Analysis and Control of Macroeconomic Trends Based on the Leontief Model

Abstract

In the present study, we consolidate the forty-five industrial sectors delineated in the U.S. input-output tables, as disseminated by the OECD, into three overarching sectors: advanced manufacturing, modern services, and a residual category termed ’others.’ We adopt gross fixed capital formation as a proxy for the proportion of net profit allocated to investment, positing that the investment requisite for augmenting output is commensurate with the requisite capital intensity. This framework enables us to forecast the trajectory of total output and GDP, taking into account the interplay of multiple determinants. In addressing the inherent linear control dynamics of the input-output model, we apply classical control theory to regulate the advanced manufacturing sector. By deriving control equations that accommodate multifactorial influences, we substantiate the efficacy of this control mechanism through rigorous numerical analysis. Moreover, we reconceptualize the dynamic input-output system as a game-theoretic model characterized by a saddle-point equilibrium. By leveraging the saddle-point equilibrium strategy, we pioneer an innovative approach to resolving the complexities of dynamic input-output analysis. This methodological innovation not only enhances the precision of our predictions but also contributes a novel perspective to the literature on economic modeling and control theory.