## a question about cycle bind

Discussion of State Space and Dynamic Stochastic General Equilibrium Models
hardmann
Posts: 185
Joined: Sat Feb 26, 2011 9:49 pm

### a question about cycle bind

Dear Tom:

When we decompose the 100 *log GDP into trend and cycle components based on UC model, supposing the trend is local linear trend process, and the cycle AR(2) process. We find that end of sample is before 2019, cycle fluctuate within [+5%,-6%] bind. Morley et al, (2003), Perron & Wada(2009), Laubach & Williams present similar result. When using 1947Q1- 2021Q4 sample, the bind narrows to ±3%. Even within sample of 1947Q1- 2021Q4, we use subsample of 1947Q1- 2019Q4, the bind restores the [+4%,-6%]. Dose the pandemic data, 2020Q1~2021Q4, change it? Why?

Best Regard
Hardmann
Attachments
US_qGDP_2021Q4.xls
UC Compare different sample.RPF
TomDoan
Posts: 7564
Joined: Wed Nov 01, 2006 4:36 pm

### Re: a question about cycle bind

You're estimating the component variances. When you add in the extra data, the variance on the trend doubles (just with 8 extra data points). So instead of a fairly stiff trend (forcing most of the variation into the cycle), the re-estimated trend picks up much of the change in 2020. You'll see a different result if you fit the SSM to the 2021 without re-estimating the variances.
hardmann
Posts: 185
Joined: Sat Feb 26, 2011 9:49 pm

### Re: a question about cycle bind

Dear：
Thanks. I get what you said. But I am still confused. I estimate different smaple ending from 2020Q1-2020Q4 respectively. I find merely the point of 2020Q2 change the result of history. There are three result, before, at, post 2020Q2. If one data changes significantly the estimation, the model will lost robustness.

Best Regard
Hardmann
Attachments
UC Compare different sample revisited.RPF
TomDoan
Posts: 7564
Joined: Wed Nov 01, 2006 4:36 pm

### Re: a question about cycle bind

Yes. That's the problem for this type of model, which is why, in practice, they require a lot of special care to produce anything resembling reasonable results.
hardmann
Posts: 185
Joined: Sat Feb 26, 2011 9:49 pm

### Re: a question about cycle bind

There is a big problem. If we estimate the output gap in real time and use the same model configuration, the estimation of specific quarter will be signifcant different, about twice as large. This is a disaster for the Taylor rule, because size of output gap will affect the interest rate decision.
I use Matlab， stamp verifies it, all get same result.
When I add a break or outlier in Stamp, the bound restores, but RATS remains.

Regard.
TomDoan
Posts: 7564
Joined: Wed Nov 01, 2006 4:36 pm

### Re: a question about cycle bind

How are you doing that with RATS? In another thread, you were doing the dummied observation incorrectly.