## wpiea2024161-print-pdf — Introduction

## Source details

**Canonical URL:** [wpiea2024161-print-pdf — Introduction](https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024161-print-pdf.pdf)

## Other formats

- [Markdown version](/-/media/files/publications/wp/2024/english/wpiea2024161-print-pdf.pdf.md)
- [Structured JSON version](/-/media/files/publications/wp/2024/english/wpiea2024161-print-pdf.pdf.json)

---

### Key questions and headline findings
- Main questions addressed:
  - Was the recent decline in real interest rates driven by a decline in 푟∗, the natural real interest rate, or by a sequence of shocks (monetary and fiscal policy, demographics, globalization) that pushed market and policy rates away from equilibrium?
  - Has the natural rate of interest been broadly stable before, during, and after the Great Recession, or has it drifted downward?
  - Conditional on the natural rate estimates, has monetary policy been too loose in response to the Great Recession and the accompanying low-inflation environment?
- Core findings:
  - Once equilibrium real exchange rate appreciation/depreciation is accounted for, the natural real interest rate in the 2000s and 2010s is no longer found to be declining to near or below zero in most countries.
  - During the first two decades of the 21st century the natural rate of interest for many advanced and emerging market economies appears to have been stable at around 2-3 percent, with a modest decline in the early 2020s.
  - The average difference of about 150 basis points between HLW (closed-economy) estimates and the open-economy framework suggests HLW-based guidance may have implied monetary policy that was too loose during the pre- and post-pandemic period.
  - Only in a couple of countries do the authors find 푟∗ dipping below the zero lower bound and only at the very end of the sample, at the height of the pandemic.

### Analytical framework and conceptual contributions
- Three main contributions:
  - Extend the 푟∗ equation to include equilibrium real exchange rate appreciation (the “Penn effect”), so that 푟∗ contains both the rate of growth of potential output and equilibrium appreciation.
  - Use an open-economy IS schedule and a full semi-structural model closed by a monetary policy rule (contrast with HLW which lacks expectations and a policy rule).
  - Apply a canonical semi-structural model across countries with Bayesian estimation to obtain country-specific parameters, extending the estimation sample through 2022Q4.
- Rationale for the exchange-rate extension:
  - Convergence in per capita income is often split between higher real GDP growth and real exchange rate appreciation.
  - Ignoring equilibrium appreciation in closed-economy HLW leads to overestimating 푟∗ in fast-growing countries with equilibrium appreciation and underestimating 푟∗ where equilibrium depreciation prevails.
  - De Broeck and Sløk (2006) argued about 2/5 of real convergence was realized through equilibrium real appreciation.

### Open-economy model specification (summary of key equations)
- Time-varying natural rate with equilibrium appreciation (equation (1)):
  - 푟푡∗ = 휌푟푡−1∗ + (1−휌)(2푐1(푐2푔푡∗ + (1−푐2)푞푡∗))
  - Contributions of potential growth and equilibrium exchange rate add up to unity; empirical estimates do not reject 푐1 ≈ 1 and 푐2 ≈ 1/2 for sample countries.
- Core model equations (semi-structural, quarterly):
  - Phillips curve (equation (2)): 휋푡 = 푎1휋푡−1 + (1−푎1)휋푡+1 + 푎2RM C푡 + 휀푡휋
    - RM C defined as weighted sum of output gap and real exchange rate gap (equation (3)): RM C푡 = 푎3푦̂푡 + (1−푎3)푞̂푡
  - Aggregate demand (equation (4)): 푦̂푡 = 푏1푦̂푡−1 − 푏2MCI + 푏3푦̂푡F + 휀푡ŷ
    - Monetary conditions index (equation (5)): MCI푡 = 푏4푟̂푡 + (1−푏4)(−푞̂푡)
  - Uncovered interest rate parity (equation (6)) allowing for alternative exchange rate regimes, FX interventions (parameters ℎ2, e1), risk premium, and UIP shock 휀푡s.
  - Policy reaction function (equation (7)) that can represent rate setting focused on inflation stability (ℎ1 = 0) or combined inflation and exchange rate objectives; includes monetary policy shock 휀푡i.
- Model flexibility:
  - Specification accommodates floats, inflation targeting, “stabilized regimes”, and currency boards by adjusting UIP and policy rule parameters.

### Estimation approach
- Bayesian estimation and Kalman filter identification:
  - Bayesian priors set at either 1/4 or 1/2 of initial parameter calibration or empirical standard deviation; robustness checks reported.
  - Foreign variables (real GDP and real rate) are prefiltered using the Hodrick-Prescott filter so foreign gaps are consistent across sample countries.
  - Trends and gaps, including the inflation objective/target, are identified jointly with parameters by the Kalman filter.
  - Bayesian regressions run from 2002Q1 to 2019Q4 to obtain coefficients; Metropolis-Hastings procedure unstable during pandemic, so Kalman filter estimates are derived for full sample 2002Q1–2022Q4.
- Estimation choices aimed to minimize ad hoc country-specific adjustments; country-specific features captured mainly via UIP and policy-rule modifications.

