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Joint estimation of technical efficiency and production risk for multi-output banks under a panel data cost frontier model

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Abstract

This article generalizes production risk from a single output production function to a multiple output cost frontier, which is able to examine input-oriented technical efficiencies and production risk simultaneously in the context of a panel data. Furthermore, the joint confidence interval estimates for technical efficiencies are constructed by means of multiple comparisons with the best approach. Whether taking production risk into account or not offers quite dissimilar implications in terms of the average technical efficiency measure and the identification of multiple efficient banks achieving the optimal cost frontier. It is suggested that inferences drawn on the basis of the confidence intervals of technical efficiency provide much more fruitful and insightful information than the point estimation alone. Bank specific risk parameters are found to be highly and positively correlated with fixed-effect estimates, implying that the more risk-averse a bank is, the more technically efficient it will be.

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Notes

  1. It is to be noted that the papers cited are all based on production frontiers, instead of a cost frontiers, as we are using.

  2. This can easily be seen by rewriting the constraint in equation (2.4) as: Y n ≤ [1+Φ −1(λ)σ ɛ ]f(Y′,X′).

  3. The same is not true for the multiple output case, while there is no natural way of selecting a dependent variable from various outputs. A cost function is preferable as it consists of multiple outputs and input prices.

  4. It is to be noted that in the panel data setting we are, in fact, parsimoniously specifying TE as both firm specific and time variant, i.e., α it = α i +α 3 t+0.5α33 t 2, as can been seen from (2.8), analogous to the formulation of R it in (2.9).

  5. One of the m cost shares must be removed in order to avoid the singularity problem occurring at the variance-covariance matrix of the random disturbances.

  6. More specifically, all the estimated cost shares of X 1 and X 3 are positive and there are only two observations having negative labor shares. As for the conditional factor demand functions, the demand for X 1 is found to be negative with respective to its own price for all sample points, while 122 sample points and six sample points are found to be positive to their own prices for X 2 and X 3, respectively, which are inconsistent with the theory. More than 339 out of 461 observations satisfy the negativity condition of a cost function.

  7. Readers are advised to refer to Horrace and Schmidt (2000) and Fraser and Horrace (2003) for details in this regard.

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Acknowledgments

The authors are grateful to the two anonymous referees of this Journal for their valuable comments and suggestions, which have promoted this paper substantially. Thanks are also due to Professor S. Kumbhakar for his constructive suggestions at various stages during the elaboration of this paper. Financial support from the National Science Council (NSC 93-2415-H-009-013), Executive Yuan, Taiwan, the Republic of China, are gratefully acknowledged.

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Authors and Affiliations

  1. Department of Money and Banking, National Chengchi University, 64, Section 2, Zhi-nan Road, Wenshan, Taipei, 11605, Taiwan, The Republic of China

    Tai-Hsin Huang

  2. Department of Insurance, Tamkang University, 151 Ying-Chuang Road, Tamsui, Taipei Hsien, 251, Taiwan, Republic of China

    Tong-Liang Kao

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Correspondence to Tai-Hsin Huang.

Appendix

Appendix

Table A.1 The fixed-effect estimates and standard errors
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Huang, TH., Kao, TL. Joint estimation of technical efficiency and production risk for multi-output banks under a panel data cost frontier model. J Prod Anal 26, 87–102 (2006). https://doi.org/10.1007/s11123-006-0007-5

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