Table formats / IOT · SUT
A SUT separates activities, which produce, from commodities, which are produced and used. Their labels and counts can differ. The supply and use blocks therefore need not be square.
Structure and native matrices#
Select a block to see its definition and default axes.
| Commodities | Activities | Final demand | |
|---|---|---|---|
| Commodities | — | UUse |
YcFinal demand |
| Activities | SSupply |
— | YaFinal demand |
| Factors | VcFactors |
VaFactors |
VYFactors |
| Satellite accounts | EcSatellite accounts |
EaSatellite accounts |
EYSatellite accounts |
UNative flows
Use transaction flows matrix
- Rows
- Region, Commodity
- Columns
- Region, Activity
YcNative flows
Final demand of commodities matrix
- Rows
- Region, Commodity
- Columns
- Region, Consumption category
SNative flows
Make transaction flows matrix
- Rows
- Region, Activity
- Columns
- Region, Commodity
YaNative flows
Final demand of activities matrix
- Rows
- Region, Activity
- Columns
- Region, Consumption category
VcNative flows
Value added transaction flows by commodity matrix
- Rows
- Factor of production*
- Columns
- Region, Commodity
VaNative flows
Value added transaction flows by activity matrix
- Rows
- Factor of production*
- Columns
- Region, Activity
VYNative flows
Value added transaction matrix for final demand
- Rows
- Factor of production*
- Columns
- Region, Consumption category
EcNative flows
Environmental transaction flows by commodity matrix
- Rows
- Satellite account*
- Columns
- Region, Commodity
EaNative flows
Environmental transaction flows by activity matrix
- Rows
- Satellite account*
- Columns
- Region, Activity
EYNative flows
Environmental transaction flows matrix for final demand
- Rows
- Satellite account*
- Columns
- Region, Consumption category
U reads commodity inputs → using activities. In MARIO, S reads
producing activities → supplied commodities; this orientation matters when
importing a source that publishes supply in the opposite orientation.
The empty diagonal cells are not additional native flow blocks.
Suffixes identify the side. a means activity and c means commodity:
Ea and Ec attach satellite accounts to those respective axes.
Yc and Ya are final-demand blocks; VY and EY attach accounts
directly to final demand. Some blocks may be zero or unavailable in a source.
Inspect a small SUT#
import mario
db = mario.load_test("SUT", tech_assumption="IT")
use = db.U
supply = db.S
activities = db.get_index("Activity")
commodities = db.get_index("Commodity")
Result · use has commodity rows and activity columns; supply
has activity rows and commodity columns. Both retain the region labels.
Indices#
A productive axis combines Region with Activity or Commodity.
MARIO’s pandas representation also stores the set label in its Level index
level. Satellite and factor accounts can carry extra levels through
matrix_layouts (marked * in the block descriptions).
| Index | Description |
|---|---|
| Region | Regions represented in the table |
| Commodity | Commodities produced by activities |
| Activity | Activities producing commodities |
| 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 |
Regional classifications can vary independently for activities and commodities. See regional classifications and the index reference for query conventions and aliases.
Coefficients and production#
Xa is activity output; Xc is commodity output/demand. Use coefficients
normalize each column of U by the output of the using activity:
Likewise, ea and va normalize activity accounts by Xa; ec and
vc normalize commodity accounts by Xc. In hybrid tables, coefficients
can express one physical unit per another: check the source units.
Technology assumptions#
The assumption controls the supply coefficients s, which connect commodity
demand to activity production. MARIO uses these two conventions:
Industry-based
IT · industry-based
Uses the observed market share of each activity in a commodity’s output.
This is the default. It supports different activity and commodity counts.
Product-based
PT · product-based
Builds the activity product mix, then inverts it:
Requires equal activity and commodity counts. On a non-square SUT, MARIO warns and falls back to IT.
The current PT builder uses a pseudoinverse if the product-mix matrix is singular. See db.s for the numerical behaviour. An invertible product mix and a singular one need different interpretation even when both return a result.
Switching assumption
db.change_assumption("PT")
assumption = db.tech_assumption
coefficients = db.s
This changes the whole database. MARIO first resets every scenario to flows,
so coefficients can be rebuilt under the new assumption. The long names
"industry-based" and "product-based" are also accepted.
See db.change_assumption().
Matrix names and default axes
| Matrix | Description | Row indices | Column indices |
|---|---|---|---|
| Xa | Total demand (or production) of activities vector | Region, Activity | - |
| Xc | Total demand (or production) of commodities vector | Region, Commodity | - |
| u | Use transaction coefficients matrix | Region, Commodity | Region, Activity |
| s | Make transaction coefficients matrix - Market share or inverted product-mix matrix** | Region, Activity | Region, Commodity |
| c | Product-mix matrix | Region, Commodity | Region, Activity |
| va | Value added transaction coefficients by activity matrix | Factor of production* | Region, Activity |
| vc | Value added transaction coefficients by commodity matrix | Factor of production* | Region, Commodity |
| ea | Environmental transaction coefficients by activity matrix | Satellite account* | Region, Activity |
| ec | Environmental transaction coefficients by commodity matrix | Satellite account* | Region, Commodity |
| waa | Leontief inverse matrix, activity-by-activity coefficients | Region, Activity | Region, Activity |
| wcc | Leontief inverse matrix, commodity-by-commodity coefficients | Region, Commodity | Region, Commodity |
| wac | Leontief inverse matrix, activity-by-commodity coefficients | Region, Activity | Region, Commodity |
| wca | Leontief inverse matrix, commodity-by-activity coefficients | Region, Commodity | Region, Activity |
| fa | Total (direct+indirect) environmental coefficients by activity matrix | Satellite account* | Region, Activity |
| fc | Total (direct+indirect) environmental coefficients by commodity matrix | Satellite account* | Region, Commodity |
| Fa | Total (direct+indirect) environmental transaction flows by actvity matrix | Satellite account* | Region, Activity |
| Fc | Total (direct+indirect) environmental transaction flows by commodity matrix | Satellite account* | Region, Commodity |
| ma | Total (direct+indirect) value added coefficients by activity matrix | Factor of production* | Region, Activity |
| mc | Total (direct+indirect) value added coefficients by commodity matrix | Factor of production* | Region, Commodity |
| pa | Price index vector by activity | Region, Activity | - |
| pc | Price index vector by commodity | Region, Commodity | - |
In a two-letter suffix, the first letter identifies the row side and the
second identifies the column side: wca has commodity rows and activity
columns. fa and fc are footprint intensities on the respective axes;
Fa and Fc are absolute allocations. The matrix reference gives their equations and dependencies.
Calculations and conversions#
MARIO can compute directly on the SUT’s native blocks:
activity_output = db.Xa
commodity_intensity = db.fc
Unified views such as Z, Y, V and E combine the split blocks for
inspection and compatible exports. They do not convert the SUT into an IOT.
Continue with calculating matrices, SUT-to-IOT conversion or importing a database.