On measures of technical inefficiency and production uncertainty in stochastic frontier production model with correlated error components |
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Authors: | Debdas Bandyopadhyay Arabinda Das |
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Institution: | (1) Department of Statistics, University of Kalyani, Kalyani, 741235, West Bengal, India |
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Abstract: | Analysis of the behavior of technical inefficiency with respect to parameters and variables of a stochastic frontier model
is a neglected area of research in frontier literature. An attempt in this direction, however, has recently been made. It
has been shown that in a “standard” stochastic frontier model that both the firm level technical inefficiency and the production
uncertainty are monotonically decreasing with observational error. In this paper we show, considering a stochastic frontier
model whose error components are jointly distributed as truncated bivariate normal, that this property holds if and only if
the distribution of observational error is negatively skewed. We also derive a necessary and sufficient condition under which
both firm level technical inefficiency and production uncertainty are monotonically increasing with noise-inefficiency correlation.
We next propose a new measure of the industry level production uncertainty and establish the necessary and sufficient condition
for firm level technical inefficiency and production uncertainty to be monotonically increasing with industry level production
uncertainty. We also study the limiting probabilistic behavior of these conditions under different parametric configuration
of our model. Finally we carry out Monte Carlo simulations to study the sample behavior of the population monotonic property
of the firm level technical inefficiency and production uncertainty in our model.
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Keywords: | Stochastic frontier model Efficiency measurement Hazard function Skew normal distribution |
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