Translation efficiency and directionally optimal scale

Abstract The aim of this paper is to show that instead of choosing the benchmark technology solely by means of maximal average productivities, a new whole range of options is opened up by using for this purpose the direction vector. By choosing any particular direction vector to evaluate technical efficiency we in fact predetermine by means of the relevant reflection vector the ray of average productivities we want to achieve. Then we may measure the extent of producing an inefficiently small (large) output by means of what we refer to as translation efficiency by comparing the average productivities of the projection of the observed input–output combination onto the best practice frontier and that of the graph translation homothetic technology. We can also determine the optimal production scale, which we refer to as directionally optimal scale , and which is defined conditionally on this vector of average productivities.