## wpiea2019230-print-pdf — Proportional Hazard Models & Parametric Models

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### Proportional Hazard (PH) model specification and AFT contrast
- PH model:
  - h(t_j|x_j) = h_0(t) exp(x_j β)
  - Cox PH model: semi-parametric; baseline hazard need not be known; relative hazards time independent: h(t|x_i) / h(t|x_j) = exp(x_i β) / exp(x_j β)
- Parametric PH variant:
  - Weibull baseline hazard: h_0(t) = θ t^{θ−1}, where θ captures duration dependence.
- Accelerated Failure-Time (AFT) specification:
  - Log(t_j) = x_j β + ε_j
  - ε_j distributions include gompertz, gamma, log normal, log logistic.
  - Coefficients interpreted as time ratios (effect on baseline duration).

### Data, definitions, and sudden stop identification
- Data source and coverage:
  - Financial Flows Analytics (FFA) database constructed by the IMF’s Research Department.
  - Coverage: 165 countries, quarterly frequency, going back to 1970.
  - Contains capital flows in real US dollar terms and capital flows as a share of GDP (latter with more limited availability).
- Focus: sudden stops in gross private capital inflows (excluding reserves and other official flows).
- Key controls:
  - Exchange rate regime (binary): Ilzetzki, Reinhart, and Rogoff (2017) collapsed to 0/1 dummy (their 1 and 2 → 0 (fixed); their 3 and 4 → 1 (flexible)).
  - GDP per capita level at episode start.
  - Change in the log commodity terms of trade index over four quarters after onset.
- Sudden stop definition (Forbes and Warnock, 2012 approach):
  - Year-over-year change in four-quarter capital inflows C_t = sum_{i=0}^3 flows_{t−i} is more than two standard deviations below the historical average during at least one quarter of the episode.
  - Historical average: rolling means over past five years of ΔC_t = C_t − C_{t−4}.
  - Episode lasts for all consecutive quarters where ΔC_t is more than one standard deviation below historical average.
- Identified episodes:
  - 1,089 quarters under sudden stops (real US dollar terms) out of 10,779 quarters with available data.
  - 714 quarters with private capital flows as share of GDP out of 7,023 quarters with available data.

### Duration descriptive statistics (sudden stops and growth decelerations)
- Sudden Stops (Real US Dollars) / Sudden Stops (Share of GDP) — All countries
  - Number of episodes: 278 / 173
  - Mean Duration (quarters): 3.89 / 4.10
  - Standard Dev.(quarters): 1.60 / 1.70
  - Min.(quarters): 1 / 1
  - Max.(quarters): 9 / 9
- Emerging Markets — Sudden Stops (Real US Dollars) / (Share of GDP)
  - Number of episodes: 157 / 69
  - Mean Duration (quarters): 3.69 / 3.86
  - Standard Dev.(quarters): 1.55 / 1.61
  - Min.(quarters): 1 / 1
  - Max.(quarters): 9 / 7
- Advanced Economies — Sudden Stops (Real US Dollars) / (Share of GDP)
  - Number of episodes: 121 / 104
  - Mean Duration (quarters): 4.15 / 4.27
  - Standard Dev.(quarters): 1.64 / 1.74
  - Min.(quarters): 1 / 1
  - Max.(quarters): 9 / 8
- Growth decelerations (only sudden stops that cause output deceleration; durations in quarters)
  - All countries: Number of episodes: 130 / 96; Mean Duration: 10.61 / 11.44; Standard Dev.: 8.88 / 9.21; Min.: 2 / 2; Max.: 45 / 40
  - Emerging Markets: Number of episodes: 53 / 35; Mean Duration: 10.34 / 10.57; Standard Dev.: 9.68 / 8.95; Min.: 2 / 2; Max.: 45 / 35
  - Advanced Economies: Number of episodes: 77 / 61; Mean Duration: 10.78 / 11.93; Standard Dev.: 8.35 / 9.39; Min.: 2 / 2; Max.: 38 / 40

### Output deceleration duration metric (alternative to standard sudden stop duration)
- Growth rate: year-on-year change in log real GDP = (LGDP_t − LGDP_{t−4}).
- Episode qualification:
  - Compare eight-quarter moving average of growth in the quarter preceding sudden stop onset with growth at onset and subsequent quarters.
  - Only sudden stops with growth deceleration at onset qualify; deceleration must last at least two quarters.
  - End of episode when growth exceeds pre-onset moving average for at least two consecutive quarters.

