Timothy Coelli

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.

Frontier Production Functions, Technical Efficiency and Panel Data: With Application to Paddy Farmers in India

Frontier production functions are important for the prediction of technical efficiencies of individual firms in an industry. A stochastic frontier production function model for panel data is presented, for which the firm effects are an exponential function of time. The best predictor for the technical efficiency of an individual firm at a particular time period is presented for this time-varying model. An empirical example is presented using agricultural data for paddy farmers in a village in India.

Prediction of firm-level technical efficiencies with a generalized frontier production function and panel data☆

Abstract A stochastic frontier production function is defined for panel data on sample firms, such that the disturbances associated with observations for a given firm involve the differences between traditional symmetric random errors and a non-negative random variable, which is associated with the technical efficiency of the firm. Given that the non-negative firm effects are time-invariant and have a general truncated normal distribution, we obtain the best predictor for the firm-effect random variable and the appropriate technical efficiency of an individual firm, given the values of the disturbances in the model. The results obtained are a generalization of those presented by Jondrow et al. (1982) for a cross-sectional model in which the firm effects have half-normal distribution. The model is applied in the analysis of three years of data for dairy farms in Australia.

A comparison of parametric and non-parametric distance functions: With application to European railways

Abstract In this paper we use multi-output distance functions to investigate technical inefficiency in European railways. The principle aim of the paper is to compare the results obtained from the three alternative methods of estimating multi-output distance functions. Namely, the construction of a parametric frontier using linear programming; data envelopment analysis (DEA) and corrected ordinary least squares (COLS). Input-orientated, output-orientated and constant returns to scale (CRS) distance functions are estimated and compared. The results indicate a strong degree of correlation between the input- and output-orientated results for each of the three methods. There are also significant correlations observed between the results obtained using the alternative estimation methods. The strongest correlations being between the parametric linear programming and the COLS methods. Finally, the paper concludes with the suggestion that a combination of the technical efficiency scores, obtained from the three different methods, be used as the preferred set of scores. This idea is borrowed from the time-series forecasting literature.

Estimators and hypothesis tests for a stochastic frontier function: A Monte Carlo analysis

This paper uses Monte Carlo experimentation to investigate the finite sample properties of the maximum likelihood (ML) and corrected ordinary least squares (COLS) estimators of the half-normal stochastic frontier production function. Results indicate substantial bias in both ML and COLS when the percentage contribution of inefficiency in the composed error (denoted by γ*) is small, and also that ML should be used in preference to COLS because of large mean square error advantages when γ* is greater than 50%. The performance of a number of tests of the existence of technical inefficiency is also investigated. The Wald and likelihood ratio (LR) tests are shown to have incorrect size. A one-sided LR test and a test of the significance of the third moment of the OLS residuals are suggested as alternatives, and are shown to have correct size, with the one-sided LR test having the better power of the two.

Technical efficiency of European railways: a distance function approach

This study has two principal objectives. The first objective is to measure and compare the performance of European railways. The second objective is to illustrate the usefulness of econometric distance functions in the analysis of production in multioutput industries, where behavioural assumptions such as cost minimization or profit maximization, are unlikely to be applicable. Using annual data on 17 railways companies during 1988–1993, multioutput distance functions are estimated using corrected ordinary least squares (COLS). The resulting technical efficiency estimates range from 0.980 for the Netherlands to 0.784 for Italy, with a mean of 0.863. The distance function results are also compared with those obtained from single-output production functions, where aggregate output measures are formed using either total revenue or a Tornqvist index. The results obtained indicate substantial differences in parameter estimates and technical efficiency rankings, casting significant doubt upon the reliability of these single-output models, particularly when a total revenue measure is used to proxy aggregate output.

Accounting for Environmental Influences in Stochastic Frontier Models: With Application to International Airlines

The principal aim of this paper is to measure the efficiency of international airlines. We obtain measures of technical efficiency from stochastic frontier production functions which have been adjusted to account for environmental influences such as network conditions, geographical factors, etc. We observe that two alternative approaches to this problem have been proposed in the efficiency measurement literature. One assumes that the environmental factors influence the shape of the technology while the other assumes that they directly influence the degree of technical inefficiency. In this paper we compare the results obtained when using these two approaches. The two sets of results provide similar rankings of airlines but suggest differing degrees of technical inefficiency. Both sets of results also suggest that Asian/Oceanic airlines are technically more efficient than European and North American airlines but that the differences are essentially due to more favourable environmental conditions. Nevertheless, it is among Asian companies that the major improvements in managerial efficiency (technical efficiency with environmental factors netted out) took place over the sample period (1977–1990).

A multi-stage methodology for the solution of orientated DEA models

The majority of DEA studies use a two-stage linear programming (LP) process to solve orientated DEA models. There are two significant problems associated with the second stage of this process. The first is that the sum of slacks is maximized rather than minimized and hence will identify not the nearest efficient point but the furthest efficient point. The second problem is that it is not invariant to units of measurement. In this paper we propose a multi-stage DEA methodology which involves a sequence of radial LPs. We observe that this new approach will identify more representative efficient points and that it is also invariant to units of measurement. The methodology is illustrated using a simple example.

A computer program for frontier production function estimation : Frontier version 2.0

Abstract The computer program FRONTIER will provide maximum-likelihood estimates for parameters of a number of stochastic frontier production function models. The most general model formulation considered is that set out in Battese and Coelli (1992), in which firm effects are assumed to be the product of an exponential function of time and a non-negative random variable having truncated normal distribution. The model considers panel data which need not be complete. The computer program permits the estimation of many other models which have appeared in the literature through the imposition of simple restrictions. Asymptotic estimates of standard errors are calculated along with individual and mean estimates of technical efficiency.

Capacity utilisation and profitability: A decomposition of short-run profit efficiency

The principal aim of this paper is to measure the amount by which the profit of a multi-input, multi-output firm deviates from maximum short-run profit, and then to decompose this profit gap into components that are of practical use to managers. In particular, our interest is in the measurement of the contribution of unused capacity, along with measures of technical inefficiency, and allocative inefficiency, in this profit gap. We survey existing definitions of capacity and, after discussing their shortcomings, we propose a new ray economic capacity measure that involves short-run profit maximisation, with the output mix held constant. We go on to describe how the gap between observed profit and maximum profit can be calculated and decomposed using linear programming methods. The paper concludes with an empirical illustration, involving data on 28 international airline companies. The empirical results indicate that these airline companies achieve profit levels which are on average US