The Morishima gross elasticity of substitution

We show that the Hotelling–Lau elasticity of substitution, an extension of the Allen–Uzawa elasticity to allow for optimal output-quantity (or utility) responses to changes in factor prices, inherits all of the failings of the Allen–Uzawa elasticity identified by Blackorby and Russell [(1989) Am Econ Rev 79: 882–888]. An analogous extension of the Morishima elasticity of substitution to allow for output quantity changes preserves the salient properties of the original Hicksian notion of elasticity of substitution. We thank Paolo Bertoletti for drawing our attention to the issue addressed in this paper and for his comments on an earlier draft.     

Directional duality theory Directional duality theory

In this paper we introduce a complete duality theory based on directional distance functions. This duality theory parallels the duality theory based on radial distance functions in Färe and Primont (1995).     

The opportunity cost of duality

A dual representation of a technology, e.g., a cost function, may not contain all of the technological information, but it will contain all of the information about input vectors that would be chosen by a cost-minimizing firm. At least this much is clear for deterministic technologies. The main question addressed in this paper is whether the same can be said about stochastic technologies and their dual representations. Despite some pessimism expressed in the stochastic frontier literature on this question, we argue that there is no extra cost imposed in the stochastic case. Thus, the conclusion of this paper is: Just dual it!     

On testing separability restrictions with flexible functional forms

In this paper, we examine the implications of imposing separability on the translog and three other flexible forms. Our results imply that the Berndt-Christensen ‘nonlinear’ test for weak separability tests not only for weak separability, but also imposes a restrictive structure on the macro and micro functions for all currently known ‘flexible’ functional forms. For example, testing for weak separability using the translog as an exact form is in fact equivalent to testing for a hybrid of strong (additive) separability and homothetic weak separability with Cobb-Douglas aggregator functions. Our results show that these ‘flexible’ functional forms are ‘separability-inflexible’. That is, they are not capable of providing a second-order approximation to an arbitrary weakly separable function in any neighbourhood of a given point.     

Luenberger Productivity Indicators: Aggregation Across Firms

Two methods of aggregating Luenberger productivity indicators across firms are considered. One method makes use of some rather implausible allocative efficiency assumptions. The second method, a superlative index number approach, relies on more palatable assumptions and is judged to be the more promising of the two methods.     

Continuous enough

In this paper we give a global condition on the cost function which is necessary and sufficient for continuity of the corresponding production function. A cost function satisfying this condition is ‘continuous enough’ in the sense discussed by Diewert (1974).     

The unification of Ronald W. Shephard's duality theory

Ronald W. Shephard developed four fundamental duality theorems. They relate the following four pairs of representations of the technology: cost function-input distance function, revenue function-output distance function, indirect cost function-indirect input distance function, and indirect revenue function-indirect output distance function. In this paper we show that all eight of these representations are equivalent. The implication of this equivalence is that there are twenty-four duality theorems and four inverse relationships involving Shephard's eight representations of technology.     

Index numbers and consistency in aggregation

This paper is an analysis of the concept of consistency in aggregation. This is the conjunction of three requirements: (i) for any given partition of the variables, two-stage aggregation is consistent, (ii) that each subaggregate and the overall aggregate have the same functional form, and (iii) that all partitions of the variables are feasible. We show that in the scalar case this results in a quasi-additive functional form. The generalization to many attributes is however shown to lead to few restrictions.