## _wp1212

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---

### I. Central findings and methodological setup
- Central message: volatility of commodity prices and export revenues (CTOT volatility) is a primary adverse channel for growth in primary commodity exporting countries; volatility matters alongside levels of resource revenues (commodity booms).
- Data and sample:
  - Annual data for the period 1970–2007.
  - Panel dataset of 118 countries; primary commodity exporters subset: 62 countries; non-primary exporters: 56 countries.
  - Five-year non-overlapping averages used for System GMM (at most seven observations per country); annual data used for CPMG (countries with at least 25 consecutive observations).
- Econometric approaches:
  - System GMM (slope homogeneous dynamic panel) applied to five-year averaged data to address endogeneity and unobserved country effects; two-step GMM with Windmeijer (2005) correction.
  - Cross-sectionally augmented Pooled Mean Group (CPMG) estimator applied to annual data to allow heterogeneous short-run dynamics and cross-sectional dependence via cross-sectional averages.
- Key interpretation:
  - For the full sample and diversified exporters, CTOT volatility is generally not significantly related to output per capita growth.
  - For the 62 primary commodity exporters, CTOT volatility reduces growth; export diversification (EXPY) raises growth and insures against price fluctuations.
  - Commodity terms of trade growth (g_CTOT) raises growth (commodity booms positive); CTOT volatility offsets positive boom effects, generating the "resource curse" via volatility rather than abundance.

### II. Data construction and volatility measures
- Commodity terms of trade (CTOT) index:
  - Country-specific index constructed from each country’s commodity export- and import-baskets using export/import shares averaged 1970–2007 and a list of 32 commodities (including gold, crude oil, copper, wheat, coffee, aluminum, etc.).
  - g_CTOT,it = Δ lnCTOT_it = Σ_j (X_ij − M_ij) Δ ln(P_jt / MUV_t).
- Volatility measures:
  - Five-year non-overlapping standard deviation of annual g_CTOT (S = 4 for five-year windows).
  - GARCH(1,1) conditional volatility on annual g_CTOT with σ^2_CTOT;it = (1 − π_1 − π_2) σ^2_CTOT;i + π_1 η^2_it−1 + π_2 σ^2_CTOT;it−1; volatility measured as sqrt(σ^2_CTOT;it).
- Constructed inputs and channels:
  - Physical capital stock via perpetual inventory with depreciation δ = 6 percent; investment I_it constructed from PWT 6.3 variables.
  - Human capital H_it = exp(φ(s_it)) using Barro and Lee (2010) schooling series and Psacharopoulos piecewise returns to schooling (0.134 first 4 years, 0.101 next 4 years, 0.068 beyond 8 years).
  - TFP computed from constant returns production function with capital share β = 1/3.

### III. Quantitative evidence — five-year averages (System GMM)
- Main regression (five-year geometric average growth of real GDP per capita):
  - Equation includes lagged GDP per capita, g_CTOT, σ_CTOT, EXPY, and controls (education, trade openness, government burden, lack of price stability).
- Key estimates (selected coefficients reported exactly as in Tables):
  - Table 3, Column [1:1] All 118 Countries:
    - Commodity Terms of Trade Growth: 0.240*** (0.072)
    - Commodity Terms of Trade Volatility: -0.105 (0.081)
    - Export Sophistication Measure, in logs: 4.818*** (1.830)
    - No. Countries/No. Observations: 118/664
    - Hansen Test (p-value): 0.121
    - Serial Correlation: First-order 0.000; Second-order 0.199
  - Table 3, Column [1:2] 62 Commodity Exporters:
    - Commodity Terms of Trade Growth: 0.255*** (0.078)
    - Commodity Terms of Trade Volatility: -0.119** (0.058)
    - Export Sophistication Measure, in logs: 2.787* (1.638)
    - No. Countries/No. Observations: 62/352
    - Hansen Test (p-value): 0.448
    - Serial Correlation: First-order 0.000; Second-order 0.252
    - "Impact of CTOT Growth and Volatility -- -0.312 -"
  - Table 5 (GARCH volatility), Column [3:2] 62 Commodity Exporters:
    - Commodity Terms of Trade Growth: 0.264*** (0.061)
    - Commodity Terms of Trade Volatility: -0.198** (0.099)
    - No. Countries/No. Observations: 62/352
    - "Impact of CTOT Growth and Volatility -- -0.509 -"
- Interpretation:
  - g_CTOT positive and statistically significant in full sample and commodity exporter subsamples.
  - σ_CTOT negative and statistically significant for commodity exporters in multiple specifications; full sample and non-exporters often show negative but insignifcant σ_CTOT.

### IV. Channels — how volatility affects growth (System GMM and robustness)
- Channel equations estimated for growth rates of TFP, physical capital per capita, and human capital per capita.
- Main channel findings (Table 4 and Table 6 highlights):
  - TFP channel:
    - Table 4 [2:1]: Commodity Terms of Trade Growth: 0.113 (0.162); Commodity Terms of Trade Volatility: 0.006 (0.102) — both statistically insignificant for TFP growth.
    - Table 6 [4:1]: Commodity Terms of Trade Growth: 0.104 (0.174); Commodity Terms of Trade Volatility: 0.071 (0.262) — insignificant.
    - Conclusion: little evidence that CTOT volatility reduces growth via TFP (no Dutch-disease effect via measured TFP).
  - Physical capital channel:
    - Table 4 [2:2]: Commodity Terms of Trade Growth: 0.186** (0.093); Commodity Terms of Trade Volatility: -0.181** (0.087).
    - Table 6 [4:2]: Commodity Terms of Trade Growth: 0.250* (0.145); Commodity Terms of Trade Volatility: -0.401** (0.182).
    - Conclusion: robust evidence that CTOT volatility reduces physical capital accumulation and that g_CTOT increases physical capital.
  - Human capital channel:
    - Table 4 [2:3]: Commodity Terms of Trade Volatility: -0.051* (0.029) — negative and significant at 10% in five-year sd specification.
    - Table 6 [4:3]: Commodity Terms of Trade Volatility: -0.026 (0.042) — insignificant with GARCH volatility.
    - Conclusion: evidence that volatility reduces human capital is present in some specifications (five-year sd) but not robust across volatility measures.

