A readily computable commodity price index: Abstract

Transcription

1 A readily computable commodity price index: Abstract This article presents an extended version of Grilli and Yang (1988) s non-fuel commodity price index (GYCPI) for the period of Specifically, the annual index under consideration comprises thirty-six commodities: the twenty-four non-fuel primary commodities considered by Grilli and Yang, two fuel commodities (i.e., oil and coal), eight additional metals and minerals (i.e., boron, cobalt, iron ore, iron & steel, manganese, phosphate rock, tungsten, and nickel), and two additional precious metals (i.e., gold and platinum). The extended index displays strong co-movement with a Divisia-version of GYCPI. In addition, this article presents a commodity price index computed at a monthly frequency for the period of January 1977-December 2017, which is compared to other existing indices such as the S&P GS Non-Energy and the World Bank Non-Energy. The annual and monthly indices here presented can be easily computed and updated from publicly available information. Keywords: Grilli-Yang commodity price index; Divisia 1 Introduction Grilli and Yang (1988) s seminal article presented a new U.S. dollar index of prices of twenty-four internationally traded nonfuel commodities, beginning in The basic version of their index Grilli-Yang Commodity Price Index (GYCPI), was base-weighted, where the weights were the values of world exports of each commodity. The idea was that the index reflected the movements of international prices of a given basket of primary commodities. Grilli and Yang also computed three additional versions of GYCPI: agricultural food commodities (GYCPIF), nonfood agricultural commodities (GYCPINF), and metals (GYCPIM). Over the years, Grilli-Yang commodity price indices have been extensively studied in the literature; see, for instance, the articles by Cuddington (1992); Cuddington and Wei (1992), Pfaffenzeller, Newbold, and Rayner (2007); Erten and Ocampo (2012); Yamada and Yoon (2014), Drechsel and Tenreyro (2017), and Harvey, Kellard, Madsen, and Wohar (2017) to cite just a few. This article generalizes GYCPI by including fuel commodities, a broader class of metals and minerals, and two additional precious metals. This extended index can be easily computed by using the Divisia-moment approach (e.g., Clements 1982; Feenstra and Reinsdorf 2000; Tcha and Takashina 2002; Chen 2010) on the basis of publicly available data from Pfaffenzeller et al. op. cit. s appendix, the US Geological Service, the International Monetary Fund, and the World Bank.

2 This article is organized as follows. Section 2 presents some methodological aspects of a Divisia price index. Section 3 in turn introduces an extended version of Grilli- Yang non-fuel commodity price index. Sections 4 and 5 present the data and discuss the empirical results, respectively. Section 6 considers higher-frequency data by proposing a Divisia monthly commodity price index. Section 7 concludes. 2 Methodology 2.1 A Divisia-based commodity price index Consider N commodities with price and quantity vectors given by p = (p 1 p 2...p N ) and q = (q 1 q 2...q N ), respectively. Total expenditure is defined as m = p q = p q. Moreover, let i = p i q i /m. Hence, where d(ln(p )) = dp d ln(m) = ω d(ln(p )) + ω d(ln(q )) (1) p and d(ln(q )) = dq q. Equation (1) can be re-written as d ln(m) = d(ln(p)) + d(ln(q)), where d(ln(p)) = ω d(ln(p )) and d(ln(q)) = ω d(ln(q )) are the Divisia price and quantity indices, respectively. 1 Furthermore, if DP ln(p t /P t 1 ) and Dp it ln(p it /p i, t 1 ) represent the log price-return on the commodity price index and on commodity i, respectively, then DP = ω Dp (2) is a budget-share weighted average of the N price log-changes, where ω = (ω, + ω ) 2. (See, for instance, Tcha and Takashina 2002). 2 On the other hand, as in Chen (2010), assume that the N commodities are divided into G subgroups, S 1, S 2,..., S G, each containing n 1, n 2,..., n G commodities, respectively, such that n = N. If commodities are equally weighted, then ω = 1/N with ω = 1. Let W, = ω = n N be the weight assigned to group g, such that W, = 1. In turn, let the share of commodity i within S g be ω = that ω = 1., =, such 1 r In particular, notice that d(ln(p ))» 1 ω = ln, is the log price-return on commodity i at time t. 1 = ω e 1, where,( ) 2 For a more technical discussion, see the derivation of a Divisia price index in the context of an Almost Ideal System Demand (AIDS) presented by Feenstra and Reinsdorf (2000). 2

