knitr::opts_chunk$set( collapse = TRUE, comment = "#>" )
Working Code Example
library(SolowVariants) theme_set(theme_bw()) # Setting up the parameter grid --------------------------------- aux_np <- 200 aux_parameter_grid <- create_parameter_grid( c("B", "alpha", "delta", "n", "s"), c(10, 1 / 3, 0.1, 0.005, 0.22), c(NA, NA, NA, NA, NA), c(NA, NA, NA, NA, NA), aux_np ) # Setting starting values for K and L --------------------------------- aux_startvalues <- list(K = 1, L = 1) # Simulate the basic Solow growth model --------------------------------- aux_simulation <- SimulateBasicSolowModel(aux_parameter_grid, aux_np, aux_startvalues) # Visualise some variables --------------------------------- VisualiseSimulation(aux_simulation, c("YpW", "Y", "KpW"), "free") # Economy in SS in the End ------------------------------------------------------------------ steadystate_checker(aux_simulation, aux_parameter_grid, "BS")
Elaboration
Parameters defining the BS
- TFP ($B$)
- Alpha ($\alpha$)
- Rate of capital depreciation ($\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 Basic Solow Growth Model
$$ \begin{aligned} Y_t &= BK_t^\alpha L_t^{1-\alpha} \ r_t &= \alpha B \left(\frac{K_t}{L_t}\right)^{\alpha -1}\ w_t &= (1-\alpha) \left(\frac{K_t}{L_t}\right)^\alpha \ S_t &= sY_t \ K_{t+1}&= sY_t + (1-\delta)K_t \ L_{t+1}&=(1+n)L_t \end{aligned} $$
