Coefficients from Frontier 4.1

Description

These methods return the coefficients and their covariance matrix from a model estimated by Frontier 4.1.

Usage

   ## S3 method for class 'front41Output'
coef( object, which = "MLE", ... )

   ## S3 method for class 'summary.front41Output'
coef( object, which = "MLE", ... )

   ## S3 method for class 'front41Output'
vcov( object, ... )

Arguments

Value

The coef method applied to an object of class front41Output returns a vector containing all coefficients estimated by Frontier 4.1.

The coef method applied to an object of class summary.front41Output returns a matrix containing the estimates, their standard errors, the t values and P values of all coefficients estimated by Frontier 4.1.

The vcov method returns the covariance matrix of all coefficients estimated by Frontier 4.1.

Author(s)

Arne Henningsen

See Also

front41ReadOutput

coef method for class frontier

Description

Extract the coefficients from stochastic frontier models returned by frontier.

Usage

## S3 method for class 'frontier'
coef( object, which = "mle", extraPar = FALSE, ... )

Arguments

Value

coef.frontier returns a named vector of the coefficients.

Author(s)

Arne Henningsen

See Also

coef.summary.frontier and sfa.

Examples

   # example included in FRONTIER 4.1
   data( front41Data )

   sfaResult <- sfa( log( output ) ~ log( capital ) + log( labour ),
      data = front41Data )
   coef( sfaResult, which = "ols" )
   coef( sfaResult, which = "grid" )
   coef( sfaResult )

coef method for class summary.frontier

Description

Extract the coefficients, their standard errors, z-values or t-values, and (asymptotic) P-values from stochastic frontier models returned by the summary method for objects of class frontier.

Usage

## S3 method for class 'summary.frontier'
coef( object, which = "mle", ... )

Arguments

Details

The standard errors of the estimated parameters are taken from the direction matrix that is used in the final iteration of the Davidon-Fletcher-Powell procedure that is used for maximising the (log) likelihood function.

If argument which of this method is "mle" (the default) and argument extraPar of summary.frontier is set to TRUE, some additional parameters, their standard errors, z-values, and (asymptotic) P-values are returned (see documentation of summary.frontier, coef.frontier, or vcov.frontier). The standard errors of the additional parameters are obtained by the delta method. Please note that the delta method might provide poor approximations of the ‘true’ standard errors, because parameter \sigma^2 is left-censored and parameter \gamma is both left-censored and right-censored so that these parameters cannot be normally distributed.

Please note further that the t statistic and the z statistic are not reliable for testing the statistical signicance of \sigma^2, \gamma, and the ‘additional parameters’, because these parameters are censored and cannot follow a normal distribution or a t distribution.

Value

The coef method for objects of class summary.frontier returns a matrix, where the four columns contain the estimated coefficients, their standard errors, z-values or t-values, and (asymptotic) P-values.

Author(s)

Arne Henningsen

See Also

coef.frontier, summary.frontier, vcov.frontier, and sfa.

Examples

   # example included in FRONTIER 4.1
   data( front41Data )

   sfaResult <- sfa( log( output ) ~ log( capital ) + log( labour ),
      data = front41Data )
   coef( summary( sfaResult ), which = "ols" )
   coef( summary( sfaResult ) )
   coef( summary( sfaResult, extraPar = TRUE ) )

Pseudo-Cook's Distance of Stochastic Frontier Models

Description

This method returns the Pseudo-Cook's distances from stochastic frontier models estimated with the frontier package (e.g., function sfa).

Usage

## S3 method for class 'frontier'
cooks.distance( model, target = "predict",
   asInData = FALSE, progressBar = TRUE, ... )

Arguments

Value

A vector of the Pseudo-Cook's distances for each observation that was used in the estimation that is provided as argument model.

Author(s)

Arne Henningsen

See Also

sfa, cooks.distance.

Examples

   # example included in FRONTIER 4.1 (cross-section data)
   data( front41Data )

   # Cobb-Douglas production frontier
   cobbDouglas <- sfa( log( output ) ~ log( capital ) + log( labour ),
      data = front41Data )
   summary( cobbDouglas )
   
   # Pseudo-Cook's distances for predicted values
   cooks.distance( cobbDouglas )

   # Pseudo-Cook's distances for efficiency estimates
   cooks.distance( cobbDouglas, "efficiencies" )

Returning Efficiency Estimates

Description

This method returns efficiency estimates from frontier models.

Usage

efficiencies( object, ... )
## Default S3 method:
efficiencies( object, ... )

Arguments

Details

This is a generic function. The default method just returns the element effic from object.

Author(s)

Arne Henningsen

See Also

efficiencies.frontier.

Returning Efficiency Estimates

Description

This method returns efficiency estimates from stochastic frontier models estimated with frontier.

