## _wp11260

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---

### I. Summary / Introduction
- Definition: The interest rate-growth differential (IRGD) is the differential between the average interest rate paid on government debt and the growth rate of the economy; central to debt dynamics and debt sustainability.
- Data construction: Database of average effective interest rates based on budget outturn data and debt stocks for a large sample of advanced and non-advanced economies, correcting for exchange rate effects on foreign-currency denominated debt and excluding about one-third of countries with concessional debt shares above 50 percent.
- Empirical summary for 1999–2008:
  - IRGDs are correlated with income levels, generally negative in non-advanced economies and often strongly so.
  - Negative IRGDs can stabilize or reduce debt ratios even with persistent primary deficits.
- Hypothesis:
  - Lower IRGDs in non-advanced economies owe as much or more to lower real interest rates than to higher growth.
  - Lower interest rates are conjectured to be related to captive financial markets, financial repression, and lack of financial development.
  - Rising IRGDs may occur relatively rapidly as financial development and global integration proceed, potentially before GDP per capita convergence.

### II. Interest Rate-Growth Differentials and Income
- Conceptual role:
  - IRGD is the rate at which the debt-to-GDP ratio would grow if the primary balance were zero and debt service were rolled over.
  - Positive IRGD → need for primary surplus proportional to IRGD and debt ratio to stabilize debt.
  - Negative IRGD → debt ratio can decline toward zero even with a primary deficit.
- Empirical observations (1999–2008 and broader samples):
  - Among G-20 advanced economies, the IRGD averaged about 1 percentage point during 1999–2008.
  - Among EMEs and LICs, IRGDs were generally markedly negative with substantial variability.
  - Average IRGD during 1999–2008:
    - almost -4 percentage points for a broad sample of EMEs,
    - below -7 percent for the total sample of non-advanced economies.
- Distributional and temporal features:
  - IRGD shows a positive correlation with GDP per capita.
  - Many non-advanced economies had average IRGDs well below -10 percentage points in 1999–2008.
  - Non-advanced economies exhibit high within-country volatility and low persistence of IRGDs relative to advanced economies.
  - Emerging economies show the highest within-country volatility, reflecting episodic crises (effects typically last 2–3 years).

### III. The Puzzle: Low IRGDs Driven by Low Real Interest Rates
- Theoretical expectation vs. evidence:
  - Theory (modified golden rule) suggests real interest rates should exceed growth rates in balanced-growth advanced economies.
  - Catch-up economies are expected to have real interest rates at least as high as advanced economies plus premia.
- Counterfactual evidence (1999–2008):
  - Real interest rates in non-advanced economies were on average almost 6 percentage points lower than the G-7 average.
  - Average GDP growth in non-advanced economies exceeded the G-7 average by about 3 percentage points.
  - The lower real interest rates accounted for about two thirds of the average IRGD difference with respect to the G-7 in 1999–2008.
- Illustrative scenario:
  - If EMEs had paid G-7 real interest rates plus an average spread of 5 percentage points, their average IRGD during 1999–2008 would have been about 3 percentage points (instead of the observed -4 percentage points), assuming fully open external financial accounts.

### IV. Why Are Interest Rates So Low in EMEs? Financial Repression and Market Distortions
- Typical elements of financial repression cited:
  - Legal ceilings on lending/deposit rates, high reserve ratios, entry barriers and public ownership of banks, quantitative credit restrictions, government-directed lending, subsidized lending rates, and restrictions on capital transactions.
- Empirical stylized facts:
  - Real interest rates are positively correlated with income per capita.
  - Country-level volatility of real interest rates is inversely related to income per capita.
  - The EMBI spread over US Treasuries contrasts with the spread of effective interest rates actually paid by non-advanced economy government debt.
  - Real interest rates are inversely related to inflation and can be negative for extended periods in many non-advanced economies; systematic low real rates associated with inflation point to financial repression and bans on indexed or foreign-currency instruments.
  - Financial development indicators (e.g., private credit, commercial bank asset shares) correlate with higher real interest rates.
- Historical reform episodes:
  - Chile, Israel, Korea, and South Africa saw real interest rates turn positive from large negative levels after financial reforms.
  - Korea and South Africa show real interest rates moving almost in tandem with private credit development.
- Persistence of repression elements (1998–2008, Abiad et al. (2008)):
  - 25 percent of non-advanced economies had deposit or lending rate regulations.
  - 13 percent had credit controls.
  - 34 percent had entry barriers to domestic banking.
  - 55 percent had significant restrictions on capital inflows and outflows.

