Price Volatility Transmission in China’s Hardwood Lumber Imports

: Hardwood lumber is the principal part of the global hardwood timber trade. China has become the largest importer of hardwood lumber in the world. However, China’s hardwood lumber imports are affected by price volatility. Thus, we investigated the price volatility transmission of China’s hardwood lumber imports. We aimed to detect the source, path, and intensity of the volatility transmission in China’s hardwood lumber imports, and reveal the intrinsic interactions between price volatilities. To date, there is little research on the price ﬂuctuations of forest products. This paper provides an empirical analysis on the volatility transmission in China’s forest product imports. We selected four types of major hardwood lumber imports to China; that is, teak ( Tectona grandis L.F.), merbau ( Merbau ), sapele ( Entandrophragma ), and casla ( Terminalia spp.) (The Latin names of tree species are given in parentheses), and used their daily prices from 4 August 2010 to 15 April 2020. The Baba–Engle–Kraft–Kroner (BEKK) multivariate models and dynamic conditional correlation (DCC) models were employed. The empirical results indicate that there is an intrinsic relationship between the price ﬂuctuations in China’s hardwood lumber imports. The volatility transmission chain originates from casla; it is transmitted along the casla → sapele → merbau → teak pathway. The direction of transmission is from lower prices to higher prices. The dynamic conditional correlation of each link in the chain does not exhibit any particular time trend. This suggests that volatility transmission is a crucial price mechanism in China’s hardwood lumber imports. Our ﬁndings have important policy implications for hedging timber price risks and designing timber trade policies.


