Determinants of international price volatility transmissions: the role of self-sufficiency rates in wheat-importing countries

Abstract

From the 1980s until the early 2000s, many developing governments adopted market liberalization policies due to relatively low agricultural prices and the implementation of structural programs by the IMF. Yet, a paradigm shift occurred with the emergence of the 2008 food crisis, which directed food-deficit governmental bodies to protectionist regimes supporting higher food self-sufficiency. Despite the importance of food autarky to shield domestic food markets, its effects have never been fully discussed in a formalized econometric framework. This article analyses wheat price volatility transmissions from global to local markets in 10 wheat importing countries, identifying the causality with conditional correlation functions (CCF), the degree of volatility transmissions using generalized autoregressive conditional heteroskedasticity (GARCH) models with the dynamic conditional correlation (DCC) specification and potential determinants with a panel analysis. The main findings reveal that a significant unidirectional Granger causality runs from international wheat price to local retail flour prices for wheat importing countries with an approximate five-month lag, the volatility correlations from international to local markets were strengthened around the period of the 2007–08 food crisis and a higher self-sufficiency rate plays a role in alleviating volatility passthroughs from international markets. This evidence that increasing the SSR of an agricultural commodity is effective in isolating the domestic market is valuable for policymakers in food importing countries. The primary beneficiaries of implementing the policy measure are risk-averse producers and consumers because their utility or welfare improves as the price volatility of foodstuffs declines.

Introduction

Between 2006 and 2014, global food price volatilities reduced national food security, particularly in the developing world (Ivanic and Martin, 2008), which caused social and political instability in developing regions, including Africa, Asia and South America (Bellemare, 2014)¹. For example, in 2008, Haiti’s senators fired the prime minister, Jacques Edouard Alexis, because he failed to decrease the price of rice (Delva and Loney, 2008). Global factors behind the food crisis such as poor grain harvests (Headey and Fan, 2008), low levels of grain stocks (Trostle, 2008), decline of investment in agricultural research and grain productivity (International Rice Research Institute, 2008; Von Braun et al., 2008), export restrictions (Von Braun et al., 2008; International Rice Research Institute, 2008; Meyers and Meyer, 2008), biofuel generated from food commodities (Von Braun et al., 2008; Headey and Fan, 2008; Mitchell, 2008; Abbott et al., 2008), energy price hikes (Yang et al., 2008; Headey and Fan, 2008) and financial speculation (Piesse and Thirtle, 2009; Cooke and Robles, 2009) were perceived as major driving forces of domestic food price inflations in importing countries rather than domestic factors. Under such national food insecurity circumstances, governments of importing nations, such as Senegal, India, the Philippines, Qatar and Bolivia, have expressed interest in increasing food self-sufficiency (Clapp, 2017).

Debates over national food autarky policies have long taken place (Hamilton, 1918; Keynes, 1993; Kako, 2009; Bishwajit et al., 2013; Clarete et al., 2013). Governmental administrations aim to enhance food self-sufficiency for various reasons such as concerns about food supply disruption due to war, extremely poor harvests by foreign producers and export restrictions, which could lead to vulnerable positions in diplomatic negotiations, environmental deterioration and the loss of concessions associated with farming or farmers (Clapp, 2015; Yamashita, 2016). However, many economists who espouse modern economic theories argue that agricultural autarky policies distort markets and create resource allocation inefficiencies (Naylor and Falcon, 2010). They also advise that subsidizing farmers or imposing additional import tariffs to hike food self-sufficiency undermine food security in the long term, precluding opportunities for gains in market efficiency (Cramer et al., 1999; Tanaka and Hosoe, 2011).

High food self-sufficiency is broadly regarded as a potent strategy for national food security by policymakers. Such a policy measure could lessen the degree of international price transmissions, which may interest aforementioned governments because this can enhance self-sufficiency rates (Tanaka, 2018). Bouët et al. (2012) discuss the rationales of export duties during global food crises, showing that export taxes contribute to stabilizing local markets.

Despite such an important policy for food security, few studies have examined the usefulness of food self-sufficiency policy using an econometric model, although some studies explore it with a general equilibrium model. Tanaka (2018) analyses the effects of wheat self-sufficiency policies for Egypt with a stochastic computable general equilibrium (CGE) model and Tanaka and Hosoe (2011) scrutinize the impact on households of a free-trade rice policy in Japan. Still, one of the major criticisms of a CGE model is that its parameters are estimated with a single-year dataset called a social accounting matrix (SAM), implying that the parameters are point-estimated and less reliable. On the contrary, an econometric model is established with longer time periods, which overcomes the primary concern of CGE.