### V. Econometric Testing: Real Effective Interest Rates and Financial Development (Panel Evidence)
- Data and specification:
  - Annual panel 1999–2008 with 128 countries (advanced and non-advanced) after exclusions.
  - Dependent variable: real effective interest rate (effective interest cost / debt stock, adjusted for currency valuation effects).
  - Dynamic panel: rit = αrit-1 + Xit′β + γZit + νi + ηt + εit, estimated by system GMM (Arellano and Bover (1995); Blundell and Bond (1998)).
- Controls (Xit): lagged public debt (% of GDP), change in public debt (% of GDP), real GDP growth, domestic private savings, population aging (not significant), and time-fixed effects.
- Financial repression/development indicators (Zit):
  - Commercial bank claims on non-financial sectors as percent of total claims (commercial + central bank assets).
  - Private credit (% of GDP).
  - Inflation.
  - Financial liberalization index (Abiad et al. (2008), normalized 0–1).
  - Capital account openness index (Chinn and Ito (2002), normalized 0–1).
  - Principal components combining commercial bank assets, private credit, liquid liabilities, capital market openness, and inflation.
- Key empirical results and magnitudes (Table 3 interpretations preserved exactly):
  - Commercial bank assets coefficient: 0.144 (Column 1).
    - 1999–2008 averages: real interest rates in non-advanced and advanced economies were -2.7 percent and 2.6 percent respectively (contemporaneous gap 5.3 percentage points).
    - Commercial bank assets averages: 84 percent (non-advanced) and 97 percent (advanced) of total (commercial + central bank) assets.
    - A rise in commercial bank assets from 84 percent to 97 percent implies a contemporaneous real interest rate increase of 1.9 percentage points (0.144 × 13), accounting for 36 percent of the 5.3 percentage point gap.
    - Long-run effect (γ/(1-α)) of this raise would be about 3 percentage points.
  - Private credit coefficient: 0.03 (Column 3).
    - Increase in private credit from 42 percent of GDP (non-advanced average) to 118 percent of GDP (advanced average) implies a contemporaneous real interest rate increase of 2.3 percentage points; long-run effect about 4 percentage points.
  - Financial liberalization and capital openness indices: positive and significant (Columns 2, 4, 5); financial liberalization increase from 0.72 (non-advanced average) to 0.94 (advanced average) implies a real interest rate rise of about 3.4 percentage points.
  - Inflation: strongly negatively associated with real interest rates and significant at 1 percent. Regression coefficient suggests a 1 percentage point increase in inflation is associated with a reduction in real interest rate around 0.69 percentage point (Column 6).
  - Principal components: first and second components significant with expected signs; second component (large weight on inflation) implies that one percentage point of inflation (0.072 increase in second component) yields an implied −0.48 percent effect on real interest rates (0.072 × -6.66).
  - Non-linear (squared) terms for financial development measures are insignificant; results robust in non-advanced-only subsample and for longer periods.
  - Excluding high-inflation episodes (>20 percent) leaves results largely unchanged, except capital account openness becomes insignificant; magnitude of financial development impacts remains similar though slightly smaller.
- Diagnostics:
  - Hansen J-test of over-identifying restrictions cannot reject validity of instruments (example p-value=0.29 for Column 1).
  - Arellano-Bond AR(2) test: cannot reject no second-order serial correlation in first-differenced errors (example p-value=0.68 for Column 1).