### Data and sample
- Sample composition and period:
  - 12 countries in or near Europe trading principally with the euro area; currencies either floating or pegged to the euro; range of monetary regimes.
  - Sample period for Kalman filter estimates: 2002Q1–2022Q4.
  - Bayesian regressions sample: 2002Q1–2019Q4.
  - Series sources: Eurostat and national statistical offices. Some country series (Türkiye, Serbia, North Macedonia, Bosnia and Herzegovina, Morocco) are slightly shorter based on availability.
- Variable definitions:
  - Inflation: annualized first difference of the log of seasonally adjusted core CPI.
  - Output: quarterly real GDP in natural logs multiplied by 100.
  - Exchange rate: country real exchange rate in domestic currency terms (a decline denotes appreciation of the domestic currency against the euro).
  - (Ex post) average real interest rate measure: based either on the policy rate or on an interbank rate closely mirroring the policy rate.

### Sample countries and descriptive statistics
- Sample period coverage: generally 2002Q1-2022Q4 for most countries; Türkiye: 2010Q1-2022Q4; Serbia: 2007Q1-2022Q4; North Macedonia: 2006Q1-2022Q4; Bosnia and Herzegovina: 2015Q1-2022Q4; Morocco: 2008Q1-2022Q4.
- 2021 GDP per capita, PPP (2017 international dollars) and average real interest rates (mean of policy interest rates minus one-period ahead inflation during 2008–2022):
  - Switzerland (CHE) GDP per capita, PPP US$ 70,764; Average real interest rate -0.3; Crawl-like arr.; 2002Q1-2022Q4
  - Norway (NOR) 64,443; 0.3; Float/IT; 2002Q1-2022Q4
  - Sweden (SWE) 54,240; -0.2; Float/IT; 2002Q1-2022Q4
  - United Kingdom (GBR) 45,989; -0.7; Float/IT; 2002Q1-2022Q4
  - Czech Republic (CZE) 40,917; -0.9; Float/IT; 2002Q1-2022Q4
  - Poland (POL) 34,587; 1.4; Float/IT; 2002Q1-2022Q4
  - Hungary (HUN) 33,863; 1.8; Float/IT; 2002Q1-2022Q4
  - Türkiye (TUR) 31,753; -2.6; Float/IT; 2010Q1-2022Q4
  - Serbia (SRB) 19,695; 3.3; Stabilized ER/IT; 2007Q1-2022Q4
  - North Macedonia (MKD) 16,372; 6.4; Soft peg; 2006Q1-2022Q4
  - Bosnia and Herzegovina (BIH) 14,813; 1.7; Currency board; 2015Q1-2022Q4
  - Morocco (MAR) 8,353; 1.1; Peg with a band; 2008Q1-2022Q4
- Data sources: IMF, World Economic Outlook Database, October 2022; IMF AREAER 2021; Eurostat; national central banks; authors’ calculations.

### Decline in global and observed real interest rates (2008–2022)
- Historical context:
  - Global real rates peaked at about 4 percent in the early 1990s and trended down over the following three decades.
  - After the GFC, real policy and short-term interbank rates dropped close to or below zero in almost all industrial countries.
- Observed sample central bank behavior:
  - Post-GFC and through the pandemic, sample central banks kept low post-GFC real policy rates.
  - Excluding Bosnia and Herzegovina, only Serbia and North Macedonia had real policy rates close to 3 percent during 2008–2022.
  - For the subsample of EU countries (all with inflation targeting), the average real policy rate was minus 50 basis points.
  - Low real rates primarily reflected nominal policy rates near the zero lower bound rather than persistent above-target inflation.
- Market expectations:
  - For Norway, Sweden, Switzerland, and the UK, the 2022 average of five-year ahead expectations of real interest rates was well below 1 percent.

