For most of the 1990s and 2000s, estimating a stochastic frontier meant running FRONTIER 4.1, Tim Coelli’s Fortran program, and its guide (Coelli, 1996) was where one learnt how. The guide works through a small example: a Cobb-Douglas production frontier for 60 firms with half-normal inefficiency, estimated by maximum likelihood. Its data are distributed with the program and, today, with the R package frontier by Coelli and Henningsen, which implements FRONTIER 4.1 in R.
This post reproduces that example twice: by maximum likelihood with frontier, which returns the guide’s printed estimates, and by Bayesian inference with bsfa. The second is the more interesting exercise, because the two approaches answer slightly different questions, and a sample of 60 is small enough for the difference to show.
Griffin and Steel (2007) is a tutorial as much as a research paper. It shows how the Bayesian stochastic frontier models that van den Broeck, Koop, Osiewalski and Steel (1994) set out can be written down and estimated in WinBUGS, and its first example is the classic of the field: the costs of 123 US electric utilities in 1970, first analysed by Christensen and Greene (1976) and used by Greene (1990) and many others since. The paper prints its WinBUGS code, its priors and the posterior summaries it obtained, which makes it an unusually complete target for a reproduction.
This post reproduces the exponential and half-normal cost frontiers of that example with the bsfa package, which samples the same models by data augmentation and elicits its priors in the way the paper does.
Work in progress (September 2023). I will try to update this page over the next few months.
This section is intended to provide an overview of the relevant issues in (macro)economic time series analysis. Again the standard disclaimer: This site does not replace a good textbook, but it should help you to get a grasp of the basic concepts more quickly than if you learned it on your own.
The intended structure of this site is: