"""
This module will define the forward and simulate behavior of
Marco Veronese Passarella's 3IO-PC model
"""
__author__ = ["Karl Naumann-Woleske"]
__credits__ = ["Karl Naumann-Woleske"]
__license__ = "MIT"
__maintainer__ = ["Karl Naumann-Woleske"]
import logging
import torch
from macrostat.core.behavior import Behavior
from macrostat.models.IOPC.parameters import ParametersIOPC
from macrostat.models.IOPC.scenarios import ScenariosIOPC
from macrostat.models.IOPC.variables import VariablesIOPC
logger = logging.getLogger(__name__)
[docs]
class BehaviorIOPC(Behavior):
"""Behavior class for Marco Veronese Passarella's 3IO-PC model"""
version = "IOPC"
[docs]
def __init__(
self,
parameters: ParametersIOPC | None = None,
scenarios: ScenariosIOPC | None = None,
variables: VariablesIOPC | None = None,
scenario: int = 0,
debug: bool = False,
):
"""Initialize the behavior of Marco Veronese Passarella's 3IO-PC model
Parameters
----------
parameters: ParametersIOPC | None
The parameters of the model.
scenarios: ScenariosIOPC | None
The scenarios of the model.
variables: VariablesIOPC | None
The variables of the model.
record: bool
Whether to record the model output.
scenario: int
The scenario to use for the model.
"""
if parameters is None:
parameters = ParametersIOPC()
if scenarios is None:
scenarios = ScenariosIOPC()
if variables is None:
variables = VariablesIOPC()
super().__init__(
parameters=parameters,
scenarios=scenarios,
variables=variables,
scenario=scenario,
debug=debug,
)
############################################################################
# Initialization
############################################################################
[docs]
def initialize(self):
r"""Initialize the behavior of Passarella's 3IO-PC model in the spirit
of Godley & Lavoie, by keeping all variables as zero. Accordingly, we
can just "pass" the function as by default the state variables are all
zero. The only exceptions are the price-indices which we initialize to
one
"""
self.state["Prices"] = torch.ones_like(self.state["Prices"])
self.state["ConsumerPriceIndex"] = torch.ones(1)
self.state["ConsumerPriceInflation"] = torch.ones(1)
self.state["GovernmentPriceIndex"] = torch.ones(1)
############################################################################
# Step
############################################################################
[docs]
def step(self, **kwargs):
"""Step function of the Godley-Lavoie 2006 PC model."""
# Scenario items
self.consumption_government(**kwargs)
self.set_interest_rate(**kwargs)
# Items based on prior
self.interest_earned_on_bills_household(**kwargs)
self.expected_disposable_income(**kwargs)
# Solution of the step
# Input-output mechanisms
self.prices(**kwargs)
self.price_indices(**kwargs)
self.inflation(**kwargs)
self.propensity_to_consume_income(**kwargs)
self.consumption(**kwargs)
self.final_demand(**kwargs)
self.real_gross_output(**kwargs)
self.national_income(**kwargs)
self.taxes(**kwargs)
self.disposable_income(**kwargs)
self.wealth(**kwargs)
self.expected_wealth(**kwargs)
self.household_bill_demand(**kwargs)
self.household_bill_holdings(**kwargs)
self.household_money_stock(**kwargs)
self.central_bank_profits(**kwargs)
self.government_bill_issuance(**kwargs)
self.central_bank_bill_holdings(**kwargs)
self.central_bank_money_stock(**kwargs)
[docs]
def consumption_government(
self,
t: int,
scenario: dict,
params: dict | None = None,
**kwargs,
):
r"""Calculate the consumption of the government. This is
given exogenously by the scenario.
Parameters
----------
t: int
The time step.
scenario: dict
The scenario.
params: dict | None
The parameters.
Dependency
----------
- scenario: ConsumptionGovernment
Sets
-----
- RealConsumptionGovernment
"""
self.state["RealConsumptionGovernment"] = scenario["GovernmentDemand"]
[docs]
def set_interest_rate(
self, t: int, scenario: dict, params: dict | None = None, **kwargs
):
r"""Set the interest rate. This is given exogenously by the scenario.
Parameters
----------
t: int
The time step.
scenario: dict
The scenario.
params: dict | None
The parameters.