3 Consequently, the log price-return on group g at time t, DP gt, is given by Moreover DP = ω Dp (3) DP = G G W g,t DP gt = W g,t g=1 g=1 ω it G W g,t g=1 i S g i S g Dp it = ω it Dp it = ω Dp (4) which is consistent with equation (2). The second-order moment of log returns for the N commodities in turn is given by Π = ω (Dp DP ) = ω Dp DP (5) whereas for the commodities in group g by Π = ω (Dp DP ) = ω Dp DP (6) so that W, Π = ω Dp W, DP. That is, ω Dp = W, Π + W, DP (7) After substituting (7) into (5) and by using the fact that DP = g=1 W g,t DP gt, Π can be expressed as the sum of within-group price variation and between-group price variation: Π = W, Π + W, (Dp DP ) (8) 2.2 A Divisia-version of Grilli-Yang non-fuel commodity price index Table 1 presents the trade-based commodity weights utilized by Grilli and Yang (1988) to construct their non-fuel commodity price index (GYCPI). The weights are based on each commodity s average export share during the base period of , and reproduced from Table 1 in Pfaffenzeller et al. (2007). In particular, GYCPI is computed as an arithmetically weighted average of commodity prices: GYCPI = ω p (9) G 3

4 where N = 24, ω is the appropriate (time-invariant) weight provided in the second column of Table 1, and p it is the commodity price in period t indexed to its average. Grilli and Yang also constructed sub-indices for agricultural food commodities, non-food agricultural commodities, and metals, which can be computed as in (9) by using the corresponding weights of each category given in the third column of Table 1. A geometric version of GYCPI (e.g., Cuddington and Wei 1992) is given by GYCPI = p (10) From (10) a Divisia version of GYCPI (DGY) is immediate. Let DP ω Dp (11) where Dp it = ln(p it /p i, t 1 ). For a given initial value of DGY 0 = GYCPI 0, DGY t can be computed recursively as DGY t = DGY t 1 exp(dp ) (12) It is apparent that DP equals the log-return on GYCPI because ln (GYCPI ) = ω ln (p ) and, hence, ln (GYCPI /GYCPI ) = ω ln (p /p, ). 3 A new commodity price index The price index proposed in this article is composed of thirty-six commodities: the twenty-four non-fuel primary commodities considered by Grilli and Yang op. cit, two fuel commodities (i.e., oil and coal), eight additional metals and minerals (i.e., boron, cobalt, iron ore, iron & steel, manganese, phosphate rock, tungsten, and nickel), and two additional precious metals (i.e., gold and platinum). These thirty-six commodities are in turn classified into seven categories: beverages, cereals, other food, agricultural raw materials, energy, metals & minerals, and precious metals. This sorting follows closely that of the World Bank Commodity Price Index but excludes fertilizers natural phosphate rock, phosphate, potassium, and nitrogenous. The exception is phosphate rock, which is added to metals & minerals in the spirit of UNCTAD. 3 Table 2 provides the details. The weights assigned to each category have been computed according to the methodology of Section 2.1. For the sake of comparison, it is worth noticing that the weights given by Grilli and Yang to agricultural food commodities, non-food agricultural commodities, and metals were 55.0%, 27.2%, and 17.8%, 3 The World Bank Commodity Price Data is available at whereas UNCTAD Stats at 4

