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.