## _wp12227

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---

### Introduction: motivation and literature context
- Two motivating views for focusing on frequency and duration of growth episodes:
  - Differences in average growth rates across countries stem from variations in the volatility of growth rather than constant differences in growth.
  - If the frequency of growth accelerations is fairly constant across regions, then differences in the duration of these episodes account for divergent average growth rates (Pritchett, 2000; Jones and Olken, 2008).
- Prior work:
  - Pritchett (2000) characterizes country growth patterns as “hills”, “mountains”, “valleys”, “cliffs”, and “plateaus”.
  - BOZ (2012) shift focus to growth duration and find duration positively related to equality of income distribution, democratic institutions, export orientation, and macroeconomic stability.
  - Lack of a unified growth theory motivates use of Bayesian Model Averaging (BMA) to formally incorporate model uncertainty.

### Contribution and empirical approach
- Primary contributions:
  - Systematic examination of determinants of growth-spell duration while accounting for model uncertainty using BMA applied to proportional hazards models for censored survival data.
  - Comparison of determinants in two samples—Africa and the rest of the world—to assess heterogeneity.
- Methodological choices:
  - Proportional hazards (Cox) models for censored survival data.
  - BMA to address model and parameter uncertainty.
  - Two samples: Africa; non-Africa/world.

### Identification of growth spells and break-detection
- Break-detection method:
  - Variant of Bai and Perron (1998) extended by Antoshin et al. (2008) allowing sequential testing and sample-specific critical values for small samples and heteroskedasticity.
- Key parameters:
  - Analysis covers 140 countries.
  - Minimum years between breaks h determines max number of breaks b via int( T / h ) - 1 (presented in the source as int(   )   1
T
b
h
 ).
  - Example: 5 minimum years between breaks (5)h and 50T imply maximum of 9 possible breaks.
  - Baseline choice: minimum length between breaks 5 years and significance p=0.10 (hp5 and p=0.10), though 8 years noted as reasonable to eliminate short-term fluctuations.

### Distribution of identified breaks and stylized facts
- Data source: Penn World Tables version 6.2 (breaks for per capita growth rates).
- Counts and sensitivity:
  - With 5 years between breaks and 0.10p, 137 upbreaks and 150 downbreaks are identified.
  - Increasing critical value to 0.25 identifies about one and a half times more upbreaks and downbreaks than 0.10.
  - Restricting minimum length of spell to 8 years increases total number of breaks by about 40 percent compared to 5 year minimum for 0.10p and 0.25.p
  - Irrespective of method, about one-third of either upbreaks or downbreaks occur in Africa.
- Temporal patterns:
  - Upbreaks most common in the 1950s, 1960s, and 1990s; Africa accounts for almost one-half of upbreaks in the 1990s.
  - Downbreaks more frequent in the 1970s and mostly occur in industrialized countries and Africa.
  - Latin America had most upbreaks and downbreaks in the 1980s.
- Stylized facts on spell duration and frequency (minimum length 5 years; p=0.10):
  - Share of spells: about a third correspond to Africa (roughly share of African countries in sample).
  - Mean length of complete growth spells:
    - Africa: about 6 years on average.
    - Industrialized countries: 13 years on average.
    - Emerging Asia: 21 years on average.
  - Distributional fact:
    - In Emerging Asia, seven out of ten spells last at least 16 years.
    - In industrialized and Latin American countries, only one in ten spells last at least 16 years.
- Growth rates before/during/after spells:
  - Spells in Emerging Asia and high income countries start from much higher per capita growth rates than in developing countries.
  - In Africa and Latin America, spells begin from high negative growth rates on average.
  - Growth during spells similar across regions; in Africa growth during spells is a bit higher than the average.
  - Growth after end of complete spell (average):
    - High income and Emerging Asian countries: about -1 percent.
    - Africa: about -3.2 percent immediately after the end of the spell, and -3.7 percent three years after the end of the spell.
- Summary: Africa’s spells are shorter than elsewhere and end in “rough landings.”

### Determinants: candidate variables and conceptual grouping
- Four broad categories and example variables:
  (i) Neoclassical/Solow and human capital:
    - initial income per capita, population growth, investment to GDP, total education years.
  (ii) External shocks and exogenous factors:
    - terms of trade growth, change in the US interest rate, change in oil price, drought, shock to terms of trade.
  (iii) Macroeconomic policy:
    - capital flows to GDP, external debt liabilities to GDP, openness, exchange rate undervaluation, inflation, government balance to GDP, aid to GDP.
  (iv) Institutions and heterogeneity:
    - changes in autocracy and ethnic heterogeneity.
- Preliminary two-way scatter insights:
  - Associated with shorter spell duration: higher per capita income, higher population growth, increases in US interest rate, increases in oil prices, terms of trade shocks, more exchange rate overvaluation, higher inflation, higher aid, higher ethnic heterogeneity.
  - Associated with increased spell duration: higher investment, higher education, openness.

### Empirical strategy: survival models with BMA
- Survival analysis basics:
  - T denotes survival time; S(t) = Pr(T > t).
  - Hazard rate h(t) = f(t) / S(t).
- Cox (1972) proportional hazards model:
  - λ(t | X_i) = λ_0(t) exp(X_i' β); estimation via partial likelihood.
- Endogeneity mitigation:
  - Right-hand-side variables lagged by one year to avoid contemporaneous feedback.
- BMA implementation:
  - Combines posterior distributions across K models weighted by posterior model probabilities.
  - Uses Volinsky et al. (1997) approximations for Cox models; uniform prior over model space.
- Interaction specification:
  - Hazard rate for model j: λ_j(t) = λ_0(t) exp(X_1 β_j + I × X_2 β_{j2}), where I = 1 for Africa.
  - Model space: 18 regressors + 18 interactions + Africa dummy = 37 variables for interactions sample; world sample uses 18 regressors.
  - Posterior inclusion probabilities computed by summing posterior model probabilities over models including the variable.

### Fragility of ad hoc specifications (kitchen sink regressions)
- Cox proportional-hazards estimates vary substantially across ad hoc specifications:
  - Hazard ratio interpretation: a hazard ratio of 1.15 suggests a unit increase in the regressor increases the risk that the spell will end in the next period by 15 percent.
  - Hazard ratios < 1 are protective; = 1 have no effect.
- Examples of fragility across columns (1)–(20) in Table 3:
  - Column (1) identifies initial income, total education, changes in US interest rate, change in oil price, external debt liabilities, and government balance to GDP as statistically significant.
  - Column (2) (“neoclassical” only) makes initial income and education insignificant.
  - Adding shocks and political variables changes significance and sign of several variables; oil price change alternates between significant protective and risky effects across specifications.
- Conclusion: ad hoc specifications produce fragile and potentially misleading inferences, motivating BMA.