### Estimates of the natural rate of interest (r*)
- Estimation approaches:
  - Two groups of estimates presented: (1) time-invariant estimates (assume constant trend real output growth g* and trend real exchange rate appreciation q* over the sample); (2) time-varying estimates (assume stochastic trends).
  - Bayesian estimation uses data up to 2020Q1 to avoid COVID-19 shock contamination.
- Time-invariant r* results (2002Q1-2022Q4; estimates in percent):
  - Modified r* equation: r*̅ =2c1(c2 g*̅ +(1−c2) q*̅)
  - Country-level point estimates:
    - Switzerland: r* 0.6; g* 1.7; q* −1.0; c1 0.8; c2 0.5
    - Norway: 2.8; 1.6; 0.8; 1.1; 0.6
    - Sweden: 2.8; 2.1; 0.8; 1.0; 0.4
    - United Kingdom: 1.9; 1.4; 0.6; 1.0; 0.4
    - Czech Republic: 1.5; 2.8; −1.1; 0.9; 0.5
    - Poland: 5.4; 3.8; 0.7; 1.1; 0.6
    - Hungary: 2.5; 2.4; 0.1; 1.0; 0.5
    - Türkiye: 9.5; 5.7; 5.0; 0.9; 0.5
    - Serbia: 2.0; 2.3; −0.6; 1.0; 0.5
    - North Macedonia: 3.4; 2.3; -0.1; 1.3; 0.6
    - Bosnia and Herzegovina: 2.2; 3.0; -0.7; 1.1; 0.5
    - Morocco: 2.3; 3.0; −0.4; 1.0; 0.5
  - Key time-invariant findings:
    - Time-invariant r* was positive in all countries and well above 1 percent.
    - Poland and Türkiye are outliers with high r* at 5.4 percent and 9.5 percent, respectively, owing to period-average real depreciation of their currencies.
    - Switzerland’s equilibrium real appreciation (q* = −1.0 percent) reduced r* by 80 basis points (calculation: 2*0.8*(1-0.5)*-1 = -0.8 percent).
    - Average r* across converging countries (Czech Republic, Poland, Hungary, Türkiye, Serbia, North Macedonia, Bosnia and Herzegovina, Morocco) is 3.6 percent; excluding Türkiye and Poland, average declines to 2.3 percent.
    - Average advanced-economy r* (Norway, Sweden, United Kingdom) is about 2.5 percent.
    - Authors do not observe the sharp secular decline in r* reported in some past literature.
- Time-varying r* results (2002Q1–2022Q4):
  - Time-varying individual-country estimates and the unweighted sample mean are relatively stable.
  - Average r* fluctuated between 2 percent and 3 percent prior to the COVID-19 pandemic, declining to close to 2 percent in the early 2020s.
  - End-of-sample decline attributed to pandemic-induced growth shock, partly offset by initially lower inflation during 2020-2021 which depreciated the real exchange rate.
  - Three highlighted findings:
    1. Time-varying estimates are close to time-invariant estimates, implying trend appreciation effects were largely stable.
    2. Limited evidence of a secular decline in r*: only in the UK, Czech Republic, Serbia, and Morocco did r* trend to or below zero toward the end of the sample; Swiss r* estimates were close to zero for most of the sample period.
    3. Observed real rates r were well below estimated r* in every advanced country during the post-GFC period, sometimes by 70–100 basis points; for some emerging countries (Serbia, North Macedonia, Bosnia and Herzegovina, Morocco) observed r was close to or above r* until 2015 or 2020, then declined below r* afterward.

### Robustness check: comparison with HLW (closed-economy benchmark)
- Two verification questions and answers:
  1. Does equilibrium appreciation lower the open-economy estimate of r* relative to HLW? Yes—evidence for 2013–2019 shows every percentage point of real equilibrium appreciation (q*) is associated with r* being about 1.3 percentage points lower.
     - Extending sample to 2002–2019 makes slope somewhat steeper at 1.6.
  2. Does the open-economy framework imply a different average r* than the closed-economy HLW framework? Yes—the HLW closed-economy estimates of r* are on average about 150 basis points lower than the open-economy estimates.
- Interpretation:
  - HLW methodology appears to put greater weight on actual real interest rates r (acting like a moving average of observed r), producing lower r* estimates.
  - The extended open-economy model places more weight on inflationary pressures and equilibrium exchange rate effects, allowing larger deviations between estimated r* and observed r.
- Country-level comparisons:
  - HLW estimates are consistently and visibly above open-economy estimates only in Switzerland, the Czech Republic, and Bosnia and Herzegovina (countries with fast trend real appreciation).
  - For most other countries, HLW estimates overlap or are lower than open-economy estimates.
  - Neither methodology suggests a secular decline in r* after 2000.

### r and r*: assessment of policy stance ("Too tight" or "Too loose?")
- Average gaps (r − r*), sample means by methodology and period (in percent):
  - Switzerland: Our methodology 2002–22 -0.8; 2013–22 -1.2. HLW 2002–19 -2.2; 2013–19 -2.3.
  - Norway: -2.4; -4.3. HLW -0.9; -2.9.
  - Sweden: -2.5; -3.8. HLW -1.0; -2.2.
  - United Kingdom: -2.2; -2.7. HLW -0.8; -1.9.
  - Czech Republic: -1.9; -3.5. HLW -2.1; -3.2.
  - Poland: -3.2; -5.0. HLW -1.2; -2.5.
  - Hungary: -0.8; -4.7. HLW 1.6; -1.3.
  - Türkiye: -12.1; -12.8. HLW -1.3; -1.2.
  - Serbia: 0.6; -0.5. HLW 3.6; 2.1.
  - North Macedonia: 1.9; 0.9. HLW 5.3; 3.4.
  - Bosnia and Herzegovina: -0.8; -0.8. HLW -4.2; -4.2.
  - Morocco: -1.1; -1.2. HLW -0.8; -0.9.
- Unweighted average (excluding Türkiye):
  - Our methodology: 2002–22 -1.2; 2013–22 -2.4.
  - HLW methodology: 2002–19 -0.2; 2013–19 -1.4.
- Interpretation:
  - Using the authors’ open-economy methodology, monetary policy was on average loose (r* > r) in all countries except Serbia and North Macedonia (which show tight policy).
  - Average gap r − r* about minus 120 basis points during 2002–2022 and about minus 240 basis points during 2013–2022.
  - For EU countries plus Switzerland, Norway, and the UK, average gap between r and r* was minus 360 basis points during 2013–2022.
  - For the Czech Republic, Poland, and Hungary (joined EU in mid-2000s), same-period gap was minus 440 basis points.
  - HLW gaps are smaller in magnitude (averages minus 20 and minus 140 basis points for comparable periods) but point in same direction.

