Modeling the Relationship between Crude Oil and Agricultural Commodity Prices

The food-energy nexus has attracted great attention from policymakers, practitioners, and academia since the food price crisis during the 2007–2008 Global Financial Crisis (GFC), and new policies that aim to increase ethanol production. This paper incorporates aggregate demand and alternative oil shocks to investigate the causal relationship between agricultural products and oil markets. For the period January 2000–July 2018, monthly spot prices of 15 commodities are examined, including Brent crude oil, biofuel-related agricultural commodities, and other agricultural commodities. The sample is divided into three sub-periods, namely: (i) January 2000–July 2006, (ii) August 2006–April 2013, and (iii) May 2013–July 2018. The structural vector autoregressive (SVAR) model, impulse response functions, and variance decomposition technique are used to examine how the shocks to agricultural markets contribute to the variance of crude oil prices. The empirical findings from the paper indicate that not every oil shock contributes the same to agricultural price fluctuations, and similarly for the effects of aggregate demand shocks on the agricultural market. These results show that the crude oil market plays a major role in explaining fluctuations in the prices and associated volatility of agricultural commodities.


Introduction
The literature on the food-energy nexus has attracted great attention from policymakers, practitioners and academia since the food price crisis during the 2007-2008 Global Financial Crisis (GFC), and new policies that aim to increase ethanol production. The depletion of fossil fuels and environmental concerns has increased demand to develop renewable energy sources that can replace oil [1,2]. The possibility of food price increases under the introduction of biofuels may hurt the welfare of the poor, and decrease the urgency and speed in eradicating world poverty [3,4]. Banse et al. [5] show that biofuels can even increase the 2 emission due to reducing oil price, and cutting down forest land for farming. The trade-off between food and energy security has encouraged an investigation of the causal links between the agricultural and energy markets. Any empirical findings would be expected to provide evidence to advise public policy makers to find counter measures against the adverse effect of biofuels.
The causal links between energy prices and agricultural markets are mostly found to run from the former to the latter [6]. Research has considered oil prices as predetermined, and have examined the contribution of oil prices to agricultural commodity price and volatility variations.
For example, Taghizadeh-hesary et al. [7] show that food prices respond positively to oil price increases in the period 2010 -2016 for eight Asian countries using a panel -VAR model. For purposes of forecasting error variance decomposition, the oil price contributed 4.81% of the food price volatility in the second period, and increased to 62.49% in the 20 th period.
The causal links from agricultural commodity prices to oil prices have been considered as less important in the empirical literature. In a theoretical model, Ciaian and Kancs [8] demonstrate possible channels through which agricultural markets could affect oil prices. First, a positive agricultural productivity shock can reduce the demand for fuel, implying that decreases in food prices can lower oil prices. This mechanism is called the input channel. Second, the socalled biofuel channel has two opposite effects. Drops in agricultural prices will make biofuels more attractive because some agricultural commodities are inputs for biofuel. Increases in demand for biofuels will increase biomass production and oil prices as oil is used as an input for agricultural commodities. However, increases in biofuel production will increase the total energy supply, and therefore lead to reductions in oil prices.
Despite being somewhat limited, there is some empirical evidence of causality from agricultural commodity prices to oil prices. Deren Unalmis's comment on Baumeister and Kilian [9] shows that the US Department of Agriculture has released a report which leads to a drop in corn prices. The decrease in corn prices is then followed by a decrease in oil prices within half an hour. As the report is specific to agricultural markets, the oil price reaction indicates that shocks to agricultural commodity prices can have an impact on energy prices. Similarly, Dimitriadis and Katrakilidis [10] observe both long-run and short-run causal relationships from corn prices to crude oil prices for the US economy from 2005m1 to 2014m12, using both the ARDL methodology and error correction models.
Other studies have also reached similar results [11][12][13][14]. However, these studies often do not recognize the empirical findings as evidence to support the impact of agricultural price shocks on oil prices. The main reason is that the co-movements between oil prices and agricultural commodity prices may reflect the global business cycle instead of causality.
Therefore, studies that have used only the time series of the two prices cannot isolate the impacts of each variable from the effects of global economic activity.
Differing from previous studies that only use time series price data, this paper adds aggregate demand and alternative oil shocks to investigate the causal relationship from agriculture to oil markets, which is a novel contribution of the paper. In recent years, there have been many studies that have used the Kilian index to disentangle the relationship between oil prices, agricultural commodity prices and macroeconomic variables [15][16][17][18]. Following these studies, another novel contribution of the paper is to address the relative importance and contribution of agricultural commodity prices to global economic activity, and hence to the total variability of oil prices.
The idea that oil prices are endogenous is not new in the literature. Kilian [19] presents an overview of the main causes of oil price fluctuations, which are argued to be better explained through the demand side than political events in oil-exporting countries that can trigger changes in the global oil supply. From the demand side, there are shocks for energy consumption (for example, transportation, heating and cooking), while other shocks are for inventory and speculative purposes. This paper considers and evaluates agricultural markets as an alternative source of shocks that can cause fluctuation in oil prices. 4 In addition, the literature has often used a limited number of agricultural commodities in the model specifications. It is recognized that the impacts on oil prices are not the same for different types of agricultural commodities. By using a wide range of different commodities, we find that commodities which are more likely to be used as inputs for biofuels have a stronger relationship with crude oil prices than others. The heterogeneity in the empirical discovery supports the hypothesis that increasing the size of the biofuel market is important in connecting the food-energy nexus.
This empirical finding suggests that oil price forecasting can be improved by observing the appropriate agricultural commodities that are more likely to impact on oil prices. In terms of public policy making, the findings suggest that policy makers can sustain energy security by increasing the supply of agricultural commodities that are inputs for biofuel production.
The paper is structured as follows. Section 2 presents an overview of the related studies in the literature, while Section 3 discusses the methodology. Sections 4 and 5 provide a discussion of the data and the results of the empirical analysis. Section 6 provides some concluding remarks.

