## 1. Median Real GDP per capita Growth

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### Key concepts and purpose
- Develops a vulnerability index to quantify low-income country risks to growth crises arising from external shocks.
- Growth crises capture combined effects of growth declines (negative growth) and level drops following shocks, which can endanger sustainability of a country’s growth path.
- Rationale: low-income countries face higher amplitude and frequency of exogenous shocks (terms-of-trade swings, export demand shocks, natural disasters, volatile financial flows) and often lack resources, instruments, and policy buffers to absorb or mitigate shocks.
- Sample and scope:
  - Sample period: 1990–2009 for 71 low-income countries (61 used in regressions).
  - Shock observations considered (first year only): 698 shock observations (out of 1420 observations).

### Drivers of vulnerability and crisis determinants
- Identified drivers:
  - Large fiscal imbalances.
  - Large external imbalances.
  - Unsustainable debt ratios.
  - Inadequate reserve buffers.
  - Weakly diversified economic structures.
  - Narrow and concentrated tax bases.
  - Institutional weaknesses.
- Key determinants from econometric results (correlated pooled probit):
  - Weaker institutions (CPIA) increase crisis probability.
  - Lower pre-shock GDP growth increases crisis probability.
  - Anemic past real per capita GDP growth increases crisis probability.
  - Higher reserve coverage and better fiscal balance reduce crisis probability.
  - Flexible exchange rate regime reduces crisis probability.
  - Larger adverse shock size (external demand, export prices) increases crisis probability.

### Methodological approaches
- Identification of large exogenous shocks:
  - A shock event occurs when annual percentage change of a shock variable falls below the 10th percentile in the left-tail of the country-specific distribution.
  - Shock types included: (i) external demand; (ii) terms-of-trade; (iii) FDI; (iv) aid; (v) remittances; (vi) climatic shocks (large natural disasters).
  - FDI, aid, and remittances measured as ratios to GDP.
  - Large natural disasters defined by top 25th percentile for people affected and economic damage (EM-DAT).
  - Only the first year of each shock event is used.
  - Result: 698 shock observations (first-year shocks) from the sample.
- Definition of growth crisis events:
  - Both conditions must hold within identified shock events:
    - (i) post-shock two-year average (t and t+1) level of real GDP per capita falls below the pre-shock three-year trend; and
    - (ii) growth of real GDP per capita is negative at time t.
  - Severe state failure events excluded (SFTPMMAX > 3.9).
  - Unconditional probability of crisis within large shock sample: 0.24.
- Econometric approach:
  - Binary response panel probit model (correlated pooled probit using Chamberlain-Mundlak device preferred).
  - Explanatory variables lagged by one year (except shock-size variables).
  - Final explanatory variables grouped into three clusters:
    - Policy variables: government balance/GDP; reserve coverage (months of imports); dummy for flexible exchange rate; exchange market pressure index (EMPI).
    - Structural and institutional variables: CPIA; real GDP growth (t-1); country-specific average real GDP per capita growth.
    - Shock size variables: growth in trading partners (weighted); change in export prices (weighted).
- Signaling (univariate) approach:
  - Defines optimal cut-offs for individual indicators minimizing misclassification errors.
  - Converts indicators to zero-one scores using cut-offs, weights indicators by predictive power, aggregates into cluster indices and overall vulnerability index.
  - Uses 13 variables grouped into three clusters: Overall economy & institutions; External sector; Fiscal sector.
  - Overall index threshold obtained by minimizing asymmetrically-weighted loss function.

### Empirical findings and quantitative results
- Sample medians and crisis statistics:
  - Table 1: Median Real GDP per capita Growth (1990-2009)
    - All: 1.8
    - Crisis Episodes: -4.0
    - Non-Crisis Episodes: 2.8
    - Sample Probability of Crisis: 0.24
    - Observations: 674; Crisis observations: 163; Non-crisis: 511
- Benchmark correlated pooled probit selected coefficients (Table 2):
  - CPIA (t-1): -0.3438*** (0.1259)
  - GDP growth (t-1): -0.0632*** (0.0198)
  - Government balance, % of GDP (t-1): -0.0162* (0.0089)
  - Reserve coverage, months of imports (t-1): -0.0852** (0.0380)
  - Exchange market pressure index (t-1): 0.0525** (0.0204)
  - Exchange rate regime (flexible:1; fixed:0) (t-1): -0.3783** (0.1630)
  - Change in export prices weighted by lagged exports to GDP: -0.0335** (0.0161)
  - Country Specific Averages Real GDP growth: -0.1847*** (0.0479)
  - Constant: 1.5295*** (0.3699)
  - Pseudo R-squared: 0.26
  - No of observations: 561; Growth decline events: 120; Normal episodes: 441; No of countries: 61
- Marginal effects (median LIC, Table 3):
  - CPIA (t-1): -0.0744*** (0.0275)
  - GDP growth (t-1): -0.0137*** (0.0040)
  - Government balance, % of GDP (t-1): -0.0035* (0.0019)
  - Reserve coverage (t-1): -0.0184** (0.0084)
  - Exchange market pressure index (t-1): 0.0113*** (0.0044)
  - Exchange rate regime (flexible:1; fixed:0) (t-1): -0.0818** (0.0345)
  - Change in export prices weighted by lagged exports to GDP: -0.0072** (0.0034)
  - Country Specific Averages Real GDP growth: -0.0400*** (0.0101)
- Marginal effects of moving from median to best quartile (Table 4; percentage point changes):
  - CPIA improvement example: 3.8 reduces probability by about 3 percent for the median country (text example: "3.8 reduces the probability of a growth crisis by about 3 percent for the median country.")
  - Reserve coverage: increase from 2.8 to 4.1 months lowers crisis probability by 2½ percentage points.
  - Exchange rate regime: shifting from fixed to flexible reduces likelihood by 9 percentage points.
- Model thresholding and classification performance:
  - Threshold probability for calling a crisis: 0.19 (asymmetric loss function).
  - Type I and Type II errors at threshold: 20 percent and 27 percent, respectively.
  - Median predicted probability: 0.38 for growth crisis episodes versus 0.10 for normal episodes (Table 5 percentiles).
  - In-sample: more than 75 percent of growth crisis episodes have predicted probabilities above the crisis threshold.
  - Out-of-sample (1990–2004 estimated, 2004–2009 predicted):
    - Model correctly calls 14 out of 15 crises.
    - Type I error: 7 percent.
    - False alarms in 34 percent of non-crisis episodes.
- Signaling approach index weights, thresholds, and fit (Table 6):
  - Overall economy and institutions cluster weight: 0.37.
  - Reserve coverage threshold: 2.30 months; Type I error: 0.42; Type II error: 0.33; Index weight: 0.09.
  - Public debt (% of GDP) threshold: < 36; Type I error: 0.05; Type II error: 0.80; Index weight: 0.05.
  - Overall Index threshold: 0.44.
  - Proportion of crises missed: 0.17.
  - Proportion of non-crises mis-specified (false alarms): 0.31.
  - Overall error: 0.28.
- Vulnerability index distribution and performance:
  - Median vulnerability index for growth crises: 0.66 versus 0.33 for normal episodes (Table 8 percentiles).
  - Seventy-five percent of growth crises have vulnerability indices above 0.50.
  - In-sample: index correctly calls 83 percent of growth crises; overall misclassification error: 28 percent.
  - Secondary threshold 0.3 (low vs medium vulnerability): at 0.3, less than 9 percent of crisis events missed; false alarms ~56 percent.
  - Out-of-sample (1990–2008 thresholds evaluated for 2009 global crisis): vulnerability index correctly flags 9 out of 13 countries (70 percent) that experienced a growth crisis in 2009; false alarms 28 percent.

