Model PC

This guide explains how to use the godley package to create the PC model — a model with government money and portfolio choice, as described by Wynne Godley and Marc Lavoie in Chapter 4 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_pc <- create_model(name = "SFC PC")
#> Empty model created

Define the variables for the model:

# Add variables
model_pc <- model_pc |>
  add_variable("B_cb", desc = "") |>
  add_variable("H_s", desc = "") |>
  add_variable("B_s", desc = "") |>
  add_variable("B_h", desc = "") |>
  add_variable("H_h1", desc = "") |>
  add_variable("H_h", desc = "") |>
  add_variable("C", desc = "") |>
  add_variable("V", desc = "") |>
  add_variable("T_x", desc = "") |>
  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("r", init = 0.025, desc = "") |>
  add_variable("G", init = 20, desc = "Government demand") |>
  add_variable("lambda0", init = 0.635, desc = "") |>
  add_variable("lambda1", init = 0.05, desc = "") |>
  add_variable("lambda2", init = 0.01, desc = "")

Establish the relationships between variables by adding equations:

# Add equations
model_pc <- model_pc |>
  add_equation("Y = C + G", desc = "") |>
  add_equation("Yd = Y - T_x + r[-1] * B_h[-1]") |>
  add_equation("T_x = theta * (Y + r[-1] * B_h[-1])") |>
  add_equation("V = V[-1] + (Yd - C)") |>
  add_equation("C = alpha1 * Yd + alpha2 * V[-1]") |>
  add_equation("H_h = V - B_h") |>
  add_equation("H_h1 = V * ((1 - lambda0) - lambda1 * r + lambda2 * ( Yd/V ))") |>
  add_equation("B_h = V * (lambda0 + lambda1 * r - lambda2 * ( Yd/V ))") |>
  add_equation("B_s = B_s[-1] + (G + r[-1] * B_s[-1]) - (T_x + r[-1] * B_cb[-1])") |>
  add_equation("H_s = H_s[-1] + B_cb - B_cb[-1]") |>
  add_equation("B_cb = B_s - B_h") |>
  add_equation("H_h = H_s", hidden = T)

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

# Simulate model
model_pc <- simulate_scenario(model_pc,
  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, visualize the results for the variables of interest:

# Plot results
plot_simulation(
  model = model_pc, scenario = c("baseline"), from = 1, to = 100,
  expressions = c("B_h / V")
)

# Plot results
plot_simulation(
  model = model_pc, scenario = c("baseline"), from = 1, to = 100,
  expressions = c("H_h / V")
)

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 propose to implement an increased rate of interest on bills.

First, initialize an empty shock object:

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

Define the shock by adding an appropriate equation:

# Add shock equation with increased rate of interest on bills
shock_pc <- add_shock(shock_pc,
  variable = "r",
  value = 0.035,
  desc = "Increase in the rate of interest on bills",
  start = 5, end = 50
)

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

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

Simulate the scenario with the shock applied:

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

Finally, plot the simulation outcomes:

# Plot results
plot_simulation(
  model = model_pc, scenario = c("expansion"), from = 1, to = 50,
  expressions = c("B_h / V")
)

# Plot results
plot_simulation(
  model = model_pc, scenario = c("expansion"), from = 1, to = 50,
  expressions = c("H_h / V")
)

References

For more details on PC model, refer to Chapter 4 of Monetary Economics. An Integrated Approach to Credit, Money, Income, Production and Wealth.