Maximum Entropy Estimators To Assess Technical Efficiency with State-Contingent Production Frontiers
Pedro Macedo1, Elvira Silva2, Manuel Scotto1
1Department of Mathematics, University of Aveiro, Portugal; 2Faculty of Economics, University of Porto, Portugal

In the last decade, the work of Chambers and Quiggin (2000) inspired a remarkable research in the production economics literature. With a more realistic representation of the economic production problems under uncertainty, the state-contingent approach provides higher estimates of technical efficiency when compared with the traditional stochastic frontier analysis. However, although the theory of state-contingent production is nowadays well-established, the empirical implementation of this approach is still in an infancy stage. Among others, there are two important difficulties: (a) the real number of states of nature may be very large (creating ill-posed models); and (b) with the increasing number of states, it is very likely to find few observations for some states of nature as well as collinearity problems. Some authors claim the urgent need to develop robust estimation techniques to overcome these difficulties.

Golan et al. (1996) developed the Generalized Cross Entropy (GCE) and the Generalized Maximum Entropy (GME) estimators, which are widely used in linear and nonlinear regression models, in particular in models with small size samples, non-normal errors and affected by collinearity, and in models where the number of parameters to be estimated exceeds the number of observations available. Later, Golan and Perloff (2002) defined the GME-α estimators by replacing the Shannon entropy measure with Tsallis and Rényi entropies in the objective function of the GME estimator. So far there have been only few attempts to estimate state-contingent production functions using the GME estimator. However, looking at the advantages of these estimators, it becomes clear that they could be the solution for some problems in the estimation of technical efficiency with state-contingent production frontiers, with the following additional important advantage: the traditional parametric assumptions on the error distributions, specifically the error inefficiency component, are not needed.

In this talk, we illustrate the performance of these estimators when compared with the Maximum Likelihood estimator through several simulation studies (including models affected by collinearity and ill-posed models). Small mean squared error loss and small differences between the true and the estimated mean of technical efficiency reveal that the GCE, GME and GME-α estimators perform better than the Maximum Likelihood estimator in most of the cases analyzed.


Chambers, R. G. and Quiggin, J. (2000). Uncertainty, Production, Choice, and Agency: The State-Contingent Approach. Cambridge University Press, Cambridge.

Golan, A. and Perloff, J. M. (2002). Comparison of maximum entropy and higher-order entropy estimators. Journal of Econometrics 107: 195-211.

Golan, A., Judge, G. and Miller, D. (1996). Maximum Entropy Econometrics: Robust Estimation with Limited Data. John Wiley & Sons, Chichester.

Keywords: Maximum entropy; State-Contingent production; Technical efficiency; Stochastic frontier analysis

Biography: Pedro Macedo has a degree in Applied Mathematics, a MSc in Economics and is concluding a PhD program in Mathematics in the University of Aveiro in Portugal. He worked as a statistician in the natural gas supply company in Portugal and is currently an assistant in the Department of Mathematics in the University of Aveiro. His research interests are in information theory and entropy econometrics.