Model SIM

This guide explains how to use the godley package to create the SIM model, the simplest model with government money, as described by Wynne Godley and Marc Lavoie in Chapter 3 of Monetary Economics: An Integrated Approach to Credit, Money, Income, Production and Wealth.

library(godley)

Base scenario

Start by initializing an empty SFC (Stock-Flow Consistent) model:

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

Define the variables for the model:

# Add variables
model_sim <- model_sim |>
  add_variable("C_d", desc = "Consumption demand by households") |>
  add_variable("C_s", desc = "Consumption supply") |>
  add_variable("G_s", desc = "Government supply") |>
  add_variable("H_h", desc = "Cash money held by households") |>
  add_variable("H_s", desc = "Cash money supplied by the government") |>
  add_variable("N_d", desc = "Demand for labor") |>
  add_variable("N_s", desc = "Supply of labor") |>
  add_variable("T_d", desc = "Taxes, demand") |>
  add_variable("T_s", desc = "Taxes, supply") |>
  add_variable("Y", desc = "Income = GDP") |>
  add_variable("Yd", desc = "Disposable income of households") |>
  add_variable("alpha1", init = 0.6, desc = "Propensity to consume out of income") |>
  add_variable("alpha2", init = 0.4, desc = "Propensity to consume out of wealth") |>
  add_variable("theta", init = 0.2, desc = "Tax rate") |>
  add_variable("G_d", init = 20, desc = "Government demand") |>
  add_variable("W", init = 1, desc = "Wage rate")

Establish the relationships between variables by adding equations:

# Add equations
model_sim <- model_sim |>
  add_equation("C_s = C_d", desc = "Consumption") |>
  add_equation("G_s = G_d") |>
  add_equation("T_s = T_d") |>
  add_equation("N_s = N_d") |>
  add_equation("Yd = W * N_s - T_s") |>
  add_equation("T_d = theta * W * N_s") |>
  add_equation("C_d = alpha1 * Yd + alpha2 * H_h[-1]") |>
  add_equation("H_s = G_d - T_d + H_s[-1]") |>
  add_equation("H_h = Yd - C_d + H_h[-1]") |>
  add_equation("Y = C_s + G_s") |>
  add_equation("N_d = Y/W") |>
  add_equation("H_s = H_h", desc = "Money equilibrium", hidden = TRUE)

Now, you can simulate the model (in this example, we calculate the baseline scenario over 100 periods using the Newton method)

# Simulate model
model_sim <- simulate_scenario(model_sim,
  scenario = "baseline", max_iter = 350, periods = 100,
  hidden_tol = 0.1, tol = 1e-05, method = "Newton"
)
#> Model prepared successfully
#> Simulating scenario baseline (1 of 1)
#> Scenario(s) successfully simulated

With the simulation estimated, visualize the results for the variables of interest:

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

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

Shock scenario

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

In this example, we apply a permanent increase in government expenditures.

First, initialize an empty shock object:

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

Define the shock by adding an appropriate equation:

# Add shock equation with increased government expenditures
shock_sim <- add_shock(shock_sim,
  variable = "G_d",
  value = 25,
  desc = "Increase in government expenditures", start = 5, end = 50
)

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

# Create new scenario with this shock
model_sim <- add_scenario(model_sim,
  name = "expansion", origin = "baseline", shock = shock_sim
)

Simulate the scenario with the shock applied:

# Simulate shock
model_sim <- simulate_scenario(model_sim,
  scenario = "expansion", max_iter = 350, periods = 100,
  hidden_tol = 0.1, tol = 1e-05, method = "Newton"
)
#> Simulating scenario expansion (1 of 1)
#> Scenario(s) successfully simulated

Finally, compare the results of the base scenario with those of the shock scenario.

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

plot_simulation(
  model = model_sim, scenario = c("baseline", "expansion"), from = 1, to = 50,
  expressions = c("C_d")
)

plot_simulation(
  model = model_sim, scenario = c("baseline", "expansion"), from = 1, to = 50,
  expressions = c("G_s")
)

References

For more details on SIM model, refer to Chapter 3 of Monetary Economics: An Integrated Approach to Credit, Money, Income, Production and Wealth.