## Annex I. Hodrick and Prescott decomposition

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### Introduction — context, questions, and contributions
- Context and motivation:
  - Frequency and severity of economic, financial and health crises have raised questions about countries' macroeconomic vulnerability and policies to build resilience, particularly in developing countries.
  - Developing countries are generally disproportionately affected by negative shocks, increasing volatility of production and amplifying vulnerability.
- Productive capacities concept and data:
  - UNCTAD's Productive Capacities Index (PCI) (2021) measures "productive resources, entrepreneurial capabilities and production linkages" that determine a country's ability to produce goods and services.
- Research question:
  - Whether strengthening productive capacities could mitigate the effects of vulnerability on growth volatility in Sub-Saharan Africa (SSA).
- Contributions:
  - Uses UNCTAD PCI (2021) to measure productive capacities in SSA.
  - Examines interaction between economic vulnerability, productive capacities, and growth volatility.

### Stylized facts: growth trends and economic vulnerability in SSA
- Growth periods and key figures:
  - 2000–2008: strong growth; "GDP per capita in the region reached 3.2% in 2007."
  - 2009: "Economic growth fell considerably, from 3.2% of GDP per capita in 2007 to 0.19% in 2009."
  - 2010: growth averaged "3.1% in 2010."
  - 2016: falling commodity prices destabilized resource-dependent countries.
  - 2018: "GDP growth slowly recovered to positive levels."
  - 2020 (COVID-19): "SSA experienced a recession, with GDP per capita falling by 4.6% in 2020," compared with "Latin America and the Caribbean, where growth fell by 7.3% of GDP."
- Economic vulnerability and productive capacities (2018 comparisons):
  - "In 2018, the region had a productive capacities level of around 31, compared with 49, and 53 respectively for Latin America and Caribbean, and East Asia and Pacific."
  - PCI dimension gaps largest in ICT; deficits also in transport infrastructure (TR), energy (EN) and human capital (HC).
  - Natural capital (NC), structural change (SCH), institutions (INST), and private sector are above average; institutions have trended downward since 2012.

### Theoretical background and literature review: vulnerability, productive capacities, and volatility
- Definitions:
  - Economic vulnerability: risk of exposure to unforeseen exogenous shocks; three components — magnitude of exogenous shocks; exposure; resilience.
  - Volatility: variability over time relative to mean or trend.
  - PCI components: structural change, human capital, natural capital, energy, ICT, transport, institutions, private sector.
- Mechanisms (component-level):
  - Structural change: movement to higher-productivity activities reduces volatility.
  - Physical capital (energy, ICT, transport): ICT diffusion linked to productivity and may affect output fluctuations.
  - Institutions: good institutions reduce uncertainty and volatility; democracy tends to reduce volatility.
  - Private sector/financial development: can absorb shocks via diversification and risk sharing; effects may be mixed and subject to thresholds.
  - Human capital: promotes diversification and reduces volatility.
  - Natural capital/resource dependence: higher natural resource shares often increase volatility through lower export diversification.
- Hypothesis:
  - "Greater productive capacities are likely to help reduce fluctuations in economic growth, i.e., the volatility of economic growth."

### Role of productive capacities in the vulnerability–volatility relationship
- Conceptual framework:
  - Vulnerability increases volatility via domestic shocks (fiscal instability, social conflicts) and exogenous shocks (commodity prices, global interest rates, natural disasters).
  - Productive capacities are resilience factors that can mitigate amplification of shocks.
- Specific mitigating mechanisms:
  - Institutions: democratic consensus reduces shock-induced volatility.
  - Financial sector: bank credit smooths production fluctuations by providing short-term loans.
  - Human capital and ICT: enhance capacity to respond to shocks and support delivery of critical services.
- General proposition:
  - "Growth is less volatile when the economy is less vulnerable and productive capacities have developed."

### Methodology and data
- Data sources and variables:
  - Data from World Bank, FERDI, UNCTAD. Variables: growth volatility, economic vulnerability (EVI), productive capacities (PCI), controls (inflation volatility, trade openness, credit, GDP per capita, government expenditure).
- Measurement:
  - Growth volatility: "rolling standard deviations of GDP per capita growth rates over five-year periods (Le, 2020)."
  - Economic vulnerability: Economic Vulnerability Index (EVI) from UNCDP and FERDI; includes exposure and shock components.
  - PCI: UNCTAD PCI with eight components, each scored 0–100; composite index uses these scores.
- Empirical model:
  - Equation (1): σ_it = α σ_i,t−1 + β′ X_it + γ EVI_it + θ PCI_it + ε_it
  - Equation (2): σ_it = α σ_i,t−1 + β′ X_it + γ EVI_it + θ PCI_it + τ (PCI∗EVI_it) + ε_it
  - Marginal effect: ∂σ/∂EV = γ + τ PCI; productive capacities expected to reduce the marginal effect of economic vulnerability (τ < 0).
- Estimation:
  - Two-stage system GMM (Arellano and Bover, 1995; Blundell and Bond, 1998) with Windmeijer (2005) finite-sample correction; Sargan/Hansen and Arellano-Bond tests reported; collapse option used to limit instruments.

