Modeling Nonlinearities in the U.S. Soybean-to-Corn Price Ratio: A Smooth Transition Autoregression Approach

ABSTRACT

The soybean-to-corn price ratio has long been considered one of the triggers that farmers use in the decision to produce corn or soybeans, but little has been done to analyze its dynamics. Recently, the soybean-to-corn price ratio options were introduced on the Chicago Board of Trade, providing the market participants with an opportunity to trade the relative prices of the crops. In this study, the author investigates potentially nonlinear dynamics of the soybean-to-corn price ratio by applying the smooth transition autoregression (STAR) modeling framework to the soybean-to-corn price ratio, derived from monthly futures prices of corn and soybeans. The estimated model demonstrates nonlinear dynamics, resulting in asymmetries in the adjustment to the long-run equilibrium of the soybean-to-corn price ratio. The findings of this research provide insightful implications to crop producers, input suppliers, and other market participants.

INTRODUCTION

In December 2010 the soybean-to-corn price ratio (STC) options were introduced on the Chicago Board of Trade (CBOT). The availability of these options has been considered a new tool for producers and market participants to hedge and trade the relative prices of corn and soybeans, thus implying additional impacts on acreage allocations of these crops. In fact, the STC has long been known as a decision-making trigger for the U.S. crop producers (Lin & Riley, 1998). Corn and soybeans are considered substitutes in production because they are typically produced in the same geographic regions of the United States, and their planting decisions are made jointly. Thus, the supply responses of corn and soybeans are somewhat peculiar, in the sense that a trade-off is seen with respect to acreage allocation decisions (e.g., Holt, 1992). For example, an increase in corn acreage happens at the expense of a reduction in soybean acreage, and vice versa.

Additionally, corn and soybeans are substitutes in consumption. Historically, these crops and their byproducts have been used in livestock feed rations. This feedstock-driven substitutability has been further strengthened recently, as a result of the increased interest and support of biofuel production. In particular, the Energy Policy Act of 2005 and the Energy Independence and Security Act of 2007 have greatly influenced both the production and alternative use of these crops in the United States (e.g., Anderson & Coble, 2010; Eidman, 2007; Gardner, 2007). However, the byproducts of corn-based ethanol and soybean-based biodiesel production, respectively, dried distillers grains with solubles (DDGS) and soybean meal, have a primary end-use in livestock production (e.g., Beckman, Keeney, & Tyner, 2010), and are close substitutes in livestock feed rations. So, despite the increase in the use of corn and soybeans for energy products, the inclusion of their byproducts in livestock feeds further strengthens the link that already exists. Finally, an additional reason for the strengthened substitutability between corn and soybeans is the energy linkage of the two crops, in that ethanol and biodiesel are blended with gasoline and diesel, respectively; both of which are processed from crude oil.

Given the aforementioned simultaneity of planting decisions and the strong market linkages between corn and soybeans, the dynamic relationship between the relative prices and the acreage allocation of corn and soybeans may be illustrated with the following example. A negative shock to the STC would favor corn production over soybeans, which in the following period will result in increased corn supply and decreased soybean supply in the respective markets. In response to these supply shocks, corn and soybean prices would possibly alter the STC to the extent that now soybeans would become a more favorable crop to plant in the subsequent year. Thus, the soybean-to-corn price ratio would impact planting decisions, which in turn would affect crop prices, and subsequently the soybean-to-corn price ratio. From this, it can be concluded that corn and soybean prices are likely to fluctuate around some long-run equilibrium, thus defining the dynamics of the soybean-to-corn price ratio.

Notably, although the supply-induced shocks will have a tendency to alter the soybean-to-corn price ratio on an annual basis, the demand-driven shocks are likely to alter the ratio at a higher frequency. However, the “feedstock link” and the “energy link,” discussed above, will ensure the co-movement of the prices between the harvest periods. In other words, corn and soybean prices are likely to be cointegrated. As discussed subsequently, one way of analyzing the cointegration between corn and soybean prices is to assess the dynamics of relative prices of corn and soybeans, or the soybean-to-corn price ratio. An additional benefit of modeling the STC in an univariate mode, as opposed to a system of two equations, is that by taking a ratio of two related prices I effectively discard any “common shocks” associated with these crop prices, and only focus on impulses associated with relative preferences and technology shocks (Carter & Smith, 2007).

