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### World Commodity Prices (Section 3.1)

- Coverage and frequency
  - International prices of 45 individual commodities are used.
  - Two database variants:
    - a monthly database based on the 45 commodities that starts in 1980.
    - an annual database using a narrower set of 40 commodity prices that starts in 1962.

- Commodity groups and items
  - Energy: coal, crude oil, and natural gas.
  - Metals: aluminum, copper, gold, iron ore, lead, nickel, tin, uranium, and zinc.
  - Food and beverages: bananas, barley, beef, cocoa, coffee, corn, fish, fish meal, groundnuts, lamb, olive oil, oranges, palm oil, poultry, rapeseed oil, rice, shrimp, soybean meal, soybean oil, soybeans, sugar, sunflower seed oil, swine meat, tea, and wheat.
  - Agricultural raw materials: cotton, hard logs, hard sawnwood, hides, natural rubber, soft logs, soft sawnwood, and wool.

- Price construction and deflation
  - Real prices = commodity price in US dollars ÷ IMF’s unit value index for manufactured exports (MUV index).
  - Primary source: IMF Primary Commodity Prices database.
  - World Bank’s Global Economic Monitor and US Energy Information Administration used to extend barley, coal, iron ore, and natural gas back to the 1960s.
  - Annex Table A2 lists individual commodities, international price, and sources (as in the source document).

- Mapping prices to trade headings
  - Trade data: United Nations Comtrade, SITC Revision 1 at 5-digit headings; oil at 3-digit aggregation.
  - Each commodity price linked to all SITC product codes for the unprocessed commodity and semi-processed products expected to comove with the primary commodity (example: copper → SITC 28311 and SITC 68212).
  - Semi-processed categories can account for a significant share of commodity trade (example: “refined copper including remelted” > half of Chile’s copper exports in 2010; “ores and concentrates of copper” ≈ one third).

- Role within broader database
  - 45-commodity monthly series and 40-commodity annual series feed country-specific commodity price indices for 182 economies over 1962–2018 (monthly series start in 1980; annual series use 40 commodities and start in 1962).
  - Indices used (after deflation by MUV) as P_{j,t} in index construction:
    - ∆Log(Index)_{i,t} = sum_{j=1}^J ∆P_{j,t} Ω_{i,j,t}
    - ∆ denotes first differences; Ω_{i,j,t} are commodity- and country-specific time-varying weights.

- Data limitations and choices
  - Annual database excludes gold, olive oil, pork, rapeseed oil, and uranium due to data availability constraints.
  - Monthly gold trade flows (1980-based monthly database) use Comtrade SITC Rev 2 because non-monetary gold not reported in SITC Rev 1.
  - MUV index chosen for deflation to avoid CPI inclusion of nontradables that may distort trends.

### Commodity terms-of-trade index (Section 4.1)

- Construction methodology
  - Indices labeled xm_gdp in the database, constructed similarly to Spatafora and Tytell (2009).
  - Annual weight of each commodity:
    - ω_{i,j,τ} = (x_{i,j,τ} − m_{i,j,τ}) / GDP_{i,τ}
    - x_{i,j,τ} (m_{i,j,τ}) = exports (imports) value of commodity j of country i in year τ in US dollars; GDP_{i,τ} = nominal GDP in US dollars.
  - Net-exports weighting rationale:
    - Allows imported-commodity price variations (x_{i,j,τ} − m_{i,j,τ} < 0) to be accounted for.
    - Sum of weights not constrained to one and can be positive or negative.
  - Economic interpretation:
    - A one percentage point change in the commodity terms-of-trade index ≈ change in aggregate disposable income equivalent to one percentage point of GDP (first-order approximation, abstracts from volume reactions).

- Stylized facts (1963–2018 unless noted)
  - Average annual growth rate across all countries: 0.3 percent.
  - Distribution and variability:
    - Interquartile range: 1.2 percentage points.
    - Interdecile range: 4.3 percentage points.
    - Standard deviation: 4.2 percent.
    - Distribution has fat tails and is skewed to the right.
  - Heterogeneity:
    - EMDEs show more extreme growth rates than AEs.
    - Commodity exporters exhibit more extreme growth rates than other economies:
      - Standard deviation for non-commodity exporters: 2.3 percent.
      - Standard deviation for commodity exporters: 6.7 percent.
    - During 2003–07 commodity price boom:
      - Commodity exporters: commodity terms of trade increased on average by 2.9 percent per year.
      - Other economies: commodity terms of trade declined by 0.5 percent per year on average.
  - Cross-country comovement:
    - Indices often differ substantially even among countries in same commodity category (examples: Australia, Chile, Peru; Colombia, Iran, Venezuela; Argentina and Sri Lanka).
    - Distribution of all pairwise correlations of annual growth is rather uniform; even among commodity exporters many pairwise correlations close to zero.

- Macro effects (local projections; Jordà, 2005 specification)
  - Panel local projection estimating cumulative responses over three years to a change in commodity terms-of-trade index:
    - y_{i,t+h−1} − y_{i,t−1} = α_h + β_{h0} Δtot_{i,t} + Σ_{j=1}^{J} β_{hj} Δtot_{i,t−j} + Σ_{j=1}^{J} ρ_{hj} Δy_{i,t−j} + μ_{hi} + ν_{ht} + ε_{i,t+h}
    - J = 3; country and time fixed effects; country-cluster robust standard errors.
    - y = log real GDP (rgdpna), real domestic absorption (rdana), or real consumption (rconna) from Penn World Table version 9.0.
  - Main results (Table 1, panel (a)):
    - Contemporaneous response (β_{1,0}) of all three aggregates indistinguishable from zero.
    - Cumulative response one year after shock (β_{2,0}) positive and statistically significant for real domestic absorption and real consumption.
    - Cumulative response after two years (β_{3,0}) significant for all three aggregates.
    - Magnitudes two years after a shock that raises aggregate disposable income by 1 percent of GDP:
      - Real GDP: on average 0.11 percent higher.
      - Real domestic absorption: 0.32 percent higher.
      - Real consumption: about 0.25 percentage points higher.
  - Selected Δtot coefficients (standard errors in parentheses) from Table 1, panel (a):
    - Output: h=1: 0.0225 (0.0311); h=2: 0.0539 (0.0442); h=3: 0.106** (0.0498).
    - Domestic Absorption: h=1: 0.0181 (0.0466); h=2: 0.190*** (0.0667); h=3: 0.320*** (0.0917).
    - Consumption: h=1: 0.00743 (0.0480); h=2: 0.119*** (0.0439); h=3: 0.252*** (0.0605).

