Augmented Gravity Model of Trade with Social Network Analysis

Abstract

The 2030 Agenda for Sustainable Development recognizes international trade as an engine for inclusive economic growth and poverty reduction, and an important means to achieve the sustainable development goals (SDGs). Given this role, international trade and global trade networks have received preeminent attention in recent times due to the sharp growth in trade volumes and their contributions to poverty reduction and sustainable development over the years. Despite the growth in global trade volumes and the associated benefits, there are worrying concerns about the unprecedented changes in international trade patterns and growing imbalances in trade in recent times. Whereas China’s trade volumes have more than tripled over recent decades and have maintained the largest trade surplus spot ahead of Germany, other major trade surplus countries such as Japan, the USA, etc., have become trade deficit countries with their trade volumes increasing at a much slower pace. In view of the growing changes in international trade patterns and the need to understand the dynamics of the widening global trade imbalances among major trading partners, this paper investigates the factors that determine the export performance of countries. More specifically, the purpose of this paper is to highlight the forces that determine the export performance of countries using an augmented gravity model that includes social networks. The paper provides useful insights into the underlying currents responsible for the changes in international trade patterns. Using data from 51 countries for 41 years, our results indicate that the GDP of both the home country and the partner country affects the home country’s exports positively. Similarly, the real effective exchange rate REER, trade openness OPEN, and dummy variables BORDER, ENGLISH, and EU have produced positive and statistically significant coefficient estimates, and these are in line with our theoretical expectations.

1. Introduction

International trade is one of the most important economic activities among countries, and its contributions towards a country’s economic growth and sustainable development are self-evident. For centuries, international trade has existed because of the mutual benefits it generates among trading countries [1]. In other words, trade improves welfare and increases production in countries that are trading with each other. From the consumers’ point of view, international trade provides households with access to cheaper and high-quality imported consumables, which raises consumers’ welfare. It also provides consumers with different varieties of products of better quality at competitive prices. This is largely due to competition between domestic producers and foreign suppliers. In terms of producers, international trade allows countries to specialize in the production of goods at which they are the most productive. Thus, domestic resources are allocated more efficiently, and productivity increases. Moreover, enlarged consumer markets allow the exporting producers to reap the benefits based on scale such as economies of scale and increasing returns to scale. It also enables producers to import high-quality raw materials at cheaper prices.

In recent times, international trade and global trade networks have received significant attention among policymakers, governments, international organizations, and other stakeholders due to their significance in poverty reduction. Research has shown that in the long run, international trade is associated on average with high economic growth and sustainable economic development. For instance, the Netherlands in the 1800s had accumulated substantial wealth through shipping and trading. Recently, the experiences of rapid growth among the Asian tigers (including Singapore, Hong Kong, Korea, and Malaysia) and other countries such as China, India, etc., have all been associated largely with international trade [2]. The high economic growth from international trade leads to job creation, increased opportunities, and a growth in labor demand and wages which are fundamental to poverty reduction.

Reports from multiple sources indicate that the number of people living in extreme poverty around the world has fallen by around one billion since 1990 due to the growth in international trade [3]. Given this evidence and the need to reduce poverty, trade has been recognized as an engine for inclusive economic growth and poverty reduction in the 2030 Agenda for Sustainable Development. The 2015 joint WTO–World Bank publication, “The Role of Trade in Ending Poverty” reinforced the evidence that trade has played a critical role in poverty reduction and that the further integration of developing economies into an open global economy will be crucial for achieving the global objective of ending extreme poverty by 2030 [3,4].

Given the benefits of international trade and its contribution to poverty reduction, there has been a sharp growth in global trade over the last three or four decades, and the growth in trade shows no signs of slowing down [5,6]. In value terms, global trade has increased considerably from approximately USD 16 trillion in 2011 to USD 28 trillion in 2021 [7]. Despite the growth in international trade value, there has been an unprecedented change in international trade patterns, and growing imbalances in trade have emerged over recent decades. Amongst the major trading economies, China’s trade volumes have more than tripled over the last decade and have maintained the largest surplus position ahead of Germany and other major trading economies in recent years [7]. Similarly, China has become the largest trade partner for large swaths of Latin America and Africa, while the United States is China’s largest trade partner [8]. On the other hand, another large trade surplus country, Japan, has become a trade deficit country in recent years, with the trade volumes of other major trading economies also increasing at a much slower pace. Much more markedly, over these decades, the US economy experienced an ever-growing trade deficit. While studies have shown that the trade flow and export performance of a country are determined by factors such as the GDP of the country and that of its trading partners, REER, distance, etc., multiple sources have shown that China’s unprecedented trade expansion over recent decades could be partly associated with digital transformations and social networks which have transformed the pattern of the country’s global interconnectedness and global trade [8,9].

In light of these changes in international trade patterns, we attempt to investigate the export performance of countries. More specifically, the purpose of this paper is to identify the factors which affect the export performance of countries. We employ the gravity model of trade which relates the export and/or trade volumes directly to the GDPs of the trade partners, and inversely to the distance between the two countries as the framework. The framework is augmented with dummy variables to account for the impacts of common borders, language, and history [10]. In addition, we test for the effects of the Linder hypothesis which posits that the more similar the per-person income levels between the countries, the greater the volume of trade between them. We also incorporate real exchange rates in our model, as it is one of the well-known international competitiveness measurements. In doing so, we examine if appreciated currencies (higher real effective exchange rate (REER))—which make the imported products cheaper on the domestic market—do increase the imports of partner countries from the USA. Finally, we combine economics with social network analysis and thus augment the model with the inclusion of social network measurements. Thus, we use reciprocity, in-degree, and out-degree centrality measurements as explanatory variables.