### BMA results: robust determinants and heterogeneous effects
- Estimation setup:
  - Africa and non-Africa samples use 37 variables (interactions included); world sample uses 18 variables.
  - Prior inclusion probability for each variable = 0.50.
  - Variables with posterior inclusion probability above 0.50 considered robust.
- Key BMA findings (posterior inclusion guidance and preserved magnitudes):
  - Non-Africa robust determinants include: initial income, terms of trade growth, inflation, exchange rate undervaluation.
  - Non-Africa estimated marginal effects (preserved phrasing and magnitudes):
    - A percentage increase in exchange rate overvaluation increases the probability that the growth spell will end by 2.7 percent.
    - A percentage increase in inflation increases the probability that the growth spell will end by 1.9 percent.
    - A one percent improvement in terms of trade increases the probability the growth spell will continue by 1.4 percent (protective effect).
  - These three variables (terms of trade growth, inflation, exchange rate overvaluation) are ineffective in the Africa sample (inclusion probabilities < 10 percent).
  - Higher initial income associated with higher probability spell will end in non-Africa (conditional convergence).
  - Africa-distinct effective variables (ineffective in non-Africa):
    - Openness (increases associated with lower spell duration).
    - Cumulative number of droughts (very large negative effect on spell duration).
  - Variables effective in both Africa and non-Africa:
    - Total years of education (human capital).
    - Investment to GDP ratio (physical capital).
    - Exogenous shocks (e.g., U.S. interest rate changes).
- Preserved marginal-effect magnitudes across samples:
  - Investment protective effect:
    - Africa: 9 percent.
    - non-Africa: 5.4 percent.
  - Additional year of education increases probability growth spell is sustained by:
    - Africa: 87 percent.
    - non-Africa: 37 percent.
  - U.S. interest rate changes reduce spell duration by:
    - non-Africa: 19.5 percent.
    - Africa: 11.1 percent.

### Interpretation and links to literature
- Results align with neoclassical/augmented Solow emphasis on physical and human capital (Solow, 1957; Mankiw, Romer, and Weil, 1992), especially for Africa.
- Negative effects of shocks consistent with Rodrik (1999) and Easterly et al. (1993).
- Macroeconomic instability (inflation and exchange rate overvaluation) negatively associated with length of growth spells, notably in non-Africa sample (Fischer, 1993).
- Inflation measure: 100log(1+π), where π is log difference of the price level; at low inflation 100log(1+π) approximately linear so one percentage point increase in 100log(1+π) similar to one point rise in the rate of inflation.

### Conclusions and policy implications
- Determinants differ between Africa and the rest of the world:
  - Initial income, terms of trade, exchange rate undervaluation, inflation, openness, and droughts have distinct impacts in only one of the two samples.
  - Openness and droughts: unique to Africa sample.
  - Terms of trade, exchange rate undervaluation, and inflation: influence only non-Africa sample.
  - Investment, total years of education, and U.S. interest rate changes affect both groups but with substantially different marginal impacts.
- Policy guidance (preserved phrasing):
  - Properly accounting for model uncertainty is important for policymakers; recommendations should not be based on a single specification.
  - What sustains growth spells globally is not necessarily what sustains growth spells in Africa.
  - Economic characteristics influencing growth spells in Africa: physical and human capital accumulation, openness, and droughts.
  - Further work needed on:
    - Relative importance of physical vs human capital accumulation.
    - How (or how fast) African economies should open to the rest of the world.
    - How to limit adverse impact of droughts (e.g., setting up crop insurance systems or shifting policy focus to sectors other than agriculture).

### Selected numeric and table highlights (preserved exact entries)
- Break counts and baseline:
  - 137 upbreaks and 150 downbreaks identified with 5 years between breaks and 0.10p.
- Mean spell lengths:
  - Africa: about 6 years.
  - Industrialized countries: 13 years.
  - Emerging Asia: 21 years.
- Post-spell growth declines (average):
  - High income and Emerging Asia: about -1 percent.
  - Africa: -3.2 percent immediately after spell end; -3.7 percent three years after.
- Table 4 example posterior entries (preserved exact figures):
  - Initial income per capita:
    - Africa P(incl) 45.2; Mean 1.515; Stand. Dev 1.339; Hazard 4.551; St.Dev 6.093.
    - Non-Africa P(incl) 100.0; Mean 0.432; Stand. Dev 0.089; Hazard 1.541; St.Dev 0.136.
    - World P(incl) 100.0; Mean 0.426; Stand. Dev 0.085; Hazard 1.531; St.Dev 0.130.
  - Total education years:
    - Africa P(incl) 69.7; Mean -2.051; Stand. Dev 1.310; Hazard 0.129; St.Dev 0.169.
    - Non-Africa P(incl) 100.0; Mean -0.478; Stand. Dev 0.181; Hazard 0.620; St.Dev 0.112.
    - World P(incl) 100.0; Mean -0.581; Stand. Dev 0.154; Hazard 0.560; St.Dev 0.086.
  - Investment to GDP:
    - Africa P(incl) 59.3; Mean -0.094; Stand. Dev 0.078; Hazard 0.910; St.Dev 0.071.
    - Non-Africa P(incl) 83.2; Mean -0.054; Stand. Dev 0.038; Hazard 0.947; St.Dev 0.036.
    - World P(incl) 69.7; Mean -0.036; Stand. Dev 0.032; Hazard 0.965; St.Dev 0.031.
  - Drought:
    - Africa P(incl) 76.5; Mean 1.240; Stand. Dev 1.571; Hazard 3.457; St.Dev 5.430.
    - Non-Africa P(incl) 0.6; Mean 0.007; Stand. Dev 0.114; Hazard 1.007; St.Dev 0.115.
    - World P(incl) 40.6; Mean 0.387; Stand. Dev 0.579; Hazard 1.472; St.Dev 0.853.
  - Overvaluation index:
    - Africa P(incl) 0.7; Mean 0.027; Stand. Dev 0.010; Hazard 1.028; St.Dev 0.010.
    - Non-Africa P(incl) 99.9; Mean 0.027; Stand. Dev 0.009; Hazard 1.027; St.Dev 0.009.
    - World P(incl) 99.9; Mean 0.023; Stand. Dev 0.007; Hazard 1.023; St.Dev 0.007.
- Table 3 sample sizes and observations (selected exact entries):
  - Observations across columns include: 563, 966, 845, 757, 680, 898, 901, 966, 884, 932, 829, 966, 966, 954, 929, 719, 864, 889, 876, 966.
  - Subjects: 50, 73, 67, 62, 66, 69, 68, 73, 71, 70, 68, 73, 73, 73, 71, 62, 65, 70, 68, 73.

