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", "beta", "delta", "n", "s", "g", "X"),
    c(1/3, 1/3, 0.2, 0.005, 0.2, 0.02, 1),
    c(NA, NA, NA, NA, NA, NA, NA),
    c(NA, NA, 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 <- SimulateExtendedSolowModelScarceResourceLand(aux_parameter_grid, aux_np,aux_startvalues)

# Visualise some variables ---------------------------------
VisualiseSimulation(aux_simulation,
                    c("YpW", "KpW", "L"), 
                    "free")

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

Elaboration

Parameters defining the ESSRL

• Alpha ($\alpha$)
• Beta ($\beta$)
• Population growth rate ($n$)
• Growth rate of total factor productivity ($g$)
• Savings rate to physical capital ($s$)
• Rate of capital depreciation ($\delta$)
• Stock of land ($X$)

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

Starting value of endogenous variables defining the ESSRL

• 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("ESSRL").

Structural Equations to the Extended Solow Growth Model with the Scarce Resource Land

$$ \begin{aligned} Y_t &= K_t^\alpha * (A_t * L_t)^{(1- \beta)} * X_t^\kappa \quad \text{ where } \alpha + \beta + \kappa = 1 \ K_{t+1} &= s_KY_t + (1-\delta)K_{t} \ L_{t+1}&=(1+n)L_t \ A_{t+1}&=(1+g)A_t \ \end{aligned} $$

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