## INTRODUCTION

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---

### Estimation: approaches, data, and challenges
- Estimation focus: how equilibrium interest rates are estimated for the euro area.
- Five common estimation approaches:
  - Univariate Statistical Filters (trend component of real rates; can include stochastic volatility).
  - VAR Models (multi-variable trends and cyclical components; can have time-varying parameters).
  - Semi-Structural Models (reduced-form relationships with economic structure; HLW frameworks).
  - Fully Structural Models (endogenous dynamics from optimizing agents; overlapping generations, DSGE).
  - Term Structure Models (decompose yield curve to infer expected future short-term risk-free rates and term premia).
- Open-economy extensions: factor VARs, open HLW variants, open-economy DSGEs.
- Data and sample:
  - Estimation period: 1995Q1 to 2024Q4.
  - Key series and definitions: seasonally adjusted HICP excluding energy and unprocessed food (Eurostat); real GDP adjusted for initial Covid-19 shock (Lenza and Primiceri 2022); primarily 3-month money market rate spliced with Krippner’s (2013) shadow rate for 2011Q2 to 2023Q1; GDP-weighted 10-year government bond yield; CPI-based real effective exchange rate with 120 trading partners; Brent oil prices; import/export prices and terms of trade; dynamically weighted 1-year and 2-year ahead Consensus Economics inflation expectations (earlier periods use GDP-weighted average of Germany, Italy, France, Spain).
  - Sensitivity checks: backward-looking inflation expectations; omitting the shadow rate adjustment.
- Measurement challenges and identification issues:
  - Equilibrium rates are unobservable, producing identification challenges in models with more shocks than observables.
  - Econometric issues: robustness to misspecification, sample dependence, reliance on identification assumptions, parameter uncertainty, structural shifts, and low power.
  - Many established models perform poorly on at least one dimension (e.g., Buncic et al. 2024).
- Role of foreign developments:
  - Ex-ante real interest rates in the United States explain nearly 40 percent of variation in euro area ex-ante real rates on average; country range between 57 percent (Finland) and 2 percent (Slovakia).
  - Global real and equilibrium rates share significant common trends.

### Results — closed economy estimates (high-level)
- Univariate stochastic volatility model (Beyer and Milivojevic 2023):
  - Baseline: trend real rate fell from just below 1 percent in 1995 to around -1 percent in 2016, stabilized, and slightly increased recently.
  - Backward-looking inflation expectations: decline from over 2 percent to below -2 percent.
  - Ignoring QE (policy rate instead of shadow rate): near-parallel upward shift of about 0.6 percentage points.
  - Baseline estimate for end-2024: -1.0 percent.
- VAR model (Del Negro et al. 2017):
  - Updated baseline: starts at 1.5 percent in 1995, falls to around 1 percent in the 2000s, declines close to 0 percent before COVID-19, and stays near 0 thereafter.
  - Versions with backward-looking expectations behave similarly to univariate filters.
- Semi-structural HLW (HLW2017 / HLW2023):
  - Medium- to long-run concept driven by trend growth and temporary factors.
  - Rates around 2 percent until the Global Financial Crisis, around 0 before COVID-19; strong increase early 2022 to mid-2023 then quick fall.
  - HLW2023 COVID control reduces fluctuation; authors’ average standard error: 3.4 percent; jumps to 5.0 percent for 24Q4.
- DSGE (Neri and Gerali 2019):
  - Short-term efficient rate with largest fluctuations: 4.4 percent before the Global Financial Crisis; below 0 percent thereafter; below -6.0 percent during the European Debt Crisis; 5.3 percent during 2022 inflation; 0.8 percent at end-2024.
  - Most variation explained by the risk premium shock.