### Key statistics and data summary (preserved exact values)
- Vulnerability index: average 38.70; maximum 70.04 (Gambia, 2015); minimum 16.38 (Côte d'Ivoire, 2016); std. dev. 10.3.
- Volatility: mean 3.1; Std. Dev. 3.0; Min 0.1; Max 20.0.
- GDP per capita: mean 2182.8; Std. Dev. 2997.5; Min 281.9; Max 16628.1.
- Trade: mean 73.5; Std. Dev. 41.5; Min 1.3; Max 348.0.
- Inflation volatility: mean 4.6; Std. Dev. 12.4; Min 0.2; Max 237.0.
- Government expenditure: mean 14.7; Std. Dev. 6.7; Min 2.0; Max 43.5.
- Credit: mean 18.1; Std. Dev. 15.6; Min 1.1; Max 106.3.
- shock: mean 38.9; Std. Dev. 17.4; Min 2.4; Max 88.2.
- Exposure to shock: mean 38.3; Std. Dev. 9.3; Min 22.8; Max 64.7.
- PCI (Productive Capacities Index): mean 23.1; Std. Dev. 4.1; Min 12.6; Max 37.4.
- PCI component means and ranges:
  - Human capital: mean 34.7; Std. Dev. 5.8; Min 20.4; Max 51.1.
  - Natural Capital: mean 57.9; Std. Dev. 8.7; Min 32.9; Max 96.7.
  - Transport: mean 12.1; Std. Dev. 5.6; Min 4.4; Max 46.6.
  - ICT: mean 5.2; Std. Dev. 2.5; Min 2.8; Max 17.1.
  - Institutions: mean 41.5; Std. Dev. 12.4; Min 18.7; Max 74.4.
  - Private Sector: mean 70.3; Std. Dev. 8.2; Min 38.2; Max 87.8.
  - Structural Change: mean 14.1; Std. Dev. 3.8; Min 1.5; Max 21.3.
  - Energy: mean 19.4; Std. Dev. 6.2; Min 5.6; Max 59.2.

### Econometric results — effect of economic vulnerability on growth volatility (GMM estimates)
- Model validity:
  - Sargan/Hansen p-values well above 10%; Arellano-Bond AR(2) p-values above 10% in reported specifications.
- Economic vulnerability:
  - Positive and statistically significant at 1% in all specifications.
  - Example: Column 1 economic vulnerability coefficient 0.039*** (standard error 0.005). Interpretation: increase of 10 units in economic vulnerability index → increase in growth volatility of around 0.4 units.
- Lagged volatility (L.volatility) coefficients reported: 0.509***, 0.696***, 0.590***, 0.564***, 0.564***, 0.534***.
- GDP per capita:
  - Negative and statistically significant in several specifications (e.g., -0.038***; other reported values include -0.440***, -0.176***, -0.082, -0.297**).
- Trade openness:
  - Positive and significant in several specifications (e.g., 0.304***, 0.336***, 0.239***, 0.453***).
- Inflation volatility:
  - Positive and significant when included; reported coefficients: 0.025***, 0.039***, 0.038***. Interpreted as increase of inflation volatility by 10 units → increase in growth volatility of around 0.25 units.
- Credit (bank credit to private sector):
  - Negative where included (e.g., -0.007**, -0.017***), suggesting higher credit reduces volatility.
- Government expenditure:
  - Positive and significant where included (coefficient 0.066***), suggesting discretionary fiscal policy may increase volatility.
- Table 2 sample sizes and diagnostics:
  - Observations: 597; 595; 565; 553; 513; 500 across columns.
  - Countries: 45; 44; 42; 42; 41; 41.
  - AR(2) p-values: 0.173; 0.182; 0.208; 0.366; 0.654; 0.546.
  - Hansen p-values: 0.270; 0.367; 0.242; 0.365; 0.316; 0.339.

### Effects of productive capacities on growth volatility
- Aggregate PCI:
  - Aggregate productive capacities coefficient -0.064** (std. error 0.029) — negative and significant at 5% (Table 3, column 1).
- PCI component effects (selected coefficients and significance):
  - Human Capital: -0.042** (significant at 5%).
  - Natural Capital: 0.012 (positive, not significant).
  - Transport: -0.037*** (significant).
  - ICT: -0.076*** (significant).
  - Institutions: -0.072*** (significant).
  - Private Sector: -0.064*** (significant).
  - Structural Change and Energy: mixed or not significant in many specifications.
- HP-filter volatility (Table 6) confirms main results:
  - Productive capacities (aggregate): -0.102**.
  - Human Capital: -0.186** (in specific column).
  - Transport: -0.160***.
  - ICT: -0.345***.
  - Institutions: -0.035** (in specific column).
  - Energy: mixed signs (e.g., 0.057 in one spec; -0.030** in another).

### Interactive effects — productive capacities mitigate vulnerability
- Interaction term results (selected coefficients):
  - Productive capacities × Economic Vulnerability: -0.003** (Table 4).
  - Human Capital × EV: -0.002***.
  - Transport × EV: -0.001***.
  - ICT × EV: -0.001**.
  - Institutions × EV: -0.001***.
  - Private Sector × EV: -0.002*.
  - Structural Change × EV: 0.003*** (positive in one specification).
  - Energy × EV and Natural Capital × EV: reported as -0.001 (not significant in summary).
- HP-filter volatility interactions (Table 7) similar:
  - Productive capacities × EV: -0.003***.
  - Human Capital × EV: -0.003***.
  - Transport × EV: -0.002*.
  - ICT × EV: -0.006***.
  - Institutions × EV: -0.001*.
  - Private Sector × EV: -0.001*.
- Interpretation:
  - Productive capacities reduce the marginal effect of economic vulnerability on growth volatility; higher PCI levels mitigate vulnerability transmission.

