New Definitions of Economic Cross-Efficiency

Abstract

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.