| Title: | Indices of Productivity Using Data Envelopment Analysis (DEA) |
|---|---|
| Description: | Levels and changes of productivity and profitability are measured with various indices. The package contains the multiplicatively complete Färe-Primont, Fisher, Hicks-Moorsteen, Laspeyres, Lowe, and Paasche indices, as well as the classic Malmquist productivity index. Färe-Primont and Lowe indices verify the transitivity property and can therefore be used for multilateral or multitemporal comparison. Fisher, Hicks-Moorsteen, Laspeyres, Malmquist, and Paasche indices are not transitive and are only to be used for binary comparison. All indices can also be decomposed into different components, providing insightful information on the sources of productivity and profitability changes. In the use of Malmquist productivity index, the technological change index can be further decomposed into bias technological change components. The package also allows to prohibit technological regression (negative technological change). In the case of the Fisher, Hicks-Moorsteen, Laspeyres, Paasche and the transitive Färe-Primont and Lowe indices, it is furthermore possible to rule out technological change. Deflated shadow prices can also be obtained. Besides, the package allows parallel computing as an option, depending on the user's computer configuration. All computations are carried out with the nonparametric Data Envelopment Analysis (DEA), and several assumptions regarding returns to scale are available. All DEA linear programs are implemented using 'lp_solve'. |
| Authors: | K Hervé Dakpo [aut], Yann Desjeux [aut, cre], Laure Latruffe [aut] |
| Maintainer: | Yann Desjeux <[email protected]> |
| License: | GPL-3 |
| Version: | 1.1.0 |
| Built: | 2024-11-01 04:38:51 UTC |
| Source: | https://github.com/cran/productivity |
This function extracts individual productivity and profitability (when available) change
indices from any object created by either fareprim, fisher,
hicksmoorsteen, laspeyres, lowe, malm,
or paasche function.
Changes(object, ...)Changes(object, ...)
object |
Object of class |
... |
Currently not used. |
An object of class 'FarePrimont' is a result of a call to fareprim.
An object of class 'Fisher' is a result of a call to fisher.
An object of class 'HicksMoorsteen' is a result of a call to hicksmoorsteen.
An object of class 'Laspeyres' is a result of a call to laspeyres.
An object of class 'Lowe' is a result of a call to lowe.
An object of class 'Malmquist' is a result of a call to malm.
An object of class 'Paasche' is a result of a call to paasche.
In the case of Färe-Primont, Fisher, Laspeyres, Lowe, Malmquist, and Paasche indices, the function returns
a data frame containing all the elements and observations included in the "Changes" component of object.
In the case of Hicks-Moorsteen index:
When components = FALSE (default) in the call to hicksmoorsteen, the function returns a data frame
containing all the elements and observations included in the "Changes" component of the object of class 'HicksMoorsteen'.
When components = TRUE in the call to hicksmoorsteen, the function returns a list of three data frames:
* HicksMoorsteen:A data frame containing all the elements and observations related to "Changes" component of the Hicks-Moorsteen index.
* MalmquistHS:A data frame containing all the elements and observations related to "Changes" component of the Malmquist-hs index.
* MalmquistIT:A data frame containing all the elements and observations related to "Changes" component of the Malmquist-it index.
Yann Desjeux, K Hervé Dakpo, Laure Latruffe
For details and information on returned values, see fareprim,
fisher, hicksmoorsteen, laspeyres, lowe,
malm, or paasche.
See also:
- Levels for productivity and profitability levels; and
- Shadowp for shadow prices.
## Not run: FAREPRIM <- fareprim(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"), w.vars = c("p.capital", "p.land", "p.labor", "p.materials"), p.vars = c("p.livestock", "p.crop", "p.other")) Fareprim.change <- Changes(FAREPRIM) head(Fareprim.change) ## End(Not run)## Not run: FAREPRIM <- fareprim(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"), w.vars = c("p.capital", "p.land", "p.labor", "p.materials"), p.vars = c("p.livestock", "p.crop", "p.other")) Fareprim.change <- Changes(FAREPRIM) head(Fareprim.change) ## End(Not run)
Using Data Envelopment Analysis (DEA), this function measures productivity and profitability in levels and changes with Färe-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 class 'FarePrimont' print(x, digits = NULL, ...)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, ...)
