Literature review

The linkage between energy and agricultural commodity markets has been extensively studied, especially in the aftermath of the 2007–2008 food and energy price spikes. Numerous studies attribute rising food prices to macroeconomic uncertainty, supply-demand imbalances, exchange rate volatility, biofuel policies, and increased speculative activity (Avalos 2014; Headey and Fan Reference Headey and Fan2008; Yuan et al. Reference Yuan, Tang, Wong and Sriboonchitta2020). Among these drivers, energy prices – particularly oil and natural gas – have received significant attention due to their central role in modern agriculture.

Energy affects agriculture through both direct and indirect channels. The direct channel encompasses input costs related to mechanization, irrigation, transportation, and processing. The indirect channel operates through the energy-dependance of key agricultural inputs, notably synthetic fertilizers and pesticides (Aye and Odhiambo Reference Aye and Odhiambo2021; Woods et al. 2010). Oil prices, for example, influence fuel and logistics costs, while natural gas serves as a primary feedstock for nitrogen-based fertilizers such as Urea (Pimentel and Pimentel Reference Pimentel and Pimentel2008).

Although this dual channel is theoretically well established, empirical studies have yielded mixed results. Some studies report weak or neutral relationships between crude oil and agricultural commodity prices (Nazlioglu Reference Nazlioglu2011; Yu et al. Reference Yu, Wang and Lai2008; Zhang et al. Reference Zhang, Lohr, Escalante and Wetzstein2010), while others find positive and significant co-movements (Avalos and Lombardi Reference Avalos and Lombardi2015; Chen et al. Reference Chen, Kuo and Chen2010; Jadidzadeh and Serletis Reference Jadidzadeh and Serletis2018; Sun et al. Reference Sun, Mirza, Qadeer and Hsueh2021). Still others suggest asymmetric spillovers or structural breaks associated with financialization and speculative behavior (Al-Maadid et al. Reference Al-Maadid, Caporale, Spagnolo and Spagnolo2017; Bonato and Taschini Reference Bonato and Taschini2016).

Fertilizers represent a critical yet underexplored component in the transmission of energy prices to agricultural commodity prices. Nitrogen (N), phosphorus (P), and potassium (K) fertilizers are essential for yield growth and are highly energy-intensive to produce. Di-Ammonium Phosphate (DAP), widely used in cereal production, relies heavily on oil-based inputs for transportation and processing. Urea, the most commonly used nitrogen fertilizer globally, is synthesized from ammonia – derived primarily from natural gas (Ding et al. Reference Ding, Ye, Fu, He, Wu, Zhang, Zhong, Kung and Fan2023; Heffer and Prud’homme Reference Heffer and Prud’homme2016). Wongpiyabovorn and Hart (Reference Wongpiyabovorn and Hart2024) conduct an ARDL analysis to examine the pass-through relationship between natural gas and corn prices on nitrogen fertilizer prices in the U.S., taking into account the biofuel mandates, improvements in shale gas extraction after 2009 and the strong dependance of corn production on fertilizer costs. Even though their study is limited to the US, they claim that the global natural gas shocks have emerged as a factor affecting fertilizer prices.

Studies highlight the global importance of fertilizers in supporting grain output and stabilizing productivity (Aghabeygi et al. Reference Aghabeygi, Louhichi and Gotor y Paloma2022; McArthur and McCord Reference McArthur and McCord2017). Increases in global fertilizer prices – driven in part by energy markets – can thus have significant delayed effects on crop markets. Despite this, the empirical literature often treats fertilizer prices as exogenous or omits them entirely from price transmission models.

A recurring limitation in the literature is the reliance on linear models or symmetric volatility frameworks that may overlook nonlinearities and evolving price dynamics. Moreover, few studies explicitly separate direct energy effects from indirect fertilizer-driven effects. The joint behavior of energy and fertilizer prices – especially their conditional covariances – has received limited attention despite its potential importance during times of global market stress.

This study addresses these gaps by modeling both direct and indirect linkages from energy to agriculture, employing conditional covariances extracted from BEKK-GARCH models, and controlling for non-linearities via the Flexible Fourier Form. To our knowledge, this approach is novel in the context of energy-agriculture price dynamics and offers a more nuanced view of co-movement and volatility spillover effects.