5 respectively. In Table 2, agricultural food commodities (beverages + cereal + other food) represent 30.6% of the index, while non-food agricultural commodities (agricultural raw materials) 19.4%. The metal categories of Table 2 (metals & minerals + precious metals) represent 44.4% of the index because of the large number of commodities involved (sixteen altogether). Finally, fuels, which were not considered by Grilli and Yang, represent only 5.6%. The World Bank Non-Energy (WBNE) Index in turn assigns weights of 31.6%, 64.9%, and 3.6% (based on developing countries' export values) to metals & minerals, agriculture, and fertilizers, respectively. As can be easily computed, Table 2 assigns altogether 36.1 % to metals & minerals and 50% to agriculture, figures not so distant from the World Bank s. Precious metals, however, are not considered in the WBNE Index, but grouped into a separate index. 4 Data The data series are drawn from various sources: Pfaffenzeller et al. (2007) s appendix S.1, for individual commodities and Grilli-Yang commodity price index and sub-indices for the period of ; the IMF s International Financial Statistics (IFS) and the World Bank Commodity Price Data (Pink Sheet) for updating the series for the period of ; and, the US Geological Service (USGS) for historical prices of metals and minerals, such as boron, cobalt, iron & steel, iron ore, manganese, nickel, phosphate rock, and tungsten, which are available at for the period of Price information updated to 2016 is taken from the Mineral Commodity Summary 2017, For most minerals and metals, the USGS provides time series of unit value per ton in US dollars starting from Unit value is defined as the value of one ton of apparent consumption (= secondary production + imports exports stock changes + government shipments.) 5 Empirical results and discussion Figure 1 depicts five commodity price indices for the period of The Divisia Non-fuels index is the one described in Section 3 after excluding coal and oil. That is, its log-return is computed on the basis of thirty-four commodities according to the methodology of Section 2.1, and its initial value corresponds to that taken by GYCPI and its Divisia version (DGY) in Similarly, GYCPI and DGY are computed according to equations (9) and (12) of Section 2.2. For completeness, the WBNE index, recorded by the World Bank from 1960 onwards, is also reproduced. As mentioned earlier, this index gives weights of 31.6% to metals & minerals, 64.9% to agriculture, and 3.6% to fertilizers, and it excludes precious metals. A Divisia Non-fuels/Non-precious metals index is also included 5

6 in the graph so that it resembles WBNE more closely. All indices have been deflated by the US CPI and expressed in 2016 US dollars. As can be seen from the figure, the indices displayed high co-movement along the sample period, which translated into high bivariate correlations of their log-returns. For instance, the Pearson correlations of the Divisia Non-fuels index with WBNE, GYCPI and DGY reached 0.93, 0.89, and 0.92, respectively, during The exclusion of precious metals from the Divisia-Non fuels index drives such correlations slightly up to 0.95, 0.93, and 0.96, respectively. On the other hand, the correlation of the log returns on GYCPI and DGY (a modified version of GYCPI with geometric weights) reached 0.97 during However, it is apparent from Figure 1 that the use of arithmetic weights has an impact on the level of GYCPI, as it evolves mostly below the other four indices. Various studies have examined the empirical validity of the Prebish-Singer hypothesis of a secular decline in relative prices of primary commodities (e.g., Cuddington Wei 1992; Yamada and Yoon 2014; Baffles and Etienne 2016; Harvet et al. 2017). Based on the methodology developed by Harvey, Kellard, Madsen and Wohar (2010), the rejection of the null hypothesis of no trend for the above five indices depends on the significance level. The only index that rejects the null at the 1% significance level is GYCPI. Its estimated annual growth rate for the period of is 0.98%, whereas a 95%- confidence interval for this rate is given by ( 1.65%, 0.31%). In the case of the Divisia Non-fuel index, the null hypothesis is rejected only at the 10% significance level. Its estimated annual growth rate is 0.47% with a 95%-confidence interval of ( 1.06%, 0.12%). Figure 2(a) in turn depicts the variance decomposition of log-price returns, t (Eq. (8)) on the Divisia price index, DP t, composed of the thirty-six commodities. As can be seen, through time a sizeable percentage of total variance corresponded to within-group variation. In particular, by focusing on averages (Table 3), the categories of other food, agricultural raw materials and metals & minerals were the ones that jointly explained nearly 80% of total within-group variance: 19.5%, 20.9%, and 38.3%, respectively. Regarding between-group variation, the seven commodity groups displayed relatively similar mean percentages, which ranged from 11% to 18% of total betweengroup variance during However, very extreme values were observed along the same period. For instance, 80% of between-group variance was explained by beverages in 1954, 79.8% by other food in 1963, 73.1% by energy in 2015, and 85.1% by precious metals in For completeness, Figure 2(b) shows the annual volatility estimate for DP t, Π, for the period of Along the 116-year period, the three most volatile years were 6

