## _wp0518 - References

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---

### I. Introduction
- Purpose: Empirically identify robust determinants of per capita growth rates across the world and Africa, addressing model uncertainty.
- Approach: Combines neoclassical and endogenous growth theory frameworks with a Limited Information Bayesian Model Averaging (LIBMA) implementation that uses a dynamic panel GMM estimator.
- Key summary findings:
  - Economic factors (initial conditions, higher investment, lower inflation, lower government consumption, better fiscal stance), improved political environment, favorable exogenous terms-of-trade shocks, and fixed geographical factors are robustly correlated with growth in both the World and Africa samples.
  - Africa’s growth process follows that of the rest of the world in principle, but marginal impacts and transmission mechanisms differ; in Africa, political/institutional factors and lower debt service to GDP are additionally robust correlates of growth.

### II. Theoretical considerations and estimation
- Baseline dynamic specification (discrete 5-year intervals):
  - ln(Y_i,t) − ln(Y_i,t−τ) = β_0 ln(Y_i,t−τ) + β_1' Z_i,t−τ + u_i + ν_t + ε_i,t with τ = 5.
  - Rewritten: ln(Y_i,t) = γ_0 ln(Y_i,t−τ) + γ_1' Z_i,t−τ + u_i + ν_t + ε_i,t.
- Solow-type nested specifications:
  - ln(Y_i,t) = η_0 ln(Y_i,t−τ) + η_1 ln(n_i,t + g + δ) + η_2 ln(s_i,t) + u_i + ν_t + ε_i,t; with human capital: + η_3 ln(h_i,t).
  - Speed of convergence λ recovered as λ = ln(1+γ_0)/t.
- Estimation issues and solutions:
  - Problems: inconsistent empirical estimates due to omitted country effects and endogeneity; model uncertainty with many correlated candidate regressors.
  - Estimator: Two-step systems GMM (difference and level equations estimated as a system) using lagged instruments (systems GMM as in Blundell and Bond (1998); Hansen (1982) framework).
  - Model uncertainty addressed via LIBMA: combines dynamic panel GMM with Bayesian model averaging over a universe of models; replaces full-information BIC with LIBIC for limited-information setting.

### III. Data and candidate determinants
- Data construction and samples:
  - Annual data from Penn World Table 6.1 (Summers and Heston) and other sources; five-year intervals τ = 5 producing panels for 1965, 1970, 1975, 1980, 1985, 1990, 1995, and 2000.
  - After filtering: unbalanced regularly spaced panel covering 149 countries over 1960-2000, maximum of 983 observations.
  - Samples: “World”: 149 countries, 983 observations; “Africa”: 41 countries, 328 observations.
- Categories of candidate determinants (selected):
  - Solow determinants and human capital: initial income; physical capital (investment to GDP); human capital (life expectancy, school enrollment); population growth.
  - Macroeconomic stability and external environment: inflation; government balance; government consumption to GDP; financial development (broad money to GDP; assets of deposit money banks to total bank assets); trade openness; terms-of-trade changes; black market premium.
  - Institutions and governance: democracy/autocracy indices; annual change in Polity index; incidence of civil war; political instability; ethnic fragmentation.
  - Geography and fixed factors: distance to coastline/sea-navigable river; percentage of land in geographical tropics; landlocked/coastal indicators.
  - Foreign aid and external debt: aid to GDP; debt stock to GDP; debt service to GDP.
  - Internal environment and resources: Gini index; arable land per capita; sectoral distribution effects.

### IV. Econometric results — Robustness design and main findings
- Universe of models and priors:
  - Universe for World and Africa samples: 2^19 = 524,288 regressions (19 potential determinants).
  - Initial prior mean model size kbar = 9; sensitivity checks with kbar = 5, 7, 9, 11, 13 reported (Tables 4a and 4b).
- Reported metrics per variable:
  - Posterior inclusion probability; posterior mean and variance (conditional on inclusion); sign certainty probability.
- Robustness classification (based on sign certainty probability and posterior inclusion):
  - Very strong: Prob(Sign certainty) ≥ 0.99 and Prob(Posterior inclusion) ≥ 0.90 (and above the prior).
  - Strong: Prob(Sign certainty) 0.95−0.98 and Prob(Posterior inclusion) ≥ 0.90 (and above the prior).
  - Mild: Prob(Sign certainty) 0.80−0.94 and Posterior inclusion above the prior.
  - Weak: Prob(Sign certainty) 0.55−0.79 and Posterior inclusion above the prior.
- Main robustness findings (common and region-specific):
  - Convergence and Solow determinants:
    - Conditional convergence holds: elasticity of per capita growth with respect to initial income is negative and very strongly significant.
    - Estimated rate of convergence λ:
      - World sample: estimated λ is on average between 2 and 2.5 percent.
      - Africa sample: λ is slightly slower, in the range of 1.5 and 2 percent.
    - Solow determinants: initial income and investment are “very strongly” robust; education is “mildly” robust; population growth shows weak robustness (sign flips frequently); life expectancy has high inclusion probability but is only mildly robust.
  - Seven variables identified as “strongly” robust common to both samples (policy, exogenous, political, geography):
    - Low inflation; small government size (government consumption); lower fiscal imbalances (fiscal balance to GDP); change in terms of trade; annual change in the polity index; geography (e.g., percentage of land in geographical tropics); black market premium (World sample).
  - Africa-specific strong robustness:
    - Additional strongly robust variables in Africa only: democracy index; incidence of civil war in the last 10 years; debt service to GDP.
  - Geography and institutions interaction:
    - Geography and black market premium are “strongly” robust in the World sample; at best “weakly” robust in Africa when institutions are controlled for.
    - Excluding institutional/political variables makes geography strongly robust in Africa, suggesting geography operates at least partly through institutions.
- Summary of “Very Strongly” Robust Growth Determinants (as reported in source):
  - World: Log(Inflation); Fiscal balance (to GDP); Log(Overall investment to GDP); Log(Government consumption to GDP); Log(Initial Income); Annual change in the polity index; Percentage of land in geographical tropics; Terms of Trade; Black market premium.
  - Africa: Log(Inflation); Fiscal balance (to GDP); Log(Overall investment to GDP); Log(Government consumption to GDP); Log(Initial Income); Annual change in the polity index; Terms of Trade; Democracy Index; Incidence of civil war in the last 10 years; Debt service to GDP.
- Other variable robustness:
  - Mildly robust in one or both samples: education, trade openness, aid to GDP (openness barely misses “strongly” robust cutoff in Africa).
  - Weakly robust or inconsistent: financial development, life expectancy, inequality, black market premium (sample-dependent).