It has been argued that the recent biofuel-oriented policies have altered the crop price levels and perhaps their dynamics (Irwin & Good, 2009). As well, over the past several years there has been increased correlation between corn and crude oil prices, something that did not exist previously (Tyner, 2010). The overall consensus is that the recent policies have triggered beginning of the new era of the crop prices. In this respect, a question remains to be addressed whether the new era has also fundamentally altered arbitrage between corn and soybean markets. In particular, a stronger cointegration between these two crop prices could be more apparent in recent years, than it was previously. In this study, I will assess a possible structural change in the soybean-to-corn price ratio over the past few years.

The soybean-to-corn price ratio may also be characterized with nonlinear dynamics, and there are a number of reasons for this. First, it is due to the very nature of the agricultural production—though crops are harvested on an annual basis, given the demand shock they can be moved into the supply chain rapidly, thus suggesting possibilities for asymmetric dynamics in the relative prices. Second, adjustments to the long-run equilibrium may have different rates depending on a direction or a magnitude of the deviation from the equilibrium. For example, there may exist some transactions cost band beyond which the relative prices behave in a strictly stationary manner, while within the price ratio may have an explosive nature (e.g., Balke & Fomby, 1997). Alternatively, because of associated fixed costs and possible differences in these costs across the considered crops, economic agents may be more reluctant to react to the relative price change that favors one crop production, but less so when the other crop production is favored by the STC. The subsequent actions on the grain market may amplify or mitigate the shock-related effects on the relative price dynamics. Finally, a number of studies report asymmetries in corn and soybean acreage responses to price shocks (de Gorter, Nielson, & Rausser, 1992; Holt, 1992; Shideed & White, 1989), as well as asymmetries in yield responses to price shocks (Choi & Helmberger, 1993). Also, government support programs likely introduce nonlinearities to these commodity prices (Chavas & Holt, 1990; Goodwin & Mishra, 2006; Holt, 1992; Lin & Dismukes, 2007). All these could possibly result in asymmetries in the relative price dynamics of these crops as well.

Nonlinearities and structural change in the STC dynamics may be captured by regime-dependent models. One such specification is a smooth transition modeling framework. The conceptual model for smooth transition regressions was originally proposed by Bacon and Watts (1971), whereas modeling and testing methods were subsequently developed by Terasvirta and colleagues (Luukkonen, Saikkonen, & Terasvirta, 1988; Terasvirta & Anderson, 1992; Terasvirta, 1994). A smooth transition autoregressive (STAR) modeling is one of the more advanced time series methods, which moreover combines elements of other regime-dependent models, such as threshold autoregressive (e.g., Tsay, 1989; Tong, 1990), Markov switching (e.g., Hamilton, 1989), and artificial neural network (e.g. Kuan & White, 1994) models. An attractive feature of the STAR modeling framework is that it allows for a possible range of switching points between the regimes, which may prove useful when considering behavior of potentially heterogeneous agents, for example. Over the past two decades the smooth transition modeling approach has gained in popularity and has been increasingly applied to macroeconomic data to examine potential nonlinearities of unemployment rates, gross domestic product (GDP), money demand, and interest rates (e.g., Eitrheim & Terasvirta, 1996; Sarantis, 1999; Skalin & Terasvirta, 2002, Terasvirta, 1995).

Relatively few studies have explored the potential for nonlinearities in commodity prices (e.g., Balagtas & Holt, 2009; Goodwin, Schnepf, & Dohlm, 2005; Holt & Craig, 2006; Mainardi, 2001; Reitz & Westerhoff, 2007). For example, Chavas and Holt (1991) adopt the “deterministic chaos” method to investigate nonlinear dynamics of the corn–hog cycle, Goodwin et al. (2005) examine structural change in a system of soybean prices and stocks-to-use ratio, and Balagtas and Holt (2009) investigate nonlinearities in the commodity terms of trade. An approach used by Holt and Craig (2006) is the closest to the motivation and the econometric implementation of the current study, as it investigates nonlinear dynamics of the corn–hog cycle, using time-varying smooth transition autoregressive (TV-STAR) modeling approach.

