npsf (version 0.8.0)

tenonradialbc: Statistical Inference Regarding the Russell Measure of Technical Efficiency

Description

Routine tenonradialbc performs bias correction of the nonradial Russell input- or output-based measure of technical efficiency, computes bias and constructs confidence intervals via bootstrapping techniques.

Usage

tenonradialbc(formula, data, subset,
            ref = NULL, data.ref = NULL, subset.ref = NULL,
            rts = c("C", "NI", "V"), base = c("output", "input"),
            homogeneous = TRUE, smoothed = TRUE, kappa = NULL,
            reps = 999, level = 95,
            print.level = 1, show.progress = TRUE, seed = NULL)

Arguments

formula

an object of class ``formula'' (or one that can be coerced to that class): a symbolic description of the model. The details of model specification are given under `Details'.

data

an optional data frame containing the variables in the model. If not found in data, the variables are taken from environment (formula), typically the environment from which teradial is called.

subset

an optional vector specifying a subset of observations for which technical efficiency is to be computed.

rts

character or numeric. string: first letter of the word ``c'' for constant, ``n'' for non-increasing, or ``v'' for variable returns to scale assumption. numeric: 3 for constant, 2 for non-increasing, or 1 for variable returns to scale assumption.

base

character or numeric. string: first letter of the word ``o'' for computing output-based or ``i'' for computing input-based technical efficiency measure. string: 2 for computing output-based or 1 for computing input-based technical efficiency measure

ref

an object of class ``formula'' (or one that can be coerced to that class): a symbolic description of inputs and outputs that are used to define the technology reference set. The details of technology reference set specification are given under `Details'. If reference is not provided, the technical efficiency measures for data points are computed relative to technology based on data points themselves.

data.ref

an optional data frame containing the variables in the technology reference set. If not found in data.ref, the variables are taken from environment(ref), typically the environment from which teradial is called.

subset.ref

an optional vector specifying a subset of observations to define the technology reference set.

smoothed

logical. If TRUE, the reference set is bootstrapped with smoothing; if FALSE, the reference set is bootstrapped with subsampling.

homogeneous

logical. Relevant if smoothed=TRUE. If TRUE, the reference set is bootstrapped with homogeneous smoothing; if FALSE, the reference set is bootstrapped with heterogeneous subsampling.

kappa

relevant if smoothed=TRUE. 'kappa' sets the size of the subsample as K^kappa, where K is the number of data points in the original reference set. The default value is 0.7. 'kappa' may be between 0.5 and 1.

reps

specifies the number of bootstrap replications to be performed. The default is 999. The minimum is 100. Adequate estimates of confidence intervals using bias-corrected methods typically require 1,000 or more replications.

level

sets confidence level for confidence intervals; default is level=95.

show.progress

logical. Relevant if print.level>=1. If TRUE, progress of the bootstrap is displayed; if FALSE, display of the bootstrap progress is suppressed.

print.level

numeric. 0 - nothing is printed; 1 - print summary of the model and data. 2 - print summary of technical efficiency measures. 3 - print estimation results observation by observation. Default is 1.

seed

numeric. The seed (for replication purposes).

Value

tenonradialbc returns a list of class npsf containing the following elements:

K

numeric: number of data points.

M

numeric: number of outputs.

N

numeric: number of inputs.

rts

string: RTS assumption.

base

string: base for efficiency measurement.

reps

numeric: number of bootstrap replications.

level

numeric: confidence level for confidence intervals.

te

numeric: radial measure (Russell) of technical efficiency.

tebc

numeric: bias-corrected radial measures of technical efficiency.

biasboot

numeric: bootstrap bias estimate for the original radial measures of technical efficiency.

varboot

numeric: bootstrap variance estimate for the radial measures of technical efficiency.

biassqvar

numeric: one-third of the ratio of bias squared to variance for radial measures of technical efficiency.

realreps

numeric: actual number of replications used for statistical inference.

telow

numeric: lower bound estimate for radial measures of technical efficiency.

teupp

numeric: upper bound estimate for radial measures of technical efficiency.

teboot

numeric: reps x K matrix containing bootstrapped measures of technical efficiency from each of reps bootstrap replications.

esample

logical: returns TRUE if the observation in user supplied data is in the estimation subsample and FALSE otherwise.

Details

Routine tenonradialbc performs bias correction of the nonradial Russell input- or output-based measure of technical efficiency, computes bias and constructs confidence intervals via bootstrapping techniques (see Badunenko and Mozharovskyi (2020), 10.1080/01605682.2019.1599778).

Models for tenonradialbc are specified symbolically. A typical model has the form outputs ~ inputs, where outputs (inputs) is a series of (numeric) terms which specifies outputs (inputs). The same goes for reference set. Refer to the examples.

Results can be summarized using summary.npsf.

References

Badunenko, O. and Mozharovskyi, P. (2020), Statistical inference for the Russell measure of technical efficiency, Journal of the Operational Research Society, 713, 517--527, 10.1080/01605682.2019.1599778

F<U+00E4>re, R., Grosskopf, S. and Lovell, C. A. K. (1994), Production Frontiers, Cambridge U.K.: Cambridge University Press, 10.1017/CBO9780511551710

See Also

teradial, tenonradial, teradialbc, nptestrts, nptestind, sf

Examples

# NOT RUN {
 
 
# }
# NOT RUN {
  
  data( ccr81 )
  head( ccr81 )
  
  # Subsampling

  t9 <- tenonradialbc(y1 + y2 + y3 ~ x1 + x2 + x3 + x4 + x5, data = ccr81,
                          ref = NULL, data.ref = NULL, subset.ref = NULL,
                          rts = "v", base = "i",
                          homogeneous = FALSE, smoothed = TRUE, kappa = .6,
                          reps = 999, level = 95,
                          print.level = 1, show.progress = TRUE, seed = NULL)
  # display the results

  cbind(te = t9$te, telow = t9$telow, tebc = t9$tebc, teupp = t9$teupp, 
        biasboot = t9$biasboot, varboot = t9$varboot, biassqvar = t9$biassqvar)
  
  # Smoothing

  t10 <- tenonradialbc(y1 + y2 + y3 ~ x1 + x2 + x3 + x4 + x5, data = ccr81,
                          ref = NULL, data.ref = NULL, subset.ref = NULL,
                          rts = "v", base = "i",
                          homogeneous = TRUE, smoothed = TRUE, kappa = .6,
                          reps = 999, level = 95,
                          print.level = 1, show.progress = TRUE, seed = NULL)
  # display the results

  cbind(te = t10$te, telow = t10$telow, tebc = t10$tebc, teupp = t10$teupp, 
        biasboot = t10$biasboot, varboot = t10$varboot, biassqvar = t10$biassqvar)
  
 
# }
# NOT RUN {
 
# }