### IV. Econometric results — Selected numeric posterior metrics (from Tables 1 and 2)
- Marginal Evidence of Importance in Africa Sample (selected entries: posterior inclusion — posterior mean — posterior variance — sign certainty):
  - 1. Log of Inflation — 0.90 — -0.0225 — 0.0004 — 1.00
  - 2. Fiscal balance (to GDP) — 0.94 — 0.8339 — 0.0828 — 1.00
  - 3. Log (overall investment to GDP) — 0.94 — 0.0475 — 0.0008 — 1.00
  - 4. Log(Government consumption to GDP) — 0.94 — -0.0688 — 0.0009 — 0.99
  - 5. Log(Initial Income) — 0.94 — -0.1595 — 0.0024 — 0.99
  - 6. Annual change in the polity index — 0.94 — -0.2937 — 0.4133 — 0.98
  - 7. Percentage of land in geographical tropics — 1.00 — -0.2868 — 0.0080 — 0.97
  - 8. Terms of Trade (Growth) — 0.94 — 0.0275 — 0.0124 — 0.96
  - 9. Black market premium — 0.94 — -0.0002 — 0.0000 — 0.95
  - 10. Overall schooling — 0.77 — 0.0572 — 0.0011 — 0.94
  - 19. Debt service to GDP — 0.87 — 0.2334 — 0.0889 — 0.30
- Marginal Evidence of Importance in World Sample (selected entries):
  - 1. Log of Inflation — 0.90 — -0.1360 — 0.0047 — 1.00
  - 2. Log(Government consumption to GDP) — 0.92 — -0.0616 — 0.0015 — 1.00
  - 3. Terms of Trade (Growth) — 0.92 — 0.2510 — 0.0238 — 1.00
  - 4. Democracy index — 0.91 — 0.6421 — 0.1660 — 1.00
  - 5. Annual change in the polity index — 0.91 — -1.2164 — 1.1457 — 1.00
  - 6. Debt service to GDP — 0.91 — -0.4808 — 0.1153 — 0.99
  - 7. Log(Initial Income) — 0.92 — -0.0947 — 0.0015 — 0.99
  - 8. Log (overall investment to GDP) — 0.92 — 0.0475 — 0.0016 — 0.99
  - 9. Incidence of civil war in the last 10 years — 0.92 — -0.0230 — 0.0008 — 0.96
  - 10. Fiscal balance (to GDP) — 0.92 — 0.1493 — 0.0503 — 0.96

### V. Marginal impacts and elasticity comparisons (Table 3 excerpts)
- Elasticities at country/sample group means — selected reported entries (World vs Africa):
  - Log of Inflation: World -0.0225 — Africa -0.1360
  - Fiscal balance (to GDP): World -0.0357 — Africa -0.0087
  - Log (overall investment to GDP): World 0.0475 — Africa 0.0475
  - Log(Government consumption to GDP): World -0.0688 — Africa -0.0616
  - Log(Initial Income): World -0.1595 — Africa -0.0947
  - Annual change in the polity index: World -0.0215 — Africa -0.0476
  - Terms of Trade (Growth): World 0.0295 — Africa 0.4761
  - Democracy Index (World figure in table): -2.5510
- Interpretation:
  - Inflation and terms of trade have larger adverse or positive magnitudes respectively for Africa than for the World sample.
  - Investment elasticity similar across samples (0.0475).
  - Fiscal balance and government consumption elasticities have smaller marginal impacts in Africa compared to the rest of the world.

### VI. Sensitivity analysis on prior model size (Tables 4a and 4b — selected ranges)
- World sample (selected robust determinants; sign certainty and min/max posterior means and variances across kbar = 5, 7, 9, 11, 13):
  - Log of Inflation — Certainty 1.00 — Minimum -0.0274 — Maximum -0.0204 — Variance minimum 0.0004 — Variance maximum 0.0006
  - Fiscal balance (to GDP) — Certainty 1.00 — Minimum 0.7878 — Maximum 0.8609 — Variance minimum 0.0574 — Variance maximum 0.1301
  - Log (overall investment to GDP) — Certainty 1.00 — Minimum 0.0418 — Maximum 0.0565 — Variance minimum 0.0006 — Variance maximum 0.0012
- Africa sample (selected robust determinants):
  - Log of Inflation — Certainty 1.00 — Minimum -0.1379 — Maximum -0.1336 — Variance minimum 0.0024 — Variance maximum 0.0081
  - Log(Government consumption to GDP) — Certainty 1.00 — Minimum -0.0672 — Maximum -0.0569 — Variance minimum 0.0012 — Variance maximum 0.0021
  - Terms of Trade (Growth) — Certainty 1.00 — Minimum 0.2323 — Maximum 0.2642 — Variance minimum 0.0203 — Variance maximum 0.0298
  - Democracy index — Certainty 1.00 — Minimum 0.6055 — Maximum 0.6816 — Variance minimum 0.1313 — Variance maximum 0.2373
  - Annual change in the polity index — Certainty 1.00 — Minimum -1.2388 — Maximum -1.2157 — Variance minimum 1.0333 — Variance maximum 1.3980
- Note: Qualitative conclusions robust to the prior mean model size choice.

### VII. Policy-relevant messages and implications
- General policy levers supported by robust correlations:
  - Improve macroeconomic stability: lower inflation.
  - Strengthen fiscal positions: sustainable fiscal balances.
  - Reduce government consumption share of GDP.
  - Raise investment (overall investment to GDP).
  - Improve political/institutional environment (annual change in polity index; democracy).
  - Respond to exogenous shocks: terms-of-trade improvements matter.
- Africa-specific priorities indicated by robustness findings:
  - Strengthen institutions and democratic governance (democracy index robust in Africa).
  - Reduce incidence of civil conflict.
  - Address high debt service burdens (debt service to GDP robust in Africa).
- Methodological caveat:
  - Results establish robust associations under LIBMA and systems GMM; they do not map explicit causal transmission mechanisms for all determinants. Further research needed on interaction mechanisms and country-specific channels.

### Appendix I — Variable definitions, sample, and group averages (selected entries)
- Dependent variable:
  - LN Y — Penn World Table 6.1 — Logarithm of real GDP per capita (1996 US dollars at PPP).
- Selected explanatory variables and sources (preserved labels):
  - LNY0 — Penn World Table 6.1 — Logarithm of initial real GDP per capita (1996 US dollars at PPP).
  - LNI — Penn World Table 6.1 — Logarithm of real investment to GDP (1996 US dollars at PPP).
  - LNINFL — International Financial Statistics — Logarithm of one plus the inflation rate.
  - BALY — World Economic Outlook — Government balance as share of GDP, current LCU.
  - LNG — Penn World Table 6.1 — Logarithm of real government consumption to GDP.
  - TOTGR — World Economic Outlook — Terms of trade (goods and services) growth.
  - DEMOC, POLITY, CHANGE — Polity IV measures; CHANGE is annual change in the Polity index.
  - PW10 — Sambanis — Incidence of civil war in the last 10 years.
  - BLK — Easterly and Sewadeh — Black market premium measure.
- Sample country-count and example country observations:
  - Panel includes 149 countries; examples list country observation counts (e.g., Algeria 8, Angola 8, Australia 8, Bangladesh 8, France 8, United States 8, etc.).
- Unweighted group averages (selected entries from Table A4):
  - LNYT-LNY0: ALL 0.08, Non-oil 0.07, Intermediate 0.08, OECD 0.11, Africa 0.03
  - 1 LNY0: ALL 8.14, OECD 9.47, Africa 7.27
  - 2 LNI: ALL 2.55, OECD 3.14, Africa 2.06
  - 4 LNINFL: ALL 0.17, OECD 0.07, Africa 0.16
  - 5 BALY: ALL -4.28, OECD -2.98, Africa -5.83
  - 7 AIDGDP: ALL 6.60, OECD 0.35, Africa 11.87
  - 11 TOTGR: ALL 1.07, OECD 0.31, Africa 1.90
  - 12 LTOTED: ALL 1.26, OECD 1.96, Africa 0.48
  - 13 LFEXP: ALL 60.23, OECD 73.34, Africa 47.29
  - 17 TROPICAR: ALL 55.16, OECD 1.76, Africa 91.65

