Correction: Does institutional openness improve the trade efficiency of China's agricultural products imported from Central Asian countries? A time-varying stochastic frontier gravity model

China first put forward the "Belt and Road Initiative" (BRI) in Central Asian countries. With the implementation and promotion of the BRI, the scale of agricultural trade from Central Asian countries to China has been growing continuously, from 9.9 million U.S. dollars in 2000 to 691 million U.S. dollars in 2022, with an average annual growth rate of 21.3% (Table 1). The economies of the Central Asian countries are in the process of transition, and the agricultural sector is one of the most important sectors in the five Central Asian countries, accounting for 10% ~ 45% of their GDP and employing 20% ~ 50% of total employment (Hamidov et al., 2016;Yu et al., 2020). This means that agricultural production and trade occupy a major position in its economic structure, which is related to the local livelihood. To cope the current international environment with steeply increasing in uncertainty and instability, the export trade of agricultural products between China and Central Asian countries, can effectively improve the farmers' employment and incomes in Central Asian countries, which will enhance the degree of openness in the agricultural sector and the resilience of the food system in Central Asian countries.However, agricultural trade in Central Asian countries still faces high costs, both for geographical reasons and institutional barriers. And institutional openness is becoming increasingly important for agricultural trade (Pomfret, 2017;Sun and Zhang, 2021). In 2023, China and Central Asia countries signed the China-Central Asian countries Summit Outcome List, which proposed the need to promote the level of agricultural trade between China and Central Asian countries in terms of mechanisms and institutions. Therefore, it is of great significance to evaluates the impact of institutional openness on the efficiency of agricultural trade between China and Central Asian countries.The research on institutional openness mainly focused on the exploration of its definition (Research Group of Institute of International Economics, National Development and Reform Commission, 2021;Zhang, 2021;Dai, 2021). Relevant studies believed that the essence of systematic opening up is the expansion, extension and deepening of "border opening up" to "internal opening up" in the past, and the formation of basic rules and systems in line with the prevailing rules of international economic and trade activities in the process of promoting rule changes and optimizing system design. In promoting rule and optimizing institution design, it forms basic rules and systems that are in line with the prevailing rules in international economic and trade activities, which is an advanced institutional arrangement that plays a leading role in the adjustment and improvement of the new round of highly standardized international economic and trade rules (Chang and Qian, 2022;Zhao and Zhang, 2022). With the deepening of the understanding of institutional openness, some researchers have also tried to sort out the characteristics of institutional openness, the mechanism and industrial chain risk, as well as the practical foundation and realization path with the Free Trade Zone (FTZ) as the core (Guo, 2022;Liu et al., 2023;Zhao and Zhang, 2022). At the same time, some studies have begun to use three dimensions of business environment, trade and investment liberalization and facilitation, and institutional innovation to measure institutional openness (Nie and Xue, 2022), as well as to quantitatively assess the impact of institutional openness on enterprise innovation (Wang and Chang, 2023). Related studies have paid less attention to institutional openness and its influence on agricultural trade (Wang and Chang, 2023).With the deepening of China's economic and trade cooperation relations with Central Asian countries, the research on China's trade in agricultural products with Central Asian countries have gradually increased. Relevant studies are mainly focused on the following aspects: first, the competitiveness and complementarity of China's agricultural products trade with Central Asian countries (He et al., 2016;Jia, 2021;Liu, 2020;Li and Li, 2011;Yi and Abula, 2008). Relevant studies have shown that Central Asian countries has strong international competitiveness in the export of land-intensive products such as cotton and silk, and China has relatively strong competitiveness in technology-intensive agricultural products such as vegetables and fruits, meat, fish, and eggs, while the complementarity of bilateral trade in agricultural products has increased significantly, and the categories of agricultural products that have strong complementarities are mainly concentrated in vegetables, sugar, flour products, and textile fibers of the cotton category (Meng, 2018). Secondly, China's trade with Central Asian countries in agricultural products is growing. The study on the growth drivers of agricultural trade between China and Central Asian countries (Gong and Zhang, 2014;Hong, 2019;Zhu et al., 2018;Guo et al., 2021). These studies point out that the growth of market demand is the primary reason for the growth of agricultural trade. Third, the potential and efficiency of agricultural trade between China and Central Asian countries (Lv et al., 2020;Qi, 2019;Tan et al., 2016;Wumuer, 2016) and trade structure studies (Yan et al., 2021). Relevant studies have shown that the trade in agricultural products between Central Asian countries and China has a high potential. Fourth, there are studies are about China and Central Asian countries' agricultural trade patterns (Chen, 2014;Li, 2018), trade costs (Hou and Abula, 2015), trade facilitation (Felipe and Kumar, 2014;Hu, 2014;Kai et al., 2021;Yu, 2022;Yu, 2020), FTA construction (Wang et al., 2019), trade margins (Fang and Li, 2023), and supply chain performance evaluation (Abula, 2022). Fifthly, rising studies focused on agricultural value chains and infrastructure in Central Asian countries (Pomfret, 2014;Pomfret, 2017), soil and water resource use Imports Year Imports Cao et al. 10.3389/fsufs.2025.1598004 Frontiers in Sustainable