On the relation between gross output and value addedbased productivity measures: The importance of the domar factor

In this paper I consider the relation between gross output and value addedbased total factor productivity (TFP) measures. It appears that, without any (micro-)economic theory being required, a conditional relationship between TFP indices can be derived, in which the Domar factor plays an important role. At the same time it turns out that gross output and value addedbased TFP indicators (difference-type measures) always coincide. In the Divisia index framework and maintaining the classical assumptions (profit maximization and a production technology that exhibits globally constant returns to scale), it appears that both TFP indices measure technological change, albeit in a dual way. In establishing this result, no separability assumptions are involved. Both indices are in general path-dependent. Path independence of the gross outputbased TFP index requires that the technology exhibit Hicks input neutrality, whereas path independence of the value addedbased TFP index requires Hicks value-added neutrality. These two concepts of neutrality are, however, not dual.

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