In their comment, Subhash C. Ray and Evangelia Desli (1997) (hereafter RD) point out that the specification of the decomposition of the Malmquist productivity index used by Fare et al. (1994) (hereafter FGNZ) is not unique, and propose and compute an alternative specification of that decomposition. We will discuss additional decompositions at the end of this note, but proceed here by comparing the RD decomposition with FGNZ based on both conceptual and computational grounds. RD provide a discussion of the overall Malmquist productivity index, including the important issue of when this index is equivalent to the traditional notion of total factor productivity (TFP) -namely under the condition that the technology be consistent with constant returns to scale (CRS). As they point out, this will yield a measure of TFP even if the true underlying technology is not CRS, for example. Both RD and FGNZ use the CRS technology to compute overall Malmquist productivity. One of the key issues raised is the role of the underlying scale properties of the benchmark technologies used to define and compute both productivity and its components. In particular, two reference technologies are employed in both RD and FGNZ: what we refer to as CRS and variable returns to scale (VRS) technologies.' By construction, these technologies are nested: the CRS technology contains the VRS technology, as in Figure 1 in RD. This nestedness provides the logical basis for our decomposition. At a very intuitive level, we would argue that these two benchmarks can be used to provide bounds on the underlying true-but unknown-technology.2 Intuitively we see the VRS technology providing a type of convex inner approximation, whereas the CRS technology provides a type of convex outer approximation. Thus these two technologies provide alternative benchmarks; they do not require that the data satisfy either CRS or VRS. Another possible intuitive interpretation is that the CRS captures a (perhaps hypothetical) long run and the VRS approximates the short run. As a technology, the CRS technology has some very useful features; for example, it captures the notion of maximal
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