### Policy implications
- Practical implications for monetary policy:
  - Underestimating 푟∗ would make monetary conditions too loose and risk overheating/higher inflation.
  - Overestimating 푟∗ would make monetary conditions too tight and risk higher unemployment and undershooting inflation targets.
  - Because HLW-style closed-economy estimates may understate 푟∗ for many open economies (by roughly 150 basis points on average in this sample), policy guided by HLW estimates alone may have been looser than optimal in pre- and post-pandemic periods.
- Study-specific implications:
  - Sample central banks likely underestimated r* on average by more than 100 basis points during 2002–2022 and by about twice as much after the taper-tantrum period, which likely contributed to keeping policy rates close to the zero lower bound for too long (r < r*).
  - The 2021–2023 period of high inflation may have had, at least partly, monetary roots consistent with an underestimation of r*.
  - For small open economies, the question remains whether they can set policy rates independently of dominant central banks (US Fed, ECB) or whether they stopped trying after the GFC; the near-zero r* narrative may have been convenient and influential.
  - The estimates do not support the claim that all advanced and emerging market economies have been operating close to the effective nominal zero lower bound: the true natural nominal rate (r* plus expected inflation or the inflation target) may have been higher by 100 basis points on average and substantially higher for some countries.
  - Only the UK and the Czech Republic show open-economy estimates of r* dipping below zero, and then only during the COVID period.

### Conclusions (summary)
- Incorporating equilibrium real exchange rate dynamics into the natural-rate equation and using an open-economy semi-structural model with a policy rule leads to materially different estimates of 푟∗ from those obtained under the HLW closed-economy framework.
- For the sample countries over 2002Q1–2022Q4, the natural real interest rate was broadly stable at around 2-3 percent for many economies, with modest declines in the early 2020s and only limited instances of 푟∗ falling below zero at the pandemic peak.
- The average 150 basis point gap relative to HLW estimates implies that closed-economy based policy assessments could have biased monetary policy toward undue looseness.

### Key numerical and procedural facts
- Sample size: 12 countries located in and around Europe.
- Sample period for Kalman filter estimates: 2002Q1–2022Q4.
- Bayesian regressions sample: 2002Q1–2019Q4; Bayesian estimation uses data up to 2020Q1 to avoid COVID-19 distortion.
- Metropolis-Hastings simulation draws: 100,000.
- Many r* differences under relaxed priors concentrated within ±100 basis points; notable exceptions: North Macedonia and Türkiye.
- Average HLW vs open-economy r* gap: about 150 basis points.
- Typical pre-pandemic average r*: between 2 percent and 3 percent; end-of-sample decline to close to 2 percent in early 2020s.

*Source: Introduction (content unit: wpiea2024161-print-pdf - Introduction) from the provided IMF PDF content.*

### Introduction ...........................................................................................................

### Introduction

### Key questions and headline findings
- Main questions addressed:
  - Was the recent decline in real interest rates driven by a decline in 푟∗, the natural real interest rate, or by a sequence of shocks (monetary and fiscal policy, demographics, globalization) that pushed market and policy rates away from equilibrium?
  - Has the natural rate of interest been broadly stable before, during, and after the Great Recession, or has it drifted downward?
  - Conditional on the natural rate estimates, has monetary policy been too loose in response to the Great Recession and the accompanying low-inflation environment?
- Core findings:
  - Once equilibrium real exchange rate appreciation/depreciation is accounted for, the natural real interest rate in the 2000s and 2010s is no longer found to be declining to near or below zero in most countries.
  - During the first two decades of the 21st century the natural rate of interest for many advanced and emerging market economies appears to have been stable at around 2-3 percent, with a modest decline in the early 2020s.
  - The average difference of about 150 basis points between HLW (closed-economy) estimates and the open-economy framework suggests HLW-based guidance may have implied monetary policy that was too loose during the pre- and post-pandemic period.
  - Only in a couple of countries do the authors find 푟∗ dipping below the zero lower bound and only at the very end of the sample, at the height of the pandemic.

### Analytical framework and conceptual contributions
- Three main contributions:
  - Extend the 푟∗ equation to include equilibrium real exchange rate appreciation (the “Penn effect”), so that 푟∗ contains both the rate of growth of potential output and equilibrium appreciation.
  - Use an open-economy IS schedule and a full semi-structural model closed by a monetary policy rule (contrast with HLW which lacks expectations and a policy rule).
  - Apply a canonical semi-structural model across countries with Bayesian estimation to obtain country-specific parameters, extending the estimation sample through 2022Q4.
- Rationale for the exchange-rate extension:
  - Convergence in per capita income is often split between higher real GDP growth and real exchange rate appreciation (Samuelson 1994).
  - Ignoring equilibrium appreciation in closed-economy HLW leads to overestimating 푟∗ in fast-growing countries with equilibrium appreciation and underestimating 푟∗ where equilibrium depreciation prevails.
  - Literature note: De Broeck and Sløk (2006) argued about 2/5 of real convergence was realized through equilibrium real appreciation.

