leontief.inv: Leontief Inverse
In ignaciomsarmiento/ioanalysis: Input-Output Analysis

Description Usage Arguments Details Value Author(s) References Examples

Computes the Leontief Inverse and Backward and Forward Linkages

1	leontief.inv(mip, X, linkages=TRUE, write.xlsx=TRUE, name="Leontief_Inv.xlsx")

`mip`	Matrix. Input output matrix
`X`	Vector. Input in each column
`linkages`	Logical. If TRUE computes Backward and Forward Linkages
`write.xlsx`	Logical. If TRUE results are presented in an excel file
`name`	String. Name of the excel file

The Leontief inverse is derived from the input-output table A=[a_ij] where

a_ij=z_ij/X_j

where z_ij is the input from i required in the production of j. X_j is the corresponding input in each column. The Leontief inverse is then computed as

(I-A)^{-1}

The user has the option to compute the Backward and Forward Linkages for Key-sector Analysis. The sector j's Backward Linkage (BL_{j}) is defined as:

BL_{j}=\frac{\frac{1}{n}∑_{i=1}^{n}b_{ij}}{\frac{1}{n^{2}}∑_{j=1}^{n}∑_{i=1}^{n}b_{ij}}

The sector j's Forward Linkage (FL_{i}) is defined as:

FL_{i}=\frac{\frac{1}{n}∑_{j=1}^{n}b_{ij}}{\frac{1}{n^{2}}∑_{j=1}^{n}∑_{i=1}^{n}b_{ij}}

Returns a data.frame with the Leontief Inverse

Ignacio Sarmiento-Barbieri

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)

mip<-mat_40x40[1:40,2:41] #Input-output coefficients

X<-mat_40x40$DT.a.PB[1:40]  #Total output vector

L<-leontief.inv(mip,X,linkages=TRUE,write.xlsx = FALSE)