Empirical Analysis of Largest Eigenvalue of Leontief Matrix

Abstract

In Input–output Analysis, consumption coefficients play an important role and reflect the production technology of the economic system. The largest eigenvalue of Leontief matrix has some economic meanings. To some degree, it indicates a limit on economic growth, which means the economic system may grow only when the gross input coefficient is bigger than the largest eigenvalue. On the other hand, it has inverse proportion relation with final demands rate. In an empirical analysis for the five countries, China, Japan, Britain, America and Australia, results are calculated for these countries’ eigenvalues of Leontief matrices. The outcomes exhibit a large degree of stability across the different years’ matrices for a country. Therefore it is confirmed that the largest eigenvalue can reflect a kind of inner regularity. List of these countries according to the average value of largest eigenvalues in a decreasing order are China, Japan, Britain, America and Australia.