Food Systems 03 frontiersin.org efficiency (Liu et al., 2021), virtual soil and water trade (Zhou et al., 2022), water resource use and food system relationships (Ma et al., 2022), trade openness and food security, and trade openness and food security (Sun and Zhang, 2021).Compared with existing studies, this study has three notable contributions. First, previous research on institutional openness mainly focused on its connotation, however, how to measure institutional openness has not formed a unified standard. Our study contributes by measuring institutional openness with multiple indicators as comprehensively as possible. Secondly, there are many existing studies on the potential and efficiency of agricultural trade in Central Asian countries, but more on the impact of trade facilitation and less on the efficiency of agricultural trade from the perspective of institutional openness. This study focuses on the impact of institutional openness on the efficiency of agricultural trade in Central Asian countries, which can fill the lack of research in this area. Third, fewer studies have considered the impact of uncertainty risks such as the Russia-Ukraine war and the Covid-19 on agricultural trade between China and Central Asian countries. Instead, this study considers it. Therefore, this study tries to adopt suitable indicators to quantitatively measure the institutional openness, and assesses its impact on the efficiency of China's agricultural trade with Central Asian countries under the background of uncertainty based on UN Comtrade database from 2000 to 2022. This study will provide policy references for improving the efficiency of agricultural trade between China and Central Asian countries.The rest of this research is constructed as follows. Section 2 describes the material and methods, we provide detailed information about the data sources and data structure; the time-varying stochastic frontier gravity model of trade and the estimation techniques involved in the analysis. Section 3 presents and discusses the estimated results under study. All the findings of the study are concluded in Section 4 of this study.In this section, we present how we conducted this study and the tools we used. First, we explain the basic idea of the Stochastic Frontier Gravity Theory equation. Second, we describe our derived model for the agriculture exports from Central Asian countries, and give information about the data source and summarize the main characteristics of the data. Finally, we provide the detailed protocol involved in the estimation of our model.This paper intends to use a stochastic frontier gravity model to investigate the impact of institutional openness on the trade efficiency of China's imports of agricultural products from Central Asian countries. The traditional gravity model does not take into account the influence of policy factors, such as institutional factors and other subjective factors, which means the trade potential it calculates does not truly reflect the trade potential between countries. To solve this problem, the stochastic frontier gravity model was introduced into the field of trade research. The stochastic frontier production function first originated from the concept of technical efficiency proposed by Farrell (1957) and Lebenstein (1966), Aigner et al. (1977) and Meeusen and Van Den Broeck (1977) subsequently used the stochastic frontier model to analyse the technical efficiency of the production function. Since the traditional trade model is essentially similar to the production function, Armstrong (2007) argues that it is equally feasible to use the stochastic production function to analyse trade efficiency, providing a theoretical basis for the stochastic frontier gravity model to study trade efficiency. As the stochastic frontier gravity model takes into account the technical inefficiency term, it is more scientific than the traditional gravity model, and has been widely used in the field of trade. According to the theoretical setting of Aigner et al. (1977), Meeusen and Van Den Broeck (1977) and Armstrong (2007), the general form of the stochastic frontier gravity model is as follows (Equations 1-3):( ) ( ) β - = it it v u ijt ijt T f x e (1) ( ) ( ) β * = it v ijt ijt T f x e (2) ( ) - * = = it ijt u ijt ijt T TE e T(3)In Equation 1where ijt T represents the actual trade value between country i and country j, and * ijt T in Equation 2 represents the trade potential value between country i and country j under the ideal condition, i.e., the maximum trade value under the frontier condition, where all the trade inefficiencies are overcome. ijtx is a vector of order 1*k, which represents the natural factors affecting the trade value, such as gross domestic product (GDP), population, and geographic distance, etc., and β is the parameter to be evaluated parameters. it v is the random error term and it u is the trade inefficiency term, where ijt TE in Equation 3 is the trade efficiency value, which is the ratio of the actual trade value and the trade potential value. The size of this value can be used to judge whether the trade is efficient or not, when the value is 1, it indicates that there is no trade inefficiency, the two sides of the trade has reached the maximum frontier value, the trade potential is fully tapped; when the value is 0, it indicates that the trade friction between the two sides of the trade reaches the maximum value so that the two sides cannot trade, and the trade potential that can be tapped in the future reaches the maximum; when the TE ∈ (0,1), it indicates that there are trade inefficiencies. In specific empirical evidence, generally take the logarithm of both sides of Equation 1 to get the following Equation 4:( ) β = + - ijt ijt it it lnT lnf x v u (4)In order to explore the influencing factors of trade inefficiency, this paper draws on the one-step method proposed by Battese and Coelli (1995) ( ) α ε = + it it it u z (5) ( ) ( ) β α ε = + - + ijt ijt it it it lnT lnf x v z it z represents the factors affecting trade inefficiency and α is the parameter to be estimated for the factors affecting trade it v and it u are of and it u a the data in this paper to in order to measure whether the trade efficiency of China's agricultural countries changes time, this