eladder {Benchmarking}

Efficiency ladder for a single firm

Description

How the efficiency changes as the most influential peer is removed sequentially one at a time. For eladder the removed peer it is the one that have the largest change in efficiency when removed and for eladder2 it is the peer with the largest weight (lambda).

Usage

eladder(n, X, Y, RTS="vrs", ORIENTATION="in", 
	XREF=NULL, YREF=NULL, DIRECT=NULL, param=NULL, MAXELAD=NULL)

eladder2(n, X, Y, RTS = "vrs", ORIENTATION = "in", 
	XREF=NULL, YREF=NULL, DIRECT = NULL, param=NULL, MAXELAD=NULL)

eladder.plot(elad, peer, TRIM = NULL, 
	xlab="Most influential peers", ylab="Efficiency", ...)

Arguments

n

The number of the firm where the ladder is calculated

X

Inputs of firms to be evaluated, a K x m matrix of observations of K firms with m inputs (firm x input). In case TRANSPOSE=TRUE the input matrix is transposed to input x firm.

Y

Outputs of firms to be evaluated, a K x n matrix of observations of K firms with n outputs (firm x input). In case TRANSPOSE=TRUE the output matrix is transposed to output x firm.

RTS

Text string or a number defining the underlying DEA technology / returns to scale assumption, se the possible values for dea.

ORIENTATION

Input efficiency "in" (1), output efficiency "out" (2), and graph efficiency "graph" (3). For use with DIRECT, an additional option is "in-out" (0).

XREF

Inputs of the firms determining the technology, defaults to X

YREF

Outputs of the firms determining the technology, defaults to Y

DIRECT

Directional efficiency, DIRECT is either a scalar, an array, or a matrix with non-negative elements. See dea for a further description of this argument.

param

Possible parameters. Now only used for RTS="fdh+" to set low and high values for restrictions on lambda; see the section details and examples in dea for its use. Future versions might also use param for other purposes.

MAXELAD

The maximum number of influential peers to remove.

elad

The sequence of efficiencies returned from eladder.

peer

The sequence of peers returned from eladder. Also used for annotations at the tick marks at the x-axis.

TRIM

The number of characters for the name of the peers on the axis in the plot.

xlab

A title for the x axis

ylab

A title for the y axis

...

Usual options for the method plot.

Details

The function eladder calculates how the efficiency for a firm changes when the most influential peer is removed sequentially one at a time. For eladder the largest effect is the largest change in efficiency and for eladder2 the largest weight, lambda.

Somewhere in the sequence the firm becomes efficient and are itself removed from the set of firms generating the technology (or the only firm left) and thereafter the efficiencies are super-efficiencies and the process stops.

When it happens that there is no solution to the dea problem after removing a series of peers then the program might stop before MAXELAD peers have been removed.

Value

The object returned from eladder is a list with components

eff

The sequence of efficiencies when the peer with the largest value of lambda has been removed.

peer

The sequence of removed peers corresponding to the largest values of lambda as index in the X rows.

Note

When the number of firms is large then the number of influential peers will also be large and the names or numbers of the peers on the x-axis might be squeeze together and be illegible. In this case restrict the number of influential peers to be removed.

The efficiency step ladder is discussed in Essay III of Dag Fjeld Edvardsen's Ph.D. thesis from 2004.

Author(s)

Peter Bogetoft and Lars Otto [e-mail]

References

Dag Fjeld Edvardsen; Four Essays on the Measurement of Productive Efficiency; University of Gothenburg 2004; http://hdl.handle.net/2077/2923

Examples

data(charnes1981)
x <- with(charnes1981, cbind(x1,x2,x3,x4,x5))
y <- with(charnes1981, cbind(y1,y2,y3))

# Choose the firm for analysis, we choose 'Tacoma'
n <- which(charnes1981$name=="Tacoma")[1]

el <- eladder(n, x, y, RTS="crs")
eladder.plot(el$eff, el$peer)

# Restrict to 20 most influential peers for 'Tacoma' and use names
# instead of number
eladder.plot(el$eff[1:20], charnes1981$name[el$peer][1:20])

# Truncate the names of the peers and put a title on top
eladder.plot(el$eff[1:20], charnes1981$name[el$peer][1:20], TRIM=5)
title("Eladder for Tacoma")