productivity (version 1.1.0)

Shadowp: Shadow prices used in productivity and profitability computations

Description

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.

Usage

Shadowp(object, …)

Arguments

object

Object of class 'FarePrimont', 'Fisher', 'HicksMoorsteen', 'Laspeyres', 'Lowe', or 'Paasche'.

…

Currently not used.

Value

• In the case of F<U+00E4>re-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.

Warning

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).

Details

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 F<U+00E4>re-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.

See Also

- Changes for productivity and profitability change indices; and - Levels for productivity and profitability levels.

Examples

# 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)
# }