Aggregation in Input–Output Models: Prices and Quantities

Abstract

This paper develops a joint theory of aggregation of input–output quantity and price models. The main emphasis is on the problem of aggregation of industries in the models. While aggregation of quantity models is a familiar topic in economic literature, the aggregation of price models is a largely unexplored subject. Here, however, quantity and price models are considered as two parts of a single, composite flow model. This understanding implies that each result in the quantity model has dual counterpart in the price model and vice versa. Through consistent use of this duality principle, significant results are developed for both model types, and a number of well-known results can be stated in a simpler way. Specifically, a number of conditions for perfect aggregation of final demands, primary inputs and industries in price models as well as quantity models are formulated. On this basis a new indicator of aggregation bias is suggested. The indicator can be decomposed into the contributions of each detaile...