### V. Annual data and long-run CPMG results (commodity exporters)
- Sample: 52 commodity exporting countries with at least 25 consecutive annual observations (1971–2007).
- Dynamic stability and homogeneity diagnostics:
  - Error-correction coefficients ϕ_i negative and statistically significant → dynamic stability and conditional convergence.
  - Hausman tests typically do not reject long-run homogeneity for parameters reported; emphasis on CPMG estimates.
- Long-run magnitudes (Table 7 CPMG and Table 8 CPMG):
  - Table 7 CPMG (dependent = growth rate of output per capita):
    - Error Correction Term: -0.131*** (0.017)
    - Commodity Terms of Trade Growth: 0.003* (0.002)
    - Commodity Terms of Trade Volatility: -0.034*** (0.008)
    - Trade Openness: 0.249*** (0.023)
    - Government Burden: -0.274*** (0.027)
    - Lack of Price Stability: -0.544*** (0.059)
    - No. Countries / No. Observations: 52/1813
    - Joint Hausman Test: 7.68 [p= 0:17]
    - "Impact of CTOT Growth and Volatility -- 0.090"
    - Quantitative summary stated: "The overall average negative impact of the two CTOT variables on output growth is -0.09 percent per year."
  - Table 8 CPMG [5:1] Dependent = TFP:
    - Error Correction Term: -0.279*** (0.033)
    - Commodity Terms of Trade Growth: -0.012*** (0.003)
    - Commodity Terms of Trade Volatility: 0.005 (0.007)
    - Trade Openness: 0.133*** (0.031)
    - Government Burden: -0.267*** (0.026)
    - Lack of Price Stability: -0.424*** (0.058)
    - No. Countries / No. Observations: 52/1816
  - Table 8 CPMG [5:2] Dependent = Physical Capital:
    - Error Correction Term: -0.075*** (0.015)
    - Commodity Terms of Trade Growth: 0.007*** (0.002)
    - Commodity Terms of Trade Volatility: -0.018*** (0.005)
    - Trade Openness: 0.542*** (0.032)
    - Government Burden: 0.135*** (0.025)
    - Lack of Price Stability: -0.047* (0.027)
    - No. Countries / No. Observations: 52/1819
- Interpretation:
  - CPMG long-run estimates confirm a statistically significant negative long-run relationship between CTOT volatility and output per capita growth (-0.034*** in Table 7 CPMG) and a negative long-run effect of volatility on physical capital accumulation (-0.018*** in Table 8 [5:2] CPMG).
  - g_CTOT remains positive for output growth and for physical capital accumulation in CPMG, while g_CTOT is estimated negatively for TFP growth in [5:1] CPMG but the overall long-run effect of g_CTOT on GDP per capita is positive.

### VI. Robustness, diagnostics, and sample heterogeneity
- Robustness checks reported:
  - Volatility measured alternatively as five-year standard deviation and GARCH(1,1) conditional volatility; main finding of negative volatility effect on growth in commodity exporters holds across measures, with some differences in magnitude and in human capital channel significance.
  - Results robust to changing the primary commodity exporter cut-off to 40 percent and 60 percent (only a few countries move groups).
  - Hansen tests and AR(2) diagnostics in GMM specifications generally support instrument validity and absence of second-order serial correlation (examples: Hansen p-values 0.121, 0.148; AR(2) p-values often >0.1).
  - CPMG diagnostics: "There is no evidence of serial correlation, non-normality, functional form misspecification, or heteroskedasticity in most of the 52 countries in the sample." Hausman p-values often above conventional levels, supporting long-run homogeneity for focused parameters.

### VII. Policy implications and recommendations
- Policy challenge: reduce negative effects of commodity price uncertainty on real output growth by mitigating volatility’s adverse impact on physical capital accumulation (and possibly human capital).
- Policy options emphasized:
  - Creation of commodity stabilization funds or Sovereign Wealth Funds (SWF) to smooth resource income shocks.
  - Improvements in the conduct of macroeconomic policy to manage booms and slumps.
  - Appropriate exchange rate regimes to absorb terms-of-trade shocks.
  - Export diversification to reduce vulnerability to commodity price volatility (EXPY shown to boost growth and physical capital).
  - Institutional reform to ensure effective use of resource income and macroeconomic policy credibility.
- Research agenda suggested:
  - Further investigation of mechanisms to offset volatility’s negative effects on physical and human capital investment.
  - Need for better data on institutional quality to test institutional reform hypotheses.
  - Development of structural models to analyze attenuation of volatility’s growth effects.

*Source: _wp1212 - References and selected sections as provided.*

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

### _wp1212 - References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

### I. INTRODUCTION — central findings and methodological setup
- Many countries specialize in the export of just a few primary products and/or depend heavily on natural resource endowments, exposing them to substantial commodity price volatility and macroeconomic instability, which may harm GDP per capita growth.
- Central message: the volatility of commodity prices and export revenues (CTOT volatility) should be considered in growth analysis alongside levels of resource revenues (price trends) and other determinants of output per capita; the source of the resource curse is volatility in commodity prices as opposed to abundance of the resource itself.
- Methodological approaches employed:
  - System GMM approach (a slope homogeneous panel) to correct for biases from joint endogeneity in dynamic panel data and unobserved country-specific effects.
  - Cross-sectionally augmented Pooled Mean Group (CPMG) estimator (a heterogeneous panel) to account for cross-country heterogeneity and cross-sectional dependence.
- Data and sample:
  - Annual data for the period 1970–2007.
  - Panel dataset of 118 countries.
  - Annual observations used for the CPMG approach; time series data transformed into at most seven non-overlapping five-year observations for the GMM estimation (to abstract from business cycle effects).
  - Use of a country-specific commodity-price index based on each country’s commodity export- and import-baskets to investigate impacts on growth of commodity terms of trade level and volatility.
- Sample splits to test heterogeneity:
  - Full sample: 118 countries.
  - Subsample (a): 62 primary commodity exporters.
  - Subsample (b): 56 other countries with more diversified export baskets.
- Key empirical findings:
  - In the full sample (118 countries) and in subsample (b) of 56 diversified exporters, CTOT volatility is not significantly related to output per capita growth.
  - In subsample (a) of 62 primary commodity exporters, lower CTOT volatility contributes to enhanced growth.
  - Export diversification is associated with faster growth and better insurance against price fluctuations; export diversification of primary commodity exporting countries contributes to faster growth.
  - Channels: CTOT volatility is associated with lower accumulation of both human- and physical-capital, and through that with lower growth.
  - No significant negative association found between CTOT volatility and Total Factor Productivity (TFP) growth.
  - Higher level of commodity terms of trade significantly raises growth (commodity booms have a positive effect on growth).
  - Conclusion: volatility, rather than abundance per se, drives the "resource curse" paradox; negative growth effects of CTOT volatility offset the positive impact of commodity booms on real GDP per capita.

