Hierarchical Clustering and Matrix Completion for the Reconstruction of World Input-Output Tables

TL;DR

This paper introduces a novel method combining hierarchical clustering and matrix completion with a LASSO-like penalty to accurately reconstruct missing entries in world input-output tables, aiding economic data analysis.

Contribution

The paper presents a new approach integrating hierarchical clustering with matrix completion techniques for imputing missing data in I/O matrices, demonstrated on synthetic and real-world datasets.

Findings

Effective prediction of missing I/O data from past and similar countries.

Method shows strong performance on synthetic matrices.

Approach is applicable to various industry-by-industry I/O tables.

Abstract

World Input-Output (I/O) matrices provide the networks of within- and cross-country economic relations. In the context of I/O analysis, the methodology adopted by national statistical offices in data collection raises the issue of obtaining reliable data in a timely fashion and it makes the reconstruction of (part of) the I/O matrices of particular interest. In this work, we propose a method combining hierarchical clustering and Matrix Completion (MC) with a LASSO-like nuclear norm penalty, to impute missing entries of a partially unknown I/O matrix. Through simulations based on synthetic matrices we study the effectiveness of the proposed method to predict missing values from both previous years data and current data related to countries similar to the one for which current data are obscured. To show the usefulness of our method, an application based on World Input-Output Database (WIOD) tables - which are an example of industry-by-industry I/O tables - is provided. Strong similarities in structure between WIOD and other I/O tables are also found, which make the proposed approach easily generalizable to them.