Effects of Regional Trade Agreement to Local and Global Trade Purity Relationships
Siyu Huang, Wensha Gou, Hongbo Cai, Xiaomeng Li, Qinghua Chen
EEffects of Regional Trade Agreement to Localand Global Trade Purity Relationships (cid:63)
Siyu Huang ,Wensha Gou , Hongbo Cai Xiaomeng Li * and Qinghua Chen , * School of Systems Science, Beijing Normal University, Beijing, China New England Complex Systems Institute, Cambridge, MA, USA Business School, Beijing Normal University, Beijing, China*corresponding author: [email protected],[email protected]
Abstract.
In contrast to the rapid integration of the world economy,many regional trade agreements (RTAs) have also emerged since theearly 1990s. This seeming contradiction has encouraged scholars and pol-icy makers to explore the true effects of RTAs, including both regionaland global trade relationships. This paper defines synthesized trade re-sistance and decomposes it into natural and artificial factors. Here, weseparate the influence of geographical distance, economic volume, overallincreases in transportation and labor costs and use the expectation max-imization algorithm to optimize the parameters and quantify the tradepurity indicator, which describes the true global trade environment andrelationships among countries. This indicates that although global andmost regional trade relations gradually deteriorated during the period2007-2017, RTAs generate trade relations among members, especiallycontributing to the relative prosperity of EU and NAFTA countries. Inaddition, we apply the network to reflect the purity of the trade relationsamong countries. The effects of RTAs can be analyzed by comparing typ-ical trade unions and trade communities, which are presented using anempirical network structure. This analysis shows that the communitystructure is quite consistent with some trade unions, and the representa-tive RTAs constitute the core structure of international trade network.However, the role of trade unions has weakened, and multilateral tradeliberalization has accelerated in the past decade. This means that morecountries have recently tended to expand their trading partners outsideof these unions rather than limit their trading activities to RTAs.
Keywords: the gravity model · international trade · regional trade agreement · trade purity indicator · EM algorithm. (cid:63)
Supported by the Chinese National Natural Science Foundation (71701018,61673070) and the National Social Sciences Fund, China (14BSH024). a r X i v : . [ q -f i n . GN ] M a y I S. Huang et al.
With the rapid development of international trade, as of 2020, the World TradeOrganization (WTO) has 164 members representing 98 percent of world trade.However, in addition to this extensive multilateral trading system, the world hasalso witnessed unprecedented proliferation of regional trade agreements (RTAs)since the 1990s [8]. In 2013, 546 notifications of RTAs were received by the Gen-eral Agreement on Tariffs and Trade (GATT)/WTO [19]. The role of RTAs raisesquestions among scholars and policy makers: what drives an increasing numberof countries to join regional trade unions, and how will this affect regional tradepatterns and globalization processes? Trade creation and trade diversion havebeen proposed to describe the effects of RTAs [14,35]. Trade creation refers tonew trade arising between member countries due to the deduction of tariffs,while trade diversion means that imports from a low-cost outsider country arereplaced by imports from a higher cost member country because of RTA [59].Some have advocated for RTAs by arguing that, unlike multilateral trade liber-alization, they promote“deeper” integration [9].Despite the controversy in the literature, previous studies usually focus on theinfluence of RTAs on countries in given regions instead of quantitative analyseson a global scale. A common approach is to operationalize RTA membership asa categorical independent variable and analyze the influence of trade unions onbilateral trade using a gravity model [57,50,29,39]. However, the roles of RTAsin regional and global trade differ, which can also be seen in the descriptionof trade creation and trade diversion. It is not comprehensive to study themseparately, and we need to break through the limitations of existing research.In fact, international trade is a complex system with global characteristics andregional structures, and we should analyze the effects of RTAs on both regionaland global trade environments. It is necessary to use quantitative models andnetwork methods to analyze global trade as a whole, and the influence of othercountries should not be ignored when discussing the trade flow between any twocountries.RTAs are usually signed between neighboring countries, so their effects onregional trade are coupled with geographical distance and other factors. Theinnovation of this paper is to study and describe the trade purity relationship ofcountries, with some other typical factors, such as economic volume, geograph-ical distance, overall increases in transportation and labor costs, are separated.In contrast to the existing literature, which consistently increases observablevariables to quantify trade costs [20,55,41], here, we