a stochastic frontier model object returned by semsfa()
log.output
logical. Is the dependent variable logged?
...
further arguments to the summary method are currently ignored
Details
The estimation of the individual efficiency score for a particular point (x,y) on a production frontier might be obtained from the Jondrow et al. (1982) procedure. Defining:
where f and F represent the standard Normal density and cumulative distribution function, respectively; alternative formulas for cost frontier models are easy to get (please see Kumbhakar and Lovell, 2000).
If the response variable is measured in logs, a point estimate of the efficiency is then provided by exp(-u) in (0,1); otherwise, (fitt-u)/fitt where fitt is the estimated output evaluated at the frontier, given the inputs.
Value
An object of class semsfa containing the following additional results:
u
the prediction of the individual efficiency score
efficiencies
point estimate of the efficiency
Author(s)
Giancarlo Ferrara and Francesco Vidoli
References
Jondrow, J., Lovell, C.A.K., Materov, I.S., Schmidt, P., 1982. On the estimation of technical inefficiency in
stochastic frontier production models. Journal of Econometrics 19, 233-238.
Kumbhakar, S.C., Lovell, C.A.K., 2000. Stochastic Frontier Analysis. Cambridge University Press, New York.
See Also
semsfa, summary.semsfa, plot.semsfa.
Examples
set.seed(0)
n<-200
#generate data
x<- runif(n, 1, 2)
fy<- 2+30*x-5*x^2
v<- rnorm(n, 0, 1)
u<- abs(rnorm(n,0,2.5))
#production frontier
y <- fy + v - u
dati<-data.frame(y,x)
#first-step: gam, second-step: fan (default)
o<-semsfa(y~s(x),dati,sem.method="gam")
#calculate efficiencies
a<-efficiencies.semsfa(o)