Background and Related Literature

DDGS are a co-product from dry-mill ethanol productions, high in both energy and protein content. Traditionally, DDGS were used in livestock feeds as a source of protein, often replacing soybean meal in the feed ration. However, the rapid rise in corn processing for ethanol since 2006 has altered this pattern (Silvestri Reference Silvestri2015). Tightening corn supplies and the increasingly volatile corn prices had led many livestock producers to replace corn in the feed ration with DDGS as an energy source. DDGS feeding rapidly expanded against this backdrop and is emerging as a mainstream animal feed in the United States. Though questions remain over the substitution rate of DDGS for energy (corn) and protein (soybean meal) in livestock and poultry rations (Hoffman and Baker Reference Hoffman and Baker2010), it is expected that both corn and soybean meal prices play a significant role in the price behavior of DDGS, with price differences reflecting their differing nutritional values. In a survey conducted by Stroade et al. (Reference Stroade, Martin, Conrad and Schroeder2010), 87 percent of the ethanol plants used corn futures prices to establish the benchmark prices of distiller's grains, while 43 percent of the respondents used soybean meal futures prices as a benchmark.

Despite its importance, studies regarding the price and volatility interactions between DDGS and other feed ingredients in the U.S. remain scant. The U.S. Grain Council (2007) highlights the role of corn and soybean meal prices on DDGS prices, but notes that DDGS prices should be most closely linked to corn prices because of similarities in their economic and nutritional values. This relationship is supported by Hoffman and Baker (Reference Hoffman and Baker2010), who find that corn and soybean meal prices explain over 95% of the variation in DDGS prices, and that corn prices play a much larger role than soybean meal prices after the expansion of ethanol production in 2006. Irwin and Good (Reference Irwin and Good2013) examine the factors affecting spot DDGS prices in Iowa from 2007 to 2013, finding that a $1/ton increase in soybean meal and corn prices would lead to $0.11/ton and 0.85/ton increases in DDGS prices, respectively. These numbers were slightly higher than the regression results reported in Hoffman and Baker (Reference Hoffman and Baker2010) using Central Illinois DDGS prices. In a follow-up study, Irwin and Good (Reference Irwin and Good2015) consider the relationship between the three markets during the period of high protein prices (2011–2014), finding that soybean meal prices to play a much more significant role on Iowa DDGS prices in 2011–2014 compared to the period prior. However, this impact is still significantly smaller than corn.

Other studies have examined the long-run or dynamic pricing relationship between corn, soybean meal, and DDGS. Anderson, Anderson and Sawyer (Reference Anderson, Anderson and Sawyer2008) examine the price of DDGS in Central Illinois and the price of corn received by producers in the Texas Triangle area, finding these two prices to be cointegrated. These authors also note that the relationship between the two prices appears to be weak prior to 1998 but has strengthened since then as the DDGS market matures. Tejeda (Reference Tejeda2012) reports that under a dynamic correlation framework, correlations exist between DDGS and other feed grains after the ethanol mandate but not prior. Johnson et al. (Reference Johnson, Yu, Griffith, Jensen and Cho2015) study the price relationship between DDGS, corn, soybean meal and livestock outputs at four locations associated with a predominant livestock sector. They show that regardless of the regions examined, the price of corn is the largest contributor to DDGS price variances, and that other factors only have limited effects on DDGS prices. Using DDGS spot prices in Iowa, Silvestri (Reference Silvestri2015) finds a stable long-run relationship between corn, soybean meal, and DDGS prices and that corn prices are the primary channel through which exogenous shocks are transmitted to the system. They attribute such findings to the higher storability of corn relative to DDGS and soybean meal.

However, not all studies agree with the significant price relationship found between the three commodities. In particular, Van Winkle and Schroeder (Reference Van Winkle and Schroeder2008) examine the pricing efficiency of local DDGS markets by investigating their price relationships with the corn and soybean meal futures markets. Out of the 11 markets examined, they find that DDGS prices of only one location to be cointegrated with corn and soybean meal prices. Schroeder (Reference Schroeder2009) finds significant price risks in the DDGS market that cannot be eliminated by hedging using corn futures contracts. Murguia and Lawrence (Reference Murguia and Lawrence2010) find that the effects of corn and soybean meal prices on DDGS are highly dependent on the empirical model specified, and that the effectiveness of using these two futures contracts to hedge against DDGS price risk varies with the period used and the model considered.