### II. LITERATURE REVIEW — context and related work
- Prior studies stressing volatility and growth:
  - Ramey and Ramey (1995): influential work on consequences of excess volatility for long-run growth.
  - Blattman et al. (2007): panel of 35 commodity-dependent countries between 1870 and 1939; adverse effects of volatility on foreign investment and growth.
  - Aghion et al. (2009): system GMM for 83 countries over the period 1960–2000; exchange rate volatility can stunt growth, especially with under-developed capital markets.
  - Bleaney and Greenaway (2001): sample of 14 sub-Saharan African countries over 1980–1995; growth negatively affected by terms of trade volatility, investment by real exchange rate instability.
- Closely related studies and contrasts:
  - van der Ploeg and Poelhekke (2009) and van der Ploeg and Poelhekke (2010): volatility of unanticipated GDP per capita growth impacts growth, with effect depending on financial development; they use Maximum Likelihood (ML) fixed effects; they find a direct positive effect of resource abundance on growth and argue against traditional resource curse.
    - Differences with current paper: current paper studies CTOT volatility (not unanticipated GDP volatility), employs GMM and CPMG rather than ML fixed effects, and explores channels (human- and physical-capital) through which CTOT volatility operates; finds volatility harms capital accumulation but not productivity.
- Resource curse literature overview:
  - Mixed empirical evidence on the resource curse (Sachs and Warner (1995) and subsequent debate).
  - Papers confirming negative effects of resource abundance: Rodriguez and Sachs (1999), Gylfason et al. (1999), Bulte et al. (2005).
  - Papers challenging the resource curse:
    - Brunnschweiler and Bulte (2008): argue resource curse disappears with correct measure of resource abundance.
    - Alexeev and Conrad (2009): allowing for omitted variables rejects unconditional resource curse.
    - Stijns (2005): no correlation of oil and mineral reserves with growth between 1970 and 1989.
    - Cavalcanti et al. (2011a): heterogeneous cointegrated panel for 53 oil and gas producing countries, accounting for cross-sectional dependence, finding natural resource abundance per se is not a determinant of growth failure.
    - Esfahani et al. (2009): long-run growth model for a major oil exporting economy showing conditions where oil revenues have lasting impact.
- Channels literature:
  - Gylfason (2001): natural resource abundance appears to crowd out human capital investment.
  - Bravo-Ortega et al. (2005): higher education levels can offset negative effects of resource abundance.
  - Papyrakis and Gerlagh (2004) and Gylfason and Zoega (2006): resource abundance leads to lower physical capital investment, dampening GDP growth.
  - Note: prior studies focus on levels of resource abundance and not on volatility in commodity prices or resource income.

### III. THE ECONOMETRIC MODEL AND METHODOLOGY — overview of estimation strategy
- Two econometric techniques introduced and employed:
  - System GMM (dynamic panel, slope homogeneous) using five-year non-overlapping averages to mitigate business cycle effects and address endogeneity and unobserved country effects.
  - Cross-sectionally augmented Pooled Mean Group (CPMG) estimator (heterogeneous panel) using annual data to exploit time-series dimension and take into account cross-country heterogeneity and cross-sectional dependence.
- Variable construction and identification:
  - Use of a country-specific commodity-price index depending on composition of each country’s commodity export- and import-baskets.
  - Investigation of impacts on growth of commodity terms of trade level and volatility.
- Empirical strategy includes:
  - Estimating effects of CTOT growth and volatility on cross-country real output per capita growth and its sources (physical capital, human capital, TFP).
  - Comparing results across estimators (GMM vs CPMG) and across sample splits (full sample, commodity exporters, diversified exporters) to assess robustness and heterogeneity.

*Source: _wp1212 - References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .*

### Section V. They are: (1) a system GMM approach which is a slope homogeneous panel

### Section V. They are: (1) a system GMM approach which is a slope homogeneous panel method and (2) a cross-sectionally augmented version of the Pooled Mean Group (CPMG) estimator (a heterogenous panel approach)

### A. The Econometric Model — setup and estimation choices
- Model specified (dynamic panel):
  - Equation (1): y_it = (ρ−1) y_it−1 + β' x_it + μ_i + γ_t + ε_it
  - y_it: growth rate of real GDP per capita in country i; y_it−1: logarithm of lagged real GDP per capita; x_it: vector of explanatory variables; γ_t: time-specific effect; μ_i: country-specific effect; ε_it: error term.
- Motivations for chosen estimators:
  - Cross-sectional regressions suffer endogeneity (initial income y_it−1 correlated with ε_it) and omitted country-specific factors.
  - Traditional static panel estimators (FE, RE) are inconsistent with lagged dependent variables because:
    - FE de-meaning induces correlation of order 1/T between transformed error and lagged dependent variable.
    - RE requires lack of correlation between μ_i and regressors, which is violated.
  - Errors with heteroscedasticity or serial correlation also invalidate FE/RE.
- Estimation strategies used:
  - System GMM: to correct endogeneity from lagged endogenous variables and simultaneity (Section B).
  - Cross-sectionally augmented Pooled Mean Group (CPMG): to account for heterogeneous time effects and cross-sectional dependencies while allowing heterogeneous short-run dynamics (Section C).

### B. GMM Methodology — implementation and limitations
- Transformation and instruments:
  - First-difference of (1) yields equation (2): Δy_it = ρ Δy_it−1 + β' Δx_it + Δγ_t + Δε_it.
  - Difference GMM moment conditions (assuming ε_it not serially correlated and x_it weakly exogenous):
    - E(y_it−s, Δε_it) = 0 for s ≥ 2 and t = 3:...:T;
    - E(x_it−s, Δε_it) = 0 for s ≥ 2 and t = 3:...:T.
  - System GMM augments differences with levels equation (1) using lagged differences as instruments, adding moment conditions for s = 1:
    - E(Δy_it−s, μ_i + ε_it) = 0 for s = 1;
    - E(Δx_it−s, μ_i + ε_it) = 0 for s = 1.
- Estimation details:
  - Solutions yield T−1 equations in first differences plus T equations in levels.
  - Two-step GMM with weighting by inverse consistent estimate of moment covariance matrix.
  - Hansen test of over-identifying restrictions and serial correlation tests (Arellano–Bond style) used to assess instrument validity and serial correlation (noting differenced errors are expected to show first-order but test targets second-order).
  - Windmeijer (2005) correction used to adjust two-step standard errors in small samples (applied in empirical section).
- Method limitations:
  - System GMM restricts slope coefficients to be identical across countries (slope homogeneity), assumes homogeneous time effects, and cross-sectional independence of errors.
  - If these conditions fail, GMM can produce inconsistent and misleading estimates, per Pesaran and Smith (1995).
  - Time-specific heterogeneity (country-specific responses to global shocks like oil price movements) is important; CPMG is designed to address heterogeneous time effects and cross-sectional dependence.

### C. CPMG Methodology — rationale and implementation
- Estimator family and positioning:
  - Mean Group (MG): fully heterogeneous; PMG (Pesaran et al. 1999): long-run coefficients homogeneous, short-run coefficients, intercepts and error variances heterogeneous.
  - CPMG: PMG augmented for cross-sectional dependence following Pesaran (2006), using cross-sectional averages to capture common factors.
- ARDL(p; q; ... ; q) baseline:
  - Equation (3): y_it = Σ_{j=1}^p φ_ij y_it−j + Σ_{j=0}^q θ'_ij x_it−j + μ_i + u_it.
  - u_it has multi-factor structure u_it = λ'_i f_t + ε_it (equation (4)), where f_t are unobserved common shocks and λ_i are country-specific loadings.
- Cross-sectional augmentation:
  - Cross-sectional averages of dependent and explanatory variables included to proxy common factors (Pesaran 2006).
  - Error correction representation derived (equation (7)) with country-specific long-run parameter ϑ_i = −(θ_i / φ_i).
  - Long-run homogeneity imposed: ϑ_i = ϑ for i = 1,...,N (equation (9)), which can be tested (Hausman test for coefficients).
- Practicalities:
  - CPMG uses maximum likelihood via Newton–Raphson.
  - Lag length chosen by criteria such as Schwarz Criterion (SBC).
  - Advantages: accommodates heterogeneous short-run dynamics and heterogeneous responses to common shocks; avoids requiring pre-testing for integration orders (valid for I(0) and I(1)).

