Difference between revisions of "Input-Output Coefficient"

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== Definition ==
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'''Input-Output Coefficient''' (also technical coefficient) is any of the numerical elements of a symmetric [[Input-Output Matrix]].
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== Interpretation ==
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The input coefficients can be interpreted as the percentage share (%) of costs for [[Intermediate Input | intermediate inputs]] (goods and services) and [[Primary Input | primary inputs]] in [[Total Output]] (production value).<ref>R.E. Miller and P.D. Blair, Input-Output Analysis: Foundations and Extensions, Second Edition, Cambridge University Press, 2009</ref>
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== Formula  ==
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The input-output coefficients, are calculated by dividing each value in the IO table by the corresponding column total (i.e., the production value).
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:<math>
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\begin{align}
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a_{ij} & = \frac{x_{ij}}{x_j} \\
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v_{ij} & = \frac{z_{ij}}{x_j}
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\end{align}
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</math>
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where
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* <math>a_{ij}</math> are the input coefficients for intermediate inputs,
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* <math>v_{ij}</math> are the input coefficients for other primary inputs,
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* <math>x_{ij}</math> is the flow of commodity i to sector j (transaction bloc of the IO table),
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* <math>z_{ij}</math> is the flow of [[Primary Input]] i to sector j ([[Value Added]] bloc of the IO table)
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* <math>x_j</math> is the output of sector j (production value).
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== See Also ==
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* [[Input-Output Model]]
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== Further Resources ==
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* [https://www.openriskacademy.com/course/view.php?id=70 Crash Course on Input-Output Model Mathematics]
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* [https://www.openriskacademy.com/course/view.php?id=64 Introduction to Input-Output Models using Python]
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== References ==
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<references/>
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[[Category:EEIO]]
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{{#set:Has Formula = HAS_FORMULA}}
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Latest revision as of 18:17, 16 November 2023

Definition

Input-Output Coefficient (also technical coefficient) is any of the numerical elements of a symmetric Input-Output Matrix.

Interpretation

The input coefficients can be interpreted as the percentage share (%) of costs for intermediate inputs (goods and services) and primary inputs in Total Output (production value).[1]

Formula

The input-output coefficients, are calculated by dividing each value in the IO table by the corresponding column total (i.e., the production value).


\begin{align}
a_{ij} & = \frac{x_{ij}}{x_j} \\
v_{ij} & = \frac{z_{ij}}{x_j}
\end{align}

where

  • a_{ij} are the input coefficients for intermediate inputs,
  • v_{ij} are the input coefficients for other primary inputs,
  • x_{ij} is the flow of commodity i to sector j (transaction bloc of the IO table),
  • z_{ij} is the flow of Primary Input i to sector j (Value Added bloc of the IO table)
  • x_j is the output of sector j (production value).

See Also

Further Resources


References

  1. R.E. Miller and P.D. Blair, Input-Output Analysis: Foundations and Extensions, Second Edition, Cambridge University Press, 2009