Persistence 훼훼
15 : 0.1
    - Real marginal costs 훼훼
25 : 0.2
    - Loading on output gap in real marginal costs 훼훼
35 : 0.9
  - Exchange rate
    - Exchange rate persistence 푐푐
1 : 0.3

### Hungary's corporate sector risk: machine learning approach — objectives, data, methodology, and key findings
- Objectives:
  - i) Explore determinants of firms’ PDs over two decades using firm-specific and macro factors.
  - ii) Examine influence of these determinants on firms’ PDs during and after the pandemic.
- Data and sample:
  - PD estimates from Credit Research Initiative, National University of Singapore (NUS-CRI) with PDs transformed via a logistic (logit) function.
  - Firms’ financial ratios from Orbis; macro variables (GDP growth, 10-year government bond yields, CDS spreads, EUR/HUF) from Haver.
  - Sample period: 2000-2022.
  - Matched sample: 527 firm-year observations, 55 unique firms, average 24 firms per year.
  - Robustness exercise expands sample to listed firms in Bulgaria, Croatia, Czech Republic, Poland, Romania, Slovakia, Slovenia — bringing firms and firm-year observations to 1,182 and 10,086 respectively.
- Methodology:
  - Candidate ML models: elastic net, decision tree, K-nearest neighbors, random forest.
  - Model selection based on out-of-sample predictive performance via cross-validation (folds by random allocation, firm size, and time).
  - Random forest had the best predictive performance (highest average coefficient of determination across cross-validation schemes).
- Determinants and interpretability:
  - Random forest results summarized via Shapley values; variables ranked by average absolute contribution to PD predictions.
  - Top contributors:
    - Return on assets (ROA) — firm profitability.
    - Firm size.
    - Cash equivalents to current liabilities (CE/CL) — liquidity buffers.
    - Sovereign risk premia (CDS) — fourth most important factor.
  - Directional effects:
    - High risks associated with low ROA, small firm size, low CE/CL.
    - High CDS associated with high risks.
    - Long-term interest rates and currency value play a relatively minor role but explain some PD variation.
    - GDP growth has very limited role in predicting corporate risk, possibly due to correlation with firm profitability ratios included in model.
  - Non-linearity and interactions (Shapley plots):
    - Contributions to predicted PDs from ROA and firm size fall sharply when returns become positive or firms are sufficiently large.
    - Contributions from sovereign risk premia and long-term interest rates increase substantially when CDS spreads rise above around 170 and when bond yields are higher than 7 percent.
    - Interaction effects:
      - Reduction in contributions of ROA and firm size to PDs is more pronounced for firms with higher CE/CL — higher liquidity buffers amplify beneficial effects of profitability and size.
      - Larger firms benefit more in risk reduction from a decline in long-term interest rates than smaller firms.

*Source: IMF staff analysis as presented in the provided content unit.*

### 10.      Risk indicators deteriorated across the board at the onset of the pandemic before

### 10.      Risk indicators deteriorated across the board at the onset of the pandemic before

### Pandemic-era changes in predicted PDs and main contributors
- Shapley values are additive and averaged across firms for each variable by year; the difference in average Shapley values across two years for a given variable captures that variable’s contribution to the change in the predicted PD between the two years.
- Waterfall-chart analysis (Figure 5) isolates main contributors to the change in predicted PDs:
  - At the onset of the pandemic in 2020:
    - "Deteriorating profitability contributed the most to the observed rise in Hungarian corporate sector risk in 2020."
    - "Other firm-specific and macro factors, namely firms’ liquidity buffers and size, GDP growth, and sovereign risk premia also played a role, although to a limited extent."
  - In 2021:
    - Reversals in contributions of risk factors occurred.
    - "An improvement in firms’ profitability playing the most significant role in reducing corporate sector risk, followed by a decline in CDS spreads and improvements in revenue growth and GDP growth."
- Note on normalization in figures:
  - For the left-hand panel (Between 2019-2020) the average value of the logit PDs across all firms in 2021 is normalized to 0, such that the sum of the individual bars captures the change in the average logit PD across firms between 2021 and 2022.
  - The same treatment applies in the right-hand panel (Between 2020-2021) with the average value of the logit PDs across all firms in 2022 normalized to 0.

### 2021–2022 developments: monetary tightening and sovereign premia
- Firm-specific risk factors continued to improve in 2022, but:
  - "Their beneficial effects were more than offset by higher interest rates and rising sovereign risk premia."
- Key analytical points:
  - "While successful at taming inflationary pressures, our analysis highlights the effects of the significant monetary tightening on corporate sector risk in 2022, especially since this occurred at a time of rising sovereign risk premia."
  - Monitoring priorities going forward:
    - "It would be important to continue monitoring interest rate and maturity risks carefully, since a significant portion of corporate loans are set to mature within the next few years and could be repriced at higher interest rates."
- Figure 6 illustrates contributions to change in predicted logit PD between 2021-2022 with the average value of the logit PDs across all firms in 2021 normalized to 0.

