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, U or S. A database contains many matrices, some parsed directly while others can be computed on demand.

Mode

A matrix can be either stored in flows or coefficients mode, 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 Z or V), while matrices named with lowercase letters are coefficient matrices (for example z or v).

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.