## _wp07258

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---

### Introduction and motivation
- Capital account crises: episodes of financial distress with abrupt capital outflows and deep macroeconomic and social consequences.
- Literature focus: causes and triggers (global financial conditions; self-fulfilling expectations; domestic balance-sheet weaknesses; limited trade openness; countries’ solvency and liquidity).
- Gaps addressed: duration of, and exit from, capital account crises received relatively little attention.
- Research questions:
  - How to measure duration and identify beginning and end of crises?
  - What has been the duration of capital account crises?
  - Relationship between crisis complexity and duration?
  - How do macroeconomic flow and balance-sheet variables evolve and where do they settle at crisis dusk?
  - What factors affect speed of crisis resolution? Role of initial conditions, exogenous factors, adjustment policies, and IMF financial support?

### Methods for identifying the beginning and end of crises (Box 1)
- Common start-of-crisis methods:
  - Numerical rules on first/second moments of capital flows (sudden stops): falls below mean by one or two standard deviations.
  - Volatility-based identification using changes in capital flows.
  - Desk-validated capital-flow measures using subjective IMF desk inputs.
  - Market-pressure indices combining REER, reserves, and sovereign spreads.
- Shortcomings of single-indicator approaches:
  - Delayed identification where capital controls exist; numerical-rule false positives; level vs. change ambiguity.
  - No unique satisfactory endpoint indicator: stabilization of pressure indicators, resumption of inflows, return of spreads to “normal”, resumption of market access, and end of reliance on exceptional financing each have cons.
- Recommendation: use a hybrid or composite measure (market pressure index) combining several indicators to identify start and end.

### IKAC index to measure crisis duration (Index for Kapital Account Crises)
- Construction and components (quarterly data; each term standardized to mean zero and standard deviation one; positive values denote financial pressure):
  - foreign exchange reserves (FX) net of IMF disbursements (in millions of U.S.$),
  - nominal effective exchange rate (NEER) in percentage changes,
  - secondary market spreads on sovereign bonds (S),
  - net private capital flows scaled to GDP (K) — WEO definition applied to quarterly IFS data, excluding FDI but including errors and omissions.
- IKAC operational rules:
  - Start of crisis: first of two consecutive quarters with IKAC value positive.
  - End of crisis: first of two consecutive quarters with IKAC value negative.
  - Two-quarter criterion sometimes discretely overridden (examples: Brazil 1998, Philippines 2002).
- Limitations:
  - Small quarterly samples require standardizing components over entire sample (including crisis observations), potentially biasing the “normality” benchmark; mitigated by calibrating zero threshold using IMF staff reports.
  - Lack of sufficiently long pre-crisis series for some countries prevents pure pre-crisis normalization.

### Empirical durations and stylized facts (Box 2 and summaries)
- Sample: 12 emerging market economies; 18 crisis episodes (Turkey, Mexico 1994 start; Uruguay 2002 end among examples).
- Central tendency (selected measures reported):
  - IKAC (Index): Mean = 8.5 (quarters); Median = 7.0 (quarters).
  - Capital outflow indicator: Mean = 6.0; Median = 5.0.
  - Spreads: Mean = 6.8; Median = 5.0.
  - Reserves: Mean = 7.2; Median = 7.0.
  - Exchange rate: Mean = 6.3; Median = 6.0.
  - Market access: Mean = 11.1; Median = 7.0.
  - Exceptional financing (excl. IMF): Mean = 11.2; Median = 10.0.
  - IMF financing: Mean = 10.9; Median = 8.5.
  - Staff assessment: Mean range = 6.2–7.3; Median range = 5.0–7.0.
- Duration distribution:
  - Range: from three quarters (1998 Turkey) to 18 quarters (1997 Thailand).
  - Average duration: about 8½ quarters.
  - Median duration: seven quarters.
  - 16 out of 18 crises lasted less than 12 quarters.
- Crisis complexity:
  - Duration tends to increase with complexity (single, twin, triple).
  - 15 out of 18 crises involved twin or triple crises.
  - All three single crises were shorter than the median; virtually all triple and half of twin crises had longer-than-median duration.
- Sequencing of recovery by indicator:
  - Large capital outflows subside first.
  - Spreads reduce next.
  - Foreign exchange reserves recover last (often not to pre-crisis levels within sample).
  - Real output often recovers before financial normalization in 10 out of 13 episodes with data.
- Exchange rate and spreads:
  - Currencies stabilize at considerably lower levels after crises; depreciation extent correlates with crisis complexity.
  - Average NEER depreciation (“Before crisis” to “After crisis”):
    - Single crises: 25.8 (percent)
    - Twin crises: 28.9 (percent)
    - Triple crises: 54.6 (percent)
- Flow and stock variable patterns (selected figures and means):
  - Capital outflows at crisis peaks typically ranged around 2 percent to about 10 percent of annual GDP; Uruguay peaked at 20 percent of GDP.
  - Average change in private net capital outflows (“Before crisis” to “Crisis Peak”):
    - Single crises: 1.8 (percent of GDP)
    - Twin crises: 3.0 (percent of GDP)
    - Triple crises: 5.4 (percent of GDP)
  - Current-account adjustment: median improvement about 5 percentage points of GDP in more complex crises.
  - Fiscal balance mean changes by crisis type:
    - Single crises: Mean = 0.5 (percent of GDP)
    - Twin crises: Mean = -1.3 (percent of GDP)
    - Triple crises: Mean = 1.4 (percent of GDP)
  - Average change in external debt (“Before crisis” to “After crisis”):
    - Single crises: 2.3 (percent of GDP)
    - Twin crises: 8.2 (percent of GDP)
    - Triple crises: 21.4 (percent of GDP)
  - Foreign exchange reserves examples across phases (U.S.$ billion): reported series include values such as 16.5; 21.7; 22.2; 15.3; 17.8; 12.3; 16.6; 26.3; 29.1 (U.S.$ billion) across crisis types/phases.
- Banking sector (Appendix I partial evidence):
  - 16 out of 18 cases involved banking sector distress.
  - Nonperforming loans (NPLs): Before crisis mean = 16.2 (percent of total loans); Crisis peak mean = 25.8; After crisis mean = 15.2.
  - Bank FX loans change (selected episodes; percent of total loans): Mean = -6.3; Median = -2.4 (country labels in figure: ARG 01, KOR 97, RUS 98, MAL 97, ARG 95, IDN 97).