- Interpretation nuances
  - Effects depend on whether terms-of-trade change stems from higher export prices or lower import prices.
  - Short-term output gains more likely with slack in commodity-sector capacity utilization; medium-term expansion via investment and higher aggregate demand plausible.
  - Consumption response depends on commodity sector characteristics and ownership concentration; perceived transitory windfalls may be saved.

- Comparison with standard terms of trade
  - Correlation between commodity and standard terms-of-trade series:
    - Median rolling correlation ≈ 0.5; interquartile range about 0.8.
    - Correlation close to 1 for ~10 percent of economies; negative for ~25 percent; lower than −.5 for ~10 percent.
  - Macro effects using IMF WEO standard terms-of-trade (Table 1, panel (b)):
    - Cumulative response of all three aggregates indistinguishable from zero at all horizons—except domestic absorption significant at 10 percent level two years after shock.
  - Reasons for differences:
    - External shocks may induce different export/import price reactions across countries due to pricing currency and price rigidity.
    - Commodity terms-of-trade series implicitly controls for trade openness since each commodity weighted by net exports over GDP.

- Exogeneity assessment
  - Market-share evidence (average global market share over 2000–15 for top country-commodity pairs):
    - Very few markets where a country’s global market share > 40 percent; examples: palm oil (Malaysia), soybeans (US), corn (US), olive oil (Spain), soybeans oil (Argentina).
    - Metals: Chile copper ≈ 20 percent; Niger uranium ≈ 30 percent.
    - Energy: Australia ≈ 30 percent of global coal exports (coal ≈ 20 percent of Australia’s total commodity exports); largest market shares for crude oil and natural gas range between 15 and 18 percent.
    - Conclusion: only a handful of countries both dominate a global commodity market and rely heavily on that commodity for total commodity exports.
  - Granger non-causality tests (Dumitrescu and Hurlin, 2012) — p-values (null: GDP growth does not Granger-cause changes in commodity terms of trade):
    - Commodity exporters (3 lags): Z p-value = 0.11; Z approx. p-value = 0.25.
    - Non-commodity exporters (8 lags): Z p-value = 0.08; Z approx. p-value = 0.19.
    - Advanced economies (2 lags): Z p-value = 0.89; Z approx. p-value = 0.95.
    - EMDE (8 lags): Z p-value = 0.12; Z approx. p-value = 0.25.
    - Large or market-dominant countries (3 lags): Z p-value = 0.07; Z approx. p-value = 0.14.
  - Interpretation:
    - Lowest p-values for large or market-dominant countries (expected), but adjusted p-value = 0.14.
    - Large p-values across groups support treating country-specific commodity terms-of-trade indices as largely determined in world markets and exogenous from individual-country perspective.

### Alternative commodity price indices (Section 4.2)

- Overview
  - Database includes country-specific commodity indices that vary by:
    - whether exports and imports are weighted by overall commodity trade or output; and
    - whether trade flows considered are only exports, only imports, or net exports.
  - Commodity weights ω_{i,j,τ} defined in Table 3.
  - Weighting by overall commodity trade similar to standard price indices but does not account for overall importance of commodities across countries.

- Definitions and weighting schemes (as in Table 3)
  - Commodity Export Price Indices:
    - ω_i,j,τ = x_i,j,τ / ∑_{J j=1} x_i,j,τ
    - ω_i,j,τ = xgdp_i,j,τ / GDP_i,τ
  - Commodity Import Price Indices:
    - ω_i,j,τ = m_i,j,τ / ∑_{J j=1} m_i,j,τ
    - ω_i,j,τ = mgdp_i,j,τ / GDP_i,τ
  - Commodity Terms-of-Trade Indices:
    - ω_i,j,τ = (x_i,j,τ − m_i,j,τ) / (∑_{J j=1} x_i,j,τ + ∑_{J j=1} m_i,j,τ)
    - ω_i,j,τ = xmgdp_i,j,τ / GDP_i,τ
  - Note: x_i,j,τ (m_i,j,τ) denote exports (imports) value of commodity j by country i in year τ in US dollars; GDP_i,τ denotes nominal GDP in US dollars.

- Key empirical illustrations and findings
  - Scaling by output (xmgdp) can produce very different windfall magnitudes than indices weighted by overall commodity trade (xm):
    - United States faced larger drop in xm over 2001–07 than Ukraine, but xmgdp shows Ukraine registered much larger losses in disposable income.
    - Average increase in xm during 2001–07 larger in Argentina than in Indonesia, but xmgdp windfall gains somewhat smaller for Argentina.
  - Export-only vs import-only vs terms-of-trade:
    - Export-only and import-only indices can diverge substantially from terms-of-trade series; relevance depends on the research question.
    - Example January 2007–July 2008, Argentina and Uruguay:
      - Export price indices improved in both as food prices increased.
      - Commodity terms-of-trade moved in opposite directions because Uruguay had a large negative oil trade balance while Argentina had a positive one.
  - Cross-country correlation evidence:
    - Distribution of correlations between annual growth rates of export price index (x) and net export price index (xm) over 1963–2018 shows many countries with high correlation but a non-negligible share with negative correlation.

- Time-varying versus fixed weights
  - Common practice:
    - Fixed weights based on average trade flows over a few years produce indices invariant to endogenous volume responses.
    - Time-varying weights capture evolving commodity importance; authors implement three-year rolling averages of trade values and output, lagged to be predetermined to price fluctuations.
  - Limitations of fixed weights:
    - May misrepresent relevance of individual commodities when mix of traded commodities or importance of net commodity exports in output changes over time.
    - Illustrative dynamics (1970–2015):
      - Equatorial Guinea: cocoa main export in 1970s–1980s (net exports > 40 percent of GDP in some years) while net oil importer; by early 2000s oil exceeded 90 percent of total commodity exports in some years.
      - Mongolia: net exports of coal > 16 percent of GDP in 2011 but insignificant before 2004.
  - Variability across commodities (1962–2015):
    - Variability of export shares typically larger than import shares.
    - Oil: standard deviation of share of oil in commodity imports between about 10 and 20 percentage points for half of economies.
    - Some food commodities (wheat, rice) show high variability in import shares.
  - Comparative index behavior (rolling vs fixed weights)
    - Rolling vs fixed weights can produce opposite signs and large magnitude differences for terms-of-trade shocks:
      - Mid-2014 commodity price collapse example:
        - Colombia: rolling weights index implies negative shock equivalent to loss in aggregate disposable income of more than 6 percent of GDP.
        - United Kingdom: rolling weights index implies windfall gains of about 1 percent of GDP.
        - Explanation: Colombia was a net oil importer and the UK a net oil exporter in early 1980s; situation reversed later — choice of reference period matters.
    - Cross-country correlations (monthly frequency, non-overlapping three-year windows):
      - Rolling vs 1980–83 weights:
        - Correlation ≈ 0.9 or higher for three-fourths of countries in first three windows.
        - Correlation ≈ 0.5 or less for one-fourth of countries in 2004–06 and 2010–12.
        - Correlation negative for one-tenth of countries in some windows.
      - Rolling vs 1980–2015 weights:
        - Correlation higher with longer-period fixed weights, but:
          - Correlation < 0.5 for ~one-tenth of countries between 1980 and 1994.
          - Correlation negative throughout 1980–2015 for 1 percent of countries.