Research has not yet fully examined the potential factors influencing the volatility pass-throughs between world and local markets in a formal statistical test. Previous studies primarily focus on the links between domestic markets within developing countries (e.g., Baulch, 1997; Abdulai, 2000; Lutz et al., 2006; Moser et al., 2009; Myers, 2013) and only a few studies examine the transmission of price from world to local markets, including volatility transmissions (Mundlak and Larson, 1992; Conforti, 2004; Minot, 2011; Ceballos et al., 2017; Hatzenbuehler et al., 2017). Most studies adopt an error correction method to examine the relationship between global and domestic prices based on a specific country. Nevertheless, these studies did not explore determining factors of the extent of a spill-over. While, along these lines, no studies explored such factors in a comprehensive manner (such as with a panel analysis), Götz et al. (2013) discovered that Russian and Ukrainian export restrictions during food crises helped to stabilize agricultural domestic prices.

Responding to this gap in the scholarly archive, this research concentrates on examining the relationship between self-sufficiency rates and the extent of spill-over effects from global to local markets (rather than that between food policy changes and the degree of international pass-throughs). More specifically, this article explores the determinants of wheat price volatility transmissions from international to local markets using a generalized autoregressive conditional heteroskedasticity (GARCH) model with dynamic conditional correlation (DCC) specification and three types of panel regressions. We concentrate on whether wheat self-sufficiency weakens international volatility pass-throughs, zooming in on 10 net importer nations that are not self-sufficient in wheat. The analysis was conducted during the period between January 2006 and December 2013. The model testing procedure is as follows. First, the direction of Granger causality was identified and the lead-lag relationships between international and domestic wheat prices using Hong’s (2001) conditional correlation function (CCF). Second, the volatility correlation pairs between global and local markets were measured with the GARCH-DCC approach based on the results of leads/lags estimated in the first step. Finally, a panel data analysis was conducted to identify factors that can influence long-term dynamic correlations between international and local wheat prices in wheat-importing countries. After detecting the appropriate causalities and estimations of the three empirical models, it was successfully determined that higher self-sufficiency in wheat effectively insulates domestic markets from international market volatilities.

This article makes several contributions to the existing literature. As stated, Ceballos et al. (2017) offer the only study that investigates international price volatility transmissions of cereals. Whiles Ceballos et al. employ the GARCH-BEKK model, the first international volatility transmission analysis of an agricultural good with a DCC approach was conducted, which enabled the identification of the time variant correlated relationship between global and regional markets. One advantage of using this method is that it more precisely estimates the link between correlated volatilities and underlying factors with an extended sample size, generating yearly correlation outputs differently from a GARCH-BEKK approach. This sort of factor identification econometric testing has never been performed in any prior study. In addition, this study tested the effectiveness of a self-sufficiency measure, one of the most important food security strategies that has not been econometrically examined in the literature. Furthermore, the pass-throughs with an explicit focus on the links between international wheat prices and local retail wheat flour prices were analyzed; in previous studies, it is uncertain whether the commodities focused on were wheat or wheat flour (e.g., Ceballos et al., 2017; Minot, 2011). This study aimed to fill these gaps and provide useful implications not only for policymakers, but also agricultural producers and consumers, assuming that most people are risk-averse with respect to market steadiness (Bar-Shira et al., 1994; Jianakoplos and Bernasek, 1998).

The remainder of this article is organized as follows. Section “Data description” offers a brief description of the data. Section “Econometric methodology” introduces the empirical methods. Section “Empirical” results and interpretations addresses the empirical findings and interprets the results. Section “Conclusion and policy implications discusses the policy implications” of the results and the limitations of the study.

Data description

We used monthly data from the Global Information and Early Warning System (GIEWS), which provides the monthly food commodity prices of various countries and international food prices. Retail flour prices from January 2006 to December 2013 for 10 wheat-importing countries (Afghanistan, Azerbaijan, Brazil, Cameroon, Georgia, Israel, Kyrgyzstan, Mauritania, Peru and Tajikistan) were obtained. While commodity price data are available for a number of countries in the GIEWS, only 10 regions met the study’s requirements for available data on the retail prices of wheat flour for a recent time period and of non-self-sufficiency in wheat. Following the literature, the local prices are in US dollars. The international price is the export price of wheat (US No. 2 hard red winter) from the US Gulf Coast, which is also quoted in the GIEWS. To eliminate the influence of seasonal fluctuations, we adjusted all data by using the X-13-ARIMA² method. Moreover, for each data series, continuously compounded returns were computed as $\ln (X_t/X_{t - 1}) \times 100$, where X_t represents international wheat prices (IWP) and local wheat prices in 10 wheat-importing countries (Afghanistan, Azerbaijan, Brazil, Cameroon, Georgia, Israel, Kyrgyzstan, Mauritania, Peru and Tajikistan). Figure 1 plots the returns of each variable.

