Effective Rank and Dimensionality Reduction: From Complex Disaggregation Back to a Simple World

Abstract

Abstract In recent years, we are witnessing renewed interest in the capital theory controversies, in which the empirically found near-linearities of the price-rate of profit and wage-rate of profit curves take centre stage. This article argues that these near-linearities are resulting from the low effective rank property characterizing the economy’s system matrices of technological coefficients. The implication is that it takes only a few eigenvalues and respective eigenvectors for an adequate representation of the movement of prices consequent upon changes in income distribution. Furthermore, a low-dimensional system may compress some of the characteristic features of the economy. JEL Classifications: B24, B51, C67, D46, D57, E11, E32