## 1. Kaplan-Meier Survivor Function by Level of Initial Deficit Level

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### I. Introduction: purpose and scope
- Study objective: assess factors determining the duration (persistence) of fiscal consolidations in a pooled sample of emerging market countries during 1980–2001 using survival analysis.
- Sample: 25 emerging market countries: Argentina, Bolivia, Brazil, China, Colombia, Côte d'Ivoire, Ecuador, Egypt, India, Indonesia, Jordan, Lebanon, Mexico, Nigeria, Pakistan, Peru, Philippines, Poland, Russia, South Africa, Thailand, Turkey, Ukraine, Uruguay, and Venezuela.
- Methodological novelty:
  - Introduces a “composite approach” that accounts for both the level and the trajectory of fiscal consolidation.
  - Uses semi-parametric (Cox proportional hazards) and parametric (Weibull) specifications.
- Baseline operational definition of failure:
  - Failure = 1 when the annual variation of the budget deficit is equal to or lower than 1 percentage point of GDP (lack of adjustment).
  - Failure = 0 when the annual variation of the budget deficit is above 1 percentage point of GDP (years of fiscal consolidation).
- Alternative definitions tested:
  - Change in fiscal deficit thresholds of 0.5 percent of GDP and 1.5 percent of GDP.
  - Alternative composite definition where failure = 1 when annual variation ≤ 1 percentage point of GDP AND the deficit is more than 2 percentage points of GDP.

### II. Analytical framework and literature
- Survival analysis fundamentals:
  - Spell length T; survival function S(t)=Pr(T>t); failure function F(t)=1−S(t); hazard h(t)=f(t)/S(t).
- Proportional hazard (PH) specifications:
  - Cox semi-parametric: h(t,X)=h0(t)*exp(X′β).
  - Weibull parametric baseline with ancillary parameter p testing duration dependence.
- Fiscal consolidation typology (Adam and Bevan, 2003):
  1. Level approach (deficit below specified threshold).
  2. Gradient approach (deficit falls relative to previous year).
  3. Composite approach (combines level and gradient).
- Motivation for composite approach: capture marginal cost of further adjustment as economy approaches sustainable deficit levels and capture credibility effects of relative deficit position.

### III. Data and empirical framework
- Period: 1980–2001.
- Data sources:
  - World Economic Outlook (WEO) for macro variables.
  - Government Finance Statistics (GFS) for disaggregated government expenditure.
  - World Development Indicators (WDI) for structure of economy variables.
- Key covariates included in hazard regressions:
  - Fiscal history: number of previous failures at fiscal consolidation.
  - Composition of spending: goods and services, interest payments, subsidies and transfers, capital spending (all in percent of GDP).
  - Total revenue and grants (percent of GDP).
  - Debt (% of GDP) — initial stock.
  - Change in international oil price deflator (percent change).
  - Exchange rate depreciation.
  - Unemployment rate.
  - Corruption (rescaled; higher values indicate weaker institutions).
  - Interaction: capital spending * corruption.
  - Dummies tested: IMF program (Stand-by/EFF, ESAF/PRGF), capital account crises.
- Composite “distance” variable:
  - Equal to specified threshold minus current deficit level; threshold fiscal deficit set to 2 percent of GDP; variable can be positive or negative.

### IV. Empirical results — nonparametric, semi-parametric, and parametric
- Non-parametric (Kaplan-Meier) findings:
  - 56 percent of episodes of fiscal consolidation end within a year.
  - Confidence interval for risk of interrupting fiscal consolidation: between 33 percent and 94 percent.
  - Splitting episodes by initial fiscal deficit relative to 2 percent of GDP:
    - Significantly lower proportion of fiscal adjustments end within a year when the initial deficit is lower than 2 percent of GDP.
    - Wilcoxon, Tarone-Ware, Fleming-Harrington tests reject equality of survival functions — supports composite approach.

- Selected semi-parametric (Cox proportional hazards) robust findings:
  - Previous number of failures: hazard ratio ~1.24 (significant at 1 percent).
  - Distance from deficit threshold: hazard ratio ~1.09 (significant at 1 percent).
  - Debt (% of GDP): coefficient ~-0.99 (significant at 1 percent) — higher debt associated with lower risk of ending a spell (i.e., higher persistence).
  - Interest payment (% of GDP): coefficient ~-0.95 (significant at 5 percent) — higher interest payments associated with lower hazard of ending consolidation.
  - Subsidies and transfers (% of GDP): hazard ratio ~1.06 (significant at 1 percent) — more subsidies/transfers increase probability of ending adjustment.
  - Total revenue and grants (% of GDP): coefficient ~-0.95 (significant at 1 percent) — higher revenues support persistence.
  - Spending on goods and services: weak positive association with hazard (marginal significance).
  - Capital spending: generally negative association with hazard (protecting/increasing capital spending is not harmful).
  - Interaction capital spending * corruption: negative — suggests corruption offsets capital spending benefits.
  - Exchange rate depreciation and corruption: positive association with failure but less robust.
  - Dummies for IMF-supported programs and capital account crises: generally insignificant.
  - Goodness-of-fit: Cox-Snell residuals indicate good fit; proportional hazard assumption not rejected (generalized Grambsch and Therneau test).

