New Keynesian 3-Equation Model

Equations

• IS: \(y_t = A - a_1 \, r_{t-1}\)

• Phillips: \(\pi_t = \pi_{t-1} + a_2 \, (y_t - y_e)\)

• Policy: \(r_s = \frac{A - y_e}{a_1}\) and \(r_t = r_s + a_3 \, (\pi_t - \pi^T)\), where \(a_3 = \frac{1}{a_1\left(\frac{1}{a_2 b} + a_2\right)}\).

API

from macrostat.models.NK3E import (
    NK3E,
    ParametersNK3E,
    VariablesNK3E,
    ScenariosNK3E,
)

# Configure horizon and (optional) progress bar
params = ParametersNK3E(hyperparameters={"timesteps": 50, "timesteps_initialization": 1, "use_tqdm": False})
variables = VariablesNK3E(parameters=params)
scenarios = ScenariosNK3E(parameters=params)
model = NK3E(parameters=params, variables=variables, scenarios=scenarios)

# Baseline simulation
model.simulate()

# Scenario examples (provided out-of-the-box)
model.simulate(scenario="Scenario.1: Rise in A")      # demand up
model.simulate(scenario="Scenario.2: Higher pi_T")    # higher inflation target
model.simulate(scenario="Scenario.3: Rise in y_e")    # higher potential output

Series

The model records time series in model.variables.timeseries with keys:

• y: output

• pi: inflation

• r: real interest rate

• r_s: stabilizing real interest rate (A - y_e)/a1

Each series has length equal to the configured timesteps. Baseline parameters A, pi_T, and y_e are available via model.parameters; scenario shocks are managed by ScenariosNK3E.

Source

The reduced-form and parameterizations follow the online note: https://macrosimulation.org/a_new_keynesian_3_equation_model.