ON THE INTERPRETATION OF FIXED INPUT COEFFICIENTS UNDER AGGREGATION

A fixed input coefficient is traditionally interpreted as the addition al input from one sector that is required for an additional unit of ou tput in another sector. It is shown that this ratio of increments is, in general, not fixed under aggregation. A tight upper and lower bound for its variation are derived. A necessary and sufficient condition f or the ratio to be fixed is obtained. As a consequence, adopting the c ommon assumption of fixed input coefficients implies that additional a ssumptions at any subaggregate level are required. Similar results are given for the Leontief inverse, whose typical element is usually inte rpreted as the additional output in one sector that is required for an additional unit of final demand in another sector.