Koffi Dumor1,2,* and Li Yao 1,2,3
1 School of Management and Economics, University of Electronic Science and Technology of China, No. 2006,Xiyuan Ave, West Hi-Tech Zone, Chengdu 611731, China; liyao@uestc.edu.cn
2 Center for West African Studies, University of Electronic Science and Technology of China, No. 2006,Xiyuan Ave, West Hi-Tech Zone, Chengdu 611731, China
3 East Asian Institute, National University of Singapore, Singapore 259770, Singapore
* Correspondence: dumor3000@yahoo.fr
Abstract: The Belt and Road Initiative (BRI) under the auspices of the Chinese government was created as a regional integration and development model between China and her trade partners.Arguments have been raised as to whether this initiative will be beneficial to participating countries in the long run. We set to examine how to estimate this trade initiative by comparing the relative estimation powers of the traditional gravity model with the neural network analysis using detailed bilateral trade exports data from 1990 to 2017. The results show that neural networks are better than the gravity model approach in learning and clarifying international trade estimation. The neural networks with fixed country effects showed a more accurate estimation compared to a baseline model with country-year fixed effects, as in the OLS estimator and Poisson pseudo-maximum likelihood. On the other hand, the analysis indicated that more than 50% of the 6 participating East African countries in the BRI were able to attain their predicted targets. Kenya achieved an 80% (4 of 5) target. Drawing from the lessons of the BRI and the use of neural network model, it will serve as an important reference point by which other international trade interventions could be measured and compared.
Keywords: belt and road initiative; trade; gravity model; neural network analysis
1. Introduction
It is well known that international trade is a key contributor to growth and poverty reduction.Thus, assessing a country’s trade performance, and estimating the extent to which it is poised for growth is highly important. Such estimation can be used by governments to adopt and devise policies according to international economic demands. The need to partner with and expand the trade frontiers to stimulate its economy lead China to introduce of the Belt and Road initiative and studies by Huang, Liu and Dunford emphasize that this strategy is focused on stimulating the socio-economic development for China and also beyond its borders to cooperating countries on this initiative for mutual benefits and improvements on the livelihood of the peoples, create employment and improve the environment. We trace the Belt and Road Initiative (BRI) to September and October of 2013,when the President of China proposed a model called “Silk Road Economic Belt” and was aimed to become a regional cooperation model of development and further incorporated a “Maritime Silk Road” as well Swaine . In their view, Huang, Johnston noted that the Belt and Road Initiative (BRI) focused on 5 key areas: policy coordination, facilities connectivity, trade facilitation, financial cooperation and bond various people. Thus, breaking away geographical limits and promoting inclusiveness and improve relationships. In the mid-2017 President Xi called the BRI as the “Project of the Century”. It must be noted, however on the contrast to this accolade an anonymous Beijing-based European diplomat echoed that “Everyone asks me about BRI but we don’t even know,what it is” SCMP thus giving a down twist to its relevance and essence as well as denying knowledge of its roles. The outpour of such comments of the BRI potential is indicative of its opposition to the extent of denying knowledge of it and this calls for a deeper reflection on the impact of BRI to partner countries. Studies into the estimation of benefits on subscribing to the BRI has been growing steadily but little has been done in the area of analyzing with neural networks approach.
In this study, we do not necessarily intend to design a novel neural network or gravity model datasets but we aim at extending this concept to BRI by an application of the neural network.This would lead to predicting accurately with the datasets while ensuring the sustainability of generating more predictive information that would increase in the quality of stockholders’ decision making, regarding the growth of this new BRI concept. In this study, sustainability is defined as the continuous use of the datasets that consistently allow for the achievement of the set of policy target and this in line with the definition of sustainability that defined as a composite by the Brundtland land commission and a determined policy objective . We employ the gravity model to further explain the benefits of such international trade agreement on participating countries. This model is often used to estimate international trade and various empirical studies on bilateral trade often rely on the traditional gravity model, which relates the volume of trade between countries to their economic scales and the distance between them . A second possible method of predicting or estimating international trade is the neural network analysis. Artificial Neural Networks (ANNs) describe a general class of non-linear models that have been successfully applied to a variety of problems such as pattern recognition, natural language processing, medical diagnostics, functional synthesis,and forecasting (e.g., econometrics), as well as exchange rate forecasting . Neural Networks are especially appropriate to learn patterns and remember complex relationships in large datasets.Recently, Wohl and Kennedy in their study exhibit an extremely starter endeavor to examine international trade with neural network and the traditional gravity model approach. The findings show that the neural network has a high degree of accuracy in prediction compared to the gravity model regarding Root-Mean-Square-Error (RMSE). Their study compares neural network predictions with actual trade between the United States and its major trading partners.