Our paper departs from the aforementioned papers in a number of ways. First, while most of the previous studies have focused on how DDGS prices can be affected by the prices of corn and soybean meal, little research has investigated the interrelationship between these three commodities and how DDGS prices can influence the price behavior of the other two feed ingredients. This reverse causality is likely as livestock and poultry farmers can reasonably change the feed ration between the three commodities based on their relative price ratios. Since DDGS prices can significantly affect the profitability of ethanol plants (Irwin, Reference Irwin2016, Irwin and Good, Reference Irwin and Good2015), the relative price of DDGS may also affect the demand of corn to be used in ethanol production and further affect corn prices. Second, previous studies have only focused on the price interactions between the three feed ingredients, without paying much attention to the volatility dynamics. Our study, by contrast, examines how volatility transmits between the three markets. As Gallagher and Twomey (Reference Gallagher and Twomey1998) point out, examining the conditional second moment could provide additional valuable insights to the interrelationships across different markets. In particular, we investigate how exogenous shocks in one market could affect the volatility in the three markets to shed light on the volatility transmission mechanism. Finally, in light of the changing dynamics between the three markets identified in previous studies, we seek to identify how the interrelations between corn, soybean meal, and DDGS prices have changed over time. We expect the DDGS market to be more correlated with corn, but less with soybean meal as the feed ration in livestock and poultry production changes. Such information is a critical input for many of the common tasks involved in risk management. If the correlations and volatilities of the three commodities are time-varying, hedgers who wish to effectively manage their price risks may find it useful to adjust the hedge ratio to account for the most recent information.

Econometric Model

Standard time series procedures are used to evaluate the price and volatility linkages between DDGS, corn, and soybean meal markets. We first investigate stationarity, co-movement, and volatility clustering properties of the three price series. As noted in the next section, there is no evidence against the unit root null hypothesis in any of the price series, and overwhelming evidence in favor of stationarity in every differenced price series. Individual series that are nonstationary, however, could be cointegrated such that each series reverts to common stochastic trends. Assuming there exists a long-run equilibrium, the following vector error correction (VEC) model is estimated to investigate the price linkages between the three price series:

(1) $$\eqalign{& \Delta {\bi P}_t = \; \mathop \sum \limits_{\,j = 1}^p {\bi \beta} _j \Delta {\bi P}_{t - j{\bi \;}} + {\bi \alpha} ECT_{t - 1} + {\bi \varepsilon} _t, \cr & {\bi \varepsilon} _t \; \vert \; {\bi I}_{t - 1} \; \sim \; \lpar {\bf 0},{\bi H}_t \rpar,}$$

where P _t is a three-component vector including prices of DDGS, corn, and soybean meal, Δ is the first difference operator such that Δ P _t  =  P _t  −  P _t−1, β _j are parameters that capture the short-run dynamics between the three price series, p is the lag length, ECT is the error correction term that characterizes the long-run relationships between the three variables, and α is a 3 × 1 vector that describes the speed of adjustment when deviations from the long-run relationship occur. Additionally, ε _t is a three-component vector of disturbance term, the variance-covariance matrix of which is characterized by matrix H _t conditional on past information I _t−1.

It is not uncommon for time series data, in particular prices, to exhibit time-varying volatility clustering, i.e. periods of large swings interspersed with periods of relative tranquility. For this matter, we consider two different multivariate generalized autoregressive conditional heteroscedasticity (MGARCH) models to account for the error structure in the VEC model. In the first specification, we consider the conditional correlation (DCC) model that assumes the conditional correlation matrix ( R _t ) between the three markets to be time-varying, as shown in equation (2):

(2) $$\eqalign{& {\bi H}_t = {\bi D}_t^{1/2} {\bi R}_t {\bi D}_t^{1/2}, \cr & {\bi R}_t = {\rm diag}\lpar {{\bi Q}_t} \rpar^{ - 1/2} {\bi Q}_t {\rm diag}\lpar {{\bi Q}_t} \rpar^{ - 1/2} \cr & {\bi Q}_t = \lpar {1 - \lambda _1 - \lambda _2} \rpar{\bi Q} + \lambda _1 \tilde \varepsilon _{t - 1} \tilde \varepsilon _{t - 1}^{\prime} + \lambda _2 {\bi Q}_{t - 1},} $$

where ${\bi D}_t = {\rm diag}\left\{ {\sqrt {h_{it}} } \right\}$ is a 3 × 3 diagonal matrix of time-varying standard deviations that evolves according to a univariate GARCH(1,1) process, R _t is a time-varying symmetric matrix of conditional correlations between the three prices, λ ₁ and λ ₂ are non-negative adjustment parameters satisfying λ ₁ + λ ₂ < 1 such that the conditional correlations are mean-reverting, $\tilde \varepsilon _t$ is the standardized residuals, and Q is the 3 × 3 uncondtional variance matrix of $\tilde \varepsilon _t$ . The DCC specification has the flexibility of a univariate GARCH but not the complexity of many conventional MGARCH models (Engle, Reference Engle2002). The DCC model allows us to estimate the time-varying conditional correlations between DDGS, corn, and soybean meal markets. Previous applications of the DCC model in agricultural commodity markets include Gardebroek and Hernandez (Reference Gardebroek and Hernandez2013), Mensi et al. (Reference Mensi, Beljid, Boubaker and Managi2013), among others.

