frontier: 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

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.

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 lengt

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.

an object of class frontier (returned by the function frontier).

...

currently unused.

Value

frontier returns a list of class frontier containing following elements:
modelTypemodel type (see above).
functionTypefunction type (see above).
logDepVarlogical. Is the dependent variable logged?
nnnumber of cross-sections.
ntnumber of time periods.
nobnumber of observations in total.
nbnumber of regressor variables (Xs).
mulogical. Indicates if a 'mu'/'delta0' is included in the estimation (see above).
etaIn 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).
iprintnumeric. Printing of information on the iterations (see above).
indicnumeric. Scaling of unidimensional search procedure (see above).
tolnumeric. Convergence tolerance.
tol2numeric. Tolerance used in uni-dimensional search procedure.
bignumnumeric. Used to set bounds on densities and distributions.
step1numeric. Size of 1st step in search procedure.
igrid2numeric. 1 = double accuracy, 0 = single accuracy.
gridnonumeric. Steps taken in single accuracy grid search on gamma.
maxitnumeric. Maximum number of iterations permitted.
startValnumeric vector. Starting values for the ML estimation (if specified by user).
dataTablematrix. Data matrix sent to Frontier 4.1.
olsParamnumeric vector. OLS estimates.
olsStdErnumeric vector. Standard errors of OLS estimates.
olsLoglnumeric. Log likelihood value of OLS estimation.
gridParamnumeric vector. Parameters obtained from the grid search (if no starting values were specified).
mleParamnumeric vector. Parameters obtained from ML estimation.
mleCovmatrix. Covariance matrix of the parameters obtained from the OLS estimation.
mleLoglnumeric. Log likelihood value of the ML estimation.
lrTestValLR test of the one-sided error (this statistic has a mixed chi-square distribution with lrTestDf degrees of freedom.
lrTestDfnumeric. Degrees of freedom of the LR test.
nIternumeric. Number of iterations of the ML estimation.
efficmatrix. Efficiency estimates: each row corresponds to a cross-section; each column corresponds to a time period.

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

Run this code

# 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 )

   rice <- frontier( riceProdPhil,
      crossSectionName = "FMERCODE", timePeriodName = "YEARDUM",
      yName = "lPROD", xNames = c( "lAREA", "lLABOR", "lNPK" ) )
   rice

   rice2 <- frontier( riceProdPhil,
      crossSectionName = "FMERCODE", timePeriodName = "YEARDUM",
      yName = "lPROD", xNames = c( "lAREA", "lLABOR", "lNPK" ),
      zNames = c( "EDYRS", "BANRAT" ) )
   rice

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