Equations
---------
.. math::
:nowrap:
\begin{align}
r(t) = \bar{r}
\end{align)
Dependency
----------
- scenario: InterestRate
Sets
-----
- InterestRate
"""
self.state["InterestRate"] = scenario["InterestRate"]
[docs]
def interest_earned_on_bills_household(
self, t: int, scenario: dict, params: dict | None = None, **kwargs
):
r"""Calculate the interest earned on bills by the household.
Parameters
----------
t: int
The time step.
scenario: dict
The scenario.
params: dict | None
The parameters.
Equations
---------
.. math::
:nowrap:
\begin{align}
r(t-1)B_h(t-1)
\end{align}
Dependency
----------
- prior: InterestRate
- prior: HouseholdBillStock
Sets
-----
- InterestEarnedOnBillsHousehold
"""
self.state["InterestEarnedOnBillsHousehold"] = (
self.prior["InterestRate"] * self.prior["HouseholdBillStock"]
)
[docs]
def expected_disposable_income(
self, t: torch.tensor, scenario: dict, params: dict | None = None
):
r"""The expected disposable income is simply the prior period's
disposable income. Equation (3.20) in the book.
Parameters
----------
t : torch.tensor
Current time step
scenario : dict
Equations
---------
.. math::
YD^e(t) = YD(t-1)
Dependency
----------
- prior: DisposableIncome
Sets
-----
- ExpectedDisposableIncome
"""
self.state["ExpectedDisposableIncome"] = self.prior["DisposableIncome"]
[docs]
def prices(self, t: int, scenario: dict, params: dict | None = None, **kwargs):
r"""Compute the sectoral prices as the sum of unit labour cost and a
markup on intermediate prices
Parameters
----------
t: int
The time step.
scenario: dict
The scenario.
params: dict | None
The parameters.
Equations
---------
.. math::
:nowrap:
\begin{align}
P_i(t) = \frac{w}{pr_i} + (1 + \mu)\sum_j a_{ij}P_j(t)
\end{align}
Dependency
----------
- scenario: WageRate
- params: LabourProductivity
- params: Requirement
- params: Markup
Sets
-----
- Prices
"""
self.state["Prices"] = torch.linalg.solve(
A=(
torch.eye(params["Requirement"].shape[0])
- (1 + params["Markup"]) * params["Requirement"].T
),
B=scenario["WageRate"] / params["LabourProductivity"],
)
[docs]
def price_indices(
self, t: int, scenario: dict, params: dict | None = None, **kwargs
):
r"""Compute the consumer and government price indices based on their
consumption shares
Parameters
----------
t: int
The time step.
scenario: dict
The scenario.
params: dict | None
The parameters.
Equations
---------
.. math::
:nowrap:
\begin{align}
p_c(t) &= \beta_{HH}^\top P(t)\\
p_g(t) &= \beta_{G}^\top P(t)
\end{align}
Dependency
----------
- state: Prices
- params: HouseholdBudgetShare
- params: GovernmentBudgetShare
Sets
-----
- ConsumerPriceIndex
- GovernmentPriceIndex
"""
self.state["ConsumerPriceIndex"] = (
self.state["Prices"] @ params["HouseholdBudgetShare"]
)
self.state["GovernmentPriceIndex"] = (
self.state["Prices"] @ params["GovernmentBudgetShare"]
)
[docs]
def inflation(self, t: int, scenario: dict, params: dict | None = None, **kwargs):
r"""Compute the inflation (i.e. term for absence of money illusion)
Parameters
----------
t: int
The time step.
scenario: dict
The scenario.
params: dict | None
The parameters.
Equations
---------
.. math::
:nowrap:
\begin{align}
\pi(t) &= \left(\frac{p_c(t) - p_c(t-1)}{p_c(t-1)}\right)\left(\frac{V(t-1)}{p_c(t-1)}\right)
\end{align}
Dependency
----------
- prior: Wealth
- prior: ConsumerPriceIndex
- state: ConsumerPriceIndex
Sets
-----
- ConsumerPriceInflation
"""
self.state["ConsumerPriceInflation"] = (
(self.state["ConsumerPriceIndex"] - self.prior["ConsumerPriceIndex"])
/ self.prior["ConsumerPriceIndex"]
) * (self.prior["Wealth"] / self.state["ConsumerPriceIndex"])
[docs]
def propensity_to_consume_income(
self, t: int, scenario: dict, params: dict | None = None, **kwargs
):
r"""Endogenous propensity to consume out of income, dependent on the
rate of interest
Parameters
----------
t: int
The time step.
scenario: dict
The scenario.
params: dict | None
The parameters.
