# Appendix 1: A Methodology for Assessing Systemic Trade Interconnectedness34

- Nagwa Riad, Luca Errico, Christian Henn, Christian Saborowski, Mika Saito, and Jarkko Turunen
- Published Date:
- January 2012

The cross-border transmission of shocks takes place through two main channels: the financial channel and the trade channel. The global crisis has drawn renewed attention to the former with recent IMF Executive Board papers discussing financial sectors of “systemic importance” and their interlinkages in the context of IMF surveillance, underscoring financial interconnectedness.^{35} Less emphasis has been placed on the trade channel—that is, the real side of the equation.^{36} Nonetheless, understanding the impact that changes in domestic demand exert through the trade channel, especially in the case of systemically important trade sectors, is important in informing the analysis of cross-border spillovers and contagion.

Typically, considerations about the “systemic” importance of a trade sector have been based on its absolute (within jurisdiction) or relative (within the global trade system) size. Interconnectedness has, however, more recently emerged as a critical complementary consideration to gauge the systemic risk that may arise through direct or indirect interlinkages among sectors in the global system. The idea is that the more linkages a given sector has to the global system, the higher the risk that distress in that sector may have repercussions on other jurisdictions or systemic stability.

Against this background, we develop a methodology for assessing systemic trade interconnectedness by defining “systemic” trade sectors and identifying the jurisdictions hosting them. The methodology draws from recent work on financial interconnectedness^{37} and leverages the IMF’s Direction of Trade Statistics (DOTS) database. The use of DOTS lends robustness to the analysis by providing data that are not only uniform, but also available for the entire IMF membership. Additionally, the regular updating of DOTS by the IMF’s Statistics Department allows for dynamic analysis and recalibrations of the findings tracking global trade developments on a timely basis. This methodology naturally complements financial interconnectedness analysis, providing a holistic view of the potential for spillovers and contagion at the bilateral, regional, and global levels.

## Methodology

The methodology entails a two-stage approach. In the first stage, jurisdictions are ranked based on trade size and interconnectedness indicators. In the second stage, the rankings of trade size and interconnectedness are combined into a composite index of systemic trade importance.

## First Stage

### Size indicators

Three measures of the absolute size of a trade sector (in nominal U.S. dollars), namely: (i) total exports (*X*); (ii) total imports (*M*); and (iii) total turnover (*X + M*) are used to capture the importance of a jurisdiction’s trade sector in the global trade system. One measure of the relative size of a trade sector—namely, total turnover relative to nominal GDP (in U.S. dollars)—is used to gauge the relative importance of the trade sector within a given jurisdiction. The four trade size indicators then are combined into a single ranking for size by ranking all jurisdictions in each of the four trade size indicators separately and taking the median rank of the four indicators for each jurisdiction as the single ranking for trade size.

### Interconnectedness indicators

Similar to the approach used for financial interconnectedness analysis, the idea is to infer from the pattern of cross-border linkages among trade sectors the extent to which a trade sector in a jurisdiction is “central” in the global trade network. The global trade network is defined as a set of bilateral trade relationships (links), either exports or imports, of different jurisdictions (nodes). A materiality threshold ensures that the analysis focuses only on economically meaningful links—that is, trade relationships representing less than 0.1 percent of a jurisdiction’s GDP are excluded.

The network is expressed in matrix form where *Aij* represents the value of total turnover between jurisdiction *i* and jurisdiction *j*. The matrix has dimension *n* equal to the number of jurisdictions. Diagonal elements are zero. Off-diagonal elements are zero for jurisdiction pairs that have no link either as exporter or importer. The indicators are based on whether a link exists, that is, they are based on the indicator *Nij* = 1 if *Aij* > 0, and 0 otherwise.

Applying network analysis, four measures of “centrality” of a jurisdiction’s trade sector within the global trade network are used:^{38}

- “In-degree” is the number of links that point to a node. It is given by the sum Σ
*j*N*ji;* - “Closeness” is the inverse of the average distance from node
*i*to all other nodes. The distance between*i*and*j*, δ*ij*equals the shortest path. The average distance from*i*to all other nodes is given by Σ*jδij*/(*n*– 1). Closeness is the inverse of this measure; - “Betweenness” looks at the nodes that the shortest path goes through. Let g
*jk*denote the number of shortest paths between*j*and*k*, and g*jk*(*i*) denote the number of such paths that go through node*i*. The probability that node*i*is on the shortest path from*j*to*k*is given by g*jk*(*i*)/g*jk*. “Betweenness” of node*i*is the sum of these probabilities over all nodes excluding*i*, divided by the maximum that the sum can attain:$(\mathrm{\Sigma}j\ne i\mathrm{\Sigma}k\ne igik\left(i\right)/gjk)/(n\u20131)(n\u20132);$ and - “Prestige” (or eigenvector centrality) considers the identity of counterparties. It is a measure of the importance of a node in the network. It assigns relative scores to all nodes in the network based on the principle that connections to high-scoring nodes contribute more to the score of the node in question than equal connections to low-scoring nodes. The “prestige” of jurisdiction
*i*(*vi*) is obtained by taking the “prestige” of its exporters, weighted by a matrix of relationships with*i*, that is,*vi*= Σ*j*R*ji vj*. This defines a linear system*v*=*R′v*where*R*is the matrix of relationship. The solution to the system is the eigenvector associated with the unit eigenvalue.

As with the ranking for trade size, a single ranking for trade interconnectedness is calculated from these four different indicators. All jurisdictions are ranked in each of the four interconnectedness indicators separately, taking the median of the four rankings as the single ranking for trade interconnectedness.

## Second Stage

An overall composite index of trade systemic importance is calculated as a combination of the trade size and trade interconnectedness rankings calculated in the first stage. The rankings of size and interconnectedness are combined into a weighted average “baseline” index to allow the analysis of the relative significance of size and interconnectedness in systemic importance. Sensitivity analysis of the composite index suggests that while weight changes affect some of the individual country ratings at the margin, they do not introduce significant changes in the listing of the jurisdictions in the upper echelons of the ranking.^{39}

^{}34

Prepared by Luca Errico and Alexander Massara (both from the Statistics Department).

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^{36}

In this analysis, trade includes goods/merchandise, but excludes services.

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^{38}

Because we consider both exports and imports, the network is “undirected” and because we assign equal weights to the four measures of centrality, the network is “unweighted” with binary values (0, 1).

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^{39}

The following combinations of size and interconnectedness breakdowns were tested: 0.8/0.2 (0.8 for size and 0.2 for interconnectedness), 0.7/0.3, 0.6/0.4, and 0.5/0.5, respectively.