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Abstract
The total factor productivity (TFP) of a multiple-output multiple-input firm can be
defined as the ratio of an aggregate output to an aggregate input. With this definition, index
numbers that measure changes in TFP can be expressed as the ratio of an output quantity index to
an input quantity index. This paper uses the term multiplicatively complete to describe TFP index
numbers that are constructed in this way. O'Donnell (2008) shows that, irrespective of the returns
to scale and/or scope properties of the production technology, all multiplicatively complete TFP
index numbers can be decomposed into widely-used measures of technical change and technical
efficiency change, as well as unambiguous measures of scale and mix efficiency change.
Members of the class of multiplicatively complete TFP index numbers include the Fisher,
Tornquist and Moorsteen-Bjurek indexes, but not the popular Malmquist index of Caves,
Christensen and Diewert (1982a). This paper uses data envelopment analysis (DEA) to compute
and decompose Moorsteen-Bjurek indexes of world agricultural TFP change for the period 1970-
2001. In a DEA model that prohibits technical regress, only two countries are found to maximize
TFP during the study period: Nepal from 1970 to 1995, and Thailand for several years in the late
1990s. The paper explains how changes in the agricultural terms of trade have drawn other larger
agricultural producers away from TFP-maximizing input-output points. The annual rate of
technical progress in global agriculture is estimated to be less than 1% per annum.