### Policy response variables and measurement
- Policy responses analyzed:
  - i) changes in real interest rates (ex-post short term real interest rates);
  - ii) sales of international reserves (percent change in reserves over four quarters after onset);
  - iii) changes in capital account restrictions (Chinn and Ito (2006) index);
  - iv) changes in fiscal primary balance (residuals from regression of primary balance on real GDP growth and commodity terms of trade growth).
- Policy variables included as changes over four quarters following onset (four-quarter window chosen because sudden stops tend to be short and later policies may not be responses to the shock).
- Measurement notes:
  - Fiscal discretionary response: change in residuals from OLS regression of primary balance on real GDP growth and commodity terms of trade growth.
  - Capital account regulations: de jure index by Chinn and Ito (2006).
  - Monetary policy: changes in ex-post short term real interest rates (CPI inflation from IFS used to compute real rates).

### Non-parametric (Kaplan-Meier) findings
- Exchange rate regime:
  - Output deceleration durations tend to be longer under fixed exchange rate regimes (fixed dashed curve above floating curve).
- Advanced vs EMDEs:
  - Differences not significant for sudden stops or output decelerations; some indication of higher probability of remaining in growth deceleration for advanced economies after 5 quarters, disappearing after 20 quarters.

### Semi-parametric Cox model results and interpretation
- Methodological caution:
  - Schoenfeld residuals tests generally reject proportionality; interpret Cox results cautiously.
  - Breslow method used for ties.
- Main estimated associations (significant effects summary):
  - Flexible exchange rate regime:
    - Shortens duration for sudden stops and output decelerations.
    - Flexible regime increases odds of exiting a growth deceleration by over 50 percent.
  - Terms of trade:
    - Improvement of 1 percent increases hazard rate by 10 percent.
    - A one standard deviation in commodities terms of trade growth (~2.5 percent) may change duration by 25 percent.
  - Monetary policy tightening:
    - Associated with increased hazard of exiting growth deceleration.
    - A tightening of 3 percent in real terms is associated with a decrease in duration of 15 percent in model (4).
  - Other policy variables: generally not significant in semi-parametric specifications.

### Baseline parametric specifications and key parametric findings
- Parametric baselines:
  - Weibull: h0(t) = θ t^{θ−1}; reported θ estimates include 2.65, 2.90.
  - Gompertz: h0(t) = exp(γ t); reported γ estimates include 1.66, 1.83.
  - θ and γ estimates point to an increasing hazard over time (higher probability of exit as quarters increase).
- Sudden stops (parametric PH results):
  - Exchange rate regime: exponentiated coefficients reported as ER Regime = 1.28, 1.62, 1.38, 1.96 (Weibull and Gompertz examples); coefficients significant and economically large.
  - Terms of trade: exponentiated coefficients = 1.12, 1.13, 1.11, 1.12; a 1 standard deviation increase in terms of trade would increase chance of leaving sudden stop by 30 percent.
  - Monetary policy: exponentiated coefficients example Monetary = 1.03, 1.06; a 1 percentage point increase in real interest rates increases chances of leaving sudden stop by 6 percent (standard sudden stop specification).
  - Reserves: positive and significant in several specifications (example Reserves = 1.01, 1.01).
  - Capital controls and fiscal policy: generally weaker or not statistically significant.
- Growth decelerations (parametric PH results):
  - Exchange rate regime: flexible regimes increase hazard by between 50 to 80 percent in several cases (examples ER Regime = 1.58, 1.84, 1.52, 1.81).
  - Terms of trade: robust positive effect (examples Terms of Trade = 1.08, 1.10, 1.08, 1.09).
  - Monetary policy: 1 percentage point increase in real interest rates increases chances of leaving low growth state by 5 percent (examples Monetary = 1.05, 1.05).
  - Other controls (fiscal policy, reserves, capital controls): mixed significance; reserves sometimes significant (Reserves = 1.01).