Literature Review
In recent years, there have been many published studies on the relationship between oil prices and agricultural commodity prices, most of which have focused on the unidirectional causal relationship from oil prices to agricultural commodity prices. López Cabrera and Schulz [20] find a cointegrating relationship between crude oil, rapeseed and biodiesel using the VECM model, where rapeseed and biodiesel react to the long run equilibrium while crude oil remains exogenous. However, there did not seem to be any long-run or short-run relationships from rapeseed to crude oil. Kapusuzoglu and Karacaer Ulusoy [21] show that crude oil prices can Granger cause corn, soybeans and wheat. Fernandez-Perez, Frijns and Tourani-Rad [22] find that oil prices can Granger cause soybeans, corn and wheat, and has a contemporaneous effect on soybeans and wheat. Wang et al. [23] find that most of the agricultural commodity prices investigated respond to oil price shocks during 2006m5 -2012m12 using impulse response functions derived from the structural VAR (SVAR). 5 However, some studies have found limited evidence for a causal relationship from oil prices to agricultural commodity prices. Fowowe [24] conducts a cointegration test with a structural break and nonlinear Granger causality tests, and finds that there is no long-run or short-run relationship between oil prices and agricultural commodity prices in South Africa. Nazlioglu and Soytas [25] use the Toda-Yamamoto procedure to test for long-run Granger causality between oil prices, agricultural commodity prices and the exchange rate in Turkey, but cannot find any Granger causal relationship from oil prices to agricultural commodity prices.
There is also no transmission from oil price shocks to agricultural commodity prices, either directly or through the exchange rate. Chiu et al. [14] find Granger causality from corn prices to oil prices, but not the reverse, in the USA, using the VAR and VECM models. According to Zhang et al. [26], there is no cointegration between agricultural commodity prices and energy prices. Sugar prices can Granger cause oil prices, but oil prices cannot Granger cause any agricultural commodity prices. Of the studies that confirm the neutrality of agricultural markets to oil price shocks, the outcomes are frequently attributed to governmental efforts to insulate the domestic agricultural sectors from international competition [24,25].
Several studies have found evidence of the bi-directional causal relationship between agricultural markets and crude oil prices. Nazlioglu and Soytas [11] examine 24 agricultural commodity variables in a panel VEC model, and find that agricultural prices and oil prices can Granger cause each other in the short run, while long-run causality is from oil prices to agricultural prices. According to Nazlioglu [27], linear Granger causality tests show that there is no relationship between agricultural prices and oil prices in either direction. However, after accounting for nonlinearity, it is possible to find bi-directional causal relationships between oil prices and soybeans prices, oil prices and wheat prices, and a unidirectional relationship from oil prices to corn prices. Rosa and Vasciaveo [28] find that wheat prices have a bi-directional relationship with oil prices after considering the Diks and Panchenko test [29] for nonlinear Granger causality.
The authors show that Granger causality goes from oil prices to corn and soybeans prices.
Avalos [13] uses the VECM model and finds that oil prices Granger cause soybeans prices, while both soybean and corn prices Granger cause oil prices. Moreover, corn prices can Granger cause oil prices in the long run, with all the relationships being discovered after the implementation of the Energy Policy Act 2005. Bi-directional relationships between the oil and agricultural markets 6 are observed not only in prices but also in the associated volatility (for a related analysis, see Chang and McAleer [30,31]).
Nazlioglu et al. [32] use the Lagrange Multiplier test for causality in variance proposed by Hafner and Herwartz [33] (see also Chang and McAleer [34] for a simple test of causality in volatility), and find that there is no causal relationship between corn, soybeans, wheat, sugar and oil volatilities in the pre-crisis period. However, the tests detect causal relationships from oil volatility to corn and wheat volatilities, and a bi-directional causal relationship between oil volatility and soybean volatility in the post-crisis period.
There are many explanations for the co-movements between the energy and agricultural markets. The extant literature recognizes four channels through which this can occur, including the cost-push effect, aggregate demand, exchange rate, and biofuels. Some authors have argued that oil prices Granger cause agricultural commodity prices as oil is an important input for the agriculture sector that is rapidly becoming more energy intensive [9,35]. Baumeister and Kilian [9] argue that such co-movements are the outcome of increasing aggregate demand for both agricultural products and crude oil. They find that fertilizer prices respond to oil price shocks, even though the main input for nitrogen fertilizer production is natural gas, which confirms the joint demand for oil and agricultural commodities. For a detailed analysis of modelling the effects of oil prices on global fertilizer prices and volatility, see Chen et al. [36].
The exchange rate is seen as an intermediate channel that connects agricultural commodities and crude oil [11,23]. Many studies have compared the pre-and post-crisis periods to identify the relevance of biofuels in explaining the relationship between the crude oil and agricultural markets. These studies have shown that the links between the two markets became stronger after the food price crisis [8,37], and attribute biofuels to such co-movements.
Recognizing that the relationships between the agricultural and oil markets may be subject to events that can occur contemporaneously, research attempts have been made to separate these mechanisms. Paris [38] uses the cointegrating smooth transition regression model proposed by Choi [39] to detach the biofuels channel from the aggregate demand effect. Wang et al. [23] use the SVAR model to differentiate oil-related shocks, including oil supply, aggregate demand and oil speculative demand shocks, and quantify their significance for the agricultural markets.

