The Impact of Global Digital Trade Development on China’s Grain Import Trade Potential: An Empirical Analysis Based on a Time-Varying Stochastic Frontier Gravity Model

Abstract

It is of great significance to clarify the impact of the rapid development of digital trade on China’s grain imports in order to enhance its efficiency and guarantee food security. From an import perspective, this article adopts a stochastic frontier gravity model and a trade inefficiency model to analyze the influence of global digital trade development on the efficiency of China’s grain imports and further estimates the potential for trade expansion. The main findings include the following: (a) Divergence in digital trade capabilities persists across nations. As countries advance their digital trade ecosystems, China’s grain import efficiency demonstrates corresponding enhancements. (b) Compared with digital infrastructure construction and digital trade competition intensity, China’s food import trade efficiency increases as the level of digital technology innovation improves. (c) China achieves the highest trade efficiency in grain import among the ASEAN (Association of Southeast Asian Nations) and North American countries, while the greatest untapped potential lies in imports from South America. Accordingly, for different countries, it is necessary to adopt different strategies to enhance cooperation with the world’s major grain-trading countries in the areas of digital trade infrastructure construction and digital technology innovation, and to use digital trade to optimize China’s grain import trade chain and improve its efficiency.

1. Introduction

With the deepening of agricultural and rural reforms, China’s comprehensive grain production capacity has steadily improved. According to the National Bureau of Statistics of China, China has maintained an annual output exceeding 650 million metric tons for nine consecutive years since 2015. However, escalating resource and environmental constraints, declining incentives for grain cultivation, and increasing meteorological risks suggest diminishing returns for future production scaling, necessitating strategic increases in grain imports to address domestic supply–demand gaps [1]. Customs statistics indicate that China’s grain imports exceeded 100 million tons for the first time in 2014, with imports increasing annually thereafter. By 2023, total grain imports surpassed 160 million tons, comprising 99.41 million tons of soybeans and 59.08 million tons of cereal grains. This longitudinal surge in imported volumes has reshaped China’s status in the global grain trade, transitioning the nation from a net exporter to a net importer [2]. China’s grain imports remain predominantly concentrated in Brazil, the United States, Argentina, and Canada, all of which are located in the Americas [3]. In fact, moderate grain imports not only effectively reconcile the discrepancy between grain supply and demand but also contribute substantially to alleviating agricultural resource constraints and strengthening national grain security [4]. However, against the backdrop of resurgent trade protectionism and escalating geopolitical tensions, the high level of grain imports poses latent market risks [5]. Consequently, it is imperative to diversify import sources by implementing a multi-channel grain procurement strategy, thereby dispersing the risks associated with concentrated imports while optimizing grain import structure and spatial distribution [6].

According to the definition in the 2018 World and China Digital Trade Development Blue Paper, digital trade, as an extension of traditional trade in the digital economy era, refers to the efficient exchange of traditional physical goods, digital products and services, and digital knowledge and information, carried out through modern information networks and facilitated by information and communication technologies [7]. With the accelerated integration of information technology into the field of international trade, the deep integration of digital trade and agricultural trade has supported the development of China’s agricultural trade [8]. According to the 2023 China Agricultural Products e-Business Development Report, in 2022, the total retail import and export volume of China’s agricultural product cross-border e-commerce reached USD 8.1 billion, representing a 25.9% growth compared to 2021 [9]. Digital trade has brought new opportunities for China’s agricultural trade [10]. According to the data of China’s agricultural products import and export in 2023 released by China’s Ministry of Agriculture and Rural Affairs, in 2023, China’s agricultural trade deficit stood at USD 135.18 billion, with the import volume of bulk agricultural products such as grains showing an increasing trend [11]. However, China’s agricultural trade is confronted with multiple external pressures, including the rise of trade protectionism, profound changes in the global agricultural trade landscape, and sustained tensions in international agricultural trade [12,13]. Facing the complex and volatile international landscape, the development of global digital trade has provided a new path for global agricultural import and export trade [14]. Accordingly, investigating the impact of digital trade on China’s grain trade holds significant implications in the context of digital trade.

Figure 1 shows the value of China’s grain imports from major grain-exporting countries and its growth rate from 2006 to 2023. Overall, China’s trade volume of imported grain from major grain-exporting countries shows a fluctuating growth trend, with imports growing from USD 8.308 billion in 2006 to USD 80.044 billion in 2022, accounting for more than 90% of China’s total grain imports, with an average annual growth rate of imports of 16.2%. In 2022, China’s imports from America, Canada, Australia, Brazil, and Argentina amounted to USD 73.104 billion, accounting for as much as 91.32% of China’s grain imports. Within the sample interval, the development of China’s grain imports can be divided into two stages: In the first stage (2006–2016), China’s grain imports increased and then slowly declined. The decline in 2008 was affected by the global financial crisis, and in 2015, China’s economy entered a new normal, affected by the decline in demand for grain imports. In the second stage (2017–2022), China’s grain imports first declined slowly and then rose rapidly, affected by China–US trade friction, resulting in a sharp decline in China’s grain imports such as soybeans and corn. In recent years, in order to cope with the risk of over-concentration of grain imports, the structure of China’s grain import sources has been gradually optimized, and it is of great practical significance to study China’s grain import trade potential and expansion space from the perspective of imports at this time.

2. Literature Review

The current literature offers limited research on the impact of digital trade on the potential of grain import trade. Scholars primarily focus on the trade potential of agricultural exports and imports, with a particular emphasis on exploring the export potential of agricultural products and its influencing factors. In terms of trade potential, Li et al. argued that agricultural trade between China and the countries along the “21st-Century Maritime Silk Road” is highly complementary and concluded that China and the countries along the road have greater potential for trade of agricultural products [15]. Abudukeremu et al. believe that the overall agricultural export efficiency from China to Central Asian countries shows an upward trend. However, compared to the Central Asian and surrounding countries, the agricultural trade efficiency between China and Central Asian countries is at a relatively low level [16]. Abdullahi found that Nigeria’s export potential for agricultural products to European Union countries has not been fully explored [17]. Romyen argued that Thailand’s agricultural export trade potential is approaching the maximum level determined by the trade agreement with partner countries [18]. Li et al. revealed a low average trade efficiency in China’s agricultural exports to RCEP (Regional Comprehensive Economic Partnership) member states, noting cross-country heterogeneity and untapped export potential [19].

Research on the factors influencing agricultural trade efficiency is relatively abundant, with scholars conducting in-depth explorations into aspects such as infrastructure, economic development levels, and trade policies. For instance, Gao et al. believe that infrastructure has a significant positive effect on agricultural trade efficiency [20]. Chen posited that economic scale positively promotes China’s agricultural exports, and shorter geographical distance facilitates agricultural trade [21]. Li et al. argued that factors such as the signing of free trade agreements and customs clearance efficiency in trading partner countries significantly impede China’s agricultural trade [22]. Fang et al. revealed that institutional quality significantly promotes the export of medium- and high-value-added citrus products but inhibits the export of low-value-added citrus products [23]. Cao et al. found that improvements in judicial efficiency, monetary freedom, investment freedom, trade freedom, and financial freedom are conducive to enhancing agricultural trade efficiency, whereas increases in government fiscal expenditure and commercial freedom are detrimental to trade efficiency [24]. In addition, some researchers have examined the impact of climate change on China’s agricultural product imports. For instance, Ding et al. revealed that climate change exerts positive impacts on China’s import trade dynamics through two primary channels: production and supply risks in agricultural origins, and energy substitution risks arising from shifting climatic conditions [25].

Additionally, there are also a small number of scholars who studied the trade efficiency of agricultural imports and its influencing factors. For example, Qi et al. believe that the efficiency of China’s main grain import trade is in a fluctuating upward trend, with the potential for trade with some countries to be further improved; reducing the level of tariffs, improving the degree of financial freedom, and signing free trade agreements will improve China’s grain import trade efficiency [26]. Cheng et al. found that the overall trade efficiency of China’s agricultural imports with RCEP countries is at a relatively low level, and there are differences between different countries. China’s trade potential needs to be improved, and factors such as the economic scale of the agricultural exporting countries and the degree of trade freedom affect the efficiency of China’s agricultural imports [27]. Cao et al. reported low average trade efficiency but considerable potential in China’s agricultural imports from Latin America, with geographical distance and exchange rate volatility as primary inhibitors [24]. Cui et al. revealed that the combined effects of food security and the Belt and Road Initiative significantly promoted the import efficiency of both agricultural products and plant-based goods [28]. However, few scholars have explored agricultural import trade potential from the perspective of digital trade.

