Exploring the time-frequency connectedness and network among crude oil and agriculture commodities V1

Journal Pre-proof Exploring the time-frequency connectedness and network among crude oil and agriculture commodities V1 Sang Hoon Kang, Aviral Kumar Tiwari, Claudiu Tiberiu Albulescu, Seong-Min Yoon

PII:

S0140-9883(19)30338-X

DOI:

https://doi.org/10.1016/j.eneco.2019.104543

Reference:

ENEECO 104543

To appear in: Received Date:

13 August 2018

Revised Date:

10 June 2019

Accepted Date:

11 October 2019

Please cite this article as: Kang SH, Kumar Tiwari A, Albulescu CT, Yoon S-Min, Exploring the time-frequency connectedness and network among crude oil and agriculture commodities V1, Energy Economics (2019), doi: https://doi.org/10.1016/j.eneco.2019.104543

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Exploring the time-frequency connectedness and network among crude oil and agriculture commodities V1 Sang Hoon Kanga, Aviral Kumar Tiwarib,c, Claudiu Tiberiu Albulescud*, Seong-Min Yoone a Department

of Business Administration, Pusan National University, Busan, Republic of Korea for Energy and Sustainable Development (CESD), Montpellier Business School, Montpellier, France. c Department of Economics, IBS-Hyderabad, IFHE University, Hyderabad, India. d Management Department, Politehnica University of Timisoara, Timisoara 300006, Romania. e Department of Economics, Pusan National University, Busan, Republic of Korea . b Center

author. E-mail address: [email protected].

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* Corresponding

Research Highlights



we examine the frequency domain connectedness between oil and agriculture

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commodity prices

and use the frequency domain spillover method of Baruník and Křehlík (2018)



we show that the vegetable oil index is the most influential price volatility source for oil



we find a bidirectional and asymmetric connectedness between oil and agriculture

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markets at all frequency bands 

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

the volatility spillover between oil and agriculture commodities increases in the long

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run

Abstract

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We examine the frequency domain connectedness among international crude oil and

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agriculture commodities, covering the period of 1990M1-2017M5. The frequency domain connectedness is examined at three frequencies, which roughly correspond to one to six months, six to twelve months, and a period of more than twelve months. We also use a network based on pairwise correlations and a net directional matrix generated from the frequency domain spillover method. We show that the vegetable oils are the most influential price volatility source for the other agriculture commodities, such as dairy, cereals, meat and

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sugar, but also for the crude oil. In addition, we find a bi-directional and asymmetric connectedness between oil and agriculture commodity markets at all different frequency bands. These findings validate the preliminary results we obtain using a rolling-based bootstrap time-varying Granger causality analysis but provide additional insights as they allow to see the direction and the strength of the volatility at different frequencies. Our findings provide novel information about the production cost channel describing the relationship between oil and agriculture commodity markets. In addition, from the

portfolio diversification benefits especially in the short run.

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financialization perspective, our results show that agriculture commodity may provide

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Keywords: oil and agriculture commodity market, prices connectedness, frequency domain

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JEL classification: Q41, Q14, C58, G11

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spillover, network analysis

1. Introduction

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Recently, agriculture commodities have experienced sharp increases and subsequent severe collapses during periods characterized by high volatility of oil price.1 As the oil price

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represents an important element of production costs for all commodities, oil penetrates all

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aspects of economy and society (He et al., 2012). Building upon Pal and Mitra (2017), the purpose of our paper is to provide additional evidence on volatility spillover between oil and agriculture commodity prices using a frequency domain spillover method with network analysis. Different from other non-linear techniques that assess the co-movement between oil

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For a detailed analysis on the role of oil in commodities spike prices, please refer to Radetzki (2006), Heady and Fan (2008), Rosegrant et al. (2008). Du et al. (2011), Ji and Fan (2012), and Wang et al. (2014), inter alia, investigated the role of oil prices in the recent food crisis from 2006 to mid-2008.

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and agriculture markets, this method allows to see the direction of volatility spillover and the strength at different frequencies. A classical way to investigate the interactions between oil and agriculture commodity markets, is to consider the impact of oil prices on the production cost of agriculture commodities (Hanson et al., 1993). However, the current debate on the nexus between oil and agriculture commodity prices shows that an oil price surge enhances the incentive to produce biofuels (Wright, 2014), and, therefore, the relationship between oil and agriculture

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commodities prices has gained a new dimension (Ciaian and Kancs, 2011). Because biofuels are obtained using agriculture products, such as corn and soybeans, an increased demand for these products ultimately leads to increases in agriculture commodities prices (for a recent

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review of the literature, please refer to Pal and Mitra, 2017).

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In this context, early empirical papers focus on the impact of oil on agriculture commodities, or on how oil prices co-move with other commodities (i.e. Natanelov et al.,

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2011; Reboredo, 2012; Byrne et al., 2013; Baumeister and Kilian, 2014; Wang et al., 2014). Several theoretical explanations sustain this approach and economic mechanisms may be at

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work, as presented in detail by Reboredo (2012) and Ahmadi et al. (2016). A first channel shows that an increase in the oil price raises the cost of production, in particular for

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agriculture products, and these costs are then transferred to agriculture commodities(Hanson et al., 1993; Tyner, 2010; Dillon and Barrett, 2016). Second, sharp increases in the oil price

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trigger demand for biofuels and, therefore, an increase in corn and soybeans prices (Chen et al., 2010a; Hochman, 2012). Further, the increase in the prices of agriculture commodities generates a second-round effect as corn and soybeans compete with other crops for land, water, and profits (Bastianin et al., 2014). More recent works consider and document a bidirectional causality between oil and agriculture commodity prices (i.e. Nazlioglu, 2011; Nazlioglu and Soytas, 2012; Lucotte, 2016; Pal and Mitra, 2017; Pal and Mitra, 2018). Their 3

co-movement are important to anticipate correctly their impacts on inflation and exchange rates (Zhang and Qu, 2015). In addition, by affecting the external balance, as well as fiscal and monetary policy, the co-movement between oil and agriculture commodity and food prices has noteworthy effects on economic stability (Lucotte, 2016).2 The literature also brings forward a financial interpretation of oil – agriculture commodity prices interactions. According to this view, the international financial assets become more and more integrated, and a financialization of the agricultural commodity

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market was recently recorded. On the one hand, international investors started to explore new category of assets, including agriculture commodities in search of higher returns (Brooks and Prokopczuk, 2013). On the other hand, prices and volatilities of agriculture commodity

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market seem to be negatively correlated with equity market, while being positively correlated with energy market (Doran and Ronn, 2008). Given the fact that oil and agriculture

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commodities represent different classes of assets, their dependencies are important for

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portfolio selection, risk management and hedging reasons (Ciner et al., 2013; Rafik and Bloch, 2016).

