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By SUBHASH C. RAY AND EVANGELIA DESLI*
In a recent issue of this Review, Rolf Fare et al. (FGNZ) (1994) analyzed the rates of productivity growth over the period 19791988 in 17 OECD countries. They used Data Envelopment Analysis to measure Malmquist productivity indices for the individual countries by the ratio of the values of the output distance functions for a reference technology exhibiting constant returns to scale (CRS ) at the input-output bundles of the same country observed in adjacent years. The Malmquist index is first decomposed into two factors: one showing technical change and the other, changes in technical efficiency, which can be interpreted as "catching up." The "catching up" term is further factored into two terms: one representing pure technical efficiency change and the other, changes in scale efficiency. This extended decomposition conceptualizes a technology characterized by variable returns to scale ( VRS ).1 Their use of CRS and VRS within the same decomposition of the Malmquist index raises a problem of internal consistency. Their technical change (TECHCH) measure corresponds to shifts over time in the CRS frontier. The other factors-pure efficiency change (PEFFCH) and scale efficiency change (SCH) -are derived from VRS frontiers from two different periods, however. If CRS is assumed to hold, the TECHCH term correctly shows the shift in the frontier. But, under CRS no scale effect exists at all. Hence, the extended decomposition is misleading. On the other hand, if the VRS assumption is correct, FGNZ's TECHCH does not show how the maximum producible output changes due to technical change holding the input bundle constant. In other words, it does not measure the autonomous shift in the frontier. As we show below, the Malmquist productivity index is correctly measured by the ratio of CRS distance functions even when the technology exhibits variable returns to scale. Thus, we measure the productivity index itself the same way as FGNZ do. There are alternative ways to decompose the same Malmquist index, which, in empirical applications, lead to different conclusions about technical change and efficiency change experienced by individual countries. We propose a decomposition using a VRS frontier as the benchmark. We measure technical change by the ratio of VRS distance functions. While this affects the measured value of the...