Despite analysts’ awareness of the soybean-to-corn price ratio as one of the defining factors of adequate acreage allocation, the dynamics of these relative prices has been largely unexplored. I intend to fill this gap in the literature by adopting the STAR modeling framework to investigate regime-dependent nonlinear dynamics of the soybean-to-corn price ratio. Moreover, I will examine the possibility of the structural change in the dynamics of the relative prices. In what follows, I will first outline the modeling framework. I will then discuss the data and the estimation procedure used in this research. I will subsequently present the main findings of this study, which I will further illustrate using the generalized impulse-response functions. Finally, I will summarize the implications of this research.

MODELING FRAMEWORK

In this section, I outline the econometric approach used in this research to investigate the potential nonlinear relationship of relative commodity prices. I will first describe the smooth transition autoregression (STAR) framework. Then I will outline the model selection and diagnostic testing procedures.

The Smooth Transition Autoregression Model

Class of smooth transition autoregressive (STAR) models of Terasvirta (1994) is widely used in studies attempting to model the asymmetric cyclical variations and turbulent periods (e.g., Hall, Skalin, & Terasvirta, 2001; Terasvirta, 1995; Terasvirta & Anderson, 1992). STAR model of order p, STAR(p), can be specified as:

• (1)

or alternatively:

• (2)

where and . is a dependent variable, x_t is a vector of right-hand-side variables, and , are vectors of parameters; finally, is an additive error process such that . Further, is a transition function, by construction bounded between zero and one, where is a transition variable, and γ and c are, respectively, smoothness and location parameters.

In empirical studies, logistic and exponential transition functions are most frequently used, forming the logistic STAR (LSTAR) and exponential STAR (ESTAR) models, respectively. Another frequently used transition function is a quadratic function, forming the quadratic STAR (QSTAR) model. These three transition functions are defined as follows:

• (3)

• (4)

• (5)

In the smooth transition functions γ is a nonnegative parameter. The LSTAR and QSTAR models converge to a linear AR model when γ → 0, and a threshold autoregressive model (TAR) when γ → ∞. On the other hand, the ESTAR converges to a linear AR in both cases, that is, when γ → 0 and γ → ∞.

Often some function of the lagged dependent variable is used as a transition variable. Alternatively, t* = t/T, where T is the length of the time series, may be used as a transition variable, leading to the time-varying autoregressive (TVAR) model. Finally, the model specified in Equations 1 and 2 is a two-regime model, which may be extended to any k-regime model (see, for example, van Dijk & Franses, 1999).

Model Selection and Diagnostics

The STAR models suffer from the presence of unidentified nuisance parameters (e.g., Davies, 1987). Thus, the conventional test statistics against linearity and/or parameter constancy are not directly applicable to the STAR models (Luukkonen et al., 1988). To circumvent the problem, the adequate hypotheses are tested using auxiliary regressions. Suitable auxiliary regressions apply Taylor series expansions of the transition functions. The third-order Taylor series expansion is a preferred form of the test because it embeds tests against logistic and exponential/quadratic STAR models, along with the general test against STAR-type nonlinearities (below I will briefly describe the algorithm of the STAR model selection, for more details of the testing procedure, refer to Eitrheim & Terasvirta, 1996; Luukkonen et al., 1988; Terasvirta & Anderson, 1992). The testable auxiliary equation is expressed as follows:

• (6)

where and x_t are the dependent and independent variables in the model, as defined above (note, that Equation (6) is equivalent to Equation (2) with a third-order Taylor series expansion substituted for the transition function). = 0,…, 3, are vectors of the auxiliary regression parameters to be estimated, and . The underlying hypotheses are: for no nonlinearity, and for no logistic nonlinearity, and for no exponential (or quadratic) nonlinearity. The F version of the LM test statistic is preferred for the small and moderate samples (e.g., van Dijk et al., 2002):

• (7)

where and are sums of squared residuals of the restricted and unrestricted models, respectively; q is the number of columns in the matrix of independent variables; l takes values 1 and 3, and m takes values 1, 2 and 3, depending on a hypothesis being tested; T is the total number of usable observations.