### IV. Data — coverage, key constructed series, and sample splits
- Time span and frequency:
  - Annual data from 1970 to 2007 used.
  - For five-year average analysis: non-overlapping five-year averages constructed, yielding at most seven five-year observations per country covering 1970–2005 (unbalanced panel).
  - For CPMG annual analysis: countries with at least 25 consecutive observations included.
- Sample sizes and splits:
  - Full sample: 118 countries.
  - Primary commodity exporters subset: 62 countries defined as those with primary commodities / total exports > 50 percent.
  - Non-primary exporters subset: 56 countries.
  - CPMG annual analysis focuses on commodity exporters with sufficient observations: 52 countries out of the 62.
- Commodity terms of trade (CTOT) index:
  - CTOT_it = Σ_j (P_jt / MUV_t) X_ij − Σ_j (P_jt / MUV_t) M_ij (equations (10)–(12) summary: lnCTOT_it = Σ_j (X_ij − M_ij) ln(P_jt / MUV_t); g_CTOT,it = lnCTOT_it − lnCTOT_it−1 = Σ_j (X_ij − M_ij) Δ ln(P_jt / MUV_t)).
  - Export/import shares X_ij and M_ij averaged between 1970 and 2007 (held fixed over time in CTOT construction).
  - Commodities in the CTOT basket (list of 32): Shrimp, beef, lamb, wheat, rice, corn, bananas, sugar, coffee, cocoa, tea, soybean meal, fish meal, hides, soybeans, natural rubber, hardlog, cotton, wool, iron ore, copper, nickel, aluminum, lead, zinc, tin, soy oil, sunflower oil, palm oil, coconut oil, gold, crude oil.
- CTOT volatility measures:
  - Five-year non-overlapping standard deviation of g_CTOT,it:
    - σ_CTOT;it;t+S = sqrt( (1/S) Σ_{s=0}^S (g_CTOT;it+s − (1/(S+1)) Σ_{s=0}^S g_CTOT;it+s)^2 ), with S = 4 (five-year averages).
  - GARCH(1,1) conditional variance approach on annual g_CTOT,it:
    - g_CTOT;it = Δ lnCTOT_it = υ_0 + η_it;
    - σ^2_CTOT;it = (1 − π_1 − π_2) σ^2_CTOT;i + π_1 η^2_it−1 + π_2 σ^2_CTOT;it−1 (equation (14)); volatility measured as sqrt(σ^2_CTOT;it).
- Constructed series for channels and inputs:
  - Physical capital stock K_it via perpetual inventory method using PWT 6.3:
    - Initial K_it^0 = I_it^0 / (g_I + δ) (equation (15)); I_it = k_it × rgdpch_it × pop_it (equation (16)); subsequent K_it = (1 − δ) K_it−1 + I_it (equation (17)).
    - Assumed depreciation rate δ = 6 percent.
  - Human capital H_it = exp(φ(s_it)) with s_it average years of schooling (Barro and Lee 2010 interpolated annually). Piecewise returns to schooling used: 0.134 for first 4 years, 0.101 for next 4 years, and 0.068 for s_it > 8 (Psacharopoulos specification).
  - Total Factor Productivity A_it computed from constant returns production function with capital share β = 1/3 (equation (21)).

### V. Empirical Results — overview and main quantitative findings
- Estimation methods applied:
  - System GMM for five-year averaged panel regressions, using Windmeijer (2005) correction for two-step standard errors.
  - Cross-sectionally augmented Pooled Mean Group (CPMG) on annual data for robustness and to allow heterogeneous time effects and cross-sectional dependence.
- A. Analysis Using Five-Year Averages — setup:
  - Dependent variable for growth regressions: g_y;is = geometric average growth of real GDP per capita over five-year period s for country i.
  - Main regression (equation (22)):
    - g_y;is = (ρ−1) y_is−1 + α_1 g_CTOT;is + α_2 σ_CTOT;is + α_3 EXPY_is + β' z_is + μ_i + γ_s + ε_is.
  - Control variables z_is: education, trade openness, government burden, lack of price stability, etc.
- A.1 Volatility and Growth — key quantitative results (system GMM, Table 3 highlights):
  - Full sample (118 countries) regression [1:1]:
    - g_CTOT coefficient: positive and highly significant.
    - CTOT volatility coefficient: negative but statistically insignificant.
    - EXPY (export diversification) coefficient: significant and positive.
  - Primary commodity exporters (62 countries) regression [1:2]:
    - g_CTOT coefficient: positive and significant (commodity booms increase growth).
    - CTOT volatility coefficient: negative and significant (volatility reduces growth).
    - Overall effect of CTOT growth and volatility on output per capita over five years (calculated from regression [1:2]): −0.312 over five years.
  - Non-resource-abundant subsample (56 countries) regression [1:3]:
    - No significant impact of g_CTOT or σ_CTOT on GDP growth.
    - EXPY positive and significant.
  - Additional diagnostics:
    - Hansen and second order serial correlation test statistics: reported as well above conventional significance levels (supporting instrument validity and absence of second-order serial correlation).
  - Interpretation:
    - Evidence against resource curse driven by abundance; instead CTOT volatility is the primary adverse channel for primary commodity exporters.
    - Export diversification (EXPY) consistently growth-enhancing across samples.
- A.2 Volatility and Channels Affecting Economic Growth — three channels (system GMM, Table 4 highlights):
  - Estimated channel equations (equation (23)):
    - g_W;is = (ρ−1) w_is−1 + α_1 g_CTOT;is + α_2 σ_CTOT;is + α_3 EXPY_is + β' z_is + μ_i + γ_s + ε_is,
    - where W ∈ {TFP, physical capital per capita, human capital per capita}.
  - TFP channel ([2:1]):
    - g_CTOT and σ_CTOT: statistically insignificant → commodity booms and volatility do not affect TFP growth in primary commodity exporters.
    - Human capital and export diversification positively associated with TFP growth.
    - Finding contradicts a Dutch disease mechanism operating through TFP declines.
  - Physical capital channel ([2:2]):
    - g_CTOT: positive and significant (commodity booms increase physical capital accumulation).
    - σ_CTOT: negative and significant (volatility reduces physical capital accumulation).
    - Conclusion: physical capital accumulation is an important channel through which CTOT volatility reduces GDP per capita growth.
  - Human capital channel ([2:3]):
    - σ_CTOT: negative and significant → CTOT volatility reduces human capital accumulation (in Table 4).
    - Possible mechanism: volatility increases inequality and credit constraints, reducing privately financed education.
  - Additional observations:
    - EXPY (diversification) increases physical capital accumulation ([2:2]) but not significantly associated with human capital accumulation ([2:3]).
    - Control variables generally have expected signs; Hansen and AR(2) tests support instrument validity and lack of second-order serial correlation.
  - Subsample of 56 net commodity importers: g_CTOT and σ_CTOT show no significant effects on TFP, physical capital, or human capital (results available upon request).
- A.3 Robustness checks — alternative volatility measure (GARCH(1,1), Tables 5–6 highlights):
  - Use of GARCH(1,1) conditional volatility of ln(CTOT) on annual data as an alternative σ_CTOT measure.
  - Results (Table 5):
    - Full sample [3:1] and non-resource-abundant [3:3]: CTOT volatility coefficients negative but statistically insignificant.
    - Primary commodity exporters [3:2]: CTOT volatility significantly negative for GDP growth.
    - Overall combined effect of g_CTOT and GARCH-based σ_CTOT on output growth: −0.509 percent (Table 5).
  - Channels (Table 6):
    - TFP ([4:1]): g_CTOT and σ_CTOT both insignificant — again no evidence of Dutch disease via TFP.
    - Physical capital ([4:2]): g_CTOT positive and σ_CTOT negative and significant → volatility harms growth via reduced physical capital accumulation.
    - Human capital ([4:3]): σ_CTOT negative but statistically insignificant in the GARCH robustness check — evidence on human capital channel is inconclusive across volatility measures.
  - Additional robustness:
    - Results robust to changing definition of primary commodity exporter cut-off to 40 percent and 60 percent (changes omit/add only a few countries).
    - Hansen tests and AR(2) diagnostics remain satisfactory across robustness checks.
  - Interpretation:
    - Main robust finding: CTOT volatility reduces growth for primary commodity exporters primarily via reductions in physical capital accumulation; evidence on human capital channel is mixed depending on volatility measure.
- B. Analysis Using Annual Data — motivation and sample for CPMG
  - Reasons to complement five-year averages with annual CPMG:
    - Five-year averaging can lose information and may understate volatility measured over business cycles.
    - Traditional GMM does not account for cross-sectional heterogeneity or residual cross-country dependencies.
  - CPMG annual analysis:
    - Applied to annual observations 1970–2007.
    - Countries included: those with at least 25 consecutive observations and focusing on commodity exporters: 52 countries (out of 62 primary commodity exporters).
    - Education variable (secondary enrollment) unavailable annually for all countries → education excluded from CPMG regressions; human capital channel cannot be analyzed in CPMG and focus is on TFP and physical capital channels.

