Difference between revisions of "Input-Output Coefficient"
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== Definition == | == Definition == | ||
| − | '''Input-Output Coefficient''' (also technical coefficient) is any of the numerical elements of | + | '''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 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> | ||
== Formula == | == Formula == | ||
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a_{ij} & = \frac{x_{ij}}{x_j} \\ | a_{ij} & = \frac{x_{ij}}{x_j} \\ | ||
v_{ij} & = \frac{z_{ij}}{x_j} | v_{ij} & = \frac{z_{ij}}{x_j} | ||
| + | \end{align} | ||
</math> | </math> | ||
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* <math>v_{ij}</math> are the input coefficients for other primary inputs, | * <math>v_{ij}</math> are the input coefficients for other primary inputs, | ||
* <math>x_{ij}</math> is the flow of commodity i to sector j (transaction bloc of the IO table), | * <math>x_{ij}</math> is the flow of commodity i to sector j (transaction bloc of the IO table), | ||
| − | * <math>z_{ij}</math> is the flow of | + | * <math>z_{ij}</math> is the flow of [[Primary Input]] i to sector j ([[Value Added]] bloc of the IO table) |
* <math>x_j</math> is the output of sector j (production value). | * <math>x_j</math> is the output of sector j (production value). | ||
| − | |||
== See Also == | == See Also == | ||
* [[Input-Output Model]] | * [[Input-Output Model]] | ||
| + | |||
| + | == Further Resources == | ||
| + | * [https://www.openriskacademy.com/course/view.php?id=70 Crash Course on Input-Output Model Mathematics] | ||
| + | * [https://www.openriskacademy.com/course/view.php?id=64 Introduction to Input-Output Models using Python] | ||
| + | |||
== References == | == References == | ||
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).
where
-
are the input coefficients for intermediate inputs, -
are the input coefficients for other primary inputs, -
is the flow of commodity i to sector j (transaction bloc of the IO table), -
is the flow of Primary Input i to sector j (Value Added bloc of the IO table) -
is the output of sector j (production value).
See Also
Further Resources
References
- ↑ R.E. Miller and P.D. Blair, Input-Output Analysis: Foundations and Extensions, Second Edition, Cambridge University Press, 2009
