Question about the measurement errors

Hello, I’m estimating multisector NK model and I got question on measurement error.

My observable includes sectoral relative price gaps(=relative price - efficient relative price), and by definition, weighted sum of sectoral relative prices (or their gaps) is zero.
So, the equation 0 = \sum_{k=1}^K n_k p_{k,t}^R is included in the model.

I have relative price gaps as an observables for whole sectors, so they are having exact linear combination. Therefore, I want to put some measurement error here.

I looked up professor Pfeifer’s guide book, and I put the measurement errors for each sectors’ observables as below.

@#for i in 1:secnum
Dpr@{i} = prhat@{i} + vpr_me@{i};

But in this case, I have to put 16 measurement errors as I have 16 sector model.
I think it is not efficient, as I only need 1 measurement error for the above equation like
0 = \sum_{k=1}^K n_k p_{k,t}^R + me.
Is there any way I can do this? Or please advice me if I am misunderstanding something.

Thank you so much!
I attached my mod and data file just in case. (28.2 KB)

In that case, I would try to just pick one of them and add measurement error. Or alternatively, just drop one of observables and work with measurement error.

I really appreciate your response, professor.

  1. Is it okay for me just pick one of them and add measurement error? I’m worrying that it might be somewhat arbitrary.

  2. For second suggestion, you mean for example I drop the data from sector 1 and add some measurement error in sector 1? How about just drop out the data from sector 1 and not including measurement error? Does it make sense?

Thank you very much for you help again!!

  1. Yes it may be somewhat arbitrary, but it seems to be the minor evil.
  2. I recommended simply not observing the data for sector 1 (a “numeraire”) and not have measurement error.

I see. I really appreciate your help professor.
Thank you!