*Source: Excerpt from _wp12227 (IMF Working Paper content unit extracted from the supplied PDF).*

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

### _wp12227 - References .............................................................................................................

### Introduction: motivation and literature context
- Two motivating views for focusing on frequency and duration of growth episodes:
  - Differences in average growth rates across countries stem from variations in the volatility of growth rather than constant differences in growth.
  - If the frequency of growth accelerations is fairly constant across regions, then differences in the duration of these episodes account for divergent average growth rates (Pritchett, 2000; Jones and Olken, 2008).
- Pritchett (2000) characterizes country growth patterns as five types: “hills”, “mountains”, “valleys”, “cliffs”, and “plateaus”.
- Prior empirical work on growth spells identifies many potential determinants (macroeconomic environment, trade, investment, institutions, geography) but broadly finds identified determinants are idiosyncratic, unrelated to “standard” growth determinants, and explain little of the variation in frequency or duration of growth spells.
- Berg, Ostry, and Zettelmeyer (BOZ, 2012) shift focus from pre/post decelerations to growth duration, defining “growth spells” as periods of high growth following an up-break and ending with a down-break or end of sample. BOZ find duration of growth spells is positively related to: equality of income distribution, democratic institutions, export orientation, and macroeconomic stability.
- Lack of a unified growth theory has led researchers to formally incorporate model uncertainty using Bayesian Model Averaging (BMA) methods to assess robustness of empirical relations.

### Contribution and empirical approach of the paper
- Two primary contributions:
  - Systematic examination of determinants of growth-spell duration while accounting for model uncertainty using BMA applied to proportional hazards models for censored survival data.
  - Comparison of determinants in two samples—Africa and the rest of the world—to assess heterogeneity in how determinants operate.
- Methodological choices:
  - Use of BMA to address model and parameter uncertainty given absence of an explicit theory for growth-spell determinants.
  - Estimation of proportional hazard models for censored survival data across two samples (Africa; non-Africa/world).

### Key empirical findings (as stated in the source)
- The analysis finds several robust determinants of growth spells including proxies for initial conditions, physical and human capital, exogenous factors, and the macroeconomic environment.
- Determinants operate differently in Africa versus the rest of the world:
  - Out of nine identified robust variables, six variables—initial income, terms of trade, exchange rate undervaluation, openness and droughts—have a distinct impact in only one of the two samples. 
  - In the non-Africa sample:
    - Spell duration is positively related to physical capital, human capital, and terms of trade growth.
    - Spell duration is negatively affected by exchange rate overvaluation, inflation, changes in the U.S. interest rate, and initial income.
  - In the Africa sample:
    - Increased openness and droughts have a distinct impact and are negatively related to growth-spell duration.
  - In both Africa and the rest of the world:
    - Physical capital, human capital, and changes in the U.S. interest rate are robustly correlated with growth spells, but estimated marginal effects and hazard ratios vary substantially between the two samples.

### Identification of growth spells: structural-break methodology
- Break-detection method:
  - Follows BOZ and uses a variant of the Bai and Perron (1998) procedure extended by Antoshin et al. (2008) to test for multiple structural breaks when both the total number and the location of breaks are unknown.
  - Antoshin et al. (2008) allow sequential testing of breaks and use sample-specific critical values to account for small samples and heteroskedasticity; their modifications perform substantially better than Bai and Perron (1998) in samples with as low as 50 observations.
- Key parameters and implications:
  - Analysis covers 140 countries.
  - The procedure requires defining the minimum years between breaks h, which determines the maximum number of breaks b with the relation int( T / h ) - 1 (presented in the source as int(   )   1
T
b
h
 ).
  - Allowing 5 minimum years between breaks (5)h results in a maximum of 9 possible breaks for a country with 50T.
  - Averaging of 5 years is typically used in panel growth regressions as a unit of averaging.
  - A larger minimum between-breaks interval such as 8h is noted as reasonable to eliminate short-term fluctuations or cyclical factors.
  - To assign statistical significance to identified breaks, the procedure follows BOZ and defines an allowable significance value p and experiments with critical values (as described in the source).

### Empirical samples and heterogeneity emphasis
- Two samples explicitly investigated:
  - Africa (regional sample).
  - Non-Africa / rest-of-world sample.
- The analysis focuses on whether determinants of growth-spell duration differ across these samples and documents notable heterogeneity in marginal effects and hazard ratios.

*Source: Excerpt from the content unit _wp12227 - References .............................................................................................................*

### 0.10 and 0.25p

### _wp12227 - 0.10 and 0.25p

### Distribution of identified breaks (per capita growth rates)
- Data source: version 6.2 of the Penn World Tables (breaks identified for per capita growth rates).
- Grouping: “upbreaks” and “downbreaks” by region, for critical values of 0.10 and 0.25, and for breaks not closer than 5 or 8 years.
- Key counts and sensitivity:
  - With 5 years between breaks and 0.10p, 137 upbreaks and 150 downbreaks are identified.
  - Increasing the critical value to 0.25 identifies about one and a half times more upbreaks and downbreaks than 0.10.
  - Restricting the minimum length of spell to 8 years increases the total number of breaks by about 40 percent compared to the 5 year minimum spell limit for 0.10p and 0.25.p
- Robustness of distributions:
  - Irrespective of method, about one-third of either upbreaks or downbreaks occur in Africa.
  - Break sizes are comparable across methods.
- Chosen baseline for analysis: the 5 and 0.10hp case (maximizes number of accurately measured breaks for a reasonable minimum number of years between breaks).
- Temporal patterns (Figures 2a and 2b, described):
  - Upbreaks are most common in the 1950s, 1960s, and 1990s.
  - For the 1950s and 1960s, breaks are evenly distributed across country groups.
  - Africa accounts for almost one-half of upbreaks in the 1990s.
  - Downbreaks are more frequent in the 1970s and mostly occur in industrialized countries and Africa.
  - Latin America had most of its upbreaks and downbreaks in the 1980s.