### Robustness and sensitivity
- Robustness checks:
  - Including all growth crises (not only those induced by large exogenous shocks) leaves qualitative results unchanged.
  - When all crises included, climatic shocks and shocks to remittances become significant.
  - Reserves are more effective in reducing likelihood of growth crisis induced by large exogenous shocks.
- Correlations among shock variables:
  - Pair-wise correlations are generally very low and statistically insignificant, except for a negative correlation between change in FDI to GDP and terms of trade shock.
  - Appendix Table 1 reports specific correlations (e.g., Growth in trading partners % Change with ToT growth % Change: 0.0601 in full sample).

### Temporal assessment of vulnerabilities (1993–2011)
- Trend and drivers:
  - Vulnerability index trended down since the 1990s until the twin crises in 2007/08.
  - Drivers of decline: build-up of reserve buffers, improvements in fiscal performance and official debt-relief, removal of policy-induced exchange market pressures, and strong growth during the “great moderation.”
  - Vulnerability index rose significantly after the global crisis but remained lower than early-1990s levels.
  - Vulnerabilities remained high during 2010–2011 as policy buffers were expended; deterioration in fiscal indicators and pronounced decline in growth in 2009 were key contributors; external sector indicators largely remained sound.
  - Aggregate index eased somewhat from its 2010 peak due to more buoyant external conditions and stronger-than-expected growth in low-income countries, but fiscal vulnerabilities remained elevated.

### Policy implications and uses of the index
- The vulnerability index provides early warning signals of growth crises in low-income countries using a parsimonious set of macroeconomic and institutional indicators aggregated via complementary approaches.
- Key policy takeaways:
  - Strengthening policy and institutional frameworks is especially effective for countries with initially weak buffers; marginal effects are larger for weaker countries.
  - Maintaining reserve coverage and sound fiscal balances lowers crisis probability (quantified examples above).
  - Flexible exchange rate regimes can materially reduce vulnerability to external shocks.
  - The index can flag underlying vulnerabilities and inform pre-emptive policy action and judgment-based mitigation strategies.
- Practical use:
  - Monitoring tool to assess risks from external shocks and to inform country-level policy discussions, with sensitivity to country-specific buffer levels and institutional contexts.

*Source: Content unit drawn from _wp12264 PDF (sections II–IV, methodology and empirical approach).*

### 1. Median Real GDP per capita Growth ..................................................................................2

### 1. Median Real GDP per capita Growth ..................................................................................28

### Key concepts and purpose
- Develops a vulnerability index to quantify low-income country risks to growth crises arising from external shocks.
- Growth crises capture combined effects of growth declines (negative growth) and level drops following shocks, which can endanger sustainability of a country’s growth path.
- Rationale: low-income countries face higher amplitude and frequency of exogenous shocks (terms-of-trade swings, export demand shocks, natural disasters, volatile financial flows) and often lack resources, instruments, and policy buffers to absorb or mitigate shocks.

### Drivers of vulnerability (as identified in the text)
- Large fiscal imbalances.
- Large external imbalances.
- Unsustainable debt ratios.
- Inadequate reserve buffers.
- Weakly diversified economic structures.
- Narrow and concentrated tax bases.
- Institutional weaknesses.

### Methodological approaches
- Multivariate regression approach:
  - Uses a correlated panel probit model to estimate the probability of a growth crisis.
  - Accounts for correlations among different variables.
  - Tests statistical significance of individual variables.
  - Assesses constancy of coefficients across country groups.
- Univariate “signaling” approach:
  - Uses each indicator separately to identify critical thresholds that minimize prediction error.
  - Averages indicators into a summary index.
  - Composite vulnerability index measures the number of indicators exceeding thresholds, weighted by their relative signaling power.
  - Accommodates differences in data availability and allows inclusion of more indicators than multivariate method.
  - Probit analysis guides conditional statistical significance of variables used in the univariate approach.

### Empirical findings (summary statements from the text)
- The overall vulnerability index declined significantly from its peak in the early 1990s.
- Contributing factors to lower vulnerabilities up to the onset of the global crisis included:
  - Better policy and economic management.
  - A favorable external environment, especially terms-of-trade improvements.
  - Official debt relief.
- More recently (relative to the text), growth crisis risks in low-income countries remain elevated and well above pre-crisis years as fiscal buffers have increasingly been used up.

### Use and implications of the index
- Flags underlying vulnerabilities that predispose countries to growth declines when hit by large external shocks.
- Can provide a first indication of potential problems and signal scope for pre-emptive policy action.
- Supports assessment of vulnerabilities to growth declines in low-income countries over time.