### Results — open economy estimates (high-level)
- Factor VAR with common factor (Del Negro et al. 2019):
  - Baseline: falls from 1.5 percent in 1995 to 0 percent in 2005, remains around 0, then declines to -1 percent between 2015 and 2020 and stabilizes at that level.
- Ferreira and Shousha (2023) state-space model with spillovers:
  - Dynamics: drop into negative territory in 2005, increase from 2017 and reach 1 percent at end of sample.
  - Historical decomposition drivers (changes, in percent) for periods 1995-1999, 2000-2004, 2005-2009, 2010-2014, 2015-2019, 2020-2024:
    - Safe Asset Supply: -0.1, -0.2, 0.4, 0.3, 0.4, 0.8
    - Safe Asset Demand: 0.0, -0.1, -0.1, -0.1, 0.0, 0.1
    - Convenience Yield: -0.5, 0.1, -0.3, -0.4, 0.4, 1.0
    - Productivity: -0.5, -0.4, -0.2, 0.2, -0.2, -0.2
    - Working Age Share: 0.0, 0.0, -0.1, -0.2, -0.2, -0.3
    - Global Spillovers: 0.2, -0.2, -0.7, 0.0, 0.0, -0.1
    - Other Factors: 0.0, -0.1, -0.2, -0.1, 0.1, 0.3
    - Total Change: -0.9, -0.7, -1.2, -0.2, 0.6, 1.6
- HLW2017 with foreign trend growth (Wynne and Zhang 2018):
  - Slightly higher point estimates than closed HLW; foreign trend growth adds around 0.5 percentage points to the euro area natural rate.
- Small open-economy DSGE (Zhang et al. 2021):
  - Equilibrium rate slowly declined from around 4 percent in 1995 to around 2 percent pre-Global Financial Crisis, dropped significantly below 0 percent, then increased sharply during recent inflation; end-sample baseline: 1.7 percent.
  - Ignoring the effective lower bound yields end-sample estimate 1.1 percent.
  - Variance decomposition: foreign growth explains about half of short-horizon variation and about 90 percent in the long run.

### Comparison of estimates and key statistics
- Range of estimated equilibrium rates in 2024Q4: -1.2 to 1.7 percent.
- Table of means, standard deviations, and 24Q4 baseline estimates (values preserved exactly):
  - Closed economy
    - Univariate SV Model (Beyer and Milivojevic (2023)): Mean -0.15; St.D. 0.53; 24Q4 -1.15
    - VAR (Del Negro et al. (2017)): Mean 0.86; St.D. 0.43; 24Q4 0.13
    - Semi Structural (Holston, Laubach, Williams (2023)): Mean 1.26; St.D. 0.87; 24Q4 -0.14
    - Our estimation of HLW2017: Mean 1.04; St.D. 1.38; 24Q4 0.77
    - DSGE model (Neri and Gerali (2019)): Mean -0.72; St.D. 3.18; 24Q4 0.83
  - Open economy
    - Factor VARs with CF (Del Negro et al. (2019)): Mean -0.04; St.D. 0.73; 24Q4 -1.15
    - HLW2017 with foreign growth (Wynne and Zhang (2018)): Mean 1.26; St.D. 1.48; 24Q4 0.55
    - VAR with Spillovers (Ferreira and Shousha (2023)): Mean -0.02; St.D. 0.94; 24Q4 1.04
    - Small DSGE (Zhang et al. (2021)): Mean -0.00; St.D. 2.29; 24Q4 1.71
  - Market implied (term structure models, IMF internal)
    - TSM: 5y5y: Mean -1.05; St.D. 0.30; 24Q4 -0.81
    - TSM: 1y5y: Mean -1.02; St.D. 0.47; 24Q4 -0.65
    - TSM: 1y1y: Mean -0.95; St.D. 1.19; 24Q4 -0.03
  - Note: “The mean and standard deviation refer to the baseline equilibrium rate over the entire period.”
- Estimation uncertainty:
  - HLW2023 authors’ standard errors: ±5 percent for 2024Q4.
  - Sensitivity to data definitions, starting values, priors, and sample composition varies across models:
    - Univariate filters: least affected by sample length adjustments.
    - VARs: more stable, especially with time-varying parameters.
    - HLW semi-structural variants: very sensitive to sample changes.
    - DSGE models tested: relatively robust but still exhibit parameter sensitivity.

### Comparison with implicit ECB and market expectations
- Implicit ECB neutral rate approximation:
  - With inflation at target in 2026 and a small negative output gap in IMF forecast (0 percent output gap in European Commission’s Autumn 2024 forecast), ECB projections suggest an implicit neutral euro area real rate of around 0.1 percent in 2026.
  - This implicit prediction varied in 2024 from 0.6 percent in June to 0.1 percent in December.
- Market-implied term structure measures:
  - The 1y1y market-implied risk-free rate is currently around 0 percent; 1y5y and 5y5y implied rates remain negative.
  - Markets expect the equilibrium rate to decline in 2025 and to remain negative in the future.
- Caveats:
  - No consensus on the best term structure model to identify the short-term risk-free rate and correct term premium.
  - Short-maturity market rates largely reflect central bank guidance.