Fig. 1

Time-series plots of continuously compounded returns of international and local wheat prices

Table 1 reports the descriptive statistics of returns on wheat prices (international and domestic markets). Data in this table reveal that most of the mean returns are positive, suggesting a rise in wheat prices during the study period. It is worth noting that the standard deviations of Afghanistan’s and Kyrgyzstan’s price returns are relatively higher than those of other countries. This indicates that these two countries tend to experience extreme changes in wheat prices more frequently for the two countries. Before proceeding with the causality test based on the CCF approach, it is necessary to check the stationarity of each variable. An augmented Dickey-Fuller (ADF)³ and Kwiatkowski-Phillips-Schmidt-Shin (KPSS)⁴ unit root tests were performed on the return series. The null hypothesis of the ADF test is that the series is nonstationary, whereas that of the KPSS test is that the data series is stationary. The results of the unit root tests presented in Table 1 indicate that all variables are stationary in their first log-differenced forms⁵ and integrated of order 1. This allows us to jointly model the price transmission between international and local wheat prices.In addition, Van Dijk et al. (2005) suggest pre-testing for structural breaks before examining causality. Following this, Bai and Perron’s (2003) structural change test, which allows for the simultaneous estimation of unknown multiple structural breaks, is applied to identify the structural break points in each wheat price series⁶.

Table 1 Summary statistics and pre-test for wheat price returns

The results of Bai and Perron’s (2003) structural breaks test in Table 1 show that, across all countries, only Georgia demonstrates a structural break in its price returns. Specifically, one break exists in the wheat price return of Georgia in August 2008.

In the next step, we employ yearly data, including the self-sufficiency rate (SSR) and domestic economic variables, to identify the common factors that could affect wheat price volatility transmission in importing countries. Table 2 provides the definitions of the potential factor variables used and Table 3 displays the summary statistics for the explanatory variables in the panel estimation. First, because a key assumption is that the SSR could be a significant factor in determining the dynamic correlation, the annualized SSR for each country is chosen. The SSR of wheat is defined as Production/(Production + Import – Export). The data source of each component of the SSR is the FAOSTAT⁷. Figure 2 plots the time-series SSR in each country. As Fig. 2 and Table 3 show, the SSR displays different characteristics in wheat-importing countries. For example, Afghanistan, Kyrgyzstan and Tajikistan have relatively high average SSR values, while Cameroon’s and Mauritania’s SSR display the lowest average values. It is also interesting that the SSRs of some countries (e.g., Afghanistan, Azerbaijan, Brazil and Peru) fluctuated dramatically during the 2007–2008 food crisis. Because SSR data are not available at monthly frequencies, we converted the estimated monthly conditional correlations between international and local prices into yearly frequency data⁸.

Table 2 Definitions of the variables in the panel analysis

Table 3 Summary statistics for the explanatory variables in the panel analysis

Fig. 2

Time-series plots of SSR for wheat in importing countries

Moreover, it is important to consider the substitutive effects of commodities; therefore, the annualized domestic consumption of maize and rice in each wheat-importing country were selected. Table 4 shows the levels of domestic consumption of wheat, rice and maize in each country. Wheat consumption is typically larger than those of maize and rice in all countries except Cameroon and Peru. In addition, we include macroeconomic factors—the annualized GDP per capita growth rate and annualized inflation rate⁹—to reflect the current economic conditions. The GDP and CPI data are sourced from FAOSTAT and the World Bank’s World Development Indicators online database¹⁰.

Table 4 Daily per capita caloric consumption of wheat, maize and rice

Econometric methodology

To perform the analysis, we used a three-step econometric methodology. First, we examined the Granger causality and lead-lag relationships between international and local wheat prices by employing the CCF approach. Second, we estimated the price volatility transmission between international and local wheat markets using a GARCH-DCC framework. In the final step, a panel analysis was applied to investigate the common factors that could affect wheat price volatility transmission in wheat-importing countries.

Testing Granger causality using a cross-correlation function

To examine the causality between international and local wheat prices in wheat-importing countries, Hong’s (2001) non-uniform weighting cross-correlation function (CCF) was applied. One of the key advantages of this approach is that it can detect the leading and lagging structures of causality, as well as the duration over which causality is exerted¹¹. The GARCH used in this model was introduced by Bollerslev (1986)¹² and has been widely used to estimate volatilities for time-series data¹³. Using the residuals obtained from the GARCH model, the standardized residuals $\hat \tau _t$ and $\hat \xi _t$ were estimated. Next, the sample cross-correlation coefficient at lag m, $\hat r_{\tau \xi }(m)$, was calculated from the consistent estimates of the conditional mean and variance for international and local wheat prices. This leaves us with

$$\hat r_{\tau \xi }\left( m \right) = \hat c_{\tau \xi }(m)\left\{ {\hat c_{\tau \tau }(0)\hat c_{\xi \xi }(0)} \right\}^{ - \frac{1}{2}},$$

