Difference between revisions of "Leontief Matrix"

From Open Risk Manual
 
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== Definition ==
 
== Definition ==
'''Leontief Matrix'''. The Leontief “A” matrix is a direct requirements table calculated from an industry-by-industry transactions table.  
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'''Leontief Matrix'''. The Leontief A matrix is a direct requirements table calculated from an industry-by-industry transactions table.  
  
The “I - A” matrix (where I is an identity matrix with ones in the diagonal cells and zeroes in other cells) can be inverted to calculate the inverse ((I - A)-1 ) or total requirements table.  
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The I - A matrix (where I is an identity matrix with ones in the diagonal cells and zeroes in other cells) can be inverted to calculate the [[Leontief Inverse Matrix]] or total requirements table.  
  
The elements of the inverse enable one to estimate both the direct and indirect impacts of a change in final uses.<ref>Concepts and Methods of the US Input-Output Accounts. K.J.Horowitz, M.A.Planting, 2009</ref>
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The elements of the inverse matrix enable one to estimate both the direct and indirect impacts of a change in final uses.<ref>Concepts and Methods of the US Input-Output Accounts. K.J.Horowitz, M.A.Planting, 2009</ref>
  
 
== References ==
 
== References ==

Latest revision as of 18:24, 16 November 2023

Definition

Leontief Matrix. The Leontief A matrix is a direct requirements table calculated from an industry-by-industry transactions table.

The I - A matrix (where I is an identity matrix with ones in the diagonal cells and zeroes in other cells) can be inverted to calculate the Leontief Inverse Matrix or total requirements table.

The elements of the inverse matrix enable one to estimate both the direct and indirect impacts of a change in final uses.[1]

References

  1. Concepts and Methods of the US Input-Output Accounts. K.J.Horowitz, M.A.Planting, 2009