### Implications — ranking, criteria, and model use
- Three proposed criteria for policy use:
  - (i) Conceptual fitness for purpose (time horizon relevance).
  - (ii) Robustness of the estimate.
  - (iii) Consistency of implied results with external indicators; assign more weight to estimates aligned with broader economic evidence.
- Complementary disciplines when model uncertainty is high:
  - Employment, productivity, income inequality, government saving, and uncertainty measures to inform judgment.
  - Qualitative assessment of drivers of investment and savings.
  - Expected directional effects:
    - Sustained debt-financed public spending should push equilibrium rates up.
    - High productivity growth or a larger workforce raises the neutral rate.
    - Increased inequality lowers it.
    - Heightened risk perceptions raise precautionary saving and lower rates.
- Illustrative model evaluation (horizon, robustness, notes):
  - Closed economy
    - Univariate SV Model (Beyer & Milivojevic): long horizon; robustness: good; note: No economic structure
    - VAR (Del Negro et al.): long horizon; robustness: good; note: Little economic structure
    - Semi Structural (HLW): medium horizon; robustness: weak; note: Large role of temporary factors
    - DSGE (Neri & Gerali): short horizon; robustness: medium; note: Large role for risk premium shocks
  - Open economy
    - Factor VARs with CF (Del Negro et al.): long; good; Little economic structure
    - VAR with Spillovers (Ferreira & Shousha): medium; good; A lot of economic structure
    - HLW2017 with PS (Wynne & Zhang): medium; weak; Little variation of spillovers
    - Small DSGE (Zhang et al.): short; good; No impact of EA on international prices
  - Market implied (TSM)
    - 5y5y: long; medium; Depends on CB guidance
    - 1y5y: medium; medium; Depends on CB guidance
    - 1y1y: short; medium; Depends strongly on CB guidance

### Policy approaches to model uncertainty
- Three practical approaches:
  - Abandon the neutral rate and adopt a gaps approach (Svensson 2003):
    - Policy rule depends on forecasted inflation gap and forecasted deviation of output growth from trend growth.
  - Model averaging (e.g., Bayesian model averaging):
    - Policy rule is a weighted average across model-specific optimal rules.
  - Robust control / max-min approach (Orphanides and Williams 2007):
    - Choose the optimal rule under the worst-case model; penalized variants restrict worst-case search to models close to baseline (entropy ball approach).

### Implications for the current monetary stance and near-term judgment
- Guidance for policy:
  - Short- to medium-term equilibrium rate measures with diverse drivers are most useful for guiding policy.
  - HLW2017 and related medium-term estimates serve as a lower bound; short-term DSGE estimates provide an upper bound for the short-term neutral rate.
  - A short-run neutral rate above 0 percent but below 1 percent aligns with 2024 point estimates.
  - Given model sensitivity, do not overweight highly data-sensitive estimates.
  - Observable trends (weaker-than-expected investment in the euro area and low loan demand) suggest the neutral rate may be lower than one year ago.
- Judgmental assessment in the paper:
  - The real neutral rate at the one-year horizon could now be between 0 and 0.25 percent, implying a monetary stance close to neutral in April 2025.
  - This range aligns with Brand, Lisack, and Mazelis (2025) ranges: -0.5 to 0.5 percent excluding HLW2017, and -0.5 to 1 percent including HLW2017.

### Implications for future equilibrium rates
- Recent hikes in equilibrium rates are likely temporary; longer-term estimates have stabilized.
- Forces likely to decrease equilibrium rates:
  - Trade fragmentation and financial fragmentation; regional effects could range from a 40-bps decline to a 20-bps increase (IMF 2023).
  - Demographic aging and increased longevity may reduce rates; immigration could offset or reverse this; net effect uncertain—could lower equilibrium rates by around 0.5 percentage points by 2030 (Bodnár and Nerlich 2022).
- Forces likely to increase equilibrium rates:
  - Potential productivity gains from AI could raise consumption, investment, GDP, and inflation.
  - Reduced convenience yield on advanced-economy sovereign bonds would raise equilibrium rates.
  - Higher defense spending financed by deficits could raise rates; crowding out could reduce them.
  - A reversal of elevated markups and higher labor shares could raise the equilibrium rate by 6 to 19 basis points by 2050 (IMF 2023).
- Net outlook:
  - Slow-moving forces push in opposite directions; net impact likely tilted to the upside, but market-implied 5y5y rates remain negative.

