godley is an R package for simulating SFC (stock-flow consistent) models. It can be used to create and simulate fully fledged post-keynesian / MMT models of the economy. It allows users to apply shocks, simulate effects of changing parameters, visualize different macro scenarios and much more.
godley is named after Wynne Godley (1926-2010), a famous British post-keynesian economist and a father of stock-flow consistent modelling.
The best way to start using godley is to install it directly grom GitHub using the devtools package.
install.packages("devtools")
devtools::install_github("gamrot/godley")Below you can find a simple example of godley in action. Let's play with the well known "SIM model" from Monetary Economics (Godley & Lavoie, 2007).
First, we need to create an empty model using create_model() function.
model_sim <- create_model(name = "SFC SIM")Now let's add some variables using the add_variable() function. This will add a $varibles tibble to the model.
model_sim <- model_sim |>
add_variable("C_d", desc = "Consumption demand by households") |>
add_variable("C_s", desc = "Consumption supply") |>
add_variable("G_s", desc = "Government supply") |>
add_variable("H_h", desc = "Cash money held by households") |>
add_variable("H_s", desc = "Cash money supplied by the government") |>
add_variable("N_d", desc = "Demand for labor") |>
add_variable("N_s", desc = "Supply of labor") |>
add_variable("T_d", desc = "Taxes, demand") |>
add_variable("T_s", desc = "Taxes, supply") |>
add_variable("Y", desc = "Income = GDP") |>
add_variable("Yd", desc = "Disposable income of households") |>
add_variable("alpha1", init = 0.6, desc = "Propensity to consume out of income") |>
add_variable("alpha2", init = 0.4, desc = "Propensity to consume out of wealth") |>
add_variable("theta", init = 0.2, desc = "Tax rate") |>
add_variable("G_d", init = 20, desc = "Government demand") |>
add_variable("W", init = 1, desc = "Wage rate")
model_sim$variables
## # A tibble: 16 x 3
## name desc init
## <chr> <chr> <dbl>
## 1 C_d Consumption demand by households 0
## 2 C_s Consumption supply 0
## 3 G_s Government supply 0
## 4 H_h Cash money held by households 0
## 5 H_s Cash money supplied by the government 0
## 6 N_d Demand for labor 0
## 7 N_s Supply of labor 0
## 8 T_d Taxes, demand 0
## 9 T_s Taxes, supply 0
## 10 Y Income = GDP 0
## 11 Yd Disposable income of households 0
## 12 alpha1 Propensity to consume out of income 0.6
## 13 alpha2 Propensity to consume out of wealth 0.4
## 14 theta Tax rate 0.2
## 15 G_d Government demand 20
## 16 W Wage rate 1Okay, let's add some equations, shall we? There's a function for that! You've guessed it, it's the add_equation() function.
It also adds a tibble to the model, this time it's called $equations
model_sim <- model_sim |>
add_equation("C_s = C_d", desc = "Consumption") |>
add_equation("G_s = G_d") |>
add_equation("T_s = T_d") |>
add_equation("N_s = N_d") |>
add_equation("Yd = W * N_s - T_s") |>
add_equation("T_d = theta * W * N_s") |>
add_equation("C_d = alpha1 * Yd + alpha2 * H_h[-1]") |>
add_equation("H_s = G_d - T_d + H_s[-1]") |>
add_equation("H_h = Yd - C_d + H_h[-1]") |>
add_equation("Y = C_s + G_s") |>
add_equation("N_d = Y/W") |>
add_equation("H_s = H_h", desc = "Money equilibrium", hidden = TRUE)
model_sim$equations
## # A tibble: 12 x 3
## equation desc hidden
## <chr> <chr> <lgl>
## 1 C_s = C_d "Consumption" FALSE
## 2 G_s = G_d "" FALSE
## 3 T_s = T_d "" FALSE
## 4 N_s = N_d "" FALSE
## 5 Yd = W * N_s - T_s "" FALSE
## 6 T_d = theta * W * N_s "" FALSE
## 7 C_d = alpha1 * Yd + alpha2 * H_h[-1] "" FALSE
## 8 H_s = G_d - T_d + H_s[-1] "" FALSE
## 9 H_h = Yd - C_d + H_h[-1] "" FALSE
## 10 Y = C_s + G_s "" FALSE
## 11 N_d = Y/W "" FALSE
## 12 H_s = H_h "Money equilibrium" TRUEWith all variables and equations defined, it's about time to run some simulations using the simulate_scenario() function. You can choose simulation method (Newton or Gauss) and number of periods (think quarters or years). Results will be stored in a $result tibble under a $baseline scenario.
model_sim <- simulate_scenario(model = model_sim, scenario = "baseline", max_iter = 350,
periods = 100, hidden_tol = 0.1, tol = 1e-08, method = "Newton")
model_sim$baseline$result
## # A tibble: 100 x 16
## C_s G_s T_s N_s Yd T_d C_d H_s H_h Y N_d alpha1
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0 0 0 0 0 0 0 0 0 0 0 0.5
## 2 13.3 20 6.67 33.3 26.7 6.67 13.3 13.3 13.3 33.3 33.3 0.5
## 3 22.2 20 8.44 42.2 33.8 8.44 22.2 24.9 24.9 42.2 42.2 0.5
## 4 29.9 20 9.99 49.9 39.9 9.99 29.9 34.9 34.9 49.9 49.9 0.5
## 5 36.6 20 11.3 56.6 45.3 11.3 36.6 43.6 43.6 56.6 56.6 0.5
## 6 42.4 20 12.5 62.4 49.9 12.5 42.4 51.1 51.1 62.4 62.4 0.5
## 7 47.4 20 13.5 67.4 53.9 13.5 47.4 57.6 57.6 67.4 67.4 0.5
## 8 51.7 20 14.3 71.7 57.4 14.3 51.7 63.3 63.3 71.7 71.7 0.5
## 9 55.5 20 15.1 75.5 60.4 15.1 55.5 68.2 68.2 75.5 75.5 0.5
## 10 58.8 20 15.8 78.8 63.0 15.8 58.8 72.4 72.4 78.8 78.8 0.5
## # ... with 90 more rows, and 4 more variables: alpha2 <dbl>, theta <dbl>,
## # G_d <dbl>, W <dbl>When everything is done, you can plot the outcome using the plot_simulation() function. You can define which variables or expressions you want. Let's plot Income, Government spending and Taxes.