### AFT model findings (time-ratio interpretation)
- Sudden stops (AFT; Table 6):
  - Terms of trade shorten durations: exponentiated coefficients ≈ 0.94–0.96 (examples Terms of Trade = 0.94, 0.95, 0.95, 0.96).
  - Weibull AFT suggests flexible ER regimes reduce sudden stop duration by 15 percent (Weibull column: ER Regime = 0.85).
- Growth decelerations (AFT; Table 7):
  - Flexible ER regimes significantly shorten durations, typically by over 30 percent in many specifications (examples ER Regime = 0.70, 0.67, 0.67, 0.70).
  - Terms of trade shorten durations (examples Terms of Trade = 0.93, 0.94, 0.94, 0.93).
  - Monetary tightening shortens durations (examples Monetary = 0.98, 0.98, 0.97, 0.98).

### Robustness checks and extensions
- Controlling for banking crises (Table 8):
  - Banking crises reduce hazard of exiting sudden stop states (examples Banking Crisis = 0.52, 0.51 in Weibull/Gompertz sudden stop columns).
  - Effects on growth decelerations not statistically significant in these specifications.
  - Exchange rate regime and terms of trade findings confirmed.
  - Monetary policy associated with a 3 to 5 percent reduction in duration of sudden stops per percentage point increase in real rates in these specifications.
- Controlling for initial public debt and initial reserves (Tables 9 and 10):
  - Initial Public Debt and Initial Reserves generally not significant (examples Initial Public Debt = 1.00; Initial Reserves = 1.00) and do not materially change main results.
  - Exchange rate regime and monetary policy effects persist.
- Alternative sudden stop definitions (Tables 11 and 12; inflows as share of GDP):
  - Findings confirmed; ER regime role becomes clearer with large and statistically significant effects in all models for sudden stops.
  - Monetary policy matters for sudden stops when using inflows in percent of GDP (examples Monetary = 1.03, 1.05).
- Shared frailty models (Table 13; Gompertz frailty, Inverse-Gaussian frailty):
  - Broad confirmation of baseline results.
  - Examples: ER Regime = 1.34, 1.86; Terms of Trade = 1.15, 1.14; Monetary = 1.04, 1.05.
  - Frailty parameter examples: v = 0.88, 0.27, 0.32, 0.00.

### Conclusions and policy implications
- Exchange rate flexibility:
  - Floating exchange rate regimes tend to shorten sudden stop episodes and growth decelerations following sudden stops.
  - Quantitative effect: flexible regimes increase probability of exiting sudden stop state by between 50 to 80 percent in several cases.
  - Positive variations in terms of trade abbreviate durations of sudden stops.
- Monetary policy:
  - Tightening can shorten durations of sudden stops and growth decelerations, though identification is nuanced.
  - Example magnitude: a 3 percent rise in real interest rates associated with roughly 15 percent reduction in sudden stop duration.
  - Mechanism consistent with containing real exchange rate depreciation and tightening collateral constraints.
- Policy interpretation:
  - Results support the view that exchange rate flexibility helps mitigate external shocks.
  - Caution against overstating insulating power of capital account restrictions; capital controls and fiscal policy show weaker and mixed effects across specifications.

*Source: wpiea2019230-print-pdf*

### 2.1    Proportional Hazard Models

### 2.1    Proportional Hazard Models

### Proportional Hazard (PH) model specification
- PH models estimate the hazard function:
  - h(t_j|x_j) = h_0(t) exp(x_j β)
  - h(t_j|x_j) is the hazard function; h_0(t) is the baseline hazard function; x_j is a vector of covariates.
- Cox PH model:
  - semi-parametric: the baseline hazard does not need to be known or estimated.
  - Relative hazards are time independent:
    - h(t|x_i) / h(t|x_j) = exp(x_i β) / exp(x_j β)
- Parametric PH variants:
  - When duration dependence is present, the Weibull distribution is an option with baseline hazard:
    - h_0(t) = θ t^{θ−1}, where θ captures duration dependence.