### VI. Financial Crises and Dynamics of the IRGD (Appendix 2)
- Methodology:
  - Uses qualitative crisis indicators and impulse response functions following Cerra and Saxena (2008).
  - Univariate autoregressive model extended with crisis dummy D, panel estimation on an unbalanced annual panel for 1980-2010 with up to 4 lags, country fixed effects, and 95 percent confidence intervals from 1000 bootstrap replications.
  - Crisis data from Reinhart and Rogoff (2009).
- Main empirical findings (IRGD responses to crises):
  - IRGD tends to sharply rise during and immediately after financial crises, but effects are relatively short-lived and tend to fade over time.
  - Currency crises: effects on IRGD are 1.3 and 2.3 percentage points in the first two years, disappearing by the fifth year.
  - Banking crises: average impact 2 and 2.5 percentage points in the first two years; severe banking crises peak with IRGD rising by more than 11 percentage points in the second year, fading within 4–5 years.
  - Sovereign domestic debt crises: IRGD rises by about 18 percentage points in the first year, followed by smaller impacts in subsequent years.
- Mechanisms:
  - Exchange-rate depreciation amplifies IRGD where foreign currency debt shares are significant.
  - Output falls and interest rates rise during crises, worsening IRGD in the short run.
  - Severity and duration of crises determine amplitude and persistence of IRGD increases.

### VII. Selected Empirical Summary Statistics and Stylized Facts
- IRGD computation: IRGD is computed as (r-g)/(1+g).
- From Table 1 (1966-2010, all available annual data on r-g):
  - Advanced Economies (No. of obs. 715): mean r-g = 3.16; S.T.D. = 3.90; Min = -14.51; Max = 25.61. Mean r = 2.58; S.T.D. = 2.48; Min = -8.02; Max = 11.51. Mean g = 0.58; S.T.D. = 0.63; Min = -18.09; Max = 30.02.
  - Non-advanced Economies (No. of obs. 2149): mean r-g = -2.02; S.T.D. = 10.17; Min = -81.45; Max = 84.09. Mean r = 4.71; S.T.D. = 6.17; Min = -19.27; Max = 149.97. Mean g = -6.73; S.T.D. = -6.10; Min = 11.46; Max = -87.50.
- Within-country volatility and persistence (Table 2, 1966-2010, countries with at least 10 observations):
  - Advanced Economies (23 countries): Mean volatility = 4.15; S.T.D. = 1.82; Min = 2.32; Max = 9.57. AR(1) coefficient mean = 0.48; S.T.D. = 0.20; Min = 0.08; Max = 0.79.
  - Emerging Economies (32 countries): Mean volatility = 9.00; S.T.D. = 6.66; Min = 3.18; Max = 34.01. AR(1) coefficient mean = 0.31; S.T.D. = 0.28; Min = -0.15; Max = 0.80.
- Panel regression highlights:
  - Lagged dependent variable positive and significant (e.g., 0.41*** in Table 3, column [1]).
  - Inflation (%) often has a negative coefficient (e.g., -0.69*** in Table 3, column [8]).
  - Estimation uses System GMM with Windmeijer correction; Arellano-Bond AR(2) test p-values and Hansen J-statistics reported.

### VIII. Conclusions and Policy Implications
- Magnitude and fiscal implications:
  - Average IRGD for non-advanced economies in 1999–2008 was about -7 percent (more than 8 percentage points lower than the G-7 average).
  - For an average non-advanced economy, the combined effect of growth and low real interest rates during 1999–2008 would have reduced the government debt ratio by half, enabling a looser fiscal stance.
- Interpretation:
  - Most of the IRGD downward pressure was due to real interest rates on government debt much lower than in G-7 economies—well below competitive-market levels—while growth played a comparatively lesser role.
  - Evidence supports that low (often negative) real interest rates stem from domestic financial market distortions, captive savings markets, and financial repression.
- Policy implication and outlook:
  - As financial development and global integration advance, non-advanced economies could experience substantial rises in IRGDs relatively quickly—well before GDP per capita converges to advanced-economy levels.
  - Countries pursuing financial development and liberalization should plan associated fiscal policy reforms to accommodate rising government debt servicing costs.
  - Emerging Eastern Europe, Western Hemisphere, and Asia exhibited higher real interest rates in 1999–2008 relative to earlier decades due to rising international financial integration; this process is likely to continue.

