MultiplierDEA (version 0.1.19)

MPI: 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)

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.

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.

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