The paper uses panel data covering 51 countries and 41 years from 1980 to 2020. Thus, the contribution of the paper to the literature is two-fold: Firstly, it uses an extensive dataset with 2091 observations. Secondly, as one of the rare studies taking this approach, it makes use of social network analysis in the model which accounts for the deep structure of all exchanges. The rest of the paper is organized as follows: Section 2 presents the literature review; Section 3 provides the model and the data for the estimation; Section 4 includes the results and discussions; and the conclusions are presented in Section 5.

2. Literature Review

Studies using gravity models of trade in the literature are replete with evidence from both developed and developing countries. The gravity model of trade posits that the trade volume between any two countries is directly proportional to the GDPs of the trading partner countries and inversely proportional to the distance between them [11]. The distance serves as a proxy for transportation costs, and in some studies, for trade barriers.

In the literature, Refs. [12,13,14] are the first studies that used gravity models in analyzing international trade. Tinbergen applied the basic gravity model and the extended version that incorporated dummy variables for trade agreements and the presence of a common border among trading countries to predict trade patterns among 42 countries. Nevertheless, the initial studies were criticized for the lack of a strong theoretical foundation supporting the gravity model of trade.

Several studies, including [15,16,17,18], became pioneering works in the field, and some provided the previously missing theoretical foundation for the gravity model. Nevertheless, Ref. [19] reports that, “despite the model’s consistently high statistical explanatory power, its use for predictive purposes has been inhibited owing to an absence of strong theoretical foundations”.

In [20], the authors explore the validity of the general gravity model of trade by reviewing studies from several authors. The paper analyses the relationship between the trade volume between two countries (dependent variable) and independent variables including the GDPs of each country, a composite term for measuring the trade barriers between the two countries, and two trade barrier terms between the given countries and the rest of the world. The transportation costs are approximated by the distance between the two countries. The model also incorporates dummies for islands, landlocked countries, common language, colonial history, and neighbors. The impact of regional trade agreements (RTAs) is investigated by differentiating between trade creation and trade diversion with “Both-in RTA” and “One-in-RTA” terms applied. The study then extends the model to address advanced issues such as zero-trade flows, and tariff equivalents for non-tariff barriers.

The author of [21] highlights that for a large selection of countries, there is support for the gravity model of trade in the literature. The literature finds strong evidence for the coefficient estimates for the GDPs of the two countries being around 1 while/and the distance coefficient of around −1. The author underscores the paradox of the distance term as he points out the huge innovations and advances in transportation technology, trade barriers, and the nature of goods traded over the century. Similarly, [22] also investigates if the effect of the distance term has changed over time. On the other hand, ref. [23] shows how to deal with different country sizes, while [24,25] address the zero-trade flows in data.

The author of [26] uses a gravity model to analyze the role of free trade area memberships on the flows of trade and inward FDI. The study relied on the UN COMTRADE and UNCTAD FDISTAT databases involving 170 countries from 1976 to 2005. The author finds evidence that the sign for coefficient estimates for distance is negative and significant at 1%, while the coefficient estimates for joint GDPs and joint per capita GDPs are positive and significant at a 1% significance level. The study also finds evidence that coefficient estimates for all FTA memberships used have a positive sign at a 1% significance level.

After observing that the scale of intra-trade within three specific regional groupings, namely the European Union, Asia-Pacific, and North America, has been considerably imbalanced, ref. [27] analyzes the trade creation and trade diversion effects of the regional trade agreements (RTAs) on trade volume among Asian countries. The study uses annual trade data for the period 1980–2009 within the framework of the gravity model. The findings of this study are mostly consistent with the literature. The coefficients of real GDP, population, and distance have the expected signs and are statistically significant at a 5% significance level in all models.

In [28], the authors use new panel data within a structural gravity approach to estimate the trade and welfare effects of Brexit. Using different post-Brexit scenarios, the authors find that the UK’s exports of goods to the EU are likely to decline within a range between 7.2% and 45.7% in six years after Brexit has taken place. For the UK, the negative trade effects are only partially offset by an increase in domestic trade and trade with third countries.

Other studies, such as [29], use panel data from the EU and the Mediterranean countries for the period of 1993–2007 to study the effects of trade agreements between them. Similarly, ref. [30] uses panel data from Turkey and 10 EU countries for the period of 1998–2002 to analyze the impact of the customs union signed between Turkey and the EU. While [30] uses exports as the dependent variable, ref. [29] uses bilateral trade as the dependent variable.

In relation to studies on the gravity model of trade and social networks, ref. [31] uses an expanded gravity model in which the predictors consist of GDPs, per capita GDPs, the distance between the trading countries, and dummies for colonial history, common language, common border, membership of the EEC and EFTA as well as NET which stands to capture the effects of network structure on bilateral trade volume. The authors find that network structure as well as GDPs are statistically significant at a 1% significance level in explaining the variation in trade volume.

Also, ref. [32] highlights that the intra-firm trades of multinational corporations are important but rigorous empirical studies in the field are limited and scanty. Although recent studies include network analyses of international trade, they consider international trade and firm-level activity in isolation. Thus, they fail to look at whether country-level patterns of trade are a result of firm-level activity. The authors try to fill this gap by combining firm- and country-level data. The study uses an ERGM (exponential random graph model) estimation method where the explanatory variables include such macro terms as reciprocity, sink, popularity, in-degree, out-degree, transitive closure, and so on. The results turn out to be largely significant.