### Robustness and sensitivity checks
- Alternative volatility measure:
  - Hodrick-Prescott (HP) filter used to compute volatility as standard deviation of the cycle; results in Tables 5–7 confirm main findings.
- Outlier sensitivity:
  - Mauritius and Lesotho identified as influential for many PCI indicators; excluding them yields results largely consistent with full-sample findings.
- Autocorrelation checks:
  - Autocorrelation tests up to order four validate absence of autocorrelation of errors of order 4.

### Conclusions and policy implications
- Main empirical conclusions:
  - Economic vulnerability contributes to higher growth volatility in SSA.
  - Productive capacities reduce growth volatility.
  - Productive capacities mitigate the adverse effect of economic vulnerability on growth volatility.
- Policy recommendations (preserved wording and domains):
  - ICT: strengthen infrastructure, improve access to electronic communications services, reduce telecommunication costs.
  - Transport: open up production areas, develop access corridors to ports for landlocked countries, improve the quality of air transport, promote river transport.
  - Energy: increase supply of electricity, improve quality of product offered, reduce electricity costs, facilitate access to electricity services.
  - Human capital: improve quality of education, public health and research and development (R&D).
  - Private sector: improve business environment by strengthening technical, human and financial capacities of institutions serving the private sector; facilitate access to financial services by reducing information asymmetry concerning SMI/SMEs.
  - Structural transformation: promote (i) diversification and sophistication of exports; (ii) strengthening links between production, processing and consumption; (iii) building value chains; (iv) strengthening links between large and small companies and between domestic and foreign companies.
  - Natural resources and agriculture: enhance value of natural resources; improve productivity of agricultural sector and its resilience to climate shocks.
  - Institutions and governance: create a stable environment conducive to growth by strengthening governance effectiveness, reducing corruption, improving political stability, eradicating insecurity and violence.
- Study limitations and future research:
  - Study period limited by data availability; future research should cover longer time series.
  - No country-level analysis in this study; future research can perform country-specific analyses.

### Annex: Hodrick–Prescott (HP) decomposition (methodological details)
- Definition:
  - Decomposes series X_t into non-stationary trend T_t and stationary cyclical component C_t: X_t = T_t + C_t.
- HP filter program (as written in source):
  - Minimize sum_{t=1}^N (X_t − T_t)^2 + λ sum_{t=2}^{N−2} (Δ^2 T_t)^2.
- Interpretation:
  - First term minimizes variance of cyclical component; second term smoothes evolution of trend.
- Smoothing parameter λ:
  - As λ → ∞: trend approaches simple linear time trend.
  - As λ → 0: filtered series approaches original series.
- Choice in literature:
  - Hodrick and Prescott recommend λ = 100 for annual data.
  - Other suggested ranges: between 100 and 400; between 6 and 10.
- Choice in this study:
  - This study uses λ = 100.

*Source: wpiea2024169-print-pdf - Annex I. Hodrick and Prescott decomposition*

### Annex I. Hodrick and Prescott decomposition ............................................................................

### Annex I. Hodrick and Prescott decomposition

### Figures and Illustrations
- Figure 1: Real GDP growth in SSA compared with other regions
- Figure 2: Comparative trends in the level of economic vulnerability in SSA with other regions and
- Figure 3. Comparison of productive capacities index in SSA and other regions
- Figure 4: Evolution of the productive capacities of SSA
- Figure 5: Productive capacities index and its components
- Figure 6: Correlations between the variables of productive capacity, economic vulnerability and growth

### Tables (selected)
- Table 1: Statistics
- Table 2: effects of economic vulnerabilities on growth volatility
- Table 3: Effects of Productive Capacities on growth volatility in SSA
- Table 4: Consideration of interactive effects
- Table 5: effects of economic vulnerabilities on growth volatility (using the HP filter as an alternative
- Table 6: Effects of Productive Capacities on growth volatility in SSA (using the HP filter as an alternative measure of volatility)
- Table 7: Consideration of interactive effects (using the HP filter as an alternative measure of volatility)