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.
|
p.vars |
Output price variables (Optional). Can be a vector of text strings or integers.
|
tech.change |
Logical. If |
tech.reg |
Logical. If |
rts |
Character string specifying the returns to scale assumption.
The default value is |
orientation |
Character string specifying the orientation.
The default value is |
parallel |
Logical. Allows parallel computation. If |
cores |
Integer. Used only if |
scaled |
Logical. If |
by.id |
Integer specifying the reference observation used for computing the indices (Optional).
|
by.year |
Integer specifying the reference year used for computing the indices (Optional).
|
shadow |
Logical. Default is |
x |
An object of class |
digits |
The minimum number of significant digits to be printed in values.
Default = |
... |
Currently not used. |
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.
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
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Changes |
Change indices of the different elements of |
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Shadowp |
Returned only if |
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 Färe-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).
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.
K Hervé Dakpo, Yann Desjeux, Laure Latruffe
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 Färe-Primont
productivity and profitability in levels and components.
See Changes to retrieve a data frame with Färe-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.
## Färe-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) ## Färe-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)## Färe-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) ## Färe-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)
Using Data Envelopment Analysis (DEA), this function measures productivity and profitability in levels and changes with Fisher index.
The Fisher productivity index is the geometric average of Laspeyres and Paasche indices.
Deflated shadow prices of inputs and outputs can also be computed.
fisher(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 = TRUE, shadow = FALSE) ## S3 method for class 'Fisher' print(x, digits = NULL, ...)fisher(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 = TRUE, shadow = FALSE) ## S3 method for class 'Fisher' print(x, digits = NULL, ...)
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 |
tech.reg |
Logical. If |
rts |
Character string specifying the returns to scale assumption.
The default value is |
orientation |
Character string specifying the orientation.
The default value is |
parallel |
Logical. Allows parallel computation. If |
cores |
Integer. Used only if |
scaled |
Logical. If |
shadow |
Logical. Default is |
x |
An object of class |
digits |
The minimum number of significant digits to be printed in values.
Default = |
... |
Currently not used. |
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.
The Fisher 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.
fisher() returns a list of class 'Fisher' for which a summary of productivity and profitability
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
|
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Changes |
Change indices of the different elements of |
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Shadowp |
Returned only if |
From an object of class 'Fisher' obtained from fisher(), 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 individual input and output deflated shadow prices.
The fisher() function will not work with unbalanced panel data.
The Fisher 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).
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.
K Hervé Dakpo, Yann Desjeux, Laure Latruffe
Diewert W.E. (1992), Fisher ideal output, input, and productivity indexes revisited. Journal of Productivity Analysis, 3(3), 211-248. https://doi.org/10.1007/BF00158354
Coelli T.J., D.S.P. Rao, C.J. O'Donnell, and G.E. Battese (2005), An Introduction to Efficiency and Productivity Analysis. Springer Eds.
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 Levels to retrieve a data frame with individual Fisher
productivity and profitability in levels and components.
See Changes to retrieve a data frame with individual Fisher
productivity and profitability changes and components.
See Shadowp to retrieve individual deflated input and output shadow prices, provided that shadow = TRUE.
See also laspeyres and paasche for computations with alternative indices.
## Fisher profitability and productivity levels and changes' computations ## Not run: Fisher.prod <- fisher(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 = "out") Fisher.prod ## End(Not run)## Fisher profitability and productivity levels and changes' computations ## Not run: Fisher.prod <- fisher(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 = "out") Fisher.prod ## End(Not run)
Using Data Envelopment Analysis (DEA), this function measures productivity and profitability in levels and changes with Hicks-Moorsteen index.
The Hicks-Moorsteen index is the geometric average of its components, i.e. Malmquist-hs and Malmquist-it indices.
