metadata: authors: 0: author: De Pace, Pierangelo
1: author: Hernandez, Manuel A.
2: author: De Nicola,Francesca
count: World
docna: 0: docna: Co-movement of major commodity price returns
            : time-series assessment
docty: Policy Research Working Paper
subtopic: Climate Change and Agriculture,Oil Refining & Gas Industry,Crops and Crop Management Systems,Rural and Renewable Energy,Energy Demand,Energy and Environment,Energy and Mining,Renewable Energy,Commodity Risk Management
teratopic: Energy,Industry,Agriculture,Macroeconomics and Economic Growth,Private Sector Development
abstracts: cdata!: This paper provides a comprehensive
            analysis of the degree of co-movement among the nominal
            price returns of 11 major energy, agricultural and food
            commodities based on monthly data between 1970 and 2013. A
            uniform-spacings testing approach, a multivariate dynamic
            conditional correlation model and a rolling regression
            procedure are used to study the extent and the
            time-evolution of unconditional and conditional
            correlations. The results indicate that (i) the price
            returns of energy and agricultural commodities are highly
            correlated; (ii) the overall level of co-movement among
            commodities increased in recent years, especially between
            energy and agricultural commodities and in particular in the
            cases of maize and soybean oil, which are important inputs
            in the production of biofuels; and (iii) particularly after
            2007, stock market volatility is positively associated with
            the co-movement of price returns across markets.
repnme: repnme: Co-movement of major commodity price
            returns : time-series assessment
display_title: Co-movement of major commodity price
            returns : time-series assessment
listing_relative_url: /research/2014/04/19446026/co-movement-major-commodity-price-returns-time-series-assessment
topicv3: Energy and Extractives m1326595 507,Biofuels Energy m1326600 532,Crop Production m1326627 174,Commodity and Resource Prices m1503849 3034,Natural Gas m1583894 4712
publishtoextweb_dt: 2014-04-01T00:00:00Z
historic_topic: Energy,Industry,Agriculture,Macroeconomics and Economic Growth,Private Sector Development
no_of_pages: 38
author_keys: 0: author_key: 941177
model_extractions: WPS6845 Policy Research Working Paper 6845 Co-Movement of Major Commodity Price Returns Time-Series Assessment _Francesca de Nicola Pierangelo De Pace Manuel A. Hernandez_ The World Bank Africa Region Finance and Private Sector Development Unit April 2014
Policy Research Working Paper 6845

# **Abstract**

This paper provides a comprehensive analysis of the degree of co-movement among the nominal price returns of 11 major energy, agricultural and food commodities based on monthly data between 1970 and 2013. A uniform-spacings testing approach, a multivariate dynamic conditional correlation model and a rolling regression procedure are used to study the extent and the time-evolution of unconditional and conditional correlations. The results indicate that (i) the price returns of energy and agricultural commodities are highly correlated; (ii) the overall level of co-movement among commodities increased in recent years, especially between energy and agricultural commodities and in particular in the cases of maize and soybean oil, which are important inputs in the production of biofuels; and (iii) particularly after 2007, stock market volatility is positively associated with the co-movement of price returns across markets.

This paper is a product of the Finance and Private Sector Development Unit, Africa Region. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The author may be contacted at fdenicola@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# **Co-Movement of Major Commodity Price Returns: Time-Series Assessment**

Francesca de Nicola<sup>i</sup> , Pierangelo De Pace<sup>ii</sup> , Manuel A. Hernandez<sup>iii</sup> JEL codes: Q02, E30, C32 Keywords: Commodity prices, co-movement, time-series models\\ i The World Bank, AFTFW ii Pomona College, Department of Economics iii International Food Policy Research Institute (IFPRI)
# **1 Introduction**

Commodity prices and their fluctuations have received substantial attention in the literature over the years.<sup>1</sup> One of the stylized facts of commodity prices that remains puzzling is their apparent co-movement.<sup>2</sup> In their seminal paper, Pindyck and Rotemberg (1990) show that the prices of seven raw commodities move together even after controlling for macroeconomic and market conditions. They label this phenomenon as excess co-movement and attribute it to herd behavior in financial markets. The excess co-movement hypothesis, however, has been challenged by subsequent studies. For example, Deb, Trivedi and Varangis (1996) argue that Pindyck and Rotemberg (1990)’s results are due to misspecification in their modeling strategy, since they do not account for possible issues of heteroskedasticity and for the potential presence of structural breaks in the dynamics of commodity prices. Cashin, McDermott and Scott (1999) find strong evidence of price co-movement within agricultural and metal commodities, but not between them. Similarly, Ai, Chatrath and Song (2006) do not find excess co-movement in the price of agricultural commodities. From a more theoretical point of view, Alquist and Coibion (2013) examine what drives the co-movement among commodity prices and build a model for thinking about the sources of commodity price co-movement and its implications in terms of macroeconomic dynamics. They suggest that commodity-related shocks have generally played a limited role in global business cycle fluctuations.

The general interest in the analysis of commodity prices is also motivated by the potentially large welfare implications of their properties. The presence of excess co-movement, for example, may cast doubts on the competitiveness and efficiency of commodity markets. Its existence might indicate that commodity traders react to herding behaviors instead of market fundamentals, missing arbitrage and hedging opportunities. Traders as well as exporting countries could also face substantial challenges to balance their portfolios and could therefore be exposed to high income volatility. In the case of agricultural commodities, farmers growing multiple crops may experience strong income fluctuations due to synchronized changes in prices, with significant effects on food security. Furthermore, a simultaneous increase in several commodity prices may generate inflation pressures on highly dependent commodity-import countries.

The recent increases in both the level and volatility of commodity prices have reignited the interest of researchers and policy makers in the behavior of commodity prices and their co-movement. According to Ivanic, Martin and Zaman (2011), the upsurge in commodity prices of 2007-2008 and 2010-2011 had an overall negative effect on the population, especially among the poor, who spend a high fraction of their income on food consumption. Several studies have lately investigated the determinants of these price fluctuations. Frankel (2008) indicates that the real interest rate may be an important determinant of oil and other mineral and agricultural prices. Svensson (2008) underscores the importance of taking into account aggregate supply and demand shifts to explain commodity price dynamics. Gilbert (2010) asserts that the recent commonality of rises

> 1See, for example, Deaton (1999), Beck (2001), Cashin, McDermott and Scott (2002), Enders and Holt (2012) and Karali and Power (2013).

> 2Saadi (2011) provides a recent review of commodity price co-movement in international markets.

1
and falls in the price of energy, metals and foods is unlikely to be coincidental and may be the result of a common set of macroeconomic and financial factors driving prices across a wide range of commodities. Byrne, Fazio and Fiess (2013) document a significant degree of price co-movement across 24 commodities and argue that such co-movement may be due to a common factor related to macroeconomic fundamentals, such as the real interest rate and stock market uncertainty.

In this paper we adopt a multivariate approach to comprehensively examine the degree of co-movement among major commodity markets. We first study the extent of cross-section correlation and the time-varying pairwise unconditional and conditional correlations between 11 energy, agricultural and food price returns using monthly data from January 1970 through May 2013. Specifically, we use the uniform spacings method developed by Ng (2006) to test for the presence and evaluate the extent of unconditional co-movement in commodity price returns. We estimate a multivariate dynamic conditional correlation (DCC) model, based on Sheppard and Engle (2001) and Engle (2002), to analyze the time-varying conditional correlations between commodity price returns. Furthermore, we investigate whether bivariate rolling unconditional correlations between commodity price returns are statistically associated with specific macroeconomic and financial factors by means of a linear regression analysis.

We contribute to the existing empirical literature on the topic along several dimensions. First, contrary to most previous studies, which mainly examine the co-movement of commodity price returns, we model the evolution over time of the interlinkages between markets by also allowing for time-variation in price-specific conditional volatilities.<sup>3</sup> Allowing for time-variation in mixed and non-mixed conditional second moments permits a more accurate assessment of the dynamic relationships between markets (Gallagher and Twomey, 1998). Second, our investigation is restricted to major energy, agricultural and food commodities. The goal is to analyze the extent of price correlations both within and across energy- and food-related markets. Agricultural commodities, for example, are expected to be correlated because they are generally close substitutes in demand, have similar input costs and share common market information. Yet, growing financial market integration and the development of agricultural futures markets might have corroborated these interdependencies in recent years. Furthermore, the interlinkages between energy and agricultural markets, typically related through production and transportation costs, may have become stronger due to the recent development of the biofuel industry and the increasing demand for agricultural produce in the production of ethanol and biodiesel (Rajagopal and Silverman, 2007). Our period of analysis is sufficiently large to allow a characterization of the evolution of commodity prices in terms of trends and structural changes, which could be associated with particular events in the commodity markets (see Figure 1). The use of monthly data allows us to capture dynamics that would otherwise be hidden in lower frequency data.<sup>4</sup> Finally, motivated by the work of Frankel

> 3Deb, Trivedi and Varangis (1996), Zhao and Goodwin (2011) and Gardebroek, Hernandez and Robles (2013) are among the few studies that focus on market interactions in terms of conditional second moments. The authors of these studies estimate BEKK models following Engle and Kroner (1995). Deb, Trivedi and Varangis (1996) analyze excess co-movement across apparently unrelated commodities using a likelihood ratio test; the other two studies examine volatility spillovers between major agricultural commodities.

> 4At the same time, we avoid higher frequency data, which could instead be characterized by a high noise-to-signal

2
(2008), Gilbert (2010), Gruber and Vigfusson (2012) and Byrne, Fazio and Fiess (2013) on the co-movement of commodity prices, we evaluate if the correlations across markets are driven by real interest rates and by the volatility of stock market returns (a proxy for uncertainty in stock markets).

The empirical results that we present show that the price returns of related commodities are generally highly correlated. The uniform spacings methodology indicates strong and positive correlations within cereal crops, between cereal crops and soybean oil (a reference agricultural commodity), and within energy commodities. We also find an increase in the degree of co-movement between energy and agricultural commodity price returns in recent years, particularly maize (another agricultural commodity that we use as a reference) and soybean oil, which are important inputs in the production of biofuels. The evolution of the estimated dynamic conditional correlations confirm the presence of high levels of co-movement between the returns of energy commodities and maize and soybean oil in the past few years and a rising level of co-movement by the end of the sample. Our results provide evidence the emergence of even stronger interlinkages between energy and agricultural markets in recent years, likely determined by the expansion of the biofuel industry. The concluding linear regression analysis that we propose suggests that several of the observed correlations within and across energy and agricultural markets are positively affected by the behavior of financial markets (measured by the volatility of stock market returns) particularly after 2007, but not by changes in macroeconomic conditions (measured by a real interest rate).

The remainder of the paper is organized as follows. In Section 2 we describe the data and the statistical properties of the price returns included in the analysis. We also present the results of the breakpoint analysis that we perform to estimate breaks in the dynamics of nominal price returns. In Section 3 we discuss empirical results concerning the extent of cross-section correlation in the data, the dynamic conditional correlations of nominal price returns and the statistical relevance of two potential driving factors (real interest rates and volatility of stock markets) of unconditional co-movement between commodity price returns. In Section 4 we draw the conclusions.