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Most existing empirical works analyse the oil – agriculture commodity markets nexus and report a positive relationship, addressing endogeneity (Chang and Su, 2010; Cha and

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Bae, 2011; Wang et al., 2014) or asymmetry issues (Bildirici and Turkmen, 2015; Rafiq and Bloch, 2016). However, a few works find no significant relationship (Zhang et al., 2010;

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Nazlioglu and Soytas, 2012) or a positive impact in specific periods only (Lucotte, 2016; Pal and Mitra, 2017). Only several studies focus on volatility spillovers between oil and

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Although the interaction between oil and agriculture commodity prices are accepted by most of researchers, there is a particular, narrow strand of literature, that sustains the neutrality hypothesis characterizing the oil – agriculture commodity prices nexus. In this line, Wiggins and Keats (2009) argue that during the recent food crisis the fall in corn prices was caused by the dismantling of public food stocks and not by an increased demand for biofuels, while Nazlioglu and Soytas (2011) documented a weakly reaction of agricultural commodity prices to crude oil prices in Turkey.

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agriculture commodities (Serra, 2011; Ji and Fan, 2012; Nazioglu et al., 2013; Jebabli et al., 2014). Nevertheless, little is known about the direction and the strength of volatility spillovers, and how spillovers manifests at different frequencies. To fill in this gap, our study moves beyond the existing literature and performs a frequency domain spillover analysis (following Baruník and Křehlík, 2018) and a volatility network analysis, to understand the complex interactions between different categories of agriculture commodities (cereals, vegetable oils, dairy, meat, and sugar) and oil prices at the

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global level. We build upon Pal and Mitra (2017) to investigate the interactions between

crude oil prices on the one hand, and the five agriculture indexes on the other hand, using

Food and Agricultural Organization (FAO) data. While Pal and Mitra (2017) perform a time-

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frequency analysis of price co-movements, we focus on the frequency domain volatility

spillovers to see if price transmissions between oil and agriculture commodity markets are

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stronger at different frequencies, and if they vary across different categories of agriculture

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commodities.

As starting point, we use a rolling-based bootstrap time-varying Granger causality (TV-

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GC) with heteroscedastic error distribution following Hurn et al. (2016), to show that the caus al relationship between our variables is non-linear. The non-linearity between oil and agricult

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ure commodity prices shows that the prices of agriculture commodities increase in greater ma gnitudes in response to rises in crude oil prices and conversely (Pal and Mitra, 2017). Howev

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er, this method does not allow to see the direction of the causality (i.e., whether variable 𝒙 is positively or negatively Granger-causing variable 𝒚) and thus provides no evidence about the strength of causality. To overcome these limits, we first use the recent frequency connectedness technique of Baruník and Křehlík (2018) (BK hereafter), who extend the spillover index of Diebold and Yi

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lmaz (2012) from time series (DY method).3 The BK technique considers regularities in time series and estimates a volatility spillover in the frequency domain. The spectral representation of variance decompositions is helpful in our case, as price volatilities on oil market might cre ate linkages with food market, with various degree of persistence (for an investigation of oil p rice transmissions to commodities in a frequency domain framework, please refer to Křehlík and Baruník, 2017). Further, using the BK approach, we can assess the connectedness for diff erent short-, medium-, and long-term cycles (also called bands or periodicities). More preciou

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sly, if the short-term risk spillovers are higher than the medium- and long-term horizons, it im plies that most of the investors behave in a similar manner at short-frequencies while in the

medium- and long-term horizons they behave more heterogeneously while investing in risky

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assets.

This way, we take a different look at the data and obtain complex results for the network

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analysis. If, for example, a volatility spillover is transmitted with only a monthly regularity,

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the frequency domain allows us to underscore this characteristic. Consequently, from the perspective of the oil-cost dependence, we are able to know which agriculture commodity

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responds to oil price volatility transmission, and for which frequencies the pass-through is higher. At the same time, from the financialization perspective, stronger spillovers at a specific frequency, show that investors on oil and agriculture commodity markets have a

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similar behaviour. In this context, oil and agriculture commodities provide limited options for

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portfolio diversification.

Another contribution of our study to the existing literature is represented by the

3

As far as we know, Kristoufek et al. (2012) is the only paper that performs a network investigation of several categories of fuel prices and agriculture commodities using minimal spanning trees and hierarchical trees for a time domain series, following Mantegna (1999). Even if network analysis does not represent the workhorse for studying the relationship between oil prices and other commodities, noteworthy investigations have been conducted for assessing the linkages between crude oil and fuel prices (Chen et al., 2010b; An et al., 2014; Yang et al., 2015; Wang et al., 2016).

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computation of pairwise (net) spillovers to see how volatility is transmitted between different groups of agriculture commodities, and oil prices. The pairwise (net) spillovers are computed for different periodicities to obtain a complete understanding of the volatility transmission. We consider the complex network of net-pairwise directional connectedness at different frequency bands. Our approach thus provides a unified vision for two competing strands of the literature, considering oil as a commodity in analysing co-movement and as a determinant of other commodities’ co-movements (Chen, 2015).

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Finally, different from other studies which investigate the oil – food prices nexus, we

consider in our analysis the relationship between oil market and five agriculture commodity markets, as in Pal and Mitra (2017). Making such a choice we identify several research

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hypotheses. First, in line with other recent studies, we assume that the volatility spillover between oil and agriculture markets is bi-directional. Second, we compare the degree of

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volatility spillover between oil prices and each category of agriculture commodities, and

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manifest at all frequency bands. For some agriculture commodities (e.g. energy-based crops) the price volatility spillovers with the oil market are expected to be stronger in the short run

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given their role in bioenergy production, for other commodities (e.g. diary and meat) the spillovers might manifest especially in the long run, given that these products require a larger period to assimilate oil price shocks in their prices. Therefore, the volatility of agriculture

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commodities prices with the oil prices should manifest at all frequencies. Third, we expect to

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observe a different intensity of spillovers between each category of agriculture commodities and the oil prices. On the one hand, in the case of cereals the volatility spillovers are usually stronger given that corn and soybeans are sources of biofuels. This is also the case of sugar, which is one of the main inputs for ethanol production, or vegetable oils, which may substitute diesel fuel. On the other hand, in the case of vegetable oils we expect weaker volatility spillovers from crude oil prices given that the production of vegetable oils is less

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dependent of petroleum products (Hanson et al., 1993). The reminder of the paper presents the literature review (Section 2), the data (Section 3) and methodology (Section 4), and different groups of results (Section 5), and the last section concludes and draws the policy implications of our findings.

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2. Literature review The relationship between oil and agriculture commodity prices is investigated in the

empirical literature from different points of view. From a methodological point of view, the literature includes linear and non-linear approaches that consider the oil price as either an

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exogenous or as an endogenous factor in the co-movement of commodities prices. From the

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perspective of the transmission effect, the literature assesses the price level transmission, the volatility transmission, and the effects of shocks to oil prices, on the co-movement of

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commodity prices. Finally, the increased production of biofuels highlights the bi-directional relationship between oil prices and agriculture commodities.