*Source: _wp11260 — IMF Staff estimates and analysis contained in the supplied content unit.*

### 1. Summary Statistics on Interest Rate Growth Differentials ..................................................24

### 1. Summary Statistics on Interest Rate Growth Differentials ..................................................24

### Major subsections listed
- 2. Average by Country Groupings: Within-Country Volatility and Persistence of Interest Rate Growth Differentials ...............................................................................25
- 3. Panel Regression: Real Effective Interest Rates and Financial Repression (Development) Dependent Variable: Real Effective Interest Rates ............................26
- 4. Panel Regression: Real Effective Interest Rates and Financial Repression— Excluding the Episodes of High Inflation ....................................................................27

### Figures enumerated
- 1. Interest Rate-Growth Differential: 1999–2008 Average  ......................................................6
- 2. Interest Rate-Growth Differential: Non-Advanced Economies, 1999–2008 .........................6
- 3. IRGD in Non-Advanced Economies Relative to G-7 Average, and Its Components ...........8
- 4. Real Interest Rates: 1999–2008 Average .............................................................................10
- 5. Real Interest Rates and Volatility: 1999–2008 Average ......................................................11
- 6. Real Interest Rates and Non-Advanced Economies and EMBI Spread ..............................11
- 7. Real Interest Rates and Inflation: 1999–2008 Average .......................................................12
- 8. Real Interest Rates and Financial Development: 1999–2008 Average ...............................13
- 9. Korea: Real Interest Rates and Private Credit .....................................................................14
- 10. South Africa: Real Interest Rates and Private Credit .........................................................14

### Appendixes
- 1. Derivation of Interest Rate-Growth Differential ..................................................................20
- 2. Financial Crises and Dynamics of the IRGD .......................................................................21

*Source: _wp11260 - 1. Summary Statistics on Interest Rate Growth Differentials ..................................................24*

### References .............................................................................................................

### _wp11260 - References

### I. INTRODUCTION
- The interest rate-growth differential (IRGD) is defined as the differential between the average interest rate paid on government debt and the growth rate of the economy; it is central to debt dynamics and debt sustainability.
- The paper constructs a database of average effective interest rates based on budget outturn data and debt stocks for a large sample of advanced and non-advanced economies, correcting for exchange rate effects on foreign-currency denominated debt and excluding about one-third of countries with concessional debt shares above 50 percent.
- Empirical summary for 1999–2008:
  - IRGDs are correlated with income levels, generally negative in non-advanced economies and often strongly so.
  - Negative IRGDs can stabilize or reduce debt ratios even with persistent primary deficits.
- Hypothesis and conjecture:
  - Lower IRGDs in non-advanced economies owe as much or more to lower real interest rates than to higher growth.
  - Lower interest rates are conjectured to be related to captive financial markets, financial repression, and lack of financial development.
  - Rising IRGDs may occur relatively rapidly as financial development and global integration proceed, potentially before GDP per capita convergence.

### II. INTEREST RATE-GROWTH DIFFERENTIALS AND INCOME
- Conceptual role:
  - IRGD is the rate at which the debt-to-GDP ratio would grow if the primary balance were zero and debt service were rolled over.
  - Positive IRGD → need for primary surplus proportional to IRGD and debt ratio to stabilize debt.
  - Negative IRGD → debt ratio can decline toward zero even with a primary deficit.
- Empirical observations:
  - Among G-20 advanced economies, the IRGD averaged about 1 percentage point during 1999–2008.
  - Among EMEs and LICs, IRGDs were generally markedly negative with substantial variability (Table 1).
  - Average IRGD during 1999–2008:
    - almost -4 percentage points for a broad sample of EMEs,
    - below -7 percent for the total sample of non-advanced economies.
- Distributional and temporal features:
  - IRGD shows a positive correlation with GDP per capita (Figure 1).
  - Many non-advanced economies had average IRGDs well below -10 percentage points in 1999–2008.
  - Non-advanced economies exhibit high within-country volatility and low persistence of IRGDs relative to advanced economies (Table 2).
  - Emerging economies show the highest within-country volatility, reflecting episodic crises (effects typically last 2–3 years, Appendix 2).

