Skip to contents

Model DISINF

Source: vignettes/Model_DISINF.Rmd
Model_DISINF.Rmd

This guide explains how to use the godley package to create the DISINF model — a model with private bank money, inventories and inflation, as described by Wynne Godley and Marc Lavoie in Chapter 9 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_disinf <- create_model(name = "SFC DISINF")
#> Empty model created

Define the variables for the model:

# Add variables
model_disinf <- model_disinf |>
  add_variable("rrc", init = 0.025) |>
  add_variable("pr", init = 1) |>
  add_variable("add", init = 0.02) |>
  add_variable("alpha0", init = 15) |>
  add_variable("alpha1", init = 0.8) |>
  add_variable("alpha2", init = 0.1) |>
  add_variable("beta", init = 0.9) |>
  add_variable("epsilon", init = 0.8) |>
  add_variable("gamma", init = 0.25) |>
  add_variable("phi", init = 0.24) |>
  add_variable("sigma_T", init = 0.2) |>
  add_variable("Omega0", init = -1.4) |>
  add_variable("Omega1", init = 1) |>
  add_variable("Omega2", init = 1.2) |>
  add_variable("Omega3", init = 0.3) |>
  add_variable("p", init = 1) |>
  add_variable("W", init = 1) |>
  add_variable("UC", init = 1) |>
  add_variable("s_E", init = .00001) |>
  add_variable("inv_T") |>
  add_variable("inv_E") |>
  add_variable("inv") |>
  add_variable("s") |>
  add_variable("c") |>
  add_variable("N") |>
  add_variable("WB") |>
  add_variable("INV") |>
  add_variable("S") |>
  add_variable("EF") |>
  add_variable("Ld") |>
  add_variable("Ls") |>
  add_variable("Ms") |>
  add_variable("rm") |>
  add_variable("EFb") |>
  add_variable("Mh") |>
  add_variable("YD") |>
  add_variable("C") |>
  add_variable("omega_T") |>
  add_variable("Nfe") |>
  add_variable("yfe") |>
  add_variable("mh") |>
  add_variable("y") |>
  add_variable("rl") |>
  add_variable("pic") |>
  add_variable("ydhs") |>
  add_variable("yd") |>
  add_variable("ydhs_E")

Establish the relationships between variables by adding equations:

# Add equations
model_disinf <- model_disinf |>
  add_equation("y = s_E + inv_E - inv[-1]") |>
  add_equation("inv_T = sigma_T * s_E") |>
  add_equation("inv_E = inv[-1] + gamma * (inv_T - inv[-1])") |>
  add_equation("inv = inv[-1] + (y - s)") |>
  add_equation("s_E = beta * s[-1] + (1 - beta) * s_E[-1]") |>
  add_equation("s = c") |>
  add_equation("N = y / pr") |>
  add_equation("WB = N * W") |>
  add_equation("UC = WB / y") |>
  add_equation("INV = inv * UC") |>
  add_equation("S = p * s") |>
  add_equation("p = (1 + phi) * (1 + rrc * sigma_T) * UC") |>
  add_equation("EF = S - WB + (INV - INV[-1]) - rl * INV[-1]") |>
  add_equation("Ld = INV") |>
  add_equation("Ls = Ld") |>
  add_equation("Ms = Ls") |>
  add_equation("rm = rl - add") |>
  add_equation("EFb = rl[-1] * Ls[-1] - rm[-1] * Mh[-1]") |>
  add_equation("pic = (UC / UC[-1]) - 1") |>
  add_equation("rl = (1 + rrc) * (1 + pic) - 1") |>
  add_equation("YD = WB + EF + EFb + rm * Mh[-1]") |>
  add_equation("Mh = Mh[-1] + YD - C") |>
  add_equation("ydhs = c + (mh - mh[-1])") |>
  add_equation("yd = YD / p") |>
  add_equation("C = c * p") |>
  add_equation("mh = Mh / p") |>
  add_equation("c = alpha0 + alpha1 * ydhs_E + alpha2 * mh[-1]") |>
  add_equation("ydhs_E = epsilon * ydhs[-1] + (1 - epsilon) * ydhs_E[-1]") |>
  add_equation("omega_T = Omega0 + Omega1 * pr + Omega2 * (N / Nfe)") |>
  add_equation("W = W[-1] * (1 + Omega3 * (omega_T[-1] - (W[-1]/p[-1])))") |>
  add_equation("yfe = (1 + sigma_T) * s - inv[-1]") |>
  add_equation("Nfe = s / pr")

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

# Simulate model
model_disinf <- simulate_scenario(model_disinf,
  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_disinf, scenario = c("baseline"),
  from = 1, to = 40,
  expressions = c("p", "UC", "UCp = UC/p")
)
# Plot results
plot_simulation(
  model = model_disinf, scenario = c("baseline"),
  from = 1, to = 40,
  expressions = c("inflation = (p - dplyr::lag(p)) / dplyr::lag(p)")
)
# Plot results
plot_simulation(
  model = model_disinf, scenario = c("baseline"),
  from = 1, to = 40,
  expressions = c(
    "ydhs_ss = alpha0 / (1 - alpha1 - alpha2*sigma_T * (UC/p))",
    "ydhs", "c", "s"
  )
)

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

Shock scenarios

With godley package you can simulate how shocks affect the base scenario.

Shock 1

The first example demonstrates the effect of the increase in costing margins.

First, initialize an empty shock object:

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

Then, define the shock by adding an appropriate equation:

# Add shock equation
shock_disinf <- add_shock(shock_disinf,
  variable = "phi",
  value = 0.3,
  desc = "Increase in the costing margins",
  start = 5, end = 50
)

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

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

Simulate the scenario with the shock applied:

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

Finally, plot the simulation results:

# Plot results
plot_simulation(
  model = model_disinf, scenario = c("expansion1"), from = 1, to = 40,
  expressions = c("p", "UC", "UCp = UC/p")
)
# Plot results
plot_simulation(
  model = model_disinf, scenario = c("expansion1"), from = 1, to = 40,
  expressions = c("inflation = (p - dplyr::lag(p)) / dplyr::lag(p)")
)
# Plot results
plot_simulation(
  model = model_disinf, scenario = c("expansion1"), from = 1, to = 40,
  expressions = c(
    "ydhs_ss = alpha0 / (1 - alpha1 - alpha2*sigma_T * (UC/p))",
    "ydhs", "c", "s"
  )
)

Shock 2

This example applies an increase in the target real wage.

First, initialize an empty shock object:

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

Define the shock by adding an appropriate equation:

# Add shock equation
shock_disinf <- add_shock(shock_disinf,
  variable = "Omega0",
  value = -1,
  desc = "Increase in the target real wage",
  start = 5, end = 100
)

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

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

Simulate the scenario with the shock applied:

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

Finally, plot the simulation outcomes:

# Plot results
plot_simulation(
  model = model_disinf, scenario = c("expansion2"), from = 1, to = 40,
  expressions = c("p", "UC", "UCp = UC/p")
)
# Plot results
plot_simulation(
  model = model_disinf, scenario = c("expansion2"), from = 1, to = 40,
  expressions = c("inflation = (p - dplyr::lag(p)) / dplyr::lag(p)")
)
# Plot results
plot_simulation(
  model = model_disinf, scenario = c("expansion2"), from = 1, to = 40,
  expressions = c(
    "ydhs_ss = alpha0 / (1 - alpha1 - alpha2*sigma_T * (UC/p))",
    "ydhs", "c", "s"
  )
)

References

For more details on DISINF model, refer to Chapter 9 of Monetary Economics. An Integrated Approach to Credit, Money, Income, Production and Wealth.