Since the pioneer works of Aigner et. al. (1977) and Meeusen and van den Broeck
(1977), stochastic frontier analysis appeared to be a promising field of study for researchers.
One of the most important purposes of stochastic frontier analysis is to estimate technical effciencies of firms based on their choices of input combinations, price of inputs and the level of outputs produced. Based on the estimates of technical efficiencies, the rank of firms in terms of efficiency can be obtained.
The main idea of stochastic frontier analysis is the introduction of composite error term which contains two components: a technical inefficiency component and a noise component.
This composite structure of the error allows each firm to be efficient or inefficient relative to its own production/cost frontier. With the distributional assumptions imposed on the two error terms, the Maximum Likelihood Method or Method of Moments can be employed to obtain estimates for firms' technical efficiencies. Various distributional assumptions have
been used in the literature for the two error components.
This thesis centered on considering some distributional assumptions for the two error terms. These assumptions are more realistic compared with the existing ones in terms of modeling financial data and allowing for the exibility in the shape of the error terms. The
main results obtained were:
* Three sets of assumptions including Normal-Uniform, Laplace-Exponential, and Cauchy-Half Cauchy were studied in the context of cross-sectional data. In each model, closed-form formulas for point estimators, lower, and upper limits of technical efficiency were
derived.
* Each set of assumptions has its own merits in certain circumstances. Flat Uniform distribution is the most neutral one in the sense that one does not impose any prior belief on the distribution of technical inefficiency term relating to its mode or shape. Laplace-Exponential and Cauchy-Half Cauchy are very useful in modeling the financial and economic data, which usually evidence fat tails.
* All models were applied to a real data set of 123 U.S electric utility companies. These assumptions generated different estimates of technical efficiency from the four existing
models in the literature.
* Ranges of skewness coefficients of the distributions of the composite error were compared.
Except for the case of Normal-Uniform with zero skewness, the other two
proposed models resulted in the wider range of skewness compared to other models
used previously, and hence could be used for broader ranges of asymmetry and accommodate
outliers.
* Two models with distribution sets Normal-Uniform and Cauchy-Half Cauchy were generalized for balanced and unbalanced panel data. Time-invariance technical efficiency models were derived and applied to a balanced panel data set of 683 U.S banks and
an unbalanced panel WHO data set.
* Allocative efficiency (relating to the ability of a firm in choosing the right combination of inputs given their choices of output levels) was considered besides technical efficiency.
These two could be uncorrelated or correlated with each other. In each case, a model
was proposed to estimate technical and allocative efficiency.
* Lastly, some models to allow for the correlation between the noise components among
rms as well as the correlation between the two error components were proposed.
In short, the dissertation proposed various models to estimate technical efficiency of firms using either cross-sectional data or panel data. These models have some advantages compared
to the existing models. Other contributions included models which account for the correlation among error terms, either among noise components of firms or between noise and technical efficiency terms of firms.