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
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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.
Aigner D, Chu SF (1968) On estimating the industry production function. Am Econ Rev 58:826–839Google Scholar
Aigner D, Lovell CAK, Schmidt P (1977) Formulation and estimation of stochastic frontier production function models. J Econom 6:21–37CrossRefGoogle Scholar
Barnett WA (2002) Tastes and technology: curvature is not sufficient for regularity. J Econom 108:199–202CrossRefGoogle Scholar
Chambers RG, Chung Y, Färe R (1996) Benefit and distance functions. J Econ Theory 70:407–419CrossRefGoogle Scholar
Chambers RG, Chung Y, Färe R (1998) Profit, distance functions and Nerlovian efficiency. J Optim Theory Appl 98:351–364CrossRefGoogle Scholar