### Determinants of crisis duration — duration-model results (Appendix II)
- Econometric framework:
  - Grouped duration model / discrete-time survival analysis.
  - Exit probability modeled as p(exit | X, t, u) = exp(λ0(t) + Xβ + u) / (1 + exp(λ0(t) + Xβ + u)) in grouped-duration formulation; alternative complementary log-log and proportional-hazard specifications also used.
  - Time-dependence specifications: logistic time dependence λ0 = α0 + α1 ln(t); linear time dependence λ0 = α0 + α1 t; and time-invariant baseline tested.
  - Robustness checks: three baseline time-dependent specifications; general-to-specific variable elimination; instrumentation for endogenous IMF financing.
- Data and sample:
  - Observations: N = 153 across reported regressions; crisis episodes: 18.
  - Log likelihood values reported across regressions: -30.822; -34.467; -35.858; -35.693; -36.955; -40.026.
  - Akaike Information Criterion values: 111.564; 92.934; 91.715; 95.386; 93.909; 102.051.
  - Bayesian Information Criterion values: 187.405; 129.299; 122.020; 131.751; 124.214; 135.386.
- Robust empirical findings (consistent across preferred specifications unless noted):
  - Initial and external conditions:
    - Larger pre-crisis current account deficits associated with longer crises (Current account balance (pre-crisis): coefficients positive and significant, e.g., 0.214***; 0.280***; 0.239***).
    - Higher external debt correlated with longer crises (External debt (lag 1) coefficients negative and significant in several regressions, e.g., -0.036**, -0.042***).
    - Benign global liquidity (lower three-month LIBOR) and stronger trade-weighted partner demand shorten crisis duration significantly (Libor coefficients negative and significant; trade-weighted demand positive and significant).
    - Net private capital flows to emerging markets weakly associated with exit probability and lacks robustness.
  - Policy responses:
    - Fiscal tightening (change in primary balance, lag 1) shortens crisis duration robustly (coefficients positive and significant; e.g., 0.174**, 0.096***).
    - Monetary policy: raising real interest rate differential shortens crisis duration with lag (mixed results across lags; lag 3 often positive and significant; lag 2 coefficients sometimes negative).
    - Exchange rate regime: more flexible regimes tend to prolong crises on average (negative coefficient; significance sensitive to specification).
  - IMF financial support:
    - Greater cumulative IMF financing associated with higher exit probability in some specifications (IMF financing*program dummy coefficient e.g., 0.272** in one regression) but significance not robust across time-dependent specifications.
  - Time in crisis:
    - Quarters in crisis (log): coefficients positive and significant (e.g., 2.719**, 2.680***, 2.501***).
    - Quarters in crisis (linear): coefficients positive and significant (e.g., 0.353***, 0.342***).
- Multicollinearity and endogeneity:
  - Cumulative IMF financing and exchange rate flexibility increase with time by construction; inclusion of time variable introduces multicollinearity affecting significance.
  - IMF financing is likely endogenous; instrumented using IMF quota, lagged debt ratios, lagged current account, real GDP growth, log of time in crisis, and lagged IKAC index.

### Counterfactual experiments and policy-relevant magnitudes (Box 3 and “0.5 probability” results)
- Median crisis duration: seven quarters.
- Largest reductions in expected duration (one-standard-deviation counterfactuals evaluated at median and at 0.5 probability of staying in crisis):
  - External and initial conditions have biggest impacts:
    - External debt-to-GDP (t-1) - 1SD → increase in exit probability = 0.43; reduction in duration = 3.30 quarters.
    - LIBOR - 1SD → increase in exit probability = 0.32; reduction in duration = 2.73 quarters.
    - CAB-to-GDP (pre-crisis) + 1SD → increase in exit probability = 0.29; reduction in duration = 2.56 quarters.
  - Policy and financial-support counterfactuals (one-standard-deviation changes; increases in exit probability and reductions in duration):
    - Trade-weighted partner country demand + 1SD: +0.14 probability; -1.53 quarters.
    - IMF financing + 1SD: +0.12 probability; -1.36 quarters (statistically not robust in preferred specification; interpret with caution).
    - Change in primary balance + 1SD: +0.10 probability; -1.12 quarters.
    - Capital flows to EM + 1SD: +0.09 probability; -1.10 quarters.
    - Maintaining pre-crisis exchange rate regime: +0.08 probability; -0.95 quarters.
    - Real interest rate differential + 1SD: +0.03 probability; -0.36 quarters.
- Interpretation:
  - Stronger initial conditions or a more benign external environment can shorten expected crisis duration by roughly 2–3 quarters (about 30–40 percent of the median).
  - Policy responses (fiscal consolidation, interest-rate measures) have meaningful but smaller effects; fiscal tightening (one-quarter lag) shortens crises robustly.
  - IMF financing can increase exit probability in some specifications; average IMF package often modest relative to needs of vulnerable countries.

### IMF financing scenarios and frontloading (Box 4 summaries)
- Average IMF package used in illustrative exercises: 3.25 percent of annual GDP.
- Two illustrative crisis scenarios (based on regression (4)):
  - Pure external contagion:
    - Good initial conditions (75th percentile); bad external environment (25th percentile); strong corrective policies (75th percentile).
    - Substantially lower IMF financing needed to resolve crisis relative to vulnerable-country case.
  - External shock to a vulnerable country:
    - Bad initial conditions (25th percentile); bad external environment (25th percentile); strong corrective policies (75th percentile).
    - Average IMF package (3.25 percent of annual GDP) appears too small to have substantial impact on pace of resolution.
- Frontloading experiment (two-year program; total access 3.25 percent of GDP disbursed over eight quarters):
  - Frontloading (half of committed funds disbursed in first two quarters) vs. evenly spread disbursements:
    - Pure external contagion scenario: frontloading raises exit probability but marginal impact small.
    - Vulnerable-country scenario: frontloading makes little difference given average package size insufficient.

### Descriptive statistics for model variables (selected)
- Exchange rate regime: N 153, Mean 6.67, Standard deviation 2.02
- Real interest rate differential (lag 2): N 153, Mean 6.27, Standard deviation 43.41
- Real interest rate differential (lag 3): N 153, Mean 6.12, Standard deviation 40.34
- Change in primary balance (lag 1): N 153, Mean 0.48, Standard deviation 4.76
- Capital flows to EM countries: N 153, Mean 1.41, Standard deviation 0.89
- Three-month Libor rate: N 153, Mean 4.54, Standard deviation 1.84
- Trade-weighted domestic demand (change): N 153, Mean 0.58, Standard deviation 0.62
- External debt (lag 1): N 153, Mean 70.04, Standard deviation 28.92
- Current account balance (pre-crisis): N 18, Mean -2.45, Standard deviation 3.89
- Cumulative IMF financing: N 151, Mean 2.96, Standard deviation 13.75
- Notes:
  - Exchange rate regime as in IMF’s AREAER classification.
  - Real interest rate differential = policy rate differential with three-month Libor, adjusted for inflation differentials.
  - Primary balance change refers to four-quarter (t/t-4) change.
  - Capital flows to EM = total net private capital flows to emerging market countries (ratio to GDP).
  - Cumulative IMF financing = cumulative disbursed IMF financing (percent of quarterly GDP), starting with four quarters preceding the crisis.

