Transforming a SUT table from Isard to Chenery-Moses model¶
This tutorial shows how to switch a SUT table from Isard to Chenery-Moses
Background¶
In the case of a multi-regional SUT, the Isard and Chenery-Moses are two possible models that differentiate mainly in how traded commodity flows are accounted.
While an Isard model shows how each commodity is imported by or exported towards each foreign industrial activity in the USE table, the Chenery-Moses model assumes a fixed shares of imports/exports for each commodity independently on activity-specific consumption patterns.
In practical terms, the regional extradiagonal blocks of the SUPPLY matrix (S) of the Isard model are null, while the regional extradiagonal blocks of the USE matrix (U) are null in the Chenery-Moses model, as shown in the following example

Alt text¶
Perform the transformation¶
From version 0.3.0 onwards, MARIO has a built-in method to perform the transormation from Isard to Chenery-Moses. Note the opposite cannot be done since the Chenery-Moses model loses information regarding the activity-specific consumption patterns of each imported commodity in a given region.
First, we need to import a SUT table into MARIO. To do so, we can load the test SUT using the “load_test” method.
import mario
test_SUT = mario.load_test(table='SUT')
It is possible to check if the table is in Isard or Chenery-Moses format
test_SUT.is_isard()
True
test_SUT.is_chenerymoses()
False
It is also possible to check the ‘S’ or ‘U’ matrices to check which of the two models shown in the Figure above the parsed table resembles
test_SUT.S
Region | Italy | RoW | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Level | Commodity | Commodity | ||||||||||||
Item | Agriculture | Construction | Manufacturing | Mining | Services | Transport | Agriculture | Construction | Manufacturing | Mining | Services | Transport | ||
Region | Level | Item | ||||||||||||
Italy | Activity | Agriculture | 6.414041e+10 | 0.000000e+00 | 8.476744e+08 | 0.000000e+00 | 1.268921e+09 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 |
Construction | 0.000000e+00 | 2.052262e+11 | 8.890008e+06 | 0.000000e+00 | 5.602012e+09 | 1.517120e+07 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ||
Manufacturing | 0.000000e+00 | 1.581203e+09 | 1.161939e+12 | 2.616691e+09 | 2.876029e+10 | 7.861768e+08 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ||
Mining | 0.000000e+00 | 1.745479e+07 | 1.271582e+09 | 9.838438e+09 | 2.453322e+09 | 1.185310e+07 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ||
Services | 2.456823e+09 | 5.639194e+09 | 6.655796e+10 | 0.000000e+00 | 1.837665e+12 | 2.160879e+10 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ||
Transport | 0.000000e+00 | 1.567515e+09 | 1.752820e+09 | 0.000000e+00 | 9.178747e+09 | 2.613827e+11 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ||
RoW | Activity | Agriculture | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 5.969584e+12 | 1.117362e+10 | 2.223620e+11 | 4.305393e+09 | 7.087351e+10 | 3.325944e+09 |
Construction | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 3.479551e+08 | 1.256801e+13 | 3.825648e+10 | 3.405690e+09 | 5.886374e+10 | 1.964438e+09 | ||
Manufacturing | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 1.079269e+10 | 1.698351e+10 | 5.259731e+13 | 2.664999e+10 | 4.536109e+11 | 1.015322e+10 | ||
Mining | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 5.145630e+08 | 1.285635e+10 | 1.869789e+11 | 3.418478e+12 | 6.750145e+10 | 4.215670e+09 | ||
Services | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 8.931201e+09 | 1.683406e+11 | 4.937088e+11 | 1.401294e+10 | 8.244055e+13 | 6.142484e+10 | ||
Transport | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 4.692799e+08 | 1.974234e+10 | 2.833988e+10 | 3.321611e+09 | 1.741595e+11 | 8.411313e+12 |
test_SUT.U
Region | Italy | RoW | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Level | Activity | Activity | ||||||||||||
