Multilateral and Bilateral Trade Agreements

In most traditional network representations of the ITN, the trade volume is represented by weighted and directed links that connect two industrial sectors or, at a coarser resolution, two countries. Here, we assess the interconnectedness between two national economies with a newly developed framework that is based upon the interpretation of the ITN as a flow network. Generally, flow networks encode the probabilities of a random walker to move from one node to another. Thus, the ITN as a flow network represents the probability that a unit good follows certain paths through different industrial sectors down the supply chain. This probabilistic approach becomes necessary as individual supply chains cannot be traced from existing data.

In this work, we utilize the idea of flow networks to define the trade interconnectedness (TI) between two countries based upon the input and output dependency measures $p_{i j}^{\bullet}$ originally used in Distributions of positive correlations in sectoral value added growth in the global economic network,

$p_{i j}^{\text {out }}=\frac{w_{i j}}{\sum_{t} w_{l l}} \text { and } p_{j i}^{i n}=\frac{w_{j t}}{\sum_{t} w_{i t}}$

Here, $w_{i j}$ describes the aggregated monetary value (in nominal US $) of all goods that have been sold in 1 year from sector $i$ to another sector $j$. The values of $p_{i j}^{\text {out }}\left(p_{j i}^{i n}\right)$ can be interpreted as the empirical probability of a unit good (respectively, of a certain monetary unit) to follow the corresponding edge in the ITN from $i$ to $j$ as a random walker. 

With the matrices $\left(P_{o u t}\right)_{i j}=p_{i j}^{\text {out }}$, the probability that a unit good follows a path of length $\alpha$ from sector $i$ to sector $j$ is given by $\left(P_{o u t}^{\alpha}\right)_{i j} .$ Analogously, $\left(P_{i n}^{\alpha}\right)_{j i}$ measures the flow of the associated monetary units. To measure how likely it is for a random walker on the ITN to start from a sector in one country and eventually end in another country, we define the trade interconnectedness $(T I)$ between two countries $\mathcal{C}_{1}$ and $\mathcal{C}_{2}$ as

$T I^{*}\left(\mathcal{C}_{1}, \mathcal{C}_{2}\right)=\frac{1}{\left|\mathcal{C}_{1}\right| \cdot\left|\mathcal{C}_{2}\right|} \sum_{i \in \mathcal{C}_{1}}\left(\sum_{\alpha=1}^{\alpha_{m a x}}\left(P_{\bullet}^{\alpha}\right)_{i j}\right)$

with $\mathcal{C}_{c}$ denoting the subset of all sectors $i$ that belong to one country $c .$ We refer to $T I^{\text {out }}\left(\mathcal{C}_{1}, \mathcal{C}_{2}\right)$ as the output TI of $\mathcal{C}_{1}$ to $\mathcal{C}_{2}$, which can be interpreted as the relative importance of $\mathcal{C}_{2}$ in the role of a consumer for $\mathcal{C}_{1}$. The relative importance of $\mathcal{C}_{1}$ in the role of a supplier for $\mathcal{C}_{2}$ is analogously quantified by the input $Ti$ of $\mathcal{C}_{2}$ to $\mathcal{C}_{1}, T I^{\text {in }}\left(\mathcal{C}_{1}, \mathcal{C}_{2}\right)$. In Equation (2), $\alpha_{\max }$ describes the maximal path length (in terms of national economic sectors) of the random walker that is to be considered. We find that a reasonable choice of $\alpha_{\max }$ is twice the average path length between the two subgraphs of the ITN spanned by the national economies of $\mathcal{C}_{1}$ and $\mathcal{C}_{2}$. A more detailed discussion of this choice and a sensitivity analysis of the results with respect to different values of $\alpha_{\max }$ will be presented in section 4.

