frontier (version 1.1-8)

summary.frontier: summary method for class frontier

Description

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

Usage

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

Arguments

object

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

x

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

extraPar

logical. If TRUE, some additional parameters, their standard errors, z-values, and P values are returned: sigmaSqU = sigmaSq * gamma (with \(u\) ~ \(N^+\)( mu, sigmaSqU )), sigmaSqV = sigmaSq * ( 1 - gamma ) (with \(v\) ~ N( 0, sigmaSqV )), sigma = sigmaSq^0.5, sigmaU = sigmaSqU^0.5, sigmaV = sigmaSqV^0.5, lambdaSq = sigmaSqU / sigmaSqV, and lambda = sigmaU / sigmaV. Please note that sigmaSqU and sigmaU are not the variance and standard error, respectively, of \(u\). If the model is an error components frontier, also the following additional parameters are returned: varU = the variance of \(u\), sdU = varU^0.5, and gammaVar = varU / ( varU + sigmaSqV ). Please note that the variance of \(u\) usually differs between observations if the model is an error component frontier with ‘time effect’ or an efficiency effects frontier.

effic

logical. Print the individual efficiency estimates?

logDepVar

logical. Is the dependent variable logged?

effMinusU

logical. If TRUE (the default), the efficiencies are calculated by E[exp(-u)]. If FALSE, the efficiencies are calculated by E[exp(u)]. For details, see documentation of argument minusU of efficiencies.frontier.

farrell

logical. This argument is only kept for backward compatibility and will be removed in the future.

…

further arguments to the summary method are currently ignored; further arguments to the print method are forwarded to printCoefmat.

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:

olsParam

matrix of OLS estimates, their standard errors, t-values, and P-values.

mleParam

matrix of ML estimates, their standard errors, z-values, and asymptotic P-values.

logDepVar

logical. Argument logDepVar (see above).

printEffic

argument effic.

effic

matrix. Efficiency estimates: each row corresponds to a cross-section; each column corresponds to a time period.

efficMean

numeric scalar. Mean efficiency.

efficYearMeans

numeric vector. Mean efficiency for each year in the sample (only for panel data but not for the Error Components Frontier without time effects).

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.

See Also

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

Examples

# NOT RUN {
   # 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 )
# }