Usage

## S3 method for class 'frontier'
efficiencies( object, asInData = FALSE,
   logDepVar = TRUE, minusU = farrell, farrell = TRUE, 
   margEff = FALSE, newdata = NULL, ... )

Arguments

Value

If argument asInData is FALSE (default), a matrix of efficiency estimates is returned, where each row corresponds to a firm (cross-section unit) and each column corresponds to a time period (only if efficiency estimates differ between time periods).

If argument asInData is TRUE, a vector of efficiency estimates is returned, where the efficiency estimates are in the same order as the corresponding observations in the data set used for the estimation.

If argument margEff is TRUE, and the model is an Efficiency Effects Frontier (EFF) with z variables, and the dependent variable is logged, the returned efficiency estimates have an attribute "margEff" that contains the marginal effects of the z variables on the efficiency measure.

If the dependent variable is logged, the marginal effect of the kth z variable on the efficiency is

\frac{\partial E[ \exp( - \kappa \, u ) ]}{\partial z_{kit}} = \frac{ \delta_{k} ( 1 - \gamma ) \exp \left( - \kappa \, \bar{\mu}_{it} + \frac{1}{2} \bar{\sigma}^{2} \right) }{ \Phi \left( \frac{\bar{\mu}_{it}}{ \bar{\sigma} } \right) }

\cdot \left( \frac{ \phi \left( -\kappa \, \bar{\sigma} + \frac{ \bar{\mu}_{it} }{ \bar{\sigma} } \right) }{ \bar{\sigma} } - \frac{ \Phi \left( -\kappa \, \bar{\sigma} + \frac{ \bar{\mu}_{it} }{ \bar{\sigma} } \right) \, \phi \left( \frac{ \bar{\mu}_{it} }{ \bar{\sigma} } \right)}{ \bar{\sigma} \, \Phi \left( \frac{ \bar{\mu}_{it} }{ \bar{\sigma}}\right) } - \kappa \, \Phi \left( -\kappa \, \bar{\sigma} + \frac{ \bar{\mu}_{it} }{ \bar{\sigma} } \right) \right),

where

\bar{\mu}_{it} = ( 1 - \gamma ) \, z_{it} ' \delta - \tau \, \gamma \, \epsilon_{it},

\bar{\sigma}^{2} = \gamma \, ( 1 - \gamma ) \, \sigma^{2},

\kappa = 1 in case of Farrell efficiencies (i.e. efficiencies have values between between 0 and 1), whereas \kappa = -1 otherwise (i.e. efficiencies have values larger than 1), and \tau = 1 if inefficiency decreases the dependent variable, whereas \tau = -1 otherwise (see Olsen and Henningsen 2011).

If argument asInData is FALSE, this attribute is a 3-dimensional array, where the first dimension represents the individual firm, the second deminsion represents the time period, and the third dimension represents the z variables. In contrast, if argument asInData is TRUE, this attribute is a matrix, where the rows represent the observations and the columns represent the z variables.

Author(s)

Arne Henningsen

References

Olsen, Jakob Vesterlund and Arne Henningsen (2011): Investment utilization and farm efficiency in Danish agriculture. FOI working paper 2011/13, Institute of Food and Resource Economics, University of Copenhagen, http://EconPapers.repec.org/RePEc:foi:wpaper:2011_13.

See Also

sfa, summary.frontier, and efficiencies.

Examples

   # rice producers in the Philippines (panel data)
   data( "riceProdPhil" )
   library( "plm" )
   riceProdPhil <- pdata.frame( riceProdPhil, c( "FMERCODE", "YEARDUM" ) )

   # Error Components Frontier (Battese & Coelli 1992), no time effect
   rice <- sfa( log( PROD ) ~ log( AREA ) + log( LABOR ) + log( NPK ),
      data = riceProdPhil )
   efficiencies( rice )
   riceProdPhil$efficiencies <- efficiencies( rice, asInData = TRUE )

   # efficiency of an 'average' farm
   efficiencies( rice, 
      newdata = data.frame( t( colMeans( riceProdPhil[ , -c(1,2) ] ) ) ) )

   # Error Components Frontier (Battese & Coelli 1992), with time effect
   riceTime <- sfa( log( PROD ) ~ log( AREA ) + log( LABOR ) + log( NPK ),
      data = riceProdPhil, timeEffect = TRUE )
   efficiencies( riceTime )
   riceProdPhil$efficienciesTime <- efficiencies( riceTime, asInData = TRUE )
   
   # Technical Efficiency Effects Frontier (Battese & Coelli 1995)
   rice2 <- sfa( log( PROD ) ~ log( AREA ) + log( LABOR ) + log( NPK ) |
      EDYRS + BANRAT - 1, data = riceProdPhil )
   eff <- efficiencies( rice2, margEff = TRUE )
   attr( eff, "margEff" )   # marginal effects

Elasticities of a Quadratic/Translog Frontier

Description

Calculate the elasticities of a quadratic or translog frontier function.