### Accelerated Failure-Time (AFT) models (contrast to PH)
- AFT model specification:
  - Log(t_j) = x_j β + ε_j
  - t is survival time; ε_j is an error term with possible distributions including the gompertz, gamma, log normal, and log logistic.
- Interpretation:
  - Coefficients are time ratios indicating how baseline duration expands or contracts following a one-unit change in explanatory variables.

### Data and definitions (overview)
- Analysis focus:
  - sudden stops in gross private capital inflows (excluding reserves and other official flows).
- Data source:
  - Financial Flows Analytics (FFA) database constructed by the IMF’s Research Department.
  - Coverage: 165 countries, quarterly frequency, going back to 1970.
  - Dataset contains capital flows in real US dollar terms and capital flows as a share of GDP (latter with more limited availability).
- Advantages of FFA:
  - Compiles IMF Balance of Payments Statistics and extends with Haver Analytics, CEIC, and EMED.
  - Presents private capital flows within “other investment” excluding general government, monetary authorities, IMF lending, and reserve asset accumulation — allows focus on market-driven flows.
- Key control variables:
  - Exchange rate regime (binary): derived from Ilzetzki, Reinhart, and Rogoff (2017) collapsed into 0/1 dummy:
    - their 1 and 2 → 0 (fixed)
    - their 3 and 4 → 1 (flexible)
  - GDP per capita level at episode start.
  - Change in the log commodity terms of trade index over four quarters after onset.
- Note on exchange rate regime:
  - Choice is slow-moving and correlated with income per capita; flexible regimes more prevalent in higher middle-income and advanced economies.
  - Empirical finding highlighted: pre-shock floaters leave the growth-reducing sudden stop state more quickly than pre-shock peggers.

### Defining sudden stops
- Sudden stop definition (following Forbes and Warnock, 2012):
  - Year-over-year change in four-quarter capital inflows C_t = sum_{i=0}^3 flows_{t−i} is more than two standard deviations below the historical average during at least one quarter of the episode.
  - Historical average calculated over past five years (rolling means of ΔC_t = C_t − C_{t−4}).
  - Episode lasts for all consecutive quarters for which the change in annual capital flows is more than one standard deviation below the historical average.
- Identified episodes (using this approach):
  - 1,089 quarters under sudden stops in gross private capital inflows (real US dollar terms) out of 10,779 quarters with available data for that variable.
  - 714 quarters with private capital flows expressed as a share of GDP out of 7,023 quarters with available data.
- Duration summary (Table 1 descriptive statistics for duration of sudden stops, in quarters)
  - Sudden Stops (Real US Dollars) / Sudden Stops (Share of GDP)
    - All countries
      - Number of episodes: 278 / 173
      - Mean Duration (quarters): 3.89 / 4.10
      - Standard Dev.(quarters): 1.60 / 1.70
      - Min.(quarters): 1 / 1
      - Max.(quarters): 9 / 9
    - Emerging Markets
      - Number of episodes: 157 / 69
      - Mean Duration (quarters): 3.69 / 3.86
      - Standard Dev.(quarters): 1.55 / 1.61
      - Min.(quarters): 1 / 1
      - Max.(quarters): 9 / 7
    - Advanced Economies
      - Number of episodes: 121 / 104
      - Mean Duration (quarters): 4.15 / 4.27
      - Standard Dev.(quarters): 1.64 / 1.74
      - Min.(quarters): 1 / 1
      - Max.(quarters): 9 / 8

