Distance Functions in Primal and Dual Spaces

Rolf Färe (), Shawna Grosskopf and Dimitri Margaritis
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Rolf Färe: Oregon State University
Dimitri Margaritis: University of Auckland

Chapter 1 in Data Envelopment Analysis, 2015, pp 1-21 from Springer

Abstract: Abstract This chapter provides an overview of the dual measurement of efficiency by means of distance functions and their value duals, the profit, revenue and cost functions. We start by showing how the Shephard (input) distance function in quantity space is a cost function in price space and how the cost function in quantity space is a distance function in price space. We then proceed to formulate a more unifying structure that allows for the simultaneous adjustment of inputs and outputs via establishing duality between the profit function and the directional (technology) distance function which also enables us to derive duality results for the revenue and cost functions as special cases. We complete our exposition by explaining how we can implement empirically dual forms of these efficiency measures either via activity analysis accounting for environmental technologies, slack-based measures and endogenous directional vectors or via parametric methods.

Keywords: DEA; Directional distance functions; Shephard distance functions; Duality theory; Profit efficiency; Cost efficiency; Revenue efficiency; Slack-based measures; Endogenous directional vectors; Generalized quadratic forms (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-1-4899-7553-9_1

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