### Annex: some more model details (selected technical points)
- Univariate Stochastic Volatility specification:
  - rt = rt* + r̃t
  - rt* = rt−1* + et, with eit ~ N(0,σe2)
  - r̃t = εit √e^{lnht}, with εit ~ N(0,1)
  - lnht = α01 + α1 lnht−1 + vt, with vit ~ N(0,σv2)
  - Bayesian MCMC; quarterly data from 1990Q1 to 2024Q3; priors and procedure follow Beyer and Milivojevic (2023).
- VAR (Del Negro et al. 2017) identification highlights:
  - Observables: yt = (πt, πte, it3m, ite, it10y)
  - Measurement: yt = Λy̅t + ỹt, with trends y̅t = (πt*, rt*, tpt*)
  - Identification via Fisher-type relations linking nominal short-term rate, trend inflation, and equilibrium rate.
  - Estimated from 1999Q1 to 2024Q3 using Haver.
- HLW model key relations:
  - yt = yt* + ỹt
  - πt = bπ πt−1 + (1−bπ) πt−1,4 + by ỹt + επt
  - ỹt dynamics with lagged gaps and r deviations.
  - y*t = y*t−1 + gt−1 + εt y*
  - gt = gt−1 + εt g
  - zt = zt−1 + εt z
  - rt* = c gt + zt, c>0
  - Used IMF (2023) code for estimation from 1995Q1.
- Neri and Gerali (2019) DSGE:
  - Representative household optimizing consumption, labor, capital, investment, safe nominal bond.
  - Firms with Cobb-Douglas production, monopolistic competition, staggered pricing, mark-up shocks.
  - Neutral rate: real short-term rate where output equals flexible-price output and inflation equals central bank target across periods and shocks.
  - Seven observables at annual frequency; estimated in Dynare with Bayesian methods.
- Open-economy model highlights:
  - Del Negro et al. (2019): adds common trend across Euro Area and a global factor jointly estimated with US.
  - Wynne and Zhang (2018): r^{h,*}_t = c_h^h g_t^h + c_f^h g_t^f + z_t^h; foreign region is GDP-weighted average covering ~70 percent of world GDP.
  - Ferreira and Shousha (2023): state representation with cyclical components (û_{j,t}, π̂_{j,t}, î_{j,t}) and trends X_{j,t}^{u}, X_{j,t}^{m}, X_{j,t}^{r}; determinants of longer-run neutral rates include ∆pt_{j,t}, ∆ωs_{j,t}, ∆cy_{t}, ∆ss_{t}, ∆sd_{t}, and g_{j,t−1}.
  - Zhang et al. (2021): small open-economy NK model with non-stationary productivity shock; equilibrium rate depends on forecastable components of productivity growth, preferences, and world output growth.

*Source: IMF Working Paper — Introduction (Real Equilibrium Interest Rates in the Euro Area), wpiea2025123-print-pdf.*

### INTRODUCTION _________________________________________________________________ 3

### INTRODUCTION _________________________________________________________________ 3

### Estimation
- Subsections listed: Notable Features; Estimation Strategies; Data.
- Indicates methodological focus on how equilibrium interest rates are estimated for the euro area.

### Results
- Subsections listed: Closed Economy Estimates; Open Economy Estimates; Comparison; Comparison with Implicit ECB and Market Expectations.
- Implies presentation of model estimates and cross-model comparisons for euro area equilibrium rates.

### Implications
- Subsections listed: A Ranking of Estimates; Implications for Monetary Policy; Implications for the Current Monetary Stance; Implications for Equilibrium Rates in the Future.
- Signals discussion of policy relevance and forward-looking implications of the estimated equilibrium rates.

### Conclusion
- Final synthesis and closing remarks are indicated under CONCLUSION.

### Supporting material listed in the unit
- Figures enumerated (by title): Closed Economy Estimates of Euro Area Equilibrium Rates; Drivers of HLW2017 and Neri and Gerali (2019) Estimates; Open-economy Models; Drivers of Wynne and Zhang’s (2018); Policy and Short-term Efficient Rates; Implicit ECB and Market Expectations About Equilibrium Interest Rates; Investment in Euro Area and U.S.
- Tables enumerated (by title): Driver of the Equilibrium Rate in Ferreira and Shousha (2023) Over Time; Overview of Latest Estimates of Different Estimations; Criteria to Assess Models.
- Annex: Some More Model Details.

*Source: https://www.imf.org/-/media/files/publications/wp/2025/english/wpiea2025123-print-pdf.pdf*

### Introduction

### Introduction

### Motivation and definitions
- Renewed interest in equilibrium interest rates stems from:
  - Inflation in the euro area approaching its target and a shift of attention to the short-term neutral rate—the policy interest rate that is neither restrictive nor accommodative (Kaplan 2018).
  - Debate on secular stagnation shifting toward a potential rise in long-term equilibrium rates due to increased public spending on climate and defense and possible productivity boosts from wider use of artificial intelligence (Schnabel 2025).
- The equilibrium rate is not singular; definitions vary by time horizon and model:
  - In a neoclassical growth model, it is a very long-term constant jointly determined by the discount factor and productivity growth.
  - Semi-structural models (e.g., HLW2017 and HLW2023) estimate a policy-relevant medium-term neutral rate linked to time-varying trend growth and temporary factors.
  - Short-term hypothetical rates from DSGE models (Platzer et al. 2022) can be interpreted as neutral in a frictionless setting; policy rates following such rates may act as bounds on the neutral rate depending on shocks.
  - The short-term efficient rate (Curdia 2015; Barsky 2024) denotes the rate that yields efficient stabilization when the central bank has complete information.