### Output decelerations following sudden stops
- Rationale for alternative duration metric:
  - Standard sudden stop durations are short and display limited dispersion.
  - Not all sudden stops coincide with reductions in growth; policy interest centers on sudden stops that cause real activity slowdowns.
- New duration metric:
  - Number of quarters of subpar growth performance ignited by a sudden stop episode (only if growth deceleration occurs).
- Growth rate definition:
  - Year-on-year change in log of real GDP: (LGDP_t − LGDP_{t−4}).
  - For each sudden stop episode, compare the eight-quarter moving average of growth in the quarter preceding the sudden stop onset with growth at onset and subsequent quarters.
  - Only sudden stops featuring a growth deceleration at onset qualify; deceleration must last at least two quarters.
  - End of episode: growth must exceed pre-onset moving average for at least two consecutive quarters.
- Descriptive statistics for duration of growth decelerations (Table 2)
  - Decelerations (Real US Dollars) / Decelerations (Share of GDP)
    - All countries
      - Number of episodes: 130 / 96
      - Mean Duration (quarters): 10.61 / 11.44
      - Standard Dev.(quarters): 8.88 / 9.21
      - Min.(quarters): 2 / 2
      - Max.(quarters): 45 / 40
    - Emerging Markets
      - Number of episodes: 53 / 35
      - Mean Duration (quarters): 10.34 / 10.57
      - Standard Dev.(quarters): 9.68 / 8.95
      - Min.(quarters): 2 / 2
      - Max.(quarters): 45 / 35
    - Advanced Economies
      - Number of episodes: 77 / 61
      - Mean Duration (quarters): 10.78 / 11.93
      - Standard Dev.(quarters): 8.35 / 9.39
      - Min.(quarters): 2 / 2
      - Max.(quarters): 38 / 40

### Policy responses (variables and measurement)
- Policy responses considered:
  - i) changes in real interest rates;
  - ii) sales of international reserves;
  - iii) changes in capital account restrictions;
  - iv) changes in fiscal primary balance.
- Measurement approaches and notes:
  - Monetary policy response: use changes in the ex-post short term real interest rates (rather than nominal-rate-based dummies).
  - Fiscal discretionary response: change in residuals from regression of primary balance (share of GDP) on real GDP growth and commodity terms of trade growth (approach in Hutchison et al. (2010)).
  - Capital account regulations: changes in the de jure capital account openness index by Chinn and Ito (2006).
  - Sales of international reserves: percent change in international reserves over four quarters after onset.
  - Policy variables included as changes over four quarters following onset (time-fixed inclusion required by duration models).
  - Rationale for four-quarter window: policies enacted long after onset are not considered responses to the shock; sudden stops tend to be short.
- Literature measurement variants:
  - Hutchison et al. (2010): fiscal response via residuals of budget balance regression; monetary tightening/loosening via discount rate changes exceeding ± two standard deviations; reserves change via two-standard-deviation threshold.
  - Forbes and Klein (2015): statistical criteria using thresholds (e.g., top 5 percent of country-quarter observations; large depreciation example: 22.6 percent year-over-year depreciation; large monetary change: ≥200 basis points increase).
  - Eichengreen and Gupta (2017): narrative approach using policy documents and IMF Article IV to classify tightening/loosening/no change; they document most countries loosen monetary policy and tighten fiscal policy in response.

### Baseline results (outline)
- Analytical approach:
  - Non-parametric Kaplan-Meier (K-M) survival functions.
  - Semi-parametric Cox regression models including controls and policy response variables.
  - Parametric models (alternative specifications) also estimated.
- Dependent variables considered:
  - i) sudden stops in gross private capital inflows (real US dollars);
  - ii) preferred specification: output decelerations following sudden stop episodes in gross private capital inflows.

### Non-parametric findings (Kaplan-Meier)
- Exchange rate regime (Figure 3):
  - Output deceleration durations tend to be longer under fixed exchange rate regimes (dashed curve lying above solid for fixed vs. floating).
  - Interpretation links to literature on flexible exchange rates and smaller output variability.
- Advanced vs EMDEs (Figure 4):
  - Differences between advanced economies and emerging markets do not look significant for sudden stops or output decelerations.
  - Some indication that probability of remaining in growth deceleration is higher for advanced economies after 5 quarters, but differences vanish after 20 quarters.

