Theory and Application of Directional Distance Functions

In 1957 Farrell demonstrated how cost inefficiency could be decomposed into two mutually exclusive and exhaustive components: technical and allocative inefficiency. This result is consequence of the fact that—as shown by Shephard—the cost function and the input distance function (the reciprocal of Farrell's technical efficiency measure) are dual to each other. Similarly, the revenue function and the output distance function are dual providing the basis for the decomposition of revenue inefficiency into technical and allocative components (see for example, Färe, Grosskopf and Lovell (1994)). Here we extend those results to include the directional distance function and its dual, the profit function. This provides the basis for defining and decomposing profit efficiency. As we show, the output and input distance functions (reciprocals of Farrell efficiency measures) are special cases of the directional distance function. We also show how to use the directional distance function as a tool for measuring capacity utilization using DEA type techniques.     

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!     

Economic Performance, Trade Restrictiveness, and Efficiency

The paper addresses the question of whether trade restrictiveness impacts economic performance, via a trade restrictiveness index that is decomposable into a trade distortion and a domestic distortion component. The paper builds on the Anderson and Neary price index measure of trade distortion, in evaluating trade restrictiveness via a distance function approach. This is accomplished by adding a “dual” version to their trade restrictiveness price index, based on distance functions that scale output quantities. The authors compute the trade restrictiveness quantity index (TRQI) using a parametric frontier approach to model the production side of the economy, and a panel of information on the agricultural sector of a set of European Community countries. The results suggest that the use of TRQI makes a considerable difference to interpretations of the efficiency impact of agricultural trade policies in EC countries, as compared to policy‐oriented aggregates or result‐oriented measures of trade restrictiveness.     

Planning Your Own Debt

We model the Danish market for mortgage backed securities with a two-factor interest rate model and use a stochastic programming approach to analyse how an individual home-owner should initially compose and subsequently readjust his mortgage in an optimal way. Results show that the 'rules of thumb' used by financial institutions are reasonable, although best suited for more aggressive mortgagors, for whom the delivery option is of some value. More risk-averse investors should also re-adjust frequently, but use more diversified portfolios. Results are insensitive to whether a one- or two-factor model is used, provided the former is suitably calibrated.     

A Comment on Weak Disposability in Nonparametric Production Analysis

In his 2005 paper in this journal, Kuosmanen argues that Shephard's specification of weak disposability in activity analysis (DEA) models is not correct. We show that Shephard's specification does satisfy weak disposability and is the "smallest" technology to do so.     

Are you really doing good things in your boss's eyes? Interactive effects of employee innovative work behavior and leader–member exchange on supervisory performance ratings

Organizations increasingly depend on employee efforts to innovate. However, the quality of relationships between leaders and employees may affect the recognition that employees receive for their innovative work behaviors. Drawing from a social cognition perspective, we tested a model in which leader–member exchange (LMX) moderates the impact of employee innovative work behavior on supervisory ratings of employee performance. Results from two multisource studies combining self, colleague, and supervisor ratings consistently showed that employees receive more favorable performance ratings by engaging in innovative work behavior when they have high‐quality LMX relationships. Moreover, we found that this interactive relationship was mediated by leader perceptions of innovative employee efforts, providing support for a moderated mediation model. Implications for the literatures on performance appraisal, LMX, and innovation are discussed.