efficiencies.semsfa: Prediction of the individual efficiency score
In semsfa: Semiparametric Estimation of Stochastic Frontier Models

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 `semsfa()`
`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.

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)

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]