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Early studies of the relationship between oil and agriculture commodities, or that between oil and global food prices, are undertaken using a linear framework (see Rafiq and

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Bloch, 2016). Most of them investigate the long-run relationship between these categories of assets using a vector autoregression (VAR) or a cointegration framework. For example,

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Baffes (2007) finds that the impact of the oil price is stronger on agriculture commodities than on metals. Using a vector error correction model, Saghaian (2010) shows that oil and agriculture prices are cointegrated. For the period from 1996 to 2008, the author reports unidirectional causality running from the oil price to agriculture commodities. Using a principal component analysis, Esmaeili and Shokoohi (2011) report that the crude oil price influences food production and, therefore, food prices. Chen et al. (2010a) develop a cropland 8

allocation model and apply an autoregressive distributed lag model to discover that each grain price in China is influenced by changes in the crude oil price. Serra et al. (2010) demonstrate the existence of long-term relationships among crude oil, fuels, and corn prices using a smooth transition vector error correction model for the United States (US). Whereas Zhang et al. (2010) use cointegration and report no long-run relationships between oil and agricultural commodity prices, Cha and Bae (2011) employ a structural VAR (SVAR) model and find that increases in the crude oil price lead, inter alia, to an increase in corn prices in

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the short run. Hassouneh et al. (2012) examine the price linkages and price transmission between food and energy prices in Spain using multivariate linear regressions and parametric error correction models and find a long-run equilibrium relationship between biodiesel,

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sunflower, and crude oil prices. Similar findings are reported by Nazlioglu and Soytas (2012) in a panel data investigation framework for the period from 1980 to 2010. The Pedroni panel

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cointegration test shows a long-run relationship between oil and agriculture commodities in

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which oil significantly affects agricultural prices. In a similar investigation, Rezitis (2015) use a panel VAR and causality analysis to assess the linkages between crude oil prices, US dollar exchange rates, and a large set of agriculture commodities. The author reports bi-

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directional panel causality effects between crude oil and international agricultural prices. However, most recent work focuses on the non-linearities characterizing this

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relationship. Modifications to the market structure, production capacities, or even price

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regulation lead to an asymmetric response of commodities to the oil price and vice-versa (Rafiq and Bloch, 2016). Several researchers report structural breaks in the relationship between oil and agriculture commodity prices. In this line of research, Pala (2013) employs a Johansen cointegration analysis and Granger causality tests and reports a significant relationship between oil and food prices for the period 1990:01 to 2011:08 as well as for subsamples representing the pre- and the post-crisis period. Along similar lines, Lucotte

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(2016) uses VAR models and impulse response functions and finds strong linkages between oil and food prices but only after the recent financial and food crisis. Similar, Wang et al. (2014) use an SVAR analysis and differentiate between oil-specific and aggregate demand shocks. They find that oil shocks hardly explain frictions in agricultural commodity prices before the 2006-2008 food crisis. Other studies (i.e. Nazlioglu, 2011; Bildirici and Turkmen, 2015) investigate the nonlinear causal relationship between oil and commodity prices at global levels and report non-

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linear feedback. More recently, De Nicola et al. (2016) employ monthly data over the period from 1970:01 to 2013:05 to investigate the time-varying properties of pairwise unconditional and conditional correlations between energy and agriculture commodity prices. They find that

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energy and agricultural commodity prices are highly correlated, but the correlation increased during the last period analysed. With a focus on South Africa, Fowowe (2016) use

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cointegration tests with structural breaks and nonlinear causality tests and, unlike in similar

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studies, show that agriculture commodity prices are neutral to oil price shocks. Pal and Mitra (2017) apply a wavelet analysis for the period from January 1990 to February 2016 and find

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that oil market leads the agriculture markets at all frequencies. Although most existing works focus on price level transmission, several studies

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investigate the volatility spillover between oil and agriculture commodities (Du et al., 2011; Serra, 2011; Nazioglu et al., 2013). Du et al. (2011) use stochastic volatility models to

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observe the volatility spillover effect of the oil price to weekly crude oil, corn, and wheat futures prices from 1998:11 to 2009:01 and find evidence of volatility spillovers after the fall of 2006. Nazioglu et al. (2013) report similar results using a causality-in-variance test. Serra (2011) investigates the volatility transmission between oil and agriculture commodity prices in Brazil, applying a semiparametric GARCH model with stochastic volatility. The author shows that ethanol and crude oil prices on the one hand, and ethanol and sugar prices on the 10

other, exhibit long-run equilibrium parity. Jebabli et al. (2014) assess the volatility spillovers between energy, financial, and food prices using a time varying parameter VAR model. They report an increase in volatility spillovers after the crisis. Decomposing oil price shocks into macroeconomic and oil-specific shocks, Ahmadi et al. (2016) use an SVAR method to investigate the volatility spillover from oil price shocks onto different agricultural and metal commodities. They find that the volatility transmission for all commodities is influenced by the underlining causes of each shock. Zhang and Qu (2015) conduct a similar investigation

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and differentiate between positive and negative oil price shocks. They underscore the fact that oil price spillovers on most agricultural commodities in China are asymmetric. In addition, the impact of unexpected oil price volatilities on agriculture commodities in China became

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more complex after the financial crisis (Zhang and Chen, 2014).

As mentioned before, biofuels development brings a new perspective to the relationship

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between oil and agriculture commodity prices. Whereas Chang and Su (2010) find significant

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price spillover effects from crude oil to corn and soybean futures in a bivariate exponential generalized autoregressive conditional heteroscedastic (EGARCH) model, Bahel et al. (2013)

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report a positive link between energy and agriculture commodity prices after the introduction of biofuels as a substitute for fossil fuels. With a focus on the US, Avalos (2014) and Baumeister and Kilian (2014) question the impact of increased biofuels consumption on the

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oil– agriculture commodity prices nexus. Whereas Avalos (2014) reports a significant

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influence of the corn price on oil and soybean prices using different cointegration tests, Baumeister and Kilian (2014), in contrast, find that the relationship between energy and agriculture commodity prices is largely driven by common macroeconomic determinants. More recently, Pal and Mitra (2018) perform a detrended cross correlation analysis and search for structural changes in the oil – food market relationship and find increased positive interdependence during the recent food crisis.

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Despite the extensive empirical literature devoted to this subject, none of the previous studies deploy an extensive investigation of the volatility spillovers between the oil price and different groups of agriculture commodity prices. Indeed, Kristoufek et al. (2012) focus on a network analysis in the time domain without considering the cycles that might appear in volatility transmission. At the same time, Křehlík and Baruník (2017) perform a frequency domain analysis for volatility shocks transmission, with a focus, however, on crude oil, heating oil, and gasoline prices, without addressing the interactions with agriculture

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commodity markets. Therefore, we extend the existing works by performing a complex network analysis between oil and agriculture commodities, using the BK frequency domain volatility spillover technique.

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3. Data

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We use monthly data for the five agriculture commodity price indexes (meat, dairy,

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cereals, vegetables oils, and sugar), relying on FAO’s data. Each of the five indexes is in its turn constructed as a weighted average index of individual prices. For example, the cereals

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index is build considering different quotations for the wheat, corn, rice and other cereals. For the crude oil price, we use average oil price index provided by the International Monetary

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Fund (IMF).4

The study period runs from January 1990 through March 2017, which covers several

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turbulent periods and crises, including all sharp fluctuations in the commodity futures markets and major global events such as the 2007 US subprime mortgage crisis, the 2008– 2009 global financial crisis (GFC), the 2007–2008 global food crisis, and the 2009–2012

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Given the fact that agriculture commodity prices are established at international level and are constructed as weighted averages of individual price quotations, we have chosen to work with the average oil price index and we report these results. However, for robustness purpose we have also used the Brent (as in Pal and Mitra, 2017), Dubai and WTI oil prices, and we have found very robust results. These estimations can be provided upon request.