Data and methodology

This study employs monthly data spanning the period from February 1991 to February 2021 to investigate the direct and indirect effects of energy prices on agricultural commodity prices. To ensure completeness and reflect recent market developments, the dataset has also been extended to cover the period up to December 2024, following the same methodological framework. The extended results, presented in the Appendix, allow for an updated comparison while maintaining the original sample as the primary focus of analysis, given its coverage of a relatively stable pre-war period that ensures methodological consistency and comparability. The focus is on three major grains – wheat, maize, and soybeans – due to their global production and trade significance (Erenstein et al. Reference Erenstein, Chamberlin and Sonder2021; Szerb et al. Reference Szerb, Csonka and Fertő2022). Crude oil and natural gas prices serve as proxies for energy inputs, while Di-Ammonium Phosphate (DAP) and Urea represent fertilizer inputs.

Crude oil is used as a benchmark for energy, represented by the average spot price of Brent, Dubai, and West Texas Intermediate. Natural gas is captured via a Laspeyres index averaging prices across Europe, the U.S., and Japan. The agricultural commodity prices are based on trade-relevant benchmarks: U.S. No. 2 yellow corn (f.o.b. Gulf ports), U.S. No. 2 hard red winter wheat (Gulf export), and U.S. No. 2 yellow soybean meal (CIF Rotterdam). Fertilizer prices are represented by DAP (spot, f.o.b. U.S. Gulf) and Urea (spot, f.o.b. Black Sea).

All price data are sourced from the World Bank’s Commodity Price Data – “Pink Sheet” (World Bank 2023). Table 1 presents an overview of variable definitions and sources.

Table 1. Variable names, and descriptions

Source: World Bank.

The descriptive statistics of the variables are presented in Table 2. There are 362 observations for each variable. Between February 1991 and February 2021, the Crude Oil price varied between 10.4 and 132.8, with a mean and standard deviation of 48.5 and 31.8. Ngas price varied between 28.9 and 222.1, with a mean and standard deviation of 77.9 and 38.4. Among fertilizer items, Urea and DAP show dramatic price movement from 62.7 to 785, 112.7 to 1075.7 respectively, with a mean and standard deviation of 208.6 and 118.7, 291 and 163.7 respectively. Maize, wheat, and soybean prices also fluctuated significantly in the sample period, ranging from 75.2 to 333, 102.1 to 439.7, and 75.2 to 333 respectively. Soybean has the highest mean value and DAP has the highest standard deviation. According to JB statistics, it is evident that all price series exhibit a non-normal distribution.

Table 2. Descriptive statistics

Source: Authors calculation.

When beginning the analysis, standard unit root tests are used to examine the stochastic properties of the variables. As seen in Table 3, only fertilizer series (Dap and Urea) are I(0), but others are I(1). Therefore, there is a unit root problem in most of the series.

Table 3. Unit root test results

Notes: *1% and **5%.

Critical values for Dickey-Fuller and Philips-Perron are −3.983, −3.422, −3.134 (1%,5%,10% respectively).

Since, in traditional tests, the null hypothesis is one of the unit-root linearity, for the identification of the nonlinear structure (state-dependent or time-dependent) of the variables, a battery of tests (Leybourne, Newbold, and Vougas (LNV), Reference Leybourne, Newbold and Vougas1998 and Kapetanios, Shin and Shell (KSS), Reference Kapetanios, Shin and Snell2003) is employed to see whether each variable is governed by a stationary process with different nonlinear structures. As seen in Table 4, LNV model-b is the most suited one, but still wheat, maize, and soybean series are insignificant.

Table 4. Unit root test results

Notes: *1%, **5% and ***10%.

1-raw data; 2-De-meaned; 3-De-meaned and de-trended; 4-Lnv Model-a; 5-Lnv Model-b; 6-Lnv Model-c.

Critical values for KSS – raw data −2.82, −2.22, −1.92; De-meaned, −3.48, −2.93, −2.66; De-trended, −3.93, −3.40,−3.13 (1%,5%,10% respectively).

Critical values for LNV – Model a, −4.88,−4.23,−3.91; Model b, −5.48, −4.77, −4.43; Model c, −5.65, −5.01, −4.70 (1%,5%,10% respectively).