### Four main findings (as stated)
- Estimates for the euro area using different methods vary significantly, but two general patterns emerge:
  - Current short-term equilibrium rates mostly exceed longer-term rates.
  - Foreign spillovers contribute positively to euro area equilibrium rates.
- Different equilibrium rate estimates serve distinct purposes:
  - Longer-term measures inform the likelihood of hitting the effective lower bound and fiscal sustainability.
  - Short-term estimates guide policy rates and the monetary stance.
- A judgement-based assessment should evaluate individual estimates by time horizon, robustness, and consistency with other economic information; using this approach, the paper assesses the real short-term neutral rate at the end of 2024 to likely be around 0 to 0.25 percent.
- The paper discusses how to incorporate uncertainty about equilibrium real rates drawing on model uncertainty literature.

### Notable features and measurement challenges
- The short-term neutral rate can fluctuate strongly due to fiscal policy, risk appetite, financial conditions, capital flows, and the degree of anchoring of inflation expectations (Obstfeld 2023).
  - Example: during the recent ECB tightening episode, real interest rates had to increase significantly above pre-pandemic medium-term neutral rate estimates to become restrictive (IMF 2024); drivers included expansionary fiscal policy and slower pass-through of policy rate hikes to bank rates (Beyer et al. 2024).
- Estimation is difficult because equilibrium rates are unobservable, creating:
  - Identification challenges in models with more shocks than observables.
  - Econometric issues: robustness to misspecification, sample dependence, reliance on identification assumptions, parameter uncertainty, structural shifts, and low power.
  - Many established models perform poorly on at least one of these dimensions (e.g., Buncic et al. 2024).
- Foreign developments and spillovers are crucial:
  - Ex-ante real interest rates in the United States explain nearly 40 percent of the variation in euro area ex-ante real rates on average; the share ranges between 57 percent (Finland) and 2 percent (Slovakia).
  - Global real and equilibrium rates share significant common trends; past factors (e.g., China's savings surplus) may have lowered global rates, while robust U.S. growth and expansionary fiscal policy could elevate them.

### Estimation strategies and data
- Five common estimation approaches:
  - Univariate Statistical Filters (trend component of real rates; can include stochastic volatility).
  - VAR Models (multi-variable trends and cyclical components; can have time-varying parameters).
  - Semi-Structural Models (reduced-form relationships with economic structure; HLW frameworks).
  - Fully Structural Models (endogenous dynamics from optimizing agents; overlapping generations, DSGE).
  - Term Structure Models (decompose yield curve to infer expected future short-term risk-free rates and term premia).
- Open-economy extensions exist across approaches (factor VARs, open HLW variants, open-economy DSGEs).
- Data and sample:
  - Estimation period: 1995Q1 to 2024Q4.
  - Primary sources and definitions:
    - Inflation: seasonally adjusted HICP excluding energy and unprocessed food (Eurostat).
    - Real GDP: adjusted for the initial Covid-19 shock (Lenza and Primiceri 2022).
    - Interest rates: primarily the 3-month money market rate, spliced with Krippner’s (2013) shadow rate for 2011Q2 to 2023Q1 to account for QE.
    - Long-term rate: GDP-weighted 10-year government bond yield of selected euro area economies.
    - Real effective exchange rate: CPI-based with 120 trading partners.
    - Brent oil prices; import/export prices and terms of trade.
    - Inflation expectations: dynamically weighted 1-year and 2-year ahead from Consensus Economics; earlier periods use a GDP-weighted average of Germany, Italy, France, and Spain.
  - Sensitivity checks include using backward-looking inflation expectations and omitting the shadow rate adjustment.