Deflated shadow prices of inputs and outputs used to compute Malmquist-hs and Malmquist-it indices can also be returned.
hicksmoorsteen(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, components = FALSE) ## S3 method for class 'HicksMoorsteen' print(x, digits = NULL, ...)hicksmoorsteen(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, components = FALSE) ## S3 method for class 'HicksMoorsteen' print(x, digits = NULL, ...)
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.
|
p.vars |
Output price variables (Optional). Can be a vector of text strings or integers.
|
tech.change |
Logical. If |
tech.reg |
Logical. If |
rts |
Character string specifying the returns to scale assumption.
The default value is |
orientation |
Character string specifying the orientation.
The default value is |
parallel |
Logical. Allows parallel computation. If |
cores |
Integer. Used only if |
scaled |
Logical. If |
components |
Logical. Default is |
x |
An object of class |
digits |
The minimum number of significant digits to be printed in values.
Default = |
... |
Currently not used. |
The Hicks-Moorsteen index is the geometric average of Malmquist-hs and Malmquist-it indices. For a firm i Malmquist-it computes the productivity index based on the reference year t. For a firm h, Malmquist-hs computes the productivity index based on the reference year s (i.e. t-1). Therefore, the Malmquist-it index uses the current period shadow prices as aggregators, while the Malmquist-hs index uses the previous period shadow prices as aggregators.
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.
The Hicks-Moorsteen 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.
hicksmoorsteen() returns a list of class 'HicksMoorsteen' for which a summary of productivity and profitability
(when price information is specified) measures in levels and changes is printed.
This list contains the following elements:
– HicksMoorsteen, containing levels and changes related to Hick-Moorsteen index per-se, with:
Levels |
Several elements are provided, depending on the
|
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Changes |
Change indices of the different elements of |
– MalmquistHS, only returned when components = TRUE and accessible using Levels, Changes,
and Shadowp, containing levels, changes, and shadow prices related to Malmquist-hs index, with:
Levels |
Several elements are provided, depending on the |
Changes |
Change indices of the different elements of |
Shadowp |
For each observation, input ( |
– MalmquistIT, only returned when components = TRUE and accessible using Levels, Changes,
and Shadowp, containing levels, changes, and shadow prices related to Malmquist-it index, with:
Levels |
Several elements are provided, depending on the |
Changes |
Change indices of the different elements of |
Shadowp |
For each observation, input ( |
From an object of class 'HicksMoorsteen' obtained from hicksmoorsteen(), the
Levels function extracts individual Hicks-Moorsteen productivity and profitability levels;
Changes function extracts individual Hicks-Moorsteen productivity and profitability change indices; and
Shadowp function extracts individual input and output deflated shadow prices of Malmquist-hs
and Malmquist-it indices, when components = TRUE.
The hicksmoorsteen() function will not work with unbalanced panel data.
The Hicks-Moorsteen index may be sensitive to the rescaling.
The productivity levels are obtained using shadow prices computed using dual (multipliers) DEA models. However, for extreme efficient observations the issue of multiple solutions may arise and the values of shadow prices may differ depending on the linear programming solver used (here lpSolveAPI).
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.
K Hervé Dakpo, Yann Desjeux, Laure Latruffe
Briec W., and Kerstens K. (2011). The Hicks-Moorsteen Productivity Index Satisfies the Determinateness Axiom. The Manchester School, 79(4), 765–775. https://doi.org/10.1111/j.1467-9957.2010.02169.x
Caves D.W., Christensen L.R., and Diewert W.E.(1982). The Economic Theory of Index Numbers and the Measurement of Input, Output, and Productivity. Econometrica, 50(6), 1393–1414. URL: http://www.jstor.org/stable/1913388
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. (2010). Measuring and decomposing agricultural productivity and profitability change. Australian Journal of Agricultural and Resource Economics, 54(4), 527–560. https://doi.org/10.1111/j.1467-8489.2010.00512.x
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 Levels to retrieve Hicks-Moorsteen (along with Malmquist-hs and Malmquist-it) productivity
and profitability in levels and components.
See Changes to retrieve Hicks-Moorsteen (along with Malmquist-hs and Malmquist-it) productivity
and profitability changes and components.
