dea {rDEA}

Data envelopment analysis scores

Description

Naive scores in input-oriented, output-oriented and cost-minimization DEA models

Usage

dea(XREF, YREF, X, Y, W=NULL, model, RTS="variable")

Arguments

XREF

a matrix of inputs for observations used for constructing the frontier.

YREF

a matrix of outputs for observations used for constructing the frontier.

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 for observations, for which DEA scores are estimated in cost-minimization model, W=NULL for input- and output-oriented models.

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".

Details

Estimates technical efficiency scores (input- and output-oriented DEA models) and cost efficiency score (cost-minimization DEA).

Value

A list containing the optimal solutions for linear optimization problem for each firm, with the following components.

thetaOpt

a vector of DEA scores in input- or output-oriented model, thetaOpt is in (0,1).

gammaOpt

a vector of DEA scores in cost-minimization model.

XOpt

the matrix of optimal values of inputs, only returned for cost-minimization model.

lambda

the matrix of values for constraint coefficients in the corresponding linear optimization problem, lambda >=0.

lambda_sum

the vector for sum of constraint coefficients in the corresponding linear optimization problem, lamdba_sum=1 for variable returns-to-scale, lambda_sum <=1 for non-increasing returns-to-scale.

Author(s)

Jaak Simm, Galina Besstremyannaya

References

Charnes, A. and Cooper, W. and Rhodes, E. 1978. Measuring the efficiency of decision making units. European Journal of Operational Research. Vol.2, pp.429–444.

Fare, R. and Grosskopf, S. and Lovell, C.A. 1985. The Measurement of Efficiency in Production. Kluwer Academic Publishers.

Coelli, T.J. and Rao, D.S.P. and Battese, G.E. 1994. An Introduction to Efficiency and Productivity Analysis. Kluwer Academic Publishers.

The Measurement of Productive Efficiency and Productivity Growth. 2008. O'Fried, H. and Lovell, C.A.K. and Schmidt, S.S., eds. Oxford University Press.

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.

Besstremyannaya G., Simm J., Golovan S. 2014. Robust non-parametric estimation of cost efficiency with an application to banking industry. Working paper.

See Also

dea.robust, dea.env.robust and hospitals.

Examples

## load data on Japanese hospitals (Besstremyannaya 2013, 2011)
data("hospitals", package="rDEA")

## inputs and outputs for analysis
Y = hospitals[c('inpatients', 'outpatients')]
X = hospitals[c('labor', 'capital')]
W = hospitals[c('labor_price', 'capital_price')]

## 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

## Naive DEA score in cost-minimization model for the first 20 firms under variable returns-to-scale
ci_naive = dea(XREF=X, YREF=Y, X=X[firms,], Y=Y[firms,], W=W[firms,],
               model="costmin", RTS="variable")
ci_naive$XOpt
ci_naive$gammaOpt