Food security under global economic policy uncertainty: fresh insights from the ocean transportation of food

Abstract

The Russian–Ukrainian conflict has led to ongoing disruptions in global agricultural prices and maritime transport markets, exacerbating food insecurity and raising concerns about the ocean transportation of food. To comprehend this complex relationship, this study employs a vector autoregression model to investigate the time-varying nonlinear connection among global economic policy uncertainty (GEPU), food prices, and maritime transport. Utilizing bivariate and multivariate wavelet frameworks, we validate and explore the lead-lag relationships, co-movements, and dynamic associations among these indicators across various time and frequency domains. The findings reveal a significant covariance among the variables, with medium- and long-term changes being more affected by short-term shocks. Furthermore, there exists both positive and negative interdependence among the variables in the long term, with the interdependence strengthening progressively from the medium to the long term. Notably, the volatility of ocean freight rates has exceeded that of food prices in recent years, thus, impacting future economic policy directions. These results provide a warning to food trade participants as well as governments that focusing on transport market volatility to smooth out food market and economic policy volatility ought to be an important preoccupation, together with increased attention to the potential consequences of global economic policy changes, in order to ensure greater market stability and sustainability in the transportation of food.

Appendices

Appendix 1: Methodology

1.1 Vector autoregression

A VAR model with k lags of N variables is expressed as follows.

$${Y}_{t}=\mu +{\Pi }_{1}{Y}_{t-1}+{\Pi }_{2}{Y}_{t-2}+\cdots +{\Pi }_{t}{Y}_{t-k}+{u}_{t}, {u}_{t}\sim {\text{IID}}\left(0,\Omega \right)$$

(1)

where ${Y}_{t}={\left({y}_{1,t}{y}_{2,t}\dots {y}_{N,t}\right)}^{\mathrm{^{\prime}}}$, $\mu ={\left({\mu }_{1}{\mu }_{2}\dots {\mu }_{N}\right)}{\prime}$, ${u}_{t}={\left({u}_{1t}{u}_{2t}\dots {u}_{Nt}\right)}^{^\prime}$,

${\Pi }_{j}=\left[\begin{array}{ccc}{\pi }_{11.j}& \cdots & {\pi }_{1N.j}\\ \vdots & \ddots & \vdots \\ {\pi }_{N1.j}& \cdots & {\pi }_{NN.j}\end{array}\right]$, j = 1,2,…k.

${Y}_{t}$ is the ${\text N}\times 1$-order time-series column vector. $\mu$ is the ${\text N}\times 1$-order constant term column vector. ${\Pi }_{1}$, …,${\Pi }_{k}$ are ${\text N}\times {\text N}$ parameter matrices. ${u}_{t}\sim\mathrm{IID}\left(0,\Omega \right)$ is a random error column vector of order ${\text N}\times 1$, where each element is non-autocorrelated, but there may be correlations between the random error terms corresponding to different equations. Since the right-hand side of each equation in the VAR model contains only lagged terms of the endogenous variables, which are uncorrelated with ${{\text{u}}}_{{\text{t}}}$, each equation can be estimated in turn using the OLS method, and the parameter estimates obtained are consistent.

In addition to satisfying the smoothness condition, the VAR model should be built with correctly determined lags k. If there are too few lags, the autocorrelation of the error terms can be severe and lead to non-consistent estimates of the parameters. This study utilizes the Akaike Information Criterion (AIC) for the selection of k values.

$${\text{AIC}} = \log \frac{{\mathop \sum \nolimits_{{t = 1}}^{{\text{T}}} \hat{u}_{t}^{2} }}{{\text{T}}} + \frac{{2k}}{{\text{T}}},$$

(2)

where ${\widehat{u}}_{t}$ denotes the residual, ${\text T}$ denotes the sample size, and k denotes the maximum lag order. The principle of choosing the value of k is to make the value of AIC as large as possible in the process of increasing the value of k.

The VAR model can be used to test whether there is a causal relationship between two variables. The test of whether there is a causal relationship between ${x}_{t}$ and ${y}_{t}$ can be done by testing whether all lags of ${x}_{t}$ can be eliminated from the equation in the VAR model with ${{\text{y}}}_{{\text{t}}}$ as the explanatory variable. For example, the equation in the VAR model with ${{\text{y}}}_{{\text{t}}}$ as the explanatory variable is expressed as follows.

$${y}_{t}=\sum_{i=1}^{k}{\alpha }_{i}{y}_{t-i}+\sum_{i=1}^{k}{\beta }_{i}{x}_{t-i}+{u}_{1,t}.$$

(3)

Then the null hypothesis for testing the existence of Granger non-causality of ${x}_{t}$ on ${y}_{t}$ is ${{\text{H}}}_{0}:{\beta }_{1}={\beta }_{2}=\dots ={\beta }_{{\text{k}}}=0$. If there is significance in the estimates of the regression parameters for any of the lagged variables of ${x}_{t}$, the original hypothesis is rejected and there is Granger causality of ${x}_{t}$ on ${y}_{t}$.

1.2 Continuous wavelet transform

The XWT ${W}_{x}\left(s\right)$ finds regions in time–frequency space where the time series show high common power. The wavelet is given as follows:

$${W}_{x}\left(s\right)={\int }_{-\infty }^{\infty }x\left(t\right)\frac{1}{\sqrt{s}}{\varphi }^{*}\left(\frac{t}{s}\right),$$

(4)

where * represents the complex conjugate and the scale parameter ${\text{s}}$ determines whether the wavelet can recognize higher or lower elements of the series $x\left(t\right)$, possible when the admissibility condition yields.