Once the suitable transition function is selected and the adequate STAR model is estimated, the next step is to test for remaining nonlinearities and parameter nonconstancy. To do so, the following auxiliary regression is applied:

• (8)

where is the residual from the estimated STAR model; , where is the estimated transition function, and and are gradients of the estimated transition function with respect to the γ and c factors of the function. The procedure of rejecting the null hypothesis of no remaining nonlinearity and parameter nonconstancy, and selecting the suitable transition variable is similar to the one used in identification of initial nonlinearities in the model. This step may be reiterated as many times as needed until the nonlinearity is absorbed at some conventional level of the statistical significance.

The final step of diagnostic testing is to evaluate the estimated model for no remaining residual autocorrelation. This is done using the following auxiliary regression:

• (9)

where is a vector of lagged residuals from the estimated smooth transition model, and other variables and parameters are as defined above.

DATA AND ESTIMATION PROCEDURE

In this research, I use monthly average CBOT nearby futures prices of corn and soybeans. I use futures prices because they closely reflect price expectations (e.g., McKenzie, 2008), and they are not averaged across different locations (as it would have been the case with the average cash prices). The series are constructed so that the futures contract rollover occurs on the last trading day prior to the delivery month. By doing so, I discard observations in the delivery month, which often appear to be excessively volatile as a result of the delivery process. Additionally, I assume that crop producers and other market participants are likely to decide on their actions throughout some extended period. In particular, I assume that farmers examine the ratio on a monthly basis to make planting decisions; or livestock producers observe crop prices on a monthly basis before making a decision regarding the feed rations, etc. For the same reasons, in this research I use monthly average prices, rather than single-day observations within a month. Furthermore, and albeit due to the reasons listed above, using monthly average prices appears to be a preferred choice in the relevant literature (e.g., Du & Hennessy, 2008; Holt & Craig, 2006; Irwin & Good, 2009).

I obtain the soybean-to-corn price ratio by simply dividing soybean futures prices by corn futures prices. I further transform the ratio to the natural logarithm form to mitigate potential heteroskedasticity usually associated with the price data, and also to analyze effects in percentage changes, which is also consistent with the existing literature (e.g., Carter & Smith, 2007; Holt & Craig, 2006).

The time series ranges between January 1976 and December 2010. The price series and the soybean-to-corn price ratio are presented in Figure 1. An apparent comovement of the prices can be seen (from here forward whenever price is mentioned it is to be considered as a natural logarithm of the futures price unless otherwise stated). Note that the given specification of the soybean-to-corn price ratio implies cointegration of a form , where and are soybean and corn prices, respectively; would be a historical mean of the soybean-to-corn price ratio, and would be an error-correction term. It is then followed that the Augmented Dickey-Fuller (ADF) test of stationarity of the price ratio becomes equivalent to a cointegration test, with being a cointegrating vector in a log-linear relationship of corn and soybean prices (see also, Goodwin et al., 2010).1

Figure 1. Corn and Soybean Prices, and the Soybean-to-Corn Price Ratio.

Linear AR models are used to examine the unit root hypothesis in the soybean-to-corn price ratio. The ADF test statistics failed to reject the stationarity hypothesis in the soybean-to-corn price ratio at α = 0.01 significance level. This result is expected, and, as mentioned above, suggests cointegration between the corn and soybean prices. Nonetheless, the ADF formulation of the AR equation is maintained, with the lag length, p, set to be equal to 2, based on Akaike Information Criterion (AIC). Finally, to account for possible seasonal effects monthly dummy variables are included in the equations. So, the linear version of the equation is expressed as follows:

• (10)

where y_t is a natural logarithm of the soybean-to-corn price ratio at time t, and D_t is a vector of monthly dummy variables; α, β, θ, and are parameters to be estimated.