To examine the volatility spillover between the three markets, we consider an alternative model for the error structure. Specifically, the conditional covariance matrix H _t is modeled using the Baba-Engle-Kraft-Kroner (BEKK) procedure with one lag, as shown in equation (3).

(3) $${\bi H}_t = {\bi CC}^{\prime} + {\bi A^{\prime}\varepsilon} _{t - 1} {\bi \varepsilon} ^{\prime}_{t - 1} {\bi A} + {\bi B^{\prime}H}_{t - 1} {\bi B},$$

where C is a 3 × 3 lower triangular matrix that corresponds to the constant, ${\bi \varepsilon }_{t - 1}{\bi \varepsilon }^{\prime}_{t - 1}$ are the squared lagged errors, A is a 3 × 3 matrix of ARCH parameters containing elements measuring the degree of innovation from one market to another, and B is a 3 × 3 matrix of GARCH parameters that shows the persistence in conditional volatility between two markets. The BEKK specification in equation (3) not only provides a direct estimation of the conditional covariance matrix, but also significantly reduces the number of parameters to be estimated in H _t while ensuring positive definiteness of the conditional covariance matrix. This specification has been widely used in the literature to investigate own- and cross-volatility spillovers and persistence between multiple markets, including Ait Sidhoum and Serra (Reference Ait Sidhoum and Serra2016), Etienne, Trujillo-Barrera and Wiggins (Reference Etienne, Trujillo-Barrera and Wiggins2016), Gardebroek and Hernandez (Reference Gardebroek and Hernandez2013), Jin, Lin and Tamvakis (Reference Jin, Lin and Tamvakis2012), Serra, Zilberman and Gil (Reference Serra, Zilberman and Gil2011), Trujillo-Barrera, Mallory and Garcia (Reference Trujillo-Barrera, Mallory and Garcia2012), among others.

The conditional mean specified in equation (1) and conditional variance specified in equations (2) or (3) jointly defines the trivariate VECM-MGARCH model used in this analysis. In both models, we first estimate the cointegration factor, and then use the maximum likelihood procedure as outlined in Seo (Reference Seo2007) and Serra, Zilberman and Gil (Reference Serra, Zilberman and Gil2011) to jointly model the mean and error processes. Estimation results are used to assess i) the long-run and short-run price dynamics (VECM), ii) the time-varying correlations (DCC), and iii) the volatility transmission mechanisms between DDGS, corn, and soybean meal markets in the US (BEKK).

It should be noted that the DCC- and BEKK-MGARCH specifications are not competing models; rather, they complement each other. We use the BEKK specification because it allows the identification of volatility spillovers from one market to the other, as well as investigation of how an exogenous shock in one market affect volatility in its own and other markets. DCC complements BEKK by uncovering the time-varying conditional correlations of price volatility, which are critical inputs for many common risk management strategies. As such, the use of both models offer a more thorough description of price volatility. We expect the results from BEKK- and DCC-MGARCH models to be robust, but offering differing information on the volatility dynamics between the three markets.

Data

Weekly nearby prices of the No.2 Yellow Corn futures contracts and soybean meal futures contracts are obtained from the Chicago Board of Trade (CBOT). Prices are rolled into the next nearby contracts on the first business day of the delivery month. We use the DDGS price in Central IL as the benchmark price for DDGS, as it is close to the corn and soybean meal delivery locations. These prices are obtained from the US Department of Agriculture (USDA) Agricultural Marketing Service (AMS). The sample period considered runs from January 2000 to May 2016, resulting in 857 weekly observations. The selection of the sample period is motivated by data availability, as the DDGS price in Central IL is not available until January 2000.

Figure 1 plots weekly DDGS, corn, and soybean meal prices in cents per unit (ton for DDGS and soybean meal and bushel for corn). All three prices experienced dramatic rises and drops. Three peaks are observed in corn prices: one in mid-2008, one in mid-2011, and another in mid-2012, all with comparable price levels. By contrast, the highest price in DDGS market is observed in 2012, significantly higher than the peak prices observed in other periods. A dramatic decline occurred in DDGS prices during 2014, dropping its value from a maximum of 252.5 cents/ton in March 2014 to a minimum of 91 cents/ton in November 2014. While similar price patterns are observed in corn and soybean meal markets during the same timeframe, the percentage price drops in these two markets were of smaller magnitudes than DDGS. Additionally, while corn prices started their run-up in mid-2006, the price of DDGS did not rise significantly until the end of 2007. The relatively low DDGS prices in the early stages of ethanol expansion quickly attracted attention from livestock producers who are constantly searching for cheaper feed ingredients. DDGS soon emerged as a mainstream substitute in animal feed rations, which eventually led to the rapid spike in DDGS prices in 2008.