*Italic: Summary based exclusively on the provided content from Section V of the source document.*

### Section III.C to estimate the following equation:

### _wp1212 - Section III.C to estimate the following equation:

### Methodology and estimated model
- Model estimated: dynamic error-correction/ARDL specification as displayed in the source (equation (24)), where:
  - y_it is the annual growth rate of real GDP per capita for country i and year t.
  - x_it is a 5×1 vector of explanatory variables: growth rate of the CTOT index g_CTOT;it and its volatility ε_CTOT;it, and conventional control variables: openness, government burden, and lack of price stability.
  - y_t, Δy_t, g_CTOT;t, and Δg_CTOT;t denote simple cross-sectional averages in year t.
- Estimation approaches:
  - Cross-sectionally augmented pooled mean group (CPMG/PMG) estimator is the primary time-series panel method used.
  - Mean group (CMG) estimates are also reported as averages of individual country coefficients.
  - System GMM dynamic panel estimator used elsewhere in the paper to address simultaneity and omitted variable bias (context provided in concluding remarks).

### Conditions and implementation details for CPMG/PMG
- Lag order selection:
  - Lag order chosen on the unrestricted model using the Schwarz Criterion (SBC) subject to a maximum lag of two on each variable, i.e., p=q2.
  - Lag orders allowed to differ across countries.
- Key conditions for consistency and efficiency:
  - Residuals of the error-correction model must be serially uncorrelated.
  - Cross-sectional independence of the residuals ε_it is required; common factors addressed by augmenting regressions with cross-sectional averages of real GDP growth and the CTOT index (y_t and g_CTOT;t).
  - Existence of a long-run relationship (dynamic stability) requires the error-correction coefficient ϕ_i (or _i) to be negative.
  - Homogeneity of long-run parameters across countries is required for efficiency of the CPMG estimator.
- Testing long-run homogeneity:
  - Hausman statistic used to test equivalence of CPMG and CMG estimates; null: equivalence (homogeneity).
  - Rejection criterion described as probability value of<0:05.
  - Note: likelihood ratio (LR) test often suggests homogeneity is not reasonable, but Hausman test typically accepts poolability when T is small relative to N.

### Diagnostic and sample features
- Sample: 52 commodity exporting countries used for the PMG/CPMG analysis in Section III.C.
- Diagnostics: "There is no evidence of serial correlation, non-normality, functional form misspecification, or heteroskedasticity in most of the 52 countries in the sample." (results available upon request).
- Hausman statistics reported in Table 7 indicate long-run homogeneity restriction is not rejected for individual parameters and jointly in all regressions; therefore emphasis placed on CPMG estimates.

### Long-run empirical findings (CPMG results)
- Error-correction coefficients (_i) are statistically significant and negative — evidence of dynamic stability and conditional convergence to country-specific steady states in the sample of 52 commodity exporters.
- Long-run relationships:
  - Growth rate of GDP per capita:
    - Negatively related to the size of government and lack of price stability.
    - Positively related to trade openness.
  - Commodity terms of trade volatility (CTOT volatility):
    - CPMG estimate is negative and statistically significant: long-run adverse link between commodity price volatility and growth.
  - Resource abundance (g_CTOT):
    - Significantly positively related to economic growth in the long run, but its impact is smaller than that of CTOT volatility.
- Quantitative summary:
  - "The overall average negative impact of the two CTOT variables on output growth is -0.09 percent per year."
- Comparison with other estimators:
  - Coefficient of ε_CTOT in the CPMG regression of Table 7 is roughly the same magnitude as in two GMM regressions referenced ([1:2] and [3:2]).
  - Imposing long-run homogeneity (CPMG vs CMG) reduces standard errors, increases measured speed of adjustment, and slightly changes long-run estimates.

