Description Usage Arguments Details Value Author(s) References See Also Examples
This function calculates and returns efficiency estimates from semiparametric stochastic frontier models estimated with semsfa()
.
1 | 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:
σ^2=σ_u^2+σ_v^2, u_{*}(x) = -σ_u^2 ε/σ^2, σ_{*}^2=σ_u^2 σ_v^2/σ^2
it can be shown that:
u|ε ~ N^+(μ_{*}(x),σ_{*}^{2}(x)).
We can use this distribution to obtain point previsions of u trought the mean of the conditional distribution:
E(u|ε)=μ_{*} + σ_{*} f(-μ_{*}/σ_{*})/(1-F(μ_{*}/σ_{*}))
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
.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | 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)
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Loading required package: mgcv
Loading required package: nlme
This is mgcv 1.8-17. For overview type 'help("mgcv-package")'.
Loading required package: np
Nonparametric Kernel Methods for Mixed Datatypes (version 0.60-3)
[vignette("np_faq",package="np") provides answers to frequently asked questions]
[vignette("np",package="np") an overview]
[vignette("entropy_np",package="np") an overview of entropy-based methods]
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