Journal of Productivity Analysis

, Volume 45, Issue 2, pp 121–130 | Cite as

A note on parameterizing input distance functions: does the choice of a functional form matter?

  • Rolf Färe
  • Michael VardanyanEmail author


We use a Monte Carlo experiment to compare the quadratic and translog functional forms in terms of their ability to approximate known frontiers that possess convex curvature. Unlike some of the existing simulation studies that have considered concave frontiers, we find that both functional forms provide a reliable approximation when a true frontier is convex. Our results lend support to existing intuitive explanations concerning the translog form’s innate propensity to yield convex, rather than concave, frontier estimates, suggesting that it should fare relatively well when modeling input isoquants. We also demonstrate that the quadratic functional form loses less of its flexibility than the translog function when shape constraints are imposed to satisfy regularity.


Distance functions Parameterization 

JEL Classification

D24 C63 



The authors would like to thank the two anonymous referees and the participants of the 13th European Workshop on Efficiency and Productivity Analysis for many helpful suggestions regarding the manuscript’s earlier drafts. Any remaining errors are our responsibility.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Economics and Department of Applied EconomicsOregon State UniversityCorvallisUSA
  2. 2.Department of Agricultural and Resource EconomicsUniversity of MarylandCollege ParkUSA
  3. 3.IÉSEG School of Management, LEM-CNRS (UMR 9221)Paris La Défense CedexFrance

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