### Stylized conclusions and policy implications
- Recovery pattern: capital outflows subside first; exchange rates stabilize at lower levels; spreads decline; reserves recover slowly; real output often recovers before financial-normalization.
- Initial and external vulnerabilities matter most: larger pre-crisis current account deficits and higher external debt are associated with longer crises—underscoring the importance of prudent policies in normal times.
- Fiscal policy: fiscal consolidation during crises (one-quarter lag) signals commitment and shortens crisis duration.
- Monetary policy: raising real interest rates can help shorten crises with lags, but evidence is mixed across specifications and lags.
- Exchange rate policy: greater exchange rate flexibility during crises tends to be associated with longer crises—likely reflecting balance-sheet and reserve-depletion effects.
- IMF financing: larger packages associated with higher exit probability in some specifications but results lack robustness; IMF financing is more effective for countries with stronger fundamentals; instrumenting IMF financing is necessary given endogeneity and multicollinearity concerns.
- Prudence in normal times, timely fiscal adjustment during crises, and attention to external-debt and current-account vulnerabilities are central to preventing and shortening capital account crises.

*Source: _wp07258 (excerpts from References, Box 1, Box 2, Appendix I, Appendix II, and related figures and tables).*

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

### _wp07258 - References

### Introduction and motivation
- Capital account crises are defined as episodes of financial distress characterized by abrupt capital outflows and tend to be highly disruptive with deep macroeconomic and social consequences.
- Existing literature has focused mainly on causes and triggers of crises, highlighting:
  - global financial conditions (liquidity and investor perceptions) and self-fulfilling investor expectations;
  - domestic balance sheet weaknesses and limited trade openness;
  - countries’ solvency and liquidity conditions.
- Prior studies typically find a large negative effect of crises on output growth; this effect appears to be short lived even without recoveries of domestic or foreign credit and investment.
- The duration of, and exit from, capital account crises has received relatively little attention in the literature.

### Research focus and objectives
- The paper provides a systematic account of how recent capital account crises came to an end using a dataset covering crisis episodes starting with Turkey and Mexico in 1994 and ending with Uruguay’s crisis in 2002.
- Primary research questions:
  - How can the duration of a capital account crisis be measured, and what marks the beginning and the end of a crisis?
  - What has been the duration of capital account crises?
  - Is there a relationship between the complexity of a crisis and its duration?
  - How do macroeconomic variables—in both flow and balance sheet dimensions—evolve during capital account crises, and where do they settle at the dusk of crises?
  - What factors affect the speed of crisis resolution? To what extent do these reflect initial conditions, exogenous factors (“good luck”), or adjustment policies? And what is the impact of IMF financial support?

### Organization of the paper (as presented)
- Section II: introduces a new methodology for measuring the duration of capital account crises and discusses key findings for the episodes in the sample.
- Section III: distils stylized facts on economic and financial conditions at the end of crises, relating them to the beginning and peak of crisis episodes.
- Section IV: provides an econometric analysis of the probability of exiting a crisis, using a duration analysis methodology.
- Section V: concludes.

### Conceptual challenge of defining the end of crises
- Identifying the start of capital account crises is relatively well established; timing the end is more complicated.
- At crisis onset, indicators (spreads on sovereign bonds, international reserves, exchange rates) tend to move sharply and in a highly correlated fashion.
- At the tail end of a crisis, these indicators often do not move together and may give conflicting signals.
- The literature on crisis identification has typically focused on beginnings; methods broadly fall into:
  - those relying solely on capital flow patterns (in particular sudden stops);
  - those relying on a broader range of indicators.

### Relevant structural elements and materials in the source (as included in the PDF)
- Boxes cited in the paper include:
  - Box 1: Methods for Identifying the Beginning of Crises
  - Box 2: Application of the Index: One Example and Two Special Cases
  - Box 3: Some Diagnostic Results for Duration Analysis
  - Box 4: IMF Financial Support and Crisis Resolution
- Figures cited include frequency and alternate measures of crisis duration, relationships between crisis duration and IMF credit repayment period and output recovery, average NEER depreciation, average secondary market spreads on sovereign bonds, changes in private net capital flows, current account, fiscal balance, external debt, foreign exchange reserves, and predicted probabilities of staying in crisis under different scenarios.
- Tables cited include timelines and durations of recent capital account crises, duration and nature of crises, estimation results for the capital account crises duration model, and descriptive statistics for the model variables.
- Appendices cited:
  - Appendix 1: Banking Sector Vulnerabilities: Some Partial Evidence
  - Appendix 2: A Model for the Duration of Capital Account Crises

*Source: _wp07258 - References (PDF).*

### Box 1. Methods for Identifying the Beginning of Crises

### Box 1. Methods for Identifying the Beginning of Crises

### Methods used to identify capital account crises
- Numerical rules applied to first and second moments of capital flow time series (sudden stops): assume a sudden stop when the financial account balance in percent of GDP falls below its mean by a certain amount, typically one or two standard deviations. References: Calvo (1998), Calvo (2005), Frankel and Cavallo (2004), Eichengreen, Gupta, and Mody (2006).
- Volatility-based identification: Calvo, Izquierdo, and Mejia (2004) look at first and second moments of changes in capital flows and rely on volatility to identify crises.
- Desk-validated capital-flow measures: Chamon, Manasse, and Prati (2006) employ capital-flow–based measures but validate and revise crisis identification using subjective inputs from IMF country desks to filter noncrisis explanations for reversals.
- Market-pressure indices: combine variables such as real effective exchange rate, international reserves, and spreads on sovereign bonds to capture pressures preceding crises. Hawkins and Klaus (2000) survey such indices; Ramakrishnan and Zalduendo (2006) use an unweighted sum of percentage changes of REER, reserves, and spreads to identify episodes of intense pressures that accompany large net private capital outflows.

### Shortcomings of single-indicator approaches
- Delayed identification when capital account restrictions exist: capital outflows can lag other indicators (example: Malaysia after the Asian crisis).
- Numerical-rule false positives: numerical rules can identify reversals with noncrisis explanations.
- Level vs. change ambiguity: indices based on changes resume “normal” values when variables pass inflection points even if levels remain in disequilibrium.
- No unique satisfactory endpoint indicator: stabilization of pressure indicators, resumption of capital inflows, return of spreads to “normal” levels, resumption of market access, and end of reliance on exceptional financing each have shortcomings (see detailed bullets below).

### Considerations for defining crisis endpoints
- Stabilization of pressure indicators
  - Pros: sudden strong pressure on exchange rate, reserves, and spreads marks onset; stabilization could mark end.
  - Cons: stabilization may reflect a new unsustainable level; crisis may no longer be deepening but large capital outflows can continue.
- Resumption of capital inflows
  - Pros: natural candidate since sudden stops/outflows define capital account crises.
  - Cons: crisis-induced structural changes can alter capital flow patterns so inflows need not resume; resumed inflows may not coincide with sustainable spread reductions (e.g., equity inflows).
- Return of spreads to “normal” levels
  - Pros: spreads are continuous investor-sentiment measures; reduction signals subsiding pressures.
  - Cons: spreads can remain elevated long after crisis due to uncertainty or contagion; choosing a specific “normal” level is arbitrary.
- Resumption of market access
  - Pros: practical marker if primary issuance resumes.
  - Cons: market access can occur at prohibitively expensive terms; observable only when issuance occurs and can lag actual end (example: Indonesian government did not tap markets during six years of IMF financing after Asian crisis).
- End of reliance on exceptional financing
  - Pros: many crises involve multilateral/bilateral emergency financing.
  - Cons: duration of exceptional financing is influenced by facility maturities and political/cost considerations and is not a reliable length-of-crisis measure.