- Parametric (Weibull) findings:
  - Estimated ancillary parameter p > 1, implying monotonically increasing baseline hazard with time (evidence of “consolidation fatigue”).
  - Oil price increases: significant negative impact on hazard in Weibull — for oil-exporting countries higher oil prices sustain consolidation.

- Alternative composite definition (failure only when annual reduction ≤ 1 percentage point of GDP AND deficit > 2 percentage points of GDP):
  - Average survival rate after one year increases from 44 percent (baseline) to 52 percent under alternative definition.
  - Regression results qualitatively similar: previous failures, distance from threshold, subsidies/transfers positively related to hazard; interest payments and total revenue negatively related.
  - Under this alternative, initial stock of debt becomes insignificant — concentration of failed episodes under baseline among high-debt countries explains difference.

- Robustness checks:
  - Alternative deficit-change thresholds (0.5 and 1.5 percentage point of GDP) — results broadly consistent.
  - Models allowing time-varying parameters, group-specific hazards, and unobserved heterogeneity (shared frailty) — baseline findings confirmed.
  - Primary deficit definition tested (smaller sample) — consistent with baseline findings.

### V. Key quantitative statistics (as reported)
- Sample period: 1980–2001.
- Number of countries (baseline Cox models): typically 15 (and variations with 19 in some specifications).
- Number of failures (baseline): typically 120 (variations reported across models).
- Nonparametric result: 56 percent of consolidation episodes end within a year; risk interval 33 percent to 94 percent.
- Deficit threshold used in composite distance variable: 2 percent of GDP.
- Baseline failure threshold (annual variation): 1 percentage point of GDP.
- Alternative failure rule combined threshold: annual variation ≤ 1 percentage point of GDP AND deficit > 2 percentage points of GDP.
- Illustrative oil-price effect: US$1 per barrel increase lowers deficit by 0.1 percentage point of GDP in Indonesia (illustrative example).

### VI. Main conclusions
- Composite approach (gradient conditioned on level) is empirically supported: distance from deficit threshold matters for persistence.
- Factors enhancing persistence:
  - Higher total revenues and grants (% of GDP).
  - Higher interest payments (% of GDP) (interpreted in context of high-debt dynamics).
  - Higher initial debt (% of GDP) associated with greater persistence in baseline specifications.
  - Higher international oil prices for oil-exporting countries.
- Factors undermining persistence:
  - Large subsidies and transfers (% of GDP).
  - A history of prior failures (previous number of failures).
  - Exchange rate depreciation and weaker institutions (corruption) show positive association with failure, though less robust.
- Role of spending composition:
  - Protecting or increasing capital spending is not harmful and may support persistence.
  - Reallocating from wages/transfers toward capital spending supports persistence, but corruption can offset capital spending benefits.
- Duration dependence:
  - Weibull p>1 indicates baseline risk of ending consolidation increases with time — evidence of “consolidation fatigue.”

### VII. Policy implications and recommendations
- Strengthen institutional quality and policy credibility to reduce “stop and go” dynamics; histories of interruptions reduce persistence.
- Base deficit reductions on:
  - Cuts in wasteful/current expenditures (subsidies, transfers, excessive wage bills).
  - Revenue mobilization: broaden tax base, remove exemptions, combat tax evasion, consider higher rates where appropriate.
  - Protect and/or increase productive capital spending while targeting inefficient current outlays.
- Maintain social safety nets given adverse effects of unemployment on persistence to build social consensus for consolidation.
- Take account of external factors and macro-policy interdependencies (oil prices, exchange rate policy); further research needed to address endogeneity and the role of accompanying monetary/exchange rate policies.

*Source: Excerpt from the IMF working paper section titled "1. Kaplan-Meier Survivor Function by Level of Initial Deficit Level" (Appendix, methodology, and empirical results for fiscal consolidation persistence in 25 emerging market countries, 1980–2001).*

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

### References

### References section
- References................................................................................................................................23

### Tables
- 1. Persistence of Fiscal Consolidation, 1980–2001: Probability of Ending Fiscal Adjustment .......................................................................................................................14
- 2. Persistence of Fiscal Consolidation, 1980–2001: Alternative Composite Approach ..........18

### Figures
- Figure

*Source: _wp03224 - References..............................................................................................................*