# **2 Commodity Prices and Breakpoints in Price Return Dynamics**

Monthly prices of 11 commodities are the core of the dataset. We focus on the main energy products (coal, crude oil and natural gas), agricultural crops (barley, maize, rice, sorghum, soybean oil and wheat) and food products (coffee and sugar). Time series from January 1970 to May 2013 are obtained from the World Bank Commodity Price Data.<sup>5</sup> Figure 2 shows the evolution of nominal commodity prices series over the period under investigation. Energy and agricultural prices follow similar patterns, in particular (i) crude oil and coal, (ii) soybean oil and rice, and (iii) maize, wheat, barley and sorghum. Most of these prices reach peaks around the global food price crisis in 2007-2008 and, generally, in the last two years of the

> ratio.

> 5 Data are publicly available from `http://go.worldbank.org/4ROCCIEQ50` . Table 4 in Appendix B provides further details on the specific commodities included in the sample.

3
sample. Natural gas also shows a price spike in the early 2000s. The surge in soybean oil prices dates back to the mid-1970s and 1980s; in both cases it is related to major supply shortages in the United States. Unlike energy and agricultural prices, the prices of sugar and coffee do not appear to co-move. Sugar prices are rather stable over the entire sample period, while coffee prices peak in the late 1970s, mid-1990s and in 2011. Such peaks are all likely associated with bad weather conditions in Brazil and, more recently, in Colombia.

Our empirical analysis is based on month-to-month nominal commodity price returns, defined as _rm,t_ = ln _Pm,t −_ ln _Pm,t−_ 1, where _Pm,t_ is the price of commodity _m_ at time _t_ .<sup>6</sup> By means of a breakpoint analysis based on Qu and Perron (2007), whose technical details are described in Appendix A.1, we estimate breakpoints in the dynamics of the 11 commodity price returns in the sample. We consider an unrestricted vector autoregressive (VAR) model for the returns and estimate three breaks at unknown dates in the model coefficients and the variance-covariance matrix of the errors. The breaks we find are 1979M11, 1987M07 and 2007M05.<sup>7</sup> The empirical investigation that follows is conducted on the full sample and on the four resulting subsamples, (S1) 1970M02-1979M10, (S2) 1979M11-1987M06, (S3) 1987M07-2007M04 and (S4) 2007M05-2013M05. As shown in Figure 1, the identified structural breaks generally coincide with significant events in energy and agricultural markets, which likely affected the dynamics of price returns. The first break can be associated with the Iranian revolution in 1979 and the subsequent war between Iran and Iraq, which led to a global oil crisis. The second break can be related to the severe droughts that occurred across most states in the United States and led to a major crop failure for soybeans and maize in 1988. The third break can be linked with the recent food price crisis, which started in 2007.

Table 1 reports summary statistics for the price returns computed over the full sample. Table 5 in Appendix B reports the same statistics computed over the four previously determined subsamples. Crude oil exhibits the highest average monthly returns (0.8%) over the full sample. The average returns of all commodities are higher in the 1970M02-1979M10 period than in the other subperiods. All average price returns fall in the subsequent 1979M11-1987M06 period, then generally and steadily rise until the end of the sample. However, in most cases, they do not reach the initial levels of the 1970s. Maize and sorghum are the only two commodities that show higher returns in the most recent subperiod relative to the first subperiod (approximately a 50 percent increase in the case of maize and a 14 percent increase in the case of sorghum). Besides crude oil, the other two energy commodities and coffee show the most pronounced return decreases over time. The patterns of volatility are more mixed. Natural gas price returns are overall the most volatile. The price returns of sugar are similarly volatile. Crude oil and sugar are the most volatile commodities until almost the end of the 1980s. Barley, sugar, natural gas and coffee exhibit the

> 6The results that we present in this paper are robust to alternative measures of price returns (real price returns computed using a seasonally adjusted and a non-seasonally adjusted consumer price index). Details are available upon request.

> 7In order to assess the robustness of these results we perform several checks. Specifically, we apply the procedure to nominal and real returns and also consider VAR(0) and VAR(1) models to jointly describe and estimate the cross-correlation structure of price returns.

4
highest levels of volatility during the 1980s and the 1990s, and up to 2007. The returns of the three energy commodities are consistently the most volatile between the end of the 1980s and 2013, with the exception of coal during between 1987 and 2007. All return volatilities (with the exception of natural gas) rise between 2007 and 2013 with respect to the previous twenty-year period.

Turning to the other distributional properties of the data, maize price returns exhibit a distribution with a long left tail, while natural gas returns are the only returns with a symmetric distribution. All other returns have distributions with long right tails and median returns almost always smaller than average returns. A battery of Shapiro-Wilk tests run on the nominal price returns rejects the null hypothesis that the data are normally distributed in all cases. The kurtosis of all price returns is greater than three, as we observe leptokurtic data. Table 1 also reports the p-values from the Ljung-Box autocorrelation tests run on the squared returns. The null hypothesis of no autocorrelation up to 12 lags is mostly rejected at conventional statistical levels, except the cases of crude oil, maize and sorghum.

All these findings are consistent with the presence of nonlinear time-dependency in the series of price returns, maybe due to the existence of time-varying conditional moments. Figure 3 plots the time-evolution of each nominal price return, whose fluctuations and volatility changes over time are apparent. These descriptive results motivate the adoption of specific econometric techniques to characterize the time-varying properties of the second moments of the commodity price returns in the sample. As already mentioned, particular attention is given to the second mixed moments, which are used in this study to measure the co-movement of price returns.

# **3 Measuring the Co-Movement of Commodity Price Returns**

In this section we describe and discuss the main empirical findings of our investigation. We study the co-movement of commodity price returns in three different ways. We assess the extent of their cross-section unconditional correlation over the full sample and four subperiods by means of Ng (2006)’s methodology. We study the time-evolution of their dynamic conditional correlations by estimating a multivariate DCC model on the data, while allowing for time-varying conditional volatilities. Finally, we model the time-evolution of their unconditional correlations using a rolling regression approach based on Tang and Xiong (2012). In this final context, we also run a regression analysis to statistically investigate the association between the unconditional co-movement of price returns and two of its possible determinants. Further details about the econometric techniques can be found in Appendix A.

## **3.1 Cross-Section Unconditional Correlations**

We formally examine the cross-section co-movement of nominal price returns in energy, agricultural and food markets by following the uniform spacings methodology developed by Ng (2006), which tests for the existence and measures the extent of cross-section unconditional correlation in a panel of data where the number of correlated series is unknown _ex ante_ . This econometric approach 5
improves upon standard tests for cross-section correlation, such as Breusch and Pagan (1980) for example, as it requires less restrictive assumptions to be satisfied in the data and allows to precisely identify the series in the panel that determine the rejection of the null hypothesis of no cross-section correlation. Ng (2006)’s methodology produces a split in the sample of all pairwise correlation coefficients (55 correlations in our sample of 11 commodity price returns) into two subsets of small and large absolute correlations. Building on the literature about spacings and adopting breakpoint analysis techniques, the procedure makes use of a spacings variance ratio test statistic (SVR) to test the null hypothesis of no correlation within groups of correlation coefficients.<sup>8</sup> We assess the cross-section unconditional correlation of the 11 commodity price returns over the full sample ( _T_ = 520 monthly observations) and over the four subsamples described in Section 2 ( _T_ = 117 monthly observations over S1, _T_ = 92 monthly observations over S2, _T_ = 238 monthly observations over S3 and _T_ = 73 monthly observations over S4). As reported in Table 2, we reject the null hypothesis of no cross-section correlation at the 10% level in most time periods and for most values of _q_ , a parameter that determines the length of the spacings needed to run the test. The only exception is the 1979M11-1987M06 period, for which we are unable to reject the null of no cross-section correlation in the entire panel. It is worth noting that, for the same 1979M111987M06 period, the extent of overall cross-section correlation is small: 12 pairs of price returns in the large correlation subset exhibit significant levels of (positive) correlation, the remaining 43 in the small correlation subset are, instead, not statistically different from zero. The results of the testing procedure also suggest a high level of generally positive co-movement (i.e., positive correlation) of price returns concerning large groups of commodity pairs in all time periods. The extent of positive co-movement increases over time. The number of positive correlation coefficients is 41 in the first period and becomes 54 in the last period. More specifically, we observe 37 positive correlation coefficients (out of 48 statistically significant correlations) in the 1970M021979M10 large correlation set, 12 positive correlation coefficients (out of 12 statistically significant correlations) in the 1979M11-1987M06 large correlation set and 23 positive correlation coefficients (out of 28 statistically significant correlations) in the 1987M07-2007M04 large correlation set. In the 2007M05-2013M05 period, the large correlation set includes 48 positive correlation coefficients (out of 48 statistically significant correlations).

Table 6 in Appendix B provides additional information about the cross-section correlation of these commodities. We sort the pairs of commodities in the large absolute correlation sets over full sample and subsamples in a descending order. Overall, the price returns of related commodities (i.e., commodities in the same category) tend to be strongly positively correlated. We observe strong and positive correlations within cereal crops (specifically maize, sorghum, barley and wheat), between cereal crops and soybean oil and within energy commodities (oil, coal and gas). Related commodities are likely affected by similar supply and demand factors since they are close substitutes in demand, have similar input costs and share common market information. Such a positive correlation between related products is typically labeled as “category based” co-movement, given

> 8We provide further methodological details in Appendix A.2

6
that investors (including hedgers and speculators) classify these crops as belonging to the same category from which they can shift resources to invest in other commodities or categories. For the full sample period, the returns of maize and sorghum exhibit the largest correlation (0.81), followed by sorghum and wheat (0.53) and barley and maize (0.49). The returns of barley and wheat are the most highly correlated for the period 1970M1-1979M10 (correlation of 0.93), whereas the returns of maize and sorghum are the most highly correlated over the subsequent subperiods (correlations of 0.68, 0.86 and 0.81).

The negative correlations between the returns of energy (coal and gas) and several agricultural commodities in the first subsample later become positive in most cases. For example, during the 1970M02-1979M10 period, the returns of coal and soybean oil, coal and barley, coal and maize, gas and maize, and gas and barley, among others, exhibit negative correlations, which change to positive in 2007M05-2013M05. Furthermore, crude oil and soybean oil show the second largest positive return correlation during the 2007M05-2013M05 period (0.76), followed by maize and soybean oil (0.67), crude oil and barley (0.66) and coal and soybean oil (0.63). The large positive correlations between the returns of energy and agricultural commodities (particularly soybean oil and maize) can be explained by the recent rapid expansion of the production of biofuels, which have begun to utilize a significant portion of planted acres of starch and sugar-based crops, such as maize and sugarcane, and oilseed crops, such as soybean and rapeseed oil (see, for example, Rajagopal and Silverman, 2007; Babcock, 2011; Tangermann, 2011). Increasing energy prices may not only directly affect agricultural prices through higher input and transportation costs, but may also create an incentive to use alternative energy sources like biofuels, which, in turn, may further stimulate agricultural prices. This possibility could also explain the recent large correlation between maize and soybean oil (0.67 in 2007M05-2013M05), as both commodities are important inputs for the production of ethanol and biodiesel in the United States.