### Open-economy model specification (summary of key equations)
- Time-varying natural rate with equilibrium appreciation (equation (1)):
  - 푟푡∗ = 휌푟푡−1∗ + (1−휌)(2푐1(푐2푔푡∗ + (1−푐2)푞푡∗))
  - Contributions of potential growth and equilibrium exchange rate add up to unity; empirical estimates do not reject 푐1 ≈ 1 and 푐2 ≈ 1/2 for sample countries.
- Core model equations (semi-structural, quarterly):
  - Phillips curve (equation (2)): 휋푡 = 푎1휋푡−1 + (1−푎1)휋푡+1 + 푎2RM C푡 + 휀푡휋
    - RM C defined as weighted sum of output gap and real exchange rate gap (equation (3)): RM C푡 = 푎3푦̂푡 + (1−푎3)푞̂푡
  - Aggregate demand (equation (4)): 푦̂푡 = 푏1푦̂푡−1 − 푏2MCI + 푏3푦̂푡F + 휀푡ŷ
    - Monetary conditions index (equation (5)): MCI푡 = 푏4푟̂푡 + (1−푏4)(−푞̂푡)
  - Uncovered interest rate parity (equation (6)) allowing for alternative exchange rate regimes, FX interventions (parameters ℎ2, e1), risk premium, and UIP shock 휀푡s.
  - Policy reaction function (equation (7)) that can represent rate setting focused on inflation stability (ℎ1 = 0) or combined inflation and exchange rate objectives; includes monetary policy shock 휀푡i.
- Model flexibility:
  - Specification accommodates floats, inflation targeting, “stabilized regimes”, and currency boards by adjusting UIP and policy rule parameters (Annex I contains parametrization).

### Estimation approach
- Bayesian estimation and Kalman filter identification:
  - Bayesian priors set at either 1/4 or 1/2 of initial parameter calibration or empirical standard deviation (Annex I); robustness checks in Annex II.
  - Foreign variables (real GDP and real rate) are prefiltered using the Hodrick-Prescott filter so foreign gaps are consistent across sample countries.
  - Trends and gaps, including the inflation objective/target, are identified jointly with parameters by the Kalman filter.
  - Bayesian regressions run from 2002Q1 to 2019Q4 to obtain coefficients; Metropolis-Hastings procedure unstable during pandemic, so Kalman filter estimates are derived for full sample 2002Q1–2022Q4.
- Estimation choices aimed to minimize ad hoc country-specific adjustments; country-specific features captured mainly via UIP and policy-rule modifications.

### Data and sample
- Sample composition and period:
  - 12 countries in or near Europe trading principally with the euro area; currencies either floating or pegged to the euro; range of monetary regimes.
  - Sample period for Kalman filter estimates: 2002Q1–2022Q4.
  - Bayesian regressions sample: 2002Q1–2019Q4.
  - Series sources: Eurostat and national statistical offices. Some country series (Türkiye, Serbia, North Macedonia, Bosnia and Herzegovina, Morocco) are slightly shorter based on availability.
- Variable definitions:
  - Inflation: annualized first difference of the log of seasonally adjusted core CPI.
  - Output: quarterly real GDP in natural logs multiplied by 100.
  - Exchange rate: country real exchange rate in domestic currency terms (a decline denotes appreciation of the domestic currency against the euro).
  - (Ex post) average real interest rate measure: based either on the policy rate or on an interbank rate closely mirroring the policy rate.

### Comparison with HLW and robustness
- HLW framework summary:
  - Closed-economy unobserved component model where 푟푡∗ = 푔푡∗ + 푧푡 (trend growth plus unexplained component).
  - HLW links natural rate evolution to trend growth via an IS schedule and a New Keynesian Phillips curve, but does not explicitly incorporate exchange-rate equilibrium effects or a policy rule with expectations.
- Identified limitation:
  - HLW's closed-economy formulation implies fast-growing emerging markets mechanically have higher 푟∗, which conflicts with observation of low observed real rates in many emerging markets.
  - Arena and others (2020) found that about one-half of the estimated decline in 푟∗ since the GFC can be attributed to the unexplained component 푧푡, which could reflect equilibrium real appreciation/depreciation.
- Robustness check result:
  - The open-economy extension that explicitly accounts for equilibrium real appreciation explains substantial differences: average 푟∗ difference of about 150 basis points versus HLW estimates.

### Policy implications
- Practical implications for monetary policy:
  - Underestimating 푟∗ would make monetary conditions too loose and risk overheating/higher inflation.
  - Overestimating 푟∗ would make monetary conditions too tight and risk higher unemployment and undershooting inflation targets.
  - Because HLW-style closed-economy estimates may understate 푟∗ for many open economies (by roughly 150 basis points on average in this sample), policy guided by HLW estimates alone may have been looser than optimal in pre- and post-pandemic periods.
- Use of 푟∗ estimates:
  - 푟∗ estimates are one input among many for central bankers; they help evaluate policy options but are uncertain and should be considered alongside other indicators.
  - The model’s ability to represent alternative exchange rate regimes and policy objectives makes it suitable for assessing country-specific monetary strategies.

