Measurement equations with model/data frequency mismatch

Dear All,

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)

with m=1/4

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?

Any comment?