# **3.2 Dynamic Conditional Correlations**

After examining the cross-sectional dimension of the panel of data, we focus on its time dimension. The objective is to assess how the degree of correlation between commodity returns evolves over the years. We estimate a dynamic conditional correlation (DCC) model following Sheppard and Engle (2001) and Engle (2002).<sup>9</sup> In particular, we first estimate a univariate GARCH model for each returns series and then derive a multivariate conditional correlation estimator from the transformed residuals of the first-stage models. The resulting conditional correlations between returns at each point in time are a function of the past correlations and of the history of conditional volatility of each series.

Figures 4 and 5 plot the estimated dynamic conditional correlations between the price returns of maize and soybean oil – which are in this section considered the two reference commodities because of their importance in the production of biofuels – and all the other commodities in the sample.<sup>10</sup>

> 9The details of this method are presented in Section A.3.

> 10Estimates of the dynamic conditional correlations between all other commodities are available upon request as well

7
As shown in Figure 4, maize price returns are highly correlated with the returns of other cereal crops like sorghum (average conditional correlation of about 0.8), barley and wheat (average conditional correlation of about 0.50), as well as with the returns of soybean oil (average conditional correlation of about 0.45). An upward trend in the degree of conditional correlation between the returns of maize and wheat, coffee and sugar starts around 2004. The dynamic correlations between the returns of maize and crude oil, natural gas, soybean oil and rice increase between 2004 and around 2009, then slowly decline until the end of the sample. The recent correlation increase between the returns of maize and crude oil to levels above 0.1 draws some attention because, prior to 2006, such conditional correlation was steadily negative or close to zero.<sup>11</sup> The conditional correlations between the returns of maize and coal, rice, barley and sorghum exhibit less steep or even nonexistent upward trends from 2004 and tend to decline towards the end of the sample. In Figure 5, the returns of soybean oil exhibit a relatively large average degree of correlation with the returns of maize (as previously argued), sorghum and barley (correlations of about 0.40) and, to a lower extent, wheat (average correlation of about 0.30). In all cases reported in the figure, the estimated dynamic conditional correlations moderately increase in the last few years of the sample, starting from about 2004, then tend to fall after reaching a peak around 2009. Sharp increases to levels close or above 0.2 occur in the conditional correlations between the returns of soybean oil and crude oil, coal and coffee starting from about 2003 to around 2009, after which such correlations mildly decline too. It is not superfluous to point out that the majority of the unreported dynamic conditional correlations between the price returns of the other 9 commodities follow similar (and more or less pronounced) hump-shaped evolutions in the last ten years of observations in the sample. The declines at the end of the sample observed in the reported and unreported dynamic correlations look relatively small in most cases, if compared to the correlation rises occurred during the previous years.

In another set of unreported results, we analyze the correlations between the estimated timevarying conditional standard deviations (volatilities) of the series of price returns. We detect large co-movements in the conditional volatilities of agricultural products and crude oil price returns. In particular, the correlation between the estimated volatilities of soybean oil and crude oil returns more than quadruples from the 1970s to the last years in the sample. It more than triples in the case of maize and crude oil price returns over the same period of time. The conditional volatilities of sorghum and barley price returns also exhibit high correlations with the conditional volatility of crude oil price returns. The conditional volatility of soybean oil returns is also characterized by high levels of co-movement with the volatilities of coal and maize returns.<sup>12</sup> Overall, these empirical outcomes represent additional evidence in support of the high levels of interrelation between agricultural and energy markets emerged in recent years. As briefly discussed above and in the related literature, such a pattern might be driven by the expansion of the biofuel

> as the full results related to the estimated DCC model.

> 11The conditional correlation between maize and coal becomes greater than 0.1 in the late 1980s; the conditional correlation between maize and natural gas permanently exceeds 0.1 starting from the late 1990s.

> 12Additional details are available upon request.

8
industry.

# **3.3 Rolling Unconditional Correlations and Determinants**

With the objective of understanding if there are factors driving the co-movement under investigation, we adopt a flexible approach to compute rolling unconditional correlations between commodity nominal price returns based on Tang and Xiong (2012).<sup>13</sup> We only report and discuss results related to rolling correlations estimated using a 24-month rolling window. Our empirical results are robust to alternative rolling windows. For example, a fixed rolling window of 60 monthly observations is also used for comparison purposes. Further details are available upon request.

Similar to the dynamic conditional correlations obtained from the estimation of the DCC model and discussed in the previous section, we focus on the unconditional correlations between maize and soybean oil price returns (here used again as reference commodities) and the returns of all other commodities. The estimated unconditional correlations are plotted in Figures 6 and 7 in Appendix B. These rolling correlations exhibit fluctuations similar to those observed in the evolution of the dynamic conditional correlations.

Real interest rates and stock market uncertainty might, in principle, affect the co-movement of commodity price returns. Some of the reasons can be found, for example, in the work of Frankel (2008), Gruber and Vigfusson (2012) and Byrne, Fazio and Fiess (2013). They argue that the correlations of commodity price returns should be inversely related to the real interest rate. The theoretical foundations of this claim can also be found in Deaton and Laroque (1992, 1996) and are based on the idea that a fall in the interest rate lowers the volatility of prices (smoothing transitory shocks through lower inventory costs) and increases the correlations of price returns if covariant shocks are more persistent than idiosyncratic shocks. Byrne, Fazio and Fiess (2013) argue that the standard deviation of stock market prices can be used as a proxy of market uncertainty, in line with Beck (1993) and Dixit and Pindyck (1994)’s suggestion that market risk and uncertainty might be associated with movements in commodity prices. According to Beck (1993), uncertainty may have a positive effect on commodity prices because volatile commodity prices are likely to reduce inventories and, consequently, their price. Dixit and Pindyck (1994) predict a negative effect of uncertainty on commodity prices as uncertainty increases the option value of waiting (since investment in the production of primary commodities may be irreversible). Gilbert (2010) also suggests that co-movements across commodity prices can be better explained by macroeconomic and financial conditions than by market-specific factors.

In this study we consider two possible determinants of the co-movement of commodity price returns: (i) a real interest rate series computed as the difference between an annualized 3-month Treasury bill interest rate series obtained from the Board of Governors of the Federal Reserve System and a series of annual inflation rates calculated from a monthly non-seasonally adjusted consumer price index series taken from the Federal Reserve Bank of St Louis Economic Dataset (FRED); and (ii) the standard deviation of Standard & Poor’s 500 (S&P500) stock price returns

> 13The technical details are presented in Section A.4.

9
(also taken from FRED), whose monthly series is derived as the standard deviation of the daily returns in each month in the sample. Motivated by the aforementioned studies about the possible effects of real interest rates and stock market uncertainty on the co-movement of commodity price returns, we regress the monthly series of estimated rolling absolute correlations between the price returns of commodities _x_ and _z_ – with _x_ = _z_ and _x, z_ = 1 _, ...,_ 11 – on the annualized real interest rate and the standard deviation of S&P500 stock price returns. Specifically, we study the statistical properties of the model � where<sup>�</sup> _ρxz,w,t_ is the estimated value of the rolling correlation between commodities _x_ and _z_ at time _t_ and _w_ is the length of the window used to compute the rolling correlations, i.e. _w_ = 24 months, in this case; _L_ = 12 is the maximum lag determined using the Schwarz criterion; _RRt_ is the real interest rate and _σSP_ 500 is the standard deviation of S&P500 returns. A Newey-West correction, based on a Bartlett kernel and a fixed bandwidth, is employed to produce reliable standard errors for the regression coefficients. The dependent variable in the regression is measured in absolute value to measure whether returns on safe assets (the real interest rates) and/or the volatility of stock markets (market uncertainty) are statistically associated with the degree of co-movement in commodity price returns, regardless of its sign.<sup>14</sup> Table 3 reports the coefficients associated with the two regressors from the model estimated on the full sample. Table 7 in Appendix B reports the coefficients estimated from the regressions run on the four different subsamples previously identified in Section 2.

Unlike Byrne, Fazio and Fiess (2013), we fail to find a statistically significant association between the real interest rate and the co-movement of commodity price returns over the full sample of data. In particular, out of 55 real interest rate coefficients estimated in 55 linear models, only 2 are statistically significant and negative as predicted by theoretical arguments. However, there seems to be some (limited) time-variation in such association from a statistical point of view. From the regression analysis run on the four subsamples, we observe statistically negative coefficients in a few cases (10 and 8) during the first two subperiods, especially when the dependent variable is the time-varying correlation between price returns of energy commodities and some agricultural commodities. Over the subsequent two subperiods, the number of statistically negative coefficients shrinks to 2 and 3. A possible explanation for this finding is that Byrne, Fazio and Fiess (2013) base their analysis on annual data spanning the 1900-2008 period of time, while we work with monthly data over a shorter period of time. The impact of macroeconomic conditions on the comovement of commodity price returns might be more easily detectable when considering long time spans. On the other hand, a statistically positive link between the standard deviation of S&P500 stock price returns and the co-movement of commodity price returns is much more evident. Over

> 14Qualitatively similar results are found when the dependent variable of the regression is the signed rolling correlation series (i.e., without absolute values), given that most of the derived pairwise rolling correlations are positive.

10
the full sample, 15 coefficients (out of 55) associated with the standard deviation of S&P500 stock price returns are statistically positive. Such a positive relationship considerably intensifies in recent years. Over the first subperiod, only one coefficient is statistically positive. In the subsequent three subperiods, this number increases to 6, 5 and 38. In other words, after 2007, increases in the stock market volatility are generally associated with increasing co-movement in most commodity price returns, both within and across energy and agricultural products. This specific finding is possible indication of a high overall level of integration of energy and agricultural markets with financial markets in the past few years (i.e., a higher “financialization” of commodity markets) and possibly a direct effect of the recent global financial distress on commodity price dynamics.

# **4 Conclusions**

The recent and recurrent increases in both the level and volatility of commodity prices has led researchers and policy makers to further analyze the behavior of commodity prices and the apparent co-movement of their returns. In this paper, we provide an extensive analysis of the degree and extent of co-movement among major energy, agricultural and food commodity nominal price returns between 1970 and 2013. We measure co-movement by means of unconditional and conditional correlations and pay particular attention to the characterization of their time-varying properties over the sample. We adopt a uniform spacings testing procedure to assess the extent of unconditional co-movement in a panel of 11 commodity price returns and run it over the full sample under investigation and over four subsequent subsamples determined by a breakpoint analysis. A dynamic conditional correlation model allows us to estimate the time-evolution of the conditional correlations of price returns while modeling the conditional volatilities of the returns of each commodity and their time-varying properties. We finally investigate whether time-varying unconditional correlations estimated by means of a rolling regression procedure are statistically associated with changes in macroeconomic and financial conditions, respectively measured by real interest rates and stock market volatility.

In general, we find positive correlations within energy and agricultural price returns. This finding is in line with the fact that related commodities are generally close substitutes in demand, share common market information and have similar input costs. Yet, we find an overall increase in the degree of co-movement between energy and agricultural price returns in recent years, especially in the cases of maize and soybean oil, which are important inputs in the production of biofuels. Our empirical results provide supporting evidence of a higher association between energy and agricultural markets in recent years, likely driven by the expansion of the biofuel industry. From a policy perspective, the higher positive correlation in returns suggests that countries that are net importers of energy and agricultural commodities, like most developing countries, could have faced stronger upward price pressures in recent past. This could be more critical among Sub-Saharan Africa countries which also maintain caps on staple food prices to support consumption among the poor. In addition, we find clear signs of the existence of a statistically positive association between 11
the co-movement of commodity price returns and stock market uncertainty, especially in the time period starting from 2007. On the other hand, from a statistical point of view, real interest rates do not seem to have much effect on the co-movement of price returns.