### Appendix II — Computational aspects, LIBMA formulation, and computed statistics
- Bayesian framework and model probabilities:
  - Posterior for parameters: p(θ|D) = p(D|θ) p(θ) / ∫ p(D|θ) p(θ) dθ.
  - Posterior model probability for Mk: p(Mk|D) = exp(−1/2 LIBICk) p(Mk) / Σ_{j=1}^K exp(−1/2 LIBICj) p(Mj) (LIBMA replaces BIC with LIBIC in limited-information setting).
  - Posterior odds ratio: p(M2|D) / p(M1|D) = [p(D|M2) / p(D|M1)] × [p(M2) / p(M1)] (first term is Bayes factor).
- Prior model probabilities:
  - Prior probability of model Mj (as presented): p(M_j) = (k k* )^{k_j} (1 − k k* )^{1−k_j} (notation preserved from source).
  - k* is total number of regressors; k is prior about expected number of non-zero regressors; k_j is number included in model Mj.
- Posterior summaries and inclusion measures:
  - Posterior mean across models: E(θk|D) = Σ_{j=1}^{2^{k*}} p(Mj|D) E(θk|D, Mj).
  - Posterior variance: Var(θk|D) formula preserved as in source.
  - Posterior inclusion probability: p(θk ≠ 0 | D) = Σ_{θk ≠ 0} p(Mj|D). If p(θk ≠ 0 | D) > p(θk ≠ 0) = k/k*, variable considered to have high marginal contribution.
  - Sign certainty probability: sign certainty for θk = p[ sgn(θk) = sgn E(θk|D) | D, θk ≠ 0 ] (formula preserved).
- Computed statistics and robustness checks:
  - Bayes factors approximated via BIC or LIBIC; prior inclusion parameter k is varied in sensitivity checks (kbar = 5, 7, 9, 11, 13) to assess robustness.
  - When exhaustive enumeration feasible (K = 2^{k*}), posterior model probabilities and derived statistics computed by summing over full model space using LIBIC-weighted model weights.

*Source: _wp0518 — Appendix II: Computational Aspects and associated tables and appendices as provided in the content unit.*

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

### _wp0518 - References .............................................................................................................

### Tables
- 1. Robustness of Growth Determinants: World Sample .....................................................22
- 2. Robustness of Growth Determinants: Africa Sample .....................................................22
- 3. Elasticities at Country/Sample Group Means: Robust Growth Determinants ...............23
- 4a. Sensitivity Analysis on Prior Model Size in World Sample ..........................................24
- 4b. Sensitivity Analysis on Prior Model Size in Africa Sample ..........................................24

### Appendix I: Tables
- A1. Sample Data: Variable Definitions and Sources ............................................................25
- A2. Sample Data: Country Group Membership ....................................................................26
- A3. Growth Regressions Compilation: Correlations from the Literature .............................27
- A4. Sample Data: Country Group Unweighted Averages ....................................................29

*Source: _wp0518 - References .............................................................................................................*

### Appendix II: Computational Aspects .....................................................................................

### Appendix II: Computational Aspects

### I. Introduction
- Purpose: Empirically identify robust determinants of per capita growth rates across the world and Africa, addressing model uncertainty.
- Approach: Draws on neoclassical and endogenous growth theories; uses Bayesian Model Averaging (limited information LIBMA) alongside a dynamic panel GMM estimator.
- Key summary findings:
  - Economic factors (initial conditions, higher investment, lower inflation, lower government consumption, better fiscal stance), improved political environment, favorable exogenous terms-of-trade shocks, and fixed geographical factors are robustly correlated with growth in both the World and Africa samples.
  - Africa’s growth process follows that of the rest of the world in principle, but marginal impacts and transmission mechanisms differ; in Africa, political/institutional factors and lower debt service to GDP are additionally robust correlates of growth.

### II. Theoretical considerations and estimation
- Model specification:
  - Baseline dynamic specification (discrete 5-year intervals):
    - ln(Y_i,t) − ln(Y_i,t−τ) = β_0 ln(Y_i,t−τ) + β_1' Z_i,t−τ + u_i + ν_t + ε_i,t
    - With τ = 5 (five-year intervals), rewritten as ln(Y_i,t) = γ_0 ln(Y_i,t−τ) + γ_1' Z_i,t−τ + u_i + ν_t + ε_i,t
  - Solow-type augmented specifications (nested):
    - ln(Y_i,t) = η_0 ln(Y_i,t−τ) + η_1 ln(n_i,t + g + δ) + η_2 ln(s_i,t) + u_i + ν_t + ε_i,t
    - With human capital: + η_3 ln(h_i,t)
  - Speed of convergence λ recovered from estimated elasticities as λ = ln(1+γ_0)/t.
- Estimation issues:
  - Two main problems: inconsistent empirical estimates (omitted country effects, endogeneity) and model uncertainty (many correlated candidate regressors).
  - Estimator:
    - Two-step systems GMM (difference and level equations estimated as a system) to address omitted effects and endogeneity, using lagged instruments (systems GMM as in Blundell and Bond (1998); Hansen (1982) framework).
  - Model uncertainty addressed via LIBMA:
    - Limited Information Bayesian Model Averaging (LIBMA) combines dynamic panel GMM with a Bayesian robustness check over a universe of models; relaxes full-information priors and allows control for endogeneity via GMM.

### III. Data and candidate determinants
- Data construction:
  - Annual data from Summers and Heston (Penn World Tables, version 6.1) and other sources.
  - Five-year time intervals with τ = 5 produce eight panels: 1965, 1970, 1975, 1980, 1985, 1990, 1995, and 2000.
  - After filtering (countries with less than two observations and extreme values), an unbalanced regularly spaced panel covering 149 countries over 1960-2000, yielding a maximum of 983 observations.
  - Two samples for comparison:
    - “World”: 149 countries, 983 observations.
    - “Africa”: 41 countries, 328 observations.
- Categories of determinants (subset of those identified by Durlauf and Quah (1999)):
  - Solow determinants and human capital: initial income, physical capital (investment to GDP), human capital (life expectancy, school enrollment), population growth.
  - Macroeconomic stability and external environment: inflation, government budget balance, government consumption to GDP, financial development (broad money to GDP; assets of deposit money banks to total bank assets), trade openness, exogenous terms-of-trade changes, black market premium.
  - Institutions and governance: democracy/autocracy indices, polity index changes, incidence of civil war, political instability, ethnic fragmentation.
  - Geography and fixed factors: distance to coastline or sea-navigable river, percentage of land in geographical tropics, landlocked/coastal indicators.
  - Foreign aid and external debt: aid flows to GDP, debt stock to GDP, debt service to GDP.
  - Internal environment and resources: Gini index (inequality), arable land to total area (agricultural productivity), sectoral distribution effects.

