# key.sector: Impact Analysis: Backward and Forward linkages In ignaciomsarmiento/ioanalysis: Input-Output Analysis

## Description

Computation of Backward and Forward linkages. It aims to identify those sectors whose economic activity exerts a greater than average influence on the whole economy. Key sectors are identified by calculating backard and forward linkages. Let

B=(I-A)^{-1}=[b_{ij}]

be the Leontief inverse matrix and let B_{j} and B_{i} be the column and row multipliers of this Leontief inverse. The sector j's backward linkage (BL_{j}) and forward linkage (FL_{i}) are 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}}

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

Both indicators are used to identify key sectors, the usual interpretation is that if

BL_{j}>1

a unit change in final demand in sector j generates an above-average increase in activity in the economy. Similarly, for

FL_{i}>1

it is asserted that a unit change in all sector's final demand would create an above average increase in sector i. Thus, a key sector is identified as one having both indicators grater than one.

## Usage

 1 key.sector(mip, X, epsilon=0.1, key=TRUE, cutoff=1, write.xlsx=TRUE, name="Key_sector.xlsx")

## Arguments

 mip Input-output matrix X Total input or output dietz Logical. If TRUE uses Dietzenbacher (1991) eigenvalues method key Logical. If TRUE identifies key sectors cutoff Numerical above cutoff level sectors are considered as key sectors write.xlsx Logical. If TRUE results are presented in an excel file ... Arguments to be passed to the write.xlsx function

## Details

The function uses the sector names from the column names on the Input-output matrix. If key=TRUE it orders the sectors first by the Backward Linkage and second by Forward Linkage

## Value

Returns a vector with the calculated Backward and Forward linkages for each sector

## 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)

Dietzenbacher, E. 1992. "The measurement of interindustry linkages: key sectors in the Netherlands". Economic Modelling, 9(4), 419-437.