I am currently working on a version of the Krusell-Smith (1998) model, but instead of a fixed transition matrix, I need to work with two continuous autoregressive processes and discretize them into the Markov chain. However, to get structure similar to KS, I need to impose a correlation between micro and macro-level shocks, which makes the stochastic system VAR, not just two independent ARs.
I would be grateful for any suggestion, how to perform this discretization. Is there some nice approach similar to Tauchen/Rouwenhorst for AR(1)s? Or I need to perform Monte-Carlo simulations and fit the Markov chain on it?