### IV. Econometric results
- Impact of model uncertainty:
  - Ad hoc growth regressions are fragile: adding variables changes significance, sign, and policy conclusions; motivates formal robustness check over the model universe.
- Robustness analysis design:
  - Universe of models estimated for the World sample: 2^19 = 524,288 regressions (19 potential determinants).
  - Same universe estimated for the Africa sample.
  - Initial prior model size set to k = 9 (sensitivity checks reported in Tables 4a and 4b indicate results robust to this choice).
  - Key reported metrics per variable: posterior inclusion probability; conditional mean and variance (conditional on inclusion); sign certainty probability (probability coefficient has same sign as posterior mean).
  - Robustness classification (based on sign certainty probability and posterior inclusion):
    - Very strong: Prob(Sign certainty) ≥ 0.99 and Prob(Posterior inclusion) ≥ 0.90 (and above the prior)
    - Strong: Prob(Sign certainty) 0.95−0.98 and Prob(Posterior inclusion) ≥ 0.90 (and above the prior)
    - Mild: Prob(Sign certainty) 0.80−0.94 and Posterior inclusion above the prior
    - Weak: Prob(Sign certainty) 0.55−0.79 and Posterior inclusion above the prior
- Main robustness findings:
  - Convergence and Solow determinants:
    - Conditional convergence holds: elasticity of per capita growth with respect to initial income is negative and very strongly significant.
    - Estimated rate of convergence λ:
      - World sample: estimated λ is on average between 2 and 2.5 percent.
      - Africa sample: λ is slightly slower, in the range of 1.5 and 2 percent.
    - Solow determinants (initial income, investment, population growth, education) have high inclusion probabilities; initial income and investment are “very strongly” robust; education is “mildly” robust; population growth shows weak robustness (sign flips frequently).
    - Life expectancy has high inclusion probability but is only mildly robust (correlation with other poverty/health education measures).
  - Other robust determinants (common to World and Africa; policy, exogenous, political):
    - Five additional variables identified as “strongly” robust in both samples (total seven strongly robust variables common to both):
      - Policy variables: low inflation; small government size (government consumption); lower fiscal imbalances (fiscal balance to GDP).
      - Exogenous factor: change in terms of trade.
      - Political environment: annual change in polity index (degree of autocracy/democracy).
  - Africa-specific strong robustness:
    - Three additional “strongly” robust variables in Africa only: democracy index; incidence of civil war in the last 10 years; debt service to GDP.
  - Geography and black market premium:
    - Enter as “strongly” robust in the World sample; at best “weakly” robust in the Africa sample when institutions are controlled for.
    - If institutional/political variables are excluded, geography becomes strongly robust in the Africa sample (indicating geography operates at least partly through institutions).
  - Summary table of “Very Strongly” Robust Growth Determinants (as reported):
    - World: Log(Inflation); Fiscal balance (to GDP); Log(Overall investment to GDP); Log(Government consumption to GDP); Log(Initial Income); Annual change in the polity index; Percentage of land in geographical tropics; Terms of Trade; Black market premium.
    - Africa: Log(Inflation); Fiscal balance (to GDP); Log(Overall investment to GDP); Log(Government consumption to GDP); Log(Initial Income); Annual change in the polity index; Terms of Trade; Democracy Index; Incidence of civil war in the last 10 years; Debt service to GDP.
  - Other variables:
    - Mildly robust in one or both samples: education, trade openness, aid to GDP (openness barely misses “strongly” robust cutoff in Africa).
    - Weakly robust or less consistent: financial development, life expectancy, inequality, black market premium (some appear weakly robust depending on sample).
- Marginal impacts (elasticities at sample group means; Table 3):
  - Common robust variables have different marginal impacts across samples:
    - Inflation and terms of trade have larger magnitudes (adverse effects) for Africa than for the World sample.
    - Investment has about the same marginal impact in Africa as in the World sample.
    - Fiscal balance and government consumption to GDP have less marginal impact in Africa compared to the rest of the world.
  - Policy implication: targeting higher investment, lowering inflation, improving fiscal balances, reducing government consumption share, and improving political environment are effective levers for raising per capita incomes, with stronger effects for some variables in Africa (e.g., inflation, terms of trade).

### V. Conclusions and implications
- Methodological strengths: combination of dynamic panel GMM, LIBMA robustness over a wide set of determinants, and panel data over five-year intervals.
- Core empirical conclusions:
  - There exist economic, political, and environmental factors that robustly affect growth once model uncertainty and estimation issues are accounted for.
  - Common robust determinants for World and Africa: initial conditions, higher investment, lower inflation, lower government consumption, better fiscal stance, improved political environment, favorable terms-of-trade shocks, and fixed geographical factors.
  - Africa shows additional robust determinants: democracy, incidence of civil war, and debt service to GDP — reflecting the region’s political instability, weak institutions, and debt burdens.
- Policy-relevant messages:
  - Policies that improve macroeconomic stability (lower inflation, sustainable fiscal balances), raise investment, and improve political/institutional environment are generally favorable for growth globally and in Africa.
  - Africa-specific priorities include strengthening institutions/democracy, reducing civil conflict, and addressing high debt service burdens.
- Limitations and further research:
  - The analysis establishes robust associations but does not map explicit causal transmission mechanisms for all determinants.
  - Understanding why certain channels influence growth differently in Africa requires further study of interactions between policies, institutions, and country-specific conditions.

*Source: Appendix II: Computational Aspects (from the provided content).*

### References

### References

### Cited literature (select themes and representative works)
- Institutional determinants of development: Acemoglu, D., S. Johnson, and J. Robinson, 2001; Acemoglu, D., S. Johnson, and J. Robinson, 2002; Knack, S., and P. Keefer, 1995; Rodrick, D., A. Subramanian, and F. Trebbi, 2002; Leite, C., and J. Weidmann, 1999.  
- Geography, endowments, and growth: Gallup, J., J. Sachs, and A. Mellinger, 1999; Easterly, W., and R. Levine, 2003; Frankel, J. A., and D. Romer, 1999.  
- Poverty, human development, and distribution: Anand, S., 1991; Anand, S., and M. Ravallion, 1993; Chen, S., and M. Ravallion, 1997; Kanbur, R., and L. Squire, 2001.  
- Growth empirics and robustness/sensitivity methods: Barro, R., 1991; Barro, R., and X. Sala-i-Martin, 1992; Levine, R., and D. Renelt, 1992; Sala-i-Martin, X., 1997; Doppelhofer, G., R. I. Miller, and X. Sala-i-Martin, 2000; Fernandez, C., E. Ley, and M. Steel, 2001; Hoeting, J. A., D. Madigan, A. E. Raftery, and C. T. Volinsky, 1999; Raftery, A. E., 1996; Kass, R., and A. Raftery, 1995.  
- Political economy, democracy, and conflict: Alesina, A., S. Olzer, N. Roubini, and P. Swagel, 1996; Przeworski, A., and F. Limongi, 1993; Helliwell J., 1994; Collier, P., and J. W. Gunning, 1999; Brunetti, A., and B. Weder, 1995; Brunetti, A., 1997.  
- Macroeconomic policy, inflation, and fiscal factors: Bruno, M. and W. Easterly, 1998; Easterly, W., and S. Fischer, 2001; Easterly, W. and S. Rebelo, 1993; Fischer, S., 1993; Ghura, D., and M. Hadjimichael, 1996.  
- Finance and debt issues: King, R., and R. Levine, 1993; Krugman, P., 1988; Leamer, E., 1978.  
- Bayesian/model averaging and panel GMM methodology: Blundell, R., and S. Bond, 1998; Hansen, L. P., 1982; Tsangarides, C., 2004; Sala-i-Martin, X., Doppelhofer, G., R., and I. Miller, 2004.