Equations
---------
.. math::
:nowrap:
\begin{align}
\alpha_1(t) = \alpha_{10} - \alpha_{11} r(t-1)
\end{align}
Dependency
----------
- prior: InterestRate
- params: PropensityToConsumeIncomeBase
- params: PropensityToConsumeIncomeInterest
Sets
-----
- PropensityToConsumeIncome
"""
self.state["PropensityToConsumeIncome"] = params[
"PropensityToConsumeIncomeBase"
] - (params["PropensityToConsumeIncomeInterest"] * self.prior["InterestRate"])
[docs]
def consumption(self, t: int, scenario: dict, params: dict | None = None, **kwargs):
r"""Calculate the consumption.
Parameters
----------
t: int
The time step.
scenario: dict
The scenario.
params: dict | None
The parameters.
Equations
---------
.. math::
:nowrap:
\begin{align}
c(t) = \alpha_1 \left(\frac{YD^e(t)}{p_c(t)} - \pi(t)\right) + \alpha_2 \frac{V(t-1)}{p_c(t)}
\end{align}
Dependency
----------
- state: PropensityToConsumeIncome
- state: ExpectedDisposableIncome
- state: ConsumerPriceIndex
- state: ConsumerPriceInflation
- prior: Wealth
- params: PropensityToConsumeSavings
Sets
-----
- RealConsumptionHousehold
"""
self.state["RealConsumptionHousehold"] = self.state[
"PropensityToConsumeIncome"
] * (
(self.state["ExpectedDisposableIncome"] / self.state["ConsumerPriceIndex"])
- self.state["ConsumerPriceInflation"]
) + params[
"PropensityToConsumeSavings"
] * (
self.prior["Wealth"] / self.state["ConsumerPriceIndex"]
)
[docs]
def final_demand(
self, t: int, scenario: dict, params: dict | None = None, **kwargs
):
r"""Calculate the final demand as the sum of household and government
demands spread over the sectors
Parameters
----------
t: int
The time step.
scenario: dict
The scenario.
params: dict | None
The parameters.
Equations
---------
.. math::
:nowrap:
\begin{align}
d_i(t) = \beta_{HH,i}C_{HH}(t) + \beta_{GOV,i}G(t)
\end{align}
Dependency
----------
- state: RealConsumptionHousehold
- state: RealConsumptionGovernment
- params: HouseholdBudgetShare
- params: GovernmentBudgetShare
Sets
-----
- RealFinalDemand
"""
self.state["RealFinalDemand"] = +(
params["HouseholdBudgetShare"] * self.state["RealConsumptionHousehold"]
) + (params["GovernmentBudgetShare"] * self.state["RealConsumptionGovernment"])
[docs]
def real_gross_output(
self, t: int, scenario: dict, params: dict | None = None, **kwargs
):
r"""Compute real gross output as the solution to the linear set of
equations
Parameters
----------
t: int
The time step.
scenario: dict
The scenario.
params: dict | None
The parameters.
Equations
---------
.. math::
:nowrap:
\begin{align}
x(t) = (I - A)^{-1}d(t)
\end{align}
Dependency
----------
- state: RealFinalDemand
- params: Requirement
Sets
-----
- RealGrossOutput
"""
self.state["RealGrossOutput"] = torch.linalg.solve(
A=(torch.eye(params["Requirement"].shape[0]) - params["Requirement"]),
B=self.state["RealFinalDemand"],
)
[docs]
def national_income(
self, t: int, scenario: dict, params: dict | None = None, **kwargs
):
r"""National income is the sum of nominal final demand
Parameters
----------
t: int
The time step.
scenario: dict
The scenario.
params: dict | None
The parameters.
Equations
---------
.. math::
:nowrap:
\begin{align}
Y(t) = P^\top(t)d(t)
\end{align}
Dependency
----------
- state: Prices
- state: RealFinalDemand
Sets
-----
- NationalIncome
"""
self.state["NationalIncome"] = (
self.state["Prices"] @ self.state["RealFinalDemand"]
)
[docs]
def taxes(self, t: int, scenario: dict, params: dict | None = None, **kwargs):
r"""Calculate the taxes.
Parameters
----------
t: int
The time step.
scenario: dict
The scenario.
params: dict | None
The parameters.
