The Difference Approach to Productivity Measurement and Exact Indicators

There are many decompositions of productivity growth for a production unit that rely on the ratio approach to index number theory. However, the business and accounting literatures tend to favour using differences rather than ratios. In this paper, three analogous decompositions for productivity growth in a difference approach to index number theory are obtained. The first approach uses the production unit’s value added function in order to obtain a suitable decomposition. It relies on various first order approximations to this function, but the decomposition can be given an axiomatic interpretation. The second approach uses the cost constrained value added function and assumes that the reference technology for the production unit can be approximated by the free disposal conical hull of past observations of inputs used and outputs produced by the unit. The final approach uses a particular flexible functional form for the producer’s value added function and provides an exact decomposition of normalized value added.