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.

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)