Battese, G. 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.

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Battese, G. 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. M o s t theoretical stochastic frontier p r o d u c t i o n functions have n o t explicitly f o r m u l a t e d a m o d e l for these technical inefficiency effects in terms of a p p r o p r i a t e e x p l a n a t o r y variables.

E a r l y e m p i r i c a l papers, in which the issue of the explanation of these inefficiency effects was raised, include Pitt a n d Lee a n d K a l i r a j a n These p a p e r s a d o p t a t w o - s t a g e a p p r o a c h , in which the first stage involves the specification a n d e s t i m a t i o n of the stochastic frontier p r o d u c t i o n function a n d the p r e d i c t i o n of the technical inefficiency 1 The authors are Associate Professor and Senior Lecturer, respectively, in the Department of Econometrics, University of New England, Armidale, NSW , Australia.

We thank Manolito Bernabe for assistance with data compilation. Battese and T. Coelli effects, under the assumption 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 , Reifschneider and Stevenson and Huang and Liu recently proposed 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 frontier production 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. T for the i-th firm i - 1, Equation 1 specifies the stochastic frontier production function in terms of the original production values. However, the technical inefficiency effects, the 2 Although it is assumed that there are T time periods for which observations are available for at least one of the N firms involved, it is not necessary that all the firms are observed for all T periods in this model specification.

The explanatory variables in the inefficiency model may include some input variables in the stochastic frontier, provided the inefficiency effects are stochastic. If the first z-variable has value one and the coefficients of all other z-variables are zero, then this case represents the model specified in Stevenson and Battese and Coelli , If interactions between firm-specific variables and input variables are included as zvariables, then a non-neutral stochastic frontier, proposed in Huang and Liu , is obtained.

These assumptions are consistent with U, being a non-negative truncation of the N zitr, g2 -distribution. The inefficiency frontier production function 1 - 2 differs from that of Reifschneider and Stevenson in that the W-random variables are not identically distributed nor are they required to be non-negative, as in the latter paper. Further, the mean, z,6, of the normal distribution, which is truncated at zero to obtain the distribution of U,, is not required to be positive for each observation, as in Reifschneider and Stevenson Alternative models are required to account for possible correlated structures of the technical inefficiency effects and the random errors in the frontier.

The method of maximum likelihood is proposed for simultaneous estimation of the parameters of the stochastic frontier and the model for the technical inefficiency effects. The likelihood function and its partial derivatives with respect to the parameters of the model are presented in Battese and Coelli Coelli The prediction of the technical efficiencies is based on its conditional expectation, given the model assumptions. This result is also given in the Appendix of Battese and Coelli Information on the age and years of schooling for 14 paddy farmers from Aurepalle are used to explain the differences in the inefficiency effects among the farmers.

Data on variables, such as the frequency of contacts with agricultural extension officers, access to credit, the use of high-yielding varieties, etc. The use of age, years of formal schooling and year of observation illustrate the methodology involved. A total of observations are involved for a ten-year period from to In fact, this random variable accounts for any factors associated with inefficiency of production, including technical inefficiency.

Use of value of output is required, given that the Indian farmers involved engaged in other agricultural activites, including mixed cropping, in addition to growing paddy.

A Model for TechnicalInefficiencyEffectsin a StochasticFrontier ProductionFunction The stochastic frontier production function in 4 can be viewed as a linearized version of the logarithm of the Cobb-Douglas production of function in which the land variable is a weighted average of the number of irrigated and unirrigated hectares of land used in the production of paddy and other crops. The variable, PILand, accounts for the differences in the productivities of irrigated and unirrigated land.

The inefficiency frontier model 4 - 5 accounts for both technical change and time-varying inefficiency effects. The Year variable in the stochastic frontier 4 accounts for Hicksian neutral technological change. However, the Year variable in the inefficiency model 5 specifies that the inefficiency effects may change linearly with respect to time.

The signs of the coefficients of the stochastic frontier are as expected, with the exception of the negative estimate of the bullock-labour variable. The negative elasticity for bullock labour may be due to the fact that it is used more extensively in years of poorer rainfall for weed control, levy bank improvements, etc.

Thus bullock labour may be an inverse proxy for rainfall. The positive coefficient of the proportion of irrigated land confirms the expected positive relationship between the proportion of irrigated land and total value of production. The estimated coefficients for the land and labour variables, 0.

