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("g", "alpha", "delta", "n", "s"),
    c(0.02, 1 / 3, 0.1, 0.005, 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(A = 1, K = 1, L = 1)

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

# Visualise some variables ---------------------------------
VisualiseSimulation(aux_simulation,
                    c("YpW", "Y", "KpEW"), 
                    "free")

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

Elaboration

Parameters defining the GS

• Growth rate of total factor productivity ($g$)
• Alpha ($\alpha$)
• Rate of capital depreciation ($\delta$)
• Population growth rate ($n$)
• Savings rate ($s$)

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

Starting value of endogenous variables defining the GS

• Starting value of total factor productivity ($A_0$)
• 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("GS").

Structural Equations to the General Solow Growth Model

$$ \begin{aligned} Y_t &= K_t^\alpha (A_tL_t)^{1-\alpha} \ r_t &= \alpha \left(\frac{K_t}{A_tL_t}\right)^{\alpha -1}\ w_t &= (1-\alpha) \left(\frac{K_t}{A_tL_t}\right)^\alpha A_t\ S_t &= sY_t \ K_{t+1}&= sY_t + (1-\delta)K_t \ L_{t+1}&=(1+n)L_t \ A_{t+1} &= (1 + g)*A_t \end{aligned} $$

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