The question, therefore, remains that how relevant is the BRI as an international trade pact going to influence or otherwise be beneficial to participating countries? The neural network gravity model will be employed and the data will be analyzed to enable us attempt to explain or evaluate the BRI on partner countries? The purpose of this study, therefore, is to test and compare the predictive power of the neural network analysis with that of the gravity models, using the case of trade between China and its trading partners within the Belt and Road Initiative, particularly the African countries. As a matter of fact, as far as Africa is concerned, the Belt and Road Initiative (BRI) is predominantly located in East Africa. This study uses the gravity model and the neural network to make an estimation of bilateral trade between China and its African partners and compares the estimates with actual trade data to note which estimation method more closely matches the actual data. Finally, this paper would help to find explanations to the question of whether this BRI is indeed a worthwhile model for both China and its partners through the data analyzed. This is essential and useful to policy and could possibly influence its sustainability among the players.
The rest of the paper is structured as follows: Section 2 offers a brief review of related literature on the application of neural network analysis and gravity model to international trade estimation;Section 3 discusses the concept of Belt and Road Initiative; Section 4 grants a closer overview of gravity and neural network models; Section 5 discusses the data, the data cleaning techniques, and provides a detailed account of features. Section 6 presents the evaluations results and analysis of the model and compares the neural network and gravity model predictions with actual data on trade among China and its BRI members. Finally, Section 7 concludes the article and proposes directions for future research.
2. Related Work
While there is an extensive existing literature on Gravity Models, applying machine learning methods to foresee trade flow remains another research theme. One precedent is Nummelin et al.that used the Support Vector Machine to break down and conjecture reciprocal exchange streams of soft sawn-wood. More applicable to our target, Elif demonstrated that neural networks accomplish a lower Mean Square Error (MSE) contrasted with panel data models by using data from 15 EU countries.Tkacz et al. also showed that Financial and monetary variables could be improved using neural network techniques. Combining neural network and market micro-structure approaches to investigate exchange rate fluctuations, Gradojevic and Yang found that macroeconomic and microeconomic variables are valuable to forecast high-frequency exchange rate variations. Similarly, Varian, Sonia Circlaeys and Kumazawa provided an overview of machine learning tools and techniques,including its effect on econometrics. Furthermore, Bajari et al. presented an overview and applied a few methods from statistics and computer science to the issue of interest estimation. The findings showed that machine learning coupled with econometrics anticipates request out of a test in standard measurements considerably more precisely than a panel data model.
The gravity model is acknowledged in many studies for its consistent accomplishment in providing explanations in areas of flows, for example, infrastructure, immigration, institution,and bilateral trade . Beverelli et al. for instance investigated the effect of institutions on trade and development within the gravity trade framework and found that institutions boost trade. Lu et al. also augments Anderson model by introducing transport infrastructure,and examined its impact on trade and growth under BRI, using gravity model estimations. The results showed that stronger transport infrastructure accelerates trade and economic growth between BRI trading partners. Similarly, following Baier model , Herrero and Xu showed that Infrastructure accelerates trade among BRI members. Fiorentini et al. also empirically assessed the relationship between immigration and trade by focusing on the Veneto region in Italy. The results obtained by using the gravity model shows that immigrants promote trade among sending and hosting countries.
Recently, Wohl and Kennedy in their study exhibited an extreme starter endeavor to examine international trade with neural network and the traditional trade gravity model approach. The findings showed that the neural network has a high degree of accuracy in prediction compared to RMSE within the gravity model. Wohl and Kennedy pointed out that neural networks have the nonlinear functional capability to withstand chaos and noise in most datasets and comparatively are more robust and have high adaptability owing to a large number of interconnectivity within its processing element . Also, Athey in his research paper presented an appraisal of the early commitments of machine learning to economics, and likewise expectations about its future contribution. They also investigated a few features from the developing econometric consolidating machine learning and causal inference, including its effects on the idea of the coordinated effort on research tools, and research questions.
