BUS613: Advanced International Business

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.