Calculations and checks

Integrity check of original data

The program checks whether the IOT is balanced. If the total outputs differ from the total inputs by a difference superior to 0.001%, it stops. You can adjust this by changing the variable called max_balancing_difference.

IOT components (aggregate structure)

The analysis starts with a given IOT provided by an external file (see Data input format and its parsing). All IOT components are read from it and stored into the actual_structure_dictionary array:

1. the primary resources r
2. the intersectoral flows Z
3. the emissions: w_m (also aggregated as``w``)
4. the final demand fd
5. the total outputs x
6. the total final outputs tot_final_outputs which is fd + w

IOA components (aggregate structure)

Then, the IOA components are calculated from the original structure and stored into actual_structure_dictionary only:

1. the technical coefficient matrix A
2. the Leontief matrix L
3. the emission intensity matrices E_m and Etot, and
4. the primary resource input coefficients r_coefs.

The Leontief inverse matrix is calculated using a non-conventional method required by PIOTs since they produce several final outputs (final goods and several (m) emissions) [AAM13].

IOT components (product based structures)

Using the IOA components from above, the IOT components for each product based structure are calculated following [AAM13]. Each set of IOT components are stored in the``product_based_structures`` array, each complete set under product_based_structures['prod_based_struct_n] where n is the sector for which the product-based decomposition was run. Recall NumPy starts numbering at 0, so product_based_structures['prod_based_struct_0] contains all IOT components of the product-based decomposition for the first sector. The IOT set is the same as for the aggregate structure:

1. the primary resources r
2. the intersectoral flows Z
3. the emissions: w_m (also aggregated as``w``)
4. the final demand fd
5. the total outputs x
6. the total final outputs tot_final_outputs which is fd + w

Macroscopic Indicators

Some top-level macroscopic indicators are then calculated for the aggregated structure and each product-based structure.

Overlapped cyclic-acyclic and direct-indirect structures for the product-based and aggregate structures

Then, the program run an n-iteration to find all cyclic-acyclic and direct-indirect structural elements of the n product-based structure. At the end of each iteration the cyclic-acyclic and direct-indirect of the aggregated structure is updated with the corresponding share of the product-based structure it has been found. So, at the end of that iteration all product-based structures and the aggregate structure are found.

TODO: explain in detail the calculations. explain last check of data.

Finding the cyclic-acyclic and direct-indirect meta-structures for the product-based and aggregate structures

Since finding the cyclic-acyclic and direct-indirect meta-structures is a matter of aggregating the overlapped cyclic-acyclic and direct-indirect components derived in the previous section, the meta-structures for each product-based structure are calculated at the end of the previous iteration.

However, since all overlapped cyclic-acyclic and direct-indirect components of the aggregate structure must be calculated before they they can be aggregated, finding the cyclic-acyclic and direct-indirect meta-structures for the aggregate structure is only performed after the iteration calculating the product-based structures.

Calculating structural indicators of the cyclic structure for the product-based structures

See [AAM13]

Calculating structural indicators of the cyclic structure for the aggregated structure

They are calculated as a weighted average of the former.

Calculating structural indicators of the indirect structure for the product-based structures

See [AAM13]

Calculating structural indicators of the indirect structure for the aggregated structure

They are calculated as a weighted average of the former.

Bibligraphy

[AAM13]

(1, 2, 3, 4) Altimiras-Martin, Aleix (2013) PhD thesis