Theoretical Productivity Indices

Theoretical productivity indices provide a framework for comparing productivity levels over time or across economic units. Prominent approaches—generalizations of the classic Solow model of technical change to encompass multiple outputs—have come to be known as the Malmquist index and the Hicks-Moorsteen index. The former employs radial distance functions to measure productivity change in either input or output space, whereas the latter employs ratios of radial distance functions in each space to measure the relative change. When production below the frontier is taken into account, the Malmquist index decomposes naturally into the effects of shifts in the production frontier and changes in inefficiency. Other decomposition concepts encompass components like scale effects. Nonradial measures of productivity change in the full input–output space have been formulated using hyperbolic and directional distance functions. Also discussed are dual productivity indices (employing cost and revenue functions) and aggregation of productivity indices across economic units.