## Inflation and Public Debt Reversals in Advanced Economies — Section 1–3

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### Abstract and key quantitative conclusion
- The paper quantitatively assesses effects of inflation shocks on the public debt-to-GDP ratio in 19 advanced economies using simulation and local-projection estimation approaches.
- Simulation and local-projection estimation both suggest that a 1 percentage point shock to inflation rate reduces the debt-to-GDP ratio by about 0.5 to 1 percentage points.
- Simulations: a temporary 1 percentage point shock to inflation in 2018 reduces public debt-to-GDP ratio by about 0.7 percentage points on average across 19 advanced economies.
- Estimations: a temporary 1 percentage point inflation shock reduces the debt-to-GDP ratio by around 1 percentage point on impact.
- Impact tends to be larger and more persistent when debt maturity is longer or debt rollover is lower, but the difference from the benchmark case is not necessarily large because benchmark long-term interest rates and rollover ratios are already low.
- Policy implication highlighted: modestly higher inflation, even if accompanied by some financial repression, could reduce public debt burden only marginally in many advanced economies.

### Context and motivation
- Public debt in advanced economies remains high ten years after the global financial crisis: as of 2017, debt-to-GDP ratios in advanced economies have plateaued since 2012 above 105 percent of GDP.
- High government debt raises concerns about rollover risks, limited room for countercyclical policies, and drag on long-term growth.
- Historical precedent: higher inflation contributed to public debt reversals after World War II, especially when accompanied by financial repression (real interest rates on government borrowing contained below-market levels).
- Key modeling assumptions:
  - The inflation shock is temporary and does not affect central bank credibility and monetary policy framework.
  - The inflation shock is not correlated with growth shocks or fiscal policy shocks.
  - The inflation shock does not affect growth or primary balance in the simulation framework.

### Simulation approach — methodology and data
- Framework:
  - Extension of standard debt dynamics distinguishing short-term debt (btS) and long-term debt (btL), and between long-term debt issued in year t (btL,new) and long-term debt issued prior to year t (btL,old).
  - Baseline debt dynamics (abstracting stock-flow adjustment): bt+1 = (1 + it+1) / (1 + gt+1 + πt+1) * bt − st+1 / (1 + gt+1 + πt+1).
  - Inflation shock affects only the real interest rate on long-term debt issued prior to the inflation shock (btL,old) because nominal interest on existing long-term debt is predetermined.
  - Debt-reduction effect from an inflation shock ∆πt measured as the difference between baseline and shock scenarios operating only through decrease in real interest rates on pre-existing long-term fixed-rate debt.
- Data and experiment design:
  - Sample: 19 advanced economies (country coverage determined by data availability on debt structure).
  - Macro variables for 2018–22 (bt, st, gt, πt) drawn from IMF WEO Projection (April 2018). πt is the GDP deflator.
  - Share of short-term and medium-and-long-term debt at start of simulation from SNA short/long debt ratio (assumed constant).
  - Rollover ratio for 2018–20 from April 2018 Fiscal Monitor; for 2021–22 assumed identical to 2020.
  - Temporary experiment: a 1 percentage point shock to inflation in 2018 only (a one-time shift in price level).
  - Countries explicitly included: Austria, Belgium, Canada, Czech Republic, Denmark, Finland, France, Germany, Hungary, Ireland, Italy, Japan, Netherlands, Poland, Portugal, Spain, Sweden, United Kingdom, and United States.

### Simulation results — temporary 1 percentage point inflation shock (benchmark)
- Benchmark case:
  - Average deviation of debt-to-GDP ratio from baseline across 19 countries is about 0.7 percentage points.
  - The debt reduction effect is concentrated in the first year.
  - Largest deviation: Japan, about 2 percentage points.
  - Smallest deviation: Czech Republic.
- Cross-country differences:
  - Initial debt level explains most variation in initial debt reduction when measured in percent of GDP.
  - Controlling initial debt-to-GDP ratio (e.g., setting it at the sample average 84 percent) removes most variation across countries.
  - Given the same initial debt level, higher rollover ratios are associated with smaller debt reduction because a larger portion of total public debt has interest rates adjusted upward in response to the inflation shock.