### III. THE PUZZLING BEHAVIOR OF THE IRGD IN DEVELOPING ECONOMIES
- Theoretical expectations:
  - Modified golden rule: in economies near balanced growth, real interest rates should exceed growth rates (consistently positive IRGD for advanced economies).
  - For catch-up economies, theory predicts faster growth and typically no lower real interest rates than advanced economies; real interest rates should be at least as high as in G-7 plus premia.
- Counterfactual evidence:
  - Real interest rates on non-advanced economy government debt are generally substantially lower than on advanced-economy debt, and this drives lower IRGDs (Figure 3).
  - During 1999–2008:
    - real interest rates in non-advanced economies were on average almost 6 percentage points lower than the G-7 average;
    - average GDP growth rate in non-advanced economies exceeded the G-7 average by about 3 percentage points (Table 1).
  - The lower real interest rates accounted for about two thirds of the average IRGD difference with respect to the G-7 in 1999–2008.
  - Illustrative scenario: If EMEs had paid G-7 real interest rates plus an average spread of 5 percentage points, their average IRGD during 1999–2008 would have been about 3 percentage points (not the observed -4 percentage points), assuming fully open external financial accounts.

### IV. WHY ARE INTEREST RATES SO LOW IN EMES?
- Financial repression and market distortions documented as likely causes:
  - Typical elements include legal ceilings on lending/deposit rates, high reserve ratios, entry barriers and public ownership of banks, quantitative credit restrictions, government-directed lending, subsidized lending rates, and restrictions on capital transactions (McKinnon (1973), Shaw (1973)).
  - Reinhart and Sbrancia (2011) show episodes where nominal interest controls, capital controls, and persistent inflation maintained low or negative real interest rates and reduced public debt burdens by 3–5 percent of GDP a year in some advanced-country historical episodes.
- Empirical stylized facts:
  - Real interest rates are positively correlated with income per capita (Figure 4).
  - Country-level volatility of real interest rates is inversely related to income per capita (Figure 5).
  - The EMBI spread over US Treasuries contrasts with the spread of effective interest rates actually paid by non-advanced economy government debt (Figure 6).
  - Real interest rates are inversely related to inflation and can be negative for extended periods in many non-advanced economies (Figure 7); systematic low real rates associated with inflation point to financial repression and bans on indexed or foreign-currency instruments.
  - Financial development indicators (e.g., private credit, commercial bank asset shares) correlate with higher real interest rates (Figure 8).
- Historical and cross-country examples:
  - Financial reform episodes in Chile, Israel, Korea, and South Africa saw real interest rates turn positive from large negative levels after reforms.
  - Korea and South Africa show real interest rates moving almost in tandem with private credit development (Figures 9 and 10).
- Persistence of repression elements (1998–2008 statistics, Abiad et al. (2008)):
  - 25 percent of non-advanced economies had deposit or lending rate regulations.
  - 13 percent had credit controls.
  - 34 percent had entry barriers to domestic banking.
  - 55 percent had significant restrictions on capital inflows and outflows.

