roc.malmquist {DJL}

Malmquist Index: time-series productivity analysis

Description

Employs distance measure over time to calculate the productivity changes.

Usage

roc.malmquist(xdata, ydata, tm=NULL, dm="dea", rts="crs", orientation,
              g=NULL, wd=NULL, ncv=NULL, env=NULL, cv="convex")

Arguments

xdata

Input(s) array (n by m by t)

ydata

Output(s) array (n by s by t)

tm

Tick mark of production dates (a vector length of t)

dm

Distance measure to calculate the productivity
"dea" Data Envelopment Analysis (default)
"sbm" Slack Based Model
"ddf" Directional Distance Function
"hdf" Hyperbolic Distance Function
"sf" Shortage Function

rts

Returns to scale assumption
"crs" Constant RTS (default)
"vrs" Variable RTS
"irs" Increasing RTS
"drs" Decreasing RTS

orientation

Orientation of the measurement
"n" Non-orientation (default)
"i" Input-orientation
"o" Output-orientation

g

Directional vector indicating a measurement direction (n by (m+s))
By default (NULL), xdata & ydata will be used

wd

Weak disposability vector indicating (an) undesirable output(s) (1 by s)

ncv

Non-controllable variable index(binary) for internal NDF (1 by (m+s))

env

Environment index for external NDF (n by 1)

cv

Convexity assumption
"convex" Convexity holds (default)
"fdh" Free disposal hull (this will override rts)

Value

$cu

Catching Up (aka technical efficiency change: TEC) index

$fs

Frontier Shift (FS) Index

$mi

Malmquist Index

Author(s)

Dong-Joon Lim, PhD

References

R. Fare, S. Grosskopf, and C. A. K. Lovell, Production Frontiers. Cambridge University Press, 1994.

See Also

dm.ddf Distance measure using DDF
dm.dea Distance measure using DEA
dm.hdf Distance measure using HDF
dm.sbm Distance measure using SBM
dm.sf Distance measure using SF

Examples

# Load data
  df <- array(c(4,     3,   9,  10,  7, 4,  3, 5,
                5,    12,   3,   8,  1, 4, 14, 3,
                1,     1,   1,   1,  1, 1,  1, 1,
                3.4,   2,  10,   8, 10, 4,  1, 5,
                6,    10, 3.5,   7,  2, 4, 12, 3,
                1,     1,   1,   1,  1, 1,  1, 1,
                2.8, 1.8,   8,   7, 10, 3,  1, 5,
                5.7, 8.8, 2.8,   5,  2, 5,  9, 3,
                1,     1,   1,   1,  1, 1,  1, 1,
                2.2, 1.5,   8,   5,  8, 3,  1, 5,
                6,     8, 2.3, 3.5,  2, 5,  7, 3,
                1,     1,   1,   1,  1, 1,  1, 1),
              c(8, 3, 4))

# Run
  roc.malmquist(df[,1:2,], df[,3,], dm = "sbm", orientation = "n")