### Recommendation on endpoints
- No single indicator is satisfactory; a hybrid or composite measure (e.g., a market pressure index) that combines several indicators may better identify both the start and the end of crises.

### An Index to Measure Crisis Duration (IKAC)
- Starting point: Ramakrishnan and Zalduendo (2006) market pressure index, modified by:
  - Adding capital flows as a component (focus on capital account crises).
  - Relying primarily on levels of components (to identify end of crises), whereas Ramakrishnan and Zalduendo focused on changes.
- Components (quarterly data):
  - foreign exchange reserves (FX) net of IMF disbursements (in millions of U.S.$),
  - nominal effective exchange rate (NEER) in percentage changes,
  - secondary market spreads on sovereign bonds (S),
  - net private capital flows scaled to GDP (K) — computed using WEO definition applied to quarterly IFS data, excluding FDI but including errors and omissions.
- IKAC formula (each term standardized to mean zero and standard deviation one; positive values denote financial pressure):
  - titititi
    trend
    tititi
    KSNEERNEERFXFXIKAC
    ,,1,,,,,
    )/ln()(−+−−−=
    −
  - The index associates crisis end with spreads and capital flows returning to the country-specific sample mean and reserves approaching their long-run trend; NEER enters as percentage changes to relate exchange rate stabilization to crisis end.
- Start and end rules:
  - Start of crisis: first of two consecutive quarters in which IKAC value is positive.
  - End of crisis: first of two consecutive quarters in which IKAC value is negative.
  - Two-quarter criterion sometimes discretely overridden (example: Brazil 1998, Philippines 2002).
- Sample for application:
  - 12 emerging market economies: Argentina, Brazil, Ecuador, Indonesia, Korea, Malaysia, Mexico, Philippines, Russia, Thailand, Turkey, Uruguay.
- Limitations:
  - Small quarterly sample sizes require standardizing components over entire sample, so the “normality” benchmark includes crisis observations and may introduce bias.
  - Mitigation: calibrating the zero threshold to yield plausible start/end dates based on comparison with IMF staff reports corrects for bias to some extent.
  - Lack of sufficiently long pre-crisis series for some countries prevented use of pre-crisis observations only; post-crisis economic changes cast doubt on using pre-crisis benchmarks alone.

### Empirical durations (selected summaries from Tables 1 and 2)
- Mean durations (months/quarters context implicit in tables):
  - IKAC (Index): 8.5
  - Capital outflow indicator: 6.0
  - Spreads: 6.8
  - Reserves: 7.2
  - Exchange rate: 6.3
  - Market access: 11.1
  - Exceptional financing (excluding IMF): 11.2
  - IMF financing: 10.9
  - Staff assessment: 6.2-7.3 (range reported in table)
- Median durations:
  - IKAC (Index): 7.0
  - Capital outflow indicator: 5.0
  - Spreads: 5.0
  - Reserves: 7.0
  - Exchange rate: 6.0
  - Market access: 7.0
  - Exceptional financing (excluding IMF): 10.0
  - IMF financing: 8.5
  - Staff assessment: 5.0-7.0 (range reported in table)

*Source: IMF staff calculations and assessments.*

### Box 2. Application of the Index: One Example and Two Special Cases

### _wp07258 - Box 2. Application of the Index: One Example and Two Special Cases

### Application of the IKAC index: examples
- Uruguay (typical capital account crisis)
  - At the start: sharp capital outflows → large reserve losses and increases in spreads; pressure on reserves led to a change in the exchange rate regime and a sharp depreciation.
  - Index rose significantly above its sample mean.
  - Subsequent quarters: most variables recovered at different speeds; exchange rate stabilized at a lower level without mean-reversion.
  - Capital flows returned to their mean by the third quarter of the crisis; spreads and reserves recovered more slowly.
  - Weighing all four variables, the IKAC index calls the end of the crisis in the sixth quarter.
- Thailand (outlier)
  - Long duration reflects that it took five years to stem capital outflows and even longer to rebuild reserves.
  - Spreads broadly normalized after some 2½ years, but the IKAC index calls the end of crisis after 18 quarters (versus 15–16 quarters implied by staff assessments).
- Korea (outlier)
  - IKAC index gives a crisis duration of 10 quarters (staff assessment at the time: 5–6 quarters).
  - Index approaches zero after six quarters but then bounces back due to volatile spreads and small but persistent capital outflows; crosses the mean only in the 10th quarter.

### Stylized facts on crisis duration and nature
- Sample and identification
  - Application to 12 emerging market economies recognized as having experienced capital account crises yields 18 crisis episodes.
- Duration distribution and central tendency
  - Estimated crisis duration range: from three quarters (1998 Turkey) to 18 quarters (1997 Thailand).
  - Average duration: about 8½ quarters.
  - Median duration: seven quarters.
  - 16 out of 18 crises in the sample lasted less than 12 quarters.
- Complexity and duration
  - Duration tends to increase with crisis complexity (single, twin, triple).
  - 15 out of 18 crises in the sample involved twin or triple crises.
  - All three “single” crises were shorter than the median duration; virtually all triple and half of twin crises had longer-than-median duration.
- Consistency with IMF staff assessments
  - IKAC-based duration estimates broadly consistent with IMF country teams’ assessments.
  - Both the upper range of staff assessment and the IKAC index result in seven quarters as the median duration in the sample.
  - Correlation between IKAC index measure and staff assessments exceeds 0.8.
  - Notable exception: 1998 Russian crisis, where IKAC duration exceeds staff assessment by 7–8 quarters.

### Sensitivity analysis and alternative measures of crisis end
- Alternative end-of-crisis measures considered (transformations of index components and broader balance-of-payments indicators): reaccess to international capital markets, duration of exceptional financing, timing of IMF disbursements.
- Typical sequencing of recovery by indicator
  - Large capital outflows tend to subside first.
  - Followed by reduction in sovereign bond risk premia (spreads).
  - Foreign exchange reserves recover last to pre-crisis levels (in several instances spreads and reserves did not recover within the sample period).
- Broader balance-of-payments viability and IMF financing
  - Graduation from IMF financing generally associated with reaccess to international capital markets.
  - Balance-of-payments dependence on exceptional financing (debt rescheduling and sizeable external arrears) tends to be more prolonged.
- Mean crisis-duration values by measure (Figure 2 mapping: Capital flows; Exchange rate; Spreads; Reserves; IMF staff assessment; Index; IMF financing; Market access; Exceptional financing (excl. IMF))
  - MEAN: 6.0; 6.3; 6.8; 7.2; 7.3; 8.5; 11.2; 11.2; 10.9 (quarters) — listed in the order of the measures above.
  - MEDIAN: 5.0; 5.0; 6.0; 7.0; 7.0; 7.0; 7.0; 8.5; 10.0 (quarters) — listed in the order of the measures above.
- Link to IMF credit repayment
  - Weak link between exit from crises and repayment of outstanding IMF credit; repayment depends on modalities of IMF financing and sometimes on “prepayment” decisions.
  - Nine out of the 12 countries in the sample have fully repaid IMF credit.
  - For repaid cases: average repayment period was about 22 quarters after the beginning of the crisis (or 13 quarters after the end of the crisis).
  - Examples: Argentina fully repaid five quarters after exiting the 2001 crisis; Indonesia fully repaid 30 quarters after the end of its crisis.
  - Crisis duration and repayment statistics (Figure 3):
    - Crisis duration: Mean = 9.6; Median = 10.0 (quarters).
    - Repayment duration: Mean = 22.2; Median = 19.0 (quarters).
- Output recovery vs. financial normalization
  - In 10 out of 13 crisis episodes with available data, output recovered to pre-crisis levels before financial conditions normalized.
  - Crisis duration and output recovery (Figure 4):
    - Crisis duration: Mean = 9.2; Median = 10.0 (quarters).
    - Output recovery: Mean = 8.1; Median = 7.0 (quarters).
  - Faster output recovery may reflect sharp current-account turnarounds or “phoenix miracles” (firms financing working capital with retained earnings and postponing investment).
  - Output recovery took longer on average as crises became more complex: twin crises average 8.7 quarters; triple crises average 10.7 quarters.