### Semi-parametric Cox model results and interpretation
- Methodological note:
  - Cox regression results assume proportional hazards; Schoenfeld residuals tests generally reject proportionality in these samples—results should be interpreted with caution.
  - Breslow method used to handle ties.
- Main estimated associations (summary of significant effects):
  - Flexible exchange rate regime:
    - Helps shorten duration for both sudden stops and output decelerations.
    - Featuring a flexible regime increases the odds of exiting a growth deceleration by over 50 percent.
  - Terms of trade:
    - An improvement of 1 percent in the terms of trade increases the hazard rate by 10 percent.
    - A one standard deviation in commodities terms of trade growth (~2.5 percent) may reduce/increase duration by 25 percent.
  - Monetary policy tightening:
    - Associated with an increase in the hazard of exiting a growth deceleration episode.
    - A tightening of 3 percent in real terms is associated with a decrease in the duration of 15 percent in model (4).
  - Other policy variables:
    - Other included variables do not present significant coefficients in the semi-parametric specifications reported.
- Caution reiterated:
  - Because proportional hazards assumption is rejected by Schoenfeld residuals tests, interpret these semi-parametric estimates cautiously.

*Source: wpiea2019230-print-pdf - 2.1    Proportional Hazard Models*

### 4.3    Parametric Models

### 4.3    Parametric Models

### Baseline parametric specifications
- Two parametric survival distributions used:
  - Weibull baseline hazard: h0(t) = θ t^(θ−1), with θ estimated jointly with exp(xj β).
  - Gompertz baseline hazard: h0(t) = exp(γ t), with γ estimated.
- In all parametric specifications for sudden stops, estimates for θ and γ point to an increasing hazard over time (i.e., countries are more likely to exit sudden stops as the number of quarters increases).
  - Reported estimates (selected): θ = 2.65, 2.90 (Weibull specifications); γ = 1.66, 1.83 (Gompertz specifications).

### Key findings for sudden stops (parametric PH results; Table 4 and related text)
- Exchange rate regime:
  - Coefficients are statistically significant and economically large.
  - Example exponentiated coefficients (selected): ER Regime = 1.28, 1.62, 1.38, 1.96 in Weibull and Gompertz specifications.
- Terms of trade:
  - Statistically significant positive effect on exit hazard.
  - An increase in the terms of trade of 1 standard deviation would increase the chance of leaving the sudden stop state by 30 percent.
  - Example exponentiated coefficients (selected): Terms of Trade = 1.12, 1.13, 1.11, 1.12.
- Monetary policy:
  - Monetary policy tightening increases the hazard rate.
  - An increase of 1 percentage point in real interest rates increases the chances of leaving the sudden stop state by 6 percent (reported for standard sudden stop specification).
  - Example exponentiated coefficients (selected): Monetary = 1.03, 1.06 (Weibull/Gompertz columns).
- Reserves:
  - Positive and statistically significant in several specifications (example: Reserves = 1.01, 1.01).
- Capital controls and fiscal policy:
  - Results are generally weaker or not statistically significant across specifications.

### Growth decelerations (parametric PH results; Table 5 and related text)
- Exchange rate regime:
  - More flexible exchange rate regimes increase the hazard by between 50 to 80 percent in several cases (coefficient magnitudes consistent with Cox model results).
  - Example exponentiated coefficients (selected): ER Regime = 1.58, 1.84, 1.52, 1.81.
- Terms of trade:
  - Statistically significant and robust across specifications.
  - Example exponentiated coefficients (selected): Terms of Trade = 1.08, 1.10, 1.08, 1.09.
- Monetary policy:
  - Monetary tightening increases the hazard rate for growth decelerations.
  - An increase of 1 percentage point in real interest rates increases the chances of leaving the low growth state by 5 percent.
  - Example exponentiated coefficients: Monetary = 1.05, 1.05 (Weibull/Gompertz).
- Other controls:
  - Fiscal policy, reserves, and capital controls show mixed significance; reserves sometimes significant (e.g., Reserves = 1.01).

### Accelerated Failure Time (AFT) models (Tables 6 and 7)
- Interpretation: exponentiated coefficients are time ratios indicating how expected duration is shortened/lengthened.
- Sudden stops (Table 6):
  - Flexible exchange rate regimes show mixed significance across AFT distributions.
  - Weibull AFT model suggests more flexible ER regimes reduce the duration of sudden stops by 15 percent (Weibull column: ER Regime = 0.85).
  - Terms of trade consistently shorten durations (exponentiated coefficients ≈ 0.94–0.96 across distributions).
  - Example: Terms of Trade = 0.94, 0.95, 0.95, 0.96 (Lognormal, Loglogistic, Exponential, Weibull).
- Growth decelerations (Table 7):
  - Flexible exchange rate regimes significantly shorten durations, typically by over 30 percent in many specifications (example coefficients: ER Regime = 0.70, 0.67, 0.67, 0.70).
  - Terms of trade shorten durations (example: Terms of Trade = 0.93, 0.94, 0.94, 0.93).
  - Monetary tightening shortens durations (example: Monetary = 0.98, 0.98, 0.97, 0.98).