Introduction
Hardwood generally has better properties and is more resilient than softwood [1]. Thus, its price is relatively higher. Major countries with rich hardwood forest resources, such as Indonesia, Malaysia, Philippines, Thailand, and Ghana, have banned the exporting of hardwood logs, but encourage hardwood lumber exports (to increase the value-added trade as well as employment) [2]. Therefore, hardwood lumber has become the principal part of global hardwood timber trade; it raises concerns for all parties involved in international wood trade [3].
In accordance with the data by the Food and Agriculture Organization of the United Nations (FAO) [4], global trade value of hardwood log declined from USD 8.60 billion to USD 6.50 billion from 2012 to 2017, and the corresponding trade volume decreased by 44%. However, the trade value of hardwood lumber worldwide increased from USD 9.64 billion to USD 12.55 billion in the same period, and its trade volume increased by 41%. Hence, the proportion of hardwood lumber trade to hardwood timber trade (hardwood timber includes hardwood logs and lumber) increased rapidly. The trade value of hardwood lumber accounted for 56.86% of the global hardwood timber trade in 2012; this rose to 64.93% in 2017. Likewise, the ratio of hardwood lumber to global trade volume of hardwood timber surged, from 29.31% to 48.99% during the same period.
China has become the largest importer of hardwood lumber in the world. As shown in Table 1, China's hardwood lumber imports grew fast from 2010 to 2018. Its import value and volume of hardwood lumber soared by 11.14% and 9.08% per year, respectively. The growth rate of China was much higher than the average growth level in the world. Accordingly, the percentage of China's hardwood lumber imports in the global hardwood lumber trade increased. China's import value of hardwood lumber reached 40.61% of the global hardwood lumber trade by 2018, and the corresponding proportion of China's import volume of hardwood lumber rose to 45.42%. The structural imbalance between domestic supply and demand of hardwood lumber in China is the main reason for the growth of China's hardwood lumber imports [5,6]. The rapid development of the real estate market and wooden furniture industry in China has driven the growth of China's demand for high-grade hardwood lumber [7]. However, domestic supply of hardwood lumber is mainly low-grade timber. It leads to the high dependency of China on the imports of high-grade hardwood lumber [8]. Thus, China's hardwood lumber imports have a significant influence on the domestic hardwood lumber market. Consequently, China's hardwood lumber imports are affected by price volatility.
There could be volatility transmission among related commodities [9]. Volatility transmission refers to the relevance of price volatility. That is, the price fluctuation of one commodity spurs the similar fluctuation of another [10,11]. The substitutability between commodities is one important reason for volatility transmission [12]. Hardwood lumber is mainly used in wooden furniture manufacturing, wooden floor production, and indoor decorating [13]. Accordingly, different types of hardwood lumber are generally in demand, and share common market information. Southeast Asia and Central Africa are China's chief origins of hardwood lumber [14]. Due to the identical or adjacent geographical distribution, the hardwood lumber imported by China usually has similar input costs. This could bring about volatility transmission between hardwood lumbers, resulting in a price of diffusion risk in the entire timber market. It would increase the risk of decision making for timber traders, increase the difficulty of cost management for wood processing enterprises, and disturb the purchasing plans of domestic consumers. Hence, we explored the volatility transmission in China's hardwood lumber imports to provide theoretical references to minimize the price risk of China's timber trade.
Volatility transmission of commodities is of great interest in regard to price [15][16][17]. Scholars have studied volatility transmission along the same industrial chain. An, Qiu, and Zheng [18] examined volatility transmission in the beef cattle supply chain of western Canada. They found that volatility transmission was unidirectional from the feed barley market to the feeder cattle market. Saghaian et al. [19] discovered that positive and negative price changes caused an asymmetric volatility transmission between corn and ethanol in the United States. Ben Abdallah et al. [20] studied whether price volatility flowed along the Finnish meat supply chain. They observed a unidirectional volatility transmission chain from consumers to producers in the Finnish pork market. Ferrer-Pérez and Graciade-Rentería [21] investigated volatility transmission in the fresh wild hake supply chain in Spain. Their studies indicated that price volatility was transmitted backward, from retailers to auction, in an asymmetric way.
Studies have focused on volatility transmission of the same commodity across various markets. Yan et al. [22] discussed volatility transmission among international and domestic prices of rice, wheat, and maize in 24 developing countries. They found that volatility of international rice and wheat markets exerted momentous positive effects on the volatility of domestic rice and wheat markets in countries with high import dependence. Sinha et al. [23] found that volatility transmission existed among different onion markets in India. Kakhki et al. [24] conducted an empirical analysis on the volatility transmission of barley between the Iran Mercantile Exchange and the world. Their results suggested that the price volatility of barley transmitted from the world to the Iran Mercantile Exchange. Capitanio, Rivieccio, and Adinolfi [25] discovered that the price fluctuation of wheat between Morocco and the world regularly moved together.
Some researchers focus on volatility transmission in substitute commodities. Fakari et al. [26] explored volatility transmission in beef, mutton, and chickens in Iran. They disclosed that beef mutton with a higher degree of substitution had more drastic volatility transmission, compared with other meat pairs. Gardebroek, Hernandez, and Robles [12] estimated the volatility transmission across the price returns of corn, wheat, and soybeans in the United States. Their studies showed that there was a bidirectional volatility interaction between corn and wheat, and wheat had a one-way volatility spillover effect on soybeans. Perifanis and Dagoumas [27] examined the volatility transmission between the wholesale markets of natural gas and crude oil in the United States. Their results showed an evident two-way volatility transmission path between both markets. Živkov, Kuzman, and Subić [28] measured the volatility transmission between four agriculture futures, i.e., corn, wheat, soybean, and rice, indicating that the price volatility of soybean and wheat was greatly affected by the exogenous shocks from others. Chen, Zheng, and Qu [29] detected volatility transmission among rare earth, crude oil, and new energy markets in China. It was inferred that price volatility was transmitted between crude oil and new energy markets.
The research on volatility transmission among goods focus on agricultural products and energy. To date, however, there have been few papers concerned with the volatility transmission of forest products. Due to the leading position of China in global hardwood lumber imports, we conducted an empirical analysis on volatility transmission on the major types of hardwood lumber imported by China to reveal the inherent interaction of price volatility.
The rest of the paper is organized as follows: we analyze the characteristics of the price volatility in China's hardwood lumber imports in Section 2. The methodology is specified in Section 3. In Section 4, the empirical results are presented to analyze the volatility transmission of hardwood lumber imported by China. The reasons for volatility transmission and the corresponding policy implications are discussed in Section 5.

Overall Trend of Price Volatility
We collected the daily import prices of hardwood lumber from Yuzhu International Timber Market (Yuzhu International Timber Market is located in the city of Guangdong, and has become one of the largest timber trading centers in China. The import prices of timber issued by Yuzhu International Timber Market are important references of decisionmaking for domestic and foreign timber traders). The time series spanned from 4 August, 2010 to 15 April, 2020. The dataset includes four types of major hardwood lumber imports to China; that is, teak, merbau, sapele, and casla. Their names are listed in the descending order of prices. They are mostly used in furniture making and indoor decoration [30].
Teak is regarded as first-class timber with a high price because of its excellent wood properties [31]. It is distributed in Southeast Asia. Indonesia, Thailand, and Burma are its main origins. Merbau originates in Southeast Asia and the Pacific Islands [32]. Its physical performance is similar to teak, but its price is relatively lower. Indonesia and Malaysia are major sources of merbau. Sapele is widespread in the African tropical zone. Cameroon, Gabon, Congo, and Equatorial Guinea are its principal exporters [33]. The price of sapele is lower than merbau. Casla is widely distributed in Southeast Asia as well as Africa. Its price is the cheapest among the hardwood lumber mentioned above.
The monthly price volatility can be measured according to Equation (1) [34].
where vm stands for volatility amplitude, p t is the import price of hardwood lumber on date t, n denotes the number of trading days in one month, ln denotes the natural logarithm operator, and SD refers to the operator of standard deviation. From Figure 1, four types of hardwood lumber have a similar volatility trend overall. In terms of the volatility range, the price volatility of casla is higher than the others (most of the time). The price volatility of merbau and sapele grew sharply since May 2015. The price volatility of teak dropped to the lowest level among them after August 2015.