### Tables: Robustness of Growth Determinants (selected posterior metrics reported in source)
- Marginal Evidence of Importance in Africa Sample — Table 1: Robustness of Growth Determinants (posterior inclusion, posterior mean, posterior variance, sign certainty)
  1. Log of Inflation — 0.90 — -0.0225 — 0.0004 — 1.00  
  2. Fiscal balance (to GDP) — 0.94 — 0.8339 — 0.0828 — 1.00  
  3. Log (overall investment to GDP) — 0.94 — 0.0475 — 0.0008 — 1.00  
  4. Log(Government consumption to GDP) — 0.94 — -0.0688 — 0.0009 — 0.99  
  5. Log(Initial Income) — 0.94 — -0.1595 — 0.0024 — 0.99  
  6. Annual change in the polity index — 0.94 — -0.2937 — 0.4133 — 0.98  
  7. Percentage of land in geographical tropics — 1.00 — -0.2868 — 0.0080 — 0.97  
  8. Terms of Trade (Growth) — 0.94 — 0.0275 — 0.0124 — 0.96  
  9. Black market premium — 0.94 — -0.0002 — 0.0000 — 0.95  
  10. Overall schooling — 0.77 — 0.0572 — 0.0011 — 0.94  
  11. Arable land — 0.94 — -0.0233 — 0.0002 — 0.93  
  12. Trade openness (X+M as share of GDP) — 0.94 — 0.0889 — 0.0027 — 0.86  
  13. Aid (to GDP) — 0.89 — -0.4519 — 0.0644 — 0.84  
  14. Democracy index — 0.94 — 0.3749 — 0.0475 — 0.78  
  15. Incidence of civil war in the last 10 years — 0.94 — 0.0258 — 0.0006 — 0.72  
  16. Life expectancy — 0.93 — 0.0012 — 0.0000 — 0.60  
  17. Population growth — 0.94 — 0.1607 — 0.0181 — 0.52  
  18. Financial depth (M2 to GDP) — 0.94 — -0.0934 — 0.0071 — 0.49  
  19. Debt service to GDP — 0.87 — 0.2334 — 0.0889 — 0.30

- Marginal Evidence of Importance in World Sample — Table 2: Robustness of Growth Determinants (posterior inclusion, posterior mean, posterior variance, sign certainty)
  1. Log of Inflation — 0.90 — -0.1360 — 0.0047 — 1.00  
  2. Log(Government consumption to GDP) — 0.92 — -0.0616 — 0.0015 — 1.00  
  3. Terms of Trade (Growth) — 0.92 — 0.2510 — 0.0238 — 1.00  
  4. Democracy index — 0.91 — 0.6421 — 0.1660 — 1.00  
  5. Annual change in the polity index — 0.91 — -1.2164 — 1.1457 — 1.00  
  6. Debt service to GDP — 0.91 — -0.4808 — 0.1153 — 0.99  
  7. Log(Initial Income) — 0.92 — -0.0947 — 0.0015 — 0.99  
  8. Log (overall investment to GDP) — 0.92 — 0.0475 — 0.0016 — 0.99  
  9. Incidence of civil war in the last 10 years — 0.92 — -0.0230 — 0.0008 — 0.96  
  10. Fiscal balance (to GDP) — 0.92 — 0.1493 — 0.0503 — 0.96  
  11. Trade openness (X+M as share of GDP) — 0.92 — 0.0516 — 0.0035 — 0.94  
  12. Aid (to GDP) — 0.91 — -0.1503 — 0.0214 — 0.89  
  13. Arable land — 0.92 — -0.0091 — 0.0005 — 0.86  
  14. Population growth — 0.92 — 0.2253 — 0.0363 — 0.81  
  15. Life expectancy — 0.90 — 0.0045 — 0.0000 — 0.81  
  16. Financial depth (M2 to GDP) — 0.92 — 0.1738 — 0.0284 — 0.81  
  17. Percentage of land in geographical tropics — 1.00 — -0.0126 — 0.0193 — 0.80  
  18. Overall schooling — 0.73 — 0.0103 — 0.0005 — 0.71  
  19. Black market premium — 0.91 — 0.0018 — 0.0001 — 0.49

### Elasticities and sensitivity findings (selected excerpts)
- Table 3: Elasticities at Country/Sample Group Means — selected reported entries (World vs Africa)
  - Log of Inflation: World -0.0225 — Africa -0.1360  
  - Fiscal balance (to GDP): World -0.0357 — Africa -0.0087  
  - Log (overall investment to GDP): World 0.0475 — Africa 0.0475  
  - Log(Government consumption to GDP): World -0.0688 — Africa -0.0616  
  - Log(Initial Income): World -0.1595 — Africa -0.0947  
  - Annual change in the polity index: World -0.0215 — Africa -0.0476  
  - Terms of Trade (Growth): World 0.0295 — Africa 0.4761  
  - Democracy Index (World): -2.5510 (reported as a World figure in the table)

- Table 4a and 4b: Sensitivity Analysis on Prior Model Size (posterior conditional means and variances with kbar = 5, 7, 9, 11, 13) — selected reported ranges and certainty metrics:
  - World sample (selected robust determinants with sign certainty, minimum/maximum posterior means and variances):
    1. Log of Inflation — Certainty 1.00 — Minimum -0.0274 — Maximum -0.0204 — Variance minimum 0.0004 — Variance maximum 0.0006  
    2. Fiscal balance (to GDP) — Certainty 1.00 — Minimum 0.7878 — Maximum 0.8609 — Variance minimum 0.0574 — Variance maximum 0.1301  
    3. Log (overall investment to GDP) — Certainty 1.00 — Minimum 0.0418 — Maximum 0.0565 — Variance minimum 0.0006 — Variance maximum 0.0012  
    (additional entries listed similarly in source)
  - Africa sample (selected robust determinants with sign certainty, minimum/maximum posterior means and variances):
    1. Log of Inflation — Certainty 1.00 — Minimum -0.1379 — Maximum -0.1336 — Variance minimum 0.0024 — Variance maximum 0.0081  
    2. Log(Government consumption to GDP) — Certainty 1.00 — Minimum -0.0672 — Maximum -0.0569 — Variance minimum 0.0012 — Variance maximum 0.0021  
    3. Terms of Trade (Growth) — Certainty 1.00 — Minimum 0.2323 — Maximum 0.2642 — Variance minimum 0.0203 — Variance maximum 0.0298  
    4. Democracy index — Certainty 1.00 — Minimum 0.6055 — Maximum 0.6816 — Variance minimum 0.1313 — Variance maximum 0.2373  
    5. Annual change in the polity index — Certainty 1.00 — Minimum -1.2388 — Maximum -1.2157 — Variance minimum 1.0333 — Variance maximum 1.3980  
    (additional entries listed similarly in source)

