On the Interpretation of Fixed Input Coefficients Under Aggregation

A fixed input coefficient is traditionally interpreted as the additional input from one sector that is required for an additional unit of output 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 for the ratio to be fixed is obtained. As a consequence, adopting the common assumption of fixed input coefficients implies that additional assumptions at any subaggregate level are required. Similar results are given for the Leontief inverse, whose typical element is usually interpreted as the additional output in one sector that is required for an additional unit of final demand in another sector