Spectral Evidence for the Structural Almost Uncontrollability of the Income Multiplier Process in Actual Economies
摘要
This paper explores the fundamental question of the degrees of controllability (in the sense of Kalman-Friedland) of Keynesian-type linear multiplier processes of income-import-primary input changes for a significant class of actual input-output table economies based on a dynamic and extended version of the Kurz multi-sector multiplier model and providing relevant spectral evidence from extensive input-output table data. The findings suggest that, irrespective of the direction of the control-policy instrument vector, (i) the degrees of controllability are not greater than the order of 10−19; (ii) for a tolerance of 10−4 (of 10−2), the normalised numerical rank of the controllability matrices is not greater than 17% (than 10%); (iii) the largest spreads between two consecutive singular values of the controllability matrices are not greater than 10−1 and, therefore, (iv) the dynamic multiplier systems are structurally almost uncontrollable. Since these controllability characteristics arise from the underlying-deep production-consumption structure of the considered class of actual input-output table economies, and since the effectiveness of demand management policies is at the centre of controversy in the post-2008 crisis world, the findings of this paper are of interest for both theoretical and applied policy studies.