bootstrap_basic function

Bootstrapping DEA

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.

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)

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).

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

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")

Author(s)

Vicente Coll-Serrano (vicente.coll@uv.es ). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolós (vicente.bolos@uv.es ). Department of Business Mathematics

Rafael Benítez (rafael.suarez@uv.es ). Department of Business Mathematics

University of Valencia (Spain)