Question on estimating Ireland model

Estimation ML/Bayesian estimation
1

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.

2
  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.
3

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

4

But then the timing does not add up.

5

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?

6

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}.