I am looking for tips, pointers, explainers, blog posts, and the like, on how to set up a monte carlo simulation for a time-series, cross-sectional / panel data generating process in R.
I would like to start with a model such as this:
$$ y_{it} = \alpha + \phi y_{it-1} + \beta_1 x_{it-1} + \beta_2 z_{it-1} + \epsilon_{it} \\ \epsilon_{it} \sim N(0, \sigma^2_{(y)}) \\ x_{it} = \mu + \eta x_{it-1} + \upsilon_{it}\\ \upsilon_{it} \sim N(0, \sigma^2_{(x)}) $$
In my use case, $i$ indexes countries and $t$, years.
The plan is to fix parameters such as $\beta_1$, $\phi$ and $\eta$ at certain values, simulate a large dataset, and test the bias of alternative panel data estimators. If I can get it set up I will add more bells and whistles to the data generating model.
