frontier {frontier} | R Documentation |
Maximum Likelihood Estimation of Stochastic Frontier Production and Cost Functions. 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). This R package uses the Fortran source code of Frontier 4.1 (Coelli 1996).
frontier( yName, xNames = NULL, zNames = NULL, data, ineffDecrease = TRUE, logDepVar = TRUE, truncNorm = FALSE, zIntercept = FALSE, timeEffect = FALSE, startVal = NULL, tol = 0.00001, maxit = 1000, muBound = 2, bignum = 1.0E+16, searchStep = 0.00001, searchTol = 0.001, searchScale = NA, gridSize = 0.1, gridDouble = TRUE, printIter = 0 ) ## S3 method for class 'frontier': print( x, ... )
yName |
string: name of the endogenous variable. |
xNames |
a vector of strings containing the names of the X variables (exogenous variables of the production or cost function). |
zNames |
a vector of strings containing the names of the Z variables (variables explaining the efficiency level). |
data |
a (panel) data frame that contains the data;
if data is a usual data.frame,
it is assumed that these are cross-section data;
if data is a panel data frame
(created with plm.data ),
it is assumed that these are panel data. |
ineffDecrease |
logical. If TRUE ,
inefficiency decreases the endogenous variable
(e.g. for estimating a production function);
if FALSE ,
inefficiency increases the endogenous variable
(e.g. for estimating a cost function). |
logDepVar |
logical. Is the dependent variable logged. |
truncNorm |
logical. If TRUE ,
the inefficiencies are assumed to have a truncated normal distribution
(i.e. parameter mu is added);
if FALSE ,
they are assumed to have a half-normal distribution
(only relevant for the ‘Error Components Frontier’). |
zIntercept |
logical. If TRUE ,
an intercept (with parameter delta_0)
is added to the Z variables
(only relevant for the ‘Efficiency Effects Frontier’). |
timeEffect |
logical. If FALSE (default),
the efficiency estimates of an ‘Error Components Frontier’
are time invariant;
if TRUE , time is allowed to have an effect on efficiency
(this argument is ignored in case of an
‘Efficiency Effects Frontier’). |
startVal |
numeric vector. Optional starting values for the ML estimation. |
tol |
numeric. Convergence tolerance (proportional). |
maxit |
numeric. Maximum number of iterations permitted. |
muBound |
numeric. Bounds on the parameter mu (see ‘details’ section). |
bignum |
numeric. Used to set bounds on densities and distributions. |
searchStep |
numeric. Size of the first step in the Coggin uni-dimensional search procedure done each iteration to determine the optimal step length for the next iteration (see Himmelblau 1972). |
searchTol |
numeric. Tolerance used in the Coggin uni-dimensional search procedure done each iteration to determine the optimal step length for the next iteration (see Himmelblau 1972). |
searchScale |
logical or NA . Scaling in the Coggin
uni-dimensional search procedure done each iteration
to determine the optimal step length for the next iteration
(see Himmelblau 1972):
if TRUE , the step length is scaled to the length of the last step;
if FALSE , the step length is not scaled;
if NA , the step length is scaled (to the length of last step)
only if the last step was smaller. |
gridSize |
numeric. The size of the increment in the first phase grid search on gamma. |
gridDouble |
logical. If TRUE ,
a second phase grid search on gamma is conducted
around the “best” value obtained in the first phase
with an increment of gridSize/10 . |
printIter |
numeric. Print info every printIter iterations;
if this argument is 0, do not print. |
x |
an object of class frontier
(returned by the function frontier ). |
... |
currently unused. |
One can use the frontier
function
to calculate the log likelihood value for a given model,
a given data set, and given parameters
by using the argument startVal
to specify the parameters
and using the other arguments to specify the model and the data.
The log likelihood value can then be retrieved by
the logLik
method
with argument which
set to "start"
.
Setting argument maxit
to 0
avoids the
(eventually time-consuming) ML estimation and allows
to retrieve the log likelihood value
with the logLik
method
without further arguments.
The frontier
function uses the Fortran source code of
Tim Coelli's software FRONTIER 4.1
(http://www.uq.edu.au/economics/cepa/frontier.htm)
and hence, provides the same features as FRONTIER 4.1.
A comprehensive documentation of FRONTIER 4.1 is available
in the file Front41.pdf
that is included in the archive FRONT41-xp1.zip
,
which is available at
http://www.uq.edu.au/economics/cepa/frontier.htm.
It is recommended to read this documentation,
because the frontier
function is based on the FRONTIER 4.1 software.
If argument zNames
is NULL
,
an ‘Error Components Frontier’ (ECF, see Battese and Coelli 1992)
is estimated.
If argument zNames
is not NULL
,
an ‘Efficiency Effects Frontier’ (EEF, see Battese and Coelli 1995)
is estimated.
Generally, there should be no reason to estimate an EEF
without z variable,
but this can done by setting argument zNames
to NA
.
