## 3.1 The Prevalence of Negative Interest-Growth Differentials in History

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### Key empirical regularities
- Negative interest-growth differentials occur for prolonged periods in history in both advanced and emerging economies.
- On average:
  - differentials are approximately negative 2.5 percentage points for advanced economies,
  - and negative 6.5 percentage points for emerging economies.
- Across time:
  - differentials are more negative post-WWII than Pre-WWII,
  - and more negative pre-GFC than post-GFC.
- Across countries:
  - emerging economies show lower (more negative) differentials than advanced economies, a difference that stems largely from 1975–1995.
- The medians for both country groups are less negative than the means, indicating more frequent extreme negative tail events than extreme positive ones.

### Summary statistics by time periods (exact values)
- Full sample (N: AE 2789, EM 1468)
  - Mean: AE -2.4, EM -6.6
  - Median: AE -1.3, EM -4.8
  - Standard Deviation: AE 9.1, EM 14.3
- Pre-WWII (1800–1938, excluding WWI) (N: AE 1009, EM 146)
  - Mean: AE 0.3, EM 2.0
  - Median: AE 0.8, EM 2.4
  - Standard Deviation: AE 8.5, EM 10.4
- Post-WWII (1950–2018) (N: AE 1579, EM 1273)
  - Mean: AE -3.1, EM -7.6
  - Median: AE -1.7, EM -5.3
  - Standard Deviation: AE 8.0, EM 14.4
- Post-1980 (N: AE 906, EM 867)
  - Mean: AE 0.1, EM -5.5
  - Median: AE 0.5, EM -3.9
  - Standard Deviation: AE 6.2, EM 12.3
- Post-GFC (2009–2018) (N: AE 306, EM 239)
  - Mean: AE 0.5, EM -2.9
  - Median: AE -0.0, EM -2.2
  - Standard Deviation: AE 3.8, EM 7.4

### Frequency and cross-country variation
- Negative differentials occur more than half of the time for both advanced and emerging economies.
- The frequency of negative differentials for emerging economies is about 15 percentage points larger than for advanced economies.
- The most negative differentials are often associated with high growth episodes (post-war), while the most positive differentials often arise from large depreciation.

### Constructed variable and sample exclusions
- Key variable: interest-growth differential = effective interest rate − nominal growth rate.
- Effective interest rate contains:
  - the ratio between the interest bill and the average of the current and previous years’ public debt stocks,
  - plus the depreciation adjustment when relevant (for foreign-currency public debt).
- Formula used: ̃r_t − g_t = r_t + α_{t−1} · s_t − g_t, where:
  - α_{t−1} denotes the last period’s share of external public debt in total public debt,
  - s_t is the depreciation (against the U.S. dollar) compared with the last period,
  - r_t is the average interest rate on public debt,
  - g_t is the nominal growth rate.
- Sample exclusions: domestic and external sovereign default years, hyperinflation (greater than 100%), and extreme exchange rate collapse (top 1 percentile depreciation of the whole sample).

### Implications highlighted
- Negative differentials have been common historically and are not a purely recent phenomenon.
- Median less-negative values relative to means signal that extreme negative episodes drive average measures.
- While negative differentials can ease debt dynamics mechanically, history shows many crises have occurred after years of low differentials, and marginal borrowing costs can spike abruptly within months.

*Source: wpiea2020052-print-pdf — 3.1 The Prevalence of Negative Interest-Growth Differentials in History*

---

### 3.3 The Role of Financial Repression and Inflation in Interest-Growth Differentials

### Overview and historical episode (1975–95)
- Financial repression (interest rate controls, capital controls, reserve requirements, government ownership of banks, etc.) combined with inflation reduced government debt servicing costs in significant historical periods.
- Divergence in interest-growth differentials between advanced and emerging economies is concentrated in 1975–95:
  - Before the early 1970s, advanced and emerging economies’ differentials moved together with virtually no gap.
  - During 1975–95 advanced economies liberalized capital markets (allowing interest rates to rise faster than inflation), while many emerging economies maintained financial repression amid rising inflation.
  - By the mid-1990s many emerging economies had also liberalized financial markets.
- Negative interest-growth differentials are common across countries and time; the 1975–95 experience should not lead to the presumption that negative differentials are unique to emerging economies.

### Identification and empirical strategy
- Financial repression and liberalization years identified using de jure measures (Abiad, Detragiache and Tressel (2008)) and de facto measures (structural breaks in UIP deviations).
- Local projection specification on a 5-year horizon estimated:
  - (r−g)_{it+j} = β_j D_{it} + γ D_{it−1} + Γ X_{it} + α_i + ε_{it}, for j = 1,...,5.
  - Controls X include: real interest rate, real growth, change in public debt, initial public debt, commodity prices, Moody’s BAA spreads.
- Augmented specification for interaction between financial repression and expected inflation:
  - y_{it} = β_0 FR_{it} + β_1 FR_{it} × π^e_{it} + Γ X_{it} + α_i + ε_{it}.
  - FR measured by continuous financial repression indexes (Abiad et al. (2008)) and Chinn-Ito index; lagged inflation instrumented for expected inflation.

