Dear Arne,

  Thank you very much for your response. I will certainly read it carefully
and if I have further questions (after our discussion on this problem), I
will go to R forge. I am relatively new in SFA and productivity analysis.

  Regarding your question on the presence of any software imposing
concavity condition, please read the book Coelli et al 2005, p227-230 (page
number of the book instead of the pdf file). According to the book, the
software Shazam can do the estimation with concavity constraint.

   The book is here:
http://facweb.knowlton.ohio-state.edu/pviton/courses/crp4700/coelli_Intro_effic.pdf

   According to my friend working on panel data, the case where efficiency
>1 is seldom/never encountered, but the book says the opposite.  Thanks,

Miao


2013/4/25 Arne Henningsen <arne.henningsen@gmail.com>

> Dear Miao
>
> On 25 April 2013 03:26, jpm miao <miaojpm@gmail.com> wrote:
> > I am trying to find out the scale efficiency and optimal scale of banks
> > by stochastic frontier analysis given the panel data of bank. I am free
> to
> > choose any model of stochastic frontier analysis.
> >
> > The only approach I know to work with R is to estimate a translog
> > production function by sfa or other related function in frontier package,
> > and then use the Ray 1998 formula to find the scale efficiency. However,
> as
> > the textbook Coelli et al 2005 point out that the concavity may not be
> > satisfied,  one needs to impose the nonpositive definiteness condition so
> > that the scale efficiency <1.
>
> It might be that the true technology is not concave and that the
> elasticity of scale is larger than one. Indeed, most empirical studies
> find increasing returns to scale (in many different sectors).
> Therefore, it is probably inappropriate to impose concavity.
>
> > How can I do it with frontier package?
>
> The frontier package cannot impose concavity on a Translog production
> function and I am not aware of any software that can do this in a
> stochastic frontier estimation -- probably, because imposing concavity
> usually does not make sense.
>
> > Is there any other SFA model/function in R recommended to find out the
> > scale efficiency and optimal scale?
>
> I suggest to plot the elasticity of scale against the firm size. If
> the elasticity of scale decreases with firm size, then the most
> productive firm size is at the firm size, where the elasticity of
> scale is one. However, there are some problems with using the Translog
> production function (and the Translog distance function) for
> determining the optimal firm size [1].
>
> [1] http://econpapers.repec.org/RePEc:foi:wpaper:2012_12
>
> If you have further questions regarding the "frontier" package, I
> suggest that you use the "help" forum at frontier's R-Forge site [2].
>
> [2] https://r-forge.r-project.org/projects/frontier/
>
> ... and please do not forget to cite the R packages that you use in
> your analysis in your publications. Thanks!
>
> Best wishes,
> Arne
>
> --
> Arne Henningsen
> http://www.arne-henningsen.name
>

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