Tillema et al., Pourebrahim et al. in their work on a comparison of neural networks and gravity models in trip distribution concluded that neural networks outperform gravity models when data is scarce, invariably in large datasets, evidence shows that gravity models outperform neural networks but they point out with less certainty in respect to the latter. Furthermore, Elif compares neural networks to a panel gravity model approach and state that both models give a satisfactory result that modified gravity model of bilateral trade which was analyzed, explained the variation in bilateral exports among European countries. The panel gravity model provided an advantage of explaining the individual effect of independent variable on bilateral trade and showed their significance as well.The neural networks in another dimension with a similar independent variable accordingly gave a 97% variation showing a much superiority to the traditional panel gravity model data analysis.The application of Neural Networks to OBOR is justified by the fact that neural networks have the benefit of comprehensively predicting dichotomous outcomes as shown in fields such as medicine Alaloul et al., also it has the capability to handle complex non-linear relationships between the dependent and independent variables. This therefore falls in line with a bilateral relationship which has a similar dichotomous characteristic, with the host proponent country, China and its partners who have subscribed to participate in this trade arrangement.
With regards to factors affecting international trade, Celine and Christopher examined the impact of infrastructure on Central Asian trade by applying a panel gravity model on 167 countries.They showed that infrastructure would raise the trade flow by 2.4%. Similarly, Limao and Venables [32]investigated the effect of transport infrastructure on bilateral trade. They found out that poor quality of infrastructure cuts bilateral trade by 28%. Since it is expected that BRI comes along with infrastructure,literature presupposes that BRI has effects on the increase (or otherwise) of bilateral trade flows.This study seeks to estimate the extent to which BRI contributes to the increase (or otherwise) of the bilateral trade between China and the African countries along the Silk Road. This is in addition to the main objective of estimation and forecasting of China’s export with the members of the Belt and Road Initiative, using a large dataset from UN-Comtrade that includes 163 countries.
3. The Concept of Belt and Road Initiative
The Belt and Road initiative pact commenced with its announcement in 2013, the first forum of Belt and Road forum (BRF) in Beijing in May 2017 led to the signing of an economic and trade agreement with 30 countries including. It underlines regional connectivity through ports and infrastructural projects. The BRI primarily include the Silk Road Economic Belt which links China to the Central and the Southern Asia, and then to Europe. The new maritime silk road developed, connects China to the nations of Southeast Asia, the Gulf countries, Northern Africa and Europe. It is also said to be open to all countries. In the past decade, bilateral trade flow between China and countries along the BRI showed a tendency to increase.
As a developmental initiative, many countries cannot cope with the pace of the relationship. Thus, to improve the quality of these relationships, countries must identify their weakness through available analytical sources, which will help them make better trade decisions. Considering the shreds of evidence shown by available data that there is actually an increase in trade, we seek to find out the extent to which the increase can be attributed to the BRI. Motivated by the above, we investigate the effect of the Belt and Road initiative (BRI) on bilateral trade using neural network analysis and the gravity model estimations. A set of economic, geographic and regional trade agreements such as GDP, infrastructure, distance between the importer and exporter, etc. serve as input to our models.
4. Overview of Framework Models
4.1. Gravity Model
The gravity model was first introduced by Leibenstein, Pöyhönen, as a model to estimate the amount of bilateral trade between two countries. Empirical studies of bilateral trade often rely on the traditional gravity model, which relates the volume of trade between countries to their economic scales and the distance between them. The traditional model for trade between two nations (iand j)
appears as:
where Tij is the trade volume between areas iandj; GDPi and GDPj is the gross domestic product of the countries(i and jthat are being measured; Dij is the distance between areas i and has strong j; a, θ1, θ2, and θ3 are the parameters to be estimated.
This model is intuitive, adaptable, has substantial hypothetical establishments, and can make reasonably accurate predictions of international trade. The gravity models can determine multilateral resistance, and also other country particular historical, cultural, and geographic components, by using country fixed effects: dummy factors for individual country exporter and individual country importer. However, a weakness of this approach is that country fixed effects will ingest whenever invariant country-specific factor of intrigue. Some gravity models use country-year fixed effects, country-pair fixed effects, or both. Gravity models can appear as Ordinary Least Squares (OLS) estimators, for example,
where Xij,t is the bilateral export between country i and country j, GDPi,t and GDPj,t, the gross domestic product of patners’ i and j, the distance between i and j,Dist ij, and dummy variables, capture a common border (Contigij), a common language (Comlangij), a common colony (Colij), infrastructure indexof the partner countries (Inf ra i and Inf raj), and regional trade agreements (Obor ij, Asean ij,Eacij, Sadcij). eijtis an error term for pair of i-th country and j-th country in year t.