According to Becker et al. (Reference Becker, Enders and Lee2006), employing a Fourier function allows smooth changes when performing a unit root test. The Fourier approach’s fundamental benefit is its capacity to accurately model the behavior of deterministic functions of unknown form, even when the function is not periodic in nature. Therefore, it is not necessary to define the location, kind, or quantity of breaks. The Flexible Fourier Form allows for greater flexibility in modeling periodic components, therefore models based on the Flexible Fourier Form may provide more accurate forecasts especially when the data have nonlinear patterns (Enders and Lee Reference Enders and Lee2012). In order to do this, the Flexible Fourier Form and DF type Unit Root test (FFF), as recommended by Enders and Lee (Reference Enders and Lee2012), is used.

The following Equation is estimated to compute the FFF test statistic:

(1) $${\rm{\Delta }}{y_t} = \alpha + \beta t + \mu {y_{t - 1}} + {\delta _{1k}}\sin \left( {2\pi kt/T} \right) + {\delta _{2k}}\cos \left( {2\pi kt/T} \right) + {e_t}$$

In Equation (1), π = 3.1416, t, T, and k indicate the trend term, sample size, and a particular frequency. To determine the optimal value of frequency, k*, Equation (1) is estimated for the values of k, and the value that produces the minimum residual sum of squares (RSS) is chosen.

As seen in Table 5, all variables in question are stationary.

Table 5. Enders and Lee (Reference Enders and Lee2012) Flexible Fourier Form and DF type unit root test results

Notes: *1% and **5%.

(Critical values for FFF – constant), −4.62, −4.01, −3.69(1%, 5%, 10% respectively for k = 2); −4.38, −3.77, −3.43(1%, 5%, 10% respectively for k = 3); Constant, trend −3.93, −3.26, −2.92(1%, 5%, 10% respectively for k = 2); –3.74, −3.06, −2.72(1%, 5%, 10% respectively for k = 3).

Since the assumption of stationarity is generally satisfied, to pretest for a nonlinear trend, Becker et al. (Reference Becker, Enders and Lee2006) followed to test the null hypothesis of linearity against the alternative of a nonlinear trend with a given frequency k. Enders and Lee (Reference Enders and Lee2012) propose the use of the following F-statistic:

(2) $$F\left( k \right) = {{\left( {SS{R_0} - SS{R_1}\left( k \right)} \right)/2} \over {SS{R_1}\left( k \right)/(T - q)}}$$

where $SS{R_1}\left( k \right)$ denotes the sum of squared residuals (SSR) when Fourier transforms enter the equation, q is the number of regressors, and $SS{R_0}$ denotes the SSR from the regression without the trigonometric terms. In all cases, the null is rejected in favor of a nonlinear trend, given the frequency k.

From the FFF unit root test result, we see that all series have stationarity features. The process is stationary after employing the detrending. It should be noted that the main contribution of the nonlinear trend is the elimination of the unit root problem which results in an explosive model. The Fourier transform of the wheat, maize, and soybean series is given in Figure 1–3. The Fourier trends of the series in question are calculated for the estimation process.

Figure 1. Fourier transformation of wheat prices.

(Source: WorldBank and Authors calculations).

Figure 2. Fourier transformation of maize prices.

(Source: WorldBank and Authors calculations).

Figure 3. Fourier transformation of soybean prices.

(Source: WorldBank and Authors calculations).

Next, it is assumed that co-movements between crude oil and DAP and Urea and natural gas may influence the price determination of wheat, maize, and soybeansFootnote ¹ . The conditional covariances can only be obtained from the BEKK-GARCH model. The aim is not to use the BEKK-GARCH model itself, but to extract conditional covariances from within the model. To that respect, conditional covariance between crude oil and DAP and Urea and Ngas is estimated in a bivariate fashion. For example, let and denote the crude oil and DAPprices (Urea and natural gas prices) respectively. The VAR system then is stated as follows:

(3) $${x_t} = {\phi _1} + \mathop \sum \nolimits_{i = 1}^{p - 1} {\varphi _{1i}}{x_{t - i}} + {\varepsilon _t}$$

where ${x_t}$ is a (2 × 1) column vector given by ${x_t} = {({X_{1t}},{X_{2t}})'}$ , ${\varphi _j}$ j = 1,2 are (2 × 1) vector of constants, ${\phi _{j,i}}$ , $j = 1,2$ , $i = 1, \ldots, p$ are (2 × 2p) matrix of parameters, and ${\varepsilon _t} = \left( {{\varepsilon _{1t}},{\varepsilon _{2t}}} \right)$ is a (2 × 1) vector of residuals. Residuals are assumed to be conditionally normal with mean vector $\boldsymbol 0$ and covariance matrix ${{\boldsymbol H}_t}$ , that is, $\left( {\left. {{\varepsilon _t}} \right|{{\it\Omega} _{t - 1}}} \right)\ {\rm{\sim N}}\left( {{\boldsymbol 0},{{\boldsymbol H}_t}} \right)$ where ${\Omega _{t - 1}}$ is the information set available at time t–1. It is assumed that the conditional covariance matrix ${{\boldsymbol H}_t}$ has the GARCH(1,1) structure proposed by Bollerslev (1990)Footnote ² :

