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Model BMW

Source: vignettes/Model_BMW.Rmd
Model_BMW.Rmd

This guide explains how to use the godley package to create the BMW model — the simplest 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.

Base scenario

Start by creating an empty SFC model:

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

Define the variables for the model:

# Add variables
model_bmw <- model_bmw |>
  add_variable("rl", init = 0.025) |>
  add_variable("alpha0", init = 20) |>
  add_variable("alpha1", init = 0.75) |>
  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("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_bmw <- model_bmw |>
  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 + alpha1 * YD + alpha2 * Mh[-1]") |>
  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_bmw <- simulate_scenario(model_bmw,
  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_bmw, scenario = c("baseline"), from = 1, to = 50,
  expressions = c("Cd", "YD")
)

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).

Shock 1

In this example we observe the effect of increased autonomous consumption expenditures.

First, initialize an empty shock object:

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

Define the shock by adding an appropriate equation:

# Add shock equation with increase in autonomous consumption expenditures
shock_bmw <- add_shock(shock_bmw,
  variable = "alpha0",
  value = 30,
  desc = "Increase in autonomous consumption expenditures",
  start = 5, end = 50
)

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

# Create new scenario with this shock
model_bmw <- add_scenario(model_bmw,
  name = "expansion1", origin = "baseline",
  origin_start = 1,
  origin_end = 100,
  shock = shock_bmw
)

Simulate the scenario with the shock applied:

# Simulate shock
model_bmw <- simulate_scenario(model_bmw,
  scenario = "expansion1", max_iter = 350, periods = 100,
  hidden_tol = 0.1, tol = 1e-08, method = "Newton"
)
#> Simulating scenario expansion1 (1 of 1)
#> Scenario(s) successfully simulated

Finally, display the results for the shock scenario:

# Plot results
plot_simulation(
  model = model_bmw, scenario = c("expansion1"), from = 1, to = 50,
  expressions = c("Cd", "YD")
)

Shock 2

In the second example, we propose to introduce an increase in the propensity to save.

First, initialize an empty shock object:

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

Define the shock by adding an appropriate equation:

# Add shock equation with increased propensity to save
shock_bmw <- add_shock(shock_bmw,
  variable = "alpha1",
  value = 0.7,
  desc = "Increase in the propensity to save",
  start = 5, end = 50
)

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

# Create new scenario with this shock
model_bmw <- add_scenario(model_bmw,
  name = "expansion2", origin = "baseline",
  origin_start = 1,
  origin_end = 100,
  shock = shock_bmw
)

Simulate the scenario with the shock applied:

# Simulate shock
model_bmw <- simulate_scenario(model_bmw,
  scenario = "expansion2", max_iter = 350, periods = 100,
  hidden_tol = 0.1, tol = 1e-08, method = "Newton"
)
#> Simulating scenario expansion2 (1 of 1)
#> Scenario(s) successfully simulated

Display the results on the plot:

# Plot results
plot_simulation(
  model = model_bmw, scenario = c("expansion2"), from = 1, to = 50,
  expressions = c("Cd", "YD")
)

References

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