a question on variance

[hardmann]

Dear Tom:

When we decompose the 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 have three vaiances of states and none of observation. When we use option var=concentrate, and still estimate three variances and not specify the pegged variance. Sometimes we get three variances, also concentrate variance. we get four ones. It usual peg the measurment error variance as 1, Should we be peg one of variance of states?


Best Regard
Hardmann

[TomDoan]

If you use VARIANCE=CONCENTRATE, you have to peg one of the variances at 1. Otherwise, the variances aren't identified.

[hardmann]

Dear Tom:

We noticed that in LW(2003), "Measuring the Natural Rate of Interest", there was five variances need to be estimated. According to Stock-Watson(1998) median unbiased estimator, LW(2003) use lambda G and lambda Z , two ratio, instead of the two variances. If we use VARIANCE=CONCENTRATE, It means that we peg one of the variances at 1, other four are ratio, is it?

Best regard
Hardmann

[TomDoan]

Ratios to the one variance that is pegged, yes.

[hardmann]

Dear Tom:

When we estimate variances in trend and cycle decomposition, some code use sw=diag||sigsqxi,sigsqeps,sigsqzeta||, other code use sw=diag||sigxi^2,sigeps^2,sigzeta^2||. We know sigsqxi = sigxi^2, and so on, thus these is no different.
However, different speicifications lead to different results. Sometimes the standard deviation is negative, is right?

Best Regard
Hardmann

[TomDoan]

The sign isn't identified if the square is used, so you can just costlessly flip a sign.