less moments than variables

[p.gelain]

Hi

I am simulating a model with 37 endogenous variables, but Dynare gives me the moments only for 23 variables and the variance decomposition and the matrix of correlations only for 20 variables.

Does someone know why?

Paolo

[iacoviel]

It is likely that you are calculating the variance decomposition and the theoretical moments of nonstationary variables. Neither of those exist. Dynare will not report moments for variable which are nonstationary, I think.

[reubenpjacob]

true, if there is a unit root, dynare will not report the moments.

[p.gelain]

Ok, thank you for your replies. But, how does Dynare establish if a (simulated?) variable is stationary or not? if I do not say Dynare to simulate the model, the only way I think it can do is checking whether the variance is finite or not (I am sure that my variables has finite means, and in particular zero mean). Contrary, if I simulate the model (periods=1000), all the moments (which are not theoretical in this context!) are computed.

Paolo

[iacoviel]

Consider the following equation

x(t)=rho*x(t-1)+u(t), u(t) iid, with variance s

If abs(rho)<1, the theoretical variance of x(t) is s/(1-rho^2)

If rho=1, the variance of x does not exist, but that does not prevent you from simulating that process for T periods and computing the variance of x, but the variance of x will explode as T grows larger. Try simulating your model doubling the number of periods. The variance of your nonstationary variable should be twice as big. In fact, the variance is not finite.

Dynare applies the same logic as the one described above for the univariate case. In the multivariate case, x(t) is a vector, rho is a matrix (call is R), etc... and the variance of x(t) can be computed using the formulas described in Hamilton chapter 13. You should start from there to establish how to find which variables are stationary and which ones are not.

[p.gelain]

many thanks!

Paolo