(1)

where $\hat c_{\varepsilon \xi }(m)$ is the m-th lag sample cross-covariance given by

$$\hat c_{\tau \xi }(m) = \left\{ {\begin{array}{*{20}{c}} {T^{ - 1}\mathop {\sum}\limits_{t = j + 1}^T {\hat \tau _t\hat \xi _{t - j}} \,\;{\mathrm{for}}\,j \ge 0} \\ {T^{ - 1}\mathop {\sum}\limits_{t = - j + 1}^T {\hat \tau _{t + 1}\hat \xi _t} \,\;{\mathrm{for}}\,j \,<\, 0} \end{array}} \right.,$$

(2)

where $\hat c_{\tau \tau }$ (0) and $\hat c_{\xi \xi }$ (0) are defined as the sample variances of $\hat \tau _t$ and $\hat \xi _t$, respectively and T is the sample size.

Causality in the mean of international and local wheat prices can be tested by examining $\hat r_{\tau \xi }(m)$, the univariate standardized residual CCF. Under the regularity condition¹⁴, the following holds:

$$S = T\mathop {\sum}\limits_{i = 1}^k {\hat r^2_{\tau \xi }} (i)\mathop{\longrightarrow}\limits^{L}\chi ^2(k),$$

(3)

where $\mathop{\longrightarrow}\limits^{L}$ shows convergence in distribution and χ²(k) indicates a chi-square distribution with k degrees of freedom. To test for a causal relationship from lag 1 to k, the S-statistic was compared with the chi-square distribution. If the test statistic was higher than the critical value of the chi-square distribution, the null hypothesis. Furthermore, Hong (2001) indicates that the S-statistic weighs each lag uniformly; therefore, it may distort the amount of the presence of causality. Thus, Hong’s (2001) method was adopted, incorporating the weighting cross-correlation, which is consistent with the intuition that more recent information should be heavily weighted. The modified test statistics are defined as

$$Q = \frac{{S - k}}{{\sqrt {2k} }}\mathop{\longrightarrow}\limits^{L}N(0,1).$$

(4)

The Q-statistic is assumed to follow an upper-tail normal distribution. This test allowed for more flexible specifications of the innovation and was suitable for analyzing the lead-lag causal relationships between two variables.

Estimating price volatility transmission by applying the GARCH-DCC model

In recent years, multivariate GARCH (MGARCH) models with dynamic covariance and conditional correlation have been shown to be more useful in analyzing volatility spill-over mechanisms¹⁵ and thus this method was used for analysis. The econometric framework of the GARCH-DCC model was formulated as follows: let p_t be a 2×1 vector of returns including the international wheat price p_1,f and local wheat price p_2,f. Thus, an autoregression (AR) model k process for p_t conditional on the information set $\Omega _{t - 1}$ can be represented as:

$$p_t = \mu + \mathop {\sum}\limits_{i = 1}^k {\phi _ip_{t - i}} + u_t = \mu + \mathop {\sum}\limits_{i = 1}^k {\phi _ip_{t - i}} + \sqrt {H_t} z_t,$$

(5)

$$\left. {u_t} \right|\Omega _{t - 1}\sim N(0,H_t),$$

(6)

$$H_t = E\left[ {u_tu_t^\prime } \right] = D_tP_tD_t,$$

(7)

where $\mu = (\mu _1,\mu _2)^\prime$ is the vector of conditional means, ϕ_i is the parameter vector, k is the lag lengths of the mean equations, $u_t = (u_{1,t},u_{2,t})^\prime$ is the vector of innovations, H_t is a 2 × 2 conditional variance-covariance matrix, z_t is a 2 × 1 i.i.d vector of standardized residuals, D_t is the diagonal matrix containing the conditional standard deviations on the diagonal and P_t is the conditional correlation matrix given by:

$$P_t = diag(q_{11,t}^{ - 1/2},q_{22,t}^{ - 1/2})Q_tdiag(q_{11,t}^{ - 1/2},q_{22,t}^{ - 1/2}),$$

(8)

where Q_t is the conditional correlation matrix of standardized residuals and q is the element of matrix Q_t. Moreover, the matrix D_t can be obtained by estimating a univariate GARCH (p, q) model, with $\sqrt {h_{i,t}} \,(i = 1,2)$ on the ith diagonal as follows:

$$h_{i,t} = \pi _{i,0} + \mathop {\sum}\limits_{p = 1}^{p_i} {\lambda _{i,p}u_{i,t - p}^2} + \mathop {\sum}\limits_{q = 1}^{q_i} {\gamma _{i,q}h_{i,t - q}} ,$$