- Implications for empirical work and index construction
  - Choice of index guided by research question:
    - Use output-weighted indices (xmgdp, mgdp, xmgdp) to estimate windfall gains/losses to aggregate disposable income.
    - Use export-only or import-only indices when focusing on export or import price dynamics and direct effects.
  - Weight selection trade-offs:
    - Fixed weights (short reference periods) ensure exogeneity to domestic volume responses but risk misrepresenting commodity relevance over long spans.
    - Time-varying, lagged rolling weights smooth short-term volatility while capturing structural changes.
  - Practical recommendation:
    - Researchers should consider multiple weighting schemes (time-invariant and time-varying) to assess robustness, particularly for long-span analyses covering structural changes in commodity composition.

### Data and Appendix highlights (Appendix A)

- Sample of economies (as reported)
  - Advanced economies: 28 (list includes Australia AUS193; Austria AUT122; ...; United States USA111).
  - Emerging market economies: 29 (list includes Albania ALB914; Algeria DZA612; ...; Venezuela VEN299). (Source lists 29 emerging market economies.)
  - Low-income developing countries: extensive list including Afghanistan AFG512; Bangladesh BGD513; ...; Zimbabwe ZWE698 (note: overlaps and counts presented as in source).

- Procedure to address trade data gaps
  - General approach: distinguish gaps at beginning/end vs intermediate gaps; use bilateral trade data to infer missing reporter values from partners.
  - Extended data gaps (≥ 30 years between 1962 and 2015):
    - Set export (import) values equal to sum of imports (exports) from (to) country i as reported by trading partners p ≠ i.
  - Gaps at beginning:
    - For commodities accounting for 20 percent or more of reporter’s commodity exports/imports, use variation in partners p ≠ i to extrapolate backward between 1970 and first available year.
    - Other commodities: set equal to values reported by trading partners.
    - Data gaps between 1962 and 1970: extrapolate backward such that share of each trade flow in output constant.
  - Intermediate gaps up to four years:
    - Linearly interpolate values adjacent to gap.
  - Intermediate gaps > four years:
    - Use variation in partners p ≠ i to infer reporter values; adjust partner-reported bilateral flows so cumulative variation over gap matches reporter’s trend.
    - Exports in gap computed recursively:
      - ∆x_{i,j,t} = ∆M_{i,j,t} − |∆M_{i,j,t}| / ∑_{t∈gap} |∆M_{i,j,t}| . (∆^{gap}M_{i,j} − ∆^{gap}x_{i,j}), with t ∈ gap.
    - Same procedure applied to imports.
  - Gaps at end:
    - > four years: extrapolate using change in sum of bilateral trade flows reported by partners p ≠ i.
    - ≤ four years: extrapolate such that share of each trade flow in output remains constant.

- Additional country notes and special cases (selected)
  - Belgium and Luxembourg: Comtrade reported jointly under BLX up to 1998; indices based on trade data starting in 1999.
  - Croatia, Slovenia, Macedonia, Bosnia and Herzegovina: indices start after breakup of Yugoslavia (1996 for Bosnia and Herzegovina; 1992 for Croatia, Slovenia, Macedonia).
  - Czech Republic and Slovak Republic: indices start in 1995 and 1993, respectively.
  - Eritrea indices start in 1993; pre-1993 Ethiopia data combined as reported under ETF with post-1993 ETH for ETH indices.
  - Germany: pre-1990 DEU corresponds to West Germany; post-1990 to reunified Germany.
  - Serbia and Montenegro: break in 2006; pre-2006 SCG combined with SRB from 2006 onward for Serbia; Montenegro series start in 2006 (MNE).
  - Sudan: break in 2012 when South Sudan independent; pre-2012 SDN combined with SUD from 2012 onward to construct SDN.
  - Yemen indices start in 1990; pre-unification North and South Yemen data discarded.

- Table A2 (commodities and price sources) — selected entries
  - Agricultural raw materials (examples):
    - Cotton: Cotton, Cotton Outlook 'A Index', Middling 1-3/32 inch staple, CIF Liverpool, US cents per pound.
    - Natural rubber: Rubber, Singapore Commodity Exchange, No. 3 Rubber Smoked Sheets, 1st contract, US cents per pound.
    - Wool: Wool Index, 2005 = 100.
  - Energy (examples):
    - Coal: Coal, Australian thermal coal, 12,000- btu/pound, less than 1% sulfur, 14% ash, FOB Newcastle/Port Kembla, US$ per metric ton.
    - Crude oil: Crude Oil (petroleum), Price index, 2005 = 100, simple average of three spot prices; Dated Brent, West Texas Intermediate, and the Dubai Fateh.
    - Natural gas: Natural Gas Price Index, 2005 = 100, includes European, Japanese, and American Natural Gas Price Indices.
  - Food and Beverages (examples):
    - Beef: Beef, Australian and New Zealand 85% lean fores, CIF U.S. import price, US cents per pound.
    - Rice: Rice, 5 percent broken milled white rice, Thailand nominal price quote, US$ per metric ton.
    - Wheat: Wheat, No.1 Hard Red Winter, ordinary protein, Kansas City, US$ per metric ton.
  - Metals (examples):
    - Aluminum: Aluminum, 99.5% minimum purity, LME spot price, CIF UK ports, US$ per metric ton.
    - Copper: Copper, grade A cathode, LME spot price, CIF European ports, US$ per metric ton.
    - Gold: Gold (UK), 99.5% fine, London afternoon fixing, Average of daily rates.
    - Iron ore: China import Iron Ore Fines 62% FE spot (CFR Tianjin port), US dollars per metric ton.
  - Primary source of price data: Primary Commodity Prices database; and authors’ compilation.