### Introduction — context, questions, and contributions
- Context and motivation:
  - The frequency and severity of economic, financial and health crises in recent decades have raised important questions about countries' macroeconomic vulnerability and the appropriate policies needed to build economic resilience to future shocks, particularly in developing countries (see Azomahou et al., 2021; Gnangnon, 2021).
  - Developing countries are generally disproportionately affected by negative shocks and do not have adequate resources to overcome them, increasing the volatility of their production and amplifying their economies' vulnerability to exogenous shocks.
- Productive capacities concept and data:
  - UNCTAD launched a new productive capacities index in 2021 to help researchers and policymakers assess the performance of productive capacities.
  - Productive capacities are defined as "the productive resources, entrepreneurial capabilities and production linkages that together determine a country's ability to produce goods and services and enable it to grow and develop" (UNCTAD, 2006; 2021.).
  - Lack of comparable cross-country data on productive capacities has historically hindered empirical assessment of their role in improving resilience.
- Problem statement for SSA:
  - Africa has the highest proportion of vulnerable countries per the economic vulnerability index drawn up by the United Nations Committee for Development Policy (UNCDP) and the Foundation for International Development Studies and Research (FERDI); African countries have a significantly higher structural economic vulnerability index than other developing economies (Azaroual, 2022).
  - When only sub-Saharan Africa (SSA) is considered, the gap in vulnerability is even greater.
  - Historical data show SSA has relatively low and volatile growth rates compared to other regions (appendix Figure 1).
  - Economies with high volatility record poor growth performance (Aghion et al., 2010; Aizenman et al., 2018; Imbs, 2007; Ramey and Ramey, 1995), with downstream effects on poverty, unemployment, income inequality and human capital accumulation (Camarena et al., 2019; Carr and Wiemers, 2018; Guillaumont et al., 2009; Aye et al., 2020; Chauvet et al., 2019; Fang et al., 2015; Hausmann and Gavin, 1996).
- Research question and rationale:
  - Whether strengthening productive capacities could mitigate the effects of vulnerability on growth volatility in SSA is the central question addressed.
  - The "Singapore paradox" (Briguglio et al., 2009) illustrates that some small, highly exposed economies achieved relatively high GDP per capita and growth despite exposure to exogenous shocks, potentially due to offsetting factors like productive capacities.
- Contributions of this paper:
  - Examines the interaction between economic vulnerability and productive capacities and the interaction between productive capacities and growth volatility.
  - Uses the recently updated UNCTAD Productive Capacities Index (2021) as a first attempt in SSA to measure productive capacities, capturing multiple multidimensional aspects.
  - Assesses direct and indirect effects of economic vulnerability on macroeconomic volatility in SSA countries.
- Organization:
  - After the introductory section, Section 2 presents stylized facts; Section 3 discusses theoretical background and the review of the empirical literature.

*Source: wpiea2024169-print-pdf - Annex I. Hodrick and Prescott decomposition*

### Section 4 presents the methodology and data. The results and discussion are presented in section 5, followed

### Section 4 presents the methodology and data. The results and discussion are presented in section 5, followed by the conclusion in section 6. (wpiea2024169-print-pdf)

### Stylized facts: growth trends and economic vulnerability in Sub-Saharan Africa (SSA)
- Three main growth periods in SSA:
  - 2000-2008: marked by significant economic growth; "GDP per capita in the region reached 3.2% in 2007."
    - Drivers: surge in commodity prices, marked increase in Foreign Direct Investment (AfDB, 2015); intensified trade partnerships; improvement in quality of governance (McMillan and Harttgen, 2014).
  - 2009 financial crisis: "Economic growth fell considerably, from 3.2% of GDP per capita in 2007 to 0.19% in 2009."
  - 2010-2015: growth averaged "3.1% in 2010." Subsequent years:
    - 2016: falling commodity prices destabilized many resource-dependent countries.
    - 2018: "GDP growth slowly recovered to positive levels" aided by resilient domestic demand and higher oil prices.
    - 2020 (COVID-19): "SSA experienced a recession, with GDP per capita falling by 4.6% in 2020," compared with "Latin America and the Caribbean, where growth fell by 7.3% of GDP."
- Economic vulnerability:
  - On average, economic vulnerability in SSA is higher than in other regions (Figure 2; 2000-2018 trends shown).
  - The paper notes current global shocks (Russo-Ukrainian crisis) transmitted through "energy and non-energy commodity prices, supply chain disruptions and financial markets" (AfDB, 2021).
- Productive capacities (2018 comparisons):
  - "In 2018, the region had a productive capacities level of around 31, compared with 49, and 53 respectively for Latin America and Caribbean, and East Asia and Pacific."
  - Cross-country variation: landlocked countries (Chad, Niger, Mali) performed poorly in 2018; Mauritius, Seychelles, Botswana and Cape Verde topped rankings in most categories.
  - Non-uniform performance across PCI categories: Zimbabwe ranks last in institutions but seventh in structural change.
- Evolution across PCI dimensions:
  - SSA gaps are largest in Information and Communication Technology (ICT); deficits also in transport infrastructure (TR), energy (EN) and human capital (HC).
  - "While ICT, energy and human capital have been growing since 2000, transport infrastructure has tended to deteriorate since 2013."
  - Natural capital (NC), structural change (SCH), institutions (INST), and the private sector are above average; institutions have shown a downward trend since 2012 (attributed to political and security crises).

### Theoretical background and literature review: vulnerability, productive capacities, and volatility
- Definitions and relationships:
  - Economic vulnerability: risk of exposure to unforeseen exogenous shocks (Guillaumont, 2006). Three components: magnitude of exogenous shocks; exposure; resilience.
  - Volatility: variability over time relative to mean or trend (Aizenman et al., 2005a); comprises stability and predictability (Nooruddin, 2010).
  - Stylized link: countries with high vulnerability are likely to experience greater growth volatility.
- Productive capacities (UNCTAD, 2006): eight components — structural change, human capital, natural capital, energy, ICT, transport, institutions, private sector.
- Mechanisms by component:
  - Structural change: movement to higher-productivity activities reduces volatility; evidence that structural transformation can explain a portion of "great moderation" (Moro, 2012 found ~28% for US).
  - Physical capital (energy, ICT, transport): ICT diffusion linked to productivity and may affect output fluctuations (King and Rebelo, 1999; Aghaei and Rezagholizadeh, 2017).
  - Institutions: good institutions reduce uncertainty and volatility; democracy tends to reduce volatility (Mobarak, 2005; Rodrik, 1999; Quinn and Woolley, 2001).
  - Private sector/financial development: can absorb shocks via diversification and risk sharing, but effects may be mixed and subject to thresholds (Acemoglu and Zilibotti, 1997; Sahay et al., 2015).
  - Human capital: promotes diversification and reduces volatility (Güneri and Yalta, 2021; Maggioni et al., 2016).
  - Natural capital/resource dependence: higher natural resource shares often reduce export diversification and increase volatility (Jetter and Ramírez Hassan, 2015).
- Hypothesis derived: "greater productive capacities are likely to help reduce fluctuations in economic growth, i.e., the volatility of economic growth."

