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THE BAYESIAN COMPARISON OF FLEXIBLE FUNCTIONAL FORMS AS STOCHASTIC COSTS FRONTIERS

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Wrobel-Rotter R.

Przegląd Statystyczny

2007

vol. 54

issue 2

5-27

Tne main goal of the paper is to discriminate among stochastic frontier cost functions. The unknown cost function is approximated by the locally flexible functional forms: the translog, generalised Leontoef and McFadden and two non-flexible forms: the Cobb-Douglas model with varying returns to scale and the Cobb-Douglas model with the Muentz-Schatz series expansion of order one for the price aggregator. Numerical approximations of moments of marginal posterior distributions are accomplished by implementation of the Markov Chain Monte Carlo techniques, that is the Metropolis-Hastings algorithms within Gibbs sampling. Marginal data density is obtained on the basis of the S. Chib's method proposed in 1995. Detailed discussion of specification of the prior distribution for the technology parameters with the posterior sensitivity analysis is included in the paper. After assuming the same prior standard deviation for the technology parameters in each model the authoress concludes that ther most probable a posteriori is the translog model, whose posterior probability is almost equal to one. The generalised Leontief and McFadden flexible forms are equally probable and are much more supported by the data than the non-flexible forms, such as the Cobb-Douglas. The ranking of models does not change when the dispersion of the prior distribution of technology parameters increases evenly but it can be noticed that the marginalised likelihood drops slightly faster for the Generalised McFadden model than for the Generalised Leontief and Muentz-Szatz series expansions of order one. After assuming the same marginal prior distribution of all individual technology parameters in each model the posterior model probabilities are not affected by the prior model probabilities. The marginal posterior distribution of technology characteristics and the cost efficiency, weighted by the posterior model probabilities, would be equal to the one obtained according to translog.

THE BAYESIAN COMPARISON OF CONDITIONAL INPUT DEMAND SYSTEMS IN THE PRESENCE OF INEFFICIENCY

100%

Wrobel-Rotter R.

Przegląd Statystyczny

2007

vol. 54

issue 1

5-19

The main goal of the paper is to discriminate among stochastic conditional demand systems. In this paper the authoress presents the Bayesian comparison of conditional input demand functions derived from stochastic cost frontiers approximated by different flexible functional forms. The advantage of applying input demand (or cost share) systems over the production of cost frontiers relays on the fact that they allow for modelling both technical and allocative efficiency. The technical efficiency is related to the excessive inputs usage in a production process while the allocative inefficiency is related to the incorrect proportions of inputs. The composed error structure of each of the equations of the conditional demand systems is defined by the Bayesian random effects model, so-called common efficiency distribution model. In the empirical analysis there are considered three demand systems derived from the microeconomic short-run variable cost function approximated by three locally flexible functional forms: the translog, the Generalised Leontief and the Generalised McFadden. Details of prior specification are discussed on the basis of the short-run Generalised Leontief input demand system. The comparison of models is conducted by marginal likelihood that is calculated by implemetation of Markov Chain Monte Carlo terchniques. An example of input demand systems estimated using data obtained from 31 Polish electric power stations illustrates the methodology. The results show insignificant differences in the description of the underlying production process by competing systems but the authoress founds our significantly different explanatory power of various conditional demand models.

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2 Przegląd Statystyczny

2 Wrobel-Rotter R.

2 2007

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THE BAYESIAN COMPARISON OF FLEXIBLE FUNCTIONAL FORMS AS STOCHASTIC COSTS FRONTIERS

THE BAYESIAN COMPARISON OF CONDITIONAL INPUT DEMAND SYSTEMS IN THE PRESENCE OF INEFFICIENCY