Changing the model parameters#

There are multiple theoretical and implemented versions of the ARIO model, each with various parameters. One objective of BoARIO is to offer an extensive, modular and adaptable implementation of these versions, in order to allow easy access to version comparison, parameters values exploration and modeling improvement.

If you are not familiar with the model, it is strongly advised to read the Model description page of this documentation, as well as [Hal13].

Parameters are set when instantiating the model. The following block shows all currently available parameters as well as their default value.

model = ARIOPsiModel(
    pym_mrio=mrio,
    order_type="alt",
    alpha_base=1.0,
    alpha_max=1.25,
    alpha_tau=365,
    rebuild_tau=60,
    main_inv_dur=90,
    monetary_factor=10**6,
    temporal_units_by_step=1,
    iotable_year_to_temporal_unit_factor=365,
    infinite_inventories_sect=None,
    inventory_dict=None,
    productive_capital_vector=None,
    productive_capital_to_VA_dict=None,
    psi_param = 0.80,
    inventory_restoration_tau = 60,
)

Here a quick description of each parameters. Please refer to both the mathematical description and the API Reference for further details.

order_type : Setting it to "alt" makes the model use the intermediate order mechanism described in [GWH+20]. Any other value makes the model use the classic order mechanism used in [Hal13] (see Orders shares variants)
alpha_base, alpha_max, alpha_tau respectively set the base overproduction, the maximum overproduction, and its characteristic time (in temporal unit).
rebuild_tau sets the default rebuilding or recovering characteristic time for events (this value is overridden if specified directly in the Event object)
inventory_dict should be a dictionary of sector:duration format, where all sector are present and duration is both the initial and goal duration for this input stock.
main_inv_dur sets the default initial/goal inventory duration in temporal unit for all sectors if inventory_dict is not given.
infinite_inventories_sect should be a list of inputs never constraining production (the stocks for these input will be virtually infinite when considering stock constraints) (overridden by inventory_dict)
monetary_factor should be equal to the monetary factor of the MRIOT used (most of the time MRIOT are in millions €/$, hence the default $10^6$)
temporal_units_by_step the number of temporal units to simulate every step. Setting it to 5 will divide the computation time by 5, but only one every 5 temporal units will actually be simulated. See Focus on the temporal dimension.

iotable_year_to_temporal_unit_factor defines the temporal unit assuming the MRIOT contains yearly values. Note that this has not been extensively tested and should be used with care.
productive_capital_to_VA_dict should be a dictionary of sector:ratio format, where ratio is an estimate of Capital Stock over Value Added ratio. This is used to estimate the capital stock of each sector. By default the ratio is 4/1 for all sectors.
productive_capital_vector can directly set the capital stock for all industries (ie regions*sectors sized). This overrides kapital_to_VA_dict.
psi_param and inventory_restoration_tau : see Model dynamics

Note

All arguments except the mrio are keyword arguments (ie not positional), meaning you always need to specify <parameter = value>. (This also means you can put them in any order). The reason for this is to make parameter setting entirely explicit.

Focus on the temporal dimension#

Warning

These features have not been extensively tested and should be handled with great care. Feedbacks are welcome!

The temporal dimension is an important aspect of dynamically modeling indirect economic impacts. Historically, ARIO has been used both using weekly and daily steps, but mostly the latter case. BoARIO’s implementation of ARIO aims at being independent of the temporal unit considered, notably to study how this aspect influences the results.

This means it is virtually possible to run ARIO on any temporal granularity of your choosing.

Furthermore, for efficiency purpose, this implementation allows to simulate only some temporal unit and interpolate state variables in between.

Hence a step can represent multiple temporal units. Although by default, a step equals a temporal unit equals a day and defaults values of characteristic times and other time related variable are accordingly expressed in number of days, these three terms are conceptually different. For this reason we will favor the term temporal unit to designate the atomic period in the model throughout this documentation.

The number of temporal units to simulate can be set when instantiating the Simulation object like so:

sim = Simulation(model, n_temporal_units_to_sim=730)

By default, simulation run for 365 temporal units, representing days.