### Conclusions (summary)
- Incorporating equilibrium real exchange rate dynamics into the natural-rate equation and using an open-economy semi-structural model with a policy rule leads to materially different estimates of 푟∗ from those obtained under the HLW closed-economy framework.
- For the sample countries over 2002Q1–2022Q4, the natural real interest rate was broadly stable at around 2-3 percent for many economies, with modest declines in the early 2020s and only limited instances of 푟∗ falling below zero at the pandemic peak.
- The average 150 basis point gap relative to HLW estimates implies that closed-economy based policy assessments could have biased monetary policy toward undue looseness.

*Source: Introduction (content unit: wpiea2024161-print-pdf - Introduction) from the provided IMF PDF content.*

### Annex III for the interest rate definitions for our sample countries). All data are either from Eurostat or from

### wpiea2024161-print-pdf - Annex III for the interest rate definitions for our sample countries). All data are either from Eurostat or from

### Sample countries and characteristics
- Sample period coverage: generally 2002Q1-2022Q4 for most countries; Türkiye: 2010Q1-2022Q4; Serbia: 2007Q1-2022Q4; North Macedonia: 2006Q1-2022Q4; Bosnia and Herzegovina: 2015Q1-2022Q4; Morocco: 2008Q1-2022Q4.
- 2021 GDP per capita, PPP (2017 international dollars) and average real interest rates (mean of policy interest rates minus one-period ahead inflation during 2008–2022):
  - Switzerland (CHE) GDP per capita, PPP US$ 70,764; Average real interest rate -0.3; Crawl-like arr.; 2002Q1-2022Q4
  - Norway (NOR) 64,443; 0.3; Float/IT; 2002Q1-2022Q4
  - Sweden (SWE) 54,240; -0.2; Float/IT; 2002Q1-2022Q4
  - United Kingdom (GBR) 45,989; -0.7; Float/IT; 2002Q1-2022Q4
  - Czech Republic (CZE) 40,917; -0.9; Float/IT; 2002Q1-2022Q4
  - Poland (POL) 34,587; 1.4; Float/IT; 2002Q1-2022Q4
  - Hungary (HUN) 33,863; 1.8; Float/IT; 2002Q1-2022Q4
  - Türkiye (TUR) 31,753; -2.6; Float/IT; 2010Q1-2022Q4
  - Serbia (SRB) 19,695; 3.3; Stabilized ER/IT; 2007Q1-2022Q4
  - North Macedonia (MKD) 16,372; 6.4; Soft peg; 2006Q1-2022Q4
  - Bosnia and Herzegovina (BIH) 14,813; 1.7; Currency board; 2015Q1-2022Q4
  - Morocco (MAR) 8,353; 1.1; Peg with a band; 2008Q1-2022Q4
- Data sources: IMF, World Economic Outlook Database, October 2022; IMF AREAER 2021; Eurostat; national central banks; authors’ calculations.

### Decline in global and observed real interest rates (2008–2022)
- Historical context:
  - Global real rates peaked at about 4 percent in the early 1990s and trended down over the following three decades.
  - After the GFC, real policy and short-term interbank rates dropped close to or below zero in almost all industrial countries.
- Observed sample central bank behavior:
  - Post-GFC and through the pandemic, sample central banks kept low post-GFC real policy rates.
  - Excluding Bosnia and Herzegovina, only Serbia and North Macedonia had real policy rates close to 3 percent during 2008–2022.
  - For the subsample of EU countries (all with inflation targeting), the average real policy rate was minus 50 basis points.
  - Low real rates primarily reflected nominal policy rates near the zero lower bound rather than persistent above-target inflation.
- Market expectations:
  - For Norway, Sweden, Switzerland, and the UK, the 2022 average of five-year ahead expectations of real interest rates was well below 1 percent.

