MPI: Malmquist Productivity Index.

In MultiplierDEA: Multiplier Data Envelopment Analysis and Cross Efficiency

Malmquist Productivity Index.

Description

MPI model to calculate MPI, Technical change, Efficiency change and Scale efficiency change.

Usage

MPI(Dataset = Dataset, DMU_colName = DMU_colName, IP_colNames = IP_colNames,
OP_ColNames = OP_ColNames, Period_ColName = Period_ColName, Periods = Periods,
rts = "crs", orientation = "input", scale = FALSE)

Arguments

Dataset	The data required for the model.
DMU_colName	Column name for the DMUs in the dataset.
IP_colNames	Column name(s) for all input data in the dataset.
OP_ColNames	Column name(s) for all output data in the dataset.
Period_ColName	Column name for the period number in the dataset.
Periods	Unique periods numbers in the dataset in ascending order.
rts	Returns to scale for the application, or industry studied. Note the default rts is crs. vrs Variable returns to scale. crs Constant returns to scale.
orientation	Orientation of the DEA model - primary emphasis on input-reduction input or output-augmentation output. Note the default is input orientation.
scale	Note default value is FALSE.

Value

DMU	DMUs
et1t1.crs	The efficiencies for period 1 with reference technology from period 1 for crs returns to scale. Note: available if returns to scale is crs or scale is TRUE.
et2t2.crs	The efficiencies for period 2 with reference technology from period 2 for crs returns to scale. Note: available if returns to scale is crs or scale is TRUE.
et1t2.crs	The efficiencies for period 2 with reference technology from period 1 for crs returns to scale. Note: available if returns to scale is crs or scale is TRUE.
et2t1.crs	The efficiencies for period 1 with reference technology from period 2 for crs returns to scale. Note: available if returns to scale is crs or scale is TRUE.
et1t1.vrs	The efficiencies for period 1 with reference technology from period 1 for vrs returns to scale. Note: available if returns to scale is vrs.
et2t2.vrs	The efficiencies for period 2 with reference technology from period 2 for vrs returns to scale. Note: available if returns to scale is vrs.
et1t2.vrs	The efficiencies for period 2 with reference technology from period 1 for vrs returns to scale. Note: available if returns to scale is vrs.
et2t1.vrs	The efficiencies for period 1 with reference technology from period 2 for vrs returns to scale. Note: available if returns to scale is vrs
sec1	First componenet of the scale efficiency change. (et1t2.crs/et1t2.vrs)/(et1t1.crs/et1t1.vrs)
sec2	Second componenet of the scale efficiency change.(et2t2.crs/et2t2.vrs)/(et2t1.crs/et2t1.vrs)
sec	Scale efficiency change. (sec1 * sec2) ^ 0.5
tc1	First component of technical change. For crs, (et1t2.crs/et2t2.crs) and (et1t2.vrs/et2t2.vrs) for vrs.
tc2	Second component of technical change. For crs, (et1t1.crs/et2t1.crs) and (et1t1.vrs/et2t1.vrs) for vrs.
tc	Technical change. (tc1 * tc2) ^ 0.5
tec or ptec	Efficiency change. Note: tec for crs and ptec for vrs returns to scale.
m.crs or m.vrs	Malmquist Productivity index for the DMUs and periods.
Year	Time period underconsideration for MPI.

References

Rolf, Fare; Grosskopf, Shawna; Norris, Mary and Zhang, Zhongyang (1994) Productivity Growth, Technical Progress, and Efficiency Change in Industrialized Countries, The American Economic Review Vol. 84, No. 1, pp. 66-83.

Examples

da_f <- data.frame(x= c(11, 29, 31, 61, 13, 27, 17, 61), y=c(6, 8, 11, 16, 7, 9, 10, 16),
d= c(1,2,3,4, 1,2,3,4), p=c(1,1,1,1,2,2,2,2))

mpi_r <- MPI(Dataset = da_f, DMU_colName = "d", IP_colNames = "x", OP_ColNames = "y",
Period_ColName = "p", Periods = c(1,2),rts = "vrs", orientation = "input", scale = TRUE)

# Examine the MPI for DMUs
mpi_r$m.vrs

MultiplierDEA documentation built on Sept. 2, 2022, 1:06 a.m.