Economic cross-efficiency

This paper introduces a series of new concepts under the name of Economic Cross-Efficiency, which is rendered operational through Data Envelopment Analysis (DEA) techniques. To achieve this goal, from a theoretical perspective, we connect two key topics in the efficiency literature that have been unrelated until now: economic efficiency and cross-efficiency. In particular, it is shown that, under input (output) homotheticity, the traditional bilateral notion of input (output) cross-efficiency for unit l, when the weights of an alternative counterpart k are used in the evaluation, coincides with the well-known Farrell notion of cost (revenue) efficiency for evaluated unit l when the weights of k are used as market prices. This motivates the introduction of the concept of Farrell Cross-Efficiency (FCE) based upon Farrell's notion of cost (revenue) efficiency. One advantage of the FCE is that it is well defined under Variable Returns to Scale (VRS), yielding scores between zero and one in a natural way, and thereby improving upon its standard cross-efficiency counterpart. To complete the analysis we extend the FCE to the notion of Nerlovian cross-inefficiency (NCI), based on the dual relationship between profit inefficiency and the directional distance function. Finally, we illustrate the new models with a recently compiled dataset of European warehousesSpanish Ministry for Science and Innovation and the State Research Agency under grants PID2019-105952GB-I00/AEI/10.13039/501100011033 and EIN2020-112260/AEI/10.13039/50110001103

Economic Cross-Efficiency

This paper is concerned with introducing a series of new concepts under the name of Economic Cross-Efficiency, which is rendered operational through Data Envelopment Analysis (DEA) techniques. To achieve this goal, from a theoretical perspective, we connect two key topics in the efficiency literature that have been unrelated until now: economic efficiency and cross-efficiency. In particular, it is shown that, under input (output) homotheticity, the traditional bilateral notion of input (output) cross-efficiency for unit l, when the weights of an alternative counterpart k are used in the evaluation, coincides with the well-known Farrell notion of cost (revenue) efficiency for evaluated unit l when the weights of k are used as market prices. This motivates the introduction of the concept of Farrell Cross-Efficiency (FCE) based upon Farrell’s notion of cost efficiency. One advantage of the FCE is that it is well defined under Variable Returns to Scale (VRS), yielding scores between zero and one in a natural way, and thereby improving upon its standard cross-efficiency counterpart. To complete the analysis we extend the FCE to the notion of Nerlovian cross-inefficiency (NCI), based on the dual relationship between profit inefficiency and the directional distance function. Finally, we illustrate the new models with a recently compiled dataset of European warehouses

New Definitions of Economic Cross-Efficiency

Overall efficiency measures were introduced in the literature for evaluating the economic performance of firms when reference prices are available. These references are usually observed market prices. Recently, Aparicio and Zofío (2019) have shown that the result of applying cross-efficiency methods (Sexton et al., 1986), yielding an aggregate multilateral index that compares the technical performance of firms using the shadow prices of competitors, can be precisely reinterpreted as a measure of economic efficiency. They termed the new approach ‘economic cross-efficiency’. However, these authors restrict their analysis to the basic definitions corresponding to the Farrell (1957) and Nerlove (1965) approaches, i.e., based on the duality between the cost function and the input distance function and between the profit function and the directional distance function, respectively. Here we complete their proposal by introducing new economic cross-efficiency measures related to other popular approaches for measuring economic performance. Specifically those based on the duality between the profitability (maximum revenue to cost) and the generalized (hyperbolic) distance function, and between the profit function and either the weighted additive or the Hölder distance function. Additionally, we introduce panel data extensions related to the so-called cost Malmquist index and the profit Luenberger indicator. Finally, we illustrate the models resorting to Data Envelopment Analysis techniques--from which shadow prices are obtained, and considering a banking industry dataset previously used in the cross-efficiency literature