As formalized in Equation (2), the dependency measures allow for the definition of the output TI which describes the probability of a unit good that is supplied from $\mathcal{C}_{1}$ to end in $\mathcal{C}_{2}$. The input TI describes this probability for a flow of successive payments. In Figure 1 , we schematically illustrate the paths that contribute to the TI using an exemplary network of trade between China (CHN) and Vietnam (VNM). The output TI of China to Vietnam, $TI^out$ (CHN, VNM), accounts for the paths of goods that originate in China and end in Vietnam (see Figure 1A). On the other hand, the input TI of China to Vietnam, $T I^{i n}(\mathrm{VNM}, \mathrm{CHN})$, takes the paths of the monetary flows into account (see Figure 1B). Here, the paths are defined in the opposite direction, as the payment flows opposite to the supply of materials, goods or services in the trade network. The definition of the TI is not symmetric: the corresponding paths of this exemplary network that contribute to the TIs of Vietnam to China are illustrated in Figure 1C for $T I^{\text {out }}$ (VNM, CHN) and Figure 1D for $T I^{\text {in }}$(CHN, VNM), respectively. Notice that we do not consider paths that traverse a third country in the definition of $T I^{*}$

BTA Impact Index

To quantify the impact of a BTA on the TI between the involved countries, we define the BTA impact index $\Pi$ • that takes both the level and local trend properties of the time series of $T I$ into account. Thus, the investigation of the BTA impact index allows for a comparison between the impacts of individual BTAs. In contrast, more traditional methods such as as a difference-in-differences approach would only assess the impact of BTAs compared to country pairs without agreement.

Firstly, we investigate if the mean level of TI has changed markedly after the date of entry into force $t_{f}$ of a specific trade agreement. For this purpose, we consider the annual TI values during a 5 -year interval before the agreement's implementation $\mathcal{I}_{p}=\left[T I_{t_{f}-5}^{\bullet}, . ., T I_{t_{f}-1}^{\bullet}\right]$ and a 5 -year interval after the implementation $\mathcal{I}_{s}=\left[T I_{t_{f}+1}^{\bullet}, \ldots, T I_{t_{f}+5}^{\bullet}\right]$ and define a corresponding score as

$z:=\frac{\mu\left(\tau_{s}\right)-\mu\left(\tau_{p}\right)}{\sigma\left(\mathcal{I}_{p}\right)}$

Here, $\mu(\cdot)$ and $\sigma(\cdot)$ represent the mean value and standard deviation of annual TI values within the respective periods. The score $z$ relates the TI values after $t_{f}$ with the previous levels of the variable. Since the $T I$ ' most commonly do not follow a Gaussian distribution, we will utilize a coarse classification of the explicit values of $z$ defined by Equation (3) in the definition of $\Pi^{*}$, as it will be described below, instead of considering the precise value of $z$. In general, a more sophisticated approach to assess potential changes in the level of a random variable would include an analysis of variance (ANOVA), most likely via the Mann-Whitney $U$ test. However, the small sample size of $T I^{*}$ prevents a meaningful interpretation of the test results in this case, which is why we refrain from performing such explicit statistical significance testing at this point.

Secondly, we are interested in the evolution of the annual TI values after the date of entry into force of an agreement. and therefore statistically characterize their trend during the interval $\left[T I_{t_{f}}^{\bullet}, \ldots, T I_{t_{f}+5}^{\bullet}\right]$ (including the year of BTA implementation and the five following years). To assess this trend, we consider two possible models: In the first model, we perform a simple linear regression

$y_{l}(t)=\beta_{0}+\beta_{1} t+\epsilon_{l}(t)$

with the parameters $\beta_{i}(i=0,1)$ and an independent and identically distributed Gaussian error $\epsilon_{l}(t)$ Alternatively, in order to better recognize oscillating or saturating behavior of the time series during the considered 6-year period, we additionally perform a two-segment piecewise linear regression. The form of this segmented linear model is

$y_{s}(t)=\gamma_{0}+\gamma_{1} t+\gamma_{2}(t-\psi) \theta(t-\psi)+\epsilon_{s}(t)$

with the Heaviside function $\theta$, the (unknown) break-point $\psi$, trend parameters $\gamma_{i}(i=1,2)$ and a Gaussian error term $\epsilon_{s}(t)$ as in the linear model. In contrast to the linear regression, the model in Equation (5) can also account for one local extreme value during the investigated time period, which would be represented by a change in the signs of the slopes between the two segments. More complex regression models that exhibit multiple breakpoints cannot be reliably applied due to the coarse (annual) resolution of the considered data. Therefore, we do not consider such more general models, emphasizing that we are only interested in the sign and statistical relevance of short-term (multi-annual) trends after BTA implementation rather than exact functional descriptions of the shape of these trends or explicit quantitative estimates thereof. Since the segmented model contains two additional parameters as compared to the linear regression model, we perform a model selection based upon the Akaike Information Criterion (AIC) to avoid overfitting by the statistical model with a higher number of degrees of freedom.

