Assessing the Efficiency and Potential of China’s Apple Exports

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Introduction
It is widely recognized that exports are an essential channel for a country's agricultural products to enter the international market and to digest domestic agricultural production capacity, which is also conducive to the economic growth of exporting countries [1][2][3].In terms of fruit products, an estimated 80% of all fruits grown globally are sold as whole fresh fruits.Te export of most international fresh fruits is growing, with an annual growth rate of nearly 7% in the last decade.China is the world's largest producer of apples and the country has also rapidly expanded its exports of fresh and processed apples [4].Signifcantly, the growing demand for fresh produce in emerging and developing economies worldwide has driven signifcant growth in the fresh apple market [5].Similarly, the global apple market is growing due to the rising popularity of fresh apples for their health benefts, the advancement of new hybrid varieties, and the increase in contract farming, among other factors [6].Emerging markets, such as China, are playing a significant role in the global fruits' market.Te fact that the export share of apples was second only to bananas in 2018, apple exports have been one of the most dynamic activities of the international fruits trade in recent years [7].At the same time, apple is the second-largest garden fruit in China, its export trade status is of great signifcance in enhancing the level of China's agricultural products in the international market [8].
According to the statistics of the Food and Agriculture Organization of the United Nations (FAO), there were about 93 countries and regions in the world that produced apples in 2022.Te apple market can be segmented based on geographical location into North America, Europe, Asia-Pacifc, South America, and the Middle East & Africa [9].
Due to a long production history and ideal climatic and geographical conditions [10], China's apple production area and output have continued to be ranked frst in the World and the Asian Pacifc region since 1988 and 1992, respectively.In 2022, China's area under apple production and output were 2.13 million hectares and 4.76 million tons, accounting for 44.10% and 49.63% of the world's total.In addition, China has dominated the global apple industry in terms of its production and consumption capacities.Despite the country's large population and the presence of a signifcant market for apples, the export of apples is also signifcant on a global scale.For instance, China's share of the global apple export market reached its peak at 20% in 2016, before dropping to 17% in 2019 and further declining to 15.6% in 2022.Although this proportion seems small when compared with the production capacity of China, from 1997 to 2022, the export volume of apples continued to increase until the fnancial crisis of 2008 when global apple market demand was sluggish [11], and the export volume of China's apples began to decline.Although it increased in the subsequent year, it could not eliminate the negative impact of the international market (Figure 1).Moreover, it is foreseeable that, with the limitation of domestic apple consumption capacity in the long run, apple exports will gradually become a meaningful way to digest apple production capacity in China.Meanwhile, changes in China's apple production and trade conditions can alter the pattern of global apple production and trade patterns.