### Exchange rates, spreads, flows, and stock variable patterns by crisis complexity
- Exchange rates and spreads
  - Almost all crises had significant depreciations and currencies stabilized at considerably lower levels than before the crisis.
  - Extent of depreciation correlates with crisis complexity.
  - Average NEER depreciation (“Before crisis” to “After crisis”) by crisis type (Figure 5):
    - Single crises: 25.8 (percent of index value “before crisis”)
    - Twin crises: 28.9 (percent)
    - Triple crises: 54.6 (percent)
  - Secondary market spreads rise sharply at crisis onset and usually subside gradually; increases in spreads are strongly related to crisis complexity.
- Flow variables (capital flows, current account, fiscal balances)
  - Capital outflows at crisis peaks typically ranged from around 2 percent to about 10 percent of annual GDP; Uruguay peaked at 20 percent of GDP (outlier).
  - Average change in private net capital outflows (“Before crisis” to “Crisis Peak”) by crisis type (Figure 7):
    - Single crises: 1.8 (percent of GDP)
    - Twin crises: 3.0 (percent of GDP)
    - Triple crises: 5.4 (percent of GDP)
  - End-of-crisis capital flow patterns:
    - Many 1997 Asian cases stabilized at substantially lower inflows than before crisis.
    - Post-2000 crisis countries tended to end with higher inflows than before (possibly reflecting benign global liquidity).
  - Current-account adjustment
    - Median improvement: 5 percentage points of GDP in more complex crises.
    - Correlation between magnitude of capital outflows and current-account adjustment indicates heavy import compression and limits to official/private financing.
  - Fiscal balance patterns
    - Three groups observed:
      - Fiscal deficits deteriorated considerably (e.g., many 1997–98 Asian crises).
      - Strong fiscal improvement where fiscal sustainability was central to the crisis (Argentina, Brazil, Russia (1998), Turkey 1994/1998).
      - Country-specific mixed patterns (e.g., Malaysia 1997, Mexico 1994).
    - Mean changes by crisis type (Figure 10):
      - Single crises: Mean = 0.5 (percent of GDP)
      - Twin crises: Mean = -1.3 (percent of GDP)
      - Triple crises: Mean = 1.4 (percent of GDP)
- Stock variables (external debt, reserves, banking sector)
  - Gross external debt ratios increased considerably in almost all twin and triple crisis cases; increases driven by exchange rate depreciation and fiscal/contingent liability realizations.
  - Average change in external debt (“Before crisis” to “After crisis”) by crisis type (Figure 11):
    - Single crises: 2.3 (percent of GDP)
    - Twin crises: 8.2 (percent of GDP)
    - Triple crises: 21.4 (percent of GDP)
  - Foreign exchange reserves
    - Substantial reserve losses at crisis height as authorities defend exchange rate; reserves usually rebuilt quickly after allowing depreciation.
    - Average foreign exchange reserves (U.S.$ billion) by crisis type (Figure 12):
      - Before crisis / Crisis peak / After crisis (shown across single, twin, triple): examples include means such as 16.5; 21.7; 22.2; 15.3; 17.8; 12.3; 16.6; 26.3; 29.1 (U.S.$ billion) — reported in series across crisis phases and types.
  - Banking sector distress
    - 16 out of 18 cases in the sample involved banking sector distress; data limitations prevent systematic testing of crisis impacts on banking systems.

### What determines crisis duration? — modeling approach
- Conceptual categories of potential determinants
  - Initial conditions: policy record, external imbalances, solvency/liquidity risks, balance-sheet vulnerabilities.
  - External conditions: investors’ appetite for emerging-market risk, global liquidity, terms of trade, export markets.
  - Policy response: fiscal adjustment, interest rate hikes, exchange rate flexibility, structural policies (not fully quantified).
  - IMF financial support: availability, extent, timing of official financing and presence of IMF-supported programs.
    - IMF-supported programs were in place in 15 out of the 18 crises; no programs (at the time) in Malaysia (1997), Philippines (2002), and Turkey (1998).
- Econometric methodology
  - Grouped duration model used for panel-like data covering 18 crisis episodes with a binary exit indicator.
  - Probability of exiting a crisis in each period modeled as a function of:
    - Time already spent in crisis (time-dependent baseline probability λ0, common to all episodes).
    - Time-varying and country-specific explanatory variables X.
  - Functional form (equation (2) in the source):
    - p( exit | X, t, u ) = (exp(λ0(t) + Xβ + u) ) / (1 + exp(λ0(t) + Xβ + u) )  [expressed in source as a grouped duration framework with alternative specifications].
  - Robustness checks include three alternative baseline time-dependent specifications: logistic time-dependent, linear time-dependent, and time-invariant baseline probability.
- Note on omitted structural policies
  - Structural policies are likely important but difficult to quantify consistently; therefore their inclusion in econometric analysis was limited.