### Role of productive capacities in the vulnerability–volatility relationship
- Conceptual framework:
  - Vulnerability increases volatility via domestic shocks (e.g., fiscal policy instability, social conflicts) and exogenous shocks (commodity price instability, global interest rates, natural disasters).
  - Resilience factors (productive capacities) can mitigate the amplification of shocks.
- Specific mechanisms:
  - Institutions: democratic consensus reduces volatility induced by shocks (Rodrik, 1999; Aizenman et al., 2012).
  - Financial sector (private sector): bank credit can smooth production fluctuations by providing short-term loans during terms-of-trade deterioration.
  - Human capital and ICT: enhance capacity to respond to shocks (e.g., pandemics) and support delivery of critical services (UNCTAD, 2021).
- General proposition: "growth is less volatile when the economy is less vulnerable and productive capacities have developed."

### Methodology and data
- Data sources: World Bank; FERDI; UNCTAD. Variables of interest: growth volatility, economic vulnerability, productive capacities. Controls: inflation volatility, trade openness, credit, GDP per capita, government expenditure (described in appendix Table 7).
- Variable measurement:
  - Growth volatility: "rolling standard deviations of GDP per capita growth rates over five-year periods (Le, 2020)."
  - Economic vulnerability: Economic Vulnerability Index (EVI) from UNCDP and FERDI; two components — exposure to shocks (population size, export concentration, share of agriculture/forestry/fisheries in GDP, remoteness) and shock index (natural/climatic shocks measured by average annual percentage of population displaced by natural disasters and instability of agricultural production; trade shocks approximated by instability of exports of goods and services).
  - Productive capacities: UNCTAD's Productive Capacities Index (PCI) with eight components; each component scored 0–100 (excluding the bounds); composite index uses these scores.
- Control variables and expected effects:
  - Inflation volatility: expected positive effect on growth volatility.
  - GDP per capita: higher incomes tend to reduce output volatility.
  - Trade openness: ambiguous effect (can increase exposure to external shocks but also insulate against domestic shocks).
  - Government expenditure: ambiguous effect (can stabilize growth or undermine macro stability).
  - Credit (financial development): ambiguous/mixed effect (can stabilize via risk management; can also increase instability).
- Empirical model (as presented):
  - Equation (1):
    σ_it = α σ_i,t−1 + β′ X_it + γ EVI_it + θ PCI_it + ε_it ...(1)
  - Equation (2):
    σ_it = α σ_i,t−1 + β′ X_it + γ EVI_it + θ PCI_it + τ (PCI∗EVI_it) + ε_it ...(2)
  - Marginal effect of vulnerability on volatility:
    ∂σ/∂EV = γ + τ PCI                                (3)
  - Interpretation: productive capacities are expected to reduce the marginal effect of economic vulnerability (τ < 0). Cases:
    - If γ and τ are all positive (negative): vulnerability increases (decreases) volatility and PCI increases (worsens) this impact.
    - If γ > 0 and τ < 0: vulnerability amplifies volatility but PCI acts as mitigating factor.
- Estimation method:
  - Challenges: omitted variables, reverse causality.
  - Estimator: two-stage system GMM (Arellano and Bover, 1995; Blundell and Bond, 1998), using lagged differences and lagged levels as instruments.
  - Small-sample correction: Windmeijer (2005) finite-sample covariance matrix correction applied to address potential downward bias in estimated standard deviations.
  - Specification tests: Sargan/Hansen test for over-identification; test for no second-order serial correlation in first-differenced residuals.
  - Instrument proliferation: collapse option used; number of lags set so number of instruments < number of countries.

### Results and discussions (preliminary findings)
- Correlations (Figure 6):
  - Strong positive correlation between economic vulnerability and growth volatility.
  - Negative correlation between productive capacities and growth volatility.
  - Country examples:
    - High vulnerability, low PCI, high volatility: Zimbabwe, Eritrea, Gambia.
    - Higher PCI, lower vulnerability, more stable growth: Mauritius, Tanzania.
- Descriptive statistics preview:
  - "Over the period considered, growth volatility has an average value of 3.13 for the region, with maximum and minimum values of 19.97 and" (text truncates here; full min not provided in supplied content).

