Skip to contents

Model DIS

Source: vignettes/Model_DIS.Rmd
Model_DIS.Rmd

This guide explains how to use the godley package to create the DIS model — a model with private bank money, inventories and disequilibrium (of a kind) in the goods market, 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_dis <- create_model(name = "SFC DIS")
#> Empty model created

Define the variables for the model:

# Add variables
model_dis <- model_dis |>
  add_variable("rl", init = 0.025) |>
  add_variable("pr", init = 1) |>
  add_variable("W", init = 0.75) |>
  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 = 0.75) |>
  add_variable("epsilon", init = 0.75) |>
  add_variable("gamma", init = 0.25) |>
  add_variable("phi", init = 0.25) |>
  add_variable("sigma_T", init = 0.15) |>
  add_variable("y", init = .001) |>
  add_variable("p", init = .001) |>
  add_variable("NHUC", init = .001) |>
  add_variable("s_E", init = .001) |>
  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("UC") |>
  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("ydhs") |>
  add_variable("mh") |>
  add_variable("ydhs_E")

Establish the relationships between variables by adding equations:

# Add equations
model_dis <- model_dis |>
  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) * NHUC") |>
  add_equation("NHUC = (1 - sigma_T) * UC + sigma_T * (1 + rl[-1]) * UC[-1]") |>
  add_equation("EF = S - WB + (INV - INV[-1]) - rl[-1] * 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("YD = WB + EF + EFb + rm[-1] * Mh[-1]") |>
  add_equation("Mh = Mh[-1] + YD - C") |>
  add_equation("ydhs = c + (mh - mh[-1])") |>
  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("Mh = Ms", hidden = TRUE)

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

# Simulate model
model_dis <- simulate_scenario(model_dis,
  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_dis, scenario = c("baseline"), from = 1, to = 40,
  expressions = c("ydhs", "c")
)
# Plot results
plot_simulation(
  model = model_dis, scenario = c("baseline"), from = 1, to = 40,
  expressions = c(
    "delta_inv = inv - dplyr::lag(inv)",
    "delta_inv_E = inv_E - dplyr::lag(inv_E)"
  )
)

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

The initial example demonstrates the effect of a one-shot increase in the costing margin.

First, initialize an empty shock object:

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

Define the shock by adding an appropriate equation:

# Add shock equation
shock_dis <- add_shock(shock_dis,
  variable = "phi",
  value = 0.35,
  desc = "One-shot increase in the costing margin",
  start = 5, end = 40
)

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

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

Simulate the scenario with the shock applied:

# Simulate shock
model_dis <- simulate_scenario(model_dis,
  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

Display the results on the plot:

# Plot results
plot_simulation(
  model = model_dis, scenario = c("expansion1"), from = 1, to = 40,
  expressions = c("c", "ydhs")
)
# Plot results
plot_simulation(
  model = model_dis, scenario = c("expansion1"), from = 1, to = 40,
  expressions = c(
    "delta_inv = inv - dplyr::lag(inv)",
    "delta_inv_E = inv_E - dplyr::lag(inv_E)"
  )
)

Shock 2

Another example conveys the impact of an increase in the target inventory-to-sales ratio.

First, initialize an empty shock object:

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

Add an appropriate equation:

# Add shock equation
shock_dis <- add_shock(shock_dis,
  variable = "sigma_T",
  value = 0.25,
  desc = "Increase in the target inventories to sales ratio",
  start = 5, end = 50
)

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

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

Simulate the model with the shock applied:

# Simulate shock
model_dis <- simulate_scenario(model_dis,
  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

Plot the results:

# Plot results
plot_simulation(
  model = model_dis, scenario = c("expansion2"), from = 1, to = 40,
  expressions = c("c", "ydhs")
)
# Plot results
plot_simulation(
  model = model_dis, scenario = c("expansion2"), from = 1, to = 40,
  expressions = c(
    "delta_inv = inv - dplyr::lag(inv)",
    "delta_inv_E = inv_E - dplyr::lag(inv_E)"
  )
)

References

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