*Source: IMF staff calculations and text from Box 2, _wp07258 - Box 2. Application of the Index: One Example and Two Special Cases*

### Appendix II discusses in further detail the application of duration analysis in this study.

### Appendix II — Application of Duration Analysis in This Study

### Methodology and Model Specification
- Sample and selection:
  - Sample includes only crisis observations, starting from the first quarter in crisis and ending with the exit quarter (no selection bias).  
  - Estimates potentially subject to endogeneity bias (exiting from crisis and certain policy options may be jointly determined).
- Baseline hazard (time dependency):
  - Hazard function assumed to depend on the number of quarters spent in crisis.
  - Exit probability increases with time if the estimated coefficient on the time variable is positive (capital account crisis treated as a finite event) and decreases if it is negative.
  - Two time-dependence specifications considered:
    - Logistic time dependence: λ0 = α0 + α1 ln(t)
    - Linear time dependence: λ0 = α0 + α1 t
- Initial general specification covers variables capturing initial conditions, external conditions, policy response channels, and IMF financial support:
  - Initial conditions:
    - Pre-crisis external debt (in percent of GDP) and its one-period lag.
    - Pre-crisis short-term debt (in percent of reserves) and its one-period lag.
    - Pre-crisis primary fiscal balance and public debt-to-GDP ratio.
    - Note: Data availability prevents inclusion of household, corporate, and banking sector balance sheet indicators.
  - External conditions:
    - Ratio to GDP of net private capital flows into emerging markets (measure of investor appetite).
    - Three-month LIBOR rate (indicator of global liquidity conditions).
    - Changes in terms of trade and trade-weighted partner-countries’ demand.
  - Policy response channels:
    - Changes in the primary fiscal balance (in percent of GDP) over a four-quarter period (contemporaneous and up to two lags).
    - Policy interest rate differentials (vis-à-vis LIBOR) adjusted for the inflation differential with the United States (contemporaneous and up to six lags).
    - Exchange rate regime (AREAER eight-category classification; higher values indicate a more flexible regime).
  - IMF financial support:
    - Measure of cumulative disbursements (in percent of GDP), interacting with an IMF program dummy.
    - Cumulative IMF financing also tested normalized by short-term external debt (similar results).
    - Contemporaneous IMF variable likely endogenous; instrumented by IMF quota, lagged debt-to-GDP ratio, lagged short-term debt-to-reserves ratio, lagged current account balance in percent of GDP, real GDP growth, log of time in crisis, and lagged IKAC index (two quarters). Second lag of IKAC yields highest likelihood value.
- Specification search:
  - General-to-specific approach: sequential elimination of least significant variables (highest p-values) guided by Bayesian and Akaike information criteria to balance parsimony and performance.

### Estimation Results and Robustness
- Model estimation:
  - Both logistic and linear time dependency specifications estimated; general-to-specific yields parsimonious specifications (regressions 2b and 3b for logistic and linear).
  - Common included explanatory variables across parsimonious specifications: external debt (with a one-quarter lag); pre-crisis current account balance; capital flows to emerging market countries; three-month LIBOR rate; change in trade-weighted partner country demand; change in primary balance (with a one-quarter lag); real interest rate differential (with two and three-quarter lags).
  - Exchange rate regime falls just short of significance in time-dependent specifications (p-values of 0.13 and 0.17 in regressions 2a and 3a).
  - Excluding the time variable makes exchange rate regime and IMF financial support variables highly significant (regression 4) — likely reflecting reduced multicollinearity with time.
- Model fit and diagnostics:
  - Logistic time specification provides the tightest fit to data, with highest likelihood value and lowest Bayesian and Akaike information criteria among alternatives.
  - Number of observations across reported regressions: 153.
  - Log likelihood values reported include: -30.822, -34.467, -35.858, -35.693, -36.955, -40.026 (by regression column).
  - Akaike Information Criterion values reported include: 111.564, 92.934, 91.715, 95.386, 93.909, 102.051.
  - Bayesian Information Criterion values reported include: 187.405, 129.299, 122.020, 131.751, 124.214, 135.386.
  - Note: Complementary log-log model with homogenous parameters across crisis episodes; allowing heterogeneity produces almost identical parameter estimates and LR test strongly rejecting presence of heterogeneity (assuming Gamma or normal distributions).
- Key empirical findings (robust results across specifications unless noted):
  - Initial and external conditions:
    - Pre-crisis current account balance (relative size of pre-crisis current account deficit) is an important determinant: larger deficits associated with longer crises.
    - Higher levels of external debt correlated with longer crises; short-term external debt strongly correlated with longer crises in the model without time dependency.
    - Benign global liquidity conditions (lower three-month LIBOR rate) and favorable partner-country demand shorten crisis duration significantly.
    - Net private capital flows to emerging markets (investor risk appetite) only weakly associated with exit probability and lacks robustness (drops out in specification without time dependency).
  - Policy responses:
    - Fiscal policy tightening (one-quarter lag) shortens crisis duration in all specifications — interpreted as confidence/signaling effects of consolidation dominating contractionary impact.
    - Monetary policy: evidence that raising real interest rates (relative to world rates) shortens crisis duration with a lag of three quarters; but the negative coefficient at two-quarter lag suggests overall effect may not be clear cut and is insignificant in some specifications.
    - Exchange rate regime variable generally negative (shift toward more flexible exchange rate tends to prolong crisis); result sensitive and may reflect balance-sheet effects and reserve depletion under stress.
  - IMF financial support:
    - Positive coefficient implies greater cumulative financing packages associated with higher probability of exiting a crisis.
    - Statistical significance of IMF financing is not robust across specifications — statistically significant only in the time-invariant baseline hazard specification.
- Specific coefficient/significance indicators excerpted from reported regressions (selected):
  - Quarters in crisis (log): 2.719**, 2.680***, 2.501*** (across columns).
  - Quarters in crisis (linear): 0.353***, 0.342*** (in linear-time columns).
  - External debt (lag 1): -0.058, -0.051*, -0.039**, -0.049*, -0.036**, -0.042*** (across regressions).
  - Current account balance (pre-crisis): 0.214***, 0.280***, 0.239***, 0.311***, 0.261***, 0.162**.
  - World interest rate (three-month LIBOR): -0.373*, -0.636**, -0.577***, -0.594**, -0.543***, -0.510***.
  - Trade-weighted partner demand (change): 1.318*, 0.985**, 1.165***, 1.282***, 1.354***, 1.159***.
  - Change in primary balance (lag 1): 0.174**, 0.092**, 0.083**, 0.087*, 0.082*, 0.096***.
  - Real interest rate differential (lag 2): -0.050, -0.035**, -0.031, -0.036**, -0.032, -0.040**.
  - Real interest rate differential (lag 3): 0.029, 0.038***, 0.032**, 0.039***, 0.035**, 0.044**.
  - Exchange rate regime: -0.370, -0.298, (not included in some), -0.277, (not included), -0.386**.
  - IMF financing*program dummy: 0.080, 0.052, (not included), 0.075, (not included), 0.272**.
  - Significance notation: ***, **, and * indicate significance at the 1 percent, 5 percent, and 10 percent levels based on robust standard errors.
- Multicollinearity considerations:
  - Cumulative IMF financing increases with time by construction; greater exchange rate flexibility also likely correlated with time variable — inclusion of time variable can introduce multicollinearity affecting significance of these variables.

### Diagnostic Results (Box 3)
- Model explanatory power and fit:
  - Baseline model predicted hazard (with logistic time dependence) closely matches Nelson-Aalen estimator based solely on the distribution of the 18 observed durations of crises — provides comfort on specification and explanatory power.
  - Time-varying explanatory variables are critical: setting explanatory variables to zero causes a dramatic upward-left shift in predicted probability curve away from Nelson-Aalen hazard.
  - Simple duration model with only time variable produces a virtually flat probability curve, inconsistent with data.
- Time-dependence specification performance:
  - Logistic formulation better predicts probability of exiting for durations less than 12 quarters — preferred for 16 out of 18 crises in sample.
  - Linear specification provides a better fit for longer crises.
- Figure summary (Box Figure 1):
  - Curves compared: Nelson-Aalen hazard; baseline model with logistic time dependence (mean explanatory variables); baseline model with logistic time dependence (zero explanatory variables); simple model with logistic time dependence (time variable only); model with linear time dependence (mean explanatory variables).

