time varying volatility

[jpfeifer]

An IRF cannot converge to the ergodic mean. They always converge to 0 as the model is stationary and the effect of a shock thus dies out over time.

[econactually]

I use basic DNK model to model time varying interest rate volatility. I wrote the code in dynare and plot impolse responses as percentage deviations from the variables' ergodic means. By using the same model I also wrote the code in mathematica in a way compatible with Eric Swanson's Perturbation aim codes and again plot impolse responses as percentage deviations from the variables' ergodic means. The two results are different. Do you know what would cause this particularly? Thanks!

[sidus87]

Hi all, could any of you experts tell me whether I got it right on how to implement the uncertainty shocks and get their IRFs?

For practicing I used the Ireland model "Technology shocks in the New Keynesian model", adding shocks to the TFP volatility and try to plot the IRFs following what's been told on this thread.

Thanks a lot

[jpfeifer]

For more on this, see the appendix and the replication files to Born/Pfeifer (2014): "Risk Matters: A comment" on my homepage.

[sidus87]

Dear all,

I have a question concerning the calculation of IRFs from the Stochastic Steady State (SSS) as done in Basu and Bundick (2015). Brent Bundick has uploaded his code on his website and what they do is basically:
"simulating" (with simult_) the model with zero shocks (starting at the deterministics steady state) for a burn in period of say 2000, then at time 2001 there's the uncertainty shock hitting (simulation continues up until period 2020, so to get an IRF of 20 periods).

What I was doing before instead, was to run once simult_ with zero shocks for to back out the SSS, then run a second simulation with simult_ starting at the SSS to obtain the IRF.

I thought the IRFs would deliver the same result, but surprisingly (to me) they don't. Can anyone explain me why this is the case? Moreover, what's the correct way of doing it? Thanks in advance

[jpfeifer]

Could you please explain what exactly you did?

[sidus87]

That's what I did:
1) "simulate" the model with simult_ with zero shocks for 2000 periods and take the variables at T=2000 as the Stochastic Steady State (SSS)
2) Simulate once again the model with simult_ (for T=length IRF) starting from the SSS, hitting the economy with an uncertainty shock at time 1 and zero shocks afterwards
3) Calculate percentage deviations from SSS.

Basu and Bundick do the following:

Let T1= burnin
T2= length IRF
1) "simulate" the model with simult_ for T=T1+T2 with zero shocks for T1 periods and a 1 std shock to uncertainty at t=T1+1.
3) Calculate percentage deviations from SSS (value of the variables at t=T1)

[jpfeifer]

I don't know what exactly you did, but the outlined approach should be correct and should yield the Basu/Bundick IRFs (apart from a small difference related to them not actually starting at the stochastic steady state, because the burnin is insufficient)
I have replicated their IRFs using my own codes. Your differences are puzzling. Did you correctly deal with percentage deviations? If the model is in logs, you must use log differences instead of actual ratios.

ADDENDUM: What I said before only applies to the case without pruning. With pruning, there is an augmented state space. Basu/Bundick with their long series set yhat1 to yhat3 to the values at the stochastic steady state. However, when you restart the simulations at the stochastic steady state, you set yhat1 to yhat1+yhat2+yhat3 and yhat2=yhat3=0.

[sidus87]

Thanks a lot for the addendum, Johannes. It's been very helpful

[sidus87]

Dear Johannes,

Do you know why sometimes I get (non negligible) movements in the level of TFP after an uncertainty shock when I compute the IRFs as Generalized IRFs? I'm using the toolbox by Andreasen et al. so it should not be a problem of not having done enough replications. I really don't see why this is the case.

[jpfeifer]

I am not that familiar with their toolkit, but it might have to do with the way the process is specified (log-normal vs. in levels)

[zhanghuifd]

Dear friends, sorry to follow this old post.
I met a simple problem when studying Basu (2016). They set the s.t.d. of preference shock and that of its volatility shock to around 0.002. Then they set the variance to 1 and report irfs multiplied by 100 to represent one percent std from steady state. Are those irfs true levels or magnified? Could anyone help me?
Thanks a lot! !

[onthetopo]

How would you estimate the parameters controlling time-variation in volatility?

[zhanghuifd]

Sorry, I've not finished it yet.

[jpfeifer]

@zhanghuifd Please explain your question in more detail. I have replicated the Basu/Bundick paper.
@onthetopo If you observe the endogenous process, you can e.g. use a particle filter to independently estimate the exogenous process from the rest of the model. In Basu/Bundick, the uncertainty shock is on a preference shock and therefore unobserved. They use a combination of impulse response function and moment matching.