Theoretical Basis for a Double Deflated Index of Real Value Added
The practice which we will refer to here as is a technique for arriving at a measure of value when one has available the value of gross output and materials inputs and also price indices for gross output and for materials inputs. The double deflation technique, despite its rather wide use, has been regarded as crudely empirical, with little, if any, justification from the point of view of theory.' The purpose of this note is to demonstrate that one can justify double-deflation as a fixed-weight linear approximation to an ideal variable-weight logarithmic index under assumptions no more restrictive than those required to justify the notion of real value added itself. Analysis of production relations is simpler if we can restrict ourselves to looking at two inputs at a time. Hence in studies using disaggregated data, it is convenient to consider the contribution of capital and labor to gross output separately from the contribution of materials inputs. In order for such separate treatment to be justified, the production function must be separable. Taking y to be gross output, K to be capital, L to be labor, and M to be materials, the separability condition required is