Nonparametric production technologies with weakly disposable inputs

Abstract

In models of production theory and efficiency analysis, the inputs and outputs are assumed to satisfy some form of disposability. In this paper, we consider the assumption of weak input disposability. It states that any activity remains feasible if its inputs are simultaneously scaled up in the same proportion. As suggested in the literature, the Shephard technology incorporating weak input disposability could be used to evaluate the effect of input congestion. We show that the Shephard technology is not convex and therefore introduces bias in evaluation of congestion. To address this, we develop an alternative convex technology whose use in the evaluation of congestion removes the noted bias. We undertake a further axiomatic investigation and obtain a range of production technologies, all of which exhibit weak input disposability but are based on different, progressively relaxed, convexity assumptions. Apart from the evaluation of input congestion, such technologies should also be useful in applications in which some inputs are closely related or are overlapping, and therefore satisfy only the weak input disposability assumption incorporated in the new models.

Selective strong and weak disposability in efficiency analysis

“…The idea is to substitute the assumption of strong disposability of the inputs in the VRS technology by their weak disposability. Then, the ratio of the technical efficiency of a DMU evaluated in the VRS technology to its efficiency in the technology based on weak input disposability is interpretable as a measure of input congestion (Byrnes, Färe, Grosskopf, & Lovell, 1988;Dervaux, Kerstens, & Vanden Eeckaut, 1998;Färe et al, 1985;Mehdiloozad & Podinovski, 2018). 1 In addition to the above relatively special usages of weak disposability, in this paper we argue that this assumption may be appropriate in a more general modelling setting in which several input or output measures are closely related to each other.…”

“…In this case, it is assumed that the inputs from the subset I S are strongly disposable and that the inputs from the subset I W are only weakly disposable, i.e., can simultaneously be increased in an arbitrary proportion ρ ≥ 1 as a group, but not individually. Mehdiloozad and Podinovski (2018) point that the same setting may also be used as a general modelling assumption, outside the congestion measuring framework.…”

“…As an illustration, consider the following example which is modified from the example given in Mehdiloozad and Podinovski (2018).…”

“…It includes the rays BL, AM , GN , BJ and HK, and incorporates technology T HD VRS as a subset. As shown by Mehdiloozad and Podinovski (2018), the intermediate not closed HD tech-nologyT defined in the previous subsection is the same as technology T HD VRS with the following exception:T does not include the relative interiors of the half-line BD and the facet CBD (but it does include the ray BC). 6…”

“…The proposed technology can be seen as a generalization of the convex technology developed by Mehdiloozad and Podinovski (2018) in two respects. First, in the latter technology, only a subset (or several disjoint subsets) of inputs could be assumed to be weakly disposable.…”