### Key empirical findings on financial repression, inflation, and differentials
- Financial repression years are associated with significantly lower interest-growth differentials, by 2 to 6 percentage points depending on type of liberalization and post-liberalization horizon.
- Timing and persistence:
  - Liberalization effects emerge after 1 to 2 years (at least one year for capital control and de facto liberalization measures; two years for interest rate and credit-control liberalizations).
  - Effects are long-lasting and remain significant after five years.
  - De jure and de facto measures produce similar magnitudes.
- Financial repression suppresses nominal interest rates and the response of interest rates to expected inflation:
  - A one standard deviation deterioration in the financial regulation index is associated with a decrease in nominal interest rates and differentials by about 3 percentage points.
  - Associated with an expected 1 percentage point inflation increase, the rise in effective rates is 0.4 percentage points lower for the most financial-repressed country (based on mean Chinn-Ito index) than for the least repressed.
  - The suppressing effect is most prominent for long-term domestic interest rates (10-year treasury bill rate or, if unavailable, 5-year or 2-year).
- Counterfactual alignment:
  - If emerging countries aligned with the median level of advanced economies’ financial repression (measured by the financial reform index), the effective interest rate gap between advanced and emerging economies would have been reduced by 1.8 percentage points (out of 3.9 percentage points), on average.

### Selected regression magnitudes and statistics (as reported)
- Financial repression coefficients (examples): -12.916 and -13.306 (standard errors in parentheses).
- Interaction term financial repression × inflation examples: -0.128 and -0.678.
- Inflation coefficient magnitudes for interest rates include: 0.755, 1.759, 1.176, 0.598, 0.590, 1.434, 1.338, 1.404.
- Instrument first-stage Wald-statistics examples: 18.74, 18.74, 31.74, 5.81, 97.12, 71.22, 0.05, 9.68.
- Example sample sizes reported in Table 2: N = 1254, 1254, 837, 893, 320, 252, 513, 031416 (as presented).

### Interest-growth differentials, fiscal variables, and sovereign defaults — stylized correlations
- Median (across countries) of country-specific correlations (sample of 55 countries, 4257 observations):
  - Corr(r−g, primary balance) = -0.03.
  - Corr(r−g, cyclically-adjusted primary balance) = 0.15.
  - Corr(cyclically-adjusted primary balance, real r) = 0.14.
  - Corr(cyclically-adjusted primary balance, real g) = -0.03.
- Decomposition (mean of country-specific correlations):
  - Full sample: corr(pb_ca, r−g) = 0.19 decomposed as corr(pb_ca, r)·σ_r/σ_{r−g} = 0.21·0.88 and −corr(pb_ca,g)·σ_g/σ_{r−g} = −0.03·0.45.
  - Advanced Economies: overall 0.22; components 0.25·0.87 and −0.03·0.50.
  - Emerging Economies: overall 0.14; components 0.15·0.89 and −0.02·0.36.
- Interpretation: real interest rate plays the dominant role in the positive association between cyclically-adjusted primary balance and interest-growth differentials; advanced economies show a stronger response than emerging economies.

### Primary fiscal response functions and implications
- Estimated fiscal response function:
  - pb_it = β_1 d_{it−1} + β_2 (r−g)_{it} + β_3 d_{it−1}×(r−g)_{it} + Γ X_{it} + α_i + ε_{it}.
- Key findings:
  - The primary balance tightens when interest-growth differentials are higher, and the tightening magnitude increases with initial debt.
  - Replicating Bohn (2008): a 10 percent increase in the debt-to-GDP ratio is associated with a 0.1 percent of GDP primary balance tightening.
  - With the interaction term included, the coefficient on lag public debt × (r−g) is positive and significant (examples: 0.001 with significance).
- Quantitative example:
  - For a country with 100% debt-to-GDP, a 100 basis points decrease in differentials is associated with an expansion in the primary fiscal balance by 0.1 percent of GDP—far less than the beneficial impact on the debt ratio (1 percent of GDP) that comes from the accounting identity ((r−g) × debt).
  - Policymakers respond to lower differentials with some fiscal expansion, but not enough to fully offset the direct beneficial impact of lower differentials on debt dynamics.

### Additional regression details (Table 5 highlights)
- Lag public debt coefficient examples: 0.010∗, 0.010∗, 0.012∗∗, 0.011∗∗, 0.011∗∗.
- Real output gap coefficients examples: 0.076, 0.117∗∗, 0.118∗∗.
- Real spending gap coefficient examples: -0.100∗∗∗, -0.103∗∗∗, -0.103∗∗∗.
- Sample sizes and fit examples: N = 4007 across columns; R^2 examples: 0.008, 0.111, 0.014, 0.024, 0.133, 0.133.

