Nomenclature#
This page defines the core terminoloty used across the MARIO documentation and collects the canonical names used for indices and matrices.
Basic definitions#
- Database
The MARIO object the users interact with. A database stores one table, its scenarios, the parsed and derived matrices, and the metadata needed to work with them.
- Table
The table is a collection of matrices arranged in a certain format. In MARIO, the structural table types are Input-Output Tables (IOTs) and Supply and Use Tables (SUTs).
- Scenarios
Different states of the same table. See the dedicated page on Scenarios.
- Matrix
One named data structure shaping a table and stored in a database, such as
Z,Y,UorS. A database contains many matrices, some parsed directly while others can be computed on demand.- Mode
A matrix can be either stored in
flowsorcoefficientsmode, depending on whether it contains absolute accounting values or technical coefficients. The mode is therefore a matrix-specific property, not related to the whole table or database. For example, an IOT table can be represented both by flow and coefficient matrices.Important
By convention, in MARIO, matrices named with capital letters are flow matrices (for example
ZorV), while matrices named with lowercase letters are coefficient matrices (for examplezorv).
Default canonical labels#
Below, the default names for indices and matrices are listed, along with their accepted aliases in the public API and their intended meaning.
Important
The tables below list MARIO’s canonical default names, but users can customize the public labels of matrices and accepted set aliases through settings. See Custom matrices and indices labels for the full workflow. Names that would collide with existing reserved built-in matrix names are blocked explicitly to avoid ambiguous API calls.
The same tables are available downloading the terminology workbook.
Indices#
Each matrix in MARIO has a set of indices that define its structure. The table below lists the canonical MARIO index names, where they apply, the accepted aliases in the public API, and their intended meaning.
| Index | Table format(s) | Acceptables | Description |
|---|---|---|---|
| Region | All | Regions, region, regions | Regions represented in the table |
| Sector | IOT | Sectors, sector, sectors | Sectors representing industrial activities (or products) |
| Commodity | SUT | Commodities, commodity, commodities, Product, Products, product, products | Commodities produced by activities |
| Activity | SUT | Activities, activitiy, activities, Industry, Industries, industry | Activities producing commodities |
| Consumption category | All | Consumption categories, consumption category, consumption categories, demand categories, Consumption_category, Consumption_categories, consumption_category, consumption_categories, demand_categories | Categories of final demand (e.g. Households, Gross fixed capital, Changes in inventories…) |
| Factor of production | All | Factors, factor, factors, Factors of production, factor of production, factors of production, Factors_of_production, factor_of_production, factors_of_production | Factors of production including value added categories including, for single-region tables, imports |
| Satellite account | All | Satellite, satellite, Satellites, satellites, Satellite accounts, satellite accounts, Satellite_accounts, satellite_accounts | Environmental extensions |
Matrices#
The table below lists the matrices currently available in MARIO, their mode, in which table format they are used, common names found in the literature, and the default row and column indices used by the package.
Download the terminology workbook
for the editable source table and the worked IOT, SUT_IT and SUT_PT
example sheets built from the MARIO test databases.
| Matrix | Mode | Table format(s) | Also known as | Description | Row indices | Column indices |
|---|---|---|---|---|---|---|
| Z | Flows | IOT | T | Intersectoral transaction flows matrix | Region, Sector | Region, Sector |
| z | Coefficients | IOT | A | Intersectoral transaction coefficients matrix | Region, Sector | Region, Sector |
| w | Coefficients | IOT | L | Leontief inverse matrix | Region, Sector | Region, Sector |
| Y | Flows | IOT | F | Final demand matrix | Region, Sector | Region, Consumption category |
| X | Flows | IOT | x, q | Total production vector | Region, Sector | - |
| V | Flows | IOT | F | Value added transaction flows matrix | Factor of production* | Region, Sector |
| v | Coefficients | IOT | f, B, S | Value added coefficients matrix | Factor of production* | Region, Sector |
| VY | Flows | All | S_Y, F_hh, F_y | Value added transaction matrix for final demand | Factor of production* | Region, Consumption category |
| E | Flows | IOT | F, D_pba, terr | Environmental transaction flows matrix | Satellite account* | Region, Sector |
| e | Coefficients | IOT | f, B, S | Environmental transaction coefficients matrix | Satellite account* | Region, Sector |
| EY | Flows | All | S_Y, F_hh, F_y | Environmental transaction flows matrix for final demand | Satellite account* | Region, Consumption category |
| M | Flows | IOT | Total (direct+indirect) value added transaction matrix | Factor of production* | Region, Sector | |
| m | Coefficients | IOT | Total (direct+indirect) value added coefficients matrix | Factor of production* | Region, Sector | |
| m_ex | Coefficients | IOT | Total (direct+indirect) value added coefficients matrix, exploded by origin region and sector | Factor of production, Region, Sector | Region, Sector | |
| F | Flows | IOT | D_cba, con | Total (direct+indirect) environmental transaction flows matrix | Satellite account* | Region, Sector |
| f | Coefficients | IOT | M | Total (direct+indirect) environmental transaction coefficients matrix | Satellite account* | Region, Sector |
| f_ex | Coefficients | IOT | Total (direct+indirect) environmental coefficients matrix, exploded by origin region and sector | Satellite account, Region, Sector | Region, Sector | |
