A Parametric Distance Function Approach for Malmquist Productivity Index Estimation

Malmquist indexes of productivity are generally estimated using index number techniques or non-parametric frontier approaches. The aim of this paper is to show that Malmquist indexes can be estimated in a similar way using parametric-deterministic or parametric-stochastic frontier approaches. To allow a multi-output multi-input technology and for technical change in production, we adopt an output distance function which is specified in a translog form. We then show that using the estimated parameters, several radial distance functions can be calculated and combined in order to estimate and decompose the productivity index. Finally, this approach is applied to a panel of Spanish insurance companies. The main results confirm those generally obtained for financial services: very low rates of growth and technical change in spite of a rapid deregulation process and expansion of activity.