- Table A3 (gaps in trade data) — selected examples
  - Afghanistan: 1978-2008; 2012-2014 — 34 missing years.
  - Albania: 1962-1995 — 34.
  - Angola: 1963-1968; 1975-2015 — 47.
  - China: 1962-1984 — 23.
  - Iraq: 1962; 1964-1971; 1977-1999; 2003-2013; 2015 — 44.
  - Vietnam: 1962-1996; 2015 — 36.
  - (Full table in source lists all countries with their missing periods and counts.)

*Source: IMF working paper chapter "3.1 World Commodity Prices", "4.1 Commodity terms-of-trade index", "4.2 Alternative commodity price indices", and Appendix A from wp1921 (as provided).*

### 3.1    World Commodity Prices   .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .

### 3.1    World Commodity Prices

### Coverage and frequency
- International prices of 45 individual commodities are used.
- Two database variants are constructed:
  - a monthly database based on the 45 commodities that starts in 1980.
  - an annual database using a narrower set of 40 commodity prices that starts in 1962.

### Commodity groups and items (as listed)
- Energy: coal, crude oil, and natural gas.
- Metals: aluminum, copper, gold, iron ore, lead, nickel, tin, uranium, and zinc.
- Food and beverages: bananas, barley, beef, cocoa, coffee, corn, fish, fish meal, groundnuts, lamb, olive oil, oranges, palm oil, poultry, rapeseed oil, rice, shrimp, soybean meal, soybean oil, soybeans, sugar, sunflower seed oil, swine meat, tea, and wheat.
- Agricultural raw materials: cotton, hard logs, hard sawnwood, hides, natural rubber, soft logs, soft sawnwood, and wool.

### Price construction and deflation
- Real prices are constructed as the commodity price in US dollars divided by the IMF’s unit value index for manufactured exports (MUV index).
- The primary source for world commodity prices is the IMF Primary Commodity Prices database.
- The World Bank’s Global Economic Monitor database and data from the US Energy Information Administration are used to extend the price series of some commodities—barley, coal, iron ore, and natural gas—back to the 1960s.
- Annex Table A2 lists the individual commodities, the corresponding international price, and their sources (as referenced in the source document).

### Mapping prices to trade headings
- Trade data are from United Nations Comtrade, SITC Revision 1 nomenclature, at 5-digit headings; oil is handled at 3-digit aggregation.
- Each commodity price is linked to all SITC product codes corresponding to the unprocessed commodity and semi-processed products expected to comove with the primary commodity (example: copper price linked to “ores and concentrates of copper” (SITC 28311) and “refined copper including remelted” (SITC 68212)).
- Semi-processed categories can account for a significant share of commodity trade (example from source: “refined copper including remelted” accounted for more than half of Chile’s exports of copper in 2010, while “ores and concentrates of copper” accounted for about one third).

### Role within the broader database
- The 45-commodity monthly series and the 40-commodity annual series feed the construction of country-specific commodity price indices for 182 economies over 1962–2018 (the database overall covers 182 economies over 1962–2018; monthly series start in 1980; annual series use 40 commodities and start in 1962).
- These commodity price series are used (after deflation by the MUV index) as P_j,t in the index construction formula:
  - ∆Log(Index)_i,t = sum_{j=1}^J ∆P_j,t Ω_i,j,t
  - where ∆ denotes first differences, and Ω_i,j,t are commodity- and country-specific time-varying weights (see Section 4 for weighting details).

### Notes on data limitations and choices relevant to world prices
- Gold, olive oil, pork, rapeseed oil, and uranium are excluded from the annual database due to data availability constraints (the annual database excludes gold, olive oil, pork, rapeseed oil, and uranium).
- For gold, trade data limitations arise because exports and imports of non-monetary gold are not reported in Comtrade SITC Rev 1 data; monthly gold trade flows in the 1980-based monthly database use Comtrade SITC Rev 2 data.
- Using the MUV index as deflator follows standard practice in the literature and is preferred to consumer price indices of major economies because CPIs include nontradables which may distort price trends.

_Source: IMF working paper chapter "3.1 World Commodity Prices" from wp1921 (as provided)._

### 4.1    Commodity terms-of-trade index

### 4.1    Commodity terms-of-trade index

### Construction methodology
- Commodity terms-of-trade indices (labeled xm_gdp in the database) are constructed similarly to Spatafora and Tytell (2009).
- Annual weight of each commodity:
  - ω_{i,j,τ} = (x_{i,j,τ} − m_{i,j,τ}) / GDP_{i,τ}
  - x_{i,j,τ} (m_{i,j,τ}) denotes exports (imports) value of commodity j of country i in year τ, expressed in US dollars; GDP_{i,τ} denotes country i’s nominal GDP in US dollars in year τ.
- Net-exports weighting rationale:
  - Using net exports ensures price variations of imported commodities (where x_{i,j,τ} − m_{i,j,τ} < 0) are taken into account.
  - Sum of weights is not constrained to be one and can be positive or negative; unlike standard terms-of-trade indices, simultaneous equal increases in export and import prices need not cancel out unless commodity trade is balanced.
- Economic interpretation:
  - A one percentage point change in the commodity terms-of-trade index can be interpreted as a change in aggregate disposable income equivalent to one percentage point of GDP (first-order approximation, abstracts from volume reactions).

### Stylized facts
- Sample and central tendency:
  - Average annual growth rate of commodity terms of trade across all countries over 1963–2018 is 0.3 percent.
- Distribution and variability:
  - Interquartile range: 1.2 percentage points.
  - Interdecile range: 4.3 percentage points.
  - Standard deviation: 4.2 percent.
  - Distribution exhibits fat tails and is skewed to the right.
- Heterogeneity by country group and exporter status:
  - Extreme growth rates more prevalent for emerging market and developing economies (EMDEs) than for advanced economies (AEs).
  - Commodity exporters exhibit more extreme growth rates than other economies:
    - Standard deviation for non-commodity exporters: 2.3 percent.
    - Standard deviation for commodity exporters: 6.7 percent.
  - During 2003–07 commodity price boom:
    - Commodity exporters: commodity terms of trade increased on average by 2.9 percent per year.
    - Other economies: commodity terms of trade declined by 0.5 percent per year on average.
- Cross-country comovement:
  - Commodity terms-of-trade indices often differ substantially even among countries within the same commodity category (examples: Australia, Chile, Peru; Colombia, Iran, Venezuela; Argentina and Sri Lanka).
  - Distribution of all pairwise correlations of annual growth in commodity terms of trade is rather uniform; even among commodity exporters there is a high incidence of pairwise correlations close to zero.

