Table formats / IOT · SUT
An IOT uses the same Sector set on the rows and columns of its square transaction matrix. A sector represents an industry or a product, depending on the source. In a multiregional table, each sector is also identified by region.
Structure and native matrices#
Select a block to see its definition and default axes.
| Sectors | Final demand | |
|---|---|---|
| Sectors | ZTransactions |
YFinal demand |
| Factors | VFactors |
VYFactors |
| Satellite accounts | ESatellite accounts |
EYSatellite accounts |
ZNative flows
Intersectoral transaction flows matrix
- Rows
- Region, Sector
- Columns
- Region, Sector
YNative flows
Final demand matrix
- Rows
- Region, Sector
- Columns
- Region, Consumption category
VNative flows
Value added transaction flows matrix
- Rows
- Factor of production*
- Columns
- Region, Sector
VYNative flows
Value added transaction matrix for final demand
- Rows
- Factor of production*
- Columns
- Region, Consumption category
ENative flows
Environmental transaction flows matrix
- Rows
- Satellite account*
- Columns
- Region, Sector
EYNative flows
Environmental transaction flows matrix for final demand
- Rows
- Satellite account*
- Columns
- Region, Consumption category
Read Z from the supplying row to the purchasing column. Y sends
output to final-demand categories. V and E attach factors of production
and satellite accounts to producing sectors; VY and EY attach them
directly to final demand.
Units follow the account. Transactions may be monetary or physical;
satellite rows may use kg, energy or other units. * in an axis description
means that an extension can carry additional index levels through
matrix_layouts. Some sources supply no values for particular blocks.
Inspect a small IOT#
import mario
db = mario.load_test("IOT")
transactions = db.Z
sectors = db.get_index("Sector")
transactions.index[:3]
Result · A pandas DataFrame. Transaction rows and columns identify
regions and sectors; sectors contains the native sector labels.
Indices#
An axis combines the relevant sets. For example, a transaction connects a
(Region, Sector) to another (Region, Sector); final-demand columns use
(Region, Consumption category). MARIO’s pandas representation also stores
the set label in its Level index level.
| Index | Description |
|---|---|
| Region | Regions represented in the table |
| Sector | Sectors representing industrial activities (or products) |
| Consumption category | Categories of final demand (e.g. Households, Gross fixed capital, Changes in inventories…) |
| Factor of production | Factors of production including value added categories including, for single-region tables, imports |
| Satellite account | Environmental extensions |
Some sources have different sector labels in each region. See regional classifications for regional queries, and the index reference for accepted aliases.
Coefficients and derived matrices#
Direct inputs
z · v · e
Divide each flow column by that sector’s output X:
The same column normalization gives v from V and e from E.
e has satellite-account units per unit of sector output.
Supply-chain requirements
w · f
The Leontief system adds direct and upstream requirements:
f is a footprint intensity per unit of final demand for sector output.
Direct final-demand accounts EY are separate.
output = db.X
intensity = db.f
MARIO resolves dependencies on demand. The formula for f does not require
materializing w when the selected computation method uses a linear solve.
Matrix names and default axes
| Matrix | Description | Row indices | Column indices |
|---|---|---|---|
| X | Total production vector | Region, Sector | - |
| z | Intersectoral transaction coefficients matrix | Region, Sector | Region, Sector |
| v | Value added coefficients matrix | Factor of production* | Region, Sector |
| e | Environmental transaction coefficients matrix | Satellite account* | Region, Sector |
| w | Leontief inverse matrix | Region, Sector | Region, Sector |
| f | Total (direct+indirect) environmental coefficients matrix | Satellite account* | Region, Sector |
| F | Total (direct+indirect) environmental transaction flows matrix | Satellite account* | Region, Sector |
| m | Total (direct+indirect) value added coefficients matrix | Factor of production* | Region, Sector |
| M | Total (direct+indirect) value added transaction matrix | Factor of production* | Region, Sector |
| p | Price index vector | Region, Sector | - |
F and M are absolute allocations to final demand; lowercase f
and m are intensities. See the calculation reference for the equations, including how direct
final-demand accounts are treated. The full matrix catalogue includes additional decompositions.
Continue with calculating matrices, GHG characterization or importing a database.