In SebastianBehrens/SolowVariants: Provide framework to simulate macroeconomic Solow growth models

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

Working Code Example

library(SolowVariants)
theme_set(theme_bw())

# Setting up the parameter grid ---------------------------------
aux_np <- 10000 # set to 10000 because the SS on FpW and VpW is only 'reached' after around 6000 periods. All others are of course reached earlier.
aux_parameter_grid <-
  create_parameter_grid(
    c("B", "alpha", "n", "s", "r"),
    c(1, 1 / 3, 0.005, 0.1, 0.04),
    c(NA, NA, NA, NA, NA),
    c(NA, NA, NA, NA, NA),
    aux_np
  )

# Setting starting values for K and L ---------------------------------
aux_startvalues <- list(L = 1, V = 1)

# Simulate the basic Solow growth model ---------------------------------
aux_simulation <- SimulateExtendedSolowModelSmallOpenEconomy(aux_parameter_grid, aux_np,aux_startvalues)

# Visualise some variables ---------------------------------
VisualiseSimulation(aux_simulation,
                    c("Y", "KpW", "VpEW", "VpW"), 
                    "free")

# Verify whether the economy is 'in' steady state in the final period ---------------------------------
steadystate_checker(aux_simulation, aux_parameter_grid, "ESSOE")

Note: The steady state of the variables FpW and Vpw as tested by steadystate_checker is only "reached" after several thousand periods. Keep that in mind regarding the TRUE or FALSE evaluation in the column "Economy in SS" in the output of steadystate_checker.

Elaboration

Parameters defining the ESSOE

• Total factor productivity ($B$)
• Alpha ($\alpha$)
• Population growth rate ($n$)
• Savings rate to physical capital ($s$)
• Real rate of return on capital ($r$)

Remark: Those parameters can be found via the command: getRequiredParams("ESSOE").

Starting value of endogenous variables defining the ESSOE

• Starting value of the labor force ($L_0$)
• Starting value of national wealth ($V_0$)

Remark: Those parameters can be found via the command: getRequiredStartingValues("ESSOE").

Structural Equations to the Extended Solow Growth Model for the Small Open Economy

$$ \begin{aligned} Y_t &= BK_t^\alpha L_t^{1-\alpha} \ Y_n &= Y_t + \bar{r}F_t \ V_t &= K_t + F_t\ r_t &= \alpha B \left(\frac{K_t}{L_t}\right)^{\alpha -1}\ w_t &= (1-\alpha) B \left(\frac{K_t}{L_t}\right)^\alpha \ S_t &= sY_t \ S_t &= V_{t+1} - V_t\ L_{t+1}&=(1+n)L_t \ \end{aligned} $$

SebastianBehrens/SolowVariants documentation built on Oct. 11, 2023, 2:49 p.m.