Triangulation of input-output tables based on mixed integer programs for inter-temporal and inter-regional comparison of production structures

Understanding the industrial structure of a national or regional economy is one of the central issues in economics. The triangulation of an input-output table (IOT) can be employed to understand the production structure of an economy. Inter-temporal and inter-regional comparisons of multiple IOTs have addressed interesting and important issues pertaining to international trade, economic growth, and inter-industry relationships in the economy. Rank correlation coefficients between sector rankings obtained by solving optimization problems have been utilized to quantify similarities among production structures. However, it is well known that calculated rank correlations might be weak even if underlying structures are similar because the optimization problem inherently has multiple optimal solutions, thus leading to erroneous interpretations. This paper proposes a new method to triangulate IOTs based on mixed integer programs (MIPs) for comparing the production structures of multiple economies. The proposed new method does not suffer from non-uniqueness of optimal solutions and is consistent with maximization of the Kendall rank correlation coefficient. The application of the proposed method to the Japanese economy demonstrates stability of the Japanese production structure during 1995 - 2005. Comparisons of triangulated IOTs further reveal similarities in production structures of the Chinese, Japanese, and the U.S. economy for the year 2009.