(9)

where h_i,t is a 2 × 1 conditional variance vector of the price series and π_i,0 is a 2 × 1 constant vector, the lag lengths of variance equations are represented as p and q and λ and γ are the parameters of the GARCH and ARCH terms, respectively

Furthermore, Engle’s (2002) DCC model and Cappiello et al.’s (2006) asymmetric DCC (henceforth, A-DCC)¹⁶ model were used to determine the volatility spill-over between international and local wheat prices in wheat-importing countries. Meanwhile, the generalized DCC (henceforth, G-DCC) and asymmetric generalized DCC (henceforth, AG-DCC) models¹⁷ were employed and the best model was selected based on the Bayesian-Schwarz information criterion (henceforth, BIC). According to Engle (2002), the dynamic correlation structure is given as:

$$Q_t = (1 - \alpha - \beta )\bar P + \alpha \nu _{t - 1}v_{t - 1}^\prime + \beta Q_{t - 1},$$

(10)

where Q_t is a symmetric positive definite matrix in Eq. (8) and $\bar P$ is the 2 × 2 unconditional correlation matrix of the standardized residuals v_t. The parameters α and β are non-negative, with a sum of less than unity. Therefore, the trend of the G-DCC model can be specified as:

$$Q_t = (\bar P - A^{\prime} \bar PA - B^{\prime} \bar PB) + A^{\prime} \nu _{t - 1}\nu _{t - 1}^{\prime} A + B^{\prime} Q_{t - 1}B,$$

(11)

where A and B are 2 × 2 parameter matrices and $\bar P$ is estimated by using the sample analogue $T^{ - 1}\mathop {\sum}\nolimits_{t = 1}^{T} {\nu _t} v_t^{\prime}$. To introduce the presence of asymmetries into the DCC model, Cappiello et al. (2006) modified the correlation evolution equations in the following expression:

$$Q_t = (1 - \alpha - \beta )\bar P - \delta \bar N + \alpha (\nu _{t - 1}\nu _{t - 1}^\prime ) + \beta Q_{t - 1} + \delta (\eta _{t - 1}\eta _{t - 1}^\prime ),$$

(12)

where $\bar N$ represents the unconditional matrices of $\eta _t = I[\nu _t \,<\, 0] \otimes \nu _t$, I[.] an indicator function equal to 1 if $\nu _t \,<\, 0$ and 0 otherwise and ‘$\otimes$’ the Hadamard product. Equation (12) is a standard A-DCC in which asymmetric terms are included. Thus, the AG-DCC model can be expressed as:

$$\begin{array} {lcc} Q_t = (\bar P - A^{\prime}\bar PA - B^{\prime}\bar PB) - G^{\prime}\bar{N}G + A^{\prime}\nu _{t - 1}\nu^{\prime}_{t - 1}A \\+ B^{\prime}Q_{t - 1}B + G^{\prime}\eta _{t - 1}\eta ^{\prime}_{t - 1}G\end{array},$$

(13)

where A, B and N are parameter metrics. In the estimation, $\bar N$ is replaced with a sample analogue, $T^{ - 1}\mathop {\sum}\nolimits_{t = 1}^T {\eta _t} \eta ^{\prime}_t$. It is worth noting that the AG-DCC model in Eq. (13) nests several specifications of these DCC, G-DCC and A-DCC models. In addition, the correlation coefficient ρ₁₂ at time t can be defined as:

$$\rho _{12,t} = \frac{{q_{12,t}}}{{\sqrt {q_{11,t}q_{22,t}} }}.$$

(14)

Finally, the parameters of the DCC, G-DCC, A-DCC, and AG-DCC models were estimated by employing the Gaussian quasi-maximum likelihood estimation (QMLE)¹⁸ with the BFGS¹⁹ optimization algorithm. The joint log-likelihood function $L(\theta ,\,\psi )$ can be written as the sum of a volatility part and a correlation part, expressed as:

$$L(\theta ,\psi ) = - \frac{1}{2}\mathop {\sum}\limits_{t - 1}^T {\left( {N{\mathrm{log}}(2\pi ) + 2{\mathrm{log}}\left| {D_t} \right| + {\mathrm{log}}\left| {P_t} \right| + v_t^\prime P_t^{ - 1}\nu _t} \right)} ,$$

(15)

where T refers to the number of observations and N denotes the number of equations. Moreover, the univariate GARCH parameters in D_t are denoted as θ, where θ = (π, λ, γ) and the dynamic correlation parameters in P_t are denoted as Ψ, where Ψ = (α, β, δ). The time-varying conditional correlation coefficients are computed based on each GARCH-DCC model.