### Results — closed economy models (high-level)
- Univariate stochastic volatility model (Beyer and Milivojevic 2023):
  - Baseline: trend real rate fell from just below 1 percent in 1995 to around -1 percent in 2016, stabilized, and slightly increased recently.
  - Using backward-looking inflation expectations yields a decline from over 2 percent to below -2 percent.
  - Ignoring QE (policy rate instead of shadow rate) produces a near-parallel upward shift of about 0.6 percentage points.
  - Baseline estimate for end-2024: -1.0 percent.
- VAR model (Del Negro et al. 2017):
  - Updated baseline: starts at 1.5 percent in 1995, falls to around 1 percent in the 2000s, declines close to 0 percent before COVID-19, and stays near 0 thereafter.
  - Versions with backward-looking expectations behave similarly to univariate filters.
- Semi-structural HLW (HLW2017 / HLW2023):
  - Medium- to long-run concept driven by trend growth and temporary factors.
  - Rates around 2 percent until the Global Financial Crisis, around 0 before COVID-19; strong increase early 2022 to mid-2023 then quick fall.
  - HLW2023's COVID control reduces fluctuation; estimates feature very wide error bands (authors’ average standard error: 3.4 percent; jumps to 5.0 percent for 24Q4).
- DSGE (Neri and Gerali 2019):
  - Short-term efficient rate with largest fluctuations.
  - Reached 4.4 percent before the Global Financial Crisis, dropped below 0 percent thereafter, fell below -6.0 percent during the European Debt Crisis, rose to 5.3 percent during 2022 inflation, and was 0.8 percent at end-2024.
  - Most variation explained by the risk premium shock.

### Results — open economy models (high-level)
- Factor VAR with common factor (Del Negro et al. 2019, applied to EA and US):
  - Baseline: falls from 1.5 percent in 1995 to 0 percent in 2005, remains around 0, then declines to -1 percent between 2015 and 2020 and stabilizes at that level.
- Ferreira and Shousha (2023) state-space model with spillovers:
  - Dynamics similar early on, drop into negative territory in 2005, then increase from 2017 and reach 1 percent at end of sample.
  - Historical decomposition drivers (Table 1 in source) for 1995-1999 through 2020-2024 (values are changes, in percent):
    - Safe Asset Supply: -0.1, -0.2, 0.4, 0.3, 0.4, 0.8
    - Safe Asset Demand: 0.0, -0.1, -0.1, -0.1, 0.0, 0.1
    - Convenience Yield: -0.5, 0.1, -0.3, -0.4, 0.4, 1.0
    - Productivity: -0.5, -0.4, -0.2, 0.2, -0.2, -0.2
    - Working Age Share: 0.0, 0.0, -0.1, -0.2, -0.2, -0.3
    - Global Spillovers: 0.2, -0.2, -0.7, 0.0, 0.0, -0.1
    - Other Factors: 0.0, -0.1, -0.2, -0.1, 0.1, 0.3
    - Total Change: -0.9, -0.7, -1.2, -0.2, 0.6, 1.6
- HLW2017 with foreign trend growth (Wynne and Zhang 2018):
  - Slightly higher point estimates than closed HLW but not statistically different given wide confidence bands; foreign trend growth adds around 0.5 percentage points to the euro area natural rate.
- Small open-economy DSGE (Zhang et al. 2021):
  - Equilibrium rate slowly declined from around 4 percent in 1995 to around 2 percent pre-Global Financial Crisis, dropped significantly below 0 percent, then increased sharply during recent inflation; end-sample baseline: 1.7 percent.
  - Ignoring the effective lower bound yields end-sample estimate 1.1 percent.
  - Variance decomposition: foreign growth explains about half of short-horizon variation and about 90 percent in the long run.

### Comparison of estimates and key statistics
- Range of estimated equilibrium rates in 2024Q4: -1.2 to 1.7 percent.
- Table of means, standard deviations, and 24Q4 baseline estimates (values preserved exactly as in source):
  - Closed economy
    - Univariate SV Model (Beyer and Milivojevic (2023)): Mean -0.15; St.D. 0.53; 24Q4 -1.15
    - VAR (Del Negro et al. (2017)): Mean 0.86; St.D. 0.43; 24Q4 0.13
    - Semi Structural (Holston, Laubach, Williams (2023)): Mean 1.26; St.D. 0.87; 24Q4 -0.14
    - Our estimation of HLW2017: Mean 1.04; St.D. 1.38; 24Q4 0.77
    - DSGE model (Neri and Gerali (2019)): Mean -0.72; St.D. 3.18; 24Q4 0.83
  - Open economy
    - Factor VARs with CF (Del Negro et al. (2019)): Mean -0.04; St.D. 0.73; 24Q4 -1.15
    - HLW2017 with foreign growth (Wynne and Zhang (2018)): Mean 1.26; St.D. 1.48; 24Q4 0.55
    - VAR with Spillovers (Ferreira and Shousha (2023)): Mean -0.02; St.D. 0.94; 24Q4 1.04
    - Small DSGE (Zhang et al. (2021)): Mean -0.00; St.D. 2.29; 24Q4 1.71
  - Market implied (term structure models, IMF internal)
    - TSM: 5y5y: Mean -1.05; St.D. 0.30; 24Q4 -0.81
    - TSM: 1y5y: Mean -1.02; St.D. 0.47; 24Q4 -0.65
    - TSM: 1y1y: Mean -0.95; St.D. 1.19; 24Q4 -0.03
  - Note: “The mean and standard deviation refer to the baseline equilibrium rate over the entire period.”
- Estimation uncertainty is very high:
  - Example: HLW2023 authors’ standard errors ±5 percent for 2024Q4.
  - Sensitivity to data definitions, starting values, priors, and sample composition varies across models:
    - Univariate filters: least affected by sample length adjustments.
    - VARs: more stable, especially with time-varying parameters.
    - HLW semi-structural variants: very sensitive to sample changes.
    - DSGE models tested: relatively robust but still exhibit parameter sensitivity.

