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The Official Journal of the Pan-Pacific Association of Input-Output Studies (PAPAIOS)

Table 5 Results of a change in accounting units in the expressions for the satellite vector for models A–D

From: Analyzing the effects of the choice of model in the context of marginal changes in final demand

Model Unit-changed formula for impact analysis Invariant
A/C (PTA-p*p/ISA-i*i) \(\Delta {\tilde{\mathbf{w}}}^{{\left( {{\text{A}}/{\text{C}}} \right)}} = {\hat{\boldsymbol{\beta }}}\Delta {\mathbf{w}}^{{\left( {{\text{A}}/{\text{C}}} \right)}}\) Yes
B/D (ITA-p*p/PSA-i*i) \(\Delta {\tilde{\mathbf{w}}}^{{\left( {{\text{B}}/{\text{D}}} \right)}} = \hat{{\boldsymbol{\beta }}}{\bf W}\left( {{\hat{\mathbf{q}}\mathbf{V}}^{ - 1} {\hat{\mathbf{g}}} - {\mathbf{U}}} \right)\Delta {\mathbf{d}} \ne \hat{\boldsymbol{\beta }}\Delta {\mathbf{w}}^{{\left( {{\text{B}}/{\text{D}}} \right)}}\) No