7 1908 (57.6%), 1921 (41%), and 1974 (34.5%). In the most recent past, 2008 stood our also a very volatile year (28.1%). In order to quantify the market risk of each of the thirty-six commodities, Table 4 presents betas computed from the regression model Dp it = + i DP t + it for the period of In this context, DP t is the log-return on the market index, which gauges global or systematic risk and it is given by the Divisia index for N = 36; Dp it in turn is the logreturn on a single commodity or group. Table 4 also presents the R 2 associated to each regression, which is a measure of the proportion of variability of each commodity/group log-return accounted for by the market as a whole. In turn (1 R 2 ) is a measure of percentage variability explained by commodity-specific factors. 4 As can be seen from the table, the least risky commodities during were boron, phosphate rock, tobacco, and banana, whose betas were not statistically different from zero. The riskiest ones by contrast were copper, tungsten, palm oil, tin, and rubber with corresponding betas of 1.48, 1.48, 1.51, 1.56, and In turn the individual commodities with the highest R 2 were timber (49%), tin (50%), and copper (53%), and with the lowest R 2 (given statistically significant betas), iron ore (5%), cobalt (7%), and beef (9%). Among commodity categories, the betas ranged from 1.11 (agricultural raw materials and precious metals) to 0.89 (beverages). The largest R 2 corresponded to metals & minerals (63%), agricultural raw materials (61%), and precious metals (44%), and the lowest R 2 to beverages (26%), energy (35%), and cereals (38%). 6 Extension: a monthly Divisia index In this section, the Divisia index of Section 2.2 is computed at a monthly frequency for January 1977-December 2017, by considering forty-six commodities of the World Bank s pink sheet. Although the latter contains price information from January 1960 onwards, complete data for all commodities is available from January In addition, prior to 1977, some prices displayed infrequent variation (e.g., crude oil, natural gas). The commodities under consideration are listed on Table 5. Similar to the pattern observed in the annual data (Figure 2a), a considerably portion of total variance corresponded to within-group variation (84.9% on average) along January 1977-December Table 6 provides details by presenting summary statistics of within- and between-group variation by commodity class. As can be seen, on average agriculture explained 68.0% of within-group variance during January 1977-December 4 For this particular regression model, R = β Var(Dp )/Var(DP), where Var denotes a sample variance. When the Var(Dp )/Var(DP) ratio is of moderate magnitude and β 0, then R 0. 7

