Standard error in level model and linear model

[hodabbbb]

Hi,
a quick question.

I calibrate a model in level, and than I linearize it.

As I use the same set of parameters in linearized model,
shouldn’t I get the same/similar standard errors for the variables as I get in my model calibrated in levels ?

If it is true I assume I should have done sth wrong during loglinearization or is it normal to get different moments ?

thanks in advance

[jpfeifer]

No, in levels you get absolute deviations. E.g. output deviations are then measured in output units. When you do log-linearization (which is presumably what you mean), output will be in percentage devations and therefore unit-less.
The standard deviation of the log-linearized model should be 1/(steady state) times the standard deviation of the level.

[hodabbbb]

Thanks for the the reply.

In my level model I was calculating the standard deviation of a variable ‘X’ as

xx = x / STEADY_STATE(X)

so when I get the STD of ‘‘xx’’ in my level model it should correspond to the STD of my x_hat in my loglinearized .

Shouldn’t it ???

[jpfeifer]

Yes, it should.

[hodabbbb]

Thanks again Prof. Pfeifer

I was tracing back for the source of the problem.
So I simplified into an RBC (both linear and level) and I got the same ST.Errors.

Then I added block to get a NK and I realized that the difference comes in the way I specify th Taylor Rule (TR).

So I am posting both my TRs (level & linear model)

Level TR (following SW2007):

log(Rn/STEADY_STATE(Rn)) = rhoR * log(Rn(-1)/STEADY_STATE(Rn))
+ (1-rhoR) * thetP * log(PIE(+1)/STEADY_STATE(PIE))
+ (1-rhoR) * thetY * log(Y/STEADY_STATE(Y))
+ log(epsR) ;

MP shock:
log(epsR)-log(STEADY_STATE(epsR)) = rhoM*(log(epsR(-1))-log(STEADY_STATE(epsR))) + epsM;

so in my linear model I wrote the TR as :

rn = rhoR* rn(-1) + (1-rhoR)* ( thetPpie(1)+thetYy+thetDP*(pie-pie(-1)) ) +epsR ;

MP shock:
epsR = rhoM * epsR(-1) + epsM;

So I could boil down the problem in the way I have translated the TR (and MP shock) from level into linear model.
I tried different ways of specifying it but I could not get the same St.Errors

Any chance you could spot some problems at a blink of an eye pls ?

Thanks a lot for your time.

[jpfeifer]

Where doe the

come from?

[hodabbbb]

Sorry for the typo.
that is not active as it is set equal to '0’
in both TR rules

[jpfeifer]

How big are the differences? And are you sure the differences come from the Taylor rule itself or the way the interest rate enters the model in other equations?