| p | Coefficients | IOT | Price index vector | Region, Sector | - | |
| U | Flows | SUT | T | Use transaction flows matrix | Region, Commodity | Region, Activity |
| u | Coefficients | SUT | A | Use transaction coefficients matrix | Region, Commodity | Region, Activity |
| S | Flows | SUT | V, M, T | Make transaction flows matrix | Region, Activity | Region, Commodity |
| s | Coefficients | SUT | A | Make transaction coefficients matrix - Market share or inverted product-mix matrix** | Region, Activity | Region, Commodity |
| c | Coefficients | SUT | Product-mix matrix | Region, Commodity | Region, Activity | |
| wcc | Coefficients | SUT | w | Leontief inverse matrix, commodity-by-commodity coefficients | Region, Commodity | Region, Commodity |
| wca | Coefficients | SUT | w | Leontief inverse matrix, commodity-by-activity coefficients | Region, Commodity | Region, Activity |
| wac | Coefficients | SUT | w | Leontief inverse matrix, activity-by-commodity coefficients | Region, Activity | Region, Commodity |
| waa | Coefficients | SUT | w | Leontief inverse matrix, activity-by-activity coefficients | Region, Activity | Region, Activity |
| Yc | Flows | SUT | F | Final demand of commodities matrix | Region, Commodity | Region, Consumption category |
| Ya | Flows | SUT | F | Final demand of activities matrix | Region, Activity | Region, Consumption category |
| Xc | Flows | SUT | Q | Total demand (or production) of commodities vector | Region, Commodity | - |
| Xa | Flows | SUT | X | Total demand (or production) of activities vector | Region, Activity | - |
| Vc | Flows | SUT | Value added transaction flows by commodity matrix | Factor of production* | Region, Commodity | |
| Va | Flows | SUT | Value added transaction flows by activity matrix | Factor of production* | Region, Activity | |
| vc | Coefficients | SUT | Value added transaction coefficients by commodity matrix | Factor of production* | Region, Commodity | |
| va | Coefficients | SUT | Value added transaction coefficients by activity matrix | Factor of production* | Region, Activity | |
| Ec | Flows | SUT | Environmental transaction flows by commodity matrix | Satellite account* | Region, Commodity | |
| Ea | Flows | SUT | Environmental transaction flows by activity matrix | Satellite account* | Region, Activity | |
| ec | Coefficients | SUT | Environmental transaction coefficients by commodity matrix | Satellite account* | Region, Commodity | |
| ea | Coefficients | SUT | Environmental transaction coefficients by activity matrix | Satellite account* | Region, Activity | |
| Mc | Flows | SUT | Total (direct+indirect) value added transaction by commodity matrix | Factor of production* | Region, Commodity | |
| Ma | Flows | SUT | Total (direct+indirect) value added transaction by activity matrix | Factor of production* | Region, Activity | |
| mc | Coefficients | SUT | Total (direct+indirect) value added coefficients by commodity matrix | Factor of production* | Region, Commodity | |
| ma | Coefficients | SUT | Total (direct+indirect) value added coefficients by activity matrix | Factor of production* | Region, Activity | |
| mc_ex | Coefficients | SUT | Total (direct+indirect) value added coefficients by commodity matrix, exploded by origin region and activity | Factor of production, Region, Activity | Region, Commodity | |
| ma_ex | Coefficients | SUT | Total (direct+indirect) value added coefficients by activity matrix, exploded by origin region and activity | Factor of production, Region, Activity | Region, Activity | |
| Fc | Flows | SUT | Total (direct+indirect) environmental transaction flows by commodity matrix | Satellite account* | Region, Commodity | |
| Fa | Flows | SUT | Total (direct+indirect) environmental transaction flows by actvity matrix | Satellite account* | Region, Activity | |
| fc | Coefficients | SUT | Total (direct+indirect) environmental transaction coefficients by commodity matrix | Satellite account* | Region, Commodity | |
| fa | Coefficients | SUT | Total (direct+indirect) environmental transaction coefficients by activity matrix | Satellite account* | Region, Activity | |
| fc_ex | Coefficients | SUT | Total (direct+indirect) environmental coefficients by commodity matrix, exploded by origin region and activity | Satellite account, Region, Activity | Region, Commodity | |
| fa_ex | Coefficients | SUT | Total (direct+indirect) environmental coefficients by activity matrix, exploded by origin region and activity | Satellite account, Region, Activity | Region, Activity | |
| pc | Coefficients | SUT | Price index vector by commodity | Region, Commodity | - | |
| pa | Coefficients | SUT | Price index vector by activity | Region, Activity | - | |
| b | Coefficients | IOT | B | Intersectoral transaction direct-output coefficients matrix | Region, Sector | Region, Sector |
| g | Coefficients | IOT | G | Ghosh coefficients matrix | Region, Sector | Region, Sector |
| bu | Coefficients | SUT | B | Use transaction direct-output coefficients matrix | Region, Commodity | Region, Activity |
| bs | Coefficients | SUT | B | Supply transaction direct-output coefficients matrix | Region, Activity | Region, Commodity |
| gcc | Coefficients | SUT | G | Ghosh inverse matrix, commodity-by-commodity coefficients | Region, Commodity | Region, Commodity |
| gca | Coefficients | SUT | G | Ghosh inverse matrix, commodity-by-activity coefficients | Region, Commodity | Region, Activity |
| gac | Coefficients | SUT | G | Ghosh inverse matrix, activity-by-commodity coefficients | Region, Activity | Region, Commodity |
| gaa | Coefficients | SUT | G | Ghosh inverse matrix, activity-by-activity coefficients | Region, Activity | Region, Activity |
Important
* means that, using matrix_layouts, MARIO can accept richer
row-index structures than the default one, for example by adding
Region or Sector levels to V and E.
** means that s in SUTs can be either a market-share matrix or a
product-mix matrix depending on the active
technology assumption.