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European debt crisis (EDC). Fig.1 plots the price behaviour of the agriculture and oil markets. A close inspection of this figure indicates that all markets decreased during 2008– 2009, corresponding to the GFC period. Furthermore, the oil markets exhibited a second important decline from mid-2014 to 2016.

We calculate the continuously compounded monthly returns by taking the difference in the log values of two consecutive prices. Fig. 2 shows the dynamic evolution of the five

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agriculture and average oil price returns. As shown in Fig. 2, the return series become more

volatile at peaks times of uncertaintiy related to future economic growth, market demand and

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market performance due to the 2007–2009 GFC.

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Table 1 provides the statistical properties of the considered returns series. Among the agriculture commodity markets, vegetable oils yield the highest average return, followed by

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dairy and cereals price returns. The unconditional volatility (standard deviation) is highest for the Ave. oils price returns, followed by sugar and daily commodity markets, while the meat

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price return is the least volatile. The skewness coefficients are negative except dairy, cereals and sugar, and the kurtosis coefficients are higher than three for all return series. These

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results indicate that the probability distribution of sample returns represents asymmetry and leptokurtic and rejects the normality confirmed by Jarque-Bera statistics. In addition, we

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report the results of three different unit root tests, namely the ADF (Dickey and Fuller, 1979), the PP (Phillip and Perron, 1988), and the ZA (Zivot and Andrew, 1992) structural break unit root test, as well as the KPSS stationarity test (Kwiatkowski et al., 1992). Two conventional ADF and PP tests reject the null hypothesis of unit root in all sample returns. The KPSS test shows a stationary process for all sample returns. Likewise, ZA unit root test results confirm that all sample series are stationary with no structural breaks. 13

Fig. 3 visualize the dependence pattern between agriculture commodity indexes and average oil prices returns using the scatterplot matrix. We see a significant positive relationship among the agriculture commodity and Ave. oil returns. More precisely, the pairwise coefficient between vegetable oils and cereals shows the highest correlation followed by the pair between vegetable oils and Ave. oil price returns. Fig.3 also reports the normality distribution plots of the variables under consideration which indicates that all

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return series are non-normally distributed.

4. Methodology

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We first discuss the methodology of Diebold and Yilmaz (2012), the DY method, and

then elaborate on the Baruník and Křehlík (2018) frequency-domain spillover index, the BK

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approach. The DY spillover index is based on a VAR model, and its focus is to compute the forecast error variance decompositions (FEVD) from a generalized vector autoregression.

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This process can be explained as follows. Let us describe the 𝑛-variate process 𝑥𝑡 =

Φ(𝐿)𝑥𝑡 = 𝜀𝑡 ,

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(𝑥𝑡,1 , ⋯ , 𝑥𝑡,𝑛 ) by the structural VAR(𝑝) at 𝑡 = 1, ⋯ , 𝑇 as:

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where 𝛷(𝐿) = ∑ℎ 𝛷ℎ 𝐿ℎ is 𝑝-th order lag-polynomial and 𝜀𝑡 is a white-noise with a possibly non-diagonal covariance matrix 𝛴. Assuming that the roots of |𝛷(𝑧)| lie outside the unit-

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circle, the VAR process has the following moving average 𝑀𝐴(∞) representation: 𝑥𝑡 = 𝛹(𝐿)𝜀𝑡 ,

where 𝛹(𝐿) is an 𝑛 × 𝑛 infinite lag polynomial matrix of coefficients. Following Diebold and Yilmaz (2012), the generalised FEVD can be written as follows: (𝛩𝐻 )𝑗,𝑘 =

−1 ∑𝐻 𝜎𝑘𝑘 ℎ=0((𝛹ℎ 𝛴)𝑗,𝑘 ) ′ ∑𝐻 ℎ=0(𝛹ℎ 𝛴𝛹ℎ )

2

,

(1)

𝑗,𝑗

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where 𝛹ℎ is an 𝑛 × 𝑛 matrix of coefficients corresponding to lag ℎ, and 𝜎𝑘𝑘 = (𝛴)𝑘,𝑘 . The term (𝛩𝐻 )𝑗,𝑘 denotes the contribution of the 𝑘-th variable of the system to the variance of the forecast error of element j. In the generalised VAR framework, the shocks to each variable are not orthogonalised, and, thus, the sum of each row of (𝛩𝐻 )𝑗,𝑘 does not generally equal one. Therefore, each element of the decomposition matrix can be normalised by dividing by the row sum, that is: (𝛩𝐻 )𝑗,𝑘

(𝛩𝐻 )𝑗,𝑘 = 𝑛 ∑

, with ∑𝑛𝑘=1(𝛩̃𝐻 )𝑗,𝑘 = 1 and ∑𝑛𝑖,𝑘=1(𝛩̃𝐻 )𝑗,𝑘 = 𝑁.

(2)

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𝑘=1(𝛩𝐻 )𝑗,𝑘

The connectedness measure is then defined as the share of variances in the forecasts

generated by other than forecast errors themselves, or, equally, as ratio of the sum of the off-

̃ 𝐻 )𝑗,𝑘 ∑𝑗≠𝑘(𝛩 ̃ 𝐻 )𝑗,𝑘 ∑(𝛩

̃𝐻} 𝑇𝑟{𝛩 ), 𝐻 )𝑗,𝑘

= 100 × (1 − ∑(𝛩̃

(3)

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𝐶𝐻 = 100 ×

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diagonal elements to the sum of the whole matrix (Diebold and Yilmaz, 2012):

where 𝑇𝑟{∙} is the trace operator. Hence, the connectedness is the relative contribution to the

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forecast variances from the other variables in the system. 𝐶𝐻 measures the connectedness of the whole system. Furthermore, we can also measure the directional spillovers received by

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market 𝑗 from all other markets 𝑘 and vice versa, and the net volatility spillovers from each market to all other markets are the difference between the directional spillover received from

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the markets and the directional spillovers to the market.

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Now, we discuss the method for measuring connectedness in the frequency domain following Baruník and Křehlík (2018). As seen in Eq. (1), the connectedness measure is based on an impulse function Ψℎ defined in the time-domain. Let us consider a frequency response function Ψ(𝑒 −𝑖𝑤 ) = ∑ℎ 𝑒 −𝑖𝑤ℎ Ψℎ , which can be obtained from Fourier transform of the coefficient Ψ with i = √−1. The generalized causation spectrum over frequencies ω =∈ (−𝜋, 𝜋) is specified as: 15

(𝑓(ω))𝑗,𝑘 ≡

−1 𝜎𝑘𝑘 |(Ψ(𝑒 −𝑖𝑤 )Σ)𝑗,𝑘 |

2

(Ψ(𝜔 −𝑖𝑤 )ΣΨ′ (𝑒 +𝑖𝑤 ))

,

(4)

𝑗,𝑗

where Ψ(𝑒 −𝑖𝑤 ) is the Fourier transform of the impulse response Ψ, as defined above. (𝑓(𝜔))𝑗,𝑘 represents the portion of the spectrum of the 𝑗-th variable at frequency ω due to shocks to the 𝑘-th variable. Thus, we can interpret the quantity as a within-frequency causation, as the denominator holds the spectrum of the 𝑗-th variable, that is, the on-diagonal elements of the cross-spectral density of 𝑥𝑖 , at a given frequency ω. To obtain a natural

