summary.frontier: summary method for class frontier

In frontier: Stochastic Frontier Analysis

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

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.

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:

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).

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 )

Example output

Loading required package: micEcon

If you have questions, suggestions, or comments regarding one of the 'micEcon' packages, please use a forum or 'tracker' at micEcon's R-Forge site:
https://r-forge.r-project.org/projects/micecon/
Loading required package: lmtest
Loading required package: zoo

Attaching package: 'zoo'

The following objects are masked from 'package:base':

    as.Date, as.Date.numeric


Please cite the 'frontier' package as:
Tim Coelli and Arne Henningsen (2013). frontier: Stochastic Frontier Analysis. R package version 1.1. http://CRAN.R-Project.org/package=frontier.

If you have questions, suggestions, or comments regarding the 'frontier' package, please use a forum or 'tracker' at frontier's R-Forge site:
https://r-forge.r-project.org/projects/frontier/
Error Components Frontier (see Battese & Coelli 1992)
Inefficiency decreases the endogenous variable (as in a production function)
The dependent variable is logged
Iterative ML estimation terminated after 7 iterations:
log likelihood values and parameters of two successive iterations
are within the tolerance limit

final maximum likelihood estimates
             Estimate Std. Error z value  Pr(>|z|)    
(Intercept)  0.561619   0.202617  2.7718 0.0055742 ** 
log(capital) 0.281102   0.047643  5.9001 3.632e-09 ***
log(labour)  0.536480   0.045252 11.8555 < 2.2e-16 ***
sigmaSq      0.217000   0.063909  3.3955 0.0006851 ***
gamma        0.797207   0.136424  5.8436 5.109e-09 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
log likelihood value: -17.02722 

cross-sectional data
total number of observations = 60 

mean efficiency: 0.7405678 
Loading required package: Formula
Error Components Frontier (see Battese & Coelli 1992)
Inefficiency decreases the endogenous variable (as in a production function)
The dependent variable is logged
Iterative ML estimation terminated after 11 iterations:
log likelihood values and parameters of two successive iterations
are within the tolerance limit

final maximum likelihood estimates
             Estimate Std. Error z value  Pr(>|z|)    
(Intercept) -0.832169   0.275249 -3.0233    0.0025 ** 
log(AREA)    0.453897   0.063801  7.1143 1.125e-12 ***
log(LABOR)   0.288924   0.063639  4.5400 5.625e-06 ***
log(NPK)     0.227544   0.040859  5.5690 2.562e-08 ***
sigmaSq      0.155377   0.024202  6.4201 1.362e-10 ***
gamma        0.464312   0.088023  5.2749 1.328e-07 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
log likelihood value: -86.43042 

panel data
number of cross-sections = 43 
number of time periods = 8 
total number of observations = 344 
thus there are 0 observations not in the panel

mean efficiency: 0.8187968 
Efficiency Effects Frontier (see Battese & Coelli 1995)
Inefficiency decreases the endogenous variable (as in a production function)
The dependent variable is logged
Iterative ML estimation terminated after 47 iterations:
log likelihood values and parameters of two successive iterations
are within the tolerance limit

final maximum likelihood estimates
               Estimate Std. Error z value  Pr(>|z|)    
(Intercept)   -1.051760   0.252988 -4.1573 3.220e-05 ***
log(AREA)      0.379767   0.059976  6.3320 2.420e-10 ***
log(LABOR)     0.321029   0.061125  5.2520 1.504e-07 ***
log(NPK)       0.263797   0.034458  7.6555 1.925e-14 ***
Z_(Intercept) -2.746459   8.499182 -0.3231    0.7466    
Z_EDYRS       -0.028610   0.215997 -0.1325    0.8946    
Z_BANRAT      -3.635528   8.096562 -0.4490    0.6534    
sigmaSq        1.666588   3.695869  0.4509    0.6520    
gamma          0.978799   0.045203 21.6536 < 2.2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
log likelihood value: -77.31363 

panel data
number of cross-sections = 43 
number of time periods = 8 
total number of observations = 344 
thus there are 0 observations not in the panel

mean efficiency of each year
        1         2         3         4         5         6         7         8 
0.7619359 0.7505762 0.8311524 0.8118776 0.7641510 0.8081221 0.7049660 0.8466347 

mean efficiency: 0.784927 

frontier documentation built on April 19, 2020, 3:54 p.m.