*Source: _wp12264 - 1. Median Real GDP per capita Growth ..................................................................................28*

### Section III describes the methodology for identifying crisis episodes. Section IV presents the

### _wp12264 - Section III describes the methodology for identifying crisis episodes. Section IV presents the

### II. Literature Review
- Adverse external shocks have a significant negative impact on short- and medium-run growth through effects on aggregate demand, external balances, and the government’s fiscal position (Collier and Goderis, 2009; Berg et al., 2010).
- Effects are asymmetric: negative shocks impede growth, while positive shocks do not necessarily contribute to long-run growth, particularly in resource-rich countries with weak institutions (Collier and Goderis, 2007).
- The paper analyzes macroeconomic, institutional, and structural correlates of growth declines focusing on the negative tail of the distribution, distinguishing sharp short-term declines from longer-term growth down-breaks (Rodrik, 1999; Pritchett, 2000; Hausmann et al., 2006; Berg et al., 2011).
- Relates to early warning literature for various crises (currency crises, sudden stops, fiscal crises, financial crises) and argues that focusing on growth captures multiple manifestations of severe economic distress in low-income countries.
- Builds on methodology and findings of Easterly et al. (2000) and Dabla-Norris et al. (2011), particularly on shock and crisis identification and the role of international reserves in smoothing absorption and consumption.

### III. Methodology
A. Identification of Large Exogenous Shocks
- Large negative external shock events are identified when the annual percentage change of the relevant shock variable falls below the 10th percentile in the left-tail of the country-specific distribution.
- Shock episodes include one or more of six shocks:
  - (i) external demand;
  - (ii) terms-of-trade;
  - (iii) FDI;
  - (iv) aid;
  - (v) remittances;
  - (vi) climatic shocks (large natural disasters).
- FDI, aid, and remittances are measured as ratios to GDP.
- Large natural disasters are identified if the number of people affected and the economic damage were among the top 25th percentile of the distribution (data from the Emergency Events Database).
- Country-specific shock thresholds imply each country experiences the same frequency of shocks; focus is on reaction to the shock.
- Sample: period 1990-2009 for 71 low-income countries.
- Only the first year of each shock event is considered in the final set, yielding a total of 698 shock observations (out of 1420 observations).
- Distributions of shock versus non-shock episodes are markedly different; lowest quartile of non-shock sample markedly higher than highest quartile of shock episodes for each shock.
- Very low and statistically insignificant correlations among shocks except for change in FDI to GDP and terms of trade growth, suggesting shocks are largely independent.

B. Identification of the Dependent Variable: Growth Crisis Events
- Within identified shock events, a growth crisis is defined when both conditions hold:
  - (i) the post-shock two-year average (t and t+1) level of real GDP per capita falls below the pre-shock three-year trend; and
  - (ii) growth of real GDP per capita is negative at time t.
- Episodes failing either condition are considered normal episodes.
- Severe state failure events are excluded (identified from Political Instability Task Force dataset; variable SFTPMMAX exceeding 3.9 denotes severe state failure).
- Summary statistics:
  - The median growth rate of real GDP per capita for the identified shock sample is positive, implying not all shocks lead to drops in real growth.
  - The unconditional probability of a crisis within the large shock sample is only about 24 percent.
  - There is a substantial difference in real GDP per capita growth of more than 6¾ percentage points between crisis and non-crisis cases (statistically significant).
- Observation: in a majority of cases, negative growth is associated with persistent decline in output; quick recoveries to pre-shock output are rare in the sample of low-income countries.

### IV. Empirical Analysis: Econometric Approach
A. Probit Model
- A binary response panel probit model is used to assess the effect of policy and structural variables on the likelihood of a growth crisis conditional on large exogenous shocks.
- General specification: y_it is observed outcome (crisis = 1, normal = 0); Φ is the cumulative normal density; x_it is 1xk vector of explanatory variables; β is kx1 vector of coefficients.
- Different estimators considered depending on panel heterogeneity assumptions (pooled probit, random effects probit, fixed effects probit, correlated pooled probit using Chamberlain-Mundlak device).
- Correlated pooled probit model is preferred based on econometric tests for significance of individual specific effect and sample average for covariates.
- Sixty-one countries are included in the sample over the 1990–2009 period (Appendix Table 2).
- Model selection followed a general-to-specific approach starting from twenty-two potential regressors (Appendix Table 3).
- Final explanatory variables grouped into three clusters:
  - Policy variables:
    - Ratio of government balance to GDP;
    - Reserve coverage (in months of imports of goods and services);
    - Dummy for flexible exchange rate regime;
    - Exchange market pressure index (EMPI) — composite of depreciation of official exchange rate, change in stock of international reserves (in months of imports), and black market premium; higher EMPI indicates increased pressures on exchange rate.
  - Structural and institutional variables:
    - World Bank’s CPIA;
    - Real GDP growth in the previous period;
    - Country-specific average of real GDP per capita growth over the sample period (proxy for underlying structural and institutional conditions).
  - Shock size:
    - Growth in trading partners weighted by lagged exports-to-GDP;
    - Change in export prices weighted by lagged exports-to-GDP.
- All explanatory variables are lagged by one year, except variables capturing exogenous shock size.

B. Estimation Results: Benchmark Probit Specifications
- Table 2 estimation (baseline probit regressions) results summarized:
  - Columns: Column 1 all countries; Columns 2–4 for sub-groups excluding commodity exporters, oil exporters, and small islands respectively.
- Key empirical findings:
  - Probability of a growth crisis increases sharply for countries with:
    - Weaker institutions (proxied by the CPIA);
    - Lower pre-shock GDP growth;
    - Track record of anemic past real per capita GDP growth.
  - Sound policy fundamentals associated with lower likelihood of growth crisis:
    - Higher reserve coverage;
    - Better fiscal balance.
  - Lower pre-shock balance of payments pressures reduce likelihood of a growth crisis.
  - Flexible exchange rate regime sharply reduces probability of a growth crisis, consistent with exchange rate flexibility facilitating adjustment to real shocks.
  - Shock size is significantly associated with likelihood of growth crisis; shock variables enter with negative sign (positive shocks to external demand and commodity prices lower probability of growth crisis).
  - Export price shock impact is largely driven by commodity exporters and becomes insignificant when that group is excluded.
  - Both contemporaneous shocks are significant at the 5 percent level in the sample excluding small islands.
- Marginal effects:
  - Table 3 presents average marginal effects and marginal effects at sample median and worst quartiles.
  - Institutional quality (CPIA) and exchange rate regime are the strongest predictors of a growth crisis.
  - Marginal effects of policy variables (fiscal balance, reserve coverage) and institutional quality on crisis probability are significantly higher for countries with weaker buffers (Column 3) versus the median country (Column 2), implying higher payoffs from improvements in weaker countries.
  - Table 4 reports marginal impact of changing each explanatory variable from its median to its best quartile; example given: an improvement in the CPIA from 3.4 to