Existing scholarship has primarily focused on the influence of the digital economy on international trade, and the majority of scholars assert that the digital economy promotes the development of international trade [29]. Some scholars argue that the application of the Internet and information and communication technology (ICT) can significantly expand the scale of international trade [30]. Others suggest that enhancing digital platform development can effectively overcome information barriers in trade, thereby reducing search and matching costs [31]. These perspectives offer valuable insights for our research. Regarding the empirical impacts of digital trade on agricultural product trade, scholars have demonstrated that digital technologies can mitigate delays and uncertainties in trade processes while enhancing custom clearance efficiency [32,33]. For instance, Zhu et al. identified that the digital trade development level in importing countries significantly improves China’s agricultural export efficiency [34]. Similarly, Hu et al. estimated the digital trade levels of RCEP countries and discovered a polarization trend in their digital economic development, which significantly boosts China’s export trade efficiency to these nations [35]. Furthermore, Wang et al. provided evidence that digital trade development diminishes traditional trade barriers and generates substantial export efficiency enhancements [36]. Despite these advancements, current research specifically addressing the impact of digital trade development on agricultural trade efficiency remains scarce, presenting a critical gap in the existing literature.

A review of the relevant literature reveals that while existing studies have explored digital trade and China’s agricultural product trade potential from diverse perspectives, few have delved into an in-depth analysis of trade efficiency and potential through the lens of digital trade development’s impact on China’s grain import trade. Building on existing research, this paper will explore the following aspects:

First, departing from conventional approaches focused on digital trade’s role in agricultural trade quality enhancement, this study pioneers an import-oriented analytical framework. Specifically, it investigates how exporters’ digital trade development facilitates China’s grain import efficiency, subsequently deconstructing impacts across three distinct dimensions of digital trade evolution. The current literature predominantly emphasizes digital trade’s influence on high-quality agricultural trade development, largely overlooking its efficiency implications. By conducting quantitative assessments of grain-exporting nations’ digital trade advancement, this study further explores China’s grain import efficiency and import source structure, thereby generating targeted policy recommendations for optimizing grain import operations.

Second, this paper introduces methodological innovation by integrating the stochastic frontier gravity model into China’s grain import efficiency research. The adoption of a one-step estimation approach for identifying efficiency determinants gains particular relevance given grain security’s elevation to national security strategy status. While existing scholarship predominantly examines digital trade in isolation from goods trade convergence, this study makes substantive contributions by incorporating digital trade as a critical determinant in China’s grain import efficiency analysis. Such analytical integration holds significant practical value for reconciling digital transformation with physical commodity flows in strategic trade sectors.

3. Materials and Methods

3.1. Materials

For the accuracy of the data source, this article excludes nations with substantially incomplete datasets and finally selects 27 samples, namely Australia, Argentina, Brazil, Canada, Chile, Cambodia, Denmark, France, Germany, India, Japan, Laos, South Korea, Italy, Pakistan, Russia, South Africa, Thailand, Ukraine, the United Kingdom, America, Uruguay, Vietnam, Kazakhstan, Mexico, Peru, and the Philippines. Due to the missing sample data both before 2006 and after 2022, this study chooses the panel data from 2007 to 2020. It should be noted that China’s grain imports from these countries account for more than 90% of the total grain imports, and the selected samples are representative. The measurement software was Frontier 4.1 and stata 15.0. The variable descriptions and data sources are shown in

Table 1. Statistical summary of variables.

Variable	Obs.	Mean	Std. Dev.	Minimum	Maximum
Ln (IMPijt)	459	27.05	1.66	22.71	30.67
Ln (GDPit)	459	22.89	0.55	21.72	23.61
Ln (GDPjt)	459	20.14	1.72	15.06	23.97
Ln (POPit)	459	14.13	0.03	14.09	14.16
Ln (POPjt)	459	10.87	1.25	8.11	14.16
BORDij	459	0.22	0.42	0	1
Ln (DISTij)	459	8.75	0.81	6.91	9.56
DELjt	459	0.17	0.12	0.01	0.63
FTAijt	459	0.37	0.48	0	1
TARIit	459	3.96	1.32	1.24	5.99
LSCIjt	459	43.30	25.71	1	115.68
MFjt	459	76.05	7.88	37.90	94.30
TFjt	459	77.61	9.13	24	90
FFjt	459	56.10	18.50	20	90

.

The data sources are as follows: The data of China’s grain import trade volume are derived from the UN Comtrade database (United Nations Commodity Trade Statistics Database), which is classified by SITC Rev.2 (Standard International Trade Classification, Revision 2). The data of the GDP (Gross Domestic Product) and total population of both parties (pop) are obtained from the World Bank WDI (World Development Indicators) database, and the GDP is denominated in the constant price of US dollars in 2015 to eliminate the impact of inflation. Data on whether there is a common border (BORD_ij) and the geographical distance (DIST_ij) between the two countries are derived from the CEPII (Centre détudes prospectives et d’informations internationals) database; in the inefficiency term model, whether to sign a free trade agreement (FTA_ij) is used as a dummy variable in the model, and the data are derived from the official website of the Ministry of Commerce of China. Data on China’s tariff level (TARI_ij) are derived from the WITS (World Integrated Trade Solution) database. Monetary freedom (MF_ij), trade freedom (TF_ij), and financial freedom (FF_ij) are sorted out by the economic freedom index released by the American Heritage Foundation and The Wall Street Journal. The measurement software was Frontier 4.1 and stata 15.0. The descriptive statistics of the main variables are detailed in Table 1.

3.1.1. Explained Variable

The current international definitions of “grain” exhibit notable discrepancies. While the Food and Agriculture Organization (FAO) of the United Nations employs a comprehensive conceptualization of grain, China’s National Bureau of Statistics adopts a narrower scope, primarily encompassing cereal crops, legumes, and tuber crops. Given the need to maintain data caliber consistency throughout this study and align with established academic definitions of grain, the authors operationalize the term “grain” as encompassing cereal crops and soybeans [37,38,39]. The explained variable in this paper is IMP_ijt, which represents the grain import trade volume of China from country j in period t, with a unit of USD 100 million. The data are from the China Statistical Yearbook (2006–2022).

3.1.2. Explanatory Variables

Digital trade is booming and gradually becoming a new engine for building a trading power. However, as a brand new trade field, it is not yet a universally recognized connotation concept, and therefore, it has not yet formed a unified evaluation system. The more common indicators are the digital economy and society index (DESI) issued by the European Union since 2014, the measuring the digital economy indicators issued by the Organisation for Economic Co-operation and Development (OECD), the network readiness index (NRI) issued by the Global Information Technology Report (GITR), and the ICT development index of the International Telecommunication Union (ITU). The NRI and DESI are used by Miroslaw Moroz to measure the development of digital economy development [40]. Regarding the measurement of the development level of the digital economy, different scholars in China have selected different indicators for measurement. Zhang et al. constructed a system of indicators for measuring the readiness of digital economy development based on the basic concept of the digital economy proposed by the G20 (Group of 20) [41]. Fan used the network readiness index to measure the level of digital economy development in various countries and concluded that the improvement in the level of digital economy development can improve trade efficiency [33]. Jia et al. constructed an index system for measuring the scale of digital trade based on the concept of ‘binary three rings’ [42]. Yao constructed a comprehensive indicator system for the development level of digital trade using 11 indicators in 5 dimensions, including e-commerce infrastructure, digital technology, digital industrialization scale and trade turnover, digital industrialization trade, and the degree of dependence on foreign trade [43]. Kong et al. measured the level of digital trade development from five dimensions: digital trade foundation, digital trade environment, digital trade capacity, digital trade industry, and digital trade potential [44]. Based on previous scholarly research on the concept of digital trade, this paper selects three primary indicators—digital infrastructure development, the intensity of digital trade competition, and digital technology innovation capability—as well as thirteen secondary indicators (see

Table 2. Indicator system for digital economy level.

Primary Indicators	Sub-Indicators	Data Sources	Indicator Attribute
Digital Infrastructure Construction (A)	Fixed broadband subscriptions	International Telecommunication Union	+
	Fixed telephone subscriptions		+
	Mobile cellular subscriptions		+
	Internet penetration rate		+
Digital Trade Competition Intensity (B)	Percentage of ICT goods exports	World Bank database	+
	Percentage of ICT service exports		+
	Percentage of high-technology exports		+
	E-Government Development Index	United Nations E-Government	+
Digital Technology Innovation Ability (C)	Research and development expenditure	World Bank database	+
	Patent applications, nonresidents		+
	Patent applications, residents		+
	Scientific and technical journal articles		+
	School enrollment, tertiary		+

) to comprehensively and accurately evaluate the level of digital trade development in 27 countries from multiple perspectives.