8 2017, whereas on average precious metals and energy accounted for 28.6% and 22.2%, respectively, of between-group variance during the same time period. Figure 3 depicts two versions of the Divisia index one excluding fuels and another excluding precious metals as well, the WBNE Index, and the S&P GSCI Non-Energy Index, SPGSNE (source: Bloomberg). The latter is a world production-weighted sub-index of the S&P GS Composite Index (SPGSCI) that contains all of the commodity groups in SPGSCI but energy (crude oil and natural gas), namely, agricultural products (wheat, corn, soybeans, coffee, sugar, cocoa, and cotton), livestock (lean hogs, live cattle, and feeder cattle), industrial metals (aluminum, copper, lead, nickel, and zinc) and precious metals (gold and silver). 5 As of 2017, the percentage dollar weights of SPGSCI assigned to energy, agriculture, livestock, industrial metals, and precious metals were 59.47%, 17.89%, 7.49%, 10.57%, and 4.58%. SPGSNE includes exactly the same commodities as S&P GSCI except for energy (source: Hence by a simple re-weighting, the 2017 weights given to agriculture, livestock, industrial metals, and precious metals in SPGSNE are 44.14%, 18.48%, 26.08%, and 11.30%, respectively. By contrast those of the Divisia Non-Energy index assigned to agriculture, fertilizers, metals & minerals, and precious metals are 64.29%, 11.91%, 16.67%, and 7.14%, respectively. The Divisia Non-Energy/Non-Precious metals index includes only agriculture, fertilizers and metals & minerals, so that the corresponding weights are 69.24%, 12.82%, and 17.95%. Table 7 presents Pearson bivariate correlations for the depicted indices, and also for the Divisia all commodities index (N = 46) and SPGSCI for the sample period. Not surprisingly, the highest correlations are those between WBNE and the different versions of the Divisia index ( ). By contrast those between SPGSNE and the Divisia indices and between SPGSNE and WBNE are considerably lower. For instance, the SPGSNE/Divisia NE and SPGSNE/WBNE pairs display correlations of 0.43 and 0.47, respectively. This is not unexpected because the commodities under consideration are not identical, and the assigned weights differ as well. An alternative way of measuring association is the predictive performance of the sign of an index return (r 1t ) with respect to the sign of another (r 2t ). To that end, define V t = 1 if r 1t > 0; 0 otherwise, U t = 1 if r 2t > 0; 0 otherwise, Z t = 1 if r 1t r 2t > 0; and 0 otherwise, and utilize Pesaran and Timmermann (1992) non-parametric statistics: S = ( ) / N(0, 1) (13) 5 SPGSCI and SPGSNE are recorded from the beginning of January

9 where P is the proportion of times the sign of r 1 is predicted correctly by the sign of r 2, that is, Pr(Z t = 1) = Pr(r 1t r 2t > 0) = Pr(r 1t > 0, r 2t > 0) + Pr(r 1t < 0, r 2t < 0). Under the null hypothesis of no predictive power (i.e., r 1 and r 2 are independently distributed) such probability equals P = P P + (1 P )(1 P ). Consistent estimates P, P and P are the samples means of Z, V, and U, respectively. Moreover, Var P = T P (1 P ) and Var P T 2P 1 P 1 P + T 2P 1 P 1 P for T large, where T is the sample size. Table 7 presents estimates of P for the same indices of Table 6. For instance, the sign of the SPGSNE return correctly predicts that of the Divisia NE return (and vice versa) 60% of the time. In turn the sign of the latter predicts correctly the sign of the WBNE return (and vice versa) 84% of the time. In all cases, the null hypothesis of no predictive performance is rejected at any significance level. 7 Conclusions This article has presented two Divisia commodity indices: annually ( )- and monthly (January 1977-December 2017)-based. Both indices are readily computable and updatable from publicly available information. Moreover, both indices are capable of tracking well-known indices, such as the World Bank and S&P GSCI non-energy indices. References Baffles, J., and X. Etienne (2016). Analysing food price trends in the context of Engel s law and the Prebisch-Singer hypothesis. Oxford Economics Papers 68, Chen, M. H (2010). Understanding world metal prices Returns, volatility, and diversification. Resources Policy 35, Clements, K. (1982). Divisia moments of Australian consumption. Economics Letters 9(1), Cuddington, J. (1992). Long-run trends in 26 primary commodity prices. Journal of Development Economics 39, Cuddington, J., and H. Wei (1992). An empirical analysis of real commodity price trends: Aggregation, model selection, and implications. Estudios Económicos 7(2): Drechsel, T, and S. Tenreyro (2017). Commodity booms and busts in emerging economies. Journal of International Economics. In Press, corrected proof. 9

