Question on Measurement Error

Estimation ML/Bayesian estimation
1

Hi, Dynare experts,
I have a question on measurement error. When the measurement error shows up in the model part (not only in the measurement equation), the only way to introduce it is make it as an additional shock. Now I have two questions: 1. Can the variance of the measurement error shock be calibrated/set directly, rather than estimated? 2. How to capture the intuition of this shock in the shock decomposition? For example, if 10% of the volatility in inflation comes from measurement error shock, does that mean the data in consumption is 10% driven by the measurement error? I’m not quite sure whether that would coincide with the right economic intuition.
Thanks a lot!

2
  1. If you specify the measurement error as a normal exogenous variable in the varexo statement you can set the variance in the shocks block. There is no reason to estimate it if you have a good idea what it is.
  2. I do not understand your question. Typically, you have an observation equation of the type:
pi_obs=pi+eps_measurement_error;

where pi is the inflation rate determined in the model and pi_obs is the observed inflation rate. The measurement error will not affect pi, but only pi_obs. The variable your are interested in for the variance decomposition should be pi, not pi_obs. If there is a spillover from your measurement error on inflation to e.g. consumption, you are not talking about a measurement error, but rather you have turned it into a structural shock.

3

Hi, Johannes,
Your answer helps a lot. Thanks a lot!

4

dear jpfeifer.When we add measurement error to the estimated_params, how do we set the prior distribution of measurement error. Is it a hunch? Or is there something else going on.

5

A prior is always subjective. But people often use uniform priors with an upper bound on the volatility.

6

Whether to add observation error, and whether there is a corresponding evaluation standard. How to set the prior distribution of observation error. How do we know the magnitude of the observation error. Thank you very much for your answer.

7

Again, a prior is subjective. If you have no clue, you may want to follow the literature, e.g. Garcia-Cicco, Pancrazi, Uribe (2010) in the AER: https://github.com/JohannesPfeifer/DSGE_mod/blob/master/GarciaCicco_et_al_2010/GarciaCicco_et_al_2010.mod