Abstract
In the context of the two-tier stochastic frontier model, we present a new closed-form stochastic specification, the half-normal one. Expressions to calculate average and conditional measures of inefficiency are provided, for regression specifications in levels and in logs. Some results related to model validation and maximum likelihood estimation are also presented.
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Notes
All proofs and calculations related to the results presented in the paper are available from the author upon request.
A word on notation related to the error terms may be in order: our notation differs from the one used by previous scholars, but it was chosen to satisfy many intuitive mnemonics. Firstly, the letters used to express the composite error term are placed in the order they have in the alphabet. Secondly, the benchmark model (with only a zero mean symmetric error) is placed first, and then is augmented by the terms that reflect the special nature of the 2TSF model (i.e. "base plus extension"). So Xβ + u should be the benchmark model, and therefore u represents the symmetric disturbance. Thirdly, to determine the order in which the one-sided error components appear, we used the fact that we usually think of the signs as "plus-minus" rather than as "minus-plus". So the positive error component appears first (v), the negative error component second (w). Fourthly, we associated the number 1 with the one-sided error that appears first (hence the v-component), and the number 2 with the one-sided error that appears second (the w-component), using the order in which the two numbers appear in the naturals.
See Azzalini (1985).
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Acknowledgments
I would like to thank professor Efthymios G. Tsionas for suggesting this research topic to me, and an anonymous referee for helpful comments.
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Papadopoulos, A. The half-normal specification for the two-tier stochastic frontier model. J Prod Anal 43, 225–230 (2015). https://doi.org/10.1007/s11123-014-0389-8
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DOI: https://doi.org/10.1007/s11123-014-0389-8
Keywords
- Two-tier stochastic frontier analysis
- Half-normal distribution
- Maximum likelihood
- Informational efficiency