define synthesized trade re-sistance [2], decompose it into natural and artificial factors, and propose a tradepurity indicator (TPI) to describe the true trade environment and relationshipsbetween countries. The role of RTAs can be studied by comparing the TPI andits evolution within and outside a trade union. Here, we apply the expectationmaximization (EM) algorithm to optimize the parameters and quantify the tradepurity indicator. Compared with the exogenous parameter estimation in the ex-isting research on trade cost quantification [5,34,15,18], the method in this paper itle Suppressed Due to Excessive Length III is more scientific and effective, and it could be extended to discuss the effects ofRTAs on a number of countries around the world.Furthermore, international trade is a system that involves numerous coun-tries and trade relations, and complex network modeling has the advantage ofanalyzing a number of entities and complex relationships [54,60,62]. Addition-ally, network theory can also facilitate the examination of both local and globalproperties [63], which is consistent with the goal of our work. However, tradeflows are a direct result of trade openness, and related studies usually applytrade flows to weight the network [54,50]. Since trade flows could be influencedby a country’s economic volume, geographical factors and artificial barriers, weprefer trade resistance, which removes the impact of the economy, to reflect thepurity of the trade relationship between countries. In addition, communities inthe international trade network are represented by clusters of countries wheretrade relations between countries in the same community are closer than those indifferent communities [50]. Therefore, comparing the members of typical tradeunions and trade communities in the global trade network could facilitate re-search on the effectiveness of RTAs.The paper is organized as follows: Section 2 briefly describes the data sourceand the gravity model with synthesized trade resistance. Here, we establish amaximum likelihood function to simultaneously estimate the unobserved pa-rameters and quantify the trade purity indicator. Section 3 presents the re-sults. Here, we focus on six typical RTAs: Belt and Road (BRI), EuropeanUnion (EU), North American Free Trade Agreement (NAFTA), Organizationof African Union (OAU), Caribbean Free Trade Area (CARIFTA), and Associ-ation of Southeast Asian Nations (ASEAN). We discuss the evolution of TPI atboth the regional and global trade levels and analyze the effects of RTAs duringthe period 2007-2017. In addition, we discuss the evolution of trade communitiesbased on network methods. This shows that the representative RTAs constitutethe core structure of international trade network, but the role of trade unionshas weakened and multilateral trade liberalization has accelerated in the pastdecade. Finally, Section 4 provides the conclusion and discussion.
In this paper, we use trade data from the UN Comtrade Database, which includes198 countries/districts. Here, we choose the “Goods” type of product and usethe annual total of all Hs commodities (Harmonized Commodity Descriptionand Coding Systems). In view of differences in time and statistical caliber, theflow data reported by the importer and exporter are not always the same. Here,we use the importer’s report, with a supplement from exporters when the dataare missing.For GDP (current US $ ), we use the World Bank national accounts data andOECD National Accounts data files. It is calculated without making deductions V S. Huang et al.
Table 1.
Data Description
Indicator Indicator Description Data SourceTrade Flows Country-to-Country Trade Flows, from UNComtrade Database. For ‘Goods’, ‘Hs’ com-modities, annual data during the period2007-2017. https://comtrade.un.org/
GDP GDP (current US $ ) for countries, fromthe World Bank database, with codeNY.GDP.MKTP.CD., annual data duringthe period 2007-2017. https://data.worldbank.org/indicator/NY.GDP.MKTP.CD Distance Geographical distance between mean posi-tions of countries. The coordinate data arefrom Blue Marble Geographics. for depreciation of fabricated assets or for the depletion and degradation ofnatural resources. Data are in current US dollars. Dollar figures for GDP areconverted from domestic currencies using single-year official exchange rates.There are several methods for calculating geographical distance. As somecountries have many import and export ports, we do not choose the coordinatesof the capital but use the mean position of the longitude and latitude to calculatethe distance. A full description of the data sources is provided in Table 1.
The gravity model is one of the most successful empirical methods in the field ofsocial science [2]. Specifically, Isard and Tinbergen were pioneers in applying thegravity model to describe the patterns of bilateral aggregate trade flows amongcountries [36,56]. Their work spawned a vast empirical literature that appearsto perform well at modeling trade flows and exploring the factors influencingthem [2,33,40], as 80% −