Usage

## S3 method for class 'frontierQuad'
elas( object, data = NULL, dataLogged = TRUE,
   yObs = FALSE, ... )

Arguments

Details

This method internally calls the functions translogEla and quadFuncEla.

Value

See documentation of translogEla and quadFuncEla.

Author(s)

Arne Henningsen

See Also

frontierQuad, translogEla, and quadFuncEla.

Examples

   # 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 )

   translog <- frontierQuad( yName = "logOutput",
      xNames = c( "logCapital", "logLabour" ),
      data = front41Data )
   elas( translog )

Fitted and Predicted (Frontier) Values

Description

This method returns the fitted and predicted “frontier” values from stochastic frontier models estimated with the frontier package (e.g. function sfa).

Usage

## S3 method for class 'frontier'
fitted( object, asInData = FALSE, ... )

## S3 method for class 'frontier'
predict( object, newdata = NULL, asInData = TRUE, ... )

Arguments

Value

If argument asInData is FALSE, a matrix of the fitted or predicted values is returned, where each row corresponds to a firm (cross-section unit) and each column corresponds to a time period.

If argument asInData is TRUE, a vector of fitted or predicted values is returned, where the fitted values are in the same order as the corresponding observations in the data set used for the estimation or the data set specified by argument newdata.

Author(s)

Arne Henningsen

See Also

sfa, fitted, predict.

Examples

   # rice producers in the Philippines (panel data)
   data( "riceProdPhil" )
   library( "plm" )
   riceProdPhil <- pdata.frame( riceProdPhil, c( "FMERCODE", "YEARDUM" ) )

   # Error Components Frontier (Battese & Coelli 1992), no time effect
   rice <- sfa( log( PROD ) ~ log( AREA ) + log( LABOR ) + log( NPK ),
      data = riceProdPhil )
   fitted( rice )
   riceProdPhil$fitted <- fitted( rice, asInData = TRUE )

   # Error Components Frontier (Battese & Coelli 1992), with time effect
   riceTime <- sfa( log( PROD ) ~ log( AREA ) + log( LABOR ) + log( NPK ),
      data = riceProdPhil, timeEffect = TRUE )
   fitted( riceTime )
   riceProdPhil$fittedTime <- fitted( riceTime, asInData = TRUE )

Data provided with Tim Coelli's Frontier 4.1

Description

The front41Data data frame contains cross-sectional data of 60 firms.

Usage

data(front41Data)

Format

This data frame contains the following columns:

firm

firm ID.

output

output quantity (value added).

capital

capital input quantity (quantity index).

labour

labour input quantity (quantity index).

Source

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.php, University of New England.

Estimate a Stochastic Frontier Model by Frontier 4.1

Description

Estimate a stochastic frontier model with a modified version of Tim Coelli's program Frontier 4.1 (NOTE: this program has to be installed separately!).

Usage

   front41Est( command = ifelse( .Platform$OS.type == "windows",
      "front41.exe", "front41.bin" ), ... )

Arguments

Details

Using the command front41Est requires the installation of a modified version of Tim Coelli's FRONTIER 4.1. It is available on http://frontier.r-forge.r-project.org/front41.html. as (FORTRAN) source code and (executable) binaries for GNU/Linux and MS-Windows.

Value

front41Est returns a list of class front41Output that is returned by front41ReadOutput with two additional elements:

Author(s)

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.php, University of New England.

See Also

front41WriteInput, front41ReadOutput

Examples

   data( front41Data )
   front41Data$logOutput  <- log( front41Data$output )
   front41Data$logCapital <- log( front41Data$capital )
   front41Data$logLabour  <- log( front41Data$labour )

   ## Not run: 
   front41Est( data = front41Data, crossSectionName = "firm",
      yName = "logOutput", xNames = c( "logCapital", "logLabour" ) )
   
## End(Not run)

Read output of Frontier 4.1

Description

Read the output file of Tim Coelli's program Frontier 4.1 that performs stochastic frontier analysis.

Usage

   front41ReadOutput( file = "front41.out" )

   ## S3 method for class 'front41Output'
print( x, efficiencies = FALSE, ... )

Arguments

Details

A modified version of Tim Coelli's FRONTIER 4.1 that can be used non-interactively is available on http://frontier.r-forge.r-project.org/front41.html. It can be called from within R using the system command (see example). This version is is available as (FORTRAN) source code and (executable) binaries for GNU/Linux and MS-Windows.

Value

a list of class front41Output containing following objects:

Author(s)

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.php, University of New England.