### Definition and stylized facts of growth spells
- Definitions (following BOZ):
  - “Complete” growth spells:
    - begin with a growth upbreak followed by a period of at least 2 percent average per capita income growth; and
    - end with a growth downbreak followed by a period of less than 2 percent average per capita income growth.
  - “Incomplete” growth spells: satisfy the begin condition and are still on-going at the end of the sample.
- Regional frequency and duration (Table 2, stylized facts):
  - About a third of identified spells correspond to Africa (roughly the share of African countries in the sample).
  - Mean length of complete growth spells:
    - Africa: about 6 years on average.
    - Industrialized countries: 13 years on average.
    - Emerging Asia: 21 years on average.
  - Distributional fact for spell lengths:
    - In Emerging Asia, seven out of ten of the spells last at least 16 years.
    - In industrialized and Latin American countries, only one in ten spells last at least 16 years.
- Growth rates before/during/after spells:
  - Spells in Emerging Asia and high income countries tend to start from much higher per capita growth rates than those in developing countries.
  - In Africa and Latin America, spells tend to begin from high negative growth rates on average.
  - Growth rates during spells are relatively similar across regions:
    - In Africa, growth during spells is a bit higher than the average.
    - In Latin America, growth during spells is lower than average.
  - Growth after the end of a complete spell (average):
    - High income and Emerging Asian countries: about -1 percent (suggesting a “soft landing”).
    - Africa: about -3.2 percent on average immediately after the end of a spell, and -3.7 percent three years after the end of the spell.
- Summary statement:
  - Africa’s spells are different: they are shorter than elsewhere in the world, and they end up in “rough landings.”

### Determinants of growth spell duration (concepts and candidate variables)
- Motivation:
  - Investigate how potential correlates influence the probability that a spell will continue or come to an end, and how these may differ in Africa.
  - Model uncertainty motivates a two-part approach: Bayesian Model Averaging (BMA) techniques and a carefully chosen pool of potential determinants drawn from literature.
- Four broad categories of potential determinants considered:
  (i) Neoclassical/Solow determinants and human capital:
    - initial income per capita, population growth, investment to GDP, total education years.
  (ii) External shocks and exogenous factors:
    - terms of trade growth, change in the US interest rate, change in oil price, drought, shock to terms of trade.
  (iii) Macroeconomic policy:
    - capital flows to GDP, external debt liabilities to GDP, openness, exchange rate undervaluation, inflation, government balance to GDP, aid to GDP.
  (iv) Institutions and heterogeneity:
    - changes in autocracy and ethnic heterogeneity.
- Preliminary two-way scatter insights (Figure 3):
  - Variables associated with shorter spell duration (ceteris paribus):
    - higher per capita income, higher population growth, increases in US interest rate, increases in oil prices, terms of trade shocks, more exchange rate overvaluation, higher inflation, higher aid, higher ethnic heterogeneity.
  - Variables associated with increased spell duration:
    - higher investment, higher education, openness.
- Note: Appendix discusses definitions and sources of variables.

### Empirical strategy: Survival models and BMA
- Survival analysis setup:
  - Let T denote survival time (duration); cumulative distribution function F(t) = Pr(T ≤ t).
  - Survival function S(t) = Pr(T > t) = 1 − F(t).
  - Hazard rate h(t) defined as the instantaneous risk of spell ending at time t, conditional on survival up to t:
    - h(t) = lim_{Δt→0} Pr(t ≤ T ≤ t+Δt | T ≥ t) / Δt = f(t) / S(t).
- Cox (1972) proportional hazards model specification:
  - λ(t | X_i) = λ_0(t) exp(X_i' β)
    - where λ_0(t) is baseline hazard at time t and β is vector of parameters.
  - Partial likelihood used for estimation (expression provided).
- Addressing feedback from spell duration to covariates:
  - Potential feedback problem recognized; to avoid contemporaneous feedback, all right-hand-side variables are lagged by one year.
- BMA for survival models:
  - BMA combines posterior distributions across K models weighted by posterior model probabilities.
  - For Cox model, closed-form integration not available; approximations (Volinsky et al. (1997)) are employed.
  - Implementation follows Volinsky (1997) with a uniform prior over model space.
- Model specification and Africa interactions:
  - Hazard rate for model j: λ_j(t) = λ_0(t) exp(X_1 β_j + I × X_2 β_{j2})
    - I is an indicator equal to one if country is in Africa, zero otherwise; X_1 is matrix of regressors; X_2 subset interacts with Africa dummy.
  - Model space includes 18 regressors, their interaction with the Africa dummy variable, and the Africa dummy itself — total of 37 variables for the interactions sample.
  - For the world sample (no interactions), only 18 regressors are used.
  - Posterior inclusion probabilities constructed for every explanatory variable k as the sum of posterior model probabilities over models including the variable.
  - For interaction interpretation:
    - For covariate k in X_2, non-Africa effect = β_1k; Africa effect = β_1k + β_2k.
    - Composite posterior variances calculated using var(β_1k + β_2k) = var(β_1k) + var(β_2k) + 2 cov(β_1k, β_2k).

### Results (overview and role of model uncertainty)
- Purpose of the “kitchen sink” exercise:
  - Demonstrate fragility of ad hoc specifications due to model uncertainty by estimating various ad hoc regressions (subset of possible models).
  - Goal: expose model uncertainty; not to draw final conclusions from ad hoc specifications.
- Table 3 (description):
  - Presents exponentiated regression coefficients (“hazard ratios”) for several ad hoc regressions using the full sample and various sub-samples of potential determinants.
  - Interpretation of hazard ratios: factor by which the hazard rate changes when the covariate increases by one unit.