*Italic: Content unit drawn from _wp12264 PDF (sections II–IV, methodology and empirical approach).*

### 3.8 reduces the probability of a growth crisis by about 3 percent for the median country.

### _wp12264 - 3.8 reduces the probability of a growth crisis by about 3 percent for the median country.

### Key findings on drivers of crisis probability
- An increase in reserve coverage from 2.8 to 4.1 months of imports lowers the crisis probability by 2½ percentage points.
- Shifting from a fixed to a flexible exchange rate regime reduces the likelihood of a growth crisis by 9 percentage points.
- A strengthening of policy and institutional frameworks yields larger reductions in crisis probability for countries with initially weak buffers.
- Countries with a stronger past track record of real GDP growth have a significantly lower likelihood of a growth crisis.
- Only extreme adverse values of some covariates (exceptionally weak institutional quality, high exchange market pressure, significantly poor past GDP growth, and negative tail shocks to external demand and export prices) can push the median country’s predicted probability above the crisis threshold.

### Model estimation, interpretation, and thresholding
- Estimated probit model is non-linear; coefficients have no direct interpretation. Marginal effects are calculated at preset values (means or medians) and averaged across the sample distribution of other covariates.
- Threshold probability for calling a crisis derived by asymmetric loss-function minimization (placing higher weight on missing crises) is 0.19.
- Associated Type I and Type II errors at the threshold are 20 and 27 percent, respectively.
- A growth crisis is predicted when a country with weak policy buffers and poor institutions is hit by adverse external shocks; in such cases the 95 percent confidence interval of predicted probabilities lies above the threshold probability.
- For the median low-income country, predicted probability (including the 95 percent confidence interval) lies comfortably below the crisis threshold.

### Predicted probabilities, distributions, and in-sample performance
- Median predicted probability for a growth crisis is 0.38 versus 0.10 for normal episodes.
- More than seventy-five percent of growth crisis episodes have predicted probabilities above the crisis threshold.
- Predicted probabilities are well dispersed in the [0,1] interval, indicating the model’s ability to differentiate outcomes.

### Out-of-sample performance
- Out-of-sample predictions obtained by estimating the sample for 1990–2004 and predicting for 2004–2009 using the 0.19 threshold:
  - Model correctly calls 14 out of 15 crises.
  - Type I error (missed crises) is 7 percent.
  - False alarms occur in 34 percent of non-crisis episodes.
- Out-of-sample results show a sharply lower Type I error than in-sample, yielding lower overall misclassification errors.

### Robustness checks
- Including all growth crises (not only those induced by large exogenous shocks) and controlling for shock covariates leaves qualitative results unchanged.
- When all growth crises are included, climatic shocks and shocks to remittances become significant.
- Reserves are far more effective in reducing the likelihood of a growth crisis induced by large exogenous shocks.

### Signaling approach: methodology and index construction
- Signaling approach defines cut-off values for individual indicators; if an indicator exceeds its cut-off, it issues a signal of an upcoming growth crisis.
- Optimal cut-offs balance Type I and Type II errors; thresholds reported are based on minimization of misclassification errors.
- The overall vulnerability index is constructed in two steps:
  1. Map indicators into zero-one scores using optimal thresholds and assign weights to indicators based on predictive power.
  2. Aggregate cluster indices into the vulnerability index based on predictive power of clusters and indicators.
- Index formula components: weights w_i.g for indicators within group g, weights w_g for groups, and dummy d_i taking value 1 if indicator is above (or below) threshold.

### Signaling approach: variables, clusters, and weights
- Analysis uses 13 variables grouped into three clusters:
  - Overall economy and institutions: CPIA index, Gini coefficient, real GDP growth, sample average of GDP per capita growth.
  - External sector: reserve coverage, growth in volume of exports of goods and services, exchange market pressure index, contemporaneous shock-size variables for external demand and export prices.
  - Fiscal sector: government balance, public debt, tax revenue (all in percent of GDP), cumulative growth in real government revenue over the past two years.
- All indicators except contemporaneous shock-size variables are lagged by one period.
- Top predictor cluster: overall economy and institutions (accounting for 37 percent of index weight).
  - Within this cluster, lagged real GDP growth and the Gini coefficient are main predictors.
- External and fiscal clusters have broadly similar aggregate weights; reserve coverage and exchange market pressure index are top predictors in external cluster; government balance and real revenue growth are top predictors in fiscal cluster.
- Overall index threshold is 0.44 (obtained by minimizing an asymmetrically-weighted loss function penalizing missed crises).

### Signaling approach: predictive performance
- Univariate probit regressions: overall index and three sub-indices are highly significant determinants of growth crises.
- Multivariate probit regressions: economy and institutions and external sector indices significant at the 1 percent level; fiscal index significant at the 10 percent level.
- For a country with weak fundamentals (indicator values in 75th/25th percentile), all indicators issue a signal and vulnerability index equals its maximum of one.
- When all indicators fixed at the sample median, overall vulnerability index is 0.11, below the index threshold of 0.44.
- For a weakly-positioned country with strong policies and benign global environment, the index would be 0.37 (medium vulnerability), and a growth crisis would not be predicted.

### Vulnerability index goodness of fit and thresholds
- Median predicted vulnerability index for growth crises is 0.66 versus 0.33 for normal episodes.
- Seventy-five percent of growth crises have vulnerability indices above 0.50.
- Only ten percent of crisis events have the vulnerability index below 0.31.
- In-sample performance:
  - Index correctly calls 83 percent of growth crises.
  - Overall model misclassification error is 28 percent.
- Secondary threshold of 0.3 differentiates low versus medium vulnerability:
  - At threshold 0.3, less than 9 percent of crisis events are missed and false alarms increase to about 56 percent.
- Out-of-sample (1990–2008 thresholds evaluated for 2009 global crisis):
  - Vulnerability index correctly flags 9 out of 13 countries (70 percent) that experienced a growth crisis in 2009.
  - False alarms occur in 28 percent of non-crisis episodes.
  - One of the four missed crisis cases would have been flagged as moderately vulnerable.