### 1. Kaplan-Meier Survivor Function by Level of Initial Deficit Level.....................................12

### 1. Kaplan-Meier Survivor Function by Level of Initial Deficit Level

### I. Introduction: purpose and scope
- Study objective: assess factors determining the duration (persistence) of fiscal consolidations in a pooled sample of emerging market countries during 1980–2001 using survival analysis.
- Sample: 25 emerging market countries (Argentina, Bolivia, Brazil, China, Colombia, Côte d'Ivoire, Ecuador, Egypt, India, Indonesia, Jordan, Lebanon, Mexico, Nigeria, Pakistan, Peru, Philippines, Poland, Russia, South Africa, Thailand, Turkey, Ukraine, Uruguay, and Venezuela).
- Novelty:
  - Introduces a “composite approach” that accounts for both the level and the trajectory of fiscal consolidation.
  - Uses semi-parametric (Cox proportional hazards) and parametric (Weibull) specifications.
- Baseline operational definition of failure (binary dummy “failure”):
  - Failure = 1 when the annual variation of the budget deficit is equal to or lower than 1 percentage point of GDP (lack of adjustment).
  - Failure = 0 when the annual variation of the budget deficit is above 1 percentage point of GDP (years of fiscal consolidation).
- Alternative definitions tested: change in fiscal deficit thresholds of 0.5 percent of GDP and 1.5 percent of GDP; an alternative composite definition where failure = 1 when annual variation ≤ 1 percentage point of GDP AND the deficit is more than 2 percentage points of GDP.

### II. Analytical framework and literature
- Survival analysis components: spell length T; survival function S(t)=Pr(T>t); failure function F(t)=1−S(t); hazard h(t)=f(t)/S(t).
- Proportional hazard (PH) specification used:
  - Cox semi-parametric model: h(t,X)=h0(t)*exp(X′β).
  - Weibull parametric alternative with baseline ho(t)=β0 p t^(p−1) exp(−β0) (as specified in text), where p tests duration dependency.
- Three definitions of fiscal consolidation typology (Adam and Bevan, 2003):
  1. Level approach (deficit below specified threshold).
  2. Gradient approach (deficit falls relative to previous year).
  3. Composite approach (combines level and gradient).
- Motivation for composite approach: capture marginal cost of further adjustment as economy approaches sustainable deficit levels and capture credibility effects of relative deficit position.

### III. Data and empirical framework
- Period: 1980–2001.
- Data sources:
  - World Economic Outlook (WEO) for macro variables.
  - Government Finance Statistics (GFS) for disaggregated government expenditure.
  - World Development Indicators (WDI) for structure of economy variables.
- Key covariates included in hazard regressions:
  - Fiscal history: number of previous failures at fiscal consolidation.
  - Composition of spending: goods and services, interest payments, subsidies and transfers, capital spending (all in percent of GDP).
  - Total revenue and grants (percent of GDP).
  - Debt (% of GDP) — initial stock.
  - Change in international oil price deflator (percent change).
  - Exchange rate depreciation.
  - Unemployment rate.
  - Corruption (rescaled; higher values indicate weaker institutions).
  - Interaction: capital spending * corruption.
  - Dummies tested: IMF program (Stand-by/EFF, ESAF/PRGF), capital account crises.
- Composite “distance” variable: equal to specified threshold minus current deficit level; threshold fiscal deficit set to 2 percent of GDP; variable can be positive or negative.

### IV. Empirical results

- Non-parametric (Kaplan-Meier) findings:
  - 56 percent of episodes of fiscal consolidation end within a year.
  - Confidence interval for risk of interrupting fiscal consolidation ranges between 33 percent and 94 percent.
  - Splitting episodes by initial fiscal deficit relative to 2 percent of GDP:
    - Significantly lower proportion of fiscal adjustments end within a year when the initial deficit is lower than 2 percent of GDP.
    - Tests for equality of survival functions (Wilcoxon, Tarone-Ware, Fleming-Harrington) reject equality — supports composite approach.

- Semi-parametric (Cox proportional hazards) baseline results (selected robust findings across specifications):
  - Previous number of failures: hazard ratio ~1.24 (significant at 1 percent in baseline; z-statistics reported).
  - Distance from deficit threshold: hazard ratio ~1.09 (significant at 1 percent in baseline).
  - Debt (% of GDP): coefficient ~-0.99 (significant at 1 percent in baseline) — higher debt associated with lower risk of ending a spell (i.e., higher persistence).
  - Interest payment (% of GDP): coefficient ~-0.95 (significant at 5 percent) — higher interest payments associated with lower hazard of ending consolidation.
  - Subsidies and transfers (% of GDP): hazard ratio ~1.06 (significant at 1 percent) — more subsidies/transfers increase probability of ending adjustment.
  - Total revenue and grants (% of GDP): coefficient ~-0.95 (significant at 1 percent) — higher revenues support persistence.
  - Spending on goods and services: weak positive association with hazard (marginal significance).
  - Capital spending: generally negative association with hazard (protecting/increasing capital spending is not harmful); interaction capital spending*corruption negative — suggests corruption offsets capital spending benefits.
  - Exchange rate depreciation and corruption show positive association with failure but less robust.
  - Dummies for IMF-supported programs and capital account crises: generally insignificant.
  - Goodness-of-fit: Cox-Snell residuals indicate good fit; proportional hazard assumption not rejected (generalized Grambsch and Therneau test).

