Using Data Envelopment Analysis (DEA), this function measures productivity and profitability in levels and changes with F<U+00E4>re-Primont index.
Profitability measures are only provided when price information is specified.
Deflated shadow prices of inputs and outputs can also be computed.
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 FarePrimont
print(x, digits = NULL, …)
A dataframe containing the required information for measuring productivity and profitability.
Firms' ID variable. Can be an integer or a text string.
Time period variable. Can be an integer or a text string.
Input quantity variables. Can be a vector of text strings or integers.
Output quantity variables. Can be a vector of text strings or integers.
Input price variables (Optional). Can be a vector of text strings or integers.
NULL by default, and in this case productivity only is measured.
Output price variables (Optional). Can be a vector of text strings or integers.
NULL by default, and in this case productivity only is measured.
Logical. If TRUE (default), the model allows for technological change.
If FALSE, technological change is prohibited. See also the Details section.
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.
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).
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.
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).
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).
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.
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.
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.
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<U+00E4>re-Primont index are returned.
An object of class 'FarePrimont'.
The minimum number of significant digits to be printed in values.
Default = max(3, getOption("digits") - 3).
Currently not used.
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:
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") |
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.).
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<U+00E4>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.
The fareprim() function will not work with unbalanced panel data.
The F<U+00E4>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).
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.
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 Levels to retrieve a data frame with F<U+00E4>re-Primont
productivity and profitability in levels and components.
See Changes to retrieve a data frame with F<U+00E4>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.
# NOT RUN {
## F<U+00E4>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
# }
# NOT RUN {
## F<U+00E4>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
# }
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