First order and third order approximations give different irfs

I am estimating a DSGE model, the Bayesian irfs for some variables look different from irfs based on stochastic simulations (third order with pruning) which follows my estimations. For some variables the impact effects are just opposite. Which irf seems more reliable? In the context of my model, I believe that third order is more reliable for financial variables like to yield to maturity, bond premium or uncertainty related terms. For real variables such as GDP growth rates etc. I will trust the first order terms more. Am I right?

In addition, I don’t get any variance decompositions from the third order approximation. Don’t know why.

First of all, the concepts differ. At third order, we are talking about generalized Impulse Response Functions.

There are obviously IRFs that are zero at first order, because a linear approximation is not sufficient to capture economic effects. An example is the response to uncertainty shocks. As you can see from this, it depends not just on the dependent variable, but also on the exogenous shock. At the same time, there are shocks that have first order effects on some variables, but only have higher order effects on other variables. So the dependent variable matters as well.

But generally, higher order approximations should deliver a more accurate approximation to your model, so you should trust those IRFs more - unless there is something really suspicious going on. In any case, it is always sensible to investigate differences between first and third order effects. You will gain important insights into the workings of your model.

Many thanks for the detailed response. You did not answer why I don’t get variance decomposition for third order.

At higher order, there is no unique way to decompose the overall variance into the contribution of individual shocks as there are interaction effects due to nonlinearity. So if you request theoretical moments, you will not get a variance decomposition. But when you request simulated moments (periods>0), Dynare will simulate the model one shock at a time and give you the contributions.

Many thanks again. Very much appreciated. Would you mind giving the command for getting simulated moments?

Never mind. I know how to do it now. Thank you again.

Dear Jpfeifer,
I am following up my question about higher order approximation that I asked you two months ago. Thank you for answering my earlier questions. I am doing a higher order approximation in stochastic simulation. How is Kalman smoothing affected by higher order approximation? I thought that the Kalman smoothing is based on a log linear state space form. However, when I go to higher order, the state space form is no no longer linear. Am I right? I think the estimation and smoothing are still done in a linear state space form. Higher order only applies to stochastic simulation which happens AFTER estimation. am I right?



You are confusing something. The Kalman filter only works with linear Gaussian models. If you want to do estimation with a nonlinear model, you need to rely on a different filter like the particle filter (unless your model is invertible in the observables)

Thanks Jpfeifer for the response. Perhaps I was not clear before. I would like to do the estimation using Kalman filtering with linear Gaussian model. Using the estimates of some key parameters and also some other calibrated parameters, I am doing stochastic simulation going higher order. I then analyse the resulting variance decompositions and impulse responses based on the higher order approximations. My understanding is that it is ok to do so because I am just using the parameter estimates based on a loglinearized model but stochastic simulation is done going higher order to pick up nonlinearity. Is it ok?

Yes, as long as the procedure is transparent, that is fine.