deaR (version 1.5.2)

bootstrap_basic: Bootstrapping DEA

Description

To bootstrap efficiency scores, deaR uses the algorithm proposed by Simar and Wilson (1998). For now, the function bootstrap_basic can only be used with basic DEA models.

Usage

bootstrap_basic(datadea,
                orientation = c("io", "oo"),
                rts = c("crs", "vrs", "nirs", "ndrs", "grs"),
                L = 1,
                U = 1,
                B = 2000,
                h = NULL,
                alpha = 0.05)

Value

A list with the results (score and score_bc components) along with any other necessary information to replicate the results, such as the name of the model and parameters orientation, rts, bandwidth, bias, CI (confidence intervals) and descriptives.

Arguments

datadea

A deadata object with n DMUs, m inputs and s outputs.

orientation

A string, equal to "io" (input oriented) or "oo" (output oriented).

rts

A string, determining the type of returns to scale, equal to "crs" (constant), "vrs" (variable), "nirs" (non-increasing), "ndrs" (non-decreasing) or "grs" (generalized).

L

Lower bound for the generalized returns to scale (grs).

U

Upper bound for the generalized returns to scale (grs).

B

Number of bootstrap iterations.

h

Bandwidth of smoothing window. By default h = 0.014 (you can set h equal to any other value). The optimal bandwidth factor can also be calculated following the proposals of Silverman (1986) and Daraio y Simar (2007). So, h = "h1" is the optimal h referred as "robust normal-reference rule" (Daraio and Simar, 2007 p.60), h = "h2" is the value of h1 but instead of the factor 1.06 with the factor 0.9, h = "h3" is the value of h1 adjusted for scale and sample size (Daraio and Simar, 2007 p.61), and h = "h4" is the bandwidth provided by a Gaussian kernel density estimate.

alpha

Between 0 and 1 (for confidence intervals).

Author

Vicente Coll-Serrano (). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolós (). Department of Business Mathematics

Rafael Benítez (). Department of Business Mathematics

University of Valencia (Spain)

References

Behr, A. (2015). Production and Efficiency Analysis with R. Springer.

Bogetoft, P.; Otto, L. (2010). Benchmarking with DEA, SFA, and R. Springer.

Daraio, C.; Simar, L. (2007). Advanced Robust and Nonparametric Methods in Efficiency Analysis: Methodology and Applications. New York: Springer.

Färe, R.; Grosskopf, S.; Kokkenlenberg, E. (1989). "Measuring Plant Capacity, Utilization and Technical Change: A Nonparametric Approach". International Economic Review, 30(3), 655-666.

Löthgren, M.; Tambour, M. (1999). "Bootstrapping the Data Envelopment Analysis Malmquist Productivity Index". Applied Economics, 31, 417-425.

Silverman, B.W. (1986). Density Estimation for Statistics and Data Analysis. London: Chapman and Hall.

Simar, L.; Wilson, P.W. (1998). "Sensitivity Analysis of Efficiency Scores: How to Bootstrap in Nonparametric Frontier Models". Management Science, 44(1), 49-61.

Simar, L.; Wilson, P.W. (1999). "Estimating and Bootstrapping Malmquist Indices". European Journal of Operational Research, 115, 459-471.

Simar, L.; Wilson, P.W. (2008). Statistical Inference in Nonparametric Frontier Models: Recent Developments and Perspective. In H.O. Fried; C.A. Knox Lovell and S.S. Schmidt (eds.) The Measurement of Productive Efficiency and Productivity Growth. New York: Oxford University Press. tools:::Rd_expr_doi("10.1093/acprof:oso/9780195183528.001.0001")

Examples

# To replicate the results in Simar y Wilson (1998, p. 58) you have to
# set B=2000 (in the example B = 100 to save time)
data("Electric_plants")
data_example <- make_deadata(Electric_plants, 
                             ni = 3, 
                             no = 1)
result <- bootstrap_basic(datadea = data_example,
                             orientation = "io",
                             rts = "vrs",
                             B = 100)
result$score_bc
result$CI