90% of the variation in the flows could be captured bythe fitted relationship [1].Scholars have introduce possible explanatory variables and performed regres-sions with panel data to confirm whether trade growth or loss is more signifi-cant [59,17,14,4]. However, it is impossible to include all the relevant factors,so the estimation of effects might be biased and inconsistent due to omittedvariables, with the possibility of significant over- or underestimation [50].In Tinbergen’s gravity model, distance d i,j is not limited to geographicaldistance, and it could be broadly construed to include all factors that mightcreate trade resistance [56,40]. More recently, some papers have estimated syn-thesized trade costs or resistance from the observed pattern of production andtrade across countries [16,48,6] and performed analyses based on quantified tradecosts.Based on defined trade resistance r i,j , the improved model used in this paperis depicted by the following formula: F i,j ∝ ( m i · m j ) α r i,j − ε ij (1) itle Suppressed Due to Excessive Length V where m i and m j are the gross domestic products of countries i and j ; r i,j isa defined composite variable; and α is the parameter to be estimated with theexpectation maximization algorithm as the latent parameter in section 2.3, ε ij iserror term. Here, if we consider r i,j to be symmetric, the mechanism describedin equation 1 is similar to Anderson’s structural gravity model [3,5] but witha simpler expression. Here, r i,j is representative of trade resistance, which weuse as a composite of all the other factors that affect trade volumes other thancountries’ GDP. Equation 1 indicates that the trade amount F i,j is proportionalto m i and m j but inversely proportional to the integrated effective distancebetween them, denoted r i,j .In contrast to the traditional gravity model, here, a country’s geographicaldistance d i,j is replaced with trade resistance r i,j . The new model not onlycaptures proximity or distance in terms of geographical distance but also fullydemonstrates the true and comprehensive relationships between entities in thesystem, which is significant for understanding the global economy, politics andculture [58].In the literature, the trade cost measure can be derived from a broader rangeof models [3], which have different methods and results in the parameter estima-tion, such as the elasticity of substitution σ [5], the Frechet parameter ϑ [22], andthe Pareto parameter γ [34,15,18]. With the estimated parameters and observedtrade flow F i,j , m i and m j , the symmetrical trade resistance can be obtainedfrom equation 1 using the least squares method.However, the existing exogenous parameter estimation method will introduceunnecessary errors and doubts about validity. However, further analysis of traderesistance will inevitably involve the estimation of latent variables or parame-ters, and here, we use the EM algorithm from machine learning. In addition,there are many zero values in bilateral migration data, which is also a problemthat has long puzzled researchers [37,51,28,24]. Here, we use the pseudo maxi-mum likelihood (PML) method to preprocess the zero value flow; for details, seeAppendix B. For each pair of countries i and j , trade resistance r i,j is quantified by equation 1,and we assume that trade resistance can be separated into two components. Thedata R = { ln r , , ..., ln r i,j , ... } can be divided into two categories: I is mainlyrelated to natural factors such as geographical distance d i,j , and II is affectedmore by artificial barriers than natural factors.ln r i,j = (cid:26) a + b ln d i,j + η i,j ( r i,j ) ∈ I ξ i,j ( r i,j ) ∈ II . (2)Here, a, b are constants. η i,j and ξ i,j are normally distributed random vari-ables with different means and standard deviations, η i,j ∼ N (0 , σ ) and ξ i,j ∼ N ( µ, σ ). How should one estimate parameters Θ = { µ, σ , σ , a, b } based onobserved data R and place each ln r i,j into the appropriate category? I S. Huang et al.
To solve the parameter problem of two mixed distributions, we apply a com-monly used method, namely, the EM algorithm. In statistics, the EM algorithmis an iterative method to find the maximum likelihood or maximum a posteriori(MAP) estimates of the parameters in statistical models, where the algorithmdepends on unobserved latent variables [21,38,45,32].The EM algorithm seeks to obtain the MLE (maximum likelihood estimate)of the marginal likelihood by iteratively applying the expectation step (E step)and maximization likelihood step (M step), with t = 1 , , ... representing thenumber of iterations. The detailed process is as follows:
1. Expectation step (E step):
In step t , based on the last estimation ofthe parameters ˆ Θ ( t − , calculate the expected value of the probability ofbelonging to a certain category.Separately calculate the probabilities of observation ln r i,j belonging to cat-egory I and category II. p ( r i,j | ˆ Θ ( t − ) = 1 √ πσ exp − [ln r i,j − ( a + b ln d i,j )] σ ,p ( r i,j | ˆ Θ ( t − ) = 1 √ πσ exp − [ln r i,j − µ ] σ . (3)Then, normalize them as follows:ˆ τ ( t ) i,j = p ( r i,j | ˆ Θ ( t − ) p ( r i,j | ˆ Θ ( t − ) + p ( r i,j | ˆ Θ ( t − ) . (4)The unobserved latent variables Θ τ = { τ , , τ , , ..., τ i,j , ... } , where τ i,j (0 ≤ τ i,j ≤
1) represents the probability of trade resistance ln r i,j belonging tocategory I.