### V. ECONOMETRIC TESTING OF THE FINANCIAL DISTORTIONS HYPOTHESIS
- Data and approach:
  - Annual panel 1999–2008 with 128 countries (advanced and non-advanced) after excluding countries with concessional external debt > 50 percent.
  - Dependent variable: real effective interest rate (effective interest cost / debt stock, adjusted for currency valuation effects).
  - Dynamic panel specification: rit = αrit-1 + Xit′β + γZit + νi + ηt + εit, estimated by system GMM (Arellano and Bover (1995); Blundell and Bond (1998)).
- Controls (Xit): lagged public debt (% of GDP), change in public debt (% of GDP), real GDP growth, domestic private savings and population aging (not significant), and time-fixed effects capturing global conditions.
- Financial repression/development indicators (Zit) include:
  - Commercial bank claims on non-financial sectors as percent of total claims (commercial + central bank assets).
  - Private credit (% of GDP).
  - Inflation.
  - Financial liberalization index (Abiad et al. (2008), normalized 0–1).
  - Capital account openness index (Chinn and Ito (2002), normalized 0–1).
  - Principal components combining commercial bank assets, private credit, liquid liabilities, capital market openness, and inflation (first component captures financial development; second assigns large weight to inflation).
- Key empirical results:
  - Indicators of financial repression or lack of financial development are significantly associated with lower real effective interest rates (Table 3).
  - Commercial bank assets coefficient: 0.144 (Column 1). Interpretation:
    - 1999–2008 averages: real interest rates in non-advanced and advanced economies were -2.7 percent and 2.6 percent respectively (contemporaneous gap 5.3 percentage points).
    - Commercial bank assets averages: 84 percent (non-advanced) and 97 percent (advanced) of total (commercial + central bank) assets.
    - A rise in commercial bank assets from 84 percent to 97 percent implies a contemporaneous real interest rate increase of 1.9 percentage points (0.144 × 13), accounting for 36 percent of the 5.3 percentage point gap.
    - Long-run effect (γ/(1-α)) of this raise would be about 3 percentage points.
  - Private credit coefficient: 0.03 (Column 3). Interpretation:
    - Increase in private credit from 42 percent of GDP (non-advanced average) to 118 percent of GDP (advanced average) implies a contemporaneous real interest rate increase of 2.3 percentage points; long-run effect about 4 percentage points.
  - Financial liberalization and capital openness indices: positive and significant (Columns 2, 4, 5); financial liberalization increase from 0.72 (non-advanced average) to 0.94 (advanced average) implies a real interest rate rise of about 3.4 percentage points.
  - Inflation: strongly negatively associated with real interest rates and significant at 1 percent. Regression coefficient suggests a 1 percentage point increase in inflation is associated with a reduction in real interest rate around 0.69 percentage point (Column 6).
  - Principal components: first and second components significant with expected signs; second component (large weight on inflation) implies that one percentage point of inflation (0.072 increase in second component) yields an implied −0.48 percent effect on real interest rates (0.072 × -6.66).
  - Non-linear (squared) terms for financial development measures are insignificant; results robust in non-advanced-only subsample and for longer periods.
  - Excluding high-inflation episodes (>20 percent) leaves results largely unchanged, except capital account openness becomes insignificant; magnitude of financial development impacts remains similar though slightly smaller (Table 4).
- Diagnostic tests:
  - Hansen J-test of over-identifying restrictions cannot reject validity of instruments (example p-value=0.29 for Column 1).
  - Arellano-Bond test for autocorrelation: cannot reject no second-order serial correlation in first-differenced errors (example p-value=0.68 for Column 1).

### VI. CONCLUSIONS
- Magnitude and fiscal implications:
  - Average IRGD for non-advanced economies in 1999–2008 was about -7 percent (more than 8 percentage points lower than the G-7 average).
  - For an average non-advanced economy, the combined effect of growth and low real interest rates during 1999–2008 would have reduced the government debt ratio by half, enabling a looser fiscal stance.
- Interpretation:
  - Most of the IRGD downward pressure was due to real interest rates on government debt much lower than in G-7 economies—well below competitive-market levels—while growth played a comparatively lesser role.
  - The evidence supports that low (often negative) real interest rates stem from domestic financial market distortions, captive savings markets, and financial repression.
- Policy implication and outlook:
  - As financial development and global integration advance, non-advanced economies could experience substantial rises in IRGDs relatively quickly—well before GDP per capita converges to advanced-economy levels.
  - Countries pursuing financial development and liberalization should plan associated fiscal policy reforms to accommodate rising government debt servicing costs.
  - Emerging Eastern Europe, Western Hemisphere, and Asia exhibited higher real interest rates in 1999–2008 relative to earlier decades due to rising international financial integration; this process is likely to continue.