The core explanatory variable in this paper is the level of digital trade development (DEL_jt), which indicates the level of digital trade development of country j in period t. For the measurement of the level of digital trade development, this paper uses three first-level indicators, digital infrastructure construction, digital trade competition intensity, and digital technology innovation ability, and 13 s-level indicators. Digital trade promotes the high-speed exchange of data and information with modern information networks as the carrier. With the rapid development of information and communication technology and the improvement in the global information highway network system, the development of digital trade reduces the cost of collecting agricultural trade information, marketing channels, and delivery transportation, and improves the efficiency of China’s grain import trade. Therefore, it is expected that the development level of digital trade is negatively correlated with the inefficiency of China’s grain import trade.

The measurement of various indicators of digital trade is shown in Table 2.

The main calculation steps are as follows:

(1)

Normalization of the data for each indicator is required to eliminate the scale problem caused by the different ranges of values for the secondary indicators:

$${X_{ijt}}^{\prime }={\displaystyle \frac{x_{ijt}-\min \left(x_{ijt}\right)}{\max \left(x_{ijt}\right)-\min \left(x_{ijt}\right)}}$$

(1)

where ${X_{ijt}}^{\prime }$ is the standardization of index j in country i in year t. X_ijt donates the original data of indicator j of country i in year t. max (X_ijt) and min (X_ijt) represent the maximum and minimum values of index j of all statistical countries in year t. After the standardization of some indicators, the calculated value will be small. In order to eliminate the deviation in the calculation results, it is necessary to translate the standardized data. H is the amplitude of the index translation, and this paper selects a value of 0.0001.

$${X_{ijt}}^{″}={X_{ijt}}^{\prime }+H$$

(2)

(2)

All indicators are normalized, and the proportion of country i in index j in year t is calculated.

$$d_{ijt}={\displaystyle \frac{{X_{ijt}}^{\prime }}{{\displaystyle \sum _{i=1}^n{X_{ijt}}^{\prime }}}}$$

(3)

(3)

The information entropy of the indicator e_j is calculated as follows:

$$e_j=-{\displaystyle \frac{1}{\ln n}}{\displaystyle \sum _{j=1}^n{X}_{ijt}\ln X_{ijt}},\left(0\le e_j\le 1\right)$$

(4)

(4)

Information entropy redundancy is calculated as follows:

$$g_j=1-e_j$$

(5)

(5)

The weight of indicator j is defined as follows:

$$w_j={\displaystyle \frac{g_j}{{\displaystyle \sum _{j=1}^n{g}_j}}}$$

(6)

(6)

The main weighted arithmetic average model is used to synthesize the digital trade development index.

$$DE{L}_{ijt}={\displaystyle \sum _{j=1}^n{d}_{ijt}{w}_j}$$

(7)

3.1.3. Control Variables

The economic meaning of each of the main explanatory variables in the regression equation is detailed in

Table 3. Meaning of variables, expected signs, and theoretical explanations.

Variable	Description	Expected Sign	Economic Interpretation
IMPijt	Import trade value of grain.	(+)	China’s grain import value from sampled countries.
GDPit	GDP of importing country i in period t.	(+)	It reflects the economic development scale of the importing country; generally, the larger the economic scale, the greater the import demand tends to be.
GDPjt	GDP of exporting country j in period t.	(+)	It reflects the economic development scale of the exporting country, and generally, the larger the economic development scale of the exporting country, the greater the scale of its export trade tends to be.
POPit	Population of the importing country i in period t.	(±)	It reflects the market size of the importing country; generally, the larger the population, the greater the import demand. Meanwhile, some research posits that the larger the market size of the importing country, the lesser its reliance on the international market.
POPjt	Population of the exporting country j in period t.	(±)	It reflects the market size of the exporting country; typically, the greater the population, the stronger its export capacity. Additionally, some research argues that the larger the market size of the exporting country, the less imperative it becomes to explore international markets to boost exports.
BORDij	Whether importing country i shares a common border with exporting country j.	(+)	It reflects whether the two countries are contiguous; the existence of a common border facilitates the reduction in transportation costs, thereby promoting trade development.
DISTij	The geographical distance between importing country i and exporting country j.	(−)	It reflects the geographic distance between countries, with longer distances leading to increased transportation costs, which in turn hinder the development of grain trade.
FTAijt	Whether the trading parties have signed a free trade agreement.	(±)	The signing of a free trade agreement is conducive to reducing trade costs, thereby fostering the development of trade.
TARIit	The tariff level of the importing country i in period t.	(−)	It reflects the tariff barriers of the importing country; the higher the tariff barriers, the more detrimental they are to trade between two countries.
LSCIjt	Linear shipping connectivity index.	(−)	The higher the index in the exporting country, the better its maritime infrastructure, which is more conducive to the development of trade between two countries.
MFjt	The currency freedom index of country j in period t.	(+)	The higher the level of currency freedom in the exporting country, the smaller the trade barriers, which in turn is more conducive to the development of grain trade between two countries.
TFjt	The trade freedom level/index of country j in period t.	(+)	The higher the level of trade freedom in the exporting country, the smaller the trade impediments, thereby fostering the development of grain trade between two countries.
FFjt	The financial freedom index/level of country j in period t.	(+)	The higher the level of financial freedom in the exporting country, the smaller the trade impediments, which is more conducive to the development of grain trade between two countries.

Note: For partially missing data, the moving average method in time-series analysis was employed for imputation.

. In the stochastic frontier model, GDP reflects the size of a country’s economy; the higher the GDP of the importing country, the greater the potential demand for grain imports, and the higher the GDP of the exporting country, the greater the domestic grain production capacity of the exporting country and the greater the ability to export grain. Population size is measured by the total population at the end of the year; the larger the population size of the importing country, the greater the increase in import demand, and the larger the population size of the exporting country, the more unfavorable the increase in exports. Geographic distance reflects the distance between the two countries; the further the distance, the higher the trade cost, and the more unfavorable the trade of grain, and the closer the distance, the lower the trade cost and the more favorable the export of grain. The signing of a free trade agreement between two countries is conducive to reducing trade friction, which is favorable for grain exports. The lower the tariff rate, the more favorable it will be for reducing trade barriers and trade costs, making it easier for exporting countries to export agricultural products, while higher tariff rates will inhibit the expansion of grain trade between the two countries.

3.2. Methods

Gravitational modeling, which first originated with Newton’s law of gravity, is now one of the most common methods used by researchers to assess international trade flows and describe factor flows. The estimation of trade efficiency in the traditional gravity model is biased due to omitted variable issues. By incorporating the stochastic frontier approach into the conventional gravity model and introducing the determinants of trade inefficiency into the model, it is possible to measure the trade potential between countries on this basis.

3.2.1. Stochastic Frontier Gravity Model

The stochastic frontier gravity model can be written as follows:

$$Y_{ijt}=f\left(X_{ijt},\beta \right)\exp \left({\nu }_{ijt}-{\mu }_{ijt}\right),\mu \ge 0$$

(8)

where Y_ijt represents the actual trade volume of imports from country j to country i in year t. X_ijt represents the determinants of bilateral trade in the gravity model, which include economic size, common language, geographical distance, etc. $\beta$ is the parameter to be estimated. ν_ijt and μ_ijt represent the random error term and the non-negative inefficiency error term, respectively, and constitute the compound error term together. μ_ijt denotes the combined effect of the economic distance factors mentioned above, which results in the difference between actual trade and potential trade. Suppose that ν_ijt is set to obey a normal distribution with a mean of zero, while μ_ijt is set to obey a truncated semi-normal distribution; the mutual independence of ν_ijt and μ_ijt are assumed as well.

Taking the logarithm of the formula, we obtain the formula shown in (9):

$$\ln Y_{ijt}=\ln f\left(X_{ijt},\beta \right)+{\nu }_{ijt}-{\mu }_{ijt}$$

(9)

When μ_ijt = 0, it indicates that there is no trade inefficiency between the two countries, and the maximum value of grain imports from country j to country i has been attained in the absence of trade barriers; when μ_ijt > 0, it indicates that there is trade resistance between the two countries, and affected by trade barriers, the trade volume of grain imports from country j to country i declines. The model’s expression is as follows:

$${Y_{ijt}}^{*}=f\left(X_{ijt},\beta \right)\exp \left({\nu }_{ijt}\right)$$

(10)

where Y_ijt* represents the potential trade level of grain imports from country j to country i in year t. However, trade efficiency is obtained via the actual trade volume to trade potential ratio, which is denoted by TE_ijt, and is given by the following:

$$T{E}_{ijt}={\displaystyle \frac{Y_{ijt}}{Y_{ijt}^{*}}}\exp \left(-{\mu }_{ijt}\right),{\mu }_{ijt}\ge 0$$

(11)

In Formula (11), the value of TE_ijt is [0, 1]. A higher value of TE_ijt means more efficient bilateral trade. Conversely, a lower value of TE_ijt indicates lower trade efficiency.

