Hierarchical Clustering and Matrix Completion for the Reconstruction of World Input-Output Tables
This work addresses the timely and reliable reconstruction of economic I/O tables for national statistical offices and researchers, though it appears incremental as it builds on existing matrix completion techniques.
The authors tackled the problem of reconstructing missing entries in World Input-Output (I/O) matrices, which are crucial for economic analysis but often incomplete, by proposing a method combining hierarchical clustering and matrix completion with a nuclear norm penalty, achieving effective prediction of missing values in simulations and demonstrating applicability on real-world WIOD tables.
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.