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decomposition of the original generalized FEVD into frequencies, we can simply weight the (𝑓(𝜔))𝑗,𝑘 by the frequency share of variance of the 𝑗-th variable. We define the

𝑗,𝑗 1 𝜋 −𝑖𝜆 )ΣΨ′ (𝑒 +𝑖𝜆 )) 𝑑𝜆 (Ψ(𝑒 ∫ 2𝜋 −𝜋 𝑗,𝑗

,

(5)

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Γ𝑗 (𝜔) =

(Ψ(𝑒 −𝑖𝑤 )ΣΨ′ (𝑒 +𝑖𝑤 ))

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weighting function as:

where the power of 𝑗-th variable at a given frequency, which sums through frequencies to

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a constant value of 2𝜋. Although the Fourier transform of the impulse response is, in general, a complex valued quantity, the generalized causation spectrum is the squared

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modulus of the weighted complex numbers and, hence, produces a real quantity. We then obtain a frequency band 𝑑 = (𝑎, 𝑏): 𝑎, 𝑏 ∈ (−𝜋, 𝜋), 𝑎 < 𝑏. Consequently, the generalized

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FEVD on a frequency band d can be defined as: 1

(Θ𝑑 )𝑗,𝑘 = ∫𝑑 Γ𝑗 (𝜔) (𝑓(𝜔)) 𝑑𝜔. 𝑗,𝑘 2𝜋

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(6)

Using the spectral representation of the generalized FEVD, connectedness can be

described on a given frequency band. Let us define the scaled generalized FEVD on the frequency band 𝑑 as: ̃ 𝑑 ) = (Θ𝑑 )𝑗,𝑘 . (Θ ∑ (Θ ) 𝑗,𝑘 𝑘

(7)

∞ 𝑗,𝑘

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The frequency connectedness on the frequency band 𝑑 is then defined as ̃ 𝑑) ∑𝑗≠𝑘(Θ

𝐶𝑑𝐹 = 100 × (

̃ ∞) ∑(Θ

𝑗,𝑘

𝑗,𝑘

̃ 𝑑} 𝑇𝑟{Θ

− ∑(Θ̃

∞ )𝑗,𝑘

).

(8)

Finally, the overall connectedness within the frequency band 𝑑 can be defined as ̃ 𝑑} 𝑇𝑟{Θ

𝐶𝑑𝑊 = 100 × (1 − ∑(Θ̃

𝑑 )𝑗,𝑘

).

(9)

It is also worth noting that the within connectedness value provides the connectedness

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effect that occurs within the frequency band and is weighted by the power of the series on the given frequency band exclusively. Convers ely, the frequency connectedness decomposes the original connectedness into separate parts that, when summed, provide the original

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connectedness measure.

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5. Empirical results

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5.1. Results of the preliminary TV-GC analysis

A first step in our empirical exercise is represented by the rolling-based bootstrap TV-

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GC analysis, a method developed by Hurn et al., (2016)5. This rolling window approach shows that in all cases there is a significant, non-linear Granger-causality relationship

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between the analysed variables (Fig. 4). The TV-GC from oil to agriculture commodities is rejected in few cases only, namely in 2013 for the dairy and in 2010 for cereals. Further, the

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TV-GC from oil to meat prices is less evident, especially after 2014. However, although this technique clearly states that the bi-directional relationship

5

Hurn et al., (2016) provide a comparative analysis of bootstrapped time-varying Granger causality tests in the time domain, using rolling-, recursive-rolling, and recursive-windows and find that the rolling method outperforms the other two methods. Therefore, we apply bootstrapped time-varying Granger causality tests in the time domain, using rolling-based bootstrap TV-GC. To this end, 20% of the observations are used as window size in the rolling analysis and the window shift is one period. Maximum 12 lags are used for the VAR modelling, while the BIC information criterion serves as reference for the lag selection. Finally, we assume heteroscedastic error distributions (for more details on the methodology please refer to Hurn et al., 2016).

17

between oil and agriculture commodities is non-linear, it does not offer any information about the direction of the causality (i.e., oil price is negatively or positively affecting agriculture commodity prices). In addition, we are not able to see if the oil price spillover to one specific agriculture commodity is more important compared to the price spillover to another commodity. The frequency domain spillover method with network analysis provides additional information regarding the complex relationship between oil and agriculture

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commodity markets.

5.2. Results for the frequency domain spillover index

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We investigate the static spillover index at different frequency bands in Table 2. As

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shown in Table 2, we decompose the connectedness into three different frequency bands of up to one month to six months, six months to twelve months, and more than twelve months,

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which are computed as 𝐶𝑑𝐹 on the bands corresponding to 𝑑1 ∈ [3.14,0.52], 𝑑2 ∈ [0.52,0.26], and 𝑑3 ∈ [0.26,0.00]. These bands are selected to allow enough time to see how oil price

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volatility is transmitted to agricultural commodity prices, and the opposite. The first band reflects a short-term transmission effect between oil price volatility and agricultural

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commodity prices. The second band is selected in such a way to cover a harvest period (about 4 months for most of the agriculture crops) and to allows for a commodity such as cereals or

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sugar, to reflect an oil price shock in their prices. Finally, the third band is selected to capture the long-run impact of an oil price shock which also allows to change in the crop-patterns. Note that the ‘within’ connectedness gives us the connectedness effect that occurs within

the frequency band and it is weighted by the power of the series on the given frequency band exclusively. In addition, the frequency connectedness decomposes the original connectedness into distinct parts that, when summed, provide the original connectedness measure. Thus, 18

FROM_ABS is the measure of frequency connectedness in absolute sense, and FROM_WTH is the measure of ‘within’ connectedness. We find that the overall spillover index ranges from 10.77% to 19.59% at different frequency bands. As the frequency band increases, the connectedness strengthens across agriculture commodity and oil markets (this result confirms the findings by Pal and Mitra (2017)). Additionally, the directional spillovers transmitted ‘TO_ABS’ indicate that the vegetable oils are the largest contributor to other agriculture commodity and crude oil prices

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at all different frequency bands. These findings contrast the ones reported by Pal and Mitra

(2017), stating that oil prices lead agriculture and global food prices at all frequency bands.

Our results confirm, however, the previous findings by Baumeister and Kilian (2014) for the

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United States’ case. If we compare the volatility spillovers from oil prices to different

agriculture commodity prices, we notice that the spillover is higher for the vegetable oils and

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cereals. Our findings confirm the results reported by (Balcombe and Rapsomanikis, 2008;

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Natanelov et al., 2013; Pal and Mitra, 2017), stating that the oil prices and the prices of

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energy-based crops exhibits strong co-movements.

