frontier {frontier}R Documentation

Stochastic Frontier Analysis

Description

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).

Usage

frontier( data, crossSectionName, timePeriodName = NULL,
   yName, xNames = NULL, qxNames = NULL, zNames = NULL, quadHalf = TRUE,
   modelType = ifelse( is.null( zNames ), 1, 2 ),
   functionType = 1, logDepVar = TRUE, mu = FALSE, eta = FALSE,
   iprint = 0, indic = 1, tol = 0.00001, tol2 = 0.001, bignum = 1.0E+16,
   step1 = 0.00001, igrid2 = 1, gridno = 0.1, maxit = 100,
   startVal = NULL )
## S3 method for class 'frontier':
print( x, ... )

Arguments

data data frame that contains the data.
crossSectionName string: name of the cross section identifier.
timePeriodName string: name of the time period identifier or NULL in case of cross-section data.
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).
qxNames a vector of strings containing the names of the variables to construct quadratic and interaction terms. As a shortcut, this argument can be set to "all" for using all variables specified in argument xNames to get a full quadratic or translog model.
zNames a vector of strings containing the names of the Z variables (variables explaining the efficiency level).
quadHalf logical. Multiply the quadratic terms by one half?
modelType model type: either 1 for an 'Error Components Frontier' or 2 for an 'Efficiency Effects Frontier'.
functionType function type: either 1 for 'production function' or 2 for 'cost function'.
logDepVar logical. Is the dependent variable logged.
mu logical. Should a 'mu' (in case of an 'Error Components Frontier', i.e. modelType = 1) or a delta0 (in case of an 'Efficiency Effects Frontier', i.e. modelType = 2) be included in the estimation.
eta logical. Should an 'eta' be included in the estimation (only in case of an 'Error Components Frontier', i.e. modelType = 1).
iprint numeric. Print info every iprint iterations; if this argument is 0, do not print.
indic numeric. Use in unidimensional search procedure: indic = 2 says do not scale step length in unidimensional search; indic = 1 says scale (to length of last step) only if last step was smaller; indic = any other number says scale (to length of last step).
tol numeric. Convergence tolerance (proportional).
tol2 numeric. Tolerance used in uni-dimensional search procedure.
bignum numeric. Used to set bounds on densities and distributions.
step1 numeric. Size of 1st step in search procedure.
igrid2 numeric. 1 = double accuracy, 0 = single accuracy.
gridno numeric. Steps taken in single accuracy grid search on gamma.
maxit numeric. Maximum number of iterations permitted.
startVal numeric vector. Optional starting values for the ML estimation.
x an object of class frontier (returned by the function frontier).
... currently unused.

Details

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.

Value

frontier returns a list of class frontier containing following elements:

modelType model type (see above).
functionType function type (see above).
logDepVar logical. Is the dependent variable logged?
nn number of cross-sections.
nt number of time periods.
nob number of observations in total.
nb number of regressor variables (Xs).
mu logical. Indicates if a 'mu'/'delta0' is included in the estimation (see above).
eta In case of an error component model: logical, indicates if an 'eta' is included in the estimation. In case of an efficiency effects model: numeric, the number of efficiency effects regressors (Zs).
iprint numeric. Printing of information on the iterations (see above).
indic numeric. Scaling of unidimensional search procedure (see above).
tol numeric. Convergence tolerance.
tol2 numeric. Tolerance used in uni-dimensional search procedure.
bignum numeric. Used to set bounds on densities and distributions.
step1 numeric. Size of 1st step in search procedure.
igrid2 numeric. 1 = double accuracy, 0 = single accuracy.
gridno numeric. Steps taken in single accuracy grid search on gamma.
maxit numeric. Maximum number of iterations permitted.
startVal numeric vector. Starting values for the ML estimation (if specified by user).
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).
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.

Author(s)

Tim Coelli and Arne Henningsen

References

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.

Examples

   # example included in FRONTIER 4.1
   data( front41Data )
   front41Data$logOutput  <- log( front41Data$output )
   front41Data$logCapital <- log( front41Data$capital )
   front41Data$logLabour  <- log( front41Data$labour )

   # Cobb-Douglas production frontier
   cobbDouglas <- frontier( front41Data, "firm", "time", "logOutput",
      c( "logCapital", "logLabour" ) )
   cobbDouglas

   # Translog production frontier
   translog <- frontier( front41Data, "firm", "time", "logOutput",
      c( "logCapital", "logLabour" ), qxNames = "all" )
   translog

   # rice producers in the Phillipines
   data( riceProdPhil )
   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( riceProdPhil,
      crossSectionName = "FMERCODE", timePeriodName = "YEARDUM",
      yName = "lPROD", xNames = c( "lAREA", "lLABOR", "lNPK" ) )
   rice

   # Technical Efficiency Effects Frontier (Battese & Coelli 1995)
   rice2 <- frontier( riceProdPhil,
      crossSectionName = "FMERCODE", timePeriodName = "YEARDUM",
      yName = "lPROD", xNames = c( "lAREA", "lLABOR", "lNPK" ),
      zNames = c( "EDYRS", "BANRAT" ) )
   rice2

[Package frontier version 0.9-8 Index]