### Assessment of vulnerabilities since the 1990s
- Vulnerability index trended down since the 1990s until the twin crises in 2007/08.
- Drivers of the trend decline: build-up of reserve buffers, improvements in fiscal performance and official debt-relief, removal of policy-induced exchange market pressures, and strong growth during the “great moderation.”
- Vulnerability index rose significantly after the global crisis but remained lower than early-1990s levels.
- Vulnerabilities remained high during 2010-2011 as policy buffers were expended; deterioration in fiscal indicators (worsening government balance and weaker revenue growth) and pronounced decline in growth in 2009 were key contributors; external sector indicators largely remained sound.
- Aggregate index eased somewhat from its 2010 peak due to more buoyant external conditions and stronger-than-expected growth in low-income countries, but fiscal vulnerabilities remained elevated.

### Concluding policy implications and uses of the index
- The vulnerability index provides early warning signals of growth crises in low-income countries using a parsimonious set of macroeconomic and institutional indicators aggregated via complementary approaches.
- Country fundamentals, exchange rate regimes, institutional quality, and the size of shocks are important determinants of growth crises.
- Sensitivity of crisis risks to policy and institutional changes differs across countries; strengthening policy and institutional frameworks is especially effective for countries with initially weak buffers.
- The index is a useful monitoring tool to assess risks from external shocks and to inform judgment-based mitigation strategies.
- While many low-income countries recovered and grew strongly since 2010, fiscal risks remain elevated relative to the pre-crisis period.

*Source: _wp12264 - 3.8 reduces the probability of a growth crisis by about 3 percent for the median country.*

### References

### _wp12264 - References

### Bibliographic references
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- International Monetary Fund, 2011, “Managing Volatility: A Vulnerability Exercise for Low-Income Countries.” Available at www.imf.org/external/np/pp/eng/2011/030911.pdf
- Kaminsky, G., S. Lizondo, and C. M. Reinhart, 1998, "Leading Indicators of Currency Crises," Staff Papers, IMF, Vol. 45(1), pp.1–48.
- Kaminsky, G. and C. Reinhart, 1999, “The Twin Crises: The Causes of Banking and Balance of Payments Problem,” American Economic Review, Vol. 89, No. 3, pp. 473–500.
- Loayza, N., and C. Raddatz, 2007, “The Structural Determinants of External Vulnerability,” World Bank Economic Review, Vol. 21, No.3, pp. 359–387.
- Mundlak, Y., 1978, “On the Pooling of Time Series and Cross Section Data,” Econometrica, Vol. 46, pp. 69–85.
- Papageorgiou C., C. Pattillo, N. Spatafora, and A. Berg, 2010. "The End of an Era? The Medium- and Long-term Effects of the Global Crisis on Growth in Low-Income Countries," IMF Working Papers 10/205.
- Perry, G., 2009, “Beyond Lending: How Multilateral Banks Can Help Developing Countries Manage Volatility” (Center for Global Development).
- Pritchett, L., 2000, “Understanding Patterns of Economic Growth: Searching for Hills among Plateaus, Mountains, and Plains,” World Bank Economic Review, Vol. 14, No.2, pp. 221–250.
- Reinhart, C. M. and K. Rogoff, 2004, “The Modern History of Exchange Rate Arrangements: A Reinterpretation,” The Quarterly Journal of Economics, Vol. CXIX, Issue 1, pp. 1–48.
- Rodrik, D., 1999, “Where Did All the Growth Go? External Shocks, Social Conflict, and Growth Collapses,” Journal of Economic Growth, Vol. 4, pp. 85–412.
- World Bank, 2006, “IDA Countries and Exogenous Shocks” (Washington).

### Figures and captions (selected items and exact numeric highlights)
- Figure 1. Identification of External Shock Episodes
  - External Demand in TPs (% Change): Shock Episodes 0.8, 2.8, 1.6, 3.7, 2.3, 4.9 (75th/50th/25th percentiles shown).
  - Terms of Trade (% Change): Shock Episodes -32.8, -4.3, -21.0, 0.3, -13.1, 6.7 (75th/50th/25th percentiles shown).
  - FDI to GDP (Change in the ratio): Shock Episodes -4.2, -0.1, -1.8, 0.0, -0.8, 0.8 (75th/50th/25th percentiles shown).
  - Aid to GDP (Change in the ratio): Shock Episodes -6.1, -0.9, -3.6, 0.0, -2.3, 1.2 (75th/50th/25th percentiles shown).
- Figure 2. Distribution of Real GDP per capita: Crises versus Normal Episodes (1980-2009)
  - Kernel densities for Real GDP per capita Growth: Crisis Episodes versus Normal Episodes (graphic presentation).
- Figure 3. Effects of Explanatory Variables on Predicted Probability of Growth Crises
  - Panels for median LIC and LIC with weak fundamentals show predicted probabilities across covariates including:
    - Real GDP Growth (t-1) range: -4.0 to 10.0.
    - CPIA (t-1) range: 1.0 to 5.0.
    - Government Balance/GDP (t-1) range: -13.0 to 3.0.
    - Reserve Coverage (t-1) range: 0.0 to 8.0.
    - Export Price Shock range: -20.0 to 20.0.
    - EMPI (t-1) range: -5.0 to 19.0.
    - Exchange Rate Regime (Fix/Flexible) and Average GDP Growth panels included.
  - Note: 95 percent confidence intervals for predicted probabilities are presented.
- Figure 4. Predicted Probability of Growth Crises: Performance of the Vulnerability Index and its Sub-Components
  - Predicted probabilities estimated from univariate probit regressions when overall index or each sub-component included as only covariate; 95 percent confidence intervals presented.
- Figure 5. Marginal Effects of Sub-components on Predicted Probability of Growth Crises
  - Predicted probabilities from multivariate probit regression including all sub-components; 95 percent confidence intervals presented.
  - For median LIC, covariates fixed at medians; for LIC with weak fundamentals, covariates fixed at 75th/25th percentiles as appropriate.
- Figure 6. Growth Decline Vulnerability Index 1993-2011
  - Quartiles displayed (25th percentile, Median, 75th Percentile) and distribution of vulnerability flags (Low/Medium/High) across 1993–2011.
- Figure 7. Vulnerability Index and its Components (Median, 1993-2011)
  - Time series (1993–2011) for Overall Index, External Index, Fiscal Index, Economy and Institutions Index.
- Appendix Figure 1. Flags Raised by Selected Indicators of the Vulnerability Index (1993-2011)
  - Time series (1993–2011) of percent of sample raising flags for: Total Debt to GDP; Real Growth in Government Revenue; Reserve Coverage; Exchange Market Pressure Index; Shock to Export Prices; Shock to External Demand; Government Balance to GDP; Growth in Exports (G&S); Real GDP Growth.

