efficiencies.semsfa {semsfa} | R Documentation |
This function calculates and returns efficiency estimates from semiparametric stochastic frontier models estimated with semsfa()
.
efficiencies.semsfa(semobj, log.output = TRUE, ...)
semobj |
a stochastic frontier model object returned by |
log.output |
logical. Is the dependent variable logged? |
... |
further arguments to the summary method are currently ignored |
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:
\sigma^2=\sigma_u^2+\sigma_v^2, u_{*}(x) = -\sigma_u^2 \epsilon/\sigma^2, \sigma_{*}^2=\sigma_u^2 \sigma_v^2/\sigma^2
it can be shown that:
u|\epsilon ~ N^+(\mu_{*}(x),\sigma_{*}^{2}(x)).
We can use this distribution to obtain point previsions of u
trought the mean of the conditional distribution:
E(u|\epsilon)=\mu_{*} + \sigma_{*} f(-\mu_{*}/\sigma_{*})/(1-F(\mu_{*}/\sigma_{*}))
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.
An object of class semsfa
containing the following additional results:
u |
the prediction of the individual efficiency score |
efficiencies |
point estimate of the efficiency |
Giancarlo Ferrara and Francesco Vidoli
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.
semsfa
, summary.semsfa
, plot.semsfa
.
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)