Item | Agriculture | Construction | Manufacturing | Mining | Services | Transport | Agriculture | Construction | Manufacturing | Mining | Services | Transport | ||
Region | Level | Item | ||||||||||||
Italy | Commodity | Agriculture | 2.613081e+09 | 1.359344e+08 | 2.540695e+10 | 1.208340e+05 | 3.196519e+09 | 6.463362e+07 | 5.040894e+08 | 3.136392e+07 | 1.499590e+09 | 4.977875e+06 | 3.137667e+08 | 4.489841e+06 |
Construction | 8.234773e+08 | 4.263157e+10 | 4.051235e+09 | 6.623822e+07 | 1.511442e+10 | 4.531470e+08 | 3.427462e+06 | 2.349299e+08 | 2.980236e+07 | 5.437685e+06 | 1.925330e+08 | 1.005801e+07 | ||
Manufacturing | 8.971053e+09 | 5.105912e+10 | 2.892146e+11 | 6.912651e+08 | 9.336397e+10 | 1.438189e+10 | 3.772554e+09 | 2.488904e+10 | 1.381512e+11 | 3.299075e+09 | 3.641855e+10 | 6.963659e+09 | ||
Mining | 1.747090e+07 | 1.737138e+09 | 5.761244e+09 | 8.144308e+08 | 1.826550e+09 | 9.785732e+06 | 2.190015e+07 | 2.286785e+08 | 1.458622e+09 | 8.452581e+07 | 9.789548e+07 | 5.874072e+06 | ||
Services | 8.610745e+09 | 2.599288e+10 | 2.440182e+11 | 3.419365e+09 | 4.507979e+11 | 4.406078e+10 | 4.470008e+08 | 1.903031e+09 | 8.410499e+09 | 5.091172e+08 | 2.542143e+10 | 2.150222e+09 | ||
Transport | 1.832589e+09 | 3.009282e+09 | 6.183923e+10 | 1.519988e+09 | 6.788441e+10 | 7.545770e+10 | 1.243929e+08 | 3.185796e+08 | 2.116153e+09 | 1.214371e+08 | 2.758496e+09 | 2.895771e+09 | ||
RoW | Commodity | Agriculture | 1.928423e+09 | 2.035605e+08 | 4.978912e+09 | 2.809890e+05 | 1.183583e+09 | 1.357204e+07 | 6.741444e+11 | 7.024518e+10 | 2.809955e+12 | 9.928531e+09 | 4.367480e+11 | 7.074663e+10 |
Construction | 3.291576e+06 | 7.186756e+08 | 3.417940e+07 | 7.828606e+05 | 9.880545e+07 | 5.576916e+06 | 2.234087e+10 | 8.923503e+11 | 1.381588e+11 | 4.529305e+10 | 9.396325e+11 | 4.069810e+10 | ||
Manufacturing | 1.310490e+09 | 5.517221e+09 | 1.391664e+11 | 1.830207e+08 | 2.300338e+10 | 2.655409e+09 | 7.645405e+11 | 3.996884e+12 | 2.305268e+13 | 3.743792e+11 | 5.655872e+12 | 9.891854e+11 | ||
Mining | 2.160979e+07 | 1.109156e+08 | 4.427849e+10 | 3.946190e+08 | 8.211453e+09 | 1.007717e+08 | 7.696685e+09 | 1.255249e+11 | 2.468205e+12 | 2.247546e+11 | 2.181119e+11 | 7.827661e+09 | ||
Services | 7.253485e+08 | 2.201842e+09 | 2.048522e+10 | 3.076060e+08 | 3.749654e+10 | 3.386092e+09 | 9.795698e+11 | 1.902371e+12 | 8.172955e+12 | 5.826631e+11 | 2.173693e+13 | 1.397942e+12 | ||
Transport | 8.591924e+07 | 1.201545e+08 | 4.389120e+09 | 1.170603e+08 | 7.436268e+09 | 6.770691e+09 | 1.261775e+11 | 5.322208e+11 | 1.346195e+12 | 1.353592e+11 | 1.882357e+12 | 1.428436e+12 |
The method to perform the transofrmation is called “to_chenery_moses”.
test_SUT.to_chenery_moses()
Database: to calculate s following matrices are need.
['z'].Trying to calculate dependencies.
Again, it is possible to check the model of the table after the transformation or to show the S and U matrices as done previosly
test_SUT.is_isard()
False
test_SUT.is_chenerymoses()
True
test_SUT.S
Region | Italy | RoW | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Level | Commodity | Commodity | ||||||||||||
Item | Agriculture | Construction | Manufacturing | Mining | Services | Transport | Agriculture | Construction | Manufacturing | Mining | Services | Transport | ||
Region | Level | Item | ||||||||||||
Italy | Activity | Agriculture | 5.709680e+10 | 0.000000e+00 | 5.329008e+08 | 0.000000e+00 | 1.216672e+09 | 0.000000e+00 | 7.043617e+09 | 0.000000e+00 | 3.147736e+08 | 0.000000e+00 | 5.224878e+07 | 0.000000e+00 |
Construction | 0.000000e+00 | 2.043568e+11 | 5.588811e+06 | 0.000000e+00 | 5.371345e+09 | 1.444179e+07 | 0.000000e+00 | 8.694767e+08 | 3.301197e+06 | 0.000000e+00 | 2.306671e+08 | 7.294106e+05 | ||
Manufacturing | 0.000000e+00 | 1.574504e+09 | 7.304668e+11 | 2.201047e+09 | 2.757607e+10 | 7.483785e+08 | 0.000000e+00 | 6.699043e+06 | 4.314718e+11 | 4.156436e+08 | 1.184227e+09 | 3.779831e+07 | ||