Studies on China's agricultural trade have mostly focused on various sectors and subsectors.For example, Suroso et al. [12] examined the factors infuencing and the potential impact of China's tea exports on economic growth in China.Te authors applied the gravity model and the Autoregression Distributed Lag (ARDL) model to a dataset covering the years 2010 to 2020.Te study identifed certain factors as the main drivers of tea exports and found a positive and signifcant relationship between tea trade and economic growth, both in the long and short term.Abdullahi et al. [13] investigated the factors that infuence China's agricultural exports by employing the fxed efect and Poisson Pseudo Maximum Likelihood (PPML) frameworks.Teir study revealed a strong correlation between China's export fows and variables such as GDP, the Chinese language, shared border, and the belt and road initiative (hereafter BRI).Dang and Pang [14] used input-output table data from the years 2002, 2007, 2010, and 2015 in order to construct a computable general equilibrium model of global trade.Te purpose of this model was to evaluate the infuence of bilateral agricultural product trade between China and the Belt and Road (B&R) countries, which is commonly known as the border efect.Tey showed that the border efect of agricultural product trade decreased by 20.9% in 2015 compared to 2010.Tis suggests that the Belt and Road (B&R) initiative has, to some degree, decreased trade barriers and facilitated bilateral agricultural trade between China and B&R countries.
Nasrullah et al. [15] presented a case study that examined China's exports of forest products to the global market using the conventional gravity model.Te study revealed that both GDP and GDP per capita have a positive infuence on Chinese exports, while distance has a negative impact.Furthermore, the study suggested that promoting the Chinese language to importing countries could enhance export relations with China's partners.Sun and Li [16] focused on the trade margins of China's agricultural exports to the Association of Southeast Asian Nations (ASEAN) by utilizing the 2000-2015 data.Te results suggest that the key driver of growth for Chinese agricultural exports to ASEAN has undergone a shift from the extensive margin, particularly prior to the establishment of the China-ASEAN Free Trade Area (CAFTA).Despite China's prominent position in the global apple industry, little is known about the factors that infuence its apple trade, the efciency of its trade operations, and whether there is potential for China to increase its revenue from apple trade.In recent decades, China's government and fruit processing industries have directed signifcant attention towards the apple industry, motivating our work.In addition, export is regarded as the main drive of economic growth and an important component of China's economy.Tus, the apple industry emerges as a signifcant focal point for China's rural revitalization eforts.Tis study aims to ofer valuable insights into the government's strategies for supporting apple farmers by enhancing both apple production and farmers' income.Terefore, to analyze the trade efciency and potential as well as the determinants of China's apple industry, this study employed the Stochastic Frontier Gravity Model (hereafter SFGM) on panel datasets from 1997 to 2019 for China and its major trading partners in apple exports.Te contribution of this study is refected in the following aspects: frst, the authors checked out the status of China's apple export trade and its share in the international market.Second, to provide an insight on the potential, determinants and efciency of apple export.Also, we used the SFGM, which combines the gravity model and the stochastic frontier analysis.Tird, with our substantial efort, we attempt a gravity model in the fruit industry.Despite the signifcance and power of the gravity model in the world trade studies, its application in the global fruits industry is relatively rare or missing in the existing literature.Tus, our study designed to flls this gap.
Te rest of this study is organized as follows.Section 2 presents the study background.Section 3 reviews the works of relevant literature.Section 4 introduces the empirical model of the SFGM and data used in this study.Section 5 presents the results and discussion.In subsection, we use the SFGM to empirically examine the potential and efciency of apple export factors.We conclude the study in the last section and propose several policy implications of our study.

