Model BMWK

This guide explains how to use the godley package to create the BMWK model — a Kaldorian model with private bank money described by Wynne Godley and Marc Lavoie in Chapter 7 of Monetary Economics. An Integrated Approach to Credit, Money, Income, Production and Wealth.

library(godley)

Base scenario

Start by creating an empty SFC model:

# Create empty model
model_bmwk <- create_model(name = "SFC BMWK")
#> Empty model created

Define the variables for the model:

# Add variables
model_bmwk <- model_bmwk |>
  add_variable("rl", init = 0.025) |>
  add_variable("alpha0", init = 20) |>
  add_variable("alpha2", init = 0.10) |>
  add_variable("delta", init = 0.10) |>
  add_variable("gamma", init = 0.15) |>
  add_variable("kappa", init = 1) |>
  add_variable("pr", init = 1) |>
  add_variable("Nd", init = .001) |>
  add_variable("Ns", init = .001) |>
  add_variable("Y", init = .001) |>
  add_variable("alpha1w", init = .8) |>
  add_variable("alpha1r", init = .15) |>
  add_variable("Cs") |>
  add_variable("Cd") |>
  add_variable("Is") |>
  add_variable("Id") |>
  add_variable("Ls") |>
  add_variable("Ld") |>
  add_variable("WBd") |>
  add_variable("AF") |>
  add_variable("K") |>
  add_variable("YD") |>
  add_variable("WBs") |>
  add_variable("rm") |>
  add_variable("Mh") |>
  add_variable("Ms") |>
  add_variable("W") |>
  add_variable("DA") |>
  add_variable("KT")

Establish the relationships between variables by adding equations:

# Add equations
model_bmwk <- model_bmwk |>
  add_equation("Cs = Cd") |>
  add_equation("Is = Id") |>
  add_equation("Ns = Nd") |>
  add_equation("Ls = Ls[-1] + Ld - Ld[-1]") |>
  add_equation("Y = Cs + Is") |>
  add_equation("WBd = Y - rl[-1] * Ld[-1] - AF") |>
  add_equation("AF = delta * K[-1]") |>
  add_equation("Ld = Ld[-1] + Id - AF") |>
  add_equation("YD = WBs + rm[-1] * Mh[-1]") |>
  add_equation("Mh = Mh[-1] + YD - Cd") |>
  add_equation("Ms = Ms[-1] + Ls - Ls[-1]") |>
  add_equation("rm = rl") |>
  add_equation("WBs = W * Ns") |>
  add_equation("Nd = Y / pr") |>
  add_equation("W = WBd / Nd") |>
  add_equation("Cd = alpha0 + alpha1w * WBs + alpha1r * rm[-1] * Mh[-1] + alpha2 * Mh") |>
  add_equation("K = K[-1] + Id - DA") |>
  add_equation("DA = delta * K[-1]") |>
  add_equation("KT = kappa * Y[-1]") |>
  add_equation("Id = gamma * (KT - K[-1]) + DA") |>
  add_equation("Ms = Mh", hidden = TRUE)

Now, you can simulate the model (in this example, the baseline scenario over 100 periods using the Gauss method):

# Simulate model
model_bmwk <- simulate_scenario(model_bmwk,
  scenario = "baseline", max_iter = 350, periods = 100,
  hidden_tol = 0.1, tol = 1e-08, method = "Gauss"
)
#> Model prepared successfully
#> Simulating scenario baseline (1 of 1)
#> Scenario(s) successfully simulated

With the simulation estimated, you can create a plot to visualize the results for the variables of interest:

# Plot results
plot_simulation(
  model = model_bmwk, scenario = c("baseline"), from = 1, to = 50,
  expressions = c("Y")
)

Note: The above example uses the new pipe operator (|>), which requires R 4.1 or later.

Shock scenario

With godley package we can simulate how shocks affect the economy (specifically, how they impact the base scenario).

In this example, we simulate the effect of an increase in the interest rate.

First, initialize an empty shock object:

# Create empty shock
shock_bmwk <- create_shock()
#> Shock object created

Define the shock by adding an appropriate equation:

# Add shock equation
shock_bmwk <- add_shock(shock_bmwk,
  variable = "rl",
  value = 0.035,
  desc = "Increase in the interest rate", start = 5, end = 50
)

Integrate the shock into the model by creating a new scenario:

# Create new scenario with this shock
model_bmwk <- add_scenario(model_bmwk,
  name = "expansion", origin = "baseline",
  origin_start = 1,
  origin_end = 100,
  shock = shock_bmwk
)

Simulate the scenario with the shock applied:

# Simulate shock
model_bmwk <- simulate_scenario(model_bmwk,
  scenario = "expansion", max_iter = 350, periods = 100,
  hidden_tol = 0.1, tol = 1e-08, method = "Gauss"
)
#> Simulating scenario expansion (1 of 1)
#> Scenario(s) successfully simulated

Plot the simulation outcomes:

# Plot results
plot_simulation(
  model = model_bmwk, scenario = c("expansion"), from = 1, to = 50,
  expressions = c("Y")
)

References

For more details on BMWK model, refer to Chapter 7 of Monetary Economics. An Integrated Approach to Credit, Money, Income, Production and Wealth.