Table 5.
Definition of symbols used in equations
| Symbol | Definition | Dimension | Used in equation |
|---|---|---|---|
| Subscripts | |||
| i | Country subscript | 41 countries: see Table 3 | |
| s | Sector subscript | 35 sectors: see Table 4 | |
| t | Time subscript | 15 years: 1995–2009 | |
| Vectors and matrices | |||
| T | Territorial emissions | ||
| Tis | … in sector s of country i | 1 × 1 | (1) |
| Ti | … in country i | 1 × 1 | (3) |
| e | Emission intensity of output | ||
| eis | … in sector s of country i | 1 × 1 | |
| ei | … in all sectors of country i | 35 × 1 | (1) |
| x | Output | (3) | |
| xis | … in sector s of country i | 1 × 1 | |
| xi | … in all sectors of country i | 35 × 1 | |
| ε | Emission intensity of value added | (1) | |
| εis | … in sector s of country i | 1 × 1 | (3) |
| z | Value added | ||
| zis | … in sector s of country i | 1 × 1 | |
| C | Consumption-based emissions | (1), (5)* | |
| Cis | … in sector s of country i | 1 × 1 | |
| Ci | … in country i | 1 × 1 | |
| φ | Emission intensity of final demand | (1) | |
| φis | … in sector s of country i | 1 × 1 | |
| … in average over all sectors and all countries | 1 × 1 | ||
| φi | … in all sectors of country i | 35 × 1 | (2) |
| … in average per sector over all countries | 35 × 1 | (3) | |
| y | Final demand | ||
| yis | … in sector s of country i | 1 × 1 | |
| yi | … in all sectors of country i | 35 × 1 | (2), (6)* |
| NCO2XP | Net CO2 exports | (4), (9)*, (10)*, (11)*, (12)* | |
| NCO2XPi | … from country i | 1 × 1 | (3), (4), (7)*, (8)* |
| A | Input-output coefficients | ||
| Ai | … in country i | 35 × 35 | (4), (7)*, (8)*, (9)*, (10)*, (11)*, (12)* |
| XP | Exports (of goods and services) | ||
| XPi | … from all sectors of country i | 35 × 1 | |
| XPij | … from all sectors of country i to country j | 35 × 1 | (2) |
| MP | Imports (of goods and services) | (3) | |
| MPi | … in all sectors of country i | 35 × 1 | |
| Auxiliary matrices | |||
| I | Identity matrix | 35 × 35 | (3) |
| u | Vector of ones | 35 × 1 | (4), (9), (10), (11), (12) |
Note: Some elements that appear in the equations are time specific as indicated by a t subscript. These elements are not explicitly listed in this table, as they are equivalent to their counterpart without time dimension. * denotes the equations in which the elements are time specific