Question on estimating Ireland model

Dear Prof. Pfeifer
I have a few questions surrounding the topic of estimation. I’m currently trying to replicate results from Ireland 2004 model from your repository Ireland using my solution and I get different results with higher likelihood than estimation I get from running the Dynare file. I was wondering if I’m handling the shocks wrong, as I’m creating the shock covariance matrix C from filling the diagonal with input variances and multiplying it by shock transition (as in transition for model equation x_{t+1} = F x_t + G_e \varepsilon_t):

G_e C G_e^T

and then using it as Q in equation from your lecture Chapter III - Kalman Filter:

x_{t+1} = F x_t + w_{t+1}, w_{t+1} \stackrel{iid}{\sim} \mathcal{N} (0, Q),

also in the model file shocks are bounded and is there a step that requires them to be mapped to unbounded variables before filtering? My second question is concerning the noise covariance for measurement in distribution \mathcal{N} (0, R), should this be generated from the model or is it just zero matrix in case of this file?

Thank you very much for any help.

  1. Is the timing in your posts correct? The \varepsilon_t and w_{t+1} should have the same timing.
  2. The R should be a zero matrix due to no measurement error being present.

Yes sorry, it was supposed to be w_{t}.

But then the timing does not add up.

But shouldn’t the distribution for \epsilon_t be the same as \epsilon_{t+1} as in estimation we’re only looking to incorporate model parameters?

I am just saying it needs to be consistent. In term of the information set, X_{t+1} is directly affected by \varepsilon_{t+1}, not \varepsilon_{t}.