Study Background
China has been a signifcant contributor to global apple production and a considerable exporter [17,18].Figure 2 illustrates that during the study period, China's apple production has seen a substantial increase, rising from 17. Figure 4 shows the trend in apple import and export volume in China and the world.Due to the increasing demand for apple consumption, the import and export trade of apples in China and the world is generally increasing [5].In terms of trade value, the export value of apples in China and the world increased from $101.34

Complexity
Similarly, Mordor Intelligence [6] shows that global demand for apples is increasing due to consumers' growing health concerns.Consequently, this fruit is in high demand among consumers worldwide, particularly in developing countries, the United States, and Europe.Business Wire [19] found that the increase in fresh apple consumption in China can be attributed to a variety of factors.Tese factors encompass the rising income levels of the population, heightened awareness of health and dietary choices, shifting preferences in food consumption, innovative marketing approaches, and advancements in cold chain logistics.Moreover, the development of e-commerce, fruit chain stores, and WeChat businesses has made fruit consumption more reachable, thus enhancing the consumption value of third-and fourth-tier cities in China [20][21][22].China has been the main consumer of fresh apples in the global market, followed by the United States, and the EU [10,23].

Brief Theoretical and Empirical Literature
Te idea of gravity model analysis was frst applied by Tinbergen in the area of global trade in 1962, and it originated from the gravitational theory of Newton, which was formulated in 1687 [2].Since then, it has become the most popular empirical tool for trade analysis, and its foundation is based on the prior theoretical literature, on which this paper builds.Te gravity equation was initially derived by an economist using the product diferentiation model [25], which assumes that consumers perceive diferences among products and tend to prefer those that are more distinct.
Anderson's model uses preference functions that are either Cobb-Douglas or exhibit a constant elasticity of substitution.Additionally, the model assumes that utility functions for traded and non-traded goods are weakly separable.Te gravity model extends this framework to understand the movement of goods, individuals, or information between diferent locations, with a particular emphasis on the impact of distance and size on these fows.Within the product diferentiation model, consumer preferences are infuenced by perceived diferences among products, leading to the idea that consumers are more likely to choose products from nearby locations due to lower transportation costs and similar preferences [26,27].Bergstrand [28,29] then used monopolistic competition models to examine the microeconomic underpinnings of trade.In his research on 18 industrial countries, Helpman [30] established a connection between the gravity model and monopolistic competition model.Later on, Mátyás [31] proposed the inclusion of dummy variable(s) for trading blocs and time-specifc efects into the specifcation of gravity models.Ever since the application of the gravity model in international trade analysis, several researches have applied the gravity equation at diferent levels to explore the determinants and export potential of emerging economies.Many researchers have also incorporated several components into the model.For instance, recently, Ravi Kumar et al. [32] studied the factors afecting Indian rice and its potential using dynamic panel gravity model analysis.Tey showed that GDP, per capita GDP, trade ties, World Trade Organization (WTO) membership, and exchange rate policy impacted Indian rice exports.Nguyen [33] who applied the SFGM to examine the aggregate efect of "behind-the-border" factors on Vietnam's exports of rice and cofee.Te results suggested that Vietnam has great potential to boost its exports of rice and cofee with its main importing nations, especially ASEAN, the European Union (EU) and Comprehensive and Progressive Agreement for Trans-Pacifc Partnership.
In a similar vein, Abdullahi & Aluko et al. [33] used the SFGM to examine the determinants, efciency, and potential of bilateral agri-food exports between Nigeria and the EU from 1995 to 2019.Te fndings obtained by the scholars show that agri-food trade performance from Nigeria to the EU is infuenced by economic size, income, bilateral exchange rate, and distance between Abuja (Nigeria) and the capital cities of trading partners.Furthermore, the results demonstrated that Nigeria is quite inefcient in its agri-food exports to the EU, and there is substantial untapped potential.Similarly, using the SFGM, Atif et al. [35] and Wang et al. [36] found untapped trade potential in Pakistan and China.Moreover, it is commonly stated that there is a huge untapped and unexploited export potential, with a gap between potential and actual exports [37,38]; Abdullahi et al. [39].Te benefts of agricultural product exports for a country depend on the extent to which the market possesses unexplored potential that can be leveraged [2,40].