See Shadowp to retrieve deflated input and output shadow prices of Malmquist-hs and Malmquist-it.
## Hicks-Moorsteen productivity, without price information ## Not run: Hicks1 <- hicksmoorsteen(data = usagri, id.var = "States", time.var = "Years", x.vars = c(7:10), y.vars = c(4:6), rts = "crs", orientation = "in") Hicks1 ## End(Not run) ## Hicks-Moorsteen productivity and profitability, with price information ## Not run: Hicks2 <- hicksmoorsteen(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)) Hicks2 ## End(Not run)## Hicks-Moorsteen productivity, without price information ## Not run: Hicks1 <- hicksmoorsteen(data = usagri, id.var = "States", time.var = "Years", x.vars = c(7:10), y.vars = c(4:6), rts = "crs", orientation = "in") Hicks1 ## End(Not run) ## Hicks-Moorsteen productivity and profitability, with price information ## Not run: Hicks2 <- hicksmoorsteen(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)) Hicks2 ## End(Not run)
Using Data Envelopment Analysis (DEA), this function measures productivity and profitability in levels and changes with Laspeyres index.
The Laspeyres productivity index uses the previous period prices as aggregators.
Deflated shadow prices of inputs and outputs can also be computed.
laspeyres(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 = TRUE, shadow = FALSE) ## S3 method for class 'Laspeyres' print(x, digits = NULL, ...)laspeyres(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 = TRUE, shadow = FALSE) ## S3 method for class 'Laspeyres' print(x, digits = NULL, ...)
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 |
tech.reg |
Logical. If |
rts |
Character string specifying the returns to scale assumption.
The default value is |
orientation |
Character string specifying the orientation.
The default value is |
parallel |
Logical. Allows parallel computation. If |
cores |
Integer. Used only if |
scaled |
Logical. If |
shadow |
Logical. Default is |
x |
An object of class |
digits |
The minimum number of significant digits to be printed in values.
Default = |
... |
Currently not used. |
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.
The Laspeyres 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.
laspeyres() returns a list of class 'Laspeyres' for which a summary of productivity and profitability
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
|
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Changes |
Change indices of the different elements of |
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Shadowp |
Returned only if |
From an object of class 'Laspeyres' obtained from laspeyres(), 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 individual input and output deflated shadow prices.
The laspeyres() function will not work with unbalanced panel data.
The Laspeyres 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).
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.
K Hervé Dakpo, Yann Desjeux, Laure Latruffe
Coelli T.J., D.S.P. Rao, C.J. O'Donnell, and G.E. Battese (2005), An Introduction to Efficiency and Productivity Analysis. Springer Eds.
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 Levels to retrieve a data frame with Laspeyres
productivity and profitability in levels and components.
See Changes to retrieve a data frame with Laspeyres
productivity and profitability changes and components.
See Shadowp to retrieve deflated input and output shadow prices, provided that shadow = TRUE.
See also fisher and paasche for computation with alternative indices.
## Laspeyres profitability and productivity levels and changes' computations ## Not run: Laspeyres.prod <- laspeyres(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 = "out") Laspeyres.prod ## End(Not run)## Laspeyres profitability and productivity levels and changes' computations ## Not run: Laspeyres.prod <- laspeyres(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 = "out") Laspeyres.prod ## End(Not run)
This function extracts individual productivity and profitability (when available)
levels from any object created by either fareprim, fisher,
hicksmoorsteen, laspeyres, lowe, malm,
or paasche function.
Levels(object, ...)Levels(object, ...)
object |
Object of class |
... |
Currently not used. |
An object of class 'FarePrimont' is a result of a call to fareprim.
An object of class 'Fisher' is a result of a call to fisher.
An object of class 'HicksMoorsteen' is a result of a call to hicksmoorsteen.
An object of class 'Laspeyres' is a result of a call to laspeyres.
An object of class 'Lowe' is a result of a call to lowe.
An object of class 'Malmquist' is a result of a call to malm.
An object of class 'Paasche' is a result of a call to paasche.
In the case of Färe-Primont, Fisher, Laspeyres, Lowe, Malmquist, and Paasche indices, the function returns
a data frame containing all the elements and observations included in the "Levels" component of object.