Identifying factors using panel analysis

In the final step, the underlying factors that influence wheat price volatility transmission from international to local markets in wheat-importing countries were investigated. To tackle the data limitation problems, a panel data approach was taken and wheat-importing countries were regarded as a whole to analyze the factors influencing price volatility transmission. Following the specification in Table 2, the following panel regression model was constructed:

$${\mathrm{DCC}}_{i,t} = c + \kappa _1{\mathrm{SSR}}_{i,t} + \kappa _2{\mathrm{GDP}}_{i,t} + \kappa _3{\mathrm{CPI}}_{i,t} + \kappa _4\Delta {\mathrm{MC}}_{i,t} + \kappa _5\Delta {\mathrm{RC}}_{i,t} + \varepsilon _{i,t},$$

(16)

where DCC is the dynamic conditional correlations at yearly frequency; c the constant; ε_i,t is the heteroskedastic error term; GDP and CPI annualized GDP per capita growth rate and inflation rate, respectively; MC and RC the log-transformed values of maize and rice consumption, respectively; Δ the first difference and k the parameters to be estimated. These parameters measure the impact of the common factors that influence the price volatility transmission²⁰.

Before performing the panel analysis, it was necessary to consider the impact of heteroskedasticity or serial correlation in the error term and any cross-sectional dependence in the cross-country panel. Therefore, a series of pre-tests was applied. Specifically, the modified Wald test (Wooldridge, 2010), Pesaran’s test (Pesaran, 2004) and Wooldridge’s test (Wooldridge, 2010) were employed for heteroskedasticity, cross-sectional correlation and autocorrelation, respectively. Notably, in a standard panel data estimation, the fixed effect model or random effect model is used to estimate the parameters. Hausman’s test was thus used to examine the appropriateness of the fixed effect model relative to the random effect model.

The feasible generalized least-squares (FGLS) regression was used to estimate the panel model. The advantage of the FGLS method is that it allows for heteroskedasticity or autocorrelation in the error term. Moreover, Monte Carlo studies²¹ have shown that the FGLS estimator generally yields better estimates than the ordinary least-squares (OLS) estimator. To guarantee the robustness of the empirical results, the Prais-Winsten regression with panel-corrected standard errors (PCSEs) was applied to compare the results. As Beck and Katz (1995) argue, a PCSE model leads to a more accurate estimation than an FGLS model.

Empirical results and interpretations

The causal relationship between global and local wheat prices

As made clear above, in this study, each model was estimated using the maximum likelihood method and the lag lengths of the mean and variance equations were determined based on BIC. The AR (1)-GARCH (1,1) model was chosen for each price series because it had the lowest BIC value²². Because structural break dates were identified in Georgia’s data, a dummy variable was included in its model. Table 5 shows the parameter estimates for each model and their corresponding statistical significance values. First, we can observe that most of the coefficients of the ARCH (λ) and GARCH (γ) are significant in the GARCH model. Notably, the coefficient of the dummy variables for Georgia is significant at the 5% level. This suggests that the dummy variable accommodates the structural break in Georgia’s data. Following the result, this structural break should be interpreted as the military conflict that broke out between Russia and Georgia in August 2008. It strongly suggests that this short war appears to have significantly affected Georgia’s wheat market and caused the structural change in domestic wheat products and prices. Furthermore, it is noticeable that the break points in the global wheat price and most local wheat prices in importing countries were not discovered. These results imply that little evidence exists to support the structural changes in the wheat price returns during the 2007–2008 food crisis. In addition, Table 5 shows the diagnostics of the empirical results. All the tests imply that the estimated models adequately fit the data.

Table 5 Empirical results of AR-GARCH model

Next, based on the CCF approach, the standardized residuals obtained from each GARCH model were used to examine the causal relationship between international and local prices. Table 6 presents the empirical results, which show that international wheat price returns demonstrate a Granger causality in local prices in all wheat-importing countries with a five-month lag²⁵. In turn, there is no statistically significant evidence of causality from local price to international price²⁶. Therefore, it can be concluded that a unidirectional causality exists from international to local prices in the sample, suggesting that international price can be considered a leading indicator of local price in wheat-importing countries²⁷. Based on these results, the local price of each wheat-importing country was lagged by five periods (five months) to capture the information from the global market to the local market with a five-month time lag.