Notes drawn from the source tables:
- Bayesian Model averaging techniques are applied using a panel data systems GMM estimator; the dependent variables in the system are lny_t - lny_0 and the first difference of lny_t - lny_0.  
- The results are ranked by the sign certainty probability. The boxed area indicates variables identified as (at least) "strongly robust".  
- The prior mean model size kbar is 9; qualitative conclusions are robust to the choice of kbar (as shown in Tables 4a and 4b).  
- See Table A2 for details on sample groupings.

*Source: References and accompanying tables as provided in the content unit "_wp0518 - References".*

### Appendix I

### Appendix I

### Variable Definitions and Sources
- Dependent Variable
  - LN Y — Penn World Table 6.1 — Logarithm of real GDP per capita (1996 US dollars at PPP).
- Explanatory Variables
  1. LNY0 — Penn World Table 6.1 — Logarithm of initial real GDP per capita (1996 US dollars at PPP).
- Solow determinants
  2. LNI — Penn World Table 6.1 — Logarithm of real investment to GDP (1996 US dollars at PPP).
  3. LNNPOPGR — Penn World Table 6.1 — Logarithm of annual population growth rate plus 0.05.
- Macroeconomic stability
  4. LNINFL — International Financial Statistics — Logarithm of one plus the inflation rate.
  5. BALY — World Economic Outlook — Government balance as share of GDP, current LCU.
  6. G — Penn World Table 6.1 — Real government consumption to GDP (1996 US dollars at PPP).
  6. LNG — Penn World Table 6.1 — Logarithm of G.
- Foreign Aid
  7. AIDGDP — Global Development Finance — Foreign aid as percentage of GDP.
- Financial development
  8. DMBCB — International Financial Statistics — Ratio of assets of deposit money banks to total bank assets.
  8. BRMY — World Economic Outlook — Ratio of broad money to GDP.
- External debt
  9. DEBTGDP — World Development Indicators — Nominal debt to GDP.
  9. DSGDP — World Development Indicators — Debt service to GDP.
  9. DSX — World Development Indicators — Debt service to exports.
  9. NPDSX — Easterly — NPV debt service to exports of goods and services.
- Trade regime
  10. OPEN — Penn World Table 6.1 — Exports plus Imports as share of GDP (1996 US dollars at PPP).
  10. OPENGRP — Penn World Table 6.1 — Average annual rate of growth of openness.
- External environment
  11. TOT — World Economic Outlook — Terms of trade (goods and services).
  11. TOTGR — World Economic Outlook — Terms of trade (goods and services) growth.
- Human capital
  12. PYR — Barro and Lee dataset — Average stock of years of primary education.
  12. SYR — Barro and Lee dataset — Average stock of years of secondary education.
  12. LTOTED — Barro and Lee dataset — Logarithm of total stock of years of primary and secondary education.
- Health
  13. LFEXP — World Development Indicators — Life expectancy at birth (total).
- Internal environment/resources
  14. GINI — Dollar and Kraay/Lynn and Squire — GINI coefficient (initial value).
  14. LLAND — World Development Indicators — Logarithm of arable land per capita, hectares, average over five years.
  14. EHET — Sambanis — Ethnic heterogeneity.
  14. ELFOS — Sambanis — Updated index of ethno linguistics fractionalization.
- Corruption/War
  15. BLK — Easterly and Sewadeh — Ratio of black market rate and official exchange rate minus one.
  15. PW10 — Sambanis — Incidence of civil war in the last 10 years.
- Institutions/governance
  16. DEMOC — Polity IV — Aggregate index of democracy.
  16. DEMOCLAG — Polity IV — Aggregate index of democracy, lagged once.
  16. POLITY — Polity IV — Aggregate index of autocracy and democracy.
  16. POLITYLAG — Polity IV — Aggregate index of autocracy and democracy, lagged once.
  16. CHANGE — Polity IV — Annual change in the Polity index.
- Geography/Physical Factors
  17. CENLAT — Gallup, Mellinger, Sachs — Latitude of country centroid.
  17. DISTCR — Gallup, Mellinger, Sachs — Mean distance to nearest ice-free coastline or sea-navigable river.
  17. CENCR — Gallup, Mellinger, Sachs — Distance of country's centroid to nearest coast/sea-navigable river.
  17. POP100CR — Gallup, Mellinger, Sachs — Percentage of population within 100 km of coast/sea-navigable river.
  17. TROPICAR — Gallup, Mellinger, Sachs — % Land area in geographical tropics.
  17. LCR100KM — Gallup, Mellinger, Sachs — % Land area within 100 km of ice-free coast/navigable river.
- Dummy variables
  18. EA — East Asia and Pacific Regional Dummy.
  19. ECA — Europe and Central Asia Dummy.
  20. MENA — Middle East and North Africa Dummy.

