Skip to main content

A model for technical inefficiency effects in a stochastic frontier production function for panel data


A stochastic frontier production function is defined for panel data on firms, in which the non-negative technical inefficiency effects 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 inefficiency effects in stochastic frontiers for cross-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.

This is a preview of subscription content, access via your institution.


  • Aigner DJ, Lovell CAK, Schmidt P (1977) Formulation and estimation of stochastic frontier production function models. Journal of Econometrics 6:21–37

    Google Scholar 

  • Battese GE (1992) Frontier production functions and technical efficiency: A survey of empirical applications in agricultural economics. Agricultural Economics 7:185–208

    Google Scholar 

  • Battese GE, Coelli TJ (1988) Prediction of firm-level technical efficiencies: With a generalized frontier production function and panel data. Journal of Econometrics 38: 387–399

    Google Scholar 

  • Battese GE, Coelli TJ (1992) Frontier production functions, technical efficiency and panel data with application to paddy farmers in india. Journal of Productivity Analysis 3:153–169

    Google Scholar 

  • Battese GE, Coelli TJ (1993) A stochastic frontier production function incorporating a model for technical inefficiency effects. Working Papers in Econometrics and Applied Statistics No 69, Department of Econometrics. University of New England. Armidale

    Google Scholar 

  • Bauer PW (1990) Recent developments in the econometric estimation of frontiers. Journal of Econometrics 46:39–56

    Google Scholar 

  • Coelli TJ (1992) A computer program for frontier production function estimation: FRONTIER Version 2.0. Economics Letters 39:29–32

    Google Scholar 

  • Førsund FR, Lovell CAK, Schmidt P (1980) A survey of frontier production functions and their relationship to efficiency measurement. Journal of Econometrics 13:5–25

    Google Scholar 

  • Greene WH (1993) The econometric approach to efficiency analysis. In: Fried HO, Lovell CAK, Schmidt SS (Eds) The measurement of productive efficiency: Techniques and applications. Oxford University Press New York 68–119

    Google Scholar 

  • Huang CJ, Liu J-T (1994) Estimation of a non-neutral stochastic frontier production function. Journal of Productivity Analysis 5:171–180

    Google Scholar 

  • Kalirajan K (1981) An econometric analysis of yield variability in paddy production. Canadian Journal of Agricultural Economics 29:283–294

    Google Scholar 

  • Kumbhakar SC, Ghosh S, McGuckin JT (1991) A generalized production frontier approach for estimating determinants of inefficiency in US dairy farms. Journal of Business and Economic Statistics 9:279–286

    Google Scholar 

  • Meeusen W, van den Broeck J (1977) Efficiency estimation from Cobb-Douglas production functions with composed error. International Economic Review 18:435–444

    Google Scholar 

  • Pitt MM, Lee M-F (1981) The measurement and sources of technical inefficiency in the Indonesian weaving industry. Journal of Development Economics 9:43–64

    Google Scholar 

  • Reifschneider D, Stevenson R (1991) Systematic departures from the frontier: A framework for the analysis of firm inefficiency. International Economic Review 32:715–723

    Google Scholar 

  • Schmidt P (1986) Frontier production functions. Econometric Reviews 4:289–328

    Google Scholar 

  • Stevenson RF (1980) Likelihood functions for generalized stochastic frontier estimation. Journal of Econometrics 13:57–66

    Google Scholar 

Download references

Author information

Authors and Affiliations


Additional information

The authors are Associate Professor and Senior Lecturer, respectively, in the Department of Econometrics, University of New England, Armidale, NSW 2351, Australia. We thank Manolito Bernabe 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.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Battese, G.E., Coelli, T.J. A model for technical inefficiency effects in a stochastic frontier production function for panel data. Empirical Economics 20, 325–332 (1995).

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI:

JEL Classification System-Numbers

  • C12
  • C13
  • C23
  • C24
  • C87