Table 6 Results for Hong’s (2001) Granger causality test

Dynamic conditional correlations between global and local wheat prices

In the second stage, as mentioned in the methodology section, standardized residuals obtained from the GARCH model were used to estimate the conditional cross-correlation coefficient ρ_12,f in Eq. (14). Table 7 gives the estimation results of the parameter metrics for all the DCC models. First, the necessary condition of α + β < 1 holds for nearly every pair of international and local prices in the DCC and A-DCC models, indicating that the dynamic conditional correlations are mean reverting for international and local prices. Second, the parameters, β, were observed to be mostly positive and significant in the DCC and A-DCC models. This indicates that the lagged dynamic conditional correlation significantly affects the current dynamic conditional correlations. Third, the asymmetry coefficients, η, are found to be significant in Afghanistan and Peru in the A-DCC model, thereby providing evidence of an asymmetric response in correlation for the two countries. Next, the most appropriate model for each country was selected based on BIC. Table 8 presents the results of the model selection, which show that the standard DCC model is selected as the best fit to Afghanistan, Georgia, Kyrgyzstan, Peru and Tajikistan and the G-DCC model is chosen for Azerbaijan, Brazil, Cameroon, Israel and Mauritania.

Table 7 Empirical results of four specifications for DCC models

Table 8 The model selection of four specifications for DCC models

Finally, the dynamic cross-correlation coefficients can be estimated by maximizing the log-likelihood functions in Eq. (15). Figure 3 plots the evolution of the estimated time-varying dynamic correlations of each country. Overall, it is interesting to ascertain that all conditional correlations display considerable variability in the sample period and exhibit different patterns across different countries. Figure 3 visually confirms that almost all the conditional correlation coefficients (except those of Afghanistan, Cameroon, Israel and Tajikistan) are positive throughout the entire sample period. Because the wheat-importing countries’ SSRs in the sample are less than 1 (net wheat-importing countries), it is not surprising that global wheat prices significantly affect local wheat prices in these countries. Moreover, it is interesting that some countries’ dynamic correlations fluctuated dramatically during the 2007–2008 global food crisis. Specifically, a substantial increase in correlation between global and local wheat markets is apparent at the beginning of the food crisis, offering further evidence of the strong impacts of global wheat prices on local prices in some countries (e.g., Azerbaijan, Brazil, Georgia, Israel, and Mauritania). Since a structural break was found in Georgia, it is necessary to check whether significant trade policy changes occurred in Georgia during the crisis. Table 9 reports Georgia’s import tariff for cereals from 2006 to 2013. It was observed that Georgia’s trade tariff rate was lowered from 6.4% to 0.3% in 2007. This policy change seems to have increased the correlation between international and local prices in Georgia. For a country such as Georgia, the autarky rate of which is extremely low²⁸, one of the best short-term counter strategies to feed citizens is to liberalize food imports rather than to raise import tariffs.

Fig. 3

Plots of dynamic correlations between international and domestic wheat prices

Table 9 Georgia’s import tariff for cereal productions

Table 10 provides the descriptive statistics for the 10 wheat-importing countries’ dynamic correlations. First, the means of the correlations are positive in all countries. This suggests that increases or declines in the volatility of international wheat prices can cause increases or declines in the volatility of domestic wheat prices in wheat-importing countries. Brazil has the highest average value (0.359) of dynamic correlation coefficients, which broadly indicates that Brazil’s domestic wheat price has a high correlation with international wheat prices. On the other hand, Tajikistan has the lowest average value (0.024), which conveys a relatively low correlation. Furthermore, as Table 10 shows, different magnitudes of correlation variability emerge across different wheat-importing countries. In particular, Azerbaijan’s correlation coefficients fluctuated more than those of other countries and thus demonstrated the highest standard deviation (0.150). Conversely, Mauritania’s dynamic correlation coefficients are the most stable and thus demonstrated the lowest standard deviation (0.011).

Table 10 Summary statistics for dynamic conditional correlations of wheat

Panel data analysis

To investigate the common factors that impact the price volatility transmission, the panel model was estimated based on Eq. (16). As mentioned in the “Econometric methodology” section of the methods, some pre-tests need to be specified in a preliminary step. Table 11 summarizes the pre-test results. The Hausman test suggests a random effects model for running the panel regression instead of a fixed effects model. Furthermore, the results indicate that the model exhibits heteroskedasticity, serial correlation and cross-sectional dependencies.

Table 11 Specification tests of panel estimation

Based on the results of the specification tests, a random effects model was employed as the base model.

