Eigenvalues and Eigenlabors. On Iliadi's, Mariolis', Soklis', and Tsoulfidis' Explanation of the Empirical Regularities in Price Curves

The paper complements Iliadi’s, Mariolis’, Soklis’, and Tsoulfidis’s (IMST) explanation of the regular monotonic/near monotonic behavior of prices and capital intensities as an effect of hypothetical changes in the rate of profit obtained in empirical production price models with data from input-output accounts. We show that the shapes of the theoretical price and capital value curves depend on the product of the eigenvalues and the eigenlabors, i.e., the representation of the labor-coefficient vector in the space spanned by the eigenvectors of the input-coefficients matrix. We report robust evidence that for each economy in the WIOD database the eigenvalues by themselves cannot produce the conditions for monotonic/near monotonic curves, as claimed by IMST, but rather it is the joint action of the eigenvalues and the eigenlabors. The tendency towards zero of the product of the eigenvalues and the eigenlabors is driven by the statistical tendency towards the proportionality (i) between the columns of the input matrix, and (ii) between the labor vector and the Perron-Frobenius eigenvector of the input-coefficient matrix. The latter constitutes a new stylized fact in the productive structures of modern middle- and high-income economies.