### Robustness checks (Section 5)
- Controlling for banking crises (Table 8):
  - Banking crises significantly reduce the hazard of exiting sudden stop states (example: Banking Crisis = 0.52, 0.51 in Weibull/Gompertz sudden stop columns).
  - Effects on growth decelerations are not statistically significant in these specifications.
  - Main findings on exchange rate regime and terms of trade confirmed.
  - Monetary policy associated with a 3 to 5 percent reduction in duration of sudden stops per percentage point increase in real rates in these specifications.
- Controlling for initial public debt and initial reserves (Tables 9 and 10):
  - Including Initial Public Debt (share of GDP) or Initial Reserves (share of imports) does not materially change main results.
  - Example coefficients: Initial Public Debt = 1.00, Initial Reserves = 1.00 (both generally not significant).
  - Exchange rate regime and monetary policy continue to affect durations.
- Alternative definitions of sudden stops (Tables 11 and 12; using gross private inflows as share of GDP):
  - Results confirm previous findings; ER regime role becomes clearer with large and statistically significant effects in all models for sudden stops.
  - Monetary policy matters for sudden stops when using inflows in percent of GDP (example Monetary = 1.03, 1.05).
- Introducing unobserved heterogeneity—shared frailty models (Table 13):
  - Gompertz frailty models (Inverse-Gaussian frailty) broadly confirm baseline results.
  - Flexible ER regimes associated with increases in the hazard of leaving a sudden stop and exiting growth decelerations.
  - Terms of trade remain significant; monetary policy significant for growth decelerations but not always for sudden stops per se.
  - Example frailty model coefficients: ER Regime = 1.34, 1.86; Terms of Trade = 1.15, 1.14; Monetary = 1.04, 1.05 (selected columns).
  - Frailty parameter estimates reported (selected): v = 0.88, 0.27, 0.32, 0.00.

### Conclusions and policy implications (Section 6)
- Exchange rate flexibility:
  - Countries with floating exchange rate regimes tend to experience shorter sudden stop episodes and shorter decelerations in growth following sudden stops.
  - Effects are quantitatively large: having a flexible exchange regime increases the probability of exiting the sudden stop state by between 50 to 80 percent in several cases.
  - Positive variations in terms of trade also abbreviate durations of sudden stops.
- Monetary policy:
  - Monetary policy tightening can abbreviate the duration of sudden stops and growth decelerations, though identification is trickier.
  - A monetary tightening generating a rise in real interest rates of 3 percent is associated with a reduction of roughly 15 percent in the duration of a sudden stop.
  - These findings are consistent with theoretical mechanisms where interest rate increases contain real exchange rate depreciation and tighten collateral constraints, helping to shorten episodes.
- Policy interpretation:
  - Results reinforce the role of exchange rate flexibility in mitigating external shocks and caution against overstating the insulating power of capital account restrictions.
  - The analysis provides additional empirical support in the “fix vs flex” debate that floating regimes help countries weather external adverse shocks.