3.2.2. Inefficiency Model

Initially, the inefficiency term is assumed to be constant. But scholars propose that the inefficiency term should be assumed to change with time, which is a more reasonable hypothesis. Battese and Coelli incorporated balanced panel data into this model, verified that the trade inefficiency term changes over time, and consequently proposed the time-varying formulation of the stochastic frontier gravity model [44], as follows:

$${\mu }_{ijt}=\left\{\exp \left[-\eta \left(t-T\right)\right]\right\}{\mu }_{ij}$$

(12)

In Formula (12), T denotes the time dimension, and η is an estimated parameter that determines how the inefficiency term varies with time. If η > 0, the inefficiency term will decline over time, and thus trade efficiency will improve. If η = 0, the inefficiency term remains invariant over time, indicating no temporal variation in the inefficiency term. Consequently, the model is transformed into a non-time-varying model. If η < 0 is considered hypothetical, the trade inefficiency term increases with temporal changes, leading to a decline in trade efficiency.

Following the estimation of trade efficiency values based on Formula (11), a further analysis of the determinants of trade inefficiency should be conducted. Drawing on the research of Battese and Coelli [45], the “one-step approach” is adopted to unify the factors affecting trade inefficiency into the stochastic frontier gravity model for regression analysis, which effectively avoids the shortcomings of omitted variables and inconsistencies in the assumption of the same distribution. The trade inefficiency term μ_ijt can be expressed as follows:

$${\mu }_{ijt}=s\left(Z_{ijt},\delta \right)+{\epsilon }_{ijt}$$

(13)

Z_ijt is the exogenous variable that affects trade inefficiency, ε_ijt is a random disturbance term, and δ_ijt is an unknown parameter vector. Combining Formulas (9) and (13), a modified stochastic frontier gravity model can be further derived:

$$\ln Y_{ijt}=\ln f\left(X_{ijt},\beta \right)+{\nu }_{ijt}-\left[s\left(Z_{ijt},\delta \right)+{\epsilon }_{ijt}\right]$$

(14)

3.2.3. Model Construction

On the basis of the general gravity model, this paper refers to the model settings of Yang et al. and Gu et al. and adds control variables to construct an extended trade gravity model to ensure the accuracy of this paper. The selected control variables are GDP, population size, the distance between the capitals of the two countries, free trade agreements, and tariff levels, which can be used to obtain the expression of the stochastic frontier gravity model as follows [46,47]:

$$\begin{array}{ll}\ln IM{P}_{ijt}=& {\beta }_0+{\beta }_1\ln GD{P}_{it}+{\beta }_2\ln GD{P}_{jt}+{\beta }_3\ln PO{P}_{it}+{\beta }_4\ln PO{P}_{jt}+\\ & {\beta }_{5}BOR{D}_{ij}+{\beta }_6\ln DIS{T}_{ij}+{\nu }_{ijt}-{\mu }_{ijt}\end{array}$$

(15)

where lnIMP_ijt represents the logarithm of value of the grain imports from country j to country i in year t. β represents the parameters that the model seeks to estimate, β₀ is a constant, and β₀ to β₆ are the coefficient parameters of the explanatory variables. Here, i is China, the grain-importing country, j is the grain-exporting country (1, …, 27), and t = 2006, 2007, …, 2022 is the time period analyzed. ν_ijt and μ_ijt are the random error term and trade inefficiency term of the model, respectively. In order to estimate the impact of the level of digital economic development of grain-exporting countries on the efficiency of China’s grain import trade, an inefficiency model is constructed as shown in Formula (16):

$$\begin{array}{ll}{\mu }_{ijt}=& {\alpha }_0+{\alpha }_{1}DE{L}_{jt}+{\alpha }_{2}FT{A}_{ijt}+{\alpha }_{3}TAR{I}_{it}+{\alpha }_{4}LSC{I}_{jt}+\\ & {\alpha }_{5}M{F}_{jt}+{\alpha }_{6}T{F}_{jt}+{\alpha }_{7}F{F}_{jt}+{\epsilon }_{ijt}\end{array}$$

(16)

In Formula (16), α is the surrogate estimation parameter.

In order to further consider the degree of influence of the three first-level indicators of the level of digital trade development on the efficiency of China’s grain import trade, this paper introduces digital infrastructure construction (A), the intensity of digital trade competition (B), and the innovation capacity of digital technology (C) into the stochastic frontier gravity model, with the following expression:

$$\begin{array}{ll}\ln IM{P}_{ijt}=& {\beta }_0+{\beta }_{1}GD{P}_{it}+{\beta }_{2}GD{P}_{jt}+{\beta }_{3}PO{P}_{it}+{\beta }_{4}PO{P}_{jt}+\\ & {\beta }_{5}BOR{D}_{ij}+{\beta }_6\ln DIS{T}_{ij}+{\nu }_{ijt}-({\alpha }_0+{\alpha }_1\ln DE{L}_{Ajt}+{\alpha }_{2}FT{A}_{ijt}+\\ & {\alpha }_{3}TAR{I}_{jt}+{\alpha }_{4}LSC{I}_{jt}+{\alpha }_{5}M{F}_{jt}+{\alpha }_{6}T{F}_{jt}+{\alpha }_{7}F{F}_{jt}+{\epsilon }_{ijt})\end{array}$$

(17)

$$\begin{array}{ll}\ln IM{P}_{ijt}=& {\beta }_0+{\beta }_{1}GD{P}_{it}+{\beta }_{2}GD{P}_{jt}+{\beta }_{3}PO{P}_{it}+{\beta }_{4}PO{P}_{jt}+\\ & {\beta }_{5}BOR{D}_{ij}+{\beta }_6\ln DIS{T}_{ij}+{\nu }_{ijt}-({\alpha }_0+{\alpha }_1\ln DE{L}_{Bjt}+{\alpha }_{2}FT{A}_{ijt}+\\ & {\alpha }_{3}TAR{I}_{jt}+{\alpha }_{4}LSC{I}_{jt}+{\alpha }_{5}M{F}_{jt}+{\alpha }_{6}T{F}_{jt}+{\alpha }_{7}F{F}_{jt}+{\epsilon }_{ijt})\end{array}$$

(18)

$$\begin{array}{ll}\ln IM{P}_{ijt}=& {\beta }_0+{\beta }_{1}GD{P}_{it}+{\beta }_{2}GD{P}_{jt}+{\beta }_{3}PO{P}_{it}+{\beta }_{4}PO{P}_{jt}+\\ & {\beta }_{5}BOR{D}_{ij}+{\beta }_6\ln DIS{T}_{ij}+{\nu }_{ijt}-({\alpha }_0+{\alpha }_1\ln DE{L}_{Cjt}+{\alpha }_{2}FT{A}_{ijt}+\\ & {\alpha }_{3}TAR{I}_{jt}+{\alpha }_{4}LSC{I}_{jt}+{\alpha }_{5}M{F}_{jt}+{\alpha }_{6}T{F}_{jt}+{\alpha }_{7}F{F}_{jt}+{\epsilon }_{ijt})\end{array}$$

(19)

4. Results

4.1. The Results of the Measurement of the Digital Trade Development Level

Based on the entropy value method, we determined the weights of each secondary index and used stata 15.0 software to measure the digital trade development level index of sample countries. The score results are shown in

Table 4. Scores reflecting development level of digital trade in sample countries from 2006 to 2022.