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In net terms (TO_ABS and FROM_ABS), we discover that vegetable oils are the net largest spillover transmitter, while meat is the largest net recipient of spillovers, at all frequency bands. The fact that vegetable oils represent the net largest transmitter of spillovers across the oil – agriculture commodity prices nexus is not surprising. Although its production consumes less petroleum-based inputs (Hanson et al., 1993), vegetable oils can be used as fuel alternative for diesel engines and heating oil burners. These results are inconsistent with

19

those of Pal and Mitra (2017). In terms of ‘within’ connectedness (TO_WTH and FROM_WTH), vegetable oils are the greatest contributor to other agriculture commodities and oil prices at all different frequency bands. More precisely, the vegetable oils index contributes 3.30% (short-term), 6.77% (medium-term), and 7.58% (long-term) of the forecasting variance to other markets. In addition, cereals are the second largest transmitter of spillovers to other markets at all different frequency bands, followed by the average crude oil. Our result underlines the role of

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vegetable oils and cereals as price volatility transmitter to the oil market and comes in contrast to more of previous reported results, stating that oil prices lead agriculture

commodity prices (i.e. Baffes, 2007; Zhang and Qu, 2015; Pal and Mitra, 2017). In fact, we

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show that the volatility spillover is bi-directional, but the agriculture commodity markets

induce more volatility in the oil market compared with the volatility transmitted from oil to

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agriculture commodity prices. We therefore state that the price policies on agriculture

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commodity markets might induce oil price shocks. In addition, agriculture crop shortage and food crisis amplify the oil price volatility, which explained the stronger co-movement

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between oil and agriculture commodity markets during the recent food crisis (see for example Lucotte, 2016). This finding also implies that oil prices provide diversification benefits in

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constructing a portfolio including agriculture products. One key shortcoming of the static spillover index (in Table 2) is that the overall

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spillovers are constant at different frequencies. More precisely, the static spillover index might ignore price jumps that are typically caused by economic and financial events such as the 2008-2009 GFC and the 2010-2012 EDC. Such events might have taken place during the sample period and may have influenced the direction or intensity of connectedness at different frequency bands. Fig. 5 presents the time-varying spillover index of the considered markets at three frequency bands. In Fig. 5, we cannot observe any clear pattern of one 20

frequency band dominating all the others. However, the overall spillovers peak during the 2007-2009 GFC and the 2010-2012 EDC.

5.3. Net connectedness results To further examine the dynamic behaviour of connectedness, we study net spillovers, which reveal information about directional spillovers between the oil and agriculture commodity markets. We decompose the total spillover index into two directional spillovers:

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1) the receiver of spillovers, termed directionally as ‘FROM’, and 2) the transmitter of connectedness, termed directionally as ‘TO’.6 The dynamic net spillover index is then

calculated by subtracting directional ‘TO’ spillovers from directional ‘FROM’ spillovers. The

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positive (negative) values indicate a source (recipient) of return and volatility to (from) other

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prices.

Fig. 6 depicts the time-varying evolution of net directional spillovers of the agriculture

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and oil markets at different frequency bands. As shown in this figure, we can identify the source or the recipient of the net directional spillovers even though the net directional

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connectedness oscillates in either a negative or positive direction, while their magnitudes often change over time. Thus, the connectedness is bi-directional and asymmetric at all

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different frequency bands because all of the graphs include asymmetric magnitudes of negative and positive values over time. More interestingly, following recent financial events,

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the net spillover makes both positive and negative jumps, and the level of net spillovers is more intense. These findings confirm one of our research hypotheses, which shows that the volatility spillover between oil and agriculture commodities manifests at different frequency bands, depending on the oil-cost dependence and stockage characteristics of each category of

6

For brevity, we report only the net spillover analysis; the directional spillover analysis is presented in Appendix.

21

commodity. Therefore, the volatility spillover is expected to manifest stronger during market turmoil and at all frequency bands.

5.4. Connectedness network results To better understand the dynamic connectedness, we consider the complex network of net-pairwise directional connectedness at different frequency bands. Note that an arrow from variable 𝑥𝑖 to variable 𝑥𝑗 denotes a positive net directional connectedness (in other words,

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variable 𝑥𝑖 explains more of variable 𝑥𝑗 than the reverse). We identify net pairwise

transmitters or recipients of connectedness in three different frequency bands (Fig. 7).

For example, the vegetable oils index is the largest net pairwise volatility transmitter of

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connectedness in all frequency bands, indicating that the vegetable oils prices have the

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strongest impact on the other agricultural commodity and on the average oil market. This result confirms our previous findings generated using the static spillover index. Interestingly,

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the meat market is one of the net largest pairwise receivers of connectedness in all frequency

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bands (Fig. 7(c)).

At the same time, we notice that for all frequency bands, the average oil price volatility

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is largely influenced by the volatility of agriculture commodities prices, and, especially, by

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that of vegetable oils. Again, this result is consistent with the one reported in the study of Pal and Mitra (2017) that showed a bi-directional causality between the agriculture market and crude oil market. However, in contrast with Pal and Mitra (2017), we argue that the cereals and in particular vegetable oils prices represents net transmitters to crude oil prices, especially in the long run. All in all, our results show that: (1) there is a bi-directional connection between crude oil 22

and agriculture commodity markets, (2) the spillover from agriculture commodity prices to oil prices are stronger compared with those from oil to agriculture markets, in particular in the case of cereals and vegetables oils, and (3) the spillover effect increases in the long run. Our findings show therefore that the relationship between crude oil and agriculture commodity prices is more complex that considered before. Given their role of substitutes for crude oil, vegetable oils and biofuels represent the main price shock transmitters. Further, given that the spillover effect increases in the long run, it seems that the production cost

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channel plays a more important role than the financialization channel in oil – agriculture markets co-movements.

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6. Conclusions

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This study examines the frequency domain connectedness between oil and agriculture commodity markets at various frequencies. To estimate the short-, medium-, and long-term

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frequency connectedness, we employ the frequency domain spillover index of Baruník and Křehlík (2018), which allows us to measure the commodity markets’ connectedness at

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different frequency bands. We start from a rolling-based bootstrap TV-GC analysis advanced by Hurn et al. (2016) and show that there is a non-linear bi-directional causality relationship

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between agriculture commodity and oil markets. However, some sources of systematic risk might be hidden when ignoring several fundamental properties of connectedness. It is

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therefore essential to identify and measure the drivers of the connectedness over the short, medium, and long terms separately, what we have done using the BK approach and the connectedness network analysis. Our empirical results are summarized as follows. First, we find that the overall spillover index between agriculture commodity and oil markets ranges from 10.77% to 19.59% at

23

different frequency bands. As the frequency band increases, the connectedness strengthens across agriculture commodities and oil price returns. Second, the vegetable oils are the greatest contributor to the other agriculture commodity and oil price fluctuations at all different frequency bands. This result contrast with most of the previous findings reported in the literature on the co-movement of agriculture commodity-oil markets. Third, the volatility spillovers between vegetable oils and cereals and the oil prices are much stronger compared to the volatility spillovers between other agriculture commodity and crude oil prices. Our

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connectedness network analysis shows that vegetable oils prices are net volatility transmitters at any frequency bands.

Several practical implications result from our findings. For example, we discover that

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the price shocks of vegetable oils and cereals are transmitted to the volatility of oil price. This means that during a food shortage period when the vegetable oils prices became more

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volatile, their volatility pass-through oil prices (vegetables oil are substitutes goods for fuels).