Methodology
Consider the VAR(1) model: where denotes global oil production, is the Kilian index that captures the global demand for industrial commodities, is the price of Brent crude oil, and represents the prices of agricultural commodities. The variables are expressed in logarithms, and is the error term that represents the shocks corresponding to each equation. The variables are non-stationary in levels, but become stationary after transformation to first differences.
The VAR(1) model with contemporaneous terms can be represented as follows: Agriculture specific shocks where , , and represent the vectors of coefficients for −1 in each equation.
Moving the contemporaneous terms to the left-hand side of the equations, the structural form of the VAR system is given as follows: where the order of is chosen by using the Akaike Information Criterion (AIC). It is assumed that the shocks are serially and mutually uncorrelated. Moreover, variables have different degrees of exogeneity. Following Kilian [40], it is assumed that oil production Δ has the highest degree of exogeneity, so that it can only be affected by its own oil supply shocks. In particular, it is assumed that changes in aggregate demand, oil price and agricultural prices cannot affect oil production contemporaneously ( 12 = 13 = 0), which means that global oil production is inelastic to shocks from other markets within time period t. This assumption is reasonable because much of global oil production is decided by the OPEC countries in the longterm trajectory, and is also often affected by political events in the oil-exporting countries.
Oil production can also respond to changes in global oil demand, but the response only arises after observing oil price trends for extended periods [41][42][43]. Furthermore, global economic activity Δ responds to innovations in oil supply and its own aggregate demand shocks. It is widely believed that changes in oil prices cannot affect global economic activity within the same calendar month [40].
Therefore, it is assumed that 23 = 0. For the last assumption, oil production, global economic activity and precautionary demand for oil are often treated as predetermined with respect to agricultural commodity prices, so it assumed that 14 = 24 = 34 = 0. Following Kilian [19], oil price Δ is affected by oil production, global economic activity and its own precautionary innovations. Agricultural commodity prices have the lowest degree of exogeneity, and are dependent on shocks from other variables and its own shocks. Innovations in agricultural markets may arise from both the supply side (such as weather impacts or natural disasters), or the demand side (such as consumer preferences) [42].
According to the above assumptions, the specification of the matrix is given as:  (1) can be obtained by multiplying both sides by the matrix −1 : After estimating the parameters in the SVAR model, we use the cumulative impulse response functions (IRF) to measure the responses of oil prices and agricultural commodity prices to changes in the other three variables. Ideally, the impulse response function will measure the reaction of the system to changes in one variable, given that there are no shocks in the other variables. However, in the reduced form VAR, variables are contemporaneously correlated, such that it is not possible to isolate the impact of specific variables [22].
In order to orthogonalize the impact of the shocks, we use the Cholesky scheme which imposes zero restrictions on contemporaneous terms. The restrictions are based on economic theory, which states that variables in the vector cannot have contemporaneously causal effects on those variables that have been ordered beforehand. The IRF illustrates the size, statistical significance and the persistence of such impacts. The Granger non-causality test is calculated to reveal the causal directional relationships among the variables. The forecasting error variance decomposition is used to examine the relative importance of each type of shock to variations in agricultural commodity prices. 1 A similar specification can be found in Wang et al. [23]. to determine the structural breaks as it is one of the most important inputs for biofuels, which helps to connect the food-energy nexus (see [30,31] which increases the demand for ethanol (or bio-ethanol) and, therefore, for corn and other biofuel-related agricultural commodities [9,13]. Table 1 shows the descriptive statistics for the crude oil and agricultural commodity prices expressed in logarithms. The mean prices and volatility of most agricultural commodity prices during the second period are larger than those in the other two periods, which add further support to the examination of three sub-sample periods.