1.3 Wavelet coherence

The wavelet coherence technique (WTC) is efficient in capturing the localized interdependence through series in the time and frequency domains (Torrence and Compo 1998). The cross-wavelet of two series $x\left(t\right)$ and $y\left(t\right)$ can be written as follows:

$${W}_{n}^{xy}\left(u,s\right)={W}_{n}^{x}\left(s,\tau \right){W}_{n}^{y*}\left(s,\tau \right),$$

(5)

where ${\text{u}}$ denotes the position, $s$ is the scale, and * denotes the complex conjugate (Torrence and Webster 1999). The WTC can be calculated as follows:

$${R}_{n}^{2}\left(s,\tau \right)=\frac{{\left|S\left({s}^{-1}{W}_{n}^{xy}\left(s,\tau \right)\right)\right|}^{2}}{S\left({s}^{-1}{\left|{W}_{x}\left(s,\tau \right)\right|}^{2}\right)S\left({s}^{-1}{\left|{W}_{y}\left(s,\tau \right)\right|}^{2}\right)},$$

(6)

where $S$ connotes the smoothing process for both time and frequency at the same time. ${R}_{n}^{2}\left(s,\tau \right)$ is in the range $0\le {R}^{2}\left(s,\tau \right)\le 1$.

The formula of the PWC tool, which allows us to determine the WTC between two series $\left(y,{x}_{1}\right)$ after cancelling out the impact of a third series $\left({x}_{2}\right)$, is as follows:

$${RP}^{2}\left(y,{x}_{1},{x}_{2}\right)=\frac{{\left|R\left(y,{x}_{1}\right)-R\left(y,{x}_{2}\right)\cdot R\left(y,{x}_{1}\right)\right|}^{*2}}{{\left[1-R\left(y,{x}_{2}\right)\right]}^{2}{\left[1-R\left({x}_{1},{x}_{2}\right)\right]}^{2}}.$$

(7)

The PWC is expressed in squared form, i.e., ${RP}^{2}$. The value of PWC is between 0 and 1 (Mensi et al. 2021). ${RP}^{2}\left(y,{x}_{1},{x}_{2}\right)$ and ${RP}^{2}\left(y,{x}_{2},{x}_{1}\right)$ demonstrate the impacts of ${x}_{1}$ on y after eliminating ${x}_{2,}$ and ${x}_{2}$ on y after eliminating ${x}_{1}$, respectively.

The MWC approach has the power to explore the coherence of multiple variables on a single-dependent variable. Multiple wavelet coherency, like PWC, can be understood in terms of multiple correlations. Multiple wavelet coherency, as opposed to PWC, identifies and estimates the contributions of multiple independent variables ${x}_{1}$ and ${x}_{2}$ on a dependent variable y. As a result, MWC can be written as follows:

$${RM}^{2}\left(y,{x}_{2},{x}_{1}\right)=\frac{{R}^{2}\left(y,{x}_{1}\right)+{R}^{2}\left(y,{x}_{2}\right)-2Re\left[R\left(y,{x}_{1}\right)\cdot {R\left(y,{x}_{2}\right)}^{*}\cdot R\left({x}_{1},{x}_{2}\right)\right]}{1-{R}^{2}\left({x}_{1},{x}_{2}\right)}.$$

(8)

Appendix 2: A detailed analysis of Fig. 4

Figure 4 illustrates the coherence plots between GEPU, CRB, and BPI during the period of analysis for both PWC and MWC. Figure 4a displays the PWC between GEPU and CRB after removing the effect of BPI. Some significant correlations can be observed between GEPU and CRB at both low and medium frequencies at different time periods, corresponding to some red significant regions identified at different levels. Similarly, in the long term (32–64 months), there are some significant regions. However, in Fig. 4b, we observe a relatively different trend. The inclusion of the BPI indicator in the association between GEPU and CRB resulted in strong correlations in the high-frequency band regions throughout the sample period. In particular, this effect widens in 2004–2008 and 2018–2022. PWC and MWC identified a dramatic effect of BPI when examining the link between GEPU and CRB.

PWC describes the relationship between CRB and BPI after the removal of GEPU, as shown in Fig. 4c. There is a synergistic movement between CRB and BPI in the short- and long-term frequencies from 2000 to 2016, with strong fluctuations also seen in the short term from 2016 to 2018 and after 2020, as well as in some small areas in the long term. Fewer areas show stronger fluctuations in medium-term frequencies. In contrast, when considering GEPU in the context of the interrelationship between CRB and BPI, it is evident that a larger region of strong fluctuations is found in the corresponding medium-term frequencies from 2006 to 2010, as shown in Fig. 4d. Overall, PWC and MWC identified a considerable influence of GEPU when examining the relationship between CRB and BPI.

Figure 4e reports the PWC between BPI and GEPU after excluding the CRB indicator. Over the sample period, there is a more dispersed and strongly volatile relationship between BPI and GEPU on short- and medium-frequency scales. Similarly, Fig. 4f shows that this relationship is significantly stronger and spreads to higher-frequency scales. Figure 4f measures the MWC between BPI and GEPU using the effect of the CRB indicator. Extremely strong joint motion is detected at all frequencies. This implies that it is appropriate to consider the use of multivariate analysis.