lowe: Lowe productivity and profitability index

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

View source: R/lowe.R

Description

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

Deflated shadow prices of inputs and outputs are also computed.

Usage

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lowe(data, id.var, time.var, x.vars, y.vars, w.vars, p.vars, 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, 
  by.id = NULL, by.year = NULL)

## S3 method for class 'Lowe'
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. Can be a vector of text strings or integers.

p.vars

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

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.

by.id

Integer specifying the reference observation used for computing the indices (Optional). by.id must range between one and the total number of firms per period. See also the Details section.

by.year

Integer specifying the reference year used for computing the indices (Optional). by.year must range between one and the total number of time periods. See also the Details section.

x

An object of class 'Lowe'.

digits

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

...

Currently not used.

Details

lowe() 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 cancels the effect of tech.reg whatever the value of the latter. 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, lowe() may issue a warning when very large (or very small) values are present in the input and output quantity variables. Note that the Lowe index may be sensitive to the rescaling, especially the mix efficiency component.

By default by.id = NULL and by.year = NULL. This means that in the computation of change indices, each observation is by default compared to itself in the first period. by.id and by.year allow to specify a reference (e.g. a specific observation in a specific period). If by.id is specified and by.year = NULL, then the reference observation is by.id in the first period. If by.year is specified and by.id = NULL, then each observation is compared to itself in the specified period of time.

Value

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

This list contains the following items:

Levels

Several elements are provided, depending on the orientation specified:

REV Revenues
COST Costs
PROF Profitability
P Aggregated output prices
W Aggregated input prices
TT Terms of trade (i.e. P/W)
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 'Lowe' obtained from lowe(), the

Warning

The lowe() function might not properly work with unbalanced panel data.

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. (2008), An aggregate quantity-price framework for measuring and decomposing productivity and profitability change. School of Economics, University of Queensland, Australia. URL: https://www.uq.edu.au/economics/cepa/docs/WP/WP072008.pdf

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

O'Donnell C.J. (2012), Nonparametric estimates of the components of productivity and profitability change in U.S. Agriculture. American Journal of Agricultural Economics, 94(4), 873–890. https://doi.org/10.1093/ajae/aas023

See Also

See Levels to retrieve a data frame with Lowe productivity and profitability in levels and components.
See Changes to retrieve a data frame with Lowe productivity and profitability changes and components.
See Shadowp to retrieve deflated input and output shadow prices.
See also fareprim for computations with an alternative transitive index.

Examples

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## Lowe profitability and productivity levels and changes' computations
## Not run: 
  Lowe.prod <- lowe(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), orientation = "in-out", scaled = TRUE, 
  by.id = 1, by.year = 1)
    Lowe.prod

## End(Not run)

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