A mathematical model on how sanctions, duties and conflicts affect commerce

Sanctions, duties, and geopolitical tensions affect commercial exchange and financial flows among countries. How are imports and exports redirected?

Economists from Ca’ Foscari University of Venice, Vrije University Amsterdam and the Study Center Gerzensee, Foundation of the Swiss National Bank have proposed a new model to predict the ‘natural’ global changes in commercial and financial exchanges following a shock due to political-economic policies or political instability (as is the case with the current war).

The study was published in the Journal of Business and Economic Statistics, a prestigious journal by the American Statistical Association.    

The model can predict possible global and local effects, both temporary and persistent in the reorganisation of exchanges. In particular, it shows that it is possible that an enormous amount of data be used to produce indications for governments and central banks. By applying the results of this study, it is possible to simulate the effects that political choices have on commerce and finance, but also to intervene to correct the effects of a ‘natural’ reorganisation of exchanges. 

One of the case studies is the reduction of 1% of imports on the part of the United States, which generates immediate consequences and different impacts from country to country. Switzerland is the most positively affected country, showing increases both in exports and in imports. There would be a decrease of Danish and Swedish exports to Switzerland, Germany and France — countries which import more from the USA, Japan and Ireland. After an initial shock, imports to the US would ‘bounce back’.

“An answer to shocks is quick. Commercial and financial exchanges soon find a new structure,” says Roberto Casarin, professor of Econometrics at Ca’ Foscari and author of the study. “Our model allows us to produce short-term scenarios that can be useful in making political decisions.”

The study required five years’ work on data with a multidimensional structure. The researchers involved combined monthly observations of commercial and financial flows among countries. In order to achieve this goal, the researchers used some recent results from mathematics applied to machine learning and econometrics.

“We needed a model that could take into account the original structure of data, so a four-dimensional matrix called ‘tensor’, and a procedure of statistical inference that can manage the ensuing amount of data,” says Casarin. “We managed to do this by extending some recent results of the research in the field of numerical analysis, machine learning, and mechanical engineering, regarding new multilinear algebra tools. Now the fruit of our labour is available to everyone, not only as an interdisciplinary methodological contribution, but also as a Matlab package, one of the reference softwares for mathematical applications.”