plot_simulation(model = model_sim, scenario = "baseline", from = 1, to = 50,
expressions = c("Y", "G_s", "T_s"))
And one more thing (if you're lazy like me), you can create models using "templates" using create_model(template = "SIM"). You can choose from SIM, SIMEX, PC, PCEX, LP, REG, OPEN, BMW, BMWK, DIS and DISINF. Basically all models from Godley & Lavoie (2007).
godley allows you to create and simulate shocks. Let's see what happens if we increase government spending.
To create the shock first we need to create an empty shock object with a create_shock(). Next let's see what's gonna happen when we use the add_shock() function to increase government spending by 5 units from 5th to 50th period.
sim_shock <- create_shock()
sim_shock <- add_shock(shock = sim_shock, equation = "G_d = 25",
desc = "permanent increase in government expenditures", start = 5, end = 50)
sim_shock
## # A tibble: 1 x 4
## equation desc start end
## <chr> <chr> <dbl> <dbl>
## 1 G_d = 25 permanent increase in government expenditures 5 50With everything defined, let's add a new scenario using the add_scenario() function. But first we need to instruct godley which scenario we will use as a starting point (and which period).
model_sim <- add_scenario(model = model_sim, name = "expansion", origin = "baseline",
origin_period = 100, shock = sim_shock)After a shock scenario is created we can simulate it using the now familiar simulate_scenario() function.
model_sim <- simulate_scenario(model = model_sim, max_iter = 350, periods = 100,
hidden_tol = 0.1, tol = 1e-08, method = "Newton")
model_sim$expansion$result
## # A tibble: 100 x 16
## C_s G_s T_s N_s Yd T_d C_d H_s H_h Y N_d alpha1
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0 0 0 0 0 0 0 0 0 0 0 0.5
## 2 13.3 20 6.67 33.3 26.7 6.67 13.3 13.3 13.3 33.3 33.3 0.5
## 3 22.2 20 8.44 42.2 33.8 8.44 22.2 24.9 24.9 42.2 42.2 0.5
## 4 29.9 20 9.99 49.9 39.9 9.99 29.9 34.9 34.9 49.9 49.9 0.5
## 5 39.9 25 13.0 64.9 51.9 13.0 39.9 46.9 46.9 64.9 64.9 0.5
## 6 47.9 25 14.6 72.9 58.4 14.6 47.9 57.3 57.3 72.9 72.9 0.5
## 7 54.9 25 16.0 79.9 63.9 16.0 54.9 66.4 66.4 79.9 79.9 0.5
## 8 60.9 25 17.2 85.9 68.7 17.2 60.9 74.2 74.2 85.9 85.9 0.5
## 9 66.1 25 18.2 91.1 72.9 18.2 66.1 80.9 80.9 91.1 91.1 0.5
## 10 70.6 25 19.1 95.6 76.5 19.1 70.6 86.8 86.8 95.6 95.6 0.5
## # ... with 90 more rows, and 4 more variables: alpha2 <dbl>, theta <dbl>,
## # G_d <dbl>, W <dbl>Now let's see the result using the plot_simulation() function. As you can see, an increase in government expenditures has a positive effect on income... And not so positive short-term effect on government balance.
plot_simulation(model = model_sim, scenario = c("expansion"), from = 1, to = 50,
expressions = c("Y", "G_s", "T_s"))
godley allows users to see if simulation results are sensitive to parameter changes. After all, we don't want to create models that make sense just for a specific combination of parameters. Let's see how small changes to alpha1 affect short-term model dynamics.
First we need to create a new object using create_sensitivity() function and define lower and upper bounds for the parameter we want to analyze.
model_sens <- create_sensitivity(model_pass = model_sim, variable = "alpha1",
lower = 0.1, upper = 0.7, step = 0.05)Now we're ready to simulate results and see it on a plot.
model_sens <- simulate_scenario(model = model_sens, max_iter = 350, periods = 100,
hidden_tol = 0.1, tol = 1e-08, method = "Newton")
plot_simulation(model = model_sens, scenario = "sensitivity", take_all = TRUE,
from = 1, to = 50, expressions = c("Y"))
Here you can find more details about package functions and other models created with godley.
Here's a list of package's most important functions.
create_model() - creates an SFC model
add_variable() - adds a variable
add_equation() - adds an equation
simulate_scenario() - simulates a selected scenario(s)
plot_simulation() - plots simulation results
create_shock() - creates an SFC_shock object
add_shock() - adds shock equations
add_scenario() - adds scenario to an existing model
create_sensitivity() - creates a new SFC model with sensitivity scenarios for selected parameters.
There are two other packages that also allows users to build stock-flow consistent models:
If you encounter a clear bug, please file an issue with a minimal reproducible example on GitHub.
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