Closing the gap between export potential and existing exports by improving export efciency provides countries with opportunities to enhance export earnings, generate new careers, and nurture their economies [41][42][43].
Ismaiel Ali Ismaiel et al. [44] conducted a study to examine the drivers of overall Egyptian trade, and specifcally Egyptian rice trade in particular with 11 rice-importing partner countries using the traditional augmented gravity model.Te results revealed that the export price stimulates Egyptian exports to its trading partners, while distance discourages them.Abdullahi et al. [3] employed three different gravity models (the PPML, Heckman and GLS) to estimate the key drivers of Nigeria's cocoa trade using a panel dataset for the period 1995 to 2018 (24 years) and it 36 importing partners.Te results showed that the potential for Nigeria's cocoa export expansion was massive, particularly with developed nations.
Abafta & Tadesse [45] exploited the gravity model by means of panel data from 18 major cofee exporters and 201 importing economies through the period from 2001 to 2015.Te results unexpectedly found that the regional trade agreements (RTAs) had no substantial infuence on the cofee trade.In a similar vein, Eshetu and Goshu [46] explored the drivers of Ethiopian cofee exports to its major partners using the Generalized Method of Moments (GMM) over the 1998-2016 period.Tey showed that population, FDI, trade openness, and institutional quality substantially enhance Ethiopian cofee export fow.Meanwhile, the populace of the trading nations, institutional distance, exchange rate, and lagged export volume exacerbate cofee exports.
Shahriar et al. [3] adopt the gravity model in the form of the PPML, the fxed and random efects models, as well as the Heckman model to study the determinants of Bangladesh's leather exports to its major trade partners.Tis study is based on a panel dataset from 1989 to 2015, which includes a total of 20 carefully chosen largest leather trading economies.Tey detected that there is great potential for Bangladesh to experience signifcant growth by exporting to China and exploring network connectivity to enhance leather trade with other nations taking part in the BRI.Bose et al. [47] analyzed the potential reasons for the decline of Oman's fsh exports to the EU.Tey used the dynamic, unbalanced panel data model for the period 2000-2013.Te study employed traditional fxed efects and random efects models and indicated that the decline of Oman's fsh exports to the EU markets is mainly afected by domestic export policy and exchange rate fuctuations.
Shahriar & Qian et al. [25] conducted a study using a distinctive dataset spanning 20 years (1997-2016) to analyze China's pork export patterns to its 31 main trading partners.Te objective was to identify the key determinants infuencing the meat industry's exports in China.Te fndings indicated that China's membership in the WTO, the BRI, and shared borders are signifcant factors that impact Chinese pork exports.Tese results were obtained using the PPML, GLS, and Heckman selection models.Bui and Chen [48] used the gravity model in the form of PPML to examine the drivers of Vietnamese rice exports using a dataset ranging from 2003 to 2014.Teir results indicated that GDP, price, exchange rates, and population exhibit a strong association with Vietnamese rice export fows.
Based on the above discussion, it is evident that the existing literature has explored various aspects of agricultural exports.However, a specifc investigation into the unexplored opportunities of apple export markets is notably absent.As the world's largest apple producer and consumer, as well as a signifcant exporter, China's apple trade has 6 Complexity a substantial impact on the global apple trade pattern.Furthermore, the apple trade holds considerable economic importance globally, encompassing both domestic and international markets.Despite this, a comprehensive understanding of the factors infuencing efciency and the realization of its full potential remains elusive.With this in mind, we are motivated to bridge this gap by focusing on China's apple exports to major trade partners worldwide.We employed a panel dataset from 1997 to 2019 and utilized the SFGM-a novel approach in the context of apple exports.
By doing so, this study provides empirical evidence to guide policy formulation for China's apple export trade.