### Tables and key numerical findings
- Table 1. Median Real GDP per capita Growth (1990-2009)
  - All: 1.8
  - Crisis Episodes: -4.0
  - Non-Crisis Episodes: 2.8
  - Sample Probability of Crisis: 0.24
  - Observations: 674; Crisis observations: 163; Non-crisis: 511
- Table 2. Probability of Growth Crisis (Correlated Pooled Probit Regression, 1990-2009)
  - Reporting selected coefficients (standard errors in parentheses), significance indicated:
    - CPIA (t-1): -0.3438*** (0.1259)
    - GDP growth (t-1): -0.0632*** (0.0198)
    - Government balance, % of GDP (t-1): -0.0162* (0.0089)
    - Reserve coverage, months of imports (t-1): -0.0852** (0.0380)
    - Exchange market pressure index (t-1): 0.0525** (0.0204)
    - Exchange rate regime (flexible:1; fixed:0) (t-1): -0.3783** (0.1630)
    - Change in export prices weighted by lagged exports to GDP: -0.0335** (0.0161)
    - Country Specific Averages Real GDP growth: -0.1847*** (0.0479)
    - Constant: 1.5295*** (0.3699)
  - Pseudo R-squared: 0.26
  - No of observations: 561; Growth decline events: 120; Normal episodes: 441
  - Sample probability: 0.21; No of countries: 61
- Table 3. Benchmark Regression: Average and Conditional Marginal Effects
  - Median LIC marginal effects:
    - CPIA (t-1): -0.0744*** (0.0275)
    - GDP growth (t-1): -0.0137*** (0.0040)
    - Government balance, % of GDP (t-1): -0.0035* (0.0019)
    - Reserve coverage (t-1): -0.0184** (0.0084)
    - Exchange market pressure index (t-1): 0.0113*** (0.0044)
    - Exchange rate regime (flexible:1; fixed:0) (t-1): -0.0818** (0.0345)
    - Change in export prices weighted by lagged exports to GDP: -0.0072** (0.0034)
    - Country Specific Averages Real GDP growth: -0.0400*** (0.0101)
  - Threshold probability: 0.19
  - Predicted probability: 0.16 (95 Percent confidence interval [0.12  0.20])
- Table 4. Marginal Effects of Explanatory Variables on Crisis Probability (Percentage point)
  - Change in predicted crisis probability (Median to best quartile examples):
    - CPIA (t-1): 3.4; 3.8; -2.9 (different comparisons shown)
    - GDP growth (t-1): 4.3; 6.3; -2.8
    - Government balance, % of GDP (t-1): -3.4; -1.7; -0.7
    - Reserve coverage (t-1): 2.8; 4.1; -2.5
    - Exchange rate regime (Fixed vs Flexible): Fixed / Flexible -9.0
    - Country Specific Averages Real GDP growth: 3.5; 4.7; -4.8
- Table 5. Predicted Probabilities (Percentiles)
  - In-sample (Growth crisis vs Normal episodes) percentiles reported; examples:
    - 50%: Growth crisis 0.38; Normal episodes 0.10
    - 75%: Growth crisis 0.60; Normal episodes 0.20
    - Obs.: 120 (growth crises), 441 (normal)
    - Type I: 0.20; Type II: 0.27; Sample probability 0.21
- Table 6. Non-parametric Signaling Approach: Performance of Indicators and Model Fit
  - Index weights and thresholds for indicators; example entries:
    - Overall economy and institutions weight: 0.37
    - Real GDP growth (t-1) direction to be safe: > ; threshold: 1? (table shows > and numeric columns)
    - Reserve coverage (months of imports) (t-1) threshold: 2.30; Type I error: 0.42; Type II error: 0.33; Index weight: 0.09
    - Public debt (% of GDP) (t-1) threshold: < 36; Type I error: 0.05; Type II error: 0.80; Index weight: 0.05
  - Fit of the Model:
    - Overall Index threshold: 0.44
    - Proportion of Crises Missed: 0.17
    - Proportion of Non-crises mis-specified (false alarms): 0.31
    - Overall error: 0.28
- Table 7. Distribution of Predicted Probabilities: Vulnerability Index versus its Sub-Components (Percentiles)
  - Examples for 50th percentile:
    - External Index: Growth crisis 0.49; Normal episodes 0.07
    - Fiscal Index: Growth crisis 0.39; Normal episodes 0.09
    - Vulnerability Index: Growth crisis 0.25; Normal episodes 0.12
    - Economy and Institutions Index: Growth crisis 0.23; Normal episodes 0.14
  - Obs. for each series: 126 growth crises, 454 normal episodes (per columns)
- Table 8. Vulnerability Index (Percentiles)
  - Growth crisis vs Normal episodes percentiles:
    - 1%: 0.18 vs 0.00
    - 25%: 0.50 vs 0.18
    - 50%: 0.66 vs 0.33
    - 75%: 0.80 vs 0.47
    - 95%: 0.91 vs 0.71
    - 99%: 0.97 vs 0.80
  - Obs.: 126 (growth crises) and 454 (normal)
  - Type I: 0.17; Type II: 0.31; Sample probability: 0.22

*Source: _wp12264 - References (authors' calculations and figures/tables as presented in the content unit).*

