Cyclicality and Sectoral Linkages : Aggregate Fluctuations from Independent Sectoral Shocks

The traditional argument against the relevance of sector-specific shocks for the aggregate phenomenon of business cycles invokes the law of large numbers: positive shocks in some sectors are offset by negative shocks in other sectors. This paper hypothesizes that the law of large numbers may be postponed if the nature of sectoral interactions provides a synchronizing force, heightening co-movement in sectoral production. The analysis is performed within the context of a multi-sector model similar in spirit to that of Long and Plosser (1983). The paper explores the role limited interaction between sectors plays in determining the response of the aggregate economy from sector-specific disturbances. A feature of limited interaction that the paper stresses is that it implies few possibilities of substitution among intermediate inputs and that this increases sectoral co-movement and hence aggregate volatility. A low degree of sectoral interaction is characterized by a sparse input-use matrix. The rate at which the law of large numbers applies for increasing levels of disaggregation is shown to be controlled by the rate of increase in the number of predominantly full rows in the input-use matrix rather than by the rate of increase in the total number of sectors.Investigations of actual input-use matrices from the U.S. economy reveal that the number of full rows increases much slower than the total number of rows upon disaggregation, and when these input-use matrices are used to parameterize the model, aggregate volatility from sectoral shocks declines at a slower rate than that implied by the law of large numbers