Methodology and Data
4.1.Te Gravity Model and the SFGM.Natural and human factors, such as distance, limit bilateral export fows.Both the exporting and importing countries have human characteristics, primarily institutional and infrastructural [49,50].Te gravity model is an excellent example of this analysis.Newton's law of gravity is the foundation of the gravity model.According to this law, the mass and distance of two bodies are said to be the causes of attraction.Some economists have proposed that bilateral exports between economies are determined by economic size and distance [25].Te gravity model is defned mathematically as follows: where EXP ij is the value of bilateral exports between China and its trading partner j; GDP i and GDP j are the GDP of China and its trading economies, respectively.Dis ij stands for the bilateral distance between China and its trading partner j; α is the constant of proportionality.Te linear version of ( 1) is obtained by taking the natural logarithm of (1).In this study, it may be written as follows for China's apple exports: where APPEXP ijt denotes the value of China's apple export to its trading partners j, j (j where Ex ijt stands for the bilateral exchange rate between China and its trading partner j, pcGDP jt represent the per capita GDP of the two countries involved in trade for a t year, Area j represents agricultural land area, Border ij is 1 if country j has a common border with China, otherwise, 0. Sea ij is a dummy variable with a value of 1 if country j has sea border, otherwise 0. β 0 − β 7 , c 1 and c 2 are the parameter to be estimated.Ϛ ijt is the error term.All other variables are as defned earlier. Te description in the (3) confronts two signifcant difculties.Tese are heteroscedasticity, or the fact that the error term is not normally distributed, in which the error term is linked with unobserved factors.Genuinely, it has a non-negative methodical component as well as a random component [52,53].Te trade boost potential is expressed in terms of the sample average rather than the greatest amount possible for a given pair of trading partners, which is the method's fundamental faw.Because the gravity model's predictive capacity reduces when the year of the input values rapidly deviates from the sample average, calculating trade potential versus average expected values might be challenging [13].Te SFGM is useful for correcting the faws in the standard gravity model.
Aigner et al. [54] and Meeusen & Van Den Broeck [55] developed the stochastic frontier analysis (SFA) model to analyze technical efciency in manufacturing.Te output was modeled as a function of the inputs and an error term.Te stochastic error term is made up of a production inefciency element and a random component.Te last part of the error may be fxed if the right policies are executed.Te SFA can be utilized to express the export frontier and can measure the extent to which actual exports fall below the maximum potential exports.Te SFGM ofers several advantages over traditional gravity models.By incorporating a stochastic frontier approach, it allows for a more accurate estimation of the parameters governing spatial interactions.Tis model also enables the identifcation of factors contributing to variations in efciency across locations, providing valuable insights for policy interventions aimed at improving efciency in trade, migration, or other fows between locations [27].Additionally, the stochastic frontier gravity model allows for the estimation of both technical efciency and allocative efciency, ofering a more Complexity comprehensive understanding of spatial interactions and their determinants.
In this paper, the SFA is introduced into the gravity equation to account for changes in trade with trading partners.Tis approach allows for the freedom to choose the optimal level of trade between countries (trade frontiers) in the analysis, and it also allows the actual size of a country's trade to be harmonized with the forecasted frontier values of the importing country in order to examine the maximum size of trade [33].To solve the matching difculties of heteroscedasticity and normalcy of the error component linked with the classic method (gravity equation), Kalirajan & Singh [49] suggested using this paradigm to study trade fows between countries.Te error term of the standard gravity model has been separated into two parts: an inefciency element and a random component.SFA is turned into SFGM as follows, after being incorporated into our extended gravity model in ( 4 In this study, we used the post estimate command created by Battese & Coelli [56] in Stata to project the point estimation of export efciency, as shown in (5), after obtaining the parameter estimates of the frontier model in (4).Te gravity model's coefcients were then utilized to calculate the export potential.
where ⌽(.) designates the density function.Te assessed efciency (c) from ( 5) can fuctuate from 0% to 100%.In this case, an efciency value of 0% indicates inefciency, and greater trade is possible with the trade variables in (4).On the other hand, an efciency score of 100% demonstrates excellent efciency, meaning that the actual trade perfectly aligns with the potential trade.

