multipliers is currently able to calculate four different multipliers: output, input, income, and employment. See details for formulas.
multipliers(io, ES, regions = "all", sectors = "all", multipliers, wage.row,
employ.closed.row, employ.physical.row)An InputOutput class object from as.inputoutput
An EasySelect class object from easy.select to specify which region and sector combinations to use.
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.
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.
Character. Any combination of the following: output, input, wage, and/or employment
Integer. The row(s) in Value Added where wages is stored. See io$V_label if you do not know. This is not to be confused with the labor located in the intermediate transaction matrix (Z)
Integer. The row(s) in the intermediate transaction matrix (Z) where labor is stored. This is not to be confused with "wages" or "employee compensation" etc.
character or Integer. The row(s) in the phtsical matrix (P) where labor is stored. This is not to be confused with "wages" or "employee compensation" etc.
Produces a list over regions of multilpliers.
There are four different multipliers able to be calculated:
(1) output - Output multipliers are calculated as the sum over rows from the Leontief matrix:
$$O_j = \sum_{i=1}^n l_{ij} $$
where \(l_{ij}\) is the ith row and jth column element of the Leontief matrix.
(2)input - Input multipliers are calculated as the sum over columns from the Ghoshian matrix:
$$I_i = \sum_{j=1}^n g_{ij}$$
where \(g_ij\) is the ith row and jth column element of the Ghoshian matrix
(3) wage - Income multipliers are calculated using value add due to employee compensation or wages. Multiple types of wages are supported. Wages are standardized and multiplied by the Leontief matrix:
$$W_j = \sum_{i=1}^n \omega _i l_{ij} $$
where \(\omega _i = w_i/X_i\) is the wage divided by the total production for that region-sector combination, and \(l_{ij}\) is the ith row and jth column element of the Leontief matrix.
(4) employment - Employment multipliers are calculated using the employment row in the matrix of technical input coefficients (A):
$$E_j = \sum_{i=1}^n \epsilon _{ei} l_{ij} $$
where \(\epsilon _{ei}\) is the row(s) corresponding to labor at the ith column, and \(l_{ij}\) is the ith row and jth column element of the Leontief matrix.
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)
# NOT RUN {
data(toy.IO)
class(toy.IO)
M1 <- multipliers(toy.IO, multipliers = "wage", wage.row = 1)
M2 <- multipliers(toy.IO, multipliers = "employment.closed", employ.closed.row = "Minions")
data(toy.ES)
class(toy.ES)
M3 <- multipliers(toy.IO, toy.ES, multipliers = c("input", "output"))
# }
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