Infeasibility and Directional Distance Functions with Application to the Determinateness of the Luenberger Productivity Indicator
AbstractThe purpose of this contribution is to highlight an underexplored property of the directional distance function, a recently introduced generalization of the Shephard distance function. It diagnoses in detail the economic conditions under which infeasibilities may occur for the case of directional distance functions and explores whether there exist any solutions that remedy the problem in an economically meaningful way. This discussion is linked to determinateness as a property in index theory and illustrated by analyzing the Luenberger total factor productivity indicator, based upon directional distance functions. This indicator turns out to be impossible to compute under certain weak conditions. A fortiori, the same problems can also occur for less general productivity indicators and indexes.
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Bibliographic InfoPaper provided by IESEG School of Management in its series Working Papers with number 2008-ECO-11.
Length: 48 pages
Date of creation: Sep 2008
Date of revision:
Publication status: Published in Journal of Optimization Theory and Applications,April 2009, 14(1), pp. 55-73
Directional distance function; Shortage function; Well-definedness; Infeasibility; Determinateness;
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