### Commodity terms of trade and macroeconomic outcomes (local projections)
- Empirical specification:
  - Local projection (Jordà, 2005) panel estimates of cumulative responses over three years to a change in the commodity terms-of-trade index:
    - y_{i,t+h−1} − y_{i,t−1} = α_h + β_{h0} Δtot_{i,t} + Σ_{j=1}^{J} β_{hj} Δtot_{i,t−j} + Σ_{j=1}^{J} ρ_{hj} Δy_{i,t−j} + μ_{hi} + ν_{ht} + ε_{i,t+h}
    - J = 3; country and time fixed effects; country-based cluster-robust standard errors.
  - y is log of real GDP, real domestic absorption, or real consumption (Penn World Table version 9.0: rgdpna, rdana, rconna).
- Main results (Table 1, panel (a)):
  - Contemporaneous response (β_{1,0}) of all three macro aggregates to a commodity terms-of-trade shock is indistinguishable from zero.
  - Cumulative response one year after the shock (β_{2,0}) is positive and statistically significant for real domestic absorption and real consumption.
  - Cumulative response after two years (β_{3,0}) is significant for all three aggregates.
  - Magnitudes two years after a shock that raises aggregate disposable income by 1 percent of GDP:
    - Real GDP: on average 0.11 percent higher.
    - Real domestic absorption: 0.32 percent higher.
    - Real consumption: about 0.25 percentage points higher.
- Selected coefficient magnitudes from Table 1, panel (a) (Δtot coefficients; standard errors in parentheses):
  - Output: h=1: 0.0225 (0.0311); h=2: 0.0539 (0.0442); h=3: 0.106** (0.0498).
  - Domestic Absorption: h=1: 0.0181 (0.0466); h=2: 0.190*** (0.0667); h=3: 0.320*** (0.0917).
  - Consumption: h=1: 0.00743 (0.0480); h=2: 0.119*** (0.0439); h=3: 0.252*** (0.0605).
- Interpretation nuances:
  - Effects depend on whether the terms-of-trade change reflects higher prices for exported commodities or lower prices for imported commodities.
  - Short-term output gains more likely if there is slack in capacity utilization in the commodity sector; medium-term expansion via investment and higher aggregate demand is plausible.
  - Response of consumption depends on commodity sector characteristics and ownership concentration; windfall perceived as transitory may be saved rather than spent.

### Comparison with standard terms of trade
- Correlation between commodity and standard terms-of-trade series:
  - Median rolling correlation ~ 0.5; interquartile range about 0.8.
  - Correlation close to 1 for about 10 percent of economies; negative for about 25 percent of the sample; lower than −.5 for about 10 percent.
- Macro effects using standard terms-of-trade (IMF WEO series) in place of commodity series (Table 1, panel (b)):
  - Cumulative response of all three macro aggregates to standard terms-of-trade change is indistinguishable from zero at all horizons—except domestic absorption is statistically significant at the 10 percent level two years after the shock.
- Possible reasons for differences:
  - A given external shock may induce different reactions in export and import prices across countries depending on pricing currency and price rigidity.
  - Commodity terms-of-trade series implicitly controls for trade openness since each commodity is weighted by net exports over GDP.

### Exogeneity assessment
- Market-share evidence (average global market share over 2000–15 for top country-commodity pairs):
  - Very few commodity markets where an individual country’s global market share exceeds 40 percent; those include palm oil (Malaysia), soybeans (US), corn (US), olive oil (Spain), soybeans oil (Argentina).
  - Metals examples: Chile copper global market share ~20 percent; Niger uranium global market share ~30 percent.
  - Energy examples: Australia accounts for about 30 percent of global coal exports (coal ≈ 20 percent of Australia’s total commodity exports); largest market shares for crude oil and natural gas range between 15 and 18 percent.
  - Conclusion: only a handful of countries both dominate a global commodity market and rely heavily on that commodity for total commodity exports.
- Granger non-causality tests (Dumitrescu and Hurlin, 2012) — p-values reported in Table 2 (null: GDP growth does not Granger-cause changes in commodity terms of trade):
  - Commodity exporters (3 lags): Z p-value = 0.11; Z approx. p-value = 0.25.
  - Non-commodity exporters (8 lags): Z p-value = 0.08; Z approx. p-value = 0.19.
  - Advanced economies (2 lags): Z p-value = 0.89; Z approx. p-value = 0.95.
  - EMDE (8 lags): Z p-value = 0.12; Z approx. p-value = 0.25.
  - Large or market-dominant countries (3 lags): Z p-value = 0.07; Z approx. p-value = 0.14.
- Interpretation:
  - Lowest p-values occur for countries that are large or have market-dominant positions (expected since domestic developments could influence world prices), but even then the adjusted p-value is 0.14.
  - Overall, large p-values across groups support treating country-specific commodity terms-of-trade indices as largely determined in world markets and as exogenous from the perspective of individual countries.

*Source: Authors’ compilation.*

### 4.2    Alternative commodity price indices

### 4.2    Alternative commodity price indices

### Overview
- The database includes country-specific commodity price indices that differ on:
  - whether exports and imports of individual commodities are weighted by overall commodity trade or output; and
  - which country-commodity trade flows are considered (only exports, only imports, or net exports).
- The commodity weights of the alternative series (ω_i,j,τ in equation [2]) are defined in Table 3.
- Weighting by overall commodity trade is similar to standard price indices but does not account for differences in the overall importance of commodities across countries.

### Definitions and weighting schemes (as in Table 3)
- Commodity Export Price Indices:
  - ω_i,j,τ = x_i,j,τ / ∑_{J j=1} x_i,j,τ
  - ω_i,j,τ = xgdp_i,j,τ / GDP_i,τ
- Commodity Import Price Indices:
  - ω_i,j,τ = m_i,j,τ / ∑_{J j=1} m_i,j,τ
  - ω_i,j,τ = mgdp_i,j,τ / GDP_i,τ
- Commodity Terms-of-Trade Indices:
  - ω_i,j,τ = (x_i,j,τ − m_i,j,τ) / (∑_{J j=1} x_i,j,τ + ∑_{J j=1} m_i,j,τ)
  - ω_i,j,τ = xmgdp_i,j,τ / GDP_i,τ
- Note: x_i,j,τ (m_i,j,τ) denote the exports (imports) value of commodity j by country i in year τ, expressed in US dollars; GDP_i,τ denotes country i’s nominal GDP in US dollars in year τ.