Similarly, ref. [33] attempts to establish a model for informal trade in developing countries by making use of social network analysis. The paper highlights the concepts of degree centrality, betweenness centrality, closeness centrality, and eigenvector centrality. It also notes that ERGM models are the most popular probability models in social network analysis.

The paper [34] analyzes patterns of international trade and financial integration using complex social network analysis. In so doing, the authors attempt to investigate the similarities and differences in real and financial market integration. The bilateral asset trade data are collected from the Coordinated Portfolio Investment Survey (CPIS), while the trade data are taken from the UN Comtrade database. Then goods market and financial markets are investigated through assortativity, clustering, and centrality. The findings are consistent with the findings of many other papers that have applied network analysis to international trade flows. The results also show that goods markets are more densely connected than financial ones and that both types of networks display a disassortative, star-shaped structure dominated by a handful of hubs.

Although there have been some studies on the export performance of countries using the gravity model of trade in the literature, studies on the gravity model of trade that incorporate social networks and digital activities in international trade flow and global trade analysis at the transnational level remain patchy and thin. Whereas social networks and digital transformations have reduced the costs of engaging in international trade, facilitated the coordination of global value chains (GVCs), and connected a greater number of businesses and consumers globally, most of the studies that incorporate social network analysis in global trade analysis have been conducted at the micro level rather than at the aggregate level. Similarly, the limited studies conducted at the country level have relied on limited datasets, which are likely to generate results that are inconsistent with empirical situations. In view of these challenges, there is a need for rigorous assessment of global trade and social networks. Hence, we contribute to the literature by adding to the few existing empirical studies on the gravity model of trade with social networks and its application to trade flow analysis at the transnational level using extended datasets.

3. Materials and Methods

This section presents the full details of the methodology and the materials used for the empirical analysis. The theoretical expectations of the variables employed in the study, the data, and the preliminary tests including the correlation coefficients and unit root test results, panel fixed effect vs. random effect, and the Hausman test results to decide which one is more appropriate are highlighted in this section.

3.1. The Model

In identifying the factors that impact the volume of exports, this study adopts the gravity model of trade and augments it with a number of other explanatory variables. The basic gravity model states that trade volume is directly proportional to the GDPs of the partner countries, and inversely proportional to the distance between the partner countries. Thus, our basic model for US exports is given as:

log(export) = β₀ + β₁log(GDP)+ β₂log(GDP_USA) + β₃log(DISTANCE) + β₄log(LINDER) + β₅log(REER) + β₆OPEN + β₇ENGLISH+ β₈BORDER + β₉EU

(1)

where,

“export” is the USA’s exports to partner countries, in USD;

“GDP” is the GDPs of the USA’s trade partners in USD;

“LINDER” is the absolute value of the difference between the GDP per capita of the trade partner country and the GDP per capita of the USA, in USD;

“DISTANCE” is the distance in kilometers between the capital city of the partner country and Washington, DC;

“REER” is the real effective exchange rate for each trade partner country;

“OPEN” is the trade openness index for each trade partner country;

“ENGLISH” is a dummy variable to capture the common language effect;

“BORDER” is a dummy variable to capture the effect of sharing a land border;

“EU” is a dummy variable for all European countries having a common history with the reference countries of the US and UK.

To improve this model, the concepts of social network analysis are incorporated into the basic model. Thus, we augment the model with variables capturing the reciprocity, and in-degree and out-degree centrality of a node (which is a trade partner of the USA). An in-degree centrality is the number of edges leading to a node; thus, it indicates the popularity of a node. In trade data, since almost all countries trade with each other, we have to define an edge as a trade link between the two countries if the exports or imports of the trade partner are a certain percentage of the total world trade. In this paper, we take this as 0.05%. Thus, the in-degree centrality for each country will be the sum of the edges leading to the node (that is, the number of countries from which the partner country imports, where the imports are more than 0.05% of world trade). Likewise, out-degree centrality is the sum of the edges directed from the node (that is, the number of countries to which the partner country exports, where the exports are more than 0.05% of world trade).

In line with these, the reciprocity measurement will be the edges, as one of the US imports from the specified partner country is more than 0.05% of the total world trade. Thus, the extended model which includes the social network analysis is given by Equation (2):

log(export) = β₀ + β₁log(GDP) + β₂log(GDP_USA) + β₃log(DISTANCE) + β₄log(LINDER) + β₅log(REER)+ β₆OPEN + β₇ENGLISH + β₈BORDER +
β₉ EU + β₁₀RECIPRO + β₁₁IN_DEG + β₁₂OUT_DEG

(2)

where,

“RECIPRO” captures the effects of reciprocity measurement;

“IN-DEG” captures the effects of in-degree centrality measurement; and “OUT-DEG” captures the effects of out-degree centrality measurement.

3.2. Theoretical Expectations

Theoretically, we expect that the GDPs of partner countries will have positive impacts on US exports. This is so because the higher income of a partner country increases its imports, which also increases its imports from the USA. On the other hand, the gravity model of trade states that the distance between the two trading countries captures the effects of transportation costs. This distance is approximated as the distance between the two capital cities, and therefore, the distance and the trade volume between the two countries are inversely related. Thus, the coefficient estimate of “distance” is expected to be negative.

