Information Theory to Assess Relations Between Energy and Structure of the U.S. Economy Over Time

Abstract

This paper describes the changing structure of the United States’ (U.S.) domestic economy by applying information theory-based metrics to the U.S. input–output (I–O) tables from 1947 to 2012. Here the I–O tables are an economic network where the sectors are the nodes. The value of these metrics is that they describe the balance or trade-off between efficiency and redundancy of network flows as well as equality and hierarchy of flows through nodes in a network. I relate these metrics to the U.S. gross power consumption and annual intermediate spending by the food and energy sectors, the latter being a proxy for the inverse of the net power ratio (or net energy) of the economy, to test hypotheses of energy–economy structural linkages. The results of this paper show that increasing gross power consumption, as well as a decreasing share of intermediate expenditures of the food and energy sectors, correlates with increased distribution of money among economic sectors, and vice versa. The information theory metrics indicate two time periods at which major structural shifts occurred. The first was between 1967 and 1972, and the second was around the turn of the twenty-first century when food and energy expenditures no longer continued to decrease after 2002. In response to the latter, it is clear that the U.S. economy did trade off structural reserves (e.g., decreasing metrics of conditional entropy, redundancy, and equality) for structural efficiency (e.g., increasing metrics of efficiency, mutual constraint, and hierarchy) after food and energy expenditures increased post-2002. I also test the structural trends with increasingly simpler (e.g., fewer sectors) representations of the I–O tables, and the results are more consistent for I–O representations that account for inputs and outputs (e.g., value added and gross domestic product) rather than only the intermediate transactions among sectors. The findings of this paper have important implications for economic modeling in at least two ways. First, the paper helps explain how fundamental shifts in resources costs relate to economic structure and economic growth. Second, the paper shows that the number of sectors used to represent economic transactions influences the systemic metrics themselves.