Analytical Problems in Decomposing the System-wide Effects of Sectoral Technical Change

The disaggregated structure of input–output (IO) analysis makes it very attractive in analyzing technical change. Various authors have applied IO models in comparative static experiments to measure the effects of observed technical changes in individual industries on economy-wide total output (or related primary input) requirements. Less often have researchers performed similar analyses on the effects of changes across all consuming industries in the productive consumption of a sector's output, because of the need to append an external analysis of substitution. Despite the obstacles to joint analyses of sectoral production and cross-sectoral consumption change, its appeal has long been recognized. In this paper, an anomaly in such analyses is presented: the sum of the separate effects of changes in production and changes in productive consumption does not equal the effects of the joint change. A comparative static exercise reveals the root cause of the anomaly: essentially, an index number problem. Empirical analyses are performed across a comprehensive set of US sectors to estimate the range of discrepancies.