*Source: _wp12227 - 0.10 and 0.25p (PDF chapter/section).*

### 1.15 suggests that a unit increase in the regressor increases the risk that the spell will end in

### _wp12227 - 1.15 suggests that a unit increase in the regressor increases the risk that the spell will end in

### Fragility of Cox proportional-hazards estimates (Table 3)
- All specifications are estimated using Cox proportional-hazards regression model with STATA’s stcox command with robust standard errors.
- A hazard ratio of 1.15 suggests that a unit increase in the regressor increases the risk that the spell will end in the next period by 15 percent.
- Hazard ratios:
  - Less than 1 have a “protective” effect (help sustain the spell).
  - Equal to 1 have no effect on spell duration.
- Column (1) (full set of variables) identifies the following as statistically significant determinants of spell duration:
  - initial income (increase → higher risk of spell ending)
  - total education (increase → lower risk)
  - changes in the US interest rate (increase → higher risk)
  - change in oil price (increase → lower risk)
  - external debt liabilities (increase → higher risk)
  - government balance to GDP (increase → higher risk)
- Small variations in the set of explanatory variables change both statistical significance and estimated elasticities:
  - Column (2) (“neoclassical” variables only) causes significance of initial income and education to disappear.
  - Adding shocks, exogenous factors, and political variables (columns (3) and (4)) makes population growth and terms of trade statistically significant and oil price change drops.
  - Removing “neoclassical” variables (column (5)) makes overvaluation index and droughts significant while oil price change, debt liabilities, and fiscal balance lose significance.
  - Columns (6)–(20) sequentially add regressors starting from column (2) and show dramatic changes in significance; variables not significant in column (1)—terms of trade growth, capital flows, inflation, autocracy—become significant in some specifications.
  - Example of fragility: oil price change alternates between statistically significant hazard ratios below one (positive effect on spell) and above one (negative effect on spell) across specifications (notably columns (1) and (8)).
- Conclusion from Table 3: empirical estimates can be fragile; ad hoc specifications can yield problematic lessons and underscore the importance of incorporating model uncertainty.

### BMA robustness analysis for proportional-hazards models (Table 4) — setup
- Baseline estimation uses a universe of all possible models for three sample groups: Africa, non-Africa, and the world.
- Variable sets:
  - Africa and non-Africa samples include 37 variables (the 18 regressors, the 18 interactions with the sub-Saharan Africa dummy variable, and the sub-Saharan Africa dummy variable itself).
  - World sample estimated using the 18 variables.
- Priors: each variable has the same probability of inclusion = 0.50.
- Table 4 outputs:
  - Posterior inclusion probabilities (first column of each panel) indicate how much the data favors including a variable.
  - Variables with posterior inclusion probability above the prior of 0.50 are considered robust.
  - Unconditional means and standard deviations computed across all possible models (third and fourth columns).
  - Hazard ratios (exponentiated coefficients) and their standard deviations are shown in subsequent columns.
- Note on interpretation: the ratio of the mean to the standard deviation cannot be strictly interpreted as a t-statistic since the posterior density is not a sampling distribution.

### Key BMA findings — non-Africa vs Africa vs world (preserved magnitudes and phrasing)
- Non-Africa sample robust determinants (posterior inclusion probabilities above 0.50) include:
  - initial income
  - terms of trade growth
  - inflation
  - exchange rate undervaluation
- Estimated marginal effects in the non-Africa sample:
  - A percentage increase in exchange rate overvaluation increases the probability that the growth spell will end by 2.7 percent.
  - A percentage increase in inflation increases the probability that the growth spell will end by 1.9 percent.
  - A one percent improvement in terms of trade increases the probability the growth spell will continue by 1.4 percent (protective effect).
- These three variables (terms of trade growth, inflation, exchange rate overvaluation) are ineffective in the Africa sample (inclusion probabilities < 10 percent).
- Higher initial income is associated with a higher probability that the spell will end in the non-Africa sample (consistent with conditional convergence).
- Two variables affect Africa distinctly and are ineffective in non-Africa:
  - openness (increases associated with lower spell duration)
  - cumulative number of droughts (very large negative effect on spell duration)
- Three variables are effective in predicting growth spells in both Africa and non-Africa:
  - total years of education (human capital)
  - investment to GDP ratio (physical capital)
  - exogenous shocks
- Marginal effects differ substantially across samples (exact magnitudes preserved):
  - Investment protective effect:
    - Africa: 9 percent
    - non-Africa: 5.4 percent
  - Additional year of education increases probability a growth spell will be sustained by:
    - Africa: 87 percent
    - non-Africa: 37 percent
  - U.S. interest rate changes (one percentage point = 100 basis points) reduce spell duration by:
    - non-Africa: 19.5 percent
    - Africa: 11.1 percent

### Interpretation and links to literature (preserved terminology)
- Results are consistent with:
  - Importance of physical and human capital (investment and years of education) in Solow (1957) and augmented Solow model (Mankiw, Romer, and Weil, 1992), especially for Africa.
  - Negative effect of shocks (changes in U.S. rate, terms of trade, droughts) on spell duration (Rodrik, 1999; Easterly et al., 1993).
  - Macroeconomic instability (inflation and exchange rate overvaluation) negatively associated with length of growth spells, particularly in the non-Africa sample (Fischer, 1993).
- Inflation measure specification:
  - The inflation measure is 100log(1+π), where π is the log difference of the price level.
  - At low inflation rates, 100log(1+π) is approximately linear; one percentage point increase in 100log(1+π) inflation is about the same as a one point rise in the rate of inflation.

### Conclusions and policy implications (preserved phrasing)
- Determinants of growth spells in Africa differ from those in the rest of the world:
  - Initial income, terms of trade, exchange rate undervaluation, inflation, openness, and droughts have distinct impacts in only one of the two samples.
  - Openness and droughts: unique to Africa sample.
  - Terms of trade, exchange rate undervaluation, and inflation: influence only non-Africa sample.
  - Investment, total years of education, and U.S. interest rate changes affect both groups but with substantially different marginal impacts.
- Policy guidance:
  - Properly accounting for model uncertainty is important for policymakers; recommendations should not be based on a single specification due to fragile conclusions.
  - What sustains growth spells globally is not necessarily what sustains growth spells in Africa.
  - Identified economic characteristics that influence growth spells in Africa: physical and human capital accumulation, openness, and droughts.
  - Further work needed to examine:
    - Relative importance of physical vs human capital accumulation.
    - How (or how fast) African economies should open to the rest of the world.
    - How to limit adverse impact of droughts (e.g., setting up crop insurance systems or shifting policy focus to sectors other than agriculture).