*Source: wpiea2024169-print-pdf (IMF Working Paper content provided).*

### 0.14 respectively for Equatorial Guinea (2001-2005) and Mauritius (2014-2018). Its dispersion in relation to the

### wpiea2024169-print-pdf - 0.14 respectively for Equatorial Guinea (2001-2005) and Mauritius (2014-2018). Its dispersion in relation to the

### Key statistics and data summary
- Vulnerability index: average 38.70; maximum 70.04 (Gambia, 2015); minimum 16.38 (Côte d'Ivoire, 2016); dispersion (std. dev.) 10.3.
- Volatility: mean 3.1; Std. Dev. 3.0; Min 0.1; Max 20.0.
- GDP per capita: mean 2182.8; Std. Dev. 2997.5; Min 281.9; Max 16628.1.
- Trade: mean 73.5; Std. Dev. 41.5; Min 1.3; Max 348.0.
- Inflation volatility: mean 4.6; Std. Dev. 12.4; Min 0.2; Max 237.0.
- Government expenditure: mean 14.7; Std. Dev. 6.7; Min 2.0; Max 43.5.
- Credit: mean 18.1; Std. Dev. 15.6; Min 1.1; Max 106.3.
- shock: mean 38.9; Std. Dev. 17.4; Min 2.4; Max 88.2.
- Exposure to shock: mean 38.3; Std. Dev. 9.3; Min 22.8; Max 64.7.
- PCI (Productive Capacities Index): mean 23.1; Std. Dev. 4.1; Min 12.6; Max 37.4.
- Component means and ranges:
  - Human capital: mean 34.7; Std. Dev. 5.8; Min 20.4; Max 51.1.
  - Natural Capital: mean 57.9; Std. Dev. 8.7; Min 32.9; Max 96.7.
  - Transport: mean 12.1; Std. Dev. 5.6; Min 4.4; Max 46.6.
  - ICT: mean 5.2; Std. Dev. 2.5; Min 2.8; Max 17.1.
  - Institutions: mean 41.5; Std. Dev. 12.4; Min 18.7; Max 74.4.
  - Private Sector: mean 70.3; Std. Dev. 8.2; Min 38.2; Max 87.8.
  - Structural Change: mean 14.1; Std. Dev. 3.8; Min 1.5; Max 21.3.
  - Energy: mean 19.4; Std. Dev. 6.2; Min 5.6; Max 59.2.
- Observed high gaps between minimum and maximum for categories: natural capital, institutions, private sector, transport, energy, human capital; smaller gaps for ICT and structural change.
- Dispersion (std. dev.) highest in: institutions, human capital, natural capital, private sector.

### Econometric results — effect of economic vulnerability on growth volatility (GMM estimates)
- Model validity: Sargan/Hansen test probabilities well above 10%; Arellano-Bond test probabilities above 10% (model considered valid).
- Economic vulnerability coefficient: positive and statistically significant at 1% in all specifications.
  - Column 1: Economic Vulnerability coefficient 0.039*** (standard error 0.005). Interpretation: increase of 10 units in economic vulnerability index → increase in growth volatility of around 0.4 units.
- Lagged volatility (L.volatility) coefficients across specifications:
  - 0.509***, 0.696***, 0.590***, 0.564***, 0.564***, 0.534*** (standard errors in parentheses).
- GDP per capita effects:
  - Negative and statistically significant in several specifications (e.g., -0.038***; other reported values include -0.440***, -0.176***, -0.082, -0.297**).
- Trade openness:
  - Positive and significant (e.g., 0.304***, 0.336***, 0.239***, 0.453*** in columns where included).
- Inflation volatility:
  - Positive and significant when included; magnitude implies increase of inflation volatility by 10 units → increase in growth volatility of around 0.25 units (as interpreted in text). Specific coefficients reported: 0.025***, 0.039***, 0.038***.
- Credit (bank credit to private sector):
  - Negative coefficient where included (e.g., -0.007**, -0.017***), suggesting easier access to bank credit reduces volatility.
- Government expenditure:
  - Positive and significant where included (coefficient 0.066***), interpreted as discretionary fiscal policy potentially increasing volatility.
- Table 2 model summary statistics (selected):
  - Observations: 597; 595; 565; 553; 513; 500 across columns.
  - Countries: 45; 44; 42; 42; 41; 41.
  - AR(2) p-values: 0.173; 0.182; 0.208; 0.366; 0.654; 0.546.
  - Hansen p-values: 0.270; 0.367; 0.242; 0.365; 0.316; 0.339.

### Effects of productive capacities on growth volatility
- Aggregate PCI:
  - Productive capacities (aggregate) coefficient -0.064** (std. error 0.029) — negative and statistically significant at 5% (Table 3, column 1).
- Component effects (Table 3 highlights):
  - Human Capital: coefficient -0.042** (significant at 5%); development of human capital reduces volatility.
  - Natural Capital: coefficient 0.012 (positive but not significant).
  - Transport: coefficient -0.037*** (significant).
  - ICT: coefficient -0.076*** (significant).
  - Institutions: coefficient -0.072*** (significant).
  - Private Sector: coefficient -0.064*** (significant).
  - Structural Change and Energy: mixed or not significant in many specifications.
- Full specification (column 10) indicates ICT and institutions appear more significant than other categories.
- Table 6 (using HP-filter volatility) confirms:
  - Productive capacities (aggregate) coefficient -0.102**.
  - Human Capital: -0.186** (in specific column).
  - Transport: -0.160***.
  - ICT: -0.345***.
  - Institutions: -0.035** (in specific column).
  - Energy: mixed signs; energy sometimes positive (notably 0.057) or negative (e.g., -0.030** in a specification).
- Overall: productive capacities directly and negatively affect growth volatility.