*Source: 4.3 Parametric Models, wpiea2019230-print-pdf*

### References

### wpiea2019230-print-pdf - References

### References (selected citations)
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- Broda, C. (2004) “Terms of Trade and Exchange Rate Regimes in Developing Countries”Journal of International Economics63: 31-58.
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- Calvo, G., Izquierdo, A., and Talvi, E., 2006. “Phoenix Miracles in Emerging Markets: Recovering without Credit from Systemic Financial Crises”.NBER Working Papers 12101.
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### Appendix A: Data Sources and Definitions
- Capital flows:
  - Total Gross Non-Official Flows (ICAPFLP) in U. S. dollars and as a share of GDP from the IMF’s Financial Flows Analytics (FFA) database.
  - Capital flows in nominal dollar terms were deflated using the U.S. GDP deflator.
- Real GDP in national currency units:
  - Series used as basis for calculations regarding growth decelerations after sudden stops as explained in the main text.
  - Primary source: quarterly data from IMF’s International Financial Statistics Database (IFS).
  - Haver Analytics used when IFS was missing or had more limited availability for the following countries: AZE; BHR; BLR; BLZ; BRA; CHN; CMR; COL; DEU; DNK; FIN; GHA; GTM; HND; IDN; IND; ITA; JOR; JPN; KAZ; KWT; LKA; LSO; MEX; MNE; MNG; MOZ; NAM; NGA; NIC; PAN; SLV; UGA; URY; VNM; ZAF; ZMB.
- Real GDP per capita:
  - Log of real GDP per capita.
  - Data from the Maddison Project database (Bolt et al., 2018).
- International reserves:
  - Official reserve assets in millions of U.S. dollars from the IMF’s IFS database.
- Monetary policy rates:
  - Policy rates from Thomson Reuters Datastream.
  - IMF’s IFS Database used for money market rates and for discount rates when data on policy rates is not available.
  - The real (ex-post) interest rate is calculated using CPI inflation data from the IMF’s IFS database.
- Fiscal balance:
  - General government primary net lending/borrowing as a share of GDP from the IMF’s World Economic Outlook (WEO) database.
  - In regressions, the fiscal policy measure is constructed using residuals from a simple OLS regression of a constant on real GDP growth and growth in the commodity terms of trade series to control for automatic stabilizers.
- Capital account restrictions:
  - Index of de jure capital account openness constructed by Chinn and Ito (2006) based on information from the IMF’s Annual Report on Exchange Arrangements and Exchange Restrictions (AREAER). Higher levels indicate a more open capital account.
- Terms of trade:
  - Log of the commodity net export price index constructed by Gruss (2014).
- Exchange rate regimes:
  - Coarse de facto exchange rate regime classification from Ilzetzki, Reinhart, and Rogoff (2017).
  - Categories 1 and 2 were classified as fixed-exchange rate regimes and categories 3 and 4 as floating exchange rate regimes.

### Appendix B: Sudden Stops and Growth Decelerations — Episodes
- Sudden Stops Episodes:
  - The appendix provides an extensive list of Sudden Stops episodes by country with Start and End quarters. Examples include:
    - United States 1980q2 – 1981q1; 1983q1 – 1983q3; 1988q3 – 1988q4; 1990q1 – 1990q4; 1998q1 – 1999q1; 2001q3 – 2002q2; 2008q1 – 2009q2.
    - United Kingdom 1991q3 – 1992q1; 2001q3 – 2002q3; 2008q1 – 2009q2.
    - Japan 1990q4 – 1991q3; 1992q2 – 1993q1; 1998q2 – 1998q4; 2005q1 – 2005q4; 2008q3 – 2009q3; 2016q1 – 2016q4.
    - Many other countries and episodes are listed in tabular form (see full appendix), covering advanced and emerging economies across multiple decades.
- Growth Decelerations Episodes:
  - The appendix also lists Growth Deceleration episodes by country with Start and End quarters. Examples include:
    - United States 1980q2 – 1982q3; 1990q1 – 1994q1; 1998q2 – 1998q3; 2001q3 – 2001q4; 2008q1 – 2010q1.
    - United Kingdom 1991q3 – 1992q2; 2002q3 – 2003q1; 2008q1 – 2013q4.
    - Japan 1991q2 – 1991q4; 1992q2 – 1997q4; 1998q2 – 1999q4; 2005q1 – 2005q3; 2008q3 – 2009q4; 2016q1 – 2016q3.
    - The full list includes episodes for a wide set of countries, matching the Sudden Stops listing where relevant and detailing multi-quarter decelerations.
- Note: Both appendices present comprehensive, country-level chronological episodes (Start and End quarter notation, e.g., 2008q1) for Sudden Stops and Growth Decelerations across the sample.

*Source: wpiea2019230-print-pdf - References*

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_Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019230-print-pdf.pdf_