*Source: content of provided IMF PDF excerpt.*

### References

### _wp12227 - References

### Major citations
- Acemoglu, D., S. Johnson and J. A. Robinson, 2001, “The Colonial Origins of Comparative Development: An Empirical Investigation,” American Economic Review, Vol. 91, pp. 1369–1401.
- Aizenman J. and M. Spiegel, 2007, “Takeoffs,” NBER Working Paper No. 13084.
- Antoshin, S., A. Berg and M. Souto, 2008, “Testing for Structural Breaks in Small Samples,” Working Paper No. 75 (Washington: International Monetary Fund).
- Artadi, E.V. and X. Sala-i-Martin, 2003, “The Economic Tragedy of the XXth Century: Growth in Africa,” NBER Working Paper No. 9865.
- Bai, J. and P. Perron, 1998, “Estimating and Testing Linear Models with Multiple Structural Changes,” Econometrica, Vol. 66, No 1 (January), pp. 47–78.
- Bai, J. and P. Perron, 2003, “Computation and Analysis of Multiple Structural Change Models,” Journal of Applied Econometrics, Vol. 18, pp. 1–22.
- Berg, A. and J. Ostry, 2011, “Inequality and Unsustainable Growth: Two Sides of the Same Coin?” Staff Discussion Note No. 11/108 (Washington: International Monetary Fund).
- Berg, A., J. Ostry and J. Zettelmeyer, 2012, “What Makes Growth Sustained,” Journal of Development Economics, forthcoming.
- Block, S.A., 2001, “Does Africa Grow Differently?” Journal of Development Economics Vol. 65, pp. 443–467.
- Brock, W. and S. Durlauf, 2001, “Growth Economics and Reality,” World Bank Economic Review, Vol.15, pp. 229–272.
- Burnside, C. and D. Dollar, 2000, “Aid, Policies, and Growth,” American Economic Review, Vol. 90, pp. 847–868.
- Chen, H., A. Mirestean and C. Tsangarides, 2009, “Limited Information Bayesian Model Averaging for Dynamic Panels with Short Time Periods,” IMF Working Paper 09/74.
- Collier, P. and J. W. Gunning, 1999, “Explaining African Economic Performance,” Journal of Economic Literature, Vol. 37, pp. 64–111.
- Cox, D. R., 1972, “Regression Models and Life Tables (with Discussion),” Journal of the Royal Statistical Society, Vol. 34, pp. 187–220.
- Durlauf, S., P. Johnson and J. Temple, 2005, “Growth Econometrics,” in P. Aghion and S. Durlauf (eds.), Handbook of Economic Growth Vol. IA.
- Durlauf, S.N., A. Kourtellos, and C.M. Tan, 2008, “Are Any Growth Theories Robust?” Economic Journal, Vol. 118, No. 527, pp. 329–46.
- Easterly, W., M. Kremer, L. Pritchett, and L. Summers, 1993, “Good Policy or Good Luck? Country Growth Performance and Temporary Shocks,” Journal of Monetary Economics, Vol. 32, pp. 459–483.
- Easterly, W. and R. Levine, 1997, “Africa’s Growth Tragedy: Policies and Ethnic Divisions,” Quarterly Journal of Economics, Vol. 112, pp. 1203–1250.
- Fernández, C., E. Ley and M. Steel, 2001, “Model Uncertainty in Cross-Country Growth Regressions,” Journal of Applied Econometrics, Vol. 16, pp. 563–576.
- Fischer, S., 1993, “The Role of Macroeconomic Factors in Growth,” Journal of Monetary Economics, Vol. 32, pp. 485–512.
- Frankel, J. A. and D. Romer, 1999, “Does Trade Cause Growth?” American Economic Review, Vol. 89, pp. 379–99.
- Hausmann, R., L. Prichett and D. Rodrik, 2005, “Growth Accelerations,” Journal of Economic Growth, Vol. 10, pp. 303–329.
- Hausmann, R., J. Hwang and D. Rodrik, 2007, “What you Export Matters,” Journal of Economic Growth, Vol. 12, pp. 1–25.
- Hausmann, R., F. Rodriguez and R. Wagner, 2006, “Growth Collapses,” Working Paper No. 136.
- Hausmann, R. and B. Klinger, 2007, “The Structure of the Product Space and the Evolution of Comparative Advantage,” CID Working Paper No. 146.
- Jerzmanowski, M., 2006, “Empirics of Hills, Plateaus, Mountains and Plains: A Markov-Switching Approach to Growth,” Journal of Development Economics, Vol. 81, pp. 357–385.
- Jones, B. F. and B. A. Olken, 2008, “The Anatomy of Start-Stop Growth,” Review of Economics and Statistics, Vol. 90, pp. 582–587.
- Knack, S., and P. Keefer, 1995, “Institutions and Economic Performance: Cross-country Tests Using Alternative Institutional Measures,” Economics and Politics, Vol. 7, pp. 207–227.
- Lancaster, T., 1985, “Generalized Residuals and Heterogeneous Duration Models with Application to the Weibull Model,” Journal of Econometrics, Vol. 28, pp. 155–169.
- Leamer, E., 1978, Specification Searches: ad hoc Inference with Non-Experimental Data, New York: Wiley.
- Levine, R., 1997, “Financial Development and Economic Growth: Views and Agenda,” Journal of Economic Literature, Vol. XXXV, pp. 688–726.
- Mankiw, G., D. Romer, and D. Weil, 1992, “A Contribution to the Empirics of Economic Growth,” Quarterly Journal of Economics, Vol. 107, pp. 407–37.
- Masanjala W. and C. Papageorgiou, 2008, “Rough and Lonely Road to Prosperity: a Reexamination of the Sources of Growth in Africa Using Bayesian Model Averaging,” Journal of Applied Econometrics, Vol. 23, pp. 671–682.
- Mirestean, A. and C. Tsangarides, 2009, “Growth Determinants Revisited,” IMF Working Paper No. 268.
- Pattillo, C., S. Gupta, and K. Carey, 2005, “Sustaining Growth Accelerations and Pro-Poor Growth in Africa,” IMF Working Paper No. 195.
- Pritchett, L., 2000, “Understanding Patterns of Economic Growth: Searching for Hills among Plateaus, Mountains, and Plains,” World Bank Economic Review, pp. 221–250.
- Raftery, A.E., 1995, “Bayesian Model Selection in Social Research,” Sociological Methodology, Vol. 25, pp. 111–163.
- Raftery, A., D. Madigan and C. Volinsky, 1996, “Accounting for Model Uncertainty in Survival Analysis Improves Predictive Performance (with discussion),” in Bayesian Statistics 5, pp. 323–349.
- Rodriguez, F. and D. Rodrik, 2000, “Trade Policy and Economic Growth: A Skeptic’s Guide to the Cross-National Evidence,” NBER Macroeconomics Annual, Vol. 15, pp. 261–325.
- Rodrik, D., 1998, “Trade Policy and Economic Performance in Sub-Saharan Africa,” NBER Working Paper No. 6562.
- Sachs, J.D. and A.M. Warner, 1995, “Natural Resource Abundance and Economic Growth,” NBER Working Paper 5398.
- Rodrik, D., 1999, “Where Did All the Growth Go? External Shocks, Social Conflict, and Growth Collapses,” Journal of Economic Growth, Vol. 4, pp. 385–412.
- Rodrik, D., 2008, “The Real Exchange and Economic Growth,” Brookings Papers on Economic Activity.
- Sala-i-Martin, X., G. Doppelhofer and R. Miller, 2004, “Determinants of Long-Term Growth: A Bayesian Averaging of Classical Estimates (BACE) Approach,” American Economic Review, Vol. 94, pp. 813–835.
- Temple, J., 1999, “The New growth Evidence,” Journal of Economic Literature, Vol. 37, pp.112–156.
- Tsangarides, C., 2004, “A Bayesian Approach to Model Uncertainty,” IMF Working Paper No.04/68.
- Tsangarides, C., 2005, “Growth Empirics under Model Uncertainty: Is Africa Different?” IMF Working Paper No.05/18.
- Volinsky, C., D. Madigan, A. Raftery and R. Kronmal, 1997, “Bayesian Model Averaging in Proportional Hazard Models: Assessing the Risk of a Stroke,” Journal of the Royal Statistical Society, pp. 433–448.
- Wacziarg, R. and K. Welch, 2003, “Trade Liberalization and Growth: New Evidence,” NBER Working Paper No. 10152.
- Woolridge, J., 2002, Econometric Analysis of Cross Section and Panel Data, Cambridge: MIT Press.

