multipliers: Multiplier Analysis
In jjpwade/ioanalysis: Input-Output Analysis

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

multipliers is currently able to calculate four different multipliers: output, input, income, and employment. See details for formulas.

1 2	multipliers(io, ES, regions = "all", sectors = "all", multipliers, wage.row, employ.closed.row, employ.physical.row)

`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`.
`multipliers`	Character. Any combination of the following: `output`, `input`, `income`, and/or `employment`
`wage.row`	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`)
`employ.closed.row`	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.
`employ.physical.row`	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.

There are four different multipliers able to be calculated:

(1) output - Output multipliers are calculated as the row sums of the Leontief matrix:

O_j = ∑_{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 row sums of the Ghoshian matrix:

I_j = ∑_{i=1}^n g_{ij}

where g_ij is the ith row and jth column element of the Ghoshian matrix

(3) income - 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 = ∑_{i=1}^n ω _i l_{ij}

where ω _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 = ∑_{i=1}^n ε _{ei} l_{ij}

where ε _{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.

Produces a list over regions of multilpliers.

John J. P. Wade, Ignacio Sarmiento-Barbieri

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, key.sector, linkages, output.decomposition

data(toy.IO)
class(toy.IO)
M1 <- multipliers(toy.IO, multipliers = "income", 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"))