Sample Size and Data.
In this study, we collected a 26year dataset, spanning 1997 to 2022, and it consists of 38 countries, which were selected based on their trade history with China and the availability of data.Te dataset comprises a total of 988 observations (t * j � 26 * 38 � 988).Table 1 presents this study's key variables and data sources, while Table 2 shows the descriptive statistics of the variables.Except for dummy variables, the natural logarithms were taken for all variables in the model.Te data is balanced, and none of the variables deviate signifcantly from the normal distribution.Tere is also no extensive range among the lowest and highest values between sample observations.

Descriptive Statistics and Correlation Matrix. Table 2
ofers the summary statistics of our study variables.All variables have a reasonable range between the minimum and maximum observations.Tis indicates a degree of variability that is neither extremely narrow nor exceptionally wide.Tis moderate range suggests that the data exhibit some level of dispersion or spread, allowing for meaningful comparisons and analyses without being excessively constrained or overly scattered.Moreover, the mean and the standard deviation of the study variables suggest that each variable's data point within the dataset deviate moderately from the mean, providing insight into the spread of the data distribution.
Analyzing the distribution of the variables within this range can help identify patterns and relationships with other variables, enhancing our understanding of the phenomenon being studied.
To identify multicollinearity among the variables used in the model, we present the results of the correlation matrix of the variables, as shown in Table 3.It also provides a quick overview of the association among the variables.LnAppExp ijt is positively linked with the explanatory variables (LnGdp it , LnGdp jt , LnArea jt , LnExchr ijt , Border ij ).Te correlation coefcients of all the variables are moderate, with the highest being 0.533.In addition, Gujarati (2019) indicated that multicollinearity is present when the correlation coefcient exceeds 0.8.Hausman (2001) suggests that a correlation coefcient below 0.8 produces more accurate results.Further multicollinearity estimation was employed to compute the variance infation factor (VIF) and tolerance levels (1/VIF) of the independent variables.VIF values below 10 and tolerance fgures exceeding 0.1 are deemed satisfactory.Te analysis fndings indicate that the equation remains unafected by multicollinearity, as the VIF values and tolerance levels for all parameters lie within the appropriate range.Tis suggests that there is no multicollinearity among the variables we used in the SFGM.specifcations follow the assumptions of the gravity model.It can be seen that the GDP of China and that of its appleimporting nations are positively associated with apple export fows at a 1% signifcance level.Te positive coefcients of GDP show that a 1% increase in GDP for both China and its trading partner enhances bilateral apple exports by 0.28% and 1.02%, respectively.Tis indicates a signifcant impact of economic growth on apple exports, highlighting the importance of economic factors in shaping bilateral trade relationships and export performance.Our results confrm the fndings of Kea et al. [57]; Abdullahi & Shahriar et al., [3] and Boadu et al. [2].Additionally, with a p value of 0.001, the bilateral distance has a detrimental efect on China's apple exports.Te coefcient of Dis i j is unfavorable and statistically signifcant indicating that a percentage increase in distance reduces China's apple exports by nearly 1.61%.Tis result aligns with the fndings of Suroso et al. [12]; who demonstrated the deterrent efect of distance on China's tea exports, as well as Abdullahi et al. [27]; who highlighted the negative impact of distance on agricultural exports in China.Te income variable (LnPcGdp jt ) for the importing nations is statistically signifcant with negative coefcients and at a 1% statistical signifcance level, implying that a percentage decrease in the per capita GDP of appleimporting nation is anticipated to exacerbate China's apple export fows by 0.31%.Te per capita GDP of the exporting country signifes the consumption capacity of the exporting nation, while in the case of the importing nation; the per capita GDP shows the import ability of the importing nation.In light of this, we anticipated that this variable would favorably afect China's apple export fows.Te outcome of this study is consistent with past research fndings that documented a negative relationship between per capita income and trade fows.For example, Hassan [58] noted the "unexpected negative sign" of South Asian countries' per capita GDP.Some scholars, such as Assane & Chiang [59]; used the gravity framework to evaluate the trade fows of the Economic Community of West African States (ECOWAS) and showed negative signs for per capita GDP.In another work, Shahriar et al. [3] proposed that nations with similar income distributions trade more with one another.Moreover, it has been reported that when a negative efect of per capita GDP is found in both the exporting and importing nations, it could be attributed to various factors such as economic recessions, exchange rate fuctuations, supply chain disruptions, trade barriers, policy changes, and commodity-specifc factors.Tese negative indicators signal broader economic challenges and disruptions that afect trade and economic performance on a global scale [32].Understanding the underlying reasons for negative per capita GDPs requires considering a range of economic, political, and external factors that impact trade dynamics and overall economic health in both nations [14,34].

