malmMS: Malmquist-MS productivity and profitability index

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

View source: R/malmMS.R

Description

Using Data Envelopment Analysis (DEA), this function measures productivity and profitability in levels and changes with Malmquist-MS index.

The Malmquist-MS index uses the previous period prices as aggregators.

Usage

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

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

Arguments

data

A dataframe containing the required information for measuring productivity and profitability.

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.

w.vars

Input price variables (Optional). Can be a vector of text strings or integers. NULL by default, so only productivity is measured.

p.vars

Output price variables (Optional). Can be a vector of text strings or integers. NULL by default, so only productivity is measured.

tech.change

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

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). Other possible options are "in" (input-orientation), and "in-out" (both input- and output-orientations). For the latter, the geometric mean of input- and output-orientations' results is returned.

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 'MalmquistMS'.

digits

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

...

Currently not used.

Details

malmMS() 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.change option allows to prohibit technological change. When tech.change is set to FALSE, this overrides the effect of tech.reg. The tech.reg option, when set to FALSE, rules out negative technological change (i.e. technological regress).

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, malmMS() may issue a warning when very large (or very small) values are present in the input and output quantity variables. Note that the Malmquist-MS index may be sensitive to the rescaling, especially the mix efficiency component.

The Malmquist-MS index is not transitive and therefore each firm is compared to itself in the previous period. Since there is no previous period for the first period, the results for this first period are replaced by NA.

Value

malmMS() returns a list of class 'MalmquistMS' for which a summary of productivity and profitability (if price information is specified) measures in levels and changes is printed, as well as input (x.vars) and output (y.vars) deflated shadow prices.

This list contains the following items:

Levels

Several elements are provided, depending on the orientation specified:

REV Revenues (if w.vars and p.vars are specified)
COST Costs (if w.vars and p.vars are specified)
PROF Profitability (if w.vars and p.vars are specified)
P Aggregated output prices (if w.vars and p.vars are specified)
W Aggregated input prices (if w.vars and p.vars are specified)
TT Terms of trade (i.e. P/W) (if w.vars and p.vars are specified)
AO Aggregated outputs
AI Aggregated inputs
TFP Total Factor Productivity (TFP)
MP Maximum productivity
TFPE TFP efficiency score
OTE Output-oriented technical efficiency score
OSE Output-oriented scale efficiency score
OME Output-oriented mix efficiency score
ROSE Residual output-oriented scale efficiency score
OSME Output-oriented scale-mix efficiency score
ITE Input-oriented technical efficiency score
ISE Input-oriented scale efficiency score
IME Input-oriented mix efficiency score
RISE Residual input-oriented scale efficiency score
ISME Input-oriented scale-mix efficiency score
OTE.ITE Geometric mean of OTE and ITE (when orientation = "in-out")
OSE.ISE Geometric mean of OSE and ISE (when orientation = "in-out")
OME.IME Geometric mean of OME and IME (when orientation = "in-out")
ROSE.RISE Geometric mean of ROSE and RISE (when orientation = "in-out")
OSME.ISME Geometric mean of OSME and ISME (when orientation = "in-out")
RME Residual mix efficiency score
Changes

Change indices of the different elements of Levels are provided. Each change is prefixed by "d" (e.g. profitability change is denoted dPROF, output-oriented efficiency change is denoted dOTE, etc.).

Shadowp

The deflated cost input shadow prices and the deflated revenue output shadow prices. These prices are derived from dual input- and output-oriented DEA models for each observation in the sample.

From an object of class 'MalmquistMS' obtained from malmMS(), the

Warning

The malmMS() function will not work with unbalanced data. The productivity levels are obtained using shadow prices computed using dual (multipliers) DEA models. However, the issue of multiple solutions can yield (for some observations) different results compared to other softwares like DPIN or other simplex algorithm packages.

Note

All output-oriented efficiency scores are computed a la Shephard, while all input-oriented efficiency scores are computed a la Farrell. Hence, all efficiency scores are greater than zero and are lower or equal to one.

Author(s)

K Hervé Dakpo, Yann Desjeux, Laure Latruffe

References

O'Donnell C.J. (2011), The sources of productivity change in the manufacturing sectors of the U.S. economy. School of Economics, University of Queensland, Australia. URL: http://www.uq.edu.au/economics/cepa/docs/WP/WP072011.pdf

See Also

See Levels to retrieve a data frame with Malmquist-MS productivity and profitability in levels and components.
See Changes to retrieve a data frame with Malmquist-MS productivity and profitability changes and components.
See Shadowp to retrieve deflated input and output shadow prices.

See also malmNT and hicksmoorsteen for computation with alternative indices.

Examples

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## Not run: 
## Malmquist-MS productivity, without price information
  MS1 <- malmMS(data = usagri, id.var = "States", time.var = "Years", x.vars = c(7:10), 
  y.vars = c(4:6), rts = "crs", orientation = "in", scaled = TRUE)
    MS1

## Malmquist-MS productivity and profitability, with price information
  MS2 <- malmMS(data = usagri, id.var = "States", time.var = "Years", x.vars = c(7:10), 
  y.vars = c(4:6), w.vars = c(14:17), p.vars = c(11:13), scaled = TRUE)
    MS2

## End(Not run)

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