Similarly, Linder’s theory of trade states that the more similar the countries are in terms of their GDP per capita values, the greater the volume of trade between them. Thus, we expect the coefficient estimate for LINDER to have a positive sign. The augmented gravity model of trade states that more trade-open economic systems would have larger trade volumes between the trading countries. Therefore, the coefficient estimates for OPEN are also expected to be positive.

In terms of real effective exchange rates, appreciated currencies make imported products cheaper, thus increasing the import volumes. Hence, we expect a positive sign for the coefficient estimates of REER as higher REER means more appreciated currencies for the partner countries, increasing their imports. In the augmented gravity model of trade, common language, common land borders, and common historical backgrounds which are captured by ENGLISH, BORDER, and EU, respectively, increase with the trade. Thus, we expect positive coefficient estimates for these dummy variables.

As for the social network measurements, they may have impacts on exports via two different channels: (i) All three measurements (reciprocity, and in-degree and out-degree centrality) may reduce transportation costs, as they represent already established trade routes or systems. Hence, they may be expected to have a positive impact on US exports. (ii) On the other hand, they may also be some of the measurements of competitiveness. Thus, the out-degree centrality measurement for the partner country may show that it is a successful exporting country while in-degree centrality may indicate lower competitiveness and thus a significant importing country. Here, the in-degree centrality of partner countries is then expected to have a positive sign for US exports while out-degree centrality may have negative coefficient estimates. Given the two opposing effects, we expect the sign for out-degree centrality to be ambiguous, and those of reciprocity and in-degree centrality to be positive. Finally, the sign of the coefficient estimate for the GDP of the USA is theoretically ambiguous.

3.3. Data

In an attempt to identify factors contributing to the increase in US exports to partner countries, our study relies on panel data that include observations for 51 countries in 41 years, (i.e., from 1980 to 2020). The list of countries included in the dataset can be found in Appendix A and Appendix B. These countries are also coded as numbers from 1 to 51 in the same order (as in country code) in the dataset. The dependent variable in the study is the export volume from the USA to the partner countries. These data are in constant USD and are obtained from the IMF DOTS (Direction of Trade Statistics) dataset.

The explanatory variables used in the study include the GDPs of the partner countries, the GDP of the USA, “LINDER”, DISTANCE, REER, “OPEN”, the dummy variables including BORDER, ENGLISH, and EU, and social network analysis variables (“RECIPRO”, “IN-DEG”, and “OUT-DEG”). The datasets for the GDPs of the partner countries and the GDP of the USA are all in constant USD and have been extracted from the World Bank database. “LINDER” captures the effects of the Linder theory. This theory states that the more similar the countries are in terms of their per capita income levels, the greater the trade volume between the paired countries. Thus, the “LINDER” variable is calculated as the absolute value of the difference between the per capita GDPs (GDPPC) of the USA and the partner countries. These data are also sourced from the World Bank datasets.

According to the gravity model of trade, the trade between a pair of countries is inversely related to the distance between the countries as the increasing transportation costs would reduce the trade between them. In the literature, the distance has been proxied as the distance between the capital cities of the paired countries. The data (in kilometers) are obtained from http://ksgleditsch.com/index.html (Kristian Skrede Gleditsch) (accessed on 25 May 2023). The real effective exchange rate (REER) is a measurement of international competitiveness. It is computed as the weighted average of bilateral real exchange rates against the trade partners, where the weights are the trade volumes. However, the bilateral real exchange rate is given by the relation, RER = NER * P/P^F, where NER is the nominal exchange rate, expressed in the indirect quotation, and thus the unit(s) of foreign currencies required to purchase a unit of the domestic currency, while the P and P^F are the consumer price indices in the home and foreign countries, respectively. Therefore, depreciated currencies make domestic products cheaper in international markets, and thus lead to increases in exports, while appreciated currencies make imports cheaper in the domestic markets, and thus increase the imports. These “REER” data are taken directly from the IMF International Financial Statistics (IFS) dataset.

In terms of trade openness (OPEN), the augmented gravity model of trade states that the trade volume between any two countries would be larger if the mentioned countries had economic systems that were more trade-open. Trade openness is calculated as the sum of total export volumes and total import volumes, divided by the GDP of the country. As such, it measures the share of the GDP that is traded internationally. To calculate trade openness, one needs the total exports and total imports of the partner countries. These data are also from the IMF DOTS dataset.

Moreover, we created dummy variables to capture the effects of (i) having a common border (“BORDER”), (ii) having a common language (“ENGLISH”), and (iii) having a common history/culture (“EU”). Thus, for the variable “ENGLISH”, countries where English is the native language are coded as one, while the other countries are coded as zero. Similarly, for “BORDER”, the countries which have a land border with the USA are coded as one, while the others are coded as zero. Finally, for “EU”, the European countries are coded as one, while the others are coded as zero.

With regard to the social network analysis, we intend to investigate the effects of the reciprocity “RECIPRO”, in-degree centrality “IN-DEG”, and out-degree centrality “OUT-DEG” measurements. In trade data, these concepts can be measured in two different ways: (i) scaled and (ii) scale-free measurements. For scaled measurements, the volume of transactions is used [31]. Thus, given that in this study the directed edges or links are the export volumes from the USA to partner countries, the scaled measurement of reciprocity would be the import volumes from partner countries to the USA. The in-degree centrality of each node (or the popularity of each US trade partner country) is measured as the total imports of these countries (that is, the trade flowing to these countries) as a percentage of world trade. Similarly, the out-degree centrality of each node is measured as the total exports of these countries (that is, the trade flowing from these countries) as a percentage of world trade. In the literature and more frequently, scale-free measurement is used for social network analysis. Therefore, the reciprocity links are coded as one if the imports from the partner country to the USA are above a certain threshold (α%) of world trade. In this paper, this is taken as 0.05% of world trade.