### Key tabular findings and numeric summaries
- Table 1. Growth Breaks by Country Group (selected numeric entries preserved exactly as in source):
  - High Income: No. of countries 1; Tot al Average break size % 37257.0115.0494.9204.4
  - Emerging Asia: No. of countries 22; Tot al Average break size % 275.5195.6405.2284.7
  - Latin America: No. of countries 29; Tot al Average break size % 336.1206.0465.8285.5
  - Africa: No. of countries 43; Tot al Average break size % 4011.82210.3739.8388.8
  - Other: No. of countries 2; Tot al Average break size % 9128.266.7138.186.1
  - Totals: Total upbreaks 140; Total downbreaks 140; aggregate figures include series like 1377.9786.92216.81226.0 and 150-7.296-6.3234-6.7131-6.0 as presented.
  - Notes: 1 Includes Japan, Korea, Singapore, Hong Kong SAR and Taiwan Province of China. 2 Includes Middle East, North Africa and Caribbean countries. Upbreaks p=0.25; Downbreaks p=0.25; Minimum length: 5 years (up), 8 years (down). Upbreaks p=0.10; Downbreaks p=0.10; Minimum lengths repeated.

- Table 2. Stylized Facts about Growth Spells (selected exact values):
  - Minimum length of spell 5 years; p=0.10.
  - Example entries:
    - High Income: 2 countries; “37912.766.711.10.67.9-0.60.2-1” (as presented).
    - Emerging Asia: 22 countries; “621.383.366.7-1.57.0-1.3-1.3-1.6” (as presented).
    - Latin America: 29 countries; “188.416.711.10.35.1-0.9-0.4-0.8” (as presented).
    - Africa: 43 countries; “115.70.00.0-0.99.5-3.2-3.1-3.7” (as presented).
  - Frequency and duration of growth spells, Average growth before, during and after spells provided in table rows as in source.

- Table 3. Evidence for Lack of Robustness from Ad hoc “Kitchen Sink” Regressions of Spell Duration:
  - Regression covariates with point estimates and standard errors preserved exactly in the table (examples):
    - Initial income per capita: coefficients include 1.209* (0.119), 1.041 (0.0446), 1.135*** (0.0522), etc., across columns (1)–(20).
    - Population growth: coefficients include 1.285 (0.351), 0.997 (0.164), 1.202* (0.115), etc.
    - Investment to GDP: coefficients include 0.983 (0.0312), 1.006 (0.0176), 1.015 (0.0143), etc.
    - Total education years: coefficients include 0.535*** (0.0908), 0.871 (0.0801), 0.832* (0.0780), etc.
    - Other variables listed: Terms of trade growth, US interest rate change, Change in oil price, Capital flows to GDP, Drought, External debt liabilities to GDP, Openness, Overvaluation index, Log(1+inflation), Government balance to GDP, Aid to GDP, Difference in autocracy, Ethnic heterogeneity, Shock to terms of trade growth, Sub-Saharan Africa dummy.
  - Observations and sample sizes: Observations listed across columns include values such as 563, 966, 845, 757, 680, 898, 901, 966, 884, 932, 829, 966, 966, 954, 929, 719, 864, 889, 876, 966.
  - Subjects: values include 50, 73, 67, 62, 66, 69, 68, 73, 71, 70, 68, 73, 73, 73, 71, 62, 65, 70, 68, 73.
  - Failures: presented as concatenated integers “253835 33 31 3535383736 33 3838 38363333 373538” in the source table.
  - Note: Specifications presented to expose the issue of model uncertainty. All specifications are estimated using Cox proportional-hazards regression model with STATA’s stcox command with robust standard errors.

