extraction: Hypothetical Extraction
In jjpwade/ioanalysis: Input-Output Analysis

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

Computes the hypothetical extraction as outlined in Dietzenbacher et al. (1993) and as outlined in Blar and Miller (2009).

Caution: Inverting large matrices will take a long time. Each individual hypothetical extraction requires the inversion of a matrix. R does a computation roughly every 8e-10 second. The number of computations per matrix inversion is n^3 where n is the dimension of the square matrix. For n = 5000 it should take 100 seconds. I trust you know how cubic functions grow.

1 2	extraction(io, ES = NULL, regions = 1, sectors = 1, type = "backward.total", aggregate = FALSE, simultaneous = FALSE, normalize = FALSE)

`io`	An `InputOutput` class object from `as.inputoutput`
`ES`	An `EasySelect` class object from `easy.select` to specify which region and sector combinations to use.
`regions`	Character or Integer. Specific regions to be used. Can either be a character that exactly matches the name of the region in `RS_label` or the number of the region in the order it appears in `RS_label`.
`sectors`	Character or Integer. Specific sectors to be used. Can either be a character that exactly matches the name of the sector in `RS_label` or the number of the sector in the order it `RS_label`.
`type`	Character. Any combination of `"backward"`, `"forward"`, `"backward.total"`, and/or `"forward.total"`. See details.
`aggregate`	`TRUE` or `FALSE`. If `TRUE` produces the value of the impact over all sectors. If `FALSE` produces the impact for each sector.
`simultaneous`	`TRUE` or `FALSE`. Determines whether to extract all specified regions sequentially or simultaneously.
`normalize`	`TRUE` or `FALSE`. Whether or not to divide each linkage by total production.

type

(1) backward - Calculates the impact of hypothetically extracting the jth region/sector using the formula

X - (I - A_c)^{-1} f

where A_c is the matrix of technical input coefficients with the jth column replaced by zeros

(2)forward - Calculates the impact of hypothetically extracting the jth region/sector using the formula

X - V (I - B_r)^{-1}

where B_r is the matrix of technical output coefficients with the jth row replaced by zeros

(3) backward.total - Calculates the impact of hypothetically extracting the jth region/sector using the formula

X - (I - A_{cr})^{-1} f

where A_{cr} is the matrix of technical input coefficients with the jth column and jth row replaced by zeros except for the diagonal element.

(4) forward.total - Calculates the impact of hypothetically extracting the jth region/sector using the formula

X - V (I - B_{cr})^{-1}

where B_{cr} is the matrix of technical output coefficients with the jth column and jth row replaced by zeros except for the diagonal element.

aggregate

If TRUE multiplies the impact vector by a vector of ones to received the summed value of the impact from hypothetical extraction.

normalize

If TRUE each component in the impact vector is divided by the total output of that sector/region combination.

Produces a list over regions of a list over type of extraction. If there is only one region and one type, then a matrix is returned. For example, items can be called by using extraction$region$type.

John J. P. Wade, Ignacio Sarmiento-Barbieri

Dietzenbacher Erik & van der Linden Jan A. & Steenge Alben E. (1993). The Regional Extraction Method: EC Input-Output Comparisons. Economic Systems Research. Vol. 5, Iss. 2, 1993

Blair, P.D. and Miller, R.E. (2009). "Input-Output Analysis: Foundations and Extensions". Cambridge University Press

Nazara, Suahasil & Guo, Dong & Hewings, Geoffrey J.D., & Dridi, Chokri, 2003. "PyIO. Input-Output Analysis with Python". REAL Discussion Paper 03-t-23. University of Illinois at Urbana-Champaign. (http://www.real.illinois.edu/d-paper/03/03-t-23.pdf)

as.inputoutput, easy.select, linkages, key.sector

data(toy.IO)
class(toy.IO)
E1 <- extraction(toy.IO)

# Using an EasySelect object
data(toy.IO)
class(toy.IO)
E2 <- extraction(toy.IO, toy.ES)
E2$Hogwarts

# Using more options
E3 <- extraction(toy.IO, regions = c(1,2), sectors = c("Wii", "Minions"), 
                 type = c("backward", "backward.total"), aggregate = TRUE)
E3$Hogwarts$backward.total

# Multiple regions and types
E4 <- extraction(toy.IO, type = c("forward","forward.total"), normalize = TRUE)
E4$Hogwarts$forward.total