Benchmarking-package {Benchmarking} | R Documentation |

The Benchmarking package contains methods to estimate technologies and measure efficiencies using DEA and SFA. Data Envelopment Analysis (DEA) are supported under different technology assumptions (fdh, vrs, drs, crs, irs, add), and using different efficiency measures (input based, output based, hyperbolic graph, additive, super, directional). Peers are available, partial price information can be included, and optimal cost, revenue and profit can be calculated. Evaluation of mergers are also supported. Comparative methods for estimating stochastic frontier function (SFA) efficiencies and for convex nonparametric least squares here for convex functions (StoNED) are also included. The methods can solve not only standard models, but also many other model variants, and they can be modified to solve new models.

The package also support simple plots of DEA technologies with two goods; either as a transformation curve (2 outputs), an isoquant (2 inputs), or a production function (1 input and 1 output). When more inputs and outputs are available they are aggregated using weights (prices, relative prices).

The package complements the book, Bogetoft and Otto,
*Benchmarking with DEA, SFA, and R*, Springer-Verlag 2011, but
can of course also be used as a stand-alone package.

Package: | Benchmarking |

Type: | Package |

Version: | 0.29 ($Revision: 232 $) |

Date: | $Date: 2020-08-07 10:47:59 +0200 (fr, 07 aug 2020) $ |

License: | Copyright |

`dea` | DEA input or output efficience measures, peers, lambdas and slacks |

`dea.dual` | Dual weights (prices), including restrictions on weights |

`dea.direct` | Directional efficiency |

`sdea` | Super efficiency. |

`dea.add` | Additive efficiency; sum of slacks in DEA technology. |

`mea` | Multidirectional efficiency analysis or potential improvements. |

`eff` | Efficiency from an object returned from any of the dea or sfa functions. |

`slack` | Slacks in DEA models |

`excess` | Calculates excess input or output compared to DEA frontier. |

`peers` | get the peers for each firm. |

`dea.boot` | Bootstrap DEA models |

`cost.opt` | Optimal input for given output and prices. |

`revenue.opt` | Optimal output for given input and prices. |

`profit.opt` | Optimal input and output for given input and output prices. |

`dea.plot` | Graphs of DEA technologies under alternative technology assumptions. |

`dea.plot.frontier` | Specialized for 1 input and 1 output. |

`dea.plot.isoquant` | Specialized for 2 inputs. |

`dea.plot.transform` | Specialized for 2 outputs. |

`eladder` | Efficiency ladder for a single firm. |

`eladder.plot` | Plot efficiency ladder for a single firm. |

`make.merge` | Make an aggregation matrix to perform mergers. |

`dea.merge` | Decompose efficiency from a merger of firms |

`sfa` | Stochastic frontier analysis, production, distance, and cost function (SFA) |

`stoned` | Convex nonparametric least squares here for convex function function |

`outlierC.ap, outlier.ap` | Detection of outliers |

`eff.dens` | Estimate and plot kernel density of efficiencies |

`critValue` | Critical values calculated from bootstrap DEA models. |

`typeIerror` | Probability of a type I error for a test in bootstrap DEA models. |

The interface for the methods are very much like the interface to the
methods in the package FEAR (Wilson 2008). One change is that
the data now are transposed to reflect how data is usually available
in applications, i.e. we have firms on rows, and inputs and output in
the columns. Also, the argument for the options `RTS`

and
`ORIENTATION`

can be given as memotechnical strings, and there
are more options to control output.

The input and output matrices can contain negative numbers, and the methods can thereby manage restricted or fixed input or output.

The return is not just the efficiency, but also slacks, dual values (shadow prices), peers, and lambdas (weights).

Peter Bogetoft and Lars Otto larsot23@gmail.com

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

Paul W. Wilson (2008), “FEAR 1.0: A Software Package for
Frontier Efficiency Analysis with R,” *Socio-Economic Planning
Sciences* 42, 247–254

# Plot of different technologies 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(x,y,RTS="vrs",ORIENTATION="in-out",txt=rownames(x)) dea.plot(x,y,RTS="drs",ORIENTATION="in-out",add=TRUE,lty="dashed",lwd=2) dea.plot(x,y,RTS="crs",ORIENTATION="in-out",add=TRUE,lty="dotted") dea.plot(x,y,RTS="fdh",ORIENTATION="in-out",txt=rownames(x),main="fdh") dea.plot(x,y,RTS="irs",ORIENTATION="in-out",txt=TRUE,main="irs") dea.plot(x,y,RTS="irs2",ORIENTATION="in-out",txt=rownames(x),main="irs2") dea.plot(x,y,RTS="add",ORIENTATION="in-out",txt=rownames(x),main="add") # A quick frontier with 1 input and 1 output dea.plot(x,y, main="Basic plot of frontier") # Calculating efficiency dea(x,y, RTS="vrs", ORIENTATION="in") e <- dea(x,y, RTS="vrs", ORIENTATION="in") e eff(e) peers(e) peers(e, NAMES=TRUE) print(peers(e, NAMES=TRUE), quote=FALSE) lambda(e) summary(e) # Calculating super efficiency esuper <- sdea(x,y, RTS="vrs", ORIENTATION="in") esuper print(peers(esuper,NAMES=TRUE),quote=FALSE) # Technology for super efficiency for firm number 3/C # Note that drop=FALSE is necessary for XREF and YREF to be matrices # when one of the dimensions is or is reduced to 1. e3 <- dea(x,y, XREF=x[-3,,drop=FALSE], YREF=y[-3,,drop=FALSE]) dea.plot(x[-3],y[-3],RTS="vrs",ORIENTATION="in-out",txt=LETTERS[c(1,2,4)]) points(x[3],y[3],cex=2) text(x[3],y[3],LETTERS[3],adj=c(-.75,.75)) e3 <- dea(x,y, XREF=x[-3,,drop=FALSE], YREF=y[-3,,drop=FALSE]) eff(e3) peers(e3) print(peers(e3,NAMES=TRUE),quote=FALSE) lambda(e3) e3$lambda # Taking care of slacks x <- matrix(c(100,200,300,500,100,600),ncol=1, dimnames=list(LETTERS[1:6],"x")) y <- matrix(c(75,100,300,400,50,400),ncol=1, dimnames=list(LETTERS[1:6],"y")) # Phase one, calculate efficiency e <- dea(x,y) print(e) peers(e) lambda(e) # Phase two, calculate slacks (maximize sum of slacks) sl <- slack(x,y,e) data.frame(sl$sx,sl$sy) peers(sl) lambda(sl) sl$lambda summary(sl) # The two phases in one function call e2 <- dea(x,y,SLACK=TRUE) print(e2) data.frame(eff(e2),e2$slack,e2$sx,e2$sy,lambda(e2)) peers(e2) lambda(e2) e2$lambda

[Package *Benchmarking* version 0.29 Index]