Shocks to the second moment and estimation

[piya_uci]

Hi,

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=rho_a*at(-1)+exp(sigma_a)*u_a;
sigma_a=(1-rho_sigma_a)*sigma_a_bar+rho_sigma_a*sigma_a(-1)+eta_a*u_sigma_a;

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.

[jpfeifer]

Depends on what you want to estimate. For just estimating the exogenous process, you can look into https://github.com/JohannesPfeifer/Particle_Filtering 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 https://www.aeaweb.org/articles.php?doi=10.1257/aer.104.12.4231.