Difference between revisions of "Environmental Impact Coefficient"
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== Definition == | == Definition == | ||
| − | '''Environmental Impact Coefficient''' is a straightforward approach to account for pollution generation associated with interindustry activity. | + | '''Environmental Impact Coefficient''' is a straightforward approach to account for pollution generation associated with interindustry activity.<ref>R.E. Miller and P.D. Blair, Input-Output Analysis: Foundations and Extensions, Second Edition, Cambridge University Press, 2009</ref> |
== Formula == | == Formula == | ||
| − | Assume a matrix of pollution output or direct impact coefficients | + | Assume a matrix of pollution output or direct impact coefficients, |
| − | + | :<math> | |
| + | D^{p} = d^p_{kj}, | ||
| + | </math> | ||
| − | + | 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 | + | :<math> |
| + | x^p = D^p x | ||
| + | <math> | ||
| + | |||
| + | where <math>x^p</math> is the vector of pollution levels. | ||
| + | |||
| + | By combining the above with the traditional [[Leontief Model]], <math>x = L f</math>, where <math>L = (I - A)^{-1}</math> , we can compute <math>x^p</math> 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: | ||
| + | |||
| + | :<math> | ||
| + | x^p = [D^p L] f | ||
| + | <math> | ||
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. | 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 == | == Further Resources == | ||
| − | * [https://www.openriskacademy.com/ | + | * [https://www.openriskacademy.com/course/view.php?id=70 Crash Course on Input-Output Model Mathematics] |
| + | * [https://www.openriskacademy.com/course/view.php?id=64 Introduction to Input-Output Models using Python] | ||
== References == | == References == | ||
Revision as of 17:48, 16 November 2023
Definition
Environmental Impact Coefficient is a straightforward approach to account for pollution generation associated with interindustry activity.[1]
Formula
Assume a matrix of pollution output or direct impact coefficients,
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
is the vector of pollution levels.
By combining the above with the traditional Leontief Model, 
, where 
, we can compute 
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:
- <math>
x^p = [D^p L] f <math>
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
References
- ↑ R.E. Miller and P.D. Blair, Input-Output Analysis: Foundations and Extensions, Second Edition, Cambridge University Press, 2009