In case of an Error Components Frontier (ECF)
with the inefficiency terms u following a
truncated normal distribution with mean mu,
argument muBound
can be used to restrict mu
to be in the interval +/-muBound
* sigma_u,
where sigma_u is the standard deviation of u.
If muBound
is infinity, zero, or negative,
no bounds on mu are imposed.
frontier
returns a list of class frontier
containing following elements:
modelType |
integer. A ‘1’ denotes an ‘Error Components Frontier’ (ECF); a ‘2’ denotes an ‘Efficiency Effects Frontier’ (EFF). |
ineffDecrease |
logical. Argument ineffDecrease (see above). |
logDepVar |
logical. Argument logDepVar (see above). |
nn |
number of cross-sections. |
nt |
number of time periods. |
nob |
number of observations in total. |
nb |
number of regressor variables (Xs). |
truncNorm |
logical. Argument truncNorm . |
zIntercept |
logical. Argument zIntercept . |
timeEffect |
logical. Argument timeEffect . |
printIter |
numeric. Argument printIter (see above). |
searchScale |
numeric. Argument searchScale (see above). |
tol |
numeric. Argument tol (see above). |
searchTol |
numeric. Argument searchTol (see above). |
bignum |
numeric. Argument bignum (see above). |
searchStep |
numeric. Argument searchStep (see above). |
gridDouble |
logical. Argument gridDouble (see above). |
gridSize |
numeric. Argument gridSize (see above). |
maxit |
numeric. Argument maxit (see above). |
startVal |
numeric vector. Argument startVal
(only if specified by user). |
call |
the matched call. |
dataTable |
matrix. Data matrix sent to Frontier 4.1. |
olsParam |
numeric vector. OLS estimates. |
olsStdEr |
numeric vector. Standard errors of OLS estimates. |
olsLogl |
numeric. Log likelihood value of OLS estimation. |
gridParam |
numeric vector. Parameters obtained from the grid search (if no starting values were specified). |
gridLogl |
numeric. Log likelihood value of the parameters obtained from the grid search (only if no starting values were specified). |
startLogl |
numeric. Log likelihood value of the starting values for the parameters (only if starting values were specified). |
mleParam |
numeric vector. Parameters obtained from ML estimation. |
mleCov |
matrix. Covariance matrix of the parameters obtained from the OLS estimation. |
mleLogl |
numeric. Log likelihood value of the ML estimation. |
lrTestVal |
LR test of the one-sided error
(this statistic has a mixed chi-square distribution
with lrTestDf degrees of freedom. |
lrTestDf |
numeric. Degrees of freedom of the LR test. |
nIter |
numeric. Number of iterations of the ML estimation. |
effic |
matrix. Efficiency estimates: each row corresponds to a cross-section; each column corresponds to a time period. |
Tim Coelli and Arne Henningsen
Battese, G.E. and T. Coelli (1992), Frontier production functions, technical efficiency and panel data: with application to paddy farmers in India. Journal of Productivity Analysis, 3, 153-169.
Battese, G.E. and T. Coelli (1995), A model for technical inefficiency effects in a stochastic frontier production function for panel data. Empirical Economics, 20, 325-332.
Coelli, T. (1996) A Guide to FRONTIER Version 4.1: A Computer Program for Stochastic Frontier Production and Cost Function Estimation, CEPA Working Paper 96/08, http://www.uq.edu.au/economics/cepa/frontier.htm, University of New England.
Himmelblau, D.M. (1972), Applied Non-Linear Programming, McGraw-Hill, New York.
frontierQuad
for quadratic/translog frontiers.
# example included in FRONTIER 4.1 (cross-section data) data( front41Data ) front41Data$logOutput <- log( front41Data$output ) front41Data$logCapital <- log( front41Data$capital ) front41Data$logLabour <- log( front41Data$labour ) # Cobb-Douglas production frontier cobbDouglas <- frontier( yName = "logOutput", xNames = c( "logCapital", "logLabour" ), data = front41Data ) cobbDouglas # rice producers in the Philippines (panel data) data( riceProdPhil ) riceProdPhil <- plm.data( riceProdPhil, c( "FMERCODE", "YEARDUM" ) ) riceProdPhil$lPROD <- log( riceProdPhil$PROD ) riceProdPhil$lAREA <- log( riceProdPhil$AREA ) riceProdPhil$lLABOR <- log( riceProdPhil$LABOR ) riceProdPhil$lNPK <- log( riceProdPhil$NPK ) # Error Components Frontier (Battese & Coelli 1992) rice <- frontier( yName = "lPROD", xNames = c( "lAREA", "lLABOR", "lNPK" ), data = riceProdPhil ) rice # Technical Efficiency Effects Frontier (Battese & Coelli 1995) rice2 <- frontier( yName = "lPROD", xNames = c( "lAREA", "lLABOR", "lNPK" ), zNames = c( "EDYRS", "BANRAT" ), data = riceProdPhil ) rice2