Shocks to the second moment and estimation


I am working with a medium-sized DSGE model with nominal rigidities and financial frictions. I am interested in estimating the impulse responses of variables to second-moment shocks for the productivity process. I model the productivity process as follows:


At present, I am examining the impulse responses of model variables to uncertainty/second-moment shocks (sigma_a in this case) by taking the 3rd order solution in conjunction with pruning. If I have to proceed with estimation what would be relevant references/codes that I could go through to understand the process?

Thank you.

Depends on what you want to estimate. For just estimating the exogenous process, you can look into which we used for Born/Pfeifer (2014): Policy risk and the business cycle, Journal of Monetary Economics. If you want to estimate the whole model, you could do a simulated method of moments as we did in that article. In that case, I would refer you to the replication files to Born/Pfeifer (2014): “Risk Matters: A comment” at