dea.env.robust {rDEA}

Bias-corrected data envelopment analysis with environmental variables

Description

Estimates bias-corrected efficiency scores in input- and output-oriented DEA models with environmental (exogenous) variables

Usage

dea.env.robust (X, Y, W=NULL, Z, model, RTS="variable",
                L1=100, L2=2000, alpha=0.05)

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".

Z

a matrix of environmental variables for observations, for which DEA scores are estimated. Constant is automatically included in Z.

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".

L1

an integer showing the number of bootstrap replications in the first loop of Simar and Wilson's (2007) algorithm, default is 100.

L2

an integer showing the number of bootstrap replications in the second loop of Simar and Wilson's (2007) algorithm, default is 2000.

alpha

a number in (0,1) denoting the size of confidence interval for the bias-corrected DEA score, default is 0.05.

Details

Implements Simar and Wilson's (2007) second algorithm for bias-correction of technical efficiency scores in input- and output-oriented DEA models. Computations are done in terms of distance function, i.e. the reciprocal of efficiency score, with the range from one to infinity.

Value

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

delta_hat

the vector of the reciprocal of DEA score (distance function), estimated in input or output-oriented model in with dea function.

beta_hat

the vector of coefficients in the truncated regression of the reciprocal of DEA score on environmental variables.

sigma_hat

the standard deviation of the errors in the truncated regression of reciprocal of DEA score on environmental variables.

beta_hat_hat

the vector of robust coefficients in the truncated regression of reciprocal of DEA score on environmental variables (after the second loop).

sigma_hat_hat

the robust standard deviation of the errors in the truncated regression of reciprocal of DEA score on environmental variables (after the second loop).

delta_hat_hat

the vector of robust reciprocal of DEA score (after the second loop).

bias

the vector of bias of the reciprocal of DEA score, bias is non-positive.

delta_ci_low

the vector of the lower bounds of confidence interval for delta_hat_hat (bias-corrected reciprocal of DEA score).

delta_ci_high

the vector of the upper bounds of confidence interval for delta_hat_hat (bias-corrected reciprocal of DEA score).

beta_ci

the matrix of lower and upper bounds for beta using alpha confidence intervals (beta is robust coefficients in the truncated regression of the reciprocal of DEA score on environmental variables).

sigma_ci

the matrix of lower and upper bounds for sigma using alpha confidence intervals (sigma is the robust standard deviation in the truncated regression of the reciprocal of DEA score on environmental variables).

Author(s)

Jaak Simm, Galina Besstremyannaya

References

Simar, L. and Wilson, P.W. 2007. Estimation and inference in two-stage, semi-parametric models of production processes. Journal of Econometrics. Vol.136, pp.31–64.

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.

Simar, L. and Wilson, P. 2011. Two-stage DEA: caveat emptor. Journal of Productivity Analysis. Vol.36, pp.205–218.

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.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')]
Z = hospitals[c('z1')]

## 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

## added only for testing of the manual
library(maxLik)

## Bias-corrected DEA score in input-oriented model
## with environmental variables, variable returns-to-scale
di_env = dea.env.robust(
             X=X[firms,], Y=Y[firms,], Z=Z[firms,], model="input",
             RTS="variable", L2=100, alpha=0.05)
di_env$delta_hat_hat