Matrix Completion of World Trade

TL;DR

This paper introduces a novel application of matrix completion techniques to economic trade data, reconstructing the RCA matrix to derive a new complexity index called MONEY, which captures the predictability and complexity of countries' trade profiles.

Contribution

It applies matrix completion to economic data, introduces the MONEY index based on MC singular vectors, and compares it with existing economic complexity measures.

Findings

MC achieves high accuracy in classifying trade advantage elements.

The MONEY index correlates with economic complexity and predictability.

MC-based classifier's false positive rate proxies GENEPY index.

Abstract

This work applies Matrix Completion (MC) -- a class of machine-learning methods commonly used in the context of recommendation systems -- to analyse economic complexity. MC is applied to reconstruct the Revealed Comparative Advantage (RCA) matrix, whose elements express the relative advantage of countries in given classes of products, as evidenced by yearly trade flows. A high-accuracy binary classifier is derived from the application of MC, with the aim of discriminating between elements of the RCA matrix that are, respectively, higher or lower than one. We introduce a novel Matrix cOmpletion iNdex of Economic complexitY (MONEY) based on MC, which is related to the predictability of countries' RCA (the lower the predictability, the higher the complexity). Differently from previously-developed indices of economic complexity, the MONEY index takes into account the various singular vectors of the matrix reconstructed by MC, whereas other indices are based only on one/two eigenvectors of a suitable symmetric matrix, derived from the RCA matrix. Finally, MC is compared with a state-of-the-art economic complexity index (GENEPY). We show that the false positive rate per country of a binary classifier constructed starting from the average entry-wise output of MC can be used as a proxy of GENEPY.