Kalman filter in a backward-looking model

Hi everyone,

I basically simulate some data using a backward-looking model (using the data_gen4.m file) and then I try to use dynare to recover the filtered shocks (using the Kalman filter or smoother). I do get values for the shocks after filtering that seem to be in line with the actual values, except for nu_M (whose values are always zero after filtering). Also, when I look at oo_.SmoothedVariables.M I get a sequence of zeros which is quite surprising, given that the actual M differs significantly from zero.

I was wondering if anyone could explain to me what I am doing wrong and why the Kalman filtering does not recover the M and the nu_M properly?

Thank you very much!

dat_gen4.m (1.32 KB)
basic_filter4.mod (538 Bytes)