*Source: IMF Staff estimates and analysis contained in the supplied content.*

### Appendix 1. Derivation of Interest Rate-Growth Differential

### Appendix 1. Derivation of Interest Rate-Growth Differential

### Derivation and key equations
- Debt dynamics with a portion of debt denominated in foreign currency is written as (equation numbering preserved from source):
  - (1) relates domestic currency debt ܦ
௧
ௗ
, foreign currency debt ܦ
௧
௙
, spot exchange rate ݁
௧
, nominal interest rates ݅
௧
ௗ
 and ݅
௧
௙
, and primary balance ܲ
௧
.
- Define total debt in domestic currency as ܦ
௧
 = ܦ
௧
ௗ
݁
௧
 + ܦ
௧
௙
; share of domestic currency debt ߙ
௧
 = ܦ
௧
ௗ
/ܦ
௧
; and nominal depreciation ߝ
௧
 = ݁
௧
/݁
௧
ିଵ
- Rearranging yields (2), which can be expressed in terms of debt-to-GDP shares by defining ܻ
௧
 = (1+ߛ
௧
)ܻ
௧
ିଵ
, ݀
௧
 = ܦ
௧
/ܻ
௧
, ݌
௧
 = ܲ
௧
/ܻ
௧
, and ߩ
௧
 = (1-ߙ
௧
ିଵ
)ߝ
௧
݅
௧
 + ߙ
௧
ିଵ
݅
௧
 (weighted effective interest rate).
- Final compact form (3):
  - ݀
௧
݀ে
௧ିଵ
 = expression involving the weighted effective interest rate and valuation term (the source labels the interest rate-growth differential as the term in brackets in equation (3)).
- Interpretation:
  - The IRGD includes a valuation-change term ሺ(1-ߙ
௧
ିଵ
)ߝ
௧
ܦ
௧
िଵሻ that captures exchange-rate-induced capital gains/losses on the foreign currency debt portion.
  - In the absence of foreign currency debt (ߙ =1), the IRGD reduces to the familiar (r-g)/(1+g), equivalent to r-g in continuous/real terms where r is the real interest rate and g is real GDP growth rate.

### Definitions (as used in the derivation)
- ܦ
௧
ௗ
 : domestic currency debt at end of period t
- ܦ
௧
௙
 : foreign currency debt at end of period t
- ݁
௧
 : spot exchange rate at end of period t
- ݅
௧
ௗ
 and ݅
௧
௙
 : nominal interest rates on domestic and foreign currency debt paid in period t on debt outstanding at end of t-1
- ܲ
௧
 : primary balance in period t
- ܦ
௧
 : total debt expressed in domestic currency (ܦ
௧
ௗ
݁
௧
 + ܦ
௧
௙
)
- ߙ
௧
 : share of domestic currency debt in total debt at t
- ߝ
௧
 : rate of nominal depreciation
- ݌
௧
 = ܲ
௧
/ܻ
௧
 and ݀
௧
 = ܦ
௧
/ܻ
௧
 when expressing in share of nominal GDP ܻ
௧

### Relevance for debt dynamics
- The IRGD is the relevant factor for public debt dynamics and is computed as (r-g)/(1+g). See Appendix 1 for the detailed algebraic derivation.

---

### Appendix 2. Financial Crises and Dynamics of the IRGD

### Methodology to assess crisis impact
- Empirical approach:
  - Uses qualitative indicators of financial crises and estimates impulse response functions (IRFs) to crisis shocks following Cerra and Saxena (2008).
  - Estimates a univariate autoregressive model extended to include current and lagged impacts of a crisis dummy D (D = 1 during a crisis).
  - Panel estimation on an unbalanced annual panel for 1980-2010.
  - Number of lags restricted to 4 (additional lags rejected by data).
  - Country fixed effects (αi) included.
  - Impulse responses obtained by simulating a one-period shock in the crisis dummy (D_t set equal to 1 for only one period, zero otherwise).
  - 95 percent confidence intervals derived from 1000 bootstrap replications.
  - Data on crises from Reinhart and Rogoff (2009).
- Notes on identification:
  - Crisis dummy captures both the crisis and the policy reaction triggered by the crisis; disentangling pure crisis effect from policy response is difficult without a counterfactual.
  - Panel unit root tests reject unit roots in the differential. Nickell (1981) bias of fixed-effects lagged dependent variable estimator is of order 1/T and judged small in this data.