### Channels: volatility and sources of growth (Section B.2 and regressions [5:1], [5:2])
- Estimated channel regressions use equation (25) where w_it = TFP or physical capital per capita; Δw_it is growth of w_it; cross-sectional averages included.
- Hausman p-values in regressions [5:1] and [5:2] are well above usual significance levels → cannot reject long-run homogeneity → focus on CPMG estimates.
- Findings for channels:
  - TFP channel (regression [5:1]):
    - CTOT volatility coefficient is statistically insignificant → TFP is not the channel through which commodity price uncertainty dampens growth.
    - Resource abundance g_CTOT negatively affects TFP growth and is statistically significant in this regression; however, the overall long-run effect of g_CTOT on real GDP per capita growth remains significantly positive (Table 7), implying offsetting channels.
    - Error-correction term _i < 0, suggesting convergence towards the technological frontier and positive knowledge spillovers.
  - Physical capital accumulation channel (regression [5:2]):
    - CTOT growth increases the capital stock and enhances real GDP per capita growth.
    - CTOT volatility reduces physical capital accumulation — identified as a primary channel through which uncertainty in commodity prices dampens output growth.
    - Error-correction term also in line with expectations (_i < 0).
  - Additional controls:
    - Government burden and lack of price stability have significantly negative effects on TFP growth.
    - Trade openness has a significant positive effect on TFP growth.
    - Lack of price stability negatively affects physical capital growth; openness positively affects it.
    - Government consumption boosts investment.

### Robustness and contrasts with other results
- GMM results also suggest CTOT volatility adversely affects human capital formation, but this effect was not robust when using an alternate GARCH methodology to compute CTOT volatility.
- Using five-year averages in earlier sections produced some differing findings regarding resource abundance and channels; PMG/CPMG results align with Section V.A in emphasizing the negative role of CTOT volatility via lower physical capital investment.
- Asymmetric effects:
  - CTOT instability produced a significant negative effect on output growth in the sample of 62 primary product exporters.
  - The same pattern was not observed in the remaining 56 countries or in the full sample of 118 countries — possibly due to greater export diversification and better insurance against price volatility.

### Policy implications and recommendations
- Main policy challenge: reduce negative effects of commodity price uncertainty on real output growth, especially given volatility’s adverse impact on physical capital accumulation (and possibly human capital per some specifications).
- Policy options highlighted:
  - Creation of commodity stabilization funds or Sovereign Wealth Funds (SWF) to offset negative effects of commodity booms and slumps.
  - Improvements in the conduct of macroeconomic policy.
  - Appropriate exchange rate regimes.
  - Export diversification to reduce vulnerability to commodity price volatility.
  - Institutional reform to ensure proper conduct of macroeconomic policy and effective use of resource income.
- Research agenda:
  - Further investigation into mechanisms to offset negative effects of commodity price uncertainty on physical and human capital investment.
  - Need for better data on institutional quality to test hypotheses regarding institutional reforms.
  - Development of fully articulated structural models to examine channels through which volatility’s negative growth effects can be attenuated.

*Source: _wp1212 - Section III.C to estimate the following equation: (IMF working paper content as provided).*

### Introduction.Oxford Economic Papers 61(4), 625–627.

### Introduction.Oxford Economic Papers 61(4), 625–627

### Sample and country classification
- Sample of 118 countries listed (alphabetical order).  
- Notes on classification:
  - "1 indicates that the country is a commodity exporter. Countries are classified as commodity exporters if primary commodities constitute more than 50 percent of their exports."
  - "62 countries in the sample are primary commodity exporters and 56 are not."
  - "The 52 countries that are included in the Cross-sectionally Augment Pooled Mean Group (CPMG) analysis of Section V.B are denoted by 2."

### Data, variables, and construction
- Unit of observation and periods used in regressions:
  - Non-overlapping five-year averages, 1970 - 2005 (used in Tables 3, 4, 5, 6).
  - Annual, 1971 - 2007 (used in Tables 7, 8).
- Volatility measures:
  - Five year standard deviation of annual CTOT growth (Tables 3 and 4).
  - GARCH (1,1) volatility (Tables 5, 6, 7, 8).
- Key variables and sources (as defined in Table 2):
  - Real GDP per Capita: Ratio of GDP (in 2000 US$) to population.
  - GDP per Capita Growth: Geometric average growth rate of real GDP per capita. "Authors’ construction using data from the World Bank (2010) World Development Indicators (WDI)."
  - Initial GDP per Capita: Initial value of GDP per capita in the beginning of each five-year period.
  - TFP, TFP Growth, Initial TFP: Total factor productivity and its growth; authors’ construction.
  - Physical Capital per Capita, Physical Capital per Capita Growth, Initial Physical Capital Per Capita: Heston et al. (2009); see Section IV for details.
  - Human Capital per Capita, Human Capital per Capita Growth, Initial Human Capital per Capita: Authors’ construction using Barro and Lee (2010); see Section IV.
  - Commodity Terms of Trade Growth: Growth rate of commodity terms of trade index. "Authors’ construction based on Spatafora and Tytell (2009)."
  - Commodity Terms of Trade Volatility: Standard deviation of commodity terms of trade growth in five-year interval.
  - Export Sophistication Measure: "Authors’ construction based on Hausmann et al. (2007) and the World Bank (2010) WDI."
  - Education: Ratio of total secondary enrollment to the population of the age group that officially corresponds to that level of education. "Authors’ construction using data from UNESCO (2010) UIS."
  - Trade Openness: Ratio of Exports and Imports to GDP. "Authors’ construction using data from the World Bank (2010) WDI."
  - Government Burden: Ratio of government consumption to GDP.
  - CPI and Inflation rate: CPI (2000=100) at end of year; annual percentage change in CPI. "Author’s calculations using data from the International Monetary Fund (2010a) World Economic Outlook."
  - Lack of Price Stability: log(100 + inflation rate).

