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A multi-output multi-input stochastic frontier system with input- and output-specific inefficiency

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  • Kumbhakar, Subal C.
  • Lai, Hung-pin

Abstract

In this paper we consider a novel stochastic frontier model with multi-output multi-input production technology that accommodates non-radial inefficiency in both inputs and outputs. These measures are also observation-specific. To identify them, we use (i) a system model consisting of the revenue and cost share equations derived from the profit function and (ii) distributional assumptions on the inefficiency components and the noise terms. The error vector of the system is shown to have a closed skew normal distribution that is used to derive the likelihood function. The ML estimator of the parameters is used to derive formulas for predicting output- and input-specific inefficiencies, which are also observation-specific. We showcase the working of our model by applying it to a farm level data with two inputs and two outputs from Norway.

Suggested Citation

  • Kumbhakar, Subal C. & Lai, Hung-pin, 2021. "A multi-output multi-input stochastic frontier system with input- and output-specific inefficiency," Economics Letters, Elsevier, vol. 201(C).
    • Handle: RePEc:eee:ecolet:v:201:y:2021:i:c:s0165176521000847
    DOI: 10.1016/j.econlet.2021.109807
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    References listed on IDEAS

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    1. Lai, Hung-pin & Kumbhakar, Subal C., 2018. "Panel data stochastic frontier model with determinants of persistent and transient inefficiency," European Journal of Operational Research, Elsevier, vol. 271(2), pages 746-755.
    2. Koop, Gary & Osiewalski, Jacek & Steel, Mark F J, 2000. "Modeling the Sources of Output Growth in a Panel of Countries," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(3), pages 284-299, July.
    3. Chen, Yi-Yi & Schmidt, Peter & Wang, Hung-Jen, 2014. "Consistent estimation of the fixed effects stochastic frontier model," Journal of Econometrics, Elsevier, vol. 181(2), pages 65-76.
    4. Lai, Hung-pin & Kumbhakar, Subal C., 2018. "Endogeneity in panel data stochastic frontier model with determinants of persistent and transient inefficiency," Economics Letters, Elsevier, vol. 162(C), pages 5-9.
    5. Parmeter, Christopher F. & Kumbhakar, Subal C., 2014. "Efficiency Analysis: A Primer on Recent Advances," Foundations and Trends(R) in Econometrics, now publishers, vol. 7(3-4), pages 191-385, December.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Input- and output-specific inefficiency; Revenue and profit shares; Closed skew normal distribution;
    All these keywords.

    JEL classification:

    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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