A QUASI-MALMQUIST PRODUCTIVITY INDEX

The Malmquist productivity index is based on distance functions, which are reciprocals of radial Debreu-Farrell efficiency measures, and whi ch have a number of desirable properties. Linear programming technique s are frequently employed to calculate the efficiency measures. Howeve r these techniques can leave slacks, which constitute a non-radial for m of inefficiency which is not incorporated into the analysis. Thus a radial efficiency measure overstates true efficiency, the reciprocal d istance function understates the distance to the relevant efficient su bset, and the Malmquist productivity index is adversely affected, alth ough in an analytically indeterminate direction. This has led us to co nsider 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 produc tivity index with an application to productivity change in Spanish ban king.