*Source: IMF Working Paper — chapter section 3.3 "The Role of Financial Repression and Inflation in Interest-Growth Differentials"*

---

### 4.2 Interest-Growth Differentials in the Run-up to Default Episodes

### Main findings on interest-growth differentials
- Interest-growth differentials in the run-up to default do not significantly differ from those in normal times; although there is an increase toward the onset of default, it is not significant.
- This pattern holds in the full sample, the post-war, advanced economies, and emerging economies subsamples.
- Decomposition of differentials:
  - Real economic growth is significantly lower than usual the year prior to default.
  - A growth deceleration is visible—while not significant—in the years prior to defaults.
  - Real interest rates are somewhat lower than usual, albeit not significantly.
- Authors conclude: "we cannot reject that interest-growth differentials are the same as in normal times."

### Depreciation adjustment and timing
- Sovereign defaults in emerging countries are often just preceded or accompanied by large depreciation, which could boost the debt ratio.
- Depreciations are, on average, 20 percent larger in the year prior to default compared with normal times.
- This leads to higher depreciation adjustment, 8.8 percentage points one year prior to default, significant at the 90% level.
- Monthly evidence: visibly large depreciations—albeit insignificant—do not show up until a few months prior to default.

### Fiscal variables and predictive power
- Both primary deficits and public debts are larger than usual in the year before default:
  - In the year prior to default, the primary fiscal balance is about 1 percent of GDP lower than in normal times, even after teasing out the cyclical component.
  - In the year prior to default, public debt is 16 percent higher, as share of GDP.
- Implication:
  - Interest-growth differentials do not help to predict defaults.
  - Primary deficits and public debt ratios seem to have some predictive power.
- Confirmation: Moreno Badia et al. (2020) reach the same conclusion using a machine learning early warning system based on a large sample and more than 100 variables.

### Sample and specification notes
- "Normal times" defined as all years except: (i) years when the country is in default, (ii) the three years after completion of debt restructuring, or (iii) the five years prior to default.
- Estimating equation includes country fixed effects and year fixed effects.
- Sample counts reported in figures:
  - No. of default episodes with all 5 pre-default years = 33; with at least 1 pre-default year = 49.
  - Monthly depreciation sample: No. of default episodes = 12.

*Source: IMF staff analysis — section 4.2 as presented*

---

### 4.3 Marginal Rates in the Run-up to Default Episodes

### Behavior of marginal rates
- Marginal interest rate responds faster than the average effective rate to changes in market participants’ sentiments.
- Abundant evidence documents the increase of marginal rates in the run-up to defaults (e.g., Greece, Argentina, Dominican Republic).
- Averaging across all default episodes, marginal rates in the run-up to defaults exceed those in normal times by about 2 percentage points, and the differences are statistically significant.
- Pattern holds for marginal rates measured on both domestic currency borrowing and foreign currency borrowing, and is slightly more pronounced on the foreign currency portion.

### Timing and policy implications
- Although marginal rate increases significantly preceding sovereign defaults, they do not give much time for policy makers to react.
- Monthly decomposition of the year before default:
  - Sizable gaps emerge about six months before default and keep growing as default approaches.
  - Increases are not robustly significant until two months prior to default.
- Interpretation:
  - Marginal rate reflects market sentiment and willingness to roll over debt; it reacts quickly but is an imperfect proxy for future developments in the average effective interest rate.
  - Marginal rates matter for debt dynamics when sentiment changes are sustained and affect the whole maturity structure of the debt.
  - Increases in marginal rates are the mirror image of a default triggered by a change in market sentiment, which is hard to predict.

### Sample counts reported
- No. of default episodes with domestic marginal rates in all 5 pre-default years = 17, foreign = 13.
- With at least 1 pre-default year = 21 (domestic), 22 (foreign).
- Monthly marginal-rate sample: No. of default episodes = 15.

*Source: IMF staff analysis — section 4.3 as presented*

---

### 5 Conclusion — Key takeaways

- Negative interest-growth differentials experienced today are not unprecedented; they prevail in the history of both advanced and emerging economies and are "if anything, the norm rather than the exception during the past two centuries."
- Low differentials based on average effective interest rates are not associated with lower frequency of sovereign defaults, whereas fiscal deficits and debts seem to have some (albeit limited) predictive power for sovereign defaults.
- Cautionary message: After prolonged periods of low differentials based on average effective interest rates, marginal borrowing costs can rise suddenly and sharply, shutting countries out of financial markets at short notice.
- The paper abstracts from a full set of exogenous contributors to interest-growth differentials; a fuller analysis would require considering the reasons why differentials are currently so low.
- Policy implication emphasized: "negative differentials do not necessarily reduce the likelihood of government defaults in the years ahead. Only with further reflection on the factors underlying the low differentials, as well as prospects for the primary fiscal balance, will we be able to make fully informed judgments on an appropriate stance of policies."