### Financial repression and alternative simulation scenarios
- Definition: Financial repression refers to situations where policy interest rates are maintained at levels lower than market rates due to regulation or institutional factors.
- Extreme financial repression (all long-term interest rates unresponsive, inclusive of long-term debt issued after the inflation shock):
  - Public debt response is a little larger than the benchmark case.
  - Additional effect is only about 0.1 percent of GDP because benchmark rollover ratio is already small (13 percent on average) and the shock is temporary.
- Negative interest rate shock case (combined shocks):
  - An additional -1 percentage point shock to the long-term interest rate occurs at the same time as the 1 percentage point inflation shock (combined shock = -2 percentage point shock to the real interest rate).
  - Zero lower bound applies; where rates are very low and close to zero, the additional shock is less than 1 percentage point.
  - Responses to the combined shock are larger but not doubled from the benchmark case because of the zero lower bound.
  - Additional debt reduction effect from this shock is about 0.5 percent of GDP.
- Overall: the effect of a given size of inflation shock on public debt becomes larger under financial repression cases, but the difference from the benchmark case is not necessarily large.

### Estimation approach — local projections, identification, and data
- Estimation method: Jordà (2005) local-projections method to estimate impulse response functions (IRFs).
  - Baseline specification (following Auerbach and Gorodnichenko (2017)):
    - Dependent variable: y_{i,t+h} is debt-to-GDP ratio.
    - Shock: ∆π_{i,t} is inflation shock.
    - Controls X_{i,t}: lagged GDP growth, lagged GDP deflator, lagged primary balance to GDP ratio, lagged long-term interest rates.
    - Fixed effects: α_i (country), κ_t (time).
- Three alternative identification methods for inflation shocks:
  - (1) Residuals from an estimated Phillips curve:
    - π_{i,t} = β_{1i} π_{i,t+1}^n + (1−β_{1i}) π_{i,t−1} + β_{2i} GDPgap_{i,t−1} + μ_i + θ_t + u_{i,t}.
    - Inflation shock proxy: û_{i,t}.
  - (2) Forecast revisions:
    - ∆π_{i,t} = π_{i,t} − π_{i,t}^n using differences between April WEO and October WEO projections.
  - (3) High inflation or deflation threshold dummies:
    - D1 = 1 if inflation rate > 3, otherwise 0.
    - D2 = 1 if the inflation shock is negative, otherwise 0.
- Data:
  - Sample: 19 advanced economies (panel: unbalanced panel from 1997 to 2017).
  - Data sources: OECD (GDP, deflator, public debt, primary balance, long-term interest rate, GDP gap), IMF WEO (projection data), OECD Sovereign Borrowing Outlook (average maturity; missing data interpolated).
  - For quarterly data: seasonal adjustments and interpolation as needed.

### Main estimation results and robustness
- Baseline estimation results:
  - Responses of public debt-to-GDP ratio to inflation shocks identified by all three methods are significantly negative.
  - Initial responses are around 1 percentage point.
  - Peak responses are somewhere around 2 to 3 percentage points for all identification methods using annual data.
  - Quarterly data (residuals from estimated Phillips curve): initial response around 0.5 percentage points; peak response around 1 percentage point.
  - Estimation responses are generally larger and more persistent than simulation responses.
    - Possible reasons: secondary effects through real GDP or primary balance captured in estimation but not in simulation; shocks identified in estimation may be somewhat persistent versus purely temporary simulation shocks.
- Asymmetry:
  - Deflation shocks have much larger impacts than inflation shocks (Identification 3).
  - Likely explanation: downward adjustment of nominal interest rates is more sluggish (downward rigidity) in response to deflation shocks.
- Robustness checks:
  - Controlling for lead variables (per Teulings and Zubanov (2014)): results broadly in line with baseline.
  - Nickel bias for annual data (exclude fixed-effects term): initial impact in line with baseline; long-run impacts larger.