The next step is to test for nonlinearities in the regression, and select the suitable transition variable and transition function. I use lagged levels, , and lagged seasonal differences, , of the soybean-to-corn price ratio as candidate transition variables, where Δ₁₂ is a seasonal difference operator, and d = 1,…, 6. Additionally, I test the model for a structural change, using t* = t/T as a transition variable. Results of these tests are presented in panel (a) of Table 1. I rank the transition variables according to the p-values associated with the H₀ hypothesis of the auxiliary regression, one with the lowest p-value being the first candidate to be considered in the STAR model. Adequate (logistic, exponential or quadratic) STAR models are estimated using candidate transition variables consecutively. The final selection of the transition variable is made if the , such that , where k = 1,…, j − 1. At this stage of the testing framework, there is no evidence of the potential structural change. Note that this finding does not necessarily imply an absence of a structural change in each respective crop price dynamics. However, the finding suggests that the dynamics in the relative terms have not been altered substantially.

Table 1. Nonlinearity and other Diagnostic Test Results

Transition variable	H0	H03	H02	H01	Transition function
Note Values in the table are p-values of the respective test statistics. The column headed H0 denotes p-values of the overall tests against nonlinearity; the columns headed H03 and H01 denote p-values of the tests against logistic nonlinearity; the column headed H02 denotes p-values of the tests against exponential (or quadratic) nonlinearity. st denotes the STC at period t, and Δ12 is a seasonal (12-month) difference operator; t* = t/T is a normalized trend variable. Finally, e2, e4, and e6 denote residual autocorrelation test statistics, and ARCH2, ARCH4, and ARCH6 denote autoregressive conditional heteroskedasticity test statistics of order 2, 4, and 6, respectively.
(a) Tests against STAR-type nonlinearities and parameter nonconstancy
st-1	0.0024	0.1683	0.3387	0.0004	LSTAR
st-2	0.0007	0.0371	0.4181	0.0004	LSTAR
st-3	0.0115	0.1442	0.6943	0.0012	LSTAR
st-4	0.0296	0.3824	0.2424	0.0096	LSTAR
st-5	0.1794	0.7437	0.4060	0.0262
st-6	0.4491	0.8013	0.7581	0.0528
Δ12st-1	0.1016	0.5621	0.0489	0.2109
Δ12st-2	0.5452	0.5875	0.3348	0.5680
Δ12st-3	0.2333	0.1607	0.3257	0.5101
Δ12st-4	0.0131	0.0242	0.0409	0.4607	LSTAR
Δ12st-5	0.0290	0.3417	0.0167	0.2002	ESTAR/QSTAR
Δ12st-6	0.0583	0.1309	0.1236	0.2543
t*	0.1567	0.2025	0.9191	0.0265
(b) Tests against remaining STAR-type nonlinearities and parameter nonconstancy
st-1	0.2294	0.2931	0.2554	0.3724
st-2	0.1074	0.9299	0.0031	0.4618
st-3	0.0457	0.1520	0.0188	0.6149	ESTAR/QSTAR
st-4	0.2296	0.1525	0.1630	0.7866
st-5	0.8279	0.5951	0.7003	0.7369
st-6	0.8772	0.7708	0.8810	0.4646
Δ12st-1	0.1113	0.5195	0.0295	0.3870
Δ12st-2	0.4782	0.4675	0.2151	0.7524
Δ12st-3	0.2024	0.1046	0.2394	0.7035
Δ12st-4	0.0375	0.0165	0.1153	0.6856	LSTAR
Δ12st-5	0.0544	0.2236	0.0638	0.2415
Δ12st-6	0.0823	0.1185	0.2174	0.2540
t*	0.2250	0.1339	0.9130	0.0972
(c) Residual autocorrelation and conditional heteroskedasticity in the STAR model
e2	0.7537
e4	0.9472
e6	0.8552
ARCH2	0.2102
ARCH4	0.4187
ARCH6	0.6881

The following step is to test the estimated STAR model for no remaining nonlinearities. In the current exercise the estimated STAR model appears to have well absorbed the nonlinearities2, and again, there is no evidence of remaining parameter nonconstancy (see panel (b) of Table 1). Therefore, proceed with estimation of a two-regime STAR model, with its final specification expressed as follows:

• (11)

Finally, I evaluate the estimated model for no remaining autocorrelation (Equation (9)) or autoregressive conditional heteroskedasticity (ARCH) effects. The results of these tests are presented in panel (c) of Table 1. There is no evidence of remaining residual autocorrelation, which allows us to proceed with the generalized impulse-response analysis (described in the following section) using residual bootstrapping procedure.

