## 7. GDP Volatility during the 15 Years after Crossing Debt Thresholds

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### I. Introduction
- Research question: Is there a particular threshold in the level of government debt above which medium-term growth prospects are dramatically compromised?
- Positioning and high-level findings:
  - Uses a long-horizon episode-based methodology intended to attenuate reverse causality from growth to debt.
  - Does not identify any clear debt threshold above which medium-term growth prospects are dramatically compromised.
  - The association between debt and medium-term growth becomes rather weak at high levels of debt, especially when controlling for average growth performance of country peers.
  - Debt trajectory matters: countries with high but declining levels of debt historically grew as fast as peers.
  - High levels of debt are weakly associated with higher output volatility.

### II. Literature context
- Selected points preserved from the chapter:
  - Reinhart and Rogoff (2010) claim a threshold effect with debt above 90 percent of GDP linked to much lower growth.
  - Herndon, Ash, and Pollin (2013) find that the threshold effect vanishes after correcting a coding error and reweighting.
  - Kumar and Woo (2010): a 10 percentage point increase in initial debt-to-GDP is associated with a slowdown of 0.15 percentage points per year in annual real per capita GDP growth in AEs; they test nonlinearities via interactions at 30, 60, and 90.
  - Cecchetti et al. (2011) find that beyond 96 percent of GDP public debt reduces real per capita GDP growth by 0.17 percent per year (sample: 18 OECD countries, 1980–2010).
  - Panizza and Presbitero (2012) using instruments reject high-debt-causes-lower-growth hypothesis.

### III. Data and methodology
- Data sources:
  - Primary: IMF Fiscal Affairs Department gross government debt to GDP ratios covering nearly the entire IMF membership back to 1875.
  - Supplementary: interest payments and primary deficits for 19 advanced economies from Abbas and others (2011); real GDP from Maddison (2003); other data from Reinhart and Rogoff (2010).
- Sample focus: advanced economies (reflecting supplementary data availability).
- Sample statistics:
  - Average debt-to-GDP level in the sample is 55 percent.
  - Average real output per capita growth rate is 2¼ percent.
- Episode definition and horizons:
  - Episodes begin when gross public debt rises above a threshold τ after being below τ the previous year; linear interpolation used when necessary.
  - Horizons analyzed: h ∈ [1,5,10,15].
  - Episodes are non-overlapping: a new episode cannot begin earlier than h years after the previous one begins.
  - For robustness and consistency, only episodes beginning by 1997 (thus ending by 2012) are considered when focusing on 15-year outcomes.
- Methodological distinctions from prior work:
  - Considers a broad range of debt thresholds (not just 90 percent).
  - Analyses growth performance over fixed horizons after crossing thresholds regardless of later debt outcomes (avoids truncation/selecting only “failures”).
  - Pools episodes and weights them equally.

### IV. Empirical results — growth
- Short-run (h = 1):
  - Average real GDP growth per capita in the year after debt crosses a given threshold: around 2 percent for countries with debt below 90 percent and about -2 percent for episodes with debt rising above 90 percent.
  - Inter-quartile range indicates diverse outcomes at high debt thresholds; short-run results are fragile and influenced by outliers (example: Japan growth -50% in 1945 following debt jump from 133 to 204 percent).
  - Reverse causality and omitted variables limit causal interpretation of short-run associations.
- Medium-run (h = 5, 10, 15):
  - Growth performance improves markedly at the 5-year horizon and more so at the 10- and 15-year horizons.
  - No clear debt-to-GDP threshold above which growth deteriorates sharply when using horizons beyond the very short run.
  - Debt dynamics are slow: countries that exceed the 140 percent debt threshold experience an average debt ratio during the subsequent 15 years of 130 percent.
- Debt trajectory effect:
  - Episodes where debt is falling (starting above a threshold but declining thereafter) do not show the sharp short-run reduction in growth observed for rising-debt episodes.
  - Even at high debt ratios (e.g., 130–140 percent) when debt is on a declining path, countries have experienced solid growth.
  - The initial debt trajectory remains an important predictor of subsequent growth even after 15 years.
- Relative growth control for contemporaneous global conditions:
  - For each episode compute (g_it(h) − g_t(h)), where g_t(h) is the simple average growth rate across economies over the same period.
  - When using relative growth, countries with high debt are generally close to peer performance — differences are less than ½ percent per year except at the lowest debt levels.
  - Debt trajectory still matters: for debt between 90 and 115 percent of GDP, average growth is ½ a percentage point higher when debt is decreasing (difference is statistically significant).
- Excluding first five years (focus on years 5–15):
  - Removing the first five years (to reduce mechanical reverse causality) flattens the relation between growth and debt still further.
  - With first five years excluded, the direction of debt (rising vs falling) is no longer a clear predictor of growth — overlaps in average growth across directions.