### Main empirical findings (IRGD responses to crises)
- General pattern:
  - IRGD tends to sharply rise during and immediately after financial crises (currency, banking, or sovereign debt crisis), but effects are relatively short-lived and tend to fade over time.
- Currency crises:
  - Effects on IRGD are 1.3 and 2.3 percentage points in the first two years, respectively.
  - Impact diminishes over time and disappears by the fifth year, with IRGD returning to pre-crisis level.
  - The coefficients of the first two lagged terms of the crisis dummy are statistically significant at the 1–5 percent level.
- Banking crises:
  - Average impact: 2 and 2.5 percentage points in the first two years, similar short-lived pattern.
  - Severe banking crises (big five plus four additional episodes) have much larger peak effects: at its peak in the second year, the IRGD rises by more than 11 percentage points above the pre-crisis level, fading within 4–5 years.
- Sovereign domestic debt crises:
  - Most pronounced impact: IRGD sharply rises in the first year of the crisis by about 18 percentage points above the pre-crisis level, followed by smaller impacts in subsequent years.
- Statistical significance:
  - Coefficients of crisis dummy and its lags in regressions for banking and sovereign debt crises are mostly significant at conventional levels.

### Interpretation and mechanisms
- For economies with significant foreign currency debt shares, exchange-rate movements produce valuation effects that amplify IRGD during currency crises (large nominal depreciation raises domestic-currency value of foreign debt and servicing costs).
- Output typically falls sharply during crisis episodes; recovery and exchange-rate effects can alter g later, creating short-run deterioration in IRGD.
- Banking and sovereign debt crises affect IRGD through higher interest rates and lower growth; magnitude depends on crisis severity (depth and duration).
- High levels of sovereign debt, even absent a debt crisis, are significantly negatively associated with subsequent growth and positively with sovereign bond yields, which in turn raise IRGD (results cited from Kumar and Woo (2010); Baldacci and Kumar (2010)).

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### Selected empirical summary statistics and stylized facts
- IRGD definition used in tables: IRGD is computed as (r-g)/(1+g).
- From Table 1 (based on all available annual data on r-g in 1966-2010):
  - Advanced Economies (No. of obs. 715): mean r-g = 3.16; S.T.D. = 3.90; Min = -14.51; Max = 25.61. Mean r = 2.58; S.T.D. = 2.48; Min = -8.02; Max = 11.51. Mean g = 0.58; S.T.D. = 0.63; Min = -18.09; Max = 30.02.
  - Non-advanced Economies (No. of obs. 2149): mean r-g = -2.02; S.T.D. = 10.17; Min = -81.45; Max = 84.09. Mean r = 4.71; S.T.D. = 6.17; Min = -19.27; Max = 149.97. Mean g = -6.73; S.T.D. = -6.10; Min = 11.46; Max = -87.50 (table preserves ordering and numbers as in source).
- Within-country volatility and persistence (Table 2, 1966-2010, countries with at least 10 observations):
  - Advanced Economies (23 countries): Mean volatility = 4.15; S.T.D. = 1.82; Min = 2.32; Max = 9.57. AR(1) coefficient (persistence) mean = 0.48; S.T.D. = 0.20; Min = 0.08; Max = 0.79.
  - Emerging Economies (32 countries): Mean volatility = 9.00; S.T.D. = 6.66; Min = 3.18; Max = 34.01. AR(1) coefficient mean = 0.31; S.T.D. = 0.28; Min = -0.15; Max = 0.80.
- Panel regressions (Tables 3 and 4) find robust associations (selected coefficient signs and significance preserved as in source):
  - Lagged dependent variable is positive and statistically significant across specifications (e.g., 0.41*** in Table 3, column [1]).
  - Initial public debt (% of GDP) and change in public debt (% of GDP) often enter positively (some coefficients significant at * / ** / *** levels as reported).
  - Private bank assets (% of total assets) and private credit (% of GDP) frequently enter positively (some coefficients significant).
  - Inflation (%) often has a negative coefficient (e.g., -0.69*** in Table 3, column [8]).
  - Estimation uses System GMM with Windmeijer correction; Arellano-Bond AR(2) test p-values and Hansen J-statistics reported for instrument validity.

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*Source: IMF Staff estimates — Appendix 1 (Derivation of Interest Rate-Growth Differential) and Appendix 2 (Financial Crises and Dynamics of the IRGD) from the provided content unit.*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2011/_wp11260.pdf_