Table 4 All emission paths of PM2.5 emission from production to consumption attribution.

From sector in Step 1

\( f_{ji}^{1 \to 0} = e_{j} A_{ji} y_{i} \)

–

–

From sector in Step 2

\( f_{kji}^{2 \to 0} = e_{k} A_{kj} A_{ji} y_{i} \)

\( f_{kj}^{2 \to 0} = e_{k} A_{kj} {\mathbf{A}}_{j:} {\mathbf{y}} \)

–

From sector in Step 3

\( f_{lkji}^{3 \to 0} = e_{l} A_{lk} A_{kj} A_{ji} y_{i} \)

\( f_{lkj}^{3 \to 1} = e_{l} A_{lk} A_{kj} {\mathbf{A}}_{j:} {\mathbf{y}} \)

\( f_{lk}^{3 \to 2} = e_{l} A_{lk} {\mathbf{A}}_{k:} {\mathbf{y}} \)