Directional output distance functions: endogenous directions based on exogenous normalization constraints

In response to a question raised by Knox Lovell, we develop a method for estimating directional output distance functions with endogenously determined direction vectors based on exogenous normalization constraints. This is reminiscent of the Russell measure proposed by Färe and Lovell (J Econ Theory 19:150–162, <CitationRef CitationID="CR8">1978</CitationRef>). Moreover it is related to the slacks-based directional distance function introduced by Färe and Grosskopf (Eur J Oper Res 200:320–322, <CitationRef CitationID="CR5">2010a</CitationRef>, Eur J Oper Res 206:702, <CitationRef CitationID="CR6">2010b</CitationRef>). Here we show how to use the slacks-based function to estimate the optimal directions. Copyright Springer Science+Business Media New York 2013