### Debt maturity: short vs long
- Modified specification includes maturity dummies:
  - D1 = 0 if average maturity < 6 years, otherwise 1.
  - D2 = 1 if average maturity > 6 years, otherwise 0.
- Results:
  - Impacts of inflation shocks are generally larger in countries with long debt maturity than those with short debt maturity.
  - However, the difference between them is not necessarily large, consistent with simulation approach.

### Persistent inflation shocks — appendix summary
- Persistent inflation shock results (Table 2):
  - Debt reduction of 10 percentage points for 19 advanced economies average.
  - Debt reduction of 15 percentage points for G7 average.
  - Higher effect on G7 mainly due to higher starting public debt (especially Italy and Japan).
  - Comparison with Akitoby et al. (2014): broadly similar for G7; exception is Canada where present paper finds a 10 percentage point reduction vs 5 percentage points in Akitoby et al. (2014), due to change in data source for debt maturity (present paper uses BIS data encompassing general government).
- Note: Canada’s subnational governments are very large, so this change in data source changes the share of medium and long-term debt more significantly than other countries.
- Table 2: 6% inflation scenario (persistent shock) noted in the appendix.

### Key policy implications and caveats
- Quantitative synthesis:
  - Both simulation and estimation approaches (19 advanced economies) suggest a temporary 1 percentage point shock to inflation rate reduces the debt-to-GDP ratio by about 0.5 to 1 percentage points.
- Policy implications:
  - Modestly higher inflation, even with some financial repression, could reduce public debt burden only marginally in many advanced economies.
  - Monetary policy or financial repression alone cannot achieve a significant reduction of public debt levels.
  - If fully relied upon, very high or hyper-inflation would likely be needed, which entails other salient costs.
  - Effects of other shocks (growth and fiscal consolidation) on debt-to-GDP ratio could be much larger than inflation shocks; identifying policies to generate sustainable growth and primary balance remains an important direction for future research.
- Caveats:
  - Simulation assumes inflation shocks are exogenous, temporary, and not correlated with growth or fiscal shocks.
  - Simulation assumes no effect of inflation shocks on primary surplus or real GDP growth.
  - Analysis assumes central bank losses from holding long-term government debt due to inflation shocks are not large enough to affect central bank credibility and monetary policy frameworks.

*Source: IMF Working Paper WP/19/297 — "Inflation and Public Debt Reversals in Advanced Economies", Section I–III (authors Ichiro Fukunaga, Takuji Komatsuzaki, and Hideaki Matsuoka).*

### Section 1

### Inflation and Public Debt Reversals in Advanced Economies — Section 1

### Abstract and key quantitative conclusion
- The paper quantitatively assesses effects of inflation shocks on the public debt-to-GDP ratio in 19 advanced economies using simulation and estimation approaches.
- Simulation and local-projection estimation both suggest that a 1 percentage point shock to inflation rate reduces the debt-to-GDP ratio by about 0.5 to 1 percentage points.
- Simulations: a temporary 1 percentage point shock to inflation in 2018 reduces public debt-to-GDP ratio by about 0.7 percentage points on average across 19 advanced economies.
- Estimations: a temporary 1 percentage point inflation shock reduces the debt-to-GDP ratio by around 1 percentage point on impact.
- Impact tends to be larger and more persistent when debt maturity is longer or debt rollover is lower, but the difference from the benchmark case is not necessarily large because benchmark long-term interest rates and rollover ratios are already low.
- Policy implication highlighted: modestly higher inflation, even if accompanied by some financial repression, could reduce public debt burden only marginally in many advanced economies.

### Context and motivation (Introduction)
- Public debt in advanced economies remains high ten years after the global financial crisis: as of 2017, debt-to-GDP ratios in advanced economies have plateaued since 2012 above 105 percent of GDP.
- High government debt raises concerns about rollover risks, limited room for countercyclical policies, and drag on long-term growth.
- Historical precedent: higher inflation contributed to public debt reversals after World War II, especially when accompanied by financial repression (defined as real interest rates on government borrowing contained below-market levels due to regulations or institutional factors).
- The paper focuses on advanced economies and assumes:
  - a temporary inflation shock (e.g., temporary overshooting of the inflation target) does not affect a central bank’s credibility and monetary policy framework;
  - the inflation shock is not correlated with growth shocks or fiscal policy shocks;
  - the inflation shock does not affect growth or primary balance in the simulation framework.