The scale-free in-degree centrality of partner countries is the number of links leading to these US trade partner countries. Since in trade data, almost all countries do trade with each other, we count the links if the imports of these countries from the remaining other countries in the dataset are above a certain percentage of world trade. Similarly, the out-degree centrality of the nodes (partner countries) is the number of links (exports) from these countries. Again, we count the number of links if the exports are above a certain percentage of world trade. Here, there is no pre-defined percentage value in the literature, and thus we choose 0.05% of world trade as the cut-off point. In fact, we tried a few different percentage values until we obtained a good variation in in-degree measurements for the US trade partner countries.

The USA is the reference country while the 51 countries with 41 years of observations (from 1980 to 2020) are the trade partner countries. This gives a total of 2091 observations. Out of the total observations, the real effective exchange rate (REER) data are not available for 11 countries. Aside from this, there are also other missing observations for other variables in some countries for some years. After omitting the missing data points, the total number of observations obtained is 1586. The REER is one of the well-known international competitive measurements, and because of its significance, it cannot be exempted. Therefore, the estimation is conducted in two set-ups: one with REER (1586 observations) and the other one without REER in the set-up (2004 observations).

3.4. Test of Results

The correlation coefficients, the unit root test, and the Hausman test for the selection between panel fixed effect and random effect are conducted. The dependent variable “exports” is the US exports to partner countries and the independent variable “RECIPRO” captures the effects of the reciprocity measurement, and thus, the US imports from the partner countries. The correlation coefficient for these two variables is 0.85, indicating that there is a comparatively high and positive correlation between these variables. The explanatory variable IN-DEG measures the in-degree centrality of partner countries and, thus, the links leading to partner countries. In scaled social network measurements, these are the total imports of the partner countries. The correlation between the dependent variable and IN-DEG (world exports to partner countries) is 0.37, indicating that there is a low correlation between these two variables. The IN-DEG variable is the world exports to partner countries, and OUT-DEG is the partner country exports to the whole world. The correlation between these variables and trade openness OPEN are −0.06 and −0.08, respectively, indicating a very low correlation. Similarly, the correlation between IN-DEG and OUT-DEG turns out to be 0.96, which is a relatively high correlation; therefore, to avoid multicollinearity, we decided to use only the OUT-DEG measurement and leave out the in-degree centrality measurement. An Augmented Dickey–Fuller unit root test was conducted to test for stationarity. All the variables, i.e., GDP, GDPPC, DISTANCE, LINDER, OPEN, and REER, turn out to be stationary based on the p-values produced. Therefore, the estimation is performed on the level data rather than using the first-differenced data. The models are estimated using fixed effects as well as panel random effects. The Hausman test to decide which one is more appropriate is applied. This was done for the model with scaled social network measurements and for the model with scale-free social network measurements. Both results produce a p-value that is less than 0.05, implying a rejection of the null hypothesis that the random effect model is appropriate. Thus, the results indicate that the fixed effects model is more appropriate for these data, and therefore we only report the fixed effect estimation results.

4. Analysis and Discussion of Results

The results from the two separate estimations, one with scaled social network measurements and the other with scale-free social network measurements, are presented in

Table 1. Estimation results (dependent variable: USA exports).

	Scaled Social Network Measurements		Scale-Free Social Network Measurements
	(1)	(2)	(3)	(4)
	REER Included	REER Excluded	REER Included	REER Excluded
Log(GDP)	0.584816 (2.2 × 10−16) ***	0.664908 (2 × 10−16) ***	0.67867 (2 × 10−16) ***	0.689333 (2 × 10−16) ***
Log(GDP_USA)	0.887051 (2.2 × 10−16) ***	0.719249 (2 × 10−16) ***	0.89316 (2 × 10−16) ***	0.764656 (2 × 10−16) ***
Log(DISTANCE)	0.535110 (0.27363)	0.387348 (0.377257)	1.23371 (0.014300) **	0.512115 (0.250825)
Log(LINDER)	0.007969 (0.71674)	0.009566 (0.661845)	0.03249 (0.149884)	0.022012 (0.324259)
Log(REER)	0.285645 (2.4 × 10−9) ***		0.30597 (7.2 × 10−10) ***
OPEN	0.557539 (2 × 10−16) ***	0.651710 (2 × 10−16) ***	0.51828 (2 × 10−16) ***	0.639878 (2 × 10−16) ***
BORDER	3.280101 (2 × 10−16) ***	2.898850 (2.8 × 10−16) ***	4.12166 (2 × 10−16) ***	3.423747 (2 × 10−16) ***
ENGLISH	0.503667 (1.6 × 10−8) ***	0.464285 (2.5 × 10−7) ***	0.38689 (2.7 × 10−5) ***	0.352279 (0.00015) ***
EU	1.406151 (2 × 10−16) ***	1.153620 (2 × 10−16) ***	1.20603 (2 × 10−16) ***	1.048181 (2 × 10−16) ***
Reciprocity	5.431874 (2 × 10−16) ***	5.379964 (2 × 10−16) ***	0.03202 (0.414094)	−0.033917 (0.305357)
In-degree
Out-degree	−0.805452 (0.60487)	−1.545762 (0.318654)	0.02283 (0.00016) ***	0.024234 (1.7 × 10−5) ***
Adjusted R-squared	0.9711	0.9654	0.9693	0.9639
sample size	1586	2004	1586	2004

Note: The numbers in parenthesis are p-values. ***, **, and * indicate significance at the 1%, 5%, and 10% significance levels.