### Key empirical illustrations and findings
- Comparisons across alternative indices:
  - Countries facing similar variations in commodity prices (as captured by the terms-of-trade index xm, weighted by overall commodity trade) can experience very different windfall gains or losses when weights scale by output (xmgdp).
  - Example comparisons:
    - The United States faced a larger drop in xm over 2001–07 than Ukraine, but xmgdp reveals that Ukraine registered much larger losses in disposable income.
    - The average increase in xm during 2001–07 was larger in Argentina than in Indonesia, but associated windfall gains (xmgdp) were somewhat smaller for Argentina.
  - Export-only and import-only indices can diverge substantially from terms-of-trade series; relevance depends on the research question.
    - Example: January 2007–July 2008, Argentina and Uruguay:
      - Export price indices improved in both countries as food commodity prices increased.
      - Commodity terms-of-trade indices moved in opposite directions because of differences in commodity import prices—Uruguay had a large negative oil trade balance while Argentina had a positive one.
- Cross-country correlation evidence:
  - The distribution of correlations between annual growth rates of the export price index (x) and the net export price index (xm) over 1963–2018 shows a substantial number of countries with high correlation, but a non-negligible share with negative correlation.

### Time-varying versus fixed weights — advantages, limitations, and evidence
- Common practice:
  - Fixed weights based on average trade flows over a few years (e.g., Deaton and Miller, 1996; Aghion et al., 2010; Ricci et al., 2013) produce indices invariant to endogenous volume responses to price fluctuations.
  - Time-varying weights (as in equation [2]) capture evolving commodity importance; authors implement three-year rolling averages of trade values and output, lagged to be predetermined to price fluctuations.
- Limitations of fixed weights:
  - Fixed weights may misrepresent the relevance of individual commodities when the mix of traded commodities or the importance of net commodity exports in output changes over time.
  - Illustrative country-level dynamics (1970–2015):
    - Equatorial Guinea: cocoa was main export in the 1970s–1980s (net exports exceeding 40 percent of GDP in some years) while the country was a net oil importer; by the early 2000s oil exceeded 90 percent of total commodity exports in some years.
    - Mongolia: net exports of coal exceeded 16 percent of GDP in 2011 but were insignificant before 2004.
- Variability across commodities (1962–2015):
  - Variability of export shares is typically larger than import shares.
  - Oil: standard deviation of share of oil in commodity imports is between about 10 and 20 percentage points for half of the economies in the sample.
  - Some food commodities (wheat, rice) also show high variability in import shares.
- Comparative index behavior and concrete magnitudes:
  - Using rolling weights versus fixed weights can produce opposite signs and large magnitude differences for terms-of-trade shocks:
    - Mid-2014 commodity price collapse example:
      - Colombia: rolling weights index implies a negative shock equivalent to a loss in aggregate disposable income of more than 6 percent of GDP.
      - United Kingdom: rolling weights index implies windfall gains of about 1 percent of GDP.
      - Explanation: Colombia was a net oil importer and the UK a net oil exporter in the early 1980s, but that situation reversed later; choice of reference period matters.
- Cross-country correlation between indices based on rolling and fixed weights (monthly frequency, non-overlapping three-year windows):
  - Panel (a) (rolling vs 1980–83 weights):
    - Correlation about 0.9 or higher for three-fourths of countries in the first three windows.
    - Correlation is about 0.5 or less for one-fourth of countries in 2004–06 and 2010–12.
    - Correlation is negative for one-tenth of countries in some windows.
  - Panel (b) (rolling vs 1980–2015 weights):
    - Correlation higher when fixed weights use average trade flows over a longer period, but:
      - Correlation lower than 0.5 for about one-tenth of countries between 1980 and 1994.
      - Correlation is negative throughout 1980–2015 for one percent of the countries in the sample.

### Implications for empirical work and index construction
- Choice of index should be guided by the research question:
  - Use indices weighted by output (xmgdp, mgdp, xmgdp) when estimating windfall gains/losses to aggregate disposable income.
  - Use export-only or import-only indices when interested specifically in export or import price dynamics and their direct effects.
- Weight selection:
  - Fixed weights (short reference periods) ensure exogeneity to domestic volume responses but risk misrepresenting commodity relevance over long samples.
  - Time-varying, lagged rolling weights smooth short-term volatility while capturing structural changes in commodity mixes and importance.
- Practical recommendation based on evidence:
  - Researchers should consider multiple weighting schemes (time-invariant and time-varying) to assess robustness, particularly for long-span analyses covering structural changes in commodity composition.