*Source: IMF staff analysis (sections 4.2, 4.3, and 5 as presented in the supplied content).*

---

### Data Appendix and Appendix B — Data sources, construction, and identification of financial repression years

### Data coverage and construction highlights
- Coverage: Unbalanced panel of 55 countries (24 advanced economies and 31 emerging economies) over 1800-2018.
- Government sector coverage: Data collected at the general government level wherever available; general government data often unavailable before 1960; sector switches recorded.
- Effective interest rate on debt: Computed as the ratio of the interest bill in yeart to the stock of government debt (average of debt stocks of year-endt and t−1).
- Marginal cost of borrowing: Compiled from Mauro, Sussman and Yafeh (2002, 2006) for 1870-1914 and Datastream—updated to June 2019.
- External public debt: Assembled from multiple sources and extended back to 1970 using the World Bank’s International Debt Statistics when possible.
- Interest-growth differentials: Calculated as differences between average effective interest rates on debt and nominal growth rates; revaluation impact of exchange rate depreciation on foreign-currency public debt allowed for via a depreciation adjustment.
- Other financial variables: Money market rates and exchange rates from Global Financial Data; money market rate defined as the 3-month treasury yield in the secondary market or 3-month interbank overnight borrowing rate if unavailable.
- Sovereign defaults: Years drawn from Reinhart and Rogoff (2009) and Moody’s "Sovereign Default and Recovery Rates, 1983-2018"; months of default from Mauro, Sussman and Yafeh (2002) and Asonuma and Trebesch (2016).
- Financial repression data: Based on Abiad, Detragiache and Tressel (2008), covering 91 countries since 1973; index normalized between zero and one.

### Identifying financial repression years (methodology and robustness)
- De jure measures: Abiad, Detragiache and Tressel (2008); liberalization year = first year index reaches highest category (free market); if index decreases after, the first year of highest value used.
- De facto measures: structural breaks in UIP deviations identified using Bai and Perron (1998); UIP deviation constructed at 3-month horizon using secondary market yields.
- Robustness and cross-validation:
  - De jure and de facto measures are complementary; median difference between liberalization years identified by UIP deviation and capital controls abolishment is 2-year.
  - Different measures of UIP deviation result in very similar liberalization years, with largest difference of 2-year.
  - De jure measures indicate a significant wave of financial liberalization:
    - Advanced economies: starting from the early 1980s (earliest as 1963, latest as 1988).
    - Emerging economies: starting from the late 1980s (earliest as 1974, latest as 2004).

*Source: Data Appendix (A) and Appendix B as presented in the supplied content.*

### 3.1  The Prevalence of Negative Interest-Growth Differentials in History  . . . . . . . . .   6

### 3.1  The Prevalence of Negative Interest-Growth Differentials in History

### Key empirical regularities
- Negative interest-growth differentials occur for prolonged periods in history in both advanced and emerging economies.
- On average:
  - differentials are approximately negative 2.5 percentage points for advanced economies,
  - and negative 6.5 percentage points for emerging economies.
- Across time:
  - differentials are more negative post-WWII than Pre-WWII,
  - and more negative pre-GFC than post-GFC.
- Across countries:
  - emerging economies show lower (more negative) differentials than advanced economies, a difference that stems largely from 1975–1995.
- The medians for both country groups are less negative than the means, indicating more frequent extreme negative tail events than extreme positive ones.

### Summary statistics by time periods (Table 1, exact values)
- Full sample (N: AE 2789, EM 1468)
  - Mean: AE -2.4, EM -6.6
  - Median: AE -1.3, EM -4.8
  - Standard Deviation: AE 9.1, EM 14.3
- Pre-WWII (1800–1938, excluding WWI) (N: AE 1009, EM 146)
  - Mean: AE 0.3, EM 2.0
  - Median: AE 0.8, EM 2.4
  - Standard Deviation: AE 8.5, EM 10.4
- Post-WWII (1950–2018) (N: AE 1579, EM 1273)
  - Mean: AE -3.1, EM -7.6
  - Median: AE -1.7, EM -5.3
  - Standard Deviation: AE 8.0, EM 14.4
- Post-1980 (N: AE 906, EM 867)
  - Mean: AE 0.1, EM -5.5
  - Median: AE 0.5, EM -3.9
  - Standard Deviation: AE 6.2, EM 12.3
- Post-GFC (2009–2018) (N: AE 306, EM 239)
  - Mean: AE 0.5, EM -2.9
  - Median: AE -0.0, EM -2.2
  - Standard Deviation: AE 3.8, EM 7.4

### Frequency and cross-country variation
- Negative differentials occur more than half of the time for both advanced and emerging economies.
- The frequency of negative differentials for emerging economies is about 15 percentage points larger than for advanced economies.
- The most negative differentials are often associated with high growth episodes (post-war), while the most positive differentials often arise from large depreciation.