### Literature overview
- Simulation-based related studies include Akitoby et al. (2014), Hilscher et al. (2017), Equiza-Goñi (2016), Aizenman and Marion (2011), End et al. (2015), and Krause and Moyen (2016). The paper updates and expands Akitoby et al. (2014) by using updated WEO data, more countries, explicit rollover treatment, and both temporary and persistent shocks.
- Empirical related studies include Afonso and Jalles (2019), End et al. (2015), and Cherif and Hasanov (2018); Afonso and Jalles (2019) uses local projections and finds broadly consistent impulse responses.
- Historical and theoretical literature cited: Hall and Sargent (2011), Abbas et al. (2011), Giannitsarou and Scott (2008), Cochrane (2011), Davig et al. (2011), Doepke and Schneider (2006).

### Simulation approach — methodology
- Framework: extension of standard debt dynamics equation distinguishing short-term debt (btS) and long-term debt (btL), and between long-term debt issued in year t (btL,new) and long-term debt issued prior to year t (btL,old).
- Baseline debt dynamics (abstracting stock-flow adjustment):
  - bt+1 = (1 + it+1) / (1 + gt+1 + πt+1) * bt − st+1 / (1 + gt+1 + πt+1)
- With maturity breakdown, the inflation shock affects only the real interest rate on long-term debt issued prior to the inflation shock (btL,old), because nominal interest on existing long-term debt is predetermined.
- The debt-reduction effect from an inflation shock ∆πt is measured as the difference between the baseline and shock scenarios and operates only through the decrease in real interest rates on pre-existing long-term fixed-rate debt.
- For a given initial debt-to-GDP ratio and size of inflation shock, a higher share of medium-to-long-term debt and a lower rollover ratio increase the portion of debt unaffected by nominal rate adjustments and thus increase the debt-reduction effect.

### Simulation approach — data and experiment design
- Sample: 19 advanced economies (country coverage determined by data availability on debt structure).
- Macro variables for 2018–22 (bt, st, gt, πt) drawn from IMF WEO Projection (April 2018) to construct baseline scenarios. πt is the GDP deflator.
- Share of short-term and medium-and-long-term debt at start of simulation from SNA short/long debt ratio (assumed constant).
- Rollover ratio for 2018–20 from April 2018 Fiscal Monitor; for 2021–22 assumed identical to 2020.
- The temporary experiment: a 1 percentage point shock to inflation in 2018 only (a one-time shift in price level), to match local projection impulse responses estimated in Section IV.
- Countries explicitly included: Austria, Belgium, Canada, Czech Republic, Denmark, Finland, France, Germany, Hungary, Ireland, Italy, Japan, Netherlands, Poland, Portugal, Spain, Sweden, United Kingdom, and United States.

### Simulation results — responses to temporary inflation shock
- Benchmark case (temporary 1 percentage point shock in 2018):
  - Average deviation of debt-to-GDP ratio from baseline across 19 countries is about 0.7 percentage points.
  - The debt reduction effect is concentrated in the first year (reflecting the temporary nature of the shock).
  - Largest deviation: Japan, about 2 percentage points.
  - Smallest deviation: Czech Republic.
- Cross-country differences:
  - Initial debt level explains most of the variation in initial debt reduction when measured in percent of GDP.
  - Controlling initial debt-to-GDP ratio (e.g., setting it at the sample average 84 percent) removes most variation across countries.
  - Given the same initial debt level, higher rollover ratios are associated with smaller debt reduction because a larger portion of total public debt has interest rates adjusted upward in response to the inflation shock.
- Financial repression scenarios:
  - Financial repression is defined as situations where policy interest rates are maintained at levels lower than market rates due to regulation or institutional factors (examples include interest rate caps, reserve requirements, captive domestic investors).
  - A lower rollover ratio associated with financial repression can increase the persistence and size of the debt-reduction effect by keeping more debt in pre-existing fixed-rate instruments unaffected by nominal rate adjustments.
  - However, because benchmark long-term interest rates and rollover ratios are already low in many advanced economies, the incremental effect of financial repression on the effectiveness of inflation-driven debt reduction is limited.

