# Theoretical Moments in Second Order Approximations

Hi there,

I am encountering an issue and I am not sure if this is a problem or not. I have programmed a DSGE in levels. Then I use stoch_simul(order=1) and stoch_simul(order=2) to compute the theoretical mean and variance of the model’s variables. I find that the mean of the variables when I take a second order approximation to be different than the mean when I take a first order approximation. This makes sense and is expected. However, and this is what puzzles me, the variance of the model’s variables is exactly the same when I take a first or a second order approximation. Is this correct? Thanks, Pau.

That comes from the way theoretical moments are computed at second order. As documented in the manual, Kim et al have shown that a first order approximation delivers second order accurate moments.

Dear Pfeifer,

I have calculated the welfare results for an nonlinear model, by using `stoch_simul(order=2)`. Now, I want to report the variance for several key variables, such as output. Maybe, there are two methods to accomplish it:

1. Just using `Stoch_simul(order=2)`, and finding them in `oo_.var`, which are the theoretical variancesh.

2. Using ‘stoch_simul(periods=10000,order=2)’, and finding them in `oo_.var`.

I am not sure which one is correct.

Thanks.

It is a matter of preference, whether you want theoretical or simulated moments. Asymptotically, the two must be the same.