*Source: wp1921 - 4.2    Alternative commodity price indices*

### Appendix A.  Data

### Appendix A.  Data

### Sample of economies
- (a) Advanced economies: 28
  - Australia AUS193; Austria AUT122; Belgium BEL124; Canada CAN156; Cyprus CYP423; Czech Republic CZE935; Denmark DNK128; Estonia EST939; Finland FIN172; France FRA132; Germany DEU134; Greece GRC174; Hong Kong SAR HKG532; Iceland ISL176; Ireland IRL178; Israel ISR436; Italy ITA136; Japan JPN158; Korea KOR542; Latvia LVA941; Lithuania LTU946; Luxembourg LUX137; Malta MLT181; Netherlands NLD138; New Zealand NZL196; Norway NOR142; Portugal PRT182; Singapore SGP576; Slovak Republic SVK936; Slovenia SVN961; Spain ESP184; Sweden SWE144; Switzerland CHE146; United Kingdom GBR112; United States USA111
- (b) Emerging market economies: 29
  - Albania ALB914; Algeria DZA612; Angola AGO614; Antigua and Barbuda ATG311; Argentina ARG213; Armenia ARM911; Azerbaijan AZE912; Bahamas, The BHS313; Bahrain BHR419; Barbados BRB316; Belarus BLR913; Belize BLZ339; Benin BEN638; Bolivia BOL218; Bosnia and Herzegovina BIH963; Botswana BWA616; Brazil BRA223; Brunei Darussalam BRN516; Bulgaria BGR918; Cabo Verde CPV624; Chile CHL228; China CHN924; Colombia COL233; Costa Rica CRI238; Croatia HRV960; Cyprus appears in advanced list above; Dominican Republic DOM243; Ecuador ECU248; Egypt EGY469; El Salvador SLV253; Equatorial Guinea GNQ642; Eswatini SWZ734; Fiji FJI819; Gabon GAB646; Georgia GEO915; Grenada GRD328; Guatemala GTM258; Guyana GUY336; Honduras HND268; Hungary HUN944; India IND534; Indonesia IDN536; Iran IRN429; Iraq IRQ433; Jamaica JAM343; Jordan JOR439; Kazakhstan KAZ916; Kuwait KWT443; Lebanon LBN446; Libya LBY672; Macedonia, FYR MKD962; Malaysia MYS548; Maldives MDV556; Mauritius MUS684; Mexico MEX273; Mongolia MNG948; Montenegro, Rep. of MNE943; Morocco MAR686; Namibia NAM728; Nepal NPL558; Nicaragua NIC278; Niger NER692; Nigeria NGA694; Oman OMN449; Pakistan PAK564; Panama PAN283; Paraguay PRY288; Peru PER293; Philippines PHL566; Poland POL964; Qatar QAT453; Romania ROM968; Russia RUS922; Samoa WSM862; Saudi Arabia SAU456; Serbia SRB942; Seychelles SYC718; Sierra Leone SLE724; Singapore SGP576 appears in advanced list; South Africa ZAF199; Sri Lanka LKA524; St. Kitts and Nevis KNA361; St. Lucia LCA362; St. Vincent and the Grenadines VCT364; Suriname SUR366; Syria SYR463; Thailand THA578; Togo TGO742; Tonga TON866; Trinidad and Tobago TTO369; Tunisia TUN744; Turkey TUR186; Turkmenistan TKM925; Tuvalu TUV869; Ukraine UKR926; United Arab Emirates ARE466; Uruguay URY298; Vanuatu VUT846; Venezuela VEN299
  - (Note: the source lists 29 emerging market economies.)
- (c) Low-income developing countries
  - Afghanistan AFG512; Bangladesh BGD513; Benin BEN638; Bhutan BTN514; Burkina Faso BFA748; Burundi BDI618; Cambodia KHM522; Cameroon CMR622; Central African Republic CAF626; Chad TCD628; Comoros COM632; Congo, Democratic Republic of the COD636; Congo, Republic of COG634; Côte d'Ivoire CIV662; Djibouti DJI611; Eritrea ERI643; Ethiopia ETH644; Gambia, The GMB648; Ghana GHA652; Guinea GIN656; Guinea‐Bissau GNB654; Haiti HTI263; Honduras HND268; Kenya KEN664; Kiribati KIR826; Kyrgyz Republic KGZ917; Lao P.D.R. LAO544; Lesotho LSO666; Liberia LBR668; Madagascar MDG674; Malawi MWI676; Mali MLI678; Mauritania MRT682; Moldova MDA921; Mongolia MNG948 (also listed above); Mozambique MOZ688; Myanmar MMR518; Namibia NAM728 (also listed above); Nepal NPL558 (also listed above); Nicaragua NIC278 (also listed above); Niger NER692; Nigeria NGA694; Pakistan PAK564 (also listed above); Papua New Guinea PNG853; Rwanda RWA714; São Tomé and Príncipe STP716; Senegal SEN722; Sierra Leone SLE724 (also listed above); Solomon Islands SLB813; Sudan SDN732; São Tomé and Príncipe appears above; Tajikistan TJK923; Tanzania TZA738; Timor‐Leste TLS537; Togo TGO742 (also listed above); Tonga TON866 (also listed above); Tuvalu TUV869 (also listed above); Uganda UGA746; Uzbekistan UZB927; Vanuatu VUT846 (also listed above); Vietnam VNM582; Yemen YEM474; Zambia ZMB754; Zimbabwe ZWE698
  - (Note: the source indicates Low-income developing countries listing continues; count and overlaps as reported in the source.)

### Procedure to address trade data gaps
- General approach:
  - Distinguish gaps due to missing data at the beginning or end of the sample period from reporting gaps in the middle of the sample, and by their length.
  - Use bilateral trade data at the commodity level to infer the reporting country missing export and import values using those reported by its trading partners.
- Detailed procedures:
  - Extended data gaps:
    - Export (import) values of each commodity j by country i, for which data are unavailable for 30 or more years between 1962 and 2015, are set equal to the sum of imports (exports) from (to) country i as reported across all trading partners p ≠ i.
  - Gaps at the beginning of the sample:
    - For each commodity j that is of primary importance for country i—defined as those that account for 20 percent or more of the reporter country’s commodity exports/imports—we use the variation in trade flows reported by all trading partner p ≠ i to extrapolate backward the country i’s export and import values of commodity j between 1970 and the first year in which country i’s data are available.
    - For other commodities, country i’s trade flows are set equal to those reported across all its trading partners (as described above for extended data gaps).
    - Data gaps between 1962 and 1970 are filled by extrapolating trade flows backward such that the share of each trade flow in output are constant.
  - Intermediate gaps of up to four years:
    - For gaps of up to four years in the middle of the sample—when the country reports trade data before and after the data gap—exports and imports of each commodity are computed by linearly interpolating the values in years adjacent to the data gap.
  - Intermediate gaps of more than four years:
    - For gaps of more than four years we use the variation in trade flows reported by all trading partner p ≠ i to infer country i’s export and import values of commodity j during the period with missing data.
    - Bilateral trade flows reported by a country and its trading partners often differ; to avoid introducing breaks, trade flows reported by trading partners are adjusted so that the cumulative variation over the gap period matches that from the reporter country.
    - Exports of commodity j by country i in year t ∈ gap are computed recursively using:
      - ∆x_{i,j,t} = ∆M_{i,j,t} − |∆M_{i,j,t}| / ∑_{t∈gap} |∆M_{i,j,t}| . (∆^{gap}M_{i,j} − ∆^{gap}x_{i,j}), with t ∈ gap (5)
      - where x_{i,j,t} are exports of commodity j at time t from country i to all trading partners (as reporter by country i); ∆ denotes first differences; ∆^{gap} denotes the cumulative change during the gap period; and .M_{i,j,t} = ∑_{p=1}^P m_{i,p,j,t} is the sum of imports of commodity j at time t by all trading countries p ≠ i from country i (as reported by countries p). The same procedure is applied to imports.
    - (Footnote context: When changes in exports/imports by trading countries are used to extend trade flows of the reported country, they need to be re-scaled accordingly so that the trend is preserved.)
  - Gaps at the end of the sample:
    - For gaps of more than four years, export and import values for each commodity by country i are extrapolated using the change in sum of bilateral trade flows reported by all trading partners p ≠ i.
    - For gaps of up to four years, exports and imports of each commodity are extrapolated such that the share of each trade flow in output remains constant.