RESULTS

The estimated STAR model indeed suggests improvement in fit (AIC = −6.144) vis-á-vis the linear AR model (AIC equals; −6.116). The transition function of the estimated STAR model is:

• (12)

where values underneath the estimated parameters, in the parentheses, are asymptotic probability values of the estimated smoothness and location parameters. The low value of the smoothness parameter ( = 2.351) suggests a smooth transition between the two extreme regimes, which is better illustrated in Figure 2. Note, that the switch between the regimes is centered around 0.747, which, in real terms, is approximately 2.11. This value is about 0.40 − 0.80 lower than the historically observed break-even price ratio (Lin & Riley, 1998), suggesting that the dynamics of the soybean-to-corn price ratio alters when relative prices of corn are well above the historically observed levels. Notably, because of the smooth transition between the regimes, I observe a continuous range of switching points, rather than a fixed switching point. That is, at a given period of time a set of parameters underlying the dynamics of the soybean-to-corn price ratio, , will be a weighted average of and , where and , and where the weights are and , respectively. This result reveals interesting features of crop producers’ and market participants’ behavior: First, crop producers and agents are possibly heterogeneous in their decision making, with different STC switching points being triggers to alter their behavior; and second, the break-even price ratio varies across different regions of the United States (Lin & Riley, 1998), so even if crop producers were homogeneous in their decisions, they would still adjust their acreage allocation with respect to the different levels of the STC, thus resulting in smooth transition between the regimes.

Figure 2. Selected Transition Variable and Estimated Transition Functions. The right-hand-side plot illustrates the ordered transition function.

To better illustrate nonlinear dynamics of the soybean-to-corn price ratio I employ generalized impulse-response functions (GIRFs) of Koop Pesaran, and Potter (1996).3 GIRFs are particularly suitable for impulse-response analyses in nonlinear framework, and this approach has been extensively used in the applied literature (e.g., Chen & Lee, 2008; Holt & Craig, 2006). In what follows, I will briefly describe a procedure used to obtain GIRFs for the purposes of this study. For a given shock, ν, and history, ω, GIRF is defined as follows:

• (13)

where is a dependent variable, and h is a horizon of the shock effect. In this research, a stochastic simulation approach is used to obtain the estimates of the GIRF. That is, given a particular subset of histories, ℑ, the GIRF is defined as:

• (14)

where

• 

and where J is a total number of histories within the subset. The expected realizations of are obtained using a bootstrap resampling procedure, so that:

• (15)

where

• 

and where R is a total number of bootstrap iterations; φ is a vector of estimated parameters defining the dynamics of the dependent variable, and is an idiosyncratic shock, randomly drawn from the pool of estimated residuals.

GIRFs associated with the positive and negative shocks to the soybean-to-corn price ratio are obtained for three distinct regimes (subsets of histories) of the soybean-to-corn price ratio: the low STC regime, the medium STC regime, and the high STC regime. A set of 20 histories with the lowest soybean-to-corn price ratio values, a set of 20 histories with the largest soybean-to-corn price ratio values, and finally, a set of 20 histories with the lowest absolute soybean-to-corn price ratio values are selected. Further, (with replacement) 1000 vectors of idiosyncratic shocks (innovations) of lengths equal to 60 (5-year horizon) are randomly drawn from the pool of residuals of the estimated model. As such, 20,000 vectors of GIRFs of 60-month horizon length are generated for each shock sign and regime combination. The shock size is set to be equal to 0.2, i.e., 20% change of the soybean-to-corn price ratio. Expected GIRFs are obtained by averaging GIRF vectors across the subset of histories and vectors of random innovations, and are presented in Figure 3. The empirical distribution of GIRF vectors are used to present statistical significance (at α = 0.05 level) of each expected impulse-response function.

Figure 3. Generalized Impulse-Responses to the Relative Price Shocks. Dots on the illustrated generalized impulse-response functions denote statistical significance at α = 0.05 level.