### Estimates of the natural rate of interest (r*)
- Estimation approaches:
  - Two groups of estimates presented: (1) time-invariant estimates (assume constant trend real output growth g* and trend real exchange rate appreciation q* over the sample); (2) time-varying estimates (assume stochastic trends).
  - Bayesian estimation uses data up to 2020Q1 to avoid COVID-19 shock contamination.
- Time-invariant r* results (2002Q1-2022Q4; estimates in percent):
  - Modified r* equation: r*̅ =2c1(c2 g*̅ +(1−c2) q*̅)
  - Country-level point estimates (r*, g*, q*, c1, c2):
    - Switzerland: r* 0.6; g* 1.7; q* −1.0; c1 0.8; c2 0.5
    - Norway: 2.8; 1.6; 0.8; 1.1; 0.6
    - Sweden: 2.8; 2.1; 0.8; 1.0; 0.4
    - United Kingdom: 1.9; 1.4; 0.6; 1.0; 0.4
    - Czech Republic: 1.5; 2.8; −1.1; 0.9; 0.5
    - Poland: 5.4; 3.8; 0.7; 1.1; 0.6
    - Hungary: 2.5; 2.4; 0.1; 1.0; 0.5
    - Türkiye: 9.5; 5.7; 5.0; 0.9; 0.5
    - Serbia: 2.0; 2.3; −0.6; 1.0; 0.5
    - North Macedonia: 3.4; 2.3; -0.1; 1.3; 0.6
    - Bosnia and Herzegovina: 2.2; 3.0; -0.7; 1.1; 0.5
    - Morocco: 2.3; 3.0; −0.4; 1.0; 0.5
  - Key time-invariant findings:
    - Time-invariant r* was positive in all countries and well above 1 percent.
    - Poland and Türkiye are outliers with high r* at 5.4 percent and 9.5 percent, respectively, owing to period-average real depreciation of their currencies.
    - Switzerland’s equilibrium real appreciation (q* = −1.0 percent) reduced r* by 80 basis points (calculation: 2*0.8*(1-0.5)*-1 = -0.8 percent).
    - Average r* across converging countries (Czech Republic, Poland, Hungary, Türkiye, Serbia, North Macedonia, Bosnia and Herzegovina, Morocco) is 3.6 percent; excluding Türkiye and Poland, average declines to 2.3 percent.
    - Average advanced-economy r* (Norway, Sweden, United Kingdom) is about 2.5 percent.
    - Authors do not observe the sharp secular decline in r* reported in some past literature.
- Time-varying r* results (2002Q1–2022Q4):
  - Time-varying individual-country estimates and the unweighted sample mean are relatively stable.
  - Average r* fluctuated between 2 percent and 3 percent prior to the COVID-19 pandemic, declining to close to 2 percent in the early 2020s.
  - End-of-sample decline attributed to pandemic-induced growth shock, partly offset by initially lower inflation during 2020-2021 which depreciated the real exchange rate.
  - Three highlighted findings from time-varying estimates:
    1. Time-varying estimates are close to time-invariant estimates, implying trend appreciation effects were largely stable.
    2. Limited evidence of a secular decline in r*: only in the UK, Czech Republic, Serbia, and Morocco did r* trend to or below zero toward the end of the sample; Swiss r* estimates were close to zero for most of the sample period.
    3. Observed real rates r were well below estimated r* in every advanced country during the post-GFC period, sometimes by 70–100 basis points; for some emerging countries (Serbia, North Macedonia, Bosnia and Herzegovina, Morocco) observed r was close to or above r* until 2015 or 2020, then declined below r* afterward.

### Robustness check: comparison with HLW (closed-economy benchmark)
- Two verification questions:
  1. Does equilibrium appreciation lower the open-economy estimate of r* relative to HLW? Yes—evidence for 2013–2019 shows every percentage point of real equilibrium appreciation (q*) is associated with r* being about 1.3 percentage points lower (Figure 4).
     - Note: Extending sample to 2002–2019 makes slope somewhat steeper at 1.6.
  2. Does the open-economy framework imply a different average r* than the closed-economy HLW framework? Yes—the HLW closed-economy estimates of r* are on average about 150 basis points lower than the open-economy estimates.
- Interpretation:
  - HLW methodology appears to put greater weight on actual real interest rates r (acting like a moving average of observed r), producing lower r* estimates.
  - The extended open-economy model places more weight on inflationary pressures and equilibrium exchange rate effects, allowing larger deviations between estimated r* and observed r.
- Country-level comparisons:
  - HLW estimates are consistently and visibly above open-economy estimates only in Switzerland, the Czech Republic, and Bosnia and Herzegovina (countries with fast trend real appreciation).
  - For most other countries, HLW estimates overlap or are lower than open-economy estimates.
  - Neither methodology suggests a secular decline in r* after 2000.

### r and r*: assessment of policy stance ("Too tight" or "Too loose?")
- Average gaps (r − r*), sample means by methodology and period (in percent):
  - Table 3 findings (each cell is sample period mean of r - r*):
    - Switzerland: Our methodology 2002–22 -0.8; 2013–22 -1.2. HLW 2002–19 -2.2; 2013–19 -2.3.
    - Norway: -2.4; -4.3. HLW -0.9; -2.9.
    - Sweden: -2.5; -3.8. HLW -1.0; -2.2.
    - United Kingdom: -2.2; -2.7. HLW -0.8; -1.9.
    - Czech Republic: -1.9; -3.5. HLW -2.1; -3.2.
    - Poland: -3.2; -5.0. HLW -1.2; -2.5.
    - Hungary: -0.8; -4.7. HLW 1.6; -1.3.
    - Türkiye: -12.1; -12.8. HLW -1.3; -1.2.
    - Serbia: 0.6; -0.5. HLW 3.6; 2.1.
    - North Macedonia: 1.9; 0.9. HLW 5.3; 3.4.
    - Bosnia and Herzegovina: -0.8; -0.8. HLW -4.2; -4.2.
    - Morocco: -1.1; -1.2. HLW -0.8; -0.9.
  - Unweighted average (excluding Türkiye):
    - Our methodology: 2002–22 -1.2; 2013–22 -2.4.
    - HLW methodology: 2002–19 -0.2; 2013–19 -1.4.
- Interpretation:
  - Using the authors’ open-economy methodology, monetary policy was on average loose (r* > r) in all countries except Serbia and North Macedonia (which show tight policy).
  - Average gap r − r* about minus 120 basis points during 2002–2022 and about minus 240 basis points during 2013–2022.
  - For EU countries plus Switzerland, Norway, and the UK, average gap between r and r* was minus 360 basis points during 2013–2022.
  - For the Czech Republic, Poland, and Hungary (joined EU in mid-2000s), same-period gap was minus 440 basis points.
  - HLW gaps are smaller in magnitude (averages minus 20 and minus 140 basis points for comparable periods) but point in same direction.

