Input-Output Coefficient

Definition

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

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

• Input-Output Model

Further Resources

• Crash Course on Input-Output Model Mathematics