dea_robust: Bias-corrected data envelopment analysis

In jaak-s/rDEA: Robust Data Envelopment Analysis (DEA) for R

Bias-corrected data envelopment analysis

Description

Estimates bias-corrected scores for input- and output-oriented models

Usage

dea.robust (X, Y, W=NULL, model, RTS="variable", B=1000, alpha=0.05, 
            bw="bw.ucv", bw_mult=1)

Arguments

X	a matrix of inputs for observations, for which DEA scores are estimated.
Y	a matrix of outputs for observations, for which DEA scores are estimated.
W	a matrix of input prices, only used if model="costmin".
model	a string for the type of DEA model to be estimated, "input" for input-oriented, "output" for output-oriented, "costmin" for cost-minimization model.
RTS	a string for returns-to-scale under which DEA scores are estimated, RTS can be "constant", "variable" or "non-increasing".
B	an integer showing the number of bootstrap replications, the default is B=1000.
alpha	a number in (0,1) for the size of confidence interval for the bias-corrected DEA score.
bw	a string for the type of bandwidth used as a smoothing parameter in sampling with reflection, "cv" or "bw.ucv" for cross-validation bandwidth, "silverman" or "bw.nrd0" for Silverman's (1986) rule.
bw_mult	bandwidth multiplier, default is 1 that means no change.

Details

Implements Simar and Wilson's (1998) bias-correction of technical efficiency scores in input- and output-oriented DEA models.

Value

A list containing bias-corrected scores for each firm, with the following components.

theta_hat_hat	the vector of bias-corrected DEA score for each firm, theta_hat_hat is in the range of zero to one.
bias	the vector of bias for naive DEA scores, bias is non-negative.
theta_ci_low	the vector for the lower bounds of confidence interval for bias-corrected DEA score.
theta_ci_high	the vector for the upper bounds of confidence interval for bias-corrected DEA score.

Author(s)

Jaak Simm, Galina Besstremyannaya

References

Silverman, B.W. 1986. Density Estimation for Statistics and Data Analysis.Chapman and Hall, New York.

Simar, L. and Wilson, P.W. 1998. Sensitivity analysis of efficiency scores: how to bootstrap in nonparametric frontier models. Management Science. Vol.44, pp.49–61.

Simar, L. and Wilson, P. 2000. A general methodology for bootstrapping in non-parametric frontier models. Journal of Applied Statistics. Vol.27, No.6, pp.779–802.

Badin, L. and Simar, L. 2003. Confidence intervals for DEA-type efficiency scores: how to avoid the computational burden of the bootstrap. IAP Statistics Network, Technical report 0322, http://sites.uclouvain.be/IAP-Stat-Phase-V-VI/PhaseV/publications_2003/TR/TR0322.pdf

Kneip, A. and Simar, L. and Wilson, P.W. 2008. Asymptotics and consistent bootstraps for DEA estimators in nonparametric frontier models. Econometric Theory. Vol.24, pp.1663–1697.

Kneip, A. and Simar, L. and Wilson, P.W. 2011. A computationally efficient, consistent bootstrap for inference with non-parametric DEA estimators. Computational Economics. Vol.38, pp.483–515.

Besstremyannaya, G. 2011. Managerial performance and cost efficiency of Japanese local public hospitals. Health Economics. Vol.20(S1), pp.19–34.

Besstremyannaya, G. 2013. The impact of Japanese hospital financing reform on hospital efficiency. Japanese Economic Review. Vol.64, No.3, pp.337–362.

See Also

dea, dea.env.robust and hospitals.

Examples

## load data on Japanese hospitals (Besstremyannaya 2013, 2011)
data("hospitals", package="rDEA")
Y = hospitals[c('inpatients', 'outpatients')]
X = hospitals[c('labor', 'capital')]

## Naive input-oriented DEA score for the first 20 firms under variable returns-to-scale
firms=1:20
di_naive = dea(XREF=X, YREF=Y, X=X[firms,], Y=Y[firms,],
               model="input", RTS="variable")
di_naive$thetaOpt

## Bias-corrected DEA score in input-oriented model under variable returns-to-scale
di_robust = dea.robust(X=X[firms,], Y=Y[firms,], model="input",
                       RTS="variable", B, alpha=0.05, bw="cv")
di_robust$theta_hat_hat
di_robust$bias

jaak-s/rDEA documentation built on July 6, 2023, noon