### Interactive effects — productive capacities mitigate vulnerability
- Interaction terms (Table 4 and Table 7) — coefficients of Productive capacities × Economic Vulnerability and of component × EV are negative and statistically significant:
  - Productive capacities×EV: -0.003** (Table 4).
  - Human Capital×EV: -0.002***.
  - Transport×EV: -0.001***.
  - ICT×EV: -0.001**.
  - Institutions×EV: -0.001***.
  - Private Sector×EV: -0.002*.
  - Structural Change ×EV: 0.003*** (positive in one specification).
  - Energy×EV and Natural Capital×EV: coefficients reported as -0.001 (not significant in summary).
- Using HP-filter volatility (Table 7) similar interaction results:
  - Productive capacities×EV: -0.003***.
  - Human Capital×EV: -0.003***.
  - Transport×EV: -0.002*.
  - ICT×EV: -0.006***.
  - Institutions×EV: -0.001*.
  - Private Sector×EV: -0.001*.
- Interpretation: productive capacities reduce the detrimental effect of economic vulnerability on growth volatility; higher productive capacities provide opportunities to mitigate vulnerability transmission.

### Robustness and sensitivity checks
- Alternative volatility measure: Hodrick-Prescott (HP) filter used to compute volatility as standard deviation of the cycle. Results in Tables 5–7 confirm main findings:
  - Economic vulnerability positively affects growth volatility using HP-filter volatility.
  - Productive capacity indicators (except natural capital, energy, structural change in some specs) have negative impacts on growth volatility.
  - Interaction terms remain negative and significant: productive capacities reduce vulnerability effect on volatility.
- Outlier sensitivity:
  - Mauritius and Lesotho identified as influential for many productive capacities indicators.
  - Excluding Mauritius and Lesotho from the sample: results for productive capacities, vulnerability, and interaction terms remain largely consistent with full-sample results—conclusion not driven by these outliers.
- Autocorrelation checks:
  - Autocorrelation tests up to order four validate absence of autocorrelation of errors of order 4.

### Conclusions and policy implications
- Main empirical conclusions:
  - Economic vulnerability contributes to higher growth volatility in Sub-Saharan Africa (SSA).
  - Productive capacities reduce growth volatility.
  - Productive capacities mitigate the adverse effect of economic vulnerability on growth volatility (both direct and indirect effects documented).
- Policy recommendations (preserve wording and domains as in source):
  - ICT: strengthen infrastructure, improve access to electronic communications services, reduce telecommunication costs.
  - Transport: open up production areas, develop access corridors to ports for landlocked countries, improve the quality of air transport, promote river transport.
  - Energy: increase supply of electricity, improve quality of product offered, reduce electricity costs, facilitate access to electricity services.
  - Human capital: improve quality of education, public health and research and development (R&D).
  - Private sector: improve business environment by strengthening technical, human and financial capacities of institutions serving the private sector; facilitate access to financial services by reducing information asymmetry concerning SMI/SMEs.
  - Structural transformation: promote (i) diversification and sophistication of exports; (ii) strengthening links between production, processing and consumption; (iii) building value chains; (iv) strengthening links between large and small companies and between domestic and foreign companies.
  - Natural resources and agriculture: enhance value of natural resources; improve productivity of agricultural sector and its resilience to climate shocks.
  - Institutions and governance: create a stable environment conducive to growth by strengthening governance effectiveness, reducing corruption, improving political stability, eradicating insecurity and violence.
- Study limitations and future research directions:
  - Study period limited due to data availability; future research should cover longer time series.
  - No country-level (individual country) analysis; future research can perform country-specific analyses.

*Source: IMF Working Paper (content unit: wpiea2024169-print-pdf).*

### Annex I.   Hodrick and Prescott decomposition

### Annex I.   Hodrick and Prescott decomposition

### Definition
- Hodrick and Prescott decompose the evolution of a series into a non-stationary trend component (푇푇푡) and a stationary cyclical component (퐶퐶푡):
  - 푋푋푡 = 푇푇푡 + 퐶퐶푡

### HP filter: optimization/program
- The HP filter isolates the cyclical component by optimizing the following program with respect to 푇푇푡:
  - mmmmm �� ( 푋푋푡 − 푇푇푡 )2 + λ � ( ∆2 푇푇푡 )2 푁푁−2 푡푡=2 푁푁 푡푡=1 �
- Interpretation of terms:
  - The first term minimizes the variance of the cyclical component.
  - The second term smoothes the evolution of the trend component.

### Properties of the smoothing parameter λ
- As λ → ∞:
  - The variance of the growth in the trend component tends towards 0.
  - The trend component (filtered series) approaches a simple linear time trend.
- As λ → 0:
  - The filtered series approaches the original series.
- Implication:
  - The choice of λ requires a trade-off between smoothness of the trend and fidelity to the original series.

### Choices of λ in the literature
- Hodrick and Prescott recommend λ = 100 for annual data.
- Other studies and suggested ranges:
  - Between 100 and 400 (Baxter and King, 1999).
  - Between 6 and 10 (Maravall and Del Rio, 2001).

