Abstract
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.
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Notes
See Wolff (2015) for a recent discussion of techniques for imposing monotonicity and curvature on parametric functional forms.
We cite these “reference” papers repeatedly throughout the text, due to their importance in motivating the present study.
Here we have chosen g = (1, 1).
In addition to these two benchmarks, Färe et al. (2010) and Chambers et al. (2013) also compute the Euclidean distance between the true and estimated frontier points. They subsequently average across these three discrepancies before assessing the results using a single criterion, which is based on that average. Here we use only two benchmarks and choose to compare the translog and quadratic functions’ ability to approximate the true MRTS separately from elasticity.
We report the median rather than the average benchmark values to deal with very large estimates of MRTS that can distort the benchmark for some replications when an isoquant has a nearly horizontal slope at certain points or over certain regions of data.
Färe et al. (2010) report that “… in the case of the true polynomial technologies, the quadratic function’s global behavior is clearly superior to that of the translog function,” and Chambers et al. (2013) mention that “… the quadratic parameterizations are overall better than translog in approximating both types of true technologies….”.
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Acknowledgments
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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Färe, R., Vardanyan, M. A note on parameterizing input distance functions: does the choice of a functional form matter?. J Prod Anal 45, 121–130 (2016). https://doi.org/10.1007/s11123-015-0448-9
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DOI: https://doi.org/10.1007/s11123-015-0448-9