### Empirical findings — growth effects of CTOT growth and volatility (Tables 3 and 5)
- Estimation method for Tables 3 and 5: "Two-step system GMM with Windmeijer (2005) small sample robust correction."
- Dependent variable: Growth rate of output per capita.
- Table 3 (Volatility measure: Five year standard deviation of annual CTOT growth)
  - Column [1:1] All 118 Countries:
    - Initial Output per Capita, in logs: -1.204** (0.471)
    - Commodity Terms of Trade Growth: 0.240*** (0.072)
    - Commodity Terms of Trade Volatility: -0.105 (0.081)
    - Export Sophistication Measure, in logs: 4.818*** (1.830)
    - Education (secondary enrollment, in logs): 0.812 (0.803)
    - Trade Openness (trade volume/GDP, in logs): 2.027** (1.024)
    - Government Burden (government consumption/GDP, in logs): -2.656** (1.163)
    - Lack of Price Stability (log [100 + inflation rate]): -6.786*** (2.412)
    - No. Countries/No. Observations: 118/664
    - Hansen Test (p-value): 0.121
    - Serial Correlation: First-order 0.000; Second-order 0.199
  - Column [1:2] 62 Commodity Exporters:
    - Initial Output per Capita, in logs: -0.872 (0.688)
    - Commodity Terms of Trade Growth: 0.255*** (0.078)
    - Commodity Terms of Trade Volatility: -0.119** (0.058)
    - Export Sophistication Measure, in logs: 2.787* (1.638)
    - Trade Openness: 2.587*** (0.860)
    - Government Burden: -4.007*** (1.064)
    - Lack of Price Stability: -6.264** (2.485)
    - No. Countries/No. Observations: 62/352
    - Hansen Test (p-value): 0.448
    - Serial Correlation: First-order 0.000; Second-order 0.252
  - Column [1:3] Other 56 Countries:
    - Initial Output per Capita, in logs: -1.738*** (0.546)
    - Commodity Terms of Trade Growth: -0.156 (0.469)
    - Commodity Terms of Trade Volatility: -0.683 (0.577)
    - Export Sophistication Measure, in logs: 3.687** (1.465)
    - Trade Openness: 2.142** (0.929)
    - Lack of Price Stability: -11.119*** (3.773)
    - No. Countries/No. Observations: 56/312
    - Hansen Test (p-value): 0.314
    - Serial Correlation: First-order 0.003; Second-order 0.674
  - "Impact of CTOT Growth and Volatility -- -0.312 -"
- Table 5 (Volatility measure: GARCH (1,1))
  - Column [3:1] All 118 Countries:
    - Initial Output per Capita, in logs: -1.101*** (0.402)
    - Commodity Terms of Trade Growth: 0.250*** (0.077)
    - Commodity Terms of Trade Volatility: -0.215 (0.141)
    - Export Sophistication Measure, in logs: 4.062** (1.628)
    - Trade Openness: 2.498*** (0.922)
    - Government Burden: -2.948*** (1.096)
    - Lack of Price Stability: -6.945*** (2.521)
    - No. Countries/No. Observations: 118/664
    - Hansen Test (p-value): 0.148
    - Serial Correlation: First-order 0.000; Second-order 0.340
  - Column [3:2] 62 Commodity Exporters:
    - Initial Output per Capita, in logs: -1.053 (0.659)
    - Commodity Terms of Trade Growth: 0.264*** (0.061)
    - Commodity Terms of Trade Volatility: -0.198** (0.099)
    - Export Sophistication Measure, in logs: 2.744* (1.629)
    - Trade Openness: 2.603*** (0.892)
    - Government Burden: -3.985*** (1.193)
    - Lack of Price Stability: -6.500** (2.633)
    - No. Countries/No. Observations: 62/352
    - Hansen Test (p-value): 0.282
    - Serial Correlation: First-order 0.001; Second-order 0.435
  - Column [3:3] Other 56 Countries:
    - Initial Output per Capita, in logs: -1.891*** (0.492)
    - Commodity Terms of Trade Growth: -0.269 (0.445)
    - Commodity Terms of Trade Volatility: -0.531 (0.663)
    - Export Sophistication Measure, in logs: 4.945*** (1.561)
    - Trade Openness: 1.614* (0.957)
    - Government Burden: -0.376 (1.423)
    - Lack of Price Stability: -10.520** (4.091)
    - No. Countries/No. Observations: 56/312
    - Hansen Test (p-value): 0.225
    - Serial Correlation: First-order 0.002; Second-order 0.853
  - "Impact of CTOT Growth and Volatility -- -0.509 -"

Interpretation from Tables 3 and 5:
- Commodity terms of trade growth is estimated positive and statistically significant for the full sample and for commodity exporters (e.g., 0.240*** in [1:1]; 0.255*** in [1:2]; 0.250*** in [3:1]; 0.264*** in [3:2]).
- Commodity terms of trade volatility is estimated negatively for commodity exporters with statistical significance in several specifications (e.g., -0.119** in [1:2]; -0.198** in [3:2]), while point estimates for the full sample and non-exporters are negative but often not statistically significant.
- Export Sophistication Measure, in logs, is positive and significant in many specifications (e.g., 4.818*** in [1:1]; 4.062** in [3:1]; 4.945*** in [3:3]).
- Lack of Price Stability (log [100 + inflation rate]) shows large negative coefficients and significance in many specifications (e.g., -6.786*** in [1:1]; -6.945*** in [3:1]; -11.119*** in [1:3]).

### Channels: volatility and sources of growth in commodity exporters (Tables 4 and 6)
- Estimation method: "Two-step system GMM with Windmeijer (2005) small sample robust correction."
- Dependent variables: growth rates of Total Factor Productivity (TFP), Physical Capital, and Human Capital for commodity exporters (62 countries).
- Table 4 (Volatility measure: Five year standard deviation)
  - [2:1] Dependent = TFP growth:
    - Initial TFP, in logs: -4.221*** (0.990)
    - Commodity Terms of Trade Growth: 0.113 (0.162)
    - Commodity Terms of Trade Volatility: 0.006 (0.102)
    - Export Sophistication Measure, in logs: 4.130*** (1.382)
    - Education: 1.837* (1.034)
    - Trade Openness: 2.106 (1.485)
    - Lack of Price Stability: -5.019* (2.897)
    - No. Countries/No. Observations: 62/354
    - Hansen Test (p-value): 0.351
    - Serial Correlation: First-order 0.001; Second-order 0.569
  - [2:2] Dependent = Physical Capital growth:
    - Initial Physical Capital Stock, in logs: -0.601 (1.020)
    - Commodity Terms of Trade Growth: 0.186** (0.093)
    - Commodity Terms of Trade Volatility: -0.181** (0.087)
    - Export Sophistication Measure, in logs: 4.979*** (1.700)
    - Education: -1.417 (1.145)
    - Trade Openness: 3.205** (1.521)
    - Lack of Price Stability: -4.143 (3.375)
    - No. Countries/No. Observations: 62/354
    - Hansen Test (p-value): 0.145
    - Serial Correlation: First-order 0.012; Second-order 0.110
  - [2:3] Dependent = Human Capital growth:
    - Initial Human Capital Stock, in logs: -0.999 (0.750)
    - Commodity Terms of Trade Growth: 0.048 (0.030)
    - Commodity Terms of Trade Volatility: -0.051* (0.029)
    - Export Sophistication Measure, in logs: -0.283 (0.465)
    - Education: 0.643*** (0.202)
    - Trade Openness: 0.442 (0.340)
    - Lack of Price Stability: -0.098 (0.445)
    - No. Countries/No. Observations: 62/354
    - Hansen Test (p-value): 0.469
    - Serial Correlation: First-order 0.006; Second-order 0.533
- Table 6 (Volatility measure: GARCH (1,1))
  - [4:1] Dependent = TFP growth:
    - Initial TFP, in logs: -4.031*** (1.182)
    - Commodity Terms of Trade Growth: 0.104 (0.174)
    - Commodity Terms of Trade Volatility: 0.071 (0.262)
    - Export Sophistication Measure, in logs: 3.870** (1.633)
    - Education: 1.683 (1.150)
    - Trade Openness: 2.405 (1.907)
    - Lack of Price Stability: -5.845 (3.729)
    - No. Countries/No. Observations: 62/354
    - Hansen Test (p-value): 0.259
    - Serial Correlation: First-order 0.001; Second-order 0.660
  - [4:2] Dependent = Physical Capital growth:
    - Initial Physical Capital Stock, in logs: -0.552 (0.964)
    - Commodity Terms of Trade Growth: 0.250* (0.145)
    - Commodity Terms of Trade Volatility: -0.401** (0.182)
    - Export Sophistication Measure, in logs: 3.863** (1.915)
    - Education: -0.975 (1.172)
    - Trade Openness: 3.961*** (1.400)
    - Lack of Price Stability: -5.138 (3.423)
    - No. Countries/No. Observations: 62/354
    - Hansen Test (p-value): 0.168
    - Serial Correlation: First-order 0.024; Second-order 0.127
  - [4:3] Dependent = Human Capital growth:
    - Initial Human Capital Stock, in logs: -0.992 (0.697)
    - Commodity Terms of Trade Growth: 0.024 (0.029)
    - Commodity Terms of Trade Volatility: -0.026 (0.042)
    - Export Sophistication Measure, in logs: -0.334 (0.431)
    - Education: 0.660*** (0.225)
    - Trade Openness: 0.496 (0.388)
    - Lack of Price Stability: -0.153 (0.390)
    - No. Countries/No. Observations: 62/354
    - Hansen Test (p-value): 0.477
    - Serial Correlation: First-order 0.014; Second-order 0.791