Figure 1. DDGS (in Cents/Short Ton), Corn (in Cents/Bushel), and Soybean Meal (in Cents/Short Ton) Prices in the U.S., (January 2000–May 2016)

Figure 2 plots the one-year rolling historical volatility (annualized standard deviation) for the three return series, along with their historical volatility for the whole sample period.Footnote ⁴ Several interesting patterns emerge. First, the three commodities experienced large volatility swings between mid-2008 and the end of 2010, a period that corresponds to the worldwide commodity price spike and financial crisis. Previous studies have detected considerable co-movement across various commodity prices during this period, an indication that commodity markets are increasingly “financialized” due to the participation of commodity index traders. Second, the overall volatility during the sample period appears to be comparable for the three markets. The corn market exhibits the highest annualized volatility (30.1%), followed by soybean meal (29.4%) and DDGS (27.8%). Third, despite the similarities, the volatility patterns of the three return series show a significant degree of heterogeneity. DDGS, for instance, has the highest annualized volatility in the first half of 2015, more than 25 percentage points higher than the average annualized volatility of the sample period. By contrast, both corn and soybean meal markets have the highest volatility in 2009. Soybean meal price volatility was also high between the end of 2004 and mid-2005. Finally, the three plots are indicative of volatility-clustering in the returns, as periods of high (low) volatilities are often followed by even higher (lower) volatilities. Accounting for time-varying volatility when modeling the interrelationships between the three markets appears to be an important task.

Figure 2. One-Year Rolling Historical Volatility (Solid Line) and Overall Historical Volatility (Dashed Line) for DDGS, Corn, and Soybean Meal Price Returns (January 2000– May 2016)

Summary statistics, unconditional correlations, and unit root test results for both log prices and returns (difference in log prices) are presented in table 1. Average returns are positive during the sample period for all three commodities, though none of them is statistically significant (panel A). All three return series appear to show a leptokurtic distribution, as the excess kurtosis is positive and statistically significant. Based on the Jarque-Bera test, the normality assumption is rejected for all three return series as well. Additionally, we find strong autocorrelation for the squared returns. For up to 3, 6 and 10 lags, the null hypothesis of no autocorrelation is uniformly rejected at the 1% significance level using the Ljung-Box test (Panel D), suggesting the existence of possible non-linear dependences in the returns.

Table 1. Summary Statistics, Contemporaneous Correlations, and Unit Root Test Results for DDGS, Corn, and Soybean Meal Prices (January 2000–May 2016)

Note: One, two, and three asterisks represent statistical significance at 10, 5, and 1 percent, respectively.

Panel B of table 1 shows the unconditional contemporaneous correlations between the three log price and return series during the whole sample period. All correlation coefficients are statistically significant, and are of much higher magnitudes between log prices than between the three return series. Corn price returns are more correlated with soybean meal than DDGS price returns, with a correlation coefficient of 0.47. The correlation between DDGS returns and the other two commodities are much lower, both below 0.20.

We next examine the stationarity property of the price and return series using the augmented Dickey-Fuller (ADF) tests. Lag lengths are selected using the Bayesian information criterion (BIC). As panel (C) of table 1 suggests, regardless of the model (trend only, constant only, and both trend and constant) used, we fail to reject the null hypothesis of a unit root in all three log price series. By contrast, there is overwhelming evidence that all return series are stationary, supporting the use of returns instead of price levels in the regression analysis.

Since we find the prices of the three commodities to be non-stationary, we next investigate whether there exists stable long-run equilibriums between these prices using the Johansen maximum likelihood procedure, the results of which are presented in table 2. Two lags are selected based on BIC. At the 5% significance level, we reject the null hypothesis of at most zero cointegration relationship between the three prices, but fail to reject the null hypothesis of at most one cointegrating factor. We hence conclude that there is a stable long-run relationship between DDGS, corn, and soybean meal prices.

Table 2. Johansen Maximum Likelihood Tests for Cointegration between Log DDGS, Corn, and Soybean Meal Prices (January 2000–May 2016)

Note: The test starts with the null hypothesis of at most zero cointegrating equation (a maximum rank of zero), and accepts the null hypothesis of at most n cointegrating equations when it is first accepted.