paper draws on the research of et al. and time-varying factors into the stochastic frontier gravity model, ) = - - ijt u T u Equation ijt u represents the trade inefficiency term, T the of and is the parameter to be which is the that whether trade efficiency it means that the technical inefficiency time, the trade potential is and the trade efficiency means that the trade inefficiency time, i.e., the trade potential is gradually and the trade efficiency means that the technical inefficiency term does not time, and a model be used this constructed a time-varying stochastic frontier gravity model based on Equation as β β β β β β β β = + + + + + + + + + 1 2 3 4 ijt it it ijt ijt it it it lnT v Equation ijt T is the of agricultural exports from China j to Central Asian country i in The of the is the GDP it and GDP are the GDP of China and the source which the level of economic and the of the and the data are from the Development it and the of the source country and which the domestic market and it is considered that the the out of the source the the domestic market demand and the the imports are to the the in the the the domestic demand and the the data from ijt represents the logarithm of the between the two countries their and it is generally considered that the the distance, the the costs, which will trade between the two countries, data from the database of the ijt represents whether Central Asian countries with it is 1, it is 0, this data is also from it the of the which the agricultural of the in the more the the the of agricultural products 2021), this data is from it is the of value of agricultural in the total GDP of the which the degree of of agricultural resource of the and it is generally believed that the more the agricultural the the of agricultural products and the data is from order to explore the impact of institutional openness on trade inefficiency, this paper constructed a trade inefficiency model that institutional openness system as α α α α α α α α ε = + + + + + + + + + + 1 2 4 it it it it it u uncertainty to existing studies, institutional openness has not the traditional "border based on the of trade but also the deepening of based on the of institutional Therefore, in order to comprehensively measure the institutional openness, we constructed the system from the following in Equation trade "border indicators two main represents whether the country the or not, with a value of 1 for and for have shown that the is in trade relations et al., represents whether countries the and Road which takes the value of 1, it takes the value of studies that can effectively promote agricultural trade et al., the of the improve the efficiency of China's agricultural trade with Central Asian countries. This paper and to measure the degree of openness of the trade of the two the agricultural trade environment mainly it and are the trade efficiency of country i and China which are derived from the efficiency of in the And the are from with 1 and agricultural products are not to be the of international agricultural trade has a great influence on the trade efficiency of agricultural products, and this can effectively Cao et al. 10.3389/fsufs.2025.1598004 Frontiers in Sustainable Food Systems frontiersin.org measure the trade facilitation degree of agricultural trade, which is an important of These trade facilitation related to can agricultural trade et al., is the most average rate of country This can effectively measure the trade of agricultural trade, which from we used economic to measure the degree of openness of it and the degree of economic of country i and China which is from the with a value of The the indicates a evaluation of the which the system and the degree of openness of the source country from dimensions and 2018), the degree of of the degree of economic efficiency, trade investment and The degree of openness in all of the the of the environment, supply chain by policy environment will have a impact on agricultural trade et al., 2020), the policy changes have a impact on the efficiency of agricultural trade. this study three to the the uncertainty represents China's economic policy uncertainty data from The by et al. is a standardized of the of related to economic policy uncertainty in China's which is used to reflect China's economic and policy And we also the impact of the war ( ) and ( The and of of all the are shown in is to an form the stochastic frontier gravity The of two the first one is to the of trade the other is to whether trade inefficiency changes As shown in the is which the of is no trade significance that there trade inefficiency in the model and suitable for the stochastic frontier gravity The time-varying that the is which the of inefficiency does not significance i.e., = is not that trade inefficiency changes time, and it is more 4 the estimation results of the time-varying stochastic frontier gravity model and the trade inefficiency model the The value of is which indicates that the trade inefficiency model the trade inefficiency information According to the it can be the stochastic frontier gravity model, the of it was and that the GDP of the export source country improve the agricultural trade with be to the that the the economic level of the country has to the export of agricultural products The of that the the GDP of China have the the demand for agricultural products, and the less on Central Asian countries The impact of it was that the the of the export source the its domestic of agricultural products, the more for agricultural The of was that the the of which The of ijt was which that the the trade and and the more it was for China to agricultural products from Central Asian countries. And the was with the existing studies et al., 2023). The impact of ijt was that the was when China agricultural products from Central Asian countries mainly to The of ijt and it which that the and agricultural of Central Asian countries are more the are more for agricultural products to the trade inefficiency model, the trade "border First, the of which was the significance that the to the can promote China's imports of agricultural products from Central Asian countries. China's to the in is also a of the which that both sides need to with the rules of trade. And the countries on both