Country	Digital Infrastructure Construction			Digital Trade Competition Intensity			Digital Technology Innovation Ability			2006–2022 Mean
	2006	2012	2022	2006	2012	2022	2006	2012	2022
Australia	0.554	0.621	0.645	0.318	0.310	0.379	0.308	0.300	0.309	0.314
Argentina	0.264	0.489	0.578	0.212	0.232	0.324	0.129	0.154	0.201	0.209
Brazil	0.226	0.416	0.481	0.222	0.204	0.297	0.109	0.139	0.176	0.172
Canada	0.567	0.650	0.680	0.352	0.347	0.352	0.202	0.201	0.220	0.256
China	0.052	0.349	0.599	0.270	0.398	0.494	0.077	0.352	0.698	0.361
Chile	0.292	0.454	0.574	0.215	0.207	0.276	0.094	0.137	0.170	0.192
Cambodia	0.019	0.208	0.332	0.058	0.047	0.188	0.012	0.027	0.029	0.052
Denmark	0.707	0.734	0.672	0.373	0.336	0.372	0.216	0.236	0.253	0.259
France	0.523	0.733	0.808	0.341	0.383	0.369	0.183	0.198	0.220	0.252
Germany	0.641	0.733	0.771	0.350	0.345	0.366	0.213	0.249	0.294	0.279
India	0.039	0.137	0.212	0.312	0.321	0.414	0.071	0.108	0.144	0.143
Japan	0.526	0.656	0.828	0.371	0.329	0.365	0.333	0.317	0.313	0.323
Laos	0.032	0.143	0.313	0.053	0.095	0.141	0.015	0.030	0.023	0.061
South Korea	0.607	0.739	0.813	0.508	0.446	0.506	0.309	0.356	0.415	0.367
Italian	0.512	0.596	0.672	0.239	0.253	0.300	0.165	0.167	0.210	0.220
Pakistan	0.053	0.117	0.181	0.086	0.082	0.252	0.026	0.026	0.082	0.049
Russia	0.306	0.535	0.635	0.186	0.249	0.312	0.175	0.189	0.206	0.234
South Africa	0.168	0.324	0.463	0.147	0.148	0.247	0.053	0.058	0.072	0.098
Thailand	0.170	0.301	0.575	0.355	0.275	0.360	0.093	0.102	0.140	0.162
Ukraine	0.254	0.401	0.506	0.179	0.187	0.447	0.152	0.165	0.130	0.193
UK	0.622	0.726	0.782	0.447	0.385	0.408	0.186	0.189	0.262	0.265
America	0.563	0.606	0.650	0.423	0.374	0.394	0.482	0.550	0.630	0.539
Uruguay	0.287	0.526	0.699	0.200	0.214	0.362	0.086	0.100	0.127	0.178
Vietnam	0.112	0.361	0.502	0.108	0.301	0.493	0.034	0.053	0.090	0.130
Kazakhstan	0.140	0.535	0.536	0.257	0.301	0.383	0.100	0.094	0.102	0.164
Mexico	0.197	0.334	0.497	0.330	0.321	0.351	0.063	0.073	0.103	0.144
Peru	0.135	0.296	0.419	0.154	0.147	0.223	0.060	0.084	0.156	0.141
Philippines	0.098	0.245	0.386	0.562	0.520	0.715	0.051	0.056	0.088	0.157

Source: Based on the previous calculation results.

. According to the score results of the digital trade development level, from the time-series analysis, the growth rate of the digital trade development level in high-income countries such as Australia, Canada, Japan, South Korea, the United Kingdom, and the United States is small. Compared with these high-income countries, digital trade in low-income countries such as Cambodia, Laos, Pakistan, and Myanmar started late and was always in a state of slow growth. In recent years, China’s digital trade development level has shown a steady growth trend. Compared with other countries, China’s residents have applied for patents and published more scientific journals. In the three different dimensions of digital trade, China’s digital trade innovation ability is strong, which is mainly due to the relatively large number of patent applications and scientific journal articles produced by Chinese residents, and the fact that the enrollment rate of higher education has been increasing in recent years. In addition to China, other countries are mainly divided into two echelons. The first echelon is represented by South Korea, Germany, Denmark, the United Kingdom, France, Japan, Canada, America, Australia, and Italy. These countries have better digital infrastructure construction and stronger digital trade innovation ability, i.e., digital trade is booming. The second echelon comprises the Philippines, Vietnam, South Africa, Pakistan, Laos, and Cambodia. Due to political turmoil and lagging social development, the level of economic development is low, which restricts their investment in digital infrastructure construction and their improvement in digital technology innovation, resulting in a low level of digital trade development.

4.2. Model Applicability Evaluation

The applicability of the stochastic frontier gravity model is significantly influenced by the variations in its equation formulation. Therefore, this paper employs the likelihood ratio (LR) test method to evaluate the scientific validity and rationality of the model specification in terms of its applicability. Specifically, two levels of applicability tests are conducted for the stochastic frontier gravity model: one is to examine the existence of trade inefficiency terms, and the other is to test whether trade inefficiency terms vary over time.We used Frontier 4.1 software to test its applicability. The empirical model test results are presented in

Table 5. Simulation likelihood ratio hypothesis testing results.

Null Hypothesis	H0	H1	LR Statistic	Degrees of Freedom	1% Cutoff	Conclusions of Test
There are no trade efficiencies	453.732	535.453	163.442	1	9.500	refuse
Trade efficiencies do not change over time	453.373	481.930	57.114	2	12.810	refuse

Note: LR statistic = −2[ln(H₀) − ln(H₁)], H₀ is the constrained model, and H₁ is the unconstrained model.

.

As can be seen from the test results in Table 5, regarding whether there is a trade inefficiency term in grain import trade, the LR statistical value is greater than the critical value of 1%, which means we can reject the original hypothesis, indicating that there is a trade inefficiency term in grain import trade, and that the use of the stochastic frontier gravity model is appropriate for measuring the efficiency of China’s grain import trade with other countries. Regarding whether the grain import trade inefficiency term is a time-varying term, the LR statistic value is also greater than the critical value of 1%, which again means we can reject the original hypothesis, indicating that the grain import trade efficiency between China and other countries during the sample period has changed over time, i.e., the trade inefficiency term is time-varying. Therefore, the selection of the time-varying stochastic frontier gravity model is reasonable and effective.

After testing the applicability of the model, we use Frontier4.1 software to estimate the import model of panel data of China’s grain imports from sample countries from 2006 to 2022. As can be seen from the test results in

Table 6. Regression of the stochastic frontier gravity model.

Variable	OLS		Time-Invariant SFA		Time-Variant SAF
	Coefficient	t-Value	Coefficient	t-Value	Coefficient	t-Value
β0	−63.889 ***	−4.533	−56.682 ***	−41.589	−57.181 ***	−51.255
lnGDPit	0.962 ***	147.251	0.474 ***	35.995	0.498 ***	30.230
lnGDPit	−0.371 ***	−7.521	−0.208 ***	−17.335	−0.176 ***	−16.413
lnPOPit	5.656 ***	5.265	5.340 ***	51.975	5.326 ***	65.234
lnPOPit	0.014	1.591	0.290 ***	17.980	0.120 ***	5.466
lnBORDij	0.049 **	2.309	−1.102 ***	−19.674	−0.292 ***	−4.322
lnDISTijt	−0.002	−0.217	−0.186 ***	−6.148	−1.347 ***	−16.844
σ2	0.024		0.109 ***	16.861	0.143 ***	19.689
γ	—	—	0.965 ***	199.272	0.974 ***	427.741
μ	—	—	0.649 ***	12.986	0.747 ***	12.041
η	—	—	—	—	−0.002 **	−2.309
log likelihood	453.732		211.655		481.930
LR	—		484.154		540.549

Note: ** = significant at the 5% level, and *** = significant at the 1% level.

, regarding whether there is a trade inefficiency term in grain import trade, the LR statistical value is greater than the critical value of 1%, which means we can reject the original hypothesis, indicating that there is a trade inefficiency term in grain import trade, and that the use of the stochastic frontier gravity model is appropriate for measuring the efficiency of China’s grain import trade with other countries. Regarding whether the grain import trade inefficiency term is a time-varying term, the LR statistic value is also greater than the critical value of 1%, which again means we can reject the original hypothesis, indicating that the grain import trade efficiency between China and other countries during the sample period has changed over time, i.e., the trade inefficiency term is time-varying. Therefore, the selection of the time-varying stochastic frontier gravity model is reasonable and effective.

4.3. Analysis of the Estimation Results of the Stochastic Frontier Gravity Model

Following the validity tests of the model, this study employs panel trade data from 2006 to 2022 between China and major grain-exporting countries for regression analysis. As demonstrated in Table 6, the γ coefficients in both the time-invariant model and time-varying model are statistically significant at the 1% level and approach unity. This indicates that the disparity between China’s actual grain import levels and the stochastic frontier-based potential imports predominantly arises from import inefficiency rather than external shocks. In the time-varying stochastic frontier gravity (SAF) model, the η eta coefficient is significantly negative at the 5% level. This result not only justifies the adoption of a time-varying specification in the empirical model but also reveals a gradual increase in import inefficiency during the sample period, reflecting emerging trade barriers. These findings underscore the necessity of enhancing agricultural trade cooperation between China and major grain-exporting nations to mitigate inefficiencies and optimize trade potential.

Based on the regression results of the time-varying SAF model, the following conclusions can be drawn: (1) China’s economic scale is significantly positive at the 1% significance level, indicating that improvements in China’s economic development level can promote an expansion of its grain import volume. This is attributable to the fact that the larger the economic scale of China, the greater its capacity to stimulate grain import trade. Conversely, the economic scale of the sample country is significantly negative at the 1% level, suggesting that an increase in the economic size of the exporting country leads to heightened domestic demand for grains within that country. Given a fixed grain production level, increased domestic consumption results in a reduced volume of grains available for export. (2) The population size of the primary grain-exporting countries and that of China are significantly positive at the 1% level, indicating that the population sizes of both trading partners exert a notable positive influence on China’s grain import trade. Moreover, the coefficient associated with the population size of major grain-exporting countries exceeds that of China, implying that the population scale of exporting countries has a stronger facilitating effect on China’s grain import trade relative to China’s own population. (3) The variable indicating whether the trading countries share a common border is significantly negative at the 1% level. This finding aligns with expectations by suggesting that when exporting and importing countries are geographically contiguous, the reduction in transportation costs fosters larger grain flows, thereby promoting the development of China’s grain import trade. (4) The coefficient for geographical distance is −1.347, statistically significant at the 1% level, signifying that the physical distance between trading countries constitutes a major impediment to China’s grain import activities from leading global grain-exporting nations. Greater distance increases transportation costs, consequently reducing import volumes. However, considering the relatively small magnitude of this coefficient, it is plausible that the negative impact of geographical distance has been progressively attenuated due to advancements in transportation infrastructure and logistics in recent years.

