A scenario-based method for projecting multi-regional input–output tables

Abstract

Multi-regional input–output (MRIO) data are a powerful tool to analyze complex interdependencies in the international trade and supply network. Their field of application is however limited by the fact that MRIO datasets are only available for past years whereas the structure of the international trade network has been found to change profoundly over time. We here propose the SPIN method, a simple and flexible algorithm that can project MRIO tables into the future based on transparent scenarios of how gross domestic product and trade relations may evolve in that time. By combining well-established input–output techniques, namely the Leontief quantity model and an RAS-type algorithm, our method provides a straightforward mean to convert quantitative scenarios of the world economy into consistent MRIO tables. We illustrate the functioning of the SPIN method by projecting the evolution of the trade network after the 2008 financial crisis under different alternative scenarios of recovery.

KEYWORDS:

• Multi-regional input–output tables
• global trade network
• updating techniques
• Leontief model
• RAS algorithm

Acknowledgments

The authors thank Anders Levermann for fruitful discussion, Robert D. Carr for helpful remarks and the three reviewers of an early version of the paper for their constructive comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 An alternative solution consists in accounting for positive changes in stocks and inventories from the demand side (i.e. as part of final demand), and negative changes in stocks and inventories from the supply side (i.e. handled along with value added). This alternative could be implemented as described in Supplementary Materials S3.1.

2 Regions themselves can comprise several countries. For the sake of simplicity, we restrict the description of the method to regions corresponding to single countries. The case of regions composed of multiple countries is covered in section S3.2 in the Supplementary Materials.

3 GDP can also be constrained at sub-regional scale, e.g. to distinguish between different countries within a region. This alternative is treated in section S3.2 of Supplementary Materials.

4 Note that the SPIN method is sign conservative: negative elements in the base table will remain negative in the projected tables, which may be an unrealistic assumption for long term projections. Section S3.1 in Supplementary Materials proposes an alternative setting for enhancing the flexibility of the method with regard to negatives.

5 The creation of new connections is not subjected to any explicit constraint in the SPIN method. These new connections may hence be technologically or technically implausible. However, since the balancing algorithm minimizes the cross-entropy between the base and the final table (Lenzen et al., 2007), pre-existing trade connections are more likely to keep being predominant in the projected matrix, even if null coefficients are transformed into small positive values. The structurally conservative properties of the SPIN method are assessed in Section 3.1. Additionally, the SPIN method relies on a variant of the RAS algorithm, that may not converge if the base matrix is too sparse (Miller & Blair, 2009, pp. 335–336). In that situation, setting very small values to null coefficients guarantees the convergence of the balancing procedure.

6 Unless the sectoral allocation of exports is exogenously prescribed.

7 Again, shares of final commodities in imports and sectoral allocation of domestic final demand can also be exogenously prescribed.

8 The basic RAS algorithm is sufficient for the resolution of this operation because trade blocks do not contain any negative coefficient. The application of the GRAS algorithm would yield the exact same result but would require more computational resources than the simpler RAS algorithm.

9 Unlike for the reference scenario in Section 3.1, trade inputs for scenario #1 (and the respective reference scenario) do not distinguish exports and imports with regard to two economic zones (BRICS countries and rest of the world) but rather considers global exports and imports for each country.

10 The difference in the domestic term ($\mathrm{\Delta }{d}_r$) is the same here as for the supply side.

11 Following the law of decreasing marginal productivity, we would rather expect a larger effect in magnitude from a decrease in international trade intensity than from an increase of the same volume.

Additional information

Funding

This work was supported by Volkswagen Foundation: [Grant Number Europe and Global Challenges].