Matrix mapping sectors to the goods they produce (makeinv)

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The G-Cubed model, in general, allows each sector to produce more than one type of good in the economy. The mapping from sector to fraction of that sector’s output that is a specific good is expressed in the makeinv matrix.

For example, in an economy, with two sectors and two goods, where sector 1 split its output 66% to good 1 and 34% to good 2 and where sector 2 split its output 34% to good 1 and 66% to good 2, the makeinv matrix would be:

\[\begin{bmatrix} 0.66 & 0.34 \\ 0.34 & 0.66 \end{bmatrix}\]

In all G-Cubed models in current use the number of goods produced is equal to the number of sectors and each sector produces 100% of the corresponding goods. Thus, the makeinv matrix is an identity matrix with order equal to the number of sectors/goods.

There is one a makeinv matrix for each region. This matrix is vectorised for the region and the makeinv matrix used stored in the calibrated parameters has a column for each region, with that column being the vectorised matrix. The elements in column j are for region j.