### V. Robustness checks
- Controls applied:
  - Controls for historical variation in average growth (e.g., post-WWII boom, Great Depression bust) by using relative growth measures versus contemporaneous advanced-economy averages.
  - Tested horizons and exclusion windows; experimented with 10-year and 20-year windows with essentially unchanged results.
  - Interpolation used when missing data prevents exact dating of threshold crossing.

### VI. Debt and GDP volatility (15-year analysis)
- Volatility measurement:
  - Episode-level output volatility in deviation from the average output volatility of advanced economies over the same period: (σ_it(h) − σ_t(h)).
  - σ_it(h) defined as the standard deviation of growth over the episode; σ_t(h) is the average standard deviation for advanced economies in the same period.
- Findings:
  - No single debt threshold where output volatility jumps sharply.
  - Suggestion of a positive relation between debt and output volatility: when debt increases above the sample mean (56 percent), countries tend to experience relatively higher volatility.
  - Relation between debt and volatility should be less affected by reverse causality (increase in volatility does not have an obvious mean effect on debt).
  - Small resurgence of volatility for debt falling at very low levels (below 20 percent) may be related to reductions in debt via hyper-inflation or default.

### VII. Conclusions
- Key takeaways:
  - No simple debt-ratio threshold found above which medium-term growth prospects are severely undermined; threshold effects are present only at the shortest horizons.
  - Association between debt and growth at high debt levels becomes weak when analyzing beyond the short-run and when controlling for peer performance.
  - Debt trajectory is an important determinant: high-but-declining debt episodes do not show systematically worse medium-term growth than peers.
  - Evidence that higher debt appears to be associated with more volatile growth; volatility itself can be damaging to welfare.
  - Caution: residual endogeneity and identification issues remain; results mitigate but do not eliminate reverse causality concerns and do not establish definitive structural causal relationships.

### VIII. Data appendix — dataset coverage (high-level)
- Main source: IMF Fiscal Affairs Department gross government debt to GDP database (coverage back to 1875).
- Supplementary sources: Abbas and others (2011) for interest payments and primary deficits (19 AEs); Maddison (2003) for real GDP; Reinhart and Rogoff (2010) for other data.
- Selected country coverage examples (as listed in the chapter):
  - Australia: Real per capita GDP 1821–2011; Debt/GDP 1901–2010
  - Japan: Real per capita GDP 1871–2011; Debt/GDP 1875–2012
  - United States: Real per capita GDP 1871–2011; Debt/GDP 1791–2010

*Source: IMF working paper chapter titled "7. GDP Volatility during the 15 Years after Crossing Debt Thresholds" (content as provided).*

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

### References .................................................................................................................................... 18

### Figures

- 1. Debt and Growth in the Short Run ............................................................................................ 8
- 2. Debt and Growth over the Medium Run.................................................................................... 9
- 3. Debt Dynamics over the Medium Term .................................................................................. 10
- 4. Debt and Growth Depend on the Debt Trajectory ................................................................... 11
- 5. Relative Growth Performance .................................................................................................. 12
- 6. Growth Performance from 5 to 15 Years after Crossing Debt Thresholds.............................. 13

*https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2014/_wp1434.pdf*

### 7. GDP Volatility during the 15 Years after Crossing Debt Thresholds ..................................... 14

### 7. GDP Volatility during the 15 Years after Crossing Debt Thresholds

### I. Introduction
- Research question: Is there a particular threshold in the level of government debt above which medium-term growth prospects are dramatically compromised?
- Key positioning:
  - Some literature (Reinhart and Rogoff (2010, 2012)) argues for a threshold effect (e.g., 90 percent of GDP) with dramatically worse growth outcomes.
  - Others dispute a clear threshold and raise endogeneity concerns (weak growth causing high debt).
- Main contributions and high-level findings:
  - Uses a long-horizon episode-based methodology intended to attenuate reverse causality from growth to debt.
  - Does not identify any clear debt threshold above which medium-term growth prospects are dramatically compromised.
  - The association between debt and medium-term growth becomes rather weak at high levels of debt, especially when controlling for average growth performance of country peers.
  - Debt trajectory matters: countries with high but declining levels of debt historically grew as fast as peers.
  - High levels of debt are weakly associated with higher output volatility.

### II. Literature context (selected points preserved)
- Reinhart and Rogoff (2010) claim a threshold effect with debt above 90 percent of GDP linked to much lower growth.
- Herdon, Ash, and Pollin (2013) find that the threshold effect vanishes after correcting a coding error and reweighting.
- Kumar and Woo (2010) report that a 10 percentage point increase in initial debt-to-GDP is associated with a slowdown of 0.15 percentage points per year in annual real per capita GDP growth in AEs; they test nonlinearities via interactions at 30, 60, and 90.
- Cecchetti et al (2011) find that beyond 96 percent of GDP public debt reduces real per capita GDP growth by 0.17 percent per year (sample: 18 OECD countries, 1980–2010).
- Panizza and Presbitero (2012) using instruments reject high-debt-causes-lower-growth hypothesis.