If the simple linear model is selected by the AIC criterion, we assess the relevance of the trend identified by the linear regression model and categorize it as relevant and positive (+), relative and negative (-) or not relevant (o). Here, we consider the trend of the linear regression model as relevant, if the estimated variance of the error $\widehat{\sigma}_{\epsilon}$ in $y_{l}$ is smaller than the difference $\Delta \hat{y}_{l}:=\left|\hat{y}_{l}\left(t_{f}\right)-\hat{y}_{l}\left(t_{f}+5\right)\right|$ of the values at the margins of the regression period. If $\widehat{\sigma}_{\epsilon}>\Delta \hat{y}_{l}$, we do not consider the estimated slope of the linear model to be relevant and categorize the trend as (o).

In the case of the segmented model, the considered time series is too short for a similar relevance assessment. Accordingly, if that model is preferred, the additional breakpoint improves the AIC score as compared to the linear regression model. We then consider the slopes of the two segments as relevant. Thus, any pairwise combination between $(+)$ and $(-)$ is possible for the segmented model. Combining both the trend properties and score parameter $z$ of the time series of TI values, we finally define the impact index of a BTA as follows:

\begin{equation} \Pi^{*} (\mathcal{C}_{1}, \mathcal{C}_{2}) = \begin{cases}1 & \text { if } z>1 \text { and }(+\mid++) \\ 0.5 & \text { if } 0 < z < 1 \text { and }(+\mid++) \\ -0.5 & \text { if }-1 < z < 0 \text { and }(-\mid--) \\ -1 & \text { if }-1 < z \text { and }(-\mid--) \\ 0 & \text { else }\end{cases}\end{equation} 

As for the TI, we refer to $\Pi^{\text {out }}\left(\mathcal{C}_{1}, \mathcal{C}_{2}\right)$ as the output BTA impact index of $\mathcal{C}_{1}$ to $\mathcal{C}_{2}\left(\Pi^{i n}\left(\mathcal{C}_{1}, \mathcal{C}_{2}\right)\right.$ as the input BTA impact index of $\mathcal{C}_{2}$ to $\left.\mathcal{C}_{1}\right)$. The average BTA impact indices $\Pi^{\text {out }}$ and $\Pi^{\text {in }}$ of a country $\mathcal{C}_{c}$ are defined as the average $\Pi^{\text {out }}\left(\mathcal{C}_{c}, \bullet\right)$ and $\Pi^{i n}\left(\bullet, \mathcal{C}_{c}\right)$ for the export and import linkages, respectively, taken over all countries that have negotiated a BTA with $\mathcal{C}_{c}$.

Other than common characteristics like the total trade volume or the absolute values of imports or exports studied in previous works, the TI also captures indirect trade effects. Such indirect effects arise, for instance, if a customer increases its output, being likely to demand more input that is required for the production of its goods. This increase in demand, in turn, affects the business of the supplying industry at the input side. Capturing effects at both, demand and supply side individually, TI can be defined in each direction and thus allows distinguishing between the input TI and output TI of one country to another country as trade partner. The input TI (output TI) thereby quantifies the relative importance of one country $\mathcal{C}_{1}$ as a supplier (consumer) for the production of another country $\mathcal{C}_{2}$. Note that the countries' relative economic relevance for each other is not symmetric. Furthermore, the TI is a relative measure in the sense that it is based on the fraction of a country's total trade activities that is accounted for by a specific partner. For instance, in a global setting in which all countries increase their international exports, the TI between two countries decreases if the growth in bilateral trade volume is smaller than the global average growth (given that the nation's sectoral structure remains the same). Here, we estimate TI for the ITN for each year between 1990 and 2013.

