# Input-Output Coefficient

## 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).

{\displaystyle {\begin{aligned}a_{ij}&={\frac {x_{ij}}{x_{j}}}\\v_{ij}&={\frac {z_{ij}}{x_{j}}}\end{aligned}}}

where

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

## References

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

{{#set:Has Formula = HAS_FORMULA}}

__SHOWFACTBOX__