### III. Data and methodology
- Primary database: IMF Fiscal Affairs Department gross government debt to GDP ratios covering nearly the entire IMF membership back to 1875.
- Supplementary data: interest payments and primary deficits for 19 advanced economies from Abbas and others (2011); real GDP from Maddison (2003); other data from Reinhart and Rogoff (2010).
- Sample focus: advanced economies (reflecting supplementary data availability).
- Sample statistics:
  - Average debt-to-GDP level in the sample is 55 percent.
  - Average real output per capita growth rate is 2¼ percent.
- Episode definition and horizons:
  - Episodes begin when gross public debt rises above a threshold τ after being below τ the previous year; linear interpolation used when necessary.
  - Horizons analyzed: h ∈ [1,5,10,15].
  - Episodes are non-overlapping: a new episode cannot begin earlier than h years after the previous one begins.
  - For robustness and consistency, only episodes beginning by 1997 (thus ending by 2012) are considered when focusing on 15-year outcomes.
- Methodological distinctions from prior work:
  - Considers a broad range of debt thresholds (not just 90 percent).
  - Analyses growth performance over fixed horizons after crossing thresholds regardless of later debt outcomes (avoids truncation/selecting only “failures”).
  - Pools episodes and weights them equally (contrast with approaches that give many observations to some countries).

### IV. Empirical results — growth
- Short-run (h = 1):
  - Figure 1 (described): average real GDP growth per capita in the year after debt crosses a given threshold shows GDP growth around 2 percent for countries with debt below 90 percent and about -2 percent for episodes with debt rising above 90 percent.
  - Inter-quartile range indicates diverse outcomes at high debt thresholds; short-run results are fragile and influenced by outliers (example: Japan growth -50% in 1945 following debt jump from 133 to 204 percent).
  - Reverse causality and omitted variables limit causal interpretation of short-run associations.
- Medium-run (h = 5, 10, 15):
  - Growth performance improves markedly at 5-year horizon and more so at 10- and 15-year horizons.
  - No clear debt-to-GDP threshold above which growth deteriorates sharply when using horizons beyond the very short run.
  - Debt dynamics are slow: example given — countries that exceed the 140 percent debt threshold experience an average debt ratio during the subsequent 15 years of 130 percent.
- Debt trajectory effect:
  - Episodes where debt is falling (starting above a threshold but declining thereafter) do not show the sharp short-run reduction in growth observed for rising-debt episodes.
  - Even at high debt ratios (e.g., 130–140 percent) when debt is on a declining path, countries have experienced solid growth.
  - The initial debt trajectory remains an important predictor of subsequent growth even after 15 years.
- Relative growth control for contemporaneous global conditions:
  - For each episode compute (g_it(h) − g_t(h)), where g_t(h) is the simple average growth rate across economies over the same period.
  - When using relative growth, countries with high debt are generally close to peer performance — differences are less than ½ percent per year except at the lowest debt levels.
  - Debt trajectory still matters: for debt between 90 and 115 percent of GDP, average growth is ½ a percentage point higher when debt is decreasing (difference is statistically significant).
- Excluding first five years (focus on years 5–15):
  - Removing the first five years (to reduce mechanical reverse causality) flattens the relation between growth and debt still further.
  - With first five years excluded, the direction of debt (rising vs falling) is no longer a clear predictor of growth — overlaps in average growth across directions.

### V. Robustness checks (summary)
- Controls for historical variation in average growth (e.g., post-WWII boom, Great Depression bust) by using relative growth measures versus contemporaneous advanced-economy averages.
- Tested horizons and exclusion windows; experimented with 10-year and 20-year windows with essentially unchanged results.
- Interpolation used when missing data prevents exact dating of threshold crossing.

### VI. Debt and GDP volatility (15-year analysis)
- Volatility measure constructed as episode-level output volatility in deviation from the average output volatility of advanced economies over the same period: (σ_it(h) − σ_t(h)).
- σ_it(h) defined as the standard deviation of growth over the episode; σ_t(h) is the average standard deviation for advanced economies in the same period.
- Findings:
  - No single debt threshold where output volatility jumps sharply.
  - Suggestion of a positive relation between debt and output volatility: when debt increases above the sample mean (56 percent), countries tend to experience relatively higher volatility.
  - Relation between debt and volatility should be less affected by reverse causality (increase in volatility does not have an obvious mean effect on debt).
  - Note: small resurgence of volatility for debt falling at very low levels (below 20 percent) may be related to reductions in debt via hyper-inflation or default.