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This in turn will create a second-round effect on production cost of all agriculture commodities. The uncertainty regarding the production costs induce by oil price volatility

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will amplify the volatility of agriculture commodity prices, which might lead to a food crisis. In addition, the volatility spillovers between agriculture commodity and oil markets

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increase in the long run, providing additional arguments for their bi-directional causality and against the neutrality hypothesis. It seems that the economic channels explaining volatility

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spillover are more important compared with the financial channels that generate short-run comovements.

Furthermore, the spillover between vegetable oils and cereals prices, and oil prices, are

stronger compared to the volatility spillover of oil prices with other categories of agriculture commodities. The crop choice in agriculture is influenced by the level of profits and thus by the market prices. On the one hand, if the demand for biofuels increases, more and more 24

farmers will cultivate cereals as corn and soybeans to meet increased demand (Pal and Mitra, 2017). This in turn will affect the prices of non-energy agriculture commodities. On the other hand, if the demand for biofuels and vegetable oils will continue to increase and the productivity does not follow a similar pattern, more land will be used for cultivating energycrops which might lead to food shortage. Finally, for agriculture commodities with a higher degree of perishability (e.g. diary and meat), the net volatility spillover to oil prices is less important. Compared with vegetable oils

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and cereals, the production of diary and meat requires a longer period. Therefore, the oil price shocks are progressively accommodated in their prices. At the same time, as it is the case of non-energy agriculture commodities, the volatility of their prices spillovers to a smaller

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extent to the oil market.

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Acknowledgements

Claudiu Tiberiu Albulescu acknowledges the receipt of a grant from the Romanian

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National Authority for Scientific Research and Innovation, CNCS – UEFISCDI, project number PN-III-P1-1.1-TE-2016-0142. Seong-Min Yoon acknowledges the research grant

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supported by the Ministry of Education of the Republic of Korea and the National Research

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Foundation of Korea (NRF-2017S1A5B8057488).

25

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Fig.1. Dynamics of prices: (a) Agriculture price indices, (b) Avg. oil price index

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0.1

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0.0

Sugar

-0.2

-0.1

0.0 -0.1

0.00

Meat

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0.0

-0.05

1990

1995

2000

2005

2010

2015

0.2

Ave.Oil

0.0 -0.2

-0.15

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ur

0.4

-0.05 0.00 0.05 0.10 0.15 -0.2

Cereals

-0.1

Dairy

0.1

0.05

0.2

lP

-0.3

-0.2

Vegetable

0.1

0.2

0.2

data

1990

1995

Index

2000

2005

Index

Fig. 2. Dynamics of sample returns

32

2010

2015

0.0 0.1 0.2

-0.3

-0.1

0.1

-0.2

0.0

0.2

0.4

Density

Vegetable

***

*** 0.43

** 0.15

*** 0.19

0.054

0.2

-0.2

0.19

0.0

0.2

-0.2

.

* 0.12

0.099

**

*

0.18

0.14

0.065

0.066

0.15

-0.2

0.0

Density

Dairy x

-0.2

lP

0.0 0.1 0.2

-0.15 -0.05

0.05

0.15

na

ur Jo

-0.05

Ave.Oil x

-0.05 0.00 0.05

Fig. 3. Scatter matrix between agriculture commodity and Ave. oil returns

33

***

0.20

Density

-0.2 0.0

0.2

re

0.4

Density

-p

Meat

x

-0.15 -0.05 0.05

*

0.11

-0.025

-0.3

-0.1

x

Density

0.1

Sugar

ro of

Density

** 0.17

0.05

Cereals x

x

ro of

re

Note: Two lags were selected according to information criteria.

-p

Fig. 4. Time-varying Granger causality of agriculture commodity and oil markets

Overall spillovers on band: 0.52 to 0.26.

25

Overall spillovers on band: 0.26 to 0.00.

1995

2000

2005

Index

15 10 5

4 2

Jo

10

ur

15

6

na

20

8

20

lP

10

Overall spillovers on band: 3.14 to 0.52.

2010

2015

1995

2000

2005 Index

2010

2015

1995

2000

2005

2010

2015

Index

Fig. 5. Dynamic frequency connectedness of the agriculture commodity and oil markets Notes: These figures represent the frequency connectedness 𝐶𝑑𝐹 with 𝑑1 ∈ [3.14,0.52], 𝑑2 ∈ [0.52,0.26], and 𝑑3 ∈ [0.26,0.00].

34

-0.5

1995 2000

1.0

-2.0

-1.5

-0.5

2005

-0.5

2010

0.0

2015

0.5

Sugar

1.5

1.0

2.0

Index 1995

1995

2000 2005

Index

Index

2000 2005

Index

35 2010

2010

2015

Net spillovers on band: 0.52 to 0.26.

2015

-4

-2

-3

-2

-1

-1

0

Ave.Oil

0

Cereals

ro of

-p

0.0

1.0

Vegetable 0.5

2015

re

0.0

0.5

2010

-1.0

Meat

0.0

Dairy

lP 1.5

-1.0

2005

0.5

1.5

2000

0.0

Ave.Oil

1.0

na

0.5

Cereals 0.0 1995

ur

Jo -0.5

1

1

2

-3 3

2 -2.0

-2

-1.5

-1.0

-1

Meat

-0.5

Dairy

0

0.0

0.5

1

1.0

-1

-1

0

0

1

Sugar

1

Vegetable

2

2

3

3

Net spillovers on band: 3.14 to 0.52.

0.5

Sugar

0.0

3 2

-3 -4

-1 -2 1995

2000

2005

2010

2015

1995

2000

2005

Index

2010

2015

Index

ro of

-1

Ave.Oil

-2

1 0

Cereals

2

0

3

1

4

-5 2

-2

-4

0

-3

-2

Meat

4 2

Dairy

6

-1

8

0

10

-1

-1.0

0

-0.5

1

Vegetable

4

1.0

5

1.5

6

Net spillovers on band: 0.26 to 0.00.

re

(b) six months to twelve months

Jo

ur

na

lP

(a) one month to six months

-p

Fig. 6. Net directional connectedness of the agriculture and oil markets at different frequency bands.

(c) more than twelve months

36

ro of

Fig. 7. Net pairwise directional connectedness at different frequency bands

Jo

ur

na

lP

re

-p

Notes: This figure shows the most important directional connections among 17 pairs at different frequency bands. The arrow colours rank the strength of the net-pairwise directional connectedness from red (strongest) to blue and grey (weakest).

37

1995

2000

2005

2010

2015

1.5

2.0

2.5

0.1

0.2

0.8

0.3

0.4

Meat

0.6

Dairy

0.5

1.0

0.0

0.5

0.5

1.0

2.0

1.0

Sugar

1.5

3.0

2.0

3.5

2015 1995

To spillovers on band: 0.52 to 0.26.

1995

Index 2000 2005

Index

Index

2000

2005

Index

38

1

1

2

3

4

Ave.Oil

3

Cereals 2

5

6

4

7

0.5

1

1.0

2

Meat

2.0

Dairy 1.5

ro of

-p

re

1.5

2.5

Vegetable

lP

0.6

1.2

2010

Ave.Oil

0.4

na

0.2

2005

1.0

2.5

2000

0.5

2.0

ur

1.5 1995

0.0

1.0

Cereals

Jo

0.5

3

2.5

3.0

4

1

1

2

2

4

3

Sugar

3

4

Vegetable

5

5

6

6

Appendix

A. To Spillovers To spillovers on band: 3.14 to 0.52.

2010

2010 2015

2015

Jo 2

1995

2000

2005

2010

2015

3

5

1

3

Meat

4

3

5

4

1

1

2

2

Sugar

3

4

Vegetable

3

4 1995

From spillovers on band: 3.14 to 0.52.