See Also

front41WriteInput, front41Est

Examples

   # read the output file that is provided with Frontier 4.1
   outFile <- system.file( "front41/EG1.OUT", package = "frontier" )
   sfa <- front41ReadOutput( outFile )
   print( sfa, efficiencies = TRUE )

   # perform an SFA and read the output
   data( front41Data )
   front41Data$logOutput  <- log( front41Data$output )
   front41Data$logCapital <- log( front41Data$capital )
   front41Data$logLabour  <- log( front41Data$labour )

   front41WriteInput( front41Data, "firm", yName = "logOutput",
      xNames = c( "logCapital", "logLabour" ), 
      path = tempdir(), insFile = "coelli.ins" )

   ## Not run: 
   system( paste0( "cd ", tempdir(), "; front41.bin coelli.ins" ) )
   sfa <- front41ReadOutput( file.path( tempdir(), "coelli.out" ) )
   summary( sfa )
   
## End(Not run)

Write input files for Frontier 4.1

Description

Write an instruction file, a data file, and a start-up file for Tim Coelli's program Frontier 4.1 that performs stochastic frontier analysis.

Usage

front41WriteInput( 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, path = ".",
   insFile = "front41.ins", dtaFile = sub( "\\.ins$", ".dta", insFile ),
   outFile = sub( "\\.ins$", ".out", insFile ), startUpFile = "front41.000",
   iprint = 5, indic = 1, tol = 0.00001, tol2 = 0.001, bignum = 1.0E+16,
   step1 = 0.00001, igrid2 = 1, gridno = 0.1, maxit = 100, ite = 1 )

Arguments

Details

A modified version of Tim Coelli's FRONTIER 4.1 that can be used non-interactively is available on http://frontier.r-forge.r-project.org/front41.html. It can be called from within R using the system command (see example). This version is is available as (FORTRAN) source code and (executable) binaries for GNU/Linux and MS-Windows.

Value

front41WriteInput writes an instruction file, a data file, and a start-up file for Frontier 4.1 to disk and it invisibly returns a list of class front41WriteInput. This list contains mainly the arguments with which front41WriteInput was called. An exception is element data, which is not the argument data but the data matrix that was written into the data file. Furthermore, in case of an Efficiency Effects Model, the element eta contains the number of Z variables. Additionally, the returned list contains following elements:

Author(s)

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.php, University of New England.

See Also

front41ReadOutput, front41Est

Examples

   data( front41Data )
   front41Data$logOutput  <- log( front41Data$output )
   front41Data$logCapital <- log( front41Data$capital )
   front41Data$logLabour  <- log( front41Data$labour )

   front41WriteInput( front41Data, "firm", yName = "logOutput",
      xNames = c( "logCapital", "logLabour" ), 
      path = tempdir(), insFile = "coelli.ins" )

   ## Not run: 
   system( paste0( "cd ", tempdir(), "; front41.bin coelli.ins" ) )
   sfa <- front41ReadOutput( file.path( tempdir(), "coelli.out" ) )
   summary( sfa )
   
## End(Not run)

Quadratic or Translog Frontiers

Description

This is a convenient interface for estimating quadratic or translog stochastic frontier functions using frontier.

Usage

frontierQuad( yName, xNames, shifterNames = NULL, zNames = NULL,
   data, lrTests = FALSE, ... )

Arguments

Value

frontierQuad returns a list of class frontierQuad (and frontier) containing the same elements as returned by frontier. If argument lrTest is set to TRUE, the returned object has a component lrTests that contains the results of likelihood-ratio tests of the statistical significance of each X variable.

Author(s)

Arne Henningsen

See Also

frontier.

Examples

   # 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 )

   # estimate the translog function
   translog <- frontierQuad( yName = "logOutput",
      xNames = c( "logCapital", "logLabour" ),
      data = front41Data )
   translog

   # estimate the same model using sfa()
   translog2 <- sfa( logOutput ~ logCapital + logLabour
      + I( 0.5 * logCapital^2 ) + I( logCapital * logLabour )
      + I( 0.5 * logLabour^2 ), data = front41Data )
   translog2
   all.equal( coef( translog ), coef( translog2 ),
      check.attributes = FALSE )

Translog Ray Frontiers

Description

This is a convenient interface for estimating translog stochastic ray frontier models using frontier.

Usage

frontierTranslogRay( yNames, xNames, shifterNames = NULL,
   zNames = NULL, data, ... )

Arguments

Value

frontierTranslogRay returns a list of class frontierTranslogRay (as well as frontierQuad and frontier) containing almost the same elements as returned by frontier. Additionally, it includes following objects:

Author(s)

Arne Henningsen and Geraldine Henningsen

References

Löthgren, M. (1997) Generalized stochastic frontier production models, Economics Letters, 57, 255-259.

Löthgren, M. (1997) A Multiple Output Stochastic Ray Frontier Production Model, Working Paper Series in Economics and Finance, No. 158, Stockholm School of Economics.