Future research on this topic should explore even further the dynamic behavior of commodity prices, the degree and evolution of market interrelations and their determinants. If increasing interdependencies across commodities occur, they may limit the effectiveness of diversification strategies aimed at reducing price risk. The steady expansion of the biofuel industry in the United States and the European Union may further strengthen the extent and size of correlations between agricultural and energy commodity prices in the near future. The growing financial integration of commodity markets may also continue stimulating cross-market dependencies, while the underlying factors driving these associations and their dynamics may keep changing over time.

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12
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# **Tables**

Table 1: Summary Statistics of Commodity Nominal Price Returns (1970M02-2013M05)

|Commodity|T|Mean|Median|SD|Min|Max|Skewness|Kurtosis|Shapiro-Wilk|Ljung-Box|
|---|---|---|---|---|---|---|---|---|---|---|
|Crude oil|520|0.008|0.000|0.099|-0.540|1.154|3.056|42.226|0.000|0.514|
|Coal|520|0.005|0.000|0.057|-0.329|0.463|1.650|21.181|0.000|0.000|
|Natural gas|520|0.006|0.000|0.107|-0.405|0.478|0.000|6.647|0.000|0.000|
|Soybean oil|520|0.003|0.000|0.065|-0.278|0.311|0.326|5.490|0.000|0.000|
|Barley|520|0.004|0.002|0.067|-0.279|0.287|0.125|6.206|0.000|0.000|
|Maize|520|0.003|0.000|0.058|-0.245|0.298|-0.028|5.907|0.000|0.509|
|Sorghum|520|0.003|0.000|0.061|-0.278|0.342|0.193|6.725|0.000|0.141|
|Rice|520|0.003|0.000|0.064|-0.242|0.582|2.326|20.935|0.000|0.000|
|Wheat|520|0.003|0.000|0.061|-0.219|0.519|1.406|13.545|0.000|0.014|
|Sugar|520|0.003|0.004|0.100|-0.308|0.376|0.244|4.265|0.000|0.000|
|Cofee|520|0.002|-0.001|0.075|-0.353|0.423|0.527|6.345|0.000|0.000|

Note. Price returns are computed as ln _Pm,t −_ ln _Pm,t−_ 1, where _Pm,t_ is the nominal price of commodity _m_ at time _t_ . Prices are measured in nominal terms. T stands for the number of monthly time observations. SD stands for standard deviation. The Shapiro-Wilk column reports the p-value of the Shapiro-Wilk test (the null hypothesis is that the series of returns has a normal distribution). The Ljung-Box column reports the p-value of the Ljung-Box test (the null hypothesis is that there is no autocorrelation in the series of squared returns up to twelve lags).

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Table 2: Uniform Spacings Analysis of Commodity Nominal Price Returns

|_Full Absolute C_|_orrelat_|_ion Set_||||||||
|---|---|---|---|---|---|---|---|---|---|
|Sample Period|Pairs|Positive<br>Correlations|Negative<br> Correlations|q<br> SVR|=2<br> Prob.|q<br> SVR|=4<br> Prob.|q<br> SVR|=6<br> Prob.|
|Full sample|55|52|3|0.42|0.678|3.24|0.001|4.39|0.000|
|S1|55|41|14|-0.52|0.605|1.90|0.058|1.85|0.065|
|S2|55|40|15|1.55|0.121|1.37|0.169|1.07|0.283|
|S3|55|43|12|1.57|0.117|3.03|0.003|3.73|0.000|
|S4|55|54|1|3.25|0.001|2.20|0.028|2.50|0.012|
|_Large Absolute _|_Correl_|_ation Set (L) _|_- First Split_|||||||
|Sample Period|Pairs|Positive<br>Correlations|Negative<br> Correlations|q<br> SVR|=2<br> Prob.|q<br> SVR|=4<br> Prob.|q<br> SVR|=6<br> Prob.|
|Full sample|45|45|0|1.78|0.075|3.34|0.001|3.39|0.001|
|S1|48|37|11|4.31|0.000|5.59|0.000|7.37|0.000|
|S2|12|12|0|4.26|0.000|4.48|0.000|2.99|0.003|
|S3|28|23|5|2.69|0.007|4.18|0.000|5.01|0.000|
|S4|48|48|0|1.98|0.048|-0.05|0.962|0.87|0.382|
|_Small Absolute _|_Correl_|_ation Set (S) _|_- First Split_|||||||
|Sample Period|Pairs|Positive<br>Correlations|Negative<br> Correlations|q<br> SVR|=2<br> Prob.|q<br> SVR|=4<br> Prob.|q<br> SVR|=6<br> Prob.|
|Full sample|10|7|3|-1.19|0.234|-1.03|0.304|-0.51|0.607|
|S1|7|4|3|-1.38|0.169|-0.28|0.777|-1.07|0.285|
|S2|43|28|15|0.92|0.359|0.36|0.717|-0.04|0.969|
|S3|27|20|7|-0.88|0.378|-0.51|0.608|-0.59|0.558|
|S4|7|6|1|2.04|0.042|0.58|0.564|-1.07|0.285|

Note. Full sample corresponds to the period 1970M02-2013M05, S1 to 1970M02-1979M10, S2 to 1979M11-1987M06, S3 to 1987M07- 2007M04 and S4 to 2007M05-2013M05. The null hypothesis of this testing procedure is that there is no cross-section correlation in the sample over the specified period of time. SVR is the standardized spacings variance ratio test statistic used to run the test. Parameter q indicates the order of the uniform spacings. The number of correlations in the L and S absolute correlation sets is estimated by maximum likelihood (see also Section A.2). The Pairs column reports the number of commodity pairs considered in the testing procedure.

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Table 3: Determinants of Absolute Rolling Correlations - Linear Regression Analysis

|||||Sample Per|iod 1970M0|2-2013M0|5||||
|---|---|---|---|---|---|---|---|---|---|---|
|||Re|gressor: St|andard Dev|iation of S&|P500 Ret|urns (_σSP_500_,_|_t_)|||
||Crude oil|Coal|Natural|Soybean|Barley|Maize|Sorghum|Rice|Wheat|Sugar|
||||gas|oil|||||||
|Coal|0.011||||||||||
|Natural gas|0.003|0.015***|||||||||
|Soybean oil|0.009|0.013|0.003||||||||
|Barley|0.019*|0.020*|0.005|0.018**|||||||
|Maize|0.016|0.015|0.013***|0.015***|0.006||||||
|Sorghum|0.009|0.009|0.011***|0.013**|0.004|-0.001|||||
|Rice|0.007|0.000|0.007|0.011**|0.004|0.002|0.009||||
|Wheat|0.007|0.013|0.003|0.006|0.005|0.007|0.007|-0.006|||
|Sugar|0.005|0.008**|0.002|0.003|0.008|0.005|0.008|0.000|0.017***||
|Cofee|0.017**|0.013*|0.006|0.015**|0.021***|0.005|0.005|-0.007|0.009|0.009|
||||R|egressor: R|eal Interest|Rate (_RR_|_t_)||||
||Crude oil|Coal|Natural|Soybean|Barley|Maize|Sorghum|Rice|Wheat|Sugar|
||||gas|oil|||||||
|Coal|-0.002||||||||||
|Natural gas|-0.002|0.000|||||||||
|Soybean oil|-0.001|-0.002***|0.001||||||||
|Barley|-0.001|-0.001|0.001|-0.001|||||||
|Maize|0.001|-0.001|0.000|-0.002**|0.000||||||
|Sorghum|-0.001|-0.001|-0.001|-0.001|0.001|0.000|||||
|Rice|0.002|0.000|0.000|0.000|0.001|0.002|0.001||||
|Wheat|0.000|0.001|0.001|-0.002|0.000|-0.002|0.000|0.000|||
|Sugar|0.001|0.000|-0.001|-0.001|-0.002|-0.001|0.000|-0.001|0.002||
|Cofee|-0.001|-0.002|-0.001|-0.001|0.000|0.000|0.001|0.001|-0.001|-0.001|

Note. This table reports the OLS estimates of _δ_ and _γ_ in the equation The model parameters are estimated over the full sample, 1970M02-2013M05.<sup>�</sup> _ρ_ � _xz,w,t_ is the estimated value of the rolling correlation between the nominal price returns of commodities _x_ and _z_ at time _t_ , where _w_ is the length of the window used to compute the rolling correlations ( _w_ = 24 months, in this case). _L_ = 12 is the maximum lag allowed in the model; _L_ is determined using the Schwarz criterion. A Newey-West correction is used to produce reliable standard errors. ***, ** and * denote statistical significance at the 1%, 5% and 10% levels.

17
# **Figures**

Figure 1: Timeline of Major Events in Commodity Markets <!-- Start of picture text --> 1988: soybeans , and to a 2007-2008: Global Food<br>lower extent maize , crop Price crisis , corn, wheat and<br>shortage due to major rice were particularly<br>drought in the US. 2001: natural gas affected<br>1980: sugar price boom, price shock, gas<br>1973-1974 (first oil shock): oil decrease in global shortage<br>crisis, members of OAPEC, production<br>OPEC + Egypt, Syria, Tunisia,<br>proclaimed an oil embargo 2006: MTBE phase-out in the<br>1990-1991 Persian Gulf War: cut US, ethanol left the sole<br>down in oil production due to Iraqi oxygenate for gasoline<br>invasion to Kuwait<br>1970 1990 2013<br>2007-2008 (third oil shock):<br>1979 (second oil shock): energy crisis oil price spike , increased<br>started with Iranian revolution and demand, monetary<br>1974: sugar price boom, continued with Iran/Iraq war, Iranian oil 1996: maize, wheat debasement and potential<br>low production in 1972 & sector suspended and then limited their and soybeans crop speculation<br>1973 and increasing exports, pushing prices up fell in the US,<br>demand reduced adverse weather<br>worldwide stocks conditions leading 2011: coffee price shock,<br>to a shock in prices poor harvest due to bad<br>weather conditions in<br>1977: coffee price shock, low harvest production in Brazil Brazil and Colombia<br>in 1976 and 1977 (bad weather conditions)<br>1994: coffee price shock,<br>frost in Brazil<br><!-- End of picture text --> 18
Figure 2: Monthly Nominal Prices <!-- Start of picture text --> Crude oil Coal<br>Natural gas<br>1970m1 1980m1 1990m1 2000m1 2010m1<br>(a) Energy<br>Soybean oil Barley<br>Maize Sorghum<br>Rice Wheat<br>1970m1 1980m1 1990m1 2000m1 2010m1<br>(b) Agriculture<br>Sugar Coffee<br>1970m1 1980m1 1990m1 2000m1 2010m1<br>(c) Food<br>200 15<br>150<br>10<br>100<br>5 US$/mmbtu (gas)<br>US$/bbl (oil), US$/MT (coal) 50<br>0 0<br>1500<br>1000<br>US$/MT<br>500<br>0<br>800<br>600<br>400<br>US$/kg<br>200<br>0<br><!-- End of picture text --> 19
Figure 3: Monthly Nominal Price Returns <!-- Start of picture text --> Crude oil Coal Natural gas<br>Soybean oil Barley Maize<br>Sorghum Rice Wheat<br>1970m1 1980m1 1990m1 2000m1 2010m1<br>Sugar Coffee<br>1970m1 1980m1 1990m1 2000m1 2010m1 1970m1 1980m1 1990m1 2000m1 2010m1<br>1.0<br>0.5<br>0.0<br>-0.5<br>1.0<br>0.5<br>0.0<br>-0.5<br>1.0<br>0.5<br>0.0<br>-0.5<br>1.0<br>0.5<br>0.0<br>-0.5<br><!-- End of picture text --> Note. The vertical lines represent the structural breaks identified with the Qu and Perron (2007)’s methodology: 1979M11, 1987M07 and 2007M05.

