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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) \({\mathbf{A}}^{{\left( {\text{D}} \right)}} = {\mathbf{B}}^{{\left( {\text{D}} \right)}} {\hat{\mathbf{g}}}^{ - 1}\) \({\mathbf{R}}^{{\left( {\text{D}} \right)}} = {\mathbf{W}}{\hat{\mathbf{g}}}^{ - 1}\)
After Eurostat (2008, p. 349)