Löthgren, M. (2000) Specification and estimation of stochastic multiple-output production and technical inefficiency Applied Economics, 32, 1533-1540.

See Also

frontier, frontierQuad.

Examples

## preparing data
data( germanFarms )
# quantity of crop outputs
germanFarms$qCrop <- germanFarms$vCrop / germanFarms$pOutput
# quantity of animal outputs
germanFarms$qAnimal <- germanFarms$vAnimal / germanFarms$pOutput
# quantity of variable inputs
germanFarms$qVarInput <- germanFarms$vVarInput / germanFarms$pVarInput

# estimate a translog ray production function
estResultRay <- frontierTranslogRay( yNames = c( "qCrop", "qAnimal" ),
   xNames = c( "qLabor", "land", "qVarInput" ),
   data = germanFarms )
summary( estResultRay )

Extract Log-Likelihood Value

Description

Extract the log-likelihood value(s) from stochastic frontier models returned by frontier.

Usage

## S3 method for class 'frontier'
logLik( object, which = "mle", newParam = NULL, ... )

Arguments

Value

logLik.frontier returns an object of class logLik, which is a numeric scalar (the log-likelihood value) with 2 attributes: nobs (total number of observations in all equations) and df (number of free parameters, i.e. length of the coefficient vector).

Author(s)

Arne Henningsen

See Also

frontier.

Examples

   # example included in FRONTIER 4.1
   data( front41Data )

   # SFA estimation with starting values obtained from a grid search
   sfaResult <- sfa( log( output ) ~ log( capital ) + log( labour ),
      data = front41Data )
   logLik( sfaResult, which = "ols" )
   logLik( sfaResult, which = "grid" )
   logLik( sfaResult )

   # SFA estimation with starting values provided by the user
   sfaResult2 <- sfa( log( output ) ~ log( capital ) + log( labour ),
      data = front41Data, startVal = 0.9 * coef( sfaResult ) )
   logLik( sfaResult2, which = "ols" )
   logLik( sfaResult2, which = "start" )
   logLik( sfaResult2 )

   # evaluate log likelihood function for a user-provided parameter vector
   logLik( sfaResult, newParam = 0.9 * coef( sfaResult ) )
      # equal to  logLik( sfaResult2, which = "start" )

   # log likelihood function for different values of gamma
   plot( t( sapply( seq( 0.05, 0.95, 0.05 ), function(x) c( x,
      logLik( sfaResult, newParam = c( coef( sfaResult )[1:4], x ) ) ) ) ) )

Likelihood Ratio test for Stochastic Frontier Models

Description

Testing parameter restrictions in stochastic frontier models by a Likelihood Ratio test.

Usage

   ## S3 method for class 'frontier'
lrtest( object, ... )

Arguments

Details

If lrtest.frontier is called with only one argument/object (i.e. argument ... is not used), it compares the fitted model to a corresponding model without inefficiency (i.e. estimated by OLS).

If lrtest.frontier is called with more than one argument/object (i.e. argument ... is used), it consecutively compares the fitted model object object with the models passed in ....

The test statistic is 2 * ( logLik( mu ) - logLik( mr ) ), where mu is the unrestricted model and mr is the restricted model.

If a Frontier model (estimated by ML) is compared to a model without inefficiency (estimated by OLS), the test statistic asymptotically has a mixed \chi^2 distribution under the null hypothesis (see Coelli, 1995).

If two Frontier models (estimated by ML) are compared, the test statistic asymptotically has a \chi^2 distribution with j degrees of freedom under the null hypothesis, where j is the number of restrictions.

Value

An object of class anova, which contains the log-likelihood value, degrees of freedom, the difference in degrees of freedom, likelihood ratio Chi-squared statistic and corresponding p value. See documentation of lrtest in package "lmtest".

Author(s)

Arne Henningsen

References

Coelli, T.J. (1995), Estimators and Hypothesis Tests for a Stochastic: A Monte Carlo Analysis, Journal of Productivity Analysis, 6, 247-268.

See Also

sfa, lrtest

Examples

# rice producers in the Philippines (panel data)
data( "riceProdPhil" )
library( "plm" )
riceProdPhil <- pdata.frame( riceProdPhil, c( "FMERCODE", "YEARDUM" ) )

# Error Components Frontier with truncated normal distribution
# and time effects (unrestricted model)
mu <- sfa( log( PROD ) ~ log( AREA ) + log( LABOR ) + log( NPK ),
   truncNorm = TRUE, timeEffect = TRUE, data = riceProdPhil )

# Error Components Frontier with half-normal distribution
# without time effects (restricted model)
mr <- sfa( log( PROD ) ~ log( AREA ) + log( LABOR ) + log( NPK ),
   data = riceProdPhil )

## compare the two models by an LR-test
lrtest( mu, mr )

## compare each of the models to a corresponding model without inefficiency
lrtest( mu )
lrtest( mr )

RESET test for Stochastic Frontier Models

Description

Generalized Ramsey's RESET test (REgression Specification Error Test) for misspecification of the functional form based on a Likelihood Ratio test.

