I am estimating a DSGE model with no capital, calibrated at quarterly frequency. I would like to get some feedback on my strategy.
I treat variable X(t) as an AR(1) shock. The OECD reports some rough measure of it at, say, annual frequency. Therefore, I specify my measurement equation as follows
X_obs(t) = m ( X(t)+e ) + (1-m) X_obs(t-1)
e is an AR(1) measurement error.
Do you think this is a plausible specification to take into account the mismatch between the model and the data?