A Bayesian analysis of multiple-output production frontiers
Journal of Econometrics
In this paper we develop Bayesian tools for estimating multi-output production frontiers in applications where only input and output data are available. Firm-speci"c ine$ciency is measured relative to such frontiers. Our work has important di!erences from the existing literature, which either assumes a classical econometric perspective with restrictive functional form assumptions, or a non-stochastic approach which directly estimates the output distance function. Bayesian inference is
... d using a Markov chain Monte Carlo algorithm. A banking application shows the ease and practicality of our approach. 2000 Elsevier Science S.A. All rights reserved. JEL classixcation: C11; D24 (M. Steel). 0304-4076/00/$ -see front matter 2000 Elsevier Science S.A. All rights reserved. PII: S 0 3 0 4 -4 0 7 6 ( 9 9 ) 0 0 0 7 4 -3 Since r'1, we have to make a choice for which type of "rm we calculate the predictive e$ciency distribution. We chose to present results for what turn out to be the the most extreme of the four possible "rm types: a big "rm with high capital/retail, time and savings deposits ratio (w J "w J "1) and a small "rm with a low ratio between physical capital and retail, time and savings deposits (w J "w J "0). For ease of reference, we shall refer to these "rm types in the text as &large' and &small'. These representative "rms are chosen based on a crude measure of size of output. That is, we simply sum all three outputs together to get a measure of aggregate output. We then choose the three "rms which have the minimum, median and maximum aggregate output levels, respectively.