Input-Output Coefficient

From Open Risk Manual


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).

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


  • 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


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