### Constructed variable and sample exclusions
- The key variable is the interest-growth differential: the difference between the effective interest rate and the nominal growth rate.
- The effective interest rate contains:
  - the ratio between the interest bill and the average of the current and previous years’ public debt stocks,
  - plus the depreciation adjustment when relevant (for foreign-currency public debt).
- The formula used (as in source) is: ̃r_t − g_t = r_t + α_{t−1} · s_t − g_t, where:
  - α_{t−1} denotes the last period’s share of external public debt in total public debt,
  - s_t is the depreciation (against the U.S. dollar) compared with the last period,
  - r_t is the average interest rate on public debt,
  - g_t is the nominal growth rate.
- Sample exclusions: domestic and external sovereign default years, hyperinflation (greater than 100%), and extreme exchange rate collapse (top 1 percentile depreciation of the whole sample).

### Implications highlighted in this section
- Negative differentials have been common historically and are not a purely recent phenomenon.
- Median less-negative values relative to means signal that extreme negative episodes drive average measures.
- While negative differentials can ease debt dynamics mechanically, history shows many crises have occurred after years of low differentials, and marginal borrowing costs can spike abruptly within months.

_Italic: Source: wpiea2020052-print-pdf — 3.1 The Prevalence of Negative Interest-Growth Differentials in History_

### 3.3  The Role of Financial Repression and Inflation in Interest-Growth Differentials

### 3.3  The Role of Financial Repression and Inflation in Interest-Growth Differentials

### Overview and historical episode (1975–95)
- Financial repression (interest rate controls, capital controls, reserve requirements, government ownership of banks, etc.) combined with inflation reduced government debt servicing costs in significant historical periods.
- The divergence in interest-growth differentials between advanced and emerging economies is concentrated in 1975–95:
  - Before the early 1970s, advanced and emerging economies’ differentials moved together with virtually no gap.
  - During 1975–95 advanced economies liberalized capital markets (allowing interest rates to rise faster than inflation), while many emerging economies maintained financial repression amid rising inflation.
  - By the mid-1990s many emerging economies had also liberalized financial markets.
- Negative interest-growth differentials are common across countries and time; the 1975–95 experience should not lead to the presumption that negative differentials are unique to emerging economies.

### Identification and empirical strategy
- Financial repression and liberalization years identified using de jure measures (Abiad, Detragiache and Tressel (2008)) and de facto measures (structural breaks in UIP deviations).
- Local projection specification on a 5-year horizon estimated to measure the gap in (r−g) before and after financial market liberalization:
  - (r−g)_{it+j} = β_j D_{it} + γ D_{it−1} + Γ X_{it} + α_i + ε_{it}, for j = 1,...,5.
  - Controls X include: real interest rate, real growth, change in public debt, initial public debt, commodity prices, Moody’s BAA spreads.
- Augmented specification used to study interaction between financial repression and expected inflation:
  - y_{it} = β_0 FR_{it} + β_1 FR_{it} × π^e_{it} + Γ X_{it} + α_i + ε_{it}.
  - FR measured by continuous financial repression indexes (Abiad et al. (2008)) and Chinn-Ito index; lagged inflation instrumented for expected inflation.

### Key empirical findings on financial repression, inflation, and differentials
- Financial repression years are associated with significantly lower interest-growth differentials, by 2 to 6 percentage points depending on type of liberalization and post-liberalization horizon.
- Timing and persistence:
  - Liberalization effects are not contemporaneous; effects emerge after 1 to 2 years (at least one year for capital control and de facto liberalization measures; two years for interest rate and credit-control liberalizations).
  - Effects are long-lasting and remain significant after five years.
  - De jure and de facto measures produce similar magnitudes.
- Financial repression suppresses nominal interest rates and the response of interest rates to expected inflation:
  - A one standard deviation deterioration in the financial regulation index is associated with a decrease in nominal interest rates and differentials by about 3 percentage points.
  - Associated with an expected 1 percentage point inflation increase, the rise in effective rates is 0.4 percentage points lower for the most financial-repressed country (based on mean Chinn-Ito index) than for the least repressed.
  - The suppressing effect is most prominent for long-term domestic interest rates (10-year treasury bill rate or, if unavailable, 5-year or 2-year).
- Counterfactual alignment:
  - If emerging countries aligned with the median level of advanced economies’ financial repression (measured by the financial reform index), the effective interest rate gap between advanced and emerging economies would have been reduced by 1.8 percentage points (out of 3.9 percentage points), on average. (This represents a partial effect holding other factors constant.)

### Selected regression magnitudes (high-level highlights from Table 2 and text)
- Financial repression coefficients indicate substantial negative associations with rates and differentials (examples reported):
  - Financial repression (financial regulation index) coefficients reported in Table 2 include values such as -12.916 and -13.306 (standard errors in parentheses).
  - Interaction term financial repression × inflation entries include values such as -0.128 and -0.678 with significance markers.
- Inflation coefficient magnitudes for interest rates in Table 2 include values such as 0.755, 1.759, 1.176, 0.598, 0.590, 1.434, 1.338, 1.404 (with standard errors reported in table).
- Instrument first-stage Wald-statistics reported (examples in Table 2): 18.74, 18.74, 31.74, 5.81, 97.12, 71.22, 0.05, 9.68.
- Sample sizes in Table 2 vary by specification (examples): N = 1254, 1254, 837, 893, 320, 252, 513, 031416 (as presented).

