rDEA (version 1.2-8)

rts.test: Test for returns-to-scale in data envelopment analysis

Description

Tests for returns-to-scale in input- and output-oriented DEA models

Usage

rts.test(X, Y, W=NULL, model, H0, bw, B, alpha)

Value

A list containing the results of returns-to-scale test, with the following components.

w_hat

the vector for the values of the test statistics 4.5.

w48_hat

the vector for the values of the test statistics 48 or statistics 4.6.

theta_H0_hat

the vector for the values of naive DEA scores under the Null hypothesis (H0).

theta_vrs_hat

the vector for the values of naive DEA scores under the alternative hypothesis.

w_hat_boot

the vector for bootstrap values of the test statistics 4.5.

w48_hat_boot

the vector for bootstrap values of the test statistics 48 or statistics 46.

pvalue

the p-value for rejecting the Null hypothesis, according to test statistics 4.5.

pvalue48

the p-value for rejecting the Null hypothesis, according to test statistics 4.6 and 48.

H0reject

FALSE if H0 is not rejected according to pvalue45 and confidence level alpha, TRUE otherwise.

H0reject48

FALSE if H0 is not rejected according to pvalue48 and confidence level alpha, TRUE otherwise.

H0level

the cut-off value of w45_hat_boot for confidence level alpha.

H0level48

the cut-off value of w48_hat_boot for confidence level alpha.

H0

the Null hypothesis tested.

bw

the type of bandwidth employed.

bw_value

the value for the bandwidth.

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 model, "costmin" for cost-minimization model.

H0

a string for the NULL hypothesis to be tested, "constant" for constant returns-to-scale, "non-increasing" for non-inscreasing returns-to-scale.

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.

B

an integer showing the number of bootstrap replications in constracting the test staticstics. Recommended is 100.

alpha

a number in (0,1) for the size of confidence interval for the test statistics.

Author

Jaak Simm, Galina Besstremyannaya

Details

Implements Simar and Wilson's (2002, 2011) returns-to-scale tests for input- and output-oriented DEA models, using ratio of means, mean of ratios or mean of ratios less unity of DEA scores under the null and the alternative hypotheses as test statistics (denoted respectively, statistics 4.5 and 4.6 in Simar and Wilson (2002) and statistics 48 in Simar and Wilson (2011)). Tests the null hypothesis of constant returns to scale vs. the alternative hypothesis of variable returns to scale, and the null hypothesis of non-increasing returns to scale vs. the alternative hypothesis of variable returns to scale.

References

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

Simar, L. and Wilson, P. 2002. Non-parametric tests of returns to scale. European Journal of Operational Research. Vol.139, No.1, pp.115--132.

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. Inference by the m out of n bootstrap in nonparametric frontier models. Journal of Productivity Analysis. Vol.36, pp.33--53.

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

Examples

## load data on Japanese hospitals (Besstremyannaya 2013, 2011)
data("hospitals", package="rDEA")
firms = 1:50
Y = hospitals[firms, c('inpatients', 'outpatients')]
X = hospitals[firms, c('labor', 'capital')]

## Returns-to-scale test in the input-oriented DEA model,
## Testing the null hypothesis of constant returns-to-scale
## vs. an alternative of variable returns-to-scale
rts_input=rts.test(X=X, Y=Y, W=NULL, model="input", H0="constant",
                bw="cv", B=100, alpha=0.05)

rts_input$pvalue
rts_input$H0reject
rts_input$H0level


## Test for cost-efficiency DEA model,
## Testing the null hypothesis of constant returns-to-scale
## vs. an alternative of variable returns-to-scale
W = hospitals[firms, c('labor_price', 'capital_price')]

rts_cost = rts.test(X=X, Y=Y, W=W, model="costmin", H0="constant",
                    bw="cv", B=100, alpha=0.05)

rts_cost$pvalue
rts_cost$H0reject
rts_cost$H0level