Methodology
We utilized the Baba-Engle-Kraft-Kroner (BEKK) generalized autoregressive conditional heteroskedasticity (GARCH) models and dynamic conditional correlation (DCC) models to evaluate the volatility transmission across hardwood lumber types. The GARCH models are the principal empirical methods for probing the volatility characteristics of the time series, thus far [35,36]. The BEKK GARCH model proposed by Engle and Kroner [37] is a powerful tool to capture the joint co-movement of conditional volatilities among multi-variables. It does not impose any restriction on the conditional correlation structure of variables, so that, to some extent, the bias of model specification could be avoided [38]. Besides, the number of its parameters is smaller than other multivariate GARCH models [39]. This shows the convenience of its estimation process. The DCC model introduced by Engle [40] allows us to evaluate the dynamic evolution of the interdependence between price volatilities. It is fit to identify the time trend of the estimated conditional correlation [41,42].
The price series are converted into price returns by Equation (2). This logarithmic transformation is a standard method for measuring price returns [43].
where p it is the import price of hardwood lumber i on date t, r it is the corresponding price return after the conversion, and ln denotes the natural logarithm operator. Then, the following conditional mean equation in the form of the vector autoregressive (VAR) model, is considered: where r t is a 2 × 1 vector of price returns. γ 0 is a 2 × 1 vector of long-term drifts. γ j , with j = 1, · · · , p, are 2 × 2 matrices of parameters. ε t is a 2 × 1 vector of innovations conditional on past information I t−1 with zero mean. H t is the 2 × 2 conditional variance matrix of ε t to assess the price volatility of hardwood lumber. The stationarity of the return series hereinafter rules out the necessity to account for the vector error correction (VEC) model (the VEC model is applied to the modeling of the non-stationary time series with co-integration relations [44]). The BEKK GARCH model with one-time lag is specified as: where H t is the corresponding conditional variance matrix. C is a 2 × 2 upper triangular matrix with constants. Volatility transmission across commodities consists of volatility spillover and persistence effects [45] (Arenas and Lafuente, 2021). The elements of a ij (i = j) in the 2 × 2 matrix A quantify the volatility spillover effect from an innovation in hardwood lumber i to hardwood lumber j. The off-diagonal parameters b ij (i = j) of the 2 × 2 matrix B evaluate the volatility persistence effect in conditional variance between hardwood lumber i and j.
The DCC model is used to probe the time-varying feature of volatility interaction between hardwood lumber. H t is decomposed as follows: where R t is the time-dependent conditional correlation matrix.
The elements u it of the vector u t are defined as: where Q is the N × N unconditional covariance matrix of u t , and α and β are non-negative adjustment parameters satisfying α + β < 1.

Results
We employed the BEKK GARCH model to measure the mean levels of the volatility spillover and persistence effects in China's hardwood lumber imports on the full sample. As illustrated in Table 2, the kurtosis indexes are all greater than 3. This points to a leptokurtic distribution of every price return. The skewness coefficients are close to zero. It implies that the distributions of the price returns are all symmetrical. The Jarque-Bera tests indicate that none of the return series followed a normal distribution. These tests suggest that the Student T distribution is suitable for the specification of the BEKK GARCH model. The Ljung-Box statistics denote that there is autocorrelation for each price return. Lagrange Multiplier tests verify that all of the price returns have the ARCH effect. The Augmented Dickey-Fuller tests signify that the return series are all stationary at a 1% significance level (see Table 3). These results support that it is proper to choose the VAR and BEKK GARCH models for data fitting.  As reported in Table 4, the maximum likelihood technique is used to estimate the parameters of the BEKK GARCH model according to the BHHH algorithm. The optimal lag number is chosen based on Schwarz's Bayesian information criterion (SBIC). The diagnostic tests are implemented with 10 and 20 lags. The statistics of the Ljung-Box tests hint that we cannot reject the null hypothesis of no autocorrelation in squared residuals. The results of the Lagrange Multiplier tests indicate that the ARCH effect does not exist in squared residuals in all instances. The Hoking Multivariate Portmanteau tests prove that there is no cross-correlation in squared residuals in most cases. These results verify the adequacy of the model specification.