. The USA is the reference country while the remaining countries are the trade partner countries. The US exports to partner countries are the dependent variable. Columns 1 and 2 of Table 1 present the results for which scaled social network measurements are used and columns 3 and 4 present the results where scale-free social network measurements are applied.

In column 1, the coefficient estimate for the GDP of the partner country is 0.58 with a p-value of 2.2 × 10⁻¹⁶. Thus, partner country GDPs have a positive coefficient estimate which is statistically significant at a 1% significance level. More specifically, a 1% increase in the partner’s GDP increases the US exports to the partner country by 0.58%. Similarly, the coefficient estimate for the GDP of the USA is 0.89 with a p-value of 2.2 × 10⁻¹⁶. Thus, the US GDP has a positive coefficient estimate which is statistically significant at a 1% significance level. The DISTANCE and LINDER variables turn out to be statistically insignificant, while the coefficient estimates for REER and OPEN variables are positive and significant at a 1% significance level. These are in line with our theoretical expectations. Similarly, the ENGLISH, BORDER, and EU dummy variables have positive coefficient estimates which are all statistically significant at a 1% significance level. These are also in line with our theoretical expectations.

For the social network measurements, the reciprocity variable has a positive coefficient estimate and is statistically significant at a 1% significance level, while the out-degree centrality has a negative coefficient estimate, but this is statistically insignificant. In column 2, the REER is omitted from the model in order to prevent loss of data as there are no REER data for 11 countries. As a result, the number of observations increased from 1586 to 2004. The results are similar to those in column 1. GDP, GDP_USA, OPEN, BORDER, ENGLISH, EU, and RECIPROCITY have positive coefficients which are statistically significant at a 1% significance level, while out-degree has a negative coefficient estimate which is statistically insignificant. Furthermore, DISTANCE and LINDER again turn out to be statistically insignificant.

In columns 3 and 4, the results of the model that applied the scale-free social network measurements with and without REER are presented. The results in column 3 are similar to those in column 1: GDP, GDP_USA, REER, OPEN, BORDER, ENGLISH, and EU have positive coefficient estimates which are statistically significant at a 1% significance level. LINDER is still statistically insignificant, while DISTANCE turns out to be statistically significant at a 5% significance level but with the wrong sign. For the social network measurements, the results are reversed compared to the column 1 results. OUT_DEG has a positive coefficient estimate which is statistically significant at a 1% significance level, while reciprocity turns out to be statistically insignificant. Similarly, the results in column 4 are similar to those in column 2, with the exception of social network measurements: GDP, GDP_USA, OPEN, BORDER, ENGLISH, and EU have positive coefficient estimates which are statistically significant at a 1% significance level, while DISTANCE and LINDER are still statistically insignificant. Regarding the social network measurements, the results are reversed compared to the column 2 results. OUT–DEG has a positive coefficient estimate which is statistically significant at a 1% significance level, while reciprocity turns out to be statistically insignificant.

To account for reverse causality between the US GDP and the US exports (dependent variable), the model is modified by incorporating the lagged form of GDP_USA so that the higher US exports cannot cause higher values for lagged GDP_USA. The results failed to find support for the LINDER variable. Instead of using the LINDER variable, a separate GDPPC variable, which is the absolute value of the difference between the US and partner GDPPC values, is applied and the results are shown in

Table 2. Estimation results (modified regression models).

	Scaled Social Network Measurements		Scale-Free Social Network Measurements
	(1)	(2)	(3)	(4)
	with Lagged US GDP	Separate GDPPCs	with Lagged US GDP	Separate GDPPCs
Log(GDP)	0.584816 (2 × 10−16) ***	0.65573 (2.3 × 10−10) ***	0.67867 (2 × 10−16) ***	0.551350 (8.9 × 10−8) ***
Log(GDP_USA)		1.81839 (0.00021) ***		2.430139 (1.7 × 10−6) ***
Log(Lag_GDP_USA)	0.887051 (2 × 10−16) ***		0.89316 (2 × 10−16) ***
Log(DISTANCE)	0.535110 (0.27363)	1.76705 (0.158159)	1.23371 (0.014300) **	0.067705 (0.957900)
Log(LINDER)	0.007969 (0.71674)		0.03249 (0.149884)
Log(GDPPC)		−0.15408 (0.196962)		0.069553 (0.572215)
Log(GDPPC_USA)		−1.40018 (0.054127) *		−2.245706 (0.002958) **
Log(REER)	0.285645 (2.4 × 10−9) ***	0.29277 (8.3e-09) ***	0.30597 (7.2 × 10−10) ***	0.260635 (6.2 × 10−7) ***
OPEN	0.557539 (2 × 10−16) ***	0.55167 (2 × 10−16) ***	0.51828 (2 × 10−16) ***	0.486475 (2 × 10−16) ***
BORDER	3.280101 (2 × 10−16) ***	4.25671 (6.8 × 10−6) ***	4.12166 (2 × 10−16) ***	3.342627 (0.00068) ***
ENGLISH	0.503667 (1.6 × 10−8) ***	0.39567 (0.001040) **	0.38689 (2.7 × 10−5) ***	0.421122 (0.00094) ***
EU	1.406151 (2 × 10−16) ***	1.78251 (5.2 × 10−10) ***	1.20603 (2 × 10−16) ***	1.106219 (0.00015) ***
Reciprocity	5.431874 (2 × 10−16) ***	5.46413 (2 × 10−16) ***	0.03202 (0.414094)	0.047215 (0.234876)
Out-degree	−0.805452 (0.60487)	0.21854 (0.891379)	0.02283 (0.00016) ***	0.028096 (1.5 × 10−5) ***
Adjusted R-squared	0.9711	0.9712	0.9693	0.9695
sample size	1586	1586	1586	1586

Note: The numbers in parenthesis are p-values. ***, **, and * indicate significance at the 1%, 5%, and 10% significance levels.