### VII. Conclusions (key takeaways)
- No simple debt-ratio threshold found above which medium-term growth prospects are severely undermined; threshold effects are present only at the shortest horizons.
- Association between debt and growth at high debt levels becomes weak when analyzing beyond the short-run and when controlling for peer performance.
- Debt trajectory is an important determinant: high-but-declining debt episodes do not show systematically worse medium-term growth than peers.
- Evidence that higher debt appears to be associated with more volatile growth; volatility itself can be damaging to welfare.
- Caution: residual endogeneity and identification issues remain; results mitigate but do not eliminate reverse causality concerns and do not establish definitive structural causal relationships.

### VIII. Data appendix — dataset coverage (high-level)
- Main source: IMF Fiscal Affairs Department gross government debt to GDP database (coverage back to 1875).
- Supplementary sources: Abbas and others (2011) for interest payments and primary deficits (19 AEs); Maddison (2003) for real GDP; Reinhart and Rogoff (2010) for other data.
- Table 1 in the source lists country coverage with start/end years for real per capita GDP and debt/GDP series (selected example entries from the table):
  - Australia: Real per capita GDP 1821–2011; Debt/GDP 1901–2010
  - Japan: Real per capita GDP 1871–2011; Debt/GDP 1875–2012
  - United States: Real per capita GDP 1871–2011; Debt/GDP 1791–2010
  - (Full country-by-country coverage table appears in the chapter.)

*Source: IMF working paper chapter titled "7. GDP Volatility during the 15 Years after Crossing Debt Thresholds" (content as provided).*

### REFERENCES

### _wp1434 - REFERENCES

### Cited works
- Abbas, S. M. Ali, Nazim Belhocine, Asmaa A. ElGanainy and Mark A. Horton, 2010, “A Historical Public Debt Database”, IMF Working Paper No. 10/245.
- __________ , 2011, “Historical Patterns and Dynamics of Public Debt – Evidence from a New Database”, IMF Economic Review, Vol.59, No.4,  pp. 717–42.
- Baum, Anja, Cristina Checherita and Philipp Rother, 2013, “Debt and Growth: New Evidence from the Euro Area”, Journal of International Money and Finance, Vol. 32, pp. 809–21.
- Blanchard, Olivier, and John Simon, 2001, “The Long and Large Decline in U.S. Output Volatility,” Brookings Papers on Economic Activity, No. 1, Vol. 2001, pp. 135–74.
- Cecchetti, S. G., Mohanty, M.S., and F. Zampolli, 2011, “The Real Effects of Debt”, Federal Reserve Bank of Kansas City, Economic Symposium 2011: Achieving Maximum Long-Run Growth, pp. 145–96.
- Dippelsman, Robert, Claudia Dziobek, and Carlos A. Gutiérrez Mangas, 2012, “What Lies Beneath: The Statistical Definition of Public Sector Debt”, IMF Staff Discussion Note No. 12/09.
- Herndon, Thomas, Michael Ash, and Robert Pollin, 2013, “Does High Public Debt Consistently Stifle Economic Growth? A Critique of Reinhart and Rogoff”, Political Economy Research Institute, Working Paper No. 322.
- International Monetary Fund, 2012, “The Good, the Bad, and the Ugly: 100 Years of Dealing with Public Debt Overhangs”, World Economic Outlook, Chapter 3 (Washington, DC).
- Kumar, Manmohan, and Jaejoon Woo, 2010, “Public Debt and Growth”, IMF Working Paper No. 10/174, July (International Monetary Fund: Washington, DC).
- Maddison, Angus, 2003, The World Economy: Historical Statistics (Paris: Organization for Economic Cooperation and Development).
- McConnell, M. and G. Perez-Quiros, 2000, “Output Fluctuations in the United States: What Has Changed Since the Early 1980s?” The American Economic Review, Vol. 90, No. 5, pp. 1464–76.
- Panizza, Ugo and Andrea F. Presbitero, 2012, "Public Debt and Economic Growth: Is There a Causal Effect?", MoFiR Working Paper No. 65.
- Reinhart, Carmen M. and Kenneth S. Rogoff, 2010, “Growth in a Time of Debt”, American Economic Review: Papers & Proceedings, Vol. 100, No. 2, pp. 573–78.
- Reinhart, Carmen M., Vincent R. Reinhart, and Kenneth S. Rogoff, 2012, “Public Debt Overhangs: Advanced-Economy Episodes since 1800”, Journal of Economic Perspectives, Vol. 26, No. 3, pp. 69–86.

*Source: _wp1434 - REFERENCES.*

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