As explained above, theory suggests that BTAs foster trade activities among the partners, which should result in a stronger TI between the involved countries. To assess empirically if this is indeed the case, we analyze the BTA impact indices $\Pi^{\bullet}$ as defined in Equation (6) for each BTA. A positive value of $\Pi^{\bullet}$ implies both an increase in the level and a positive trend of the TI and thus reflects that business between the involved countries has gained in relative importance during the first years after BTA implementation. Accordingly, we consider a BTA to be effective if its BTA impact indices are positive.

The resulting probability distributions of BTA impact indices for all partners with a BTA are depicted in dark colors in Figure 2. Note that the underlying distributions of $\Pi^{out}$ and $\Pi^{\text {in }}$ are based on 214 entries each, since in general, $\Pi^{\text {out }}\left(\mathcal{C}_{1}, \mathcal{C}_{2}\right) \neq \Pi^{\text {out }}\left(\mathcal{C}_{2}, \mathcal{C}_{1}\right)$. To put these results into context, we further assess the relevance of the empirically identified impacts of the BTAs by comparing the estimated BTA impact indices with the corresponding values for those pairs of countries that have not entered a trade agreement until 2014. For the latter purpose, we calculate the BTA index for the 15,199 country pairs that have not signed such an agreement within the study period and assume an arbitrary reference year of 2002. As shown in Figure 2 , the existence of a BTA commonly coincides with an elevated probability of a positive BTA index. Note that this simple analysis does not allow directly drawing a causal link of the BTA implementation resulting in stronger entangled economic ties, since it would also be compatible with the explanation that countries with generally more p. economic development have a higher tendency toward negotiating trade agreements. Further studies on this economic development have a higher tendency toward negotiating trade agreements. Further studies on this aspect would be necessary to further address this point. In general, from the estimated probability distributions, it becomes evident that positive BTA indices are more common than negative values. These results are consistent with the general increase of international trade volumes in the course of the globalization that also affects country pairs without a dedicated trade agreement.

FIGURE 2

Figure 2. Distribution of the BTA impact indices $\Pi^{i n}$ (purple) and $\Pi^{out}$ (blue) for all 107 BTAs that have been implemented between 1995 and 2008 (dark colors, see Table 1 in Appendix for a complete list). Light colors show the corresponding results for all 15,199 pairs of countries that have not negotiated bilateral agreements assuming an arbitrary reference year of 2002 . Each of the four distributions is normalized to one and thus depicts the relative frequency. Note the logarithmic scaling of the displayed empirical frequencies.

Studying these results in more detail, we find that most countries with BTAs actually exhibit a positive average BTA impact index in both their export $\Pi^{out}$, Figure 3, top panel] and import linkages $\left(\Pi^{i n}\right.$, Figure 3 , bottom panel] to their partners. For some countries, especially the US, Australia, India and Columbia, the relative importance of the export linkages to their partners has increased more strongly than the relative importance of the import linkages from their partners. On the other hand, for other countries, such as the Philippines, Algeria, the southern African countries and Uruguay, the import linkages from their partners have gained in importance to a larger extent than their corresponding export linkages. Some notable exceptions that exhibit non-positive values of $\Pi$ for both, exports and imports include the Ukraine, Bahrain, Jordan, and Belarus. The only G2o members with non-positive values are Indonesia and China.

FIGURE 3

Figure 3. Global maps of average BTA impact indices. Shown are the country's export ($\Pi^{out}$, top) and import linkages ($\Pi^{in}$, bottom). Red values indicate that on average, the relative importances of the partners have increased for the respective countries. The average is taken over all the trade partners with which a specific country has implemented a BTA between 1995 and 2008.

In this context, it is particularly remarkable that China as one of the world's leading economies did not increase the relative importance of its agreement partners for its domestic production. When examining the composition of the average BTA impact index for China in more detail (Figure 4], the positive values of the score parameter z (see section 2) indicate that for most BTAs, the level of both input and output TI of China to its partners has increased after the date of entry into force. However, there is no continuing positive trend in the TI of China to its partners for any of these agreements (see the red shaded area in the top panels of Figure 4]. This suggests that China's agreement partners did not experience any persistent increase in importance for China's production after the BTAs have been established. In turn, considering the reciprocal TI of China's partners, the relative importance of their export and import linkages to China continuously increased during the first 5 years of the implementation period of the agreement (see bottom panels of Figure 4].