Alternatively, with the addition of country fixed effects :
This equation is the same as Equation (2), however we extended Equation (2) and introduced mi+ aj, where mi+ aj represent exporter and importer fixed effects respectively.
Alternatively, with country-year fixed effects:
In addition,we extended Equation (3) to introduce the variables mit+ ajt, where mit+ ajt denote exporter-year and importer-year fixed effects respectively.
This study in addition introduces the use of Poisson pseudo maximum likelihood (PPML) as proposed by Silva and Tenreyro, a non-linear estimator that does not depend on a log change of trade flows. Subsequently, we consider our work to pursue the spirit of time series models, for example, AR, MA, ARMA type models. Lacking thorough hypothetical support, our models will not be valuable in studying the fundamental mechanisms of bilateral exports flow. However, we trust this is a critical research objective since the measure of exports impacts governments’ domestic and trade arrangements, and a model that provides more great trade volume prediction would be of good use to policymakers.
4.2. Neural Network Model
An Artificial Neural Network (ANN) is a computational model that is inspired by the way biological neural networks in the human brain process information. It represents a general class of non-linear models that have been successfully applied to a variety of problems such as pattern recognition,natural language processing, medical diagnostics, functional synthesis, and forecasting (e.g., econometrics), as well as exchange rate forecasting. Neural Networks are especially appropriate to learn patterns and remember complex relationships in large datasets. Fully Connected Layers are a very basic but yet very powerful neural networks types. The basic unit of computation in a neural network is the neuron, aka node or unit. It receives input from some other nodes and computes an output.
Each input has an associated weight (w), which is assigned on the basis of its relative importance to other inputs. The node applies a function f defined as weighted sum of its inputs as follows:
The neuron illustrated in Figure 1takes numerical inputs X1, X2 and b (called the bias) and has weights w1 and w2. The output Y is computed as shown in Equation (5). The function f is non-linear and is called Activation Function. The purpose of such activation functions is to introduce non-linearity into the output of a neuron. This is important because most real world data is non linear and we want neurons to learn these non linear representations.
There exists different types of activation function in the literature (sigmoid, tanh, ReLu) defined
as follows:
Figure 2 shows the graphical representation of each activation function. In this work, we use ReLU as the activation function. In this paper, we follow the implementation details of Wohland Kennedy and modify the hidden fully connected layers to be 20 × 15× 10× 5 as illustrated in Figure3. Our feed forward network model is made of one input layer, four hidden layers and one output layer. First, The input layer receives information from our dataset called the input feature. Therefore, the number of input nodes in the first layer reflects the number of independent variables in the dataset. In our work, the input feature of the network are the standard gravity model variables such as GDP, distance, border, colonial relationship, trade agreement etc. These input features are summarized in Table 1. No computation is performed in any of the input node. Second, The four hidden layers have no direct connection with the dataset features, but perform computations and transfer information from the input nodes to the output node.
Each node in a hidden layer receives weighted inputs from each node in the input layer. Finally, our output layer gives the result of the computation by the neural network. In this work, the output layer is the predicted amount of bilateral trade between China and its partners along the BRI. In order to train our neural network, we calculate the total error at the output node using Equation (10) and propagate the error back through the network. We use an optimization method called Gradient Descent to adjust all the weights in the network with an aim of reducing the error at the output layer. The network was trained for 100 epoch with a batch size of 16 and a learning rate of 0.
5. Dataset
5.1. Dataset
The data for this study covers a panel data set of 163 countries from 1990 to 2017. Thus, our data set consists of 4536 observations of bilateral export flows (162 × 161 country pairs). Various sources of data were used. Used the United Nations Trade Statistics Database, the International Prospect Research and Information Center, CEPII Distance Database, WDI(WB,2018) and other databases are used as data sources for bilateral trade (exports) data, gross domestic product (importers, exporters), proximity (common border), common language (official language), colony (colonial relations), transport infrastructure variables, etc.