Data and Tests
Following Wang et al. [23], oil price shocks are separated into different sources, including oil supply shocks, oil demand shocks from aggregate demand, and other oil demand shocks that are either precautionary or speculative in nature. World crude oil production is collected from the US Energy Information Administration, while the Kilian index is used as a proxy for global real economic activity (see [40]). This paper uses the updated version of the index, which has been corrected by Kilian [45], and can be found at the following website (http://wwwpersonal.umich.edu/~lkilian).   prices, the three test statistics fail to find any cointegration at the 5% significance level, except 2 In this paper, the innovative outlier model is used.
for rice when using the Z t statistic with the constant and slope specifications. In the third period, only corn is indicative of cointegration for the ADF and Z t statistics, while for most of other cases the test statistics cannot reject the null hypothesis at the 5% significance level.
Therefore, the structural VAR model will be used to analyze the dynamic relationship between oil and agricultural commodity prices. Before considering the impulse response functions 3 , we calculate some diagnostic tests to check the stability condition and the assumption that the SVAR residuals are not autocorrelated. The diagnostic tests show that the model is stable, and that there is no indication of model misspecification. 4 The optimal lag length for the individual subsample periods is determined according to the Akaike Information Criterion. The significance level used for the impulse response functions is set at 5%. Figure 1 shows that oil supply shocks do not have significant impacts on any agricultural commodity returns for all three periods under investigation. The empirical result confirms the findings from Wang et al. [23], who attribute such an outcome to the insignificant response of oil prices to oil supply shocks. By increasing the number of agricultural commodities, it is found that the effects of aggregate demand on agricultural commodity returns are not as strong as suggested in Wang et al. [23]. Figure 2 shows that aggregate demand has marginally significant effects on only 4 commodities (namely, soybeans, coconut oil, palm oil, and palm kernel oil) from 14 commodities in the first period. The effects on soybeans, coconut oil and palm kernel oil are highly significant and persistent, even after 12 months.