Table 12 reports the empirical results of the panel regression based on these three model specifications. The empirical results revealed several interesting findings. First, it was verified that the coefficients of SSR are negative and significant for all models. These results confirm that the self-sufficiency rate of wheat is a determining factor affecting the dynamic conditional correlation between international and local wheat prices in wheat-importing countries. Furthermore, the negative coefficient indicates that an increase in the SSR will decrease the dynamic correlations. This suggests that raising the SSR of wheat can be a reasonable strategy to buffer importing countries from excessive fluctuations in international wheat prices. Second, the panel results show that the coefficients of CPI are negative and significant for the PCSEs and FGLS models. Theoretically, an increase in the inflation rate will decrease the real value of currency in local countries, which in turn weakens purchasing power and amplifies correlation with the global wheat market. One possible explanation for the negative sign of CPIs coefficients is that some monopoly or oligopoly exists among wheat importers. They may weaken the price transmission to local wheat markets if international prices decrease. Third, the results show that the coefficients of GDP are not robust to model change (k₂ is positive and significant only in the FGLS model). GDP per capita growth represents the livelihood of nationals, which may accelerate volatility pass-throughs because wealthier citizens tend to import more foodstuffs. For instance, Israel has the higher GDP per capita and one of the lowest SSRs²⁹. Because the results of CPI and GDP are not robust against a change in the model selection, they may not be the more important factors in determining the degree of price volatility transmission. Finally, it is interesting that the coefficients of ΔMC and ΔRC are mostly not significant across different estimation methods, implying that a substitutive effect does not exist between wheat, maize and rice. Typically, substituting the consumption of a good that becomes more expensive with one that is relatively cheap could buffer price shocks transmitted from external markets, causing demand for the expensive product to fall. For instance, the high price of wheat induces substitution behavior between cereal goods such as rice and maize, which may partly prevent volatility conveyances. A potential explanation for the findings might be that very different food preferences exist in different countries. Compared with maize and rice, wheat accounts for a huge amount of domestic demand (e.g., as in Afghanistan, Azerbaijan, Israel, Kyrgyzstan, and Tajikistan)³⁰. This phenomenon might cause a lower price elasticity of demand in wheat markets. Therefore, it is reasonable to consider that cultural, religious, or demographic factors may be more formative than the price of food in consumers’ food choices.

Table 12 Estimation results of panel data analysis

Conclusion and policy implications

This article explored potential factors of international wheat volatility transmissions using econometric methods such as the CCF, GARCH-DCC and panel data analysis. The primary findings are as follows. First, the analysis found a significant unidirectional Granger causality of wheat price running from international to local markets with approximately five months of lag length as the countries analyzed in this article are small wheat producers that cannot influence international prices. Second, the results show positive dynamic conditional correlations between international and local wheat prices for most wheat-importing countries. It is concluded that the international wheat price considerably affects the local price in wheat-importing countries. Third, it was found that the self-sufficiency rate has a significant negative effect on the dynamic correlation between international and local prices in all panel models. This indicates that a high SSR in wheat helps reduce volatility pass-throughs from the global market. Therefore, by adopting practices that increase the level of its wheat self-sufficiency rate, the government of a wheat-importing country can diminish the impact of unexpected excess volatility from international markets on its local markets. A point that that must made here is that this paper focused on the connectivity between the degree of price spill-overs and self-sufficiency in wheat, not between the extent of price pass-throughs and food policy changes. The panel method estimates coefficients, simultaneously comparing results both between regions and years. All 10 selected countries may not have necessarily altered food policy regimes, such as boosting export taxes, although policy information on the subject was not fully available for these nations during the sample period. Accordingly, the outcomes should not be simply interpreted as showing that any autarky policy assists local market stabilization. Nonetheless, it suggests that such policy measures may be useful for reducing price volatilities in domestic markets. For future research, import tariff or a dummy variable might be used as an explaining variable in the model.

This evidence that increasing the SSR of an agricultural commodity is effective in isolating the domestic market is valuable for policymakers in food importing countries. The primary beneficiaries of implementing the policy measure are risk-averse producers and consumers because their utility or welfare improves as the price volatility of foodstuffs declines. While this paper makes these key interventions, several tasks remain. The Arrow-Pratt coefficient, a measure of risk preference intensity, needs to be estimated to gauge the monetary values of the benefit from stabilized price movements³¹. Another subject that needs to be discussed is the cost to raise the SSR. While the potential cost to achieve a targeted SSR may vary across countries, it is likely to be substantial in cases in which farmers are continuously given subsidies to stimulate crop production or raise import tariffs and refuse cheaper foreign products. As Tanaka (2018) suggests, a revenue-neutral approach of increasing tax revenues by raising import tariffs that are then expended as subsidies for agricultural production may increase household welfare and lower its variance without hurting the government’s budget. However, evidence on this topic has only been obtained for the Egyptian economy and this is not applicable to all nations or regions. Thus, the cost benefit of the policy has not been fully analyzed and therefore calls for future studies. On the other hand, although Bai and Perron’s (2003) structural breaks test is used to identify the structural changes in each price return, the main weakness of the GARCH model is that it assumes that conditional volatility is based on only one regime over the sample period. In light of this, it would be interesting to apply a Markov-switching GARCH³², which has the advantage of allowing for time-varying causality across regime (structural) changes to estimate volatility. This would enable the present study’s findings to be compared with the empirical results derived from different models. However, this exercise must be left for a future research project.