Factors Afecting China's Apple Exports 1997-2022.
Te fndings showed that the efect of importing nations agricultural land area (LnArea jt ) on China's apple export efciency turns out to be positive and with a p value of 0.018.Tis indicates that an increase in the LnArea jt of the importing country could worsen China's apple export efciencies by 1.56%.Tis exacerbation is statistically signifcant at the 5% level, indicating a meaningful impact.Te reason behind this could be heightened competition as domestic production of apples or similar fruits increases in the importing country.Tis increased competition may lead to reduced market share, lower prices, or higher marketing costs for China's exported apples, contributing to export inefciencies.Similarly, Zhang et al. [8] studied the contributory factors for increased fruit production in China from 1978 to 2016.Te study found that except for the increase in apple yield which mainly depends on yield per unit, the increase in the yield of citrus, pears, grapes and bananas mainly depends on the expansion of the planting area.
Based on the inefciency model, export inefciency is the response variable.Te literature suggests that a negative sign associated with a specifc variable indicates a positive efect on export efciency.Te coefcient of LnExchr ijt is negative and signifcant at a 5% signifcance level (p � 0.046).Tis shows that the appreciation of China's local currency (RMB) relative to that of importing countries reduces the transaction cost of the exporting nation, thereby enhancing the export efciency of China's apple [60,61].Abdullahi & Huo et al. [51] document a similar result for Nigeria's agri-food trade.
Te coefcient of the dummy variable (Border ij ) is statistically signifcant at a 5% level (p � 0.028) and exhibits a positive efect.Drawing from this result, we can infer that those countries that have territorial adjacency with China rise the country's apple exports inefciency to those countries by 9.49 units.According to Abdullahi & Shahriar, et al. [3]; the existence of a shared border between countries can ofer potential trade advantages, such as increased proximity and market accessibility.However, this condition can also give rise to certain challenges that impede export efciency, including transportation expenses, trade barriers, political tensions, and logistical intricacies.
Finally, the coefcient of Sea j indicates that when an importing country does not have access to a seaport, China's apple export efciency would decrease by 6.70 units.Tis result is statistically signifcant at a 5% level (p � 0.010), and it also suggests that due to lower trade costs, China is more likely to export apples to countries with seaports.Several studies have also confrmed that trade costs can impact a country's competitive advantage in exports [62][63][64].Landlocked countries, compared to non-landlocked countries, face disadvantages in trade due to their geographic location [50,57,65].

Robustness Check.
To confrm the robustness of our estimation, we generate the gravity model parameters calculated for the composed error term variance, and the ratio of the standard deviation of the inefciency component to the standard deviation of the random error component, λ � σ 2 u /σ 2 .Te λ values indicate the ftness of the SFA across our estimated model.Te value of 0.999 for λ shows that variation in output is accounted for by technical efciency (99.90%).Furthermore, an extra test for the 10 Complexity presence of technical efciency (TE) in the model is carried out via a one-sided ratio (LR) test of the null hypothesis, H 0 : σ 2 u � 0, against the alternative, H 1 : σ 2 u > 0. Furthermore, the LR statistic is 1562.324,which is much higher than the critical value of 2.706.As a result, the null hypothesis of no export inefciency is rejected.In other words, the robustness test presented in Table 4 validates the SFGM estimations. .Table 5 presents the technical efciency scores of China's apple exports, while Table 6 reports their potential scores.On average, between 1997 and 2022, the efciency of the countries in this study is 33.71%, which is below the average value of 50%.In short, it is safe to say that China's apple exports are far from efcient.An efciency score of over 50% indicates that China is relatively efcient in exporting apples, whereas a score below 50% suggests that China's efciency in exporting apples is low.Although some countries, such as the Philippines (62.6%),Malaysia (60.0%),Vietnam (59.3%),Nepal (57.0%),Indonesia (56.7%),Tailand (54.6%),Sri Lanka (54.5%), and Singapore (52.3%), achieved relatively high efciency, none of the countries in this study reached 100% efciency.Tis could be attributed to factors such as favorable trade agreements, efcient supply chains, market demand, or competitive pricing strategies that make exporting apples to those countries more efcient for China.Furthermore, these countries are the only ones that recorded efciency scores above 50%, while most of the countries in this study showed relatively poor efciency.Interestingly, despite their economic and market sizes, Italy, the USA, and Sweden were the least efcient countries for China's apple exports during the study period, with efciency scores of 13.5%, 14.2%, and 20.9%, respectively.One possible reason for this is that due to the relatively high level of economic development and per capita income in these countries, they have higher requirements for the quality and variety of imported Chinese apples [6,66].Another reason may be attributed to various factors such as, trade barriers, transportation costs, market dynamics, or lower demand for Chinese apples in the Canadian market.Based on the fndings of the study, several key policy suggestions can be made to optimize China's apple export strategy.Policymakers should consider strategies for currency management to ensure that the Renminbi (RMB) remains competitive.Tis can be achieved by enhancing export efciency, which includes reducing transaction costs for international buyers.Additionally, China could beneft from negotiating and entering into trade agreements that specifcally address and mitigate the negative impacts of distance on trade fows.Tis can be done through terms that lower tarifs, simplify customs procedures, and enhance logistical connectivity with distant markets.Te identifcation of countries with untapped export potential suggests a need for targeted marketing and trade initiatives.Tese initiatives should focus on expanding market presence through promotional activities, trade fairs, and businessto-business meetings.To address competitive challenges, China should invest in research and development to improve apple quality, diversify varieties, and implement sustainable farming practices.Moreover, improving infrastructure and logistics in regions with shared borders and seaports can signifcantly boost export efciency, reducing costs and delivery times.Understanding and adapting to market preferences, as well as implementing trade facilitation measures such as digitalization of trade procedures and reducing bureaucratic hurdles, will further enhance China's apple exports.By adopting these policy suggestions, China can efectively navigate the complexities of the global trade environment.Tis will maximize the potential of its apple exports and sustain growth in this vital agricultural sector. 12 Complexity