2. Maximization likelihood step (M step):
Based on the ˆ Θ ( t ) τ obtainedfrom the E step, we find the parameter estimate Θ ( t ) that maximizes thislikelihood. The likelihood function L of R occurring is multiplied by theexpected probability of all trade resistances as follows: L ( R ; Θ, Θ τ ) = (cid:89) i (cid:54) = j { τ i,j · p ( r i,j | Θ ) (cid:124) (cid:123)(cid:122) (cid:125) Category I + (1 − τ i,j ) · p ( r i,j | Θ ) (cid:124) (cid:123)(cid:122) (cid:125) Category II } . The optimum value of Θ ( t ) based on R and ˆ Θ ( t ) τ can be calculated from thatfunction:ˆ Θ ( t ) = max Θ log L ( R ; Θ | ˆ Θ ( t ) τ )= max Θ (cid:88) i (cid:54) = j log { ˆ τ ( t ) i,j · p ( r i,j | Θ ) + (1 − ˆ τ ( t ) i,j ) · p ( r i,j | Θ ) } . (5) itle Suppressed Due to Excessive Length VII Here, we regard countries as the nodes, and the relationship between two nodescan be described by an edge. The reciprocal of trade resistance is the weight ofthe edge. Since trade resistance is symmetric for country pair ( i, j ), the networkis also symmetric. For node i , the node cluster coefficient C i is calculated by theequation below [31]: C i = 2 e i k i ( k i −
1) (6)where e i is the number of edges connected to adjacent nodes and k i denotesthe number of nodes that are adjacent to node i . The cluster coefficient of thenetwork is the mean of the cluster coefficients of all nodes.To make the community classification more efficient, we apply the disparityfilter method to obtain a backbone network [52]. α ij = 1 − ( k − (cid:90) p ij (1 − x ) k − dx < α s (7)where α ij is the probability of an edge between node i and j , k indicatesthe degree of a given node, p ij is the normalized weight of the edge and α s is asignificance level for the null hypothesis.After extracting the backbone network, to classify the network into severalcommunities, we apply the Louvain community detection algorithm [10] andevaluate the result using the Q index [47]. Q = 12 m (cid:88) i,j (cid:20) w i,j − A i A j m (cid:21) δ ( c i , c j ) , (8)where w ij is the weight of the edge between nodes i and j , A i = (cid:80) j w i,j is thesum of the weights of the edges attached to node i , c i is the community to whichnode i belongs, and δ ( c i , c j ) is 1 if c i = c j and 0 otherwise. m = (cid:80) i,j w i,j isthe sum of the edge weights. Based on the quantified trade resistances duringthe period 2007-2017, we can construct the backbone network of global trade foreach year and attempt to explore the community classification of the network. Based on the extended gravitymodel, we can quantify the international trade resistance r i,j for 198 entities(Figure 1). We suppose that most trade resistance can be divided into two cat-egories. The first has low expected barriers, which are mainly related to naturalfactors such as geographical distance, and the other includes countries with rel-atively high artificial trade barriers, such as trade restrictions, border blockades, III S. Huang et al. cultural differences and political policies. It shows that most of the trade rela-tions among the United States (red dot), China (green dot) and other countriesbelong to the first category, that is, most of the trade resistances are positivelyrelated to geographical distance, so they are concentrated near the blue dottedline (Figure 1 (a,c,e)). For the United States and China, only a small number ofbilateral trade relations are affected by more artificial barriers.Using the EM algorithm and the defined latent parameter θ = [ a, b, µ, σ , σ ],we can fit the distribution of trade resistance r i,j well and obtain the charac-teristics of the two categories [38]. The fits of the distribution for 2007, 2012and 2017 all pass the Kolmogorov-Smirnov test, and the parameters efficientlyconvert to the optimal values (Figure 1 (b,d,f)), which confirms our hypothesisof two categories of trade relations.Here, the trade resistance of each pair has a probability of belonging to thelimited trade resistance group (natural barriers, or category I). For each country i , we define the trade purity indicator T P I i by summing the probability that itstrade relation r i,j belongs to category I as T P I i = 1 /N (cid:80) j P ( z ij = 1 | ˆ θ ), where N is the number of countries, z ij equals 1 when the trade relations between i and j belong to category I, 0 otherwise. The TPI indicator provides a quantitativemeasure of the openness of a country’s trade environment.
2. Alienation of Trade Relationships between Countries.
Figure 2 (a)shows the evolution of trade resistance. Different colors represent the distribu-tion of trade resistance for corresponding years. With optimized parameters, inthe decade considered, the distribution of trade resistance (the expectations ofcategories I and II) shifts to the right overall, which indicates an average increasein global trade resistance during the period 2007-2017.Considering that global trade resistance could be affected by the growth oftransportation costs or other factors, we also analyze the trend of the tradepurity indicator from a more rigorous perspective. The distribution of the tradepurity indicator (Figure 2(b)) also indicates the alienation of the global tradenetwork. Obviously, the mean TPI decreased in from 2007 to 2017. itle Suppressed Due to Excessive Length IX(a) 2007 (b) 2007(c) 2012 (d) 2012(e) 2017 (f) 2017
Fig. 1.
Fitting the Distribution Characteristics of Trade Resistance, based on the Hy-pothesis of Two Categories. (a, c, e) Gray dots show the trade resistance betweencountries around the world. (b, d, f) Gray bars express the trade resistance quantifiedfrom the extended gravity model; the blue dotted line is the fitted results with the EMalgorithm. S. Huang et al.(a) (b)
Fig. 2.