### Sample Data (Table A1 / Table A2 highlights)
- The sample lists countries and number of observations per country (examples as presented):
  - Albania 1, Algeria 8, Angola 8, Antigua 4, Argentina 8, Armenia 1, Australia 8, Austria 8, Azerbaijan 1, Bangladesh 8, Barbados 8, Belarus 2, Belgium 8, Belize 4, Benin 8, Bolivia 8, Botswana 8, Brazil 8, Bulgaria 1, Burkina Faso 8, Burundi 8, Cambodia 1, Cameroon 8, Canada 8, Cape Verde 8, Central African Republic 8, Chad 8, Chile 8, China 8, Colombia 8, Comoros 8, Congo, Dem. Rep. 8, Congo, Republic of 8, Costa Rica 8, Cote d'Ivoire 8, Croatia 1, Cuba 2, Cyprus 7, Czech Republic 2, Denmark 8, Dominica 3, Dominican Republic 8, Ecuador 8, Egypt 8, El Salvador 8, Equatorial Guinea 8, Estonia 1, Ethiopia 8, Fiji 8, Finland 8, France 8, Gabon 8, Gambia, The 8, Germany 6, Ghana 8, Greece 8, Grenada 4, Guatemala 8, Guinea 8, Guinea-Bissau 8, Guyana 8, Haiti 7, Honduras 8, Hong Kong 8, Hungary 6, Iceland 8, India 8, Indonesia 8, Iran 8, Ireland 8, Israel 8, Italy 8, Jamaica 8, Japan 8, Jordan 8, Kazakhstan 1, Kenya 8, Korea, Republic of 8, Kyrgyzstan 1, Latvia 2, Lesotho 8, Lithuania 1, Luxembourg 8, Macao 2, Macedonia 1, Madagascar 8, Malawi 8, Malaysia 8, Mali 8, Mauritania 8, Mauritius 8, Mexico 8, Moldova 1, Morocco 8, Mozambique 8, Namibia 8, Nepal 8, Netherlands 8, New Zealand 8, Nicaragua 8, Niger 8, Nigeria 8, Norway 8, Pakistan 8, Panama 8, Papua New Guinea 8, Paraguay 8, Peru 8, Philippines 8, Poland 6, Portugal 8, Puerto Rico 5, Romania 8, Russia 1, Rwanda 8, Sao Tome and Principe 5, Senegal 8, Seychelles 8, Sierra Leone 6, Singapore 7, Slovak Republic 2, Slovenia 2, South Africa 8, Spain 8, Sri Lanka 8, St. Kitts & Nevis 4, St. Lucia 4, St. Vincent & Grenadines 4, Sweden 8, Switzerland 8, Syria 8, Taiwan 7, Tanzania 8, Thailand 8, Togo 8, Trinidad & Tobago 8, Tunisia 7, Turkey 8, Uganda 8, Ukraine 2, United Kingdom 8, United States 8, Uruguay 8, Venezuela 8, Vietnam 1, Yemen 2, Zambia 8, Zimbabwe 8.
- Memorandum: Number of countries in groups presented in Table A4:
  - Number of countries: 149, 94, 74, 24, 1 (as presented across columns).

### Sample Data Unweighted Averages (Table A4)
- Dependent Variable
  - LNYT-LNY0: ALL 0.08, Non-oil 0.07, Intermediate 0.08, OECD 0.11, Africa 0.03
- Explanatory Variables (group averages as presented)
  - 1 LNY0: ALL 8.14, Non-oil 8.11, Intermediate 8.36, OECD 9.47, Africa 7.27
  - 2 LNI: ALL 2.55, Non-oil 2.52, Intermediate 2.71, OECD 3.14, Africa 2.06
  - 3 LNNPOPGR: ALL 1.92, Non-oil 1.95, Intermediate 1.93, OECD 1.74, Africa 2.01
  - 4 LNINFL: ALL 0.17, Non-oil 0.17, Intermediate 0.16, OECD 0.07, Africa 0.16
  - 5 BALY: ALL -4.28, Non-oil -4.10, Intermediate -3.76, OECD -2.98, Africa -5.83
  - 6 LNG: ALL 2.88, Non-oil 2.82, Intermediate 2.72, OECD 2.48, Africa 3.01
  - 7 AIDGDP: ALL 6.60, Non-oil 5.52, Intermediate 3.98, OECD 0.35, Africa 11.87
  - 8 BRMY: ALL 40.41, Non-oil 37.13, Intermediate 40.76, OECD 57.60, Africa 25.02
  - 9 DSGDP: ALL 5.31, Non-oil 5.56, Intermediate 6.03, OECD 4.38, Africa 4.55
  - 10 OPEN: ALL 69.26, Non-oil 58.57, Intermediate 57.42, OECD 44.78, Africa 73.73
  - 11 TOTGR: ALL 1.07, Non-oil 0.75, Intermediate 0.84, OECD 0.31, Africa 1.90
  - 12 LTOTED: ALL 1.26, Non-oil 1.22, Intermediate 1.44, OECD 1.96, Africa 0.48
  - 13 LFEXP: ALL 60.23, Non-oil 59.79, Intermediate 63.09, OECD 73.34, Africa 47.29
  - 14 GINI: ALL 38.77, Non-oil 39.33, Intermediate 39.12, OECD 32.14, Africa 47.15
  - 14 LLAND: ALL -1.58, Non-oil -1.53, Intermediate -1.53, OECD -1.23, Africa -1.32
  - 15 BLK: ALL 122.90, Non-oil 56.58, Intermediate 52.66, OECD 1.50, Africa 56.85
  - 15 PW10: ALL 0.19, Non-oil 0.21, Intermediate 0.19, OECD 0.05, Africa 0.22
  - 16 POLITYLAG: ALL 10.71, Non-oil 10.95, Intermediate 2.28, OECD 8.74, Africa -3.97
  - 16 CHANGE: ALL 0.07, Non-oil 0.08, Intermediate 0.09, OECD 0.06, Africa 0.04
  - 17 TROPICAR: ALL 55.16, Non-oil 58.32, Intermediate 50.51, OECD 1.76, Africa 91.65
  - 17 LCR100KM: ALL 46.57, Non-oil 43.33, Intermediate 51.05, OECD 65.85, Africa 18.49
- Notes:
  - See Table A2 for details on sample groupings.
  - The average number of periods is the average number of observations of each group in the data set. A period consists of two observations that are, at minimum five years apart.

