malm: Malmquist productivity index

Description Usage Arguments Details Value Warning Note Author(s) References See Also Examples

View source: R/malm.R

Description

Using Data Envelopment Analysis (DEA), this function measures productivity with Malmquist index.

Usage

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malm(data, id.var, time.var, x.vars, y.vars, tech.reg = TRUE, rts = c("vrs", "crs", 
  "nirs", "ndrs"), orientation = c("out", "in"), parallel = FALSE, cores = max(1, 
  detectCores() - 1), scaled = FALSE)

## S3 method for class 'Malmquist'
print(x, digits = NULL, ...)

Arguments

data

A dataframe containing the required information for measuring productivity.

id.var

Firms' ID variable. Can be an integer or a text string.

time.var

Time period variable. Can be an integer or a text string.

x.vars

Input quantity variables. Can be a vector of text strings or integers.

y.vars

Output quantity variables. Can be a vector of text strings or integers.

tech.reg

Logical. If TRUE (default), the model allows for negative technological change (i.e. technological regress). See also the Details section.

rts

Character string specifying the returns to scale assumption. The default value is "vrs" (variable returns to scale). Other possible options are "crs" (constant returns to scale), "nirs" (non-increasing returns to scale), or "ndrs" (non-decreasing returns to scale).

orientation

Character string specifying the orientation. The default value is "out" (output-orientation). The other possible option is "in" (input-orientation).

parallel

Logical. Allows parallel computation. If FALSE (default) the estimation is conducted in sequential mode. If TRUE parallel mode is activated using the number of cores specified in cores.

cores

Integer. Used only if parallel = TRUE. It specifies the number of cores to be used for parallel computation. By default, cores = max(1, detectCores() - 1).

scaled

Logical. Default is FALSE. When set to TRUE, the input and output quantities are rescaled. See also the Details section.

x

An object of class 'Malmquist'.

digits

The minimum number of significant digits to be printed in values. Default = max(3, getOption("digits") - 3).

...

Currently not used.

Details

malm() allows for parallel computations (when parallel = TRUE, possibly by registering a parallel backend (doParallel and foreach packages)). The cores argument can be used to specify the number of cores to use. However, when the sample size is small, it is recommended to keep the parallel option to its default value (FALSE).

All DEA linear programs are implemented using the package Rglpk.

The tech.reg option, when set to FALSE, rules out negative technological change (i.e. technological regress). In this case, technological change will increment between consecutive periods.

The scaled option is useful when working with very large (>1e5) and/or very small (<1e-4) values. By default scaled = FALSE. In such case, malm() may issue a warning when very large (or very small) values are present in the input and output quantity variables. Note that all the distance functions required for computing the Malmquist index are radial measures which verify the translation invariance property. Hence, unless very large or very small values are present, the Malmquist index is insensitive to the rescaling option.

Value

malm() returns a list of class 'Malmquist' for which a summary of productivity measures in levels and changes is printed.

This list contains the following items:

Levels

It contains the Shephard distance function estimates, useful to compute and decompose the Malmquist productivity index. These distance functions use input and output quantities for period 1 and period 0. The prefix "c" stands for constant returns to scale ("crs") and "v" for all the other types of returns to scale (i.e. "vrs", "nirs", or "ndrs"). The suffix "o" means output-oriented while "i" refers to input-oriented. The distance function names are displayed with three digits: (i) the first digit represents the period of the reference technology, (ii) the second digit represents the period of the inputs, and (iii) the third digit represents the period of the outputs. For instance c010o means output-oriented efficiency under constant returns to scale ("crs"), with the reference technology of period 0, inputs of period 1 and outputs of period 0.

In addition to the id.var variable and periods 1 and 0, the dataframe therefore contains, depending on the orientation: c111o, c100o, c011o, c000o, c110o, c010o, c111i, c100i, c011i, c000i, c110i, and c010i.

When the returns to scale option (rts) is different from "crs", then v111o, v000o, v111i and v000i are also provided depending on the orientation.

Changes

Malmquist productivity index and its components are provided, depending on the orientation.

malmquist Malmquist productivity index
effch Efficiency change
tech Technological change
obtech Output-biased technological change
ibtech Input-biased technological change
matech Magnitude component
pure.out.effch Pure output efficiency change
out.scalech Output scale efficiency change
pure.inp.effch Pure input efficiency change
inp.scalech Input scale efficiency change

Note that:

  1. obtech (Output-biased technological change), ibtech (Input-biased technological change), and matech (Magnitude component) are components of technological change (tech).

  2. pure.out.effch (Pure output efficiency change) and out.scalech (Output scale efficiency change) are components of efficiency change (effch), when rts != "crs" and orientation = "out".

  3. pure.inp.effch (Pure input efficiency change), and inp.scalech (Input scale efficiency change) are components of efficiency change (effch), when rts != "crs" and orientation = "in".

From an object of class 'Malmquist' obtained from malm(), the

Warning

The malm() function will not work with unbalanced data.

Note

The Malmquist productivity index and its components are computed such that both orientation's results can be read in the same way (growth when greater than one and decline when lower than one). Moreover under rts = "crs", both orientation options (i.e. "out" and "in") yield the same results.

