I have a question regarding the assumptions behind the shock processes in dynare. I have a log linearized two country model. Suppose, I want to shock both countries with a 1 SD monetary shock and the shocks have a correlation of 0.5. When I use the periods option to simulate the model does that imply that a new shock drawn from a N(0,1) as specified hits each country every period? So, if I run the simulation for 2100 periods, the end result would be an average response of the variables over all periods i. e a Monte Carlo simulation? I am not quite sure if that is correct. If that is not what is happening, I would appreciate it if someone can help me do what I just described.
Thanks in advance.
Are you talking about simulations or IRFs? For IRFs, at order=1 there is no reason to do simulations due to certainty equivalence. At higher order, Generalized IRFs will be created which do what you describe. Regarding simulations when you specify the
In every period there will be shocks drawn from a multivariate normal distribution with the specified covariance matrix. So if you correctly specify the correlation in Dynare, the simulation will do what you describe.
Thanks for your response. I believe you confirmed what I had in mind. However, what do you mean by if you specify the correlation between the shocks properly? Suppose, I have the following:
var u = u_SD^2;
var u_for = u_for_SD^2;
corr u, u_for=0.5;
(with u_SD and u_SD specified earlier)
And I have the periods option specified in stoch_simul. Is that going to do what I just described?
Yes, the will result shock being drawn from a multivariate normal with correlation 0.5.
If without specifying correlation between shocks, then shocks are drawn from a multivariate normal with 0 correlation , equals that
each shock is drawn form an univariate normal?
Thanks in advance,
Yes, exactly. It will be a multivariate normal with diagonal covariance matrix with the individual variances on the diagonal. This is equivalent to a series of univariate normals.