| Type: | Package |
| Title: | Copula-Based Simultaneous Stochastic Frontier Models |
| Version: | 0.1.0 |
| Description: | Provides estimation procedures for copula-based stochastic frontier models for cross-sectional data. The package implements maximum likelihood estimation of stochastic frontier models allowing flexible dependence structures between inefficiency and noise terms through various copula families (e.g., Gaussian and Student-t). It enables estimation of technical efficiency scores, log-likelihood values, and information criteria (AIC and BIC). The implemented framework builds upon stochastic frontier analysis introduced by Aigner, Lovell and Schmidt (1977) <doi:10.1016/0304-4076(77)90052-5> and the copula theory described in Joe (2014, ISBN:9781466583221). Empirical applications of copula-based stochastic frontier models can be found in Wiboonpongse et al. (2015) <doi:10.1016/j.ijar.2015.06.001> and Maneejuk et al. (2017, ISBN:9783319562176). |
| License: | GPL-3 |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.3.3 |
| Imports: | stats, graphics, truncnorm, VineCopula |
| NeedsCompilation: | no |
| Packaged: | 2026-02-15 04:02:34 UTC; Acer |
| Author: | Woraphon Yamaka [aut, cre], Paravee Maneejuk [aut], Nuttaphong Kaewtathip [aut] |
| Maintainer: | Woraphon Yamaka <woraphon.econ@gmail.com> |
| Repository: | CRAN |
| Date/Publication: | 2026-02-18 19:00:02 UTC |
Technical efficiency measure.
Description
Computing and plotting the technical efficiency.
Usage
TE1(theta,Y,X,family)
Arguments
theta |
The estimated parameters form the model |
Y |
Vector of dependent variable |
X |
Matrix of independent variable |
family |
Copula function eg. Gaussain=1, Student-t=2 (see, Vinecopula package) |
Details
Computing and plotting the technical efficiency.
Value
- Output
Technical efficiency series.
- plot
Plot of technical efficiency.
Author(s)
Woraphon Yamaka
References
Wiboonpongse, A., Liu, J., Sriboonchitta, S., & Denoeux, T. (2015). Modeling dependence between error components of the stochastic frontier model using copula: application to intercrop coffee production in Northern Thailand. International Journal of Approximate Reasoning, 65, 34-44.
Examples
## Required packages
#example simulation data
data=sfa.simu(nob=50, alpha=c(1,2,0.5),sigV=1,sigU=0.5,family=1,rho=0.5)
# Select familty copula upper and lower bouubd ( look at CDVine package)
# family=1 # 1 is Gaussian, 2 is Student-t, 3 is Clayton and so on....
#Gaussian (-.99, .99)
#Student t (-.99, .99)
#Clayton (0.1, Inf)
model=copSFM(Y=data$Y,X=data$X,family=1,RHO=0.5,LB=-0.99,UB=0.99)
#EX: Plot the technical efficiency
te1=TE1(model$result[,1],Y=data$Y,X=data$X,family=1)
Copula based Stochastic frontier Model
Description
In the standard stochastic frontier model, the two-sided error term V and the one-sided technical inefficiency error term W are assumed to be independent. In this paper, we relax this assumption by modeling the dependence between V and W using copulas. Nine copula families are considered and their parameters are estimated using maximum simulated likelihood.
Usage
copSFM(Y,X,family,RHO,LB,UB,verbose = FALSE)
Arguments
Y |
vector of dependent variable |
X |
matrix of independent variable |
family |
Copula function eg. Gaussain=1, Student-t=2 (see, Vinecopula package) |
RHO |
The initail value of the copula parameter |
LB |
The lower bound of the copula parameter |
UB |
The upper bound of the copula parameter |
verbose |
Logical; if TRUE, prints progress messages during optimization. |
Details
herefore, the above copula families and relevant rotated copula can potentially capture the appropriate dependence between two random variables. Other popular copula families, such as Gaussain, Student,t Clayton, Gumbel etc.
Value
result |
The result contain the estimated parameters, standard errors, t-stat, and p-value |
AIC |
Akaiki Information Criteria |
BIC |
Bayesian Information Criteria |
Loglikelihood |
Maximum Log-likelihood function |
Author(s)
Woraphon Yamaka and Paravee MAneejuk
References
Wiboonpongse, A., Liu, J., Sriboonchitta, S., & Denoeux, T.(2015). Modeling dependence between error components of the stochastic frontier model using copula: application to intercrop coffee production in Northern Thailand. International Journal of Approximate Reasoning, 65, 34-44.
Maneejuk, P., Yamaka, W., & Sriboonchitta, S.(2017). Analysis of global competitiveness using copula-based stochastic frontier kink model. In Robustness in Econometrics (pp. 543-559). Springer, Cham.
Examples
#example simulation data
data=sfa.simu(nob=50, alpha=c(1,2,0.5),sigV=1,sigU=0.5,family=1,rho=0.5)
# Select familty copula upper and lower bouubd ( look at CDVine package)
# family=1 # 1 is Gaussian, 2 is Student-t, 3 is Clayton and so on....
#Gaussian (-.99, .99)
#Student t (-.99, .99)
#Clayton (0.1, Inf)
model=copSFM(Y=data$Y,X=data$X,family=1,RHO=0.5,LB=-0.99,UB=0.99)
Simulate Data for Stochastic Frontier Analysis
Description
Simulates data for the copula-based stochastic frontier model.
Usage
sfa.simu(nob, alpha, sigV, sigU, family, rho)
Arguments
nob |
Number of observations. |
alpha |
Coefficient vector. |
sigV |
Standard deviation of noise term V. |
sigU |
Standard deviation of inefficiency term U. |
family |
Copula family code. |
rho |
Copula dependence parameter. |
Value
A list containing simulated output and inputs.
Examples
set.seed(1)
sim <- sfa.simu(nob = 20, alpha = c(1, 0.5, -0.2), sigV = 1, sigU = 1, family = 1, rho = 0.2)