[R] Stochastic Frontier: Finding the optimal scale/scale efficiency by "frontier" package

Arne Henningsen arne.henningsen at gmail.com
Thu Apr 25 12:46:55 CEST 2013

Dear Miao

On 25 April 2013 03:26, jpm miao <miaojpm at 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 Henningsen

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