### Comparison with implicit ECB and market expectations
- Implicit ECB neutral rate approximation:
  - With inflation at target in 2026 and a small negative output gap in IMF forecast (0 percent output gap in European Commission’s Autumn 2024 forecast), ECB projections suggest an implicit neutral euro area real rate of around 0.1 percent in 2026.
  - This implicit prediction varied in 2024 from 0.6 percent in June to 0.1 percent in December.
- Market-implied term structure measures:
  - The 1y1y market-implied risk-free rate (one year ahead for one year) is conceptually closest to the short-term efficient rate two periods ahead in DSGE models; currently around 0 percent (market-implied rate considerably lower than DSGE short-term efficient rate).
  - 1y5y and 5y5y implied rates remain negative.
  - Markets expect the equilibrium rate to decline in 2025 and to remain negative in the future, consistent with some negative longer-run model estimates.
- Caveats on market-based measures:
  - No consensus on the best term structure model to identify the short-term risk-free rate and correct term premium.
  - Short-maturity market rates largely reflect central bank guidance, complicating use for independent estimates of equilibrium rates.

### Implications — ranking and criteria for model use
- Proposed three criteria to assess estimates for policy use:
  - (i) Conceptual fitness for purpose (time horizon relevance).
  - (ii) Robustness of the estimate.
  - (iii) Consistency of implied results (e.g., implied monetary stance, output gap) with external indicators; assign more weight to estimates aligned with broader economic evidence.
- Complementary disciplines when model uncertainty is high:
  - Use employment, productivity, income inequality, government saving, and uncertainty measures to inform judgment.
  - Qualitative assessment of drivers of investment and savings helps indicate likely trends of the neutral rate (demand and supply of loanable funds).
  - Sustained debt-financed public spending should push equilibrium rates up; high productivity growth or a larger workforce raises the neutral rate; increased inequality lowers it; heightened risk perceptions raise precautionary saving and lower rates.

- Table of criteria (summary as in source) — illustrative model evaluation (horizon, robustness, notes):
  - Closed economy
    - Univariate SV Model (Beyer & Milivojevic): long horizon; robustness: good; note: No economic structure
    - VAR (Del Negro et al.): long horizon; robustness: good; note: Little economic structure
    - Semi Structural (HLW): medium horizon; robustness: weak; note: Large role of temporary factors
    - DSGE (Neri & Gerali): short horizon; robustness: medium; note: Large role for risk premium shocks
  - Open economy
    - Factor VARs with CF (Del Negro et al.): long; good; Little economic structure
    - VAR with Spillovers (Ferreira & Shousha): medium; good; A lot of economic structure
    - HLW2017 with PS (Wynne & Zhang): medium; weak; Little variation of spillovers
    - Small DSGE (Zhang et al.): short; good; No impact of EA on international prices
  - Market implied (TSM)
    - 5y5y: long; medium; Depends on CB guidance
    - 1y5y: medium; medium; Depends on CB guidance
    - 1y1y: short; medium; Depends strongly on CB guidance

### Policy approaches to model uncertainty
- Three practical approaches for central banks handling model uncertainty:
  - Abandon the neutral rate and adopt a gaps approach (Svensson 2003):
    - Policy rule depends on forecasted inflation gap and forecasted deviation of output growth from trend growth.
    - Advantages: avoids latent-variable estimation; drawbacks: simplicity and reliance on judgement.
  - Model averaging (e.g., Bayesian model averaging):
    - Policy rule is a weighted average across model-specific optimal rules.
    - Works if model uncertainty is well-structured and priors are sensible; difficult when model set is vast.
  - Robust control / max-min approach (Orphanides and Williams 2007):
    - Choose the optimal rule under the worst-case model; implies more aggressive response to inflation gaps and greater interest-rate smoothing.
    - Penalized variants restrict the worst-case search to models close to the baseline (entropy ball approach).