### Growth Regressions Compilation (Table A3: Correlations from the Literature)
- Solow determinants and initial income
  - Initial Income: Barro (1991), (1997); Barro and Sala-i-Martin (1992); Caselli, Esquivel and Lefort (1996); Kormendi and Meguire (1985); Levine and Renelt (1992); Mankiw, Romer and Weil (1992) — Negative (significant) / Negative (robust) as reported.
  - Investment: Barro (1991); Barro (1997); Barro and Lee (1994); Caselli, Esquivel and Lefort (1996); Levine and Renelt (1992); Mankiw, Romer and Weil (1992) — Positive (significant) / Positive (not significant) / Positive (robust) as reported.
  - Population growth: Barro and Lee (1994) Positive (not significant); Kormendi and Meguire (1985) Negative (significant); Levine and Renelt (1992) Negative (not robust); Mankiw, Romer and Weil (1992) Negative (significant).
- Macroeconomic stability
  - Inflation and growth/levels/variability: Mixed negative/positive findings across Kormendi and Meguire (1985); Barro (1997); Bruno and Easterly (1995); Fischer (1993); Levine and Renelt (1992).
  - Government deficit as share of GDP: Easterly and Levine (1997), Fischer (1993) Negative (significant); Levine and Renelt (1992) Negative (not robust).
  - Government consumption to GDP: Mixed findings across Kormendi and Meguire (1985); Barro (1991),(1997); Barro and Lee (1994); Caselli, Esquivel and Lefort (1996); Levine and Renelt (1992).
- Foreign Aid
  - External transfers: Easterly, Kremer, Pritchett and Summers (1993) Mixed (not significant); Burnside and Dollar (1998) Positive (significant).
- Financial development
  - Financial sophistication and money: Easterly and Levine (1997); King and Levine (1993); Levine and Zervos (1993); Kormendi and Meguire (1985) — Positive (significant/robust) / Positive (not significant).
- External debt
  - Dummy and debt levels: Easterly, Kremer, Pritchett and Summers (1993) Negative (not significant); Patillo, Poirson and Ricci (2002) Debt to GDP (Level above 35%) Negative (significant).
- Trade regime
  - Openness and trade shares: Frankel and Romer (1996); Frankel, Romer and Cyrus (1996); Harrison (1995); Sachs and Warner (1995) — Positive (significant) / Not robust in some studies.
- External environment
  - Terms of trade improvement: Barro (1997); Barro and Lee (1994); Caselli, Esquivel and Lefort (1996); Easterly, Kremer, Pritchett and Summers (1993); Fischer (1993) — Positive (significant or not significant depending on study).
- Human capital/education proxies
  - Overall level and primary/secondary levels: Azariadis and Drazen (1990); Barro (1991); Easterly and Levine (1997); Levine and Renelt (1992); Mankiw, Romer and Weil (1992); Barro (1997); Sachs and Warner (1995) — Mixed Positive/Negative (significance varies by level).
- Health
  - Various proxies: Barro (1997); Barro and Lee (1994); Knowles and Owen (1995) — Positive (significant).
- Internal environment/resources
  - GINI coefficient and fractionalization: Alesina and Rodrik (1994) Negative (significant); Forbes (1997) Positive (significant); Easterly and Levine (1997) Ethno-linguistic fractionalization Negative (significant).
- Corruption/War
  - Black market premium and civil war incidence: Many studies report Negative (significant) effects on growth (Barro (1996); Barro and Lee (1994); Easterly and Levine (1997); Fischer (1993); Harrison (1995); Levine and Zervos (1992); Sala-i-Martin (1997); Sala-i-Martin (1997) for civil war incidence).
- Institutions/governance
  - Civil liberties, political rights, overall indices, political instability: Mixed findings across Barro and Lee (1994); Kormendi and Meguire (1985); Levine and Renelt (1992); Sala-i-Martin (1997); Sachs and Warner (1995); Alesina, Ozler, Roubini and Swagel (1996).
- Geography/Physical Factors
  - Latitude, location and climate, tropics: Sala-i-Martin (1997) Positive (significant); Gallup, Sachs, Mellinger (1999) Negative (significant); Hall and Jones (1997) Tropics Negative (significant).
- Dummy variables/regional effects
  - East Asia and Pacific, Latin America and Caribbean, Sub-Saharan Africa dummies: Mixed positive/negative and significance across Barro (1997); Barro and Lee (1994); Easterly and Levine (1997); Sala-i-Martin (1997).

### Notes on Correlations
- Correlations include results from Durlauf and Quah (1999) and author's calculations as noted.

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### Appendix II — Computational Aspects (LIBMA and Computed Statistics)
### Bayesian Hypothesis Testing and BMA / LIBMA formulation
- Posterior for parameters θ given data D:
  - p(θ|D) = p(D|θ) p(θ) / ∫ p(D|θ) p(θ) dθ
- Posterior probability of model M1 vs M2:
  - p(M1|D) = p(D|M1) p(M1) / [p(D|M1) p(M1) + p(D|M2) p(M2)]
- Posterior odds ratio (M2 against M1):
  - p(M2|D) / p(M1|D) = [p(D|M2) / p(D|M1)] × [p(M2) / p(M1)]
  - First term is Bayes factor B21; second term is prior odds ratio.
- Marginal likelihood:
  - p(D|Mk) = ∫ p(D|θk, Mk) p(θk|Mk) dθk
- BIC approximation to Bayes factor:
  - BIC = 2 log B21 = 2[log p(D|θ̂2, M2) − log p(D|θ̂1, M1)] − (d2 − d1) log n + O(n−1/2)
- Bayesian Model Averaging posterior for quantity of interest Δ:
  - p(Δ|D) = Σ_{k=1}^K p(Δ|D, Mk) p(Mk|D)
- Posterior model probabilities via BIC:
  - p(Mk|D) = exp(−1/2 BICk) p(Mk) / Σ_{j=1}^K exp(−1/2 BICj) p(Mj)
- LIBMA modification (limited information):
  - Replace BIC with LIBIC to obtain LIBMA:
    - p(Mk|D) = exp(−1/2 LIBICk) p(Mk) / Σ_{j=1}^K exp(−1/2 LIBICj) p(Mj)
  - LIBMA incorporates a dynamic panel GMM estimator and a Bayesian robustness check across a universe of models.

### Prior model probabilities and prior odds
- Represent model Mj as length-k* binary vector; each variable has equal inclusion probability.
- Prior probability of model Mj:
  - p(Mj) = (k k* )^{k_j} (1 − k k* )^{1−k_j} (as presented)
  - (notation in source: p(M_j) = (k/k*)^{k_j} (1 - k/k*)^{1-k_j} — preserved as in source formatting)
- Prior odds ratio between models Mj and Ml:
  - p(Mj) / p(Ml) = (k k* )^{k_j − k_l} (1 − k k* )^{k_j − k_l}
- k* is total number of regressors; k is researcher's prior about the number of regressors with non-zero coefficients; kj is number of included variables in model Mj.
- Posterior model probabilities when exhaustive enumeration is possible (K = 2^{k*}):
  - p(Mj|D) = exp(−1/2 LIBICj) p(Mj) / Σ_{l=1}^{2^{k*}} exp(−1/2 LIBICl) p(Ml)

### Posterior summaries and inclusion measures
- Posterior mean across models:
  - E(θk|D) = Σ_{j=1}^{2^{k*}} p(Mj|D) E(θk|D, Mj)
- Posterior variance:
  - Var(θk|D) = Σ_{j=1}^{2^{k*}} p(Mj|D) [ Var(θk|D, Mj) + E(θk|D, Mj)^2 ] − E(θk|D)^2
- Posterior inclusion probability:
  - p(θk ≠ 0 | D) = Σ_{θk ≠ 0} p(Mj|D)
  - If p(θk ≠ 0 | D) > p(θk ≠ 0) = k/k* then variable has high marginal contribution.
- Posterior mean and variance conditional on inclusion:
  - E(θk|D) / Σ_{θk ≠ 0} p(Mj|D) and Var(θk|D) / Σ_{θk ≠ 0} p(Mj|D) respectively (as ratios of unconditional quantities to inclusion probability).
- Sign certainty probability:
  - sign certainty for θk = p[ sgn(θk) = sgn E(θk|D) | D, θk ≠ 0 ] = Σ_{j=1}^{2^{k*}} p(Mj|D) { p[ sgn(θk) = sgn E(θk|D) | Mj, D ] }

### Computed Statistics for Robustness Simulations
- Posterior odds ratios B_jl = p(Mj|D) / p(Ml|D) = [p(D|Mj) / p(D|Ml)] × [p(Mj) / p(Ml)].
- Bayes factors approximated via BIC (or LIBIC in limited information setting).
- Prior inclusion parameter k is the primary arbitrary prior; robustness checks vary k to assess sensitivity of posterior model probabilities and derived statistics.
- When exhaustive calculation is feasible, posterior model probabilities, posterior means, variances, inclusion probabilities, conditional moments, and sign-certainty probabilities are computed by summing over the full model space using LIBIC-weighted model weights.

*Source: _wp0518 - Appendix I*

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