### Interest-growth differentials, fiscal variables, and sovereign defaults — stylized correlations
- Median (across countries) of country-specific correlations (sample of 55 countries, 4257 observations):
  - Correlation between r−g and primary balance: -0.03.
  - Correlation between r−g and cyclically-adjusted primary balance: 0.15.
  - Correlation of cyclically-adjusted primary balance with real r: 0.14.
  - Correlation of cyclically-adjusted primary balance with real g: -0.03.
- Decomposition (mean of country-specific correlations) highlights role of real interest rate:
  - Full sample: corr(pb_ca, r−g) = 0.19 decomposed as corr(pb_ca, r)·σ_r/σ_{r−g} = 0.21·0.88 and −corr(pb_ca,g)·σ_g/σ_{r−g} = −0.03·0.45.
  - Advanced Economies: overall 0.22; components 0.25·0.87 and −0.03·0.50.
  - Emerging Economies: overall 0.14; components 0.15·0.89 and −0.02·0.36.
- Interpretation: real interest rate plays the dominant role in the positive association between cyclically-adjusted primary balance and interest-growth differentials; advanced economies show a stronger response (fiscal expansions when real interest rates are low) than emerging economies.

### Primary fiscal response functions and implications
- Estimated fiscal response function (pb_it = β_1 d_{it−1} + β_2 (r−g)_{it} + β_3 d_{it−1}×(r−g)_{it} + Γ X_{it} + α_i + ε_{it}) finds:
  - The primary balance tightens when interest-growth differentials are higher, and the tightening magnitude increases with initial debt.
  - Replicating Bohn (2008): a 10 percent increase in the debt-to-GDP ratio is associated with a 0.1 percent of GDP primary balance tightening.
  - With the interaction term included, the coefficient on lag public debt × (r−g) is positive and significant (Table 5 reports values such as 0.001 with significance).
- Quantitative example and policy implication:
  - For a country with 100% debt-to-GDP, a 100 basis points decrease in differentials is associated with an expansion in the primary fiscal balance by 0.1 percent of GDP—far less than the beneficial impact on the debt ratio (1 percent of GDP) that comes from the accounting identity ((r−g) × debt).
  - In practice, policymakers respond to lower differentials with some fiscal expansion, but not enough to fully offset the direct beneficial impact of lower differentials on debt dynamics.

### Additional reported regression details (Table 5 highlights)
- Lag public debt coefficient examples: 0.010∗, 0.010∗, 0.012∗∗, 0.011∗∗, 0.011∗∗ (standard errors in parentheses).
- Real output gap coefficients in some specifications: 0.076, 0.117∗∗, 0.118∗∗.
- Real spending gap coefficient examples: -0.100∗∗∗, -0.103∗∗∗, -0.103∗∗∗.
- Sample sizes and fit examples: N = 4007, 4007, 4007, 4007, 4007, 4007 across columns; R^2 examples: 0.008, 0.111, 0.014, 0.024, 0.133, 0.133 (as presented).

*Source: IMF Working Paper — chapter section 3.3 "The Role of Financial Repression and Inflation in Interest-Growth Differentials" from the provided PDF content.*

### 4.2  Interest-Growth Differentials in the Run-up to Default Episodes

### 4.2 Interest-Growth Differentials in the Run-up to Default Episodes

### Main findings on interest-growth differentials
- Interest-growth differentials in the run-up to default do not significantly differ from those in normal times; although there is an increase toward the onset of default, it is not significant.
- This pattern holds in the full sample, the post-war, advanced economies, and emerging economies subsamples.
- Decomposition of differentials:
  - Real economic growth is significantly lower than usual the year prior to default.
  - A growth deceleration is visible—while not significant—in the years prior to defaults.
  - Real interest rates are somewhat lower than usual, albeit not significantly.
- On balance, the authors state: "we cannot reject that interest-growth differentials are the same as in normal times."

### Depreciation adjustment and timing
- Sovereign defaults in emerging countries are often just preceded or accompanied by large depreciation, which could boost the debt ratio.
- Depreciations are, on average, 20 percent larger in the year prior to default compared with normal times.
- This leads to higher depreciation adjustment, 8.8 percentage points one year prior to default, significant at the 90% level.
- Monthly evidence: visibly large depreciations—albeit insignificant—do not show up until a few months prior to default.

### Fiscal variables and predictive power
- Both primary deficits and public debts are larger than usual in the year before default:
  - In the year prior to default, the primary fiscal balance is about 1 percent of GDP lower than in normal times, even after teasing out the cyclical component.
  - In the year prior to default, public debt is 16 percent higher, as share of GDP.
- These results suggest:
  - Interest-growth differentials do not help to predict defaults.
  - Primary deficits and public debt ratios seem to have some predictive power.
- Confirmation: Moreno Badia et al. (2020) reach the same conclusion using a machine learning method in the context of an early warning system for fiscal crises, based on a large sample of countries and more than 100 variables over a shorter sample period.