Evolution of Trade Resistance during the Period 2007-2017. (a) Distributionof trade resistance ln r ij . (b) Distribution of the trade purity indicator (TPI) in 2007,2012, and 2017. The alienation of global trade is thought-provoking. In recent years, somescholars have highlighted this trend in international trade [13,46]. To protecttrade interests, some countries seek to maintain the friendly regional trade re-lations by signing trade agreements and creating trade unions. Since the 1990s,RTAs have proliferated, including regional unions with members that are geo-graphically near one another (e.g., EU, NAFTA) and countries or regional blocswith diverse and geographically distant partners (e.g., ASEAN and BRI) [27,7].The impact of RTAs has always interested politicians and scholars. Can RTAsadapt to such an international trade environment? Why might a governmentbe willing to compromise its sovereignty and sign an agreement? The answer isinterdependence. Based on the quantified TPI, we attempt to analyze the effectsof regional trade unions in the following sections.
The policies imposed by any government could affect the wellbeing not onlyof its own citizens but also those in other countries. Trade creation and tradediversion are common effects of RTAs identified in the recent literature [23,49],and in empirical work, their mixed effects are more complex; the results aredifficult to quantify [11,42]. This paper attempts to describe the effects of RTAson both global and local trade relationships through a quantitative model andempirical analysis.
1. Relatively Closer Trade Relationships between Union Members.
Here, we analyze six typical RTAs, including those between the 28 EU countries, itle Suppressed Due to Excessive Length XI
Table 2.
Average Trade Resistance Within and Outside Trade Unions
Year BRI EU OAU CARIFTA ASEAN NAFAT WorldMember Others Member Others Member Others Member Others Member Others Member Others2007 36.66 39.57 33.40 37.14 38.51 40.31 33.38 40.63 32.85 38.51 33.50 36.68 39.182008 38.16 41.10 34.92 38.59 40.01 41.80 34.59 41.97 34.57 39.87 35.09 38.17 40.662009 37.65 40.47 34.27 38.08 39.55 41.16 34.33 41.42 33.83 39.27 34.34 37.45 40.062010 39.45 42.33 36.30 40.04 41.24 42.98 36.42 43.43 35.95 41.10 36.71 39.71 41.972011 40.68 43.47 37.37 41.13 42.43 44.11 37.18 44.45 37.01 42.31 37.92 40.84 43.072012 41.22 43.93 37.86 41.61 42.83 44.62 37.63 44.90 37.61 42.63 38.54 41.31 43.542013 41.26 44.00 37.85 41.68 43.02 44.74 37.79 45.07 37.74 42.54 38.52 41.39 43.662014 41.27 43.94 37.81 41.44 43.38 44.73 37.95 45.11 37.41 42.71 38.48 41.39 43.652015 41.51 44.21 36.91 42.03 44.69 45.37 39.87 45.34 36.85 42.93 37.58 42.32 44.132016 40.18 42.96 36.79 40.45 42.99 43.95 38.16 44.46 36.49 41.65 37.41 40.33 42.792017 41.59 44.23 37.27 41.41 43.90 45.14 38.75 45.47 39.47 43.44 37.89 40.80 43.98
52 OAU countries, 13 CARIFTA countries, 10 ASEAN countries, 3 NAFTAcountries and 66 BRI countries.First, we compare the trade resistance within and outside the six unions. InTable 2, the average trade resistance between member countries is lower thanthat outside the unions. This demonstrates that the member countries of a uniongenerally have closer trade relations with one another.
Fig. 3.
Trade Purity Indicator Within and Outside Unions During the Period 2007-2017. The X-coordinate expresses the TPI inside the union, and the y-coordinate ex-presses the TPI outside the union.
In addition, in Figure 3, with the x-coordinate expressing the TPI within theunion and the y-coordinate expressing the TPI beyond the union, the size of thedots is proportional to its proximity to the present (TPI in 2007 has the smallest
II S. Huang et al. radius, and TPI in 2017 has the largest radius); the solid three spots of the samecolor indicate the TPI in 2007, 2012 and 2017. Obviously, most spots are locatedbelow the diagonal, which means that the relationships between union membersare closer than those with other countries outside the union.Therefore, it indicates that all trade unions help to lower average trade re-sistances and create closer trade relations among the members compared withother countries.
2. Decreasing Trend in Trade Relationships for Union Members.
Thesesix unions can be divided into two types. Specifically, the EU and NAFTA aretype one, and most countries in these unions are developed countries. For thesetwo RTAs, the spots move vertically over time (Figure 3). The TPI inside theunions barely changes, but the TPI outside the unions fluctuates and tended toincrease. BRI, OAU, CARIFTA and OAU are type two, and the spots of theseunions move towards the bottom left. In brief, by comparing the TPIs in 2007and 2017, except for the EU and NAFTA, the TPIs within unions all declined.The trade environments of the EU and NAFTA are more friendly than those inthe other four unions.In Figure 6 (in the Appendix), we can more clearly see these two typesof unions. The red labels indicate a trade deficit, while blue labels indicate atrade surplus, and the size of spots represents the net trade flow (exports minusimports). The EU and NAFTA (Figure 6(a)(e)) have fewer member countries,and have higher economic development and surplus trade flows. Therefore, thedots are highly concentrated. Other unions (BRI, OAU, CARIFTA and ASEAN(Figure 6(b)(c)(d)(f)) are more uneven, as the dots distributed from low TPI tohigh TPI, and some member countries have trade surplus, while the others havea trade deficit. In addition, this indicates that the countries with surplus tradeflows (blue label) have a higher TPI both inside and outside their unions.