4.4. Analysis of the Regression Results from the Import Trade Inefficiency Model

The results of the likelihood ratio test in Table 6 indicate the presence of inefficiency components within the time-varying stochastic frontier gravity model of grain import trade. Therefore, based on the previously introduced “one-step method” and Equation (16), Frontier4.1 software was used to further estimate the factors affecting inefficiency; the detailed results are presented in

Table 7. Estimation results of trade inefficiency model.

Variable	SAF		Variable	Trade Inefficiency Model
	Coefficient	t-Value		Coefficient	t-Value
β0	−32.6759 **	−2.3449	α0	0.5144 ***	3.1356
lnGDPit	−0.2786 ***	−5.5208	DELjt	−3.6157 ***	−3.4866
lnGDPjt	0.9092 ***	67.7781	FTAijt	0.0004	0.2614
lnPOPit	3.3584 ***	3.1680	TAFijt	−0.603 ***	−2.7620
lnPOPjt	0.0291 **	2.1387	LSCIjt	−2.0281 ***	−4.9074
BORDij	0.1019 ***	4.4590	MFjt	0.0004	0.2614
lnDISTijt	0.0380 ***	3.9131	TFjt	0.0028 *	1.8612
			FFjt	−0.0226 ***	−4.1895
σ2	—	—	σ2	0.0229 ***	11.4768
γ	—	—	γ	0.9616 ***	36.3814
LLF	264.9277
LR	106.5453

Note: * = significant at the 10% level, ** = significant at the 5% level, and *** = significant at the 1% level.

. As shown in the table, the γ coefficient is statistically significant at the 1% level, with a likelihood ratio (LR) value of 106.545. Besides the variables representing whether a free trade agreement is signed and the degree of financial liberalization, which are found to be insignificant, all the other key explanatory variables regarding the inefficiency effects exhibit highly significant coefficients. This suggests that the overall estimation of the grain import trade inefficiency model yields robust and reliable results.

In the model, the coefficient of the inefficiency variable related to trade is negative, indicating that this variable effectively promotes the efficiency of China’s grain import trade by contributing to an increase in import volumes and facilitating improvements in trade efficiency. Conversely, a positive coefficient would suggest that the variable hampers the development of China’s grain import trade and impedes efficiency gains. Concerning the estimation results of specific explanatory variables, the following are proposed:

(1)

The key explanatory variable (lnDEL_jt), the level of digital trade development, passes the significance test at the 1% level, with a negative coefficient, indicating that the digital trade development level of major grain-exporting countries can suppress the decline in China’s grain trade efficiency. Digital trade, through advanced digital tools, such as electronic information systems and the Internet, breaks traditional geographical constraints, enabling more efficient dissemination of global grain trade information, thereby reducing trade costs. Additionally, digital trade can facilitate the establishment of high-speed and efficient cross-border electronic payment platforms, accelerating the exchange of grain and financial transactions between exporting countries and promoting fintech and trade cooperation among major exporters. Digital platforms established at both demand and supply sides enable producers to more rapidly perceive market demand changes, allowing targeted product design, which further enhances the grain export quality and trade efficiency of the main exporting nations.

(2)

The virtual variable representing whether the grain trade parties have signed free trade agreements (FTA_ijt) does not show significant effects, contrary to expectations. This may be due to the insufficient number of free trade agreements signed between China and the sample countries, leading to an underestimation of their roles in removing trade barriers and facilitating trade facilitation.

(3)

The tariff level of the importing country (TAF_ijt) is significantly positive at the 1% level, which is consistent with the expected outcome, implying that higher tariffs in import countries are associated with greater restrictive effects on China’s grain imports. Nonetheless, the coefficient is relatively small, indicating a limited impact.

(4)

The linear shipping connectivity index (LSCI_jt) is significant and passes the significance test at the 1% level, suggesting that the development level of transportation infrastructure in grain-exporting countries significantly influences their export efficiency. Higher levels of trade facilities and freight infrastructure in export nations lead to lower inefficiency in China’s grain imports from these countries, thereby contributing to an improvement in trade efficiency. Consequently, China should strengthen cooperation with major grain-exporting countries, enhance the transportation environment for trade, reduce trade costs, and promote the efficiency of its grain import trade.

(5)

The three indices of economic freedom—namely monetary freedom, trade freedom, and financial freedom—reflect the overall business environment of a country. Among these control variables, only financial freedom passes the significance test at the 1% level and bears a negative sign, indicating that higher levels of financial freedom in grain-exporting countries facilitate the reduction in trade costs and enhance the efficiency of grain exports to China. Conversely, monetary freedom does not show a significant effect, and trade freedom exhibits a significant positive correlation at the 10% level, which somewhat inhibits China’s import efficiency from these countries. This may be attributable to the prevalence of trade barriers, as countries prioritize grain security and impose various restrictions on grain exports, thereby hindering China’s grain imports. The non-significance of financial freedom could be explained by the fact that the majority of the sampled countries are developing nations with limited financial liberalization and outreach, reducing the potential impact of financial freedom on import trade efficiency.

4.5. The Regression Results of the Stochastic Frontier Gravity Model Across Multiple Dimensions of the Digital Economy

We employed Frontier 4.1 software to integrate digital infrastructure construction (DELA_jt), digital trade competition intensity (DELB_jt), and digital technology innovation ability (DELC_jt) into the stochastic frontier gravity model, and further analyzed how these digital trade development indicators influence China’s grain import efficiency, as demonstrated in Equations (17)–(19). These are denoted as Model 1, Model 2, and Model 3, with the regression results presented in

Table 8. Regression results of hierarchical indicators.

Variable	Model (1)		Model (2)		Model (3)
	Coefficient	t-Value	Coefficient	t-Value	Coefficient	t-Value
DELAjt	−3.733 **	−2.2928	—	—	—	—
DELBjt	—	—	−1.813 *	−1.8419	—	—
DELCjt	—	—	—	—	−4.175 ***	−2.9172
FTAijt	−0.0752 **	−2.2460	−0.0498	−1.3128	−0.0450 *	−1.8238
TAFijt	0.0368 **	2.6702	0.0162	1.5218	0.0179 *	1.8889
LSCIjt	−0.0057 ***	−6.6560	−0.0037 ***	−6.5187	−0.0031 ***	−5.3369
MFjt	0.0049 **	2.7884	0.0017	1.0232	0.0016	1.1676
TFjt	0.0038 **	2.3079	0.0046 ***	3.1057	0.0040 ***	3.1896
FFjt	−0.0032 ***	−4.2018	−0.0027 ***	−3.6549	−0.0027 ***	−4.1883
Constant	−0.3733 ***	−2.2928	0.1124	0.5741	0.1687	1.3142
σ2	0.0263 ***	8.5431	0.0240 ***	9.1810	0.0236 ***	11.3717
γ	0.7792 ***	9.9645	0.9371 ***	15.2370	0.9627 ***	40.4533
LLF	263.0523		259.9443		262.6948
LR	102.7944		96.5785		102.0794

Note: * = significant at the 10% level, ** = significant at the 5% level, and *** = significant at the 1% level.

.

As demonstrated in Model (1), the variable of digital infrastructure construction (DELA_jt) passes the significance test at the 5% level, with a negative coefficient sign. This indicates that the improvement in digital infrastructure construction in grain-exporting countries contributes to enhancing the efficiency of China’s grain import trade. In the context of digital trade, strengthening digital infrastructure construction—including the deep integration of digital technologies such as the Internet and big data into various links of agricultural product trade—promotes greater intensification of the trade processes in China’s grain import trade, encompassing grain production, marketing, transaction settlement, transportation and payment, customs clearance, and other relevant stages. Such intensification reduces grain inventory backlogs, alleviates information asymmetry between supply and demand enterprises, lowers operational costs, and effectively elevates the efficiency of China’s grain import trade.

