mea {Benchmarking}

MEA multi-directional efficiency analysis

Description

Potential improvements PI or multi-directional efficiency analysis. The result is an excess value measures by the direction.

The direction is determined by the direction corresponding to the minimum input/maximum direction each good can be changed when they are changed one at a time.

Usage

mea(X, Y, RTS = "vrs", ORIENTATION = "in", XREF = NULL, YREF = NULL, 
    FRONT.IDX = NULL, param=NULL, TRANSPOSE = FALSE, 
    LP = FALSE, CONTROL = NULL, LPK = NULL)
mea.lines(N, X, Y, ORIENTATION="in")  

Arguments

X

K times m matrix with K firms and m inputs as in dea

Y

K times n matrix with K firms and n outputs as in dea

RTS

Text string or a number defining the underlying DEA technology / returns to scale assumption.

0	fdh	Free disposability hull, no convexity assumption
1	vrs	Variable returns to scale, convexity and free disposability
2	drs	Decreasing returns to scale, convexity, down-scaling and free disposability
3	crs	Constant returns to scale, convexity and free disposability
4	irs	Increasing returns to scale, (up-scaling, but not down-scaling), convexity and free disposability
6	add	Additivity (scaling up and down, but only with integers), and free disposability
7	fdh+	A combination of free disposability and restricted or local constant return to scale

ORIENTATION

Input efficiency "in" (1) or output efficiency "out" (2), and also the additional option "in-out" (0) for both input and output direction.

XREF

Inputs of the firms determining the technology, defaults to X

YREF

Outputs of the firms determining the technology, defaults to Y

FRONT.IDX

Index for firms determining the technology

param

Possible parameters. At the moment 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.

TRANSPOSE

as in dea

LP

as in dea

CONTROL

as in dea

LPK

as in dea

N

Number of firms where directional lines are to be drawn on an already existing frontier plot (dea.plot.frontier)

Details

Details can be found in Bogetoft and Otto (2011, 121–124).

This method is for input directional efficiency only interesting when there are 2 or more inputs, and for output only when there are 2 or more outputs.

Value

The results are returned in a Farrell object with the following components.

eff

Excess value in DIRECT units of measurement, this is not Farrell efficiency

lambda

The lambdas, i.e. the weight of the peers, for each firm

objval

The objective value as returned from the LP program, normally the same as eff

RTS

The return to scale assumption as in the option RTS in the call

ORIENTATION

The efficiency orientation as in the call

direct

A K times m|n|m+n matrix with directions for each firm: the number of columns depends on whether it is input, output or in-out orientated.

TRANSPOSE

As in the call

Note

The calculation is done in dea after a calculation of the direction that then is used in the argument DIRECT. The calculation of the direction is done in a series LP programs, one for each good in the direction.

Author(s)

Peter Bogetoft and Lars Otto [e-mail]

References

Peter Bogetoft and Lars Otto; Benchmarking with DEA, SFA, and R; Springer 2011

See Also

dea and the argument DIRECT.

Examples

X <- matrix(c(2, 2, 5, 10, 10, 3,    12, 8, 5, 4, 6,12), ncol=2)
Y <- matrix(rep(1,dim(X)[1]), ncol=1)

dea.plot.isoquant(X[,1], X[,2],txt=1:dim(X)[1])
mea.lines(c(5,6),X,Y)

me <- mea(X,Y)
me
peers(me)
# MEA potential saving in inputs, exces inputs
eff(me) * me$direct
me$eff *  me$direct

# Compare to traditionally Farrell efficiency
e <- dea(X,Y)
e
peers(e)
# Farrell potential saving in inputs, excess inputs
(1-eff(e)) * X