Trade unions are formed through agreements signed by countries. With the de-velopment of globalization, it is worth further exploring whether they can reflectreal trade affinity. As mentioned in section 2.4, we extract the backbone of theglobal trade network based on quantified trade resistance and classify it intoseveral communities. Trade communities are obtained from the analysis of thenetwork structure, which can objectively describe the trade relationships be-tween countries.
1. Communities in the Global Trade Network.
In Figure 4, the nodesthat share the same color are assigned to the same community. The modularityof classification is Q = 0 .
780 in 2007 and Q = 0 .
769 in 2017, which means thatthe classification is credible. There were some structural changes between 2007and 2017. itle Suppressed Due to Excessive Length XIII(a) 2007(b) 2017
Fig. 4.
Communities in the Global Trade Network in 2007 (a) and 2017 (b).
First, in 2007, the communities show significant regionality. The map (Figure4 (a)) shows that countries on the same continent are more likely to be clusteredin the same community, confirming that geographical characteristics play an im-portant role in forming trade patterns. For most members, the six trade unionsare signed among regional countries, and based on their relatively close trade re-lations, it is not difficult to understand that most members of RTAs are clusteredin the same community. In 2017, the distribution of community members wasmore divergent. With the development of globalization, trade between countriesis no longer restricted by geographical or transportation factors.Second, from the empirical results, over these ten years, the network densitydecreased, which means that countries in the global trade network are connectedmore loosely (the cluster coefficient changed from 0.1370 to 0.1006).
IV S. Huang et al.
There is another interesting phenomenon. Some countries are on the samecontinent and belong to the same RTA but are more closely related to coun-tries in other unions than the members of their RTAs. Most African countrieshave multiple RTA memberships [30], and the continent’s east and west coastsbelong to different marine routes in the global marine transport network [61].Therefore, it is easy to understand why eastern and western Africa are clus-tered into different communities. France, Spain, Portugal, and Belgium are EUcountries, but they are classified into the community where most members areAfrican countries. This shows that they have closer trade relations with Africancountries than with other EU members, which may be due to language, culture,colonial influence and their trade structures.Here, we apply the external-internal index (E-I Index) and compare regionaltrade cohesion and global trade cohesion as follows:E-I index ( degree ) = − EK − IKEK + IK E-I index ( weight ) = − EW − IWEW + IW (9)External edges connect nodes from different communities, while internaledges connect two nodes belonging to the same community. EK and IK arethe sum of external and internal degrees for all nodes; EW and IW are thesum of external and internal weights for all nodes. Based on the results of thebackbone network in 2007 and 2017, the E-I index (degree) dropped from 0.2711to 0.1000, and the E-I index (weight) increased from -0.1019 to 0.0281. The re-lationships in the global trade network are more diversified, but trade intensityis concentrated in local communities.
2. Correlation and Evolution of Unions and Communities.
We haveidentified the trade unions resulting from negotiations between countries, andthe trade communities clustered from the empirical data. What is the correlationbetween them? Do the members of trade unions truly have closer trade relations?Which trade unions have no obvious effect on restraining and helping membercountries? To answer these questions, we measure the correlation coefficient be-tween the members of trade unions and trade communities. Figure 5 shows thematrix of the Jaccard similarity coefficient of six trade unions and ten typicalcommunities. ‘Others’ indicates countries that do not belong to the six unions.Green color means a greater correlation and a higher commonality of membersbetween trade unions and communities. In contrast, yellow color means that themembers of the union and community are basically different.In general, the similarity matrices of 2007 and 2017 have similar structures.Each trade union has only one or two grids with a great deal of green, whichindicates that some trade unions and communities have high consistency in mem-bership. Several very green grids are shown in Figure 5 (a), which presents theoverlap of ASEAN and community 6, BRI and community 0, CARIFTA andcommunity 4, OAU and community 1, etc. The EU and NAFTA are relatively itle Suppressed Due to Excessive Length XV(a) 2007(b) 2017
Fig. 5.