20
Figure 4: Dynamic Conditional Correlations of Maize Nominal Price Returns <!-- Start of picture text --> 0.8 0.8 0.8<br>0.6 0.6 0.6<br>0.4 0.4 0.4<br>0.2 0.2 0.2<br>0 0 0<br>−0.21970 1978 1987 1996 2004 2013 −0.21970 1978 1987 1996 2004 2013 −0.21970 1978 1987 1996 2004 2013<br>(a) Crude oil (b) Coal (c) Natural gas<br>0.8 0.8 0.8<br>0.6 0.6 0.6<br>0.4 0.4 0.4<br>0.2 0.2 0.2<br>0 0 0<br>−0.21970 1978 1987 1996 2004 2013 −0.21970 1978 1987 1996 2004 2013 −0.21970 1978 1987 1996 2004 2013<br>(d) Soybean oil (e) Barley (f) Sorghum<br>0.8 0.8 0.8<br>0.6 0.6 0.6<br>0.4 0.4 0.4<br>0.2 0.2 0.2<br>0 0 0<br>−0.21970 1978 1987 1996 2004 2013 −0.21970 1978 1987 1996 2004 2013 −0.21970 1978 1987 1996 2004 2013<br>(g) Rice (h) Wheat (i) Sugar<br>0.8<br>0.6<br>0.4<br>0.2<br>0<br>−0.21970 1978 1987 1996 2004 2013<br>(j) Coffee<br><!-- End of picture text --> Note. The solid thin lines plot the estimated dynamic conditional correlations (DCC), the solid thick lines represent their trends estimated by HP (Hodrick-Prescott) filter. The dashed lines are the estimated constant conditional correlations (CCC) based on Bollerslev (1990) and their corresponding 95% confidence intervals.

21
Figure 5: Dynamic Conditional Correlations of Soybean Oil Nominal Price Returns <!-- Start of picture text --> 0.8 0.8 0.8<br>0.6 0.6 0.6<br>0.4 0.4 0.4<br>0.2 0.2 0.2<br>0 0 0<br>−0.21970 1978 1987 1996 2004 2013 −0.21970 1978 1987 1996 2004 2013 −0.21970 1978 1987 1996 2004 2013<br>(a) Crude oil (b) Coal (c) Natural gas<br>0.8 0.8 0.8<br>0.6 0.6 0.6<br>0.4 0.4 0.4<br>0.2 0.2 0.2<br>0 0 0<br>−0.21970 1978 1987 1996 2004 2013 −0.21970 1978 1987 1996 2004 2013 −0.21970 1978 1987 1996 2004 2013<br>(d) Barley (e) Maize (f) Sorghum<br>0.8 0.8 0.8<br>0.6 0.6 0.6<br>0.4 0.4 0.4<br>0.2 0.2 0.2<br>0 0 0<br>−0.21970 1978 1987 1996 2004 2013 −0.21970 1978 1987 1996 2004 2013 −0.21970 1978 1987 1996 2004 2013<br>(g) Rice (h) Wheat (i) Sugar<br>0.8<br>0.6<br>0.4<br>0.2<br>0<br>−0.21970 1978 1987 1996 2004 2013<br>(j) Coffee<br><!-- End of picture text --> Note. The solid thin lines plot the estimated dynamic conditional correlations (DCC), the solid thick lines represent their trends estimated by HP (Hodrick-Prescott) filter. The dashed lines are the estimated constant conditional correlations (CCC) based on Bollerslev (1990) and their corresponding 95% confidence intervals.

22
# **A Econometric Techniques**

In this Appendix we briefly describe the econometric techniques that we adopt to produce the results presented in the main body of the paper, in the tables, and in the figures. The nominal commodity price returns are defined as _rm,t_ = ln _Pm,t −_ ln _Pm,t−_ 1, where _Pm,t_ is the nominal price of commodity _m_ at time _t_ .

## **A.1 Qu and Perron (2007)’s Breakpoint Analysis**

We estimate two unrestricted vector autoregressions (VAR) of orders 0 and 1 for the nominal price returns of the eleven commodities over the full sample of data (1970M02-2013M05). Both model specifications satisfy the conventional stability conditions ensuring stationarity. We evaluate the presence of structural breaks at unknown dates in the coefficients of the VAR equations and in the variance-covariance matrices of the error terms.

The errors are assumed to be normally distributed (quasi-maximum likelihood technique). The distribution of the relevant test statistic becomes degenerate as the estimated breaks approach the beginning or the end of the sample, or if any two breakpoints are too close to each other. In order to address this statistical issue, we set a trimming parameter of 15%; that is, 78 months (6.5 years) is the minimum distance between any two breakpoints, between the beginning of the sample and the first break, and between the last break and the end of the sample. The covariance matrices of the errors and the distributions of the regressors in the VAR models are allowed to change from each regime to the next, but no pre-whitening is applied for the construction of the breakpoint intervals.

The multivariate approach that we adopt in this context is consistent with the rest of the analysis.<sup>15</sup> The breaks detected may differ from the breaks in individual bivariate correlation coefficients. Our assumption is that only some parameters of the VAR equations present structural breaks at some point in time and that, when a break occurs, it occurs simultaneously in all model parameters and the variance-covariance matrix of the errors.

Our preferred specification is a VAR(1) model of the eleven nominal price returns. We generally allow for the presence of two breaks, which are estimated to occur in 1979M11 and 1987M07. When we allow for the presence of a third structural break, we generally come across a corner solution, due to the 15% trimming at the two ends of the sample. The implication is that the third structural break is likely to lie to the right of the identified value (corner solution), closer to the end of the sample period. We investigate this possibility by testing for the presence of a structural break only on a restricted sample of data ranging from 1990M01 to 2013M05. By restricting the sample in this way, we reduce the number of trimmed observations from 6.5 years down to 3.5 years, while keeping the trimming parameter constant at 15%. We find an additional structural break in 2007M05, at the onset of several agricultural price spikes.

> 15In fact, the unconditional correlations analyzed in Section 3.2 can be expressed as scalar functions of the VAR parameters.

23
# **A.2 Ng (2006)’s Uniform Spacings Test for Cross-Section Unconditional Correlation**

Let _M_ = 11 be the number of nominal commodity price returns in the sample and _T_ the number of monthly observations. As long as the data sample is sufficiently large, the returns do not need to satisfy any specific distributional assumptions. The number of unique elements above (or below) the main diagonal of the sample unconditional correlation matrix is _N ≡_<sup>_M_</sup><sup><u>(</u></sup><sup>_M_</sup> 2<sup>_−_1)</sup> = 55. � � � _<u>ρ</u> ≡_ ( _|ρ_ 1 _|, |ρ_ 2 _|, ..., |ρN |_ )<sup>_′_</sup> is the vector of sample absolute correlation coefficients that collects the estimates of the absolute values of the population correlations in _ρ ≡_ ( _ρ_ 1 _, ρ_ 2 _,_ ..., _ρN_ )<sup>_′_</sup> . These _N_ sample absolute correlation coefficients are then ordered from the smallest to the largest, _′_ � _<u>ρ</u>_ [1: _N_ ] _,_ _<u>ρ</u>_ [2: _N_ ] _, ...,_ _<u>ρ</u>_ [ _N_ : _N_ ]� . Finally, define the objects _φs ≡_ Φ � _√T_ _<u>ρ</u>_ [ _s_ : _N_ ]�, where Φ ( _·_ ) is the cumulative distribution function of a standard normal random variable and _s_ = 1 _,_ 2 _, ..., N_ . Given that _<u>ρ</u>_ [ _s_ : _N_ ] _∈_ [0 _,_ 1] _∀s_ = 1 _,_ 2 _, ..., N_ , then _φs ∈_ [0 _._ 5 _,_ 1] _∀s_ = 1 _,_ 2 _, ..., N_ . The _q_ -order uniform spacings is defined as _{_ � _φs − φs−q_ � _}_<sup>_N_</sup> _s_ = _q_ +1<sup>.</sup>

The _N_ sample absolute correlations can be partitioned into two groups (first split), a group _S_ containing the smallest absolute correlations and a group _L_ containing the largest absolute correlations. The fraction of correlations in the sample contained in _S_ is _θ ∈_ [0 _,_ 1]. The statistical procedure, based on maximum likelihood techniques, determines the location of a slope change in the sequence of _φs_ ’s to estimate the parameter _θ_ . The estimated number of correlations in _S_ is then _K_<sup>ˆ</sup> _≡ θN_<sup>ˆ</sup> , whereas the estimated number of correlations in _L_ is _N − K_<sup>ˆ</sup> = 1 _− θ_<sup>ˆ</sup> _N_ . � � As proved in Ng (2006), the null hypothesis _H_ 0 : _ρs_ = 0 is equivalent to the null _H_ 0 : _φs ∼ U_ [0 _._ 5 _,_ 1]. We use a standardized spacings variance ratio test statistic, _SV R_ ( _n_ ), to test the hypothesis of zero absolute correlation within each group. Such a statistic has a standard normal probability density function under the null of no correlation in a subsample of absolute correlations of size _n −→∞_ . Ng (2006) also shows that this testing strategy exhibits reliable small-sample properties. _SV R_ ( _n_ ) depends on the choice of the lag-length parameter _q_ and is based on a transformation of the return correlation spacings, which are exchangeable by construction – that is, the structure of dependence in � _φs − φs−q_ � is the same for any _s_ . With uncorrelated data, the _φs_ ’s all <u>1</u> lie along a straight line with slope equal to 2( _n_ +1)<sup>inaCartesianspace.Thestrongerthecorre-</sup> lation intensity, the further away the _φs_ ’s are from that straight line. As proposed in the original theoretical framework, we test for each group ( _S_ or _L_ ) whether the variance of _{_ � _φs − φs−q_ � _}_<sup>_N_</sup> _s_ = _q_ +1 is a linear function of _q_ . The problem is then to test the uniformity and nonstationarity of a specific transformation of sample absolute correlations.<sup>16</sup> If the uniformity hypothesis on the _φs_ ’s is rejected for _S_ , testing whether the same hypothesis holds for _L_ becomes uninformative. In fact, if the small correlations are statistically different from zero, then the absolute correlations in _L_ must also be different from zero by construction.