- Parametric (Weibull) findings:
  - Estimated ancillary parameter p > 1, implying monotonically increasing baseline hazard with time (evidence of “consolidation fatigue” in baseline risk).
  - Oil price increases: significant negative impact on hazard in Weibull — for oil-exporting countries higher oil prices sustain consolidation.

- Alternative composite definition (failure only when annual reduction ≤ 1 percentage point of GDP AND deficit > 2 percent of GDP):
  - Average survival rate after one year increases from 44 percent (baseline) to 52 percent under alternative definition.
  - Regression results qualitatively similar: previous failures, distance from threshold, subsidies/transfers positively related to hazard; interest payments and total revenue negatively related.
  - Under this alternative, initial stock of debt becomes insignificant — concentration of failed episodes under baseline among high-debt countries explains difference.

- Robustness checks:
  - Alternative deficit-change thresholds (0.5 and 1.5 percentage point of GDP) — results broadly consistent.
  - Models allowing time-varying parameters, group-specific hazards, and unobserved heterogeneity (shared frailty) — baseline findings confirmed.
  - Primary deficit definition tested (smaller sample) — consistent with baseline findings.

### V. Key quantitative statistics (preserved as reported)
- Sample period: 1980–2001.
- Number of countries (baseline Cox models): typically 15 (and variations with 19 in some specifications).
- Number of failures (baseline): typically 120 (variations reported across models).
- Nonparametric result: 56 percent of consolidation episodes end within a year; risk interval 33 percent to 94 percent.
- Deficit threshold used in composite distance variable: 2 percent of GDP.
- Baseline failure threshold (annual variation): 1 percentage point of GDP.
- Alternative failure rule combined threshold: annual variation ≤ 1 percentage point of GDP AND deficit > 2 percentage points of GDP.
- Change in crude oil example: US$1 per barrel increase lowers deficit by 0.1 percentage point of GDP in Indonesia (illustrative example).

### VI. Main conclusions
- Composite approach (gradient conditioned on level) is empirically supported: distance from deficit threshold matters for persistence.
- Fiscal consolidation persistence in emerging markets:
  - Enhanced by higher total revenues and interest payments (the latter likely reflecting high-debt dynamics where interest reductions deliver gains).
  - Undermined by large subsidies and transfers and by a history of prior failures.
  - Not undermined by protecting or increasing capital spending; reallocating from wages/transfers toward capital spending supports persistence.
  - Supported in oil-exporting countries by oil price increases.
- Baseline risk of ending consolidation increases with time (Weibull p>1), indicating potential “consolidation fatigue.”

### VII. Policy implications and recommendations
- Strengthen institutional quality and policy credibility: histories of “stop and go” adjustments reduce persistence.
- Base deficit reductions on:
  - Cuts in wasteful/current expenditures (subsidies, transfers, excessive wage bills).
  - Revenue mobilization: broaden tax base, remove exemptions, combat tax evasion, consider higher rates where appropriate.
  - Protect and/or increase productive capital spending while targeting inefficient current outlays.
- Maintain social safety nets given adverse effects of unemployment on persistence to build social consensus for consolidation.
- Take account of external factors (oil prices, exchange rate policy) and macro policy interdependencies; further research needed to address endogeneity and the role of accompanying monetary/exchange rate policies.

### VIII. Appendix / Methodology (summarized)
- Survival analysis foundations: hazard h(t)=f(t)/S(t); survivor S(t)=exp(−H(t)), H(t)=∫0^t h(u) du.
- Cox proportional hazards model used for semi-parametric estimation; Grambsch and Therneau test applied to check proportionality via Schoenfeld residuals.
- Goodness-of-fit assessed via Cox-Snell residuals and Nelson-Aalen cumulative hazard plotting.
- Weibull parametric model used to test duration dependence; p>1 implies positive duration dependence, p=1 exponential (no duration dependence), p<1 negative duration dependence.
- Robustness: stratified Cox models, time-varying coefficients, shared frailty to allow within-country correlation, alternative fiscal definitions.

*Source: Excerpt from the IMF working paper section titled "1. Kaplan-Meier Survivor Function by Level of Initial Deficit Level" (Appendix, methodology, and empirical results for fiscal consolidation persistence in 25 emerging market countries, 1980–2001).*

### REFERENCES

### REFERENCES

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*Source: _wp03224 - REFERENCES*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2003/_wp03224.pdf_