.

In columns 1 and 3 of Table 2, the estimation of the model including the lagged version of the US GDP is shown; however, the results in column 1 include social network measurements, while those in column 3 are the scale-free social network measurements. The results from both columns show that the coefficient estimates for the lagged GDP_USA are positive and statistically significant at a 1% level of significance. This suggests a causality from the US GDP towards the US exports. Notwithstanding this indication, in column 3, the coefficient estimate for distance turns out to be wrongly signed but significant at a 5% significance level. Similarly, in both columns and as before, the coefficient estimates for LINDER and DISTANCE are statistically insignificant but statistically significant in column 3.

In terms of social network measurements, reciprocity has a positive and statistically significant coefficient estimate in column 1 but not in column 3, while out-degree centrality has a positive and statistically significant coefficient estimate in column 3 but not in column 1. All other explanatory variables turn out to be statistically significant, mostly at a 1% significance level and with signs similar to those in Table 1. For columns 2 and 4, the results from the use of separate GDPPC values rather than LINDER variables are presented. The results show that both DISTANCE and GDPPC are statistically insignificant, while US GDPPC is statistically significant with a negative sign. This implies that a higher GDPPC in the USA reduces the USA’s competitiveness, and thus its exports. Once again, reciprocity has a positive and statistically significant coefficient estimate in column 2 but not in column 4, while out-degree centrality has a positive and statistically significant coefficient estimate in column 4 but not in column 2.

Until this point, the presented estimation results are those of the model with US exports as the dependent variable. However, given that the US economy is the leading economy in the world and the fact that the US dollar is extensively used as the vehicle currency in international trade flows that sometimes do not directly involve the US, it is prudent that we consider if the above results might be any different for other reference countries. Therefore, we examine the dynamics by using UK exports as the dependent variable, and the results are presented in

Table 3. Estimation results (dependent variable: UK exports).

	Scaled Social Network Measurements		Scale-Free Social Network Measurements
	(1)	(2)	(3)	(4)
	REER Included	REER Excluded	REER Included	REER Excluded
Log(GDP)	0.513410 (2 × 10−16) ***	0.51406 (2 × 10−16) ***	0.428009 (2.6 × 10−15) ***	0.422822 (2 × 10−16) ***
Log(GDP_UK)	0.942027 (2 × 10−16) ***	0.75332 (8 × 10−16) ***	1.088107 (2 × 10−16) ***	0.919985 (2 × 10−16) ***
Log(DISTANCE)	−0.125626 (0.01230) *	−0.23953 (5.7 × 10−6) ***	−0.248889 (2.7 × 10−5) ***	−0.459105 (2 × 10−14) ***
Log(LINDER)	−0.004150 (0.78967)	−0.01008 (0.580742)	0.009142 (0.554432)	0.004389 (0.806319)
Log(REER)	0.508890 (2 × 10−16) ***		0.465936 (2 × 10−16) ***
OPEN	0.386562 (2 × 10−15) ***	0.54471 (2 × 10−16) ***	0.426153 (2 × 10−16) ***	0.567025 (2 × 10−16) ***
BORDER	−0.775380 (1.4 × 10−5) ***	−0.68608 (0.00027) ***	−0.476886 (0.004348) **	−0.417453 (0.018768) *
ENGLISH	2.123227 (2 × 10−16) ***	1.93018 (2 × 10−16) ***	1.844347 (2 × 10−16) ***	1.654926 (2 × 10−16) ***
EU	2.332903 (2 × 10−16) ***	1.99510 (2 × 10−16) ***	2.112321 (2 × 10−16) ***	1.531027 (2 × 10−16) ***
Reciprocity	3.250929 (1.3 × 10−12) ***	3.64948 (4 × 10−12) ***	0.365421 (0.00022) ***	0.717157 (5.8 × 10−12) ***
Out-deg. (partner exp.)	7.532099 (1.6 × 10−8) ***	7.87072 (1.2 × 10−7) ***	0.067185 (2 × 10−16) ***	0.071794 (2 × 10−16) ***
Adj. R-square	0.9715	0.9714	0.9595	0.9603
sample size	1545	1962	1545	1962

Note: The numbers in parenthesis are p-values. ***, **, and * indicate significance at the 1%, 5%, and 10% significance levels.

.

The results show that in all four columns, the results are relatively different from the previous case where the US is the reference country, and the US exports are the dependent variable. Interestingly, the DISTANCE variable has a negative coefficient estimate (as theoretically expected) and is highly significant at a 1% significance level. Coefficient estimates for both partner GDP and UK GDP turn out to be positive and statistically significant at a 1% significance level, while the coefficient estimate for the LINDER variable once again turns out to be statistically insignificant. Furthermore, trade openness OPEN, real effective exchange rate REER as well as the dummy variables EU and ENGLISH turn out to have positive coefficient estimates in line with our theoretical expectations, and these are all statistically significant at least at a 1% significance level.