The plots show apparent shock sign- and history-specific asymmetries in the soybean-to-corn price ratio. Several features of interest are revealed in these plots. First, there is a faster mean-reversion following a shock in the low STC regime, compared to the medium and high STC regimes. This outcome suggests that when the relative prices of corn are higher than the historical average, the adjustment to the long-run equilibrium happens in a matter of just a few months. Alternatively, when the relative corn prices are low in comparison to the historical average the price adjustment following a shock is rather slow and takes up to 2 years before prices converge to their long-run equilibrium.

Second, the shock sign-specific asymmetries are especially apparent in the medium STC regime, that is, when corn and soybean prices are in their long-run equilibrium. In which case, a positive or a negative shock will almost surely bring the soybean-to-corn price ratio to one of the extreme regimes. The prices return to their long-run equilibrium faster (within a few months) after a negative shock, compared to a positive shock when it takes up to 1 year for prices to converge.

The implication of this type of asymmetric behavior is that (more) farmers and other market participants are likely to react to higher relative corn prices, rather than to higher relative soybean prices. For example, given the favorable relative prices, farmers are more likely to switch to corn production, rather than soybean production.

Conclusions

This study applies recent advancements in time series econometrics to analyze nonlinear dynamics of the soybean-to-corn price ratio. The expectations were that the co-movement of corn and soybean prices could have been characterized with an asymmetric behavior, partly due to nonlinearities in supply response elasticities, and possibly also because of presence of a transactions cost threshold, beyond which agents are more likely to react on the relative price changes; otherwise, they would be reluctant to do so. Additionally, a possible structural change in the soybean-to-corn price ratio was investigated, which may have occurred in response to the recent government policies favoring biofuel production.

The results of this study did not reveal a statistically significant evidence of the structural change in the soybean-to-corn price ratio dynamics. This is an interesting finding, especially given that the mid-2000s are considered the beginning of a new era, potentially with distinct crop price dynamics (e.g., Irwin & Good, 2009). There is hardly any doubt that the biofuel era has affected crop production and use practices, and has brought a structural change in corn-energy and, perhaps, soybean-energy price relationships. However, the results of this study also suggest that nothing has happened to fundamentally alter the arbitrage between corn and soybean markets.

Asymmetries in the soybean-to-corn price ratio dynamics were found. After examination of the results, it can be argued that these asymmetries well depict the fact that given the circumstances, crop producers are more eager to switch to corn production than soybean production. In addition, a range of switching points was found linking the two extreme regimes in a smooth and continuous manner. This may be suggestive of heterogeneity of crop producers, which could also be a factor of farmers facing different break-even price ratios across different U.S. regions. These findings have apparent implications to market participants, as well as crop input suppliers. For example, considering that corn and soybean production require different amounts of fertilizer, the demand for the latter, is likely to vary to some extent depending on current and past levels of the relative prices of corn and soybeans.

Finally, the results of this study also motivate a few directions for future research. First, it would be interesting to examine nonlinear dynamics of other crop pairs, for example the wheat-to-corn price ratio (see also, Lin & Riley, 1998). As well, it would be interesting to investigate nonlinear dynamics and structural change in a system of prices of more than two crops, in which case a multivariate version of the current modeling framework would be a suitable approach.

1. 1

   Alternatively, cointegration between the price series can be examined using more conventional methods, such as maximum likelihood approach of Johansen (1988) and Johansen and Juselius (1990). Cointegration using Johansen's procedure was investigated and the presence of one cointegrating vector was suggested. Moreover, the hypothesis of β_STC = 1,−1,−β′_μ as a cointegrating vector could not be rejected. The test results are available upon request.

2. 2

   There are a couple of exceptions as seen in panel (b) of Table 1. However, multiple-regime STAR models did not improve fit, based on AIC. Therefore, a two-regime STAR model was settled on.

3. 3

   For the sake of brevity, the estimated model parameters are not presented here, but they are available upon request.

Biography

• Dr. David Ubilava is a Post-Doctoral Researcher at the Department of Agricultural Economics, Mississippi State University. He obtained his doctorate degree from the Department of Agricultural Economics, Purdue University. Dr. His current research includes modeling and forecasting agricultural commodity prices using nonlinear time series techniques, with particular interests in effects of large-scale medium-frequency weather anomalies on commodity price dynamics.