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 <- 200
aux_parameter_grid <-
  create_parameter_grid(
    c("alpha", "phi", "delta", "n", "s"),
    c(1 / 3, 0.99, 0.15, 0, 0.22),
    c(NA, NA, NA, NA, NA),
    c(NA, NA, NA, NA, NA),
    aux_np
  )

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

# Simulate the basic Solow growth model ---------------------------------
aux_simulation <-
    SimulateExtendedSolowModelEndogenousGrowth(aux_parameter_grid,
                                               aux_np,
                                               aux_startvalues
    )
# Visualise some variables ---------------------------------
VisualiseSimulation(
  aux_simulation,
  c("gYpW", "gKpW"),
  "free"
)

# Economy in SS in the End ---------------------------------
steadystate_checker(aux_simulation, aux_parameter_grid, "ESEG")

Elaboration

Parameters defining the ESEG

• Alpha ($\alpha$)
• Phi ($\phi$)
• Rate of capital depreciation ($\delta$)
• Population growth rate ($n$)
• Savings rate ($s$)

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

Starting value of endogenous variables defining the BS

• Starting value of physical capital ($K_0$)
• Starting value of the labor force ($L_0$)

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

Structural Equations to the Extended Solow Model with

a) Semi-Endogenous Growth

$$\begin{aligned} Y_t &= K_t^\alpha (AL_t)^{1-\alpha} \ A_t &= K_t^\phi \ K_{t+1}&= sY_t + (1-\delta)K_t \ L_{t+1}&=(1+n)L_t \ \end{aligned}$$

b) Fully Endogenous Growth

$$\begin{aligned} Y_t &= AK_t : A = L^{(1- \alpha)}\ K_{t+1}&= sY_t + (1-\delta)K_t \ L_{t+1}&=(1+n)L_t \quad \text{ where } n = 0 \end{aligned}$$

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