### Sample and specification notes (as reported)
- "Normal times" are defined as all years except: (i) those when the country is in default, (ii) the three years after the completion of debt restructuring, or (iii) the five years prior to default.
- The estimating equation includes country fixed effects and year fixed effects to control for global factors affecting interest-growth differentials.
- Sample sizes reported in figures (annual and monthly): e.g., No. of default episodes with all 5 pre-default years = 33; with at least 1 pre-default year = 49; monthly depreciation sample: No. of default episodes = 12. (These counts are reported in the figure notes.)

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### 4.3 Marginal Rates in the Run-up to Default Episodes

### Behavior of marginal rates
- The marginal interest rate responds faster than the average effective rate to changes in market participants’ sentiments.
- There is abundant evidence documenting the increase of marginal rates in the run-up to defaults (e.g., Greece, Argentina, Dominican Republic).
- Averaging across all default episodes, marginal rates in the run-up to defaults exceed those in normal times by about 2 percentage points, and the differences are statistically significant.
- The pattern holds for marginal rates measured on both domestic currency borrowing and foreign currency borrowing, and is slightly more pronounced on the foreign currency portion.

### Timing and policy implications
- Although the marginal rate increases significantly preceding sovereign defaults, it does not give much time for policy makers to react.
- Unpacking the year before default into months:
  - Sizable gaps emerge about six months before default and keep growing as default approaches.
  - However, the increases are not robustly significant until two months prior to default.
- Interpretation:
  - The marginal rate reflects market sentiment and willingness to roll over debt; it reacts quickly but is an imperfect proxy for future developments in the average effective interest rate.
  - Marginal rates are relevant for debt dynamics when sentiment changes are sustained and affect the whole maturity structure of the debt.
  - Increases in marginal rates are the mirror image of a default triggered by a change in market sentiment, which is hard to predict.
- Reported sample counts in figures: e.g., No. of default episodes with domestic marginal rates in all 5 pre-default years = 17, foreign = 13; with at least 1 pre-default year = 21 (domestic), 22 (foreign). Monthly marginal-rate sample: No. of default episodes = 15.

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### 5 Conclusion (key takeaways)
- Negative interest-growth differentials experienced today are not unprecedented; they prevail in the history of both advanced and emerging economies and are "if anything, the norm rather than the exception during the past two centuries."
- Low differentials based on average effective interest rates are not associated with lower frequency of sovereign defaults, whereas fiscal deficits and debts seem to have some (albeit limited) predictive power for sovereign defaults.
- Cautionary message: After prolonged periods of low differentials based on average effective interest rates, marginal borrowing costs can rise suddenly and sharply, shutting countries out of financial markets at short notice.
- The paper abstracts from a full set of exogenous contributors to interest-growth differentials; a fuller analysis would require considering the reasons why differentials are currently so low.
- Policy implication emphasized: "negative differentials do not necessarily reduce the likelihood of government defaults in the years ahead. Only with further reflection on the factors underlying the low differentials, as well as prospects for the primary fiscal balance, will we be able to make fully informed judgments on an appropriate stance of policies."

*Source: IMF staff analysis (4.2 and 4.3 sections, as presented in the supplied content).*

### References

### wpiea2020052-print-pdf - References

### References list (overview)
- The References cite extensive literature on sovereign debt, public debt databases, financial repression, interest-growth differentials, historical real interest rates, sovereign defaults, and fiscal sustainability. Notable cited authors and works include Abbas; Reinhart and Rogoff; Jordà, Schularick and Taylor; Mauro, Sussman and Yafeh; Abiad, Detragiache and Tressel; Bai and Perron; Blanchard; Piketty; Rachel and Summers; and others as listed in the source.

