extraction {ioanalysis} | R Documentation |
Hypothetical Extraction
Description
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.
Usage
extraction(io, ES = NULL, regions = 1, sectors = 1, type = "backward.total",
aggregate = FALSE, simultaneous = FALSE, normalize = FALSE)
Arguments
io |
An |
ES |
An |
regions |
Character or Integer. Specific regions to be used. Can either be a character that exactly matches the name of the region in |
sectors |
Character or Integer. Specific sectors to be used. Can either be a character that exactly matches the name of the sector in |
type |
Character. Any combination of |
aggregate |
|
simultaneous |
|
normalize |
|
Details
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.
Value
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
.
Author(s)
John J. P. Wade, Ignacio Sarmiento-Barbieri
References
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)
See Also
as.inputoutput
, easy.select
, linkages
, key.sector
Examples
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