### Choice in this study
- This study uses λ = 100.

*wpiea2024169-print-pdf - Annex I.   Hodrick and Prescott decomposition*

### 5.713 Rwanda 48.297 Comoros 76.199 Seychelles 17.717

### wpiea2024169-print-pdf - 5.713 Rwanda 48.297 Comoros 76.199 Seychelles 17.717

### Key statistics and ranked entries (excerpt as presented)
- 5.713 Rwanda 48.297 Comoros 76.199 Seychelles 17.717
- 10 Eswatini 5.581 Benin 48.198 Ghana 75.967 Senegal 17.704
- 11 Cote d'Ivoire 5.449 Sao Tome and Pri 47.633 Sierra Leone 75.706 Kenya 16.430
- 12 Senegal 5.410 Zambia 47.494 Guinea 75.598 Sao Tome and Pri 16.092
- 13 Lesotho 5.224 Burkina Faso 46.777 Benin 74.847 Cameroon 15.871
- 14 Zimbabwe 5.065 Malawi 46.434 Mozambique 74.384 Botswana 15.702
- 15 Mauritania 5.041 Mozambique 44.115 Madagascar 74.313 Uganda 15.564
- 16 Nigeria 4.987 Mali 42.742 Nigeria 74.281 Equatorial Guine 15.540
- 17 Kenya 4.934 Madagascar 41.976 Cameroon 73.921 Congo. Rep. 15.068
- 18 Congo. Rep. 4.910 Uganda 41.823 Sao Tome and Pri 73.517 Madagascar 14.919
- 19 Cameroon 4.812 Gabon 41.652 Mauritania 73.436 Zambia 14.851
- 20 Mali 4.805 Gambia. The 41.639 Cote d'Ivoire 73.253 Gabon 14.701
- 21 Equatorial Guine 4.795 Eswatini 41.015 Kenya 73.115 Benin 14.438
- 22 Zambia 4.775 Niger 40.964 Eswatini 72.964 Mauritania 14.422
- 23 Benin 4.676 Kenya 40.406 Gabon 72.450 Guinea 14.250
- 24 Uganda 4.435 Tanzania 38.757 Lesotho 70.548 Congo. Dem. Rep. 14.225
- 25 Togo 4.330 Djibouti 38.512 Equatorial Guine 69.541 Togo 14.093
- 26 Tanzania 4.285 Sierra Leone 38.154 Uganda 69.069 Cote d'Ivoire 14.052
- 27 Angola 4.282 Mauritania 37.759 Malawi 68.889 Gambia. The 13.876
- 28 Burkina Faso 4.281 Togo 35.191 Mali 68.412 Mozambique 13.332
- 29 Rwanda 4.240 Ethiopia 34.194 Ethiopia 67.595 Ghana 13.097
- 30 Sierra Leone 4.221 Cameroon 34.173 Botswana 67.446 Angola 12.691
- 31 Djibouti 4.195 Comoros 34.059 Tanzania 66.722 Rwanda 12.678
- 32 Guinea 4.148 Cote d'Ivoire 32.886 Burkina Faso 66.232 Tanzania 12.668
- 33 Comoros 4.128 Guinea-Bissau 32.191 Rwanda 65.507 Malawi 11.332
- 34 Mozambique 4.126 Angola 30.723 Eritrea 65.356 Comoros 10.683
- 35 Ethiopia 3.749 Congo. Rep. 30.581 Burundi 64.081 Ethiopia 10.593
- 36 Madagascar 3.682 Nigeria 30.163 Guinea-Bissau 63.172 Niger 10.443
- 37 Malawi 3.641 Congo. Dem. Rep. 29.854 Angola 63.011 Nigeria 10.237
- 38 Guinea-Bissau 3.599 Guinea 29.159 Congo. Dem. Rep. 60.451 Burkina Faso 9.890
- 39 Niger 3.567 Burundi 28.068 Niger 59.675 Mali 9.279
- 40 Chad 3.558 Equatorial Guine 25.424 Zambia 58.941 Burundi 8.997
- 41 Congo. Dem. Rep. 3.519 Chad 24.247 Zimbabwe 58.221 Sierra Leone 8.294
- 42 Burundi 3.447 Eritrea 22.996 Congo. Rep. 57.533 Guinea-Bissau 4.595
- 43 Eritrea 3.006 Zimbabwe 22.859 Chad 41.346 Chad 3.633

### Selected observations from the excerpted table
- The content presents multiple country-level numeric entries aligned in columns; each line pairs country names with numeric values exactly as listed above.
- Numeric values are preserved exactly as shown (examples: 5.713; 48.297; 76.199; 17.717; 3.006; 41.346).
- Country name formatting and punctuation (e.g., "Congo. Rep.", "Congo. Dem. Rep.", "Gambia. The", "Equatorial Guine", "Sao Tome and Pri") are preserved as in the source.

### References (selection from the source)
- Acemoglu, D., & Johnson, S. (2005). Unbundling institutions. Journal of political Economy, 113(5), 949‑995.
- Aghion, P., Angeletos, G.-M., Banerjee, A., & Manova, K. (2010). Volatility and growth : Credit constraints and the composition of investment. Journal of Monetary Economics, 57(3), 246‑265.
- Aizenman, J., Edwards, S., & Riera-Crichton, D. (2012). Adjustment patterns to commodity terms of trade shocks : The role of exchange rate and international reserves policies. Journal of International Money and Finance, 31(8), 1990‑2016.
- Guillaumont, P. (2008). An economic vulnerability index : Its design and use for international development policy.
- Hidalgo, C. A., & Hausmann, R. (2009a). The building blocks of economic complexity. Proceedings of the national academy of sciences, 106(26), 10570‑10575.
- Imbs, J. (2007). Growth and volatility. Journal of Monetary Economics, 54(7), 1848‑1862.
- Kose, M. A., Prasad, E. S., & Terrones, M. E. (2003). Financial integration and macroeconomic volatility. IMF Staff papers, 50(Suppl 1), 119‑142.

*Source: wpiea2024169-print-pdf - 5.713 Rwanda 48.297 Comoros 76.199 Seychelles 17.717*

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_Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024169-print-pdf.pdf_