Equations
---------
.. math::
:nowrap:
\begin{align}
T(t) = \theta (Y(t) + r(t-1)B_h(t-1))
\end{align}
Dependency
----------
- params: TaxRate
- state: NationalIncome
- state: InterestEarnedOnBillsHousehold
Sets
-----
- Taxes
"""
self.state["Taxes"] = params["TaxRate"] * (
self.state["NationalIncome"] + self.state["InterestEarnedOnBillsHousehold"]
)
[docs]
def disposable_income(
self, t: int, scenario: dict, params: dict | None = None, **kwargs
):
r"""Calculate the disposable income.
Parameters
----------
t: int
The time step.
scenario: dict
The scenario.
params: dict | None
The parameters.
Equations
---------
.. math::
:nowrap:
\begin{align}
YD(t) = Y(t) - T(t) + r(t-1)B_h(t-1)
\end{align}
Dependency
----------
- state: NationalIncome
- state: Taxes
- state: InterestEarnedOnBillsHousehold
Sets
-----
- DisposableIncome
"""
self.state["DisposableIncome"] = (
self.state["NationalIncome"]
- self.state["Taxes"]
+ self.state["InterestEarnedOnBillsHousehold"]
)
[docs]
def wealth(self, t: int, scenario: dict, params: dict | None = None, **kwargs):
r"""Calculate the wealth.
Parameters
----------
t: int
The time step.
scenario: dict
The scenario.
params: dict | None
The parameters.
Equations
---------
.. math::
:nowrap:
\begin{align}
V(t) = V(t-1) + YD(t) - C(t)
\end{align}
Dependency
----------
- state: DisposableIncome
- state: ConsumerPriceIndex
- state: RealConsumptionHousehold
- prior: Wealth
Sets
-----
- Wealth
"""
self.state["Wealth"] = (
self.prior["Wealth"]
+ self.state["DisposableIncome"]
- (
self.state["ConsumerPriceIndex"]
* self.state["RealConsumptionHousehold"]
)
)
[docs]
def expected_wealth(
self, t: int, scenario: dict, params: dict | None = None, **kwargs
):
r"""Calculate the expected wealth.
Parameters
----------
t: int
The time step.
scenario: dict
The scenario.
params: dict | None
The parameters.
Equations
---------
.. math::
:nowrap:
\begin{align}
V^e(t) = V(t-1) + YD^e(t) - C(t)
\end{align}
Dependency
----------
- state: ExpectedDisposableIncome
- state: RealConsumptionHousehold
- state: ConsumerPriceIndex
- prior: Wealth
Sets
-----
- ExpectedWealth
"""
self.state["ExpectedWealth"] = (
self.prior["Wealth"]
+ self.state["ExpectedDisposableIncome"]
- (
self.state["ConsumerPriceIndex"]
* self.state["RealConsumptionHousehold"]
)
)
[docs]
def household_bill_demand(
self, t: int, scenario: dict, params: dict | None = None, **kwargs
):
r"""Calculate the household bill demand.
Parameters
----------
t: int
The time step.
scenario: dict
The scenario.
params: dict | None
The parameters.
Equations
---------
.. math::
:nowrap:
\begin{align}
\frac{B_h(t)}{V^e(t)} = \lambda_0 + \lambda_1 r(t) - \lambda_2 \frac{YD^e(t)}{V^e(t)}
\end{align}
Dependency
----------
- state: ExpectedWealth
- state: ExpectedDisposableIncome
- state: InterestRate
- params: WealthShareBills_Constant
- params: WealthShareBills_InterestRate
- params: WealthShareBills_Income
Sets
-----
- HouseholdBillDemand
"""
self.state["HouseholdBillDemand"] = self.state["ExpectedWealth"] * (
# Baseline share
params["WealthShareBills_Constant"]
# Interest rate effect
+ params["WealthShareBills_InterestRate"] * self.state["InterestRate"]
# Income-to-wealth ratio effect
- params["WealthShareBills_Income"]
* torch.where(
self.state["ExpectedWealth"] > 0,
self.state["ExpectedDisposableIncome"] / self.state["ExpectedWealth"],
torch.zeros_like(self.state["ExpectedDisposableIncome"]),
)
)
[docs]
def household_bill_holdings(
self, t: int, scenario: dict, params: dict | None = None, **kwargs
):
r"""Calculate the household bill holdings.
Parameters
----------
t: int
The time step.
scenario: dict
The scenario.
params: dict | None
The parameters.
