Lauback-Williams Natural Interest Rate Paper

[macro_man]

Estima:

Would like to put a request in for a RATs coding of a paper: "Measuring the Natural Rate of Interest" by Laubach and Williams (2003). This paper uses a Kalman Filter to estimate the unobserved natural rate of interest. Here is the link to the paper: http://www.federalreserve.gov/pubs/feds ... 156pap.pdf Thanks.

[TomDoan]

The only tricky part about that is the identity linking the three state variables r*, g and z. That has to be substituted out in forming the transition matrices:

states.gif (9.65 KiB) Viewed 22037 times

The two measurement equations have a combination of observables (y, pi and the x's) and states (the y* and r*). The lagged observables go into "MU" options, while the states go into the "C" matrix. (The Fabiani-Mestre example is somewhat similar).

[TomDoan]

It's now posted at:

http://www.estima.com/forum/viewtopic.php?f=8&t=2036

[fioramanti]

Dear Tom,
I'm trying to apply Laubach and Williams (2003) to Italian data.
I have two questions about the RATS code:
1. There are 2 statements like "equation stage1eq * " while the manual says it should be "equation stage1eq depvar". What the "*" stands for?
2. It is not clear to me where did you get the value for "lamg=.11" or "lamg=.042" and "lamz=sqrt(2)*.058". Why you didn't calculate them inside the code?

Thanks,
Marco

[TomDoan]

Dear Tom,
I'm trying to apply Laubach and Williams (2003) to Italian data.
I have two questions about the RATS code:
1. There are 2 statements like "equation stage1eq * " while the manual says it should be "equation stage1eq depvar". What the "*" stands for?

* (in this case) means that there is no dependent variable. The STAGE1EQ is used only to provide a convenient way to calculate the linear part of the regression.

2. It is not clear to me where did you get the value for "lamg=.11" or "lamg=.042" and "lamz=sqrt(2)*.058". Why you didn't calculate them inside the code?

There's now a fairly substantial thread on this paper at viewtopic.php?f=8&t=2036 which addresses this. Those are pegged by the authors. They may have (at some point) used Stock and Watson to calculate those but it's not included in their Gauss code which just has the hard values.

[TomDoan]

I would note, by the way, that the LW model is (like some other similar models) incapable of determining the "gap" without really strong restrictions. The basic model has effectively a flat likelihood on everything from gap=0 to gap=data.

[fioramanti]

Dear Tom,
Thank you.
I found out that Williams has now posted a set R codes releted to the recent "Measuring the Natural Rate of Interest: International Trends and Determinants" (http://www.frbsf.org/economic-research/ ... W_Code.zip).
In the zip there is also the code for the median unbiased estimator by S&W.

Best,
M

[TomDoan]

That's actually a separate issue. The S&W lookup table apparently was done with a very small number of replications and the one that's actually used (which is more detailed than the one in the paper) has some rather serious Monte Carlo simulation problems (some of the values actually decrease when they should be increasing).

[TomDoan]

And that doesn't change the fact that the results are highly dependent upon the sample, and are even highly dependent upon the method used for initializing the Kalman filter.

[fioramanti]

And that doesn't change the fact that the results are highly dependent upon the sample, and are even highly dependent upon the method used for initializing the Kalman filter.

I can't help but ...

[fioramanti]

Tom,
Just a clarification. In your file of L&W(2003), by the end, the second "header" of the graph for the "agrate" should't be "Trend/Potential Output Growth Rate"?
Thanks

[TomDoan]

Correct. The graph is mislabeled.