Third order approximation and its discontents

Stochastic simulations
1

Hi everyone,

I am using dynare 4.5.6. My key question is related to understanding the third order approximation of the type used in Basu & Bundick (2017), henceforth BB (2017) and generating IRFs.

Here is what I am doing:

I want to understand what happens to output when there is uncertainty about productivity. I take the standard RBC model (Listing 6). I include a lagged term in the productivity equation (similar to what is done in BB (2017) – they explain this on page 13 here: https://fmwww.bc.edu/ec-p/wp774.pdf).

I include a shock process for this term. I then add stoch_simul(order=3,irf=20) because I want to extract the effect of uncertainty on output. Given the small size of the shocks my IRFs are well behaved.

I noticed, however, that there has been an active discussion on this forum (Simult_ and nonzero IRFs in higher-order approximations)
Also, the excellent BB (2017) replication and the Born/Pfeifer (2014): “Risk Matters: A comment” goes beyond the simple stoch_simul to generate IRFs. My questions:

  1. Do I need to use the simult_ function to compute IRFs around the stochastic steady state?
  2. I also noticed that when I change the irf = 20 to irf = 10, the second order IRF change. Why is that?

Attaching the code here.RBC.mod (1.5 KB)

2
  1. Yes, you need to use the simult_-function to generate IRFs at the stochastic steady state. Using the standard Dynare stoch_simul-command will generate IRFs at the ergodic mean.
  2. That implies that your IRFs have not yet converged to the ergodic distribution, i…e. you need to increase replic. Using a different IRF length results in different random numbers being drawn across the replications.