Interpretation from Tables 4 and 6:
- Commodity terms of trade volatility is associated with significantly lower physical capital growth for commodity exporters in several specifications (e.g., -0.181** in [2:2]; -0.401** in [4:2]).
- Commodity terms of trade volatility has smaller or mixed associations with TFP growth and human capital growth across specifications (e.g., small positive 0.006 in [2:1]; -0.051* for human capital in [2:3]).

### Long-run and panel estimators for commodity exporters (Tables 7 and 8)
- Estimation methods: Cross Sectionally Augmented Mean Group (CMG) and Pooled Mean Group (CPMG) Estimators.
- Table 7 (Annual 1971 - 2007, Volatility: GARCH (1,1), Dependent: growth rate of output per capita)
  - CMG results:
    - Error Correction Term: -0.248*** (0.037)
    - Commodity Terms of Trade Growth: 0.011 (0.133)
    - Commodity Terms of Trade Volatility: 0.589 (0.645)
    - Trade Openness: -0.004 (0.464)
    - Government Burden: 0.060 (0.417)
    - Lack of Price Stability: -0.536 (1.033)
    - No. Countries / No. Observations: 52/1813
  - CPMG results:
    - Error Correction Term: -0.131*** (0.017)
    - Commodity Terms of Trade Growth: 0.003* (0.002)
    - Commodity Terms of Trade Volatility: -0.034*** (0.008)
    - Trade Openness: 0.249*** (0.023)
    - Government Burden: -0.274*** (0.027)
    - Lack of Price Stability: -0.544*** (0.059)
    - No. Countries / No. Observations: 52/1813
    - Joint Hausman Test: 7.68 [p= 0:17]
    - "Impact of CTOT Growth and Volatility -- 0.090"
- Table 8 (Dependent variables: TFP and Physical Capital; CMG and CPMG; Annual 1971 - 2007; Volatility: GARCH (1,1))
  - [5:1] Dependent = Total Factor Productivity
    - CMG:
      - Error Correction Term: -0.376*** (0.045)
      - Commodity Terms of Trade Growth: 0.013 (0.033)
      - Commodity Terms of Trade Volatility: -0.130 (0.197)
      - Trade Openness: -0.059 (0.288)
      - Government Burden: -0.362 (0.401)
      - Lack of Price Stability: -1.359 (1.984)
      - No. Countries / No. Observations: 52/1816
      - Joint Hausman Test: 2:31 [p= 0:80]
    - CPMG:
      - Error Correction Term: -0.279*** (0.033)
      - Commodity Terms of Trade Growth: -0.012*** (0.003)
      - Commodity Terms of Trade Volatility: 0.005 (0.007)
      - Trade Openness: 0.133*** (0.031)
      - Government Burden: -0.267*** (0.026)
      - Lack of Price Stability: -0.424*** (0.058)
      - No. Countries / No. Observations: 52/1816
  - [5:2] Dependent = Physical Capital
    - CMG:
      - Error Correction Term: -0.136*** (0.022)
      - Commodity Terms of Trade Growth: 0.107 (0.129)
      - Commodity Terms of Trade Volatility: -0.633 (0.816)
      - Trade Openness: 0.755 (0.486)
      - Government Burden: 4.279 (3.696)
      - Lack of Price Stability: -5.131* (2.791)
      - No. Countries / No. Observations: 52/1819
      - Joint Hausman Test: 6:43 [p= 0:27]
    - CPMG:
      - Error Correction Term: -0.075*** (0.015)
      - Commodity Terms of Trade Growth: 0.007*** (0.002)
      - Commodity Terms of Trade Volatility: -0.018*** (0.005)
      - Trade Openness: 0.542*** (0.032)
      - Government Burden: 0.135*** (0.025)
      - Lack of Price Stability: -0.047* (0.027)
      - No. Countries / No. Observations: 52/1819

Interpretation from Tables 7 and 8:
- In CPMG panel estimates for commodity exporters:
  - Commodity terms of trade volatility shows a negative and statistically significant long-run effect on output per capita growth (-0.034*** in Table 7 CPMG) and on physical capital growth (-0.018*** in Table 8 [5:2] CPMG).
  - Error correction terms are negative and statistically significant in all reported CMG and CPMG specifications (e.g., -0.248*** in Table 7 CMG; -0.131*** in Table 7 CPMG), indicating adjustment toward long-run equilibria.
  - Trade openness and lack of price stability frequently show statistically significant coefficients in CPMG estimates (e.g., Trade Openness 0.249*** in Table 7 CPMG; Lack of Price Stability -0.544*** in Table 7 CPMG).

### Robustness, specification, and diagnostic notes
- All regressions include time and fixed effects (Tables 3–6) or a constant country specific term (Tables 7–8) as noted.
- Standard errors are presented in parentheses under coefficients.
- Symbols ***, **, and * denote significance at 1%, 5%, and at 10% respectively.
- Specification and diagnostic statistics reported as p-values:
  - Hansen test p-values are reported for GMM estimations (e.g., 0.121 in [1:1]; 0.148 in [3:1]).
  - Serial correlation tests (first- and second-order) are reported (e.g., first-order often 0.000–0.001 in GMM regressions).
  - Joint Hausman tests for CMG vs CPMG choices are reported (e.g., 7.68 [p= 0:17] in Table 7).

*Source: Introduction.Oxford Economic Papers 61(4), 625–627. _wp1212 - Introduction.Oxford Economic Papers 61(4), 625–627._*

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