### Appendix Table 1. Correlation Matrix for Exogenous Shocks

### Appendix Table 1. Correlation Matrix for Exogenous Shocks (1990-2008)

### Correlation matrix — Full Sample (630 observations)
- Growth in trading partners % Change correlated with:
  - ToT growth % Change: 0.0601
  - FDI to GDP Change: 0.0480
  - Remittances to GDP Change: -0.001
  - Aid to GDP Change: -0.008
- ToT growth % Change correlated with:
  - Growth in trading partners % Change: 0.0601
  - FDI to GDP Change: 0.0821
  - Remittances to GDP Change: -0.043
  - Aid to GDP Change: -0.024
- FDI to GDP Change correlated with:
  - Growth in trading partners % Change: 0.0480
  - ToT growth % Change: 0.0821
  - Remittances to GDP Change: -0.017
  - Aid to GDP Change: -0.010
- Remittances to GDP Change correlated with:
  - Growth in trading partners % Change: -0.001
  - ToT growth % Change: -0.043
  - FDI to GDP Change: -0.017
  - Aid to GDP Change: 0.044
- Aid to GDP Change correlated with:
  - Growth in trading partners % Change: -0.008
  - ToT growth % Change: -0.024
  - FDI to GDP Change: -0.010
  - Remittances to GDP Change: 0.044

### Correlation matrix — Large Shock Episodes (316 observations)
- Growth in trading partners % Change correlated with:
  - ToT growth % Change: 0.0331
  - FDI to GDP Change: 0.0290
  - Remittances to GDP Change: 0.018
  - Aid to GDP Change: -0.060
- ToT growth % Change correlated with:
  - Growth in trading partners % Change: 0.0331
  - FDI to GDP Change: 0.0761
  - Remittances to GDP Change: -0.053
  - Aid to GDP Change: -0.084
- FDI to GDP Change correlated with:
  - Growth in trading partners % Change: 0.0290
  - ToT growth % Change: 0.0761
  - Remittances to GDP Change: -0.050
  - Aid to GDP Change: -0.014
- Remittances to GDP Change correlated with:
  - Growth in trading partners % Change: 0.018
  - ToT growth % Change: -0.053
  - FDI to GDP Change: -0.050
  - Aid to GDP Change: 0.070
- Aid to GDP Change correlated with:
  - Growth in trading partners % Change: -0.060
  - ToT growth % Change: -0.084
  - FDI to GDP Change: -0.014
  - Remittances to GDP Change: 0.070

### Key notes on correlations
- Source: Authors' calculations.
- Note: Correlations among variables are reported for the common sample for which all shock variables are available.
- Results are very similar for the pair-wise correlation matrix relaxing the common sample restriction and in the sub-sample excluding commodity exporters.
- Pair-wise correlations are not statistically significant except for the negative correlation between a change in FDI to GDP and a terms of trade shock.

### Appendix Table 2 — Sample composition
- 71 LICs listed; 61 countries used in the regressions.
- Representative country listing includes (selected order preserved from source): Afghanistan, I.S. of; Armenia; Bangladesh; Benin; Bhutan; Bolivia; Burkina Faso; Burundi; Cambodia; Cameroon; Cape Verde; Central African Republic; Chad; Comoros; Congo, Dem. Rep. of; Congo, Republic of; Côte d'Ivoire; Djibouti; Dominica; Eritrea; Ethiopia; Gambia, The; Georgia; Ghana; Grenada; Guinea; Guinea-Bissau; Guyana; Haiti; Honduras; Kenya; Kiribati; Kyrgyz Republic; Lao PDR; Lesotho; Liberia; Madagascar; Malawi; Maldives; Mali; Mauritania; Moldova; Mongolia; Mozambique; Myanmar; Nicaragua; Niger; Nigeria; Nepal; Papua New Guinea; Rwanda; São Tomé and Príncipe; Senegal; Sierra Leone; Solomon Islands; Samoa; St. Lucia; St. Vincent and the Grenadines; Sudan; Tajikistan; Tanzania; Togo; Uganda; Uzbekistan; Vietnam; Zambia; (and others as listed).
- Note line: "71 LICs 61 countries used in the regressions"

### Appendix Table 3 — Variables used in the Probit Regressions and the Signalling Approach
- Identification of growth crises
  - Real GDP per capita: WEO
  - Growth: WEO
  - Lag of real GDP growth: WEO
  - Country-specific average real GDP growth over 1980-2009
- Fiscal Policy
  - Lag of fiscal balance to GDP: WEO
- Monetary policy
  - Lag of inflation rate: WEO
- External vulnerability
  - Lag of gross international reserves in months of imports: WEO
  - Lag of exchange market pressure index: WEO
  - Lag of current account deficit to GDP: WEO
  - Lag of current account deficit plus FDI to GDP and its interaction with a dummy excluding small islands: WEO
  - Lag of volume growth in exports of goods: WEO
  - Lag of black market premium: Reinhart&Rogoff (2004)
- Exchange rate regime
  - De facto exchange rate regime dummies: Reinhart&Rogoff (2004)
  - De jure exchange rate regime dummies: AREAR, IMF
- Institutions
  - CPIA index: World Bank
- Shock variables
  - Natural Disasters: Large natural disasters identified by the number of people affected and the economic damage among the top 25th percentile of the distribution. Source: Emergency Events Database (EM-DAT) published by the Center for Research on the Epidemiology of Disasters (CRED).
  - Lag of aid to GDP: OECD
  - FDI to GDP: WEO
  - Remittances to GDP
  - External demand growth in trading partners: WEO
  - External demand growth in trading partners weighted by lagged exports (goods) to GDP ratio: WEO
  - Growth in terms of trade: WEO
  - Growth in export prices of goods weighted by lagged exports (goods) to GDP ratio: WEO
- Additional variables examined (in addition to probit regressions)
  - Fiscal policy: Lag of total public debt to GDP (WEO); Growth in government revenue in previous two years deflated by CPI (WEO); Lag of tax revenue to GDP (WEO); Lag of total government revenue to GDP (WEO)
  - Monetary policy: Lag of growth in private sector credit deflated by CPI in previous three years (Beck, Demirguc-Kunt and Levine dataset (2010)); Lag of non-performing loans (above dataset complemented by staff reports); Lag of capital adequacy ratio (above dataset complemented by staff reports); A dummy variable indicating a banking crisis in the last two years (above dataset complemented by staff reports)
  - External vulnerability: Lag of change in real effective exchange rate (IMF INS dataset); Lag of trade balance to GDP (WEO); Lag of exchange rate overvaluation to GDP (REER minus HP-filtered REER) (IMF INS dataset and authors' calculations); Lag of monthly standard deviation of NEER and REER (IMF INS dataset and authors' calculations); Lag of external debt to GDP (WEO)
  - Structural variables: Lag of Gini coefficient (WB GDI (Global Development Indicators)); Lag of commodity exports to GDP (WB GDI); Lag of agricultural value added to GDP (WB GDI)

