Input-Output Coefficient

Definition

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

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]

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).