Usage

   resettestFrontier( object, power = 2:3 )

Arguments

Value

An object of class anova as returned by lrtest.frontier.

Author(s)

Arne Henningsen

References

Ramsey, J.B. (1969), Tests for Specification Error in Classical Linear Least Squares Regression Analysis. Journal of the Royal Statistical Society, Series B 31, 350-371.

See Also

sfa, resettest, and lrtest.frontier

Examples

   # load data set
   data( front41Data )

   # estimate a Cobb-Douglas production frontier
   cobbDouglas <- sfa( log( output ) ~ log( capital ) + log( labour ),
      data = front41Data )
   
   # conduct the RESET test
   resettestFrontier( cobbDouglas )

Returning Residuals

Description

This method returns the residuals from stochastic frontier models estimated with the frontier package (e.g. function sfa).

Usage

## S3 method for class 'frontier'
residuals( object, asInData = FALSE, ... )

Arguments

Value

If argument asInData is FALSE (default), a matrix of the residuals is returned, where each row corresponds to a firm (cross-section unit) and each column corresponds to a time period.

If argument asInData is TRUE, a vector of residuals is returned, where the residuals are in the same order as the corresponding observations in the data set used for the estimation.

Author(s)

Arne Henningsen

See Also

sfa, residuals.

Examples

   # rice producers in the Philippines (panel data)
   data( "riceProdPhil" )
   library( "plm" )
   riceProdPhil <- pdata.frame( riceProdPhil, c( "FMERCODE", "YEARDUM" ) )

   # Error Components Frontier (Battese & Coelli 1992), no time effect
   rice <- sfa( log( PROD ) ~ log( AREA ) + log( LABOR ) + log( NPK ),
      data = riceProdPhil )
   residuals( rice )
   riceProdPhil$residuals <- residuals( rice, asInData = TRUE )

   # Error Components Frontier (Battese & Coelli 1992), with time effect
   riceTime <- sfa( log( PROD ) ~ log( AREA ) + log( LABOR ) + log( NPK ),
      data = riceProdPhil, timeEffect = TRUE )
   residuals( riceTime )
   riceProdPhil$residualsTime <- residuals( riceTime, asInData = TRUE )

Rice Production in the Philippines

Description

The riceProdPhil data frame contains annual data collected from 43 smallholder rice producers in the Tarlac region of the Philippines between 1990 and 1997.

Usage

data( riceProdPhil )

Format

This data frame contains the following variables (columns):

YEARDUM

Time period (1= 1990, ..., 8 = 1997).

FMERCODE

Farmer code (1, ..., 43).

PROD

Output (tonnes of freshly threshed rice).

AREA

Area planted (hectares).

LABOR

Labour used (man-days of family and hired labour).

NPK

Fertiliser used (kg of active ingredients).

OTHER

Other inputs used (Laspeyres index = 100 for Firm 17 in 1991).

PRICE

Output price (pesos per kg).

AREAP

Rental price of land (pesos per hectare).

LABORP

Labour price (pesos per hired man-day.

NPKP

Fertiliser price (pesos per kg of active ingredient).

OTHERP

Price of other inputs (implicit price index).

AGE

Age of the household head (years).

EDYRS

Education of the household head (years).

HHSIZE

Household size.

NADULT

Number of adults in the household.

BANRAT

Percentage of area classified as bantog (upland) fields.

Details

This data set is published as supplement to Coelli et al. (2005). While most variables of this data set were supplied by the International Rice Research Institute (IRRI), some were calculated by Coelli et al. (2005, see p. 325–326). The survey is described in Pandey et al. (1999).

Source

Supplementary files for Coelli et al. (2005), http://www.uq.edu.au/economics/cepa/crob2005/software/CROB2005.zip

References

Coelli, T. J., Rao, D. S. P., O'Donnell, C. J., and Battese, G. E. (2005) An Introduction to Efficiency and Productivity Analysis, Springer, New York.

Pandey, S., Masciat, P., Velasco, L, and Villano, R. (1999) Risk analysis of a rainfed rice production system system in Tarlac, Central Luzon, Philippines, Experimental Agriculture, 35, 225-237.

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

sfa( formula, data = sys.frame( sys.parent() ),
   ineffDecrease = TRUE, truncNorm = 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,
   restartMax = 10, restartFactor = 0.999, printIter = 0 )

frontier( yName, xNames = NULL, zNames = NULL, data,
   zIntercept = FALSE, ... )

## S3 method for class 'frontier'
print( x, digits = NULL, ... )

Arguments

Details

Function frontier is a wrapper function that calls sfa for the estimation. The two functions differ only in the user interface; function frontier has the “old” user interface and is kept to maintain compatibility with older versions of the frontier package.