### Appendix Table 4 — Distribution of Explanatory Variables (1990-2009) (estimation sample)
- CPIA:
  - 10th Percentile: 2.48
  - 25th Percentile: 2.98
  - Median: 3.38
  - 75th Percentile: 3.75
  - 90th Percentile: 4.00
- GDP growth:
  - 10th Percentile: -0.98
  - 25th Percentile: 1.78
  - Median: 4.33
  - 75th Percentile: 6.32
  - 90th Percentile: 8.37
- Real GDP growth (country-specific sample average):
  - 10th Percentile: 1.58
  - 25th Percentile: 2.69
  - Median: 3.48
  - 75th Percentile: 4.69
  - 90th Percentile: 6.47
- Government balance (% of GDP):
  - 10th Percentile: -9.35
  - 25th Percentile: -5.83
  - Median: -3.42
  - 75th Percentile: -1.70
  - 90th Percentile: 0.49
- Reserve coverage (months of imports):
  - 10th Percentile: 0.93
  - 25th Percentile: 1.68
  - Median: 2.81
  - 75th Percentile: 4.11
  - 90th Percentile: 6.35
- Exchange market pressure index:
  - 10th Percentile: -1.76
  - 25th Percentile: -0.60
  - Median: 0.19
  - 75th Percentile: 1.70
  - 90th Percentile: 4.82
- Growth in trading partners weighted by lagged exports to GDP:
  - 10th Percentile: 0.07
  - 25th Percentile: 0.23
  - Median: 0.52
  - 75th Percentile: 0.99
  - 90th Percentile: 1.74
- Change in export prices weighted by lagged exports to GDP:
  - 10th Percentile: -3.39
  - 25th Percentile: -1.14
  - Median: 0.00
  - 75th Percentile: 1.56
  - 90th Percentile: 4.51
- Source: Authors' calculations.
- Note: The distribution of explanatory variables is provided for the estimation sample.

### Appendix Table 5 — Robustness Check with Alternative Specifications: All Growth Crisis Events
- Estimation variants: (1) All crises, (2) Average marginal effects 1/ Benchmark specification (large shocks), (3) All crises (column 3), (4) Average marginal effects 1/ (column 4)
- Coefficient estimates with standard errors in parentheses; significance: 10 percent:*; 5 percent:**; and 1 percent:***.
- Selected coefficient estimates (columns labelled as in source; standard errors retained in parentheses below coefficients):
  - CPIA (t-1)
    - (1): -0.3627*** (0.1107)
    - (2): -0.0666*** (0.0203)
    - (3): -0.3438*** (0.1259)
    - (4): -0.0744*** (0.0275)
  - GDP growth (t-1)
    - (1): -0.0861*** (0.0146)
    - (2): -0.0158*** (0.0027)
    - (3): -0.0632*** (0.0198)
    - (4): -0.0137*** (0.0040)
  - Government balance, % of GDP (t-1)
    - (1): -0.0205* (0.0107)
    - (2): -0.0038* (0.0020)
    - (3): -0.0162* (0.0089)
    - (4): -0.0035* (0.0019)
  - Reserve coverage, months of imports (t-1)
    - (1): -0.0502 (0.0322)
    - (2): -0.0092 (0.0059)
    - (3): -0.0852** (0.0380)
    - (4): -0.0184** (0.0084)
  - Exchange market pressure index (t-1)
    - (1): 0.0460** (0.0194)
    - (2): 0.0084** (0.0036)
    - (3): 0.0525** (0.0204)
    - (4): 0.0113*** (0.0044)
  - Exchange rate regime (flexible:1; fixed:0) (t-1)
    - (1): -0.4638*** (0.1475)
    - (2): -0.0852*** (0.0273)
    - (3): -0.3783** (0.1630)
    - (4): -0.0818** (0.0345)
  - Growth in trading partners weighted by lagged exports to GDP
    - (1): -0.1738* (0.0926)
    - (2): -0.0319* (0.0169)
    - (3): -0.1899* (0.1119)
    - (4): -0.0411* (0.0235)
  - Change in export prices weighted by lagged exports to GDP
    - (1): -0.0226* (0.0124)
    - (2): -0.0042* (0.0023)
    - (3): -0.0335** (0.0161)
    - (4): -0.0072** (0.0034)
  - Change in remittances weighted by lagged remittances to GDP
    - (1): (-0.0483)* (0.0281)
    - (2): (-0.0089) (0.0051)
  - Climatic shocks
    - (1): (0.2505)* (0.1447)
    - (2): (0.0460) (0.0265)
  - Country Specific Averages for 1990-2008 — Real GDP growth
    - (1): -0.1974*** (0.0577)
    - (2): -0.0362*** (0.0104)
    - (3): -0.1847*** (0.0479)
    - (4): -0.0400*** (0.0101)
  - Constant
    - (1): 1.4169*** (0.4009)
    - (2): 1.5295*** (0.3699)
    - (3): 0.0000 (0.0000)
- Model fit and sample statistics
  - Pseudo R-squared: 0.20 (column 1); 0.26 (column 2)
  - No of observations: 1042561 (column 1)
  - Growth decline events: 210 (column 1); 120 (column 3)
  - Normal episodes: 832441 (column 1)
  - Sample probability: 0.20 (column 1); 0.21 (column 2)
  - No of countries: 61 (all columns)
  - Wald test (Chi-square): 148(0.00) (column 1); 119(0.00) (column 2)
- Source: Authors' calculations.
- Note: (1) is estimated by correlated random effects probit model based on the significance of country-specific effect and (2) is estimated by a correlated pooled probit model with cluster-robust standard errors. 1/ Marginal effects of a specific covariate on the response probability averaged across the distribution of covariates in the sample.

*Source: Authors' calculations.*

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