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Journal of Productivity Analysis

, Volume 43, Issue 2, pp 215–223 | Cite as

Closed-form solution for a bivariate distribution in stochastic frontier models with dependent errors

  • Emilio Gómez-Déniz
  • Jorge V. Pérez-Rodríguez
Article

Abstract

This paper proposes a bivariate continuous model based on normal–half normal distributions for testing the independence of idiosyncratic and inefficiency terms in the stochastic frontier model in a maximum likelihood framework. This model allows us to construct a closed-form of the marginal distribution of the composite error term dependent on a parameter which gives a flexible covariance structure (positive and negative correlations are possible), but also nests classical models utilised in stochastic frontier studies. In addition, we obtain the point estimator for technical efficiency using the Battese and Coelli (J Econom 38:387–399, 1988) expression.

Keywords

Technical and cost efficiencies Stochastic frontier Marginal distribution Dependence Sarmanov model 

JEL Classification

C01 C13 C21 C51 

Notes

Acknowledgments

The research was partially funded by Emilio Gómez-Déniz: ECO2009-14152 (MICINN, Spain) and J.V. Pérez-Rodríguez: ECO2011-23189 (Ministerio de Economía y Competitividad, Spain). Also, J.V. Pérez-Rodríguez acknowledges the Department of Statistics and CRiSM, at the University of Warwick for their special support, since part of this paper was written while he was visiting the University of Warwick in 2013.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Emilio Gómez-Déniz
    • 1
  • Jorge V. Pérez-Rodríguez
    • 2
  1. 1.Department of Quantitative Methods in Economics and TiDES InstituteUniversity of Las Palmas de Gran CanariaLas Palmas de Gran CanariaSpain
  2. 2.Department of Quantitative Methods in EconomicsUniversity of Las Palmas de Gran CanariaLas Palmas de Gran CanariaSpain

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