10 Erten, B., and J. Ocampo (2012). Super cycles of commodity prices since the midnineteenth century. World Development 44, Feenstra, R., and M. Reinsdorf (2000). An exact price index for the almost ideal demand system. Economic Letters 66, Grilli, E., and M. Yang (1988). Primary commodity prices, manufactured goods prices, and the terms of trade of developing countries. World Bank Economic Review 2, Harvey, D., N. Kellard, J. Madsen, and M. Wohar (2010). The Prebisch-Singer hypothesis: Four centuries of evidence. The Review of Economics and Statistics 92(2), Harvey, D., N. Kellard, J. Madsen, and M. Wohar (2017). Long-run commodity prices, economic growth, and interest rates: 17 th century to present day. World Development 89, Pesaran, M.H, and A. Timmermann (1992). A simple nonparametric test of predictive performance. Journal of Business & Economic Statistics 10, Pfaffenzeller, S., P. Newbold, and A. Rayner (2007). A short note on updating the Grilli and Yang commodity price index. The World Bank Economic Review 21(1), Tcha, M., and G. Takashina (2002). Is world metal consumption in disarray? Resources Policy, 28 (1 2), Yamada, H., and G. Yoon (2014). When Grilli and Yang meet Prebisch and Singer: Piecewise linear trends in primary commodity prices. Journal of International Money and Finance 42,

11 Tables Table 1 Grilli-Yang weights of non-fuel commodity price index (GYCPI) and sub-indices Source: Table 1 in Pfaffenzeller et al. (2007). Commodity Weights (% share) GYCPI Sub-indices Food Bananas Beef Cocoa Coffee Lamb Maize Palm oil Rice Sugar Tea Wheat Non-food Cotton Hides Jute Rubber Timber Tobacco Wool Metals Aluminum Copper Lead Silver Tin Zinc

12 Table 2 Commodity groups Commodity group Components % group weight in Divisia index Beverages Cocoa, coffee, and tea 8.33 Cereals Maize, rice, and wheat 8.33 Other food Banana, beef, lamb, and palm oil Agricultural raw materials Cotton, hides, jute, rubber, timber, tobacco, and wool Fuels Coal and oil 5.56 Metals & minerals Aluminum, boron, cobalt, copper, iron & steel, iron ore, lead, manganese, nickel, phosphate rock, tin, tungsten, and zinc Precious metals Gold, platinum, and silver 8.33 Note: The data sources are Pfaffenzeller et al. (2007) for individual commodities and Grilli-Yang Commodity Price Index and sub-indices for the period of , the IMF s International Financial Statistics (IFS) and the World Bank for updating the series for the period of And, the US Geological Service (USGS) for metals and minerals, such as boron, cobalt, iron & steel, iron ore, manganese, nickel, phosphate rock, and tungsten. Table 3 Percentage-variance decomposition: Within-group variation (percentage explained) Beverages Cereals Other food Agri. raw mat. Energy Metals & min. Precious metals Mean 8.8% 4.6% 19.5% 20.9% 3.2% 38.3% 4.6% Std. 4.6% 6.9% 17.7% 16.1% 6.1% 19.8% 7.2% Min 1.3% 0.0% 0.1% 0.6% 0.0% 5.7% 0.0% Max 18.2% 44.7% 81.1% 67.1% 37.1% 78.9% 52.1% Between-group variation (percentage explained) Beverages Cereals Other food Agri. raw mat. Energy Metals & min. Precious metals Mean 18.1% 14.2% 13.8% 14.7% 11.0% 15.7% 12.6% Std. 18.7% 14.9% 18.0% 18.2% 14.6% 14.5% 16.5% Min 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% Max 80.1% 61.9% 79.8% 71.3% 73.1% 52.4% 85.1% Note: Decomposition according to Equation (8). 12

13 Table 4 Betas: Commodity Beta R 2 Commodity Beta R 2 Cocoa Aluminum Coffee Boron (2) Tea Cobalt Beverages Copper Maize Iron & steel Rice Iron ore Wheat Lead Cereals Manganese Banana (1) Nickel Beef Phosphate rock (2) Cereal Tin Lamb Tungsten Palm oil Zinc Sugar Metals & Minerals Other food Gold Cotton Platinum Hides Silver Jute Precious metals Rubber Coal Timber Oil Tobacco (2) Energy Wool Agri. raw materials Notes: (1) : Statistically significant at the 10% but not at the 5% level. (2) Not statistically different from zero. The market index is the Divisia index composed of thirty-six commodities. 13

