inverse.important {ioanalysis}

Inverse.Important Coefficients

Description

Calculates the inverse-important coefficients as in Blair and Miller (2009)

Usage

inverse.important(io, i, j, delta.aij)

Arguments

io

An InputOutput class object from as.inputoutput

i

Integer. The row component of the change in the matrix of technical input coefficients

j

Integer. The column component of the change in the matrix of technical input coefficients

delta.aij

Integer. By how much aij should change by

Details

The inverse-important coefficients is the change in the Leontief matrix due to a specified change in one element of the matrix of technical input coefficients (A). This uses the formula:

\Delta L = \frac{\Delta a_{ij}}{1-l_{ji}\Delta a_{ij}} F_1(i,j)

where F_1(X,Y) is the first order field of influence.

Value

Returns the change in the Leontief matrix due the change in one element of the matrix of technical input coefficients. To find the new Leontief inverse induced by this change, use io$L + inverse.important().

Author(s)

John J. P. Wade, Ignacio Sarmiento-Barbieri

References

Blair, P.D. and Miller, R.E. (2009). "Input-Output Analysis: Foundations and Extensions". Cambridge University Press

Examples

data(toy.IO)
class(toy.IO)
i <- 3
j <- 4
delta.aij <- 0.5
II <- inverse.important(toy.IO, i, j, delta.aij)