fareprim: F<c3><a4>re-Primont productivity and profitability index

In productivity: Indices of Productivity Using Data Envelopment Analysis (DEA)

Description

Using Data Envelopment Analysis (DEA), this function measures productivity and profitability in levels and changes with F<c3><a4>re-Primont index.

Profitability measures are only provided when price information is specified.

Deflated shadow prices of inputs and outputs can also be computed.

Usage

fareprim(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 = TRUE, by.id = NULL, by.year = NULL, shadow = FALSE)

## S3 method for class 'FarePrimont'
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, and in this case productivity only is measured.
p.vars	Output price variables (Optional). Can be a vector of text strings or integers. NULL by default, and in this case productivity only is measured.
tech.change	Logical. If TRUE (default), the model allows for technological change. If FALSE, technological change is prohibited. See also the Details section.
tech.reg	Logical. If TRUE (default), the model allows for negative technological change (i.e. technological regress). If FALSE, only positive technological change (i.e. technological progress) is allowed. 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 "in-out", 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. When the sample size is small, it is recommended to keep the parallel option to its default value (FALSE).
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. If TRUE (default), input and output quantities are rescaled. If FALSE, a warning message is displayed when very large (>1e5) and/or very small (<1e-4) values are present in the input and output quantity variables. 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.
shadow	Logical. Default is FALSE (no shadow prices are returned). When set to TRUE, the deflated input and output shadow prices of the 'representative observation' (i.e. the sample means of quantities and prices) used to compute the F<c3><a4>re-Primont index are returned.
x	An object of class 'FarePrimont'.
digits	The minimum number of significant digits to be printed in values. Default = max(3, getOption("digits") - 3).
...	Currently not used.

Details

When tech.change is set to FALSE, this overrides the effect of tech.reg.

Setting scaled = FALSE (no rescaling of data) may lead to numerical problems in solving LP problems while optimizing DEA models. In extreme cases it may also prevent models from being optimized.

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

fareprim() returns a list of class 'FarePrimont' for which a summary of productivity and profitability (when price information is specified) measures in levels and changes, as well as a summary shadow prices (if shadow = TRUE), is printed.

This list contains the following items:

Levels	Several elements are provided, depending on the orientation specified: REV Revenues (when w.vars and p.vars are specified) COST Costs (when w.vars and p.vars are specified) PROF Profitability (when w.vars and p.vars are specified) P Aggregated output prices (when w.vars and p.vars are specified) W Aggregated input prices (when w.vars and p.vars are specified) TT Terms of trade (i.e. P/W) (when 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 (orientation = "out") OSE Output-oriented scale efficiency score (orientation = "out") OME Output-oriented mix efficiency score (orientation = "out") ROSE Residual output-oriented scale efficiency score (orientation = "out") OSME Output-oriented scale-mix efficiency score (orientation = "out") ITE Input-oriented technical efficiency score (orientation = "in") ISE Input-oriented scale efficiency score (orientation = "in") IME Input-oriented mix efficiency score (orientation = "in") RISE Residual input-oriented scale efficiency score (orientation = "in") ISME Input-oriented scale-mix efficiency score (orientation = "in") OTE.ITE Geometric mean of OTE and ITE (orientation = "in-out") OSE.ISE Geometric mean of OSE and ISE (orientation = "in-out") OME.IME Geometric mean of OME and IME (orientation = "in-out") ROSE.RISE Geometric mean of ROSE and RISE (orientation = "in-out") OSME.ISME Geometric mean of OSME and ISME (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	Returned only if shadow = TRUE. It contains the deflated cost input (x.vars) shadow prices and the deflated revenue output (y.vars) shadow prices of the 'representative observation' used to compute the F<c3><a4>re-Primont index.

From an object of class 'FarePrimont' obtained from fareprim(), the

• Levels function extracts individual productivity and profitability levels;

• Changes function extracts individual productivity and profitability change indices; and

• If shadow = TRUE, the Shadowp function extracts input and output deflated shadow prices.

Warning

The fareprim() function will not work with unbalanced panel data.

The F<c3><a4>re-Primont index may be sensitive to the rescaling.

For extreme efficient observations, the problem of multiple solutions may arise and the values of shadow prices may differ depending on the linear programming solver used (here lpSolveAPI).

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 Herv<c3><a9> 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 F<c3><a4>re-Primont productivity and profitability in levels and components.
See Changes to retrieve a data frame with F<c3><a4>re-Primont productivity and profitability changes and components.
See Shadowp to retrieve deflated input and output shadow prices, provided that shadow = TRUE.

See also lowe for computations with an alternative transitive index.

Examples

## F<c3><a4>re-Primont productivity, without price information
## Not run: 
  FareP1 <- fareprim(data = usagri, id.var = "States", time.var = "Years", x.vars = c(7:10), 
  y.vars = c(4:6), rts = "crs", orientation = "in", by.id = 1, by.year = 1)
  FareP1

## End(Not run)
## F<c3><a4>re-Primont productivity and profitability, with price information
## Not run: 
  FareP2 <- fareprim(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), by.id = 1, by.year = 1)
  FareP2

## End(Not run)

productivity documentation built on May 2, 2019, 4:44 p.m.