$${h_{{x_1}t}} = {\alpha _{{x_1}}} + {\beta _{{x_1}}}{h_{{x_1},t - 1}} + {\gamma _{{x_1}}}\varepsilon _{{x_1},t - 1}^2,$$

(4) $${h_{{x_2}t}} = {\alpha _{{x_2}}} + {\beta _{{x_2}}}{h_{{x_2},t - 1}} + {\gamma _{{x_2}}}\varepsilon _{{x_2},t - 1}^2$$

$${h_{{x_{1,2}}t}} = {\alpha _{{{\rm{x}}_{1,2}}}} + {\beta _{{{\rm{x}}_{1,2}}}}{h_{{x_1},t - 1}}{h_{{x_2},t - 1}} + {\gamma _{{x_{1,2}}}}\varepsilon _{{x_{1,}},t - 1}^2\varepsilon _{{x_2},t - 1}^2$$

where ${h_{{x_1}t}}$ and ${h_{{x_2}t}}$ are the conditional variances of oil and DAP (Urea and natural gas) respectively, and ${h_{{x_1}{,_2}t}}$ is the conditional covariance between di-ammonium phosphate (Urea) residuals ${\varepsilon _{st}}$ and crude oil (natural gas) residuals ${\varepsilon _{ot}}$ . It is assumed that ${\alpha _i}$ and $\;{\gamma _i} \gt 0$ , ${\alpha _i} \ge 0$ for $i = 1,2$ and $ - 1 \le p \le 1$ in (4).

The conditional covariance between di-ammonium phosphate and crude oil, estimated by BEKK GARCH(1,1) is given in Equation (5) and Urea, natural gas is presented in Equation (6) with p-values in parenthesis.

(5) $$\eqalign{{h_{{x_{1,2}}t}} = \; & - 0.921 + 0.044{h_{{x_1},t - 1}}{h_{{x_2},t - 1}} + 1.015\varepsilon _{{x_{1,}},t - 1}^2\varepsilon _{{x_2},t - 1}^2 \cr & \ \ \ (0.451) \quad \quad (0.009) \quad \quad \quad \quad \quad (0.000)}$$

(6) $$\eqalign{{h_{{x_{1,2}}t}} = & \; - 8.501 + 0.023{h_{{x_1},t - 1}}{h_{{x_2},t - 1}} + 0.956\varepsilon _{{x_{1,}},t - 1}^2\varepsilon _{{x_2},t - 1}^2 \cr & \ \ \ (0.095) \quad \quad (0.000) \quad \quad \quad \quad \quad \quad (0.000)}$$

The price of Di-ammonium Phosphate (Urea) and the price of crude oil (natural gas) are both assumed to be I(0) processes in the econometric approach described above. Figures 4 and 5 show the covariance’s in detail. In light of this, it is shown that covariances accurately reflect the obvious peaks around the 2008 financial crisis and the volatile period aftermath.

Figure 4. Conditional covariance of crude oil and Di Ammonium phosphate.

(Source: World Bank and Authors calculations).

Figure 5. Conditional covariance of urea and natural gas.

(Source: World Bank and Authors calculations).

Analyzing the pairwise conditional covariances from Equations (5) and (6) the p-values (0.009 and 0.000 respectively) indicate strong statistical significance, suggesting the conditional covariance between the respective commodity pairs is dynamic and non-zero, and varies over time. Thus it is possible to confer that the conditional covariance estimates from the BEKK GARCH(1,1) model indicate significant time-varying co-movement between Crude Oil and Di-Ammonium Phosphate, and between Urea and Natural Gas. Additionally, the covariance series capture strong co-movement during systemic shocks such as the 2008 financial crisis, suggesting that external macroeconomic volatility propagates through both energy and fertilizer markets. The pattern is especially pronounced for the Urea–Natural Gas pair, reflecting the technological link via ammonia synthesis (gas-intensive), whereas the Oil–DAP pair additionally embeds broader energy-related pass-through via transport and processing costs. These facts support the hypothesis that fertilizer markets are partially integrated with global energy markets, with nontrivial implications for input price hedging and agricultural risk management.