5.2. Cleaning Techniques
Firstly, we remove all the entries that have no trade flow value as they are not economically significant and cause outlier problems. Secondly, we extrapolate the missing data using backward and forward linear interpolation. Fourthly, we took the log of data to achieve a smoother distribution of the data as illustrated in Figure 4. After this process, we left with 3936 observations. For the neural network, we standardize the persistent variables (exporter’s GDP, importer’s GDP), scaling them with the goal that their means equal up to zero and their standard deviation equal up to one using Equation (6).
where µ is mean of the distribution and σ the standard deviation, both defined as:
Table 2 illustrates the descriptive statistics for each variable in the aggregated regions. The average value of China’s bilateral exports for the sample aggregated regions (Asian, Europe, Africa and the rest of the world), 163 countries listed in the Appendix A, is 4.73% with a standard deviation of 2.19%. China is increasingly active in trading with its partners under BRI. The mean value of importer’s GDP and exporter’s GDP for the aggregated regions is respectively 10.14% and 12.34% with a standard deviation of 1.82% and 0.49%. This proves that China’s has a fast-growing economy. In the whole world, China has recently become well-known for its resilient growth and has appeared as the second largest economy in the world after the United States. Therefore, it is not surprising that the average exporter’s GDP, China is higher than that of its trading partners in BRI. The mean of geographical distance between China and its trading partners under BRI is 3.914411 km with a standard deviation 0.2320467 km. The statistics show that importer and exporter transport infrastructure index respectively has average value of 3.854467 ton-km and 5.743929 ton-km with a standard deviation of Sustainability 2019, 11, 1449 11 of 22 0.9630493 ton-km and 0.2032265 ton-km. The maximum value of transport infrastructure index refers to China among its BRI members with 6.228716 ton-km. This is because of China being vigorously occupied with the advancement of infrastructure in accordance with the OBOR initiative .
6. Evaluation Results and Analysis
6.1. Evaluation Metrics
To compare the predictive performance of our neural network model against gravity model. It is useful to quantify the performance with pre-defined metrics. In this work, we use R 2 , known as the coefficient of determination and mean square error (MSE) as our metrics.
6.1.1. Coefficient of Determination
The coefficient of determination R2 portrays how great our model is at making expectations: it speaks to the extent of the variance in the dependent variable Trade export flow that is predictable from the independent feature space variables.
It is generally characterized as:
where SSres is the residual sum of squares, SStot the total sum of square or the proportion to the variance of the data, yi the input vector associated with a predicted value yˆi and y¯ the mean of the observed data. To avoid division by zero, we modify Equation (8) to produce:
where ϵ is an empiric parameter which value was set to 1e − 8. R 2 ranges from 0 to 1: If R 2 = 0, the model always fails to predict the target variable, and if R 2 = 1 the model perfectly predicts the target variable. Any value between 0 and 1 indicates what percentage of the target variable, using the model, can be explained by the features. If R 2 < 0 it indicates that the model is no better than one that constantly predicts the mean of the target variable.
6.1.2. Mean-Square-Error (MSE)
The loss function (MSE) is used to indicate how far our predictions deviate from the target. MSE is defined as
where yi is the actual observation, yˆi the predicted observation and N is the number of observations.
The root-mean-square error RMSE, which is mainly characterized by the square root of the difference between the predicted value and the observed value, namely RMSE = pMSE, is used to measure the difference between the value predicted by the estimator or model and the actual observed value.
6.2. Analysis and Predictions
Table 3 shows the results of the evaluations.
To illustrate the predictive application of the model, we trained the neural network on a complete dataset from 1990 to 2012 and used it to predict bilateral trade exports between China and its major trading partners in the Silk Road Initiative.Table 4 shows the predicted results.The neural network's estimates closely matched actual trade values, even five years after the training period.In addition, we observed that the neural network model still made good predictions for 2017, and the prediction results are shown in Figure 6.
7. Conclusions
We have investigated the relative predictive powers of the neural network analysis and the gravity models. Results based on the analysis and comparison have demonstrated the ability of the neural network to predict efficiently and more effectively the bilateral trade flow using other economic variables. This is based on its capacity to capture nonlinear interactions between features. The neural network is also able to improve the prediction of the Gravity Model performance by a test set R2 score of 0.15, using the same set of features. This will be a useful aid to policymakers, analysts and firms engaged in the international trade business and provide impetus for all players in the industry to gauge the effects of this trade collaboration. The influence and sustainability of the BRI programme will heavily rely on the benefits that the partner countries derive from such arrangements. The estimation of these trades using the neural network model offers one of many ways by which partner countries can measure its impact and possible sustainability of such partnership.
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