The Malmquist Total Factor Productivity Index: Some Remarks

Based on work by S. Malmquist (1953); Caves, Christensen and Diewert (1982) introduced what has been called the Malmquist productivity index. Their theoretical index was given an activity analysis interpretation by Färe, Grosskopf, Lindgren and Roos (1989), who showed how it could be computed using data on inputs and outputs. Färe, Grosskopf, Lindgren and Roos (1989) and Färe and Grosskopf (1994) discovered that under certain conditions the Malmquist index could be ill-defined. This prompted Bjurek (1994) to redefine the index as ratios of Malmquist input and output quantity indexes. In this paper, we investigate the specific conditions under which the Malmquist productivity index is ill-defined and we provide conditions on the data and the reference technologies sufficient for the index to yield appropriate outcomes.