<p>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<sup>−19</sup>; (ii) for a tolerance of 10<sup>−4</sup> (of 10<sup>−2</sup>), 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<sup>−1</sup> 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.</p>

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Spectral Evidence for the Structural Almost Uncontrollability of the Income Multiplier Process in Actual Economies

  • Theodore Mariolis,
  • Nikolaos Ntemiroglou,
  • Christos Palantzidis

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.