A Package for Stochastic Frontier Analysis (SFA) in
What is frontier?
frontier is an extension package
for the "language and environment for statistical computing
and graphics" called R.
stochastic frontier production and cost functions
by maximum likelihood.
Two specifications are available:
the error components specification with time-varying efficiencies
(Battese and Coelli, 1992) and
a model specification in which the firm effects are directly
influenced by a number of variables (Battese and Coelli, 1995).
frontier includes an improved version
of the Fortran source code of
Tim Coelli's software
and hence, provides the same features as FRONTIER 4.1.
A comprehensive documentation of FRONTIER 4.1 is available
in the working paper:
Coelli, T.J. (1996),
A Guide to FRONTIER Version 4.1: A Computer Program
for Stochastic Frontier Production and Cost Function Estimation,
Working Paper No. 7/96,
Centre for Efficiency and Productivity Analysis (CEPA),
Department of Econometrics,
University of New England, Armidale, Australia.
This working paper is available as the file "Front41.pdf"
that is included in the archive "FRONT41-xp1.zip",
which is available at
Alternatively, the this file can be downloaded from
This documentation of FRONTIER 4.1 is also helpful to users of
the frontier package,
because this package is based on the FRONTIER 4.1 software.
Furthermore, frontier includes functions for:
writing input files for
FRONTIER 4.1 (function "front41WriteInput")
reading output files of
FRONTIER 4.1 (function "front41ReadOutput")
What are the differences between
and the R package frontier?
- FRONTIER 4.1 is a stand-alone software,
while the R package frontier is an add-on package to the software R.
- FRONTIER 4.1 only runs under MS-Windows,
while the R package frontier runs under all major operating systems.
- Running FRONTIER 4.1 requires the preparation of an instruction file and
a data file and possibly the modification of a file with settings,
while the R package frontier has a much simpler user interface.
- The coefficients and efficiencies estimated by the R package frontier
are directly available for further calculations.
- The Fortran code in FRONTIER 4.1 includes two bugs
that in specific circumstances can result in wrong estimates (see below),
while these bugs have been fixed in the R package frontier.
- The Fortran code in the R package frontier
has been optimised for numerical stability
so that the estimates are numerically more stable.
- The user can control more details of the estimation procedure
and the calculation of the efficiency estimates
when using the R package frontier.
- The R package frontier can calculate the marginal effects
of the "z variable" on the efficiency estimates
when using the efficiency effects model of Battese and Coelli (1995).
Who has written frontier?
Tim Coelli has written the Fortran source code,
which is the main component of this package.
Arne Henningsen has improved the Fortran code,
included it into an R package,
and has written the R interface.
Where can I get frontier?
- The released version is available on
- The current development version is available on
Under which license is frontier released?
Where can I ask questions, report bugs, or suggest new features?
Which two bugs are in FRONTIER 4.1 that are fixed in the R package "frontier"?
- In case of unbalanced panel data sets,
FRONTIER 4.1 returns some arbitray numbers
for the efficiency estimates of the unobserved observations.
- When estimating an "Error Components Frontier" (ECF)
with unbalanced panel data sets,
FRONTIER 4.1 uses arbitrary numbers
for the derivatives of the log-likelihood function
for the unobserved observations,
which usually leads the optimisation solver into a wrong direction.
Last Update: 23 August 2016