Responses of agricultural commodity prices to oil shocks
However, the significant responses of these 4 commodities disappear, whereas the effects on 3 commodities, specifically sugar, barley and tea, become significant during the second period. The effects on barley and tea are highly significant and persistent, even after 12 months, whereas the effects of aggregate demand on each and every agricultural commodity price loses its significance during the third period. In some cases, the prices of agricultural commodities 3 The analysis is based on the cumulative orthogonalized impulse response functions. 4 The results of the tests are available from the authors upon request. 13 decrease when aggregate shocks occur, even though the effects are not statistically significant.
Overall, these empirical findings confirm the decreasing impact of aggregate demand on agricultural commodity returns over time in the periods under investigation, which is similar to the outcomes mentioned in Wang et al. [23]. It is worth noting that there are two common patterns among the commodities. For vegetable oils, sugar, cotton and tea, the oil-specific shocks cause increasingly positive responses within the first 4 months. Subsequently, the responses are still positive, but the sizes remain relatively constant, with some cases becoming marginally significant (such as sugar and coconut oil), or even becoming insignificant (as in the cases of palm oil, palm kernel oil, and cotton).
For corn, soybeans, wheat, cocoa and coffee, the responses are also positive, but the sizes are reduced over time for the first 2 months. Subsequently, the effects also become insignificant.
In the third period, only palm oil, soybean oil and tea show significant responses. The responses are either insignificant after two months (for palm oil), marginally significant (for soybean oil), or relatively small in size (for tea).

Responses of crude oil price to agricultural shocks
The extant literature raises the serious issue as to why co-movements only occur during the second period. Some authors have argued that the popularization of biofuels after 2006 is responsible for the linkages between the agricultural and oil markets becoming more intense.
This paper has found evidence for the reverse causality from agricultural commodity prices to crude oil prices during the second period. Figure 4 shows the response of crude oil prices to the agricultural commodity price shocks. In the first period, oil prices show no response to the agricultural commodity price shocks, but the situation changes sharply in the second period, where it can be seen that, during the first few months, the responses are positive and increasing in magnitude, and subsequently becoming relatively constant thereafter.
Only certain commodities have significant impacts on oil prices, including corn, sugar, soybeans, wheat and vegetable oils (namely, coconut oil, palm oil, palm kernel oil, and soybean oil). The impacts of these commodities increase in size for the first 4 months and thereafter remain constant. The proportions of the effects are relatively large, at approximately 0.04% -0.05%. Moreover, the significance of the effects does not fade over time, but last over the horizon of 12 months. Such effects cannot be found for other agricultural commodities, including barley, cocoa, coffee, cotton, rice, and tea. However, the impacts of agricultural markets on oil prices disappear completely during the third period. In some cases, oil prices have negative responses to agricultural commodity price increases (such as for corn, wheat, coconut oil, cocoa, rice and tea), although such effects are not always significant.

Granger causality tests
The Granger causality tests are calculated after fitting the data to the SVAR model. Table 4 shows the results of the tests for the three sample periods.

Variance decomposition
In order to verify how the shocks to agricultural markets contribute to the variance of crude oil prices, we use the variance decomposition technique, which evaluates the relative importance of each shock to oil prices. Tables 5 and 6  Among agricultural markets, it is observed that there are commodities which are more important to oil price variations than the others. In particular, shocks from the corn, sugar, soybeans, wheat, coconut oil, palm oil, palm kernel oil, and soybean oil markets contribute more to oil price variations than do the barley, cocoa, coffee, cotton, rice and tea markets. Shocks from the first group contribute 6.37% -17.02%, while shocks from the second group contribute only 0.28% -4.43% to oil price variations. It is worth noting that, during this period, vegetable oils, such as palm oil, palm kernel oil and soybean oil, can somewhat surprisingly explain a higher proportion of crude oil price variations than can aggregate demand shocks.

