IDEAS home Printed from
   My bibliography  Save this article

The profit function system with output- and input-specific technical efficiency


  • Tsionas, Mike G.


In a recent paper Kumbhakar and Lai (2016) proposed an output-oriented non-radial measure of technical inefficiency derived from the revenue function. They proposed a closed skew-normal distribution for maximum likelihood estimation but they did not apply the model to data and their technique depends on multiple evaluations of multivariate normal integrals for each observation which can be very costly. In this paper we extend their approach to the profit function and we propose both input- and output-oriented non-radial measures of technical inefficiencies. Although the extension to the translog profit function is trivial many observations, in practice, may contain negative profits. For this reason we provide a nontrivial extension to the Symmetric Generalized McFadden (SGM) profit function. We propose and apply (to a large sample of US banks) Bayesian analysis of the SGM model (augmented with latent technical inefficiencies resulting in a highly nonlinear mixed effects model) using the integrated nested Laplace approximation.

Suggested Citation

  • Tsionas, Mike G., 2017. "The profit function system with output- and input-specific technical efficiency," Economics Letters, Elsevier, vol. 151(C), pages 111-114.
  • Handle: RePEc:eee:ecolet:v:151:y:2017:i:c:p:111-114
    DOI: 10.1016/j.econlet.2016.12.020

    Download full text from publisher

    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    1. Berger, Allen N. & Mester, Loretta J., 2003. "Explaining the dramatic changes in performance of US banks: technological change, deregulation, and dynamic changes in competition," Journal of Financial Intermediation, Elsevier, vol. 12(1), pages 57-95, January.
    2. Berger, Allen N. & Mester, Loretta J., 1997. "Inside the black box: What explains differences in the efficiencies of financial institutions?," Journal of Banking & Finance, Elsevier, vol. 21(7), pages 895-947, July.
    3. Joseph P. Hughes & Loretta J. Mester, 1998. "Bank Capitalization And Cost: Evidence Of Scale Economies In Risk Management And Signaling," The Review of Economics and Statistics, MIT Press, vol. 80(2), pages 314-325, May.
    4. Diewert, Walter E & Wales, Terence J, 1987. "Flexible Functional Forms and Global Curvature Conditions," Econometrica, Econometric Society, vol. 55(1), pages 43-68, January.
    5. Håvard Rue & Sara Martino & Nicolas Chopin, 2009. "Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 319-392, April.
    6. Guohua Feng & Apostolos Serletis, 2009. "Efficiency and productivity of the US banking industry, 1998-2005: evidence from the Fourier cost function satisfying global regularity conditions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(1), pages 105-138.
    7. Michael Koetter & James W. Kolari & Laura Spierdijk, 2012. "Enjoying the Quiet Life under Deregulation? Evidence from Adjusted Lerner Indices for U.S. Banks," The Review of Economics and Statistics, MIT Press, vol. 94(2), pages 462-480, May.
    8. Kumbhakar, Subal C. & Lai, Hung-pin, 2016. "Maximum likelihood estimation of the revenue function system with output-specific technical efficiency," Economics Letters, Elsevier, vol. 138(C), pages 42-45.
    9. Kumbhakar, Subal C. & Tsionas, Efthymios G., 2005. "Measuring technical and allocative inefficiency in the translog cost system: a Bayesian approach," Journal of Econometrics, Elsevier, vol. 126(2), pages 355-384, June.
    10. Diego Restrepo‐Tobón & Subal C. Kumbhakar, 2014. "Enjoying The Quiet Life Under Deregulation? Not Quite," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(2), pages 333-343, March.
    Full references (including those not matched with items on IDEAS)

    More about this item


    Profit function; Non-radial technical inefficiency; Symmetric Generalized McFadden form; Integrated nested Laplace approximation; Bayesian analysis;

    JEL classification:

    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • D22 - Microeconomics - - Production and Organizations - - - Firm Behavior: Empirical Analysis


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ecolet:v:151:y:2017:i:c:p:111-114. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.