hyperbolicDEA (version 1.0.2)

wrDEA: Estimation of DEA efficiency scores with linear input or output orientation and trade-off weight restrictions

Description

Linear DEA estimation including the possibility of trade-off weight restrictions, external referencing, and super-efficiency scores. Furthermore, in a second stage slacks can be estimated. The function returns efficiency scores and adjusted lambdas according to the imposed weight restrictions and slack estimation. Additionally, mus are returned if weight restrictions are imposed that highlight binding restrictions for DMUs and the absolute slack values if slack-based estimation is applied.

Usage

wrDEA(
  X,
  Y,
  ORIENTATION = "out",
  RTS = "vrs",
  WR = NULL,
  XREF = NULL,
  YREF = NULL,
  SUPEREFF = FALSE,
  SLACK = FALSE,
  ECONOMIC = FALSE
)

Value

A list object containing the following information:

eff

Are the estimated efficiency scores for the DMUs under observation stored in a vector with the length nrow(X).

lambdas

Estimated values for the composition of the respective Benchmarks. The lambdas are stored in a matrix with the dimensions nrow(X) x nrow(X), where the row is the DMU under observation and the columns the peers used for the Benchmark. NOTE: Lambdas are automatically slack optimized.

mus

If WR != NULL, the estimated decision variables for the imposed weight restrictions are stored in a matrix with the dimensions nrow(X) x nrow(WR), where the rows are the DMUs and columns the weight restrictions. If the values are positive, the WR is binding for the respective DMU.

slack

If SLACK = TRUE, the slacks are estimated and stored in a matrix with the dimensions nrow(X) x (ncol(X) + ncol(Y)). Showing the Slack of each DMU (row) for each input and output (column).

Arguments

X

Vector, matrix or dataframe with DMUs as rows and inputs as columns

Y

Vector, matrix or dataframe with DMUs as rows and outputs as columns

ORIENTATION

Character string indicating the orientation of the DEA model, e.g. "in", "out"

RTS

Character string indicating the returns-to-scale, e.g. "crs", "vrs", "ndrs", "nirs", "fdh"

WR

Matrix with one row per homogeneous linear weight restriction in standard form. The columns are ncol(WR) = ncol(Y) + ncol(X). Hence the first ncol(Y) columns are the restrictions on outputs and the last ncol(X) columns are the restrictions on inputs.

XREF

Vector, matrix or dataframe with firms defining the technology as rows and inputs as columns

YREF

Vector, matrix or dataframe with firms defining the technology as rows and outputs as columns

SUPEREFF

Boolean variable indicating whether super-efficiencies shall be estimated

SLACK

Boolean variable indicating whether slack-based estimation should be applied

ECONOMIC

Boolean variable indicating whether economic efficiency (cost or revenue) is estimated using trade-off weight restrictions. Therefore mus can be positive and negative when set to TRUE and you have a multi-stage optimization where the first stage is the efficiency estimation and the second stage is the minimization of the mus. You have to use single trade-off, hence a 1 to 1 substitution of either inputs or outputs given by the focus on either cost or revenue efficiency. The data must be value data.

Author

Alexander Öttl

Examples

X <- c(1,1,2,4,1.5,2,4,3)
Y <- c(1,2,4,4,0.5,2.5,3.5,4)

# Two weight restrictions in standard form first on output then input.
# The first WR shows the trade-off that inputs can be reduced by one unit
# which reduces outputs by four units. The second WR shows that outputs can 
# be increased by one unit when inputs are increased by four units.

WR <- matrix(c(-4,-1,1,4), nrow = 2, byrow = TRUE)

wrDEA(X, Y, ORIENTATION = "in", RTS="vrs", WR = WR)

# For an estimation just focusing on one DMU one can for example use 
# XREF and YREF to define the technology and then estimate the efficiency for 
# the DMU under observation (here DMU 1). Let's additionally estimate the slacks. 

wrDEA(X[1], Y[1], ORIENTATION = "in", RTS="vrs", XREF = X, YREF = Y, SLACK = TRUE, WR = WR)