The Official Journal of the Pan-Pacific Association of Input-Output Studies (PAPAIOS)
Table 3 Basic transformation models to derive IO coefficient matrices \({\mathbf{A}}\) and \({\mathbf{R}}\) from a SUT.
From: Analyzing the effects of the choice of model in the context of marginal changes in final demand
Model | Formulas for \({\mathbf{A}}\) | Formulas for \({\mathbf{R}}\) |
|---|---|---|
A (PTA-p*p) | \({\mathbf{A}}^{{\left( {\text{A}} \right)}} = {\mathbf{S}}^{{\left( {\text{A}} \right)}} {\hat{\mathbf{q}}}^{ - 1}\) | \({\mathbf{R}}^{{\left( {\text{A}} \right)}} = {\mathbf{E}}^{{\left( {\text{A}} \right)}} {\hat{\mathbf{q}}}^{ - 1}\) |
B (ITA-p*p) | \({\mathbf{A}}^{{\left( {\text{B}} \right)}} = {\mathbf{S}}^{{\left( {\text{B}} \right)}} {\hat{\mathbf{q}}}^{ - 1}\) | \({\mathbf{R}}^{{\left( {\text{B}} \right)}} = {\mathbf{E}}^{{\left( {\text{B}} \right)}} {\hat{\mathbf{q}}}^{ - 1}\) |
C (ISA-i*i) | \({\mathbf{A}}^{{\left( {\text{C}} \right)}} = {\mathbf{B}}^{{\left( {\text{C}} \right)}} {\hat{\mathbf{g}}}^{ - 1}\) | \({\mathbf{R}}^{{\left( {\text{C}} \right)}} = {\mathbf{W}}{\hat{\mathbf{g}}}^{ - 1}\) |
D (PSA-i*i) | \({\mathbf{A}}^{{\left( {\text{D}} \right)}} = {\mathbf{B}}^{{\left( {\text{D}} \right)}} {\hat{\mathbf{g}}}^{ - 1}\) | \({\mathbf{R}}^{{\left( {\text{D}} \right)}} = {\mathbf{W}}{\hat{\mathbf{g}}}^{ - 1}\) |