On Inverse Homotheticity

Maintaining the Regular Ultra Passum Law in data envelopment analysis

“…Unfortunately, a straight forward approach based on the joint assumption of both input and output homotheticity requires some rather restrictive additional assumptions. As noted in (Färe and Primont 1995) the notion of inverse homotheticity was introduced by ((Shephard 1970), page 255-57), where it is shown that this structure is sufficient for both input and output homotheticity. This result is generalized in (Färe and Primont 1995), where it is shown that we have inverse homotheticity if and only if the technology exhibits simultaneous input and output homotheticity 12 .…”

“…As noted in (Färe and Primont 1995) the notion of inverse homotheticity was introduced by ((Shephard 1970), page 255-57), where it is shown that this structure is sufficient for both input and output homotheticity. This result is generalized in (Färe and Primont 1995), where it is shown that we have inverse homotheticity if and only if the technology exhibits simultaneous input and output homotheticity 12 . Hence, extending our approach to multiple inputs and multiple outputs is straightforward if the technology simultaneously exhibits input and output homotheticity, i.e., inverse homotheticity and if these "mild" additional conditions are maintained.…”

Drivers of Regional Efficiency Differentials in Italy: Technical Inefficiency or Allocative Distortions?

“…The input distance function has several advantages over the traditional cost function model (see, among others, Coelli and Perelman 2000; Färe and Grosskopf 1990; Färe and Primont 1995; Grosskopf et al. 2001).…”

“…In contrast to cost functions, input distance functions are robust to deviations from the neoclassical cost‐minimising paradigm. The duality between the input distance function and the shadow cost function makes the former free from cost‐minimising assumptions because it is based on the assumption that input levels are selected according to shadow (implicit) rather than to market input prices, as is often the case for regulated or publicly owned firms, or when bureaucratic behaviour—based on principal‐agent information asymmetries—imposes private utility maximisation (Färe and Primont 1995). Similarly, this behaviour‐free characteristic makes the input distance function suitable for any situation where exogenous market forces might fail to organise available resources in an economically convenient way so that public intervention is needed to promote input adjustments.…”

“…The distance function must satisfy some regularity conditions (Färe and Primont 1995): It must be non‐decreasing, linearly homogeneous, and concave in the input vector x and non‐increasing in the output vector y .…”