As illustrated in Model (2), the variable of digital trade competition intensity (DELB_jt) passes the significance test at the 10% level, with a negative coefficient sign, indicating that an increase in digital trade competition intensity is conducive to enhancing the efficiency of China’s grain import trade. Digital trade competition intensity serves as a metric for assessing a country or region’s comprehensive digital trade competitiveness [48]. The augmentation in digital trade competition intensity facilitates the elevation of a grain-exporting country’s market share in the international arena, enhances its grain trade openness, and expands both the depth and breadth of its grain export trade openness. Furthermore, it optimizes the structure of grain export trade, elevates the quality of grain export trade, and creates favorable conditions for importing countries to engage in grain import trade.

As depicted in Model (3), the variable of digital technology innovation ability (DELC_jt) passes the significance test at the 1% level, with a notably negative coefficient, suggesting that the enhancement in digital technology innovation ability contributes to the improvement in China’s grain import trade efficiency. Advancing digital technology innovation facilitates the refinement of grain trade regulations, stimulates the emergence of new business forms and models in grain trade between exporting and importing countries, and fosters new advantages and driving forces in grain trade. This process propels the continuous digitization of grain trade means between the two parties, leveraging the functional role of improved digital technology innovation ability in “reducing costs and enhancing efficiency” for grain trade. Consequently, it drives the transformation and upgrading of traditional grain trade, thereby achieving an elevation in China’s grain import efficiency.

4.6. Regression Results of Hierarchical Indicators

Another important objective of this study is to employ the stochastic frontier gravity model to further estimate the efficiency of China’s grain import trade. Accordingly, based on the estimation results from Frontier 4.1, this paper presents the average trade efficiency of China’s grain imports from major exporting countries under both the time-varying stochastic frontier gravity model and the “one-step approach”.

As illustrated in Figure 2, the analysis indicates that the average efficiency of China’s grain import trade derived via the “one-step approach” generally surpasses that obtained through the time-varying model. Furthermore, when ranking the average trade efficiencies of China’s grain imports from various countries from highest to lowest, both estimation approaches produce largely consistent orderings. According to the computed results, the average trade efficiencies under the time-varying model and the “one-step approach” are 0.351 and 0.735, respectively, highlighting that there remains considerable potential and scope for expanding China’s grain import trade with major global exporters. The results presented in Figure 2 reveal notable inter-country variation in trade efficiencies. The top five countries in terms of average grain import trade efficiency are America, Australia, Canada, Argentina, and Ukraine. In 2022, grain imports from these five nations accounted for approximately 79.68% of China’s total grain import volume, indicating substantial trade volume with these counterparts. Conversely, the five lowest efficiency countries—South Africa, Brazil, Mexico, South Korea, and the United Kingdom—formed a minimal share of China’s total grain imports from the selected nations, collectively representing less than 1% of the total import volume in 2022. This disparity suggests that China’s grain import trade with these countries is still constrained by certain artificial barriers and impediments. Over a longer temporal horizon, China’s grain imports from Latin American and African countries primarily consist of labor-intensive and resource-intensive products, characterized by a relatively simple product structure and low-value-added content. These import efficiencies are largely influenced by geographical distance, which contributes to their relatively low levels. The case of South Korea illustrates this phenomenon: with a comparatively small agricultural sector and a heavy reliance on imported agricultural products, China’s grain imports from South Korea are limited, resulting in lower trade efficiency. Additionally, around 2010, China’s imports of grain from the United Kingdom were notably high; however, due to intensified fluctuations in exchange rates, commodity prices, and the rising trend of trade protectionism, the volume of Chinese grain imports from the UK has experienced a continuous decline, posing significant challenges to maintaining or increasing such imports.

To further analyze the market potential of China’s grain import trade, this study categorizes export countries into four distinct market typologies based on the efficiency values derived from the “one-step estimation approach”, following the classification framework proposed by Zhao [49]. Specifically, markets are segmented as follows: saturated markets (efficiency range: 0.9–1.0), expansion-oriented markets (efficiency range: 0.6–0.9), developing markets (efficiency range: 0.3–0.6), and iceberg-type markets (efficiency range: 0–0.3).

Higher trade efficiency values indicate stronger bilateral trade linkages and diminishing marginal potential for efficiency improvements. Aligning with China’s calculated grain import efficiency values (

Table 9. China’s average grain import trade efficiency and import market typology.

Market Typology	Grain Importing Countries (Efficiency Score)
Saturated markets	USA (0.945), Canada (0.903)
Expansion-oriented markets	Australia (0.876), Argentina (0.840), Ukraine (0.821), Vietnam (0.816), France (0.782), Cambodia (0.778), Thailand (0.771), Kazakhstan (0.763), Pakistan (0.763), Russia (0.682), Laos (0.661), India (0.654), Uruguay (0.610)
Developing markets	Italy (0.562), Denmark (0.547), Peru (0.532), Germany (0.517), Japan (0.507), Chile (0.471), South Africa (0.462), Philippines (0.434), South Korea (0.426), UK (0.389), Brazil (0.384)
Iceberg-type markets	Mexico (0.292)

Source: Compiled based on the operation results of Frontier 4.1.

), the analysis reveals that saturated markets are exclusively represented by two developed economies—America and Canada. This dominance is attributed to their status as global agricultural powerhouses [50], with China’s grain imports from these nations demonstrating sustained annual growth.

The expansion-oriented market cohort comprises 13 countries, including Australia, Argentina, and Ukraine. Despite substantial existing import volumes, these markets exhibit potential for further trade growth through structural optimization and efficiency-enhancing measures. Developing markets encompass 11 nations, such as Italy, Denmark, and Peru, while Mexico alone constitutes the iceberg-type market. Notably, Latin American countries within the latter categories—despite possessing abundant arable land and significant grain production capacities—currently contribute minimally to China’s import portfolio, underscoring substantial untapped efficiency gains in bilateral trade.

For analytical clarity, the sampled countries are categorized into six regions: South America, North America, South Asia, Europe, Africa, and the ASEAN bloc, with Australia incorporated into the ASEAN grouping and Kazakhstan assigned to South Asia. As depicted in Figure 3, the average trade efficiency of China’s grain imports ranges from 0 to 1, where values approaching 1 indicate higher efficiency. Overall, China’s grain import efficiency from major exporters exhibits a fluctuating upward trajectory. Notably, the ASEAN and North American regions demonstrate consistently elevated efficiency levels throughout the sample period, attributable to the dominant roles of Australia, America, Canada, Vietnam, and Cambodia in China’s grain import portfolio. Conversely, trade efficiencies with African and South American counterparts remain comparatively subdued.

A critical inflection point emerges post-2009, marked by a pronounced decline in efficiency followed by gradual recovery. This pattern aligns with the systemic shocks induced by the 2008 global financial crisis. As evidenced by prior analysis of trade inefficiency factors, financial liberalization constitutes a statistically significant determinant of China’s grain imports, potentially explaining this cyclical downturn. Post-2020, the efficiency metrics reached new troughs, primarily driven by COVID-19 pandemic disruptions—including widespread export restrictions and logistical constraints in global grain trade.

Furthermore, persistently low efficiency levels in the China–South Africa and China–Mexico grain trade may reflect structural impediments rooted in geopolitical tensions. Regional disparities are particularly pronounced in Latin America and Africa, where trade remains concentrated in bulk commodity imports with limited value chain integration, despite these regions’ theoretical comparative advantages in agricultural production.

4.7. Measurement of Import Trade Potential and Expansion Space

Trade potential is defined as the maximum attainable trade volume between partners under conditions of optimal efficiency, assuming the absence of inefficiency constraints. In this study, China’s grain import potential is quantified as the ratio of actual import values to estimated trade efficiency. To enhance measurement precision, this analysis introduces the concept of trade growth margins to assess proportional expansion opportunities in China’s grain imports across partner nations. Table 8 presents a longitudinal examination of import potential and growth margins using sampled data from 2006, 2010, 2014, 2018, and 2022.

From 2006 to 2022, China’s grain import potential from sampled countries exhibited cyclical growth, peaking in 2022, with Brazil ranking first at USD 122.754 billion, followed by the United States (USD 30.519 billion), Australia (USD 2.954 billion), Argentina (USD 4.670 billion), and Ukraine (USD 2.279 billion). These figures align closely with China’s actual import volumes from these economies.

In terms of trade growth margins, the top five countries in 2022—Mexico, Brazil, Denmark, the United Kingdom, and the Philippines—demonstrated significant expansion opportunities despite their current low efficiency classifications (

Table 10. Grain import trade potential and expansion space of China: 2006–2022.