Author(s)

K Hervé Dakpo, Yann Desjeux, Laure Latruffe

References

Färe R., and Grosskopf S. (1996), Intertemporal Production Frontiers: With Dynamic DEA. Springer Eds.

See Also

See Levels to retrieve a data frame with Shephard distance function estimates.
See Changes to retrieve a data frame with Malmquist productivity index and its components.

Examples

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## Malmquist productivity index compares each observation in period 1
## to the same observation in period 0
## Not run: 
  Malmquist <- malm(data = usagri, id.var = "States", time.var = "Years", 
  x.vars = c("q.capital", "q.land","q.labor","q.materials"), 
  y.vars = c("q.livestock", "q.crop", "q.other"), rts = "nirs", scaled = TRUE)
    Malmquist

## End(Not run)

Example output

* Please cite the 'productivity' package as:
  Dakpo K.H., Desjeux Y. and Latruffe L. (2017). productivity: Indices of Productivity and Profitability Using Data Envelopment Analysis (DEA). R package version 1.0.0.

See also: citation("productivity")

* For any questions, suggestions, or comments on the 'productivity' package, please make use of Tracker facilities at:
  https://r-forge.r-project.org/projects/productivity/

Loading required package: slam
Using the GLPK callable library version 4.52
Loading required package: foreach
Loading required package: iterators
Loading required package: parallel

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DONE!          

Shephard distance function estimates (summary):

     States        Year.1         Year.0         c111o            c100o       
 AL     :  9   Min.   :1996   Min.   :1995   Min.   :0.5316   Min.   :0.5050  
 AR     :  9   1st Qu.:1998   1st Qu.:1997   1st Qu.:0.8039   1st Qu.:0.7904  
 AZ     :  9   Median :2000   Median :1999   Median :0.8957   Median :0.8767  
 CA     :  9   Mean   :2000   Mean   :1999   Mean   :0.8769   Mean   :0.8809  
 CO     :  9   3rd Qu.:2002   3rd Qu.:2001   3rd Qu.:1.0000   3rd Qu.:0.9657  
 CT     :  9   Max.   :2004   Max.   :2003   Max.   :1.0000   Max.   :1.3886  
 (Other):378                                                                  
     c011o            c000o            c110o            c010o       
 Min.   :0.4986   Min.   :0.5316   Min.   :0.5159   Min.   :0.5173  
 1st Qu.:0.8109   1st Qu.:0.7996   1st Qu.:0.7931   1st Qu.:0.7970  
 Median :0.9127   Median :0.8902   Median :0.8766   Median :0.8902  
 Mean   :0.9121   Mean   :0.8744   Mean   :0.8788   Mean   :0.8903  
 3rd Qu.:1.0166   3rd Qu.:0.9930   3rd Qu.:0.9782   3rd Qu.:0.9950  
 Max.   :1.7092   Max.   :1.0000   Max.   :1.4037   Max.   :1.3392  
                                                                    
     v111o            v000o       
 Min.   :0.5316   Min.   :0.5316  
 1st Qu.:0.8214   1st Qu.:0.8145  
 Median :0.9278   Median :0.9236  
 Mean   :0.8965   Mean   :0.8947  
 3rd Qu.:1.0000   3rd Qu.:1.0000  
 Max.   :1.0000   Max.   :1.0000  
                                  


Malmquist productivity index results (summary):

     States        Year.1         Year.0       malmquist          effch       
 AL     :  9   Min.   :1996   Min.   :1995   Min.   :0.8065   Min.   :0.7948  
 AR     :  9   1st Qu.:1998   1st Qu.:1997   1st Qu.:0.9641   1st Qu.:0.9705  
 AZ     :  9   Median :2000   Median :1999   Median :1.0177   Median :1.0000  
 CA     :  9   Mean   :2000   Mean   :1999   Mean   :1.0212   Mean   :1.0048  
 CO     :  9   3rd Qu.:2002   3rd Qu.:2001   3rd Qu.:1.0698   3rd Qu.:1.0361  
 CT     :  9   Max.   :2004   Max.   :2003   Max.   :1.2877   Max.   :1.2547  
 (Other):378                                                                  
      tech            obtech           ibtech           matech      
 Min.   :0.8573   Min.   :0.9726   Min.   :0.9720   Min.   :0.7202  
 1st Qu.:0.9823   1st Qu.:0.9992   1st Qu.:0.9998   1st Qu.:0.9646  
 Median :1.0153   Median :1.0016   Median :1.0017   Median :1.0065  
 Mean   :1.0169   Mean   :1.0109   Mean   :1.0086   Mean   :0.9987  
 3rd Qu.:1.0507   3rd Qu.:1.0122   3rd Qu.:1.0108   3rd Qu.:1.0395  
 Max.   :1.2671   Max.   :1.2261   Max.   :1.1597   Max.   :1.1564  
                                                                    
 pure.out.effch    out.scalech    
 Min.   :0.7924   Min.   :0.8406  
 1st Qu.:0.9789   1st Qu.:1.0000  
 Median :1.0000   Median :1.0000  
 Mean   :1.0036   Mean   :1.0014  
 3rd Qu.:1.0281   3rd Qu.:1.0001  
 Max.   :1.2106   Max.   :1.2547  
                                  

productivity documentation built on Dec. 29, 2017, 3:01 a.m.