Aggregation Matrix
Contents
Definition
Aggregation Matrix in the context of Input-Output Analysis is a Boolean Matrix that aims to produce a coarse-grained version of a more granular Input-Output Model.
Aggregation can be for example along sectoral or regional dimensions.
Vectors and Matrices can be aggregated by multiplying with the aggregation matrix. Mathematically a aggregation matrix S is a matrix, where each value is either zero or one.
An aggregation matrix with K rows and N columns is used to aggregate a dimension of size N into a smaller dimension of size K.
Vector Quantity Aggregation
A vector Y of dimension N is aggregated into a vector K through its pre-multiplication with the aggregation matrix.
or in more explicitly:
Matrix Quantity Aggregation
A matrix of dimension N is aggregated through its pre-multiplication with the aggregation matrix and the post-multiplication with the aggregation matrix transpose.