I have a question about the observation equation after I have red your paper “A Guide to Specifying Observation Equations for the Estimation of DSGE Models”.
Would you please help me ?

Q1:
The model I am dealing with (as attached ) is a nonlinear model, but the Taylor Rule is linear form, like:

You need to match ReXU to the data. ReXU is the log deviation of the quarterly gross nominal interest from its mean. Thus, just follow the advice in my Guide to compute this observable. For the purpose of this observed variable, the treatment is exactly the same for a loglinearized model, because this variable is loglinearized. You just need to make sure that in other equations you remember that ReXU is a log-deviation and not a level. Currently, you seem to only take the log of the interest rate, but not the devation from the mean of log interest rate

I cannot replicate this issue. When I add that shock, there is no singularity.

Finally, your estimation routine looks incorrect due the steady state not being correctly updated. After running estimation, Dynare will update the estimated parameters but not take any dependence into account that you did not specify. Rather, your calibration only once updates the other parameters depending on the estimated one. That’s why you should use model-local variables (the ones with the pound operator) or a steady state file. See Remark 4 (Parameter dependence and the use of model-local variables) in Pfeifer(2013): “A Guide to Specifying Observation Equations for the Estimation of DSGE Models” sites.google.com/site/pfeiferecon/Pfeifer_2013_Observation_Equations.pdf.