> 16The extent of cross-section correlation in the panel of data can be graphically assessed by means of a quantile-quantile (q-q) plot of the _φs_ ’s. If all correlations are nonzero, then the q-q plot will be shifted upward and its intercept will be larger than 0 _._ 5. If there is homogeneity in a subset of the correlations, then the q-q <u>plot</u> will be flat over a certain range. If _S_ is characterized by zero correlations while _L_ is not, then, in the q-q plot, the _φs_ ’s would be approximately linear in _s_ until _s_ = _K_<sup>ˆ</sup> , then would rise steeply for _s > K_<sup>ˆ</sup> , and eventually would flatten at the boundary of 1.

24
# **A.3 Dynamic Conditional Correlations**

The multivariate (MV) GARCH model assumes that the _M_ demeaned nominal commodity price returns are conditionally multivariate normal with zero expected value and covariance matrix _Ht_ . A dynamic conditional correlation DCC(J,K) MV-GARCH(P,Q) model is used on the transformed _T_ returns _r_ � _m,t_ = _rm,t −_ _<u>rm</u>_ , where _<u>rm</u>_ = <u>�</u> _<u>t</u>_ <u>=1</u> _T_<sup>_rm,t_</sup> . Let _<u>r</u>_ = <u>(</u> _<u>r</u>_ 1 _,_ _<u>r</u>_ 2 _, ...,_ _<u>rM</u>_ )<sup>_′_</sup> , _r_ � _t_ = ( _r_ �1 _,t,_ � _r_ 2 _,t, ...,_ � _rM,t_ )<sup>_′_</sup> , � _rt ∼N_ (0 _, Ht_ ), and _Ht_ = _DtRtDt_ . _Dt_ is the _M × M_ diagonal matrix of time-varying standard deviations from _M_ univariate GARCH models. ~~�~~ _hm,t_ is the _m_<sup>_th_</sup> element of the main diagonal of _Dt_ and _Rt_ is a time-varying correlation matrix.<sup>17</sup> Each element _hm,t_ is described by a univariate GARCH model, _hm,t_ = _ωm_ +<sup>�</sup><sup>_P_</sup> _p_ =1<sup>_mαm,pr_�</sup> _m,t_<sup>2</sup> _−p_<sup>+</sup> _Qm_ � _q_ =1<sup>_βm,phm,t−q_for</sup><sup>_m_=1</sup><sup>_,_2</sup><sup>_, ..., M_.18Foreachpricereturn,</sup><sup>_Pm_and</sup><sup>_Qm_areintegersbetween</sup> 1 and 4, chosen according to the Schwarz criterion. They need not be the same. Also let _P_ = ( _P_ 1 _, P_ 2 _, ..., PM_ )<sup>_′_</sup> and _Q_ = ( _Q_ 1 _, Q_ 2 _, ..., QM_ )<sup>_′_</sup> .

The process _Ut_ = �1 _−_<sup>�</sup><sup>_J_</sup> _j_ =1<sup>_γj−_�</sup><sup>_K_</sup> _k_ =1<sup>_δk_</sup> � _U_ +<sup>�</sup><sup>_J_</sup> _j_ =1<sup>_γj_(</sup><sup>_ε_�</sup><sup>_t−jε_�</sup> _t_<sup>_′_</sup> _−j_<sup>) + �</sup> _k_<sup>_K_</sup> =1<sup>_δkUt−k_isassumed</sup> to describe the conditional dynamic correlation structure used to model the data. _ε_ � _t ∼N_ (0 _, Rt_ ) � is the vector of residuals obtained from the multiple OLS regressions _rt_ = _θ_ + _εt_ and standardized by their conditional standard deviations. _U_ is the unconditional covariance of the standardized residuals resulting from the first-stage estimation. We assume that _Rt_ = ( _Ut_<sup>_∗_)</sup><sup>_−_1</sup><sup>_Ut_(</sup><sup>_U_</sup> _t_<sup>_∗_)</sup><sup>_−_1,where</sup> such that _Ut_<sup>_∗_is a diagonal matrix composed of the square root of the diagonal elements of</sup><sup>_Ut_.Under</sup> suitable conditions, the elements of _Rt_ have the form _ρ_<sup>_∗_</sup> _xz,t_<sup>=</sup> _~~√~~_ _<u>uxx,tuxz,utzz,t</u>_<sup>,with</sup><sup>_x, z_= 1</sup><sup>_,_2</sup><sup>_, ..., M_.</sup> Note that _Rt_ can also be constant and equal to _R_ . In such a case, the DCC(J,K) MVGARCH(P,Q) model becomes a constant conditional correlation CCC MV-GARCH(P,Q) model (Bollerslev, 1990). In this paper, _J_ and _K_ are always set equal to 1. While the main focus of our work is on the multivariate analysis of commodity price returns and their correlations, we also estimate bivariate (BV) models, DCC(J,K) BV-GARCH(P,Q), between all pairs of commodity returns and find qualitatively similar results.

> 17The assumption of multivariate normality is not strictly required for consistency and asymptotic normality of the estimators. If returns have non-normal innovations, the DCC estimator corresponds to a quasi-maximum likelihood estimator.

> 18Conventional GARCH restrictions for non-negativity of variances and stationarity are imposed.

25
# **A.4 Rolling Unconditional Correlations**

Following Tang and Xiong (2012), we normalize the regular monthly commodity price returns by _rm,t−rm_ their respective averages and standard deviations, _rm,t_<sup>_∗_=</sup> <u>�</u> _Tt_ <u>=1</u><sup><u>(</u></sup><sup>_rm,t−_</sup> _<u>rm</u>_ <u>)</u><sup>2</sup> . We then regress the ~~<u>�</u>~~ _T −_ 1 normalized return of commodity _x_ , _rx,t_<sup>_∗_,ontothenormalizedreturnofcommodity</sup><sup>_z_,</sup><sup>_r_</sup> _z,t_<sup>_∗_,with</sup> _x, z_ = 1 _,_ 2 _, ..., M_ and _x_ = _z_ .<sup>�</sup> _ρ_ � _xz_ obtained from the regression _rx,t_<sup>_∗_=</sup><sup>_μ_+ �</sup><sup>_ρxzr_</sup> _z,t_<sup>_∗_+</sup><sup>_ηt_is the estimated</sup> unconditional correlation between the two commodity price returns. We assess the time-variation in the correlation coefficients between all pairs of commodity price returns by estimating rolling regressions with fixed windows of size equal to two and five years – i.e., 24 and 60 months. NeweyWest standard errors, based on a Bartlett kernel and a fixed bandwidth, correct for autocorrelation in the regression residuals and are used to derive reliable rolling 95% confidence intervals for _ρ_ � _xz_ .

26
# **B Supplementary Tables and Figures**

## Table 4: Commodities

|Crude oil|Crude oil, Dubai Fateh 32‘ API for years 1985-present; 1960-84 refer to Saudi Arabian Light, 34‘ API|
|---|---|
|Coal|Coal (Australia), thermal GAR, f.o.b. piers, Newcastle/Port Kembla from 2002 onwards, 6,300 kcal/kg<br>(11,340 btu/lb), less than 0.8%, sulfur 13% ash; previously 6,667 kcal/kg (12,000 btu/lb), less than 1.0%<br>sulfur, 14% ash|
|Natural gas|Natural Gas (US), spot price at Henry Hub, Louisiana|
|Soybean oil|Soybean oil (Any origin), crude, f.o.b. ex-mill Netherlands|
|Barley|Barley (US) feed, No. 2, spot, 20 days To-Arrive, delivered Minneapolis from May 2012 onwards; during<br>1980 - 2012 April Canadian, feed, Western No. 1, Winnipeg Commodity Exchange, spot, wholesale<br>farmers’ price|
|Maize|Maize (US), No. 2, yellow, f.o.b. US Gulf ports|
|Sorghum|Sorghum (US), No. 2 milo yellow, f.o.b. Gulf ports|
|Rice|Rice (Thailand), 5% broken, white rice (WR), milled, indicative price based on weekly surveys of export<br>transactions, government standard, f.o.b. Bangkok|
|Wheat|Wheat (US), No. 1, hard red winter, ordinary protein, export price delivered at the US Gulf port for<br>prompt or 30 days shipment|
|Sugar|Sugar (World), International Sugar Agreement (ISA) daily price, raw, f.o.b. and stowed at greater<br>Caribbean ports|
|Cofee|Cofee (ICO), International Cofee Organization indicator price, other mild Arabicas, average New York<br>and Bremen/Hamburg markets, ex-dock|

27
Table 5: Summary Statistics of Commodity Nominal Price Returns - Subsample Analysis

|1970M02-1979M10|T|Mean|Median|SD|Min|Max|Skewness|Kurtosis|Shapiro-Wilk|Ljung-Box|
|---|---|---|---|---|---|---|---|---|---|---|
|Crude oil|117|0.029|0.000|0.128|-0.204|1.154|6.487|53.539|0.000|1.000|
|Coal|117|0.012|0.000|0.060|-0.029|0.463|6.118|42.426|0.000|0.384|
|Natural gas|117|0.017|0.000|0.053|-0.022|0.394|5.278|33.486|0.000|0.004|
|Soybean oil|117|0.008|0.007|0.083|-0.195|0.216|0.207|3.224|0.219|0.330|
|Barley|117|0.009|0.004|0.047|-0.108|0.278|1.588|10.973|0.000|0.984|
|Maize|117|0.006|0.000|0.057|-0.134|0.166|0.226|3.597|0.004|0.000|
|Sorghum|117|0.007|0.000|0.058|-0.164|0.214|0.817|5.134|0.000|0.004|
|Rice|117|0.008|0.004|0.082|-0.144|0.582|3.400|24.545|0.000|1.000|
|Wheat|117|0.010|0.000|0.075|-0.163|0.519|2.697|20.279|0.000|1.000|
|Sugar|117|0.010|0.010|0.118|-0.301|0.352|0.178|4.081|0.009|0.294|
|Cofee|117|0.012|0.009|0.078|-0.231|0.254|0.351|4.310|0.018|0.000|
|1979M11-1987M06|T|Mean|Median|SD|Min|Max|Skewness|Kurtosis|Shapiro-Wilk|Ljung-Box|
|Crude oil|92|-0.008|-0.003|0.093|-0.540|0.437|-1.173|19.038|0.000|0.871|
|Coal|92|-0.003|0.000|0.052|-0.213|0.228|-0.121|13.266|0.000|0.289|
|Natural gas|92|0.003|0.005|0.024|-0.069|0.045|-0.578|2.951|0.029|0.894|
|Soybean oil|92|-0.007|-0.009|0.072|-0.215|0.311|0.806|7.040|0.000|0.949|
|Barley|92|-0.002|0.000|0.092|-0.215|0.287|0.266|3.823|0.139|0.432|
|Maize|92|-0.004|-0.008|0.057|-0.221|0.126|-0.385|4.705|0.003|1.000|
|Sorghum|92|-0.005|-0.006|0.058|-0.211|0.118|-0.759|4.488|0.006|0.373|
|Rice|92|-0.006|0.000|0.043|-0.127|0.143|0.128|3.996|0.236|0.982|
|Wheat|92|-0.005|-0.005|0.035|-0.121|0.068|-0.585|3.714|0.069|0.745|
|Sugar|92|-0.007|-0.017|0.133|-0.275|0.376|0.425|2.972|0.155|0.973|
|Cofee|92|-0.008|-0.006|0.068|-0.177|0.235|0.290|4.741|0.003|0.005|
|1987M07-2007M04|T|Mean|Median|SD|Min|Max|Skewness|Kurtosis|Shapiro-Wilk|Ljung-Box|
|Crude oil|238|0.005|0.014|0.085|-0.309|0.491|0.237|7.899|0.000|0.864|
|Coal|238|0.003|0.000|0.040|-0.135|0.159|0.280|5.630|0.000|0.000|
|Natural gas|238|0.006|0.005|0.139|-0.405|0.478|-0.207|4.209|0.001|0.072|
|Soybean oil|238|0.003|0.002|0.053|-0.117|0.261|0.826|5.764|0.000|0.970|
|Barley|238|0.004|0.001|0.059|-0.203|0.283|0.115|6.365|0.000|0.001|
|Maize|238|0.003|0.004|0.054|-0.244|0.298|0.073|8.104|0.000|1.000|
|Sorghum|238|0.003|0.000|0.057|-0.180|0.342|0.720|8.689|0.000|1.000|
|Rice|238|0.002|0.003|0.055|-0.242|0.235|0.195|6.395|0.000|0.017|
|Wheat|238|0.003|0.000|0.051|-0.151|0.179|0.285|3.946|0.007|0.002|
|Sugar<br>|238|0.002|0.007|0.078|-0.230|0.283|0.226|3.531|0.311|0.007|
|Cofee|238|0.000|-0.005|0.082|-0.353|0.423|0.684|7.151|0.000|0.060|
|2007M05-2013M05|T|Mean|Median|SD|Min|Max|Skewness|Kurtosis|Shapiro-Wilk|Ljung-Box|
|Crude oil|73|0.006|0.021|0.089|-0.335|0.187|-1.484|6.486|0.000|0.005|
|Coal|73|0.006|0.005|0.093|-0.329|0.364|-0.002|6.725|0.001|0.709|
|Natural gas|73|-0.009|-0.025|0.117|-0.301|0.375|0.598|3.987|0.092|0.680|
|Soybean oil|73|0.005|0.008|0.064|-0.278|0.117|-1.244|6.864|0.000|0.991|
|Barley|73|0.005|0.011|0.079|-0.279|0.233|-0.411|5.213|0.003|0.016|
|Maize|73|0.009|0.004|0.074|-0.245|0.220|-0.251|4.679|0.082|0.979|
|Sorghum|73|0.008|0.017|0.078|-0.278|0.254|-0.517|5.324|0.007|0.472|
|Rice|73|0.007|-0.004|0.079|-0.175|0.423|2.331|13.029|0.000|0.996|
|Wheat|73|0.007|0.006|0.088|-0.219|0.229|0.375|3.750|0.075|0.966|
|Sugar|73|0.008|-0.001|0.083|-0.308|0.197|-0.312|4.794|0.026|0.736|
|Cofee|73|0.003|0.002|0.054|-0.148|0.121|-0.170|3.092|0.927|0.977|