Conclusion and Policy Recommendations
Te study presents several limitations, including a constrained data scope that may not fully the most recent trends, such as the efect of the COVID-19 pandemic on trade.Te reliance on the stochastic frontier gravity model, while robust, may overlook complexities such as informal trade barriers and cultural infuences on trade dynamics.Additionally, geopolitical intricacies and specifc trade policies that can signifcantly impact trade fows might not be adequately considered.Te analysis also might not fully account for market demand variables, including consumer preferences and brand recognition, which are crucial in determining export efciency and potential in various markets.
For future research, it would be insightful to investigate the impacts of global disruptions, notably the COVID-19 pandemic, on trade patterns and recovery strategies.Incorporating micro-level data, such as consumer preferences and brand presence, could ofer deeper insights into market dynamics.A detailed evaluation of trade policies and their efects on exports, along with comparative analyses of other export commodities, could reveal broader trade challenges and opportunities.Moreover, exploring the roles of technological advancements and environmental sustainability practices in agriculture could provide valuable perspectives on enhancing the global competitiveness of China's agricultural exports [67][68][69][70][71][72][73][74][75][76].

Figure 6 :
Figure 6: Mean percentage of top ten China's apple exports terminals for the period 1997-2022.Source: authors' compilation using data from UNCOMTRADE [24].
million annually and accounted for 42.54% of the market share.Based on China's [50], ..., 38) is for trading partners, t is the time period, i.e., 1997, 1998, ..., 2022."ln"stands for a natural logarithm.β0−β 3 are the parameter to be estimated.εijtisthe error term.Te traditional gravity model is extended by separating demand and supply-side elements and including literatureidentifed export stimulating (such as exchange rate, per capita GDP and area) and resistant (such as distance, border and sea) variables[50].As a result, the model is as follows: ):

Table 4
presents the outcomes of the maximum likelihood estimate of the SFGM and the inefciency model.Te results of the extended gravity model with the stochastic frontier 8 Complexity

Table 1 :
Description and sources of data used in this study.

Table 2 :
Descriptive statistics of the variables.

Table 3 :
Correlation matric of the variables.

Table 4 :
Maximum likelihood estimates from the SFGM.
trading partners in apple exports.China's apple exports are less than optimal in all the countries considered in this study.
from apple production and relieving pressure on the domestic apple market.In light of this context, this study employs a Stochastic Frontier Gravity Model (SFGM) to dissect the complexities of China's apple exports, ofering a nuanced understanding of the factors shaping trade fows from 1997 to 2022 across 38 countries.Te analysis also uncovers signifcant untapped export potential in several countries, highlighting opportunities for strategic market expansion.Te study's limitations and proposed future research directions pave the way for a deeper exploration of global trade intricacies, ofering valuable insights for policymakers and exporters aiming to optimize China's agricultural export landscape in a rapidly evolving global market.
As China holds the position of the world's largest apple producer, the nation's apple exports play a vital role in generating income