Countries	2006		2012		2017		2022
	Import Trade Potential (USD 10 Thousand)	Expansion Space (Times)	Import Trade Potential (USD 10 Thousand)	Expansion Space (Times)	Import Trade Potential (USD 10 Thousand)	Expansion Space (Times)	Import Trade Potential (USD 10 Thousand)	Expansion Space (Times)
Australia	51,819.06	0.40	152,304.26	0.14	192,208.63	0.03	295,370.26	0.03
Argentina	181,573.68	0.12	545,571.81	0.46	299,358.07	0.12	467,220.47	0.18
Brazil	1,102,450.31	2.65	3,035,507.38	1.13	5,623,822.99	1.69	12,275,389.72	2.29
Canada	15,749.91	0.36	71,036.39	0.06	158,223.47	0.15	195,361.48	0.02
Chile	2.39	1.48	63.54	1.44	30.03	0.82	79.00	0.68
Cambodia	0.01	0.04	382.65	0.27	15,501.82	0.53	27,616.51	0.53
Denmark	0.46	0.43	121.16	0.51	656.71	1.43	566.64	1.30
France	402.59	0.43	1605.01	0.27	5947.23	0.18	113,024.06	0.16
Germany	67.41	1.14	892.54	1.05	284.85	1.06	184.36	0.59
India	120.50	0.73	87.28	0.76	2.06	0.22	118,988.56	0.53
Japan	17.77	0.38	39.55	0.88	349.03	0.86	193.07	0.70
Laos	352.42	0.21	3292.33	0.53	12,364.24	0.59	6649.92	0.52
South Korea	1.50	0.74	63.30	0.78	59.47	1.85	0.44	0.85
Italy	0.25	0.72	0.12	1.30	0.36	1.06	41.89	0.28
Pakistan	10.81	0.50	36,689.53	0.37	11,137.87	0.19	60,732.15	0.33
Russia	55.22	0.93	5822.51	0.57	20,897.81	0.23	56,991.13	0.21
South Africa	0.05	0.76	0.82	1.56	10.16	1.16	23,785.82	0.72
Thailand	33,659.53	0.21	22,510.62	0.40	68,850.94	0.26	51,597.31	0.23
Ukraine	1.04	0.04	14.30	0.43	75,290.29	0.43	227,853.77	0.28
UK	0.05	3.62	36.33	3.54	2.13	1.66	0.79	1.19
America	314,142.52	0.14	1,776,400.77	0.03	1,625,446.08	0.05	3,051,922.81	0.13
Uruguay	23,661.90	0.87	168,885.50	0.39	190,079.76	0.84	177,965.46	0.34
Vietnam	1171.68	0.36	100,263.20	0.47	116,593.67	0.14	44,184.30	0.01
Kazakhstan	0.75	0.50	5890.89	0.34	7071.68	0.19	7568.57	0.13
Mexico	0.01	3.91	0.91	2.64	1.00	1.70	0.39	3.17
Peru	29.86	0.88	86.33	0.97	91.63	0.63	370.52	0.60
Philippines	31.11	1.12	0.05	1.55	0.11	1.27	0.49	0.92

Source: Calculated based on data from the UN Comtrade database.

). Mexico, categorized as an iceberg-type market, and Brazil, Denmark, the UK, and the Philippines as developing markets, exhibit substantial untapped potential. Notably, Brazil’s import potential reached USD 122.754 billion with a growth margin of 2.29 times, attributable to its comparative advantages in land-intensive agricultural exports. As fellow BRICS nations, China and Brazil share strong complementarities in agro-trade, underpinned by Brazil’s vast arable land and fertile soils, warranting deepened bilateral cooperation to harness these synergies.

5. Conclusions and Policy Implications

5.1. Conclusions

This study employs the entropy method to evaluate the development level of digital trade among global grain trading nations, including China, over the period 2006–2022. By incorporating the digital trade development level as a core explanatory variable, the analysis examines its impact on the efficiency of China’s grain import trade. Building upon this framework, the research further quantifies China’s grain import potential from major global grain exporters and identifies future expansion opportunities. This study’s conclusions are as follows:

Firstly, the digital trade development levels among the sampled countries exhibit significant variation, with high-income nations demonstrating the most advanced progression in this domain, followed by middle-income countries, while low-income economies display the least developed digital trade capabilities. Furthermore, our investigation demonstrates that enhancing the digital trade development level of grain-exporting countries can effectively improve the efficiency of China’s grain import trade, which aligns with the research findings of Xiao [29]. Our empirical findings demonstrate that Wang et al.’s conclusions align with ours, confirming that the development of digital trade in importing countries significantly enhances the import efficiency of their technology-intensive products [51].

Secondly, digital infrastructure construction, digital trade competition intensity, and digital technology innovation ability in grain-exporting countries significantly impact China’s efficiency in grain import trade. However, digital technology innovation ability has a more significant positive effect on this efficiency. Scholars such as Castro have highlighted the importance of digital infrastructure construction in enhancing trade efficiency [52], which differs from our findings.

Thirdly, our research findings indicate that China has the highest efficiency in grain import trade from ASEAN and North American countries. When analyzing the potential and expansion space for China’s grain import trade, we found that the potential and the expansion space for importing grain from South American countries are the largest, surpassing the average of the sample countries. This is consistent with Cheng’s research, and there are large country differences in the potential of agricultural imports and the space for growth expansion [19].

5.2. Limitations and Future Development Direction

The breadth and depth of data collection remain insufficient. While the actual digital delivery value serves as a critical indicator for assessing the impact of digital trade on agricultural trade, academic research on the measurement of digital trade remains limited, and there is a lack of standardized databases. This poses a risk of omitting relevant variables during the construction of the indicator system. Furthermore, there is room for further exploration regarding the actual factors influencing China’s grain import trade potential. Due to limitations in the available statistical data, the current study is only able to conduct research at the macro level. However, differences among countries in terms of institutional frameworks, grain demand, and national reserves have not been incorporated into the analysis.

In our follow-up study, we plan to improve our research in two aspects. On one hand, we plan to expand the digital trade indicator system to the present, thereby enabling a comprehensive and accurate measurement of the development level of digital trade across countries worldwide. On the other hand, we intend to incorporate additional variables into the stochastic frontier gravity model to examine their relationship with digital trade development, thereby providing a more accurate assessment of the impact of digital trade on China’s grain import trade potential.

5.3. Policy Implications

Based on the aforementioned findings, this study proposes the following policy recommendations:

First, international cooperation in digital trade with major grain exporters should be strengthened. On one hand, China should leverage global public platforms to share cutting-edge achievements in digital trade innovation with leading nations, integrating these advancements with traditional agricultural trade to accelerate the development of new models and formats in grain import. On the other hand, given that many countries exporting grain to China are developing economies, the government should enhance assistance in digital trade capacity building to narrow the gap between the two sides of trade at the level of digital trade development. Disparities in digital trade development levels across countries currently hinder the efficiency of China’s grain imports. Therefore, China should incentivize its leading digital enterprises to invest in technologically lagging nations, facilitating the integration of digital technologies with agricultural trade, improving digital infrastructure, and mitigating information asymmetry risks. These measures will foster a favorable ecosystem for high-quality grain imports.

Second, heterogeneity in import efficiency across countries should be assessed. For countries with lower efficiency in grain import trade but greater potential for trade expansion, such as Mexico, Brazil, and the Philippines, China should encourage leading digital trade enterprises to assist in establishing localized digital platforms for grain trade. This initiative aims to address challenges in developing target markets and expanding distribution channels for grain production and operations, thereby broadening traditional grain trade channels. By leveraging digital technological innovation to facilitate the deep integration of digital technologies with traditional agricultural trade, this approach cultivates high-caliber human capital in the digital trade sector, establishes collaborative ecosystems for joint digital technology research and development, and strategically aligns open cooperation with national security imperatives, thereby enhancing the stability of China’s grain trade. By leveraging digital trade platforms, China will further enhance the diversification and operational efficiency of its grain import systems, ensuring more resilient and streamlined supply chains. For countries with relatively high efficiency in grain import trade but limited potential for trade expansion—such as Australia, Argentina, Canada, America, and Vietnam—China should capitalize on digital trade technologies to reduce import costs, enhance quality standards, and optimize the structural composition of grain imports. By strategically deploying these technologies, China can effectively expand the trade potential with these nations, thereby upgrading its grain import framework through cost efficiency, quality assurance, and diversified sourcing models. This approach aligns with the dual objectives of securing stable agricultural supplies and advancing systemic modernization in global trade governance.

Third, digital trade agreements with grain exporters should be accelerated. The unbalanced development of digital trade has led to obstacles in intergovernmental cooperation in the field of digital trade. Finalizing and upgrading digital trade agreements will serve as institutional catalysts for bilateral digital commerce advancement. In order to further promote the implementation of food import trade cooperation between China and grain-exporting countries, reduce the risks brought about by digital trade barriers, and actively play the role of digital trade in improving the efficiency of China’s food import trade, it is necessary to establish and improve the relevant provisions of digital trade as soon as possible.