malmq {Benchmarking} | R Documentation |

Estimates Malmquist indices for productivity and its decomposition beteween two periods. The units in the two periods does not have to be exactly the same, but the Malmquist index is only calculated for units present in both periods.

malmq(X0, Y0, ID0 = NULL, X1, Y1, ID1 = NULL, RTS = "vrs", ORIENTATION = "in", SLACK = FALSE, DUAL = FALSE, DIRECT = NULL, param = NULL, TRANSPOSE = FALSE, FAST = TRUE, LP = FALSE, CONTROL = NULL, LPK = NULL)

`X0` |
Inputs of firms in period 0, a K0 x m matrix of observations of K0 firms with m inputs (firm x input). |

`Y0` |
Outputs of firms in period 0, a K0 x n matrix of observations of K0 firms with n outputs (firm x input). |

`ID0` |
Index for firms in period 0; could be numbers or labels. Length K0. |

`X1` |
Inputs of firms in period 1, a K1 x m matrix of observations of K1 firms with m inputs (firm x input). |

`Y1` |
Outputs of firms in period 1, a K1 x n matrix of observations of K1 firms with n outputs (firm x input). |

`ID1` |
Index for firms in period 0; could be numbers or labels. Length K0. |

`RTS` |
Returns to scale assumption as in |

`ORIENTATION` |
Input efficiency "in" (1), output
efficiency "out" (2), and graph efficiency "graph" (3) as in |

`SLACK` |
See |

`DUAL` |
See |

`DIRECT` |
See |

`param` |
See |

`TRANSPOSE` |
See |

`FAST` |
See |

`LP` |
See |

`CONTROL` |
See |

`LPK` |
See |

The *index for technical changes* `tc`

is calculated as `sqrt(e10/e11 * e00/e01)`

where `e<s><t>`

is the efficience for period `s`

when the refenrece technology is
for period `t`

, i.e. determined from the observations for period `t`

and
`XREF=X_t, YREF=Y_t`

, as is the option for the function `dea`

.

The *Malmquist index for productivity* `mq`

is calculates as `sqrt(e10/e00 * e11/e01)`

and the
*index for change in efficiency* `ec`

is `e11/e00`

. Note that `mq = tc * ec`

.

`m` |
Malmquist index for productivity. |

`tc` |
Index for technoligy change. |

`ec` |
Index for efficiency change. |

`mq` |
Malmquist index for productivity; same as |

`id` |
Index for firms present in both period 0 and period 1. |

`id0` |
Index for firms in period 0 that are also in period 1. |

`id1` |
Index for firms in period 1 that are also in period 0. |

`e00` |
The efficiencies for period 0 with reference technoligy from period 0. |

`e10` |
The efficiencies for period 1 with reference technoligy from period 0. |

`e11` |
The efficiencies for period 1 with reference technoligy from period 1. |

`e01` |
The efficiencies for period 0 with reference technoligy from period 1. |

The calculations of efficiencies are only done for units present in both periods.

Peter Bogetoft and Lars Otto larsot23@gmail.com

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

x0 <- matrix(c(10, 28, 30, 60),ncol=1) y0 <- matrix(c(5, 7, 10, 15),ncol=1) x1 <- matrix(c(12, 26, 16, 60 ),ncol=1) y1 <- matrix(c(6, 8, 9, 15 ),ncol=1) dea.plot(x0, y0, RTS="vrs", txt=TRUE) dea.plot(x1, y1, RTS="vrs", add=TRUE, col="red") points(x1, y1, col="red", pch=16) text(x1, y1, 1:dim(x1)[1], col="red", adj=-1) m <- malmq(x0,y0,,x1,y1,,RTS="vrs") print("Malmquist index for change in productivity, technoligy change:") print(m$mq) print("Index for change of frontier:") print(m$tc)

[Package *Benchmarking* version 0.29 Index]