This paper shows how scale efficiency can be measured from an arbitrary parametric hyperbolic distance function with multiple outputs and multiple inputs. It extends the methods introduced by Ray (J Product Anal 11:183–194, <CitationRef CitationID="CR8">1998</CitationRef>), and Balk (J Product Anal 15:159–183, <CitationRef CitationID="CR1">2001</CitationRef>) and Ray (<CitationRef CitationID="CR9">2003</CitationRef>)...</citationref></citationref></citationref>

In this paper, we measure and analyse profit efficiency and productivity of Vietnamese banks using a newly developed index approach which is based on the directional distance function. Our findings indicate that the average bank operates quite far below the frontier of the best-practice bank,...