One can use functions sfa and frontier 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 formula of sfa is a (usual) one-part formula (or argument zNames of frontier is NULL), an ‘Error Components Frontier’ (ECF, see Battese and Coelli 1992) is estimated. If argument formula is a two-part formula (or zNames is not NULL), an ‘Efficiency Effects Frontier’ (EEF, see Battese and Coelli 1995) is estimated. In this case, the first part of the formula (i.e. the part before the “|” symbol) is used to explain the endogenous variable directly (X variables), while the second part of the formula (i.e. the part after the “|” symbol) is used to explain the efficiency levels (Z variables). Generally, there should be no reason for estimating an EEF without Z variables, but this can done by setting the second part of argument formula to 1 (with Z intercept) or - 1 (without Z intercept) (or 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 \pmmuBound * \sigma_u, where \sigma_u is the standard deviation of u. If muBound is infinity, zero, or negative, no bounds on \mu are imposed.

Value

sfa and frontier return a list of class frontier containing following elements:

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.php, University of New England.

Himmelblau, D.M. (1972), Applied Non-Linear Programming, McGraw-Hill, New York.

See Also

frontierQuad for quadratic/translog frontiers, summary.frontier for creating and printing summary results, efficiencies.frontier for calculating efficiency estimates, lrtest.frontier for comparing models by LR tests, fitted.frontier for obtaining the fitted “frontier” values, ang residuals.frontier for obtaining the residuals.

Examples

   # example included in FRONTIER 4.1 (cross-section data)
   data( front41Data )

   # Cobb-Douglas production frontier
   cobbDouglas <- sfa( log( output ) ~ log( capital ) + log( labour ),
      data = front41Data )
   summary( cobbDouglas )

   # load data about rice producers in the Philippines (panel data)
   data( riceProdPhil )

   # Error Components Frontier (Battese & Coelli 1992)
   # with observation-specific efficiencies (ignoring the panel structure)
   rice <- sfa( log( PROD ) ~ log( AREA ) + log( LABOR ) + log( NPK ),
      data = riceProdPhil )
   summary( rice )

   # Error Components Frontier (Battese & Coelli 1992)
   # with "true" fixed individual effects and observation-specific efficiencies
   riceTrue <- sfa( log( PROD ) ~ log( AREA ) + log( LABOR ) + log( NPK ) + 
      factor( FMERCODE ),  data = riceProdPhil )
   summary( riceTrue )

   # add data set with information about its panel structure
   library( "plm" )
   ricePanel <- pdata.frame( riceProdPhil, c( "FMERCODE", "YEARDUM" ) )

   # Error Components Frontier (Battese & Coelli 1992)
   # with time-invariant efficiencies
   riceTimeInv <- sfa( log( PROD ) ~ log( AREA ) + log( LABOR ) + log( NPK ),
      data = ricePanel )
   summary( riceTimeInv )

   # Error Components Frontier (Battese & Coelli 1992)
   # with time-variant efficiencies
   riceTimeVar <- sfa( log( PROD ) ~ log( AREA ) + log( LABOR ) + log( NPK ),
      data = ricePanel, timeEffect = TRUE )
   summary( riceTimeVar )

   # Technical Efficiency Effects Frontier (Battese & Coelli 1995)
   # (efficiency effects model with intercept)
   riceZ <- sfa( log( PROD ) ~ log( AREA ) + log( LABOR ) + log( NPK ) |
      EDYRS + BANRAT, data = riceProdPhil )
   summary( riceZ )

   # Technical Efficiency Effects Frontier (Battese & Coelli 1995)
   # (efficiency effects model without intercept)
   riceZ2 <- sfa( log( PROD ) ~ log( AREA ) + log( LABOR ) + log( NPK ) |
      EDYRS + BANRAT - 1, data = riceProdPhil )
   summary( riceZ2 )

   # Cost Frontier (with land as quasi-fixed input)
   riceProdPhil$cost <- riceProdPhil$LABOR * riceProdPhil$LABORP +
      riceProdPhil$NPK * riceProdPhil$NPKP
   riceCost <- sfa( log( cost ) ~ log( PROD ) + log( AREA ) + log( LABORP )
      + log( NPKP ), data = riceProdPhil, ineffDecrease = FALSE )
   summary( riceCost )

Summarizing the Estimation of Frontier 4.1

Description

summary.front41Output summarizes the estimation results of a model estimated by Frontier 4.1..

