dea.merge {Benchmarking}

Estimate potential merger gains and their decompositions

Description

Calculate and decompose potential gains from mergers of similar firms (horizontal integration).

Usage

dea.merge(X, Y, M, RTS = "vrs", ORIENTATION = "in",
          XREF = NULL, YREF = NULL, FRONT.IDX = NULL, TRANSPOSE=FALSE,
          CONTROL=NULL)

Arguments

X

K times m matrix as in dea

Y

K times n matrix as in dea

M

Kg times K matrix where each row defines a merger by the firms (columns) included in the matrix as returned from method make.merge

RTS

as in dea

ORIENTATION

as in dea

XREF

as in dea

YREF

as in dea

FRONT.IDX

as in dea

TRANSPOSE

as in dea

CONTROL

Possible controls to lpSolveAPI, see the documentation for that package. For examples of use see the function dea.

Details

The K firms are merged into Kg new, merged firms.

Most of the arguments correspond to the arguments in dea, with K firms, m inputs, and n outputs.

The decomposition is summarized on page 275 and in table 9.1 page 276 in Bogetoft and Otto (2011) and is based on Bogetoft and Wang (2005)

Value

Eff

Overall efficiencies of mergers, Kg vector

Estar

Adjusted overall efficiencies of mergers after the removal of individual learning, Kg vector

learning

Learning effects, Kg vector

harmony

Harmony (scope) effects, Kg vector

size

Size (scale) effects, Kg vector

Note

If a numerical problem occurs, status=5, or if no solution can be found, the best solution is often to scale the input X and output Y yourself or use the option CONTROL to change scaling in the program itself, as described in the notes for dea.

Author(s)

Peter Bogetoft and Lars Otto [e-mail]

References

Bogetoft and Otto; Benchmarking with DEA, SFA, and R; chapter 9; Springer 2011.

Bogetoft and Wang; “Estimating the Potential Gains from Mergers”; Journal of Productivity Ana-lysis, 23, pp. 145-171, 2005.

See Also

dea and make.merge

Examples

x <- matrix(c(100,200,300,500),ncol=1,dimnames=list(LETTERS[1:4],"x"))
y <- matrix(c(75,100,300,400),ncol=1,dimnames=list(LETTERS[1:4], "y"))

dea.plot.frontier(x,y,RTS="vrs",txt=LETTERS[1:length(x)],
    xlim=c(0,1000),ylim=c(0,1000) )
dea.plot.frontier(x,y,RTS="drs", add=TRUE, lty="dashed", lwd=2)
dea.plot.frontier(x,y,RTS="crs", add=TRUE, lty="dotted")

dea(x,y,RTS="crs")
M <- make.merge(list(c(1,2), c(3,4)), X=x)
xmer <- M %*% x
ymer <- M %*% y
points(xmer,ymer,pch=8)
text(xmer,ymer,labels=c("A+B","C+D"),pos=4)
dea.merge(x,y,M, RTS="vrs")
dea.merge(x,y,M, RTS="crs")