FIGURE 4

Figure 4. Trade profile for China. The TI of China to its partners (top) and of the partners to China (bottom) in the 5-year period after the date of entry into force t_f of the respective BTA. The left and right panels present the results for the export (import) linkages. The partners of China with a BTA include Chile (CHL), Hong Kong (HKG), New Zealand (NZL), Pakistan (PAK) and the Association of Southeast Asian Nations (AS). Values of the score parameter z shown in red (purple) imply a higher (lower) level of TI in the 5-year period after t_f . Trade agreements in the red (purple) shaded regions indicate a positive (negative) trend of the TI between the partners after t_f . A positive (negative) value of the BTA impact index Π is assigned to a trade agreement if it is succeeded by both a positive trend and a higher level (negative trend and lower level) of the TI.

A distinctively different picture emerges for the BTAs involving the US (Figure 5]. All 8 US partners but Jordan have become more important for US exports. While the importance of the partners' imports for the US reached higher levels after BTA implementation, only Australia, the Central American Common Market and Jordan showed an enduring positive trend in the input TI of the US. In the opposite direction, the US have not become relatively more important for their aforementioned partners. This applies to both, export and import linkages of the partners to the US (except for the import linkages of Morocco). In some cases, we even observe values of Π < 0 with both negative trends and lower levels after the agreement in the TI of the US' partners.

FIGURE 5

Figure 5. Trade profile for the US, with definitions as in Figure 4. The US have negotiated BTAs with Australia (AUS), Bahrain (BHR), Chile (CHL), the Dominican Republic (DOM), Jordan (JOR), Morocco (MAR), Singapore (SGP) and the Central American Common Market (CA) that became effective between 1995 and 2008.

The consideration of higher-order (indirect) effects of trade flows is crucial to account for the potential existence of strong mutual production dependencies between industries that are not direct suppliers or consumers of each other but still members of the same supply chain. These dependencies arise, for example, if two industries have the same trade partner $j$, i.e., if the industries $i$ and $k$ are connected by a path of length 2. Specifically, in a scenario in which $j$ buys commodities (inputs) from $k$ and sells goods to $i$, the node $i$ might be affected by a supply shortage of $k$ which is further mediated via j. To further assess the impact of these higher-order dependencies, we investigate the role of the maximal path length $\alpha_{\max }$ in the definition of the TI.

The nodes representing the final demand take the role of sinks in the economic flow network of goods, causing a fast saturation in $TI^{out}$ with increasing $\alpha_{\max }$. In contrast, these nodes become sources of payment flows for which a converging behavior of $TI^{in}$ is not observed. This is illustrated in Figure 6 showing the distributions of $TI^{out}$ and $TI^{in}$, respectively, for different values of $\alpha_{\max }$. Here, all pairs of countries are accounted for that have negotiated a BTA in the investigated time period. It can be seen that the values of $T I^{\dot{m}}$ do not converge for economically reasonable path lengths. Furthermore, we observe in Figure 7 that the BTA impact indices $\Pi^{\text {in }}$ of the countries' inputs show a tendency toward smaller values with increasing $\alpha_{\max }$. In Figures $7 \mathrm{~A}, \mathrm{~B}$, the input BTA impact indices $\Pi^{i n}$ of all countries are shown for $\alpha_{\max }=1\left(\alpha_{\max }=10\right)$. A trend toward smaller values can be observed, for example, in Europe, Australia, Algeria and Central America. This general trend occurs because loops within one country of the trade network gain importance for the $T^{in}$ for higher values $\mathrm{a}_{\max }$. The probabilities of these national loops decrease with time, as international trade has increased in the investigated time period. An example of the time series of $T I^{\text {in }}$ of Algeria to the European Union is displayed in Figure 8 . With increasing maximal path length, the BTA impact index decreases, as national loops become less probable in the more recent years.

