| efficiencies.frontier {frontier} | R Documentation |
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
object |
a stochastic frontier model
returned by |
asInData |
logical. If |
logDepVar |
logical. Is the dependent variable logged? |
minusU |
logical. If |
farrell |
logical. This argument is only kept for backward compatibility and will be removed in the future. |
margEff |
logical. If |
newdata |
an optional data frame from which the values
of explanatory variables and the dependent variable are taken
to calculate the efficiency estimates.
If this argument is |
... |
currently ignored. |
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