- Table 4. Posterior Coefficient Estimates for Growth Spells for Africa, Non-Africa and World (selected exact entries):
  - Columns present P(incl), Mean, Stand. Dev, Hazard, St.Dev for Africa, Non-Africa and World samples with interaction and composite hazard specifications.
  - Example entries (Africa sample, Non-Africa sample, World sample):
    - Initial income per capita: Africa P(incl) 45.2; Mean 1.515; Stand. Dev 1.339; Hazard 4.551; St.Dev 6.093. Non-Africa P(incl) 100.0; Mean 0.432; Stand. Dev 0.089; Hazard 1.541; St.Dev 0.136. World P(incl) 100.0; Mean 0.426; Stand. Dev 0.085; Hazard 1.531; St.Dev 0.130.
    - Total education years: Africa P(incl) 69.7; Mean -2.051; Stand. Dev 1.310; Hazard 0.129; St.Dev 0.169. Non-Africa P(incl) 100.0; Mean -0.478; Stand. Dev 0.181; Hazard 0.620; St.Dev 0.112. World P(incl) 100.0; Mean -0.581; Stand. Dev 0.154; Hazard 0.560; St.Dev 0.086.
    - Investment to GDP: Africa P(incl) 59.3; Mean -0.094; Stand. Dev 0.078; Hazard 0.910; St.Dev 0.071. Non-Africa P(incl) 83.2; Mean -0.054; Stand. Dev 0.038; Hazard 0.947; St.Dev 0.036. World P(incl) 69.7; Mean -0.036; Stand. Dev 0.032; Hazard 0.965; St.Dev 0.031.
    - Drought: Africa P(incl) 76.5; Mean 1.240; Stand. Dev 1.571; Hazard 3.457; St.Dev 5.430. Non-Africa P(incl) 0.6; Mean 0.007; Stand. Dev 0.114; Hazard 1.007; St.Dev 0.115. World P(incl) 40.6; Mean 0.387; Stand. Dev 0.579; Hazard 1.472; St.Dev 0.853.
    - Overvaluation index: Africa P(incl) 0.7; Mean 0.027; Stand. Dev 0.010; Hazard 1.028; St.Dev 0.010. Non-Africa P(incl) 99.9; Mean 0.027; Stand. Dev 0.009; Hazard 1.027; St.Dev 0.009. World P(incl) 99.9; Mean 0.023; Stand. Dev 0.007; Hazard 1.023; St.Dev 0.007.
  - Notes:
    - 1 Minimum length of spell 5 years; p=0.10. Boxed posterior coefficient estimates represent variables that pass the threshold of 0.50.
    - 2 Africa sample: composite posterior coefficient estimates are obtained from the specification with interactions.
    - 3 Non-Africa sample: posterior coefficient estimates are obtained from the specification with interactions.
    - 4 World sample: posterior coefficient estimates are obtained from the specification using all countries and no interactions.

### Figures: descriptions and data sources
- Figure 1a. Upbreaks and Downbreaks: Hills, Cliffs, Moutnails, and Plateaus
  - Minimum length of spell 5 years; p=0.10.
  - X-axis: Log of real GDP per capita (1940 1960 1980 2000 2020).
  - Long dashed lines: upbreaks; short dash lines: downbreaks.
  - Data source: Penn World Tables 6.2.
  - Country panels include USA, Canada, Chile, Haiti, China, Korea_Republic_of, Jordan, Egypt with log GDP per capita ranges shown (e.g., USA 9 9.5 10 10.5; Chile 8.5 9 9.5; Haiti 7.4–7.9; China 6–9 etc. as presented).

- Figure 1b. Upbreaks and Downbreaks: Hills, Cliffs, Mountains, and Plateaus in Africa
  - Minimum length of spell 5 years; p=0.10.
  - Same plotting conventions and data source (Penn World Tables 6.2).
  - Country panels include Botswana (6.5–9), Mauritius (8–10), South_Africa (8.2–9.2), Cameroon (7.4–8.2), Burundi (6.4–7), Zambia (6.6–7.4), Ghana (5.5–7.5), Comoros (7–7.6) as presented.

- Figure 2a. Distribution of Upbreaks (By country group and period)
  - Minimum length of spell 5 years; p=0.10.
  - Country groups shown: All industrial, Emerging Asia, Latin America and Caribbean, Africa, Other.
  - Periods: 50-60s, 70s, 80s, 90-00s.

- Figure 2b. Distribution of Downbreaks (By country group and period)
  - Same notes as Figure 2a.

- Figure 3 series. Duration of Growth Spells and Explanatory Variables (multiple panels)
  - Panels plot Duration of Growth Spell against:
    - Population growth (h=5; p=10).
    - Income per capita (h=5; p=10).
    - Total education (h=5; p=10).
    - Investment to GDP (h=5; p=10).
    - Terms of trade growth (h=5; p=10).
    - US interest rate change (h=5; p=10).
    - Droughts, Change in oil price, Total capital flows, Shock to terms of trade, Undervaluation Index, Openness, Debt liabilities (LM), Aid to GDP, Increase in autocracy, Ethnic heterogeneity, Fiscal balance to GDP, Log(1+inflation).
  - Source for plotted variables: Penn World Tables and author's calculation (panels repeat across pages with identical labeling and source).

### Appendix: Data and summary statistics; variable definitions and sources
- Appendix Table 1: Variable Definitions and Sources (entries preserved exactly)
  - Initial income per capita — Source: PWT 6.2 — Details: Initial real GDP per capita (2000 US dollars at PPP).
  - Population growth — Source: PWT 6.2 — Details: Annual population growth rate.
  - Investment to GDP — Source: PWT 6.2 — Details: Real investment as ratio to GDP (2000 US dollars at PPP).
  - Total education years — Source: Barro and Lee dataset — Details: Total average stock of years of primary and secondary education.
  - Terms of trade growth — Source: WEO — Details: Ratio of export prices to import prices (2000=100).
  - US interest rate change — Source: FED 3 month Treasury bill — Details: Percent change.
  - Change in oil price — Source: IFS — Details: Growth rate of average petroleum crude price, in USD per barrel.
  - Drought — Source: EM-DAT International Disaster Database — Details: Cumulative number of drought disasters recorded by EM-DAT (1974-2004).
  - Shock to terms of trade growth — Source: WEO — Details: Shock to TOT growth if above 50th pctile for all countries each year.
  - Capital flows to GDP — Source: WEO — Details: Total net capital flows to GDP.
  - External debt liabilities to GDP — Source: Lane and Milesi-Ferretti, 2003 — Details: External debt liabilities from IMF's (WEO) and World Bank's Global Development Finance database.
  - Openness — Source: PWT 6.2 — Details: Exports plus Imports divided by GDP, percent.
  - Undervaluation index — Source: PWT 6.2 — Details: Over/undervaluation index based on Rodrik (2008).
  - Log(1+inflation) — Source: IFS — Details: Percent.
  - Government balance to GDP — Source: WEO — Details: Government fiscal balance in percent of GDP.
  - Aid to GDP — Source: WDI — Details: Aid in % of GDP.
  - Difference in autocracy — Source: Polity IV — Details: Change in the index (scale from 0 to 10 (most autocratic)).
  - Ethnic heterogeneity — Source: Sambanis 2001 (extended) — Details: Ethnic heterogeneity (Vanhanen's measure): sum of racial, linguistic, and religious division rescaled 0-1.

*Source: _wp12227 - References (content unit extracted from the supplied PDF)._

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