Environmental Impact Coefficient

Definition

Environmental Impact Coefficient is a straightforward approach to account for pollution generation associated with interindustry activity.

Formula

Assume a matrix of pollution output or direct impact coefficients,

$D^{p} = d^p_{kj},$

Each element of this matrix expresses the amount of pollutant (more broadly environmental impact) of type k, e.g., CO2 or sulfur dioxide, generated per dollar’s worth of industry j’s output.

The level of pollution associated with a given vector of Total Output can be expressed as

$x^p = D^p x$

where $x^p$ is the vector of pollution levels.

By combining the above with the traditional Leontief Model, $x = L f$, where $L = (I - A)^{-1}$ , we can compute $x^p$ as a function of final demand, that is, the total pollution of each type generated by the economy directly and indirectly in supporting that final demand:

$x^p = [D^p L] f$

We can view the bracketed quantity as a matrix of total environmental impact coefficients; that is, an element of this matrix is the total pollution impact generated per dollar’s worth of final demand presented to the economy.

Further Resources

• Crash Course on Input-Output Model Mathematics
• Introduction to Input-Output Models using Python