A Quasi-Malmquist Productivity Index

The Malmquist productivity index is based on distance functions, which are reciprocals of radial Debreu-Farrell efficiency measures, and which have a number of desirable properties. Linear programming techniques are frequently employed to calculate the efficiency measures. However these techniques can leave slacks, which constitute a non-radial form of inefficiency which is not incorporated into the analysis. Thus a radial efficiency measure overstates true efficiency, the reciprocal distance function understates the distance to the relevant efficient subset, and the Malmquist productivity index is adversely affected, although in an analytically indeterminate direction. This has led us to consider a new definition of one-sided efficiency, and to develop a new nonradial efficiency measure which incorporates all slacks on the selected side. Replacing conventional radial efficiency measures with our new non-radial efficiency measures generates what we call a quasi-Malmquist productivity index. We illustrate our quasi-Malmquist productivity index with an application to productivity change in Spanish banking.     

The Rise and Fall of Slacks: Comments on Quasi-Malmquist Productivity Indices

Journal of Productivity Analysis - The Malmquist productivity index has been based on ratios of radial Farrell efficiency scores. Calculating these relative to piecewise linear production frontiers...     

Radial and non-radial decompositions of Luenberger productivity indicator with an illustrative application

Viewing slacks as one possible source of inefficiency, and that inputs have differential importance in the production process, this paper develops, based on the directional Russell measure of inefficiency, the non-radial Luenberger indicator. This indicator is then shown as the sum of the individual input-specific Luenberger indicators. The Luenberger indicator and its various input-specific indicators are also then shown as the composite measure of efficiency change and technical change. This decomposition enables the researcher to empirically examine the contributions of each factor input towards the productivity change and its components—efficiency change and technical change. Our proposed decomposition scheme is then empirically illustrated to analyze the eco-productivity performance behavior of the 22 OECD countries during the period 1995-2004. Our results indicate that first, the productivity change estimates yielded from the non-radial Luenberger indicator are different from those yielded from its radial counterpart, when slacks are present; second, most of these countries are found experiencing productivity growth due to technical progress alone; and finally, as regards the order of input-specific contributions towards productivity growth, capital contributes the most, followed by savings in emissions and labor, respectively.