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

## Description

Computes the Leontief Inverse and Backward and Forward Linkages

## Usage

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

## Arguments

 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

## Details

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}}

## Value

Returns a data.frame with the Leontief Inverse

## Author(s)

Ignacio Sarmiento-Barbieri

## References

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)

## Examples

 1 2 3 4 5 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) 

ignaciomsarmiento/ioanalysis documentation built on May 21, 2019, 9:52 a.m.