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Empirical Economics (1995) 20:325-332

A Model for Technical Inefficiency Effects in a Stochastic Frontier Production Function for Panel Data
G. E. BATTESE AND T. J.
Department of Econometrics, The University of New England, Armidale, NSW 2351, Australia

Abstract: A stochastic frontier production function is defined for panel data on firms, in which the non-negative technical inetGciencyeffects are assumed to be a function of firm-specific variables and time. The inefficiency effects are assumed to be independently distributed as truncations of normal distributions with constant variance, but with means which are a linear function of observable variables. This panel data model is an extension of recently proposed models for inefTiciency effects in stochastic frontiers forcross-sectional data. An empirical application of the model is obtained using up to ten years of data on paddy farmers from an Indian village. The null hypotheses, that the inefficiency effects are not stochastic or do not depend on the farmer-specific variables and time of observation, are rejected for these data. JEL Classification System-Numbers: C12, C13, C23, C24, C87

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Introduction

Sincethe stochastic frontier production function was independently proposed in Aigner, Lovell and Schmidt (1977) and Meeusen and van den Broeck (1977), there has been considerable research to extend and apply the model. Reviews of much of this research are provided in F0rsund, Lovell and Schmidt (1980), Schmidt (1986), Bauer (1990), Battese (1992) and Greene (1993). The stochastic frontier productionfunction postulates the existence of technical inefficiencies of production of firms involved in producing a particular output. Most theoretical stochastic frontier production functions have not explicitly formulated a model for these technical inefficiency effects in terms of appropriate explanatory variables. Early empirical papers, in which the issue of the explanation of these inefficiencyeffects was raised, include Pitt and Lee (1981) and Kalirajan (1981). These papers adopt a two-stage approach, in which the first stage involves the specification and estimation of the stochastic frontier production function and the prediction of the technical inefficiency
' The authors are Associate Professor and Senior Lecturer, respectively, in the Department of Econometrics, University of NewEngland, Armidale, NSW 2351, Australia. We thank ManoUto Bemabe for assistance with data compilation. We gratefully acknowledge the International Crops Research Institute for the Semi-Arid Tropics (ICRISAT) for providing the panel data from its Village Level Studies.

0377-7332/95/2/325-332 $2.50 © 1995 Physica-Verlag, Heidelberg

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G. E. Battese and T. J. Coelli

effects, under theassumption that these inefficiency effects are identically distributed. The second stage involves the specification of a regression model for the predicted technical inefficiency effects, which contradicts the assumption of identically distributed inefficiency effects in the stochastic frontier. Kumbhakar, Ghosh and McGuckin (1991), Reifschneider and Stevenson (1991) and Huang and Liu (1994) recentlyproposed models for the technical inefficiency effects involved in stochastic frontier functions. The parameters of the stochastic frontier and the inefficiency model are estimated simultaneously, given appropriate distributional assumptions associated with cross-sectional data on the sample firms. The present paper proposes a model for technical inefficiency effects in a stochastic frontierproduction function for panel data. Provided the inefficiency effects are stochastic, the model permits the estimation of both technical change in the stochastic frontier and time-varying technical inefficiencies.

2 Inefiiciency Frontier Model for Panel Data

Consider the stochastic frontier production function for panel data, 1^. = exp(xj -\-V,,- l/J (1) where J^-, denotes the production at the...
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