### Additional country notes and special cases
- Belgium and Luxembourg:
  - Trade for Belgium and Luxemburg in Comtrade are reported jointly under Belgium-Luxemburg (ISO code BLX) up to 1998. Indices in this database for Belgium and Luxemburg are based on trade data starting in 1999.
- Croatia, Slovenia, Macedonia, Bosnia and Herzegovina:
  - Indices start after the breakup of Yugoslavia—in 1996 for Bosnia and Herzegovina and in 1992 for Croatia, Slovenia, and Macedonia.
- Czech Republic and Slovak Republic:
  - Indices start after the dissolution of Czechoslovakia—starting in 1995 and 1993, respectively.
- Ethiopia and Eritrea:
  - Indices for independent Eritrea start in 1993. Pre-1993 data for Ethiopia (reported under ISO code ETF in Comtrade) is combined with post-1993 data (reported under ISO code ETH) to construct indices reported under ISO code ETH.
- Former Soviet Union economies:
  - Initial year of indices varies by country depending on data availability:
    - Armenia 1992; Azerbaijan 1992; Belarus 1992; Estonia 1993; Georgia 1994; Kazakhstan 1992; Kyrgyz Republic 1992; Latvia 1992; Lithuania 1995; Moldova 1992; Russia 1990; Tajikistan 1992; Turkmenistan 1992; Ukraine 1992; Uzbekistan 1992.
- Germany:
  - Comtrade data reported under ISO code DEU before 1990 correspond to West Germany and to reunified Germany thereafter.
- Serbia and Montenegro:
  - Comtrade data present a break in 2006 when Montenegro became independent. Pre-2006 data reported under ISO code SCG is combined with data reported under ISO code SRB from 2006 onward to construct indices for Serbia (SRB). Montenegro series start in 2006 and are reported under ISO code MNE.
- Sudan:
  - Comtrade data present a break in 2012 as South Sudan became independent in 2011. Pre-2012 data reported under ISO code SDN is combined with data reported under ISO code SUD from 2012 onward to construct indices reported under ISO code SDN.
- Yemen:
  - Indices of Yemen start in 1990. Data of North and South Yemen preceding the unification are discarded.

### Table A2: List of commodities and price sources (selected categories and examples)
- Agricultural raw materials:
  - Cotton: Cotton, Cotton Outlook 'A Index', Middling 1-3/32 inch staple, CIF Liverpool, US cents per pound
  - Natural rubber: Rubber, Singapore Commodity Exchange, No. 3 Rubber Smoked Sheets, 1st contract, US cents per pound
  - Wool: Wool Index, 2005 = 100, includes Coarse and Fine Wool Price Indices
  - (Other items: Hard logs, Hard sawnwood, Hides, Soft logs, Soft sawnwood)
- Energy:
  - Coal: Coal, Australian thermal coal, 12,000- btu/pound, less than 1% sulfur, 14% ash, FOB Newcastle/Port Kembla, US$ per metric ton
  - Crude oil: Crude Oil (petroleum), Price index, 2005 = 100, simple average of three spot prices; Dated Brent, West Texas Intermediate, and the Dubai Fateh
  - Natural gas: Natural Gas Price Index, 2005 = 100, includes European, Japanese, and American Natural Gas Price Indices
- Food and Beverages (selected):
  - Beef: Beef, Australian and New Zealand 85% lean fores, CIF U.S. import price, US cents per pound
  - Coffee: Coffee Price Index, 2005 = 100
  - Rice: Rice, 5 percent broken milled white rice, Thailand nominal price quote, US$ per metric ton
  - Wheat: Wheat, No.1 Hard Red Winter, ordinary protein, Kansas City, US$ per metric ton
  - (Other items include Bananas, Barley, Chicken, Cocoa, Corn, Fish, Fish meal, Groundnuts, Lamb, Olive oil, Oranges, Palm oil, Pork, Rapeseed oil, Shrimp, Soybean meal, Soybean oil, Soybeans, Sugar, Sunflower seed oil, Tea)
- Metals (selected):
  - Aluminum: Aluminum, 99.5% minimum purity, LME spot price, CIF UK ports, US$ per metric ton
  - Copper: Copper, grade A cathode, LME spot price, CIF European ports, US$ per metric ton
  - Gold: Gold (UK), 99.5% fine, London afternoon fixing, Average of daily rates
  - Iron ore: China import Iron Ore Fines 62% FE spot (CFR Tianjin port), US dollars per metric ton
  - (Other items include Lead, Nickel, Tin, Uranium, Zinc)
- Source of price data:
  - Primary Commodity Prices database; and authors’ compilation.

### Table A3: Gaps in trade data (overview and examples)
- The table lists periods of missing data between 1962 and 2015 and the total number of missing years for each country.
- Examples from the table (country — periods of missing data — Missing years):
  - Afghanistan 1978-2008; 2012-2014 — 34
  - Albania 1962-1995 — 34
  - Algeria 1962-1965; 1967; 1972 — 6
  - Angola 1963-1968; 1975-2015 — 47
  - Antigua and Barbuda 1970-1972; 1976; 1979-1980; 1982-1998; 2001-2004; 2006; 2008 — 29
  - Argentina 1982 — 1
  - Australia 1962 — 1
  - Austria 1962 — 1
  - China 1962-1984 — 23
  - India 1982 — 1
  - Indonesia 1962-1966; 2015 — 6
  - Iraq 1962; 1964-1971; 1977-1999; 2003-2013; 2015 — 44
  - Libya 1982; 1990; 1992-1996; 1999-2006; 2011-2015 — 20
  - Russia 1992-1995 — 4
  - Venezuela 2007; 2014-2015 — 3
  - Vietnam 1962-1996; 2015 — 36
- (The source table provides a comprehensive list of all countries with their specific missing periods and counts as compiled by the authors.)

*Source: Authors’ compilation; income classifications are according to the IMF World Economic Outlook database and as of October 2018.*

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_Source: https://www.imf.org/-/media/files/publications/wp/2019/wp1921.pdf_