sides of the to which the trade inefficiency in of China's imports of agricultural This is with the research of previous which the of countries to the is an institutional arrangement that effectively the trade efficiency of both sides et al., Second, the impact of on trade inefficiency was which that the of the between China and Central Asian countries trade inefficiency and promote China's imports of agricultural products from Central Asia countries et al., is mainly to the that can enhance trade policy and which the of in agricultural trade (Liu and the impact of agricultural trade environment, the of it was which that the the efficiency of China's trade with Central Asian countries, the more it the inefficiency of agricultural trade. And the of it was also which that the the of agricultural trade between the two sides of the trade, the more trade inefficiency can be the degree of openness of the of it was for Central Asian countries, which that the economic of Central Asian countries trade inefficiency, i.e., trade efficiency and 2022). the of for China was and which that the the economic of the more it was to agricultural products from the rest of the and its on Central Asia countries the of the environment, China's economic policy uncertainty uncertainty was which that when China's economic policy it the inefficiency of agricultural trade. The reason is that when there was a in the policy environment, in order to the of China's domestic supply of agricultural products, China the of agricultural products from Central Asian countries. And the impact of Russia-Ukraine war it was which that the of Russia-Ukraine war has the efficiency of Central Asian countries in agricultural products to The war and the of the efficiency of Central Asian countries in agricultural products to which is in line with the of existing studies that have a impact on agricultural trade et al., on the previous we the trade efficiency and trade potential of China's agricultural products from Central Asian countries. 1 Trade efficiency of China's agricultural products from Central Asian countries from 2000 to 2022. Cao et al. 10.3389/fsufs.2025.1598004 Frontiers in Sustainable Food Systems frontiersin.org environment the trade efficiency the "Belt and was put forward in the trade environment also trade potential value, and the trade efficiency, which the trade potential value up to a new to 2022, with the of the and the Russia-Ukraine the trade efficiency value was which also that the trade potential value the the trade efficiency of both sides from the current ~ about ~ The changes in and more the two countries with a degree of economic have been more by the of international uncertainty In it be that in 1, the value of trade potential for the is to the that trade with China was the same terms of trade there is still more for China to agricultural products from Central Asian countries. According to China a total of million from Central Asian countries in 2022, with an trade efficiency of and a trade potential value of which means that of the trade potential to be As for countries, the trade efficiency of and and was while was in 2022. To the of a on the of trade efficiency, this paper to measure the average trade efficiency of country in The results shown that and and And the average value of trade potential was million dollars and the value of trade potential is In the trade potential of China's trade with Central Asian countries is less than and the is with a trade potential value of between ~ that the trade potential is fully China's trade potential for agricultural products from Central Asian countries by ~ on the current that the trade will be between China and Central Asian countries. and are the countries, and and need agricultural investment and cooperation in order to fully the trade on the data of UN Comtrade database from 2000 to 2022, this study a time-varying stochastic frontier gravity model to investigate the impact of institutional openness on China's trade efficiency of agricultural products from Central Asian countries in the of and the trade efficiency and trade potential of China's imports of agricultural products from Central Asian countries. The following can be from the China's agricultural imports from Central Asian countries will have a of for As the ~ 2022, the scale of China's agricultural imports from Central Asia countries from less than million to a average annual growth rate of And China's average export trade efficiency to Central Asian countries for ~ is between and and the potential is about that ~ of the trade potential can still be and there is a institutional openness improve the trade efficiency in generally of China's imports of agricultural products from Central Asian countries. As for the and implementation of the and the have effectively China's trade in agricultural products from Central Asia countries, which that opening such as the of trade contributes to trade efficiency. As for trade environment, the the efficiency of the trade and and the the most the more to improving the trade efficiency of China's imports of Central Asia agricultural the the the trade of the Central Asia countries the more to promoting the export of agricultural products to such as the and war have the scale of when China's economic uncertainty risk, China in agricultural products from Central Asian countries, which promote the trade on can be In order to promote the efficiency of China's agricultural imports to Central Asian countries, both countries on the following of institutional from the of liberalization of the trade international as the to promote trade, and the of the trade and the implementation of the and other on agricultural products, can effectively promote the efficiency of China's agricultural Secondly, as for the infrastructure of agricultural trade, our take to with countries in many such as agricultural to improve the to the efficiency of the trade, to the of on agricultural products, and to improve their agricultural production and export are feasible in the of economic environment China or agricultural and mechanisms with Central Asian countries in to the trade so as to enhance the trade efficiency in a which will the cooperation and opening up of the agricultural field the trade of agricultural