Equations
---------
.. math::
:nowrap:
\begin{align}
B_h(t) = B_h(t-1) + (B_h^d(t) - B_h(t-1))
\end{align}
Dependency
----------
- state: HouseholdBillDemand
Sets
-----
- HouseholdBillStock
"""
self.state["HouseholdBillStock"] = self.state["HouseholdBillDemand"]
[docs]
def household_money_stock(
self, t: int, scenario: dict, params: dict | None = None, **kwargs
):
r"""Calculate the household deposits as a residual.
Parameters
----------
t: int
The time step.
scenario: dict
The scenario.
params: dict | None
The parameters.
Equations
---------
.. math::
:nowrap:
\begin{align}
H_h(t) = V(t) - B_h(t)
\end{align}
Dependency
----------
- state: Wealth
- state: HouseholdBillStock
Sets
-----
- HouseholdMoneyStock
"""
self.state["HouseholdMoneyStock"] = (
self.state["Wealth"] - self.state["HouseholdBillStock"]
)
[docs]
def central_bank_profits(
self, t: int, scenario: dict, params: dict | None = None, **kwargs
):
r"""Calculate the central bank profits (income on bills held).
Parameters
----------
t: int
The time step.
scenario: dict
The scenario.
params: dict | None
The parameters.
Equations
---------
.. math::
:nowrap:
\begin{align}
r(t-1)B_{CB}(t-1)
\end{align}
Dependency
----------
- prior: InterestRate
- prior: CentralBankBillStock
Sets
-----
- CentralBankProfits
"""
self.state["CentralBankProfits"] = (
self.prior["InterestRate"] * self.prior["CentralBankBillStock"]
)
[docs]
def government_bill_issuance(
self, t: int, scenario: dict, params: dict | None = None, **kwargs
):
r"""Calculate the government bill issuance.
Parameters
----------
t: int
The time step.
scenario: dict
The scenario.
params: dict | None
The parameters.
Equations
---------
.. math::
:nowrap:
\begin{align}
B_s(t) = B_s(t-1) + (G(t) - r(t-1)B_s(t-1)) - (T(t) + r(t-1)B_{CB}(t-1))
\end{align}
Dependency
----------
- prior: InterestRate
- prior: GovernmentBillStock
- state: GovernmentPriceIndex
- state: RealConsumptionGovernment
- state: Taxes
- state: CentralBankProfits
Sets
-----
- GovernmentBillStock
"""
self.state["GovernmentBillStock"] = (
self.prior["GovernmentBillStock"]
+ (
# Government demand
self.state["GovernmentPriceIndex"]
* self.state["RealConsumptionGovernment"]
# Interest expense on bills issued
+ self.prior["InterestRate"] * self.prior["GovernmentBillStock"]
)
- (
# Tax revenue
self.state["Taxes"]
# Central bank profits
+ self.state["CentralBankProfits"]
)
)
[docs]
def central_bank_bill_holdings(
self, t: int, scenario: dict, params: dict | None = None, **kwargs
):
r"""Calculate the central bank bill holdings.
Parameters
----------
t: int
The time step.
scenario: dict
The scenario.
params: dict | None
The parameters.
Equations
---------
.. math::
:nowrap:
\begin{align}
B_{CB}(t) = B_{s}(t) - B_{h}(t)
\end{align}
Dependency
----------
- state: GovernmentBillStock
- state: HouseholdBillStock
Sets
-----
- CentralBankBillStock
"""
self.state["CentralBankBillStock"] = (
self.state["GovernmentBillStock"] - self.state["HouseholdBillStock"]
)
[docs]
def central_bank_money_stock(
self, t: int, scenario: dict, params: dict | None = None, **kwargs
):
r"""Calculate the central bank money stock.
Parameters
----------
t: int
The time step.
scenario: dict
The scenario.
params: dict | None
The parameters.
Equations
---------
.. math::
:nowrap:
\begin{align}
H_{s}(t) = H_{s}(t-1) + (B_{CB}(t) - B_{CB}(t-1))
\end{align}
Dependency
----------
- state: CentralBankBillStock
- prior: CentralBankMoneyStock
- prior: CentralBankBillStock
Sets
-----
- CentralBankMoneyStock
"""
self.state["CentralBankMoneyStock"] = (
self.prior["CentralBankMoneyStock"]
+ self.state["CentralBankBillStock"]
- self.prior["CentralBankBillStock"]
)
