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Efficiency Measures in the Agricultural Sector pp 13–35Cite as

Review of Frontier Models and Efficiency Analysis: A Parametric Approach

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Abstract

The parametric frontier approach to efficiency measurement has been extensively used in applied research. Within this conceptual framework, techniques for econometric frontier analysis will be described. The purpose of this paper is to present an overview of parametric frontier methods related to the measurement of economic efficiency, focusing on both deterministic and stochastic perspectives. In addition, development and extension of the cross-sectional and panel data context associated with specification of functional forms are also revisited.

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Notes

  1. 1.

    These two authors proposed an exponential and a half-normal to model the error term of the model, respectively.

  2. 2.

    The residuals of the within estimation are given by \( \hat{\varepsilon }^{\prime}\hat{\varepsilon } = \sum\limits_{i = 1}^N {} {{\sum\limits_{t = 1}^T {\left[ {{y_{it }} - \overline {y_i } - {{{\hat{\beta }^{\prime}}}_{\mathrm{Within}}}\left( {{x_{it }} - \overline {x_i } } \right)} \right]}}^2}. \)

  3. 3.

    \( {\varepsilon^{*}}^{\prime }{\varepsilon^{*}} = \sum\limits_{i = 1}^N {{{{\left( {\overline {y_i } - \hat{\beta}_{\mathrm{Between}}^{*} - {{{\hat{\beta }^{\prime}}}_{\mathrm{Between}}}\overline {x_i } } \right)}}^2}} \). The latter residuals are the result of applying the OLS technique to the model: \( {\overline y_{it }} = {\beta^{*}} + \beta ^{\prime}\overline {x_i } + \overline {v_i } - \overline {u_i^{*}} \).

  4. 4.

    These estimates are consistent as long as N and T → ∞.

  5. 5.

    When the variances of the components of the error term are unknown, the FGLS estimator of \( \sigma_v^2 \) is consistent with N or T → ∞, whereas for \( \sigma_u^2 \) consistency is ensured only with T → ∞.

  6. 6.

    The effects where the inefficiency is contained are given by the product of time effects (common to all firms) and individual effects: \( {\beta_{it }} = {\theta_t}{\delta_i} \).

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Authors and Affiliations

  1. ISCTE Business School Scientific Research & Development Unit, Évora University, Rua Romão Ramalho, 59, 7000-671, Évora, Portugal

    Ana Sampaio

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  1. Ana Sampaio
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Correspondence to Ana Sampaio .

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Editors and Affiliations

  1. , Mathematics, Azores University, Mãe de Deus, Ponta Delgada, 9501-801, Portugal

    Armando B. Mendes

  2. , Agricultural Sciences Department, University of Azores, Rua Capitão João de Ávila, Angra do Heroísmo, 9700-042, Portugal

    Emiliana L. D. G. Soares da Silva

  3. , Mathematics, Escola de Ciências e Tecnologia, R. Romão Ramalho 59, Évora, 7000-671, Portugal

    Jorge M Azevedo Santos

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Sampaio, A. (2013). Review of Frontier Models and Efficiency Analysis: A Parametric Approach. In: Mendes, A., L. D. G. Soares da Silva, E., Azevedo Santos, J. (eds) Efficiency Measures in the Agricultural Sector. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5739-4_2

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