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2013 | OriginalPaper | Buchkapitel

2. Review of Frontier Models and Efficiency Analysis: A Parametric Approach

verfasst von : Ana Sampaio

Erschienen in: Efficiency Measures in the Agricultural Sector

Verlag: Springer Netherlands

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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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Vorheriges Kapitel Efficiency Measures in the Agricultural Sector: The Beginning

Nächstes Kapitel Introduction to Data Envelopment Analysis

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

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

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

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

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 → ∞.

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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Titel: Review of Frontier Models and Efficiency Analysis: A Parametric Approach
verfasst von: Ana Sampaio
Verlag: Springer Netherlands
Buch: Efficiency Measures in the Agricultural Sector
Print ISBN: 978-94-007-5738-7

Electronic ISBN: 978-94-007-5739-4

Copyright-Jahr: 2013
DOI: https://doi.org/10.1007/978-94-007-5739-4_2

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