### Assumptions and caveats highlighted
- Inflation shocks are modeled as exogenous, temporary, and not correlated with growth or fiscal shocks.
- The simulation assumes no effect of inflation shocks on primary surplus or real GDP growth.
- The analysis assumes that losses to central banks from holding long-term government debt due to inflation shocks are not large enough to affect central bank credibility and monetary policy frameworks.

*Source: IMF Working Paper WP/19/297 — "Inflation and Public Debt Reversals in Advanced Economies", Section I–III (authors Ichiro Fukunaga, Takuji Komatsuzaki, and Hideaki Matsuoka).*

### Section 2

### wpiea2019297-print-pdf - Section 2

### Financial repression scenarios and simulation findings
- Extreme financial repression: all long-term interest rates unresponsive to the shock (inclusive of long-term debt issued after the inflation shock).
  - Public debt response is a little larger than the benchmark case without financial repression (Figure 3).
  - Additional effect is only about 0.1 percent of GDP, because the rollover ratio in the benchmark case is already small (13% on average) and the shock is only temporary.
- Negative interest rate shock case: an additional -1 percentage point shock to the long-term interest rate occurs at the same time as the 1 percentage point inflation shock (combined shock = -2 percentage point shock to the real interest rate).
  - The interest rate shock is subject to the zero lower bound; in a country where the rate is already very low and close to zero, this additional shock is less than 1 percentage point.
  - Responses to the combined shock are larger but not doubled from the benchmark case because of the zero lower bound.
  - The additional debt reduction effect from this shock is about 0.5 percent of GDP.
- Overall: the effect of a given size of inflation shock on public debt becomes larger under financial repression cases, but the difference from the benchmark case is not necessarily large.

### Estimation approach — methodology
- Estimation method: Jordà (2005) local-projections method to estimate impulse response functions (IRFs).
  - IRF estimated as a coefficient on an exogenous shock in a regression for each forecasting horizon h.
  - Baseline specification (following Auerbach and Gorodnichenko (2017)) is given in equation (1):
    - Dependent variable: y_{i,t+h} is debt-to-GDP ratio.
    - Shock: ∆π_{i,t} is inflation shock (identified by alternative methods).
    - Controls X_{i,t}: lagged GDP growth, lagged GDP deflator, lagged primary balance to GDP ratio, lagged long-term interest rates.
    - Fixed effects: α_i (country), κ_t (time).
    - Impulse response to ∆π_{i,t} constructed as {φ_0(h)}_{h=0}^H estimated from sequence of OLS regressions through horizon h.

### Identification of inflation shocks — three alternative methods
- (1) Residuals from an estimated Phillips curve:
  - Estimate the hybrid new Keynesian Phillips curve (equation (2)):
    - π_{i,t} = β_{1i} π_{i,t+1}^n + (1−β_{1i}) π_{i,t−1} + β_{2i} GDPgap_{i,t−1} + μ_i + θ_t + u_{i,t}.
    - 1 year-ahead inflation expectation: π_{i,t+1}^n.
    - GDP gap: GDPgap_{i,t−1} (estimated by OECD).
    - Inflation shock proxy for local projection: û_{i,t} from equation (2).
- (2) Forecast revisions:
  - Use IMF WEO projections; define
    - ∆π_{i,t} = π_{i,t} − π_{i,t}^n
    - where π_{i,t}^n is the previously-projected inflation rate in the WEO.
  - Note: difference between projections in April WEO and October WEO for the current year is used.
- (3) High inflation or deflation threshold dummies:
  - D1 = 1 if inflation rate > 3, otherwise 0.
  - D2 = 1 if the inflation shock is negative, otherwise 0.
  - Nonlinear specification allows asymmetric impacts of inflation and deflation shocks.