Sapele (i = 2)
Teak (i = 1) The parameters a 21 and b 21 in the groups of teak-merbau, merbau-sapele, and sapele-casla are all statistically significant at a 1% level. The Wald tests for these groups reject the null hypothesis that a 21 and b 21 are jointly equal to zero at 5% significance level. It means that the volatility spillover and persistence effects simultaneously exist in China's hardwood lumber imports. The paths of both effects are highly consistent by comparison. Therefore, we infer that the overall volatility transmission chain is casla→sapele→merbau→teak. The volatility in China's hardwood lumber imports is transmitted from a lower price to a higher price. The source of volatility transmission is casla. Through the comparison of the coefficients along the volatility transmission path, the absolute values of a 21 and b 21 are positively correlated, and the former are larger than the latter. This demonstrates that the volatility spillover and persistence effects move together, and intensify the price volatility of the entire market. The impact of exogenous shocks plays a dominant role in the process of the volatility transmission.
The foregoing analysis uncovers that the volatility transmission in China's hardwood lumber imports conforms to "meteor shower hypothesis" instead of a "heat wave hypothesis". Both hypotheses are put forward by Engle, Ito, and Lin [46]. Exogenous shocks follow a process like a meteor shower hitting the Earth. The impact of this process is displayed as the volatility spillover from one kind of hardwood lumber to another one. In contrast, in the "heat wave hypothesis", the interdependence of volatility across commodities does not exist. A volatile day of one good tends to be followed by another volatile day of itself, but not a volatile day of others.
We investigate the dynamic change of interrelation between price volatility of hardwood lumber via the DCC model. The diagnostic tests illustrate that there is no autocorrelation, ARCH effect, or cross-correlation in the squared residuals (see Table 5). The estimated coefficients α and β in each link of the volatility transmission chain are both significant at the 1% level. The null hypotheses that the parameters α and β are jointly equal to zero are rejected by the Wald tests at the 1% significance level. These signify the appropriateness of the DCC model assumption. Figure 2 displays the time-variant characteristics of the conditional correlation between the price volatility of hardwood lumber. The conditional correlation of each hardwood lumber pair does not exhibit any particular time trend. The variability in the conditional correlation of teak-merbau and sapele-casla is higher than merbau-sapele. In light of constant conditional correlation, the interdependence of merbau-sapele is the greatest, followed by sapele-casla and teak-merbau. This coincides with the results of the BEKK GARCH model.

Discussion
The empirical analysis confirms that there is an intrinsic interconnection between the price fluctuations in China's hardwood lumber imports. The volatility transmission chain originates from casla, and is transmitted along the casla→sapele→merbau→teak path. The direction of transmission is from lower to higher prices. This phenomenon could be explained as follows. Low-priced hardwood lumber would have generally wider geographical distribution and larger living wood growing stock than high-priced hardwood lumber. For example, casla stems from Southeast Asia and Africa, and sapele is distributed in a number of countries in Central Africa. However, the main production of teak is in Myanmar, and the chief origin of merbau is Indonesia. Consequently, their stock would be smaller than casla and sapele. In line with the classical price theory, price is the dominant influencing factor of demand [47][48][49]. The lower the price, the greater the demand. These would result in a higher proportion of cheap hardwood lumber in China's imports, and accordingly, cheap hardwood lumber would have a larger influence on the import price system, compared to expensive hardwood lumber. This could be the main reason why the volatility transmission from less expensive hardwood lumber to more expensive hardwood lumber occurs.
This study has important policy implications. It suggests that volatility transmission is a crucial price mechanism of the timber trade. Thus, it is beneficial to consider volatility transmission for hedging timber price risk and designing timber trade policies. Firms could forecast the fluctuation trends of timber import prices more accurately by means of the insights gained from volatility transmission. It would help timber traders to optimize the price strategies, considering risk aversion, and assist wood processing enterprises in managing the costs of imported timber. For the government, it may provide policy reference to control the overall timber market import price risk. The restriction on the source of volatility transmission or the disconnection of the volatility transmission chain might be feasible approaches to mitigate the market price risk.

Conclusions
We employed the BEKK GARCH and DCC models to explore the price volatility transmission in China's hardwood lumber imports. The empirical results demonstrate that volatility transmission, as a vital price mechanism, exists in China's hardwood lumber imports. Volatility transmission presents unidirectional diffusion characteristics. The influence of exogenous shock plays a key role in the process of volatility transmission. The dynamic change of volatility transmission has no obvious time trend. The finding reflects the formation patterns of price risks in China's hardwood lumber market. This provides theoretical references for price risk control. It is helpful for timber traders to optimize a price risk aversion strategy, for wood processing enterprises to manage the costs of timber, and for the government to control the price risk of the overall timber market.
Further research on this topic could be expanded to include other forest products imported by China, such as logs, paper pulp, and paper products. This would assist us in examining whether volatility transmission is widespread in China's forest product imports. On this basis, we would verify the underlying factors driving volatility transmission across forest products through quantitative methods. These studies would help us to understand the nature of price fluctuation in China's forest product imports more completely.