In the case of Hicks-Moorsteen index:
When components = FALSE (default) in the call to hicksmoorsteen, the function returns a data frame
containing all the elements and observations included in the "Levels" component of the object of class 'HicksMoorsteen'.
When components = TRUE in the call to hicksmoorsteen, the function returns a list of three data frames:
* HicksMoorsteen:A data frame containing all the elements and observations related to "Levels" component of the Hicks-Moorsteen index.
* MalmquistHS:A data frame containing all the elements and observations related to "Levels" component of the Malmquist-hs index.
* MalmquistIT:A data frame containing all the elements and observations related to "Levels" component of the Malmquist-it index.
Yann Desjeux, K Hervé Dakpo, Laure Latruffe
For details and information on returned values, see fareprim,
fisher, hicksmoorsteen, laspeyres, lowe,
malm, or paasche.
See also:
- Changes for productivity and profitability change indices; and
- Shadowp for shadow prices.
## Not run: LOWE <- 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)) Lowe.levels <- Levels(LOWE) head(Lowe.levels) ## End(Not run)## Not run: LOWE <- 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)) Lowe.levels <- Levels(LOWE) head(Lowe.levels) ## End(Not run)
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 can also be computed.
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 = TRUE, by.id = NULL, by.year = NULL, shadow = FALSE) ## S3 method for class 'Lowe' print(x, digits = NULL, ...)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 = TRUE, by.id = NULL, by.year = NULL, shadow = FALSE) ## S3 method for class 'Lowe' print(x, digits = NULL, ...)
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 |
tech.reg |
Logical. If |
rts |
Character string specifying the returns to scale assumption.
The default value is |
orientation |
Character string specifying the orientation.
The default value is |
parallel |
Logical. Allows parallel computation. If |
cores |
Integer. Used only if |
scaled |
Logical. If |
by.id |
Integer specifying the reference observation used for computing the indices (Optional).
|
by.year |
Integer specifying the reference year used for computing the indices (Optional).
|
shadow |
Logical. Default is |
x |
An object of class |
digits |
The minimum number of significant digits to be printed in values.
Default = |
... |
Currently not used. |
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.
The Lowe index is also a fixed-weights-based TFP index as the Färe-Primont. The Lowe index uses the average observed input and output prices as aggregators.
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 shadow prices (if shadow = TRUE), is printed.
This list contains the following items:
Levels |
Several elements are provided, depending on the
|
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Changes |
Change indices of the different elements of |
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Shadowp |
Returned only if |
From an object of class 'Lowe' obtained from lowe(), 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 individual input and output deflated shadow prices.
The lowe() function will not work with unbalanced panel data.
The Lowe 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).
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.
K Hervé Dakpo, Yann Desjeux, Laure Latruffe
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 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, provided that shadow = TRUE.
See also fareprim for computations with an alternative transitive index.
## 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", by.id = 1, by.year = 1) Lowe.prod ## End(Not run)## 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", by.id = 1, by.year = 1) Lowe.prod ## End(Not run)
Using Data Envelopment Analysis (DEA), this function measures productivity with Malmquist index.
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 = TRUE) ## S3 method for class 'Malmquist' print(x, digits = NULL, ...)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 = TRUE) ## S3 method for class 'Malmquist' print(x, digits = NULL, ...)
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 |
rts |
Character string specifying the returns to scale assumption.
The default value is |
orientation |
Character string specifying the orientation. The default value is |
parallel |
Logical. Allows parallel computation. If |
cores |
Integer. Used only if |
scaled |
Logical. If |
x |
An object of class |
digits |
The minimum number of significant digits to be printed in values.
Default = |
... |
Currently not used. |
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 (scaled).
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 In addition to the 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 |
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Changes |
Malmquist productivity index and its components are provided, depending on the orientation.
|
Note that:
obtech (Output-biased technological change), ibtech (Input-biased technological change),
and matech (Magnitude component) are components of technological change (tech).
pure.out.effch (Pure output efficiency change) and out.scalech (Output scale efficiency change)
are components of efficiency change (effch).
pure.inp.effch (Pure input efficiency change), and inp.scalech (Input scale efficiency change)
are components of efficiency change (effch).
