Approximate aggregation and error in input-output models

Abstract

Each industry in an input-output model is an aggregate of related, but not identical, production processes. As a result, the industry's input-output coefficients and demand multipliers are averages over the underlying disaggregated parameters. We provide a method for disaggregating an input-output model to obtain more precise estimates of its demand multipliers. This method is then applied to the problem of estimating the sensitivity of the demand multipliers to aggregation errors in the input-output matrix. We prove a theorem which provides upper bounds on the variances of aggregation errors in the multiplier matrix in terms of the variances of errors in the input-output matrix.