### Implications for the current monetary stance and near-term judgment
- Applying the assessment criteria:
  - Short- to medium-term equilibrium rate measures with diverse drivers are most useful for guiding policy.
  - HLW2017 and related medium-term estimates serve as a lower bound; short-term DSGE estimates provide an upper bound for the short-term neutral rate.
  - A short-run neutral rate above 0 percent but below 1 percent aligns with 2024 point estimates.
  - Given model sensitivity (e.g., HLW variants), do not overweight highly data-sensitive estimates.
  - Observable trends (weaker-than-expected investment in the euro area and low loan demand) suggest the neutral rate may be lower than one year ago.
- Judgmental assessment provided in the paper:
  - The real neutral rate at the one-year horizon could now be between 0 and 0.25 percent, implying a monetary stance close to neutral in April 2025.
  - This range aligns with the implicit short-term equilibrium rate discussed earlier and with Brand, Lisack, and Mazelis (2025) ranges: -0.5 to 0.5 percent excluding HLW2017, and -0.5 to 1 percent including HLW2017.

### Implications for future equilibrium rates
- Longer-term estimates have stabilized; recent hikes in equilibrium rates are likely temporary.
- Higher inflation and inflation expectations may have lowered the near-term likelihood of hitting the zero lower bound, but long-term risks of hitting the effective lower bound have not materially changed.
- Forces likely to decrease equilibrium rates:
  - Trade fragmentation and financial fragmentation; regional effects could range from a 40-bps decline to a 20-bps increase (IMF 2023).
  - Demographic aging and increased longevity may reduce rates; immigration could offset or reverse this; net effect uncertain—could lower equilibrium rates by around 0.5 percentage points by 2030 (Bodnár and Nerlich 2022).
- Forces likely to increase equilibrium rates:
  - Potential productivity gains from AI could raise consumption, investment, GDP, and inflation, requiring higher rates (Aldasoro et al. 2024), though euro-area data do not suggest a consumption boom and effects depend on realized productivity gains.
  - Reduced convenience yield on advanced-economy sovereign bonds would raise equilibrium rates.
  - Higher defense spending financed by deficits could raise rates; crowding out could reduce them.
  - A reversal of elevated markups and higher labor shares could raise the equilibrium rate by 6 to 19 basis points by 2050 (IMF 2023).
- Net outlook:
  - Slow-moving forces push in opposite directions; net impact likely tilted to the upside, but market-implied 5y5y rates remain negative, indicating markets do not expect a rebound.
  - Some future changes will be captured by existing models; others may introduce structural breaks requiring new modeling channels.

*Source: IMF Working Paper — Introduction (wpiea2025123-print-pdf).*

### Conclusion

### Conclusion

### Significance and challenges
- Estimating real equilibrium interest rates in the euro area is significant for understanding monetary conditions and policy.
- Estimation is complex; results vary across methods due to inherent methodological differences and model-specific theoretical constructs.
- Equilibrium interest rates should be interpreted with caution because:
  - The rate is a specific theoretical construct that makes sense only within a particular model or approach.
  - Different models may use different and not strictly comparable concepts of equilibrium rates.
  - Selection of estimates should consider conceptual fit, robustness, and consistency with other economic indicators.

### Approaches reviewed
- The paper details multiple approaches used to calculate equilibrium interest rates:
  - Univariate statistical filters
  - VAR models
  - Semi-structural models
  - Fully structural models
- Each method presents unique strengths and weaknesses, contributing to varied results observed in the literature.

### Key empirical finding for the euro area
- The range of estimates derived from both closed and open economy models shows that recent short-term equilibrium rates are likely above longer-term rates in the euro area.
- These findings reflect underlying euro area dynamics and external influences.

### Research and policy implications / Recommendations
- Rather than accumulating more methods to estimate specific equilibrium rates, future research could focus on developing unifying frameworks and cohesive approaches that synthesize existing models.
- A cited example of a unifying approach is Reis (2025), who:
  - Provides a general framework that conceptually distinguishes between four equilibrium rates.
  - Establishes what fundamentals separately or jointly drive them.
  - Explains how these rates relate to each other in general equilibrium.

*IMF Working Paper — Conclusion (Real Equilibrium Interest Rates in the Euro Area)*

### 2024. Sveriges Riksbank.

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_Source: https://www.imf.org/-/media/files/publications/wp/2025/english/wpiea2025123-print-pdf.pdf_