### Robustness checks: expanded country sample
- Two concerns with the baseline sample addressed by expanding the sample of countries:
  - "The sample contains a relatively limited number of firms," potentially limiting variation in dependent and explanatory firm-specific variables.
  - "The focus on only one country also implies relatively limited variations in the values of macroeconomic variables, with each variable only having just over 20 likely non-independent observations."
- Replication on an expanded sample shows:
  - Baseline results are robust regarding "both the general determinants of credit risk as well as the assessment on the evolution of Hungary’s corporate sector risk during and after the pandemic."
- Figures referenced:
  - "Figure 8. Shapley Values of Selected Firm-Specific and Macro Variables (Expanded Sample)"
  - "Figure 7. Contributions to Risk Assessment (Expanded Sample)"
  - "Figure 9. Top Three Contributors to Hungary’s Corporate Sector Risk Evolution (Expanded Sample)"

*Source: IMF staff calculations based on the content provided in the source unit.*

### 15.      Model results point to AI-induced widening in regional labor productivity gaps. To

### 15. Model results point to AI-induced widening in regional labor productivity gaps. To

### AI model, calibration, and main findings
- Cazzaniga and others (2024) employed a Cobb-Douglas aggregated task-based model—à la Acemoglu and Restrepo (2022)—that integrates differences in labor productivity, asset holdings, AI exposure, and the complementarity between human labor and AI.
- The model is calibrated to Hungary, specifically linking the productivity effects of AI7 to the share of digitally skilled labor force in each region.
- The results suggest that thriving regions are likely to enjoy higher productivity gains, potentially widening regional income disparities (Figure 7, left panel).
- A caveat: “With AI technologies still being developed and adoption currently at low levels in many economies, particularly at sub-national levels, model-based estimates of AI-induced productivity are highly stylized and should be interpreted with caution (see Acemoglu, 2024).”

### Mitigation via digital infrastructure investment
- Increased investment in digital infrastructure (e.g., internet access and digitized public services) can help narrow the income gap (Figure 5, right panel).
- The IMF AI Preparedness Index, constructed by Cazzaniga and others (2024), is noted as a standard IMF indicator and is referenced in the text.6

### References and related methodological points cited in the source text
- The modeling approach references Acemoglu and Restrepo (2022) and Acemoglu (2024) for context on tasks, automation, and macroeconomics of AI.
- The source connects region-level AI productivity effects to the share of digitally skilled labor force in each region.

---

### Green transition and regional labor markets

### Patterns and mechanisms
- The green transition may deepen disparities, especially through regional differences in labor market outcomes.
- Local effects of national green policies differ across regions, often depending on regional heterogeneity in carbon intensity of activity and employment.
- In Hungary, the green share of total employment tends to be larger in higher-income regions (Figure 6, left panel).
- The greenness of labor markets is positively correlated with educational attainment (Figure 6, right panel), consistent with literature showing green-intensive jobs provide wage premium (Bergant and others, 2022) largely owing to their higher skill requirement.
- These trends position higher-income regions to thrive in the transition to carbon neutrality, potentially widening regional income disparities (Maucorps and others, 2023).

### Policy levers to reduce green-transition disparities
- Targeted spending and incentives for green investments can help green regional labor markets.
- Reskilling workers (training) can reduce disparities in green employment.
- Prioritizing and incentivizing private R&D investment can also have similar positive effect.
- Empirical approach: the green job share of total employment in each Hungarian region is regressed on controls including the share of workers benefiting from training and R&D spending as separate independent variables; results (in Figure 7) suggest training and R&D incentives reduce disparities.

---

### Conclusions and policy recommendations

### Current convergence and risks
- Hungary’s convergence to the average EU income level is underway, but at a slow and uneven pace amid persistently high regional disparities.
- Budapest and its surrounding areas have surged ahead; many rural and less developed regions have lagged, characterized by low productivity and higher unemployment rates.
- The ongoing twin digital and green transitions could worsen these disparities.
- Budapest and other thriving regions are better positioned to capitalize on emerging opportunities, while lagging regions risk falling further behind amid lower levels of digital readiness and concentration of employment in carbon-intensive, low-value added sectors.

### Recommended policy agenda
- Invest in digital infrastructure and education in lagging regions.
- Provide incentives for green private investments and prioritize green R&D.
- Invest in reskilling workers to transition to greener opportunities.
- Improve governance at the regional level (anti-corruption, regulatory quality of public institutions) to promote dynamism and growth in regional economies.
- Undertake deeper, targeted reforms to facilitate a balanced and sustainable income convergence path.

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*Source: 1hunea2024002-print-pdf - 15.      Model results point to AI-induced widening in regional labor productivity gaps. To*

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_Source: https://www.imf.org/-/media/files/publications/cr/2024/english/1hunea2024002-print-pdf.pdf_