### Data
- Sample: 19 advanced economies (consistent with simulation approach).
- Data sources:
  - OECD: GDP, deflator, public debt, primary balance, long-term interest rate.
  - OECD: GDP gap (for identification).
  - IMF WEO: projection data (for identification).
  - OECD Sovereign Borrowing Outlook: average maturity data for debt maturity analysis (missing data interpolated).
- Panel: unbalanced panel from 1997 to 2017.
- For quarterly data: seasonal adjustments and interpolation as needed.

### Main estimation results
- Baseline specification (equation (1)) results (Figure 4.1):
  - Responses of public debt-to-GDP ratio to inflation shocks identified by all three methods are significantly negative.
  - Size and persistence vary by identification method, but:
    - Initial responses are around 1 percentage point.
    - Peak responses are somewhere around 2 to 3 percentage points for all identification methods using annual data (panels A and C).
  - Quarterly data (panel B), with residuals from estimated Phillips curve:
    - Initial response around 0.5 percentage points.
    - Peak response around 1 percentage point.
  - Compared with simulation approach: estimation responses are generally larger and more persistent.
    - Possible reasons: secondary effects through real GDP or primary balance are captured in estimation but not in simulation; shocks identified in estimation may be somewhat persistent versus purely temporary simulation shocks.
- Asymmetry between inflation and deflation (Identification 3, panel D):
  - Deflation shocks have much larger impacts than inflation shocks.
  - Likely explanation: downward adjustment of nominal interest rates is more sluggish (downward rigidity) in response to deflation shocks.

### Robustness checks
- Two robustness checks:
  - (1) Controlling for lead variables:
    - Add lead variable for the inflation shock to baseline specification (per Teulings and Zubanov (2014)).
    - Figure 4.2 results: broadly in line with baseline results.
  - (2) Nickel bias for annual data:
    - For annual data with short time-series dimension, exclude fixed-effects term when using annual data (Nickell (1981) concern).
    - Figure 4.3 results: in line with baseline for initial impact although long-run impacts are larger.

### Comparison: short vs long debt maturity
- Modified specification (equation (5)) includes maturity dummies:
  - D1 = 0 if average maturity < 6 years, otherwise 1.
  - D2 = 1 if average maturity > 6 years, otherwise 0.
- Results (Figure 4.4):
  - Impacts of inflation shocks are generally larger in countries with long debt maturity than those with short debt maturity.
  - However, the difference between them is not necessarily large, consistent with simulation approach.

### Conclusion — quantitative synthesis and policy implication
- Both simulation and estimation approaches (19 advanced economies) suggest:
  - A temporary 1 percentage point shock to inflation rate reduces the debt-to-GDP ratio by about 0.5 to 1 percentage points.
- Debt maturity:
  - Impact is larger and more persistent when debt maturity is longer, but difference from benchmark case is not that significant.
- Policy implication:
  - Modestly higher inflation, even with some financial repression, could reduce public debt burden only marginally in many advanced economies.
  - Monetary policy or financial repression alone cannot achieve a significant reduction of public debt levels.
  - If fully relied upon, very high or hyper-inflation would likely be needed, which entails other salient costs.
- Additional note:
  - Effects of other shocks (growth and fiscal consolidation) on debt-to-GDP ratio could be much larger than inflation shocks; identifying policies to generate sustainable growth and primary balance remains challenging and an important direction for future research.

### Appendix — persistent inflation shocks (summary)
- Persistent inflation shock results (Table 2):
  - Debt reduction of 10 percentage points for 19 advanced economies average.
  - Debt reduction of 15 percentage points for G7 average.
  - Higher effect on G7 mainly due to higher starting public debt (especially Italy and Japan).
  - Comparison with Akitoby et al. (2014): broadly similar for G7; exception is Canada where present paper finds a 10 percentage point reduction vs 5 percentage points in Akitoby et al. (2014), due to change in data source for debt maturity (present paper uses BIS data encompassing general government).

*Source: wpiea2019297-print-pdf - Section 2*

### Section 3

### Section 3

### Key finding(s)
- Since Canada’s subnational governments are very large, this change in data source changes the share of medium and long-term debt more significantly than other countries.
- Table 2: 6% inflation scenario (persistent shock)

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*wpiea2019297-print-pdf - Section 3*

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_Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019297-print-pdf.pdf_