### Interpretation and Policy Implications
- Initial and external vulnerabilities matter:
  - Larger pre-crisis current account deficits and higher external debt correlate with longer crises — suggests policy focus on reducing external imbalances and foreign-currency exposure to shorten crisis duration.
- Fiscal policy:
  - Fiscal consolidation that signals commitment to adjustment appears to shorten crisis duration via confidence effects; fiscal tightening with a one-quarter lag is robustly associated with earlier exits from crisis.
- Monetary policy:
  - Tightening via higher real interest rates may help stem capital outflows and shorten crisis duration with lags (notably three quarters), but effects are mixed across lags and specifications.
- Exchange rate policy:
  - Moving toward greater exchange rate flexibility during a crisis tends to prolong the crisis on average, possibly due to balance-sheet and reserve depletion effects; floating amid crisis risks overshooting and deeper sectoral balance-sheet deterioration.
- IMF financing:
  - Larger cumulative IMF financing packages are associated with a higher probability of exiting a crisis in some specifications, but this result lacks robustness across specifications and may be endogenous; instrumenting the IMF financing measure is necessary to mitigate endogeneity concerns.
- Multicollinearity and model specification:
  - Inclusion of the time variable can introduce multicollinearity with cumulative IMF financing and exchange rate flexibility, affecting statistical significance — policymakers and analysts should account for such interactions in inference.

### Counterfactual Experiments (based on regression (2a), logistic time specification)
- Approach:
  - Baseline predicted probability of exiting from crisis constructed using estimated parameters and mean values of model variables.
  - Counterfactuals: change mean value of individual explanatory variables by one standard deviation and compute impact on predicted probability and estimated crisis duration.
  - Differences evaluated at median crisis duration of seven quarters; alternative gauge: quarters required for predicted probability of exit to reach one-half.
- Scenario types illustrated in Figure 13:
  - Baseline probability (mean explanatory variables).
  - Strong initial conditions.
  - Benign external conditions.
  - Strong policy response.
  - Greater IMF financing.
- Use of counterfactuals:
  - Vertical comparison at median duration (seven quarters) shows relative importance of factors on exit probability.
  - Horizontal comparison shows changes in expected crisis duration by comparing quarters to reach a given exit probability threshold (one-half).

*Source: IMF staff calculations.*

### 0.5 probability of exit from the crisis.

### _wp07258 - 0.5 probability of exit from the crisis.

### Key empirical findings on crisis duration and determinants
- Median duration of capital account crises: seven quarters.
- Largest gain in shortening expected duration: roughly 2–3 quarters, or about 30–40 percent of the median duration, associated with either:
  - Stronger initial conditions (lower pre-crisis current account deficits and relatively moderate external debt burden), or
  - A more benign external environment (more favorable international liquidity conditions and buoyant trade partners’ demand).
- Initial and external conditions are the strongest influences on crisis duration and are largely outside policymakers’ control once a crisis erupts.
- Policy response matters:
  - A stronger improvement in the primary fiscal balance (by one standard deviation) or maintaining the pre-crisis exchange rate regime increases the probability of exiting from a crisis by about 10 percent and shortens crisis duration by about one quarter.
  - A one standard deviation higher real interest rate differential is predicted to raise the probability of exiting from crisis marginally by 3 percent, and to shorten duration by about 0.4 quarters.
- Marginal impact of one standard deviation higher IMF financing is estimated to increase the probability of exiting from a crisis by about 12 percent, but this coefficient is not statistically significant in the preferred specification and must be interpreted with caution.

### Counterfactual scenario impacts (evaluated at median duration of seven quarters and at 0.5 probability of staying in crisis)
- Increase in predicted probability of exit from crisis (change in probability when the mean of the explanatory variable is changed by one standard deviation, evaluated at median crisis duration of seven quarters):
  - Real interest rate differential + 1SD: 0.03
  - Maintaining pre-crisis exchange rate regime: 0.08
  - Capital flows to EM + 1SD: 0.09
  - Change in primary balance + 1SD: 0.10
  - IMF financing + 1SD: 0.12
  - Trade-weighted partner country demand + 1SD: 0.14
  - CAB-to-GDP (pre-crisis) + 1SD: 0.29
  - LIBOR - 1SD: 0.32
  - External debt-to-GDP (t-1) - 1SD: 0.43

- Reduction in predicted crisis duration (quarters) under the same one-standard-deviation counterfactuals (evaluated at 0.5 probability of staying in crisis):
  - Real interest rate differential + 1SD: 0.36 quarters
  - Maintaining pre-crisis exchange rate regime: 0.95 quarters
  - Capital flows to EM + 1SD: 1.10 quarters
  - Change in primary balance + 1SD: 1.12 quarters
  - IMF financing + 1SD: 1.36 quarters
  - Trade-weighted partner country demand + 1SD: 1.53 quarters
  - CAB-to-GDP (pre-crisis) + 1SD: 2.56 quarters
  - LIBOR - 1SD: 2.73 quarters
  - External debt-to-GDP (t-1) - 1SD: 3.30 quarters

### IMF financing: Box 4 — scenarios and frontloading
- Average IMF package used in illustrative exercises: 3.25 percent of annual GDP.
- Two crisis scenarios evaluated (based on regression (4) in Table 4):
  - Pure external contagion:
    - Good initial conditions (75th percentile); bad external environment (25th percentile); strong corrective policies (75th percentile).
    - Substantially lower IMF financing needed to resolve crisis relative to vulnerable-country case.
  - External shock to a vulnerable country:
    - Bad initial conditions (25th percentile); bad external environment (25th percentile); strong corrective policies (75th percentile).
    - Average IMF package (3.25 percent of annual GDP) appears too small to have a substantial impact on pace of crisis resolution.
- Frontloading experiment (two-year program; total access 3.25 percent of GDP disbursed over eight quarters):
  - Comparison: half of committed funds disbursed in the first two quarters (frontloaded) versus equal quarterly disbursements over eight quarters.
  - Results:
    - In pure external contagion scenario, frontloading helps raise the probability of exiting the crisis, but the marginal impact is quite small.
    - In the vulnerable-country scenario, frontloading makes little difference given the insufficient size of the average package.

