Productivity and efficiency with discrete variables and quadratic cost function

We propose an index of productivity based on a quadratic cost function and developed for discrete data including technical and allocative inefficiency, jointly with technical change and returns to scale, as determinants of Total Factor Productivity. This new index is applied to Spanish stevedoring industry so as to identify the sources of change in the productivity of a multiproductive activity, where some companies do not produce some of the outputs. In this context, the functional quadratic form and the productivity index proposed prove particularly useful.