From an object of class 'Malmquist' obtained from malm(), the
Levels function extracts Shephard distance function estimates; and
Changes function extracts Malmquist productivity index and components.
The malm() function will not work with unbalanced panel data.
The Malmquist productivity index and components are computed such that both orientation's
results provide the same information: growth when index greater than one and decline when index lower
than one. Moreover under rts = "crs", both orientation options (i.e. "out" and
"in") yield the same results.
K Hervé Dakpo, Yann Desjeux, Laure Latruffe
Färe R., and Grosskopf S. (1996), Intertemporal Production Frontiers: With Dynamic DEA. Springer Eds.
See Levels to retrieve a data frame with Shephard distance function estimates.
See Changes to retrieve a data frame with Malmquist productivity index and components.
## 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") Malmquist ## End(Not run)## 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") Malmquist ## End(Not run)
Using Data Envelopment Analysis (DEA), this function measures productivity and profitability in levels and changes with Paasche index.
The Paasche index uses current period prices as aggregators.
Deflated shadow prices of inputs and outputs can also be computed.
paasche(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 = TRUE, shadow = FALSE) ## S3 method for class 'Paasche' print(x, digits = NULL, ...)paasche(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 = TRUE, shadow = FALSE) ## S3 method for class 'Paasche' print(x, digits = NULL, ...)
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 |
tech.reg |
Logical. If |
rts |
Character string specifying the returns to scale assumption.
The default value is |
orientation |
Character string specifying the orientation.
The default value is |
parallel |
Logical. Allows parallel computation. If |
cores |
Integer. Used only if |
scaled |
Logical. If |
shadow |
Logical. Default is |
x |
An object of class |
digits |
The minimum number of significant digits to be printed in values.
Default = |
... |
Currently not used. |
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.
The Paasche 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.
paasche() returns a list of class 'Paasche' for which a summary of productivity and profitability
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
|
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Changes |
Change indices of the different elements of |
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Shadowp |
Returned only if |
From an object of class 'Paasche' obtained from paasche(), 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 individual input and output deflated shadow prices.
The paasche() function will not work with unbalanced panel data.
The Paasche 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).
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.
K Hervé Dakpo, Yann Desjeux, Laure Latruffe
Coelli T.J., D.S.P. Rao, C.J. O'Donnell, and G.E. Battese (2005), An Introduction to Efficiency and Productivity Analysis. Springer Eds.
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 Levels to retrieve a data frame with Paasche
productivity and profitability in levels and components.
See Changes to retrieve a data frame with Paasche
productivity and profitability change indices and components.
See Shadowp to retrieve deflated input and output shadow prices, provided that shadow = TRUE.
See also fisher and laspeyres for computations with alternative indices.
## Paasche profitability and productivity levels and changes' computations ## Not run: Paasche.prod <- paasche(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 = "out") Paasche.prod ## End(Not run)## Paasche profitability and productivity levels and changes' computations ## Not run: Paasche.prod <- paasche(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 = "out") Paasche.prod ## End(Not run)
From any object created by either fareprim, fisher,
hicksmoorsteen, laspeyres, lowe, or paasche
function, and provided that the argument shadow (or components in the case of hicksmoorsteen)
is set to TRUE in the function's call, this function extracts the deflated cost input and revenue output
shadow prices.
Shadowp(object, ...)Shadowp(object, ...)
object |
Object of class |
... |
Currently not used. |
Shadow prices are derived from dual input- and output-oriented DEA models.
In the case of Fisher, Hicks-Moorsteen, Laspeyres, Lowe and Paasche indices, deflated input and output shadow
prices for each observation are returned (if the argument shadow = TRUE in the function's call).
In the case of Hicks-Moorsteen index, shadow prices used to compute Malmquist-hs and Malmquist-it
for each observation are returned (if the argument components = TRUE in the function's call).
In the case of Färe-Primont index, the deflated input and output shadow prices of the representative observation
(i.e. the sample means of quantities and prices) are returned (if the argument shadow = TRUE in the function's call).