### Descriptive statistics (model explanatory variables)
- Selected means and standard deviations (from Table 5; N and units preserved as in source):
  - Exchange rate regime 1/: N 153, Mean 6.67, Standard deviation 2.02
  - Real interest rate differential (lag 2) 2/: N 153, Mean 6.27, Standard deviation 43.41
  - Real interest rate differential (lag 3) 2/: N 153, Mean 6.12, Standard deviation 40.34
  - Change in primary balance (lag 1) 3/ 4/: N 153, Mean 0.48, Standard deviation 4.76
  - Capital flows to EM countries 5/: N 153, Mean 1.41, Standard deviation 0.89
  - Three-month Libor rate: N 153, Mean 4.54, Standard deviation 1.84
  - Trade-weighted domestic demand (change): N 153, Mean 0.58, Standard deviation 0.62
  - External debt (lag 1) 3/: N 153, Mean 70.04, Standard deviation 28.92
  - Current account balance (pre-crisis) 3/: N 18, Mean -2.45, Standard deviation 3.89
  - Cumulative IMF financing 6/: N 151, Mean 2.96, Standard deviation 13.75
- Notes from source:
  - 1/ As in IMF’s “Annual Report on Exchange Rate Arrangements and Exchange Restrictions.”
  - 2/ Policy rate differential with the three-month Libor rate, adjusted for the difference between the country’s inflation and U.S. inflation.
  - 3/ In percent of GDP.
  - 4/ Refers to four-quarter (t/t-4) change in primary balance.
  - 5/ Total net private capital flows to emerging market countries (ratio to GDP).
  - 6/ Cumulative sum of disbursed IMF financing (in percent of quarterly GDP), starting with four quarters preceding the crisis.

### Stylized facts and conclusions
- Recovery pattern: capital outflows tend to subside first, followed by exchange rate stabilization, reductions in the risk premium on sovereign bonds, and gradual recovery of foreign exchange reserves; real output tends to recover ahead of the financial indicators.
- Crisis complexity:
  - More complex (“twin” and “triple”) crises are associated with more severe capital outflows, sharper currency depreciations, larger increases in spreads, and more wrenching current account adjustments.
  - Countries emerging from more complex crises tend to have greater post-crisis debt-related vulnerabilities.
- Fiscal positions and capital flow patterns toward end of crises vary widely; external debt levels substantially rise in many cases, particularly with significant exchange rate depreciations.
- Policy implications:
  - Consistent implementation of sustainable macroeconomic policies (prudent policies) in normal times is critical for strengthening initial conditions and preventing protracted crises.
  - Appropriate fiscal adjustment during crises can shorten duration significantly.
  - Raising (real) interest rates may help shorten crises, though evidence is mixed.
  - Changes in exchange rate regimes during a crisis (often large depreciations) tend to be associated with longer crises, likely reflecting adverse balance sheet effects.
  - The effectiveness of IMF financing in shortening crisis duration appears more pronounced for countries with relatively strong fundamentals; econometric sensitivity cautions against definitive claims.

### Appendix I — Banking sector vulnerabilities (partial evidence)
- Data limitations (annual frequency; sample size) restrict systematic analysis; central bank liquidity provision may mask acute banking-sector liquidity pressures.
- Bank liquid assets:
  - Considerable cross-crisis differences in evolution of banks’ liquid assets; mean change “Before crisis” to “After crisis”: Mean = 0.8; Median = 0.2 (in percent of total assets).
- Deposits in foreign currency (bank liabilities dollarization):
  - Tended to increase somewhat during most recent crises, reflecting valuation effects and currency substitution; mean change “Before crisis” to “After crisis”: Mean = -1.3; Median = 0.5 (in percent of total deposits).
- Foreign currency loans:
  - Rose largely reflecting valuation effects; partly offset by refinancing in domestic currency as crisis progressed.
- Bank claims on government:
  - Generally rose, particularly sharply in Argentina in 2001 due to steep depreciation and swap of sovereign bonds into loans.
- Nonperforming loans (NPLs):
  - NPLs rose substantially during the crisis in several cases; toward the end of crises, strong improvements in NPL ratios are observed, reflecting restructurings, write-offs, and recovery.
  - Before crisis: Mean = 16.2 (in percent of total loans)
  - Crisis peak: Mean = 25.8
  - After crisis: Mean = 15.2

*Source: IMF staff calculations, from _wp07258 - 0.5 probability of exit from the crisis.*

### Appendix I, Figure 3. Change in Bank FX Loans 1/

### _wp07258 - Appendix I, Figure 3. Change in Bank FX Loans 1/

### Figure context and measurement
- Figure title: Change in Bank FX Loans 1/ (in percent of total loans)
- Source: IMF staff calculations.
- Footnote 1/: “Before crisis” and “After crisis” refer to an average of four quarters immediately preceding or succeeding the crisis (where data are available).
- Horizontal axis range shown in figure: -50 -40 -30 -20 -10 0 10 20 30
- Country labels shown in figure: ARG 01, KOR 97, RUS 98, MAL 97, ARG 95, IDN 97
- Summary statistics shown in figure:
  - Mean = -6.3
  - Median = -2.4

### Empirical finding illustrated by the figure
- The plotted changes report the difference from “Before crisis” to “After crisis” in bank foreign-currency (FX) loans measured as percent of total loans for selected crisis episodes.
- The sample of labeled episodes includes: ARG 01, KOR 97, RUS 98, MAL 97, ARG 95, IDN 97.
- The central tendency measures for the plotted changes are:
  - Mean = -6.3
  - Median = -2.4

### Appendix II: A model for the duration of capital account crises — key model elements
- Objective:
  - Apply survival analysis to identify factors influencing the duration of capital account crises.
  - Investigate how covariates—including initial conditions, the external environment, policy responses, and the extent of IMF financial involvement—affect the “survival” time T of a country in a capital account crisis.
- Definition:
  - Let T ≥ 0 denote the time at which an economy exits from a capital account crisis, and t denote a particular value of T.
  - Survivor function: S(t) ≡ P(T > t) = 1 − F(t), where F(t) = P(T ≤ t). (Equation (AII.1))
- Conditional hazard (discrete-time) definition:
  - The conditional hazard function at time t is defined as the probability of leaving crisis in [t, t+h], given being in crisis up until time t and conditional on time-variant explanatory variables summarized by vector X:
    - λ(t; X) = lim_{h→0+} P(t ≤ T < t + h | T ≥ t, X) / h. (Equation (AII.2))
- Proportional hazards specification with time-varying covariates:
  - λ(t; X) = λ0(t) κ(X(t)), where κ(.) is a nonnegative function of X and λ0(t) is the baseline hazard common to all countries in crisis. (Equation (AII.3))
- Complementary log-log discrete hazard specification used:
  - p_{t,u}(X) = 1 − exp(−exp(log(t) + Xβ + u)), where the baseline hazard is, for example, λ0(t) = log(t), Xβ includes an intercept, and u is an error term summarizing omitted-variable impacts on the hazard. (Equation (AII.4))
- Role and treatment of the error term u:
  - u captures omitted heterogeneity across crisis episodes and can be interpreted as capturing measurement errors in recorded regressors or recorded survival times (footnote 45).
  - To account for unobserved heterogeneity, u for different crises can be assumed to be drawn from a distribution (Normal, Gamma, or Inverse Gaussian) with estimable parameters.
  - Key identifying assumption in models with unobserved heterogeneity: the heterogeneity is independent of the observed covariates.
- Estimation approach:
  - Probabilities defined by (AII.4) are used to construct a likelihood function.
  - Parameters are estimated by maximizing the log-likelihood.

*Source: _wp07258 - Appendix I, Figure 3. Change in Bank FX Loans 1/ (excerpt).*

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