Stochastic frontier models with threshold efficiency
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This paper proposes a tail-truncated stochastic frontier model that allows for the truncation of technical efficiency from below. The truncation bound implies the inefficiency threshold for survival. Specifically, this paper assumes a uniform distribution of technical inefficiency and derives the likelihood function. Even though this distributional assumption imposes a strong restriction that technical inefficiency has a uniform probability density over [0, θ], where θ is the threshold parameter, this model has two advantages: (1) the reduction in the number of parameters compared with more complicated tail-truncated models allows better performance in numerical optimization; and (2) it is useful for empirical studies of the distribution of efficiency or productivity, particularly the truncation of the distribution. The Monte Carlo simulation results support the argument that this model approximates the distribution of inefficiency precisely, as the data-generating process not only follows the uniform distribution but also the truncated half-normal distribution if the inefficiency threshold is small.
KeywordsStochastic frontier Technical efficiency Threshold inefficiency Uniform distribution Productivity distribution
JEL classificationC13 C21 D24 L11
Young Hoon Lee would like to acknowledge the supports by the National Research Foundation of Korea Grant funded by Korean Government (NRF-2010-330-B00069) and Sogang University Research Grant.
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