In this framework, a high covariance between energy and fertilizer prices signifies periods of joint volatility, typically occurring during shocks (e.g., the 2008 financial crisis). During such episodes, uncertainty regarding input costs becomes more pronounced, prompting risk-averse behavior among producers and intermediaries. This behavior may manifest in the form of delayed production decisions, increased hedging activities, or restricted speculative inventory holdings, all of which can exert downward pressure on grain prices in the short term. In other words, elevated covariances act as “joint volatility states” that trigger a set of economic mechanisms – precautionary adjustment, de-stocking, and improved hedging alignment – that collectively dampen spot grain prices despite rising input costs. This interpretation, may be labeled as the “risk-intensification effect,” highlighting that stronger co-movement in input markets tempers short-run commodity price surges rather than amplifying them. Hence, the negative and statistically significant coefficients associated with conditional covariances should be interpreted as indicators of this risk – intensification effect. We should underline that, this negative effect of covariances does not contradict the positive pass-through of energy price levels into grain prices, but rather reflects an additional state variable that is activated in turbulent periods, offsetting part of the upward price pressure with a distinct short-run dampening mechanism.

Furthermore, the incorporation of conditional covariances aids in mitigating multicollinearity between energy and fertilizer price series, which are otherwise highly correlated. By capturing their joint variance dynamics within a single measure, the model avoids redundant information and improves coefficient estimation. The inclusion of covariances refines the computation of standard errors and t-statistics, as part of the heteroskedasticity is filtered out through the variance-covariance structure. In this regard, covariances serve both as an indicators of market co-movement and as econometric adjustments that improve the reliability and interpretability of the results. This dual role underscores their substantive contribution to the empirical framework.

More specifically, including conditional covariances allows the joint variance structure of the variables to be explicitly incorporated into the model. This reduces the impact of heteroskedasticity and potential autocorrelation in the residuals, leading to more accurate computation of standard errors and, consequently, more reliable t-statistics (Su and Hung Reference Su and Hung2018). Such an adjustment is particularly valuable in settings where market series exhibit high volatility and strong co-movement, as it helps to reduce parameter uncertainty and enhances the overall robustness of the estimation results (Brooks et al. Reference Brooks, Burke and Persand2003). Consistent with this interpretation, our estimates show that even relatively small negative covariance coefficients (≈−0.001) are statistically significant and state-dependent, aligning with the prediction that their magnitude should increase during high-volatility subsamples such as 2007–2010 or 2020.

A potential concern is whether fertilizer prices can be considered exogenous in the crop-price regressions, since they are strongly shaped by developments in energy markets. We address this by making the identification strategy explicit: crude oil and natural gas are treated as the primary drivers, while fertilizer prices are interpreted as contingent outcomes of energy cost pass-through. This structure reflects the technological asymmetry in production – fertilizer manufacturing is highly energy-intensive, with natural gas accounting for roughly 70% of ammonia/urea variable costs, and with the sector representing only a fraction of the scale of global oil and gas markets. Ammonia production accounts for about 2% of global final energy use, while the oil and gas market is much larger and deeper. Given these scale differences, feedback from fertilizers to energy is regarded as economically and theoretically negligible.

Within this framework, fertilizers are not modeled as independent shocks but as transmission channels of energy into agriculture. To further limit spurious attribution, the baseline already controls for oil and gas prices directly and incorporates conditional covariances between energy and fertilizers, ensuring that fertilizer coefficients are interpreted net of contemporaneous energy shocks. This treatment acknowledges the close link between the two markets while remaining consistent with the one-way cost-push causality from energy to fertilizers and to grains.

As mentioned earlier, the effects of the post-2021 crisis are reflected in the covariance dynamics presented in Appendix Figure 2. Although the covariances – i.e., co-movements – between DAP and crude oil exhibit a similar pattern to those between urea and natural gas, the magnitude of the urea – natural gas covariance is considerably higher. It is worth noting that in contrast to the 2007 crisis, the 2021 crisis has not yet stabilized, which accounts for the heightened volatility observed in both covariance measures. Moreover, it should be noted that the descriptive statistics and standard unit root test results provided in the section are based on the full sample, while the main statistical properties and test results of the variables are valid for both samples.