Coelli Table 1. The coefficient of Year indicates that the value of o u t p u t has tended to increase by a small, but insignificant, rate over the ten-year period. The estimated coefficients in the inefficiency model are of particular interest to this study. The Age coefficient is positive, which indicates that the older farmers are m o r e inefficient than the y o u n g e r ones.

The negative estimate for Schooling implies that farmers with greater years of schooling tend to be less inefficient. However, the relationship is very weak, because the coefficient is very small relative to its estimated standard error. The negative coefficient for Year suggests that the inefficiencies of p r o d u c t i o n of the p a d d y farmers tended to decline t h r o u g h o u t the ten-year period.

Generalized likelihood-ratio tests 5 of null hypotheses, that the inefficiency effects are absent or that they have simpler distributions, are presented in Table 1. The first null hypothesis, which specifies that the inefficiency effects are absent from the model, is strongly rejected. The second null hypothesis, which specifies that the inefficiency effects are n o t stochastic, 6 is also strongly rejected.

T h e third null hypothesis, considered in Table 1, specifies that the inefficiency effects are n o t a linear function of the age and schooling of the farmers and the year of observation. This indicates that the joint effects of these three explanatory variables on the inefficiencies of p r o d u c t i o n is significant a l t h o u g h the individual effects of one or m o r e of the variables m a y not be statistically significant.

In this case, the parameters, 6o and 63, are not identified. Hence the critical value for the test statistic for this second null hypothesis is obtained from the z]-distribution. Thus it appears that, in this application, the proposed inefficiency stochastic frontier production function is a significant improvement over the corresponding stochastic frontier which does not involve a model for the technical inefficiency effects.

An application of the model is presented using data from 14 Indian paddy farmers, observed over a ten-year period. The results indicate that the model for the technical inefficiency effects, involving a constant term, age and schooling of farmers and year of observation, is a significant component in the stochastic frontier production function. The application also illustrates that the model specification permits the estimation of both technical change and time-varying technical inefficiency, given that inefficiency effects are stochastic and have a known distribution.

Further theoretical and applied work is obviously required to obtain better and more general models for stochastic frontiers and the technical inefficiency effects associated with the analysis of panel data. Journal of Econometrics Battese GE Frontier production functions and technical efficiency: A survey of empirical applications in agricultural economics. Agricultural Economics Battese GE, Coelli TJ Prediction of firm-level technical efficiencies: With a generalized frontier production function and panel data.

Journal of Econometrics Battese GE, CoeUi TJ Frontier production functions, technical efficiency and panel data with application to paddy farmers in india. Journal of Productivity Analysis Battese GE, Coelli TJ A stochastic frontier production function incorporating a model for technical inefficiency effects. University of New England. Armidale Bauer PW Recent developments in the econometric estimation of frontiers. Journal of Econometrics G. Coelli Greene WH The econometric approach to efficiency analysis.

Journal of Productivity Analysis Kalirajan K An econometric analysis of yield variability in paddy production. Journal of Development Economics Reifschneider D, Stevenson R Systematic departures from the frontier: A framework for the analysis of finn inefficiency.

Econometric Reviews Stevenson RF Likelihood functions for generalized stochastic frontier estimation.

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## BATTESE AND COELLI 1992 PDF

Rambaldi The University of Queensland Verified email at uq. Articles Cited by Co-authors. The journal of development studies 36 3, Baytese Journal of Agricultural Economics 40 2, Here is how to contribute. Journal of the American Statistical Association 83, Australian nattese of agricultural economics 21 3, Firm size, age and efficiency: Functional forms of stochastic frontier production functions and models for technical inefficiency effects: A stochastic frontier production function incorporating a model for technical wnd effects GE Battese Working Papers in Econometrics and Applied Statistics 70 A model for technical inefficiency effects in a stochastic frontier production function for panel data GE Battese, TJ Coelli Empirical economics 20 2, Journal of productivity analysis 3, Estimation of a production frontier model: Bibliographic data for series maintained by Christopher F Baum. Their combined citations are counted only for the first article. Working Papers in Econometrics and Applied Statistics 70 Technical efficiency and productivity of maize producers in eastern Ethiopia: Windows users should not attempt to download these files with a web browser.

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