Hi, I have a question about pruning and second approximation of theoretical moments.

When I run a second-order approx. with Dynare using stoch_simul(order=2,nograph,irf = 20) I get the “Approximated theoretical moments” printed out and they are then stored in oo_.mean. I found these means are very largely deviated from the steady state. Meanwhile, I get the message that “irfs cannot be displayed” because they are explosive.

I then use pruning with Dynare using stoch_simul(order=2,nograph,irf = 20,pruning), now I can obtain the irfs. However, the variable means reported under “Approximated theoretical moments” does not change and still are very largely deviated from the steady state. I just wonder if something goes wrong. Should I trust these means?

The theoretical moments at second order are based on the first order state space representation. Thus, they are not affected by pruning and will always be the same. It is different for GIRFs, which are simulation based.

If the moments look strange, you need to check your equations.

Thank you for your reply. But I don’t understand that “the theoretical moments at second order are based on the first order state space representation”. And if that’s the case, what are the theoretical moments at first order based on?

I thought the theoretical expected mean of a variable would be calculated based on the second order Taylor expansion, which should be the sum of the variable’s steady state plus some correction for the variance of the variable.

Another question is that, if I want to estimate the mean of a variable based on simulation, can I do that?

[quote=“jpfeifer”]The theoretical moments at second order are based on the first order state space representation. Thus, they are not affected by pruning and will always be the same. It is different for GIRFs, which are simulation based.

If the moments look strange, you need to check your equations.[/quote]

To get second-order accurate moments, you only need to consider a linear solution (at second order including the constant uncertainty correction term). Pruning only affects higher order terms. Thus, the theoretical moments are identical.

Generally, see [What are "theoretical moments" referring to?)