Note. Price returns are computed as ln _Pm,t −_ ln _Pm,t−_ 1, where _Pm,t_ is the nominal price of commodity _m_ at time _t_ . Prices are measured in nominal terms. T stands for the number of monthly time observations. SD stands for standard deviation. The Shapiro-Wilk column reports the p-value of the Shapiro-Wilk test (the null hypothesis is that the series of returns has a normal distribution). The Ljung-Box column reports the p-value of the Ljung-Box test (the null hypothesis is that there is no autocorrelation in the series of squared returns up to twelve lags).

28
Table 6: Large Absolute Correlation Sets Based on Ng (2006) 1970M02-2013M05 (45 Pairs)

**Positive Correlations** : Maize-Sorghum (0.807), Sorghum-Wheat (0.527), Barley-Maize (0.491), Maize-Wheat (0.479), Barley-Sorghum (0.470), Soybean oil-Maize (0.465), Barley-Wheat (0.449), Soybean oil-Sorghum (0.419), Soybean oil-Barley (0.395), Crude oil-Coal (0.311), Soybean oil-Wheat (0.279), Coal-Natural gas (0.229), Wheat-Sugar (0.190), Soybean oil-Sugar (0.177), Sorghum-Sugar (0.176), Crude oil-Natural gas (0.172), Maize-Sugar (0.160), Wheat-Coffee (0.144), Coal-Maize (0.143), Sorghum-Coffee (0.138), Barley-Rice (0.136), Maize-Rice (0.134), Crude oil-Soybean oil (0.129), Coal-Sorghum (0.128), Sorghum-Rice (0.127), Soybean oil-Coffee (0.126), Soybean oil-Rice (0.125), Maize-Coffee (0.121), Coal-Sugar (0.112), Natural gas-Barley (0.112), Coal-Barley (0.109), Crude oil-Barley (0.108), Coal-Soybean oil (0.106), Coal-Wheat (0.093), Barley-Coffee (0.086), Crude oil-Sugar (0.086), Crude oil-Coffee (0.081), Natural gas-Maize (0.081), Crude oil-Wheat (0.080), Coal-Coffee (0.077), Rice-Wheat (0.075), Crude oil-Sorghum (0.069), Coal-Rice (0.069), Natural gas-Sugar (0.067), Barley-Sugar (0.063)

# 1970M02-1979M10 (48 Pairs)

**Positive Correlations** : Barley-Wheat (0.933), Coal-Natural gas (0.869), Maize-Sorghum (0.804), Barley-Maize (0.780), Barley-Sorghum (0.779), Sorghum-Wheat (0.614), Crude oil-Coal (0.527), Crude oil-Natural gas (0.514), Maize-Wheat (0.502), Soybean oil-Maize (0.489), Soybean oil-Sorghum (0.400), Soybean oil-Barley (0.352), Sorghum-Sugar (0.302), Maize-Coffee (0.276), Soybean oil-Sugar (0.265), Barley-Sugar (0.257), Wheat-Sugar (0.243), Soybean oil-Coffee (0.231), Soybean oil-Wheat (0.205), Crude oil-Sugar (0.199), Sorghum-Rice (0.195), Maize-Sugar (0.194), Barley-Rice (0.185), Soybean oil-Rice (0.171), Rice-Wheat (0.169), Barley-Coffee (0.163), Sorghum-Coffee (0.161), Maize-Rice (0.151), Crude oil-Sorghum (0.138), Sugar-Coffee (0.131), Crude oil-Soybean oil (0.117), Natural gas-Coffee (0.100), Coal-Sugar (0.084), Crude oil-Wheat (0.077), Crude oil-Coffee (0.077), Crude oil-Barley (0.067), Wheat-Coffee (0.067)

**Negative Correlations** : Natural gas-Sorghum (-0.162), Coal-Sorghum (-0.125), Natural gas-Rice (-0.120), Natural gas-Barley (-0.115), Natural gas-Maize (-0.109), Coal-Maize (-0.104), Natural gas-Wheat (-0.097), Coal-Barley (-0.096), Coal-Rice (-0.089), Coal-Soybean oil (-0.080), Coal-Wheat (-0.072)

# 1979M11-1987M06 (12 Pairs)

**Positive Correlations** : Maize-Sorghum (0.681), Soybean oil-Barley (0.566), Barley-Sorghum (0.538), Soybean oil-Sorghum (0.469), Sorghum-Wheat (0.468), Soybean oil-Maize (0.450), Barley-Maize (0.408), Barley-Wheat (0.376), Maize-Wheat (0.292), Coal-Natural gas (0.259), Natural gas-Wheat (0.242), Soybean oil-Wheat (0.236)

# 1987M07-2007M04 (28 Pairs)

**Positive Correlations** : Maize-Sorghum (0.859), Sorghum-Wheat (0.531), Maize-Wheat (0.455), Barley-Maize (0.424), Soybean oil-Maize (0.371), Barley-Sorghum (0.362), Soybean oil-Sorghum (0.330), Barley-Wheat (0.279), Soybean oil-Barley (0.223), Soybean oil-Wheat (0.218), Coal-Maize (0.191), Soybean oil-Sugar (0.166), Coal-Sorghum (0.149), Wheat-Sugar (0.148), Crude oil-Natural gas (0.135), Coal-Natural gas (0.115), Coal-Barley (0.106), Natural gas-Barley (0.104), Natural gas-Sugar (0.101), Maize-Sugar (0.097), Coal-Sugar (0.096), Sorghum-Sugar (0.095), Coal-Wheat (0.093)

**Negative Correlations** : Crude oil-Maize (-0.190), Crude oil-Sorghum (-0.158), Natural gas-Coffee (-0.103), Natural gas-Rice (-0.112), Crude oil-Rice (-0.098)

2007M05-2013M05 (48 Pairs)

**Positive Correlations** : Maize-Sorghum (0.806), Crude oil-Soybean oil (0.758), Soybean oil-Maize (0.668), Crude oil-Barley (0.655), Coal-Soybean oil (0.631), Soybean oil-Sorghum (0.609), Soybean oil-Barley (0.607), Maize-Wheat (0.595), Crude oil-Coal (0.575), Soybean oil-Wheat (0.563), Barley-Maize (0.539), Crude oil-Maize (0.538), Wheat-Coffee (0.535), Soybean oil-Coffee (0.526), Barley-Wheat (0.497), Sorghum-Wheat (0.497), Maize-Coffee (0.495), Crude oil-Sorghum (0.474), Coal-Barley (0.450), Coal-Coffee (0.430), Barley-Sorghum (0.412), Sorghum-Coffee (0.403), Soybean oil-Sugar (0.395), Coal-Maize (0.380), Crude oil-Coffee (0.372), Sugar-Coffee (0.347), Coal-Sorghum (0.338), Barley-Coffee (0.332), Crude oil-Wheat (0.313), Natural gas-Maize (0.312), Coal-Sugar (0.312), Natural gas-Barley (0.309), Barley-Rice (0.282), Coal-Natural gas (0.271), Coal-Wheat (0.263), Maize-Sugar (0.252), Natural gas-Coffee (0.246), Wheat-Sugar (0.246), Crude oil-Rice (0.231), Natural gas-Sorghum (0.221), Coal-Rice (0.220), Sorghum-Rice (0.219), Natural gas-Rice (0.208), Natural gas-Soybean oil (0.207), Sorghum-Sugar (0.206), Soybean oil-Rice (0.205), Crude oil-Sugar (0.188), Maize-Rice (0.172)

Note. Commodity pairs are ordered from largest to smallest absolute correlation (correlations are reported in parenthesis). The number of correlations in the large absolute correlation set is estimated by maximum likelihood (see Section A.2).