An object of class 'FarePrimont' is a result of a call to fareprim.
An object of class 'Fisher' is a result of a call to fisher.
An object of class 'HicksMoorsteen' is a result of a call to hicksmoorsteen.
An object of class 'Laspeyres' is a result of a call to laspeyres.
An object of class 'Lowe' is a result of a call to lowe.
An object of class 'Paasche' is a result of a call to paasche.
In the case of Färe-Primont, Fisher, Laspeyres, Lowe and Paasche indices, the function returns
a data frame containing all the elements and observations included in the "Shadowp" component of object.
In the case of Hicks-Moorsteen index, the function returns a list of two data frames containing, for each observation, input and output deflated shadow prices related to Malmquist-hs and Malmquist-it indices (and therefore not Hicks-Moorsteen shadow prices per se).
* MalmquistHS:A data frame containing, for each observation, input and output shadow prices of the Malmquist-hs index.
* MalmquistIT:A data frame containing, for each observation, input and output shadow prices of the Malmquist-it index.
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).
Yann Desjeux, K Hervé Dakpo, Laure Latruffe
- Changes for productivity and profitability change indices; and
- Levels for productivity and profitability levels.
## Not run: FISHER <- fisher(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 = "out", shadow = TRUE) Fisher.shadowprices <- Shadowp(FISHER) head(Fisher.shadowprices) ## End(Not run)## Not run: FISHER <- fisher(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 = "out", shadow = TRUE) Fisher.shadowprices <- Shadowp(FISHER) head(Fisher.shadowprices) ## End(Not run)
This data set from the United States Department of Agriculture (USDA) and its Economic Research Service department contains USA agriculture's input and output quantities along with their respective price indices for 48 States.
All quantities are expressed in thousand US$1996 and prices are relative to Alabama 1996 = 1.
usagriusagri
A data frame with 480 observations on the following 17 variables:
- p.livestock: |
Livestock and animal products' relative price (reference is 1 = Alabama 1996). |
- States: |
48 States of the USA identified with two capital letters. |
- States.num: |
State number. |
- Years: |
Year. |
- q.livestock: |
Livestock and animal products' quantity, in thousand US$1996. |
- q.crop: |
Crops' quantity, in thousand US$1996. |
- q.other: |
Other farm-related productions' quantity, in thousand US$1996. |
- q.capital: |
Capital services' quantity, in thousand US$1996. |
- q.land: |
Land services' quantity, in thousand US$1996. |
- q.labor: |
Labor services' quantity, in thousand US$1996. |
- q.materials: |
Total intermediate input quantity, in thousand US$1996. |
- p.livestock: |
Livestock and animal products' relative price (reference is 1 = Alabama 1996). |
- p.crop: |
Crops' relative price (reference is 1 = Alabama 1996). |
- p.other: |
Other farm-related productions' relative price (reference is 1 = Alabama 1996). |
- p.capital: |
Capital services' relative price (reference is 1 = Alabama 1996). |
- p.land: |
Land service flows' relative price (reference is 1 = Alabama 1996). |
- p.labor: |
Labor services' relative price (reference is 1 = Alabama 1996). |
- p.materials: |
Total intermediate inputs' relative price (reference is 1 = Alabama 1996). |
Further details on the data and the different variables can be found in the references.
http://www.ers.usda.gov/data-products/agricultural-productivity-in-the-us.aspx
Ball V.E., Gollop F.M., Kelly-Hawke A., and Swinand G.P. (1999), Patterns of state productivity growth in the US farm sector: Linking state and aggregate models. American Journal of Agricultural Economics, 81(1], 164–179. https://doi.org/10.2307/1244458
Ball V.E., Hallahan C., and Nehring R. (2004), Convergence of productivity: An analysis of the catch-up hypothesis within a panel of states. American Journal of Agricultural Economics, 86(5), 1315–1321. https://doi.org/10.1111/j.0002-9092.2004.00683.x
head(usagri) str(usagri) summary(usagri)head(usagri) str(usagri) summary(usagri)