Output Multiplier

From Open Risk Manual

Definition

An Output-to-Output Multiplier, or simply output multiplier, indicates how total production will change as Final Demand is changed in any one sector of the economy. The output multiplier measures the amount of output generated by a $1 change in final demand for the output of the jth sector.[1]

Output multipliers are an example of the questions tackled by Input-Output Analysis.

Formula

The output multiplier for sector j is the sum of column j of the Leontief Inverse Matrix. If we represent the elements of the Leontief Inverse Matrix L=(I-A)^{-1} as l_{ij}, then the output multiplier is defined as the column sum:


O_{j} = \sum_{i=1}^{n} l_{ij}

Further Resources

References

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