frontierTranslogRay: Translog Ray Frontiers
In frontier: Stochastic Frontier Analysis

Description Usage Arguments Value Author(s) References See Also Examples

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

1 2	frontierTranslogRay( yNames, xNames, shifterNames = NULL, zNames = NULL, data, ... )

`yNames`	a vector of two or more character strings containing the names of the output variables.
`xNames`	a vector of strings containing the names of the input variables that should be included as linear, quadratic, and interaction terms.
`shifterNames`	a vector of strings containing the names of the explanatory variables that should be included as shifters only (not in quadratic or interaction terms).
`zNames`	a vector of strings containing the names of the Z variables (variables explaining the efficiency level).
`data`	a (panel) data frame that contains the data (see documentation of `frontier`) NOTE: the variables defined by arguments `yNames` and `xNames` must be in natural units; the variables defined by argument `xNames` are logarithmized internally; the variables defined by arguments `shifterNames` and `zNames` are NOT logarithmized internally and hence must be specified as they should be used in the model.
`...`	further arguments passed to `frontierQuad` and possibly further to `frontier`.

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:

`distance`	the “distance” from the origin (zero) to the point of the dependent variables.
`theta_i`	the “direction” from the origin (zero) to the point of the dependent variables (with `i` = 1, ..., N-1 and N is the number of outputs).

Arne Henningsen and Geraldine Henningsen

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

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

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

frontier, frontierQuad.

## 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 )

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/
restarting with starting values multiplied by
[1] 0.999
Warning messages:
1: In sfa(formula = sfaFormula, data = data, ...) :
  the residuals of the OLS estimates are right-skewed and the likelihood value of the ML estimation is less than that obtained using OLS; this usually indicates that there is no inefficiency or that the model is misspecified
2: In sfa(formula = sfaFormula, data = data, ...) :
  the parameter 'gamma' is close to the boundary of the parameter space [0,1]: this can cause convergence problems and can negatively affect the validity and reliability of statistical tests and might be caused by model misspecification
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 19 iterations:
log likelihood values and parameters of two successive iterations
are within the tolerance limit
Multiplied the initial values 1 time(s) by 0.999 before the search procedure could start
You could try to use different starting values or try to reduce the step size specified in argument 'searchStep'

final maximum likelihood estimates
           Estimate  Std. Error   z value  Pr(>|z|)    
a_0     -1.1363e+02  9.6590e-01 -117.6425 < 2.2e-16 ***
a_1     -6.0431e+01  9.8998e-01  -61.0434 < 2.2e-16 ***
a_2      8.7865e+01  8.8858e-01   98.8826 < 2.2e-16 ***
a_3     -7.0398e+01  5.3416e-01 -131.7926 < 2.2e-16 ***
a_t1     3.3140e+02  9.7905e-01  338.4911 < 2.2e-16 ***
b_1_1   -2.5341e+01  9.9934e-01  -25.3581 < 2.2e-16 ***
b_1_2    1.2099e+01  9.1149e-01   13.2738 < 2.2e-16 ***
b_1_3   -1.7739e+01  5.0020e-01  -35.4639 < 2.2e-16 ***
b_1_t1   1.1418e+02  9.8398e-01  116.0431 < 2.2e-16 ***
b_2_2   -6.7051e+00  8.6451e-01   -7.7560 8.763e-15 ***
b_2_3   -3.6261e+00  4.7896e-01   -7.5708 3.709e-14 ***
b_2_t1  -3.5665e+01  8.7930e-01  -40.5611 < 2.2e-16 ***
b_3_3    1.6567e+01  3.0631e-01   54.0856 < 2.2e-16 ***
b_3_t1  -1.3646e+01  4.8508e-01  -28.1317 < 2.2e-16 ***
b_t1_t1 -1.3370e+02  9.8486e-01 -135.7540 < 2.2e-16 ***
sigmaSq  9.3204e-05  3.1047e-05    3.0021  0.002682 ** 
gamma    4.8633e-03  7.0233e-02    0.0692  0.944795    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
log likelihood value: 64.45806 

cross-sectional data
total number of observations = 20 

mean efficiency: 0.999463