### Policy implications
- Core message:
  - Misjudging the natural real interest rate r* can have long-term consequences for output, unemployment, and inflation if estimation errors are large and persistent.
- Specific implications from the study:
  - Sample central banks likely underestimated r* on average by more than 100 basis points during 2002–2022 and by about twice as much after the taper-tantrum period, which likely contributed to keeping policy rates close to the zero lower bound for too long (r < r*).
  - The 2021–2023 period of high inflation may have had, at least partly, monetary roots consistent with an underestimation of r*.
  - For small open economies, the question remains whether they can set policy rates independently of dominant central banks (US Fed, ECB) or whether they stopped trying after the GFC; the near-zero r* narrative may have been convenient and influential.
  - The estimates do not support the claim that all advanced and emerging market economies have been operating close to the effective nominal zero lower bound: the true natural nominal rate (r* plus expected inflation or the inflation target) may have been higher by 100 basis points on average and substantially higher for some countries.
  - Only the UK and the Czech Republic show open-economy estimates of r* dipping below zero, and then only during the COVID period.

*Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024161-print-pdf.pdf*

### Conclusions

Conclusions
========

Methodology
-----------
- Modified the Holston, Laubach and Williams (2017) framework to account for equilibrium real exchange rate appreciation or depreciation by:
  - including the real exchange rate as a gap in the IS schedule; and
  - including the real exchange rate trend in the natural rate estimation as the estimated real exchange rate trend.
- Model parameters estimated using Bayesian techniques; latent variables filtered with the Kalman filter.
- Calibration and estimation approach:
  - Assign monetary policy and exchange rate regime using AREAER (IMF 2022) and choose parameters ℎ1 and ℎ2 in the UIP and monetary policy reaction function.
  - Calibrate remaining UIP, policy rule, and natural rate equation parameters identically across countries conditional on monetary regime; compute standard deviations of shocks from data.
  - Use Bayesian estimation for remaining parameters and shock standard deviations in the Phillips curve and IS curve.
  - Use the Kalman smoother to filter historical data and obtain smoothed latent variables (trends and gaps in real interest rates, exchange rate, and output).
- Estimation details:
  - Bayesian estimation uses data up to the first quarter of 2020 to avoid COVID-19 distortion.
  - Posterior constructed via Metropolis-Hastings simulation with 100,000 draws.
  - Priors for key parameters 푐1 and 푐2 initially set “tight”; sensitivity analysis considered priors with standard deviations increased fivefold.
  - Data series used: short-term policy/interbank interest rate, real GDP, exchange rate against the euro, and core CPI.

Main findings
-------------
- Aggregate empirical scope:
  - Sample covers 12 countries located in and around Europe.
- Three principal results:
  1. Cannot reject the hypothesis that 푟∗ should be lower in countries with currencies appreciating in real terms.
  2. The open-economy extension of the HLW framework implies that in the sample the natural real rate of interest has been stable and more than 100 basis points higher than in the original, closed-economy HLW framework.
  3. The sizable negative difference between real observed interest rates and real natural interest rates, 푟−푟∗, suggests monetary policy may have been too loose during the 2013–2022 period in most of the sample countries.
- Sensitivity results:
  - Relaxing priors on 푐1 and 푐2:
    - Estimated 푐1 parameters differ by less than 20 percent on average; 푐2 by about 30 percent on average.
    - Differences in 푟∗ estimates between tight and relaxed priors mostly lie within ±100 basis points for all countries except North Macedonia and Türkiye.
    - Relaxed priors push 푟∗ down by about 75 basis points in the Czech Republic, by less than 50 basis points in Norway, and by about 50 basis points in Serbia.
    - Post-GFC estimates of 푟∗ are about 100 basis points higher in the U.K. and even higher in North Macedonia and Türkiye.
- Additional technical points:
  - The parameter denoting inflation persistence in the Phillips curve, 푎1, is calibrated to 0.5 for all countries.
  - Country-specific priors and posteriors are presented in Annex II (country results and Bayesian estimation outputs).
  - Final smoothed-state estimates use all available data, including the COVID-19 period of 2020–2022.

Policy implications
-------------------
- The negative gaps (푟−푟∗) over 2013–2022 imply that monetary policy may have been too loose in most sample countries, warranting reassessment of policy stance relative to country-specific 푟∗ that accounts for real exchange rate trends.
- Incorporating real exchange rate trend into 푟∗ estimation can materially affect the level of the estimated natural rate (more than 100 basis points higher versus closed-economy HLW), with implications for how policy neutrality is assessed.

Key numerical and procedural facts
----------------------------------
- Sample size: 12 countries located in and around Europe.
- Historical period flagged for policy looseness: 2013–2022.
- Bayesian estimation uses data up to the first quarter of 2020.
- Metropolis-Hastings simulation draws: 100,000.
- Priors on 푐1 and 푐2 tested with standard deviations increased fivefold in sensitivity analysis.
- Many 푟∗ differences under relaxed priors concentrated within ±100 basis points; notable exceptions: North Macedonia and Türkiye.

*Source: IMF staff calculations and analysis in “Conclusions” (wpiea2024161-print-pdf).*

---


_Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024161-print-pdf.pdf_