29
Table 7: Determinants of Absolute Rolling Correlations - Subsample Analysis

||||Pane|l A: Sampl|e Period 197|0M02-1979|M10||||
|---|---|---|---|---|---|---|---|---|---|---|
|||Re|gressor: St|andard Dev|iation of S&|P500 Retu|rns (_σSP_500_,_|_t_)|||
||Crude oil|Coal|Natural|Soybean|Barley|Maize|Sorghum|Rice|Wheat|Sugar|
||||gas|oil|||||||
|Coal|0.018||||||||||
|Natural gas|0.021|0.030|||||||||
|Soybean oil|0.006|0.013|-0.012||||||||
|Barley|-0.015|-0.021|-0.014|0.004|||||||
|Maize|0.000|-0.040**|-0.009|0.008|0.005||||||
|Sorghum|0.001|-0.023|0.000|-0.008|-0.001|-0.005|||||
|Rice|0.028|0.003|-0.014|-0.010|-0.035**|-0.033*|-0.024||||
|Wheat|-0.011|-0.006|-0.003|-0.004|0.000|-0.015|-0.003|-0.026**|||
|Sugar|0.006|0.007|0.012|-0.038|-0.011|-0.019|0.016|-0.035|-0.007||
|Cofee|0.017|0.034*|0.008|0.002|0.014|-0.002|-0.021|-0.003|-0.027|0.001|
||||R|egressor: R|eal Interest|Rate (_RRt_|)||||
||Crude oil|Coal|Natural|Soybean|Barley|Maize|Sorghum|Rice|Wheat|Sugar|
||||gas|oil|||||||
|Coal|-0.002||||||||||
|Natural gas|-0.002|0.002|||||||||
|Soybean oil|0.000|0.000|-0.001||||||||
|Barley|-0.001|-0.008***|-0.006*|-0.008|||||||
|Maize|0.006|-0.011***|-0.007|-0.005|-0.002||||||
|Sorghum|-0.003|-0.010***|-0.005*|-0.009|0.001|0.001|||||
|Rice|0.015**|0.005|0.001|0.003|0.001|0.001|0.008||||
|Wheat|-0.005**|-0.003*|-0.001|-0.007|0.000|-0.005*|0.000|0.001|||
|Sugar|-0.005|0.004|0.004|-0.01*|-0.006|-0.009**|-0.003|-0.006|-0.001||
|Cofee|-0.002|0.001|0.003|-0.003|0.000|0.000|-0.003|0.003|-0.002|-0.001|

30
Determinants of Absolute Rolling Correlations - Subsample Analysis (Cont’d) Panel B: Sample Period 1979M11-1987M06

|||Re|gressor: St|andard Dev|iation of S&|P500 Retu|rns (_σSP_500|_,t_)|||
|---|---|---|---|---|---|---|---|---|---|---|
||Crude oil|Coal|Natural|Soybean|Barley|Maize|Sorghum|Rice|Wheat|Sugar|
||||gas|oil|||||||
|Coal|-0.014||||||||||
|Natural gas|0.004|0.041*|||||||||
|Soybean oil|0.011|0.014|0.053*||||||||
|Barley|-0.039*|0.030|0.002|-0.071**|||||||
|Maize|-0.019|-0.016|0.005|0.007|-0.007||||||
|Sorghum|-0.002|-0.032**|0.035|-0.052*|-0.015|-0.004|||||
|Rice|0.062**|0.000|-0.008|-0.025|-0.008|0.001|0.000||||
|Wheat|-0.022|-0.036|0.011|-0.039|-0.035*|0.002|0.014|-0.010|||
|Sugar|-0.018|0.016|0.002|0.076**|0.006|-0.010|0.018|0.038*|0.012||
|Cofee|-0.009|-0.004|-0.008|0.029|0.091**|-0.041|-0.006|0.029|-0.029|-0.025|
||||R|egressor: R|eal Interest|Rate (_RR_|_t_)||||
||Crude oil|Coal|Natural|Soybean|Barley|Maize|Sorghum|Rice|Wheat|Sugar|
||||gas|oil|||||||
|Coal|0.000||||||||||
|Natural gas|-0.001|0.007|||||||||
|Soybean oil|0.002|-0.008***|0.005***||||||||
|Barley|0.001|-0.002|0.001|-0.001|||||||
|Maize|0.002|0.001|0.004*|-0.003**|0.000||||||
|Sorghum|0.001|-0.001|0.001|-0.004**|0.000|-0.002*|||||
|Rice|0.001|0.002|-0.003|0.003|0.002|-0.001|-0.002||||
|Wheat|0.004|-0.004*|0.002|-0.005**|-0.003|-0.003*|-0.002|0.002|||
|Sugar|0.002|0.000|0.001|0.000|-0.007***|0.004*|0.005*|-0.002|0.007***||
|Cofee|0.000|-0.001|-0.001|0.003|0.004|0.003|0.003|0.001|-0.002|0.000|

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Determinants of Absolute Rolling Correlations - Subsample Analysis (Cont’d) Panel C: Sample Period 1987M07-2007M04

|||R|egressor: St|andard Dev|iation of S|&P500 Ret|urns (_σSP_500|_,t_)|||
|---|---|---|---|---|---|---|---|---|---|---|
||Crude oil|Coal|Natural|Soybean|Barley|Maize|Sorghum|Rice|Wheat|Sugar|
||||gas|oil|||||||
|Coal|0.003||||||||||
|Natural gas|0.003|0.018*|||||||||
|Soybean oil|-0.008|-0.002|-0.008||||||||
|Barley|0.004|0.014|-0.001|0.015**|||||||
|Maize|-0.003|0.006|0.013**|0.010*|0.006||||||
|Sorghum|-0.007|-0.003|0.006|0.006|0.006|-0.007|||||
|Rice|-0.009|-0.009|0.003|0.005|-0.001|-0.008|0.005||||
|Wheat|-0.001|0.010|0.008|-0.006|0.006|0.005|0.005|0.005|||
|Sugar|-0.008|-0.002|0.007|-0.012**|0.001|0.004|0.019**|-0.012**|0.019*||
|Cofee|0.001|-0.004|0.006|0.004|0.007|-0.009|-0.010|-0.005|0.002|0.004|
||||R|egressor: R|eal Interes|t Rate (_RR_|_t_)||||
||Crude oil|Coal|Natural|Soybean|Barley|Maize|Sorghum|Rice|Wheat|Sugar|
||||gas|oil|||||||
|Coal|0.001||||||||||
|Natural gas|-0.001|-0.001|||||||||
|Soybean oil|-0.002|0.000|0.003||||||||
|Barley|-0.001|0.001|0.003|0.000|||||||
|Maize|0.004*|0.002|0.001|-0.003|0.002||||||
|Sorghum|0.000|0.003|0.001|-0.001|0.006|0.002|||||
|Rice|0.001|-0.001|0.002|0.000|0.001|0.002|0.001||||
|Wheat|-0.002|0.005*|0.001|0.003|0.005|0.004|0.002|0.001|||
|Sugar|-0.002|0.002|-0.005**|0.004|0.000|0.000|0.000|0.001|0.000||
|Cofee|-0.004*|-0.003|-0.002|0.002|0.000|0.002|0.004*|-0.001|0.001|-0.003|

32
Determinants of Absolute Rolling Correlations - Subsample Analysis (Cont’d) Panel D: Sample Period 2007M05-2013M05

|||Re|gressor: Sta|ndard Devi|ation of S&|P500 Retu|rns (_σSP_500_,_|_t_)|||
|---|---|---|---|---|---|---|---|---|---|---|
||Crude oil|Coal|Natural|Soybean|Barley|Maize|Sorghum|Rice|Wheat|Sugar|
||||gas|oil|||||||
|Coal|0.017||||||||||
|Natural gas|0.007|0.018***|||||||||
|Soybean oil|0.011|0.022*|0.003||||||||
|Barley|0.043***|0.034*|0.012**|0.033***|||||||
|Maize|0.038***|0.039***|0.009|0.026***|0.016***||||||
|Sorghum|0.024**|0.030***|0.009|0.029***|0.020***|0.004**|||||
|Rice|0.015**|0.004|0.016***|0.021***|0.020|0.017**|0.026***||||
|Wheat|0.022*|0.028**|0.003|0.021***|0.017**|0.014*|0.018***|-0.021***|||
|Sugar|0.021***|0.015**|-0.001|0.009|0.023|0.011**|-0.010|0.011|0.026***||
|Cofee|0.030**|0.031***|-0.008|0.024***|0.040***|0.019**|0.020**|-0.014**|0.021***|0.021**|
||||R|egressor: R|eal Interest|Rate (_RR_|_t_)||||
||Crude oil|Coal|Natural|Soybean|Barley|Maize|Sorghum|Rice|Wheat|Sugar|
||||gas|oil|||||||
|Coal|0.006||||||||||
|Natural gas|-0.001|0.001|||||||||
|Soybean oil|0.001|0.000|0.003||||||||
|Barley|-0.005|0.002|0.005|-0.007*|||||||
|Maize|0.002|0.002|0.001|-0.005|0.004||||||
|Sorghum|0.001|-0.004|0.000|-0.001|0.000|0.001|||||
|Rice|0.006*|0.019**|0.017***|-0.004|0.006|0.009*|0.000||||
|Wheat|0.003|0.002|0.000|0.000|0.004|-0.001|0.000|-0.009*|||
|Sugar|0.010***|0.001|-0.006|-0.005|0.004|-0.005|-0.004|0.003|0.005||
|Cofee|0.003|-0.002|-0.004|0.000|0.003|0.001|0.003|-0.008*|-0.004|0.008*|

Note. This table reports the OLS estimates of _δ_ and _γ_ in the equation The model parameters are estimated over the indicated subsamples.<sup>�</sup> _ρ_ � _xz,w,t_ is the estimated value of the rolling correlation between the nominal price returns of _x_ and _z_ at time _t_ , where _w_ is the length of the window used to compute the rolling correlations ( _w_ = 24 months, in this case). _L_ = 12 is the maximum lag allowed in the model; _L_ is determined using the Schwarz criterion. A Newey-West correction is used to produce reliable standard errors. ***, ** and * denote statistical significance at the 1%, 5% and 10% levels.

33
Figure 6: Rolling Correlations of Maize Nominal Price Returns - 24-Month Window <!-- Start of picture text --> Crude oil Coal Natural gas<br>Soybean oil Barley Sorghum<br>Rice Wheat Sugar<br>1970m1 1980m1 1990m1 2000m1 2010m1 1970m1 1980m1 1990m1 2000m1 2010m1<br>Coffee<br>1970m1 1980m1 1990m1 2000m1 2010m1<br>1<br>0<br>-1<br>1<br>0<br>-1<br>1<br>0<br>-1<br>1<br>0<br>-1<br><!-- End of picture text --> � Note. This figure reports a graphical representation of the evolution of<sup>�</sup> _ρxz,w,t_ – i.e., the rolling correlation between the nominal price returns of commodities _x_ (maize) and _z_ , where _w_ is the length of the window used to compute the rolling correlations ( _w_ = 24 months, in this case). 95% confidence bands are also plotted.

34
Figure 7: Rolling Correlations of Soybean Oil Nominal Price Returns - 24-Month Window <!-- Start of picture text --> Crude oil Coal Natural gas<br>Barley Maize Sorghum<br>Rice Wheat Sugar<br>1970m1 1980m1 1990m1 2000m1 2010m1 1970m1 1980m1 1990m1 2000m1 2010m1<br>Coffee<br>1970m1 1980m1 1990m1 2000m1 2010m1<br>1<br>0<br>-1<br>1<br>0<br>-1<br>1<br>0<br>-1<br>1<br>0<br>-1<br><!-- End of picture text --> � Note. This figure reports a graphical representation of the evolution of<sup>�</sup> _ρxz,w,t_ – i.e., the rolling correlation between the nominal price returns of commodities _x_ (soybean oil) and _z_ , where _w_ is the length of the window used to compute the rolling correlations ( _w_ = 24 months, in this case). 95% confidence bands are also plotted.

35