In contrast to our theoretical expectation, the coefficient estimate for BORDER turns out to be negative, and significant at a 1% significance level. The explanation could be that the only land border the UK has is with the Irish Republic, and a substantial part of UK trade with Ireland is carried via the sea rather than via Northern Ireland. With respect to the social network measurements, the coefficient estimates for reciprocity and out-degree centrality are both positive and statistically significant at a 1% significance level. These are in line with our theoretical expectations and provide more supportive evidence compared to previous results.

In comparing the results from the two estimations, i.e., the one with the US as the reference country with the one with the UK as the reference country, the two results are very much similar to each other except for the DISTANCE variable, which turns out to be insignificant. Similarly, and as before, the LINDER variable is statistically insignificant, while the BORDER variable is significant but wrongly signed. All the other variables are statistically significant with the correct signs. Although the DISTANCE variable is insignificant in this case, the adjusted R-square is nevertheless slightly increased.

The two datasets were combined and the two countries, that is, the USA and the UK, were made the reference or home country for further estimation and analysis. This led to an increased number of observations (n = 3131) as shown in

Table 4. Results with optimized cutoff points and combined datasets.

			Reference USA + UK
Log(GDP)			0.563578 (2 × 10−16) ***
Log(GDP_HOME)			0.984432 (2 × 10−16) ***
Log(DISTANCE)			−0.447620 (2 × 10−16) ***
Log(LINDER)			0.056736 (1.3 × 10−6) ***
Log(REER)			0.414841 (2 × 10−16) ***
OPEN			0.451708 (2 × 10−16) ***
BORDER			1.148974 (2 × 10−16) ***
ENGLISH			0.635567 (3 × 10−10) ***
EU			1.103454 (2 × 10−16) ***
Reciprocity			0.338378 (2 × 10−16) ***
Out-degree (partner exp.)			0.039728 (6.3 × 10−13) ***
Adjusted R-squared			0.951
sample size	1586	1545	3131

Note: The numbers in parenthesis are p-values. *** indicates significance at 1% significance level.

. The estimation results turn out to be ‘improved’ as all variables now turn out to be statistically significant at 1% significance and with the correct sign. The DISTANCE variable turns out to be statistically significant with a negative sign as is theoretically expected; LINDER turns out to be statistically significant with a positive sign but this is not what is theoretically expected; BORDER turns out to be statistically significant with a positive sign as theoretically expected; and finally, RECIPROCITY turns out to be statistically significant with a positive sign, as theoretically expected. Therefore, combining the datasets seems to improve the results. This can be simply due to the increased number of observations in the dataset, or due to reduced bias as we introduce two countries as reference countries rather than just the USA.

5. Conclusions

This paper investigates the factors that impact the export performance of countries using explanatory variables derived from the augmented gravity model of trade, Linder theory, and social network measurements. The study uses panel data from 51 countries and 41 years from 1980 to 2020. The estimation and analysis were conducted for three separate cases. For the first case, the USA is used as the reference or home country, so the US exports to partner countries are used as the dependent variable. In the second case, the UK exports to partner countries are set as the dependent variable, while in the third case, the data are combined and both the USA and the UK are set as the reference or home country. Similarly, the estimation and analysis are performed with and without REER as well as for the cases with scaled and scale-free social network analysis.

For the case of the USA as the home country, the results show that the GDP of both the home country and partner country affect the US exports positively (as expected from the gravity model of trade). On the other hand, there is no statistical evidence for the DISTANCE and LINDER variables. The real effective exchange rate (REER), trade openness (OPEN), and the dummy variables BORDER, ENGLISH, and EU produced positive and statistically significant coefficient estimates, and these are in line with our theoretical expectations. The results are also mixed for the social network measurements of reciprocity and out-degree. Using separate GDPPC values rather than LINDER variables or using lagged values of the US GDP due to reverse causality issues did not change the results. Similarly, using only a subset of the data for the years before the year 2000 did not change the results for DISTANCE (a proxy for transportation costs).

When we use the UK as the home country, or the US and the UK combined as the home country, the results for DISTANCE, reciprocity, and out-degree measurements improve. The DISTANCE variable produces a statistically significant negative coefficient estimate which is in line with theoretical expectations. The reciprocity and out-degree coefficient estimates turn out to be statistically significant and positive, implying that social networks affect export performance positively. This suggests that the expansion of social networks of a country is likely to affect its trade volumes positively, although this paper does not address the magnitude of this impact and potential difficulties in calculating the magnitude of the impact of social networks on the export performance and trade volumes of countries. This could be a subject of further research. Similarly, our results indicate that the effects of social networks on the export performance of countries are consistent for all the scenarios at the macro and transnational levels compared to most of the previous studies conducted at the micro level, with results that are inconsistent and could barely be used for further projections and analysis. All other results are similar to those in the base model where the US is the home country.

With regard to the REER, our results show that it is a major determinant of trade and is positively related to the export performance and trade volume of a trading country. Therefore, a positive REER means that more appreciated currencies of the partner countries increase the imports of the partner countries and by implication boost the export performance and trade volume of the country. In terms of policy, an increasing REER of a partner country relative to the home country indicates a surge in the competitiveness and export performance of the home country. Therefore, based on our results, we can conclude that a lower REER of a country relative to that of a partner country leads to trade growth, although this may depend on other parameters such as the responsiveness of exports to REER, etc., which have not been considered in this study. Similarly, our estimations indicate that the openness of a country improves its export performance and boosts its international trade.