# multipliers: Multiplier Analysis In ignaciomsarmiento/ioanalysis: Input-Output Analysis

## Description

According to Nazara et al. (2003) and Blair and Miller (2009), at least four multipliers can be calculated from an input-output matrix: (i) output multiplier, (ii) input multiplier, (iii) income multiplier and (iv) employment multiplier.

(i) Output multiplier: it is computed from the Leontief inverse. Let

B=[b_{ij}]

be the Leontief inverse matrix, then the output multiplier for sector j is

O_{j}=∑_{i=1}^{n}b_{ij}

(ii) Input multiplier: it is computed from the Goshian inverse. Let

G=[g_{ij}]

be the Goshian inverse matrix the input multiplier for sector j,

I_{j}=∑_{i=1}^{n}g_{ij}

I(iii) ncome multiplier: the calculation of this multiplier requires a wage vector (z) to calculate the household input coefficient (a):

a_{n+1,i}=\frac{z_{n+1,i}}{X_{i}}

with the Leontief inverse, the household income multiplier for sector j is

H_{j}=∑_{i=1}^{n}a_{n+1,i}b_{ij}

(iv) Employment multiplier: the calculation of this multiplier requires a sectoral employment vector (e) to calculate the labor input coefficient (w):

w_(n+1,i)=e_i / X_i

with the Leontief inverse, the employment multiplier for sector j is

E_{j}=∑_{i=1}^{n}w_{n+1,i}b_{ij}

## Usage

 1 multipliers(mip, X, z, e,write.xlsx=TRUE, name="output_multiplier.xlsx") 

## Arguments

 mip Input-output matrix X Vector. Total input or output z Vector. Household wage to calculate household input coefficient e Vector. Sectoral employment to calculate labor input coefficient write.xlsx Logical. If TRUE results are presented in an excel file name String. Name of the excel file

## Value

Returns a data frame with the calculated multipliers for each sector

## Author(s)

Ignacio Sarmiento-Barbieri

## References

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)

Wu, P.C (2009). "PyIO 2.0 Quick Start". (http://www.real.illinois.edu/pyio/)

See Also leontief.inv gosh.inv
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 #Follows the example in PyIO 2.0 Quick Start mip<-matrix(c(16,5,24,0,6,17,10,0,7,17,11,48,26,0, 8,0,43,82,33,13,17,81,51,4,35,9,93,7, 19,99,30,2,19,20,19,6,59,16,16,0,15,15, 99,45,66,11,12,7,25,22,47,4,42,26,45,1, 0,0,75,0,12,7,12,3), ncol=8, byrow=TRUE) X<-c(700,320,607,432,375,345,561,187) e<-c(10,20,30,52,10,75,51,40) z<-c(29870.9,18720,66563.8,2607,19007.7,69883,10194.2,173.1) L<-multipliers(mip=mip,X=X,z=z,e=e)