FIGURE 6

Figure 6. Box plot of the distributions of the trade interconnectedness (A) $TT^{\text {out }}$ and (B) $T I^{\text {in }}$ taken over all country pairs with a BTA (see Table 1 in the Appendix for different choices of the maximal path length $\mathrm{a}_{\max }$ ). The distributions depict the $T I$ ' values in the ITN of 2002. In both panels, the ratio of $T I^{\prime}$ with respect to its value at a reference maximal path length of $\alpha_{\max }=20$ is shown. The box depicts the quartiles of the distributions with the median indicated within the box. Outliers are displayed if they exceed 1.5 times the inter-quartile range.

FIGURE 7

Figure 7. Global maps of the average input BTA impact indices $\Pi^{i n}$ for different choices of the maximal length (A) $\alpha_{\max }=1$ and (B) $\alpha_{\max }=10$. The colors and averages can be interpreted as described in Figure 3 .

FIGURE 8

Figure 8. The input trade interconnectedness $T I^{\text {in }}$ of Algeria to the European Union for different choices of the maximal path length: (A) $\alpha_{\max }=1$ and (B) $a_{\max }=10$. The year of 2005 in which the BTA came into effect is indicated by the red vertical line. The regression model selected by the AIC criterion is displayed by the green line indicating the corresponding maximum likelihood fit.

In order to provide a more detailed view on the trade profile of China, we illustrate China's input TI to its partners for the choices of $\alpha_{\max }=1$ in Figure 9A and for $\alpha_{\max }=10$ in Figure 9B. We observe that the trade agreements of China with New Zealand and Hong Kong follow the general tendency toward a lower BTA impact index with increasing maximal path length. However, in the input TI of China to Pakistan, a higher maximal path length increases the BTA impact index. The corresponding time series of the TI are shown in Figure 10. It can be seen that the higher BTA impact index can be attributed to a changing behavior of the $T I^{\text {in }}$ in 2009 with increasing $\alpha_{\max }$. In this year, the Great Recession triggered by the global financial crisis caused a decline in international trade, interrupting the general globalization trend in this year. Thus, in this exceptional year, higher probabilities for national loops were likely to be observed as compared to the previous and following years. This exception is responsible for the increase of the input BTA impact index of China to Pakistan for increasing $\alpha_{\max }$.

FIGURE 9

Figure 9. Trade profile for the input TI of China to its partners for a maximal path length of (A) $\alpha_{\max }=1$ and (B) $\alpha_{\max }=10$. The definitions and labels correspond to Figure 4 .

FIGURE 10

Figure 10. Input TI of China to Pakistan for (A) $\alpha_{\max }=1$ and (B) $\alpha_{\max }=10$ with definitions as in Figure 8 .

The above discussion illustrates that the maximal path length $\alpha_{\max }$ should not be chosen arbitrarily large, since otherwise longer paths within one country would be increasingly overrepresented in $T I^{\text {in }}$. Studying this effect in more detail by means of probabilistic methods based upon the flow network representation used in this study might present an interesting research avenue for further methodological work, but may have limited economic value since such longer paths may crucially depend on the individual supply chains calling for case-specific interpretations. On the other hand, our analysis also demonstrates that higher-order effects, that are mediated through supply chains, affect the TI.

In view of this trade-off, we have set $\alpha_{\max }$ to twice the average path length between the two subgraphs $\mathcal{C}_{1}$ and $\mathcal{C}_{2}$ of the ITN in all calculations presented in section 3. This choice has been motivated by the probability distribution of the average path lengths $\langle d\rangle$ for all country pairs with a trade agreement (Figure 11]. It thus allows the consideration of sufficiently high-order paths between these subgraphs while at the same time avoiding too large contributions from loops within any of them.

FIGURE 11

Figure 11. Probability distribution of the average path length of subnetworks of the ITN spanned by all pairs of countries with a bilateral trade agreement (solid purple) and without any agreement (light purple), given that a direct path between the countries exists. The values are obtained from the ITN for the year 2002.

We finally emphasize that the methodological framework used in this work can potentially provide a basis for addressing further more specific research questions in the context of BTAs, including the dependency of the efficiency of such agreements on their overall number and/or affected trade volume, respectively. Another interesting issue would be the existence of interferences between different BTAs affecting the same national economic sectors directly or indirectly via BTAs affecting some relevant trade partner. We outline further in-depth investigations along these lines as a relevant topic of future research.