### Data Appendix (A) — data sources and construction
- Coverage:
  - Unbalanced panel of 55 countries (24 advanced economies and 31 emerging economies) over 1800-2018.
- Government sector coverage:
  - Data are collected at the general government level wherever available; in most cases, general government data are unavailable before 1960.
  - Sector reported commonly switches from central government to general government in nearly all final spliced series, generally in the 1960s or 70s. Breaks in series are recorded in the database.
- Effective interest rate on debt:
  - Computed as the ratio of the interest bill in yeart to the stock of government debt (average of debt stocks of year-endt and t−1).
- Marginal cost of borrowing:
  - Compiled from Mauro, Sussman and Yafeh (2002, 2006) for 1870-1914 and Datastream—updated to June 2019.
- External public debt:
  - Assembled using WB-IMF Quarterly Public Sector Debt, OECD Central Government Debt, WEO, Guscina and Jeanne (2006), Morsy et al. (2007), Abbas and Christensen (2010), Abbas et al. (2010), and Abbas et al. (2014).
  - Extended back to 1970 using the World Bank’s International Debt Statistics when possible.
- Source composition:
  - "Half of the observations for the fiscal variables in the dataset are drawn from various cross-country sources, including the IMF’s World Economic Outlook (WEO) and International Financial Statistics (IFS) and the OECD Analytical Database for the past 20 to 50 years (subject to availability); the Statistical Yearbooks of the League of Nations and the United Nations (as well as their Public Debt Supplements) for the period between World War I and the 1970s; and Flandreau and Zumer (2004) for the pre-World War I era; in addition, long-run historical series are drawn from Mitchell’s International Historical Statistics and the Montevideo-Oxford Latin American Database (MOXLAD). The other half of the data is hand-collected from country-specific sources."
  - Examples of country-specific sources: Fregert and Gustafsson (2005) for Sweden over 1800-2004; Fernandez and Acha (1976) for Spain over 1850–1975; Junguito and Rincon (2004) for Colombia over 1923-2003.
- GDP data:
  - Main sources for distant past: Mitchell and MOXLAD.
  - For most countries, GDP does not exist before World War I; proxied by Gross National Product or Net National Product from Mitchell’s International Historical Statistics when necessary.
  - UN statistical yearbooks used to fill gaps between 1940 and 1975; OECD database used for some countries beginning as early as 1960.
  - Starting in the mid 1990s, GDP data for almost all countries are taken from the WEO.
  - Fiscal and GDP data crosschecked with Jordà, Schularick and Taylor (2017) for 17 advanced economies from 1870 to 2016.
- Interest-growth differentials:
  - Calculated as the differences between average effective interest rates on debt and nominal growth rates.
  - Revaluation impact of exchange rate depreciation on public debt denominated in foreign currency is allowed for via a depreciation adjustment (details in Section 3.3).
- Other financial variables:
  - Money market rates and exchange rates drawn from Global Financial Data. Money market rate defined as the 3-month treasury yield in the secondary market; if unavailable, the 3-month interbank overnight borrowing rate is used.
  - Sovereign defaults: years drawn from Reinhart and Rogoff (2009) and, for 2009 to 2018, Moody’s “Sovereign Default and Recovery Rates, 1983-2018”; months of default from Mauro, Sussman and Yafeh (2002) and Asonuma and Trebesch (2016).
  - Financial repression: based on Abiad, Detragiache and Tressel (2008), covering 91 countries since 1973. Database records financial policy changes along seven dimensions and combines liberalization scores into a normalized graded index between zero and one.

### Identifying financial repression years (Appendix B) — methodology and key findings
- Measures used:
  - De jure measures: from Abiad, Detragiache and Tressel (2008). Define the liberalization year as the first year the index of interest rate controls and capital controls reach the highest category (free market). If the index decreases after reaching the highest category, the most recent year when the highest value is first reached is used; estimates can be viewed as a lower bound.
  - De facto measures: structural breaks in UIP deviations identified by applying Bai and Perron (1998).
- UIP deviation construction:
  - Calculate the 3-month horizon UIP deviation using secondary market yields of sovereign bonds. The 3-month horizon chosen because 3-month interest rates provide the largest country and year coverage and sufficient frequency to identify structural breaks.
  - Note: 3-month interest rate structural breaks are not automatically nor substantially leading to structural breaks on the effective interest rate used in interest-growth differentials.
- Rationale and complementarities:
  - De jure measures are objectively defined by policy regulation changes but can miss non-legislated forms of financial repression (e.g., moral suasion).
  - De facto measures are market-based and can capture changes resulting from explicit and implicit regulations.
- Challenges with de facto measures:
  - UIP deviation measurement error because the expected exchange rate is unobservable.
  - Approaches used to calculate expected future exchange rates to minimize measurement error: the actual exchange rate, last period’s exchange rate, the average of last three periods, and the expected future exchange rate backed from Purchasing Power Parity.
  - Because UIP usually does not hold, benchmarking a counterfactual for no financial repression is difficult; focus placed on structural breaks rather than all deviations.
- Cross-validation and timing results:
  - De jure and de facto measures are complementary and provide cross-validation.
  - Median difference between liberalization years identified by UIP deviation and capital controls abolishment is 2-year.
  - Different measures of UIP deviation result in very similar liberalization years, with the largest difference of 2-year.
  - De jure measures indicate a significant wave of financial liberalization:
    - Advanced economies: starting from the early 1980s (earliest as 1963, latest as 1988).
    - Emerging economies: starting from the late 1980s (earliest as 1974, latest as 2004).
    - Examples: Bank of England stopped publishing the Minimum Lending Rate in 1981; interest rate ceilings abolished in 1967 in Canada; deposit rates liberalized in 1988-89 in Mexico; restrictions on capital movements lifted after August 1989 in Turkey.
    - By the end of 1990s, the majority of advanced economies abolished interest controls and capital controls; liberalization in emerging economies was still ongoing.
- Empirical procedure notes:
  - Structural breaks in UIP deviations are identified using Bai and Perron (1998).
  - The 3-month horizon is used because it provides the largest country and year coverage.
  - Various expected exchange rate measures are employed to check robustness.

*Source: wpiea2020052-print-pdf - References*

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_Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020052-print-pdf.pdf_