The Similarity Matrix between Trade Unions and Trade Communities in 2007(a) and 2017 (b). ‘Num’ means the number of members in the corresponding tradeunion or community.VI S. Huang et al. ‘free’ trade unions, and their members are not limited to one or two commu-nities, which overlap with several separate communities. In addition, in 2007,the ‘Other’ countries that do not belong to six trade unions are also relativelyconcentrated in three communities, with a certain aggregation, and it is quitedifferent from the results from 2017.The similarity was higher in 2007; that is, the trade unions were more simi-lar to the actual trading clustering result. In 2017, the role of the trade unionsweakened. For most trade unions, the maximum matching of members to com-munities is decreasing. Here, the EU and NAFTA remain exceptions, havingrelatively higher similarity with communities 1 and 8. This might be due totheir mature trading background. In addition, the TPIs of the EU and NAFTAremained stable, while the TPIs of other trade unions decreased (Figure 3). TPIindicates a trade-friendly relationship with other countries, while communitiesalso reflect the different trade relations between countries inside and outside thecommunity. Therefore, it is reasonable and scientific to conclude that EU andNAFTA have particularities in both results. Compared with 2007, the commu-nity structure of “Other” countries has become more decentralized.In short, RTAs appear to have an impact that strengthened the formationof true trade relations [50]. Based on the similarity matrix, each trade union ismainly concentrated in one or two communities. However, in 2017, this kind ofconsistency clearly weakened, and multilateral trade liberalization has acceler-ated over the past decade.
The innovation of this paper is to study and describe the trade purity relation-ships between countries, considering some other typical factors, such as economicvolume, geographical distance, overall increased transportation and labor costs,are separated. In addition, this paper does not use the exogenous parameter esti-mation method, and we define latent parameters and use the likelihood functionand EM algorithm to quantify and analyze the trade purity indicator more sci-entifically and effectively. In brief, the extended model prompts the developmentof the gravity model in theoretical research on international trade.In the empirical analysis, some unobserved characteristics of the trade re-lationships can simultaneously be defined and optimized, and the analysis usesa trade purity indicator to describe the trade environments and positions ofcountries in both regional and global trade relationships.With the data from the UN Comtrade Database, we quantify the interna-tional trade resistance of 198 countries/districts. This analysis shows that thetrade relationships of the 198 entities can be divided into two categories. Thetrade resistance of countries in category I has an approximate log-linear rela-tion with geographical distance, and these countries have a relatively open andfriendly trade environment, where the main trade barriers are natural factors.The countries in category II have higher artificial trade barriers, and countrieswith poor trading environments frequently fall into category II. Here, we obtain itle Suppressed Due to Excessive Length XVII well fitted results using the EM algorithm from machine learning. All latent vari-ables converge rapidly to optimal points, which validates the extended gravitymodel proposed in this paper.In addition, this paper defines and identifies a trade purity indicator for dif-ferent RTA countries during the period 2007-2017. It can describe the true tradeenvironment and relationships. Countries with higher indicators have friendlytrade environments and obtain large trade flows, such as the United States,China, Japan, Korea, South Africa, Singapore, Australia, and Malaysia. Forthese countries, most trade partnerships are mainly related to natural factorssuch as geographical distance, and they have no obvious trade barriers. Theanalysis of the indicator and its evolution could help to research the characteris-tics and trends of international trade. This indicates that although the global andmost regional trade relations gradually deteriorated over the period 2007-2017,the RTAs bring closer trade relations between members, especially contributingto the relative prosperity of the EU and NAFTA.Finally, based on the trade resistance matrix, we build a network mappingthe relationship of 198 countries/districts. The Louvain community detectionmethod identifies several communities in the global trade network. Here, weanalyze the effects of RTAs by comparing the members of trade unions andcommunities. The results show that the representative RTAs constitute the corestructure of international trade network, but the role of trade unions has weak-ened and multilateral trade liberalization has accelerated in the past decade.This means that more countries have recently tended to expand their tradingpartners outside their unions rather than limit their trading activities to theirRTAs.
VIII S. Huang et al.
Conflicts of Interest
The authors declare no conflict of interest including any financial, personal orother relationships with other people or organizations.
Funding Statement
This work was supported by the Chinese National Natural Science Foundation(71701018, 61673070), the National Social Sciences Fund, China (14BSH024),and the Beijing Normal University Cross-Discipline Project.
Data Availability statement
The empirical data used in this paper could be downloaded from sources listedin Table 1. Or please contact with Dr. Xiaomeng Li ([email protected]) torequest the data.
Acknowledgement
We appreciate comments and helpful suggestions from Prof. Zengru Di, Hong-gang Li, Handong Li and Jiang Zhang. itle Suppressed Due to Excessive Length XIX
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Fig. 6.
