Thoeretical varicance-covariance matrix

Dear all,
My question is that I have got the evolution function of a simple RBC model as in the picture, with c is consumption, k is capital and a is technology, and e is white noise, (all variables are log linearized). and thus I have got the policy function. So how do I calculate the theoretical covariance matrix based on these equations? Thanks ahead!


Usually, that involves computing the fixed point of the Lyapunov equation. There exists an explicit but slow formula for that.

Yep, I first calculate the covariance matrix of (kt , at) by solving a matrix equation, and then I calculate the covariance of ct and (kt, at). But I have a new question, how do I calculate the autoregression matrix of these variables?

You mean the first order autocorrelation? That should be straightforward based on the state space representation.

This is of great help to me! Thanks jpfeifer! BTW, can you share the rest of the slides?

Chapter_2.pdf (718.3 KB)

Thanks again!

If the formula above is the solution to your model (endogenous as a function of states, a, k), then you can obtain the covariance matrix of the states, and the corresponding variance of your decision variables vector implied by the parameters you got:

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