Mining | 0.000000e+00 | 1.738084e+07 | 7.993953e+08 | 8.275669e+09 | 2.352305e+09 | 1.128322e+07 | 0.000000e+00 | 7.395026e+04 | 4.721865e+08 | 1.562769e+09 | 1.010174e+08 | 5.698811e+05 | ||
Services | 2.187026e+09 | 5.615303e+09 | 4.184247e+10 | 0.000000e+00 | 1.761998e+12 | 2.056987e+10 | 2.697975e+08 | 2.389143e+07 | 2.471549e+10 | 0.000000e+00 | 7.566728e+10 | 1.038921e+09 | ||
Transport | 0.000000e+00 | 1.560874e+09 | 1.101931e+09 | 0.000000e+00 | 8.800805e+09 | 2.488158e+11 | 0.000000e+00 | 6.641049e+06 | 6.508884e+08 | 0.000000e+00 | 3.779420e+08 | 1.256693e+10 | ||
RoW | Activity | Agriculture | 1.883560e+10 | 1.483250e+06 | 1.233132e+09 | 6.596405e+07 | 8.987178e+07 | 1.069405e+07 | 5.950748e+12 | 1.117214e+10 | 2.211289e+11 | 4.239429e+09 | 7.078364e+10 | 3.315250e+09 |
Construction | 1.097890e+06 | 1.668350e+09 | 2.121553e+08 | 5.217947e+07 | 7.464268e+07 | 6.316343e+06 | 3.468572e+08 | 1.256635e+13 | 3.804432e+10 | 3.353511e+09 | 5.878910e+10 | 1.958122e+09 | ||
Manufacturing | 3.405376e+07 | 2.254489e+06 | 2.916839e+11 | 4.083114e+08 | 5.752053e+08 | 3.264608e+07 | 1.075863e+10 | 1.698126e+10 | 5.230563e+13 | 2.624168e+10 | 4.530357e+11 | 1.012057e+10 | ||
Mining | 1.623581e+06 | 1.706626e+06 | 1.036911e+09 | 5.237539e+10 | 8.559581e+07 | 1.355482e+07 | 5.129395e+08 | 1.285465e+10 | 1.859420e+11 | 3.366102e+12 | 6.741586e+10 | 4.202115e+09 | ||
Services | 2.818028e+07 | 2.234649e+07 | 2.737914e+09 | 2.146958e+08 | 1.045395e+11 | 1.975019e+08 | 8.903021e+09 | 1.683182e+11 | 4.909709e+11 | 1.379824e+10 | 8.233601e+13 | 6.122733e+10 | ||
Transport | 1.480701e+06 | 2.620712e+06 | 1.571618e+08 | 5.089126e+07 | 2.208445e+08 | 2.704525e+10 | 4.677992e+08 | 1.973972e+10 | 2.818272e+10 | 3.270719e+09 | 1.739387e+11 | 8.384268e+12 |
test_SUT.U
Region | Italy | RoW | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Level | Activity | Activity | ||||||||||||
Item | Agriculture | Construction | Manufacturing | Mining | Services | Transport | Agriculture | Construction | Manufacturing | Mining | Services | Transport | ||
Region | Level | Item | ||||||||||||
Italy | Commodity | Agriculture | 4.541504e+09 | 3.394949e+08 | 3.038586e+10 | 4.018230e+05 | 4.380102e+09 | 7.820566e+07 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 |
Construction | 8.267689e+08 | 4.335025e+10 | 4.085415e+09 | 6.702108e+07 | 1.521323e+10 | 4.587239e+08 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ||
Manufacturing | 1.028154e+10 | 5.657634e+10 | 4.283810e+11 | 8.742859e+08 | 1.163674e+11 | 1.703730e+10 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ||
Mining | 3.908070e+07 | 1.848054e+09 | 5.003973e+10 | 1.209050e+09 | 1.003800e+10 | 1.105574e+08 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ||
Services | 9.336094e+09 | 2.819472e+10 | 2.645034e+11 | 3.726971e+09 | 4.882944e+11 | 4.744687e+10 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ||
Transport | 1.918508e+09 | 3.129436e+09 | 6.622835e+10 | 1.637049e+09 | 7.532068e+10 | 8.222839e+10 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ||
RoW | Commodity | Agriculture | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 6.746485e+11 | 7.027655e+10 | 2.811455e+12 | 9.933509e+09 | 4.370617e+11 | 7.075112e+10 |
Construction | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 2.234430e+10 | 8.925852e+11 | 1.381886e+11 | 4.529848e+10 | 9.398250e+11 | 4.070816e+10 | ||
Manufacturing | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 7.683131e+11 | 4.021773e+12 | 2.319083e+13 | 3.776783e+11 | 5.692290e+12 | 9.961491e+11 | ||
Mining | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 7.718585e+09 | 1.257536e+11 | 2.469663e+12 | 2.248392e+11 | 2.182098e+11 | 7.833536e+09 | ||
Services | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 9.800168e+11 | 1.904274e+12 | 8.181366e+12 | 5.831722e+11 | 2.176235e+13 | 1.400092e+12 | ||
Transport | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 1.263019e+11 | 5.325394e+11 | 1.348311e+12 | 1.354806e+11 | 1.885116e+12 | 1.431332e+12 |
Link to the jupyter notebook file
.