Trade resistance in six different trade unions for the year 2017. (a) for EuropeanUnion (EU) countries. (b) for Belt and Road (BRI) countries. (c) for Organizationof African Union (OAU) countries. (d) for Caribbean Free Trade Area (CARIFTA)countries. (e) for North American Free Trade Agreement (NAFTA) countries. (f) forAssociation of Southeast Asian Nations (ASEAN) countries.itle Suppressed Due to Excessive Length XXIII
Figure 6 (Appendix) presents some detailed information. The x-coordinate ex-presses the TPI between a specific country and other countries in the same union,while the y-coordinate expresses the TPI between a specific country and othercountries outside the union. The size of dots is proportional to the net trade flow,measured as the absolute value of the difference between exports and imports;a red label means that the country had a trade deficit, while a blue label meansa trade surplus flow. Most dots are below the diagonal, which means that theTPIs of most countries inside the union are lower than those outside the union.In addition, countries with surplus trade flow (blue labels) have a higher TPIboth inside and outside the union.
B Pretreatment of Flow Zero Value
For the gravity model (equation 1), F i,j is the trade flow from country i tocountry j ; m i and m j is the combined size of their economies; r i,j is the traderesistance need to be quantified. It is generally believed that the model cannotdescribe zero flow because the gravity is universal [25], even if the size of twocountries is very small and the geographical distance or trade resistance is verylarge, as long as the volume m i · m j is not equal to zero and the resistance r ij are not infinite, the trade flow between them may be very small, but not zero. F i,j (cid:39) ( m i · m j ) α r i,j − ε ij = exp ( α ln( m i · m j ) − ln r i,j ) − ε ij (10)However, the situation of zero-value flow is very common in the empiricaldata, around 50% in the global trade network [34], and it creates an additionalproblem for the log linear form of the gravity equation (including the traditionaland structural gravity model in trade studies). In the early studies, some schol-ars often deal with the zeroes trade observation by truncation method, such asdeleting them completely or substitute by small positive constant [26,12]. It’s ob-viously not rigorous enough [25]. In reality, the zero-value trade flow is generallyconsidered to be not observable or due to measurement errors from rounding.So stochastic versions of equation are used in empirical studies [53,34]. Here wecan add an error term ε ij , and assume that the error function is positive andobeys lognormal distribution [53], as ln ε ij ∼ N ( µ, σ ) in equation 10. E ( ε ij ) = e µ + σ / V ar ( ε ij ) = ( e σ − e µ + σ . For clarity, we assume X = ε ij , and Y = X + F i,j . The probability densityfunction of the random variable X is, f X ( x ) = √ πσx exp [ − σ (ln x − µ ) ] x > x ≤ XIV S. Huang et al.
The probability density function of Y is calculated as follows: F Y ( y ) = P ( Y ≤ y ) = P ( F i,j + X ≤ y ) = P ( X ≤ y − F i,j ) = F X ( y − F i,j ) f Y ( y ) = F (cid:48) Y ( y ) = f X ( y − F i,j ) × ⇒ f Y ( y ) = √ πσ ( y − F i,j ) exp [ − σ (ln( y − F i,j ) − µ ) ] y − F i,j > y − F i,j ≤ r i,j for each pair of countries by the least square method with, min ( φ = ( F i,j + ε ij − G ( m i · m j ) α r i,j ) + ( F j,i + ε ji − G ( m i · m j ) α r i,j ) ) ∂φ∂r i,j = 0 ⇒ r ∗ i,j (cid:39) m i · m j ) α F i,j + F j,i + ε ij + ε ji Different kind of Pseudo Maximum Likelihood (PML) methods are proved tobe effective to deal with the zero-valued trade flow and the logarithm transforma-tion [43,44,53]. The method in this paper is not exactly the same as the gravitymodel, and the main different is that we replace the geographical distance with r i,j which needs to be quantified. So we use the idea of PML, but improve thelikelihood function here. Then, we maximize the probability E ( Y ) = E ( X )+ F i,j ,with the defined likelihood function, L = (cid:89) i,j p ( E ( X ) + F i,j | µ, σ ) = (cid:89) i,j p ( E ( G ( m i · m j ) α r i,j ) | µ, σ ) (cid:39) (cid:89) i,j p ( 2( m i · m j ) α F i,j + F j,i + 2 E ( ε ij ) | µ, σ )With the method of maximum likelihood estimation, we can optimize theparameters µ and σ to get the max µ,σ ( L ), which make E ( Y ) = E ( X ) + F i,j themost likely to occur in reality.The optimized parameters are listed in Table 3, and Figure 7 shows thedistribution of random error ε ij during 2007-2017. It can be seen that the meanvalue of random variables is basically around 1-2, and the variance is relativelysmall, which conforms to the basic assumption of statistical error in trade flows. itle Suppressed Due to Excessive Length XXV µ σ E ( ε ij )2007 0.00694 0.00050 1.006972008 0.00228 0.00020 1.002292009 0.02364 0.00047 1.023922010 0.56409 0.00027 1.757852011 0.00339 0.00024 1.003402012 0.01529 0.00072 1.015402013 0.81314 0.00018 2.254982014 0.05607 0.00061 1.057672015 0.40263 0.00017 1.495752016 0.31945 0.00028 1.376372017 0.02362 0.00047 1.02390 Table 3.
Optimized Parameters