Usage

## S3 method for class 'front41Output'
summary( object, ... )

## S3 method for class 'summary.front41Output'
print( x, efficiencies = FALSE, ... )

Arguments

Value

The summary method returns a list of class summary.front41Output with the same elements as object returned by front41ReadOutput. However, the elements olsResults, gridResults, and mleResults have an additional culumn with marginal significance levels (P values). The P values of the OLS estimates are calculated using the t distribution, while the (asymptotic) P values of the ML estimates are calculated based on the assumption that their t values follow an (asymptotic) standard normal distribution.

Author(s)

Arne Henningsen

See Also

front41ReadOutput, front41WriteInput.

Examples

   # read the output file that is provided with Frontier 4.1
   outFile <- system.file( "front41/EG1.OUT", package = "frontier" )
   sfa <- front41ReadOutput( outFile )
   summary( sfa )

summary method for class frontier

Description

Create and print summary results of a stochastic frontier analysis returned by frontier.

Usage

## S3 method for class 'frontier'
summary( object, extraPar = FALSE, effic = FALSE,
   logDepVar = TRUE, effMinusU = farrell, farrell = TRUE, ... )
## S3 method for class 'summary.frontier'
print( x, effic = x$printEffic, ... )

Arguments

Details

The standard errors of the estimated parameters are taken from the direction matrix that is used in the final iteration of the Davidon-Fletcher-Powell procedure that is used for maximising the (log) likelihood function.

If argument extraPar is TRUE, the standard errors of the additional parameters are obtained by the delta method. Please note that the delta method might provide poor approximations of the ‘true’ standard errors, because parameter \sigma^2 is left-censored and parameter \gamma is both left-censored and right-censored so that these parameters cannot be normally distributed.

Please note further that the t statistic and the z statistic are not reliable for testing the statistical signicance of \sigma^2, \gamma, and the ‘additional parameters’, because these parameters are censored and cannot follow a normal distribution or a t distribution.

Value

summary.frontier returns a list of class summary.frontier that is identical to an object returned by frontier with two modifications and (up to) four additional elements:

Author(s)

Arne Henningsen

See Also

sfa, efficiencies.frontier, vcov.frontier, and lrtest.frontier.

Examples

   # example included in FRONTIER 4.1 (cross-section data)
   data( front41Data )

   sfaResult <- sfa( log( output ) ~ log( capital ) + log( labour ),
      data = front41Data )
   summary( sfaResult )

   # rice producers in the Phillipines (panel data)
   data( "riceProdPhil" )
   library( "plm" )
   riceProdPhil <- pdata.frame( riceProdPhil, c( "FMERCODE", "YEARDUM" ) )

   # Error Components Frontier
   rice <- sfa( log( PROD ) ~ log( AREA ) + log( LABOR ) + log( NPK ),
      data = riceProdPhil )
   summary( rice )

   # Efficiency Effects Frontier
   rice2 <- sfa( log( PROD ) ~ log( AREA ) + log( LABOR ) + log( NPK ) |
      EDYRS + BANRAT, data = riceProdPhil )
   summary( rice2 )

Telecommunications Providers

Description

The telecom data frame contains data on telecommunications providers in 21 countries in 1990.

Usage

data( telecom )

Format

This data frame contains the following variables (columns):

country

The name of the country.

output

Output (index).

mainlines

Mainlines (M km).

employees

Number of employees (10,000 persons).

Source

Supplementary files for Coelli et al. (1998), p. 193.

References

Coelli, T. J., Rao, D. S. P., and Battese, G. E. (1998) An Introduction to Efficiency and Productivity Analysis, Springer, New York.

vcov method for class frontier

Description

Extract the covariance matrix of the maximum likelihood coefficients of a stochastic frontier model returned by frontier.

Usage

## S3 method for class 'frontier'
vcov( object, extraPar = FALSE, ... )

Arguments

Details

The variance-covariance matrix of the estimated parameters is taken from the direction matrix that is used in the final iteration of the Davidon-Fletcher-Powell procedure that is used for maximising the (log) likelihood function.

If argument extraPar is TRUE, the variances and covariances of the additional parameters are obtained by the delta method. Please note that the delta method might provide poor approximations of the ‘true’ variances and covariances, because parameter \sigma^2 is left-censored and parameter \gamma is both left-censored and right-censored so that these parameters cannot be normally distributed.

Please note further that it might not be appropriate to use standard statistical tests (e.g. t-tests or other Wald tests) that are based on the variances and covariances of \sigma^2, \gamma, and the ‘additional parameters’, because these parameters are censored and cannot follow normal distributions.

Value

vcov.frontier returns the covariance matrix of the maximum likelihood coefficients.

Author(s)

Arne Henningsen

See Also

coef.frontier, coef.summary.frontier, summary.frontier, and sfa.

Examples

   # example included in FRONTIER 4.1
   data( front41Data )

   sfaResult <- sfa( log( output ) ~ log( capital ) + log( labour ),
      data = front41Data )
   vcov( sfaResult )