1995

Index 2000 2005

Index

Index

2000

2005

Index

39 2010

2010

2015

B. From spillovers

2015

0.0

0

0.5

1

1.0

2

4

1.5

2.0

Ave.Oil

3

Cereals

ro of

-p

5

2015

re

lP

2

2

Dairy

2010

Ave.Oil 4

1

2005

2

5

2000

1

4

na

3

Cereals 1995

ur

1

5

2.5

6

0

3.0 0.0

7

2

0.5

4

1.0

Meat

6

Dairy 8

1.5

10

12

2.00.0

0

0.5

2

6

1.5

Sugar 1.0

4

Vegetable 8

2.0

10

2.5

To spillovers on band: 0.26 to 0.00.

1995

1

2

2000

4

4

5

5

1

1

2

2

2005

2010

5

6

0.0

7 0

1

4

2015

5

1.5

6

Index 1995

1995

2000 2005

Index

Index

2000 2005

Index

40 2010

2010

2015

From spillovers on band: 0.26 to 0.00.

2015

0.0

0.5

0.2

0.4

0.8

1.0

Ave.Oil

0.6

1.0

1.5

Cereals

ro of

-p

1.0

Sugar

3

Vegetable

0.5

2

2015

re

4

5

2010

3

Meat

4

Dairy 3

lP 6 0

6 0

2005

3

Ave.Oil

3

Cereals

2000

0

2

na

1 1995

ur

Jo 0

2.0

1.2

0.0

1.4

0.5

0.5

1.0

1.5

Meat

1.0

Dairy

2.0

1.5

2.5

0.2

0.5

0.4

0.6

Sugar

1.0

Vegetable

0.8

1.0

1.5

From spillovers on band: 0.52 to 0.26.

Table 1. Statistical properties for the agriculture commodities sub-indexes, and average oil index returns Vegetable

Dairy

Cereals

Sugar

Meat

Ave.Oil

Mean

0.003

0.002

0.001

0.000

0.001

0.003

Median

0.001

0.001

0.000

-0.001

0.001

0.011

Max

0.205

0.258

0.153

0.216

0.091

0.457

Min

-0.275

-0.223

-0.167

-0.309

-0.091

-0.312

Std.Dev.

0.052

0.047

0.039

0.074

0.028

0.087

Skewness

-0.401*

0.028

0.280

0.117

-0.188

-0.182

3.701

3.587

5.860*

6.098

Jarque-Bera

*

*

8.376

5.504

140.0*

395.0*

90.00*

7.466*

6.628*

113.6*

ADF

-4.627*

-4.839*

-5.168*

-5.703*

-4.718*

-5.038*

PP

-12.64*

-12.22*

-11.66*

-13.31*

-15.67*

-12.75*

ro of

Kurtosis

*

Jo

ur

na

lP

re

-p

KPSS 0.055 0.039 0.078 0.078 0.087 0.074 * * * ZA -5.157 -5.039 -5.638 -6.014 -5.459 -5.698* Notes: ADF, PP, ZA, and KPSS are the empirical statistics of the augmented Dickey-Fuller (1979) and Phillips-Perron (1988), ZA (Zivot and Andrew, 1992) unit root tests, and the Kwiatkowski et al. (1992) stationarity test, respectively. * denotes significant at 1% level of significance.

41

Table 2. Static spillovers at different frequency bands Freq1: The spillover table for band: 3.14 to 0.52 roughly corresponds to 1 month to 6 months.

1.33

FROM _ABS 1.85

FROM _WTH 2.78

1.01

1.39

0.91

1.36

1.92

0.21

0.39

1.75

2.62

1.80

65.87

0.16

0.44

0.68

1.01

1.17

0.63

0.12

66.88

5.71

1.32

1.97

1.84

0.53

0.26

0.55

0.92

62.47

0.68

1.02

2.20

0.55

1.83

0.67

0.40

1.54

7.19

TO_WTH

3.30

0.82

2.74

1.00

0.59

2.31

NET

0.3513

-0.3639

0.0813

-0.0081

-0.9215

0.8608

Dairy

Cereals

Sugar

Meat

Ave.Oil

Vegetable

53.89

0.86

7.63

1.22

0.08

Dairy

2.23

55.99

0.65

0.20

Cereals

7.71

0.25

52.28

Sugar

1.18

0.47

Meat

0.27

Ave.Oil TO_ABS

10.77

ro of

Vegetable

Freq2: The spillover table for band: 0.52 to 0.26 roughly corresponds to 6 months to 12 months. Dairy

Cereals

Sugar

Meat

Vegetable

11.55

0.47

2.61

0.09

0.03

Dairy

1.49

13.34

0.50

0.06

0.23

Cereals

2.73

0.10

13.17

0.12

0.01

Sugar

0.52

0.28

0.66

11.88

Meat

0.18

0.18

0.28

0.03

Ave.Oil

0.96

0.35

0.09

0.20

TO_ABS

0.98

0.23

0.69

TO_WTH

6.77

1.59

4.76

NET

0.3943

-0.2602

0.1905

0.32

FROM _ABS 0.59

FROM _WTH 4.04

0.66

0.49

3.39

0.03

0.50

3.44

Ave.Oil

-p

Vegetable

0.13

0.27

1.83

8.71

2.01

0.45

3.09

0.30

12.59

0.32

2.20

0.08

0.10

0.53

2.61

0.58

0.66

3.63

-0.1808

-0.3513

0.2075

lP

re

0.00

17.99

Freq3: The spillover table for band: 0.26 to 0.00 roughly corresponds to more than 12 months.

0.43

FROM _ABS 0.81

FROM _WTH 4.32

0.32

0.95

0.74

3.95

0.05

0.01

0.01

0.65

3.46

0.97

14.23

0.00

0.20

0.40

2.12

0.40

0.04

10.20

2.62

0.60

3.21

0.53

0.17

0.26

0.41

16.08

0.47

2.53

1.42

0.34

1.00

0.08

0.13

0.70

3.68

7.58

1.83

5.34

0.43

0.68

3.73

0.6107

-0.3986

0.3542

-0.3162

-0.4753

0.2252

Dairy

Vegetable

15.07

0.68

Dairy

2.30

Cereals

3.69

Sugar

0.80

Meat

0.28

TO_ABS

Meat

Ave.Oil

3.67

0.06

0.03

17.81

0.81

0.06

0.13

17.19

0.42 0.29

1.47

Jo

TO_WTH

Sugar

ur

Ave.Oil

Cereals

NET

na

Vegetable

19.59

Notes: The ‘within’ connectedness gives the connectedness effect that occurs within the frequency band and is weighted by the power of the series on the given frequency band exclusively. On the other hand, the frequency connectedness decomposes the original connectedness into distinct parts that, when summed, give the original connectedness measure. Thus, FROM_ABS is the measure of frequency connectedness, and FROM_WTH is the measure of ‘within’ connectedness. 42