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

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.