14 Table 5 Commodity groups: January 1977-December2017 Group Sub-group Components % group weight in Divisia index Energy Crude oil, coal; liquefied natural gas. Japan; natural gas index Agriculture Beverages Cocoa; coffee, Robusta; tea, average 3 auctions. Fertilizers Vegetable oils & meals Cereals Other food Agricultural raw materials Coconut oil, copra, groundnut oil, palm oil, soybeans, soybean oil, and soybean meal. Barley; maize; sorghum; rice, Thai 5%; and wheat, US hard red winter (HRW). Banana, orange, beef; meat, chicken; meat, sheep; and sugar. Tobacco, US imports; logs, Cameroon; logs, Malaysian; sawn-wood, Malaysian; cotton, A index; and rubber, Singapore/Malaysia (SGP/MYS) Phosphate rock, diammonium phosphate (DAP); triple superphosphate (TSP), urea, and potassium chloride. Metals & minerals Aluminum, iron ore, copper, lead, tin, nickel, and zinc Precious metals Gold, platinum, and silver Source: World Bank s pink sheet. The total number of commodities is Table 6 Percentage-variance decomposition: January 1977-December 2017 Within-group variation (percentage explained) Energy Agriculture Fertilizers Metals & min. Precious metals Mean 8.0% 68.0% 7.5% 12.4% 4.0% Std. 10.2% 18.7% 10.0% 11.1% 5.1% Min 0.0% 12.1% 0.0% 0.3% 0.0% Max 62.3% 98.3% 68.1% 79.3% 37.8% Between-group variation (percentage explained) Energy Agriculture Fertilizers Metals & min. Precious metals Mean 22.2% 13.0% 19.3% 17.0% 28.6% Std. 23.3% 11.5% 21.1% 18.1% 25.7% Min 0.0% 0.0% 0.0% 0.0% 0.0% Max 87.6% 40.9% 85.5% 84.1% 92.7% Note: Decomposition according to Equation (8). 14

15 Table 7 Pearson bivariate correlations of nominal returns: January 1977-December 2017 SPGSCI SPGSNE Divisia All Divisia NE Divisia NE/NPM WBNE SPGSCI 1.00 SPGSNE Divisia All Divisia NE Divisia NE/NPM WBNE Note: SPGSCI and SPGSNE are the S&P GS composite and Non-Energy indices, respectively. Divisia All involves N = 46 commodities. Divisia NE excludes energy (N = 42) and Divisia NE/NPM excludes energy and precious metals (N = 39). Table 8 Pesaran-Timmermann P: January 1977-December 2017 SPGSCI SPGSNE Divisia All Divisia NE Divisia NE/NPM WBNE SPGSCI 1.00 SPGSNE Divisia All Divisia NE Divisia NE/NPM WBNE Notes: (1) SPGSCI and SPGSNE are the S&P GS composite and Non-Energy indices, respectively. Divisia All involves N = 46 commodities. Divisia NE excludes energy (N = 42) and Divisia NE/NPM excludes energy and precious metals (N = 39). (2) In all cases S n, as given by (13), is statistically different from zero at any significance level. 15

16 Figure 1 Alternative commodity price indices: Note: Divisia Non-fuels is the index computed from the commodities of Table 2, excluding coal and oil; similarly, the Divisia Non-fuels /Non-Precious metals index also excludes precious metals; GYCPI is the Grilli-Yang Commodity Price Index, and DGY is its Divisia version; WBNE is the World Bank Non-Energy Price Index, available since All indices have been deflated by the US CPI and expressed in 2016 USD.

17 Figure 2 Variability of Divisia price index, DP t, (N = 36): (a) Variance decomposition of DP t (b) Annual volatility of DP t

18 Figure 3 Monthly nominal indices: January 1977-December 2017 Note: The initial values of the indices correspond to that of S&P GS Non-Energy (SPGSNE) in December 1976: WBNE is the World Bank Non-Energy Price Index. Nominal returns are continuously compounded. 18