The Official Journal of the Pan-Pacific Association of Input-Output Studies (PAPAIOS)
Table 2 Basic transformation models to derive an IOT (\({\mathbf{S}}\) and \({\mathbf{E}}\) or \({\mathbf{B}}\) and \({\mathbf{h}}\)) from a SUT (\({\mathbf{V}}\) and \({\mathbf{U}}\)).
From: Analyzing the effects of the choice of model in the context of marginal changes in final demand
Model | Formulas for \({\mathbf{S}}\) or \({\mathbf{B}}\) | Formulas for \({\mathbf{E}}\) | Formulas for \({\mathbf{h}}\) |
|---|---|---|---|
A (PTA-p*p) | \({\mathbf{S}}^{{\left( {\text{A}} \right)}} = {\mathbf{UV}}^{{ - {\text{T}}}} {\hat{\mathbf{q}}}\) | \({\mathbf{E}}^{{\left( {\text{A}} \right)}} = {\mathbf{WV}}^{{ - {\text{T}}}} {\hat{\mathbf{q}}}\) | – |
B (ITA-p*p) | \({\mathbf{S}}^{{\left( {\text{B}} \right)}} = {\mathbf{U}}{\hat{\mathbf{g}}}^{ - 1} {\mathbf{V}}\) | \({\mathbf{E}}^{{\left( {\text{B}} \right)}} = {\mathbf{W}}{\hat{\mathbf{g}}}^{ - 1} {\mathbf{V}}\) | – |
C (ISA-i*i) | \({\mathbf{B}}^{{\left( {\text{C}} \right)}} = {\hat{\mathbf{g}}}{\mathbf{V}}^{{ - {\text{T}}}} {\mathbf{U}}\) | – | \({\mathbf{h}}^{{\left( {\text{C}} \right)}} = {\hat{\mathbf{g}}}{\mathbf{V}}^{{ - {\text{T}}}} {\mathbf{d}}\) |
D (PSA-i*i) | \({\mathbf{B}}^{{\left( {\text{D}} \right)}} = {\mathbf{V}}{\hat{\mathbf{q}}}^{ - 1} {\mathbf{U}}\) | – | \({\mathbf{h}}^{{\left( {\text{D}} \right)}} = {\mathbf{V}}{\hat{\mathbf{q}}}^{ - 1} {\mathbf{d}}\) |