Discussion
Estimation of the causal relationships between agricultural commodities and crude oil can suffers from the problems of simultaneity and endogeneity. Theoretically, the causal relationship between the two variables can run in both directions. Baumeister and Kilian [9] have emphasized that the increasing use of machinery in agriculture can lead to the situation whereby the increase in demand for agricultural commodities will lead to an increase in the demand for crude oil. In response, VAR models have been used widely in the literature to deal with the problem of reverse causality.
The relationship between the agricultural and oil markets may reflect an increase in aggregate demand. By applying the structural VAR model and the Kilian index, Wang et al. [23] filter out the impacts of the business cycle to isolate the true effects of oil price shocks on agricultural commodity prices. Following Wang et al. [23], it has been found that the impact of oil price shocks on agricultural commodity prices becomes stronger after the US Government decided to increase the mandated amount of biofuels in energy consumption. The policy increased the substitutability between oil and biofuels, thereby transmitting an increase from oil prices to agricultural commodity prices.
Considering reverse causality, the same procedure can be applied to disentangle the impacts of agricultural shocks from aggregate demand shocks. It has been found that oil prices react to agricultural commodity price shocks after the biofuel mandated policy was issued. Such effects cannot be found prior to the mandated policy act. However, there are many reasons that may lead to such reactions, such as the increasing usage of machinery mentioned above, as well as the popularization of biofuels.
The empirical results from the impulse response functions, Granger causality tests and variance decomposition analysis all point to the heterogeneity of oil price responses to agricultural commodity prices for different commodities. Different commodities may affect oil prices through different channels. For the commodities that are less likely to be factor in biofuel production, these commodities primarily affect oil prices because of the increasing use of machinery in agricultural activities. For other commodities that are more likely to be factor in biofuel production, the effects should be stronger because there are additional effects through the biofuel channel. Therefore, the identification of the causal relationship between energy and food can be determined through identifying the heterogeneity of oil price responses to different agricultural commodity prices.

Concluding Remarks
In this paper, we have replicated the results in Wang et al. [23] and related research using Furthermore, the influences of agricultural shocks on oil prices were investigated after controlling for aggregate demand shocks. Using the impulse response function, it was shown that the shocks do not have any significant impacts on oil prices during the first period. However, the situation changed sharply in the second period, where more than one-half of the agricultural commodity prices were found to trigger significant responses in oil prices. Moreover, the same commodities could also Granger cause oil prices in the same period. These new empirical findings cannot be found in the period before implementation of the energy policy act. It was also observed that the commodities that have an impact on oil price are not arbitrary as these commodities are likely to be used as inputs for biofuels, as suggested in the literature.
The same effect could not be determined for the other agricultural commodities. Variance decomposition was used to determine the contribution of agricultural shocks to oil price variations, relative to aggregate demand shocks, oil supply shocks, and oil-specific demand shocks. The empirical outcomes show that shocks related to speculative and precautionary oil demand contributed the largest proportion of oil price variations. However, agricultural fluctuations explained a relatively large proportion of oil price variations during the second period, the contribution being even larger than the aggregate demand for some commodities.
As the size of the biofuel market becomes larger, the possibility that shocks in agricultural markets can influence the oil market also increases. The implications of the empirical results in this paper for public policy are two-fold. First, oil price forecasting should consider shocks from agricultural markets as an additional information source to predict oil price fluctuations.
However, not all shocks from agricultural markets should be treated equally. Policy makers should differentiate shocks that affect agricultural commodities often used as inputs for biofuels from other agricultural shocks that are not used as inputs. Second, policy makers can turn their focus on agricultural markets to solve the problem of energy security. Increases in the production and productivity of the agricultural markets that are direct inputs into the production of biofuels may reduce oil prices in times of economic and financial crises.